𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, June 22, 2022
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Generated Thu 23 Jun 02:39:42 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
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Gemini index for the day: gemini://gemini.techrights.org/2022/06/22/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ [Meme] Trying to Circumvent the European Patent Convention is Like Playing With Fire | Techrights

⦿ At the EPO, “Bringing Teams Together” or “New Management of Office Space” is Another Step Towards EPO Outsourcing | Techrights

⦿ EPO Management Severely Harms the Health of Staff by Bullying Them | Techrights

⦿ EPO Abolishing Workers’ Rights and Creating Second-Class Workers in Direct Violation of the European Patent Convention (EPC) | Techrights

⦿ [Meme] Battistelli the Second (Battistelli II) | Techrights

⦿ [Meme] Executing the EPC (as in Killing It, Not Following It) | Techrights

⦿ IRC Proceedings: Tuesday, June 21, 2022 | Techrights

⦿ So Far Today 67% of Phoronix Articles Are About AMD | Techrights

⦿ New Article by Richard Stallman: Many Governments Encourage Schools to Let Companies Snoop on Students | Techrights

⦿ The Future of the EPO’s Work-to-Rule Industrial Action (Examiners Following the Law Rather Than Unlawful Instructions From Management) | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/06/22/antonio-campinos-playing-with-fire/#comments
		http://techrights.org/2022/06/22/at-the-epo-bringing-teams-together-or-new-management-of-office-space-is-another-step-towards-epo-outsourcing/#comments
		http://techrights.org/2022/06/22/bullying-epo-staff/#comments
		http://techrights.org/2022/06/22/epo-abolishing-rights/#comments
		http://techrights.org/2022/06/22/epo-dumpster-fire/#comments
		http://techrights.org/2022/06/22/executing-epc/#comments
		http://techrights.org/2022/06/22/irc-log-210622/#comments
		http://techrights.org/2022/06/22/phoronix-amd/#comments
		http://techrights.org/2022/06/22/school-spyware/#comments
		http://techrights.org/2022/06/22/unfit-to-lead-epo/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/06/22/clonezilla-live-3-0-1/#comments
		http://techrights.org/2022/06/22/flameshot-12-0-0/#comments
		http://techrights.org/2022/06/22/microsoft-very-long-downtimes/#comments
		http://techrights.org/2022/06/22/turkey-gnu-linux/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 77

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/22/antonio-campinos-playing-with-fire/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/22/antonio-campinos-playing-with-fire/

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Gemini_version_available_♊︎


✐ [Meme]_Trying_to_Circumvent_the_European_Patent_Convention_is_Like_Playing
With_Fire⠀✐


Posted in Europe, Law, Patents at 4:54 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇António_Campinos_calling_himself_'the_f***ing_president'...
                       hits_European_Patent_Convention⦈_
               To use only a metaphor (don’t try this at home)…


Summary: The EPO‘s repeated violations of the European Patent Convention (EPC)
will make António_Campinos an asylum seeker like his father, seeking political
shelter like Benoît_Battistelli, who virtually went into hiding in 2018 (when
his diplomatic immunity ended and his EPO crimes, like the_Benalla_affair, came
to light)


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⣧⢀⣿⣿⣿⢀⣿⣿⣇⣾⣿⣿⢸⣿⣿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢻⣿⡆⠀⠠
⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣿⣿⣷⠶⣔⡆⣉⣁⣀⡀⣸⣿⣇⣿⡿⣼⣿⣿⣿⣘⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⢿⣷⣤⡀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡚⢹⣿⡏⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⡟⣿⣿⢸⣿⣟⣟⡃⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣶⢽⣿⡗⠒⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣿⠞⡛⠷⠛⠋⡟⠃⠛⠛⠘⣿⣿⣿⣷⢻⠛⣼⣿⣿⡟⠻⠎⣛⠿⠟⠩⠈⠻⢿⣿⣷⠿⣹
⣭⣽⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢭⣼⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣯⣭⣿⣿⣿⡟⢀⡁⠈⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠈⡏⠉⡉⣉⠉⠳⠟⠓⠂⠹⣄⢠⠿⡿⢾⡿⢿
⣿⣿⣽⣿⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⡆⢸⣶⡇⠀⠀⠈⠙⠛⠛⠙⠉⢉⠑⠀⠘⢣⠛⠛⠑⠒⠒⢠⡖⠁⠀⠠⠀⠀⠉⢸
⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣧⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⢁⠙⠉⡁⠸⠭⠑⠶⠂⠂⠹⡿⠍⠉⠀⠁⠶⣶⢷⣺
⣤⡼⠛⢻⢿⣋⢝⣛⣧⣬⣽⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣿⣿⣛⣿⣟⣏⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢤⠶⣶⡖⣀⠖⠚⠀⡈⠁⠀⠜⡠⠟⠛⠐⡆⣀⣠⣄⢾⠄⡠⠔⣀⣐⡿⠃⠙⢺
⠙⠓⠒⠺⢪⣷⣶⣿⣻⣿⣿⣿⣿⣿⣿⠛⡿⠿⣿⣿⣿⣿⣿⢿⡟⠛⣿⣟⣛⣿⣽⣿⣿⣿⣿⣿⣯⣭⣽⣿⡿⣿⣿⣿⡟⢛⢻⠒⠛⠓⣭⣥⣤⣈⡉⠁⢀⠠⠰⣦⡵⡶⣶⠶⠂⠯⡏⠙⠂⢲⡗⡒⠓⠂⣶⣦⣤⣤
⣀⣀⢀⣸⣿⢷⣿⣿⢿⢿⣿⣿⣧⣯⣽⣿⣦⣼⣿⣷⣟⣿⣯⣼⣿⢿⠿⠿⢿⢻⣗⠀⣤⣤⣼⣻⣿⣿⣿⣿⣿⣿⣽⢿⣛⣶⣶⣿⣟⣿⣁⣀⣀⣠⣔⣟⣉⡉⠁⠉⠀⠀⠀⠄⠀⠤⠃⢐⣛⣿⣷⣤⣤⣿⣿⣿⡽⣹
⠿⢿⣿⢿⣿⣿⣿⣷⣶⡿⢶⣾⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⠟⠿⣾⣶⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠋⡉⠻⣿⣯⣤⣎⣸⣭⣭⣉⣉⢐⣦⠄⠀⠀⠀⠀⠀⠀⡤⣩⣍⣻⣿⣾⣿⠣⠁⢻
⣶⣼⣿⣿⣷⣾⣫⣟⣽⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⣿⢿⡟⣷⣶⠶⠽⣻⣏⣷⣿⣿⣭⣾⣻⣿⣯⣭⡁⣀⡈⠀⠀⠸⠛⠉⠸⠷⢿⣿⣿⡿⢾⣿⣿⡿⢿⣿⣿⣷⣾⡿⣦⣶⣾⡿⣀⣲⡚⣛⡹⢿⣟⢩⣛⢯⢁⣄⢹
⠿⠭⣿⣿⢟⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⣫⣏⣸⣻⣷⣿⡎⢦⣶⣆⣤⣿⢿⣿⣿⣿⣿⣷⣶⣿⢿⣿⣤⠤⣄⣀⣀⣠⣤⣺⣿⣿⣿⣻⣿⣭⠴⢷⣤⣹⣿⣿⣿⣿⣤⡥⣽⣿⣭⣿⣻⣧⣿⠿⡿⠟⠛⠀⠀⢸
⣶⣶⣿⠟⣫⣿⣿⣿⣼⡿⣿⣿⣯⣭⢿⣓⣲⣩⣩⣟⣿⡿⢿⣿⣶⣿⣿⣿⣛⣛⣋⣶⣿⣿⣿⢏⠘⠛⡿⡟⢿⠲⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⣭⡍⠀⠈⡛⠹⠋⡿⢿⣿⣿⣿⣯⣷⣖⣿⣿⣋⣿⣼⣳⣆⣤⣔⣖⢺
⠻⡅⠁⢠⣅⠹⠁⠹⢸⠿⠟⠿⠞⠻⣟⣩⡨⣟⣏⡉⠉⠰⠾⠿⡿⠿⣿⣿⣿⡿⠿⠿⣯⣟⣳⣧⣶⣞⠿⣖⣿⡿⢿⠿⣿⢮⢟⣟⠟⢵⣾⣟⣍⣿⡿⣶⣇⣶⣶⣿⣿⠿⡶⣿⣿⣹⣋⣽⣿⣋⣷⠿⣟⣿⣿⣿⣿⢽
⡿⠇⠀⢘⣣⡤⣄⠄⠊⣹⣿⡴⠦⠄⠐⣓⡈⡥⢉⠀⠀⡀⠀⠀⢠⠘⣈⣫⣙⣛⣟⣟⡿⢿⣞⡛⠝⠀⠠⠸⠛⢃⢡⣍⠉⠈⡁⠐⠣⠂⠦⠜⣙⣻⣟⣿⣷⣞⣿⠿⢟⣿⣟⣟⣟⣟⣧⣽⣾⡟⣿⠷⠯⠿⢿⡿⡿⢿
⠶⠒⠒⠒⠚⠛⣥⣽⣭⣠⣿⣿⣿⣿⡒⡻⠷⠥⠈⠰⣦⣘⣵⣶⣮⡽⣤⣞⣽⡗⠛⠍⣟⡎⠁⠁⠀⠀⠀⠀⠀⠈⣨⠝⣠⡖⠌⢲⡞⢶⣴⣦⣯⡛⣿⡭⢾⣩⡛⣤⣤⣟⣻⢛⡛⣿⢣⡛⡍⢉⣽⣿⣦⣤⡄⠁⠖⣾
⠀⠀⣀⠈⠉⠉⡉⣁⠤⠼⣿⠟⠋⠈⠒⠀⢀⠈⣁⠰⠁⠐⡖⣠⡿⠈⢀⠉⠰⠦⠀⠉⠀⠀⠀⠀⠀⠴⠀⠈⢁⠁⠁⠖⠀⠀⠀⠀⠀⠀⠀⠈⠁⡙⠛⠿⠾⠿⠿⣿⣛⣊⣿⣷⣟⣷⣤⣶⣤⣨⣿⠟⠉⠁⢁⠈⠱⢈
⠿⠟⠲⠿⠛⢛⠛⠙⠛⠒⠠⠈⠸⢀⡀⠬⣅⠽⠀⠄⠀⢀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⢤⡄⠀⠀⡀⣀⠐⠀⠤⠢⠌⠀⣀⠓⣿⣣⣡⣦⣟⣻⡻⠁⢺⠤⢿⠖⠙⠃⢘⠛⢙⠟⢗⠯⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠁⠀⠀⠀⠈⣁⡰⣀⡄⠰⣄⠀⠀⢄⣈⠁⠀⠀⢀⡀⠩⠱⠶⣈⣺⢇⢠⡀⠛⠑⠰⠂⠀⢀⣀⣔⠉⢄⣀⣄⣘⣻⣿⣿⣷⢀⡎⣉⠭⢀⡀⡉⠬⢀⡱⠆⡉⣒⣦⣹⣻
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣛⠁⠘⠤⣂⣰⡿⡶⠟⡓⡿⠟⠛⠀⠃⡀⠔⠀⠁⠀⠄⠐⠀⠂⠀⡀⠀⠞⢦⠀⢘⢀⢀⢀⣄⡀⢀⡀⢀⡃⣸⡟⠃⠠⣫⣘⣩⡇⠀⠉⢸⣻⣟⠸⠈⠀⠀⠀⠁⢀⠂⡩⠄⠤⢿
⠅⠀⠀⠀⠀⠀⠀⠛⠀⡈⠀⠒⠈⣁⣴⢶⣶⣝⠣⠠⢓⢞⠃⠀⠀⠀⣠⠌⠁⠁⠀⠂⠀⢀⡐⠀⠀⠀⠀⠖⠃⠀⠈⠉⠀⢀⠉⠉⣓⡜⣯⡟⢉⠘⠉⠙⠞⠊⠉⡩⣥⡀⣶⡄⠒⠕⢢⣰⣽⣧⣶⣠⡆⠀⠀⠈⠉⢾
⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠠⣍⡉⠈⠿⠉⠱⠄⠤⠠⡲⠀⠰⠖⠀⠀⡤⠀⠀⠈⠀⠀⠀⠀⠤⠆⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠕⡀⠀⠊⠁⠰⢄⠰⢤⡄⣰⣮⣴⡾⡈⣨⣷⣂⣞⣿⣿⡿⡹⢛⣃⢀⣐⡦⡕⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠄⠀⢄⠠⠀⢢⡘⠋⠀⠀⠀⠀⠠⣊⢠⣤⡜⡠⠐⣂⣤⡴⠇⢁⠄⠐⠀⠀⠐⢀⡤⠃⠀⠘⠓⠀⠀⠀⠀⢔⡚⠈⡇⡁⠻⠒⢀⠀⠎⠝⡛⠋⣀⠾⣻⡅⢽⣧⠏⠠⢅⡘⢻
⠀⠀⠀⢠⣄⠀⢀⠀⡀⠐⠂⠀⠀⢠⡀⢈⠉⡀⠀⠀⠀⠀⠀⠀⠠⡄⠠⢺⡏⠯⠹⡧⠓⠂⡾⠪⠀⠐⠂⠀⠀⠓⠒⠛⠉⣐⠄⠀⠀⠀⠀⣔⣶⠒⠻⢓⠔⠋⠉⠁⠀⢂⡤⢠⡀⣤⡔⠢⠒⠕⠪⡐⢋⢰⢛⣟⠟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠖⠂⣾⣿⣷⡀⢀⠠⠄⢀⢁⢠⡮⠱⠄⠠⠀⠄⠉⠀⠀⠀⢈⠑⠂⠀⡉⠉⢃⠒⠀⠉⢰⠺⠄⠀⠶⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠠⠿⢒⠹⡟⠶⠑⣹⣶⣻⢿⣉⠠⠋⠻⣹
⠀⠀⠀⠀⠀⡤⠀⠀⠤⠆⠀⠘⠀⠀⠀⠀⠒⠉⣩⡿⠿⡛⠛⢬⡳⠛⠂⠘⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠜⡯⠝⠛⠠⠋⡰⠁⠐⢀⠀⠘⠁⢀⠀⠀⠀⠀⢀⣀⠀⠀⢠⣤⠄⠆⠀⡄⠦⠝⢨⠁⠦⠞⠉⠛⣴⣬
⠀⠀⠒⠀⠈⠀⣤⠤⠀⠀⠀⠀⣠⡤⢤⡦⠈⠌⠉⠀⠀⠀⠀⠈⠂⠒⠈⠋⠁⠀⠌⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⠁⠀⠀⠠⠀⣴⢲⡆⡌⠀⠀⠀⠐⠢⢠⣤⡦⢿⣚⠂⠑⠚⠓⠊⢂⣤⣈⠠⠖⢰⣰⠶⡤⡝⠂⠀⠙
⠠⣾⡿⠽⢾⡷⢿⣷⣿⣧⠻⠏⠿⠿⠏⠇⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠀⠀⢀⡀⠀⠀⢀⢀⠁⡋⣩⡎⢉⢉⡙⡠⠭⠶⢆⣸⡶⢿⠏⠉⢋⡹⠀⡸⣷⣤⣮⢿⡕⠁⢟⢇⢉⠈⠄⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠁⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠐⠂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠓⠈⠁⠀⠀
⣿⣶⣭⡉⢩⣹⣿⡿⠟⠉⠻⠋⠉⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠿⠿⠿⠻⣿⣿⡿⡟⠿⠟⠁⠀⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣴⣧⡀⠀⠀⣀⣀⡐⠿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠣⢴⣄⠈⠋⠁⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠛⠉⠉⠉⠉⠉⠁⠀⢻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠁⢧⡕⠛⠋⠒⠓⠂⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠛⠛⠉⠉⠛⠛⠛⠉⠁⠀⠙⠛⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠁⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠺⠬⠛⠿⠿⠿⠿⠿⣿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢹⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣾⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢹⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⢛⠟⠛⠈⠛⠃⠀⠛⡛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡣⣦⣲⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣀⢀⣀⣀⣀⡀⢀⠀⠀⠀⠀⢰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⣇⣾⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢻⣿⡆⠀⢠
⣷⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣾⣻⣿⣿⣦⢸⣿⣧⣻⣿⣼⣿⣿⣿⡜⣿⡿⣿⣿⣿⣿⢽⣿⣿⣿⣧⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⣿⣷⣤⡀⢀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣓⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡟⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣶⣾⣹⣿⣷⢺⣺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠞⡛⠗⠛⠋⡟⠃⠛⠛⣿⣻⣿⣿⣿⡟⡿⠼⣿⣿⣿⠟⠬⢛⣿⠟⠁⠭⠻⠿⢻⣷⣾⣿
⣥⣬⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡯⣥⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣽⣿⣿⡇⢘⠁⠈⠀⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⢹⠉⠙⠙⠛⢻⠿⠛⠾⠙⢿⣇⣬⣿⠿⣿⢿
⣿⣿⣿⣿⣶⡷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⡄⢰⣶⡆⠐⠀⠐⠛⠛⠛⠛⠛⠁⠉⠛⠒⠚⡜⠟⠃⠢⠂⠂⣰⠊⠁⢁⡀⠁⠈⠸
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠻⠁⠈⠉⠀⠀⠀⠀⠀⠀⣀⣤⡌⡈⠉⠉⠀⠯⠅⠶⠆⠸⠀⢿⠯⠉⠑⠊⠈⢶⡴⣶
⣤⣤⠟⠛⡻⣿⡥⢟⣻⣥⣯⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣼⣿⣿⣻⣿⣿⣙⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⣴⢦⣶⢆⣠⠖⠋⢀⠉⠁⠠⢆⠸⠟⠂⢶⠠⣀⣤⡀⡢⠀⠤⢄⡀⣲⠟⢣⢻
⠉⠙⠛⠛⠗⣭⣶⣾⣯⣽⣿⣿⣿⣿⣿⡟⢻⠿⢿⡿⣿⣿⣿⡿⣿⠟⢻⣿⣟⣿⣭⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⢿⣿⣿⣿⡛⠛⡿⠖⠛⢊⣭⣥⣀⡈⠉⠈⠄⠠⢶⣬⣶⢲⣶⡞⠨⢽⠟⠓⠑⣶⠒⠚⠓⢠⣴⣤⣴
⣀⣀⣄⣖⣿⣿⣿⣿⡿⢿⡿⣿⣿⣼⣭⣿⣿⣤⣿⣿⣿⣿⣿⣷⣾⡿⣿⠿⠿⣿⢿⣓⠠⣤⣠⣟⣿⣿⣿⣿⣿⣿⣯⡿⣟⣳⣳⣶⣿⣿⣟⣀⣀⣁⣡⣢⣟⠋⠉⠈⠁⠀⠀⠠⠀⠀⠜⢠⢒⣺⣿⣀⣤⣴⣟⣻⣻⣿
⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢷⣷⣿⣾⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⡿⠟⢁⠙⣿⣽⣭⣤⢉⣭⣭⣍⠉⠁⣰⣄⠄⠀⠀⠀⠀⠀⢩⣍⣝⣟⣿⣿⣿⡽⠍⢸
⣶⢶⣿⣿⣿⣷⣏⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣻⡿⢿⣻⣶⡶⠮⢟⣿⡽⣾⣿⣯⣭⣟⣻⣿⣯⣏⢀⣉⠃⠈⠅⠽⠛⠉⠿⠶⣿⣿⣿⠷⣿⣿⣿⡿⣿⣿⣿⣷⣾⣷⣴⣶⣿⠇⣐⣖⠟⣏⠿⣿⡟⢙⣻⡕⣂⣸
⠿⠿⢿⣿⣿⣛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣁⣟⣻⣿⣷⠺⣶⣶⣠⣤⣿⣿⣿⣿⣿⣿⣷⣶⡿⣿⣯⡤⢤⣄⣀⣀⣤⣴⣻⣿⣿⣟⣿⣯⡯⠴⣤⣝⣿⣻⣿⣿⣯⣨⣬⣿⣯⣿⣛⣿⣥⣿⢷⡿⠻⠧⠠⢘
⢶⣶⣶⡿⢛⣽⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣓⣮⣍⣽⣻⡿⠿⣿⣷⣾⣿⣿⣿⣛⣻⣷⣾⣻⣿⣽⡋⠛⢻⢿⡟⡗⢶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣯⣭⠃⠀⢙⠋⠟⢛⣿⣿⣿⣿⣿⣿⣵⣛⣿⡟⣹⣣⡾⣷⢠⣠⣒⣾
⡾⢻⠉⠠⢶⡆⠏⠁⠏⣿⠿⠛⠿⢛⢷⣏⣯⣽⣿⣯⠉⠉⠶⠿⢿⢿⣿⣿⣿⣿⠿⠿⢿⣹⣋⣶⣴⡶⡿⢿⣾⣿⣿⣿⣿⡷⡭⣻⡻⠫⣶⣿⣿⣹⣯⠷⣾⣠⣶⣶⣶⣯⣷⣾⣿⣏⣿⣙⣿⣟⣹⡿⢿⡿⣿⢿⣿⣿
⢻⠿⠀⠀⠛⣤⢢⣀⣀⡫⣽⣧⡷⢶⠒⢊⢓⣫⠌⡁⠤⢀⡀⠀⠀⡀⠃⣙⣉⣛⣻⣻⣛⡿⣷⣛⡫⠃⠂⠄⠻⠛⣈⣼⡉⠁⢉⠀⠘⠔⠐⠢⢛⡛⣷⣛⣿⣾⣻⣿⠿⣟⣿⣿⣿⣿⣻⣽⣷⣿⣿⡿⢶⠿⠿⣿⢿⣿
⠙⠻⠐⠒⠒⡛⢫⣬⢿⣥⣭⣿⣿⣿⣷⢞⣾⣿⠄⠑⢿⡦⣯⣷⣶⡯⢧⣼⣫⣿⠚⠳⣽⢳⠉⢀⠀⠀⠀⠀⠀⠀⢁⣽⣒⣴⢲⡵⠶⠺⣶⣶⣴⣻⢻⣿⠽⣯⣍⠥⣠⣼⡛⡿⣛⢿⡟⣸⢫⠹⣹⣿⣷⣤⣤⠘⠬⢿
⠀⢀⡀⢄⣹⣉⣹⣉⡤⠷⢿⡿⠻⠋⠙⠊⢐⣀⢈⡄⠏⡠⢻⠒⣼⠗⠀⡈⠁⠾⠀⠈⠁⠀⠀⠀⠀⠠⠮⠀⠈⡉⠸⠱⠂⠀⠀⠀⠀⢀⠀⠀⠉⠈⠛⠻⢷⡾⣿⢾⣿⣗⣻⣿⣿⣿⣧⣤⣬⣄⣽⣿⡏⠋⠘⡋⢀⢶
⠿⠿⠛⠻⠟⡛⠟⠛⠛⠛⠛⠄⠡⠯⠤⠡⠬⣠⠇⠠⠃⠀⣂⠀⠃⠉⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⣄⠀⠁⠀⠠⢤⠀⠀⢄⣀⡀⠂⠸⠄⢠⠀⢀⡐⢺⣟⣌⣠⣼⣿⣟⠏⠔⣿⠬⡧⠞⠟⠁⠟⠛⡻⡿⠶⣷⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⠎⡀⠀⠀⠀⢉⣠⢆⣠⠀⢦⣀⠀⠠⣀⡈⠀⠀⠀⠀⠈⠍⠖⠆⣁⡿⠠⣄⠘⠋⠂⠖⠀⠀⣰⣠⡛⠡⢀⢩⣙⣟⣿⣿⣿⣖⣰⠙⢙⣇⡀⣉⣡⠞⢀⡳⠒⡛⢶⣏⣿
⢀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣀⠀⠠⣘⠇⠀⠣⠂⣃⣶⢿⠾⣛⢻⠿⠟⠃⠘⢀⠠⡂⠈⠀⠠⠀⠂⠐⠂⢀⠄⠠⠛⡞⠀⡃⡤⣈⣀⣄⠠⣀⡄⣘⡀⡻⠟⠁⢝⣇⣿⣽⠁⠘⠣⣿⣿⣃⠏⠋⠀⠈⠘⠀⡤⢀⣋⡀⣾
⠻⠀⠀⠀⠀⠀⠀⠘⠁⠠⠁⠖⠂⢩⣤⣶⣶⣿⣟⠔⠚⡢⠟⠀⠀⠐⢀⡴⠉⠀⠁⠐⠀⠀⣀⠂⠀⠀⠀⠰⠚⠀⠀⢛⠁⠀⢨⠉⠙⣂⢻⣽⠟⣉⠛⠁⡷⠖⠋⠉⢭⣀⢰⣦⡔⠾⠗⣌⣯⣷⣴⣦⢸⠁⠀⠀⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠯⢭⡉⠹⠯⡹⠶⠴⢆⢀⠆⠀⠴⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠴⢀⠐⠀⠀⠀⠀⠀⠅⢀⣀⣮⠔⠠⠑⠋⠁⠧⡈⠦⣀⢀⣮⣍⣿⢽⣑⣽⣷⣸⣿⣿⣿⠿⡟⠿⡲⣐⢶⣐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡠⠄⠄⠐⣕⠛⠁⠄⠀⠀⠐⢼⣀⣤⣴⢃⠤⢓⣢⢤⠼⠀⡠⠀⠃⠀⠀⠂⣨⠜⠅⠀⠛⠁⠐⠀⠀⢠⣴⠛⢹⠈⠙⠇⠒⡀⠰⠻⠟⠟⢋⡑⣟⣛⣈⡿⣼⠁⢜⡄⢿
⠀⠀⠀⠀⢲⡄⠀⠄⢀⠐⠚⠀⠐⠀⣦⠄⠄⢀⣀⡀⠀⠔⠀⠀⠀⢤⠄⢔⣿⢻⠭⢿⡜⠖⢢⠗⠆⠀⠒⠀⠀⠘⠒⠚⠛⢁⣢⠐⠀⠀⠀⢠⣲⡖⠚⠟⡣⠊⠉⠈⠀⠀⣡⡀⣀⢆⣥⠰⡕⢮⠗⣗⠝⡁⣶⢒⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠛⢸⣿⣿⣦⡀⢀⠤⣀⡈⣤⣴⠎⠶⠀⠄⠠⠈⠁⠀⠀⠀⡁⠒⠊⠈⣉⠙⣀⠆⠈⠁⡔⠥⡄⢰⠌⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⡾⢿⠿⠜⠆⣧⣾⡷⣿⡉⢸⡻⢭
⠀⠀⠀⠀⠀⡠⠄⠀⠀⠸⠀⠀⠃⠀⠐⠀⠘⠅⢘⣿⢿⢟⠛⠓⢟⠟⠛⢀⢋⠀⠀⠀⠀⠈⠄⠄⠀⠈⠀⠀⣠⢻⠯⠟⠃⠜⢃⠏⠀⠂⡀⠈⠟⠀⡀⠀⠀⠀⠀⠀⣁⠀⠀⣠⣤⠐⢈⢁⠰⠭⢒⡛⠳⢤⠛⠛⠧⣼
⡄⠰⠉⠁⠀⠁⣥⠤⠀⠀⢀⠀⣠⣤⠤⡼⠐⢡⠈⠙⠁⠀⠈⠀⠑⠐⠊⠙⠉⡀⠠⠁⠉⠀⠀⠀⠀⠀⠈⠠⠚⡯⠀⠀⠀⡄⢠⡶⣶⣢⠁⠀⠀⠀⢱⡄⣤⣴⠴⣷⠳⠺⠖⠛⠒⠁⣠⡌⡥⣴⠂⡥⡴⣤⣄⠲⠚⠹
⢀⢾⣿⠿⢾⡷⢿⣿⣿⣿⣿⠿⠿⠿⠏⢇⠀⠀⠀⠀⠀⢀⡆⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢂⠀⠀⠀⡉⡈⠸⢊⣥⠁⡛⣉⢇⣼⠭⢶⣀⣷⠾⣷⢉⠫⣉⡆⢄⢿⣆⣱⣿⢯⣟⡳⡫⡙⠃⣶⠈⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠁⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠐⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠐⠘⠀⠀
⣿⣿⣶⣦⡈⣩⢹⣿⠛⠉⠀⠹⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣙⠺⠿⠿⢻⣿⡿⠿⡛⠿⠏⠁⠀⠂⠀⠀
⠻⣿⣿⣿⣿⣿⣾⣧⣀⠀⠀⣀⣀⠀⠼⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠣⢤⣀⠘⠉⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀
⠀⠙⠛⠋⠉⠉⠀⠉⠉⠁⠀⠻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠁⣧⡉⠏⠃⠒⠓⠂⠊⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⠿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉⠛⠉⠉⠀⠀⠈⠛⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠔⠈⠛⠻⠿⠿⠿⠿⡿⢟⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢹⣿⡌⣿⡇⣿⣿⠀⣾⡟⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢹⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⢛⡞⠛⠈⠛⠃⠀⠛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⢀⣄⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣾⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢻⣿⡆⠀⢠
⣶⣶⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣾⣺⣍⡀⣸⣿⣇⣛⣻⣼⣿⣿⣿⡈⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⣧⣿⣿⢸⣿⣿⣿⣿⢸⣿⣟⣿⣿⠻⢿⣷⣤⡀⢀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⢛⣺⣿⡟⣿⣿⣿⣿⣿⣿⡇⣿⣷⣿⡟⣿⣿⢸⣿⣿⣿⣟⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣶⣹⣿⡇⣖⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⠞⡛⠗⠛⠋⡟⠃⠛⠛⢘⣛⣿⣿⣿⣿⣻⡞⣻⣿⣿⣿⠌⠿⢿⡟⠉⠘⢻⠿⠛⢷⣾⢿
⣤⣤⣶⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣽⣿⡇⠘⠣⠙⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⡓⢇⠛⠛⠛⠛⠓⠿⠳⠖⠸⣷⢈⣽⣿⣿⣿
⣿⣿⣿⣿⣶⣶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢔⣢⠀⠀⣤⡆⠀⠀⠀⠻⠟⠛⠛⠻⠋⠉⠙⠓⠒⠞⡾⠿⠃⠴⠄⠄⣰⠈⠀⠁⡈⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣇⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠙⡈⠍⠁⠐⠎⠱⢶⠄⡧⠘⣾⠉⠉⠑⠀⠡⢦⢾
⣤⣤⣴⠟⠛⡻⣯⠤⢿⣯⣤⣷⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣼⣿⣟⣻⣿⣯⣻⣛⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡤⠤⡤⢦⡤⢀⡠⠐⠁⠈⠋⠁⠠⠄⠫⠒⠀⢤⠀⣀⣀⢐⡆⠀⠄⠀⢀⣰⠟⣸
⠉⠉⠉⠛⠋⠛⣵⣶⣿⣭⣽⣿⣿⣿⣿⣿⣛⡿⠻⢿⠿⣿⣿⣿⡿⣿⠙⢿⣿⣛⣽⣯⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⢿⣿⣿⣟⠛⢻⡷⠒⠓⢪⣭⣄⣀⠈⠀⠀⠀⠠⣤⣭⣦⢠⣤⠟⢨⣽⠉⠃⠠⡾⠔⠋⠤⢠⣤⣬
⣤⣤⣤⣄⣄⣿⣿⣿⣿⡿⢿⠿⢿⣿⣼⣼⣿⣧⣴⣿⣿⣿⣻⣿⣾⣿⠿⡿⠿⠿⡻⡟⡂⢤⣄⣜⣿⣿⣿⣿⣿⣿⣿⣯⡿⣛⡖⣶⣾⣟⣿⣃⣀⣀⣀⣤⣼⡚⠉⠙⠌⡁⠀⠀⠄⠀⠀⠔⡀⢒⣾⣿⣀⣀⣼⣟⣗⣻
⠛⠛⠛⣿⡞⢿⢿⣿⣿⣿⣿⠒⣶⣿⣯⣾⣿⣿⣷⣿⣿⣿⣿⡟⠓⢷⣷⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣾⣿⣿⠿⠋⠉⠛⣯⣯⣭⡭⢩⣭⣍⣉⠈⠀⣦⣀⠀⠀⠀⠀⠀⠀⢩⣍⣙⠛⣿⣯⣯⣯⢹
⣶⢶⣾⣿⣿⣿⣿⣩⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⣿⡻⢟⣻⣾⠖⠼⢿⣯⣷⣿⣿⣭⣽⢛⣿⣯⣽⡍⣀⣘⠀⠈⠀⠝⠋⠩⠷⠾⣿⣾⣿⢶⣿⣿⣿⣿⣿⣿⣿⣷⣿⢦⣴⣶⣿⢆⣰⡶⠻⠏⢿⣷⠛⣻⢙⡳⢸
⠿⠿⠿⢿⣿⣟⣹⣯⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⣿⣿⣯⣸⣛⣿⣿⡷⢳⣶⣶⣤⣼⡿⣿⣿⣿⣿⣿⣶⣼⢿⣿⣧⡤⢤⣀⣀⣀⣤⣞⣿⣿⣿⡟⣽⣯⡥⢶⣤⣻⣻⣻⣿⣿⣏⣸⣹⣞⣿⣟⣛⣯⣴⣿⣷⠿⠿⠇⢙
⠒⢲⣶⣾⠟⣩⢽⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣶⣯⣭⣿⣿⡿⠿⣿⣷⣿⡿⣿⣞⣞⣻⣶⣿⣿⣿⡿⠁⠛⡻⣿⢿⠲⣶⣿⣿⣿⣿⣿⣿⣿⣷⣴⣭⡝⠀⠂⠙⠉⠛⣹⣏⣿⣿⣷⣿⣯⣭⢻⣿⡋⣹⣳⠾⡆⣄⣠⢲
⣶⡟⢻⠀⠰⣶⡰⠇⠈⠩⣟⠿⠛⠿⡙⢿⣽⢥⢿⣻⡍⠉⠀⠾⠟⢟⠿⣿⣿⣿⣿⡿⠛⢏⣝⣹⣦⣶⢞⠻⣗⣿⡿⢿⡿⣿⢶⠕⣟⠟⢽⣾⣿⣏⣿⡯⢶⣆⣠⣶⣴⣾⣽⣷⣾⣿⣿⣟⣻⣿⣟⣭⡿⣿⢿⡿⣿⣿
⠟⢻⠟⠀⠀⢩⣔⣦⣀⣘⠩⢿⣱⣓⣖⠐⡉⡒⡾⠌⠀⡀⢀⡀⠀⢀⡀⢃⣉⣉⣫⣟⣿⣻⢿⣟⠛⠛⠀⠠⠈⠟⢇⣠⣍⠉⠉⡉⠀⠢⠘⠰⢼⢛⢻⣗⣻⣿⡾⣿⡿⢿⣻⣿⣿⣿⣟⣻⣿⣽⣿⣿⡧⣴⣿⣿⡿⣿
⠀⠙⠋⠉⠉⠈⡉⣠⡴⢯⠤⡿⣿⣿⣿⡞⣳⠿⡷⠀⠀⣷⣼⣭⢵⣶⠭⣧⣶⣭⡟⠚⢬⡟⣯⠁⡀⠀⠀⠀⠀⠀⠈⢉⡟⣢⡶⠦⠷⡖⢷⣶⣦⣾⠚⣿⣭⢹⣻⡙⢥⣠⣿⢻⡿⣻⢿⠋⡻⢫⢩⢸⣶⣦⣤⡄⠹⣽
⠀⢀⣀⡠⢄⣋⣉⣙⣡⠴⠖⠿⠟⠋⠉⠁⠁⡀⡀⣡⠘⢁⠸⠛⠣⠿⠊⠀⠍⠐⠆⠄⠉⠀⠑⠀⠀⠀⠤⠅⠀⢉⡀⠙⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠽⣶⠾⡷⣾⣿⣞⢿⣿⣿⣾⣀⣠⣅⣀⣽⣿⠟⠛⠾⠰⢲
⠿⠟⠛⠙⠛⠛⠫⠍⠁⠛⠃⠓⠀⠠⠣⠄⠠⠥⡜⠂⠐⠁⢐⡀⠘⠀⠀⠀⠙⠀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡄⠀⠠⢀⣀⠐⠀⠧⢄⣠⠀⢁⠒⣾⣃⣃⣤⡼⣿⡻⠏⢵⣯⢽⠥⠻⠟⠉⠿⠛⣷⡦⢼⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡲⢃⠀⠀⠀⠀⣁⡰⣆⣆⠐⡦⠀⠀⠄⣀⠁⢀⠀⠀⡀⠩⠱⠶⢈⣹⠷⠠⡀⠺⠁⠠⠖⠀⢀⣀⣐⠋⠀⠈⣉⣹⣻⣿⣿⣷⡆⣼⠛⣺⢀⠀⣀⣰⠇⢘⠶⠖⡢⢿⣹
⢐⣀⠀⠀⠀⠀⠀⠀⣤⡀⢀⡀⠀⢠⣛⠀⠈⠴⢈⣐⡾⣧⠿⣛⠹⠿⠙⠃⠘⣀⢔⠃⠉⠀⠀⠐⠀⠘⠀⢠⠠⠜⢣⢘⢘⣡⡠⢂⣠⡀⢀⢠⢀⡛⢑⡿⠛⠈⢙⣙⣏⣷⠀⠛⢡⡿⣟⣸⠙⠃⠀⠀⠋⢀⠤⢘⣉⢸
⠘⠋⡂⠀⠀⠀⠀⡀⠉⠁⢠⠀⠒⠈⣠⣼⠻⣾⣿⣷⠒⢊⠖⠓⠀⠀⠂⠤⠌⠉⠀⠀⠂⠀⠀⡀⠂⠀⠀⠀⠒⠓⠀⠘⡋⠀⠁⡍⠉⠓⣘⢯⡺⠛⡙⠓⠒⡶⠚⠋⠋⣩⠀⢤⣬⠩⡿⢢⢱⣷⣶⣴⡆⡼⠀⠉⠍⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡰⠷⢬⠉⠻⢇⠸⠦⠶⡨⡐⠈⠰⠖⠀⠀⠤⠀⠀⠈⠀⠀⠀⠀⠄⠆⡀⠀⠀⠀⠀⠀⠨⠀⢀⣠⡍⠄⡌⠚⠋⢰⣄⠠⢄⣀⣠⣥⣘⡯⡏⢹⣿⣄⡨⣿⣿⡿⢿⠿⠟⡆⡰⣤⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠐⢀⠀⠤⠀⢢⡊⠉⠀⠀⠀⠀⠐⣏⣠⣆⡞⡠⠘⣒⡠⡤⠇⢀⠄⠀⠀⠀⠀⢂⡤⠋⠄⠰⠓⠁⠂⠀⠀⢀⡔⠏⡇⠋⠻⠄⢀⡀⠄⠿⢿⠛⢉⢹⣓⣋⣸⢯⡟⠁⣁⢸
⠀⠀⠀⠀⠀⠦⠀⠀⠀⡄⠐⠁⠀⠈⢰⡤⠐⠀⢄⣤⡀⠠⠀⠀⠀⠀⡖⠀⢺⡗⡯⠽⣧⠳⠒⣼⠲⠀⠐⠂⠀⠀⠓⠒⠛⠊⢁⡤⠂⠀⠀⠀⣴⣶⠒⠺⠟⡔⠋⠁⠀⢀⠈⣀⠀⠀⣠⡤⢬⡴⣽⢝⡪⠞⢰⣔⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠋⢹⣿⣿⣆⠀⡤⢄⣠⢑⢴⡶⠑⠂⢠⠀⠄⠈⠀⠀⠀⢈⡐⠒⠀⢈⢁⢃⡰⠐⠉⢠⠲⠄⠠⡴⠀⠋⠈⠈⠀⠀⠀⠀⠈⠀⢀⡽⠷⠯⡯⠦⠢⢘⣠⡿⡦⡏⢃⣽⢿
⡀⠀⠀⣀⠈⢀⠴⠃⠀⠐⢛⠀⠈⠁⠀⠁⠀⢉⠀⣘⡿⡿⠛⠙⢺⣹⠛⠃⡈⡁⠀⠀⠀⡀⠈⠠⠀⠀⠀⠀⠂⡜⡯⠵⠛⠂⠞⡠⠃⠁⢀⠀⠘⠃⢀⠀⠀⠀⠀⠀⢈⡀⠀⢀⣀⡄⠀⡸⠀⢬⡽⢘⠛⠤⡽⠟⠲⢰
⣶⠤⠀⠉⡁⠀⣤⠤⠀⠀⠀⠀⢂⣤⡆⠠⠟⠃⡆⠀⠀⠀⠀⠀⠈⠒⡒⠈⠉⠁⠀⠈⠀⠁⠀⠀⠀⠀⢠⠁⠐⠛⡅⠀⠀⢠⠀⣤⢶⣖⡜⠃⠀⠀⠈⢦⢠⣤⣦⣼⡞⠖⠢⠚⠛⠒⠀⣠⠉⢤⣴⢨⣤⣦⣥⡔⣦⢘
⢠⣴⣿⠽⢻⡷⠿⢿⣷⠷⢿⡟⠿⠺⠏⠇⣀⠀⠀⢀⠀⠀⢰⠁⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⡀⡀⠀⠀⠀⠁⠁⠐⢋⡍⢉⠋⡩⢀⡏⠥⢞⣰⡶⣿⡞⠙⢏⡰⡂⣒⢷⣈⡭⡿⢹⠾⡼⢏⠲⢑⡎⠀⢨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠁⣀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡄⢀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠘⠸
⣿⣿⣿⣶⣶⣌⡭⢹⣿⠟⠋⠉⠻⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡛⠿⠿⢷⢹⣿⣿⢿⡻⠿⠟⠃⠀⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣾⣷⣀⡀⠀⣀⣀⡚⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡌⠡⢤⣀⠉⠉⠀⢀⢀⡄⠃⠀⠀⠀⠀⠀
⠀⠀⠙⠛⠋⠉⠁⠀⠀⠉⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠈⠙⣧⠸⠟⠓⠚⠓⠊⠊⠁⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⢿⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠛⠋⠉⠀⠀⠙⠻⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠱⠻⠛⠻⠿⠿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣾⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡏⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣧⢸⣿⢹⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⡚⠛⠈⠛⠃⠀⠛⢛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⢀⣀⠀⣀⠀⠀⠀⠀⢰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣾⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢻⣿⡆⠀⢀
⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⣊⣈⣁⢸⣿⡇⣛⣛⣼⣿⣿⣿⡀⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⣧⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⢿⣷⣤⡀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣟⢻⣿⡏⣿⣿⣿⣿⣾⣿⡇⣿⣷⣿⡟⣿⡿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢺⣿⣿⣿⣿⣶⣶⣹⣿⡇⡀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠛⠃⠛⠛⡟⠃⠛⠛⢸⣿⣏⣹⣿⣿⣿⣼⣛⣇⣟⣻⠎⠛⠿⢟⡁⠈⢻⡿⠛⠳⣶⣿
⣿⣷⣶⣶⣿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣿⡏⠰⢃⠘⠀⠀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⢒⡍⠋⠙⠓⠒⠶⡿⠷⠄⢰⣢⢈⣽⣿⣿
⣿⣿⣿⣿⣷⣶⡾⢖⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠄⠀⢠⡄⠠⡄⠀⠿⡿⠻⠛⠛⠛⠋⠁⠛⠐⠒⢢⠿⠷⠲⠤⠠⢀⣰⠉⠈⠁⠁⠘
⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠿⢟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢑⠉⠉⢁⠰⠈⠳⢦⠄⡇⠸⡾⠉⠉⠠⠀⢠⢴
⣥⣤⣶⣶⣛⣛⡻⡧⠴⣭⣥⣴⣾⣿⣿⣟⣻⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣛⣿⣿⣏⣋⢻⣿⣿⣿⣿⣿⣷⣤⣤⣠⣤⡤⠤⡤⣤⣆⣀⡴⠐⠁⡘⠛⠀⠰⠀⠞⠒⠠⡄⠄⣀⡀⣴⠌⢠⠠⠀⢠⣼⢻
⠉⠉⠈⠉⠉⠉⢊⣶⢿⣿⣭⢿⣿⣿⣿⣿⣿⢛⡟⠛⢻⠿⣿⣿⣿⢿⡿⠛⢿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣯⣽⣿⣿⡟⣿⣿⣿⡟⠛⠛⠒⠚⠒⣩⣩⣀⡀⠈⠀⢡⠀⠤⣤⣵⣦⣤⣤⠇⣬⣽⠛⠂⢤⡦⠴⠭⠬⣥⣴
⣤⣤⣤⣤⣄⢼⣟⣟⣿⣿⠿⣿⠿⠿⣷⣴⣾⣿⣧⣶⣿⣿⣯⣻⣷⣾⣿⢿⡿⠿⢿⣻⣛⠠⣤⣀⣸⣻⣿⣿⡿⣿⣿⣿⣽⢟⣛⢲⣤⣾⣻⣿⣃⣀⣉⣉⡤⣔⠛⠙⠣⠍⠀⠀⠀⠄⠀⡀⠇⡠⢐⣿⣇⣀⣠⣼⣿⣾
⠛⠛⠛⠋⣿⣞⠿⠿⣿⣿⣿⣿⣺⣾⣿⣯⣾⣿⣿⣷⣿⣾⣿⣿⡟⠛⢾⣾⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣾⣿⣿⠿⠋⠉⢻⣯⣯⣭⡍⢩⣭⣉⠑⠀⢀⣆⡐⠀⠀⠁⠀⠀⠉⣩⠉⣙⢻⣿⣽⣿⣿
⣀⣰⣶⣿⣿⣿⣿⣿⣽⣧⣴⣿⣿⣿⣿⣿⣟⣿⣿⣉⣛⣻⡻⣏⣳⣷⠲⠾⢿⣿⢷⣿⣿⣭⣿⣻⣿⣯⣿⣁⣀⡁⠀⠀⠸⠙⠋⠽⠶⢾⣷⣷⡿⢾⣿⣿⣿⣿⣟⣿⣿⣶⣻⣄⣴⣶⣿⣀⣴⠶⠿⠻⣿⣿⢛⡿⣛⢼
⣟⠛⠛⠛⢿⣿⣇⣽⣦⣿⢿⣻⣿⣯⣟⣿⣿⣿⠿⣿⣿⣦⣼⣻⢿⣿⠟⣳⣿⣦⣤⣾⢿⣿⣿⣿⣿⣷⣶⣿⢿⣿⣦⠤⣄⣀⣀⣠⣴⣺⣿⣿⣿⣻⣿⣽⡤⣦⣌⣻⣛⣿⣿⣿⣉⣏⣳⣿⣛⣛⣻⣿⣼⣿⣴⡿⠿⢸
⠋⠉⢰⣿⠿⠋⡝⢿⣿⣿⣾⣿⣿⣿⣯⣶⡟⣯⣼⣭⣭⣯⣿⠟⢻⣿⣾⣿⠿⣿⣟⣟⣷⣶⣿⣿⣿⢏⠘⠛⡿⡿⠷⠶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⣭⡟⠀⠈⠛⠩⠛⣻⣻⣿⣿⣳⣿⣭⡽⢿⣿⠛⡟⣹⣿⡆⡀⣴
⡱⣾⡏⢁⠀⠰⡦⠐⠀⠘⢸⣛⠋⠙⠋⠉⠯⡽⢴⢟⣻⡍⠈⠘⠾⠻⡿⢿⣿⣿⣿⣿⠟⠛⣋⣋⣱⣦⣶⢞⠿⣖⣿⡿⣿⢿⡿⠬⢝⣿⠟⣱⣾⣿⣻⣷⣵⣶⣇⣴⣦⣴⣾⣽⣶⣿⣿⣻⢟⣻⣿⣟⣫⣿⣿⣿⡿⣿
⡖⠂⣛⡃⣀⠠⢥⡔⠦⢀⣀⢴⢿⣜⣛⣂⠈⡈⡗⡧⢄⠀⠀⣀⡀⠀⣠⠘⠀⣩⣙⣭⣟⣟⣿⣿⣞⡛⠛⠀⠰⠹⠛⢀⣡⣉⠉⠈⡁⠐⠤⠃⠤⡙⡻⢿⣖⣻⣯⢿⣿⡿⣿⣿⡿⣿⣿⣟⣿⣯⣽⣿⣿⣦⣼⣾⣿⣿
⠃⠀⠙⠃⠉⢉⣉⡉⣴⡞⠧⢰⣾⣿⣿⢿⡟⣿⢳⠒⠊⠘⣷⢸⡭⣵⣶⠽⣤⣦⣽⡗⠙⢬⣟⡞⠁⠀⠀⠀⠀⠀⠀⠈⣨⢑⣠⡖⠌⢲⠲⣶⣶⣦⣗⠿⣿⡍⣝⣛⠩⣄⣨⡟⢽⠟⠿⣿⠉⡿⡏⡇⢻⣶⣅⣀⡉⢻
⡶⠆⣀⣀⡰⣀⣃⣀⢃⣴⠶⠘⠻⠋⠉⠀⠀⠀⡀⣀⡥⠘⠀⠈⠃⠥⠿⠀⠠⢁⠐⠢⠈⠉⠈⠈⠀⠀⠀⠬⠀⠈⢁⠁⠃⡖⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠿⠷⣶⢿⡷⣿⣿⠞⣿⣿⣷⣯⣀⣨⣁⣈⣻⡿⠻⠋⠷⢸
⡤⠝⠛⠋⠈⠛⠋⠡⠀⠈⠋⠈⠑⠀⠐⠠⠄⠀⠤⡞⠀⠀⠀⣐⡀⠀⠈⠀⠀⠁⠠⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⢤⡀⠀⠀⡀⡀⠐⢀⠥⢄⡀⡀⢀⠒⣞⣇⣀⣤⠿⣿⠻⠫⢼⣫⡿⠭⠻⠛⠹⠟⠻⣦⠤⣼⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡜⢀⠀⠀⠀⢈⣠⣾⣤⡆⠐⡆⠄⠠⢀⡈⠁⠀⠀⢀⠀⠩⠱⠴⣈⡺⠇⢄⡀⠛⠁⠰⠂⠀⠀⣐⡰⠋⠀⠉⣉⣿⣿⣿⣿⣶⠀⡝⠒⣾⠀⠀⣒⡰⠀⠪⡬⠖⠮⣽
⠀⢐⣀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢤⠅⠀⠈⠎⣁⡺⠻⡿⢟⡃⠯⠏⠙⠀⢃⡀⢘⠀⠁⠀⠀⠂⠀⠃⠀⡀⠄⠞⢦⠃⢘⢄⠄⢀⣄⠀⡀⡠⢘⠃⢱⠟⠋⠈⣚⢹⢟⡏⠘⠛⢽⢿⡟⣸⠙⠃⠀⠀⠃⠠⠅⢛⣹
⠈⠈⢡⠀⠀⠀⠀⠀⠀⠉⠁⣀⠐⠋⢀⣤⣾⢻⣿⣿⡕⠒⢫⢚⠃⠀⠀⠂⠤⠉⠉⠁⠐⠀⠀⢀⠐⠀⠀⠀⠀⠚⠃⠀⠘⠉⠈⢀⠉⠉⠒⣺⣗⡟⢋⠛⠂⢲⠶⠛⠙⢋⡁⠀⣤⣌⢭⡿⢅⢰⣲⡆⣤⣄⡇⠀⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⡆⠉⠛⠀⠛⠖⢆⢀⡁⠀⠴⠊⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠤⢆⡀⠀⠀⠀⠀⠀⠈⠀⣀⣰⠥⢠⠈⠛⠁⢠⣀⠠⣀⡀⣬⣅⣫⡭⠈⣛⣧⣔⣭⣿⣿⣿⢻⠿⠧⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⠀⠀⠀⠂⠀⠠⠀⠐⠳⠉⠁⠀⠀⠀⠀⢢⢅⣐⣤⣃⠤⠓⣂⣴⠼⠇⠀⠄⠀⠀⠀⠐⣀⡤⠣⠀⠜⠊⠐⠀⠀⠀⣤⡐⠛⡀⠉⠫⠠⢀⠀⠜⠿⠿⠟⡋⣽⢐⡃⣺⣛⡞⠉⣉
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠈⠁⠀⠀⡴⡄⠂⠀⣤⣤⠀⠀⠀⠀⠀⠠⡆⠐⣾⡞⠏⢻⡧⠇⠂⡖⠮⠀⠐⠂⠀⠈⠒⠒⠓⠋⣐⠄⠀⠀⠀⠀⡴⡶⠒⢿⠓⡐⠁⠁⠀⡀⢈⡀⢀⢀⢁⣠⣍⢬⣪⢝⢩⠚⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠁⣿⣿⣷⣄⢀⠴⣄⣌⣁⠶⡶⠑⠀⠀⠠⠀⠉⠀⠀⠀⢇⠐⠆⠀⡩⡉⣃⠆⠀⠁⠠⠢⠀⠠⠆⠈⠃⠁⠀⠀⠀⠀⠀⠁⠀⣀⠿⠤⢩⠥⢆⠆⢶⣰⢷⣾⠞⢉⢿
⠤⡤⠀⢀⣃⠀⠀⠞⠀⠀⠚⠃⠀⠈⠀⠀⠀⡀⠀⠀⣷⢿⠻⠋⠙⢢⠌⠋⢁⢈⠀⠀⡀⢀⠀⠁⠄⠀⠀⠀⠐⢀⢸⡽⠜⠓⠰⢋⠘⠉⠀⠀⠀⠛⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⡀⢀⠃⡠⢜⡫⠙⠋⣼⡿⠓⢼
⣾⡷⠂⠀⠉⡄⣤⠤⠀⠀⠀⠀⠀⢤⠔⠒⠒⠓⠠⠂⠀⠀⠀⠁⠀⠀⠀⠂⠉⠉⠁⠐⠀⠈⠀⠀⠀⠀⠀⡎⠀⠒⢡⠀⠀⠀⠠⢠⡴⢶⡂⡜⠀⠀⠀⠘⡄⢠⣀⣤⣷⠳⠖⠆⠚⠫⠂⠀⣀⢀⣄⡤⢡⣤⣤⣁⠲⢰
⠉⣿⡿⡿⢾⡿⠿⠿⡿⠷⠿⣿⡿⠾⠇⠇⠀⡀⠀⠀⡀⠀⠀⠌⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡉⠁⠀⢀⢀⠀⠀⠀⢈⠀⠉⠊⣩⡈⡘⢉⠑⡸⠩⠥⢃⢴⣶⣷⠎⠻⣀⠒⠀⡲⣆⣈⣽⡿⡳⢷⠾⡋⠶⢱⡁⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠁⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠁⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠄⢨
⣿⣿⣿⡿⡿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠐⢸
⢿⣿⣿⣿⣶⣶⡌⡭⢹⣿⠏⠋⠀⠛⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡉⠿⠿⠷⢹⣿⣿⢾⡻⠿⠋⠃⠀⢸
⠘⠿⠿⣿⣿⣿⣿⣿⢿⣧⣀⠀⢀⣀⣄⡐⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡜⠠⣤⡀⠉⠉⠀⠀⢀⡈⠂⠀⠀⠀⠘
⠀⠀⠀⠈⠛⠉⠉⠀⠀⠀⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠈⠙⣄⠘⠙⠓⠚⠓⠈⠊⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⢿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⠁⠉⠉⠉⠉⠁⠀⠀⠘⠛⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠋⠑⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠕⠉⠛⠿⠿⠿⠿⢿⡿⢛⣻⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡏⣿⣿⠀⣾⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡏⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢹⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⡞⠛⠈⠛⠃⠀⠛⢛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⠀⢰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣾⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢻⣿⡆⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣾⣟⡂⢸⣿⡇⣿⣛⣸⣿⣿⣿⡀⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⣧⣿⣿⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⢿⣷⣤⡀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣾⣿⡇⣿⣷⣿⡟⣿⡿⢸⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣶⢹⣿⡇⢈⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⣿⡿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠛⡃⠛⠛⡛⠃⠛⠛⢸⣿⣿⣿⣿⣿⡿⣾⣻⣫⣟⣟⣾⡿⡿⠿⣁⡈⠻⢿⡛⠛⠿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⠿⢟⣛⣿⣿⣿⣿⣿⣿⣳⣮⣝⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣽⡏⠰⢃⠴⠀⠀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢲⡏⠛⠛⠓⠒⢦⠿⠷⠆⢲⡎⢉⣿⣿
⣿⣿⣿⣿⣿⣾⣿⡟⢛⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡆⢀⡄⠀⢀⡄⢠⡄⠃⣾⣿⡿⠿⠛⠛⠟⠃⠈⠓⠐⠲⢻⠿⠗⠠⠤⠠⢀⡤⠉⠈⠉⠙
⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡿⢏⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣟⣿⡀⢹⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⢓⠩⠉⠀⠲⠈⠲⠤⠀⡇⢰⡞⠉⠉⠰⠁⢰
⣽⣷⣶⣶⣾⣉⣩⣿⠷⠪⣭⣴⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣛⣿⣽⣽⣜⣻⣿⣿⣿⣿⣷⣄⣄⣄⡠⣤⠤⢤⠤⣤⡄⣀⠄⠘⠁⠛⠋⠀⠤⠈⠞⠂⠠⡄⠄⣀⡀⢰⠄⠀⠠⠀⠠⣼
⠀⠀⠀⠀⠉⠉⢙⣡⣾⢿⣿⣽⣿⣿⣿⡿⣿⣿⣻⠟⠛⣿⠻⣿⣿⣿⢻⡏⠛⢿⣿⣭⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠛⠛⠓⠒⠚⠒⣭⣅⣀⠀⠁⠀⠀⠀⠤⣬⣵⡤⣤⣤⠇⣮⡝⠉⠈⢤⡦⠤⢥⠭⣽
⣷⣦⣤⣤⣤⣠⢼⣟⣿⣿⣿⣿⣿⠿⢿⣷⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣛⣹⣉⣠⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⡽⢟⣳⢢⡦⣞⣻⣟⣀⡀⣉⣩⡤⣖⠋⠙⠢⢉⠀⠀⠀⠀⠀⠀⠅⠠⢴⣾⣧⣀⣀⣶⣿
⠙⠋⠛⠛⢃⣿⣟⣟⢻⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡛⠛⢾⣾⣿⣯⣿⣿⣿⣿⢻⣯⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⠟⠁⠙⢻⣯⣭⣭⠍⣭⣭⣉⠁⠀⢸⣄⡐⠀⠀⠀⠀⠈⠀⣩⠋⠛⢻⣿⣽⣿
⣀⣀⣲⣟⣿⣿⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣍⣙⣟⠿⣟⣿⡟⠓⠿⠿⠟⣿⣿⣯⣾⣟⣹⣿⣿⣏⣀⣀⡃⠀⠀⠨⠛⠉⠿⠶⣿⣷⣿⠿⢾⣿⣿⣿⣿⣻⣿⣷⣾⡳⣄⣶⣾⡷⡀⡤⠴⠷⢿⣿⡿⢻⡿⣿
⣿⣿⡛⠛⠛⣿⣿⣧⣿⣿⣿⣿⣿⣿⣧⣿⠿⣿⡿⢿⣿⣿⣦⣿⣻⣿⣿⢟⣛⣿⣦⡤⣿⣿⢿⣿⣿⣿⣷⣶⡿⢿⣿⣤⠤⣄⣀⣀⣤⣴⣻⣿⣿⣿⣻⣿⣿⣴⣦⣈⣛⣛⣿⣷⣿⣉⣏⣷⣿⣛⣻⣿⣇⣶⣿⣴⡿⠿
⡛⠋⠉⣻⣿⠟⡫⡵⣿⡿⣿⣿⣿⣿⣿⢷⣶⣻⣭⣿⣤⣼⣯⣿⡛⢻⣿⣿⣿⢿⣵⣯⣽⣷⣿⣿⣿⡿⠁⠘⢛⣿⡿⡷⢶⣾⣿⣿⣿⣿⣿⣿⣿⣦⣮⣍⠃⠒⠈⠋⠝⠛⣿⣻⣿⣿⣳⣿⡭⡭⣽⠿⠛⡟⣽⣧⠄⢠
⡺⢽⢿⣏⣱⠀⢸⡶⠘⠀⠘⣾⣙⣋⠋⠩⠹⠿⡷⣾⣏⣿⠁⠀⠸⠟⠻⠿⢿⣿⣿⣿⣿⢛⢛⣹⣉⡿⣴⡶⡟⢿⣺⣿⠿⣿⢿⡷⡮⢿⣿⢫⣷⣿⢿⣻⣿⣵⣴⣢⣰⣤⣶⣯⣷⣶⣿⣿⣿⣿⣿⣿⣟⣻⣾⣿⣿⣿
⣿⡟⠀⣻⢃⣀⣀⣠⣯⠧⢶⡃⣾⣷⣟⣛⣋⢁⢨⣳⠇⢀⢐⠀⣀⣀⠀⢀⣈⠌⣩⣙⢽⡻⣯⣿⣿⡙⠛⠃⠀⠀⠹⠛⣀⣬⣉⠉⢈⠁⠐⠄⠃⠬⡟⡻⢿⣚⣿⣯⢿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣮⣵⣿⣿
⠋⠁⠀⠉⠀⠈⢩⣥⣭⣶⡚⠲⢲⣻⣿⣿⣿⠛⡿⢻⢒⠊⢸⡧⣿⠯⣭⡾⢻⣴⣯⣽⠓⠁⢸⠱⠀⢠⠀⠀⠀⠀⠀⠀⠀⣸⢓⣴⠒⠽⢶⢲⣶⣶⣦⡷⠻⣯⡭⣟⡋⢭⣄⣹⡏⣿⠿⣿⡿⠙⠿⡛⡗⣿⣾⣅⣉⢹
⣴⡖⣂⣀⣀⣒⣔⣠⣄⣥⣶⣊⢛⠿⣉⢁⠀⠁⢀⠄⡀⠄⠙⠀⠫⠉⠾⠟⠁⠤⠁⠐⠠⠈⠁⠉⠁⠀⠀⠠⠬⠀⠈⡉⠈⢳⠖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠫⠷⣾⢿⣶⣿⡿⠿⡿⣿⣷⣏⣀⣌⣁⢘⣿⡿⠿⠿⢶
⠴⠤⠟⠛⠃⠈⠛⠡⠐⠀⠈⠉⠀⠙⠀⠚⠰⠐⠒⢴⠋⠐⠈⠀⣃⠀⡀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠀⢄⠀⠀⠀⠠⢤⠀⠀⠀⣀⡀⠂⢸⠤⣀⣀⠈⠀⢲⣿⣐⣠⣬⠿⣟⠟⠯⢽⣛⡯⡽⡻⠛⡻⠿⢷⡤⢤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣁⠋⡀⠀⣀⠀⣠⣴⣷⣴⠀⠰⠤⠀⠐⣠⡀⠀⡅⠀⣀⠈⠍⠲⠆⣉⡿⠢⣄⠘⠋⠄⠴⠂⠀⢀⣒⡞⠃⠈⢉⡉⣿⣿⣿⣿⣶⢠⠿⢶⡇⠀⠐⢂⡴⠀⢎⡭⠶⢹
⠀⢀⣭⡄⠀⠀⠀⠀⠀⢰⣆⠀⠠⠄⡀⡦⠝⢀⡐⢃⣤⠿⠯⡿⢏⠉⠿⠇⠉⠈⣁⡀⡉⠀⠀⠀⠀⠂⠐⠃⠀⠀⠤⠛⡔⡂⣃⣄⡘⣀⣄⢀⡀⠍⣘⠋⣺⠟⠋⠙⣏⣽⣛⡇⠙⠋⡽⢷⠇⡗⠛⠁⠀⠸⠃⢈⠉⢺
⠀⠈⠉⠠⠀⠀⠀⠀⠠⠈⠈⠐⣆⠘⠁⢠⣤⣟⢻⣿⡯⡗⠚⠝⠛⠀⠀⠐⠀⠤⠉⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠐⠚⠀⠀⠛⠁⠉⢈⠉⠙⢂⡻⣵⠟⢛⠛⠒⢲⡶⠛⠛⣙⡁⠠⣤⡩⣼⡯⡕⣔⣶⡄⣤⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠲⠆⠉⠛⠄⠛⠚⡂⣊⡅⠁⠖⠉⠀⠰⠆⠀⠀⡀⠀⠀⠀⠠⠴⢀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣬⠤⢠⠙⠚⠁⣦⡀⣤⣀⠀⣬⣒⣫⣽⠩⣷⣆⢐⣹⣿⣿⡿⢿⢾⢧⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠇⠀⠀⠀⠁⠀⠦⠄⠘⠞⠁⠀⠀⠀⠀⠀⣫⣄⣶⣸⢡⠄⠛⣠⣶⠬⠀⠠⠀⠀⠀⠂⠂⣠⠜⠁⠀⠞⠊⠀⠀⢀⠀⣥⠲⢹⠘⠓⠯⠌⠠⠡⠹⠿⡿⠟⡛⡿⠴⠃⣶⣣⠞⢻
⠀⠀⠀⠀⠀⠀⠙⠂⠀⠐⠀⠀⠋⠀⠀⢠⡶⠂⠃⠀⣤⣄⠀⠂⠀⠀⠀⢰⠂⠒⣿⠚⠉⢻⠎⠄⢲⡗⠅⠀⠒⠀⠀⠘⠒⠚⠓⠁⣠⠔⠀⠀⠀⢠⡶⡶⠒⠿⢓⠈⠀⠐⠀⠠⢉⠀⠀⠀⣀⣠⣁⣭⢯⠏⣱⠋⣤⣼
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠈⠉⣈⣿⣿⣷⣄⢰⠶⣀⡌⡐⢶⢆⠐⠀⠆⠰⠀⠁⠀⠀⠸⡁⠒⠊⢀⣍⠙⡀⠂⠈⠁⡴⠇⠀⢤⠆⠘⠀⠁⠁⠀⠀⠀⠀⠁⠁⣐⠯⠬⢿⢲⣐⠀⢆⣸⣶⣸⠾⢹
⡤⢴⡦⠀⠀⣅⠀⠠⠋⠀⠀⠙⠁⠁⠀⠀⠀⢀⡀⠀⠠⠿⡿⠻⠉⠙⠦⠍⠉⣂⣀⠀⠀⡀⢀⠈⠀⠀⠀⠀⠀⠂⠠⢻⠭⠟⠓⠜⢃⠞⠈⠀⡀⠈⠟⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⠀⠈⠇⠠⣓⡯⠛⢋⣘⡷⠾
⣿⣿⠗⠀⠀⢠⣤⠤⠀⠀⠀⠀⢀⡈⠤⠒⡒⠚⢃⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠀⠀⠀⠀⠐⠈⠀⠚⡭⠀⠀⠀⡄⢠⣴⣶⢢⠓⠀⠀⠀⢳⡄⣤⣠⣤⣶⢷⢶⡄⠟⠯⠢⢀⡄⢂⣉⣄⣁⢠⣄⣀⢴
⠻⠿⣿⡿⢿⡟⠿⢿⣿⠿⠿⠿⣿⠿⠇⠇⠀⢀⠀⠀⠀⡀⠀⠀⠍⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⡀⠀⠀⠀⡁⠈⠁⢚⣡⠉⡙⣉⠇⣘⠩⠴⠃⣧⣾⣶⠛⠿⡐⡦⠠⣶⣄⣉⣹⣷⡵⢇⡿⠻⠎⢭⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡚⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢤
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢸
⡭⢹⣿⣿⣿⣶⣶⣄⡠⢹⣿⠋⠉⠁⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡉⠿⠿⠟⢹⣿⠽⢿⡙⠿⠋⠁⢸
⠀⠈⠻⠿⣿⣿⣿⣿⡿⢿⣷⣀⠀⢀⣠⣄⡑⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡜⠤⣆⣀⠈⠉⠀⢀⢀⡠⠁⠀⠀⠘
⠀⠀⠀⠀⠈⠋⠉⠈⠀⠀⠀⠈⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠈⠙⣬⠚⠛⠑⠚⠛⠀⠊⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠿⢿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠁⠁⠉⠉⠋⠉⠀⠀⠀⠙⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠣⠉⠻⠿⠿⠿⠿⠿⠟⢿⣿⣿⣿⡿⣇⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡌⣿⡇⣿⣿⠀⣾⡟⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣧⢸⣿⢻⣿⡇⠀⣿⣿⠄⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⠞⠛⠈⠛⠃⠀⠛⢛⠀⠈⠛⠟⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⠀⢰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣾⣿⣿⢸⣿⣿⣿⣇⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣧⣾⣿⢻⣿⡆⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡂⣸⣿⡇⢛⣻⣸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣧⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⢿⣷⣤⡀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣾⣿⡇⣿⣷⣿⡟⣿⡿⢸⣿⣿⣿⣏⣿⣿⣻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣶⣽⣿⡇⡀⣸
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⡃⢛⠛⡛⠃⠛⠛⢘⣿⣿⣿⣯⣿⣿⣿⣿⣿⡟⣟⣎⣿⠿⠿⠅⢈⡻⠿⣛⠃⠙⢾
⣿⣿⣿⣿⣿⣿⠿⡿⣿⢟⣛⣻⣿⣿⣿⣿⣿⣿⣻⣾⣝⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣽⡟⠠⢂⠤⢀⠀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⡲⡉⠉⠙⠓⠒⠦⠿⠶⠆⢺⡎⣉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠈⡀⠘⠀⡄⢰⡀⠃⣼⣿⣿⡿⠛⠛⠛⠛⠃⢋⠓⠐⠺⢷⠻⠟⠠⠤⠀⣄⡦⠁⠉⢈
⣿⣟⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣻⣿⠀⠳⢦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣌⠒⠩⠉⡁⠳⠍⠷⡦⢐⠄⢱⡟⡉⠉⠦⢸
⣥⣶⠷⠾⠿⣿⣁⣩⡻⢗⣓⣤⣶⣾⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣯⣽⣜⣌⣻⣿⣽⣿⣧⣌⣉⠀⢠⡤⡶⠤⢴⠶⣤⡀⣀⠆⠛⠀⠙⠉⠀⠄⠸⠝⠂⠠⠤⢄⣠⡄⣶⠀⠀⠠⠀⢸
⣍⠁⠀⠀⠀⠈⠉⢉⣵⣞⣿⣿⣾⣿⣿⣿⡿⣿⣯⣽⠛⢛⣟⢻⣿⣿⡟⣻⡏⠙⣿⣯⣽⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢻⣯⣽⣿⠘⠛⡒⠒⠛⠂⣭⣥⣀⡀⠉⠀⠄⠀⢤⣬⣴⣠⣤⣤⠧⣮⡟⠑⠎⣤⡧⠴⢥⢭
⣈⣿⣷⣶⣦⣶⣴⣼⣯⣿⣿⣿⣛⣿⣛⢿⣷⡿⢿⣿⣶⢿⣿⣿⣮⣿⣿⠿⣿⢿⣛⣛⣋⣹⣁⣠⣄⣰⣿⣟⣿⣿⢿⣿⣿⣯⡽⣛⣓⣲⣶⣟⣿⣟⣀⣀⣈⣠⡠⣛⠋⠙⠢⢉⠀⠀⠠⠀⠀⡨⢀⠤⣴⣿⣆⣀⣠⣾
⠉⠉⠉⠉⠉⣹⣿⣿⡿⢻⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⢿⡿⡿⣻⣻⣯⣿⣿⣿⡿⣿⣿⣿⣿⣷⣿⣯⡿⠚⠀⠘⢻⣽⣭⣭⠉⣭⣭⣉⠃⠁⢸⣀⡂⠀⠀⠀⠀⠈⠈⣩⢉⠛⢻⣿⣽
⠇⣀⣀⣨⣉⢿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣍⣭⡏⢿⣍⣿⡏⠓⠿⠿⠟⢿⣿⣿⣶⣏⣹⣿⣾⣯⣠⣈⡁⠀⠂⠍⠋⠉⠿⠶⣿⣿⣿⠷⣿⣿⣿⣿⡿⣻⣿⣷⣞⡷⣠⣶⣾⣷⡀⡤⠾⠷⢿⣿⡿⢻⢿
⣿⣿⣟⡉⣛⣙⣻⣿⡥⣿⣿⣿⢿⣿⣿⣷⡿⠿⣿⣟⣻⡿⣿⣤⣯⣿⣿⡿⣘⣿⣿⣤⣴⣿⡿⢿⣿⣿⣿⡿⣶⡿⣿⣿⠦⠴⣀⣀⣀⣬⣖⣻⣿⢿⡟⣿⣯⣯⣴⣤⣈⣟⣛⣿⣿⣟⣉⣉⣷⣟⣛⣷⣿⣗⣼⣷⣼⢿
⣟⣋⠁⢀⣽⡿⠛⠁⠚⢻⡿⣿⢿⣯⣿⣝⣶⣿⣻⣭⢿⣦⣼⣭⣿⠛⣿⣿⣿⡟⢫⣷⣭⣽⣷⣿⣿⣿⠟⠅⠉⢹⡻⠿⠒⢲⣿⣿⣿⣿⣿⣿⣿⣿⣦⣯⣽⠃⠒⠙⠋⠝⢛⣟⣻⣿⣿⣿⣻⣭⠽⣿⠿⠛⡟⣽⣯⢸
⣍⠷⢾⢿⣁⡇⠀⢘⠧⠈⠀⠀⣾⣉⡉⠉⠱⠸⢷⡷⣲⣯⡷⠀⠀⠙⠋⠹⠛⣿⣿⣿⣿⣛⣋⢋⣽⣉⡿⣾⡾⡹⢿⣻⣿⢿⠿⣿⡷⠽⣻⠻⢫⣶⣿⣿⣻⣯⣶⣼⣠⣴⣤⣶⣯⣶⣾⣿⣟⡿⢿⣿⣿⣟⣹⣾⣿⣿
⣧⣿⡏⠁⣿⠁⣀⣒⣲⠯⠇⢵⠅⠛⣷⣏⣹⣄⣠⣠⣹⠂⣀⣐⠠⣀⣀⠀⢄⣁⠄⢤⣡⢼⡽⣭⡿⣿⠝⠋⠃⠀⠂⠛⠛⣀⣬⠉⠁⢉⠀⠒⠔⠀⠤⢛⠻⣿⣚⣿⡿⣿⣿⢿⣿⣿⢿⣿⢿⣿⣟⣯⣿⡿⣷⢬⡷⣿
⠉⠉⠁⠀⠉⠀⠀⢠⣤⣤⣶⠛⠒⢶⣻⣿⣿⢿⢉⠟⠟⢂⠈⢺⠇⡷⠊⢭⣖⣧⣾⡥⣿⠃⠁⡯⠵⠀⢠⠀⠀⠀⠀⠀⠀⢀⡞⣢⣴⠂⠑⠒⢲⣶⣶⣼⡻⢻⣿⢭⣟⠋⢭⣀⣹⠫⣿⠿⣿⡟⠙⠟⡙⡓⣿⣾⣅⣸
⡶⢤⠋⣀⣤⣄⢀⣠⣦⣤⣴⣶⣁⡉⠊⠉⢀⠈⠀⢀⠠⡰⠆⠁⠄⠹⠹⠾⠏⠀⢬⠀⠒⠂⠉⠀⠉⠁⠀⠀⠰⠆⠀⠉⠈⠘⢰⠂⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠿⢶⡾⣿⣾⣿⠷⢻⡿⣿⣿⣇⣀⣌⡀⣙⣹⡿⠿⠿
⠀⠼⠶⠋⠉⠀⠀⠉⠀⠐⠀⠀⠁⠀⠀⠀⠋⠒⠘⠛⡼⠃⠈⠀⠀⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢂⡀⠀⠀⡠⣔⠀⠀⢄⣀⡀⠂⡸⠤⡀⠀⠀⠐⢲⣟⣀⣠⡼⢿⣿⠟⠯⣜⣛⡭⡽⠿⠛⡿⠛⢲⡤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡨⢁⡄⠀⣀⢀⣠⢶⣳⣶⡀⢰⠴⠀⠀⣤⠀⠈⠀⠀⡀⠀⠍⠂⢂⣘⠿⠠⣄⠘⠉⠀⠖⠀⠀⢀⣂⠞⠁⠈⢉⡩⣿⣿⣿⣟⣆⢠⠻⢶⡇⠀⠐⢂⡕⠀⢎⠭⢾
⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠸⢆⠀⠤⢀⡐⠦⠄⣀⣘⣃⣤⠿⢻⡚⣩⠸⠞⠁⠁⢈⣠⣐⠁⠀⠀⠀⠀⠀⠘⠀⠠⠠⢐⠻⠌⡂⡡⡠⠀⣠⡀⢀⢀⠄⡚⠉⡺⠟⠁⢙⡋⡿⣻⠃⠘⠋⡿⣷⠇⡗⠛⠁⠀⢸⠃⢈⢙
⠀⠀⠀⠈⠐⠀⠀⠀⠀⠐⠀⠀⢠⡄⠈⠁⡰⢶⣟⣻⣷⠎⡇⡉⠝⠋⠀⠀⠂⠀⠀⠉⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠐⠉⠀⠀⠉⠀⠁⡈⠉⠑⣒⢿⣿⠛⠓⠓⠒⣶⠞⠋⠛⣙⠀⢠⣤⡩⣽⡯⡁⣔⣲⡀⣤⢠⠆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠰⠆⠀⠉⠄⠉⠈⠁⣠⡁⠐⠊⠁⠀⠰⠀⠀⠀⡀⠀⠀⠀⠔⠔⣀⠀⠀⠀⠀⠀⠀⠁⢀⣀⡦⠄⡀⠙⠊⠁⣄⡀⠤⣀⠀⣌⣚⣭⠉⠈⣓⣀⢀⣹⣿⣿⡿⡿⢾⠄⢰
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠃⠀⠀⠈⡄⠄⠂⠀⠁⠇⠀⠀⠀⠀⠀⠈⡡⣀⣢⣞⢀⠘⠛⡖⡶⠯⠀⠐⠀⠀⠀⠀⢀⡠⠜⠄⠠⠃⠁⠂⠀⠀⢠⣥⠒⢩⠘⠙⠥⠄⠨⠠⠻⠿⠿⠟⠻⡯⠴⠁⣞⣣⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠀⠁⠀⠀⢠⠳⢂⣇⢀⣤⣤⠀⠀⠀⠀⠀⢒⠀⠚⣷⠚⠀⠫⠊⠀⣰⠚⠀⠈⡂⠀⠀⠙⠒⠚⠋⢁⡢⠀⠀⠀⠀⢠⢶⠔⠚⠟⣂⠊⠈⠂⠀⠤⢁⠀⠀⠀⣀⣨⣡⡕⣯⠉⡱⠋⣴
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⢀⡀⠀⡀⠀⠀⠈⢁⡈⢿⢿⣷⣄⣐⢲⣠⣆⠰⠾⣂⠁⠐⠀⠀⠀⠀⠀⠀⢘⡀⠐⠀⣈⢇⢉⡑⠀⠈⠀⠖⠄⠀⠤⠀⠙⠈⠀⠀⠀⠀⠀⠈⠀⢀⣰⠧⠌⢟⢲⡰⡰⣆⣽⣦⣴⢹
⠀⡒⣻⡇⠀⠠⠤⠀⠘⠅⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠆⠠⠟⠟⢋⠀⠉⠦⠉⢀⡀⣀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠄⠃⠀⣿⠅⠛⠂⠜⡁⠋⠐⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⢀⢤⣚⠭⠛⢣⣛⢶
⠒⣶⣿⠋⢀⡀⣴⠤⠀⠀⢀⠀⢀⠠⠀⠒⠚⠀⠚⠀⠘⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠐⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠐⠊⠆⠀⠀⠀⠆⣤⠶⣖⣠⠃⠀⠀⠀⢣⠀⣄⣠⣴⡶⠧⢲⠐⠟⠽⠀⢀⡐⣀⢁⣀⣂⣠⣉⢰
⠈⠹⡿⠿⢿⡟⢿⢿⣯⣣⠿⠿⢿⣿⠏⠇⠀⠀⠠⠀⠀⠀⡀⠀⠰⠁⢀⠠⠀⠀⠂⠐⠀⠀⠀⠀⠀⢈⠀⠀⠀⢀⡀⠀⠀⠀⡁⠀⠐⢉⣅⢁⠋⡩⢇⣏⠥⠜⠀⣶⣶⡶⠻⠗⠰⠄⠰⣶⣀⣉⣷⢶⠼⢆⢷⠱⠏⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢛⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻
⠉⠉⢹⣿⣿⣿⣶⣶⣤⡰⠽⣿⠋⠉⠈⠈⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡁⠿⠿⠟⢹⣿⡿⠿⡙⠿⠋⠉
⠀⠀⠈⠻⠿⢾⣿⣿⣿⡿⠿⣿⣀⠀⠀⣠⣄⡊⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡌⠠⣦⣀⠉⠀⠀⢀⢀⡀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠙⠉⠈⠀⠀⠀⠈⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠈⠘⣍⠚⠛⠃⠘⠓⠀⠊⠁⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⠉⠉⠁⠀⠀⠀⠙⠛⢹⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠉⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⠿⠿⠿⠿⠿⠟⠛⢿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣾⡟⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡏⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢻⣿⡗⠀⣿⣿⠄⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⠞⠛⠈⠛⠃⠀⠛⠛⡀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣠⣤⣀⣄⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣾⣿⣿⢸⣿⣿⣿⣆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢻⣿⡆⠀⢈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣪⢸⣿⣇⡛⢛⣸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⢿⣷⣤⣀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣾⣿⡏⣿⣿⣿⣿⣿⣿⡇⣿⣧⣿⡟⣿⡿⢹⣿⡟⣿⣯⣿⣿⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣶⢹⣿⡇⠁⢸
⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠛⡃⢛⠛⠛⠃⠛⠛⠘⣿⣷⣿⣯⣛⣿⣻⣿⣏⣿⢛⣈⣟⣿⡟⠁⠈⠻⠿⠛⣑⡛⠻
⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠛⢛⣛⣿⣿⣿⣿⣿⣿⣻⣦⣜⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣽⡄⢠⢆⢤⠀⠀⠀⠐⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠠⡈⠛⠛⠃⠓⡶⠿⠦⠀⢲⡀⣸
⣿⣿⣿⣿⣿⣿⣷⣿⣿⢟⣻⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡄⠈⠀⠀⠀⡄⢠⣀⠀⢸⣿⣿⣿⠟⠛⠛⠻⠟⠀⠙⠂⠀⠲⣲⠿⠞⠠⡄⠄⣄⡌⠁⢙
⣿⣿⣛⡿⠿⠿⢿⣿⣿⣿⣿⢿⣿⡷⠭⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠀⢳⣂⠁⠀⠀⠙⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⣀⡈⠂⠩⠉⠀⠶⡉⠦⡤⢠⠀⢶⡟⠉⠀⢸
⣭⣵⠶⠾⠿⠿⣟⣠⣠⡹⢖⣓⣤⣶⣾⣿⣿⣿⣛⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣯⣿⣯⣷⣜⣈⣿⣯⣿⣇⠘⠛⠀⠀⢤⣤⠤⠤⠴⢤⣤⢀⡠⠄⠋⢀⠛⠉⠀⠄⠸⢔⠀⠤⠠⠀⣀⢄⣤⠀⠀⡠⢸
⣭⣭⠁⠀⠀⠀⠀⠀⢈⣵⣟⣿⣳⣴⣿⣿⣿⡟⡿⣏⣽⠛⢛⣟⠻⣿⣿⡟⣿⡋⠙⣿⣭⣽⣳⠿⠟⠿⢿⣿⣿⣿⣿⣿⣟⢩⢶⣶⡴⠀⠒⡒⠒⠐⢊⣭⣄⣀⠀⠉⠈⠄⡠⢤⣬⣶⣠⣤⣼⢰⣮⡟⠙⠈⣤⣧⠴⣼
⢉⣩⣽⣿⣶⣶⣶⣴⣼⣯⣿⣿⣟⣛⣿⣛⣿⣷⡿⣿⣿⣾⣿⢾⣿⣭⣿⣿⡿⡿⢟⣛⣛⣃⣯⣁⣠⣄⣴⣟⣟⣿⣿⢿⡾⣿⣯⡿⡉⣒⢰⢴⣟⢻⣏⣀⣀⣁⣡⠠⡚⠋⠛⠪⢁⠀⠈⠠⠀⠀⡠⠀⠠⢤⣿⠬⣀⣠
⠀⠀⠈⠉⠉⠉⢹⣿⣭⡋⢻⣽⡿⢿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣼⢿⡟⣽⣛⣿⣯⣿⣿⣿⡾⣾⣿⡿⣿⣿⣷⣯⡯⠊⠀⠘⣿⣭⣭⡭⠉⣭⣉⡉⠀⠀⢰⡀⡂⠀⠀⠀⠀⠈⠀⣉⠉⠛⢿⣻
⠒⠂⣤⣤⣬⣩⠿⢿⣿⡿⣷⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⡏⢿⣩⢿⡏⠰⠿⠿⠝⢿⣿⣷⣶⣋⣿⣿⣾⣌⣀⣈⠀⠀⠀⠏⠋⠉⠷⠾⣿⣾⣾⠷⣿⣿⣿⢿⡿⣻⣿⣷⣿⣧⣠⣴⣾⡇⠐⡤⡼⠷⢽⣿⡿⢻
⣿⣿⣿⣏⡉⢉⣙⣿⣿⠴⣿⣿⣟⣯⣿⣿⣷⠽⢿⣿⣟⣻⠿⣿⣠⣭⣿⣿⡿⣘⣻⣿⣤⣼⣿⠿⢿⣿⣿⣿⡾⣾⡿⣿⣶⠦⠴⣀⣀⣀⣤⣔⣿⣻⢽⡟⣿⣯⣧⢴⣄⣙⠛⣛⣿⣶⣏⣉⣘⣧⣟⣻⡷⣿⣓⣼⣿⣸
⠿⠯⢉⡀⣀⣼⡟⠛⠑⠊⢿⠟⣿⣿⣿⣿⣟⣶⡟⣿⡽⢧⣦⣼⣽⣿⠛⣿⣿⣿⡟⢫⣮⣭⣽⣾⣿⣿⣿⠏⠁⠉⢹⠿⠻⠒⢲⣿⣿⣿⢿⣟⣿⣿⣷⣦⣭⣙⠁⠀⠉⠉⡝⢛⣟⣿⣿⣿⣿⣻⣍⠽⡽⡿⠛⡏⣭⣽
⣭⡭⠵⠚⠿⣀⡇⠀⢹⠇⢈⠀⠀⢿⢍⡁⣉⠀⠘⢷⡓⢲⢭⡶⠀⠀⠙⠋⠻⠛⡿⣿⣿⣿⣛⣉⢋⣯⣩⣶⣾⠾⡹⢿⣿⣻⢿⡿⣿⡶⠹⣻⡻⢩⣶⣿⣟⣹⡯⢶⣼⣠⣤⣤⣶⣏⣶⣼⣿⡟⣿⠿⣷⣿⢟⣩⣿⣿
⣤⣤⢿⡏⠀⡯⠠⠤⢒⠺⢅⠃⢵⠄⠟⣏⣭⣭⣄⣠⣠⡹⠂⡄⣒⠠⣀⣀⠀⣆⡠⠌⣤⣡⢼⢻⣽⡻⣿⠙⠃⠁⠀⠂⠛⢃⣀⣬⡈⠁⢉⠀⠢⠜⠠⢅⢛⠛⣷⣚⣿⡽⢻⡿⣾⢷⣶⢿⣿⢿⢿⣛⣿⣿⠿⣧⣈⢼
⠟⠋⠈⠁⠀⠈⠀⠀⢠⡴⡤⡷⠙⠒⣺⣿⣿⣟⠿⢉⠏⠓⢂⠂⢺⠆⠷⢨⢭⠖⣣⣮⠥⠿⠁⠁⡉⠷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣢⣴⠂⠑⡖⢶⣦⣶⢼⠺⢿⣿⢩⣗⠫⢥⢀⣹⠫⣿⠾⣿⡟⠹⡟⠛⠚⣧⣯⣹
⣾⡶⢶⠉⣀⣦⡄⣉⣬⣦⣄⠰⢎⣁⢉⠊⠀⡀⠈⠀⢠⠀⡰⠆⠁⠀⠩⠱⠞⠃⠀⢆⠀⠂⠆⠉⠀⠉⠁⠀⠀⠰⠇⠀⢁⡈⠐⠴⠂⠀⠀⠀⠀⠀⠀⠀⠉⠈⠿⢻⢶⡾⣷⣾⣿⠿⢿⡿⣽⣿⣁⣈⣈⡀⢛⣻⡿⠿
⠀⠀⠾⠞⠃⠉⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠉⠒⠘⠓⡼⠁⠈⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢂⡠⣔⠀⠠⢀⣀⡐⠀⡤⠄⣀⠀⠀⠐⣴⣇⣐⣠⡼⠿⡻⠟⠻⣝⣛⣏⡽⡿⠛⡿⠻⢦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠆⡸⢁⠄⢀⣀⣀⣰⣖⣳⣦⠀⢰⠤⠀⠀⣄⠀⠈⠀⢀⡀⠈⠅⠂⢂⣹⠿⠠⣄⠚⠁⠠⠖⠀⠀⣀⣂⠞⠃⠉⢉⠩⢿⣷⣿⣷⡄⢀⠿⢿⡇⠀⠠⠆⠇⠠⢈⢸
⠀⠀⠀⠀⣢⠄⠀⠀⠀⠀⠀⠸⠆⠀⠀⢀⡀⠦⠂⣀⣘⡣⣤⠛⢻⡛⣤⠘⠚⠀⠁⢀⣤⢀⠁⠀⠀⠀⠈⠠⠘⠀⠠⠠⠒⠳⠜⢈⡡⡠⠀⣠⡀⢀⠠⠁⠛⠑⡺⠛⠉⠓⡋⡟⣻⠉⠑⠋⡶⣿⠂⡗⠛⠁⠀⠸⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠈⠀⠰⠶⢏⣿⡷⠏⡉⠉⢚⠍⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠐⠁⠀⠀⠋⠀⠀⡈⠉⠑⢘⣯⣲⠚⠒⠓⠒⣶⠮⠛⠛⠙⠀⢠⣄⢡⣜⠬⠁⡐⣤⠀⣄⢠⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠈⠉⠀⠉⢈⠀⣠⠁⠐⠋⠁⠀⠴⠀⠀⢀⡀⠀⠀⠀⠔⠖⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡮⠄⡈⠙⠊⢑⣀⡀⡄⣀⢀⣈⣚⣉⡉⠋⣶⡀⢀⣻⣿⣿⡿⡷⣾⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡠⠀⢃⠀⠀⠀⠄⠈⠂⠀⠀⢥⠀⠐⠀⠀⠀⠈⡠⣀⣧⣏⠀⠘⢓⡖⡶⠧⠀⠀⠀⠀⠀⠀⢂⡬⠞⠄⠀⠃⠃⠠⠀⡀⢀⡔⠎⢋⠘⠺⠥⠅⠈⠨⢻⠿⠿⠛⢛⡿⠴⠠⣔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠀⢰⠓⠀⣄⢠⣴⣄⠀⠀⠀⠀⠀⡒⠐⠘⣧⠚⠘⡟⠊⠀⣼⠪⠀⠁⡂⠀⠀⠑⠒⠚⠋⢁⡦⠀⠀⠀⠀⣠⢶⠔⠺⠏⠂⠭⠂⠂⠀⠀⠁⠀⠀⠀⠀⣈⢫⡵⣿⠤⣻⢻
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⣀⠀⠀⡀⠀⠀⠈⢀⠸⢿⢿⣷⡄⣖⢢⣰⢀⠰⠾⣀⠡⠐⠀⠂⢀⠀⠀⠀⢈⡐⠒⠀⣨⠁⢁⠰⠀⠉⠠⠖⠀⠀⢤⡁⠉⠈⠈⠀⠀⠀⠀⠈⠀⠈⣲⠧⠜⣛⣢⡡⠨⡆⣱⡦⣾
⠀⠀⠛⣻⣆⠀⠠⠤⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠄⠤⠟⠟⢉⠀⠙⠤⠁⢀⡀⡀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠄⠂⠌⡧⠥⠛⠂⠞⡠⠃⠁⠀⠀⠘⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢱⠀⢀⣲⠻⠷⢋⣻
⠒⠲⣾⡿⠋⢠⣤⠴⢀⡀⠀⢀⠀⢠⠠⠀⠒⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠀⠀⠂⠀⠀⠀⠀⢀⠀⠐⠀⠐⠋⠆⠀⠀⢠⠀⣤⢶⣖⡜⠂⠀⠀⠈⢦⢠⣄⣤⣴⡶⣵⢂⠴⠿⡽⠄⢁⠐⠈⢉⡀⠃⣨⢹
⠀⠹⠿⡹⢿⡿⠿⢿⣿⣣⡼⠿⠿⠻⡷⠏⠀⠀⠀⡠⠀⠀⠀⠀⠀⠰⠁⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⢉⠀⠀⠀⢀⡀⠀⠀⠀⠁⠁⠑⢉⡅⢁⠋⡫⢀⢇⠁⠼⢨⣦⣿⡾⠻⠗⠢⠄⠠⣦⡐⣙⣶⢿⣹⢰⡷⢩⠽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠉⠈⠉⠩⣿⣿⣿⣷⣶⣦⣀⢽⣿⠛⠉⠉⠘⠃⢀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡉⠿⠿⠿⢹⣿⡿⠷⣛⢿
⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⠿⣿⣄⡀⠀⣀⣤⣘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠡⢤⣀⠈⠉⠀⠀⢀⣠⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠁⠀⠀⠈⠁⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠑⣧⠜⠟⠃⠚⠓⠂⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠈⠈⠉⠉⠉⠉⠀⠈⠉⠛⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉⠹⠿⠿⠿⠿⢿⡿⢿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡟⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢻⣿⡗⠂⣿⣿⢢⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⡺⠛⠈⠛⠃⠀⠛⠛⠀⠈⠛⠟⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣀⣀⣈⣨⣥⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣾⣿⣿⢸⣿⣿⣿⡆⣿⣿⣸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢻⣿⡆⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⢺⣿⣇⡛⣛⣸⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⢿⣷⣤⡀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣏⣿⣯⣿⡟⣿⣿⢸⣿⣿⣿⡟⣿⣿⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣶⣻⣿⣇⣀⢸
⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓⠻⠛⠛⠃⠛⠛⠘⢻⣷⣿⣧⣿⣿⣙⣿⣿⣿⣟⣾⣻⣿⣿⣿⣎⣻⡿⠛⠉⠙⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⢛⣻⣿⣿⣿⣻⣿⣿⣻⣾⣜⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡏⢀⡄⣀⡀⠃⠘⠂⠒⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢠⠛⠛⠛⠃⠶⢴⡿⠧⠤⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡞⠁⠋⠁⠀⠀⠀⡀⢠⠆⣼⣿⣿⣿⣿⣿⣿⠛⣿⡟⠛⠒⠟⠢⢴⢆⣶⡶⢠⣤⢠⡀⣼
⣙⣿⣿⣏⣉⡿⠿⠿⢿⣿⣿⣿⡿⢿⣟⡛⢯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣏⠀⡷⠀⡈⠁⠀⠘⠇⠈⠀⠈⢹⣿⣿⡿⠛⠱⠢⠁⣀⡘⡶⠚⠉⠀⢦⡛⢦⣀⠀⠀⢦⣾⢻
⠭⠠⣸⣿⣿⠿⠿⠿⣿⣤⣤⡻⢟⣛⣷⣾⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⣿⣯⣧⣧⣙⣿⠀⠣⠤⠀⠀⠀⠀⠀⠀⠀⠤⣤⢤⢠⠄⠠⠄⠞⠁⠛⠋⠁⡄⣰⠦⠀⢤⢀⡀⢀⠀⣬⡁⢸
⣵⣶⣦⣮⡀⠀⠁⠀⠀⠀⢨⣵⣟⣿⣷⣶⣿⣿⣿⡟⡿⣯⣽⠛⢛⣟⣻⣿⣿⡟⣿⡋⠛⣿⣭⣽⣷⠿⠿⠿⢿⣿⣿⣥⣧⣶⣖⠀⠂⢐⡄⠐⠒⠐⠒⠂⢊⣉⣉⠀⠀⠀⠀⡀⠀⣤⣀⣄⣠⣠⣤⢤⣒⡟⠢⢁⣄⣾
⠄⠀⠁⡤⠵⣿⣿⣶⣿⣼⣺⣿⣿⣿⣿⣻⣿⣛⣿⣿⡿⣿⣿⣿⣾⣿⣿⣽⣿⣿⡿⡟⣟⣛⣛⣃⣏⣁⣤⣄⣴⡿⣿⣿⣿⢿⡿⣿⣫⡯⠛⡒⢀⣴⣓⢶⠎⡈⠉⣉⣣⢄⠔⠓⠒⠘⠋⠁⠉⢉⠁⠀⢀⠁⠠⢤⣼⢿
⠀⢰⣠⣤⠀⠀⠉⡉⣡⣿⣭⣭⣿⣿⣿⢿⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣷⣽⢿⣿⢿⣟⣿⣯⣿⣿⣿⣾⣾⣿⡿⢽⣷⣷⣯⣾⠏⠁⠙⣿⣍⣩⣭⠩⣗⡑⠒⠒⠀⢨⠀⠐⠀⠀⠀⠁⠀⠐⠊⠛⢾
⡀⠀⣉⣁⣶⣴⣾⣿⣿⣿⣿⡿⣷⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡏⣿⣽⣿⡏⡱⠿⠿⠝⢿⣿⣷⣾⣋⣿⣿⣿⣏⣀⣈⠀⠀⠀⠉⠛⠀⠶⡶⣷⣾⣿⠿⣿⣿⣿⣿⡿⣿⣶⣤⣿⣇⣀⣠⣶⣆⠀⣀⣸⡿⢿⣾
⣿⣿⣿⣿⣿⣿⠄⣈⣄⣽⡿⢴⣿⣿⣿⣿⣿⣿⣿⠽⢿⣿⣟⣻⠿⣿⣤⣭⣿⣿⡿⣘⣿⣿⣤⣼⣿⠿⣿⣿⣿⣿⣶⣾⠿⣿⣦⡤⢤⣀⣀⣠⣤⡴⣯⣺⣻⡞⣟⣟⣇⣤⣀⣛⠿⢿⣛⣵⡟⢛⠛⣧⣿⠷⠦⢶⣆⣽
⣿⠀⢻⠛⢭⣅⣠⣼⡟⠋⢑⠊⠿⠟⣿⣿⣿⣿⣟⣾⣿⣿⡿⣷⣦⣾⣽⣟⠛⣿⣿⣿⡟⢻⣾⣭⣽⣾⣿⣿⣿⠏⠅⠉⢿⢿⢿⠒⢶⣿⣿⣿⣿⣿⣿⣿⣿⣥⣙⡛⠋⠈⠯⠝⡿⠛⡿⣻⣿⣿⣿⢟⣛⣻⣳⣾⠿⣿
⠶⠶⣿⡿⠟⣋⡹⣧⡇⠀⠨⠗⣈⠀⠀⢻⢭⡀⣉⣐⣙⣳⣓⣷⠿⠶⠀⠀⠙⠉⠻⠛⡿⣿⣿⣿⣛⣉⣋⣏⣹⢷⣴⢾⠹⣗⣿⣿⢿⡿⣿⢢⠱⣿⡟⣛⣼⡿⣿⣿⣶⣦⡼⢀⣀⣀⣼⣟⣯⣹⣿⡿⣶⡷⣵⣶⡶⢿
⢀⣀⣒⣶⣿⡇⠀⣭⠤⠤⠽⠿⢟⡃⣠⠜⢿⣿⣧⣼⣄⣠⣠⡿⠃⡄⣃⢠⣤⣀⡠⢄⡡⠄⣤⣥⢬⢿⣽⠻⣏⠝⠙⠰⠀⠊⠟⢃⣠⣜⡛⠁⡉⠀⠢⠼⠠⢹⢛⠛⡧⢴⣿⣿⢿⣿⣾⣧⡽⣿⣿⣿⢿⣻⣟⣻⣿⣿
⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠐⠶⠶⠿⠉⢩⣿⣿⣿⡿⠟⡙⠛⠟⢣⠀⣿⢞⣷⠺⣻⣖⡷⣯⠥⡟⠙⠡⠯⠆⠀⡄⠀⠀⠀⠀⠠⠈⢉⡏⣂⡖⠊⡤⡴⣶⣆⣎⣼⢶⣷⣟⢻⡗⢻⢋⠉⢸⣗⣾⣿⣿⣾⢻⡿⠻⠧⣿
⠶⠾⠿⣷⢾⠍⣵⣶⡶⢽⣶⠶⠶⠶⢿⡧⢠⠉⠤⠠⠀⠀⠠⠦⡴⠂⡠⠌⠻⠱⠞⠁⠰⢎⠀⠑⠆⠉⠀⠉⠀⠀⠀⠴⠅⠀⢉⡉⠀⢴⠂⠁⠀⠀⠀⠀⠀⠀⠋⠸⠾⣻⣤⣿⣷⣼⣿⣯⣶⣷⣶⣾⡇⠈⡒⠃⠰⢿
⣀⣀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠛⠉⣙⡾⠁⠈⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣀⠀⠀⠀⠤⡄⠀⠀⠀⢀⠀⠀⣀⢄⣀⠀⠃⡠⣴⠯⡀⣁⣹⣿⠷⠾⣛⣻⣛⣛⡻⣿⠗⣿⢿
⠋⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠢⡜⢡⢆⣀⣀⣀⣴⣶⣳⣦⠀⢡⠄⠀⢂⣄⠀⠨⠈⢀⡀⠨⠁⠶⢈⣰⠷⠠⣀⠞⠫⠠⠶⠁⠀⢑⣚⠶⡇⠙⣉⢹⢿⣷⣾⣷⡁⣰⠯⢭⡏⠁⠁⠄⡈⢈
⣀⠀⠂⠀⠀⠤⢷⣇⠀⠀⠀⠀⠀⠸⠧⢀⡒⣀⡼⠲⢃⣀⣘⡤⣬⠻⣻⡛⡤⠘⠚⠀⠀⢈⣤⠊⠁⠀⠀⠂⠈⠠⠘⠀⠀⠠⠸⢣⢔⢘⢠⣀⠀⡠⠄⣀⠠⠁⠿⠣⣴⠗⠛⣳⠛⣟⣻⠛⠧⢞⣤⣾⠗⡆⠶⠚⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠸⠂⠁⢀⡴⠾⢿⣿⡿⢿⠉⡉⢊⢉⠀⠐⠀⠐⠊⠉⠀⠀⢁⠀⠠⠄⠀⠀⠀⠀⠒⠓⠀⠘⠋⠀⠉⡈⡉⠣⠘⣶⢺⠛⠘⠗⠲⣤⣾⠇⠻⢛⠀⣀⠘⢓⢻⡖⠡⠤⣤⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡊⠉⠙⢀⠉⠁⠊⠉⣉⢄⣴⠀⠘⠉⠀⠀⢶⠀⠀⢀⠀⠀⠀⠀⠤⠖⡀⠀⠀⠀⠂⠀⠈⠁⢀⣀⡍⠅⡈⠵⠎⢁⡀⢀⡀⡀⢀⣒⠽⣲⡞⡿⢮⠉⠰⣷⣿⣿⣾⣿
⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠤⠀⠃⠀⠀⢀⠀⠈⠓⠀⠀⠁⠀⠀⠀⠀⠀⢘⡤⣀⣷⣏⡄⠚⢃⣒⡶⠅⢀⠄⠀⠀⠀⠀⢀⣠⠟⠁⠰⠇⠃⠀⠀⡀⡘⡥⠜⠇⠘⠽⣋⠋⠐⣘⢿⣿⣿⠿⣿⣿⡡⢸
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠈⠀⠀⠀⠰⠓⣬⣤⣰⣶⣄⠀⠀⠀⠀⠀⡒⠐⠹⡇⠓⠘⠟⠉⢀⣜⠪⠀⠁⠂⠀⠀⠓⠒⠛⠚⠑⡠⠀⠀⠀⠀⣠⣶⠥⣼⣧⠠⡖⠐⠀⠀⠀⠂⠀⠈⠑⠁⠐⠊⢳⠖⣲
⠇⠀⣀⠀⠀⣀⡀⠀⠠⠄⠀⢀⡀⠀⠀⣠⠀⠀⠄⠀⠀⠀⠠⠼⢿⢿⣷⣄⣖⡱⣰⣠⡲⢾⣀⠁⠐⠀⠂⠀⠀⠀⠀⢈⠐⠒⠀⡉⠉⢒⠴⠐⠀⠠⢄⣀⠀⣉⠉⠆⠐⠐⠁⠀⠀⠀⠘⠐⠉⢴⣆⡾⡿⢍⢋⢑⡉⣺
⠒⢀⣀⣠⣍⣿⣇⠀⠔⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⠀⡀⡺⠛⠟⢀⠀⠙⠴⠀⣁⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢂⠜⡯⠷⠓⠀⠞⠰⠋⠣⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢣⠈⡁⠥⣻⣿
⠀⠤⠉⣉⣿⣟⣭⢤⡀⡘⣤⡤⠀⣠⠀⣤⠀⠀⠊⠉⠉⠋⠄⠃⠀⠀⠀⠀⡀⡀⠁⠉⠈⠁⢀⠀⠂⠀⠀⠀⠀⣀⠀⠐⠁⠐⢫⠅⠀⠀⢠⠀⣥⣤⡄⡸⠀⠀⠀⠈⡄⢀⠀⡄⣰⣴⣆⣤⣰⣟⣣⠀⠘⠰⠙⠊⠁⠐
⠠⠿⠿⠹⢸⡿⠿⠟⡿⣣⢾⣿⠿⠻⡏⡿⡷⠀⠀⠀⢀⠖⠀⠀⡰⠀⠀⠘⠀⠄⠄⠀⠐⠀⠐⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀⠀⠀⠀⢈⠂⠉⠖⢋⡌⠱⠳⡶⢐⢖⣂⡨⢸⣉⣯⡹⢷⡧⢌⠀⣀⣄⠠⠾⣷⣥⣸⢡⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢯⣿⡟⣻⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢅⠀⠀⠉⠉⠩⣿⣿⣿⣷⣶⣦⣀⡌⢿⠏⠉⠉⠘⠃⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⠹⠷⠿⠊⣿⡿⠿⣿
⠇⠀⠀⠀⠀⠀⠘⠿⠯⣿⣿⣿⣿⠿⣿⣆⡀⠀⣀⣤⣀⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠣⢤⣀⠈⠉⠁⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠈⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠈⠁⢣⠀⠋⠃⠐⠓⠂⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠉⠛⢩⣿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠻⠿⠿⠿⠿⡿⠻⢿⣿⣿⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠁⣾⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⣏⠀⣿⣿⡀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢿⣿⡇⠂⣿⣿⠱⣼⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠈⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⢘⠛⠈⠛⠃⠀⠛⠛⢀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣠⣀⣀⣠⣄⣤⣄⣀⣀⣀⣀⣀⢀⣀⣀⢰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣾⣿⣿⢸⣿⣿⣿⡆⣿⣿⣸⣿⣇⣿⣿⢰⣿⣿⣿⣧⣾⣿⢻⣿⡆⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⢛⣸⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣼⣿⣿⣿⣿⠻⢿⣷⣤⡀⠠⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⣿⣯⣿⡟⣿⣿⢸⣿⡿⣿⡇⣿⣿⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣶⣶⢻⣿⣇⣶⢸
⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣋⣋⣙⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠓⠻⠋⠛⡃⠛⠛⠘⠛⣷⣿⣷⣿⣿⣜⣛⣿⣿⣿⣮⣿⣿⣟⣁⣼⣿⣿⡛⠁⠈⢹
⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣋⣽⣿⣿⣿⣿⣿⣿⣟⣷⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢁⡄⣐⡀⢠⠀⠇⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢔⡛⠛⠛⠃⠤⢤⡿⠧⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⡞⠁⠋⠃⠸⠀⠀⢀⠀⡄⢰⣿⣿⣿⣿⣿⡿⡿⠻⢻⡟⠛⠓⠞⠡⢴⢲⣶⣦⢪⣡⢠⢸
⣿⣉⣻⣿⣿⣉⠽⠿⡛⢻⣿⣿⣿⡿⣿⣟⡛⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⡿⣿⣿⣷⣶⣾⣿⣿⡏⠸⡇⠀⠀⠁⢀⢰⣆⠈⠁⠁⠈⢿⣿⣿⠟⠋⠰⠆⢇⢀⡐⠶⠊⠂⠀⢴⣛⢆⣀⠀⡂⢠⣾
⡿⠭⠄⠚⣾⣿⠿⠿⠿⠯⢤⠤⡺⢛⣙⣷⠿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣧⣿⣿⠀⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⢴⢤⠄⠠⠤⠞⠁⠛⠃⠈⡤⢰⢥⠀⠤⡀⡀⢀⡀⣬⣻
⣯⣭⣶⣶⣶⣀⠀⠀⠀⠀⠀⢈⣵⣿⣿⣻⣶⣿⣷⣿⡟⡟⣯⣽⠋⢹⣟⣻⣿⣿⡟⣿⡋⢛⣿⣭⣽⡳⠿⠿⠿⢿⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠚⣉⡈⠉⠀⠀⠈⠀⢀⣤⣀⣠⢈⣠⣤⡇⣒⡿⠳⡝⣩
⠀⠀⠀⠀⠤⠤⣿⣿⣿⡯⣴⣲⣷⣷⣿⣿⣿⣿⣛⣻⣿⣟⣿⣿⣿⢿⣿⣿⣬⣿⣿⡿⡟⣟⣛⣛⣃⣭⣁⣤⣄⣶⡯⣿⣿⣟⢿⠾⣶⣫⡮⠛⡂⢀⢴⣓⢶⡎⣈⠉⢋⣩⠄⠔⠚⠂⠈⠛⠉⠙⢉⠁⠀⢈⠇⢀⢠⣼
⠀⠀⢀⣤⣤⠀⠀⠀⣀⣰⢿⣭⣭⣭⢿⣟⢻⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⢿⣿⣿⡽⢿⡟⢟⣟⣿⣯⣿⣿⣿⣾⣾⣶⡿⢿⣶⣷⣏⡾⠎⠈⠙⣟⣭⣋⣭⠉⣕⡓⠒⠒⠂⢨⠀⠐⠀⠀⠀⠉⠀⠐⠒⢻
⢻⣀⠀⢉⣉⣶⣶⣾⣷⣛⣻⣿⡿⣿⠿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣷⣦⣽⡏⣻⣭⢿⡉⡑⠻⠿⠝⢿⣿⣷⣾⣉⣿⣿⣿⣋⣀⣈⠀⠀⠀⠍⠋⠀⠶⠶⣷⣶⣾⠿⣿⣿⣿⣿⣿⣿⣶⣧⣼⣏⣀⣠⣴⣆⠀⣀⣰⣯⢾
⢽⣿⠿⣿⣿⣿⡿⠤⣠⣤⣼⡿⢞⣿⣿⣿⣻⣽⣿⣿⠼⢻⣿⣟⣻⠿⢿⣦⣥⣟⣿⣟⣘⣿⣿⢤⣼⣟⠿⢿⣿⣿⣿⣶⣼⠿⣿⣧⡤⢤⣀⣀⣀⣤⡴⣿⣺⢳⡞⣿⣟⣃⣤⣄⡙⠿⢿⣿⣥⡿⠛⡛⣧⣿⠷⠦⣤⣼
⡿⠿⠂⢺⣛⣣⢥⣤⡭⡏⠉⢀⠊⢛⠛⢻⢻⣿⣿⣿⣾⡟⣽⡶⢷⣶⣶⡾⠿⣙⣿⣿⣿⣟⣻⣮⣭⣽⣾⣿⣿⣿⠍⠀⠉⠙⢿⠻⠒⣶⣿⣿⣿⣿⣿⣿⣿⣾⣥⣙⠛⠁⠈⠻⠍⡻⠛⣿⢻⣿⣿⣿⣿⠛⣛⣷⣾⣿
⠙⠹⠿⢷⣶⢊⣉⡙⣷⡆⠀⠸⢇⡀⡀⠀⠹⠮⡄⣀⣀⡈⡳⣑⡿⠾⠗⠀⠀⠉⠉⠻⠙⡿⣿⣿⣿⣛⣉⢋⣎⣹⢷⣶⠾⡹⣗⣿⡿⢿⠿⣿⢦⠱⣿⡻⣋⣽⣿⢟⣿⣒⣆⣸⢀⣀⣀⣨⣟⣭⣹⣿⡿⣿⣷⣿⣶⣾
⠀⠀⣀⣸⣷⠻⠇⠀⠦⡀⠠⠬⠽⠷⣋⣺⡀⢋⣧⣦⡤⣄⣰⣠⡼⠑⠄⣁⠠⡤⣀⡠⢄⡠⠄⣤⣥⢬⢿⣽⠻⡯⠙⠉⠀⠀⠊⠟⢃⣀⣑⡙⠁⡈⠀⠠⠄⠠⢫⢛⠟⡧⢴⣿⣿⢿⣿⣼⣧⣭⣭⢿⣿⢷⠶⣟⣿⣿
⣆⠀⠉⠛⠉⠀⢀⠀⠀⠀⠀⠐⠒⠒⠛⠉⢉⣻⣽⣿⠟⠓⡐⠋⠉⠩⠀⡽⠒⣓⠒⢻⡒⡷⣯⠴⠏⠁⠀⡯⠖⠀⡄⠀⠀⠀⠀⠀⠈⢁⠟⢂⡖⠁⠠⡴⣦⣆⣞⣘⢰⣾⣟⢛⠳⢛⠋⠉⢺⣟⣾⣽⣾⣶⢻⡟⠻⢻
⡻⠝⠟⠿⠷⠺⠋⣴⣶⡶⠲⠶⠶⠶⠄⠻⡤⠌⠉⠀⡤⠀⠀⠠⠠⡔⠁⡠⠀⠋⠐⠛⡁⠰⣎⠀⠁⠂⠁⠀⠉⠀⠀⠀⠴⠅⠀⢉⡀⠘⡴⠂⠁⠀⠀⠀⠀⠁⠀⠋⠸⠾⣿⣨⣽⣦⣸⣿⣏⣶⣿⣶⣾⡃⠀⡰⠁⢰
⠄⠀⡀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢙⡋⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡈⠀⠀⠠⡄⠀⠀⠀⢀⠀⠀⣇⢀⣀⠀⠂⠠⣤⠎⠀⣉⢸⣿⠶⡾⣃⡻⠺⣛⡻⢿⠷⢾
⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡴⠂⡔⡠⠂⣀⡄⣀⣴⢂⣶⣇⡈⢵⠆⠀⠂⣄⠀⠨⠀⢀⠀⠨⠑⠶⢊⣹⠷⢠⡀⠛⠩⠠⠶⠁⠈⢁⡦⠶⠀⠉⠘⢑⢿⣷⣶⣇⡁⠀⢯⣍⡏⠁⠁⡀⣸
⠤⢤⠄⠂⠀⠀⠀⠸⠃⠄⠀⠀⠀⠀⠘⠣⢀⠒⢀⠄⠓⢂⣠⣌⡄⣦⢉⡻⡛⣤⠘⠛⠀⠉⢈⣤⡊⠁⠀⠀⠀⠈⠠⠘⠀⠀⠠⠜⢣⠐⢘⢠⣀⠂⠠⠀⡀⠀⠉⠿⠢⣴⠷⠚⠻⠛⣿⢿⠛⠣⠜⣤⣼⠅⡤⠴⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠂⠁⠀⡔⠚⠫⢥⡜⢲⡉⠅⠪⢉⠀⠀⠁⠐⠂⠀⠀⠀⠁⠀⠀⠄⠀⠐⠀⠀⠒⠃⠀⠘⠋⠈⠀⠈⠙⠣⠹⣖⢶⠒⠺⠇⠤⣮⣴⠖⠖⠛⠀⢀⠀⠋⢻⡖⠃⣠⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠙⢀⠀⠀⠈⠉⡉⢄⠴⠁⠀⠉⠀⠀⣂⠀⠀⢀⡀⠀⠀⠀⠠⠆⡀⠀⠀⠀⠀⠀⠈⠀⣀⣀⣉⠁⡙⠵⠎⠁⡀⢀⡀⠀⢀⡢⠹⣲⠎⡟⢬⠉⠀⢷⣷⣿⣾
⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⡀⠀⠀⠤⠀⠁⠀⡀⠀⠀⠂⠃⠀⠀⠀⠀⠈⠀⠀⠀⢈⡠⣼⢵⡏⡄⠚⢋⣖⠶⠅⠀⠄⠀⠀⠀⠀⢀⡀⠋⠁⠠⠇⠃⠄⠀⠀⠘⡥⠜⠟⠺⢹⣛⡋⠀⣐⢿⣷⣾⠽⡿⣿⣻
⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠙⣠⡆⢰⣶⣤⠈⠀⠀⠀⠀⡎⠀⠙⡏⠓⠘⠓⠉⠀⡞⠂⠀⠀⠂⠀⠀⠓⠒⠒⠊⠑⡠⠀⠀⠀⠀⢠⣤⠥⣴⣷⢀⡖⠀⠀⠀⠀⠂⠈⠉⠁⠉⠐⠎⢃⢾
⠀⠋⠀⡀⠀⣀⣀⡀⠀⠠⠄⠀⢀⡤⠀⠀⢠⠀⠀⠄⠀⠀⠀⠠⠼⢿⢿⣷⣄⣎⡱⣴⣨⡸⢟⡈⠁⠐⠀⠂⠀⠀⠀⠀⣋⠐⠒⠀⡨⠁⢒⠀⠒⠀⠢⢔⡀⠀⣉⠉⠆⠐⠀⠁⠀⠀⠀⠰⠀⠐⢠⣆⡰⡶⢉⢊⢑⣹
⠀⠅⠁⣀⣀⣀⣼⣧⠀⠘⢛⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⡀⠒⠛⠍⢀⠀⠸⡖⠀⢀⢠⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠔⠀⠜⡯⠵⠓⠠⠞⠰⠋⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢫⠉⠃⢠⢿
⠸⠤⠀⢀⡀⢿⣿⣥⡀⣆⡈⠤⠄⠀⣤⣀⣤⠐⢀⠈⠉⠈⠉⠀⠁⠀⠀⠀⠀⡀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢣⠅⠀⠀⢠⠀⣥⣤⡆⡐⠀⠀⠀⢸⡀⠀⠀⡀⣠⣴⣂⣤⢠⣶⣢⠀⠀⢠⠑⠒⠩
⠀⠸⠿⠿⢸⡯⠿⠿⡯⠣⠼⠿⣿⠿⠏⠏⠉⡗⠀⠀⠀⠀⠖⠀⠀⠰⠀⠀⠐⠀⠤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⢀⠀⠀⠀⢈⠂⠉⠖⣋⡈⠑⠷⠶⢀⠖⣂⡈⢸⣉⣯⡹⢷⡧⢈⠀⣀⣅⠀⠶⣤⣲⢲⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣟⣿⣿⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠈⠉⠉⠉⢽⣿⣿⣿⣶⣶⣄⡈⢿⡟⠉⠉⠀⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠹⠿⠿⠎⣿⣿
⠀⠀⡿⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⡿⢿⣆⡀⠀⢀⣠⣀⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠋⢤⣄⠀⠙⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠈⠁⠀⠈⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠉⢒⡈⠭⠓⠐⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠈⠉⠙⠉⠁⠀⠀⠉⠛⢛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠈⠹⠻⠿⠿⠿⠿⡿⢻⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡏⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣿⡟⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⣟⠀⣿⣿⡀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢨⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣧⢸⣿⣿⣿⡏⠀⣿⣿⠱⣼⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⠘⡟⠈⠛⠃⠀⠛⠛⠀⠈⠛⠿⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠁⠀⡀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣈⣨⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⣇⣼⣿⣿⢹⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣧⣾⣿⢻⣿⡆⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⢼⣿⣧⣿⣇⣿⣿⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⠻⢿⣷⣤⡐⠠⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡟⣿⣿⢸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣶⢹⣿⡷⣖⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣋⣋⣙⣿⣿⣿⣿⡿⠿⢿⣿⣻⢿⣿⣿⣽⣿⣿⣿⡿⠛⢻⠛⠛⠃⠛⠛⠘⠛⢃⣾⣿⣿⣿⣜⣿⣯⣛⣻⠿⣿⣿⣿⣁⣈⣻⣿⣟⠁⣈⢹
⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣋⣽⣿⣿⣿⣿⣿⣿⣟⣷⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢃⠀⠄⠀⢄⠀⢠⠀⠀⡘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠀⡙⠻⠛⠯⢥⣬⣽
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡞⢸⠲⠀⢸⠀⠀⠀⠀⢡⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠟⢷⢤⣤⡔⣶⣦⠄⣹
⣿⣾⣷⣧⣹⣿⣿⡭⠽⠿⣛⢙⣿⣿⣿⡿⢿⣛⡻⠳⢿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣷⣶⣾⡅⢸⡇⠀⠀⠂⠀⣀⣄⠀⣦⡼⠠⣿⣿⣿⣿⣿⡿⠛⠰⠶⠋⢀⡐⢶⠞⠖⠂⢠⠼⢄⣀⡀⣾
⣿⣿⣭⡭⠤⠚⢿⣿⠿⠿⠿⠿⠤⠤⡿⢟⣙⣷⠿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣯⣻⣫⡁⠘⠁⢀⡗⠀⠾⠋⠙⠀⠀⠀⢀⠟⠿⡿⢽⢿⠆⠀⠤⠔⠋⠛⠛⠘⡀⠀⡠⠀⢀⡀⡈⠀⢘
⡛⢻⣿⣭⠷⣶⣶⣤⡀⠉⠀⠀⠀⢠⣵⣿⣿⣿⣶⣿⣷⣿⡟⡟⣯⣽⠋⢹⣟⣻⣿⣿⠟⣿⡋⢛⣿⣭⣝⡳⠿⠿⠿⠷⠀⡁⢨⣤⣄⠀⠀⠀⠀⠀⠐⠂⠠⠖⠁⠘⠛⡂⠉⠐⠂⠀⠀⠀⣀⠑⠨⡀⢀⣀⣆⠅⠲⢺
⢿⠛⠃⠀⠀⠀⠤⠴⠿⢿⣿⡿⣷⣳⣿⣾⣿⣿⣿⣿⣛⣻⣿⢟⣿⣿⣿⢿⣿⣿⣬⣿⣿⡿⡟⣟⣛⣛⣁⣏⡁⣤⣄⣀⡋⡳⣿⣿⢇⡶⣤⢚⠨⠓⡄⢀⢤⡲⢦⠎⡈⠙⠛⢂⢄⠄⠐⠀⢈⠛⠋⠘⢛⠋⠀⠉⡏⢘
⠀⢠⠀⠀⠀⠭⠦⠄⠀⢀⣀⣀⢻⣯⣭⣭⢿⣟⢻⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⢿⣿⣧⡽⣿⣿⢟⡟⣿⣯⣥⣿⣿⢾⣾⣶⠻⢴⢰⢢⣇⡎⠎⠁⠨⣞⡙⢂⣉⠉⡒⠓⠒⠀⠂⢀⠀⠀⠈⠀⠀⠈⠀⢸
⡛⢛⢋⣥⠀⣈⣉⣵⣶⣶⣶⣚⣛⣿⡿⢷⠿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣶⣦⢽⠍⣫⣭⣿⠉⡘⠻⠷⠝⢿⣿⣷⣾⣉⣍⣷⣤⡉⣀⡐⠀⠀⠀⠉⠟⠈⠦⣴⣶⣶⣿⣫⣿⣷⣶⣿⣿⢿⣶⣒⡺⣇⠀⣀⣤⣤⠀⢀⣰
⡥⡀⣩⣿⡿⢿⣿⣿⡿⠤⢠⣤⣼⡿⢞⣻⣿⣿⣡⣼⣿⣿⠜⣻⣿⣗⡻⠷⢟⣤⣥⣗⣿⡗⣘⣻⣿⣤⢼⣟⠯⢿⣿⣿⣷⢴⣼⠿⣯⣤⡤⣤⡀⢀⢀⣀⠴⣟⣺⣧⠶⣿⣟⣋⣨⣁⠻⡿⠿⣿⣣⣿⠛⠟⣏⡦⢮⣬
⣧⣔⡻⠛⠃⢺⣟⣂⠤⣤⡤⠍⠉⢀⡁⢙⠛⢻⢹⣶⣿⣿⣿⣟⡽⡶⢷⣶⣶⡼⡏⢙⣿⣿⣿⣞⣻⣮⣭⣭⣾⣿⣿⣿⠈⠀⠉⣔⠟⠻⠲⠾⣿⣿⣿⡿⢿⣿⣿⣮⣥⠛⠛⠉⠉⢛⡓⠒⠾⣿⢿⣿⣶⣷⣿⠗⠶⢾
⠶⠂⢉⡙⠿⠷⠶⠊⣉⡈⣷⡞⠀⠀⢏⡠⡀⡀⠸⣶⡄⣀⣀⠈⡰⢉⠽⠾⠶⠀⠀⠙⠉⡫⠙⡿⣿⣿⣟⣋⣉⣩⣍⣹⢥⣴⢖⠻⣖⣾⣷⢿⡯⣿⢄⠩⡿⡿⡛⣩⣻⠿⣷⡰⣄⣰⢀⢀⠀⣁⡮⣉⣹⣿⣿⣷⣿⣿
⠀⠀⠀⠀⣠⣬⣿⠟⠗⠀⠒⠀⠂⠀⠜⠣⣉⣲⡀⣈⣿⣧⡤⣄⣰⣰⡸⠙⠄⣅⢠⡤⣀⡠⢄⡠⢄⡤⣤⢯⢯⣽⢻⣏⠛⠛⠀⠀⠘⠟⠇⢁⣐⡛⠐⠚⠀⢄⠠⠈⡻⠟⠟⠄⠔⣟⣺⣿⣿⣽⣏⣿⣿⣿⣧⣮⠤⣼
⣦⣤⣶⠀⠈⢋⡁⠀⣀⡀⠀⠀⢀⠐⠒⠒⠛⠉⡉⣯⣿⢿⠏⠓⠐⠃⠈⠩⠀⡽⠒⣓⢒⢻⡒⡶⣯⠴⡏⠉⢀⠭⠎⠀⡄⠀⠀⠀⠄⠀⠈⢩⡝⢂⡄⠁⢤⣤⣦⠤⡌⠐⢴⣶⡾⠛⠯⠞⠛⠙⢻⠻⣽⣯⣽⣾⠓⣿
⣿⡿⠙⠋⠛⠛⠿⠉⡂⡰⢶⠞⠰⠶⠶⠂⠒⠹⠦⠄⡉⠀⡠⠀⠀⠴⠢⡔⠁⡠⠈⠫⠐⠚⡀⠰⡆⠀⠑⠂⠁⠀⠉⠀⠀⠀⠴⠁⠀⢁⡃⠉⡴⠉⠁⠀⠀⠁⠈⠉⠉⠎⠰⡼⡿⣈⣰⣆⣨⣶⣞⣠⣯⡿⣍⡇⠰⠩
⠀⠉⡂⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢙⡋⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠠⠀⣀⡀⡀⠀⠒⠀⣠⣌⠉⠛⢹⢧⣤⠽⠏⢻⢿⠳⠦⣿
⣃⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠴⡖⠀⠞⠠⢀⣠⣄⡠⣴⣆⣷⣆⠨⠣⠆⠀⢢⣄⠀⠠⠈⢀⠀⠩⠱⠴⢈⣾⠇⢀⡀⠶⠋⢀⠄⠉⠈⠩⠔⠶⡇⠛⠲⢲⣾⣯⣵⣆⠀⢈⣕⣒⡓⠋⢛
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠸⠃⠄⠀⠀⠀⠀⠀⠓⢀⠈⠠⠄⠛⢀⣤⣌⠤⣔⢃⣻⣋⡤⠘⠛⠀⠀⢀⣄⡊⠀⠀⠀⠀⠘⠀⠂⠀⡀⠀⠜⢦⠂⢘⢄⡀⠀⡀⠀⠀⢀⠛⠿⠠⣵⠦⠛⢎⠖⠿⢿⠛⢂⡽⣀⣔⡆⡄⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠐⠂⠀⢀⡘⠛⠪⢡⡛⢸⡉⡁⠊⢉⠀⠀⠀⠐⠂⠀⠀⠀⢁⠀⡠⠀⠀⠀⠀⠀⠒⠂⠀⠘⠊⠈⠙⠐⠒⠦⢹⣖⢴⠴⠴⡯⢤⣤⣴⡦⣵⠞⠀⠀⠀⠭⢿⡤⠃⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠉⡉⢠⠴⠀⠘⠉⠀⠐⣂⠀⠀⢀⠀⢀⠀⠠⠤⠆⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣁⠁⡘⠣⠶⠀⠀⠀⠉⠅⠀⠄⣰⠶⡽⣷⣉⠛⢁⣆⣿
⠀⠐⡒⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⢠⠔⠀⠁⠀⠀⢠⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢘⠤⣸⣽⡁⡀⠚⢃⢰⠶⠅⣀⠄⠐⠀⠀⠠⢀⣀⢟⠋⢰⠆⠂⠀⠀⠈⢙⡊⡝⡇⠰⢻⠗⡛⠣⠠⣾⣧⣔⣿⣿
⠀⢒⡒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⠠⠄⢴⣶⣤⠀⠀⠀⠀⠐⡏⠀⠹⡇⠒⠸⠓⠁⢀⣾⠅⠀⠐⠂⠀⠀⠲⠖⠒⠋⠙⡀⠀⠀⠀⠀⢠⣤⣀⣽⣗⠁⠦⠄⡄⠈⠁⠁⠈⠐⠩⠉⢡⡔
⠉⠀⠀⠁⠀⠄⠀⣀⣤⡀⠀⠐⠂⠀⢀⠄⠀⠀⠴⠀⠀⠆⠀⠀⠀⠤⠞⢿⣿⣷⣴⣉⡧⣶⣨⠲⢟⡈⠄⠀⠀⠀⡈⠀⠀⠀⣅⠒⠆⠀⡙⡐⠖⡅⠑⠒⠀⢐⠀⢀⣑⠋⡆⠌⠰⠀⠀⠀⠀⠰⠠⠶⣠⡄⣴⣶⡒⢼
⠀⠤⢤⠇⠀⠤⠀⣆⣼⡧⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⡀⠚⠋⠈⠂⠀⠹⡐⠀⣀⣤⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠐⠠⠜⡽⠳⠂⠠⠆⢠⠒⠄⠀⠀⢯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠐⢗⠚⠸
⡄⢤⠘⠃⠀⠠⣤⠿⠋⡄⢐⣤⠌⠀⠂⠀⣤⣀⣄⠐⢀⠉⠀⠀⠁⠀⠁⠀⠀⠀⢀⠀⠀⠁⠉⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠀⠐⢢⠀⠀⠀⢠⢈⣤⣤⠄⢰⠀⠀⠀⢐⡀⠀⠀⠀⣤⡤⠄⣀⢠⣶⠆⠀⠈⡀⢲
⠀⠸⠏⠹⢻⡿⠿⠿⡿⠫⠹⠟⠿⠿⣿⠏⠉⠁⠸⡇⠀⠀⠀⠀⠆⠀⠀⢰⠀⠀⠐⠀⠤⠆⠀⠀⠀⠀⠀⠁⠀⠀⠀⡉⠀⠀⠀⢂⠀⠀⠀⠑⠀⠁⡾⢛⠘⠱⠷⢆⢰⠤⠄⡁⢸⣒⣏⣻⣭⣉⡙⠉⠁⡉⢀⣰⣀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⡿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⡀⠉⠉⠉⠉⢻⣿⣿⣿⣶⣶⣄⡨⢿⡟⠉⠁⠀⠇⠀⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠹⡿⠿⠗⣿
⠀⠀⠀⠶⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣷⣿⣇⣀⠀⢀⣠⡈⠡⠮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢋⣠⡄⠈⠃⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠈⠁⠀⢈⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⢒⡢⠭⠓⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠙⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠋⠙⠛⠁⠺⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠛⠿⠿⠿⠿⣿⡿⢟⢿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠺⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡏⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣾⡟⣿⣷⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡟⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⣿⣿⡧⠄⣿⣿⢡⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⠘⡟⠈⠛⠃⠀⠛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣣⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⢰⣿⡟⣿⣇⢀⣿⣿⣿⠀⣿⣿⣇⣼⣿⣿⢸⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⣰⣿⣿⣿⣧⣾⣿⢻⣿⡆⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⠿⢛⣸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⢼⣿⣧⣿⣇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣷⣤⣀⠠⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡟⣿⡿⣿⣿⢸⣿⡯⢷⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⢹⣿⡧⢾⣾
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣿⣿⠿⢿⢿⣻⢿⣿⣿⣿⣿⣿⡿⠛⢛⠛⠛⠇⠛⠛⠘⠛⠃⣾⣿⣿⣿⣜⣛⣻⣛⣛⣿⢿⣿⡟⣵⣈⡻⣿⣿⡷⠐⣺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣋⣽⣿⣿⣿⣿⣿⣿⣛⣷⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢃⠀⡀⠈⣄⠀⢀⠀⠀⠐⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠭⡻⠿⠿⠧⠩⣽
⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡾⢰⣶⠀⠹⠀⠊⠀⠀⠃⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⡷⢶⢧⣤⡆⣦⣤⢼
⣿⣿⣷⣿⣿⣹⣿⣿⡭⠽⠟⣛⣙⣿⣿⣿⡿⢿⣟⡛⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⡁⠀⢠⠀⡀⠀⠒⠀⢄⡼⢁⣿⣿⣿⣿⣿⣿⡿⠿⠱⠶⡏⢈⡱⣶⡞⠶⠂⢀⠼⢝⡀⢘
⣿⣿⣯⣭⣭⠤⠿⠿⣿⠿⠿⠿⠻⠤⢤⡾⢛⣙⣷⠿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡏⠀⠋⠀⠀⠟⠠⢽⡶⠀⠀⠛⠃⠀⠿⣿⢿⡿⢽⣿⠇⢀⡄⠔⠋⠟⠛⠐⣀⢠⡠⠀⢈⡀⠉⢸
⠛⠒⢻⣿⣯⣿⣷⣶⣤⡀⠈⠀⠀⠀⢼⡷⣿⣿⣿⣶⣿⣷⣿⡟⡟⣯⣽⠋⣻⣟⣻⣿⣿⡟⣿⠉⢻⣿⣭⣟⡯⠯⠿⠀⠀⠀⠀⠀⢀⣈⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠈⠛⠀⠀⠐⠒⠐⠀⠀⠀⠁⢬⠑⠀⣈⡇⡥⢾
⠿⠿⠃⠀⠀⠀⠀⠤⠶⠿⢿⣿⡿⣷⣻⣷⣶⣿⣿⣿⣿⣛⣻⣿⢟⣿⣿⡿⣿⣿⣿⣭⣿⣿⡿⡻⣟⣛⢛⣉⣏⡀⢤⣄⡀⠛⠣⢼⡿⣏⢧⣤⢘⠜⠚⠄⣠⢤⠦⢤⠜⠙⠛⠛⢒⢀⡤⠄⠤⠙⠿⠛⠋⠛⠛⠈⠛⢻
⠀⠀⢤⠀⠀⠈⢭⣤⠄⠀⠀⣄⣀⣛⣭⣭⣽⢿⡗⢻⣿⣽⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⠙⠛⢿⣿⣯⡽⣿⣿⢿⠿⡿⣥⣄⣿⣿⣶⣾⣶⣻⣾⢰⢸⠒⣻⠎⠉⠸⡞⡓⠂⡙⠛⠒⠒⠂⠄⠀⢐⠀⠀⠈⠀⠀⠂⠸
⢻⠻⢛⣋⣴⡀⣈⣩⣵⣶⣶⣶⣚⣿⣿⡿⢿⢿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣷⣦⢽⠟⣻⣽⣿⠉⡺⠿⠿⢻⢿⣿⣽⣿⡋⣝⣯⣭⡁⣀⡐⠀⠀⠈⠉⠟⠉⣦⣴⣶⣴⣽⣏⣿⣷⣶⣿⣿⣷⣶⣆⣺⣖⠀⣀⣀⣄⠀⠀
⣭⡀⠆⣹⢿⡿⢿⣿⣿⡿⠄⢠⣤⣼⡿⢟⣿⣿⣿⣻⣽⣿⣿⠜⣻⣿⣛⡻⠿⢿⣦⣥⣻⣿⡇⣛⣿⣿⢤⢼⣿⠯⣿⣿⣿⣷⣤⣼⣿⣿⣤⣤⣤⠀⠀⢀⣀⡴⣟⣿⢧⠴⣿⣿⣛⣉⡃⠻⢿⢿⣿⣫⣿⠿⠿⣟⣤⣿
⣿⣧⣴⡿⠛⠃⢺⣿⣒⢄⣤⡾⠏⠉⢀⠁⢹⠛⠻⢿⣾⣿⣿⣿⣏⡿⡞⠷⣶⣾⣾⠏⢙⣿⣿⣿⡛⣿⣬⣭⣿⣾⣿⣿⣿⠋⠈⠙⡲⡿⠿⠰⡾⣿⣿⣿⣿⣷⣿⣻⣯⣠⠻⠻⠉⠙⢛⡒⢲⣶⣿⣿⣷⣶⣶⣿⠷⢾
⠰⠶⠂⢉⠙⠿⠷⢶⢊⣡⡈⣷⡆⠀⠰⢏⡠⡀⡀⠹⣶⡄⣀⣀⠉⠻⣙⢵⠾⠖⠀⠀⠙⠉⠋⠛⣿⣿⣿⣟⣛⡛⣫⣍⣹⣥⣶⣖⢺⣶⣿⡶⢿⣿⡿⣍⠩⡿⡿⢛⣹⣿⡿⣧⡴⣀⣰⠀⢁⠀⣉⡿⣙⣻⣾⣿⣧⣽
⠠⠀⠀⠀⠀⣤⣬⣿⠽⠏⠀⠒⠖⠒⠀⠘⠯⣉⣪⡂⣋⣧⣦⣤⣄⣤⣦⣐⠁⡄⣅⢠⠤⣀⡤⢀⡠⢄⣬⡤⣏⣯⡟⢿⡞⡛⠛⠀⠠⠘⠿⠇⢃⣒⡛⠀⠒⠁⢄⠠⢉⠳⠿⢿⣌⢩⣗⣾⣿⣿⣿⣟⣛⣟⣿⣧⣿⢬
⣶⣶⣤⣶⠀⠈⢉⡁⠀⣤⡄⠀⠀⣀⢐⠚⠒⡛⢉⣉⣭⡿⣿⠟⢃⠔⠋⠉⠭⢀⡟⠒⡒⠚⣿⣒⡶⣯⢼⡏⠈⢪⠽⠆⠀⡀⠀⠀⠀⠀⡀⠈⠩⡝⠇⡤⠁⣤⣬⣤⣤⡅⡒⣤⣾⡾⠻⣯⠞⠛⠛⢽⡫⣽⣻⣽⣭⢾
⡿⣿⣿⠙⠋⠉⠛⠿⠉⣇⡲⠿⠟⠲⠷⠾⢛⠨⠱⠶⠌⠁⠂⡄⠀⠀⠔⠢⠒⠀⡠⠀⠉⠐⢛⠀⠰⡂⠀⠲⠈⠉⠈⠉⠀⠀⠀⠤⠁⠐⠁⡂⠉⡤⠉⠁⠀⠀⠁⠈⠉⠩⠆⢠⣽⠟⣈⣶⢌⣸⣶⣿⣭⣟⣭⡵⡯⠸
⠒⡄⢛⣃⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢙⠃⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⠀⠀⠀⠀⣀⡀⠁⢀⠀⠀⠠⠀⣆⡀⠠⠀⠄⢀⣩⣜⠉⠛⢻⣯⣭⣿⠿⢿⢿⡧⢴
⢀⣃⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠴⡒⡁⢎⠰⢀⣠⡄⡠⣶⣆⣶⣇⠨⠧⠆⠀⢀⡀⠀⠠⠀⢀⠈⠉⠱⠤⣈⢾⡇⣀⡠⠶⠋⢀⡀⠉⠈⠁⢀⡴⠀⠳⠶⠦⣾⣏⣭⣎⠂⠀⢼⡶⡗⠾
⠀⠀⠀⠀⠢⠀⠀⠀⠀⠐⠸⢃⠄⠀⠀⠀⠀⠘⠓⢀⠙⠠⠄⠛⢁⣤⡬⢴⣖⣚⡋⣋⡄⠘⠛⠀⠀⢀⣄⡊⠀⠀⠐⠀⠒⠂⠂⠀⡀⠀⠽⣆⠢⠚⢁⡀⠀⠀⠀⠀⣐⠛⡷⠀⣥⡤⠿⢜⠼⣿⢿⠿⢇⡾⣈⣩⡅⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠚⠂⠀⢀⣘⠛⢨⢢⡜⢺⠉⡑⠉⣉⠀⠀⠁⠐⠂⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠡⠒⠂⠈⠐⠊⠘⠁⠒⠒⣦⢵⡮⣴⡤⣴⣯⣤⣀⣸⣤⣷⢾⠀⠈⠀⣟⢫⣥⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⢉⡁⣨⠦⠀⠈⠉⠀⠐⡆⠀⠀⢀⠀⢀⠀⠀⠀⢆⡀⠀⠀⠠⠀⠀⠀⠈⡀⢀⣒⠃⠹⣫⠶⠂⠀⠀⠉⠉⠀⢐⢲⢤⡸⡶⣐⠺⠁⣾
⠀⠀⠐⠚⠓⠤⠐⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⢠⠆⠀⠁⢀⠀⢠⠐⠈⠈⠀⠜⠀⠀⠀⠀⠀⠀⣐⢤⣸⣼⠁⠀⠒⣂⢴⠴⡀⡁⠄⠀⠀⠀⠠⢀⣀⢟⠋⢱⠄⠠⣀⠀⠘⠳⣈⡳⡆⠼⢳⠖⠟⠣⠠⣾⣦⣴⣾
⠀⠀⢒⡖⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠚⠉⡤⠄⢵⣶⣄⠀⠀⠀⠀⢐⠃⠈⢻⡄⠃⠛⠧⠁⢂⠗⠇⠀⠒⠂⠀⠐⠦⠤⠖⠊⠹⣈⠄⠀⠀⠀⢠⣄⢂⣼⡇⠁⣅⡆⡘⠉⠡⠄⠐⠛⢛⠛⢻
⠀⠀⠀⠀⠉⠠⠠⠀⣀⣤⡄⠀⠰⠂⠀⢠⠖⠀⠠⠶⠀⠐⠄⠀⠀⠀⠤⠞⢿⣿⣷⣰⣉⢇⣶⣥⡰⢟⡈⠀⠀⠀⠀⠉⠀⠀⠀⡅⠲⠄⠀⡑⠰⠆⡀⠽⠂⣀⣘⠀⢀⣛⠋⡄⠌⠡⠊⠁⠀⠀⠠⠠⠦⣀⡀⢠⣤⠾
⠀⠀⠀⢄⡂⠀⠤⠤⣷⣼⡧⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⡀⠚⠉⠉⠀⠄⠱⡐⠀⣀⣄⠀⠀⢀⢀⠀⠀⠀⠀⠈⠀⣐⠠⢻⣟⠴⠇⢠⠄⡠⠐⠈⠁⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠓⠃⠞⠺
⠀⠤⠴⠚⠃⠀⣤⠤⠛⠋⡄⢰⣦⠈⠐⠂⠀⢤⣠⣔⠐⠈⠁⠁⠈⠁⠀⠁⠀⠀⠀⢀⠀⠌⠁⠉⠁⠁⠂⠐⠀⠀⠀⠀⠀⠀⠀⡄⠀⠬⢪⠀⠀⠀⢠⢈⣀⣤⡄⡤⠀⠀⠀⢠⠀⠀⠀⠀⣄⡠⠄⠀⢠⣤⡆⠠⠘⢠
⠀⠸⠗⠹⣸⡿⠿⠿⡧⠣⠻⠗⠿⠿⠿⣷⠋⠉⠀⠰⡇⠀⠀⠀⠠⠂⠀⢠⠴⠀⠀⠈⠀⠄⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⡉⠁⠀⠀⢂⠀⠀⠀⠙⠀⠁⠼⢟⠙⢳⡧⠆⢠⠠⠌⡆⠷⢺⣗⢿⣍⣋⠓⠈⠉⡋⠀⣀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⡿⣻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡀⠉⠉⠉⢉⣿⣿⣿⣷⣶⣶⣀⡬⢿⡏⠋⠁⠸⠇⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⢹⠿⠿
⠀⠀⠀⠀⠀⡷⠁⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⡿⣿⣄⡀⠀⣂⣤⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠣⢴⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁⠀⠀⠈⠁⡠⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⢫⡅⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢻⢿⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠉⠙⠉⠉⠁⠀⠉⠙⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠛⠿⠿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣅⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣾⡟⣿⣿⠁⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣷⣿⡟⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣧⢸⣿⢻⣿⡧⠀⣿⣿⢢⢸⣿⣿⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⣸⠛⠈⠛⠃⠀⠛⠛⠀⠈⠛⠿⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣀⢠⣀⣀⣀⣀⣀⣨⣴⣶⣦⣤⣦⣤⣀⣀⣤⣤⣀⣀⣤⣤⣤⣤⣀⣀⣀⣰⣿⡟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣼⣿⣷⢸⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⣴⣿⣿⣿⣧⣾⣿⢿⣿⡆⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⣺⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⢸⣿⣧⣿⡇⣿⣿⣸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⡿⣿⣿⢸⣿⡏⡵⡤⣿⣿⣹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢻⣿⡗⠳⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣩⣉⣻⣿⣿⣿⣿⡿⠿⠿⣿⣿⣻⣿⣿⣿⡛⠋⡛⠓⠻⠧⠛⠛⠘⠛⠃⣷⣿⣿⣟⣞⣿⣯⣿⣿⣏⣛⣿⢿⣿⣾⣿⣿⣛⣥⣼⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣋⣩⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡀⢀⠀⢣⠀⠀⡀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣤⡟⠛⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⢟⣻⣿⣿⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣴⣇⣿⡆⢸⠅⠀⠇⠀⠀⠊⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠞⠾⢥⢴⡆⣾
⣿⣿⣿⣳⣶⣶⣾⡽⣿⣿⡭⢟⣛⣋⣙⡿⢿⣿⡿⣿⠭⠟⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⡇⢰⡇⠈⠁⡇⢰⠀⠀⠀⠀⠀⣐⠃⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠷⠾⡍⣀⡲⣶⢾⠖⠀⢠⠾⢼
⣿⣿⣿⣿⣯⣥⣶⠦⠿⠿⠿⠛⡛⠛⠿⠦⢴⡿⣫⣹⡿⢿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠸⠁⠀⠀⠀⠀⠀⠀⠛⠀⠸⠇⠸⠿⠿⢿⢿⢿⡷⣿⣿⠆⠠⠤⠐⠙⠟⠃⠃⡀⢀⢢⠀⢀⣨
⣭⡬⡋⣓⠻⢿⡷⠿⣷⡶⣤⣄⠀⠀⠀⠀⢸⡾⣯⣿⣿⣮⣿⣿⣿⡻⣟⣿⣟⠉⡽⣿⣿⣿⣿⢛⣿⡉⣻⣯⣭⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠰⠒⠃⠊⠓⠈⠁⠐⠂⠀⡀⠀⣀⠐⣨⠀⢀⣀⢛
⣓⣓⡛⠿⠁⠀⠘⠀⠀⠒⠺⠿⠿⠿⠿⣿⣿⣿⣾⣿⣿⣭⣿⣙⣻⣿⢟⣿⣿⡿⣿⣿⣿⣼⣿⣿⣿⣻⣟⣛⣋⣀⣀⣀⣤⣀⡐⠀⢠⣼⡿⣧⢧⣤⢀⠜⠓⠄⣀⣴⡲⢦⠎⠉⠛⠛⡂⢀⡀⠇⠠⣘⠛⠛⠘⢛⠛⠘
⠀⠀⢀⠀⠤⡠⠀⠨⢭⡶⠆⠀⣠⣤⣴⣿⣿⣿⡿⢿⣿⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠻⣿⣿⣯⠿⣾⠫⣛⣛⣿⣥⣴⣿⣷⣷⣶⣦⠿⡎⣰⣼⣱⡿⠋⠉⠸⢞⡝⢈⣉⢋⠚⠓⠒⠀⠂⢐⠀⠄⠈⠀⠐
⣧⡿⢟⡉⢍⣁⣧⣀⣤⣬⣾⣶⣾⣶⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⢟⣿⣿⣿⣉⠛⠿⠿⠹⣿⣿⣶⣞⣩⣹⣳⣤⢁⣀⡀⠀⠀⠨⠉⠛⠱⢦⢶⣷⣶⣿⣩⣿⣶⣾⣿⣿⣷⣶⣒⣺⣇⠀⣐⣠⣤
⣿⣿⣦⡴⢅⣴⣿⡟⢿⣿⠿⡟⢖⢤⣤⣼⠿⣛⣿⣿⣯⣿⣿⣿⣿⢚⣻⣿⢋⡿⠿⢿⣾⣼⣻⣿⣣⣽⣿⣧⣴⣿⡻⠾⣿⣿⣿⣷⢦⡾⢿⣯⣤⠤⣄⡀⡀⢀⣠⠴⣟⣻⡵⠾⣿⣟⣋⣉⡁⠛⣿⢿⣿⣫⣿⠻⠟⣿
⣯⣭⣿⣷⠞⣟⡛⠃⣽⣧⣴⣢⣴⡾⡏⠁⢨⡅⢻⠋⡟⣿⣿⡿⣿⣿⣯⣷⠚⡶⣶⣿⠿⢯⣹⣿⣿⣿⣛⣿⣭⣭⣷⣿⣿⣿⡿⠀⠘⠙⣲⡟⠗⠲⠾⣿⣿⣿⣿⢺⣿⣳⣬⣹⠛⠛⠉⠉⣛⡒⢲⢾⣷⣿⣿⣶⣷⣿
⠉⠉⠹⠟⠁⠁⠟⠛⢿⣯⢉⣴⠎⣷⡇⠀⣘⣋⣵⡀⢀⢿⣲⣆⣤⣨⠉⠽⢕⣵⠾⠋⠀⠈⠉⠉⠯⢹⢿⣿⣿⣟⣋⡙⣡⣍⣽⣦⣶⣿⠿⣶⣿⡿⣿⣿⡿⣌⢩⡿⡿⣫⣩⣿⡿⣷⣤⣀⣖⠀⣁⠀⣁⡟⣝⣻⣿⣿
⣂⣀⡠⠀⠠⠀⢀⠤⣤⡿⠛⠏⠀⠻⠟⠛⠒⢛⢯⣄⣟⣋⣣⣿⣷⣾⣦⢧⣧⣏⡡⠌⣄⢠⠤⣀⣼⢀⠤⢤⣤⡴⡿⣯⣟⢿⠯⠛⠋⠈⠀⠸⠻⠀⣁⣚⠛⠐⠚⠡⢄⠜⢉⡻⠿⢿⣌⢹⣷⣿⣿⣿⣿⣟⣻⣿⣿⣿
⣛⣿⢿⣿⣽⣷⢀⣀⣭⣤⢀⣤⣄⣀⣀⡤⢼⡋⢺⢛⣠⣥⣿⣿⠿⠛⠯⠟⠈⠋⠍⢠⠟⢲⣓⡖⣿⣺⠾⡽⠾⠋⠈⣸⠱⠆⠀⠀⠀⠀⠀⠀⠀⠉⢹⠟⣀⡦⡰⣥⡬⣤⢡⡅⡐⣴⣷⠾⠻⣿⢟⠞⠛⢽⠿⣽⣻⣻
⠿⢿⠿⠿⣿⠉⠉⠉⠉⠻⣹⣍⡿⠿⠏⠹⠿⠛⢛⠛⠿⠗⠲⠁⢂⣆⡀⣀⡊⣲⠈⢰⡄⢁⠀⠚⢋⠀⠲⡢⠈⠐⠈⠀⠈⠁⠀⠀⠠⠬⠀⠈⢁⠁⠇⡤⠉⠁⠀⠈⠀⠁⠉⠁⠎⢢⣽⢯⣉⣶⣌⣸⣶⣾⣭⣏⣭⣽
⢛⠛⠛⡄⠨⠉⢠⠤⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⢨⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠂⢀⣠⣝⠙⢛⣻⣯⣭⣿⠿⢿⢿
⠒⢂⠀⠩⢄⠀⠀⠀⠉⠀⠀⠀⣐⡀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠀⢀⠲⠊⠱⢊⠰⢠⣰⣄⣴⡮⣮⣶⣆⠨⡳⠀⠀⢠⡀⠀⠅⠀⢀⠀⠍⠰⠤⣉⣾⠆⣀⡠⠶⠁⢀⠌⠉⠈⠁⢀⡴⠀⠻⠶⢶⣾⣏⣭⣏⠂⢉⣽⠶
⠀⠀⠀⠀⠀⠛⠹⠂⠀⠀⠀⠉⠘⢡⠂⠀⠀⠀⢀⠘⠃⢠⠁⠤⠚⢉⣠⣦⡤⣺⢟⣛⡯⣡⣆⠛⠃⠀⠀⣠⡄⠈⠀⠀⠐⠀⠁⠄⠃⠀⠀⠠⠟⡄⠢⠊⣄⡠⠀⡀⠀⠀⣐⠻⠷⠄⣥⠤⠳⢼⠼⣿⢿⠿⣇⡾⣈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠁⠀⢠⣬⣟⢻⣧⡛⣾⡀⡘⢙⣄⠀⠈⣐⠒⠀⠀⠀⠈⠀⠀⠠⠐⠀⠂⠀⠐⠒⠂⠀⠓⠋⠉⠑⠒⠒⡤⢵⡦⣴⠤⣶⣯⣤⣀⣼⣬⣵⡞⠀⠈⠰⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡅⠀⠁⠀⠀⣈⢐⠀⣕⠲⠦⠀⠉⠁⠀⢐⡂⠀⠀⣀⠀⠀⠀⠡⠰⢀⠀⠀⠀⠀⠀⠀⡀⠈⡀⢀⢒⠃⠻⡃⠶⡀⠀⠐⠉⠅⠀⢔⢲⢤⡹⣶⣐⠺
⠀⠀⠀⠀⠈⠉⠁⠒⠘⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢀⠰⠃⠀⠔⢠⣀⢹⠘⡀⠀⠀⡘⠄⠀⠁⠀⠀⠀⣰⢤⡯⣬⠡⠐⠛⣰⢲⠾⠀⡠⠄⠂⠀⠀⠠⢀⡸⢛⠉⡰⠜⠀⡀⠀⠘⢳⣘⠱⡇⠼⣻⠖⠟⠣⠱⣾⢶
⢀⠀⣤⣤⠍⠉⣥⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⡴⠂⣿⣷⣤⠁⠀⠀⠀⢸⠁⠈⢻⠝⠂⠻⠊⠁⢠⠓⠅⠀⠒⠀⠀⠐⠶⠔⠒⠋⠁⡠⠀⠀⠀⠀⢠⣄⣀⣿⣇⠀⢇⡄⡉⠉⠡⠄⠐⠙⢻
⠉⠉⠈⠀⠐⠂⡀⢐⠖⠀⡶⣶⡆⠀⢀⡁⠀⡰⠆⠀⠐⠖⠠⠐⠂⠀⠂⠀⢒⠋⢟⣿⣷⡼⢍⡷⣆⣝⠻⢇⠉⠆⠆⠐⠀⠀⠀⠀⠈⡁⠒⠆⠀⡃⠰⠆⠀⠝⠢⣀⡀⠀⢀⡓⠋⡄⠍⠱⠈⠁⠀⠀⠠⠠⠦⣀⡀⣸
⠀⠀⠀⠀⠐⢲⡇⠀⠧⠴⢿⣿⠿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄⡇⠘⡀⠛⠙⠀⠆⠀⢙⡃⡀⣤⡤⠐⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠠⢻⠟⠴⠁⠠⠆⡠⠓⠀⠁⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠓⢻
⠀⠠⠀⠀⠒⠈⣥⣤⠐⠒⠛⠛⣖⠬⡗⢒⠒⠂⢠⣶⣴⣦⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠀⠒⢪⠀⠀⠀⡄⢨⣤⣤⡄⠰⠀⠀⠀⢢⠀⠀⠀⠀⣀⡠⠄⢀⢠⣴⡄⢰
⠀⠨⠍⠹⢸⡏⠿⠿⡿⠳⠺⠟⠿⠻⠇⠏⠙⡿⠉⡀⠀⠺⡁⠀⠀⠀⠴⠋⠀⠠⠰⢀⡀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⠀⠀⠀⠱⠀⠁⠼⢟⠟⠻⠧⠆⢠⠠⠈⡆⠱⢲⡗⢿⣉⡋⠷⠙⠑⠊⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠙⠛⠛⠛⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡛⣻⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡀⠈⠉⠉⠉⢻⣿⣿⣷⣶⣶⣀⠆⢿⠏⠉⠉⠘⠃⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢩⠙⢻
⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⠿⠿⣆⡀⠀⢀⣤⣈⠛⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡠⡺⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠩⠅⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⠉⠋⣹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠉⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠻⠻⠿⠿⠏⠿⢿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣾⡟⣿⣷⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣿⣿⡏⠀⣿⣿⠀⢸⣿⢿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣧⢸⣿⢻⣿⡇⠀⣿⣿⠆⢸⣿⣺⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⢛⡞⠛⠈⠛⠃⠀⠛⠛⠀⠈⠛⠟⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣄⣀⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣀⣰⣿⡟⣿⣧⣠⣿⣿⣿⠀⣿⣿⡇⣾⣿⡿⢸⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⣴⣿⣿⣿⣧⣾⣿⢿⣿⡆⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⢸⣿⣧⣿⡇⣿⣿⢸⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣷⣤⣥⣔⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⡿⣿⣿⢸⣿⡏⠁⠀⣿⣿⢹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣯⣭⣭⣽⣿⣿⣿⣿⢿⢿⣿⣟⣹⣛⣿⣿⠛⢃⠛⠃⠻⠇⠛⠋⠘⠛⠣⣶⣷⣟⣛⣾⣿⣿⣿⣿⣬⣿⣿⣿⡿⣿⣿⣿⣛⣁⣶⣾
⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣽⣏⣡⣬⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣀⠈⢧⠀⠀⡀⠀⠀⢰⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡞⠛⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣾⢱⣿⠀⢸⠀⠰⠁⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⡟⠻⠛⠿⠡⢴⣾
⣿⣿⣿⣿⣻⣷⣶⣶⡽⢿⢿⢶⣞⣋⣉⣙⡿⠿⣿⡟⡻⠯⠍⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠁⢸⠁⠌⢀⠁⠈⠀⠀⠀⠀⠀⣰⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠶⠿⣇⣤⡸⠶⠟⠓⠀⠢⢿
⠿⢿⣿⣿⡿⣷⣴⣒⣂⡻⠿⠿⠛⣛⠛⠻⠦⢼⢝⣫⣬⡿⢿⣿⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠀⠀⠈⠀⠀⠀⠀⠴⠀⠸⠇⠸⠿⠿⢿⢿⠿⢿⡿⢿⣿⢧⡠⠆⠚⠑⠛⠋⠑⡄⢠⡠⠤⢬
⣻⣭⡭⣋⣹⠻⢿⠶⠛⠿⠿⢤⣄⣀⣀⢀⣀⢰⡞⣯⣿⣿⣿⣷⣿⣿⡹⣻⣷⣏⠉⡽⣭⣿⣿⣿⣹⣿⣉⣻⣯⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠒⠓⢊⣋⡈⠁⠐⠀⠈⡀⢀⣄⠐⣠⠌⣀⣸
⣨⣟⣛⠛⠿⠍⠀⠈⣀⡀⠒⠛⠻⠿⠿⠟⣿⢿⣿⣿⣿⡯⣭⣯⣭⣿⡿⢟⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣻⣟⣛⣻⢰⣠⣐⣤⣀⠀⢀⢀⡰⠕⠤⠧⣖⢀⠜⢓⠂⣀⢴⣓⢶⢆⡈⠉⢋⣣⢤⠔⠒⠀⠘⠛⠉⠙⢛⠛
⠉⠀⠀⢀⣀⢀⣤⠀⠈⢓⣶⠂⠀⢠⣤⣴⣿⣷⣶⡟⢻⡟⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣍⡛⢿⣿⣷⠛⡽⡁⣛⢻⣯⣤⣬⣿⡷⠷⣶⣶⠟⣟⢸⣾⣱⠴⠋⠀⠸⣏⡝⣈⣩⠭⠚⠓⠒⠐⠂⢨⠀⠀⠀⠘
⣀⣆⡿⢉⡉⢩⣭⣾⣠⣤⣴⣾⣿⠿⠷⠾⣿⣿⠟⣿⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣶⡾⢊⣷⣿⣏⡉⡙⣚⠷⠹⢽⣷⣶⣎⣩⣽⢴⣶⣀⣀⡁⠀⠀⠠⠉⠋⠠⠲⢶⣷⣶⣿⢯⣿⣷⣾⣿⣿⣿⣶⣆⣼⣇⢁⣀⣰
⣿⣿⣿⣧⡤⠧⣼⣻⡟⢻⣿⠿⠟⠓⢠⣶⣾⢟⡫⣿⣿⣯⣿⢿⣿⣿⣛⣻⡿⢭⠟⠛⡿⣶⣦⣿⣿⣃⣭⢿⣷⣶⣻⡻⣾⣿⣿⣿⡷⢶⡿⠿⣷⡤⠤⢄⣀⣀⣠⣠⢸⡟⣻⢰⠾⣿⣟⣋⣨⡁⠛⠿⠿⣿⣫⡟⠛⣿
⣤⡦⢬⢿⠷⠞⢻⣟⣃⡸⠯⢽⣦⣶⡞⠃⠀⢨⡅⠩⠉⠋⣿⣿⠿⣯⠿⣧⢷⠚⡾⣶⠿⠺⢩⣽⣿⣿⣿⣿⣾⣽⣭⣧⣿⣿⣿⡟⠀⠈⠉⡙⠟⠓⠒⣞⣿⣿⣿⣿⢻⣷⣳⣮⣵⠛⠛⠉⠉⢛⡓⠲⠾⣿⣿⣿⣶⣿
⠉⠁⠈⠙⠛⠉⠀⠆⠉⢙⣿⢩⡴⠎⠿⠇⠀⣈⣡⣴⡄⢀⠙⣳⣆⠦⠬⠌⠽⢕⣿⠻⠁⠀⠀⠉⠈⠋⢹⢿⡿⣿⣯⣉⣈⣴⣍⢷⢷⣷⢏⠷⣖⣿⡿⣿⢿⡇⣌⢼⣿⡿⢩⣹⣿⡿⣷⡶⣄⡐⠀⣀⡈⣉⡿⣉⣹⣿
⣀⣉⣀⣀⣀⠠⠀⠀⠴⣶⡾⠛⠃⠀⠛⠍⠙⢛⣚⢓⣤⢽⣑⣤⣿⣷⣻⡢⢧⠷⣃⡀⢤⡄⢢⠤⢄⣰⢤⢦⣴⢤⣾⣭⢧⡟⠿⠬⠉⠉⠀⠀⠘⠛⣂⣡⣋⠉⠘⠋⠠⢄⠎⠉⡻⠻⢻⡡⢼⣿⣻⢿⣿⣽⣯⣻⣿⣿
⢛⣯⣿⢛⣿⣺⣿⣄⣀⣨⣄⣀⠴⠄⣀⢀⠤⠈⠉⢉⢉⣤⠤⢷⣿⠛⠛⠃⠈⠀⠉⠂⠠⠛⢰⣇⡶⣿⠽⠺⡷⠺⠉⢊⣺⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠑⣂⡆⢀⠤⡴⣤⠦⡅⡀⣵⣷⡞⢛⣯⢞⠋⠙⣻⠽⣽⣼
⡿⣿⡿⢿⠿⢿⣈⠉⠉⠉⠙⢈⣧⡿⠽⠏⠙⠛⠉⠁⠉⠙⠗⠐⠀⠀⢆⡀⣀⡊⡐⠉⠠⠄⢀⠀⠉⠉⠀⠐⡠⠈⠁⠀⠀⠈⠁⠀⠀⠀⠾⠀⠈⣁⠁⠃⡶⠈⠁⠀⠈⠀⠀⠉⠁⠊⠢⣼⢯⣈⣿⣆⣸⣦⣻⣮⣿⣽
⠉⠉⠉⠉⣇⠀⠄⠅⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡨⠃⠀⠀⠀⠠⠀⢀⠀⠀⢀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⣀⠀⠀⠀⢥⠀⠀⠀⠀⡀⠀⠀⣂⠀⠀⠀⠂⢀⣠⡜⠍⢛⣻⣧⣤⠽⠿⢿
⣛⡛⠃⠀⠽⠦⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠸⠉⠁⣁⠐⢠⣴⣤⣴⠿⡿⡾⣂⠘⡖⠀⢀⠰⡀⠀⠆⠁⠀⠀⠭⠐⠶⣉⡾⠆⢄⡰⠷⠉⢠⠌⠁⠈⠡⢠⠴⠀⠻⠶⢶⣽⣯⣽⣎⠀⠉⢿
⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠈⠘⠡⠂⠀⠀⠀⢀⠘⠋⠠⠀⠔⠂⢉⣠⢶⠤⢺⢏⢩⠧⣡⡂⠋⠁⠀⠀⠤⠌⠁⠀⠀⠀⠀⠁⠄⠃⠀⡄⠀⠟⠆⠀⠋⢄⡀⠀⡀⠀⠀⢘⠻⠗⠠⣥⠦⠻⢞⠾⡿⢿⠿⢇⡾⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣭⣍⠚⢦⡞⣷⣀⡈⠉⢄⠀⢀⣀⠐⠀⠀⠀⠈⡀⠀⠄⠀⠀⠀⠀⠐⠚⡂⠀⠛⠋⠈⠈⠘⠒⡤⢵⡦⣴⠤⢸⡭⣤⣤⣰⣴⣷⡾⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⢀⠀⢄⠴⠇⠀⠉⠀⠀⡀⠁⠀⠀⡀⠀⠀⠀⠐⠰⢀⡀⠀⠀⠀⠀⠀⡈⠀⡀⣀⣀⠁⠙⠧⠒⠀⠀⠀⠉⠁⠀⢀⣲⢤⡹⠶⣸
⠄⡐⠄⠀⠀⣀⣈⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠒⠃⠀⠀⢀⡀⠰⠈⡈⠀⠀⠘⠂⠁⠀⢀⡀⢀⣰⣦⡵⣮⢠⡒⠩⡴⠲⠮⠀⠠⠀⠂⠀⠀⠀⢀⣠⢛⠉⠰⠜⠠⠀⠀⠘⢓⣈⡹⡇⠼⢻⠖⠟⠢⠠⣾
⣀⣠⣄⠤⢤⠍⠋⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠖⠂⢺⣿⣦⡀⠀⠀⠀⠨⠁⠈⠻⠉⠂⠹⠊⠁⣡⠓⠁⠈⠐⠀⠀⠘⠒⠒⠒⠋⠙⡠⠀⠀⠀⠀⢠⣄⣠⣽⣂⠁⢇⠄⡈⠉⠡⠄⠐⠛
⠀⠈⠉⠉⠈⠈⠁⠄⠀⠂⠀⣶⢶⡆⠀⢈⣁⠀⠰⠂⠀⠐⠛⠐⠀⠀⠀⠀⠀⠒⠈⢻⣿⡷⠼⠧⡳⢏⣎⠙⢃⠉⠆⠀⠀⢀⠀⠀⠀⠀⡁⠒⠂⠀⡉⠐⡂⡌⠑⠂⡀⣀⠀⢀⣑⠩⡆⠌⠐⠀⠁⠀⠀⠰⠠⠦⡀⡤
⡀⠀⠀⠀⠀⠈⢩⡅⠀⠒⠒⢶⣿⠟⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠇⠈⡄⠉⠘⠀⠅⠀⢘⠃⡀⢤⠤⠀⠀⠀⠀⠀⠓⠀⠀⠀⠠⠀⠠⢻⠽⠶⠀⠠⢆⠴⠒⠄⠀⠐⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠚
⠀⠠⠀⠀⠀⠘⣬⠤⠀⠀⠀⠉⢃⠦⠚⠗⠢⠍⠁⣀⣶⠴⠶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠚⡨⠀⠀⠀⣠⢨⣤⣤⠄⠶⠀⠀⠀⢱⠀⠀⠀⠀⣤⠠⠄⢀⢀⣤⣮
⢀⠠⠧⠹⢸⡏⠯⠿⡯⠣⠻⠟⠿⠻⠏⠇⠉⠉⠿⠉⡀⠐⠈⠅⠀⠀⠀⠐⠁⠀⠰⠰⢀⡀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠑⠀⠁⠾⣛⠙⠹⠶⡆⢰⠤⠌⡃⠹⢲⣗⣿⣏⡋⠟⠘⠉⡚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠏⠙⠉⠛⠛⠛⠻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣯⡟⣻⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠉⠉⠉⢻⣿⣿⣿⣶⣶⣀⡤⢿⠏⠉⠁⠘⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⠿⠿⣄⡀⠀⣠⣤⣈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠦⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠁⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠁⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠉⠋⢽⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠻⠟⠻⠿⠿⠛⠿⢿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⢀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣿⣿⡏⠠⣿⣿⠀⢸⣿⢸⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢻⣿⡇⠀⣿⣿⡄⢸⣿⣸⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⣻⠛⠛⠈⠛⠃⠀⠛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣀⣀⣄⣔⣶⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣴⣤⣴⣿⣟⣿⣧⣼⣿⣿⣿⠀⣿⣿⡇⣾⣿⣟⢹⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣧⣾⣿⢻⣿⡆⢢⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣽⣿⣿⣿⡀⣿⣿⣿⣿⣿⣏⢸⣿⣷⣿⡇⣿⣿⢸⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡟⣿⣿⢸⣿⡏⠁⠀⣿⣿⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹
⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣽⣭⣽⣿⣿⣿⡿⠿⣿⡿⣛⣛⡟⣛⠃⠛⠓⣟⡃⠛⠛⠘⠻⢇⣷⣷⣟⣛⣚⣛⣿⣿⣿⣾⣿⣿⣿⣉⣿⣻⣿⣟⣽⣠⣼
⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣫⣽⣯⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢁⠀⢣⡀⠀⠈⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻
⣟⢛⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡏⢸⣆⠈⣅⠀⠼⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠻⠟⠿⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠿⣿⣶⣞⣉⣉⣩⠿⠿⣿⣟⡻⠿⢏⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡏⠀⠏⢹⠀⡇⠀⠀⠀⠀⠀⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⣯⣀⡘⢶⠾⠛⢿
⠻⠛⠿⢿⣿⣿⡿⣷⣶⡚⣓⣉⠻⠿⠛⠛⠛⠛⠦⢼⢿⣣⣬⣿⢿⣿⢿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠇⠀⠀⠀⠀⠃⠀⢀⣀⠀⣠⠃⣸⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⢧⣠⠢⠞⠙⠛⠛⠘⡀⢠⣸
⣛⣟⣟⣭⡍⢋⣽⡛⠻⠷⠛⠿⠛⠦⣴⣂⣀⣀⣀⣰⡾⣯⣿⣿⣿⣷⣿⣿⣟⣿⣷⣯⣉⣽⣭⣿⣿⣿⣹⣯⣉⣇⠈⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠈⠉⠉⠃⡀⠘⠂⠒⠒⠓⢊⣁⡈⠉⠐⠀⠀⡀⠀⣄⡐⢢⢸
⣻⣯⣽⣿⣿⠛⠻⠆⠀⠀⢀⣀⠘⠛⠛⠿⠿⠿⣿⢽⡿⣿⣿⣿⣴⡯⣬⣿⣿⣿⣿⣿⣟⣿⣿⣷⣾⣿⣿⣿⣻⣟⠀⠀⠀⢀⣀⢤⣀⠀⠀⢀⡰⠖⠴⠧⣖⢄⠈⢙⡂⣀⣴⡓⢶⢏⠉⠉⢋⣣⢄⠐⠓⠀⠈⠛⠋⠸
⢻⡏⠉⠁⠀⣠⣤⣔⣠⡀⠀⢲⣷⡂⠀⢠⣤⣤⣿⣿⣶⣟⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣍⡙⢿⣿⡶⠒⠀⠀⣛⢙⣡⣤⣤⣿⡷⠶⢶⡶⠟⣇⣸⣾⣹⠾⠋⠀⠸⣋⣝⣉⣭⠭⡖⠓⠒⠒⠂⢸⠀⢠
⡿⡧⣠⣶⣾⠿⡍⠻⡥⣾⣆⣴⣶⣾⣿⠿⠿⠿⣿⣿⢟⣿⣻⣿⡿⣿⣿⣻⡿⣿⣿⣿⣷⣶⡿⣩⣷⣿⣏⣩⣉⣛⠊⠽⣽⣷⣴⣌⣠⣽⢶⣎⣀⣀⡁⠀⠀⠀⠁⠉⠰⠦⢶⣷⣶⣿⢹⣿⣷⣾⣿⣿⣿⣶⣂⣸⣿⢈
⠿⠿⠿⠿⣿⣷⡆⠗⣼⣿⡟⣻⣿⣿⠟⠋⠲⣿⡾⢟⡫⣿⣿⣿⣿⣿⣿⣟⣫⣿⡿⢭⠟⠛⡿⣷⣾⣿⣿⣣⣭⣽⡷⣖⣿⡻⣺⣼⣿⣿⡷⢷⡿⢿⣴⡤⠤⢄⣀⣀⣠⣠⢺⣗⣻⠲⠾⣿⣛⣋⣨⠉⠛⠿⠿⣿⣏⣿
⣡⣤⣴⡦⠤⣿⡗⠚⢻⣭⣅⣼⢻⣶⣵⢾⡟⣇⠀⠠⡄⠩⠉⠟⣿⢿⠿⡿⠿⣧⣻⡋⡿⣿⠿⠛⢫⣽⣿⣿⣿⣽⣶⣽⣽⣽⣿⣿⣿⡟⠀⠈⠉⡽⠟⠓⠒⡞⣿⣿⣿⣿⢻⣿⣷⣮⣹⠛⠛⠉⠉⣻⡚⠲⠾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠁⠠⠆⠉⢙⣻⣴⣶⠏⢿⡇⠀⠈⣡⣾⣄⢄⠯⣵⣦⠶⢬⠤⠽⠥⣿⡻⠁⡀⠀⠉⠈⠛⢹⢿⡿⣿⣭⣉⣨⣴⡍⢷⢶⡷⢯⠿⣺⣟⡿⣿⢿⡷⣮⢽⣿⣿⣫⣽⣿⡿⣷⣶⣄⣲⠀⣁⠀⣉⡿⢻
⢀⣃⣀⣨⣠⣐⣐⣀⣀⠀⠶⢿⠿⠋⠛⠀⠙⠋⠙⢛⣋⣳⣤⠽⣕⣴⣿⣿⣿⣦⢧⡷⣇⣐⢠⡄⠲⠤⠄⣰⢤⢂⣴⣤⣾⣿⢧⡛⠿⠭⠭⠋⠀⠀⠐⠛⣀⣡⣘⠛⠐⠋⠀⢤⠼⢭⡻⠿⢻⣦⢽⣿⣻⣿⣿⣽⣟⣻
⢈⣿⣛⣭⣽⣻⣿⣶⣾⢤⣤⣤⣦⣄⡒⢂⣤⣠⣔⣈⣍⣩⣩⣤⠄⢷⡿⠛⠊⠇⠋⠐⠁⠂⠠⠛⢹⣧⠷⣯⠽⠚⡗⠺⠉⢀⡲⠙⠃⠀⠀⠀⠀⠀⠀⠀⠁⣰⠑⣀⡦⡕⢤⡴⣤⢠⡅⡈⣼⣷⡾⢻⣿⢞⠋⠙⢻⣹
⣸⣿⣟⣻⣿⢿⠟⠿⣈⡁⠀⠀⠙⢠⣧⡿⠛⠛⠈⠙⠉⠩⠁⠙⠏⠑⠄⠩⠆⡀⢀⣀⡁⠉⠰⠆⠀⠀⠉⠉⠀⠒⡄⠈⠀⠀⠀⠈⠀⠀⠀⠐⠮⠀⠈⣁⠁⠇⡶⠈⠁⠀⠈⠀⠀⠉⠑⠊⠲⣼⢿⣉⣺⣦⣉⣶⣾⣾
⢃⡀⣀⣀⡈⠀⢹⠐⠤⠶⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠃⠀⠀⠀⠐⢀⢄⢀⠀⢀⠀⠐⠀⠀⠠⠀⡀⠀⠀⢀⣀⠀⠀⠀⢅⠀⠀⠀⠀⡀⠠⢀⣂⠀⠀⠀⠂⢀⣠⣝⠋⢛⣻⣿⣬⣽
⠮⣁⣉⠉⠉⠀⠲⠶⢀⡁⠀⡀⠀⠁⢀⢌⣤⠀⠀⠀⠀⠀⢰⡀⠀⣀⠀⢈⣘⠉⠕⣡⠂⢠⣶⣦⣶⠿⣿⡾⢆⢘⡓⠀⢀⠰⡄⠀⠆⠁⠀⠀⠭⠒⠖⣉⡾⠆⢄⡠⠗⠉⠠⠌⠁⠈⠡⢤⠶⠀⠛⠶⢶⣿⣯⣽⣯⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠳⠃⠀⠀⠀⠠⠈⠁⢰⡀⠞⠊⣀⣴⣶⠶⣻⢯⠥⠧⣰⠇⠉⢁⠀⠀⠤⠌⠄⢀⠀⠀⠀⠁⠄⠃⠀⠀⠴⠟⣦⠂⢊⣄⡀⠀⡀⠀⠀⢘⠻⠗⠠⣥⠤⠻⢼⠼⡿⢿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡐⠬⣭⠹⢶⡏⢷⣔⡌⢉⢤⠀⢀⣤⠀⠀⠀⠀⠈⡀⠀⠄⠀⠀⠂⠀⠐⠚⠂⠀⠛⠋⠈⠀⠈⠒⠤⢵⡦⡴⠤⣶⣯⣤⣤⣰⣾⣵⡾⠀⠨
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆⠀⠀⠄⠀⢀⡀⠠⢆⠴⠓⡀⠁⠀⠀⣈⠁⠀⠀⡀⠀⡀⠀⠐⠰⢀⠀⠀⠀⠀⠀⠀⡈⠀⡀⣀⢂⠁⠛⠧⠖⠀⠀⠐⠉⠅⠀⠄⣺⢤⡸
⡖⣒⣐⠊⠖⠀⠀⢀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠙⠋⠀⠂⢨⡀⠸⠈⣄⡀⠀⡊⠀⠀⠀⢀⡀⢀⣼⣦⠿⣯⢠⡒⠩⡵⠲⠮⠄⠠⠂⠊⠀⠀⠀⣀⡺⢛⠉⠰⠔⠠⠀⠀⠘⢳⣊⡱⡇⠼⣻⠖⠷⠸
⣤⡀⠡⢠⣤⣐⣒⠂⠂⠰⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠂⢾⣿⣦⠀⠀⢀⠀⠸⠁⠁⡻⠙⠀⠙⠚⠋⣡⡓⠀⠈⠐⠀⠀⠘⠒⠚⠚⠋⠘⡠⠀⠀⠀⠀⢠⣄⣠⣽⣇⠀⢇⡀⡈⠉⠁⠄
⠉⠀⠀⠀⠀⠀⠁⠀⠁⡀⠨⡉⠁⣰⣻⣗⠀⠠⠅⠀⠴⠁⠈⠀⠉⠐⠈⠁⠀⠀⠀⠀⠉⣫⣿⡷⠼⠧⡳⠧⣮⡛⠥⠄⠂⠃⠀⢀⡀⠀⠀⢘⡁⠒⠊⠀⡉⡐⡊⠄⠕⠢⡀⣀⠀⢀⡓⠫⡆⠌⠱⠀⠁⠀⠀⠠⠀⢴
⠀⠀⠂⠀⠀⠀⠀⠀⣀⣇⠀⠛⠛⣻⡿⠟⠁⡀⠰⣀⣀⠀⠀⠀⠀⢀⠂⠤⠤⠤⠧⠀⠄⠉⠘⠀⠅⠀⠘⠇⡀⠤⠤⠀⠀⠀⠠⠀⠃⠀⠀⠀⠠⠂⠠⢻⠿⠞⠂⠠⠆⠰⠓⠄⠀⠀⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣤⠭⠀⠀⠀⠌⠉⠉⣣⠬⠐⠛⠩⡉⣉⣱⢿⠒⢻⣌⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠈⠀⠚⢩⠀⠀⠀⡄⢨⣤⣤⠄⠰⠀⠀⠀⢐⠀⠀⠀⠀⣠⢠⡄⠀⠀
⠁⠀⠥⠼⢸⡷⠿⠿⠧⠳⠻⠟⠿⠻⠏⠇⠀⠀⠀⠈⠿⠁⡀⠀⠈⠅⠀⠀⠀⠒⠁⠀⠐⠁⢀⠀⠁⠀⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠀⠁⠾⣛⠛⠹⠧⠆⢠⠤⠌⡇⢰⠶⡗⢿⣏⡛⠹⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⢻⠛⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⡛⣻⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠈⠉⠉⠉⣿⣿⣿⣷⣶⣦⣀⠤⢿⠏⠉⠁⠘⠂⢀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⠿⠿⣄⡀⠀⢠⣤⣙⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠁⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠉⠃⣽⣿⡻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋⠁⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠋⠿⠿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⢀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⣿⣿⡏⠠⣿⣿⠀⢸⣿⢹⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣧⣼⣿⢻⣿⡇⠀⣿⣿⠀⢸⣿⣸⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⢛⡟⠛⠛⠘⠛⠃⠀⠛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣤⣤⣬⣴⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣴⣿⣟⣿⣧⣏⣿⣿⣿⠀⣿⣿⡇⣾⣿⣟⢸⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣷⣾⣿⣿⣿⣆⣘⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣽⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⡷⣿⣿⢸⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣷⣿⡟⣿⣿⢸⣿⡏⠁⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⣿⣭⣽⣿⣿⣿⣿⣿⣿⣟⣿⡻⠛⠃⠛⠓⣛⠃⠛⠛⠘⢛⢃⣿⣷⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿
⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣿⣯⣴⣼⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠘⣆⠀⠀⠟⠀⠀⠀⡆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⠀⣷⠀⢩⡀⠀⡏⠀⠀⠀⠃⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⠿⢿⣿⣶⣞⣋⣍⣹⠿⢿⣿⣟⣽⡿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡏⠰⠟⠃⢸⠃⠀⠁⠀⠀⠀⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣆⡸⢶⢿⢻
⠛⠛⠛⡻⣿⣿⣿⣿⣿⣶⡟⣓⣛⢻⠿⠛⠛⠛⠛⠿⢾⢟⣡⣬⣿⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠇⣸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢧⣤⠶⠟⠛⠛⠛⠘⣠⢸
⣉⣛⣯⣯⣥⣎⣫⣹⣟⣿⠷⠛⠿⠛⠦⣴⣂⣀⣠⣄⣸⡞⢿⣿⣿⣿⣿⣿⣿⣹⣿⣶⣏⡩⣽⣽⣿⣿⣿⣹⣯⡀⠈⠀⠀⠀⠀⠃⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠉⠻⡁⠙⠂⠒⠒⠓⢊⣋⡉⠉⠐⠂⠈⡀⠀⣀⠐⣺
⣛⣻⣧⣬⣿⠿⠟⠻⠆⠁⠨⣀⣀⠚⠛⠛⠛⠿⠿⣿⢿⡿⣿⣿⣷⣶⡯⢬⣿⡿⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣣⡀⠀⠀⠀⢀⣐⣤⣀⠀⠀⢀⡰⠢⠤⢥⣞⢌⠍⢓⠒⣄⣼⣓⢷⢏⠩⠙⣋⣫⢤⠔⠓⠀⠘⠛⠻
⠛⢻⡏⠉⠀⣀⣠⣤⣶⣦⣄⠐⢺⣶⠂⠀⢠⠦⣴⣽⣿⣶⣟⣿⣯⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡛⣿⣿⡶⠒⠀⠀⡛⢉⢡⣤⣼⣿⡷⠷⢶⡾⠿⣟⣿⣾⣹⠿⠋⠁⠻⣏⣝⣉⣭⢭⡚⠓⠒⠖⠂⢸⠰
⣿⡿⣷⣮⣦⣾⠿⣿⢿⣭⣾⣦⣶⣶⣾⣿⠿⠿⠿⣿⣿⢏⣿⣻⣿⡿⣿⣿⣻⣿⣿⣿⣿⣷⣶⡿⣩⣶⣿⣇⡠⣁⡛⠊⠫⣿⣷⣴⣏⣰⡽⣶⣦⣠⣀⡁⠀⠀⠀⠙⠑⠰⠶⢶⣷⣶⣿⢹⣿⣷⣾⣿⣿⣿⣶⣶⣺⣿
⠿⠿⡿⠿⠿⢿⣿⣦⠟⣼⣿⡟⣻⣿⣿⠟⠋⠿⣿⡿⢟⡫⣿⣿⣷⣿⣿⣿⣟⣫⣿⡿⣬⢟⠛⡿⣷⣮⣿⣟⣡⣥⣿⠷⣞⣿⡻⣺⣼⣿⣿⡿⣷⡿⢿⣶⡤⠤⣄⣀⣀⣠⣠⢾⣟⣿⢶⠾⣿⣟⣛⣠⡉⠻⡿⢿⣿⣿
⠢⣤⣤⣴⣶⣤⣿⡛⠛⢻⣭⣥⣼⣻⣾⡷⢾⡟⣣⠈⢠⡆⠩⠉⠏⣿⢿⠟⠿⠻⣷⣻⢛⡿⣿⠟⠛⢫⣽⣿⣿⣿⣵⣶⣷⣿⣽⣿⣿⣿⢏⠀⠈⠩⡿⠛⠓⠲⣾⣿⣿⣿⣿⢻⣿⣷⣮⣽⠛⠻⠉⠉⣻⡛⢲⣿⣿⣿
⠀⠈⠀⠀⠀⠀⠀⠉⠁⠤⠓⠉⢹⣿⣰⣾⠆⢿⡇⠀⠈⢵⣾⡄⢄⢯⣵⣦⠶⠴⠬⠻⠕⣋⠛⠁⡀⠀⠁⠨⠊⠽⢿⠿⣿⣭⣉⣩⣴⡍⣿⢾⡾⡯⢿⣺⣿⡿⣿⢿⡷⣮⢽⣿⣿⣫⣹⣿⡿⣷⣶⣄⣰⠀⣁⡀⣉⣽
⠀⢐⣃⣀⣤⣤⣐⣒⣐⣂⠀⠿⢿⠿⠛⠋⠀⠛⠂⠙⣋⣉⣓⣤⠼⠿⡼⣿⣿⣿⡧⣧⣿⣇⣘⢠⡄⠶⠤⢄⣺⡤⢂⣴⣴⣾⣼⢤⡛⢿⠭⠏⠋⠇⠀⠑⠛⣀⣀⣚⠋⠐⠉⠠⢤⠏⣝⡻⠿⢿⣯⢽⣿⣿⣿⣿⣽⣿
⡀⠹⣿⣿⣭⣿⣿⣿⣶⣾⢦⣤⣴⣶⣴⡒⣂⣤⣤⣐⣼⣍⣩⣩⡤⠈⢷⡟⠛⠉⠓⠋⠀⠑⢂⠐⠋⢻⣭⢷⣯⠝⢺⡖⠻⠉⢙⡞⠙⠀⠠⠀⠀⠀⠀⠀⠀⠁⣸⠑⣠⡶⣠⣤⡴⣤⢦⡍⡒⣼⣷⡾⢻⣿⠟⠟⠛⢻
⢯⣹⣿⣟⣹⣿⣿⠿⣿⣾⡁⠀⠀⠉⢬⣶⡟⠛⠋⠉⠋⠉⠭⠉⠙⠋⠓⠄⠩⢇⡀⢀⣉⡡⠉⠰⠆⠈⠁⠉⠉⠀⢒⠔⠉⠁⠀⠀⠈⠁⠀⠀⠰⠮⠀⠉⡉⠁⠁⡶⠉⠁⠀⠈⠀⠉⠉⠉⠋⢢⣿⣿⣙⣺⣦⣨⣶⣾
⠛⢛⡀⣀⣠⡄⠀⢻⠐⠳⡷⠔⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠁⠀⠀⠀⠒⣀⢄⢀⠀⢀⠀⠂⠀⠀⠠⠄⠀⠀⠀⣄⣀⠁⠀⡀⢥⠀⠀⠀⠀⡀⠠⠀⣂⡀⠀⠀⠆⢀⣩⣝⠫⢛⣻⣿⣽
⠶⠶⠥⣭⠉⠁⠔⠚⠖⣀⣀⠀⡠⠀⠁⢀⢬⡄⠀⠀⠀⠀⠀⢰⡀⠀⣀⠀⢠⣻⠍⠘⡥⠀⢠⣶⣴⡶⠿⣿⡿⣆⣺⠒⠀⣈⠴⠄⠀⠆⠁⡀⠀⠏⠰⠶⣁⡾⠆⣄⡰⠷⠉⢠⠌⠁⠈⠉⢢⡴⠀⠻⠷⢶⣿⣏⣭⣾
⠛⠉⠀⠉⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠈⠲⠃⠀⠀⠀⠠⠈⠁⢰⡀⠞⠉⣄⣼⣶⠖⣻⣧⠬⢧⣴⠇⠉⢁⠀⠀⠴⠌⠄⢀⠀⠀⠀⠁⠜⠃⠀⡄⠰⠛⡖⠀⡃⣄⡀⠀⡀⠀⠀⢘⠻⡗⠤⣥⠤⠳⢜⠼⡿⢿⠿
⣴⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡐⠭⣭⠺⣷⡏⠷⣤⡌⢊⠄⠀⢀⡤⠈⠀⠀⠀⠈⠄⠠⠄⠀⠀⠁⠀⠐⠚⠀⠀⠛⠃⠈⠈⠘⠒⡤⢷⡦⣴⠤⢸⣭⣤⣄⢼⣬⣵⣾⠀
⠠⠤⠀⠀⢀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠂⠀⢀⡀⠤⠆⠶⠃⡀⠁⠀⠀⣈⠁⠀⢀⡀⠀⠀⠀⠐⠴⢀⠀⠀⠀⠀⠀⠀⡈⠈⡀⢀⢒⠉⠻⡧⠶⠂⠀⠀⠉⠉⠀⢐⢲⢴
⠻⠟⡒⡒⠉⠛⠀⠀⢀⣆⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠠⠉⠁⠀⠈⣠⡠⠸⠀⣀⡀⠀⠈⠀⠀⠀⢀⡀⢀⣼⣦⠿⣿⢨⡚⠹⡵⡲⠯⠀⠠⠂⠃⠀⠀⠀⢀⡠⢛⠋⡰⠐⠠⣀⠀⠘⠳⣘⡳⡆⢼⣳⠦⠿
⣠⣤⣀⡄⢤⣤⣖⣲⡂⡀⠰⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠂⢾⣿⣦⠀⠀⣀⠀⠹⡀⠁⠻⠉⠀⠙⠊⢋⣱⡋⠀⠈⠂⠀⠀⠘⠲⠒⠒⠋⠙⡠⠀⠀⠀⠀⢠⣔⣂⣼⣏⡁⣅⡀⡈⠀⠁
⠉⠉⠀⠀⠀⠀⠀⠀⠀⢁⣐⠨⡉⠀⣞⣻⣗⠀⠠⠥⠀⠞⠁⠀⠈⠉⠀⠈⠁⠀⠀⠀⠉⢉⣯⣿⡷⠾⠦⡳⠧⡮⡹⠡⠀⠂⠁⠀⢀⠀⠀⠠⢘⡀⠒⠀⠀⣉⠐⠎⠌⠗⠂⡀⣂⠀⢀⣻⠫⡄⠭⠩⠊⠁⠀⠀⢠⢰
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣸⠷⠀⠛⢛⣻⡿⢟⠀⡀⢐⣀⣀⠀⡀⠀⠀⣄⠣⠤⣦⠸⠧⠠⠄⠉⠈⠀⠀⠀⠸⠁⡠⠤⠤⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠂⠠⢻⠟⠖⠀⠠⠆⡴⠂⠀⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⠤⠉⠁⠀⠀⠌⠉⠉⣥⠛⠓⠋⢉⣈⣡⣴⠿⠚⢻⡄⠐⠀⠀⠁⣀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⢀⡀⠀⠀⠠⠚⡬⠀⠀⠀⡄⢨⣤⣤⠄⠦⠐⠀⠀⢰⠀⠀⠀⠀⣀⢠⡄⢀
⠀⠩⠅⠸⢺⡷⠿⠿⠧⠣⠸⠟⠿⠻⠏⠇⠀⠀⠀⠀⠈⠛⠀⡄⠀⠈⠇⠀⠀⠀⠈⠀⠀⠰⠡⡀⠀⠁⠐⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠀⠑⠾⣏⠙⠳⠦⢆⢠⠀⠌⠶⠰⠶⡷⢿⣟⡛⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⠟⠋⠙⡋⠻⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢯⣿⠛⣻⣿⣿⠻⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡈⠉⠉⠉⠉⢿⣿⣿⣿⣶⣦⣀⠼⢿⠉⠉⠉⠘⠂⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⠿⢯⣿⣿⣿⣿⠿⠿⣄⡀⠀⣠⣤⣙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠟⠛⠻⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⣽⡿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠛⠟⠿⠙⠿⠿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡗⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⢀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣸⣿⣿⣿⡷⢆⣿⣿⠀⢸⣿⢸⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣷⢻⣿⢻⣿⡇⠈⣿⣿⠀⢸⣿⣸⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢃⡟⠛⠚⠛⠈⠛⠃⠀⠛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣰⣄⣀⣀⣀⣤⣶⣾⣷⣶⣶⣶⣶⣤⣤⣦⣤⣤⣤⣤⣶⣿⣟⣿⣯⢀⣿⣿⣿⢀⣿⣿⣇⣾⣿⣟⢸⣿⣿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣧⣾⣿⣿⣿⣆⣀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣟⣸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣯⣿⡿⣿⣿⢸⣿⣏⣥⣀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣯⣿⣭⣿⣿⣿⣿⣿⣿⡿⠿⠛⠃⢛⣛⠛⠃⠛⠛⠘⡛⣿⣿⣿⣿⣿⣞⣛⣋⣛⣛⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣛⣻⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣽⣧⣴⣾⣿⣿⣿⣿⣿⣯⣽⡧⣿⣿⣻⣿⣿⣿⣿⣿⠟⠋⠉⢷⡀⢸⣿⡟⠀⠀⠠⠄⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣤⣰⡄⠘⠃⠈⢻⡆⠀⠀⠘⢀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣶⣛⣉⣍⣭⠿⢿⣿⣋⣽⣿⣏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⠃⡾⢿⠀⣄⠀⠈⠀⠀⠀⠀⡸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣧⣺⢾
⣉⣉⡉⠛⠛⡛⡻⠿⣿⣿⣿⣶⡿⣛⣛⣻⠿⠛⠻⠛⠛⠳⢺⢞⣥⣴⣟⣻⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⡧⠀⠀⠘⠀⠧⠀⠀⠀⠀⣀⠀⠆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⢷⡴⠷⠞⠛⠛⠛⢹
⣭⣭⣉⣙⣭⣭⣥⣶⣏⣭⣿⡿⡷⠛⠿⠛⠲⣤⣤⣀⣠⣢⣻⡟⢷⣿⣿⣿⣿⣿⣿⣽⣿⣾⣏⣩⣿⣽⣿⣿⡇⠀⠓⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⢉⡟⢛⠉⠉⡙⠻⡁⠛⠒⠒⠚⠓⢛⣏⡉⠉⠒⠠⠀⡀⠀⣼
⣛⣛⣟⣻⣧⣬⡿⠿⠟⠛⠂⠁⠀⢀⣀⡚⠻⠛⠻⠛⠟⣷⡿⠿⣿⣿⣷⣾⡧⣬⣿⡿⣿⣿⣿⣻⣿⣿⣷⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠼⠒⠼⢴⣮⣵⢝⢓⠂⣤⣞⡳⣶⢏⠉⠙⣋⣫⢄⠔⠖⠀⢸
⠛⠛⠛⢫⡟⠀⠀⢀⣤⣤⣴⣦⣆⠐⠲⣾⡖⡀⢠⠤⣼⣿⣿⣾⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣄⣀⠀⠠⢠⠀⢂⠀⠀⡀⢀⢡⣤⣼⣿⡖⠶⢿⡾⠛⣇⣿⣿⣹⠿⠉⠁⢸⣏⡝⣉⣭⢯⡚⠓⠒⠂⠲
⣶⣶⡿⣟⣿⣮⣿⣿⡿⠯⣻⡷⣿⣦⣶⣶⣿⣿⠿⠿⠿⢾⣿⣋⣻⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣷⣶⡟⣭⣶⣿⣀⢈⣁⡃⠊⠉⣿⣷⣴⣁⣠⡽⠶⢎⣠⣀⡁⠀⠂⠈⠙⠁⠰⠶⢾⣷⣶⣿⢽⣿⣷⣾⣿⣿⣿⣶⣶
⡿⡿⠿⡿⠿⠿⠿⢿⣿⣧⢛⣾⣿⡟⢻⣿⣟⠟⠛⣿⣿⠿⢛⠥⣿⣿⣷⣿⣿⣿⣟⣭⣿⡿⣬⡛⢛⡿⣷⣮⣿⣟⣠⡤⡿⢶⣚⣟⢗⣺⣾⣿⣿⡿⣷⠿⢯⣦⡤⠤⣄⣀⡀⣀⣠⢾⣗⣿⣶⢾⣿⣟⣋⣨⡉⠻⢿⣿
⡀⠀⠒⣥⣤⣶⣶⣲⣿⣟⣛⡿⢭⣥⣼⣻⣺⡵⢾⡏⣯⠈⢰⣆⠋⠁⢋⡿⠿⠻⠟⠻⣷⣻⢹⠻⣿⠛⠛⢩⣽⣿⣿⣯⣵⣦⣶⣿⣽⣿⣿⣿⢿⠄⠉⢩⠻⠛⠒⠲⣾⣿⣿⣿⣿⣿⣿⣿⣮⣹⠛⠻⠉⠉⣿⡟⢺⣿
⠀⠢⠀⠂⠀⠀⣀⠀⠀⠉⠀⠀⠋⠉⠉⣿⣶⣿⠂⣟⣃⣀⠬⣵⣲⣄⡦⢩⣽⣶⠶⠶⠲⠳⠵⣏⠋⢁⠀⠀⠁⠉⠈⠽⢿⢿⣿⣭⣁⣩⣶⡭⡿⣾⡾⡍⢷⣸⡿⠿⣿⢿⡷⡏⢽⣿⣿⣫⣹⣿⡿⣷⣶⣄⣰⠀⣉⢸
⣀⡀⠀⢀⣭⣤⣤⣤⣬⣭⠔⢂⠠⠛⠿⠿⠙⠋⠀⠛⠃⠈⢉⣩⣳⣤⠿⢭⡼⣿⣿⣿⣶⣿⣿⣁⠰⢰⡜⢖⡤⢔⡢⡔⢂⡧⣴⣻⡼⣬⡛⡿⠭⠝⠃⠃⠂⠙⠛⣈⣀⣚⠛⠒⠋⠠⢄⠜⢝⡳⠿⢿⣯⢽⣿⣿⣿⣿
⣩⢬⣅⠩⣿⣭⣽⣿⣯⣿⣿⢿⣯⣤⣴⣶⣶⣒⣢⣤⣤⣒⣴⣬⣽⣭⣴⠒⢿⡟⠛⠉⠓⠋⠈⠐⠂⠘⠋⣿⡭⢹⡯⠟⢺⠖⠻⠉⣁⡟⡙⡁⢠⠀⠀⠀⠀⠠⠀⠁⣸⡑⣀⣮⣰⣤⣴⣤⢥⡅⣒⣽⣷⡾⠻⣿⡿⢿
⢴⠶⢿⣽⣿⣟⣹⣿⣻⡟⢿⣦⡆⠀⠀⠈⠦⠶⠏⠉⠓⠈⠉⠩⠮⠍⠛⠋⠑⠊⠹⢅⡀⠈⣀⠍⠁⠲⠁⠈⠈⠍⠅⠀⢢⠆⠉⠁⠀⠀⠈⠁⠀⠀⠰⠮⠀⠉⡙⠀⠫⡶⠉⠁⠀⠈⠀⠉⠉⠹⠏⢦⣽⣿⣉⣺⣮⣸
⠚⠋⠛⢫⣄⣠⣄⣀⠀⢸⠘⠛⠓⠛⠠⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣐⡀⡴⠁⠀⠀⠀⠓⣀⣄⢀⠀⣀⠀⠂⠀⠠⠤⠀⠀⠀⠀⣆⣀⠀⢀⡠⢥⠀⠀⡀⠀⠀⠠⢀⣂⡀⠠⠀⠆⢀⣩⣟⡛⠛⢻
⣶⣶⡶⠶⠦⠿⠎⠉⠂⠘⠛⣀⣀⣀⠤⠀⠀⢀⢪⡆⠀⠀⠀⠀⠀⢰⡀⠀⣀⠀⢨⣻⠁⠘⠵⠂⢴⣶⣶⡾⠿⣿⡿⡄⣺⡂⠀⡀⢦⠄⠀⠂⠀⡀⠈⠍⠒⢆⣁⡿⠆⣀⡠⠷⠁⢀⠌⠉⠈⠁⢰⡴⠀⠷⠽⢦⣾⣽
⡿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡈⠑⠁⠀⠀⠀⠠⠈⠀⣘⡀⠛⠁⣠⣼⢿⠾⣽⡧⠤⢧⡼⠇⠉⢁⠀⠠⠴⠬⠄⢀⠀⠂⠈⠁⠘⠁⢠⠀⠰⠛⡄⠂⠋⣀⡀⠀⡀⠀⠀⣘⠻⡷⢄⣧⡤⠶⢜⠮⣿
⠛⠑⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠯⡭⠨⠶⡉⠧⣴⡍⠂⠄⠀⣁⡤⠉⠀⠀⠀⢁⠀⠠⠄⠀⠀⠁⠀⠐⠚⠀⠂⠓⠋⠉⠁⠐⠲⡤⣷⣢⣴⣤⣰⣯⣠⣀⣨⣦⣽
⠤⠀⠠⠶⠀⠀⢀⠀⠀⠀⠀⠀⠄⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠰⠂⠀⠀⢂⠀⢄⡀⠤⡨⠞⠃⠀⠁⠀⢀⣨⠀⡀⢀⡀⠀⡀⠀⠔⠶⢀⠀⠀⠀⠀⠀⠀⡈⠈⡀⢐⢒⠃⠿⣇⠶⠂⠀⠀⠉⠍⠀⢘
⠿⠿⠻⠿⠛⡫⠄⠛⠀⠀⠠⠥⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠂⠄⠘⠁⠀⠂⡸⡤⢀⠀⣀⡀⠀⠉⠀⠀⠀⣀⡀⣀⣝⣮⠿⣯⢨⡚⠩⡵⠶⠯⠀⠠⠀⠊⠀⠀⠄⢀⡸⠟⠋⡰⠸⠀⣀⠀⠘⠳⣘⡣⡇⢤⣾
⠀⠀⣰⣶⣤⡄⢲⣦⣶⡶⠂⡍⠘⠀⡀⠀⠀⠀⠀⠀⢀⡀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠚⠂⣿⣿⣦⠀⢀⣀⠀⠙⡀⠁⡻⠉⠀⠙⠚⢉⣽⠋⠀⠈⠒⠀⠀⠘⠲⠖⠒⠋⠄⡠⠀⠀⠀⠀⢀⣐⢂⣾⡭⠁⣇⡀⠙
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠐⣍⠀⡏⣹⣇⡀⠰⠦⠀⠞⠅⠀⠈⠁⠀⠈⠁⠀⠀⠈⠉⢉⣯⡿⡷⠾⠶⡾⠷⢮⡙⠡⠀⠀⠁⠀⢀⠀⠀⠀⢘⡁⠒⠂⢀⠉⠰⠎⠈⠕⠢⣀⡂⠀⠀⠻⠏⡌⡉⠩⠊⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡬⠇⠀⢉⣁⣻⣿⣋⠀⣄⣐⣀⣀⠀⡀⠀⡀⣀⠠⠴⢖⠰⠇⠠⠀⠐⠊⠀⠐⠀⠩⠁⠠⠴⠤⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠂⠠⢻⠿⠴⠄⡠⠆⡤⠂⠈⠁⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⡄⠀⠀⡤⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⢥⠓⠋⠋⢱⣆⣥⡝⠿⠚⢻⡄⠂⠀⠀⢀⡈⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⢀⡀⠰⠉⠀⠚⡬⠀⠀⠀⡄⢀⣀⣤⡄⢴⠀⠀⠀⢢⠀⠀⠀⠀⠀⢀
⠀⠈⠉⠹⢲⡷⠿⠿⡯⠣⠸⠇⠿⠿⠇⠇⠀⠀⠀⠀⠀⠀⠈⠛⢀⠤⠈⠉⠂⠀⠀⠀⠈⠀⠀⠀⠁⠠⠀⢀⠐⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠈⡑⠀⠑⠼⢿⠻⢻⣤⡄⢀⡀⠈⠆⢲⠦⡶⢾⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠻⠿⠛⠋⢙⠛⠛⠛⠛⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢛⣻⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡈⠉⠉⠉⢉⣿⣿⣿⣷⣶⣦⣀⠼⢿⠛⠙⠁⠻⠂⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⢿⢿⣿⣿⣿⣿⠿⣿⣄⡀⠀⣤⣤⡙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠁⠀⠀⠈⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏⠛⠻⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠁⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⠛⠛⠿⠉⠻⠿⣿⡿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⢿⣿⡆⢸⣿⡄⣿⡇⣿⣿⢀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣇⣸⣿⣿⣿⡷⢄⣿⣿⠀⢸⣿⢸⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢻⣿⢹⣿⡇⠈⣿⣿⠀⢸⣿⣸⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣳⠛⠛⠘⠛⠘⠛⠃⠀⠛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⢰
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣈⣀⣀⣀⣀⣀⣀⣰⣀⣀⣀⣤⣀⣾⣷⣷⣶⣶⣶⣶⣤⣦⣦⣤⣤⣤⣴⣿⣟⣿⣇⢀⣿⣿⣿⣀⣿⣿⡇⣾⣿⣿⢸⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣧⣾⣿⣿⣿⣶⣦⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⢺⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⡿⣿⣿⢸⣿⣏⣁⣠⣿⣿⢸⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣭⣿⣿⣿⣿⣿⠿⠟⠛⠃⣛⡛⠛⠃⠛⠋⠘⡛⣿⣿⣿⣿⣿⣾⣟⣫⣛⣛⣹⣿⣿⣿⣷⣾⣿⣿⣿⣿⣻⣿
⣛⣛⣛⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣭⣭⣥⣶⣾⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⠟⠂⠱⡄⠀⣿⣿⠃⠀⠀⠤⠀⢰⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡄⣦⠀⠛⠀⠘⢻⠀⠀⠀⠐⢀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⣶⣾⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠿⣿⣿⣶⣚⣉⣍⣹⠿⢿⣿⣋⣽⣿⣋⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡾⢃⣿⡇⠀⠀⠀⠸⠀⠀⠀⠀⡸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣧⡆⣿
⣭⣉⣉⡉⠛⡛⣛⠻⣿⣿⣿⣿⣿⠿⣓⣉⣻⠟⠛⠻⠛⠛⠳⠻⢜⣤⣼⣟⣻⣿⣿⣿⣷⣾⢿⣿⣿⣿⣿⣿⡇⢸⡇⠘⠀⠀⠀⡆⠀⠀⠀⠀⢠⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⢿⡿⣿⣿⢷⣹⠗⠛⠁⠛⢻
⣭⣭⣭⣍⣙⣭⣯⣥⣶⣿⣭⣟⡿⢗⠛⠟⠛⢢⣦⣤⣄⣠⣂⣻⡿⢷⣿⣿⣿⣿⣿⣿⣹⣿⣾⣍⣩⣿⣽⣿⠀⢸⡁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⠉⡉⠉⠻⡁⠙⠒⠒⠚⠓⢊⣉⡈⡁⠀⠀⠈⡀⢈
⣿⣛⣛⣟⣛⣧⣽⣿⠯⠟⠛⠂⠀⠀⢁⣀⠛⠙⠟⠛⠛⠟⣷⣿⠿⣿⣿⣷⣶⠧⣬⣿⣿⣿⣿⣿⣻⣿⣿⣿⣇⠀⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠰⠲⠾⢤⡎⢄⢉⢑⠂⣠⣜⡓⢷⢇⡩⢉⣋⣫⢦⡔⠚⠰
⠛⠛⠛⠛⢛⡿⠀⠀⣀⣤⣤⣶⣶⣤⡐⠺⣾⣂⡀⢠⡦⣬⣿⣿⣿⣞⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡄⣀⠈⠠⠰⠆⠀⠀⠀⡀⢠⢡⣤⣼⣿⡶⠷⢿⠾⠛⣇⣿⣾⣹⠿⠁⠀⠻⣯⣝⣉⣭⠭⡟⠓⠒⠲
⣷⣶⣶⡾⢟⣿⣶⣾⣿⡿⠞⣛⣶⣿⣶⣶⣶⣿⣿⠿⠿⠷⢿⣿⣋⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣷⢶⡟⠹⠶⣉⠀⢈⣁⠃⠈⠈⢹⣶⣴⣀⣰⡭⠦⢎⣠⣈⡁⠀⠀⠀⠙⠁⠰⠶⢶⣷⣶⣿⢽⣿⣷⣾⣿⣿⣿⣾
⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣦⣛⣼⣿⡏⢻⣿⣟⠟⠋⣹⣿⢿⢋⠥⣿⣿⣧⣿⣿⣿⣟⣭⣿⠿⡼⡛⢛⡿⣷⣬⣾⣏⣠⡤⡾⠶⣚⣏⢓⣺⣾⣿⣿⡿⣷⠿⢯⣦⡤⠤⣄⣀⡀⣠⣠⢾⣟⣿⢶⠾⣿⣟⣋⣨⡁⠛⢿
⠠⠤⠀⠒⢠⡤⣶⣶⣒⣿⣟⣛⡻⠭⣭⣴⣳⣺⡵⢾⡏⡅⠈⢲⣆⠛⠀⢋⡟⠿⠻⠟⢻⣿⣿⢸⠻⣿⠛⠛⢩⣿⣿⣿⣯⣵⣦⣶⣾⣿⣽⣿⣿⢂⠄⠉⠩⡸⠛⠒⠲⣾⣿⣿⣿⣿⢻⣿⣳⣮⣽⠛⠻⠉⠉⢻⡗⢻
⠀⠀⠢⠀⠈⠀⠀⢀⠀⠈⠉⠀⠐⠋⠉⠩⣿⣴⣾⠀⣟⣃⣀⠬⢷⣺⠄⡲⠫⠿⣶⠶⠶⠰⠻⢵⣏⠋⣀⠀⠀⠁⠘⠈⠟⢿⠿⠿⢍⣁⣩⣶⡍⡿⢾⡿⡭⢶⣺⣿⡿⣿⢿⡧⣏⢽⣿⣿⣋⣹⣿⡿⣷⣶⣄⣰⠀⣉
⣃⣀⡀⠀⢀⣭⣤⣤⣤⣬⣭⠔⢂⡀⠟⠿⠿⠉⠉⠀⠛⠃⠈⢉⣡⣱⣤⠮⠭⠼⣿⣿⣿⡺⣾⢾⡥⠐⢰⡜⢖⡤⢔⡢⡔⢂⡶⣴⡺⡼⣴⡛⠿⠬⠙⠃⠃⠀⠙⠛⣈⣀⣛⠛⠘⠋⠠⢄⠞⢙⡳⠿⠻⣣⢱⣟⣿⣿
⠉⣩⠤⣍⠉⣿⢭⣵⣿⣭⣿⣿⣿⣏⣤⣴⣶⢤⣖⣂⣤⣤⣒⣴⣤⣽⣭⣔⠒⢿⠟⠋⠈⠓⠉⡈⠐⡂⠚⠋⣽⡭⢻⡯⠓⢲⠖⠛⠁⣀⠘⡙⠀⠠⠀⠀⠀⠀⠀⠀⠀⣸⠑⣰⣦⣰⣤⡴⣤⢄⡅⡒⢼⣷⡾⢿⣿⢿
⠠⠤⠶⢾⣟⣿⣋⣩⣿⣛⡏⢻⣦⣄⠀⠀⠨⠨⠷⠎⠉⠁⠈⠉⠉⠫⠍⠉⠉⠁⠂⠰⢡⡀⠬⣈⠍⠁⠲⠀⠉⠈⠍⠅⠀⠡⠒⠉⠁⠀⠀⠀⠀⠀⠀⠰⠮⠀⠉⡉⢨⠉⠶⠉⠉⠀⠈⠀⠉⠉⠁⠆⢢⣽⣿⣈⣶⣼
⢶⠆⠋⠉⠫⣄⢠⣀⣀⠀⠸⡘⠓⠛⠚⠠⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠒⡔⠀⠀⠀⠀⠓⣀⡄⢀⠀⣀⠀⠀⠀⠀⠤⢀⠀⠀⠀⢀⣀⠀⢀⡀⢥⠀⠀⡀⠀⡀⠀⠀⣀⡀⠀⠀⠆⢀⣩⣝⡛⢻
⡤⢤⢴⡼⠷⠶⠶⠆⠁⠂⠈⠙⢀⢀⣀⡤⠀⠁⢀⢺⡆⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢠⣙⠅⠈⠄⠀⢴⣶⣴⡾⢾⣾⡿⡄⢺⠂⠀⡀⠶⠄⠀⠀⠀⡀⠈⠍⠒⠎⣑⡿⠀⣀⡰⠶⠁⢠⠌⠉⠈⠉⢢⡴⠀⠷⠵⢦⣾
⡛⠹⡻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⠠⠀⠀⣺⠀⠛⠀⣤⣼⢿⠚⣼⡧⠬⢣⡾⠌⢉⣀⠀⠠⠴⠬⠄⢀⠀⠀⠀⠁⠜⠁⢀⠠⠰⠓⡔⠀⠃⣄⡀⠀⡀⠀⠀⣘⠛⡷⢄⣧⡤⠶⢼⢼
⡖⠈⠑⠺⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡍⠙⠾⠍⠷⣤⡄⠊⡄⠀⣀⡄⠈⠀⠀⠀⠁⠀⠠⠄⠀⠀⠁⠀⠐⠚⠀⠂⠓⠁⠈⠁⠐⠲⣤⣷⡮⣴⣤⣰⣯⣠⣄⠨⣼
⠶⠶⠄⠰⢶⠀⠀⢀⡀⠀⠀⠀⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⢀⠀⢄⠀⠴⡪⠞⠀⠀⠁⠀⢀⡈⠀⡀⢀⡀⠀⠀⠀⠔⠶⢀⠀⠀⠀⠀⠀⠀⡀⠈⡀⢐⢒⠉⠹⣏⠶⠂⠀⠀⠋⠉⠈
⣿⠿⠿⠟⠿⠿⠏⠄⠛⠃⠀⠠⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠂⠀⠘⠀⠐⠁⡤⡄⢐⠀⣄⣀⠀⠌⠀⠀⠀⣀⡀⣠⣼⡮⠷⣥⢘⡊⠩⠵⠳⠯⠁⠠⠀⠃⠀⠀⠀⢀⣠⣛⠋⣰⢀⠀⣀⠀⠘⠳⣘⣳⡦⢼
⠁⠀⠀⢠⣶⣤⣔⠒⣶⣴⡶⠆⡅⠘⠀⣀⠀⠀⠀⠀⠀⢀⡄⠤⠀⡀⠀⠀⣀⠀⠀⠀⠁⠐⠛⠀⣿⣿⣦⠀⢀⣀⡀⠙⡀⢉⠻⠉⠈⠙⠊⢉⣵⡋⠀⠈⠒⠀⠀⠐⠲⠒⠒⠋⠙⣠⠀⠀⠀⠀⢀⣀⢂⣬⡭⡁⣅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠐⢈⣀⡭⢹⣏⠀⠰⠦⠀⠎⠁⠀⠈⠡⠀⠈⠀⠀⢁⠀⡍⢉⣻⡿⡷⠿⠶⡿⠷⠮⡹⠡⠀⠀⠁⠀⢀⠀⠀⠀⢘⡀⠲⠈⢀⡁⠰⠆⠈⠵⠂⣀⡨⠀⠀⠻⠏⡌⡉⠉⠎⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠷⠀⢈⣁⣹⣿⣋⣀⣄⣘⢀⣀⠀⡀⠀⡀⣀⠠⠔⢖⠺⠁⠠⠀⠀⠁⠀⠀⠀⠩⠀⡠⠴⠤⠀⠀⠀⠄⠘⠂⠀⠀⠀⠄⠂⠠⢻⠟⠶⠄⠠⠄⡤⠂⠈⠁⠈⣟⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣄⠀⡄⠀⠀⠀⠈⠀⠁⠀⠐⠂⠀⠀⠵⠒⠋⠉⣑⣦⣤⡼⠛⠚⢻⡄⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠔⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠐⠁⠠⠚⡬⠀⠀⠀⡄⢈⣠⣤⡄⢤⠐⠈⠀⢠⠀⠀⠀⠀⠀
⠀⠐⠋⠹⢺⡷⠷⠿⠿⠣⠸⠟⠿⠿⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠆⠈⠈⠂⠀⠀⠀⠈⠀⠀⠀⠁⠠⠀⢀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠀⠱⠾⢯⠹⢳⣤⠄⢀⡀⠈⠶⢰⠦⡶⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠉⠸⠋⠅⠉⠉⠁⠀⣻⡿⠿⠿⠿⠿⣿⣿⣿⣾⣮⣉⢉⣹⣾⢿⠿⠿⠻⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠸⠹⣿⣿⣿⣿⣿⣿⣴⣿⣀⠀⢀⣀⣔⠻⠦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠘⠿⠛⠋⠉⠉⠉⠉⢁⡨⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡏⠛⠻⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠙⠋⠋⠉⠉⠀⠉⠙⢩⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠈⠙⠟⠛⠟⠿⠿⠿⠻⠿⢿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⣼⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⢀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣟⣻⣿⣿⣿⣇⡀⣿⣿⠀⢸⣿⢻⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣷⣿⣿⢻⣿⡟⢱⣿⣿⠀⢸⣿⣸⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠏⠛⠛⠚⠛⠘⠛⠃⠀⡛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⢀⡀⢰
⣀⣀⣀⡀⣀⠀⠀⠀⠀⢀⠀⣀⣀⣀⡈⠁⠀⡀⠀⣀⢀⢀⡀⢀⣀⣀⣀⣭⣿⣿⣦⣶⣶⣦⣤⣤⣤⣤⣰⣿⣟⣿⣧⢀⣿⣿⣿⠀⣿⣿⡇⣾⣿⣿⢸⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣧⣾⣿⢿⣿⣶⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢸⣿⢿⣿⡀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⡿⣿⣿⢸⣿⣟⣇⣄⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣯⣿⣿⣿⣿⣿⣿⠛⠛⠓⠛⢻⠟⠗⠛⠛⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣊⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⠏⠥⡄⠀⣿⣷⡄⠀⠀⠀⣀⠘⢿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣛⣿⣿⣿⣿⣟⣿⣿⣿⠛⠉⢀⠀⠡⠀⠘⢿⡇⠀⠀⠀⢧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⡽⣭⢿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠿⣿⣾⣾⣛⣋⣙⡿⢿⣿⢟⣻⠽⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⡇⣺⣆⠀⠀⠀⠈⠟⠀⠀⠀⠀⠂⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿
⣛⣚⣿⠙⠛⠛⠛⠿⠿⠿⢿⣿⡿⢿⣷⣖⣓⡟⠿⠿⠛⢛⠟⠻⠦⢼⢝⣫⣽⡿⢿⣿⣿⣿⣧⣽⣿⣿⣿⡇⢰⡿⠁⡿⠛⡀⠀⡀⠀⠀⠀⠀⠠⠀⠃⢀⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠟⠻
⣿⢿⣯⣭⣭⡑⠓⣒⣛⣯⣥⣏⣽⣿⣿⡷⠟⠿⠿⠦⣶⣀⡀⣀⣠⢺⣾⣯⣯⣿⣿⣿⣿⣿⢻⣿⣿⡍⣿⠁⢸⡃⠀⠀⠀⠃⢐⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠉⡉⡙⢿⠋⠛⠫⠓⠚⠛⢛⣟⡈⠉⠐⠒⠸
⠟⣿⣿⣟⣛⣿⣛⣯⣭⣿⣻⡛⠿⠧⠁⠈⢀⣀⡘⠛⠿⠿⠿⠿⣫⣽⣿⣿⣿⣧⣴⡯⣽⣿⡿⣻⣿⣿⣿⡀⠘⣅⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠻⡾⢧⡿⢽⠝⢓⠒⣤⣴⡲⢶⠏⠙⠛⡛⣓⢄⣤
⠿⠿⠛⠛⠻⠟⠛⣿⠉⠁⠀⣀⣤⣔⣢⣤⠀⢻⣷⡒⠀⢠⣤⣴⣿⣿⣶⣞⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢷⠀⠛⠢⠔⠀⠀⠀⠠⡄⠀⠀⠀⠀⢘⢣⣄⣼⣿⡶⠶⣶⡾⢿⣎⣾⣾⣱⣿⠋⠉⢸⣟⡝⣋⣉⣏⡞⠚
⢻⣿⣶⣶⣶⣶⡾⢿⣾⣾⣿⡿⢾⢛⣭⣾⣧⣶⣶⣾⣿⡿⠿⠿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡆⠀⠀⠀⠠⢀⠀⠀⠐⠂⠈⠈⢾⣦⣠⣉⣠⡛⣤⣌⣀⣀⡀⠀⠄⠈⠙⠑⠱⣦⢶⣷⣶⣿⣽⣿⣷⣶⣿⣿
⣿⠿⢿⣿⣿⡿⢿⢿⡿⢿⠿⣿⣦⠸⣬⣿⣿⣻⣿⣿⠿⠻⠲⣷⡾⢟⡯⣿⣿⣯⣿⣿⣿⣟⣋⣿⡿⠬⠓⠠⠤⣦⣜⣨⣟⣈⠁⣾⢴⣞⢟⠳⠾⣼⣿⣿⡶⣶⡿⢿⣧⣤⣤⣄⠀⡀⢀⣠⠼⣟⣿⣵⠶⣿⣿⣟⣉⢙
⠒⠂⠀⣄⠨⠐⢌⣤⣤⣶⠦⣿⣟⠛⢻⣯⣭⣼⢻⣿⣶⣾⡟⣫⠈⢠⡄⠫⠉⢟⡿⣿⠻⡿⠿⡽⢓⢐⠻⣾⠗⠟⢍⣽⣿⣿⣗⣳⣮⣥⣭⣼⣿⣿⣿⢏⡄⠈⢱⣺⠟⠗⠶⣾⣿⣿⣿⣿⢾⣿⣻⣷⣡⠛⠻⡏⠙⢹
⢀⣀⡀⠀⣰⠀⠘⠁⠀⠀⠀⠀⠉⠩⠄⠜⠉⠉⣿⣽⣶⠆⣿⠇⠀⠈⣥⣶⡄⢄⠫⣵⣤⠦⠥⠨⠫⢐⣝⠋⠁⠀⠈⠁⠙⠈⠽⢿⢿⣿⣍⣁⣩⣮⡉⣿⣾⡶⣏⢷⣺⣿⡾⣿⣿⣯⣟⣹⣿⣿⣿⣹⣿⡿⣿⣴⣀⣰
⣀⣐⠒⣀⣀⠀⠀⣙⣀⣤⣤⣤⣟⡐⢀⡀⠴⢿⠿⠟⠛⠁⠙⠃⠙⢛⣉⣣⣤⠾⠽⡼⣿⣿⣿⡴⢿⣾⣃⡰⢠⡐⢦⠤⣀⡦⡄⢤⣦⣴⣾⡽⣭⡛⣿⠽⡋⠋⠆⠀⠻⠿⠈⣀⣚⠛⠐⠚⠉⢇⠸⢛⢣⠿⠿⣿⣻⣿
⠉⠉⠉⢛⣩⣅⡈⢹⣿⣯⣽⣯⣽⣷⣾⣯⣤⣤⣶⣤⡖⣂⣠⣤⡐⣨⣍⣹⣭⣤⠾⢷⡟⠛⠋⠗⠋⠈⠑⠂⠘⠋⣼⣽⢲⣯⠗⢺⡖⠻⠉⠁⡺⠵⠂⢠⠀⠀⠀⠀⠀⠀⠉⢹⠻⠀⣤⣰⣄⣬⣤⣌⡕⢰⣼⣿⣴⢿
⠀⠀⠀⢄⡴⠾⣿⣿⣿⣻⣿⣿⣿⡿⣧⣷⠂⠀⠉⠆⡷⠞⠛⠛⠈⠛⠉⠩⠉⠙⠋⠓⠀⠠⢄⡀⢀⣉⡆⢁⠰⠂⡈⠀⡉⠁⠐⢒⡄⠉⠂⠀⠀⠉⠁⠀⠀⠠⠬⠀⠈⢐⠈⣏⡬⠉⠉⠉⠀⠁⠉⠛⠋⠿⣾⣹⣿⢸
⠿⠷⢼⡦⠘⠛⠛⣀⢀⣄⣀⠀⢸⡔⠓⣾⠲⠃⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡬⠀⠀⠀⠀⠒⠀⡄⢀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⢀⣃⠄⠀⡀⠀⠀⠠⠀⡄⡀⠀⠀⠤⢀⣙⣿
⠿⣶⣀⣥⣤⣴⠶⠾⠼⢭⣉⠶⠒⠳⢄⣀⣀⡤⠄⠁⢀⢸⣤⠀⠀⠀⠀⠀⢰⡀⠀⣀⠀⢈⣻⠉⠘⡥⠂⢠⣶⣴⡾⠿⣿⡾⣠⢹⡒⠀⡀⢤⠀⠀⠄⠀⡀⠨⠍⠤⠎⣁⣾⢆⣀⠁⡶⢃⢀⡀⠉⠑⢒⣠⣀⡎⠽⢽
⣤⣤⠽⠿⢿⠛⠛⠉⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠠⠈⠉⢰⡂⠚⠀⣀⣴⣶⢶⣹⡧⠬⢧⣴⠎⠋⢁⠀⠀⢤⠘⠄⠀⠀⠀⠈⠂⠘⠃⢀⠀⠠⠷⡄⠆⠞⡁⠀⠀⢀⠀⠀⡀⠖⣷⢅⣠⣤⡸
⣿⣿⣶⠒⠛⠲⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡰⠭⣭⠹⢶⠉⣧⣰⡌⠂⠄⠄⢉⣀⠀⠀⠀⠀⠈⠀⣀⠄⠀⠀⠃⠀⠰⠒⠂⠁⠐⠒⠙⠑⠒⠷⣄⣶⡬⣠⣬⢀⡟⠉⣈
⠉⠉⣤⠶⢄⠀⠴⠆⠀⠀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⡆⠀⢀⠀⠤⡄⠵⠃⠀⠁⠀⠀⢘⠁⠀⠀⡀⠀⡀⠀⠡⠴⢀⠀⠀⠀⠀⠈⠀⠒⠈⠀⠀⠶⠞⠿⢎⡠⠄⠁⠈⠽
⡓⣒⣟⡿⠿⠿⠿⠛⣛⠩⠘⠃⠀⠀⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠠⠈⠉⠀⠊⢸⡀⠨⠀⣄⡀⠀⡉⠀⠀⠀⢀⡀⢀⣵⣶⠷⣾⢱⠐⠛⣢⠦⠞⡈⡠⠄⠀⠀⠀⠠⠁⢀⡿⠛⢣⣄⠅⡀⠀⠐⠢⠤⠲
⣀⡉⠁⠀⠀⠀⣶⣦⣤⡐⣶⣴⣖⡲⣉⠰⠂⠀⡀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⣿⣿⣦⠀⠀⢀⠀⠸⠁⠉⢻⠙⠒⠻⠊⠁⢠⠳⠄⠠⠒⠁⠀⠰⢤⡴⠶⠞⠹⠈⠀⠈⠈⠀⠉⠀⠀⢲⣦⠻
⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣁⣰⠐⢯⡀⢸⢹⣟⡀⠠⠦⠀⠶⠁⠀⠈⠉⠀⠈⠁⠀⠀⠀⠉⠉⢫⣿⡷⠼⠧⡲⢧⣎⠻⠁⠉⠀⠂⠐⠀⠀⠀⠀⠰⡀⠦⠄⠀⡲⠰⠄⡀⠪⠅⠀⡀⠀⠀⠼⠽⣉⢹⠛⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣤⡿⠀⢊⣉⣘⣿⢟⡁⣤⢐⣂⣀⠀⢀⠀⢀⢠⠡⠤⢤⠠⠧⢠⠄⠈⠚⠀⠄⠀⠙⢁⡀⠤⠤⠀⠀⠀⠀⠀⠂⠀⠀⠈⢀⢀⢠⢾⣗⡤⠭⢡⡄⢠⠥⡘⠒⠀⣟⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠁⠀⢩⡜⠚⠋⢁⣂⣩⣴⠯⠒⢻⣎⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠔⢮⠀⠀⠀⢈⠐⠈⣀⡀⢠⠀⠈⠁⠠⡀⠀⠀
⠀⠀⠁⠸⢰⡏⠷⠷⡷⠢⠺⠟⠿⠛⠇⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡤⠀⠁⠇⠀⠀⠀⠐⠁⠀⠰⠠⠀⡀⠁⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀⠀⠲⠠⠁⣸⠿⠹⢧⣆⣀⢀⡀⡀⢃⠰⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡘⠂⠈⠉⠉⠉⠈⠉⠋⠿⢙⠉⠉⠁⠃⣾⡿⠿⠿⠿⢿⣿⣿⣿⣮⣬⣉⡉⣹⣾⣿⠿⠏⠿⠂⠩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⡻⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣴⣾⡀⠀⢀⣀⣠⠿⠦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠚⠉⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠙⠿⠟⠋⠋⠀⠉⠙⢁⡈⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠛⠉⠉⠙⠛⠉⠉⠁⠈⠉⠛⢫⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠉⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠁⠸⠏⠿⠿⠻⠿⠿⠿⠻⠿⢿⣿⣿⣻⠧⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⢀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡟⣻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⢿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣷⢹⣿⢻⣿⡏⣢⣿⣿⠀⢸⣿⣸⣿⡇⢸⣿⢻⣿⡇⣿⣿⠘⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⠃⠛⠛⠚⠛⠘⠛⠓⠂⡟⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣬⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣄⣄⢸
⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠉⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⣅⣿⣧⣤⣴⣦⣤⣀⣀⣀⣰⣿⣟⣿⣇⢀⣿⣿⣿⠀⣿⣿⣗⣾⣿⣯⢸⣿⡿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣧⣾⣿⢿⣿⣾⣿⣿
⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠛⢸⣿⢿⣿⡀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⢼⣿⣿⣧⣤⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣿⣿⠘⠛⠓⢿⣿⡿⠻⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⣛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣟⣭⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⣁⠀⢠⣿⣦⡉⠀⠢⢋⡀⠘⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣛⣿⣿⣿⣿⣟⣿⣿⠛⠋⠐⠘⠇⠀⠻⣿⡇⠀⠀⠀⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣍⣉⣿⢯⣽⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣽⢿⣿⡮⢽⣟⣋⣙⣿⢿⣿⠿⣻⣿⠟⣶⣿⣿⣿⣿⣿⣿⠟⢁⣶⡇⣷⠀⠀⠀⡀⠻⡷⠀⠀⠀⠈⠇⠀⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿
⢟⡟⣖⣻⡟⠛⡛⠛⠻⠿⠿⠿⣿⣿⣿⣯⣖⡒⡘⠿⠟⠟⣛⠿⠻⠦⢴⣿⣫⣽⣿⢿⣿⣿⣿⣿⣼⣿⡟⠀⣼⡿⢃⡿⢳⡀⠀⠃⠀⠁⠀⠀⠀⠀⠀⢀⣏⣜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠼
⡷⠿⠿⣯⣭⣤⡐⠒⠒⣒⣒⣤⡜⢉⣞⣿⣿⠞⠿⠷⠧⣔⣀⡀⢀⡀⢺⣾⣿⣿⣿⣿⣿⣿⣿⢻⣻⣿⡇⠀⣟⠃⠈⠀⠉⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⠋⣻⡉⢿⡟⠛⠯⠱⠶⠛⠚⣛⡋⠉⠑⢲
⠿⠛⠐⣿⣿⠛⢿⣟⣻⣭⣽⣟⣿⠻⠯⠉⠀⢁⣀⡐⠛⠿⠿⠿⠿⣻⣽⣿⣿⣿⣯⣥⣯⣽⣿⡿⣻⣿⡃⠀⡯⣀⣀⣀⠛⠀⠘⠛⠋⠀⠀⠀⠀⠃⡄⠀⠈⢀⣽⡿⡹⣷⣧⣿⣽⠝⢛⠲⣤⣴⣖⢶⡞⠹⠛⠛⢓⣰
⠀⣴⣶⡟⠛⠛⠿⠍⣻⡏⠉⠀⣀⣠⡄⢲⣤⠀⢶⣿⡒⠀⠠⣤⣴⣯⣿⣷⣼⣻⣿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠉⣾⣽⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣤⣸⣿⣷⡷⣿⣾⠿⣾⢸⣿⣓⣟⠏⠉⠨⡾⣫⠊⣋⣛⢻
⡟⠛⣿⣷⣶⣶⣴⣶⠿⣷⣶⣼⡿⢖⢻⣭⣴⣧⣴⣶⣾⣿⡿⠿⠯⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡶⠀⠈⠁⠀⢀⠀⠀⠐⠆⠈⠈⢱⣷⣠⣈⣡⣻⣤⣄⢀⣀⡀⠀⠀⠈⠉⠛⢉⣦⣴⣶⣴⣼⣏⣿⣷⣶⣾
⠿⢿⡿⠿⣿⣿⣿⠿⠿⣿⠿⠿⣿⣷⡜⢧⣿⣿⢛⣿⣿⠿⢛⠶⣾⡾⠟⡫⣿⣿⣿⣿⢿⡿⣿⣛⡷⠿⠄⠃⠂⡤⣤⣜⣠⣞⢀⠁⢼⠤⣔⡟⠳⠼⢽⣿⣿⡷⢦⡿⢿⣧⣠⣤⣄⠀⠀⢀⣀⡴⣿⣿⣯⡤⣿⡿⢟⢻
⢶⣾⡓⠂⣈⢡⡄⠄⣤⣤⣶⡦⢼⣿⡛⢛⣯⡭⣤⡛⡿⣧⣾⡿⢫⠀⢢⣥⠩⠉⠛⣿⣿⢿⡿⠻⡧⢲⠐⠲⣖⠗⠚⠍⣽⣯⣿⣗⣲⣦⣭⣬⣴⣿⣿⣿⡏⠀⠘⠓⢲⡟⠯⠶⡼⣿⣿⣾⣿⣷⣿⣻⣷⡖⡟⠿⠟⢹
⠶⠆⣁⣀⠀⣐⡄⠈⠃⡀⠀⠀⠀⠀⠉⠤⠔⠈⠉⣻⣯⣷⡆⣹⡋⠀⠈⢥⡔⣄⢄⠉⣵⡆⠶⠬⠩⠿⠑⡗⠛⠀⠀⠀⠁⠈⠉⠹⢿⡿⣿⣙⣁⢉⣨⣉⣯⣴⣶⣖⢷⣶⣿⡶⢿⣿⣿⣙⣋⣿⣿⣿⣛⣿⣿⢿⣄⣸
⠀⠀⣤⢔⣀⡀⡀⠀⢘⣃⣠⣤⣤⣞⣃⢐⡢⠔⠿⠿⠟⠛⠁⠘⠚⠙⢙⣙⣛⣤⡼⢗⣥⣷⣿⣿⡢⢧⠧⣃⡰⢠⡐⢢⠤⢀⡸⡀⠦⡤⢤⣾⣽⣭⠟⢿⡛⡻⠛⠀⠀⠹⠻⠇⢃⣀⠛⠚⠐⠋⢁⡩⢚⢻⡼⠿⣿⣹
⡈⠀⠉⠙⢛⡣⣄⡀⢩⡯⣿⣭⣯⣭⣷⣶⣿⣥⣤⣶⣆⡐⢒⣠⣀⡐⣪⣋⣉⣯⣤⠖⢷⡿⠛⠋⠓⠉⠐⠈⠂⠸⠓⢰⣗⢶⣯⡵⢺⡷⠿⠉⠋⡩⠵⠞⢀⡁⠀⠀⠀⠀⡀⠈⢨⡯⠅⣠⡁⣆⣠⣤⣬⣱⠐⢲⣿⣼
⠀⠀⠀⠀⢠⡤⠾⢯⣿⣿⣛⣿⣿⣿⡿⣷⣨⠖⠀⠈⠑⣷⠾⠟⠛⠈⠙⠉⠩⠈⠙⠛⠙⠂⢈⢆⣀⢀⡋⡑⠉⠰⠂⠀⠂⠉⠉⠀⢒⡠⠉⠑⠈⠀⠈⠉⠀⠀⠠⠬⠀⠀⠀⠂⠉⡨⠉⠁⠉⠀⠀⠈⠛⠛⠮⢿⣹⣿
⡾⠿⠿⠤⣧⠜⠛⠛⢃⣀⣀⣀⡀⠀⡧⠒⢺⡷⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⡬⠃⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⠀⠀⠠⠁⣀⡀⠁⠀⠀⠂⠀⠀⠄⢀⠀⠀⠠⢀⢸
⡻⠿⣆⣂⣭⣤⢴⡶⠶⠿⠭⣍⠱⠰⠘⢦⣀⣀⣀⠄⠈⢀⡰⣡⠂⢀⠀⠀⠀⢠⡆⠀⣀⠀⢀⣺⠍⠑⣁⠐⢠⣶⣦⣶⠿⡿⣾⣀⢸⡶⠀⠀⢠⡀⠀⠁⠀⢀⠈⢉⠠⠤⡀⢾⡇⣀⠈⣰⢖⠀⣐⠋⠉⠲⡠⣀⡄⢹
⣨⣡⣤⡤⠿⠿⡟⠛⠉⠈⠉⠀⠀⠀⠀⠀⠑⠘⠀⠀⠂⠁⢀⠑⠎⠀⠀⠀⠠⠈⠈⠠⡀⠔⠄⣅⣰⣶⣴⣾⣯⢭⠧⣴⡆⠋⠉⡀⠁⣠⣔⡃⠀⠀⠀⠀⠒⠀⠃⢀⡀⡠⡽⣅⠄⠸⠃⠀⠄⠀⠀⠀⠀⠴⣶⢅⣐⣸
⣿⣿⣿⣷⠖⠚⠳⠾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡰⠬⣍⠹⢴⡟⢿⣀⡈⢑⡄⠀⠉⣀⠐⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠡⠒⠂⠈⠰⠖⠘⠉⠐⠪⣅⢢⣬⣁⣌⡈⣽⠛
⠛⠛⠉⣡⠶⠄⠀⠰⠆⠀⠀⣀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠄⠂⢈⡐⠀⢔⠰⠇⠀⠉⠁⠀⠐⡃⠀⠀⣀⠀⢀⠀⠠⢀⢄⡐⠀⠀⠠⠀⠀⠰⠀⠀⠀⠬⠶⠻⢾⢠⠤⠉⠉
⣚⠛⢒⡊⠻⠿⠿⠿⠟⢃⠨⠄⠛⠀⠀⡤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠄⠋⠀⠐⢀⣤⠠⠈⡀⠀⠀⠘⠂⠀⠁⠀⠀⢀⣱⢤⡪⣼⠁⡤⠓⣂⢤⢴⡀⢁⡄⠀⠀⠀⠀⠈⠄⡿⠚⠓⣅⠆⡀⠀⠈⠦⣬
⠒⣠⡌⠁⠀⠀⠁⣴⣦⣤⣄⢲⣦⣶⡒⣈⠀⠃⠀⠠⠀⠀⠀⠀⠄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠲⠂⢻⣿⣦⡀⠀⠀⠀⠨⠁⠈⢻⠝⠒⢻⠦⠁⢂⠷⠎⠀⠂⠁⠀⠀⣦⣤⡦⠔⢫⠈⡀⠈⠁⠁⠈⠀⠠⠀⣺
⠈⠡⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢯⡁⠀⢍⣿⡀⠠⠶⠀⠰⠉⠀⠀⠙⠀⠀⠁⠀⠀⠀⠀⠉⠻⣻⣷⠶⢯⡲⠆⣭⡹⢏⡉⠆⠂⠰⠀⠉⠀⠀⠀⠆⠤⠀⠀⢲⠤⡄⢂⢒⠭⡀⠀⠀⠀⠰⣻⢏⠙⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣄⣠⠼⠂⠘⣋⣈⣿⠿⣁⢠⣄⣂⣀⠀⠀⠀⢀⢀⡀⠤⢤⠤⠧⠌⡤⠉⠙⠁⠁⠀⠘⡃⣀⠠⠤⠀⠀⠀⠀⠀⠂⠄⠀⠀⠈⡀⠀⠴⣷⣤⠖⢀⡤⢀⡨⠌⠃⠀⢚⡆⠘⠀⠈
⠀⠀⠀⠀⠀⠀⡄⠠⡄⠀⠀⠀⠀⠀⠁⠉⠁⠀⠒⠁⠀⠨⡜⠚⠙⠉⣲⣈⣠⠾⠖⠛⣌⠐⠂⠀⠀⠐⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⢢⠋⠁⠀⠈⠁⠈⠀⠈⢀⡄⠈⠉⠀⡄⠀
⠀⠀⠏⠹⢰⡗⠏⠱⡷⠢⠺⠗⠿⠻⠏⠇⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠃⡠⠔⠀⠇⠀⠁⠀⠐⠃⠀⠰⢘⢀⡀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡈⠉⠀⠀⠀⠀⠈⠀⠒⠀⠌⢀⣿⡹⠿⣖⣀⠀⡀⠀⠳⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢟⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢘⣉⣀⠂⠉⠉⠈⠉⠉⠁⠌⠢⠑⠈⠁⠉⠘⢹⠿⠿⠿⠿⠿⣿⣿⣿⣮⣭⣉⢘⣻⣾⢻⠏⠉⠰⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣯⠀⠀⢀⣀⡰⠿⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠊⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠙⠿⠟⠛⠋⠈⠉⠙⠀⠘⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠋⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠋⠉⠉⠙⠋⠉⠉⠀⠀⠉⠛⢩⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠻⠿⠿⠻⠿⢿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠠⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⣸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡟⢻⣿⣷⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢻⣿⣷⡄⣿⣿⠀⢸⣿⣸⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠃⠛⠛⠚⠛⡈⠛⠏⢰⠛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠟⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣼⡔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡦⣸
⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⠃⠀⠀⠀⡀⡀⢀⡀⣀⣀⣀⣐⣩⣿⣯⣤⣶⣄⣄⣰⣿⡿⣿⣇⢀⣿⣿⣿⠀⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢿⣿⡞⠟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢸⣿⢿⣿⡀⣿⡿⣿⣿⣿⣿⢺⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣼⣿⣧⣿⣿⠻⢿⣷⣤⣴⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣾⣿⣾⣿⡟⣿⣷⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣟⣿⣿⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⣿⠛⠙⠛⢻⠿⠿⠛⠋⠻⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣙⣻⣿⣿⣷⣶⣿
⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣋⣭⣿⣿⣿⣿⣿⣿⣟⣿⣼⣿⠿⠀⠀⠀⣤⣀⠀⠀⢆⠄⠀⢰⣴⣿⣿⣿⣿⣿⣿⣦⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣻⣿⣿⣿⣿⠞⠲⢰⡄⠀⢠⣿⣿⠇⠀⠈⠀⣆⠀⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣭⣭⣿⢯⣽⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣷⡽⠿⠿⠾⣟⣛⣉⣹⡿⢿⣿⢟⡿⠽⣗⣾⣿⣿⠏⢁⣠⡀⢀⠀⠁⠀⠀⠙⣿⡆⠀⠀⠀⠙⢠⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠒⣚⢿⣛⢚⣻⡧⠝⡟⠛⡿⠿⠿⠿⣿⣿⢿⣷⣖⢒⣉⠿⠿⠛⡛⠟⠳⠦⢾⢝⣥⣽⡿⣿⣿⡿⠀⣠⣿⣿⡇⣿⣶⣄⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠀⣿⣿⣥⣍⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣼⢿⢿⠟⡿⠿⣫⣭⣬⣌⠓⢚⣒⣯⣥⠊⣙⣿⣿⣷⠚⠻⠿⠤⣔⣀⡀⣀⣠⢶⡾⣯⣿⣿⣿⣿⡇⠀⣿⣿⡟⠀⠈⢉⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣯⣿⣿⣿⠛⣟⠛⣿⡟⠛⠽⠳⠖⠛⠛⣛⢘
⠷⠿⡿⠟⠃⠼⢿⣟⢛⣻⣟⣻⣤⣝⡙⠛⠛⠧⠀⠀⢀⣀⡚⠻⠿⠿⠿⢿⣯⢿⣿⣿⣿⣧⣾⣭⡅⠀⣿⣿⣧⡀⠀⠀⠿⠀⠀⠀⠘⠛⠀⠀⠀⠞⠃⠀⢀⣄⡀⠉⢨⣿⢿⢿⣿⣼⣯⣽⠛⢓⠤⣤⣴⠦⢦⠞⠛⢛
⣶⣶⣷⣆⢖⡾⠛⠛⠛⠿⠙⣽⠏⠁⠀⣠⣤⣔⣒⣤⠀⢲⣗⠒⠀⢠⡤⣼⣽⣾⣦⣟⣿⣿⣿⣶⣧⠀⢻⣿⣿⣷⣾⣶⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⣡⣄⣿⣿⣶⣾⣿⡿⠷⡏⣾⣾⢰⢻⠋⠁⢼⠞⡓⢚
⣉⣉⣉⣉⣙⣿⣷⣶⣶⣶⣾⢿⣷⣷⣾⡗⠦⢻⡥⣾⣴⣶⣶⣾⣿⠿⠿⠿⣿⣿⣟⣿⣿⣿⡿⣿⣟⣦⠀⡙⠻⠏⠂⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⠉⢲⣄⣄⢁⣈⣏⣬⡉⣀⣀⠀⠀⠀⠉⠹⠋⢹⣄⣴⣶⣤⣿⣏⣿
⢿⡟⢿⠻⢿⡛⠿⣿⣿⡿⠿⠻⠿⠿⠿⣿⣧⢘⣣⣿⣿⢹⣿⣿⠟⠻⢿⣿⠿⢟⣫⣿⣿⣿⣿⣿⠿⣗⣹⢶⠦⠄⠀⠠⢤⣤⣀⣤⡂⡈⠡⡧⢤⣼⠛⠦⠯⢽⣿⣷⡴⣼⠿⣟⣥⣤⣤⡀⠀⠀⢀⣠⢼⡿⢿⢯⡤⣿
⠒⠲⠦⠹⢿⡁⠁⢄⠠⠀⠊⣤⢴⣶⣖⢺⡟⣛⢙⠯⢭⣴⣻⣺⠥⣾⡟⠣⠉⢶⣆⠉⠙⢏⡿⠟⢷⠿⢻⠜⡆⡒⢷⣺⠒⠯⢉⣽⣽⣿⣒⣷⣬⣥⣭⣾⣲⣾⣿⠁⡁⠋⠒⢺⠻⠭⣦⣿⣶⣷⣿⣿⢶⣿⢿⣴⠂⢻
⠒⠒⠺⠚⠂⠄⠄⠀⠀⠄⠈⠁⠀⠀⠀⠀⠈⠑⠠⠞⠈⠉⣽⣰⣶⠂⣿⢃⡀⠭⢥⣾⡠⠈⠩⢶⠴⠦⡄⠌⠏⢺⡑⠏⠀⠀⠈⠉⠑⠉⡿⣿⣿⣟⣀⡉⣉⣄⣉⣌⣴⣶⣚⣶⢶⣷⡾⣿⢻⡏⡙⣹⣾⣿⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠠⢞⣀⠀⠀⢀⣨⢅⣤⣤⣤⣌⡔⢂⡠⠜⠿⠿⠛⠋⠀⡙⠂⠉⢉⣉⣣⣤⠯⠯⢼⣾⣿⣿⠼⠼⢞⣀⠠⣤⡐⡤⢄⣀⠇⠠⠤⠤⣤⢯⣿⡱⠻⣷⢛⠛⠃⠅⠄⠿⠿⠙⠀⠼⠗⠡⠜⠛⡁⡉⠛⢯⣽
⠀⠀⠀⠀⠀⠀⠀⢩⡱⢦⡍⢡⠮⣽⣿⣯⣭⣿⡟⣿⣥⣴⣶⢤⡖⣂⣥⣠⡒⣼⣏⣹⣡⣔⠛⣿⡟⠛⠉⠙⠉⠂⠑⠀⠟⠃⣾⡶⢾⣷⠶⢪⠴⠯⠁⠁⠩⠲⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⠫⠀⣤⢐⠂⣉⣄⡈⣛⢸
⠶⠞⠂⠀⠀⠀⠈⠤⠴⣶⣯⡿⣿⣭⣿⣋⡿⠿⣷⣕⠂⠀⠈⠢⠷⠾⠋⠓⠈⠉⠉⠭⠉⠙⠉⠃⠀⠸⢀⡀⣐⠈⠎⢁⠖⠂⡉⠈⠉⠁⠐⢂⠀⠛⠂⠉⠀⠁⠁⠀⠀⠀⡔⠀⠚⠐⠈⠋⣈⠙⠉⠈⠉⠁⠉⠒⠓⢹
⡤⡤⠭⢟⣛⠛⠶⡷⠚⠉⠉⠤⢠⣄⣀⡀⠀⠇⠛⣚⠾⠣⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⣀⠠⠭⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠄⠀⠂⠀⢁⣂⠀⠁⠀⠀⠀⢀⠀⡄⠀⠀⠈
⠀⠀⠀⠼⢿⣿⣤⢶⣶⢶⣏⠶⠶⠶⢠⠀⠀⠉⢂⡀⣀⡤⠄⢁⢀⢸⡴⠀⡀⠀⠀⠀⣰⡀⠀⡀⠀⢉⡫⠉⠘⡀⠆⣄⣶⣠⡾⢽⣵⡷⡀⠹⠆⠀⠂⣀⠀⠀⠀⠀⠈⠉⡀⠀⡄⠊⣿⡀⠀⢀⣦⠖⠀⣠⠓⠰⠦⢸
⣤⣤⣤⣤⣄⣒⡚⠛⢙⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠂⠀⡀⠱⠃⠀⠀⠀⠤⠈⠁⣐⠀⠓⠀⣀⡴⣶⢶⡻⡅⠙⢌⣴⠘⠋⢁⠀⢀⣤⢐⠁⠀⠀⠀⠀⠀⠰⠀⢀⢀⢠⠯⡡⠀⠟⡃⠀⠀⠈⠁⠀⠠⠤⣼
⣿⣿⣿⣿⣿⣿⡷⠂⠉⠑⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡼⢭⡍⢪⣮⠩⣧⣀⡈⠠⠀⠌⠉⡂⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠠⠤⠅⠁⠶⠖⠑⠀⠤⢤⡀⢢⣴⢀⢹
⠶⠶⠋⢉⣹⠀⢶⣖⢶⣀⣐⣆⠀⢀⣄⡀⠀⠀⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠠⠀⠀⣁⠀⠠⡢⠶⠀⠈⠉⠀⠀⢒⠀⠀⠀⣀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⠭⠌⢳⡿⢩
⠀⠀⠉⢍⠉⢛⠅⠝⠛⠚⠋⠉⠥⠄⠘⠃⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠘⠁⠀⠂⣠⡄⠌⢁⢀⠀⠀⡓⠈⠀⠀⠀⠀⢈⣢⣔⣧⣟⢠⠜⢒⣠⢤⣄⠘⢀⠀⠄⠀⠀⢀⠃⠀⡷⠾⢂⡅⠆⠉⠈
⠀⣀⣀⢩⡤⠄⠀⠀⠀⠀⣼⡶⢰⡔⠶⠦⡭⠩⣉⠘⠁⣀⡄⠀⢀⡀⠠⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠒⠘⣿⣷⣄⠀⠀⠀⠀⢹⠀⠙⣿⠛⠚⡿⠼⠒⢠⢷⡀⠐⠭⠁⠀⢠⣤⣰⣤⡖⢺⠁⠀⠈⠈⠀⠀⠐
⠀⠀⠀⠈⠠⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠉⢲⣀⡸⢹⣟⠀⠰⠦⠀⠊⠁⠀⠈⠉⠀⠈⠀⠀⠀⠀⠈⠙⣏⣿⣷⠾⣝⡶⣂⣍⠿⣃⠁⠀⠀⠄⠈⠉⠀⠀⠰⠀⢀⠀⠠⠮⢀⡀⠤⢖⡈⠁⢀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠛⠀⠈⡄⠸⡿⢏⣀⣤⣐⣂⡀⠀⡀⠀⡀⣄⠡⠤⡄⠸⠧⢡⠌⠉⠃⠨⠀⠀⢛⢀⣀⣥⡄⠂⠀⠀⡀⠸⠤⠀⠀⠘⠁⠄⢀⢴⣧⣠⡂⢃⡐⢀⡚⠳⠄⠀⡠⠸
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠰⡞⠊⠉⣑⣦⣥⣴⠽⠚⢻⡅⠂⠀⠀⠈⡂⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠈⣬⡘⠉⠁⠀⠈⠑⠈⠀⠀⢀⠀⠙⠸
⠀⠀⠥⠹⢸⡇⠇⠀⠯⠡⠸⠗⠿⠻⠏⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢙⠀⠤⠊⠈⠂⠀⠀⠀⠈⠀⠀⠀⠃⣀⠈⠀⠔⠒⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⢆⠀⠎⢰⣿⢿⣇⡌⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣛⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠇⠁⢈⣁⣀⠂⠁⠈⠀⠉⠈⠑⠗⠟⡉⠉⠉⠉⠡⣿⡿⠿⠿⠿⢿⣿⣿⣿⣷⣯⣉⣉⡿⣿⡿⡿⠛⠗⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣿⣧⣀⢀⣨⣤⣝⠿⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠻⠛⠋⠉⠁⠈⠉⠉⣌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠙⠟⠛⠫⠿⠿⠿⠻⠿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⣸⣿⡆⣿⡇⠿⣿⣿⠿⢰⣿⣿⣿⡆⢸⣿⡄⣿⡇⣿⣿⠀⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡟⢻⣿⣷⣿⡇⠀⣿⣿⠀⢸⣿⢿⣿⡇⢸⣿⣿⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⢸⣿⢻⣿⣷⡄⣿⣿⠀⢸⣿⣻⣿⡇⢸⣿⢻⣿⡇⣿⣿⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠟⠃⠛⠛⠚⠛⡈⠛⠋⡁⠛⠛⠀⠈⠛⠛⠛⠁⠘⠛⠈⠛⠃⠛⠛⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⡀⠀⠀⠀⢀⠨⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼
⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣤⣄⣈⣁⣀⣀⣀⣀⣀⣠⣠⣀⣀⣠⣼⣽⣿⣷⣶⣶⣴⣿⡟⣿⣇⢀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡆⣿⣿⢸⣿⣇⣿⣿⢰⣿⣿⣿⣦⣾⣿⢻⣿⡾⢿⢿
⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣸⣿⢿⣿⣠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣸⣿⣷⣿⣿⣻⣿⣷⣤⣤⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣷⣼⣿⣾⣿⣯⣿⣿⣿⡿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⠻⠟⠛⠛⠛⠋⠙⠃⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⣀⠀⠀⢀⠄⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠗⠒⣶⣤⠀⠀⣿⣿⡇⠀⠈⠀⣶⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⠿⣶⣾⣿⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠾⠿⣷⣶⣋⣻⣉⣽⠿⢿⣿⣻⣿⣿⣳⠿⠉⢀⣄⠀⠀⠈⠙⠆⠀⠉⣿⡇⠀⠀⠀⠹⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⡟⠛⣛⣛⣿⣿⣭⣿⣏⣣⣄⣋⣿⣛⣻⠿⣿⣿⣿⣿⡿⣛⣋⣻⠙⠛⠿⠛⠛⠶⠿⣫⣤⣿⣿⠇⢀⣴⣿⣿⠀⣷⣶⡀⠀⠀⠀⠹⠇⠀⢀⠀⠀⠀⠇⢈⣿⣿⣿⣾⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠓⢲⣿⣿⣟⣿⢻⣷⣶⣶⣬⣩⣭⣭⣭⣴⣯⣭⣯⣿⣿⠛⠛⠛⢺⣥⣤⣠⣤⣶⣿⠻⣿⣿⣿⠀⢸⣿⣻⠏⠀⠉⢹⣧⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⡇⠸⢿⣿⠿⣿⣿⣿⣿⣿⣿⡟⢙⣟⣻⣿⠛⠻⡿⠷⠾⠛⢻
⣿⣿⣿⡿⣿⠛⢛⣻⣿⣿⣙⣿⣯⣿⣶⡿⠿⠟⠛⠃⠀⠘⠦⠤⡛⠽⠛⠟⠻⣿⣷⣿⢿⣿⣿⡇⠀⢸⣿⣿⡄⠀⠐⣘⣿⠀⠀⠀⠀⠛⠀⠈⠀⠀⠘⠀⠀⢀⣤⣄⡀⠀⣸⡿⢿⣿⣿⣼⣯⡿⠛⡳⢦⣥⣶⣶⣦⢻
⣿⣿⣿⣿⣿⣯⣿⣿⡛⠍⠙⠛⢫⣿⠀⢀⣤⣤⣦⣤⣶⢦⠐⠻⢿⣅⣀⣶⣶⣿⣿⣾⣼⣿⣿⣇⡀⠘⣿⣿⣿⣶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠛⠋⣥⣬⣿⣷⣾⣾⣿⡿⣷⣧⣿⡟⢚⣻⠉⠉⣿⢿
⣶⣴⣤⣭⣭⣍⣉⣿⣿⣿⣷⣾⣿⣻⣿⣿⣿⣛⠿⣹⣶⣿⣷⣿⣷⣿⣿⠛⠿⠶⣿⣟⣹⣯⣿⣿⢷⡀⠙⠿⠿⠻⠷⠃⠀⠀⠀⠀⠀⡀⠀⠀⠒⠂⠉⠁⣷⣶⣈⣁⣹⣣⣤⣁⣀⡀⠀⠀⠀⠉⠿⠏⣱⣤⣶⣧⣮⣿
⣿⣿⡿⠿⣿⣟⣿⣟⡻⠿⠿⠿⢛⠛⠿⢿⠿⣿⣿⣙⣾⣿⣯⢿⣿⣛⠏⣟⣿⠿⣛⡯⢸⣿⣿⣾⡿⣿⢀⣀⡼⡶⠤⠀⠀⠠⢤⣤⣄⣴⣀⡠⢠⠷⣶⣻⡻⠾⢥⣿⣿⣿⢶⡾⢿⣯⣦⣤⣤⡀⠀⡀⣠⣠⢾⡿⣿⣿
⡹⠛⠛⠓⠚⢉⣻⠗⠀⢢⠰⠀⢢⡖⠾⣿⠶⢿⢿⣿⡽⢻⣿⣾⣿⣾⠿⣿⣋⡏⠑⣶⡄⠋⠹⢹⠛⠛⠷⠛⢷⠚⡁⡚⠖⠗⠓⠩⢩⣿⣿⣿⣾⣶⣽⣬⣭⣿⣿⣿⣿⢩⠘⠓⠒⣾⢻⠵⣮⣿⣶⣷⣿⣿⣾⣿⣿⣾
⠖⠀⠉⠉⠉⠉⠳⠶⠇⠤⠼⠂⠈⣁⠀⠀⠀⠀⠉⠐⠒⠁⠀⠹⣿⣾⣟⢸⣏⣀⣠⣽⣶⡷⣐⠌⠹⣷⠲⠶⠀⠛⠦⣾⡙⠁⠀⠀⠁⠈⠋⢹⠿⡿⣿⣏⣉⡘⣡⣍⣹⣥⣷⣶⣿⣶⣾⣶⢾⣿⣿⣏⣿⣻⣿⣿⣟⣻
⠤⠀⠀⠀⠀⠀⡴⠾⣥⣤⠤⠄⣀⣤⣤⣾⢶⣤⣤⣼⣥⣕⠛⠿⢟⠈⡁⠀⠙⠃⠁⣀⣝⣶⡶⢬⢴⣿⣿⣿⣇⠷⡷⢟⡀⠦⣆⠲⡦⠤⣐⢤⠦⣴⢤⣴⣯⣯⡽⢿⡿⣛⠟⠻⠀⠘⠿⠏⠚⠠⠼⠯⠧⠛⢛⡉⡹⣻
⡀⠀⣀⣤⡄⠀⠀⠀⢁⡨⠔⢢⣄⣾⣻⣷⣾⣷⣿⣿⡿⡷⢶⣾⡿⢹⠭⣥⣶⣴⣲⣶⣤⣯⣴⣗⢚⡿⠛⠁⠙⠊⠁⠀⢒⠠⠛⢡⣯⠗⣿⣽⠒⣷⠾⠍⠚⢫⣭⠖⠁⡀⠀⠀⠀⠀⠀⠀⠀⣟⢭⢠⣔⢐⠂⣩⣀⢚
⣀⣾⣿⣿⣁⣀⣀⣀⢀⡳⢞⣛⣽⡿⠿⠿⠿⠽⢿⢿⡿⣏⢉⣀⠈⠻⠾⠋⠉⠁⠈⠩⠔⠢⠈⠉⠉⠁⠀⠏⢄⠀⢐⡩⠉⠰⠖⠀⠁⢉⠉⠀⠒⡠⠌⠑⠂⠁⠈⠉⠀⠀⠀⢠⠂⠀⠒⠰⠘⢋⣈⠛⠋⢋⠙⠉⠻⠿
⣻⣿⡿⠿⠻⣯⣭⣙⣟⠿⢃⢀⣀⣴⢰⠴⠬⡀⣘⣏⡙⠿⠿⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢢⠂⠀⠀⠀⠐⠂⠠⠀⡀⢐⡀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡀⠐⠀⠘⢁⣈⠘⠀⠀⠀⠀⡀⢀⠀⠘
⠉⠉⠀⠀⠀⠚⠹⠿⢶⣿⣿⣿⣏⡛⢋⡳⠶⠕⠁⠉⢷⣤⡴⠖⠀⣀⠤⢲⢎⡀⠄⠀⠀⠀⣶⡀⢈⠀⠀⣍⡋⠀⠡⠘⠠⣴⣶⣶⡾⣿⣿⢇⠈⡷⠂⠐⢀⣄⠀⢀⠀⠀⡈⢙⡀⢠⡔⢪⣿⠀⠀⣠⡶⠦⠀⡾⠒⢼
⣤⣴⣶⣷⣾⣷⣾⣿⣏⣛⣿⣃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠐⠛⠀⠀⠀⠀⠆⠀⣀⡫⠘⠃⢠⣤⡿⣿⣯⣯⠭⠽⣴⠷⠛⠉⡐⠀⣠⣄⡊⠀⠀⠀⠀⠐⢂⠒⢀⣀⣀⢼⢯⡡⠨⠟⠀⠠⠀⠉⠁⠀⢸
⠉⠩⠿⢿⣿⣿⡿⠿⠛⠁⠀⠈⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⢯⠉⠴⠏⠹⣄⣬⠁⢤⠠⠉⢁⠐⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠤⠬⠌⠁⠶⠂⠒⠠⠴⣤⠀⣤⣖
⣶⣶⠟⠋⢉⣤⣌⣲⣿⣍⣱⣤⣽⣅⣀⡠⢆⡀⠀⠀⠒⠖⠤⠴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣈⠉⠇⠀⠀⠐⡀⠠⡀⠀⢔⠶⠗⠀⠈⠁⠀⠀⡋⠀⠀⢀⡀⠀⠀⠀⢀⡄⠀⠄⠀⠀⡀⠀⠀⠄⠐⠀⠀⡩⠿⣿
⡾⠿⡌⡀⠀⣀⠀⠤⠤⠛⠻⠛⢛⡐⠖⠊⡈⢀⣀⣰⡓⢒⠠⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠈⠀⠂⠀⠀⠈⢠⣤⠄⠃⢀⣀⠀⢈⠃⠀⠀⠀⡀⠀⣸⣦⣾⣼⡏⡤⠓⣒⡤⣤⣂⠋⡀⠠⠀⠀⠀⡀⠀⢰⠦⠶⢐⢠⠸
⠈⠁⢀⠤⠄⢰⢒⠂⠀⠀⠀⣴⠛⠓⠲⠙⠛⠓⠛⠓⠆⠈⣠⣤⠂⣠⣤⡄⠒⢠⠄⠈⢀⡄⠀⢀⡀⠀⠀⠈⠁⠐⠃⢸⣿⣷⡄⠀⠀⠀⠈⠏⠈⠹⡏⠓⢚⠧⠿⠒⣼⣷⠀⠻⠍⠁⠀⣦⣤⣤⣤⠖⡈⠂⠀⠊⠙⠈
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠐⠶⣶⡈⣷⡤⣒⣽⣷⠀⠒⠂⠀⠁⠀⠀⠈⠅⠁⠀⠀⠈⠀⠈⠉⢙⣽⣿⡶⠷⣚⠞⣸⡙⢟⡈⠱⠐⠠⠄⠉⠁⠀⠀⠖⠠⣀⠆⠰⡄⣀⠠⠠⣖⡈⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠿⠛⠀⡠⠧⠼⡿⡢⣠⣆⠭⢤⠄⣀⣀⣀⡀⡀⠤⠲⠒⡟⠀⠤⠀⠙⠁⠀⠀⠈⡛⣀⢠⡤⠄⠀⠀⠀⠀⠡⠄⠀⠀⠋⠀⠀⡠⣼⢔⣠⡀⣀⡐⣀⠚⠦⠄⢰
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⠀⠀⢠⠈⠁⠠⠄⠒⠍⠉⠡⠬⣤⣤⠟⠛⠛⣧⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⢡⣦⠛⠉⠁⠀⠋⠤⠃⠀⠀⡐⢘
⠀⠈⠷⠸⢺⡷⠿⠀⡧⠣⠸⡗⠿⠻⠇⡇⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠉⠰⠆⠁⠘⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠈⠠⠂⠂⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠠⠀⠀⠁⠠⠄⠠⠅⣰⣾⣿⣥⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣁⣀⣀⢨⠟⠿⢿⣿⣿⡿⠟⠙⠛⠿⣿⢟⡝⠉⢿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠂⠋⠹⠯⠩⢵⡏⠶⣤⠿⣿⣿⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢹⣅⡀⣠⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢼⣶⡬⠌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠫⢩⡤⠉⠉⠉⠀⠈⠆⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾
⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠙⠛⠉⠉⠉⠉⠉⠉⠈⠙⠿⠿⠿⣉⡙⣸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠏⠀⣻
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣂⣦⠠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⡌⠀⠀⠰⢛⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠑⠂⠐⠀⠀⠈⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠐⠀⠂⠐⠀⣵⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣤⣄⣀⣀⠀⣀⡀⠀⠀⣀⡀⠲⠶⠶⠶⣾⣿⠿⣳⣤⣿⣤⠒⢻⡷⣽⣿⣿⣦⣶⣦⣾⣿⣿⣿⣿⣤⠃⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣦⠀⢀⣀⡶⠋⠉⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣷⣷⣴⣖⣂⠒⢂⣀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠛⢿⡶⠟⢃⣀⣠⡄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣦⠈⣿⣿⣿⣿⣿⡟⠃⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠻⠿⠀⠀⠘⠆⠀⠈⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠛⢿⠇⠀⣤⣀⠀⢠⠦⠐⠒⠂⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢿⣿⣿⣿⣿⠟⠛⠛⠉⢹⣿⣦⡌⠀⠀⣿⣿⠀⠸⣤⣰⣶⣶⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣀⣴⣶⡆⣀⣀⠀⠉⢷⡀⠀⢹⣿⠾⢷⣬⡏⠹⡿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣿⣧⣿⣿⣿⣿⣿⣿⣿⣛⣛⡿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣵⣿⣦⣥⣭⢛⣓⣂⡉⠀⣾⣿⣿⣿⡧⣿⣿⣿⡄⠈⢣⠀⠘⢿⠀⠸⣏⠀⠠⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣻⠛⣿⡛⢯⢿⣿⣾⣿⣿⠀⣼⣿⣿⣿⡟⠀⠀⣿⣿⣷⠀⠸⠀⠀⠀⠀⢨⣶⣤⣀⣵⣿⠃⣼⣿⡿⢛⣛⠛⣻⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⠉⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⢿⡿⢿⣿⠛⢛⣛⣉⣠⣤⣤⣫⣿⣿⣭⣉⣙⣉⣽⠀⢻⣿⣿⣿⣿⣤⣾⣿⣿⣿⠀⣼⠆⠀⠠⠳⠀⠘⠉⢉⡉⠃⢐⣿⣿⣿⣯⣿⣿⡿⣾⣾⣿⣛⣿⣿⣿⣿⣾⣛⣩⣛⣿
⣿⡿⢿⣿⣿⣿⣿⣿⣿⠛⡟⢻⣿⣿⣤⣤⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⣷⢚⡟⣿⣿⣿⠟⠛⣿⣿⣿⢿⣿⠛⣿⡿⠿⡿⣿⣿⣿⣿⢿
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣷⣿⣯⣿⣦⡀⠙⣿⣿⣿⣿⡿⠁⠀⣀⠀⠀⠀⠀⠀⠀⡀⢆⡄⠤⢬⡌⠀⣸⣿⡿⣿⣶⣿⣿⣿⢯⣶⣴⣅⠀⠀⠰⠾⠛⠸⠿
⣿⣿⣿⣿⡿⣻⡿⠿⠿⢿⣿⣿⣿⢟⣻⣿⠤⣻⣭⣵⣧⣼⣿⣿⢿⣿⣟⣿⢿⣿⣯⣽⡿⣿⠿⣟⡃⡶⢻⣿⣿⣿⣷⣾⣟⣻⡍⣥⣄⣼⣻⡿⠷⣿⣧⣾⣻⣿⠿⠽⣿⣻⣿⣿⣿⣿⡿⣿⣛⣿⣿⡿⠶⣶⣀⣤⣤⣿
⣿⣿⣽⣿⣽⣿⣤⡴⠶⣾⢿⣯⣭⣄⣿⣯⡀⠿⠛⠉⠉⠉⠛⢻⣭⡿⠿⣻⣿⣿⣿⡟⣷⡟⣶⠿⣇⣅⠀⢹⡯⣭⢩⡓⠛⢹⡗⣻⣽⣿⠉⠙⢶⠻⡿⣿⣾⣿⣷⣿⣷⣿⣿⣿⣿⣿⢃⠙⣩⡿⠛⣟⢻⣿⣿⣿⣿⣿
⣿⣏⣉⣹⣟⣿⠟⢛⡂⠀⣀⣴⣶⣞⣀⣁⠹⢑⣋⣈⣭⣑⣒⣲⣶⣶⡴⢶⣿⡿⠿⠏⠿⣿⣿⡿⢿⢏⣑⣿⠿⣽⣩⣭⣅⣡⣭⣿⡶⡰⣶⣀⠀⠀⠉⡉⡉⢟⠿⠷⣶⣦⣷⣷⣾⣿⣾⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣽
⣿⣿⠅⢀⠰⠏⢺⣀⣀⣙⠙⢋⡹⠛⣛⣭⣛⢿⡿⣛⣯⣿⣿⣿⣾⣿⣿⣠⣤⣶⣶⣾⣻⣤⠤⣿⣟⣻⣛⣻⣿⣽⣿⡿⢿⣿⢟⠿⣟⠋⣿⣼⣿⣗⣮⣷⣛⡿⣿⡿⢿⣿⣾⣟⡿⠾⢝⠭⠓⠂⠛⠛⣂⣭⣟⡛⠛⣻
⣿⣧⣦⣥⣶⣥⣽⣿⣿⡇⠀⠈⠉⢿⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢛⣿⣯⣿⡿⢯⠟⡿⢟⣿⠟⣿⣿⣿⠅⢴⠬⡁⣬⢦⣭⠎⣯⡼⣶⣿⣿⡟⠋⢻⢫⣿⠩⢽⠿⣟⡍⠰⠀⠀⣀⠀⢠⡀⢀⣺⣝⣦⣶⣿
⣿⣿⣻⢿⢿⣿⣿⣿⣿⣿⣿⣟⢷⣿⣶⣿⠉⢏⣈⣭⣽⡿⠉⣿⠿⢿⣷⣏⡉⢄⠉⠉⠁⠀⠀⠀⠁⠈⠉⠀⡠⠸⠄⠉⠛⣎⣑⡾⠷⠚⠋⢐⣂⠲⠘⠓⣉⠿⠁⠈⠉⠀⠠⠊⠀⠀⠀⢲⠗⠀⠉⣉⢩⡯⡷⣯⠉⢻
⣉⣬⣤⣤⣿⠿⠛⠛⠓⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣽⡾⠻⢿⣍⣁⣤⠌⣣⢀⣼⣤⠐⣀⠀⠂⠀⣤⠹⠠⠤⠄⡤⣶⣾⣼⣁⡄⣀⣀⣀⣠⣼⣇⣄⢤⣥⣀⠀⡀⠠⠤⢀⠀⠀⠰⢧⣀⠁⢀⡠⢥⠀⠀⡀⠀⢸
⣷⣶⣾⣯⣼⣶⣶⣶⣶⣾⣿⣷⣶⣿⣿⣿⣭⡛⠃⠉⠉⠉⠀⠀⠈⣓⠙⠟⢻⣟⠊⢸⣿⡞⠙⠠⠶⡀⠿⠆⣽⣧⣤⢷⠋⣈⣈⣡⣽⠿⢿⠿⣻⣿⣿⣛⡯⢿⠁⣄⡱⠶⠀⡰⠤⠀⢄⡐⠏⡲⢿⣹⣿⠇⣔⣣⠷⣻
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣟⢿⣇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢘⠯⠀⠀⠀⠀⠀⠈⠂⢖⠚⠁⠈⣿⣿⠿⣿⣿⢯⡟⡛⢟⡟⠋⠠⠤⣀⡰⠿⠰⡀⡀⠀⠁⠀⠀⠘⡙⠤⠠⠲⣟⣾⠠⣟⣅⣀⢞
⠉⠉⠀⢀⣤⣶⣿⣿⣟⢫⣽⣿⣶⣶⣲⣿⣻⣿⡀⠀⣤⠀⠀⠤⣤⣤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣤⣾⠋⠙⢋⣩⠉⢞⡓⠓⣨⣻⠀⢠⡶⠂⠁⣤⠀⠁⠠⠀⠄⠂⠁⡐⠁⠄⠐⠺⠒⠋⠓⠛⠙⠙⢲
⣀⣀⣀⣬⣿⣿⣿⣿⣿⣿⣭⢍⣽⣿⠿⣿⠿⠿⢽⣯⠟⣏⠀⠀⣤⢤⣍⡑⠋⠀⠀⠀⠀⠀⠈⢿⡄⠀⠄⣔⡲⠆⢈⠄⡦⠞⡾⠎⠗⠈⢙⢏⠹⠭⠀⠀⠀⢠⡿⢀⣀⣠⡦⢂⣄⡖⠖⠶⢄⡁⠈⠀⠠⠈⠀⡒⠈⢹
⠷⠠⠄⠋⠙⠛⠛⣿⣿⡇⣽⣶⣄⠀⠀⢀⣴⡿⠦⣾⠿⢶⣿⣿⣿⡭⠏⣀⣄⠀⢀⡀⢀⣀⣐⣒⡠⠀⠈⠁⠀⠀⠀⠰⠿⢧⣽⢼⣦⣄⠐⠂⠠⠀⠠⣤⣀⢼⣿⣿⢿⣯⣿⣫⢭⢿⡿⡯⢋⡰⠂⠋⢀⠄⡤⠥⣄⣿
⠀⠀⠀⠴⠀⠀⠀⠈⠒⠒⠙⠿⠏⠠⠄⠐⠁⠀⠀⣀⠀⡈⠉⠉⣩⣰⣾⣿⣍⣾⣿⣿⣶⢪⣿⢁⣔⡣⠀⠐⠖⠤⠒⠀⠠⠉⢡⠼⢻⣿⣷⡄⣤⢴⣲⡯⣤⣬⣿⡍⠉⠛⠛⢩⣽⡟⠂⠉⡒⠁⠀⢲⣤⣾⠷⠞⢹⢩
⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡊⠁⠀⠀⣅⣾⣿⣏⣿⣿⣹⣿⣿⡓⣀⣰⡄⠀⠀⠀⠀⠉⡠⢆⣀⣀⣸⣤⣷⡴⢿⡿⢿⢽⠻⣟⠾⠿⠿⠖⡚⡘⠀⠁⢀⠀⣀⠠⣸⡑⠲⠌⠐⡖⠶⢔⡒⣾⢭
⠀⠈⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠦⠀⠀⠀⢀⠀⢁⠀⠣⡐⠿⣚⣀⠫⣿⣟⣛⣫⣽⣋⣳⣷⣼⣷⡃⢬⠘⠓⠬⠤⠋⠀⠀⠠⠈⢀⣀⢒⣰⠟⠛⢓⠁⡠⠄⠦⠘⠓⠀⠀⠈⣈⠋⠤⢿⣿⡤⠯⢡⡬⢩
⠀⣠⠀⠀⠀⠈⣭⣤⡀⣤⠀⠀⠀⠀⠀⠁⣠⠀⠒⢈⠋⠈⠂⠀⠀⠠⠛⠀⠀⠉⠀⠁⠉⠀⠉⣍⠿⠉⣼⠗⢻⠁⠐⠂⠠⠴⠂⠀⣤⡄⠂⠰⠁⣇⣀⠀⢠⡀⢘⠀⡁⠀⠀⠀⢀⣤⣀⢹⠉⠰⠿⣾⠋⠀⠄⣈⠔⢹
⠀⠸⠿⠹⢹⡿⠿⠿⡿⠣⠻⠟⢿⣿⠯⢧⠾⡀⠋⢉⡀⠸⠧⠰⣖⠂⠀⢠⡄⠀⠀⠀⠁⠈⠰⠀⠈⠉⠀⢀⠀⠀⠂⠀⠀⡀⠀⠠⠀⠑⠓⢂⠤⠁⠀⠀⠑⠊⣀⠀⠀⢀⠀⠀⢠⠀⠀⠨⡐⣀⠀⠁⠑⠲⠰⠯⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠁⠉⣯⡇⠃⠿⠋⢩⡙⠙⠛⠙⠛⠻⠿⣽⡟⠿⠛⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡛⢛⢻⣶⣾⣿⡿⢿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠃⠄⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢈⣿⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣾⣵⣿⠀⠀⣀⣂⡴⢷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠛⠹⡿⠿⠛⠛⠉⠙⠛⠃⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⠻⠛⠛⠛⠛⠛⠛⠛⠉⠋⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠿⠿⠿⠿⠻⠻⠿⠿⠿⠿⣿⣿⣿⣿
⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡧⠶⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢒⠀⠀⠀⠀⢟⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠈⠀⠀⠀⠀⠨⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠈⠀⣰⠶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⡀⠀⠐⠠⣀⠾⣿⣾⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣰⣶⣶⢱⣶⣶⣠⣶⢿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣶⣶⣀⣤⣴⣦⣀⣀⣀⣀⣠⣀⣤⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣛⠛⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⢿⣿⣻⣿⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⡿⠟⣿⣿⣛⣻⣿⡟⠛⠛⠛⠛⠘⠛⠛⠛⠈⠻⠿⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣋⡀⣈⣻⣟⡀⢀⣀⣀⡀⣀⣀⣀⠁⣀⡐⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⢽⣿⣿⢯⣭⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣿⣯⣿⡟⣿⣿⣻⣿⠛⠉⣿⣿⢿⣷⣿⣿⢻⣷⢸⣿⡟⢳⣿⡏⠿⠗⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⠉⣿⣿⣿⣿⢸⣿⡿⣟⡧⣿⣿⡿⠻⠿⠿⢿⣿⣶⣿⣽⣿⢾⣿⣿⣿⡟⣿⣿⢶⣶⣶⣶⣿⣿⢿⠇⣿⣿⣿⣯⢸⣿⠿⢇⣙⣿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣾⣿⣿⣦⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣯⣥⣽⣿⣟⣛⣛⣿⣵⣜⣹⣿⣿⣿⢿⣿⡿⣿⡇⠻⣿⣼⣿⣿⣿⣿⣿⢺⣿⣿⣿⢿⣿⢸⣿⣤⡌⢿⣧⣿⠇⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠿⡿⣿⣿
⣿⣿⣿⣿⣭⣷⣮⠀⢐⡖⡖⢳⡟⠉⡂⢾⣿⣝⣻⣿⣻⣷⣿⣿⡿⠛⠏⠁⠀⣄⣀⠒⣾⡇⠀⣿⣷⣾⡟⠁⠀⠀⣾⣯⣴⠀⠀⡀⠀⠀⠀⠀⢤⣭⣀⠀⣴⣶⠀⢰⣿⡟⢻⡋⣉⣉⠉⠛⠛⢻⣿⣿⣿⣿⣰⡶⢾⣿
⣛⣛⣛⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣽⣿⣽⡛⠛⠛⠛⣿⡇⠀⣀⣄⣤⣐⣶⢤⠰⢾⣗⡃⠃⠀⢿⣿⣿⣁⠀⣀⣰⣿⣿⡿⠀⢰⡷⠀⠀⠘⠂⠀⠋⠆⢀⠀⠀⠀⣑⣰⣿⣿⣷⣶⣿⣿⡏⡠⣾⣿⣻⣻⣿⣿⣟⡾⣹
⠛⢿⡏⠋⠉⠉⢭⣿⣿⣿⣮⣬⣭⣭⣽⣿⣷⣶⣶⡿⢻⣿⣿⣿⡟⢾⣻⣯⣾⣷⣶⣦⣿⣷⠀⠀⠨⣿⣿⢷⣶⣿⣿⣿⠃⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⡟⡫⠭⢿⡇⠐⢸⢿⣿⡗⠛⠟⠛⢻⠛⠛⠻⣧⣿
⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠻⢿⣿⠿⢿⠛⡿⢿⠿⣿⣷⢻⣾⣿⣏⣻⣿⡿⠿⡷⠄⠀⠘⠿⡩⣥⡿⠉⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠐⡠⠰⠖⣠⣀⣀⣼⢟⣻⠷⣾⣿⣘⡛⣦⣶⣶⠀⠀⠀⠀⠹
⠀⠀⠈⠛⠛⠿⠛⠛⠼⠋⠛⢛⣛⣻⠟⠀⠠⡤⠆⢓⡶⠼⠿⠷⠿⢟⣛⠻⢯⣭⣞⣻⡮⢵⣿⢃⠁⠠⣄⠠⠀⠟⡦⠤⢶⣾⠶⣀⠤⠠⢠⢀⡥⣿⡛⢻⣷⣼⣯⢟⡫⢅⠧⢬⣭⣿⣿⣿⠿⢻⣟⣛⣻⣿⠷⡻⣦⣠
⠈⠙⢻⣿⠾⠶⣶⠒⠒⠘⠉⠉⠋⠑⠒⠒⠀⠨⠖⠠⢁⡄⢠⣀⠀⠉⠑⠒⠋⠉⠹⣿⣶⡖⢹⡛⠀⢠⣭⡤⡄⠄⢓⣲⣀⣤⣀⣠⢎⢸⠢⡮⠀⠀⠐⠛⢻⠻⢿⣾⣿⣿⣿⡿⢿⠛⡿⣯⡆⡀⣈⣬⡛⢹⣉⣻⣿⣿
⣶⣤⣄⣤⡰⠶⠖⠲⠆⠀⠀⠀⠀⢤⠶⢯⣴⡤⠒⣀⡴⣦⣶⣶⣶⣯⡯⢥⣶⡛⠿⠿⠉⠁⢈⠐⠉⠙⣉⣛⣤⣝⣐⣐⣷⣶⣶⣠⣶⡼⠇⢀⢀⠠⣀⡀⠀⡀⠉⡙⠙⠛⣻⢶⡦⣾⣷⡸⣿⣿⡻⠞⢯⣿⣿⢿⠿⢿
⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣤⣤⠄⠀⠀⠀⡠⠌⢳⣤⣿⣳⣾⣾⣷⣾⣿⡿⡷⣤⣼⡯⢽⢟⣠⣄⣔⣢⣀⣉⣏⣤⡨⢷⡽⠿⠛⡧⠚⠡⠛⠁⣸⠧⡱⠭⢷⡬⢏⣨⣛⣿⠿⣻⠻⢧⡹⠗⠖⠃⠘⠀⠁⠛⠛⣀⣬⣽
⣋⢉⣉⣹⣿⣶⣶⣤⣴⣻⣻⣯⣤⣤⣤⡀⣕⢻⣿⣿⡟⠿⠽⣿⡿⢿⠿⡿⣶⠀⣀⠉⠾⠾⠛⠛⠊⠙⠭⠩⣉⠙⠃⠛⡁⢐⡄⠀⠀⠒⠄⠂⢨⠄⠙⠏⠼⡏⠉⣙⠋⢭⣅⠀⠘⠣⣥⠀⠂⠀⠀⡀⠀⡠⠀⢠⣾⣻
⠈⠩⠭⠅⠀⠈⢉⣉⣟⡿⠿⠋⠻⣯⣍⠩⣿⣋⢀⣀⡶⢶⠶⠶⡅⢸⣎⡉⠽⠿⠦⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠁⠈⣑⠑⠈⠉⠀⣁⠀⠀⠀⠀⡐⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢁⠈⠘⢴⠺
⠿⣿⣦⣔⡚⡓⠎⠉⠁⣀⣀⡀⡈⢭⣛⣛⣻⣿⡿⠯⡿⠛⠿⠷⠕⠀⠀⢡⠤⡤⠔⠀⣄⠔⣴⢃⠠⠀⠀⠀⢠⣄⠀⣀⠀⢐⣺⠛⠳⣃⠄⣀⣤⣀⣠⣤⣵⣤⠀⣤⣄⠀⠀⠀⠒⠂⠀⠀⠀⠸⣄⡀⠀⣀⡤⡄⠀⠀
⣀⣿⣿⣿⣿⣽⣷⣶⣾⣿⣿⣿⣿⣿⣷⣏⡉⢽⣗⣤⠀⠀⠀⠀⠀⠀⠀⢠⠤⠁⠀⠈⠀⢀⠘⠏⠀⠀⠀⠠⠈⠉⠰⠏⠶⡈⣉⣠⣦⣥⣲⡞⠻⡟⢋⡉⠿⠏⠙⠜⠇⢐⠤⠘⠆⠀⠀⡀⠠⣂⠰⠐⠚⢊⣸⡷⠀⣸
⠿⣿⡧⠟⠛⠛⠋⠉⠀⣟⣛⣛⠿⢿⡛⣛⣁⡀⠀⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡰⣿⣟⢻⣿⠛⣎⢉⠜⢛⠋⠀⠔⠂⠐⠛⠓⠃⠠⠀⠀⠀⠀⠀⢁⠀⠄⠄⠺⢳⡜⠀⣫
⣶⣿⣅⠀⠀⠀⢰⣾⣿⡟⡉⣡⠴⠶⣥⣿⢯⣭⣦⣽⣥⡄⠤⢢⡄⠀⠐⠒⢒⠤⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⠲⡅⠀⠉⡄⠈⠑⠉⠉⡡⢪⡅⠁⠒⠂⠀⣠⡄⠀⠀⠂⠀⠒⠈⢀⠈⠀⠀⠒⠓⠀⠐⠛⠙
⠉⢲⡷⠆⠐⠶⠾⠿⠿⠯⠸⢆⠱⠄⡐⠊⠉⠉⠏⢉⡁⠒⢈⣈⢀⣀⣐⡒⣒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠰⠬⠋⠀⠀⢐⣀⢩⠐⡈⠁⠈⠿⠀⠀⠀⠀⠀⠀⢖⠀⡄⣠⠶⠂⣀⡐⠐⠰⠂⡀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠿⠉⠀⠀⠀⠰⠛⠛⠛⠒⠛⠻⠓⠲⠆⣉⡠⠴⠀⣀⣄⡀⠀⣤⠤⠍⢀⠀⠀⢀⠀⠀⠀⠛⠃⠴⠄⣿⣷⣄⠃⠀⠀⠀⠠⠄⠴⣿⢿⣛⣿⡐⡍⡀⣬⡻⢻⡤⠀⠖⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⢲⡖⡉⣦⣤⣋⣿⡯⠁⠒⠀⠐⠁⠀⠀⠘⠔⠈⠀⠀⠂⠀⢒⠛⢿⣿⣦⢰⡒⣤⡌⡀⣤⡝⠥⠀⠈⠉⠁⠴⠟⠃⠀⠙⠀⠀⠀⠷⠦⠶⢼
⢀⡀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⢿⠉⢀⡼⠦⢿⢟⡉⣰⣆⣃⣀⡀⢀⠀⢀⢠⠀⡤⣤⠤⡇⠈⡂⠚⠿⠙⡏⠉⠯⠍⠛⠎⠀⠀⠁⠁⠈⠀⡄⠀⠀⠀⣃⠐⠂⠁⣙⠒⠦⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠤⠀⠀⠀⠀⠀⢡⠀⠋⠤⠄⠻⠛⠉⠠⠾⣤⡼⠯⡟⢻⣇⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⠀⠘⠓⠂⠃⠛⠀⢀⠂⠀⠀⠉⠁⠀⠀⢀⠜⠄⠜⣿⣧⠾⢌
⠀⠠⠀⠀⠂⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⡀⢀⣀⠄⠀⡤⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠐⠙⡃⠤⠃⠉⠃⠀⠀⠀⠒⠋⠀⢠⠀⠀⠀⠃⢀⢤⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠆⠀⠐⢳⡅⠀⠀⢨
⠀⠸⠿⠽⢸⡇⠿⠿⡧⠣⠸⠗⢿⠻⠇⠿⡏⠀⠀⠀⠀⠀⠀⡀⠉⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠔⠆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠄⠀⠀⢀⢀⠀⠀⠀⠐⠄⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠬⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣂⣸⢞⣞⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢛⡻⠛⢿⣱⣤⣷⣾⣷⡊⡋⠭⠏⢿⠟⠱⣛⣉⠿⠉⠉⠉⠙⠹⠿⣿⣿⣿⠟⠛⠛⣿⣿⣿⠛⠟⠿⣿⣿⣿⣿⣿⣭⡉⣭⣿⣿⠿⣿⠛⠃⢊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠚⠉⠘⠈⠈⠘⠫⠁⠀⠀⠟⠋⢐⡢⢰⠀⠀⠁⠀⠈⠉⠉⠀⠀⠀⢀⣝⠇⠂⠀⠀⠿⢿⣿⣿⣿⣿⣿⣷⣿⣄⣀⣿⣄⣼⡻⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠛⠿⠿⠋⠉⠁⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠻⠟⠟⠛⠁⠈⠙⠛⠛⠁⠀⠁⠈⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠓⠒⠒⠢⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠻⠟⠿⠟⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠊⠀⠀⠱⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡏⡁⢀⠀⠀⠚⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠠⡀⠀⠐⠁⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠰⣶⣶⠀⢀⣄⣀⠀⡤⠀⣤⣀⠀⠀⡀⡈⠀⠀⠀⠀⠀⠀⣾⠿⠤⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣴⣴⣶⣶⣴⣶⣤⣴⣿⣿⣿⣿⣿⣷⣶⣾⣶⣤⣤⣄⣀⣄⣀⣀⣠⣀⣡⣤⣴⣝⡛⣛⣀⣦⣤⣞⣿⣿⣿⣿⠁⠀⢀⡄⠀⠀⠠⡟⠀⠀⠀⠙⣷⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⡀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣶⢰⣶⣶⣠⣶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣶⣾⢹⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣿⣟⣛⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠛⠛⠛⠛⠛⠛⣻⠎⠛⠟⠋⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣀⣈⣛⣿⡀⢀⣀⣀⡈⣀⣠⣤⠤⣒⡒⢀⣰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣟⣿⣛⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⢿⣿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⠛⢳⣿⡟⠿⠇⣿⣷⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⢿⣿⣿⣿⣿⣿⡿⠭⠶⣤⣿⣋⣹⣿⢿⣿⣿⣿⡏⣿⣿⢶⣶⡾⢷⣿⣿⢿⠏⣿⣿⣿⣯⢸⣿⡿⢇⣙⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⡦⣼⣿⣹⣿⡿⣿⡇⢿⣿⣼⣿⣤⡤⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⡞⢿⣿⣿⠇⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣽⣯⣤⣼⣿⣿⣷⣿⣿⣾⡿⠿⠓⠋⠉⠁⠀⠀⢸⡋⠑⠒⠏⠁⠀⣰⣿⣿⡆⠀⢸⣶⠀⠀⠀⠀⠀⣩⣥⡀⠀⠀⣴⣾⠃⢰⣿⣿⣿⣿⣟⣻⣯⣩⣭⡍⡟⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢯⣶⣤⣭⠿⠿⣿⣿⣿⣿⣿⠿⠿⡿⢿⣿⣿⣀⣉⣡⣿⣧⣤⣶⣶⣿⣿⡇⠀⢈⠑⢹⣤⣠⣠⣼⣿⣿⣿⡇⠀⣼⣿⣷⣄⡀⣠⡄⠈⠿⢿⣾⣿⣿⠇⢀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿
⡿⠿⡃⠉⠀⠠⣿⣿⣷⣶⣤⣽⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣟⣿⣷⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣿⠿⠿⢿⠛⠛⠀⠀⠀⠀⠘⠛⠁⠀⠚⠛⠀⠹⡿⡿⠿⢿⣿⣓⣻⠿⣿⡿⠛⠿⠛⢻
⣿⣿⣿⣿⣿⠾⠛⠻⣿⣿⣿⣿⣿⢿⡿⠿⣿⣿⣿⣿⡾⠛⠻⣋⡹⢟⢛⣹⣛⣿⣿⣿⣿⣧⡄⠈⠙⢿⠀⣈⡀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⡀⠀⠀⣀⣀⣒⢈⡴⠐⣒⣶⣄⣀⣿⢿⣻⡿⣶⣿⣟⣛⣳⣶⣾
⣿⣿⣿⣿⣿⣷⣦⣤⣤⣬⣭⣽⣿⣟⡤⠤⠤⠶⢿⣛⣡⡈⣻⣅⠸⠿⠛⠛⠛⠻⠿⣗⢚⡿⠧⣢⡴⢖⡘⢯⣠⠀⢐⡦⠐⠀⠀⡇⠜⠿⠿⢻⠤⢷⢠⢶⢰⠶⠿⣛⣻⣿⣿⡧⢟⣅⢓⣻⣬⣭⣽⣿⣿⣿⠛⣿⣛⣿
⣿⣿⣿⡏⠉⠁⣀⣸⣟⣋⣉⣹⣊⣉⠉⠐⠂⠀⠀⣠⣭⠊⠉⠉⠒⠐⠂⢐⡒⠠⠤⣍⣉⡅⣤⣽⣷⣿⡇⢸⢭⣤⣔⣲⠰⢆⣠⠫⢕⡴⠤⡤⠤⠮⣩⡖⠗⠂⠀⠉⠋⠻⡛⢻⣿⣿⣿⣿⠿⢻⡟⠿⣿⣾⢀⢈⣩⣻
⣿⣮⣿⣷⣶⣿⣿⣿⣿⡏⠁⠀⠀⠉⠀⠀⠀⠀⠉⠉⠻⢛⡋⣁⠒⣚⣿⣿⣻⣿⣿⣯⣾⡯⠍⣛⣁⣀⣀⠠⠉⠈⢡⣽⣱⣶⠾⣥⡾⣿⣿⣷⠴⢴⣾⢋⠮⢩⡰⣀⣀⠀⣰⢈⣈⢉⢛⣻⠶⡶⢿⣷⡚⣟⣿⣿⡿⢿
⣿⣿⣿⣿⣿⠿⠟⠛⠿⠦⣄⣀⣠⣀⣼⠿⡿⠓⠂⠀⠀⢧⣭⣼⢿⣿⣾⢿⡿⣿⣿⣿⣹⣟⡟⠻⢟⣻⣩⣼⣯⠭⣿⣥⣼⣷⣴⣚⣿⠟⠛⠙⠿⠋⠘⠩⠄⡸⠷⣽⣾⣽⣯⢯⣠⣛⣻⣿⣿⠿⡯⣹⠟⠳⠫⠘⠁⢸
⢭⣍⠉⠉⠉⠁⠒⠒⠛⠛⠛⠿⠿⢿⣿⣿⣿⣷⠟⠒⢶⣶⡾⠛⢛⣋⢉⣉⣿⠛⢹⡿⣭⣧⣤⠒⢊⠙⠛⠋⠉⠀⠉⠙⠻⠣⠙⠋⢋⠀⠬⢧⣀⣐⢑⣖⠃⣤⠀⠙⠏⠻⠟⠉⣼⠋⢭⣍⠀⠐⠻⣭⠄⠂⠀⠀⡀⠘
⠀⠀⠐⠾⠿⣷⣶⣄⣀⠠⠴⣤⡾⠿⠋⠉⠀⠸⠿⣿⣭⣽⣶⢴⡶⢾⡼⣍⣉⢦⠼⠷⡆⠉⢁⡉⠰⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠆⠁⠁⠀⢀⣰⠆⡽⠈⠈⠀⠀⣥⠄⡁⠈⠀⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀
⠀⠀⢀⣠⣀⣀⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣦⣼⣵⣶⣾⡿⣽⡿⢙⠛⠈⠉⠉⠁⠀⠀⠹⠙⠟⠃⠤⠂⠛⢟⡠⠒⢀⣀⠀⢸⣤⠠⡥⠀⢬⡻⠡⠛⡄⠆⣤⣤⣤⣤⣶⣽⣴⠐⣠⣆⠀⠠⠀⠒⠒⠀⠀⠀⠸⢇⡀⠘
⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠱⣿⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠈⠀⣲⠉⠁⠀⠀⠈⠲⠈⢀⣛⡱⠛⢅⣆⣴⣶⣶⣶⣛⣻⣏⣭⣽⠿⠏⠙⠗⢇⢀⠤⠚⠆⢀⠒⡀⠠⣂⠰⠄⢾
⠤⠀⣀⣯⣤⣭⣿⣿⠁⠀⠀⢀⣤⣶⣿⢿⢞⣭⣽⡷⣶⣾⣷⣛⣠⣄⠀⢀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠿⠯⡟⣿⣿⠛⣇⢀⡚⢏⡁⠀⠐⠀⠀⠛⠓⠃⠠⠀⠈⠀⠀⠀⢉⠠⠤⢨
⠀⠈⣉⠛⠛⡿⣯⣿⣇⠠⣤⣾⣿⣿⣿⣷⣾⢛⡍⢩⣯⠙⠛⡛⠻⠯⣯⡭⠙⡂⠀⢐⣉⣛⠉⠍⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⣀⡗⠹⠄⠀⠁⠐⠀⡂⠊⣩⢥⣭⡇⠀⠖⠂⠀⣠⡄⠀⠀⠀⠀⠐⠈⢀⠘⠀⠀⠚
⠶⠿⠿⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠈⠉⢩⠼⠆⡷⠶⠀⠀⠀⣀⣼⡦⢴⡶⣷⣴⣶⣚⡂⡶⠉⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠚⠈⠁⠀⠁⣠⡤⢏⢁⠈⠁⠀⢳⠐⠒⠈⠀⠀⠀⣖⣂⣠⣀⡶⠀⣠⣠⠐⠲⠦⣀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠈⠀⠀⠀⡀⢀⠀⠀⢈⣀⣄⢾⡃⢰⣾⣷⡬⢑⡶⠒⢂⠄⠀⢀⡄⠀⣀⡀⠉⠹⠟⠚⣿⣷⣄⠀⠀⠀⠀⣶⡄⠴⣿⢿⣛⣿⣼⡟⡍⡽⡿⢿⠭⣀⢴
⠒⠂⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠃⠈⠀⢀⣨⣽⡏⠚⢛⢻⣿⡿⠯⠈⢉⡀⠉⠈⠀⠀⠑⠈⠉⠁⠈⠀⠐⡞⠙⣿⣿⣦⣶⣲⣤⠍⡢⣵⡝⢥⠀⡛⠉⠀⡽⠟⠃⠈⠑⠂⠈
⠀⠀⠀⠘⠻⠏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈⠉⠄⠴⡍⠉⢹⣹⣲⢿⢿⣳⠶⢀⣄⣀⣄⡄⠰⢶⣖⢾⠷⢫⠌⠙⠏⠙⠠⠉⠷⠍⠛⢎⡊⠁⠁⠁⠈⠀⡀⠀⠀⢄⣏⠲⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⡠⠈⠛⠋⡁⠀⠀⠀⠀⠀⠜⠀⠈⠙⠀⠋⠑⠈⠒⠻⣿⡛⠙⣏⢿⠅⢉⠀⠀⢈⡋⠀⠀⠀⠐⠀⡀⠠⠘⠼⠟⠓⠻⠀⢠⠂⠀⠀⠉⠂⠀⠀⠀⡐⣹
⠀⠠⠀⠀⠀⠀⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠐⢂⠐⠈⡁⠀⡧⠀⢄⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⡉⠘⠐⠛⠁⠈⠁⠀⠀⠀⠉⠀⠀⠐⡆⢀⠀⠀⡠⠤⠀⢠⠄⠀⡁⠨⠀⠀⠀⠀⢠⣀⠀⡎⠁⣸
⡀⠸⠇⠹⢸⡿⠿⠿⡧⠣⠸⠟⠿⠻⣿⠇⠀⠈⠁⠀⠀⠃⠀⠀⠀⠖⠀⠈⠁⠀⣠⠼⠉⠀⠀⠀⠀⠀⢀⡀⠈⢀⠀⠐⠀⠀⢀⠀⠀⠀⠠⠄⠶⠀⠀⠀⠂⠈⠠⠒⠂⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⢇⠂⡘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠫⠉⡯⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⠿⠛⠐⢀⠊⢑⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡖⡈⠁⢱⢨⢠⢅⣺⣥⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠑⠃⠘⠂⠃⠂⠀⠃⢿⣙⡿⣾⣽⣿⣿⣿⡿⣿⣿⣿⣿⠗⣟⣛⡻⠋⠉⠉⠻⢙⠻⣿⣿⣿⣿⠟⠟⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣯⣍⣭⢿⣿⣿⣿⣟⠿⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠷⠻⠚⠛⠣⠹⠟⠏⠀⠀⠻⠋⢰⡶⢰⡆⠀⠁⠀⠈⠙⠉⠁⠀⠀⢀⣾⠇⠂⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣿⣿⣿⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠛⠻⠿⠋⠉⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠚⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⣴⣧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠿⠟⠟⠛⠁⠀⠈⠙⠋⠋⠁⠉⠈⠘⢿⣾⣿⣿⣿⣿⣿⣿
⠉⠉⠛⠋⠀⠛⠛⠒⠒⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠟⠻⠛⠛⢿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠁⠀⠀⠟⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡄⠀⠀⠀⠿⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⠀⠀⠀⠒⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠰⣶⣶⠀⣀⣄⣀⢠⣦⣠⣸⠀⠀⠀⠀⠀⠀⣿⡷⣤⠇⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣴⣤⣤⣤⣤⣄⣤⣤⣯⣤⣶⣾⣿⣟⣷⣔⣦⣯⡆⠀⠀⢠⡀⠀⣠⠿⠀⠀⠀⠘⠛⣦⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣶⢰⣶⣶⣰⣶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⠿⣿⣬⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣶⣾⢹⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡛⠛⠛⠺⡿⣿⠛⠈⠛⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣃⣄⣈⣻⣛⡀⢀⣀⣀⡉⣀⣀⣀⣀⣀⡠⢄⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⡿⣿⣿⢻⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠟⢳⣿⡟⠿⠇⣿⣧⣼⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣏⡩⣿⣿⣿⣐⣷⣶⣿⣿⣿⡿⢾⣿⢸⣿⣿⣿⡇⣿⣿⣶⣿⣷⡆⣿⣿⠿⠏⣿⣿⣿⣿⢸⣿⠿⢇⣙⣿⣷⣦⣿⣏⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣼⣿⣿⡿⣿⣿⣿⣿⣿⣼⣿⡟⣿⣧⣿⣿⣼⣿⡼⢠⣿⣿⣷⡄⣿⣿⣿⣿⢸⣿⣶⡞⢿⣧⣿⠇⣿⡟⢿⣿⣿⣿⠫⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣾⣿⣿⣷⣶⣷⣾⠀⢰⡏⠁⠉⠁⠀⠀⠀⣰⣿⣿⣷⠀⢰⣶⣾⣥⡄⠀⠀⠀⠉⠉⠒⠀⠀⢤⣴⣶⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⢟⢻⣯⣉⣍⣍⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠿⠿⣿⣿⣿⣿⣿⣿⣟⡟⢿⣿⣷⣤⣤⣴⣿⠀⠈⣫⠰⣂⣠⣀⣠⣾⣿⣿⣿⡟⠀⣸⣿⣿⣀⣀⡀⠀⠀⠺⣿⣿⣷⣤⣼⣿⡟⠀⣼⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠛⠛⠛⠛⠛⣿⣿⣿⣭⣍⠈⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠻⣿⣿⣿⣿⣿⣽⣿⣿⠟⠁⠰⣛⣿⣿⣋⣿⣿⠿⠇⠀⠉⠋⣛⠛⡿⡏⠀⠰⠟⠻⣿⣿⠿⠛⠿⣿⣿⣽⣿⣿⣟⢻⣿⣿
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠋⠙⠿⡿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣶⣉⢻⡯⣜⣊⣻⣦⡀⠈⠳⠯⢿⠍⠺⠟⠁⠀⠀⠁⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⣀⣈⣯⣻⡵⠐⢶⣶⣆⣀⣿⣿⣿⣿⣶⣿
⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣷⣷⣿⣾⣧⣭⣷⡖⠻⠿⠿⢭⣠⣄⣳⣄⠘⠟⠉⠋⠉⠀⠤⣄⣚⠅⣄⠠⠀⢀⠀⣅⠀⠀⠀⠀⠀⠀⠠⡏⠚⠻⠟⢯⠤⢗⣲⢶⡴⠤⡿⡛⣻⣿⣿⣿⢿⣻⢯⣾⣭⣯⣿⣿⣿
⠛⠛⢻⣿⣿⠿⣿⣿⣷⠁⢨⣤⣽⣿⣯⣬⣼⢯⣿⠙⠋⠅⠀⣠⣴⣶⣂⢀⣀⠙⢚⣃⣭⣅⣀⠄⣥⠥⠀⣤⣤⠘⣻⠁⡍⠀⠀⠀⠀⠰⢄⡌⠩⢶⡴⠤⡄⠸⢮⣽⡖⠗⠀⠀⠘⠛⠻⡿⢿⣾⣿⣿⣿⣿⣿⡿⣿⣿
⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⣀⣀⡠⠉⢉⠘⢉⣱⢎⣉⣽⣟⣯⣽⣛⣻⣿⣿⣶⣈⣉⠄⣀⣀⠤⠉⠀⠤⢬⣹⡶⢿⣥⠿⣿⣽⣷⠴⣴⡼⠋⣮⢉⡠⣀⣀⢈⣰⠈⡙⢛⠿⣷⣶⣦⣿⣷⣸
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣛⣛⣻⣛⣧⣤⣾⣶⣾⣿⣿⣋⣀⣀⠀⡷⢴⣾⣿⣿⣿⣻⣿⣿⣿⣿⣽⡯⠟⠛⣏⣖⣠⣿⣷⠭⣯⣥⣼⣴⣶⣚⣿⠟⢛⠙⠿⠋⠐⠨⠀⡼⠷⠿⠮⢽⣾⣿⣩⣟⣻⡿⣿⣿⣿⣙⣿
⠛⠛⠛⠋⠋⠛⠷⢀⣀⣤⣤⠋⠯⣿⠟⠝⠛⢛⣓⣿⣿⡟⣻⣯⣝⣛⣿⣾⡍⠹⣧⣭⣭⣿⠉⣿⠻⣽⣧⡖⠊⠍⠙⠛⠋⠀⠀⠙⠂⠺⠢⠉⠉⢻⠀⡼⣂⣀⣐⠕⡔⠂⣥⠄⠹⡯⢽⡿⠉⣙⡛⢭⣏⠉⡽⠿⣟⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠿⢿⣷⣶⣖⣲⣶⠏⠉⠉⣁⠈⢙⣍⡿⢿⣿⣿⣿⣿⣷⢾⣿⣯⣧⠚⢷⣎⠉⣁⣉⠂⠀⢰⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⡀⣱⠄⡽⠃⠈⠁⠀⣁⠀⠃⠈⠀⣘⠟⠀⠈⠉⠀⠀⠀⠈
⠀⠀⢀⣀⣀⠀⠀⣠⣴⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣤⠁⠀⠀⠈⠀⠀⠀⢛⡙⠻⠠⡔⠚⠓⣿⡤⠛⠀⣀⠀⣿⡄⡠⠅⠃⢌⡿⠩⢻⡄⢆⣀⣤⣀⣤⣾⣽⣤⠀⣤⣄⡀⢀⡀⠤⠤⠀⠀
⣿⣿⡿⠿⡿⠆⠀⠉⣿⠿⣿⣿⣿⡿⠟⠛⠉⠉⢉⣿⣿⢿⡿⣿⡿⠿⠃⢁⡙⣯⠀⠀⠀⠀⠀⡀⠀⠚⠁⠀⠀⠀⠠⢖⠈⠁⠀⠀⠈⠒⠀⢀⣫⠜⠹⢵⣤⣶⣶⣶⣿⣟⣻⣟⣩⣽⡿⡏⡻⠽⠏⢀⣨⠴⠶⠀⠀⢘
⠈⠀⠀⠀⠀⠀⠠⠤⣿⣿⣿⣿⣿⣅⠀⠀⠀⣿⣿⣿⣻⣧⣼⢾⣷⣿⣿⣿⣭⣿⣇⣀⣠⣄⠀⠀⢄⣀⣀⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⢿⡟⣿⣿⢻⣏⢅⠚⢟⠋⠠⠴⢂⢀⠚⠇⢔⢀⠀⠈⠀⠈
⠒⠀⠀⠀⠀⠀⣠⣶⠀⠉⠹⣷⣿⣷⠐⠒⠚⠛⢿⣿⣿⣿⠹⡶⠐⠒⠏⠩⠉⠛⠛⠿⠒⣻⠅⠀⣤⣤⣌⠉⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⣨⡍⠱⠀⠀⢱⠐⠀⡋⠍⣉⣥⣪⡇⠡⠶⠂⠀⢠⡄⠀⠀⠄⢠⠤⠐
⣀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠰⡛⢃⣿⡝⠠⠀⠇⢤⠿⠗⢾⠿⠿⣿⣯⣯⡥⠟⡉⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠈⠁⠀⢁⣧⡄⢏⠃⠈⠁⠀⢧⠠⠒⠆⠀⠀⠠⣬⠆⣀⢀⣠⠄⣀⢨
⣿⣇⠑⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⢀⣠⡟⢿⣇⣶⣿⣷⣤⢜⣻⠛⣡⠄⠄⣠⡄⠀⣀⠀⠉⠹⠟⠸⣿⣧⡀⠁⠀⠀⠀⢤⠄⠤⣿⣿⡟⣿⣭⡶⠛⣻
⠋⠁⠀⠀⠠⠬⠍⠀⢠⣤⣄⣤⡄⠀⠐⠫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠨⠀⠀⢀⡬⣴⣿⢧⡜⣿⢹⣿⡿⠍⠈⢩⡈⠁⠉⠀⠀⠑⠉⠉⠁⠀⢀⠐⡖⠹⣿⣿⣆⣶⢲⣦⡝⣤⣭⡝⣬⠉⠙⠛⠃⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢂⣀⣀⠀⠀⠁⡐⠑⣊⣾⢏⠉⢹⣽⠽⠿⢟⡒⠆⣠⣆⣄⣄⡄⠶⢶⣖⠾⠶⣥⠘⠻⠟⢛⢻⠙⠯⠝⠻⠏⠖⠒⠃⠃⠀⠀⡀⠸
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⢠⠀⠀⢀⡀⣈⣀⠄⢈⡀⠀⠀⠠⠛⠂⠀⠉⠀⠁⠋⠀⠛⡛⣿⡋⠻⣟⢿⠄⢉⠀⠀⢘⡋⠀⠀⠀⠀⠀⣀⢀⠘⠰⠞⠛⢓⡀⢀⠄⠠⠀⠓⠨
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠸⡏⠀⠈⠁⠉⡉⣄⡐⠓⠀⢆⢀⠀⢠⡄⠁⠀⠀⠀⠐⠠⠁⠒⠐⠉⠁⠘⠀⡠⠀⠀⠉⠀⠀⠔⡂⠀⠐⠃⢢⣤⠀⢀⡄⠀⠂⢈⠂⠀⠀⠀⢀
⠀⠸⠏⠹⢻⣿⠿⠿⡧⠣⠻⠟⠿⠻⠏⠇⠀⡀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠁⠀⠴⠎⠁⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠐⠀⠀⢀⠀⠀⢈⠐⠄⠆⠀⠀⠀⠀⠉⢠⠲⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢟⡿⠟⢟⠿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⣿⡟⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣭⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠟⠛⠿⣿⣿⣿⣿⠿⡿⠿⢿⠗⠾⠿⠁⣶⣶⣶⢮⠙⠉⠘⠻⠛⠉⠀⠀⠀⣾⡏⠑⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⢿⣿⣬⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠬⠱⠛⠹⠿⠟⠗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠛⠻⠿⡛⠋⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢁⢨⣧⣤⣘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠉⠙⠂⠻⠿⠿⠛⣛⡉⠙⠛⠛⠛⠉⡍⠀⠀⠝⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠙⡟⠃⠸⠶⠶⠶⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠟⠛⢻
⣿⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠸⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⢀⠀⠀⠘⢷⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠐⠋⠙⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⠰⣶⡶⢂⣀⣤⣀⠀⣼⠀⠀⠀⠀⠀⢠⣿⣷⣾⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣦⣤⣤⣤⣤⣤⣬⣷⣧⣶⣾⣿⣿⣻⣴⠂⠀⠀⣠⡄⠀⣼⠇⠀⠁⠀⢿⣿⣿⣿⣿⣶⣶⣶⣾⣾⣶⣶⣶⣶⣦⣴⣦⣤⣤⣤⣤⣤⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣶⣾⣿⣷⣶⢸⣶⣶⣰⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⠿⣿⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣿⢻⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣛⠛⠟⠛⢘⣿⡟⠛⠈⠛⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣛⣉⣄⡀⣙⣃⣀⡀⢸⣛⣀⡐⣈⣀⣀⡀⣀⣀⣀⣉⣉⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⣿⣽⣿⣿⣿⡟⣿⣿⢹⣿⠉⠁⣿⣿⣿⣷⣿⣿⣿⣿⢸⣿⡟⢷⣿⡟⠿⠏⣿⣧⣼⣿⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⣲⣿⣀⣶⣶⣾⣿⣿⣿⢼⣿⣿⣿⡇⣿⣿⣿⣿⡦⠀⣿⣿⠿⠏⣿⣿⣿⣿⢼⣿⠿⢇⣙⣿⣷⣆⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⣷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣷⣴⣿⣿⡿⢿⣸⣿⣿⣿⡟⣿⣇⣿⣿⣼⣿⢦⡆⣿⣿⣆⠀⣿⣿⣿⣿⢸⣿⣶⡞⢿⣷⣿⠇⣿⡿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣾⣿⠿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠀⢰⣿⣿⡇⠉⠁⠀⠀⢠⣯⣿⣿⠀⢸⣶⣶⠄⠀⠀⠀⠀⠀⠯⠉⠀⠀⢀⣀⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣟⣛⡻⣿⣿⣤⠀⠸⣿⣿⣧⣦⣀⣠⣾⣿⣿⣿⡟⠀⣸⣿⣿⡦⠄⠘⠀⣀⠀⢿⣿⣇⣂⣀⣰⣿⡿⠃⢠⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣾
⠉⠙⠛⠛⠛⠋⠋⢻⣿⣿⣯⣭⣀⣰⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣿⣷⣿⡁⢤⣤⣬⢹⠄⠈⠛⢻⣿⡟⠿⣟⢁⣴⣯⣭⣿⣿⣿⣿⡿⠟⠿⣿⣿⣯⣿⣿⣿⣻
⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⡉⠉⠹⢿⢿⣿⣿⣏⡽⠛⠿⠿⣿⣿⣷⢋⣙⣿⠦⠀⠈⠻⢿⣛⡭⠽⠟⠀⠀⠀⠉⠈⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡠⠟⢉⠻⠿⣿⣿⣯⣿⣷⡆⠶⣶⣦⣀⣹⣿⣿⣿
⠀⠰⣷⣴⣶⣿⣿⣿⣿⣿⡿⠿⢿⠟⢿⣿⣿⣿⣿⣷⣶⣵⣶⡚⠻⠛⡧⢥⠤⣻⡧⠀⠤⡀⠀⠀⠈⠷⢀⣀⡄⠀⠀⠀⢀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡟⠐⠻⠿⠻⡤⢼⢒⢶⣶⠧⣿⢟⣻⣿⣷⣿⡿⣟⡽⡽⢧⣻⣿
⠀⠀⠈⠉⠉⠿⠿⣟⡻⠿⡿⠆⢠⣤⣴⣿⣿⣤⡬⠽⣯⡅⠈⠉⠀⢀⣤⣶⣖⣀⣠⠈⢐⡃⣨⣥⣀⡀⣤⠤⠀⣤⣤⣄⣻⡅⠈⠀⢄⠀⠀⠠⠆⣀⠩⢵⣤⠦⣤⠤⠧⣩⡗⠻⠂⠀⠈⠛⠛⣿⠿⣷⣿⣿⣿⣿⣿⣿
⣀⣾⣿⣿⣶⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢀⣀⣀⣠⠀⠁⠜⢉⣭⢦⣉⣭⣟⣻⣽⣟⣛⣿⣿⣶⣂⣉⡡⣀⣀⠠⠈⠈⠨⠴⣽⣶⠿⣭⠾⣿⣿⣿⠤⢦⣶⠏⣱⣁⣁⢄⣀⡀⢁⡌⣉⢟⠻⠿⣶⣶⣽
⡿⢿⣿⣿⣿⣿⣿⣟⡿⠿⠿⠿⢿⣟⣉⣭⣿⣿⣦⣼⣧⣾⣿⣿⣏⣀⣀⡀⣻⢶⣾⣿⣿⣿⣟⣿⣿⣿⣿⣽⣯⠿⠛⣯⣖⣠⣾⣷⠯⣽⣥⣼⣷⣶⣞⣿⡟⢛⠛⠿⠟⠄⠘⠅⣰⠿⠬⠷⡽⣷⢿⣋⣿⣿⣿⣿⣾⣾
⠀⠈⠉⠉⠉⠉⠉⠉⠓⢂⣤⣤⣴⣄⠙⠻⠟⠃⠙⢛⣿⣾⣿⣿⢻⣯⣭⣹⣿⣿⣯⠉⢧⣬⣭⣿⡏⢹⡟⢿⣷⡶⠒⢡⠉⠛⠋⠀⠀⠉⠒⠸⠣⠘⠉⠛⡇⢹⢖⣀⣐⠢⢢⠚⢨⡤⠘⢿⢭⣿⠛⢉⡻⢛⣿⠎⢭⣽
⠈⠁⠁⠀⠀⠀⠀⠀⠀⠐⠀⠉⡙⠿⣿⣷⣶⣉⣹⠟⠉⠉⣀⡀⠈⡩⣽⣷⣾⣿⣿⣿⣿⣿⣾⣯⣻⠞⠿⣎⣉⣁⣈⠐⠀⢰⢄⡀⠀⠀⠀⠀⠀⠠⠆⠁⠁⠀⠀⢹⡤⣩⠛⠊⠉⠀⢈⡀⠒⠀⠒⣈⠿⠁⠈⠉⠀⠰
⣀⣀⣀⣀⣀⣀⣀⡀⠀⢠⣴⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡌⠀⠀⠀⠀⠀⠀⢘⡘⠛⠃⢤⠓⠃⣿⣤⠞⠀⣀⠀⢸⣤⢠⠬⠁⢬⣻⠍⠳⣧⠖⣀⣤⣄⣀⣴⣽⣦⡄⣠⣤⣀⠀⡀⠠⠤
⣿⣛⣛⡿⢿⠟⠛⠹⣄⠀⢹⡿⢿⢿⣿⡿⠟⠉⠉⠉⢉⣰⣛⣿⡿⢿⣿⣿⣋⣀⡈⠿⡅⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⢴⠀⠁⠀⠀⠈⠰⠀⢀⣸⡵⠛⢯⣯⣰⣶⣴⣶⣿⡿⣿⢏⣍⣿⣿⢻⠯⢿⠁⣄⡡⠶⠔
⠨⠛⠃⠀⠀⠀⠀⠀⠉⠰⠾⣿⣿⣿⣿⣧⠄⠀⢀⣺⣿⣿⣿⣡⣤⡷⢿⣿⣿⣿⣦⣼⣯⣀⣀⣄⡀⠀⠤⢤⡄⣀⣀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠿⣟⣻⣿⡿⣿⡩⠹⣻⠛⠁⠤⠄⣀⡰⠿⠠⡂⡀⢀
⠀⠀⠉⠁⠀⠀⢀⣀⣠⣴⣶⠀⠨⡻⣾⣿⣆⠀⠛⠛⠛⠿⢿⣟⡏⠷⣐⠚⠛⠉⠋⢙⡃⠳⠒⡉⠇⠀⢤⢤⣤⡉⠉⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⣕⠻⡎⠀⠁⠔⡈⡓⠫⠋⣫⣜⣽⠈⢴⠶⠂⠁⣄⠀⠁⢠⠘
⡶⠿⣇⣀⣀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠉⠼⣽⠥⠀⠀⢸⠿⠟⠺⠿⠿⢿⣯⣯⡭⠿⢀⣀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠁⠚⠈⠉⠀⠈⣨⣈⢹⠙⡈⠉⠈⠽⡍⠥⠄⠀⠀⠀⢈⠽⢀⡀⣀⣨
⢀⠀⣴⡾⠀⠓⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠠⣤⣿⣿⣏⣰⣿⣿⣤⢌⣻⠛⣃⠄⠠⢀⣄⠀⢀⡀⠉⠹⠾⠒⣿⣷⣄⠉⠀⠀⠀⢠⡤⠠⣼⣿⡾⢿⣿⣼
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣤⡄⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⢠⣴⣿⠿⡌⢻⣝⣿⣿⠏⠉⢩⡀⠉⠈⠀⠀⠑⠈⠉⠉⠀⠀⡐⢒⠛⣿⣿⣶⢰⡒⣖⡬⢣⣤⣼⢛⡉⠸⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣃⣀⣀⠀⠀⠀⡀⠘⣂⡻⣿⠉⢙⣽⡿⠿⢟⣓⠶⢀⣦⣀⣄⣠⠰⠶⣶⢶⠷⢼⡀⢻⡿⠛⡏⠋⢯⡑⠿⢯⠻⠶⠔⠐⠀⠒
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣄⠄⠀⣂⢀⣁⡤⠀⣀⠀⠀⠀⠚⠃⠀⠈⠀⠀⠉⠀⠙⡛⢿⡟⠙⣟⣻⡇⢉⡁⠀⢘⣛⠉⠀⠀⠀⠀⢀⣀⡐⣃⣴⠾⠿⡄⠁⠀⠀⢰
⠀⠠⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢄⠀⠀⢀⠄⠀⠘⣯⠉⠘⠉⠀⡀⢰⡀⠚⠂⢲⣀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠍⠐⠐⠛⠉⠈⠁⢀⠀⠀⠚⠁⠄⠠⠂⠐⠀⠋⠐⣀⡀⠀⣀⠀⠹⠀⡃⠀⠈
⠀⠰⠯⠹⢸⡏⠿⠿⡿⠣⠸⠟⠿⠿⠇⠇⠀⢀⣀⢀⠀⠘⠃⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠴⠞⢀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠂⠀⢀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠈⠁⠴⠄⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠚⠿⢳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⢿⡿⠿⡋⡻⢋⠽⢫⢕⢂⠅⢠⠀⣄⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠈⠡⠓⠊⠱⢜⡁⢘⡀⠵⡌⡢⡮⢻⡴⡓⣻⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠉⠜⠻⠷⣛⣻⣿⡿⢿⣿⡿⢿⠏⠈⢿⡶⢎⣀⣀⡀⠀⠶⠈⠻⠿⠿⠉⠈⠀⢉⣻⠏⠇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⢙⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠼⢣⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠹⠿⠿⡿⠿⠛⠃⠈⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠘⢿⡿⠿⠟⠛⠙⠛⠛⠛⠟⠛⠛⠉⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⣿⠍⢰⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸
⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⢠⠀⠀⠀⠈⠁⠈⠉⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠋⠀⠀⠘⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⡀⠀⠀⠼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⡄⠀⠀⢠⠝⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠷⠶⠆⠹⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠀⢀⣀⠀⣿⡆⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⢈⣁⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⡠⠀⠈⠛⠙⡉⢡⡿⠃⠀⠀⠀⠰⡄⠀⢸⡇⠙⡟⠀⣿⣷⣴⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣠⣄⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⣶⡆⣶⣶⣿⣿⣿⣷⣿⢰⣶⣶⣰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⢸⣿⢹⣿⣿⣿⣶⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠟⠛⠘⣛⡘⢻⣿⡛⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣃⣘⣳⡄⣀⣀⣀⡉⢳⣿⣟⡀⣀⣀⣀⡙⣿⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢻⣿⣷⣿⡿⣿⣿⢻⣿⢒⣄⣿⣿⣿⣷⣿⣿⣿⣷⢸⣿⡟⢳⣿⣿⠿⠗⣿⡗⢺⣿⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⣽⡏⢹⣿⣽⣿⣿⣿⣇⣿⣿⢶⣶⠈⠈⣿⣿⣿⡏⣿⣿⣿⣿⢸⣿⡿⢇⣙⣿⣷⡦⣿⡇⢾⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⢸⣿⣿⣿⣿⣿⣿⡼⣿⣰⣤⣿⣿⢿⣿⣿⣿⣿⣿⢸⣿⣷⡌⢿⣧⣿⠟⣿⣧⢼⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣶⣿⣿⠀⢠⣾⣿⣿⣿⠟⠉⠙⠣⣿⡿⠂⠀⢙⠋⠉⠀⠀⠀⠀⠀⠀⠀⣼⠯⠅⠀⠀⠋⣰⣿⣿⡇⠀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣶⡾⠿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣟⡀⠀⢠⣿⣼⣿⠇⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⢘⣟⣉⣉⡀⠀⢠⣼⣿⣿⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠉⠉⠉⠛⠻⠟⠿⠛⠛⢿⣿⣿⣏⠉⠀⣸⣿⣿⣷⣶⣽⣿⣿⣿⣷⠀⠸⣿⣿⣿⣿⣿⣶⣾⣿⣿⡟⠀⢠⣿⣿⣿⣿⣖⠀⠀⠠⠀⠈⠻⣿⡧⣼⣶⣾⣿⡟⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣟⠛⠛⢿⡿⣿⣿⡿⣻⡿⠿⣤⡀⠘⢿⣿⣿⣻⠿⠿⠿⠉⠀⠀⠿⣿⣿⣿⠿⠋⠀⠀⠀⠚⠀⠀⠉⠳⠾⢿⣯⡉⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣉⣙⣻
⠀⠀⠀⠀⠀⠀⣽⣤⣤⣼⠿⣿⣿⣿⣿⣿⣿⡿⠓⣶⣶⣾⣼⣿⣯⣿⣀⡤⠤⠴⣄⣀⣈⡙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠛⢻⣄⣸⣽⣿⣿⣿⣿⣿⣉⡙⣿⣿⣿⣿⣿⣡⣴⣿⣿
⠀⠀⠀⡀⠀⠀⠈⠉⠙⢛⣿⣿⡿⢿⣿⣷⠉⣁⣤⣾⣿⣯⣭⣭⣿⣯⠋⢛⡂⠀⢀⣬⡥⠋⠉⠁⠂⠲⠀⠂⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⡀⡀⠀⠘⠦⡄⢩⠉⠙⠩⡫⢸⣝⣝⡉⠛⢳⣾⣿⣿⣿⣿⣿
⣿⣯⣋⣉⣀⣀⣾⣿⣶⣶⣶⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⣀⣀⡈⠉⢉⠍⢛⣉⡀⢒⣩⠿⣟⣿⠿⢞⣰⣆⠈⠹⠟⡀⠁⠀⡰⠒⠀⠀⡰⣭⣩⣶⢌⣽⣭⣭⣇⢈⢉⣹⡷⡡⠤⢀⠀⠀⠈⠋⠹⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣛⣛⣛⣛⣦⣤⣿⣤⡿⢻⣿⠋⡂⠀⢸⣧⣤⡿⣿⣷⣿⣿⣿⣿⣿⣟⣿⣻⠿⢿⢹⡟⣂⣤⣀⣤⡭⣙⣿⣃⣸⣿⣼⡿⡿⢿⣭⠟⡣⠶⠟⢸⣆⣻⣷⣦⣼⣧⠶⣼
⠛⠙⠣⣶⠈⠀⠈⢉⠉⠛⠛⠉⠛⠓⠆⢀⣠⣤⠉⠹⡿⠋⠙⠛⠛⠛⣷⣿⠿⢿⣛⡛⠾⣷⣿⡛⢛⡉⣛⣿⡿⠛⣾⣿⣿⣩⣤⠔⠛⠶⠿⠛⠃⠙⢛⡻⣟⠛⠿⠲⢟⠀⢤⠌⠁⣠⢄⢈⡄⠚⠉⣯⡭⠯⣿⣽⠶⣿
⡀⠀⠀⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣴⣒⣲⡶⠟⠉⠉⠁⠀⢺⣟⠿⡽⣿⣿⣿⡶⠯⣯⣩⡳⡠⢵⣤⠿⡟⠐⠂⡅⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠀⠋⠑⣂⠲⢵⣧⠠⠿⠁⠌⠁⣉⠉⡀⠲⣿
⠛⠀⡀⣠⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⣠⣴⣯⣭⣽⣿⣿⣿⣿⣿⣶⣔⣿⣿⣿⣿⣶⣿⣿⣷⣿⢯⡟⠃⠙⠛⠛⠀⠀⠘⠟⠾⠿⣃⡰⠠⢣⢎⣠⠄⠀⠀⠀⣄⠈⠀⠤⠀⢤⣤⠾⣡⢋⡀⠀⠀⠀⠛⣀⣤⠀⠀⠀⢸
⠻⠾⠆⠸⣿⣟⣻⣛⣿⣿⠛⠛⢇⣀⠈⣿⡿⢿⣿⣿⠿⠟⠛⠉⠉⠁⣿⢿⢿⣿⣿⠿⠿⠉⠉⠾⣇⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠃⢀⡄⠻⠉⠀⠀⠂⡀⠛⠁⡮⢡⣤⢗⠏⣀⣘⣋⣱⣶⣿⣶⡾⢿⣿⣾⣏⡺⣿
⠀⢀⠨⠥⠈⠛⠛⠀⠀⠀⠀⠀⠀⠛⠤⢾⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⣿⣟⣏⣴⣼⣷⣿⣿⣿⣅⣶⡀⠀⢀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠀⣿⣿⢿⣿⣿⣿⡦⠬⣧⣿⣿⠟⠛⡊⠉⣹
⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣠⣶⡆⠉⠉⣷⣾⣗⠐⠒⠛⠻⢿⣿⣿⠟⣷⡎⠽⡿⠝⢻⠛⠻⢹⣯⠝⢷⠀⠀⣉⠉⠑⢒⠂⠀⠈⠄⠀⠀⣀⠀⠀⠀⠀⠀⠠⠤⣮⠋⠙⠂⠛⠛⣩⠷⣤⠍⣧⡅⠠⠉⢑⠒⠉
⢦⣀⢁⣶⣶⡶⢿⣇⣀⡀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠺⠾⢀⣟⡷⡀⠀⠀⣲⣿⠦⣶⣾⣶⣶⣶⣛⣻⠗⠂⠀⠀⠀⠀⠀⠀⠀⠱⠀⠐⢂⡔⠺⠇⠈⠆⡄⠸⡴⡀⠦⠥⠶⡾⠾⠇⠀⠉⠁⠀⠸
⠁⠐⠎⠿⠟⠃⢀⣤⠧⠘⠃⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠁⠀⠀⢀⠀⡈⠉⠙⣋⣠⣴⣿⠃⣤⣴⣄⣂⢤⡤⠭⢁⡀⠀⠀⠀⠀⠀⠰⠿⣃⣅⣸⣤⡀⠐⠽⠈⠉⠁⠀⠀⠀⢻
⠈⠁⣤⣦⠶⣿⡟⠉⠀⠀⠀⠀⠀⠈⠤⠠⣤⣄⣤⠄⠀⠘⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣭⣿⡛⢿⡖⣿⣿⣿⠋⠓⠃⠔⠫⠀⠁⠚⣂⠀⠒⠀⢠⠉⣉⣸⣿⣿⣦⠀⠀⠀⠀⣻⠗⠒⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠀⠀⠀⠀⠀⠉⠉⠅⢩⣶⠟⠛⠿⣷⣴⣶⣿⣀⡀⠀⠀⠀⠀⠐⣀⣀⣀⣰⠀⢆⣈⣿⣿⣿⠿⣽⡶⣆⣕⢶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⢀⠀⠤⠈⠙⢉⡕⠀⠀⠈⠀⠸⠧⠉⠒⠖⠙⠋⠥⠡⠿⣧⣤⡿⢷⡿⣿⡃⠤⠚⠃⢿⡉⠜⠃⠚⠃⠈⠐⠀⢛⠃⣉⣓⣹
⠀⠀⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⣿⡒⠂⠚⡁⠉⠩⡄⢸⡧⢠⠠⠀⠀⠀⠀⠂⠀⠠⠀⢀⠐⢚⡛⣠⠜⠒⢻⢁⠐⠀⢠⣴⠂⠀⠀⡀⠈⠁⠖⠐⠈⠊⠋⠉⠙
⠀⠸⠍⠹⢸⡇⠿⠿⡧⠣⠸⠟⢿⡿⠇⠇⠀⠈⠀⠀⠀⠀⢀⢀⡀⠀⠿⠀⠀⠁⠀⠀⠈⠀⠀⠀⠒⠈⠀⠉⠀⢀⡠⠏⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠇⢤⠀⠀⠴⠲⠀⠠⠆⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠉⢿⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠟⡛⡛⡃⡁⠈⠀⢀⠪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⡿⣟⢏⡹⠉⢟⠬⠐⢀⠀⠪⣂⠀⢘⡡⠤⣇⣶⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⢿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠞⠃⠍⠘⠁⠃⠕⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⠟⠙⢿⣭⡝⠁⠀⠀⠀⣠⠙⢻⣿⣿⡟⠉⠉⠙⢿⡏⠉⠉⠉⣿⣿⣿⣿⣿⣿⣷⣏⣭⡿⠋⢻⣿⢽⣴⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠋⠋⠋⠀⠉⠀⠀⠈⠉⣨⠯⣺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠃⠀⠀⠀⠈⠹⣿⣿⣿⠿⠿⠛⠛⠻⠾⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⠀⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠛⣿⣿⣿⣿⡿⠟⠿⠿⠿⠿⠟⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣺⣟⠒⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢉⠁⠀⠉⠉⠉⠉⠒⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠾⠁⠀⠈⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀⠀⠀⢀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⡆⠀⠄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠁⠀⠀⠀⢺⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠧⠷⠾⠷⠦⠦⠄⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠛⠁⠀⠀⠀⠀⠘⠁⠈⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⣀⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⢶⡟⠃⠀⠀⠀⠠⡀⠀⢀⡷⠀⣿⡇⢸⣷⣄⠠⣢⣄⣠⣦⣦⣤⣤⣤⣤⣠⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠏⢰⣶⣦⣶⣾⣶⣿⣶⣾⣷⢰⣿⣷⣰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣟⣿⣿⣿⣿⢸⣿⢹⣿⣿⣿⣴⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⠻⢿⠿⠿⠛⢛⣘⡛⠘⢻⡿⠛⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣠⣤⣀⡀⣀⣀⣈⣿⣿⣿⣃⡀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⢹⣿⣯⣿⣯⣿⣿⢿⣿⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠛⢳⣿⡿⢿⣇⣿⣏⢹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⣛⣸⣿⢻⣿⣿⣿⡇⣿⣿⢶⣾⠸⢿⣿⣿⠿⢿⣿⣿⣿⣿⢸⣿⠿⣇⣛⣿⣷⡄⣿⣇⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣺⣿⢸⣿⡿⣿⣇⣿⣿⡼⣿⡀⠀⣿⣿⣦⡈⣿⣿⣿⣿⢸⣿⣦⡌⢿⣧⣿⠇⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣶⣾⣭⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⣼⣿⣿⣿⡟⠋⣼⢳⣾⣿⠀⠀⣿⠿⠷⡄⠐⠀⠀⠀⠀⠀⢴⡶⠏⠁⠀⣶⢀⣾⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⡇⠀⣼⣿⣿⣿⣿⡀⠀⡀⠙⢻⢿⠄⠀⣇⣀⣠⡄⠀⠀⠀⠀⠀⠀⠨⠯⠥⠤⠀⡀⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠙⠁⠉⠀⠁⠘⠛⠿⠿⠟⠛⠿⢿⡿⠉⠉⠉⢹⣿⣿⣤⣤⣭⡀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡏⠀⣰⣿⣿⣿⣷⡄⡀⠀⠀⠀⠀⣲⡶⡂⠀⠀⢉⣿⣿⡟⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⣭⣷⡶⠿⠿⢿⣿⣿⣿⣧⠀⠀⣽⣿⣿⣿⣿⣿⣿⠟⠋⠀⠐⠉⠻⢿⣿⣿⣷⡆⠀⠀⠀⠀⠘⠀⣠⣤⣀⠀⠴⠌⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡟⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⣄⣤⡼⢿⣿⣿⣿⣿⣿⣷⠦⢤⣤⣤⣀⣿⢟⣁⡀⠀⢛⣥⠬⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⢿⣿⣿⣿⣿⣽⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢲⣶⣿⣿⣿⣿⡏⠁⢀⣠⣟⢋⢉⣙⣒⡋⠁⠀⠀⠀⠀⢠⣤⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⢸⣿⡛⠛⠿⠻⠛⣻⢻⠻⡏⠟⠿⣟⣻⣿⣿⣿
⣦⣶⣻⣍⡁⠈⠉⠀⣰⣶⣶⣴⣦⡶⣾⣶⣶⣶⣶⣶⣿⣿⣿⡻⠉⠁⠈⠉⠀⠀⠀⠀⠚⠋⠛⠶⢂⠀⠤⢔⣶⡶⣰⢶⣤⢀⡀⠰⢶⡶⠀⠂⠀⠀⠀⠀⠉⢁⣘⢺⣦⡓⣻⢞⣲⡖⠚⠓⢴⣏⡛⠁⠀⠈⠋⠹⠟⢿
⠴⠿⠿⠟⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢻⣿⡟⠛⠛⠛⠾⢄⣀⣠⠀⣼⠿⠿⠃⠀⠀⠀⣈⣁⣹⣼⣧⣵⣿⣷⣶⣬⡟⣧⠤⣴⣶⢃⡶⠄⣃⠀⣀⣒⠳⢾⠟⠳⢾⣺⣿⣿⣿⡚⣶⠿⢃⡰⠤⡄⢢⢤⣀⣀⣼
⣶⠂⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠛⠳⠄⠉⢉⣀⠐⢛⣛⠋⠉⠛⠻⠬⣥⣴⣤⣶⠶⠲⣦⣯⡽⠛⠻⠛⠛⠚⠚⠛⣽⠳⣷⠚⢁⣩⢶⣯⣿⠿⠇⠲⠷⠶⡾⠟⣿⣭⣿⠋⠉⠙⠛⠩⠊⠈⠀⣼⠗⠚⠛⣿⣷⢿
⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠻⣶⣦⣀⠴⠦⣦⠾⠛⠉⠉⠀⠨⠿⢷⣂⣯⣪⣴⣮⣉⣛⡾⢆⠀⣋⣉⠹⠿⠣⠄⡂⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠨⡀⠞⠥⡤⢌⣏⡖⠉⣰⠆⠘⠏⠽⠿⢿
⠀⠴⢚⠃⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣃⣚⣿⣿⣿⣟⣷⣤⡤⣴⣶⣴⣤⣤⣤⣴⠿⢷⣟⠣⠆⠐⠛⠒⠃⠀⠹⡤⣤⡦⠀⢡⢀⢝⡤⢈⡀⠀⠀⠀⣀⠐⠀⠀⠀⣀⣀⣰⠂⡬⠋⠀⠀⠀⠤⠄⢛⠀⢸
⠻⠿⠥⠦⠆⠰⠶⠇⠛⡛⠟⠽⠿⠛⠂⠀⠀⢻⡿⢿⣿⣿⡿⠻⠟⠛⠛⠋⣹⣿⣿⣿⣿⣿⣷⠒⠚⢿⡇⠀⠀⠀⠀⠀⠀⠀⡥⠈⠀⠀⠊⠁⠈⠶⠊⠁⠀⠀⠀⠿⠆⣰⠆⡁⣎⣿⠫⠙⡄⠆⣀⣤⣄⣀⣶⣿⣦⣼
⠀⠀⠀⠀⠀⠥⠀⠐⠐⠀⠀⠀⠀⠀⠀⠘⠠⢼⣷⣴⣿⣯⣄⠀⠀⠀⣶⣾⣿⠷⢚⣡⣹⣷⣶⣶⣆⡂⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠃⠀⠤⠥⠘⠙⣸⣤⣼⣷⣾⣿⣟⣛⣟⣣⣅⡿⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⢀⣤⡄⠉⠙⢫⣽⣯⠀⠰⢶⣿⣿⣿⣾⠏⣻⡉⢹⡟⠙⠟⠿⠟⢓⡒⣚⡦⠀⠀⡐⢒⡢⠤⡄⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⡠⠟⢻⡭⡿⣾⠛⣯⠉⠙⡻⠋⠁⠀⠘
⠀⠀⠀⠀⠁⢰⠶⣤⢾⣇⣀⡀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠵⠼⠄⣷⡆⠀⠀⠀⢀⣶⣆⣉⣰⣀⣤⣤⠯⢖⡠⠌⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⢨⡏⠹⡀⡀⢰⣀⠀⣈⠄⣉⡡⣎⣏⠈⠠⢾
⠂⠀⠀⠀⠀⠸⠉⠀⠀⢠⠐⠀⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠂⠀⠀⠀⠛⠀⠀⠉⠈⠘⠛⠛⠟⠋⣀⢤⠄⣀⣠⡀⠤⢀⣀⣀⠀⠀⠀⠁⠁⠀⠈⢀⣧⡄⠪⠃⡌⠀⠀⠭⠄⠅⠄⠀⠀
⠀⠀⠀⠀⠠⠠⠠⢾⣖⠂⠀⠀⠀⠀⠠⠉⠁⢀⣤⣄⣀⡀⠀⠐⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠄⠒⣶⢚⣹⣦⣽⣽⣷⡖⢮⡏⢡⡴⣂⠀⢤⡄⠀⣀⠀⠉⠙⠗⠸⣿⣶⣄⠉⠀⠀⠀⢠⣤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⠀⠀⠀⠀⠉⠻⠏⠰⣤⠷⠽⣿⣏⣀⣀⣴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢀⠐⡒⠹⣿⣿⣦⣴⣶⣖⣈⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⢀⠀⠢⠐⠂⠀⠀⠀⠀⢀⣄⠘⠡⡤⠰⠟⡛⢛⣩⣝⣃⣤⣦⣤⣤⠇⠚⢻⠗⢼⠧⢩⠝⠻⠿⠛⡉⠛⢿⡕⢻
⠀⠠⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠬⠌⠔⠀⠒⠒⠁⢰⣆⠀⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢉⡙⢿⠉⠹⣫⢿⠂⢉⠀⠀⢈⡈⠈⠀⠀⠀⠂⠀⠀⠐⠂⣼
⠀⠸⠏⠹⢸⡇⠧⠀⠧⠣⠸⠗⠿⠻⢿⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠈⠀⠀⠈⠀⠀⠀⠠⠔⠀⠷⠆⠀⢀⡳⠆⠀⠐⠂⠀⠀⠀⠀⠈⠐⠀⠁⠈⠉⠀⠈⠀⡠⠀⠀⠉⠀⠀⠤⡆⠀⠀⠏⠌⢀⡀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠀⠀⠉⠑⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡽⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠱⢐⡀⠀⡀⠐⢶⢠⣠⢨⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠙⠟⠉⠛⠋⠁⠫⠉⠓⠣⢂⣀⢩⠅⡥⣠⡤⠙⡏⡟⣓⣵⣷⣿⣿⣿⢿⣿⣿⣻⡿⠻⢿⣟⡿⠏⠉⠉⠉⠝⠻⢿⣿⣿⠿⠟⠝⠻⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣷⣆⡶⣿⡿⠛⢻⢋⣉⣡⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠘⠙⠘⠿⡿⠿⠔⠿⠽⠓⠡⠀⠘⠟⢑⡦⣤⡤⣀⠈⠀⠈⠛⠛⠁⠀⠀⢀⣾⠃⠃⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠿⢧⣤⣾⣷⣾⣯⣌⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠱⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠁⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠉⠙⢿⣿⣿⣿⣿⣿⡿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠀⠀⠹
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⠀⠷⠷⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠉⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡰⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠆⠀⢸⣿⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢛⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠅⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠚⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⠄⠀⠇⣵⣾⣷⣤⣄⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠾⠁⠀⠀⠀⠀⣀⠋⠻⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡇⢻⣧⣄⠀⠠⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣄⠀⢰⣶⣶⣶⣶⣶⣶⣼⣶⣶⣹⣷⣾⣿⣿⣿⣾⣿⣷⣷⣷⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⢹⣿⢻⣿⣿⣿⢴⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢛⣛⣻⡟⠛⠛⠘⠛⢸⣟⠛⠛⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠘⠛⣛⣛⣋⡀⣠⣾⣿⣿⣿⣃⣀⡀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠈⠓⣿⣿⣿⣧⣿⣿⢿⣿⣿⣿⠟⢳⣿⡟⠿⠏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⣿⣿⣶⣾⣦⡀⣿⣿⣿⣟⣿⣿⣿⣿⢹⣿⡿⢧⣟⣿⣷⡆⣿⡗⢼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡾⣿⡇⠻⣿⡼⣿⣿⣷⣿⣿⠽⠟⣿⣿⣻⣿⢸⣿⣶⡞⢿⣧⣿⠇⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣶⣿⣿⡇⠀⠀⣨⣧⠀⢸⣿⣿⣦⡄⠀⠀⢠⡄⠀⠀⠀⠀⢀⠐⠏⢁⡤⢠⣴⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⣻⣿⣿⠏⠀⠴⢻⣿⡗⠀⢸⣿⠿⠿⠃⠀⠀⠀⠃⠀⠀⠀⠀⠈⠄⠀⠘⠃⠈⢿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠿⢻⣶⣶⠶⡿⠿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡛⠀⠀⣿⣯⣉⣭⡀⠀⣠⣬⣯⡅⠀⣸⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠀⢤⣶⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣶⡆⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⣿⣿⣿⣷⣶⡶⠀⠀⠀⠀⣠⣶⡤⠁⢠⣾⣿⡿⠁⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⢻⣿⠟⠿⠟⠚⠉⠉⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠿⢿⠀⠀⠠⠔⠀⠤⠀⣈⠈⠉⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣯⠙⢩⣧⠄⠀⠈⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣄⡀⠉⢽⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿
⣋⠉⠉⣀⣰⣶⣿⣿⣿⡿⠿⠟⠇⣰⣶⣦⣬⣭⣽⣿⣾⣭⣭⣶⣮⣤⡀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⣀⡀⣀⣀⠠⠀⠀⣠⣤⡄⢀⠀⠀⠉⡀⡀⠬⡄⣦⢀⡻⣷⣦⠈⣑⣘⣳⣷⣺⣍⣯⡉⠉
⠿⠿⠯⠥⠤⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢻⣿⢿⠿⠿⠯⢤⣀⣀⡀⣂⣤⢤⡔⠀⠀⠂⢀⠀⠓⣄⣀⣈⣽⣼⣯⣿⣶⣿⣐⣀⣛⡥⢀⣀⠠⠈⠀⠀⣀⣜⣦⣼⣟⣣⣾⣤⣼⣥⣠⣠⣼⠗⢄⠤⢤
⣶⣾⣶⣶⣾⣷⡟⠉⠉⠉⢩⠉⠉⠙⠛⠛⠛⠛⠛⠺⣯⡅⠉⠉⠀⠐⠒⠲⠒⠻⣿⣷⣚⣥⣤⣥⣴⣤⣄⣼⣒⣿⣷⣿⣿⡫⣿⣛⣟⣿⣽⣭⠝⠛⢣⣺⢡⣴⣦⢴⣲⣲⣭⣯⣥⣌⢿⣾⠿⡿⢿⣭⡝⣡⠶⠊⢨⣼
⣭⢭⡭⠭⠄⠀⣀⡀⠀⠈⠉⠓⠐⠶⠂⠀⢀⠀⠀⠀⠀⠈⠙⠿⢷⣶⣄⣁⠀⣀⣠⠶⠶⠻⠉⠀⣳⣶⡮⢿⣿⡇⣄⡶⢶⣶⣶⡀⢸⠟⠿⣷⣶⠒⢉⠉⠛⠋⠈⠁⠉⠭⠽⡏⡉⠟⠻⢫⠀⣦⠈⠀⢈⢄⣈⡥⢸⢻
⠀⠀⠀⠀⠀⠀⠴⠶⠃⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣀⣸⣿⣿⣷⢾⣅⣀⢠⣤⣤⣤⣔⣲⣝⣯⣿⣿⠿⣿⠛⣳⣶⡣⠚⠻⣇⡉⢁⣉⠐⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠁⠛⣚⡓⢴⡿⠠⠀⢸
⠀⠀⠂⠉⠙⠛⠿⠿⡶⡦⠸⠿⠿⠿⠾⣿⣾⠷⠷⢆⠀⠚⣿⣿⣿⣿⣿⣹⠿⠿⠿⠿⠚⣿⣿⣿⣿⣿⣿⡿⠽⣟⣷⡌⠀⠀⠀⠀⠀⠀⢙⡛⠿⠋⢀⠷⠚⢾⣁⡰⠆⠀⠀⢀⣆⠀⠀⠠⠀⢶⣶⠾⣡⠏⡀⠀⠀⠘
⠀⠀⠀⢀⠀⠀⠀⠀⠀⣨⣭⠁⠺⠛⠀⠉⠀⠀⠀⠀⠷⣀⣽⣤⣭⣿⣟⡀⠀⠀⢠⣤⣴⣦⠼⠟⡛⣿⣭⣥⣤⡬⢟⣆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣤⠌⠛⠀⠀⠀⠣⠜⠛⠡⢬⢡⢄⢟⠋⣈⣘⣃⣥⣶⣿⣾
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⢀⣬⡍⠉⠛⢯⣿⣧⠠⣤⣼⣿⣿⣷⣾⣾⣟⠛⠿⣷⣾⣷⣾⣯⣤⣤⣤⡀⠀⠤⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠉⠁⠈⣿⣿⣿⣿⣿⣿⣯⢭⢿
⠀⠠⠀⡀⢀⠀⡀⢀⡀⡁⣴⣤⣤⣾⣄⣀⠀⠀⠛⠛⠛⠟⠃⣀⠀⠀⠋⠙⠀⠀⠀⠀⠉⢉⣀⡌⢹⣤⡉⠁⠀⠃⢉⣉⠓⠎⡉⠅⠀⢨⢤⣀⠉⠍⠁⠀⠀⠂⠀⠀⢀⡀⠈⠁⠀⠀⠰⠴⣏⠋⠙⠇⢛⠻⣉⢷⣤⣸
⠙⠐⠀⠈⠿⠇⠃⠘⠉⠿⠿⠿⠃⠀⣭⣿⠹⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⡂⢀⠀⠸⠟⠛⠛⠿⠛⠿⢿⢿⡭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⣡⠀⠐⠠⠖⠟⠂⠩⠆⠄⠨⡼⡀⠤⠧⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣤⣴⣾⣶⠋⠁⠀⠀⠠⣬⠉⢁⢀⣤⠀⣀⡀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠀⠀⢨⣥⣴⣺⣏⢱⡶⣷⣄⣁⣦⡄⠉⢀⠀⠀⠀⠀⠀⠀⠰⠷⣅⣅⢠⣄⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⢸⢴⣾⣧⣙⢿⡛⣿⣿⡟⠈⠙⠢⠒⠩⠂⠀⠹⡉⠴⠶⠀⢀⠉⢋⣈⣿⣿⣦⠀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠒⠂⠘⠁⠀⠒⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠉⡀⢤⠀⠀⠀⠀⠀⢂⠹⣯⠛⠙⣻⣦⣿⡾⠧⣤⡀⢀⠀⠀⢀⠀⣀⣀⣀⣠⡀⣆⣘⣿⣿⣿
⠀⠤⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣆⣐⠂⣤⢠⣤⡔⠀⣄⠀⠀⠀⠘⠂⠈⠙⠂⠙⠓⠂⠠⢿⣬⣼⠿⣷⣾⣶⠡⠍⠹⠋⣟⣃⢴⠊⠙⠛⢹
⠀⠻⠿⠹⢻⡇⠿⠿⡧⠣⠸⠇⠿⠻⠇⠇⠀⠀⠀⢸⡀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠐⠆⠀⠈⠓⠀⠀⠐⣀⡀⢲⣀⠛⠂⢰⣀⠀⠀⣀⠈⠀⠀⠠⠀⠀⠐⢈⡃⡤⠼⠂⢏⠀⠒⠀⢀⣤⠆⠀⠀⠀⠀⢘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡀⡤⢳⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢍⠉⠉⠍⢗⠡⠘⠈⡀⡱⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠒⠿⠿⠿⢿⠿⠿⢻⠟⢯⠽⠋⢫⠨⠀⣀⠤⠕⣍⡄⠠⡓⣒⠭⣋⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣍⣩⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠂⠊⠪⠓⢿⢿⣟⡻⠿⣿⣿⠟⠏⠝⢿⠟⣤⣀⣠⠀⠘⠒⠀⠻⠿⠏⠀⠀⠀⢽⣿⠰⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣨⣿⣿⣿⣛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠁⠀⠀⠀⠀⠀⠤⠛⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠛⠿⠿⠛⠛⠋⠀⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠂⠀⠀⠛⢾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠋⠹⡿⠿⠿⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣿⠇⢹⣶⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠰⠀⠀⢸⣇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢛⡋⠀⠀⠀⠻⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢈⠰⠂⠀⠀⢠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣆⠀⠨⡇⣷⣖⣆⢀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⠾⠀⠀⠀⠀⠠⡾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠟⠀⠀⠀⠉⠉⠙⠛⠛⠃⠘⠛⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⡟⠘⢸⣧⣄⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣴⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⣶⣄⣶⣶⣶⣀⣶⣶⣠⣶⣶⣴⣶⣶⣰⣶⣦⣶⣶⣶⣶⣿⣄⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣿⣰⣾⣿⣿⣶⢶⣶⣰⣶⣾⣶⣾⣿⣤⣶⣶⣾⣿⣿⣿⣿⣾⣷⣶⣶⣶⣦⣴⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢹⣿⣿⣿⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠙⢻⢿⣿⠛⠛⠛⠘⠛⣘⣛⠛⠛⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠤⠼⣿⣿⣋⠀⣀⣤⣤⣼⣿⣋⣀⡀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠒⢦⣿⣿⣿⣷⣿⣿⣿⣿⢹⣿⡟⢳⣿⡿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⢶⣶⡀⠀⣿⣿⣿⠇⣿⣿⣿⣯⢸⣿⠿⣇⣿⣿⣷⡆⣿⣇⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢹⣿⡙⣿⡇⠻⣿⡼⣿⣿⣆⣿⣿⣿⠖⣿⣿⣿⣿⣸⣿⣦⡌⢿⣧⣿⠧⣿⡇⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣠⣴⣶⣿⠂⠀⠀⣨⡀⠈⣿⣿⣥⠀⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⣴⡉⠁⠀⢈⣴⣤⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣴⣿⣿⡿⠟⢀⣰⣶⣿⡇⠀⣻⣿⣿⣷⡤⠀⠀⢻⠀⠀⠀⠀⠀⠃⠀⠀⠺⠀⢹⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠿⠿⠿⠿⠿⠟⠿⣷⣶⣶⣶⠿⠿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣸⡿⢻⡛⠃⠀⠈⠁⣾⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⣀⣰⣶⣿⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⢻⣯⠀⠀⣿⣾⣿⣿⣆⣀⣶⣿⣿⡟⠀⢠⣿⣿⣿⣿⣷⣄⣀⣀⠀⠀⠀⠀⠩⠭⢒⠀⢠⣾⡊⠿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣠⣾⣿⣿⣿⡄⠀⢻⣟⠋⠙⠛⠁⠙⠟⠛⠀⠐⠺⠟⠛⠛⠛⠻⠛⠋⠠⡤⠆⠀⠀⠠⠂⠀⠀⠙⠉⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣷⣶⣤⣆⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣯⣭⣿⣿⣿⣧⡀⠀⠁⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠿⠛⢻⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻
⣿⣿⣍⣉⠉⠀⠀⣠⣶⣶⣶⣶⠒⠶⠶⠀⣤⣤⣀⣀⣉⣽⣯⣙⣛⣁⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠐⢀⠀⠿⠋⠀⢘⣋⢀⡀⠹⣿⣍⠙⠟⠛⢛⣻⡏⡿⢿
⠛⠙⠛⠻⠶⠭⡭⠭⣭⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⡾⣿⣿⢿⣿⡥⠛⠻⠦⢄⡀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠠⣀⠀⠀⣛⣗⣞⢻⠦⣤⠄⠈⠻⢛⠀⠁⠀⡀⠋⠋⠀⠸⢜⣓⡷⠼⢻⣷⣛⣓⠀⡛⡛⣿⣽
⣒⣒⣒⣶⣶⣶⣶⣦⣤⠉⠏⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠲⣿⣝⠚⠛⠁⠀⠤⠄⠬⠵⣶⣦⠤⠋⠀⠀⣠⣤⣀⢀⠦⠴⡞⣴⣶⠖⢻⠛⢿⢿⣏⠒⣒⠾⣿⢡⡟⢀⣤⡠⠤⣽⠛⢺⠛⠉⢶⣟⣿⣿⣿⡔⠳⡷⢋⢼
⡤⠶⢏⣙⣩⣍⡭⠉⠁⣀⠀⠀⠀⠚⠆⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣀⣀⠀⢀⣀⣀⣠⣭⠿⠟⠉⠹⣥⣌⣻⡿⡯⠉⢉⣈⣉⣈⠁⠉⡯⣿⣻⣁⣠⠐⠹⠷⠿⠟⠛⠙⢷⣟⣻⠟⢿⣯⡿⠋⣉⡉⠃⠉⢎⠉⢺
⠛⠉⠉⠀⠀⠀⠀⠀⠠⠭⠿⠂⠀⣀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⠤⠭⣿⣿⣦⣤⣝⡁⠀⣀⣀⣀⣈⠉⣙⣲⡻⣿⣿⣛⠦⠯⣭⡡⡠⠧⢤⠚⠛⠐⠀⠅⠀⣀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⡅⠚⠣⠤⠤⢇⣻⣾
⠶⣦⠀⠀⠐⠒⠛⠛⠶⡶⢦⠴⠌⠽⠶⠶⠶⠶⣶⣶⠶⢦⠀⠰⢾⣿⣿⣷⣿⡿⣿⣷⣿⣿⠦⢿⣿⣿⣿⣽⣿⣟⣑⣻⢯⡝⠁⠉⠉⠉⠀⠀⠘⠖⢶⠗⠀⢀⠠⢎⡔⠀⣀⠀⠀⠀⢀⠀⠁⠀⠀⢀⣀⣀⡶⢨⠏⠘
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣘⣂⠀⠿⠉⠉⠉⠀⠀⠀⠸⣀⣘⣯⣨⣿⣿⠋⠀⠀⠀⣀⣠⣿⣽⡿⠿⢿⣛⣛⣀⣀⣛⢇⠀⠀⠀⠀⠀⠀⠀⠟⠂⠀⠘⠃⢀⡀⠻⠃⠀⠀⠤⡀⠾⠦⣀⠤⣀⢠⣽⠇⠝⠧⠸⢰
⠀⠀⠄⠀⠀⠀⠈⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢈⡍⠙⠛⢟⣻⣗⡀⢀⣠⣿⣿⣯⣽⣴⡶⢾⣶⣿⣭⣿⣥⣶⡀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠈⠌⠃⠀⠀⠀⠀⠀⠉⠀⠤⠽⠒⠉⢢⣦⣴⣶⣶⣾⣿
⠦⣀⣷⢬⣔⠀⢀⣀⡀⡈⠀⠀⢀⣤⣤⢴⣶⠀⠀⠀⠒⠲⠲⠿⠿⢀⡀⠀⠙⠿⠆⠀⠉⠉⠉⠛⠉⢈⠿⣇⡐⠂⠈⠹⠉⠙⠻⠽⠞⠻⠀⢀⣌⠩⠔⢒⠄⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⣀⠾⠿⣯⢹⣷⡟⣿
⠀⠀⠋⠀⠈⠀⠫⠽⠕⠉⠈⠙⠿⠟⠷⠀⠈⡿⡟⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢯⡏⠀⠀⠀⡾⠿⠲⣶⠾⢤⣶⣶⣒⣩⠔⠀⠀⠀⠀⠀⠀⠀⡈⢽⠀⠀⠀⡀⢤⣍⠹⢇⢀⠀⠄⡂⢐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⡶⠁⠀⠀⠀⣀⡚⠂⠀⣀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠈⠋⠠⢴⡶⠂⣠⣤⡀⠠⢀⣀⣐⠂⠀⠀⠉⠉⠀⠀⠁⣼⣤⠹⡑⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠍⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣿⠉⢿⡶⣿⣿⣿⠏⠾⣅⢀⠶⡃⠂⠠⡦⠄⣀⠀⠉⠹⡿⠖⣿⣶
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠈⠈⠙⢁⠹⣤⡿⠼⣿⣏⣡⣤⣴⣄⠀⠀⠀⠀⠐⢀⡀⠀⠐⠃⡀⢒⠛⢿
⠀⠤⠀⠀⠀⠀⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⢠⠤⢀⠈⠉⢉⡁⠈⠀⠈⠀⢐⡆⠙⠂⠤⠲⢟⣋⢛⣩⡝⠃⣴⣦⣤⣤⡤⠐⠒⣶⢢⣷⡼⣖⢺
⠀⠹⠿⠹⢻⡿⠿⠿⡧⠣⠸⠟⠿⠋⠇⠇⠀⠀⠀⠀⠀⠐⡖⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠖⣄⠀⠀⠤⠀⠀⢿⠉⠁⠉⠁⠉⢡⡀⠸⠇⡠⠤⠀⠀⠀⠀⠄⠀⢀⠀⠀⠉⡙⢿⠁⢹⣏⢽⡇⢉⠀⠁⠀⠒⠀⠁⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠊⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢉⢹⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠛⠟⠽⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⢿⠿⢷⢕⡍⠡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢖⣯⢟⢿⡯⡶⣙⠊⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⢻⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠈⠉⠛⠋⠋⠊⠀⠁⠞⠝⡇⠪⠭⠇⠺⠹⠯⢿⡻⣯⣿⣿⣿⣿⣿⣿⣿⣿⡻⢻⣭⡟⠋⠀⡀⠀⡒⠏⢿⣿⣿⡟⠋⠋⠛⣻⣿⣟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⡟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠻⠛⠛⠛⠛⠏⠛⠛⠇⠉⠉⣨⣿⣷⣿⠟⠀⠀⠀⠈⠈⠀⠀⠀⠠⣿⠃⠉⠀⠀⠈⠙⣿⣿⣿⡿⡿⠟⠛⠻⢟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠀⠀⠄⠀⢀⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⡗⢶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠏⠀⠈⠙⠛⠛⠛⢻⣦⣠⣀⣀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⠀⠀⠀⢀⠀⠀⣾⡇⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢀⡀⢀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⢰⠀⠀⣿⡇⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠗⠚⠀⠀⠀⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⢸⠀⠀⣿⡇⠀⠀⠀⡎⠠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠐⠂⡄⠀⠀⠀⣵⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢸⡇⣇⣔⡀⠈⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣠⡇⠀⠀⠀⠈⣭⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠈⠑⠛⠻⠿⠿⠧⠄⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⠈⠉⠀⠀⠀⠀⠀⡎⠀⢻⠛⠟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣶⢶⣶⣄⣶⣶⣶⡀⣶⣶⠀⣿⣶⠀⣶⣶⢰⣶⡄⣶⣆⣶⣶⣶⣇⠀⢰⣶⣆⣶⣶⣶⣶⢰⣾⣷⢰⣿⣿⣷⣶⢶⣶⢰⣶⣶⣶⣶⣶⣀⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣛⣀⣼⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⢻⣿⣿⣿⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠹⠟⢿⣿⣿⣿⠛⠛⠚⠛⠘⠛⠛⠛⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣀⣠⣶⣾⣟⠀⣀⣀⣠⡿⢛⣀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⣿⣿⣿⣷⣿⣿⣿⣿⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⠈⠹⣿⣿⠿⢧⣿⣿⣿⣯⢸⣿⠿⢇⣿⣿⣷⡆⣿⣟⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⣿⡇⠻⣿⣼⣿⣤⡀⣿⣿⠀⠀⣿⣿⣿⣿⢸⣿⣷⡞⢿⣧⣿⠇⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⣠⣤⣶⠀⠀⠀⠉⠙⢻⣿⣷⡄⠛⠀⢀⣤⠀⠀⠛⠆⠀⠀⠀⣘⠉⠁⠨⠰⢢⡀⠙⣿⣿⣯⣭⡝⠉⡙⠛⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣠⣾⣿⣿⡿⠀⢇⣠⣧⡀⠈⠿⠿⠃⠀⠀⠐⣘⣦⠀⠀⠀⠀⠠⡜⠛⠇⢠⠀⢰⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⠻⢿⣿⠿⣿⡿⣿⣿⣿⣧⣤⣤⣼⣿⣿⡿⢿⣿⣿⡿⠃⠀⣴⣿⣿⣿⠋⠀⠰⠛⣿⣿⠁⠀⣶⣤⣤⡀⠀⠈⠁⠘⠀⠀⠀⠀⠠⡕⠀⠀⠈⠀⠀⠉⣥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣻⣿⡇⠀⠀⣀⣴⣿⡟⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⢇⠀⠐⢂⣀⠀⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢸⣿⣿⣿⣥⣀⠜⠛⠛⠟⠀⠀⠻⡿⡻⣿⠿⢿⣶⠶⡾⡶⢄⡄⠀⠀⠘⠿⠀⠘⠟⠛⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠐⠻⡆⠀⠈⣿⣿⢹⣿⣦⣂⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠀⢁⣤⣶⣶⣶⣶⣶⣶⠆⢤⣄⣀⡀⠀⠀⠘⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣟⣿⣿⠀⠀⣿⡿⠉⠹⣿⣿⣿⣿⣿
⠋⠉⠉⠉⠉⠉⠋⠛⠛⠻⢷⡿⡭⠭⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣤⣤⣤⠤⠶⠞⠿⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠔⢠⡦⣠⣤⣄⠀⡀⠠⢶⣶⡟⠿⠇⠈⢤⣤⢄⣺⣿⣶⣤⣽⣿⣦⣀⣸
⠀⠀⠠⡄⢀⣀⣀⣲⣶⣶⣾⣿⣷⣶⣏⠿⠟⠛⢉⠛⠉⠉⠙⠛⠛⠀⠣⣼⣏⠀⠒⠒⠀⢀⡀⢈⣳⣤⣄⢀⡠⠈⠉⠀⠀⠈⠀⣀⣁⣵⣦⣤⣴⣷⣷⣾⣿⣿⣯⣀⣤⣭⡤⢠⣤⠀⠈⠁⠡⣬⣍⣷⣾⣿⣣⣽⣿⣽
⠀⠀⣀⣀⣀⣤⠴⠶⢊⣍⣭⡭⠭⠉⢁⡀⠀⠀⠑⠶⠀⠴⠔⠀⠀⠀⠀⠀⠈⠀⠠⢶⠀⡀⠀⠄⠀⠈⠉⣓⣲⣿⠶⠾⡛⠳⢶⣯⣴⠾⠾⠟⠿⠸⠧⠽⣽⢷⣾⡶⠏⠉⢯⣿⣲⣾⣷⠍⣽⣧⣤⣿⣥⣼⠿⣾⣿⣿
⣤⣤⣿⣿⠻⠋⠉⠉⠀⠀⠀⠀⠀⠀⠨⠭⠞⠀⠀⣀⡀⠀⠀⠀⠈⠑⠂⠀⠀⠀⢀⡀⠙⣿⣶⣯⣙⠻⠛⠁⠀⠀⠀⠀⣛⡻⢿⢯⣭⣤⣮⣟⣿⡷⠧⡀⣿⣙⢻⣷⡞⣋⠁⠙⠛⠃⠀⠀⠉⠭⠈⠯⡉⠻⠻⢿⠀⢸
⠛⠙⠙⠇⠀⠐⠲⡦⠀⠀⠐⠂⠛⠛⢶⣶⣤⡤⡩⣿⣶⡶⢄⣰⣴⣶⣦⡀⠠⢶⣏⣵⣶⣾⡿⣿⣿⣽⣶⣆⣾⣿⣷⣶⣶⣶⣶⡾⢽⣿⡿⠏⠹⠿⠧⠗⠉⠻⣅⣁⣠⣈⠐⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠀⢹
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣒⡊⠹⠿⠋⠋⠉⠀⠂⠱⣄⣈⣿⣚⣻⣿⠿⠋⠉⠉⠉⠁⣰⣟⢿⡿⣿⣿⡿⠟⠟⢷⡿⠀⠀⠀⠀⠀⠀⠀⢘⡙⠛⠀⡴⠛⠃⢟⣤⡤⠀⠀⠀⢀⣄⠈⠀⠤⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠁⠠⠤⠄⠀⠀⠀⠀⠈⣉⠛⠻⣿⡿⢷⠄⠀⠀⣺⣿⣿⣛⣩⣥⣼⣥⣶⣖⣶⠒⣭⡄⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠅⣴⠈⠁⠀⠀⠀⠃⡌⠋⠩⡮⢥⣤⣿
⠀⠀⠀⠀⣤⣤⠄⣀⣻⣒⡤⠀⢀⣀⡀⣈⣀⠁⢠⣤⣤⣴⡆⠀⠀⠠⠶⠶⠾⠿⠆⠀⠠⡼⣿⡏⡈⠙⠛⠻⠿⠿⠛⢻⡞⢩⣿⠻⢿⠿⣿⣶⡶⠶⣶⠀⠐⠲⢦⢄⢀⣀⠀⠈⡀⠂⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠈⣺
⠀⠀⠀⠀⠀⠁⠀⠐⠉⠂⠈⠉⠹⠟⠀⠈⠘⠻⠿⠿⠇⠈⣛⣿⢣⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡖⠂⣾⣷⠀⠀⠀⣠⣤⣄⣙⣠⣜⣀⣀⣴⡤⢅⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠠⠴⣾⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣤⣶⣶⠛⠁⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠈⠓⠀⠀⠀⠙⠉⠉⠙⠛⠛⠿⠿⢫⡝⠋⠉⣄⠀⠀⠀⠀⠀⠠⠈⠅⠀⠐⢠⡖⡶⠂⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⡖⠖⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⣤⡏⣿⡍⣶⣶⣷⣈⣰⣦⠤⠭⢀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⢠⡀⠀⠀⠀⠀⠶⠶⡾⠯⡽⣿⣻⣿⣿⠟⠚⠛⠠⠚⠫⠀⠀⠺⠂⠠⠤⢸
⠀⠴⠓⠂⠀⠀⣤⡤⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠈⢀⠀⠠⠄⠤⠀⠀⠀⠐⠐⣀⢻⡿⠉⢹⣻⣶⣶⣶⣧⣤⠀⠀⠀⠀⠁⠠⠀⠈
⠀⠸⠿⠹⢹⡿⠿⠿⡿⠣⠹⠟⠿⠿⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠠⠀⠉⠁⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢸⡶⠍⠴⠆⠴⠶⠇⠀⡄⠀⠀⠐⠛⠀⠈⠙⠋⠙⠳⠎⠴⣿⣬⣴⢿⣶⣶⣾⠇⠛⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣀⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠁⠀⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠖⠀⠉⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⡿⠿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⠈⠊⣾⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠋⠁⠀⠘⠛⠻⠛⠻⣿⣿⡿⠿⣿⣿⡿⢟⡿⡻⣋⣩⣿⣿⣿⣿⡟⠁⠉⠉⠉⠁⠀⠀⠠⣿⠋⠉⠀⠀⠈⠛⣿⣿⣿⣿⣿⡟⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠻⠑⠛⠛⠋⠛⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢡⣤⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢾⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⡗⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠠⠀⠀⢠⡄⠀⠀⠀⢛⠁⠘⠛⠛⠛⠓⢶⣄⣀⣀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⠀⠘⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⣿⣀⢀⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿⣿⣿⡞⠁⠀⠀⠠⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠀⢸⠀⠀⢸⣇⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⡀⠀⠀⢠⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣇⣧⣠⡆⠈⠀⠀⢸⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠋⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠋⠿⠿⠿⠿⠷⠄⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠁⠀⠀⠀⠀⠀⠏⠘⢿⡟⢺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣶⣀⣶⣶⣶⣀⣶⣶⣀⣶⣶⠀⣿⣶⢰⣶⡄⣶⣆⣴⣶⣶⣆⠀⢰⣶⣆⣶⣶⣶⣶⢰⣾⣷⢰⣿⣿⣷⣶⢶⣶⢰⣶⣶⣶⣶⣶⣆⣶⣶⣶⣪⣶⣶⣷⣶⣴⣲⣶⣶⣶⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣛⣛⣀⣸⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⢿⣿⣿⣿⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠹⠿⢿⣿⣿⣿⠟⠛⠛⠛⠘⠛⠛⠛⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣀⣰⣶⣾⣟⡀⣀⣀⣼⡟⢃⣀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⣿⣿⣿⣷⣿⣿⣿⣿⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢷⣶⠈⣿⣿⣿⠿⣿⣿⣿⣿⣯⢸⣿⠿⢇⣙⣿⣷⡏⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⣿⡇⠿⣿⣼⣿⣄⠈⣿⣿⠀⠀⣿⣿⣿⣿⢸⣿⣷⡞⢿⣯⣿⠏⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⣠⣤⣦⠀⠀⠀⠉⠙⣿⣿⣧⡌⠳⠀⣤⣄⠀⠈⠳⣶⠂⠀⠀⠰⡍⡇⠐⢦⡄⠀⠹⣿⣿⣿⣿⣯⣭⣙⡛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿
⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡟⠁⢀⣰⣿⣿⣿⡟⠰⢃⣠⣧⠀⠘⣿⣿⠿⠆⠀⢿⣿⣧⠀⠀⠐⠀⡠⡄⠿⡇⢀⠈⢸⠸⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⡿⠿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⠏⠁⠀⣾⣿⣿⣿⠋⠁⡶⠛⣿⣿⠁⠀⠛⠛⠀⠀⠀⠘⠉⠙⠀⠀⠀⠐⠋⣵⡀⠀⠘⠀⠈⠀⢙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣰⣿⡿⠂⠀⣶⣴⣤⣤⡄⠀⠀⠀⠨⠀⠀⠀⠀⠰⠋⠀⠠⢴⣀⢦⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣸⣿⣿⡿⠃⠀⠸⣿⣿⣿⣿⣧⣤⢤⣤⣤⣤⣤⣤⠄⠀⠾⠥⢤⣿⡿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠍⠁⠀⠀⠀⢴⣾⣿⣯⢏⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⠃⠀⣤⣶⣷⣶⣶⣶⣶⠶⠀⠀⠀⠀⣉⡉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢻⠿⠿⢿⣿⣿⣿⣿⣿⡙⠙⣿⣿⠟⠻⣿⣿
⣿⣿⡿⠋⠉⠉⡁⠀⠉⠉⠙⠛⠛⢷⣽⡭⣭⢿⣿⣿⣿⣷⣶⣴⣦⣦⡀⢀⡀⢀⣀⡐⠶⠶⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⣤⣄⣄⣀⠀⢀⠀⣤⣤⡿⣿⡏⢻⣋⣀⡠⢭⣷⣤⣀⣻⣿
⠀⠀⠀⠀⠀⠀⠤⠀⣤⣤⣶⣶⣶⣶⣿⣶⣶⣼⠝⠟⠛⠉⠉⠉⠁⠛⠛⠻⠉⠠⣤⣖⠀⠰⠗⠀⢀⡀⣀⣂⣤⠀⠀⠠⠈⠈⠁⠀⠈⠀⠀⢈⣰⣀⣆⣫⣷⣯⣭⣿⣾⣟⠐⠈⣩⣥⢀⣀⠠⠉⠋⠙⣚⡛⣯⣽⣿⢿
⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠶⣚⣭⣭⣯⠭⠍⢁⣀⠀⠀⠀⠳⠀⠠⠖⠀⠀⠀⠀⠀⠉⠀⠀⣶⣀⡀⠀⠤⠀⠈⠛⠓⣶⣶⡦⢤⠷⠢⣤⣎⣹⠿⢿⠿⣯⢽⣏⣹⣿⣿⣿⣩⠟⠻⣇⣾⢭⣴⣖⣒⣶⣏⣉⣹⣋⣹⣿
⣤⣤⣤⣤⣤⣾⣿⡟⠫⠑⠉⠀⠀⠀⠀⠀⣀⠠⠼⠞⠀⠀⣀⡀⠀⠀⠀⠈⠑⠒⠀⠀⠀⢀⣀⠙⣿⣷⣞⣛⡻⠟⠉⠀⠁⠀⠠⠿⢿⣛⣿⣝⣠⣔⣦⣶⢾⣇⠀⣿⠻⢿⣧⡴⠖⠛⠻⠿⠿⠙⠂⠛⢛⠻⣿⡛⣿⣿
⣿⠟⠻⠟⢏⠘⠛⡃⠀⠚⠷⠀⠀⠀⠉⠉⠙⢻⠿⢥⢤⢩⣿⣶⣦⣄⣰⣶⣶⣦⡀⠠⢶⣏⣷⣶⣼⡿⣿⣯⣿⣶⣄⣷⣿⣶⣶⣯⣷⣿⣾⣿⣿⢿⡟⢛⣶⣆⡷⠻⢷⡈⠉⢉⡉⠰⠀⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⢘
⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠤⣀⣀⢀⡀⠀⢀⣒⣛⠹⠿⠟⠛⠋⠁⠀⠹⣄⣈⣟⣛⣻⣿⠟⠛⠋⠉⠙⠃⣹⠿⣿⣿⣿⣿⣷⠶⠾⢿⡧⠀⠀⠀⠀⠀⠀⠀⢻⡛⠟⠁⣀⠆⠜⣴⣃⣠⠀⠐⠀⠀⣄⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⢀⡨⠉⠈⠁⠀⠀⠤⠀⠀⠀⠀⠀⠈⣛⠻⢿⣿⡿⣷⡄⠀⠀⣶⣿⣿⣛⣋⣉⣹⣟⣧⢤⡴⠛⣷⡀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠉⢂⣤⠙⠛⠉⠀⠒⢆⡐⠿⠖⣼
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣂⢤⣿⣭⡿⣆⢀⣀⢀⣠⣈⡉⣠⣤⣤⣴⡆⠀⠠⠤⠶⠶⢾⡿⠂⠀⢚⢽⣿⣏⠈⡻⠿⠿⣿⢿⠿⣿⡭⣹⣿⢿⣿⣷⣾⢧⣄⠴⣄⠀⠠⢀⣀⡀⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠁⠰⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠩⠟⠊⠈⠛⠻⠿⠿⠟⠈⣛⣿⢣⠄⠀⠀⠀⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠼⠀⣷⣦⠀⠀⠌⣀⣤⣝⣛⣋⡙⠀⠀⣷⣶⡚⠛⠛⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣥⣤⣶⣶⠟⠉⠀⠀⢀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠯⠁⢠⠀⠛⠉⠉⠛⠛⠛⣿⣿⣽⡷⠞⠃⠀⠀⠀⠀⠀⠀⢀⠙⣃⠀⣠⢀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠁⢙⠷⠒⠶⠀⠈⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⢉⣁⣶⣾⡿⣠⣤⣦⠰⢄⣀⣀⣲⠆⠐⠈⠁⢉
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣤⠀⠤⠄⢀⡀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⠀⠀⡬⣤⣿⣯⡺⣿⢿⣿⣿⡿⠽⠯⢂⠠⢶⠀⠀⢤⣬
⠀⠤⠀⠀⠀⠉⣭⠤⠀⠀⠀⠀⠀⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⣀⠈⠁⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠈⠩⣥⣤⣄⠠⠀⠁⠈⠣⠌⢷⣾⠓⢻⣿⣭⣥⣤⡆⠀⠀⠀⠀⠀⢲
⠀⠿⠿⠹⢻⡿⠿⠿⡿⠣⠸⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠠⠀⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⢤⣂⣨⠇⡠⣠⠎⢀⡀⠀⠀⠠⠿⠈⠁⠲⠞⠿⣏⠹⣩⣿⡛⢢⣴⣄⣀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠉⠁⠀⠙⢺⢖⠂⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⢠⣄⡀⠲⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢩⢯⣅⣀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⡿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⠛⢹⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠿⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠈⠀⠀⠀⠈⠛⠛⠟⠛⠛⠛⠉⠙⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣲⣶⣿⣷⣿⡟⠙⠛⠛⠛⠋⠀⠀⢨⣿⠋⠘⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⠁⠈⠉⠉⠙⠶⡿⡿⣽⡿⡛⠿⠟⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⢄⠀⠀⣀⠈⠉⠉⠻⡛⠀⠻⠟⠓⠦⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠨⠀⠀⣿⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠀⠀⠀⢸⠀⠀⣿⠇⠀⠀⠀⢇⡀⠀⢀⡀⠀⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⣸⠃⠛⠛⠀⠀⠀⠐⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⠀⠀⣿⠀⠀⠀⢀⡏⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣇⣴⠀⠙⠀⢀⣿⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢋⢿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠘⠻⣿⣿⣷⣷⣄⠈⣿⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⡏⠐⢻⡏⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣦⣄⣀⣀⣀⠀⠀⢠⣶⢶⣶⡀⣴⣶⣶⣈⣷⣶⠀⣶⣶⠀⣶⣶⢰⣶⡄⣶⡞⣶⣶⣶⣾⠁⢰⣶⣆⣶⣶⣶⣶⢰⣶⣿⣰⣿⣷⣴⣶⢶⣦⢰⣶⣶⣶⣶⣶⣂⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣛⣛⠀⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡛⠛⠛⢻⣿⣿⡿⠛⠛⠛⠘⣛⣙⠛⠛⠛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣼⡿⣿⣛⣁⡀⣀⣠⣾⡟⢁⣀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢷⣶⠹⣶⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⠿⢇⣙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡇⢿⣿⣼⣿⡀⢹⣿⣿⠀⠀⣿⣿⣿⣿⢸⣿⣷⣞⣿⣧⣿⠧⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢀⣤⣤⡀⠀⠀⠘⠙⢿⣿⣿⡌⠻⣧⠀⠀⣤⡀⠀⠘⢧⡄⠂⠁⢀⡌⡄⢠⡄⠀⠙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠟⠿⠿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⣠⣿⣿⣿⣿⡇⣤⠀⣤⡀⠈⢻⣿⣿⣆⠈⠀⣸⣿⣿⣄⠀⠀⠈⣦⡼⣬⡇⠃⠠⠻⠇⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣭⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⢻⠿⢿⠿⣿⣿⣿⡟⠁⢠⣾⣿⣿⣿⣿⠟⢡⣿⣷⣿⣷⠀⠈⣿⣿⣿⣧⡀⢸⠿⢻⢿⠋⠀⠀⠉⢁⣿⣇⢰⠀⠐⣯⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠈⠀⠛⢻⣿⠀⠀⣿⣿⠋⠉⠁⠀⠀⠂⡀⠀⣰⡀⡀⠀⣀⡀⠙⢰⣿⣷⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⠟⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢋⣀⣀⣀⠀⠐⣾⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠀⠀⠘⢿⣊⠠⡆⠂⢂⣶⣲⢠⠀⠀⠉⠉⠉⠉⠂⠀⢻⡿⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⡃⣀⠀⠀⠱⣄⣤⣶⠆⠀⠀⠊⠀⠀⠀⠀⢨⠿⣿⣅⡀⠀⠉⠉⠉⠙⢲⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠍⠙⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠅⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣯⣽⡧⠄⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⣰⣤⢾⣿⣿⣿⡯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣐⠛⢉⣙⣿⣿⣿⠿⣿⡿⢿
⠉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠐⠀⠐⠒⠠⠤⠴⢽⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠂⠾⠿⠁⠁⠀⠐⠂⣠⣀⠀⢀⠀⠒⠆⠀⠐⠀⠀⠐⢢⡌⢼⣿⣿⣿⡟⢿⣦⣶⣀⡘⢻⠿⠛⠛⠐⢻⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣖⣉⣥⣾⠭⡿⠏⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣄⣰⢆⠈⠀⠀⠉⠹⠿⠯⢥⣴⣄⣀⣶⣤⣀⣐⢒⣲⣿⣿⣿⢿⣿⢿⣿⣿⣿⡶⢶⣶⣿⢇⡶⠖⣁⣠⣿
⠀⠀⠠⠾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⠀⠀⠀⠀⣀⣀⣒⢶⣾⠋⢀⣀⣀⠀⠀⠀⠉⠛⠒⠃⠀⠀⢀⣀⣘⣿⣦⣄⡲⣦⠾⠛⠛⠛⠁⢀⣶⣦⡬⣿⡿⠯⣉⢥⣫⣭⡿⠛⢻⣿⣿⣿⣋⣁⡸⢿⣯⣿⡿⣿⣿
⣤⣴⣦⣤⡄⢤⠴⢿⠿⠿⢿⣯⣭⣿⣣⠾⠹⠇⠀⠀⠉⠉⠉⠉⢿⢿⢶⠦⢿⠶⣷⣦⣐⣦⣶⣴⣆⠠⣶⣞⣻⣧⣽⣿⣿⣿⣿⣦⣀⢦⣶⣦⣴⣖⣎⣛⣿⣿⣿⣿⣶⠿⣭⣉⢦⣸⣇⣉⠿⠿⠯⠀⠂⠉⠉⠁⠀⢹
⠿⠿⠿⠿⠷⠦⡀⠰⠀⠈⠀⠈⠋⠀⠀⣀⡀⠀⠀⠀⠀⠤⠀⠀⣀⠀⣀⣸⣯⡻⠿⠿⠛⠛⠱⠃⠙⣦⣁⣿⣟⣿⣿⣿⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠈⠙⠛⠋⠀⠀⢻⣤⣤⡶⠀⢁⣀⣲⡢⠀⢸
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢐⣢⣤⡀⡔⠒⠒⠢⣭⠉⠀⠈⠉⠑⠒⠒⠀⠀⠀⠀⠈⢛⡻⣿⣿⣿⣷⣤⠀⠀⢰⣶⣾⣶⠿⢛⣻⡿⢟⣃⣩⣿⣿⡅⠀⠀⠀⠀⠀⠀⢀⠃⠉⠁⠲⣎⠉⢸⣷⣶⣾
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣇⣤⣴⣴⣦⣀⣁⣶⣤⣴⣶⠀⠄⠤⠴⠶⢶⣿⡇⠂⢼⣳⣿⣿⠐⢶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⣻⣇⠀⠁⡰⠀⡀⠀⠀⠀⠀⠀⠀⠰⡾⡇⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠈⠀⠀⠀⠹⠿⠟⠛⠈⣛⠿⠿⠿⠂⢹⣿⣟⡤⠀⠀⠀⠀⠀⠓⠂⠀⠉⠀⠀⠀⠀⠀⠉⢡⣥⡟⣻⣌⡛⠋⠉⠟⢛⠻⢿⡯⢿⣇⡀⠙⠛⣓⣄⣠⡄⠀⠠⠀⠀⠀⠀
⠀⠀⠀⢀⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣯⣴⣶⣶⡾⠛⠁⠀⡀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠐⠻⣿⡇⠀⠀⢰⡿⠷⢶⣶⣿⣽⣤⣼⣷⣖⣤⣀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⣀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠙⢚⣷⣴⡶⠆⠀⠛⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠉⠻⠿⠷⣉⢁⣀⡄⠀⢈⠀⠀⠀⢶
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠠⡀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠁⠠⣀⣀⣀⡀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⡓⠈⠀⢀⢔⠶⣾⣼⣿⣙⣿⣿⣯⡍⡤⣼
⡤⠤⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠉⠁⠈⠀⠈⠉⠀⠀⠠⣀⣴⣤⣴⡀⠀⠀⠀⠠⠐⠐⠂⠀⠀⠀⠀⠚⠚⢿⣿⣿⣻⣯⣻⣿⡿⢅⠛⠛
⠀⠾⠿⠿⢺⡿⠿⠿⡿⠣⠹⠟⠿⠻⠏⢇⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⠀⣀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠈⠈⠁⠀⢠⣀⡤⠤⡤⠙⠋⣹⠦⠆⠀⠊⠉⢩⡏⢿⣊⠉⣻⣿⣶⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠳⣶⣶⠀⠉⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣿⣿⣿⣿⣿⡯⠀⠀⠀⣤⣄⡀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⡿⠻⢿⣿⣥⣀⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠁⠀⠉⠙⠛⠛⠙⠐⠀⠀⠀⠀⠘⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⡛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⠿⣿⠿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣶⣾⣿⣿⣿⡟⠛⠛⠛⠛⠋⠀⠀⢨⣿⠃⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠋⠙⠋⠉⠉⠛⠻⢿⣿⡿⣿⣿⡿⢿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⡀⠀⢀⣀⠉⠉⠙⠛⠛⠚⠿⠿⠦⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹⠀⠀⠀⠇⠀⢸⣿⠀⠀⠠⢀⣀⠀⠀⢰⣀⡀⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⡇⠀⢸⡇⠀⠀⠘⠻⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⢸⡅⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣾⣤⡆⢈⠁⠀⢸⡏⠀⠀⠀⠀⡀⠀⠀⠀⠃⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⡇⠀⠛⢿⣿⣿⣾⣦⡀⢹⡇⠀⠀⢀⣤⠃⠀⠂⠀⠀⠇⠘⢻⣟⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣠⣶⢶⣶⡀⣴⣶⣶⠀⣶⣶⣀⣿⣶⡀⣶⣶⢰⣶⡄⣶⣆⣴⣶⣶⣿⠎⢰⣶⡆⣶⣶⣶⣶⢰⣶⣿⣰⣿⣷⣶⣶⢶⣦⢰⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⢸⣿⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⡛⢛⣉⣿⣿⠟⠛⠛⠛⠛⣘⣛⡛⠛⠛⠛⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡻⡿⠛⣀⣀⣀⣤⣴⣿⣿⡃⢀⣀⣀⡀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⢷⣶⣿⣿⠿⠏⣿⣿⢿⣯⢸⣿⠿⢇⣙⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡇⢿⣿⣿⣿⡀⢿⣿⣿⠀⠀⣿⣿⣿⣿⣼⣿⣷⣞⣿⣧⣿⠇⣿⡧⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⢀⣠⣤⡀⠀⠀⠈⠛⣿⣿⣷⣌⢻⣿⡆⠀⢰⣄⠀⠈⠙⢢⡂⠉⢀⣬⢠⠀⡄⠀⠈⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣽⣿⡟⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣴⣿⠿⣿⣿⡇⣀⢀⣀⠀⠘⢿⣿⣿⣇⠉⠀⠀⣸⣿⣿⣀⠄⠀⠿⢿⣤⣟⠈⠀⡜⡿⣠⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡿⠿⠿⠛⠉⠀⣰⣿⣿⣿⣶⣾⡿⢂⣿⣾⣿⡷⠀⠈⣿⣿⣿⣷⡀⢀⡿⢻⣿⣿⡀⠀⠀⠰⠻⡿⡠⠆⠀⢿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣄⣤⣄⣀⣀⣀⡈⠁⠀⠀⠀⠀⣰⡏⠙⠉⠉⠁⠉⠀⠈⠀⠉⠋⠉⠀⠀⣿⣿⣿⡿⡇⠀⠃⠸⠠⠿⠿⡶⢁⣐⣂⣀⡀⠀⣶⣾⣿⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡬⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⠤⢀⣀⠀⢶⣿⣿⣿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣷⣴⣤⣀⠀⠀⠀⠀⠀⠐⠁⠀⠀⣧⣀⣀⢀⣄⣤⣤⣴⣦⠀⠀⠀⠀⠀⠈⠉⠀⠘⢿⡟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⡀⠀⠘⢖⣀⡂⢇⣷⣷⡂⠀⠀⠀⠀⠀⠀⠉⠿⠛⡹⢿⣧⣁⡈⠉⠄⠂⠀⠀⠰⠤⠤⠤⠄⠀⠀⠀⠙⠻⠿⠟⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠀⠤⠀⠀⠀⠀⢙⠛⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⠺⣾⣿⠿⠿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⣀⠀⡀⠀⠀⠛⠟⠛⢻⣿⣿⣿
⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠛⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡂⠠⠿⠀⠀⠀⠀⠂⢀⡀⠄⢀⡀⠲⠲⠀⠀⠀⠂⠥⠤⣀⢘⣽⣿⣟⣿⣿⣷⣉⣥⠀⠒⣿⣿⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣬⡵⠶⠶⠶⠶⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⡆⠈⠁⠀⠈⠉⠿⢷⣊⣤⣦⣀⣴⣄⡀⢀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣥⣴⣶⣦⣼
⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⡏⣹⣅⠀⠀⢀⣀⣀⣘⣓⣾⡋⢀⣀⣀⠀⠀⠀⠈⠉⠓⠂⠀⠀⠀⣀⣘⣿⣧⣤⣰⣤⣴⠖⠚⠛⠋⠈⣣⣤⣭⣿⣿⣿⠛⢛⣛⣿⣟⡿⠿⣿⣿⣿⣷⠛⣘⣻⣾⣻
⠀⠀⠀⢠⣶⣶⡶⣖⡰⠠⠺⠿⠟⠻⠻⡣⣶⡶⡻⠙⠛⠃⠀⢀⠉⠈⠉⠹⠿⡷⠶⠾⡶⢿⣷⣆⣶⣶⣶⣶⡀⢶⣾⣻⣷⣼⣿⣿⣿⣿⣦⣄⢠⣶⣦⣤⣿⣿⣛⣿⣿⣶⣾⣿⣯⣿⣿⣶⣀⣽⣉⣻⣿⣾⣋⠉⠙⢿
⠿⠤⠂⠀⠋⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠒⠃⠳⠤⠤⠤⣤⣀⡨⣭⣍⣿⠿⠟⠛⠋⠉⠘⢳⣄⢽⣿⣿⣿⣿⡞⠿⠟⠛⠿⠛⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⡟⠛⠛⠻⠛⠛⠈⠻⣧⢄⣠⣤⠙⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣤⣤⣤⡀⠚⠛⠛⢦⣭⡄⠈⠉⠀⠒⠒⠂⠀⠀⠀⠀⠙⣻⢿⣿⣿⣿⣤⡀⠀⢠⣶⣶⣿⣿⠟⡛⣿⣛⠛⠉⣯⣿⣗⠀⠀⠀⠀⠀⠀⠀⢭⡍⠛⠓⢤⠖⢺
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⢿⠿⢿⣿⣿⡿⣷⣶⣶⣶⣶⣤⣤⣶⣶⣶⣿⠀⠐⠰⠴⠶⠶⣿⣿⠢⠖⣿⣾⣿⡒⠶⣾⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣽⣾⠂⠀⠂⠀⠀⠆⠀⠁⠀⠀⠀⠈⢉⣾
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠁⣉⣿⡿⠟⠟⠨⣿⣟⠳⠄⠀⠀⠤⠀⠘⠊⠀⠈⠁⠉⠉⡀⢀⠚⠛⣏⣾⢛⣧⡛⠿⠛⠿⠻⠿⢿⣖⡚⣷⠀⠑⣒⢦⢄⣀⣀⡀⠈⣛
⣰⢤⡔⠄⠀⠀⠠⠹⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⣾⣾⠋⠁⠀⢀⠀⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠽⠍⠘⣿⣿⡄⠩⠠⣶⣷⣦⣭⣴⣮⣭⣄⣿⡿⢍⡉⠉⠁⠀⠈
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠰⢤⠄⠀⠁⠀⠉⠁⠀⠀⠀⠀⠉⠉⠙⠓⣻⣦⠶⠶⠀⠘⣳⠆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⠈⠉⠀⠀⠉⠉⠙⠿⢿⣿⡾⠋⢉⣀⠀⠀⢰
⠠⠤⠦⠶⠶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠶⠤⠐⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠋⠀⢄⣀⣀⣀⠀⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠝⠀⠂⠀⡠⢤⣬⣿⣿⣿⣣⣴⣿
⠀⠠⠀⠒⠂⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠉⠀⠁⠀⠉⠀⠀⠀⠄⢀⡆⣠⡄⠀⠀⠀⠀⡀⠅⢤⠀⠁⠀⠀⠰⡗⣾⣿⣿⡿⣿⣻⣿⣿
⠀⠸⠏⠹⢸⡿⠿⠿⡿⠣⠻⠟⠿⠻⠏⠇⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⣀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⡀⢀⣀⣄⡐⠶⠒⣆⠰⠐⠠⠐⠓⣞⣿⣿⠿⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣯⢠⣤⣤⡀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⢛⡹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣗⠀⠀⠀⢉⠙⢓⣀⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠛⠛⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠺⢿⣿⣶⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠛⢿⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠙⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⣶⣿⣶⣿⣿⠛⠛⠿⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⠛⠋⠛⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢴⠖⠀⠖⣾⠷⠸⠷⠶⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠣⠀⠀⠙⠄⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠇⠀⡀⢀⣀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠄⠀⢿⡿⠁⠀⠀⠀⠿⣿⣶⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡄⠀⢨⡇⠀⠀⠀⠀⠀⣶⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⣶⠀⡇⠀⠀⠀⠀⢼⣿⣿⣿⣷⣄⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⡀⣀⡀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠻⣼⣿⣿⣴⡄⠸⠀⠀⠀⠈⠀⠙⣿⣿⣿⣦⡀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢤⣶⢶⣶⡶⣶⣶⣶⠀⣶⣶⠀⣶⣶⠀⣶⣶⢰⣾⡟⣷⡆⣴⣶⣾⣍⢉⢵⣶⡆⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣼⣿⢿⣯⢹⣿⣶⡆⣶⣶⠀⣶⣶⣶⠀⠀⢀⣠⣶⣴⣾⣶⣶⣶⣶⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣧⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⢾⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣿⣿⣿⠿⡿⠟⠛⠛⢛⣛⣿⡿⠛⠚⠛⠛⠛⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣤⣤⣴⣶⣶⣾⣿⣿⣛⣁⡀⢀⣀⣀⡀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡿⣿⣿⢶⣿⣶⣦⣿⣿⠿⠏⣿⣿⣿⣯⢸⣿⠿⢇⣹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢻⣿⡟⣿⣧⢿⣿⣿⣿⠹⣿⣿⣿⣿⡆⣿⣿⣿⣿⣸⣿⣷⡾⢿⣧⣿⡇⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⣀⣠⣤⣤⡄⠀⠀⠊⠘⣿⣿⣿⣦⠹⣿⣿⣿⡇⠀⢠⡄⠈⢱⣤⣦⠒⠒⠉⠁⠀⠀⠀⠀⢶⣟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠟⠛⠋⠛⠛⠛⠟⠿⠿⡿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⠆⠀⣄⣄⠀⠻⣿⣿⣷⡈⠻⢿⣿⣧⠘⠃⠀⠘⠛⢷⣤⣀⣿⡇⠟⠰⣂⡄⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⠿⡴⣾⣿⣿⡆⠀⠘⣿⣿⣿⡆⠈⣿⢁⣶⣶⢀⡀⠰⣿⣿⡭⣿⡗⢠⠈⢹⣵⣿⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⢀⣠⣀⡀⠀⠀⣀⣴⣶⠀⠀⢀⣀⡀⠈⠀⠁⠀⠁⠘⠁⠈⠈⠉⠑⠀⠀⠉⠋⠙⠻⠂⠈⠀⠈⠀⠀⠀⢰⣿⡟⣀⠙⠑⠨⠀⣼⣏⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣍⣠⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⣠⣀⣒⠂⠀⣀⣼⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢻⣿⣿⣿⣿⣿⣿⣶⣦⡶⠶⣤⡠⠀⠀⠀⢀⣀⣠⡴⠂⠀⠀⠀⢰⡂⠐⢻⣿⠋⠉⠐⠆⠉⠹⢻⣿⡟⠁⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠻⣿⣿⣿⣿⣿⢿⠋⠁⠀⠀⠀⠀⡀⡖⣫⠁⠀⠀⠀⠀⠀⠀⠪⢷⡀⠀⠉⠹⢿⣿⣆⣤⠿⠿⠉⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠘⠛⠧⠬⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠈⠛⠒⠚⠃⠀⠀⠀⠀⠈⠙⠃⠙⠋⣻⣿⡿⠛⠛⠈⠈⠃⠉⠙⠛⠛⢻
⣿⣿⣿⠿⠖⠒⠚⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡃⠀⠀⠀⠀⠐⠒⡋⠀⠀⠀⠀⠀⣀⣄⡀⠀⡈⣹⠓⠀⢀⣤⣤⣤⣤⣤⣤⣤⣸
⣿⣿⣽⢿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣐⣶⣦⢀⣤⣤⡤⠠⠶⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⠀⢀⡀⠀⠀⠀⠲⢶⣾⣿⠴⣋⣉⠏⣀⠀⠀⢰⣏⣉⣳⣤⣿⣿⣿⣿⣟⣿⣿
⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⢧⣖⣨⣅⠀⠀⢀⣀⣀⣸⣶⣶⡟⢁⣀⣀⡀⠀⠀⠒⠒⠤⠄⠀⠀⠀⠈⢹⣶⣄⣀⢀⣀⣀⣬⣭⢿⣿⠻⢟⣛⡳⢼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⢾⣿⣿⢿⡓⠀⠀⠉⠉⠋⣅⢿⣶⢷⡗⠓⠘⠁⠀⣀⠉⠉⠉⠹⣿⡷⡿⣿⣿⣶⣦⣤⣤⣤⣀⣀⢀⣀⣴⢶⣖⣺⣿⣿⣶⣿⣋⠁⢀⣀⡀⠁⢻⡿⣿⣾⣿⣿⣳⣐⠶⣿⣿⣿⠉⢹⣿
⠀⠀⠀⠰⠿⠿⠀⠓⠒⠂⠀⠀⠀⠉⠹⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠌⠛⠉⠒⠤⠄⢀⣀⣐⣘⣿⣻⣿⣿⡿⠿⠿⠿⠻⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣼⣿⣿⣿⣷⣿⣶⣽⣿⣿⣿⣿⣿⢿⣯⣭⣷⠾⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣭⣤⣤⣄⠛⠒⠂⣤⣭⡍⠉⠛⠉⠭⠭⠄⠀⠀⠀⠉⠳⢿⣿⣿⣿⣿⡃⠀⠀⢀⣉⣠⣟⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⠁⠀⠉⠉⠉⠀⢸
⠛⠛⠒⠒⠠⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⡿⠿⣿⣿⣿⣿⣴⣶⣶⣶⣄⣝⣶⣴⣴⣶⡔⠴⢤⣠⣤⣴⣾⣿⡩⢿⣿⣽⣿⣇⣀⣼⣿⣿⣿⣯⣭⣾⣿⣰⣶⣶⣿⣿⣷⡀⢀⠀⠀⠀⠀⠸
⣤⣤⠤⣄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⣛⣿⡿⠿⠿⢟⣿⡗⣄⡀⠀⠁⣻⠛⠧⠜⠛⠛⠛⠂⠘⠛⠛⡿⠿⡿⣻⣯⡍⣿⣿⣿⣿⣿⣿⣇⣀⣀⣔⠀⢉⢀
⠷⠱⠇⠀⠀⠀⠀⠀⠁⠙⠋⠀⠀⠀⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣵⣶⣿⣾⠟⠛⠉⡠⠀⢾⣬⠀⠀⠀⠀⠀⠂⠀⠰⠂⠘⠂⠀⢻⠚⣺⣷⣮⠟⢫⡙⡉⣭⡛⢻⠗⣻⣧⠤⢽
⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⢄⡀⠈⠉⠁⠙⠃⠀⠀⠈⠉⠉⠓⠶⡦⣦⣀⣀⣀⡀⢠⣄⣀⠀⠀⠀⠉⠉⠁⠻⣿⠃⣨⠀⢿⠿⠟⢿⣾⣷⣶⣶⣿
⠀⠀⠠⠤⠤⠤⠤⠄⠐⠙⢉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠖⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⢨⡙⠻⠛⠀⠀⠐⠚⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣈⠛⠻⢿
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠙⠛⠚⠃⠀⠶⠄⠈⠁⠒⠂⡀⠀⠀⠀⠀⠐⠂⠀⠤⠀⠀⢈⢁⠁⠀⢰⢾
⠀⠸⠯⠹⢸⡇⠿⠿⡧⠣⠸⠟⠿⠿⠏⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠠⠀⠴⠶⠀⠀⠀⠀⠁⠘⠷⠾⡗⠀⠀⠀⠀⠂⠁⢙⡀⠀⠀⠀⠀⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⡛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣮⡔⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣄⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠉⠉⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡉⠛⣓⣤⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣗⣀⠀⠸⠛⠃⠉⣩⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠛⠉⠯⠻⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠛⠛⠛⠋⠋⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠛⠻⠿⠛⠟⠿⠛⠻⠻⠿⢿⣿⣿⣿⣿⡿⣿⠿⠿⣿⢿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠀⠀⠀⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢠⡀⠀⠀⠀⠐⠒⠾⠿⠿⠿⠿⠦⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠓⠐⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⣆⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠘⠿⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠘⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠘⣿⣿⣿⠀⠂⠀⠁⠃⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⢶⣶⡔⣶⣶⣶⣂⣶⣶⠀⣶⣶⠀⣶⣶⢰⣶⡀⣶⡎⣿⣿⣶⣄⠀⣽⣷⡆⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⢶⣮⢹⣿⣿⡏⣿⣷⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣶⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⡟⢸⣿⣧⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢀⣼⣿⣿⣿⣿⣿⣿⢿⣿⢹⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠙⠛⣃⣛⣻⣿⣿⠟⠛⠛⠛⠛⠛⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣿⣿⣿⣿⣿⡿⣛⣀⣀⡀⢀⣀⣀⡀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⠿⣿⣿⣿⣷⣿⣿⣿⣿⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢶⣿⣷⣶⣿⣿⡿⠏⣿⣿⣿⣯⢸⣿⠿⠇⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⢻⣿⡟⣿⡧⢿⣿⣿⣿⠘⣿⣿⣿⣿⣷⣿⣿⣿⣿⣸⣿⣷⡞⢿⣷⣿⣏⣿⡟⣻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣤⣤⣤⣤⣤⠀⠀⠁⠙⢿⣿⣿⣦⡹⢿⣿⣿⣿⠀⠀⠀⠀⣿⣦⣰⡔⠊⠉⠁⠀⠀⠀⠈⠀⢾⣣⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⠛⠉⠉⠙⠛⠛⠋⠀⢠⣾⢿⡿⣿⣿⣿⣿⣃⢀⣦⣄⠀⠙⢿⣿⣿⣄⠻⢿⣿⣿⠀⠀⠀⠘⢿⣇⡘⢀⠀⢽⢸⠀⢟⣠⠀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢻⠟⢿⢟⣿⣿⣿⡆⠀⠈⣿⣿⣿⣦⠀⢻⠿⡿⠧⠀⠐⠚⣻⣷⣌⢵⡿⠊⡄⠀⢩⣾⣷⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⢀⣠⣀⣀⡀⡀⠀⢀⣠⣤⣤⣠⣠⡀⠀⠀⠈⠈⠉⠉⠈⠁⠀⠀⠉⠉⠉⠹⠇⠈⠁⠀⠀⠀⠀⠐⢿⠿⢛⡈⠊⠀⠃⢀⣼⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⣀⣐⡂⠀⢀⣠⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠒⠀⠚⣿⠛⠉⠁⠀⠈⠉⣻⣿⣿⡏⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠛⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠋⠀⣰⣾⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⢀⢿⣿⠿⠉⠀⣠⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⣤⣤⣤⣤⣿⡿⠿⢿⣿⣿⣿⣿⠿⠿⠻⠟⠻⠿⠛⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠛⠛⠋⠘⠙⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣙⢾⣾⣶⣦⠆⢀⠾⣿⣯⣃⣋⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣽⣿⣿⢿⡷⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⣀⣀⠀⠀⢀⣠⢤⠤⠠⠀⠂⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⢈⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣛⡉⠉⠉⢉⣿⣿⣏⢂⠀⢠⣀⣠⢤⣀⠀⠀⣀⣀⣀⣀⣒⣛⢁⣀⣀⡀⠀⠀⠐⠒⠂⠀⠀⠒⠛⠚⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠾⣿⣿⣿⣿⡯⡀⠉⠉⠍⠈⢔⡶⡿⠶⠏⠀⠉⠀⠀⠀⠈⠉⠩⠿⣿⠾⣿⣿⣾⣦⣤⣤⣤⣀⣀⣄⣄⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣤⣤⡀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠊⠙⠉⠗⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⢀⠂⠀⠘⠢⠤⠤⣄⣀⣐⣿⣽⣿⣿⠟⠻⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠉⠀⠀⣴⣶⣤⣬⣥⣴⣤⠋⠛⠻⣭⣽⡉⠉⠉⠻⠦⠭⠤⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⡏⠉⠋⠉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢻
⣿⣿⣉⡁⠉⠉⠉⠁⠀⠠⢤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠹⠿⢿⢿⣿⢿⢿⣶⣶⣶⣶⣆⣥⣶⣶⣶⣶⣦⣴⢤⣀⣠⣤⣶⣿⣏⣹⣿⣻⣿⣷⢀⣈⣿⣿⣿⣿⣿⣯⣿⣿⣯⣭⣩⣿⣿⣯⡂⠀⢸
⣿⣿⣿⣧⡄⠀⠀⠀⠀⢄⠀⡀⣀⣀⠀⠀⠀⠀⢴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠫⣻⣻⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⢙⠛⠃⠽⠿⠿⠿⠧⠬⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸
⣿⣿⣿⢟⢘⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣶⣾⣿⣿⣿⢿⣷⣤⣶⣭⣭⣀⠀⠀⠀⠀⠀⠀⠦⠀⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿
⠉⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⠜⠉⠛⠙⠉⠛⠉⠀⠈⠛⠻⠾⣿⣷⣄⣀⡀⠀⢀⣀⡀⠀⠀⢀⠈⠛⠙⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠀⠻⠻⠛⠛⠓⠊⠁⠀⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠿⠋⠟⡅⠀⠀⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢼⣿⣿⡿⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠉⠀⠀⠈⢹
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠛⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠉⠛⠛⠒⠒⠠⡄⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠐⠛⢺
⠀⠸⠿⠻⢻⡟⠿⠿⡧⠣⠸⠗⠿⠻⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠰⢴⣶⢶⡄⠀⠀⠀⠀⠀⠐⠂⠀⠈⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢛⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⣿⣿⣿⣿⣿⡥⡇⠲⠚⠿⠟⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⡀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠟⠇⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠋⠿⢿⣆⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣽⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠐⠿⠗⠘⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠤⠀⠀⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣿⣿⠛⡻⣻⣿⣿⣎⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⠀⠈⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠁⠀⠋⠈⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⠀⠀⠺⠿⠻⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠩⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠛⠛⠻⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠻⠿⠿⠿⠦⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⣿⢿⠋⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠀⠀⠀⢷⣶⣏⠁⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠅⠀⠀⠀⠈⢸⣿⣿⣦⣄⠀⠀⣿⣿⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⣿⣿⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡹⣿⣿⣿⣿⣧⡀⣿⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣤⣤⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⢰⣶⡄⣶⡆⣴⡶⣶⣄⠀⢰⣶⡆⣶⣾⣿⣾⣿⣿⣿⢹⣿⣿⣿⣿⣶⣦⢰⣶⣶⡆⣶⣶⠀⣾⣿⣿⠉⠉⠉⣁⣀⣀⡀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣶⣺⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡟⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣴⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⢀⣘⣿⣷⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⣿⣿⣿⣟⣛⡋⣀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣍⠙⣿⣿⣿⣷⣿⣿⣿⣷⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⢹⣿⣿⣿⣿⠏⣿⣿⣿⣯⢸⣿⠿⢇⣙⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⢸⣿⢸⣿⡟⣿⡟⢿⣿⣿⣿⣄⢻⣿⣿⣿⡇⣿⣿⣿⣿⣼⣿⣶⣞⣿⣿⣿⣧⣿⡧⣽⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢀⣴⣶⣿⣿⣿⣿⡄⠀⢀⠀⠉⢻⣿⣿⣦⡙⢿⣿⣷⣦⠀⢰⣿⣿⣻⣶⡼⡏⠉⠁⠀⠀⠀⠀⠀⠑⠫⣿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⠀⠠⠁⠀⠀⠙⠻⠿⣿⣷⢠⣿⣿⡄⠀⠙⣿⣿⣿⣌⣟⣿⣋⠀⠿⣿⣾⣿⠟⠁⠘⢄⣐⣿⡇⡗⠠⠇⣤⢀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠈⠟⠄⠀⠹⣿⣿⣿⣿⣿⣿⡄⣤⣾⣾⠇⠀⣰⣿⣾⠻⣿⡷⠃⠘⠔⣱⣿⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⢠⣤⣤⣤⣄⣄⠀⠀⢀⣴⣦⣤⣤⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠛⣛⠊⠢⠘⢀⣾⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⡇⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⠄⢀⣼⣿⣿⣿⣿⠅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⣿⣿⣿⣿⣿⣶⣤⡄⠀⠁⠐⠒⠚⠿⣿⣷⣶⣤⡄⠉⠹⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠋⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣷⣆⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠰⠿⠿⣿⠿⠿⣿⢿⣯⣦⣤⣤⡀⠀⠀⠈⠉⠈⠀⠀⠶⢾⣿⣿⡿⠉⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣉⣿⣿⣿
⣶⣶⣾⣿⣾⣤⣤⣤⣵⣶⣶⣾⣿⣿⣿⣟⣛⣛⡿⠿⠛⠛⠃⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠈⠂⠆⠀⠀⠐⠐⠾⠿⠿⠟⠉⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢹⠿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠟⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣦⣤⣤⣄⡀⠀⠀⠄⡢⢀⠀⠀⠀⠐⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠠⢹
⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⡀⢠⣿⡷⠀⠀⢀⡄⢄⡠⢤⡀⠀⠀⣀⣀⣀⣀⢰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠘⡿⣿⣿⣿⣶⣀⠉⠉⢘⡕⠹⠾⠷⠌⠀⠈⠁⠀⠀⠀⠉⠉⠹⢿⣥⣖⣽⣥⣤⣠⣄⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠋⠉⠋⠁⠀⠀⠀⡀⠀⠀⠘⠒⠀⡀⠒⠀⠲⠤⠤⢤⣀⣀⣘⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿
⣤⣤⣤⣤⣤⣤⡤⠶⣿⡿⣿⠿⠳⣶⣤⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⡄⠃⠀⠘⣶⣶⣦⣶⣶⣶⣶⣿⡟⡻⣿⣿⣿⠛⠻⣻⣯⣭⡍⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣆⠀⠀⠀⠀⠈⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⣀⣀⣀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⡾⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡟⠟⠁⠀⠀⠀⠀⠄⠤⣤⠄⠀⠀⢐⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⡿⣟⢿⣿⣿⣿⣿⣿⣿⣾⣿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠻⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠉⠛⣯⣥⣽⣿⣿⣿⣿⣿⣤⣤⣴⣷⣾⢈⠉⠙⠙⡿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⣀⣀⣀⣀⣀⡀⠤⠶⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡄⠿⠿⠟⠛⠛⠋⠄⠘⠿⢿⣿⣿⣯⣟⡀⠀⠀⠀⠀⠘⠛⠋⠉⠙⠽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠀⠀⠀⠀⠀⠀⠸⠀⠄⠈⠛⠛⠑⠛⡃⢀⢰⣦⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⣿⣿⣷⠷⠀⠙⠛⠓⠂⠀⠀⠀⠀⠀⠈⠻⢿
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠈⠉⠛⠻⣿⣯⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢘
⠀⠸⠏⠹⢸⡟⠿⠿⡧⠣⠸⠟⠿⠻⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⢈⠁⣦⣀⡀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠉⠉⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣄⡀⠀⠈⠉⠉⠉⠀⢹⣿⣿⣿⣿⣷⣶⡆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠻⣿⣷⣆⣀⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⡤⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠟⠿⣿⣿⣿⠃⠀⢀⡀⠀⠀⢀⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠈⠛⠂⠀⣼⣿⣦⠀⠸⢿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠌⢋⠉⠉⠛⠐⠁⠀⠀⠉⠙⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠤⣤⠀⢴⣦⢀⣸⣿⡟⠀⠀⣀⠼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠨⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠉⠙⠛⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠼⠿⠿⣿⣷⣤⣤⣄⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠟⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠀⠀⠀⢳⣶⣤⣀⠀⠀⠀⠀⠀⣽⣿⡟⠀⠁⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣨⣽⣿⣿⡄⠀⠀⠀⢺⣿⣧⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⠀⠀⠀⣼⣿⣿⣿⣿⣾⠀⢼⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡡⢿⡿⣿⣿⣿⣶⣀⠀⣿⣿⣿⣿⣿⡟⠀⣿⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣵⢸⣿⡇⢸⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⡦⣶⣶⣶⣶⣶⣆⠀⢰⣶⣦⣾⣿⣷⣾⣿⣷⣶⢰⣶⣾⣽⣿⣿⣯⣹⣿⣿⡖⣿⣿⠀⣶⣶⣶⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣾⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣤⣶⣶⣶⣤⣤⣤⣤⣤⣴⣴⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠉⢹⣿⡏⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢴⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⣘⣿⣷⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣼⣿⣿⣿⣿⣿⣿⣟⣃⡀⢀⣀⣀⡀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣍⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠛⣳⣿⡏⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠉⣻⣿⣿⣿⡏⣿⣿⢿⣯⢸⣿⡿⠇⣹⣿⣷⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢸⣿⣸⣿⡟⣿⡷⠿⣿⣿⣿⣷⡜⣿⣿⣿⠄⣿⣿⣾⣿⣼⣿⣷⡞⢿⣷⣿⣿⣿⣇⣹⣿⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣠⣴⣾⣿⣿⣿⣧⡀⠀⣄⠈⠙⢿⣿⣿⣮⢻⣿⡆⠀⠀⠀⠈⣿⣿⢳⣶⣶⡟⠛⠋⠉⠉⠀⠉⠀⠈⠲⢢⡶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣷⠂⠀⠛⠳⠀⠈⢻⣿⣿⣧⡻⠟⠀⣠⣤⡀⢘⣣⣿⡿⠃⠑⣀⠠⣿⣿⠀⢶⡤⢀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⠉⠘⠋⠀⠀⠀⠀⠀⠀⠈⣉⣉⣩⣥⡀⠀⣸⣿⣷⡾⠛⠋⠀⣠⣾⡟⢻⣿⣿⡄⠀⢡⢫⣶⣦⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣵⣶⣿⣿⣿⣿⡇⠀⢹⣿⡿⠟⠛⠉⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⣿⡿⠿⠄⠀⣈⣽⡿⠁⠀⠀⠀⠛⠿⠿⠃⠹⢟⠀⠀⣰⣿⢿⣿⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣷⣦⡀⠈⠉⠁⠀⠠⠤⠠⠤⠬⠭⠭⠤⠈⠀⠀⠁⠁⠸⣾⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠐⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣋⣉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⡉⠉⠁⠀⠈⠙⣀⡀⠙⠿⣿⣿⣿⣿⣿⢿⠿⠋⠀⣰⣾⣿⡿⣿⠿⠿⠿⠿⢿⣿⣿⣶⣦⠀⠀⠀⡀⠀⣀⣀⣀⣀⠀⣠⣿⣿⠟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣶⣤⣶⣾⣿⣿⣿⣿⣿⣛⣃⡂⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠘⠺⠿⣿⣿⡿⠿⠟⠛⠁⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⡿⠃⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡿⠿⠍⠉⠈⠈⠉⠉⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⠿⣟⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠀⡀⠀⠀⠀⠈⠀⠀⠀⣠⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⣚⣓⡠⠄⠈⠛⠛⠛⠂⠀⠀⠀⢹⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠿⢿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⢼⣿⣿⣷⣀⣀⣀⠀⢠⣶⣿⣿⣿⠛⠻⣦⠄⠀⠐⠒⠶⣶⣶⣦⣠⣴⢴⣄⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣖⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠛⠁⠈⢙⣿⣣⣤⡄⠀⠛⠤⠤⢄⣀⢘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠋⠉⠉⠈⠀⠀⣤⣴⣶⣶⡶⣶⢶⢛⣻⣛⡛⠛⠻⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⡐⠞⠿⣿⣿⣿⣤⣶⣤⣤⣤⣶⣿⣿⣿⣿⡟⢿⣿⣿⡿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠶⠶⢶⣆⣀⠀⠀⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣾⣿⣿⣂⣀⡉⠘⠒⠒⠂⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⢸⣿⣿⣿⣤⠐⠛⠛⠛⠛⠛⠛⠻⢿⢿⣿⣿⠿⠿⠉⠀⠁⠁⠂⠀⡤⣤⡆⠀⠀⠐⠿⣿⣦⡀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠶⠴⠆⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⣉⣛⣿⣿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣄⣀⠴⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣨⣿⢿⣿⣿⣿⣿⡿⢿⣶⣶⣾⣿⣿⡂⠀⠀⠀⠉⣿⣿⣇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠗⢒⠀⠀⠀⢀⣀⣀⡀⠀⠈⠉⠋⠀⠀⠀⠀⠈⠁⠀⠈⠉⠛⠛⠿⣿⣷⣄⣀⡀⠀⢀⣈⡛⢺
⠀⠤⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢽⢿⣿⡻⠋⠀⠉⠉⠉⢸
⠄⠿⠿⠹⢺⡿⠿⠿⡿⠣⠸⠗⠿⠛⠇⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⡀⠀⠈⠀⠹⠿⠷⠶⠤⢄⣤⣠⣺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢿⣿⣿⡗⢿⣿⣿⣿⣿⣿⢍⡙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⣤⣤⣄⠀⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠋⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣈⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⡠⠛⠋⢰⣾⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠋⠘⠻⠿⢿⣿⣿⡟⠀⠉⠉⠻⣿⡇⠀⢀⣶⣄⠀⢰⣾⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠻⡻⠿⣿⠷⡂⡀⠀⠙⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⡀⠀⠀⣀⠀⠺⣿⣿⠂⠀⠙⢻⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠈⢻⣆⠐⢻⣿⠀⠀⠒⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠈⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠻⠿⠿⢿⠿⠿⠿⠿⠿⠻⢿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⢹
⠿⠿⠿⠿⠿⠶⠿⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣧⣤
⠀⢀⣤⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⡄⠀⠀⢀⣤⣄⠀⠈⠉⠉⠉⠛⠛
⣾⣾⣿⣿⣷⣶⡌⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠀⠀⠀⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠠⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣀⣭⣭⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠄⠀⠀
⠀⢹⣿⣿⣿⣿⣿⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⡲⠀⣾⣿⠁⠀⠀⠀⣼⠅⠀⠀
⠀⠀⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⢿⣿⣿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⢀⠀⡀⣀⣀⣤⣠⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⢸⣷⡟⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⣀⣀⠀⢸⣿⣿⣿⣿⣿⡀⠀⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣠⣶⣶⣴⣶⣦⣶⣦⣶⣶⣶⣆⣄⣰⣶⣶⣿⣷⣾⣿⣷⣶⣶⢰⣶⣾⣹⣿⣶⣦⢸⣿⣿⡆⣾⣿⠿⣿⣿⣿⠷⣀⣿⣟⡀⡀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣤⣿⣿⣤⣤⣤⣤⣤⣖⣛⣀⣀⣀⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⡏⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢶⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣛⡛⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠈⠻⢿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣁⣀⡀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠛⢳⣿⡟⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⠘⣿⣿⣿⣿⣟⣿⣿⣿⣯⢸⣿⣿⠇⣙⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢹⣿⢸⣿⡝⣿⡧⠿⣿⣿⣿⣦⡝⣿⣿⣿⣿⣿⣿⣻⣿⢼⣿⣷⡜⢿⣧⣿⡇⣿⣟⢻⣿⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢀⣤⣶⣿⣿⣿⣧⡀⠀⣀⠉⠹⣿⣿⣷⣌⢻⣿⣿⣿⣷⡀⠀⠈⢻⣷⣦⣴⡛⠗⠚⠛⠛⠀⠘⠃⠀⢠⡶⣢⢄⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⠆⢰⣿⣧⡄⠘⢿⣿⠿⠟⠻⣿⣿⣿⣿⣧⡄⠀⠸⠿⠇⠳⡀⠀⣤⣤⡤⢠⣤⠀⠀⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣷⠀⠀⠁⠀⠀⠀⠉⠿⡯⠛⢿⡇⠀⠀⠀⠀⠀⢿⣶⣿⣿⡇⠈⠉⡰⣫⣶⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⠀⠀⣿⣿⣿⢿⠿⢏⣁⣠⣿⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⢠⣿⣧⡀⠀⠁⠀⠀⠀⠀⠀⠹⠇⠻⡿⠃⠀⠈⣴⣿⣿⣿⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡿⠀⠈⠿⢿⠁⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⡘⠂⠀⠘⠁⠀⠈⠿⠇⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣾⣿⣯⣄⣀⣶⣶⣶⣄⣠⣦⠀⠀⠠⠦⠄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⡙⠙⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠙⠿⣿⣿⣿⣿⡿⠿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢶⣶⣶⣦⣦⠀⣀⠀⠀⠀⠂⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣿⣦⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠘⠛⠋⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⢿⡿⡿⠉⠉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿
⣋⣉⣫⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣫⣿⣿⣿⣿⣿⠟⠙⠙⠉⠛⠛⠛⠈⠉⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣉⡁⠀⠀⠀⠀⠠⠀⠺⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⢿⡿⢿⡿⣿⣿⠿⢿⣿⣛⣻⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⠛⠛⠛⠛⠛⠓⠀⠈⣴⣿⣷⡷⠀⠀⠛⠛⠛⠿⢦⣀⣀⡀⠀⠘⢿⣯⣿⣿⠛⠻⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢁⣀⣀⣈⠉⠉⠉⠉⠉⠛⠿⢷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠠⣝⣿⣶⣀⣄⣴⡀⠂⢂⣹⣿⣿⣷⣶⣶⣆⡀⠀⣀⣀⣈⠿⠷⠷⠒⠀⠀⠉⠉⠉⠀⠀⠀⠀⣹⣿⣿⣿⣿
⠀⠀⣀⣀⢉⣿⣿⣿⣿⣿⣿⣷⣶⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⢿⡿⠿⠟⠗⠘⠿⡿⠿⠋⠀⠀⢹⡇⠀⠀⠀⠉⣿⣿⣿⣤⣾⣻⣳⣄⣀⣀⠀⠀⠀⠀⠀⠉⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣟⡻⠋⠁⠀⠀⠀⠀⠀⣤⣶⣶⣶⢶⠖⠂⣚⣛⠛⠛⠛⠶⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢴⣷⣾⣷⣿⠀⠉⠁⠀⠐⠒⠠⣬⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣮⣲⠶⠶⢶⣄⣀⠀⠈⣉⣉⣹⣿⣿⣿⣿⣿⣿⣏⣁⣀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠷⠖⠉⣑⣿⣿⣿⣿⣿⣿⣶⣾⡟⠛⠻⣟⣿⣟⠉⠿⣿⣿⠿⠟⠋⠛⠿⢿⣿⣿⣿⣿
⠉⠁⠀⠈⠋⠈⠉⠀⠀⠀⠀⠸⣿⡿⣿⡤⠀⠙⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⡟⠛⠃⠀⠘⠀⠀⢀⣀⣤⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠻⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣉⣉⡙⠁⠀⠀⠀⠙⠻⣿⣿
⣦⣦⣀⠀⠀⠀⠀⠀⠐⠒⠛⠓⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠶⠶⣶⣾⣿⣿⣿
⣿⣿⣿⣧⣄⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣀⣁⢿
⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠷⠦⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡾⠿⠻⠿⣿⣿⠿⠟⣿⣿⣷⢶⢮⣯⢸
⣶⣷⡶⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⢀⠀⠀⠀⠈⠁⠁⠀⠈⠉⠛⠁⠀⣐⣶⣦⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⣿⣾
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢟⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠈⢿⣿⣿⡧⢿⣿⣿⣿⣿⡷⠚⠟⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢤⣤⣤⣀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠻⠛⠀⠀⠘⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢘⠛⣻⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⠛⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠙⠿⠿⠿⣿⣿⣿⠈⠉⠙⠿⣿⡏⠀⠀⣤⡀⠀⢠⣾⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡟⠽⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⣀⠀⠸⣿⣿⠇⠀⠙⢻⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⠛⠛⠿⠋⠀⠙⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠐⢛⣦⠐⢿⣿⠀⠀⠂⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠉⠻⠿⠿⣿⠿⠿⡿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣧⡄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹
⠿⠿⠿⠿⠿⠿⠭⠥⠤⠴⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣤⣄⠀⠠⢤⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⣀⣀⠈⠉⠉
⣷⡶⠿⢿⣶⣶⣹⣿⣶⣦⣌⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡲⠀⠀⠀⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠰⣨⣬⣭⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀
⠉⠉⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣴⣄⡄⠀⢸⣿⡇⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠉⠁⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠤⣿⢻⡏⢿⠿⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⡌⠀⣾⣿⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⡀⠀⠀⠀⠀⣀⡀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡄⣿⣿⠇⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠂⠀⣿⣿⠀⠀⠀⠀
⣤⣤⣤⣄⣀⡀⠀⠀⢀⣀⣀⣰⣯⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢰⣶⣦⣶⣶⣶⣶⣶⣦⣤⣴⣶⣾⣿⣶⣿⣿⢰⣶⣶⢰⣶⣾⣹⣿⣶⣦⢰⣶⣶⡆⣾⣿⣿⣷⣾⣿⢿⣿⣿⣿⣆⣀⣿⣿⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⠻⣿⣿⣿⣸⣿⣧⣄⣿⣿⣿⣿⣿⣤⣤⣤⣀⣀⣀⣀⣀⣠⣐⣒⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⡏⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢶⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢛⠛⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠈⠻⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⡀⣀⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠛⢳⣿⡏⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⠇⣙⣿⣷⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⢸⣿⡝⣿⡇⠿⣿⣽⣿⣷⡟⣿⣿⣿⣿⣿⣿⣺⣿⢸⣿⣷⡌⢿⣧⣿⠇⣿⣏⢻⣿⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣤⣶⣾⣿⣿⣷⡀⠀⣀⠈⠙⢿⣿⣷⣮⢿⣿⣿⣿⣷⣶⣤⠀⠘⣷⣢⣴⡛⠷⠚⠛⠛⠀⠛⠀⠐⣤⣶⢦⡄⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿⣿⣿⣟⡅⢀⣿⣷⡄⠈⢿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⠃⠀⠈⠛⠣⡀⠀⣤⣤⣤⢤⣤⢀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⠟⠀⣼⣿⣿⣿⡄⠀⣿⣿⣿⠁⠙⡋⠛⠉⠋⠋⠀⠀⠀⠀⠀⠑⣶⣿⣿⡇⠈⠉⣸⢻⣶⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣹⣉⣍⣽⠿⠏⠁⢠⣾⣿⣿⣿⣿⡇⠀⠹⣿⣅⡀⢀⢐⣶⡀⠀⠁⠀⠀⠀⠀⠀⠠⠍⠿⡿⠋⠀⢈⣰⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣵⡽⢰⣿⣟⠁⠀⠀⠀⣀⠀⠀⠀⣐⣂⣀⡘⠀⠀⠈⠁⠈⠙⠙⠛⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⣿⣿⡿⠁⠀⣉⣷⣄⣠⣦⠄⠀⠤⣶⣶⣶⣿⣯⣥⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠈⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⡉⠉⠉⠉⠉⠉⠁⠀⠉⠛⠉⠉⠹⢿⣿⠿⠋⠁⣠⣾⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣀⣰⣿⣿⣷⠆⠀⠀⠀⠀⠀⠸⣶⣶⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠘⠛⠛⠻⠿⠿⠿⠟⠿⠟⠿⠻⠿⠿⠛⠀⠀⠀⠙⠻⠿⠛⠻⢿⣿⣿⣿⠿⠃⠀⠀⣼⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿
⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣭⣅⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣉⢉⣿⣿⣿⠿⠿⠏⠉⠉⠉⠙⠋⠁⠈⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣉⣛⡳⠂⠀⢠⡻⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⠿⠿⠿⠟⠟⠟⠿⣿⣿⣻⣛⣛⣛⣻⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠿⠿⢾⣦⣤⣠⣿⣿⣿⡿⠄⠀⠶⠶⢶⣾⣆⣀⠀⠈⠈⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⠉⠉⠉⠁⠀⠀⠀⠀⣀⣀⣄⣉⣉⠉⠉⠉⠙⠻⠧⢤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⢹⣿⣯⣷⡴⠬⠙⠿⠿⠿⠟⠀⠈⢹⣿
⠿⠿⠿⣀⣀⣀⣠⣄⣀⣸⣿⣿⣿⣿⡿⠯⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣿⣿⠿⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⢷⣶⣦⣄⣤⣤⣤⡀⠀⠀⠀⠛⠿⢿
⣴⣶⣶⣿⣿⣿⣿⣿⣿⣦⢿⡻⠛⠋⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⢶⣾⣿⣿⡛⠛⠻⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠁⠉⣿⣿⣿⣿⣿⣿⣿⠋⠁⠰⣤⡀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣼
⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢾⡗⠄⠒⠛⢻⣦⣀⡀⠀⠉⢉⣹⣿⣿⣿⣿⣿⣿⣍⣁⣀⠀⠀⠀⠀⡀⠶⠦⠀⠀⠀⠀⢀⠀⠀⠀⠿⣿⣿⣶⣾⠿⠿⢿⣿⣿⣿⣿⣶⣶⣶⣶⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿
⣿⣿⣿⣿⠋⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⡸⢿⡿⠿⠦⠀⠙⠛⠛⠉⠙⠻⢿⣿⣿⣿⣿⣿⣛⠛⠛⠻⠆⠀⢀⣀⣄⠀⠀⠀⣄⣄⡀⠀⠀⠁⠀⠀⠼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣛⡃⠙⠓⠲⠶⠤⠤⠼⢿
⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠁⠁⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠠⠭⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣼
⣿⣿⣿⠿⠿⠿⣿⣿⣦⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⠉⢹
⢉⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠁⠀⠤⢤⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⣿⣿⣿⣿⠿⣿⣶⣾
⣿⣿⣿⣿⡿⠛⣿⡧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠊⠈⠉⠙⢿⣿⣧⡠⣤⣤⣀⡀⠐⢲⠛⠛⠛⠉⠁⠉⠛⠛⠉⠀⠛⠻⢿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠣⠻⠟⠿⠻⠏⠇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⣿⣿⣿⣿⣿⠛⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⣿⣿⣿⣧⢿⣿⣿⣿⣿⡾⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢿⢄⣄⣀⣀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠉⠉⠁⠘⢿⣿⣿⣿⣷⠟⠓⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⠛⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⡘⠻⠃⣾⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠹⢿⣿⣿⣿⣿⣿⠉⠻⠿⢿⣿⡏⠀⠀⣄⡀⠀⢠⣾⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡟⢽⣿⣿⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣥⡄⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠈⠛⠀⢰⣿⣷⠀⠘⠛⢛⣻⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠬⠀⠀⠈⠛⠿⠿⠛⠉⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠆⠀⢿⡆⠠⣿⣿⠀⠀⠀⠚⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠻⠿⢿⣿⣿⣿⢿⠿⠿⠿⢻
⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸
⠽⠯⠭⠭⠭⠭⠭⠕⠐⠂⠒⣒⣀⣒⣶⣶⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣤⣤⠀⠀⢠⡄⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠠⠀⠀⠀⢀
⣠⣿⣿⣿⣷⡴⠿⢿⣶⣎⢸⣿⣧⣤⡘⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡲⠀⠀⢀⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠈⠀⠀⠀⠀⣿
⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢄⣭⣭⣭⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⢰⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡠⢄⠀⢸⣿
⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⢽⣿⣿⠛⣿⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠷⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣾⣿⡇⠀⠀⠀⠘⢿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⠀⠀⣿⣿
⠀⠀⢀⣀⣀⣤⣄⣀⡀⠀⠀⠀⢠⣶⢶⣶⣄⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣆⣶⣆⣶⣶⣶⣆⣀⣰⣶⣿⣷⣿⣿⣷⢰⣶⣶⢰⣶⣿⣹⣿⣶⣦⢰⣶⣶⡆⣶⣶⠀⣶⣾⣿⣿⠀⠹⢿⣿⣿⣿⣿⣆⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣸⣿⣧⣄⣿⣿⢀⣿⣿⣿⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣁⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⠛⠛⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⢛⣛⡿⣿⣿⣿⣿⣿⡃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡀⣀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣭⡙⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠛⢳⣿⡟⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⠸⢿⣿⣿⣿⡏⣿⣿⣿⣯⢸⣿⠿⠇⣹⣿⣷⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢹⣿⣸⣿⡟⣿⡇⠿⣿⣿⣿⣷⡟⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣜⣿⣧⣿⢇⣿⣏⢻⣿⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣤⣶⣿⣿⣿⣷⡄⠀⢠⠈⠙⢻⣿⣷⣮⢿⣿⣿⣿⣧⣤⣤⣤⡀⠀⢪⣴⠻⠗⠚⠛⠋⠀⠛⠀⠐⣤⡦⣤⡄⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⠃⢀⣼⣿⣿⣿⣿⣿⣟⠄⢀⣿⣿⣄⠀⢻⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠃⠃⠀⠠⣤⣤⡄⣤⣤⣀⡀⠈⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿⠛⠀⣼⣿⣿⣿⡄⠀⣿⣿⣿⣿⣦⣿⠟⠛⠀⡄⠀⠀⠀⠀⠀⠓⣖⣿⣿⠇⠘⠉⡽⣫⣴⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣶⣿⣶⣦⣶⣿⣿⣿⣿⣿⣯⠀⢸⣿⣿⣿⣉⣉⣀⣠⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⡿⠀⠉⣤⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⡿⠃⠀⠈⣴⣿⣿⣿⡆⠀⠹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣯⡀⣀⣰⡫⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⣀⠘⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣼⣿⣿⣿⡇⠘⠻⣷⣄⣤⣦⡀⠀⠤⣶⣶⣶⣿⣯⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⡉⠉⠁⠀⠀⠉⠙⠿⠏⠿⠿⠟⠉⠀⠀⠾⠿⣿⣿⣉⣀⣀⣴⣾⣿⣿⣿⣿⡄⠀⠿⣿⣯⣿⣿⣛⣓⣀⣰⣿⣿⣶⡆⠀⠀⣀⣀⡀⠀⠀⠀⠀⢰⣶⣤⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⢾⣦⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠙⠻⠟⠛⠛⠿⠿⣿⣿⠿⠃⠀⠀⣼⣿⣿⣿⣧⣤⣀⣄⣂⣻⣿⣿
⠿⣿⣿⣿⣿⠿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⢟⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠂⠀⠀⠀⠀⣽⣡⣀⣤⣿⣿⣿⣿⣿⣿⣿⡿⣍⣉⠩⣿⣿⣿⠿⠿⠋⠉⠉⠉⠉⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠁⠀⠠⣶⣿⣿⡿⠻⠛⠿⠿⠛⠗⢺⣿⣏⣊⣑⣉⣉⣧⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠷⢦⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⣈⣉⡉⠉⠉⠙⠛⠧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣶⣶⣦⣤⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣏⣉⡉⠉⠉⠉⠛⣿⣶⣶⣶⣈⡙⠿⣿⣿⣶⣿
⢿⣷⠜⠛⠟⠿⠻⣀⣀⣀⣤⣤⣀⡨⣿⣿⣿⣿⠯⠯⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⠿⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠒⠺⠿⣭⣭⣍⣀⣀⣀⣀⠀⠀⢸
⣿⣧⣴⣬⣥⣾⣿⣿⣿⣿⣿⣿⣭⣶⢾⡛⠋⠁⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⡶⣶⣶⣿⣿⠛⠛⢓⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠉⢹⣿⣿⣿⣿⣶⣿⡟⠁⠀⣤⡀⠐⠻⢿⣿⣶⣷⣿⣿⣶⣦⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠗⠶⠖⠀⠙⠉⣻⣤⣀⡀⠀⠉⣉⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⠀⠀⠀⢀⠰⠦⠄⠀⠀⠀⠀⠀⠀⠀⠸⣽⣶⣶⣤⣾⠿⢻⣿⣿⣿⣿⣧⣄⣀⣰⣯⣅⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⠿⠿⠿⠤⠈⠙⠛⠉⠁⠛⠻⣿⣿⣿⣿⣿⠟⡻⠛⠻⠶⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⠀⠀⠉⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⣄⣺⣿⣿⣿⠿⠛⠟⢿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⢨⡽⢿⠇⠀⠀⠀⠀⠀⠀⠁⠈⠉⠛⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣼
⣀⣀⣀⣸⣿⠿⠿⠿⠿⠿⠿⠿⡶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣗⣀⣀⣀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠨⣭⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⡡⢿⢿⣿⡿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠈⠀⠤⠙⠛⠓⣶⣶⡆⠀⣀⡀⠀⠀⠀⡔⠲⠖⠻⠛⠛⠻⢿⣿⢿
⠻⠿⠿⠿⢻⡿⠿⠿⡿⠣⠹⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠱⠿⣿⣿⡶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢹⣿⣿⣿⡁⣿⣿⣿⣿⣿⢍⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣃⣀⣀⡀⠀⠸⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠛⠛⠛⠃⢻⣿⣿⣿⢇⠤⢤⠤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⢿⣛⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⠈⣽⣿⣿⣿⠁⠀⠀⠀⠀⠈⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡀⠐⠒⢮⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⡏⠉⢿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢀⣿⣿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⠨⣿⣿⣿⣿⣷⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠉⠀⠀⠀⠀⠙⠛⠟⠃⠀⠀⠀⠈⠛⠇⠀⣼⣿⣤⠀⠻⠿⢿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠉⠉⠉⠉⠛⠛⠿⠿⠟⠁⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡄⢲⣦⠀⣹⣿⡏⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠨⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⢿⢿⣿⣿⣿⢿
⠛⠛⠛⢛⣿⣿⣿⣷⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸
⠀⠀⠀⠘⠛⠛⣛⣿⣿⣿⣿⠦⠦⠤⠤⠄⠀⠠⢤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀
⠀⠀⠀⠀⣀⣿⣿⣷⣆⠀⢿⣧⣀⡀⣸⣿⣀⡀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸
⠀⠀⠐⠿⠿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣙⣿⣿⣿⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸
⠀⠀⠀⠀⠚⠛⠛⠛⠛⠋⠉⠉⠉⠛⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡤⣰
⠀⠀⠀⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠙⠋⠉⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣿⣿⡿⣿⢿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⠁⠀⠃⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢠⣶⢶⣶⡀⣴⣶⣶⣀⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣆⣀⣰⣶⣟⣿⣿⣿⣶⢰⣶⣶⢹⣿⣾⣿⣿⣶⣦⢰⣶⣶⡆⣶⣶⠀⣶⣶⣶⠀⠀⣶⣶⣶⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣸⣿⣧⡄⣿⣿⠀⣿⣿⣤⠀⢀⣻⣿⣿⣀⢀⠈⠉⠉⠉⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡏⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠀⢘⣻⣿⣿⣿⣿⣿⣿⡟⠘⠛⠛⠛⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡷⢶⣤⣖⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⡀⣀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣉⡛⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠛⢳⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⠻⣿⣿⣿⣿⣇⣿⣿⣿⣯⢸⣿⠿⣇⣟⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⢸⣿⡝⣿⡧⠿⣿⣿⣿⣮⠻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣶⡞⢿⣧⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣴⣶⣿⣿⣿⣷⡀⠀⣠⠈⠙⣿⣿⣷⡝⣿⣿⣿⣿⣷⣄⣤⣤⡄⠀⠡⣶⠿⠗⠚⠛⠃⠐⠃⠐⠠⣶⡤⣤⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⠄⢠⣿⣷⡄⠈⢿⣿⣿⣿⡻⠿⣿⣿⣿⣿⡟⠀⠀⠀⠘⠄⠀⣠⣤⣤⣤⣤⡄⡀⠀⠙⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⢸⣿⣿⣿⣿⣿⡿⠋⠀⣾⣿⣿⣷⠀⠈⣿⣿⣿⣷⣄⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⢢⣺⣿⡿⠀⠛⠙⠿⣤⣦⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣉⣽⣿⣿⣿⣿⣿⣷⣴⣦⣴⣴⣾⣿⣷⠀⢸⣿⣿⣿⣿⣏⣀⣠⣟⣛⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠟⠁⠀⠀⠾⢿⣿⣿⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⡀⠀⠀⠀⣀⣀⡈⠃⠀⠀⢀⣀⡀⠀⠘⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⣾⣿⣿⣿⣿⣟⢿⣧⣤⣴⡦⠀⠀⢴⣶⣶⣾⣿⣥⡄⠀⣤⣾⣿⣿⣶⣤⠀⠀⠀⠁⠈⠈⠈⠛⠙⠛⠙⠛⢹
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠈⠻⠿⠟⠛⠉⠀⠐⠺⠋⠻⠿⠿⠏⠀⢀⡉⣻⣿⣿⣷⡀⠀⢿⣿⣿⣿⣿⣿⣂⣀⣽⣿⣿⣿⠿⠀⢀⣰⣶⣦⣄⡀⠀⠀⠀⠀⢀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣄⣀⣀⣀⣀⣀⠀⣀⣀⣠⠠⠦⢴⣿⣿⣿⣿⣿⡿⣿⡆⠀⠙⠿⢿⣿⡿⠿⠿⢿⣿⠿⠋⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⢸
⣿⣿⣿⡿⠿⣿⣿⢿⣿⢏⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⢀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣯⣁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣯⣉⣹⣻⣿⣿⣿⡿⢛⠛⠙⠛⠻⠟⠗⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣀⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣙⣛⡛⠛⠋⠀⠀⢰⣶⣿⣿⡿⠿⠿⠿⠿⠻⠟⣿⣿⣛⣟⣛⣋⣿⣽⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⣤⣤⣤⣤⣀⣀⣴⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿
⣿⣽⠅⠀⠠⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢤⣤⣤⣌⣉⣉⠉⠉⠙⠿⢿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⢠⣴⣶⣦⣀⣀⣍⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⢿⣋⣁⣀⡀⠺⢿⣿
⠉⠉⠀⠸⠘⠂⠛⠿⠿⠿⢇⣀⣀⣀⣤⣄⣠⣿⣿⣿⣿⣿⢿⠯⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⡄⠀⠀⠛⠛⠃⠀⠙⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠠⢤⣼⣿⣿⠿⠿⠓⠀⢹
⣿⣿⣷⣶⣾⣤⣤⣤⣷⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠋⠁⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠶⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠟⠟⠛⠉⠛⠻⣿⣿⣿⣿⣯⣽⣿⣿⡇⠀⠀⠈⢹⣿⣿⣶⣶⣶⣾
⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⡟⠫⠏⠛⢻⣿⣆⣀⠀⢉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠈⠀⠀⣀⣀⠀⠉⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣏⠀⠉⢑⣶⢤⣬⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠿⢿⣿⠷⠖⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⡿⢶⠦⠰⢤⡀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠉⠻⠿⠿⠻⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿
⣭⣭⣭⡍⠙⠿⠿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡟⠁⠀⠀⠈⠁⠀⢐⡲⣗⠀⡀⢸⣿⣿⣦⣄⠀⠀⠀⠀⠙⠟⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣈
⣿⣿⣿⣷⣤⣀⣀⣿⣿⠿⠿⠿⠿⠿⠿⣿⣶⡤⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣿⣿⣿⣿⣿⣿⢏⣁⣀⣤⣤⣄⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠛⠻⠷⠖⠚⠛⣟⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿
⠿⠿⢟⣿⣿⣿⣭⣽⢿⣿⣿⡿⠛⠛⠃⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣷⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⣿⣿
⠿⠿⠿⠿⢿⡿⠿⠿⡿⠣⠹⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠤⠄⠀⠀⠽⠟⠃⠀⠀⠙⠿⠿⡷⢴⣶⣦⣤⣀⠉⢱⠉⠉⠁⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣽⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⢻⣿⣿⡧⢸⣿⣿⣿⡿⠂⣀⡚⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠒⢶⣶⣤⣀⣈⣉⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣥⠚⠛⠉⠀⠀⠙⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣤⣌⣲⣾⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢸⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⡏⢹⣿⣿⣿⣀⣤⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠛⠿⠿⣿⣿⣿⠀⠘⠛⠻⣿⣏⠀⢀⣠⡀⠀⢠⣾⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠗⠈⠉⠛⠻⠻⠿⠿⠆⢀⣼⣿⠛⠉⠻⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢨⣍⠀⢸⣿⡿⠀⠀⠉⢩⣽⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠘⣻⡆⠐⣿⡇⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣖⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠓⠚⠒⠒⠒⠒⠂⠉⠉⠉⠉⠨⠤⠬⠽⠿⠷⠾⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣆⠀⢰⣆⠀⠀⢲⣶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣉⣻⣿⣦⣼⣿⣿⣶⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠇⠀⠀⢘⣛⣛⣛⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⡿⣿⠿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡞⠛⠛⠛⠛⠃⠀⠀⠈⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣧⣿⠀⠹⠁⢰⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣦⡀⣰⣶⣶⠀⣶⣶⠀⣶⣶⠀⣶⣶⢰⣶⡄⣶⣆⣶⣶⣶⣆⣀⢰⣿⣿⣿⣿⣶⣶⢰⣾⣿⣿⣿⣿⣿⣶⣶⣦⢰⣶⣶⡆⣶⣶⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣼⣿⣿⣿⣿⣿⣄⣿⣿⣀⣿⣿⣤⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⣤⣿⣿⠀⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠉⢸⣿⡟⣿⣿⣿⣿⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣿⣿⣭⣤⣤⣠⣄⣀⣀⣀⣠⣤⣤⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⣿⠛⠛⠀⢘⣻⣿⣿⣿⣿⡿⠘⠛⠘⠛⠛⠛⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⣀⣠⣾⣿⣿⣿⣛⠛⣁⣀⣀⣰⣶⣂⣄⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠹⣿⣿⣿⣿⣧⣿⣿⣿⣿⢹⣿⡛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⢿⣶⣿⣿⡿⠏⣿⣿⣿⣿⢸⣿⣿⣧⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⢹⣿⡛⣿⡧⢻⣿⣽⣿⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣧⣿⡏⣿⡟⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣴⣶⣶⣶⣆⠀⠀⡀⠉⠻⣿⣷⣜⢿⣿⣿⣿⣿⣷⠀⠀⠀⠿⠁⣤⣿⡿⠗⠛⠂⠐⠂⠀⢂⣤⣭⢍⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿⣟⠀⢰⣿⣦⡀⠘⣿⣿⣧⣻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢇⠀⢠⣤⣤⡤⢠⡄⢀⠀⠙⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠟⠀⣾⣿⣿⣧⠀⠘⣿⣿⣿⣆⠈⣿⣿⣿⣿⣦⡄⠀⠀⣠⣶⣼⣿⣿⠃⠘⠁⠫⢃⣤⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣟⠛⠉⠉⢀⣿⣾⠾⢿⣿⣿⣿⣿⣿⣛⡻⠿⢿⣿⣿⣏⣽⠀⠀⢀⢉⣹⣿⡏⠁⣠⣾⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⠿⠧⠏⠛⠛⠁⠀⣾⡿⠿⠿⣮⢹⠁⠀⠀⠀⠈⠉⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⠆⠛⢻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡿⠿⠿⠿⢿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣶⣶⣿⣿⣿⡄⠀⠀⠀⠀⢀⠀⠁⢀⣀⡀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⠁⢠⣤⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣾⣿⡆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣾⣿⣿⣿⣿⣿⣿⡀⡀⠀⣀⠀⠠⣴⣶⣾⣯⣭⣤⠀⠀⣶⣶⣶⣶⣶⣶⠀⠀⢀⣀⡀⠁⠉⠀⠁⠀⠀⠉⢻
⣶⣶⣾⠟⠿⠻⠛⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠉⠉⠁⠀⠰⠾⠿⠿⣿⣿⣿⣿⠟⠈⠛⠾⣿⣦⠀⠸⣿⣷⣶⣿⣿⣽⣆⣀⣽⣿⣿⡿⠋⠀⣰⣿⣿⣿⣷⣆⣀⣀⡀⣀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣽⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠙⠛⠃⠀⠀⠲⠶⣿⣿⣧⣄⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠐⠒⣲⣶⣾⣿⣿⣿⣿⡿⢿⣿⣿⠿⠟⠏⠉⣽⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠓⠂⠀⠀⠀⠀⠀⠠⠏⠀⠉⠉⠉⠉⠓⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⢈⢁⣀⣀⣹⠿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣇⣈⣉⡁⠉⠙⠩⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣈⠛⠛⠛⠛⠁⠀⢀⣤⣤⡶⠿⠻⠛⠛⠛⠀⠀⠈⠉⠙⠀⠑⠒⠀⣁⠽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠑⠤⠤⢤⣶⣿⣿⣿⣿
⣀⣀⣀⣀⡀⠀⠀⣭⡥⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠑⠒⠒⠶⠶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠾⠿⠶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠛⠛⠛⢛⡓⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⠻⠿⠿⣀⣀⣀⣀⣀⠀⢸⣿⣿⣿⡦⡄⣀⣀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢤⣤⠀⠤⢤⡀⠸⣿⣿⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡋⠉⠙⠛⠛⢿
⠒⠒⠻⠿⢿⠿⠿⠿⠶⣶⣶⣦⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣷⣨⣮⣿⡿⠟⠁⠀⠉⠉⠀⠀⣠⣤⣤⣤⣄⣀⣈⣴⣼⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠠⠴⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⠷⠶⠶⠶⣦⡀⠀⠈⠻⠿⣿⣯⣿⣿⣿⣾⣯⣭⠉⠹⠿⠶⠆⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠉⣿⣿⣿⣫⣡⣉⣻⣿⡿⠀⠀⠀
⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣤⠈⠡⠿⠿⢿⣿⣿⣿⣿⣿⣶⣄⣀⣀⡀⡀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣄⣤⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠉⣻
⣿⣿⣿⠿⠿⠿⣿⣭⣭⣭⡍⠙⠿⠿⣿⣿⣿⣿⣶⣶⢦⡄⠀⠀⠀⠀⠀⠐⠚⠂⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⢿⡿⠛⠛⠑⠒⠆⠀⠀⣀⡄⠀⠀⠀⣀⣀⠀⠙⠛⠛⠉⠁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣶⣶⣾⣿⣿⣋⣉⣃⣀⡀⢀⣿⣿⠿⠿⠿⠿⠿⠿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠉⠛⠙⠙⠻⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣩⣭⣿⣿⣭⣽⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿
⠋⠩⠉⠹⣿⣿⣿⡦⠂⠈⢛⢛⣟⠉⠀⠺⠿⠿⠟⠓⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹
⠀⠘⠟⠹⢻⡿⠿⠿⡿⠫⠻⠟⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⣷⣦⠈⠿⣶⣆⣀⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⠂⠀⠀⠘⣿⣿⣿⡄⣿⣿⣿⣿⠇⠀⠀⠚⠻⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠂⠰⢶⣦⣤⠀⢉⣉⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠉⠉⠀⠸⢿⡿⡋⠀⠐⠒⠂⠀⠀⠻⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢠⣄⠉⢵⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡟⠋⢻⣿⣿⣅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠼⠿⣿⣿⣿⡇⠀⠛⠿⢿⣿⠀⠀⠀⠀⠀⠀⣤⣾⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠆⠀⠙⠟⠿⠏⠁⠤⠀⠀⢨⠛⠹⠟⠛⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡅⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠈⡉⠀⠀⣾⣿⡆⠀⠙⢛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠀⠻⠧⠀⢼⣿⠁⠀⠀⠘⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⠿⠛⠛⠉⠉⠁⠉⠈⠉⠀⠈⣩⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠉⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠍⠭⠟⠛⠛⠛⠒⠂⠀⠒⠒⠦⠠⠤⠤⠄⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦⠀⠀⠀⠀⠀⠠⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡄⠂⢶⣤⣄⣼⣷⣦⣤⠛⠃⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⡀⢛⣛⣛⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠓⠳⠲⠶⠀⠀⠀⠙⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣼⡇⠈⠛⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣶⢶⣦⡀⣰⣶⣶⠀⣶⣶⠀⣶⣶⠀⣴⣶⢰⣶⡄⣶⡆⣴⣶⣶⣄⠀⢰⣶⣿⣿⣷⣶⣶⢰⣿⣿⣿⣿⣿⣿⣶⢶⣦⢰⣶⣶⡆⣶⡆⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣤⣀⣀⣀⣀⣀⣸⣿⣸⣿⣇⣿⣿⣿⣶⣿⣿⣄⣿⣿⠀⣿⣿⣸⣿⣷⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⣤⣿⣿⢀⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠁⢸⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⡿⠛⠛⠀⢘⣻⣿⣿⣿⡟⠛⠘⠛⠘⠛⠛⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢀⣀⣀⣠⣶⣿⣿⣿⣋⠁⣀⣀⣀⡟⢂⣀⣀⡀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠙⣿⣿⣿⣿⣇⣿⣿⣿⣿⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⣷⣶⣿⣿⠿⠇⣿⣿⣿⣯⢸⣿⣿⡇⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠹⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⢹⣿⠛⣿⡇⢻⣿⣽⣿⡺⣿⣿⣿⣿⣷⣿⣿⣿⣿⢸⣿⣿⡧⣿⣧⣿⠟⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣤⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣤⣶⣶⣶⡄⠀⠀⠀⠉⢻⣿⣷⡝⣿⣿⣿⣿⣿⣧⠀⠀⠠⠟⠠⣬⣿⠿⠗⠒⠂⠐⠂⠀⢠⣤⣭⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠈⠛⠛⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣴⣿⣿⣿⣿⣿⣟⠀⢸⣿⣦⠀⠙⣿⣿⣧⡻⠿⣿⣿⣿⣿⣿⠀⠀⠰⠛⠀⠀⢀⣠⣤⡄⣤⠀⠀⠈⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣤⣤⣤⣤⣤⣤⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⠋⠀⣾⣿⣿⣧⠀⠙⣿⣿⣿⡄⠉⣿⣿⡿⣿⣦⠜⠀⢀⣬⣦⣸⣿⡿⠋⢿⡐⠙⠀⠄⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⡛⠋⠉⠉⠀⣉⣩⠾⢿⣿⣿⣿⣽⣿⣿⠿⠿⠇⠀⢸⣿⢻⣿⡟⠋⠀⣠⣾⣻⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⢿⡇⠀⠙⡏⠀⢀⣿⣿⣿⣿⣍⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡷⠀⠐⢲⣿⣿⣿⣿⣷⣴⣶⣶⣾⣿⣿⣿⣿⡀⠀⢿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⢀⣿⣿⣿⣥⣼⡀⠀⠀⠀⠇⣀⣸⣟⣛⣂⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠋⠁⣠⣤⡘⢻⣿⣿⣯⣶⣾⣿⣿⣿⣿⣿⣷⣾⣷⣆⠈⠛⡿⢿⣿⣿⣿⣿⣿⣿⠛⠁⢀⣾⣿⣷⣿⣿⣿⣷⠀⠀⠀⢀⠀⠠⣶⣶⣿⣭⣥⣄⠀⢠⣤⣤⣤⣤⣤⡄⠀⢀⣠⣀⣠⣤⣤⡄⠉⠙⠙⠉⠙
⣿⡿⠋⠁⣠⡴⠘⠛⠛⠛⠛⣿⣿⣿⣿⡿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣷⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⡿⠂⠀⠙⢷⣆⠀⢻⣿⣷⣶⣯⣭⣳⣀⣈⣿⣿⣿⡿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣆⢀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣁⣀⣩⢉⠉⣻⣿⣷⣤⣄⠀⠀⠀⠀⠀⢀⠈⠛⠛⠃⠀⠀⠒⠻⠿⠂⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠀⠀⠐⠒⣆⣄⣿⣿⣿⣿⣿⠿⢿⣿⡿⠟⠉⠉⢹⣿⣿⣿⣿⣿⡿⠻⠿⣿⣿⣿⣯⣭⡿⠟⠛⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠁⠀⣀⠈⠻⠿⢶⠆⠿⡿⡿⠿⠿⠿⠿⢶⡢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠿⠿⠟⠋⠛⠙⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⠛⠛⠃⠀⠀⣀⣠⡄⠜⠛⠛⠛⠛⠃⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠛⢀⣀⣀⣠⢽
⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠶⠔⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣄⣀⣀⣀⡀⣤⣤⣤⣄⣉⣉⣹⣿
⠛⠫⠤⠬⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠶⠆⣀⣀⣀⡀⠀⠀⣰⣿⣿⣦⠄⡀⠀⠀⠑⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⠀⣤⣤⣤⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠾⠻
⠀⠀⠀⡀⠂⠂⠲⠟⠟⠳⠖⠶⠶⢶⣦⣦⣤⣤⣤⣴⣶⣾⣿⣿⢿⢟⠀⡠⠸⢿⣿⠋⠀⠉⠉⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⣰⣶⡿⠷⠂⠀⠀⠉⠉⠁⠀⠘⠃⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⢿⣿⢿⡦⢯⡶⠶⠤⠤⢔⡀⠀⠀⠹⠿⣿⣿⣛⣿⣉⣉⣉⣛⡛⠛⠟⢆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠛⢻⣿⡿⠛⠉⠻⣿⣿
⠀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢿⣶⣄⡀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⢸⣿⣿⣿⣿⣿⣞⣿⢻
⣟⣿⣿⣿⣿⣿⡟⠛⠛⢻⣭⣭⣭⣭⠉⠙⠿⠿⣿⣿⣿⣷⣶⠒⠄⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⡟⠛⠖⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠟⠻⠋⣉⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣉⣉⣉⣀⣀⠀⢀⣿⠿⠿⠿⠿⠿⠿⠶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⣲⣿⣶⡄⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣬⣽⣿⡿⠤⢿⣿⣿⣿⣿⡷⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹
⣿⣿⠟⠉⠉⠉⣤⡽⠿⢿⠃⠀⠀⠈⡛⣛⡉⠀⠀⠙⠟⠟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠀⠒⢒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⠏⠹⢹⡇⠿⠿⡿⠫⠻⠟⠿⠻⠟⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⢴⣤⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠍⠉⢶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢘⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⣄⣆⣎⡿⠟⠛⠁⠈⠉⢻⣿⣿⣏⢸⣿⣿⣿⣧⠀⠀⠈⠿⠿⠛⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠿⠥⠀⠤⣤⣄⡀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠙⠋⠉⠀⢿⣿⡿⠃⠀⠰⠆⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠩⣤⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⠀⠠⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⡿⠈⠉⠻⢟⠏⠀⠀⠀⠈⠉⠀⠸⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠨⣿⣿⣿⣿⣦⠀⠹⠿⣿⣯⠁⠀⠀⠀⠀⠀⢀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠅⠄⠀⠀⠛⠲⠁⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡉⠉⠀⠀⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠙⠂⠀⢠⣶⣦⠀⠈⠛⠛⢛⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠛⢦⠀⠈⣿⡏⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠉⠉⠉⠉⠉⠉⠉⠉⣙⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠉⠁⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠍⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠠⠤⠀⠀⣀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣶⣄⠀⠠⣤⣄⢀⣾⣥⣄⠀⠀⠀⠀⠀⠀⠦⠀⠀⠘⠛⣛⣛⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡔⣿⣿⣿⣯⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠈⢹⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⢀⠚⣿⣿⡿⣿⢿⡿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⡀⠀⠀⠀⠀⠀⠠⠤⠦⠤⠤⠤⠀⠀⠀⠒⠒⠒⠒⠤⠤⠀⠀⠀⠀⠀⠈⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⣧⣼⠁⠉⠂⠀⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢒⣾⣶⣦⣤⣴⣶⣿⣿⡀⠀⠀⢠⣶⢶⣦⡀⣴⣶⣶⠀⣶⣶⠀⣶⣶⠀⢰⣶⢰⣶⡀⣶⡆⣴⡶⣶⣄⠀⣰⣾⣿⣿⣶⣶⣶⢰⣿⣿⣿⣿⣿⣷⣶⢶⣦⢰⣶⣶⡆⣶⡆⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣸⣿⢸⠿⠇⣿⣿⣿⡄⣿⣿⣤⣿⣿⡀⣼⣿⢸⣿⣧⣿⣿⣿⣧⣛⣻⠎⢻⣿⣧⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣍⢸⣿⣧⣄⣿⣿⠀⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⣿⣿⠁⢸⣿⡏⣿⣿⣿⣿⢸⣿⢹⣿⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠿⠛⠛⠀⢘⣻⣿⣿⡿⠟⠛⠘⠛⠘⠛⠚⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣁⣀⣠⣼⣿⣿⣟⣋⠀⣀⣀⣀⡋⢀⣀⣀⡐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢹⣿⢻⣯⣿⣿⢻⡇⣿⣿⣿⣷⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣷⣶⣄⣿⣿⠿⠇⣿⣿⣿⣯⢸⣿⣿⠇⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⠉⠉⠁⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⠛⣿⠛⣿⡇⢻⣿⣼⣿⢼⣿⣿⣿⣷⣦⣿⣿⣿⣿⣸⣿⣷⡄⢿⣧⣿⠟⣿⡟⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⣠⣤⣤⣶⠀⠀⠀⠀⠛⢿⣿⣮⡹⣿⣿⣿⣿⣿⡀⠀⢠⡟⠀⢠⣬⣭⡭⠷⠒⠀⠂⠀⠄⣠⣄⡁⠒⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⣿⣿⣿⣿⣿⣟⠀⢸⣷⣄⠀⠻⣿⣷⣜⠿⢿⡿⣽⢽⣿⣇⢠⣦⠞⠃⠀⠀⣀⣀⡀⢀⣀⠀⠀⠙⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣤⣤⣤⣤⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡻⠋⠀⣾⣿⣿⣆⠀⢹⣿⣿⣦⠈⠛⠉⠈⠙⢻⣾⠋⠀⢀⣰⣄⢻⣿⡇⠘⠃⠞⢳⣦⡀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣔⠙⠉⠉⠁⠈⠀⠀⠭⣿⣭⣭⣯⣽⠇⠀⢾⣿⣽⣿⡉⠈⠀⠀⠀⠀⣈⣛⣿⠀⠀⣿⣿⣿⣷⣾⢷⠀⠀⠀⡅⠀⣰⣿⣿⣿⣧⡙⡄⠀⠀⠐⠿⠿⠇⠀⠀⠙⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⢤⣿⣿⣿⣿⢤⣤⣤⣶⣴⠀⠘⣿⣿⣿⡿⣦⣾⣷⣶⣿⣿⣿⡟⠀⢠⣿⠿⣿⣯⣧⠀⠀⠀⠀⠃⠀⢛⣛⣀⣀⠀⠓⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⡤⠀⠈⣸⣥⣥⣠⣀⣬⣙⠋⢻⣧⡄⠈⠻⡿⡤⠠⠤⠽⣿⣿⣿⠛⠁⢀⣾⣷⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⣶⣶⣦⣭⣭⡤⠀⠀⣤⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⣿⣿⣿⣿⣿⠟⠁⠀⡤⠒⠘⠈⠉⠁⠉⣿⣿⣿⠛⠛⠛⠛⠛⠉⠁⢐⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠐⠛⠉⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⣀⠈⢿⣿⡀⣀⣈⣑⠆⢀⣸⣿⣿⡿⠏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦⣸
⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣀⣀⣀⣤⣴⣶⣶⣧⣄⡀⠀⠀⠀⠀⠈⠹⣿⣆⢄⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠚⠛⠋⠁⠀⠑⠷⠟⠫⢹⣿⣿⣿⣿⠿⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣀⣰⣿⣿⣿⣿⠛⠿⡟⡟⠛⠛⠛⠉⢿⣿⣿⣿⡟⠂⠠⣴⣶⣷⣄⠀⠀⡒⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠢⠂⠀⠀⠓⠺⠶⠶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⢿⡿⠿⠿⢿⠿⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡀⢸
⣴⣶⣶⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⡿⠿⠛⠛⠋⠒⠒⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣀⠋⠛⠛⠛⣿⣿⣶⣷⣷⣿⣿⣿⣿
⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠋⠀⠀⠰⠶⠶⢤⡀⣀⣀⣠⣤⣶⣤⣿⠛⠓⠀⠀⠄⠀⡸⡺⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡤⠀⠀⠐⠛⠓⠀⠛⣷⠀⠛⣿⣿⣿⣶⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣾⣷⣿⣿⢿⣿⣿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠇⠀⢈⠻⠿⠷⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⢿⣿⣿⠇⡟⠛⠛⠿⢿⣿⣿⣿
⣤⣤⣤⡀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⣶⣶⣿⣿⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⢸
⣿⣿⣿⣛⣻⣿⠿⣿⣿⠉⠙⠛⠋⢁⣭⣭⣭⠍⠉⠻⠿⠣⢠⣤⣤⡶⠂⠀⠀⠀⠀⠀⠀⠠⢤⠄⠀⠀⠉⠛⠂⠀⠈⠉⠉⠉⠉⢻⣿⣿⣿⣿⣶⠶⡤⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣤⡄⠈⠙⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣉⣉⡁⠀⠀⠀⠀⠀⠿⠛⠾⠶⠶⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿
⣇⣀⣘⣿⣿⡿⠛⡿⢝⡀⠀⣠⡼⠿⠤⠴⠷⢿⡮⣷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠉⠭⠙⠎⠯⠀⣤⠤⠀⠀⠀⠛⠛⠃⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⣤⣤⣠⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠹⠟⠹⢸⡏⠏⠉⡧⠣⠸⠟⠿⠻⠏⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠭⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢹⣿⣿⣿⣿⣿⣿⠉⢙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⡀⣦⣻⠿⠿⠛⠙⠛⠛⣿⣿⣿⠃⢾⣿⣿⣿⡅⠁⢉⢛⣿⠿⢿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⡿⠭⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠛⠛⠛⠃⢸⣿⣿⡟⠁⢠⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣷⣶⡦⠀⠀⠀⠀⠀⠀⣩⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⡿⠍⠻⠿⣿⠟⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣹⣿⣿⣿⣆⡀⠈⢿⣿⡿⡇⠀⠀⠀⠀⠀⠀⢀⣸⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⡄⡀⠀⠉⠟⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠀⠀⠉⠉⠛⠿⠿⠃⠀⠀⠉⠑⠣⠀⠀⣤⣤⡄⠀⠻⠿⠿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣤⡄⠀⣿⣿⠃⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠋⠙⠙⠻⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⠟⠟⠛⠛⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⡒⠒⠲⠦⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⣄⡀⠀⣀⣀⠀⢠⣮⣀⠀⠀⠀⠀⠀⠀⠲⠿⠿⠷⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣦⣤⣿⣿⣷⣿⣿⣿⣷⡄⠀⠀⠀⠀⣶⣾⣿⣿⣵⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⠉⠙⣿⣿⣿⣿⣷⠤⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡄⠀⠀⠠⠤⠤⠤⢤⣤⡀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠿⠀⠀⠀⢸⣅⡏⠀⠁⠈⢠⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠤⢤⣶⣦⣠⣀⣤⣶⣶⣦⣶⢶⣶⡀⣴⣶⣶⠀⣶⣶⠀⣶⣶⠀⢰⣶⢰⣶⠀⣶⡆⣴⡶⣶⣄⢀⣶⣾⣿⣷⣶⣲⣶⢼⣿⣿⣽⣿⣿⣶⣶⢶⣦⢰⣶⣶⡆⣶⣆⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠇⣿⣿⣿⡀⣿⣿⠀⣿⣿⠀⣼⣿⢸⣿⣧⣿⣇⣿⣇⣛⣛⠐⢼⣿⣧⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣮⣉⢸⣿⣧⡄⣿⣿⠀⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣷⣶⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡟⣿⣿⠀⢸⣿⡏⣿⣿⣿⣿⢸⣿⣹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣏⣽⣿⣿⣆⣿⣿⣩⣶⣾⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢙⠿⠛⠛⠀⣘⣿⣿⣿⣿⡟⠛⠘⠛⠘⠛⠛⠛⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶
⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⣀⣀⣠⣾⣿⣿⣟⣛⠁⣀⣀⣐⡀⢀⣀⣀⡒⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢹⣿⢻⣿⣿⡟⢻⡇⣿⣿⣿⣷⢸⣿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⣦⣄⣿⡿⠿⠃⣿⣿⢿⣯⢸⣿⡿⠇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⠋⠁⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⠛⣿⠛⣿⡇⢻⣿⣼⣿⣽⣿⣿⣿⣶⣤⣿⣿⢸⣿⣿⣿⣷⡄⢿⣧⣿⠟⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣄⠀⠀⠀⠀⢠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⣤⣤⣤⣶⠀⠀⠀⠀⠛⢷⣾⣌⢻⣿⣿⣿⣿⡇⠀⣀⡼⠃⠀⣤⣬⣤⣭⠷⠄⠠⠄⠠⠀⣀⡒⠐⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⠙⠛⠛⠟⢿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣼⣿⣿⣿⣿⣿⡃⠀⣸⣶⡄⠈⢻⣿⣷⡙⠿⣿⣿⢯⣿⣿⣇⢠⣦⠛⠀⠀⠀⣀⣀⡀⣀⠀⠀⠙⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣀⣀⣤⣬⣬⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣟⠻⠃⠀⢿⣿⣿⡄⠀⢻⣿⣿⡄⠘⠃⠁⠉⠙⣿⡞⠁⠀⡀⣠⠰⡿⢻⠀⠹⠁⠒⢢⡄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡚⠛⠉⠉⠁⠈⠁⠉⢭⣫⡅⠀⠋⠩⠼⢿⣿⡇⠀⠀⠀⠀⠘⠂⠁⠀⢸⣿⣿⣇⠀⠹⣆⠀⠀⠀⡅⠀⣾⣿⣿⣿⣞⢿⡀⠂⠀⢶⣿⣿⣆⠀⠹⠟⠛⠙⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠠⣼⣿⣶⡾⣧⣤⠀⠈⣴⣱⣤⣀⣷⣿⣶⣦⣤⣤⣾⠇⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠐⣛⣓⠀⠀⠘⠦⠀⠀⠀⠰⢟⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⢀⡀⠀⠈⢉⣁⣀⡀⠀⠦⠀⠙⢿⣿⣭⣭⣉⡀⠀⠀⠘⠉⠀⣠⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠠⣰⣥⣤⣭⣭⣤⡀⠀⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠉⠻⢿⣿⣿⣿⣿⣿⡿⠋⠁⠀⡐⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠙⠂⠀⠀⠀⠉⠉⠁⠀⠁⠀⠀⡀⣎⡹⠿⠿⠻⠿⠿⢿⣿⡷⠀⠀⢀⣀⣿⣿⣿⣆⠀⠈⠒⠀⢀⣶⣶⣶⡂⠀⠀⣴⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠈⠑⠁⠃⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠘⠻⠿⠁⠀⠀⠺⢿⣿⡿⠟⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣀⣀⣾⣿⣷⣦⠀⠀⠀⠀⠙⠛⠛⠛⢉⣿⣶⣶⡶⠂⠀⢠⢄⣤⡀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⠀⠁⠉⠈⠁⠦⠀⠀⠀⠀⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸
⠀⠀⠀⢰⣶⣶⣶⣦⣤⡄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⠛⠛⠛⠃⠀⠒⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⢦⣤⣤⣀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠂⠀⢀⣀⣀⣀⣤⣤⡶⠒⠂⠀⠀⠀⠀⠒⣺⠐⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠶⣦⠀⠐⣦⠀⠀⢲⣶⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣽⡟⠛⢿⠿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⡦⠀⠠⠾⣾⣯⣭⣉⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢿⣿⣿⣿⣿⠉⠻⠟⢿⣿
⠀⠀⢠⣤⣤⣤⣄⢀⣀⣀⣀⣀⣤⣤⣤⡤⡴⣲⣶⣤⣤⣤⣾⣿⡿⠓⠕⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄⡀⠀⠀⠀⢡⣶⣤⣦⣤⣷⣶⡶⠄⠐⠚⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠈⠁⠀⠀⢸
⣶⣶⣼⣿⣿⣿⣧⣙⡙⠛⠿⠿⠋⠉⠉⠉⠀⣉⢍⢭⡍⠉⠹⠿⠇⠀⣀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠑⠒⠒⠀⠀⠘⠛⠛⠛⠻⣿⣿⣿⣷⣤⣤⣀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢸
⣿⡿⣿⣿⠿⠿⣿⣿⣿⣷⣶⣶⣿⢿⣿⢿⣶⣅⣁⢈⠁⠀⠀⠀⢀⢘⠯⠯⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⠀⠀⠁⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸
⣶⣶⣶⣦⣄⣀⣈⣸⡟⠟⠛⡏⠅⠀⠄⣴⢿⠧⠤⠶⠿⢤⢾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠻⠷⡄⠀⠀⠀⠀⠈
⣿⠿⠀⠈⠉⠉⣶⠿⠁⠀⠀⠀⠀⠀⠘⠛⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠿⠿⠹⢹⡏⠿⠫⡧⠣⠸⠇⠽⠈⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠠⣶⡴⠟⠛⠿⢿⣿⣿⣿⠁⣾⣿⣿⣿⠛⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠘⣿⣿⣿⠀⢻⣿⣿⠟⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣋⣀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⡿⠀⢻
⠿⠿⠿⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠀⠀⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠐⠚⠿⣿⣿⣷⠀⠈⠛⠻⣰⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣿⣿⠀⠀⠈⢠⣬⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠈⠙⠂⠀⢻⡏⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠛⠛⠀⠀⠘⠿⣿⡿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠉⠉⠉⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣆⠀⢀⣶⣦⡄⠀⢀⣭⣬⣭⡉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠿⠿⠿⠛⠛⠿⠿⢿⣷⣹⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡜⣿⠛⠛⠙⠛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣶⢶⣦⡀⣴⣶⣾⠉⣿⣿⠉⣶⣶⠀⣴⣶⢰⣿⡉⣿⡆⣰⡶⣶⡄⠀⢸⣷⣿⣶⡶⣲⣾⢷⣿⣿⣿⣷⣦⣠⣶⢶⣦⢰⣶⣶⡆⣶⡆⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠿⠇⣿⣿⣿⡀⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣧⣿⣇⣿⣇⣛⣛⠁⢸⣿⣷⣿⣧⣽⣿⢹⣿⣿⣿⣿⣿⣿⣿⣬⣉⢸⣿⣤⡄⣿⣇⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣄⣄⣠⣤⣴⣶⣶⣶⣶⣶⣾⣿⢰⣷⣧⣿⣿⣿⣧⣿⣿⣤⣿⣿⣤⣿⣿⣸⣿⣿⣿⣿⣿⡟⣿⣿⠀⢸⣿⣏⣿⣿⣿⣿⢸⣿⣹⣿⣿⣿⣿⣿⢻⣿⢸⣿⣏⣁⣿⣿⡀⣿⣿⣭⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⣀⠠
⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠻⠛⠛⠀⣘⣟⣿⣟⣛⣛⠛⠘⠛⠘⠛⠛⣿⣿⣿⣿⣫⣘⣛⣛⢛⢛⣛⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣉⣙⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣂⡀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣛⣀⣀⡀⢀⣀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣾⣿⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⢻⣷⢸⣿⡛⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⣿⣿⢶⣶⣉⡁⣿⣿⠿⠏⣿⣿⢿⣯⢸⣿⠿⢷⣙⣿⣷⡆⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⡏⠁⣿⣿⡿⣿⣿⣿⣿⣿⡿⠟⢻⣿⠛⣿⠛⣿⣇⣿⣿⣼⣿⣿⠇⣿⣿⠀⠀⣿⣿⢸⣿⢸⣿⣤⡌⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢀⣤⣤⣤⣼⣿⣿⠟⠁⠀⣠⣤⣤⣤⡀⠀⠀⠀⠑⢿⣷⣮⠻⣦⣄⣀⠀⠀⢠⣤⣤⠀⠀⣀⣤⣤⣤⡭⠅⢠⠀⢠⠀⠐⠚⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠙⠛⠛⠿⢿⠃⠀⣰⣿⣿⣿⣿⣿⣟⠀⣰⣷⣄⠀⠻⣿⣷⡙⠿⣿⣆⠀⢸⣿⣇⢠⡠⠟⠀⠀⠀⣀⡀⠀⣀⠀⠈⠛⠀⣠⣦⣶⣹⠏⠋⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⠀⠀⠀⡈⠀⠀⣻⣭⡟⠿⠛⠋⠏⠀⠻⣿⣿⡆⠀⠹⣿⣧⣤⠈⡇⠀⠈⠉⠻⡞⠁⠀⠀⠀⢰⠟⠗⠀⠟⠰⠂⣄⠀⠉⢿⣿⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠿⠛⠁⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⣀⣈⣀⠁⠀⠀⠇⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣼⣿⣿⣷⡙⢆⠀⠀⢠⣾⣿⣷⡀⠀⢹⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⡿⠿⣿⣿
⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠐⡀⣠⣩⠆⠀⢠⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠘⠻⢂⠀⠠⠙⠄⠀⠀⠀⠘⠿⣿⣿⠀⠀⢻⣿⣿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣑⡟⠉⠀⢀⣾⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠋⣱⣂⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠁⠹⠇⠦⠀⠄⠴⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣶⣶⠈⠀⢀⣾⣿⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠘⠂⠒⠂⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣱⣾⠿⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⠀⠀⠀⠀⠀⠙⠿⠟⠛⠢⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠛⣏⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⢿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠉⠉⠙⠁⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣄⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⠟⠟⠛⠓⠠⠀⠉⠙⠛⠛⠛⠛⠻⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣦⣤⠄⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠁⠒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⠿⠿⣿⣿⣶⠦⠀⡤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠠⠶⣶⣶⠄⠀⠀⠐⠷⠆⠀⠐⠀⠀⠘⢿⣿⣷⣤⢰
⠁⠀⠀⠐⠀⠐⠂⠀⠀⣤⣴⣦⣤⡀⢀⣀⣀⣠⣤⡠⢤⣤⠠⢤⣤⣤⣤⣤⣤⣶⡿⠷⠤⢾⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢛⠓⠀⡀⢙⣛⣛⠷⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⢖⠲⠢⢺⣿⣷⣶⣶⣶⣄⣯⣿⣯⣤⣁⠛⠻⠿⡋⠉⠁⠉⠀⠈⢉⢉⡉⠉⠙⡿⢇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⣄⡀⠀⠀⢀⣿⣿⣿⣿⣾⣭⣿⡂⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠹⠉⠙⠿⠿⠿⠿⠿⢿⣻⣿⣿⣶⣶⣾⠿⡲⢶⣶⣆⣉⠈⠁⠀⠀⠀⠀⢀⠀⢜⡉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⠰⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣆⡀⢠⣴⣷⣟⣛⡿⠿⢤⣤⡀⢀⡍⠛⠛⢋⠄⠀⠀⢠⠼⠧⠭⠭⡧⣀⢠⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠹⠽⠿⢿⣿⡿⣿⠿⠉⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹
⠀⠸⠏⢹⣻⣟⣿⣿⡿⠣⠸⠏⠿⠉⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢀⣀⡀⠀⡀⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⢤⡭⠝⠻⠿⠿⣿⣿⣿⡇⢰⣿⣿⣛⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⣄⡀⠀⠈⠉⠀⠀⠀⠀⢻⣿⣿⡅⠸⣿⣿⡿⠆⠀⠀⠀⠈⠀⠈⣽⣿⣿⣿⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠉⠀⠀⠀⠿⠟⠁⠀⠀⠉⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠃⠀⢹⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠸⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠴⢶⣿⣿⣦⠀⠈⠛⠿⢡⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠙⠀⠠⣾⣿⠄⠀⠈⠋⣙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈⠳⠄⠀⢹⣿⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠴⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠺⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠃⠀⠠⠿⣿⣿⣿⡿⠿⢿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣈⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⢀⣾⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣨⣭⣭⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣆⠀⠀⠀⠀⣉⣉⣉⣳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⡷⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⠿⢶⡦⣿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢻⡿⢛⠛⣿⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣶⡀⣰⣶⣶⠀⣶⣶⠉⣿⣿⠁⢶⣶⢰⣾⡉⣿⡏⣹⡶⣶⡄⠀⣿⣾⡇⣶⡶⢶⣾⣷⣿⣿⣿⣶⡆⢠⣶⢶⣦⢰⣶⣶⡆⣶⡆⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠿⠇⣿⣿⣿⡼⣿⣿⠀⣿⣿⠀⢽⣿⢸⣿⣧⣿⡇⣿⡇⣛⣛⠈⢻⣿⣧⣿⣇⣿⣿⢺⣿⣿⣿⣿⣿⣾⣿⣬⣉⢸⣿⣥⡄⣿⣇⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣀⣤⣀⣀⣀⣀⣴⣦⣦⣼⣿⢰⣶⣦⣿⣿⣿⣧⣿⣿⣀⣿⣿⣀⣿⣿⢸⣿⣿⣿⣷⣿⡏⣿⣿⠀⢸⣿⡏⣿⣿⣿⣿⢸⣿⢹⣿⣿⣿⣿⣿⢻⣿⢸⣿⣏⣁⣿⣿⡀⣿⣿⠉⠀⢀⣀⣀⡀⢀⣀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠳⠙⠛⠛⠛⢀⣘⣟⣻⣛⣛⠛⠛⠘⠛⠘⠛⢿⣿⣿⣿⣿⡋⢘⠛⢛⣻⢛⣛⣛⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣧⣆⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⣀⡀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⢀⣀⣀⣨⣿⣿⣿⣯⣾⣷⣦⣼⣽⣵⣽⣥⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣟⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⢻⣿⣻⡟⣿⣿⣿⣷⣿⣿⢻⣷⢸⣿⡟⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢹⣿⣿⣿⡟⣿⣿⢶⣶⣉⠀⣿⣿⠿⠇⣿⣿⢿⣯⢸⣿⠿⣇⣙⣿⣷⡆⣿⣏⣻⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡟⠛⢻⣿⠋⠻⡿⣿⣿⠿⠟⠛⢹⣿⠘⣿⠛⣿⣇⣿⣿⡼⣿⢽⠟⣿⡏⠀⠀⣿⣿⢸⣿⢸⣿⣤⡌⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⣀⣤⣼⠋⠀⣀⣤⣴⣦⣆⠀⠀⠀⠀⠳⣿⣷⡕⣾⣤⡀⠀⠀⢠⣤⣤⠀⠀⢀⣐⣂⣠⣤⠍⢠⡄⢀⡀⠁⠉⠩⠭⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠈⠻⠿⠁⠀⢼⢿⣿⣿⣿⣿⡃⠀⣿⣦⡀⠘⢻⣿⣌⠻⢿⣧⡀⠈⠿⣿⡀⣆⡼⠃⠀⠀⠀⣀⠀⠀⠀⠀⠛⠁⢀⣤⡜⠽⠿⣿⠟⠛⠛⠛⠛⠻⣽⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠁⠙⠆⠃⠘⠁⠀⠙⠻⢷⠀⠈⣿⣯⣦⠀⠛⠃⠀⠀⠘⢳⡏⠁⠀⢀⠰⡏⠁⠀⠹⠀⠖⢀⠀⠈⢻⣿⣶⣶⣿⣷⣶⣤⣴⣦⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠉⠉⠀⠀⢷⠀⠀⠀⠀⠁⢰⣿⢿⣷⡍⢖⠀⠀⠀⣰⣿⣷⡄⠀⢹⣿⣷⣿⣿⡯⣻⣾⣿⣿⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠦⠠⠙⠄⠁⠀⠀⠀⠘⢿⣳⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣿⠟⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠁⠀⠸⠏⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⡁⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣠⠀⠀⠀⣼⣦⣶⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢽⡿⠛⠀⠀⢼⠿⡿⠿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣾⣿
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⠀⠀⠀⠀⠀⠸⠿⡿⠿⢆⢀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠊⠀⠀⠀⠀⠙⡟⢿⣿⣿⣿⣿⣿⣿
⠉⠀⠒⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠿⠿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠙⠛⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣰⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⣿⠿⠿⠿⠭⢈⣙⠛⠻⠿⢿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢛⣓⡛⠻⢿⣷⣤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠠⢤⣄⠀⠀⠀⠀⠀⢶⣴
⣭⣥⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢤⣤⣤⡤⡀⠀⢀⣀⠠⠄⠀⠀⠀⠀⠄⣀⣄⣀⣀⣤⣴⣤⠆⠠⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⠾⠆⠀⠀⠠⠶⠾⣭⣍⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠿⢿⡷⠄⠂⠐⠘⠿⣿⣶⣶⣤⣀⣡⣯⣭⣤⡀⠛⠛⠿⠋⠁⠀⠀⠀⠈⠉⠉⠉⠋⠛⣿⡁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠀⠀⣶⣶⣶⣦⣔⡖⠲⡄⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠉⠙⠛⠙⠉⢽⣶⣶⣶⣶⠶⠶⠒⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠉⠛⠿⣿⣻⣣⠀⣀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀
⠒⠂⠸⠯⠧⠀⠀⣠⣾⣒⣿⡿⠷⠤⢤⠀⠀⠂⠁⠋⢉⠀⠀⠀⠀⢘⠮⣭⣭⣤⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠈⠛⠛⣿⣯⠻⠛⠋⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠸⢸⡿⢿⣿⣯⣫⡹⠟⠿⠉⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠀⢈⣛⣻⢿⢿⣿⣿⣿⣿⣿⠁⣼⣿⣿⡿⠿⠿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠰⡠⠙⠛⠉⠀⠈⠉⢹⣿⣿⡏⠀⣿⣿⣿⣷⠄⠀⠀⠀⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡄⠀⠀⠀⠈⠉⠉⠁⠀⢾⣿⠿⠀⠀⠐⠖⠀⠀⠀
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠀⢻⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠠⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣹⣯⣿⣿⣧⠀⠈⢿⣿⣟⣙⠀⠀⠀⠀⠀⠀⠀⣤⣬⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠘⠷⠀⠀⣤⣤⡄⠀⠘⠛⢻⣶⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠐⣲⣄⠀⢹⣿⠁⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡿⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠛⣶⣤⡀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡶⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣦⠀⣰⣶⣶⠀⣶⣶⠀⣶⣶⠀⣶⣶⢲⣶⡖⣶⡆⣴⡶⣶⣆⢂⣸⣶⡆⣶⣶⣾⣿⣿⣿⣿⣽⣿⡿⢠⣶⢶⣦⢰⣶⣶⡆⣶⡆⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡷⠤⠦⠤⠀⠀⠀⠀⠀⢸⣿⠘⠿⠇⣿⡿⣿⡄⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣧⣿⡇⣿⣇⣛⣛⠛⢸⣿⣧⣿⣧⣿⣿⢹⣿⣿⣿⣿⣧⠸⣿⣬⣉⢸⣿⣦⡄⣿⣧⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣤⣤⣤⣄⣀⡀⢀⠀⢸⣿⢰⣶⣦⣿⣷⣿⣧⣿⣿⣀⣿⣿⣀⣿⣿⢸⣿⣿⣿⡇⣿⡏⣿⣿⠀⢈⣿⡏⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⢹⣿⢸⣿⣏⣁⣿⣿⣀⣿⣿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣫⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠛⠙⠛⠃⠙⠛⣛⣻⣶⣿⣿⣟⣟⡛⠙⠛⠘⠛⠘⣿⣿⣿⣿⣿⣿⣫⣸⣛⣛⣻⣛⣛⢛⢛⢛⣾⣿⣿⣶⣶⣶⣷⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣛⣛⡛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣁⣀⡀⣀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠛⣀⣀⣀⡀⢀⣘⣻⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣍⣀⣁⣉⣙⣛⢉⣁⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣧⣄⣾⣿⡟⣻⣿⣷⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⣾⣿⢻⣿⣿⠟⣿⡟⢻⡇⣿⣿⢻⣷⢸⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⣿⣿⢶⣶⠀⠀⣿⡿⠿⠇⣿⣿⢿⣏⢸⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠛⠛⠋⠀⠀⢸⣿⠀⣿⠘⣿⡇⢿⣿⣾⣿⠀⠀⣿⣧⢀⠀⣿⣿⢸⣿⢸⣿⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⡄⠀⠀⠀⣤⠀⠀⠀⠈⠹⣿⣯⡝⣷⣦⡄⠀⠀⠹⣦⠀⠀⢠⡀⢠⡤⠤⠄⠠⠄⢠⠀⠀⠚⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠈⢀⣀⣺⣿⣎⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢫⠀⢀⣼⣧⡀⠘⣿⣿⣌⠟⢿⣤⣀⡀⠈⠲⢾⡟⠃⠀⠀⢀⡀⠀⣀⠀⠈⠛⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠪⠿⢿⠛⠛⠃⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣤⡀⠀⠀⠀⠉⠀⠈⠉⣿⡇⠀⠸⠛⠓⠂⠘⣯⠋⠃⠀⠀⠈⠁⣀⣠⠀⡏⠃⠀⠘⠰⠖⢀⠀⠉⢿⣿⣿⣿⣿⣿⣶⣽⣭⣭⣿⣽⣿⣯⣽⡉⠉⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣁⠀⠀⠛⠟⠂⠉⠇⠀⠀⠆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⠋⠊⢻⣌⢇⠀⠀⠀⠀⠀⣵⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⢽⣷⠀⠈⣻⣿⣿⠿⣿⣿⣿⡿⣿⣿⣯⣵⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣷⣤⠈⠛⠿⠟⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⣉⠉⠓⠚⠚⠻⢵⣼⣱⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣶⣴⡄⠓⡒⡒⣟⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣨
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡀⠀⠀⠀⠀⠀⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠉⠋⠛⢿⠏⠉⠙⠋⠟⢻⣿⣿
⠀⠀⠀⠀⠤⠊⠉⠉⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠿⢿⣿⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠶⠤⣿⠋⠀⠀⠀⠠⣄⡀⠀⠀⠤⠤⣤⣴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠶⢶⣤⠉⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⣤⣤⣤⣤⣤⣤⠶⠾⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠻⢟⠿⠛⠋⠉⠛⠰⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠉⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⣶⣶⣗⣌⣉⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⠈⠑⢀⣀⡀⠀⠀⠀⢤⣶⣶⣤⠄⠀⣀⣀⠤⠄⠀⠀⡀⠄⠀⢀⡀⢀⣉⣩⣭⣧⣆⡀⣀⠛⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣀⠀⠀⠀⣠⣾⡿⠶⠄⠀⠀⠀⠿⠦⠸
⠀⠀⠀⠀⠉⠉⠉⠙⠓⠊⠉⠀⠈⠻⠽⢶⣶⣦⣀⣨⣿⣥⣄⠀⠛⠻⠿⠉⠀⠀⠀⠀⠈⠉⠛⠛⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠉⠋⠋⣝⣉⠀⠀⣉⣛⣛⡓⠲⠤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠛⠋⡉⢵⣶⣶⣶⡶⠖⠶⠶⣆⡀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠡⠦⣄⠀⠀⠰⣿⣿⢿⣿⣿⣯⣝⡃⠀⠈⠉⠉⠀⠀⠀⠀
⠤⠄⠄⠀⠀⠀⠀⠀⠱⢳⣦⣀⣀⣤⣿⣯⣭⠿⠧⠤⠤⠄⠀⠁⠀⠉⣉⠀⠀⠀⢀⠽⣙⣓⣂⠀⢀⣀⣀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⠃⠤⢤⡀⠀⠀⠐⠚
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠚⠚⠛⢉⢛⣛⡉⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⠉⠁⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠐⠀⠀⠀⠀⠀⢰
⠀⠀⠉⠹⢠⡇⠇⠀⠧⠡⠸⠟⠿⣿⣧⡇⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⢀⢰⢿⠻⠟⠋⠉⠉⠛⢿⣿⣿⡟⠀⣿⣿⣿⣷⡅⠀⢠
⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⡄⠀⠀⠀⠈⠛⠋⠉⠀⢼⣿⡿⠃⠀⠰⠺
⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠏⠈⢿⣿⣿⣷⣤⡤⠀⠀⠀⠀⠀⠀⠠⣵⣶⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢉⣽⣿⣿⣿⡄⠀⠈⣿⣿⡟⠏⠀⠀⠀⠀⠀⠀⠀⣀⣮⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠀⠀⠀⠉⠙⠻⠿⠟⠀⠀⠀⠉⠹⡧⠀⠀⣠⣤⡀⠀⠸⠿⠿⢦⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠘⣧⡀⠀⢻⣿⠃⠀⠀⠀⢾⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠀⠈⣠⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡙⠛⠛⣦⠀⠀⢀⡀⠀⠠⣧⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣿⣷⣦⣶⣿⣿⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠷⠤⠛⠛⢿⣿⣿⣿⡀⠀⠙⢿⣿⣿⣿⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣦⠀⣰⣶⣶⠀⣶⣶⠀⣶⣶⠀⣶⣶⢰⣶⡶⣶⡶⣶⡶⣶⣄⠀⢰⣶⡆⣶⣶⣿⣿⣿⣷⣶⢰⣶⣶⢩⣿⢷⣦⢰⣶⣶⡆⣶⡆⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡥⠤⡤⠀⠀⠀⢸⣿⠸⠿⠇⣿⡿⣿⡀⣿⣿⠁⣿⣿⠀⣿⣿⢼⣿⣧⣿⣇⣿⣇⣛⣛⠀⠘⣿⣧⣿⡯⣿⣿⢹⣿⣿⣿⣿⣿⠸⣿⣬⣉⢸⣿⣦⡄⣿⣯⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣀⠀⢸⣿⢰⣶⣦⣿⣷⣿⣧⣿⣿⣀⣿⣿⣀⣿⣿⢸⣿⣿⣿⡇⣿⡏⣿⣿⠀⢠⣿⡏⣿⣷⣿⣿⢸⣿⣿⣿⣿⣿⣴⣾⢹⣿⢸⣿⣏⡁⣿⣿⣀⣿⣿⣩⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⡿⣯⣙⣛⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠛⠈⠛⠃⢙⣿⣛⣿⣶⣿⣿⣿⠛⠋⠚⠛⠘⠛⢻⣿⣿⣿⣌⣻⣿⡫⣜⣛⣛⡛⠛⣛⣛⣛⣻⣿⠿⣿⣿⣶⣶⣶⣴⣶⣶⣶⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⠛⣛⣛⣛⡻⣿⢿⣿⢿⣿⣿⣤⣄⣀⣀⡀⣀⡠⣿⣿⣿⣿⣿⡿⣋⣁⣀⠀⣀⣀⣀⡀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣁⣁⣑⢻⣙⣛⣁⣃⣉⣩⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⢹⣿⣿⣿⣤⣾⣿⡟⣻⢿⣍⡿⣿⣿⣿⣽⣿⢸⣿⣷⣿⡇⣽⣿⢻⣿⠁⠀⣿⡟⢻⡇⣿⣿⢻⣷⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⢸⣿⣿⣿⡏⣿⣿⢶⣶⠀⠀⣿⣿⠿⠇⣿⣿⢿⣧⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⢸⣿⠀⣿⠚⣿⣇⣿⣿⣼⣿⠀⠀⣿⣷⡀⠀⣿⣿⢸⣿⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣷⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿
⣉⣭⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢻⣷⣍⢿⣶⣤⣤⠀⠈⢳⡀⠀⢠⣄⠀⠀⠐⠀⠀⠀⠌⢀⠐⠊⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣏⢉⡀⣀⣺⣿⣗⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣤⡀⠀⠀⠀⠀⠀⡼⢿⣆⠀⠸⣿⣎⠉⢿⣿⡇⠀⠀⠷⠶⠟⠁⠀⠀⢀⡀⠀⠀⠀⠈⠛⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠁⠿⢻⠟⠛⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣷⣦⠀⠀⠀⠀⠀⠈⠉⠀⠀⡟⡛⠒⠀⣿⠇⠀⠀⠀⣠⣄⣀⣤⡰⡎⠃⠀⠀⠒⢢⣄⠀⠙⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣭⣭⣭⣿⣛⣿⣿⣿⡛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠹⣿⣿⣿⣿⣶⣈⠀⠀⠲⠶⠂⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠘⠋⠉⢹⣎⢇⠀⠀⠀⠈⢻⣧⠀⠈⠉⠉⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣧⡀⠛⢿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢤⢸⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣷⣦⣌⠙⠛⠟⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠉⠉⠚⠃⢿⣭⡽⣽⣿⣿⣯⡫⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠐⠐⢰⣤⣶⠼⠧⠭⠍⣹⣿⣿⣿
⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⠀⠀⢀⣌⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿
⠋⠉⠉⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢰⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠘⠱⡿⡻⠟⠻⢿⣿⣟⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠏⠉⠉⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠾⢿⣿⣿⣿⣶⣀⣀⠀⠀⠀⠉⠉⠁⠨⣥⣶⣿⠃⠀⠀⣀⣰⣔⠙⠃⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠭⣤⣴⣖⡒⠊⠁⠀⠀⠈⠉⠠⠄⡀⠀⢀⣄⣀⣀⣀⣀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⢄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⠿⠿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠈⠉⠀⠤⠬⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠋⠉⠊⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⣶⡶⠾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⢤⣴⣶⣒⡁⠉⠀⠀⠀⠀⠀⣷⠄⠀⠀⠀⣀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣷⠀⢈⡉⠁⢀⣀⡀⠀⠀⢤⣴⣶⣦⡠⠀⢀⣀⠠⠤⠄⠀⣀⣀⢀⢀⡀⠀⠈⠙⣳⣿⣇⡀⣈⡉⠟⠉⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⢠
⠲⠒⠒⠂⠀⠀⠀⠉⠉⠙⠛⠛⠋⣉⣀⠹⡿⢿⢿⣶⣤⣀⣽⣯⣥⡀⠘⠻⠿⠟⠁⠀⠀⠀⠁⠒⠚⠒⠚⢿⣿⡛⠉⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⠿⣿⠿⠂⠀⠐⠲⢾⣿⣯⣍⣁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣂⠀⠀⠀⠀⠀⠘⠋⠛⠉⠛⠻⢋⡩⢧⣶⣦⣴⡶⠶⢶⣶⣀⠀⠀⠉⠀⠀⠉⠁⠀⠀⣤⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢂⣀⡀⠀⠀⣨⣿⣿⣶⣶⣼⡿⢷⠀⠐⠓⠶⠦⠐
⠀⠀⠠⠤⠄⠤⠄⠀⠀⠀⠙⠛⣲⣆⣀⣠⣾⣿⣭⣽⠿⠦⠤⠤⡀⠀⠉⠘⢛⣋⠀⠀⠀⣨⣿⣛⣂⣤⠀⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠙⠛⣿⣿⣿⣧⢀⣀⡀⠀⠀
⠀⠤⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠛⠛⢛⣛⣛⣛⡁⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠉⠉⠉⠘⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠯⠀⠍⠉⠁⢐
⣀⣼⡏⠹⢸⡇⠇⠀⠧⠢⠸⠇⠿⠻⠧⢷⢶⣤⣄⠉⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸
⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡬⠟⠛⢿⣿⣿⣿⣿⡗⢽⣿⣿⡿⠀⣿
⠁⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣶⡶⠉⠙⠻⠇⣾⣿⣿⠇⢠⣿
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣦⠀⣀⣀⡀⠀⠀⠀⠀⠿⠿⠿⠆⠈⣿
⠀⠀⠀⠀⠙⠟⠋⠉⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣟⣛⣻⣿⣟⠛⠐⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⡅⠀⠀⣿⣿⣿⢟⠋⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⢿⣿⠿⠛⠁⠀⠚⠿⢿⣿⣿⠀⠀⠈⠛⠛⣔⡂⠀⠀⣀⡀⠀⠀⢰⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⢰⣿⡿⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⣓⠀⠀⢿⡇⠀⠀⠀⠀
⣇⡀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠛⢻⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⠟⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠘⠿⣿⡿⠿⠀⠻⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣁⣀⣀⣠⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠦⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠛⠳⣤⠀⠀⠀⠀⣷⡂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠿⣿⣿⣾⣿⣷⣤⣼⣿⣽⣿⣆⡀⣀⣶⣦⣀⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠐⠚⠛⢿⣿⣿⣿⡅⠬⢿⣿⠛⠑⠉⠙⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣶⢶⣦⠀⣹⣿⣿⠁⣶⣶⠀⣶⣶⠀⢰⣶⢰⣶⡀⣶⡆⣴⡶⣶⣄⠀⠰⣶⡆⣶⣿⣿⣿⣿⣶⣶⢰⣶⡆⢠⣶⢶⣮⢻⣿⣿⡿⣿⡆⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡀⢸⣿⠸⠿⠇⣿⣿⣿⡀⣿⣿⠀⣿⣿⠀⢼⣿⢸⣿⣧⣿⡇⣿⣇⣛⣛⠀⠀⣿⣧⣿⡟⢿⣿⢾⣿⣿⣿⢿⡇⠸⣿⣬⡉⢸⣿⣥⡄⣿⣇⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⢰⣶⣆⣿⣷⣿⡇⣿⣿⡀⣿⣿⣀⣼⣿⢸⣿⢻⣿⡇⣿⡏⣿⣿⠀⠀⣿⡏⣿⡧⢼⣿⢸⣿⣿⣿⣼⡇⢰⣮⢹⣿⢸⣿⡏⠁⣿⣿⡀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣛⣃⣟⡛⠛⣛⡛⣻⣟⣛⣛⠛⠘⠛⢈⠛⠃⢙⣿⣿⣻⠆⠚⠛⠃⠛⠋⠘⠛⠘⢻⣿⣿⣿⣛⣈⣻⢿⡋⢘⣛⣛⣓⣛⣛⣛⢛⣛⣤⣶⣶⣶⣶⣿⣿⣷⣦⣀⣀⡀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣏⡩⣹⠿⢿⠿⢿⡿⢿⣿⢏⣠⣄⣀⡼⢿⣋⣀⡀⠀⠀⣀⣀⣀⠀⣀⣀⣀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣓⣉⣘⣿⢿⣋⣉⣛⣙⣛⣟⡻⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⡛⢣⠈⢻⣿⣿⣿⠿⠅⠿⠇⠽⠿⢸⣿⢸⣿⣯⣿⣧⣾⣿⢹⣿⠀⠀⣿⡟⣻⡇⣿⣿⢻⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿⣇⣠⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡷⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡿⣿⣿⢶⣶⠀⡀⣿⣿⠿⠃⣿⣿⢿⣿⢹⣿⣿⣷⣟⣿⣷⡏⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠛⣿⣿⣿⣿⠏⢀⣄⡰⠻⠛⢹⣿⠀⣿⠙⣿⡇⢿⣿⡼⣿⠀⠡⣿⣇⠀⠀⣿⣿⢸⣿⢸⣿⣿⡟⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⢿⣿⠀⣿⣿⠉⠉⠉⢻⣿
⠟⠛⠛⠛⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⡟⠀⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡦⠀⠀⣷⠀⠀⠀⣶⠄⠀⠒⠀⠀⠀⠀⠀⠉⠁⠉⣭⡍⡉⠻⣿⣿⡿⠻⣿⣿⣿⣿⣷⣾⣷⣷⣶⣶⣶⣶⣿⣿
⠀⠀⠀⢼⣿⣿⣿⣧⠄⠐⠚⠠⣬⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠼⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⣤⣄⡀⠀⠀⠈⠛⢀⣤⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠁⠑⠲⣷⣿⡿⠛⢻⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢀⣴⣌⢿⡏⠁⠀⠘⢀⡄⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠲⠄⠀⢠⣄⠀⠀⠀⠀⠀⠀⠉⠀⠹⣎⠁⠀⠀⠀⠀⠀⠄⠀⠉⠉⠉⠙⠛⠛⠻⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣄⠈⠻⢿⣿⣿⣿⠟⠋⢀⣤⣄⣀⠉⠀⠀⢀⠀⠀⠀⠀⠀⡀⠠⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣴⣶⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⠊⢍⠉⡙⠛⠛⠛⢻⣿⠿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠍⠙⠁⠀⠀⠀⠀⠀⠈⠁⠒⠚⠛⠛⠿⠶⢼
⠤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⣤⠀⠀⠄⠀⠀⠀⠀⢰⣷⣿⣉⣉⣛
⠀⠀⠉⠙⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠒⠲⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣷⡀⠀⠀⠀⠀⠘⠻⠿⠿⠓⠀⢀⣀⡀⠀⠀⠈⢙⢻⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠘⠀⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠾⠤⠀⠀⠒⣒⣶⡶⠶⠦⠀⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠲⠶⢾⡍⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠟⠛⢃⣀⡚⠒⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⠀⠀⢀⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣦⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢽⡻⠛⠻⣿⣤⠄⠀⢠⣀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⠤⠀⠀⠀⠀⠀⠰⠖⠶⠄⠀⠀⠉⠉⠙⠿⠷⠂⠑⠂⠛⢿⣶⣦⣤⡌⠉⢹⣇⠀⠀⢱⣶⣶⡏⠀⠀⠐⠀⠀⣴⣤⣤⣴⣴⣶⠷⠚⠀⣦⡎⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣄⣀⠀⠀⠀⠀⢤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠛⠣⠴⠾⠿⠛⠀⣀⣀⣈⣀⣀⣀⣀⠀⡀⠀⠤⠀⠀⠙⠧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠈⠛⠻⢛⡋⠀⠀⠙⠻⢿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠠⠀⠀⠈⠋⠽⢭⣄⣀⣀⣴⣖⣐⣒⠶⣄⣀⣀⠀⠀⠛⠻⠟⠛⠀⠀⠘⠻⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠤⠄⠀⠀⠠⣿⣿⣿⣿⣿⣟⣛⣀
⢠⣤⣤⣤⣤⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠛⠋⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠒⠲⠒⠀⠠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿
⠀⠹⠿⢻⣻⣿⢿⡯⡧⠡⠸⠇⠼⠈⠇⠇⠀⠀⠀⠀⣀⣈⣉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⠿⠃⠀⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⡛⠿⠿⣿⣿⣿⣿⣿⡝⣿⣿⣿
⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⣤⣭⠉⠛⠻⡿⣀⣽⣿⣿
⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡁⣀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢻⠿⠿⣿⣿⠿⠇⢸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⠹⢿⣿⣿⣟⠂⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀
⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⡿⠟⠀⠠⠤⣤⣿⣷⡄⠀⠈⠻⠿⢃⡔⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠊⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢨⠗⠂⠀⣶⣶⡆⠀
⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠷⠆⠀⢹⣿⠀⠀
⣿⣿⣷⡄⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠰⠗⠀⠀
⠉⠉⠉⠃⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⣶⣾⣿⣿⡏⠈⠉⠋⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣤⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠈⣈⣙⠛⢷⣄⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠛⢻⣿⣷⣾⣿⣦⡀⠀⠀⢠⣶⣛⣷⣦⠀⠀⢠⣄⡀⣲⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠛⣿⣿⣿⣧⠀⠀⠘⣛⣿⣿⡿⠛⠘⠛⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⣶⢶⣦⠀⣰⣶⣶⠒⣶⣶⠀⣶⣶⠀⢰⣶⢰⣶⡄⣶⡆⣴⡶⣶⡄⠀⠀⣶⡆⣾⣿⣿⣿⣿⣶⣶⢰⣶⡆⢠⣶⢶⣦⢰⣾⣿⡿⣿⣿⠖⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⠸⠿⠇⣿⡿⣿⡀⣿⣿⠀⣿⣿⠀⢸⣿⢸⣿⣧⣿⡇⣿⣇⣛⣛⠀⠀⣿⣧⣿⡿⢿⣿⢿⣿⣿⣿⢿⡟⠸⣿⣬⡉⢸⣿⣥⡄⣿⡟⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢰⣶⣆⣿⣷⣿⡇⣿⣿⠀⣿⣿⣤⣾⣿⢸⣿⢻⣿⡇⣿⡏⣿⣿⠀⠀⣿⡏⣿⣗⣺⣿⢸⣿⣿⣿⢸⡇⢰⣮⢹⣿⢸⣿⡉⠁⣿⣇⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⠛⣛⡛⠛⠛⡛⢛⣿⣛⠘⠛⡘⠛⠃⣙⣿⡛⠻⠆⠚⠛⠃⠛⠃⠘⠛⠘⣿⣿⣿⣞⣛⠈⡻⠿⠋⠘⡛⢛⠃⢛⠛⠓⢛⠛⢀⣤⣄⣤⣶⣶⣶⣶⣶⣶⣦⣀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣋⠉⢁⠀⢀⡈⢉⣛⢃⣉⣤⣀⡸⢿⣃⣀⡀⠀⠀⣀⣀⣀⠀⣀⣀⣐⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⢛⣛⣛⣛⣛⣉⣈⡛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢹⣿⠛⣿⣿⡅⠿⠇⠽⠯⢸⣿⢸⣿⣧⣿⣧⣿⣿⢹⣷⠀⠀⣿⣟⣻⡇⣿⣿⢻⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣟⣿⣇⣈⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢩⣿⣿⣿⣌⡻⣿⠇⠀⠀⣀⣸⣿⠀⣿⣿⣿⡏⣿⣿⢶⣶⠀⠀⣿⡿⠿⠃⣿⣿⢿⣯⢼⣿⣿⣇⣛⣿⣷⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣴⣿⡿⠋⢸⣿⠀⣿⠘⣿⡇⢿⣿⡼⣿⠀⠀⣿⡇⠀⠀⣿⣿⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⣿⣿⠋⠙⠛⠛⠻
⠉⠒⠻⠿⠿⠿⠛⠛⠛⠛⠛⠉⠛⠋⠈⠉⠉⠉⢀⣤⡿⠀⣼⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠀⢠⣤⡀⠀⠀⢰⠆⠀⠀⠂⠀⠀⠠⠀⠀⠉⠩⢻⡻⠿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴
⠀⠀⠀⠀⠀⢤⣦⣤⣴⣖⣀⣠⡤⠀⢀⣠⣴⣿⣿⣿⣷⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⠜⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠈⠙⠂⣠⣀⠀⠀⠀⠀⠉⠀⢘⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠢⠀⠀⠀⠀⠀⠉⠉⠉⠛⢀⣠⣤⣴⣾⣟⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⢀⣤⣧⢻⡍⠁⠀⠐⢂⣄⠀⠙⡆⠲⠴⡲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⢿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠈⠁⠩⢷⠹⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠨⠈⠯⠿⠿⠿⠿⠿⡿⣿⣿⣿⣷⣷⣶⣷⣶⣮⣈⣽
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣀⡈⠛⠿⠿⠿⠛⢂⣠⣤⣀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣻⣯⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢍⡛⡻⢿⢿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠻⠶⠀⠀⠀⠁⠀⠐⠀⠀⠠⣶⣾⣼
⠀⠠⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠉⠀⠀⠀⠀⠀⢠⣤⣠
⠀⠀⠀⠈⠉⠙⠛⠻⠛⠗⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⢀⠠⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠒⠠⠤⠼⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣦⡀⠀⠀⠀⠀⠀⡿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠼⠽⢟⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠠⠿⠤⣿⠟⠀⠀⠀⣤⣆⡉⠛⠁⣤⣠⣀⣠⣀⡀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠩⢥⣤⣐⡒⠚⠋⠉⠉⠀⠙⠓⣄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠿⠿⠟⠁⠠⠤⢠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠡⠀⠀⠀⠀⠐⠒⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⠂⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣭⡉⠀⠠⠤⠀⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣀⣛⣓⣶⣶⣿⣶⣏⡉⠉⠀⠀⠀⠀⢄⣠⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⡤⠀⠀⠀⠠⢤⣤⣤⣤⠀⠀⠉⠉⠛⣿⣧⠄⠂⠤⡠⣶⣶⣤⣀⡀⠛⠛⠛⠒⠀⠀⣤⣭⣥⣆⠀⠀⠄⠄⠀⢀⠀⠀⢈⣭⣯⣽⡀⣩⣿⠛⠉⠀⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠒⠀⠀⠋⠙⠿⠷⠀⣨⣿⣿⢦⠀⠉⠉⠋⠀⠀⠀⠀⠀⠈⠉⢉⠉⠙⣿⡍⠀⠀⠘⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⡶⡶⠀⠀⢀⣸
⠈⠰⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠉⠁⠷⢶⣂⠀⠀⢀⡤⠀⠠⢤⣤⡀⠀⠈⠓⠻⠿⠿⡿⠛⠉⠙⠳⣆⣀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢗⣀⠀⠀⠀⠀⢐⣤⣤⣤⣤⣴
⠀⠠⠀⢀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠵⢶⠉⠻⡿⠋⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣭⣥⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠉⠉⠁⠀⠀⠙⠛⠛⠛⠿⣿
⠀⠙⠋⠹⢻⡿⣿⢿⡯⡣⠸⠇⠿⠋⠇⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠻⢿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠉⠉⠀⠈⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠒⠉⠉⠙⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠙⠿⠇⠀⠈⠹
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣦⣾⣿⡆⢠⣦⣤⠄⠀⠀⠀
⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⡤⠸⣭⣭⣽⣿⡏⠁⢰⣿⣿⣷⣦⣤⢤
⣤⣤⣬⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣿⣿⡿⠃⠀⣘⣻⣿⣟⡀⠀⠀⣿⣿⡟⡛⠅⠀
⠉⢉⣛⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⢻⣙⠿⠋⠁⠀⠈⠙⠛⠻⠿⠇⠀⠀⠈⠉⠙⣯⡄⠀
⣵⣤⣀⣈⡁⠂⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⢇⡀⠀
⣿⣿⠿⢿⣿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠨⢿⠀
⣿⣿⡃⠈⠙⣾⣿⣷⣶⡄⢀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⢛⠛⠉⠁⠀⠻⠿⢿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠻⠿⠿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣶⣶⣿⣧⡀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠴⢷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣈⡹⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢠⣶⣶⣭⡙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⠉⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠐⠒⠚⠓⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⣬⠈⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣇⡀⠀⠀⠀⠀⠀⢶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡟⠛⠓⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⣿⣐⣿⣧⡄⢀⢼⣿⣦⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢶⣦⠀⣰⣶⣶⠀⣶⣶⠀⣾⣿⣋⣷⣶⢹⣷⠀⣶⡆⣴⣶⣿⡄⠀⠀⣶⡞⣿⣿⣿⣿⣴⣶⣶⢰⣶⣶⢰⣶⢾⣿⢳⣶⣶⡆⣶⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡯⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣼⠿⠇⣿⣿⣿⡀⣿⣿⠀⣿⣿⠀⣹⣿⢸⣿⣧⣿⡇⣿⣿⣛⣛⠀⠀⣿⣧⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⠸⣿⣬⣉⢸⣿⣤⡄⣿⡿⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡟⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⣷⣿⣇⣿⣿⡀⣿⣿⡀⢿⣿⢸⣿⢻⣿⡇⣿⡏⣿⣿⠀⠀⣿⡏⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⢰⣮⢹⣿⢸⣿⡉⠁⣿⣇⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣃⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠘⠛⠘⠛⠃⢙⣿⠛⠛⠀⠘⠛⠃⠛⠛⠛⠛⠻⣿⣿⠛⠘⠛⠈⠛⠟⢋⠘⢛⠛⠃⠛⠛⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣷⣟⣖⣲⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢒⠀⢀⡀⢀⣀⢀⣀⡀⣀⡀⢀⣀⣀⡀⠀⠀⣀⣀⣀⠀⣀⣈⣉⡿⢿⣦⣶⣄⣤⣀⣀⣠⣀⣠⣍⣀⣀⣀⣄⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢹
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣷⣿⡇⠽⠿⢸⣿⢸⣿⣧⣿⡇⣾⣿⢹⣷⠀⠀⣿⡟⢻⡇⣿⣿⢻⣷⢸⣿⡟⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣼⣿⠛⣿⣿⡛⣿⡇⠀⢸
⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣀⡻⣿⡶⠀⢸⣿⣀⣿⣿⣿⡇⣿⣿⢶⣶⠀⠀⣿⡿⠿⠃⣿⣿⢿⣇⢸⣿⡿⣷⣿⣿⣷⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣾
⣶⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣾⣿⢹⣿⠘⣿⡇⠹⣿⡼⣿⠀⠀⣿⣷⢶⡄⣿⣿⢸⣿⢸⣿⣶⡞⢿⣯⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠶⢾⣿⣿⡿⠛⠻⠿⠟⠛⠛⠛⠃⠙⠿⠟⠉⠉⢉⠁⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠰⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣤⣤⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⣀⣀⠀⠀⣀⣠⣤⣾⣿⡄⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⣀⣀⡀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠉⠉⠙⠳⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠷⠆⠀⠀⠀⠀⠈⠉⠛⠛⠻⠭⢩⣤⣤⣶⣿⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⣴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣤⣤⣬⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⠇⠉⠻⣿⣿⣿⣿⣇⠈⢿⣿⣿⣿⡄⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠉⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢽⡙⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢛⢻
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⣀⠙⠛⠿⠿⠟⠋⣀⣀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⢿⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠴⠻⢣⠉⡙⢻
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠦⠉⠛⠀⠀⠄⠀⠀⠈⠘⠚
⠀⠀⠀⠀⠀⠈⠉⠙⠓⢶⣶⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣄⠀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⢠⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠂⠤⠤⢤⠰⣶⣆⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣾⣿⣿⣄⠀⠀⠀⠀⠘⠛⠛⠛⠻⣤⢀⣤⣤⠀⠀⠀⠉⣿⣷⣶⡄⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠈⠛⠛⠿⠋⠀⠀⠰⢶⢿⡄⠉⠰⠶⠶⣶⣶⣦⡤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠓⠶⠮⡭⡍⠃⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠤⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣛⠛⠛⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⢀⠄⡀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠛⠿⢿⣿⣇⡀⡈⠉⢀⣤⡀⠀⠀⠠⣤⣴⡄⠀⢀⣀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠬⣭⡟⠛⠻⣟⡂⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀
⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠌⠉⠀⠁⢰⣶⡄⠀⠠⣤⣀⡀⠁⠿⢷⡖⠂⠀⠀⠀⠀⠀⠶⣄⣀⣀⣲⠶⠃⠀⠰⡆⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⣶⡤⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⢄⠤⠀⠀⠀⠀⡀⠀⠀⢀⠀⠉⠉⠁⠁⠀⠠⣀⠀⠤⠤⠀⡀⠀⠀⠀⠄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠛⠿⠿⢻
⠋⠠⢀⣀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠈⠈⠙⠷⣤⣤⠾⣿⡤⠌⠙⠲⠤⢤⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⣀⠀⠀⠀⠀⣼
⠀⠘⠛⠹⢸⡿⠿⠿⡿⠻⠿⠟⠿⠻⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⢁⡀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣏⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠿⠿⠿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠛⠛⠃⠀⢙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠊⠉⠙⠻⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠸⠿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣤⣴⣶⠄⢀⣤⣤⠀⠀
⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⠈⠙⢛⣿⣿⣿⡛⠁⢸⣿⣿⣤⣤
⣉⣁⣀⣀⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡿⠀⠀⠻⠿⣿⡇⠀⠀⢸⣿⣿⡿⣿
⠉⠙⠛⠛⠻⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠿⡏⢽⡿⠋⠁⠀⠐⠚⠺⣿⣿⠄⠀⠀⠉⠋⢻⡿
⣿⣷⣄⡉⠉⠐⠮⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⣿⣿⣿⣿⠿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢻
⣿⣿⣿⣿⠀⠘⢳⣿⣿⡆⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠙⠛⠁⠀⠀⠛⠿⢻⣿⣿⣷⣶⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⡀⠀⠀⠀⠀⠀⠿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣾⣿⣷⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⣀⠀⠀⡸⢿⣿⣿⣿⣿⡇⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡾⢻⣿⣶⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠺⡿⠑⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠦⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲⠒⠉⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⡶⠶⣿⣿⣿⣿⣿⢿⣿⣿⣧⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠘⣷⣿⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⢹⣿⣄⠀⢀⣻⣦⣤⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⣰⣶⣶⠀⣶⣶⠀⣶⣶⠿⣿⣿⢱⣷⠀⣶⡆⣴⡶⣿⡅⠀⠀⣶⡆⣿⣿⣿⣷⣴⣶⣶⢰⣶⣶⢠⣶⢶⣾⢿⣿⣷⡆⣶⡾⠛⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣧⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⡀⣿⣿⠀⣿⣿⠉⣻⣿⢸⣿⣧⣿⡇⣿⣇⣛⣛⠀⠀⣿⣧⣿⣟⣿⣿⣿⣿⣿⣾⢿⣿⠸⣿⣬⣉⣸⣿⣤⡄⣿⡇⠀⣿⣿⡿⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣿⣇⣿⣿⡀⣿⣿⡀⣿⣿⢸⣿⢿⣿⡇⣿⡏⣿⣿⠀⢠⣿⡏⣿⡏⣽⣿⣿⣿⢹⣿⢸⡇⢰⣾⢹⣿⢸⣿⡉⠁⣿⣇⠀⣿⣿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠽⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠘⠛⠈⠛⠃⠙⠛⠛⠛⠀⠘⠛⠃⠛⠛⠛⠛⢿⣿⡟⠛⠘⠛⠈⠛⠛⠋⠘⡛⠛⠃⠛⠛⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢠⠠⢀⡀⢀⣀⢀⣀⡀⣀⡀⢀⣀⣀⡀⠀⠀⣀⣀⣀⠀⣀⣀⣚⡛⢂⣀⣠⣤⣄⣀⣀⡀⣀⣃⣀⣘⣀⣀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸
⠈⠛⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⡿⠿⢸⣿⢸⣿⣧⣿⡇⣾⣿⢹⣿⠀⠀⣿⡟⢻⣇⣿⣿⣿⣷⢸⣿⠛⢳⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣼⣿⠛⣿⣿⠛⣿⡇⠀⢸
⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣀⣄⡉⢿⣿⣦⣸⣿⠈⣿⣿⣿⡇⣿⣿⢶⣶⠀⠀⣿⡿⠿⠋⣿⣿⢿⣏⢸⣿⠿⢇⣙⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣤⣿⣿⣦⣶⣶⣿⣾
⣤⣤⣄⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣠⣿⡾⣿⡇⠹⣿⡼⣿⠀⢀⣿⣿⠲⣦⣿⣿⣸⣿⢸⣿⣤⡌⢿⣧⣿⠇⣿⡟⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠛⠛⠻⠃⠀⠀⠠⠾⠿⠿⠿⠛⠛⠿⠟⠛⠛⠛⠋⠹⠿⠟⠋⠉⢉⣽⠀⣴⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⣿⣷⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣷⣽⣿⣿⣾⣷⣿⣿⣿⣿⣷⣦⣤⡄⠈⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠄⢀⣀⠀⠀⢀⣀⣤⣴⣿⣿⣿⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠙⠛⡛⠛⣿⣿⣿⠿⢿⣿⣿⣿⣷⣾
⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠉⠉⠉⠙⠫⠉⣥⣤⣤⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠀⠀⠀⠀⠀⠀⢲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⣸⣿⣛⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠉⠹⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣷⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⡟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻
⠀⠀⠀⠀⠁⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⡀⠙⠿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠒⠒⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠐⠐⠿⠿⠻⠻⠿⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣤⣈⣉⡉⣁⣤⣴⣶⣶⣤⣄⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣭⣾
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⡨⠫⠉⢻
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣜⠛⡓⡀⣀⠀⠈⢐⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠶⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⡀⠈⠉⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠰⠦⣢⣀⣀⣀⣠⡄⠀⠈⠈⠉⠉⠉⠁⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⣤⠀⠀⠀⠀⠀⠸⠿⠿⠿⢦⡀⢀⣀⣀⠉⠈⠙⠻⣷⣤⣤⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠸⠿⠾⣿⠏⠀⠀⢀⣴⣞⡉⠛⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠭⠥⣤⣄⣒⠒⠉⠙⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⢠⣀⠒⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠀⢠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠐⠆⠀⠀⠀⠀
⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣶⠀⠀⡀⠂⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⣙⣒⡶⠰⢲⣆⠉⠁⠀⠀⠀⠀⠀⠐⢦⠀⠀⣀⠀⠀⠀⠀⠀⠒⠀
⠶⠦⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠋⠂⠀⣈⡀⠊⠉⠁⢠⡤⠀⠉⣉⣀⠈⠈⢳⣶⣶⠎⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⡤⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⢀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠛⠙⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠙⠝⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣼
⠉⠽⠛⠁⢀⠀⣤⠬⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂⠐⠂⠀⠀⠀⠊⠓⣲⣤⣀⣀⣶⣦⣄⡒⢶⣤⣤⡀⠈⠀⠀⠙⠉⠈⠀⠉⠈⠀⣤⡀⠁⠁⠀⠀⠀⠀⠀⠀⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡄⠀⠀⠀⢘
⠀⠘⠋⠹⢻⡟⠿⠿⠿⠳⠿⢿⡿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢑⡂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠛⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠝⠻⠟⣿⣿⣿⣿⣿⣇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠉⠛⠛⠛⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣯⣭⣭⡥⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣀⣄⡀⠀⣰
⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠻⠿⠿⢿⣿⠿⠇⠀⣿
⠀⠀⣠⢴⠿⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣨⣿⣿⣿⡇⠐⠇⣿⣿⡟⠁⠀⠀⣿
⠀⠀⠀⢰⣶⣶⣦⣤⣽⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⣿⡿⢻⣿⡿⠋⠀⠠⣤⣼⣿⣧⡄⠀⠀⠙
⣶⣶⣴⢆⣀⡀⠩⣉⣙⡛⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡑⠚⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣷⣤⣤⣌⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢿⣿⣿⣿⣿⣿⣿⣿⡞⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⠟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⣷⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠟⠛⠛⠛⠃⠀⠀⠻⠿⠗⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡏⠉⢹⣿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠁⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⠛⠿⡅⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠟⣻⣿⣧⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⠶⠆⣼⡏⣿⣿⣿⣿⣷⣄⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⠹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢉⡀⢸⣿⣿⣿⣿⣿⣻⣿⣇⢀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⢸⠀⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⣷⡄⠀⠀⢤⣀⠀⢹⣤⣤⡀⠚⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⠉⠉⠙⠛⠻⣿⣷⣾⣿⣿⣿⣿⣶⠀⣶⣶⠀⣶⣶⠀⢰⣶⢸⣿⡿⣶⡆⣴⡶⣶⡌⠀⠀⣶⡆⣶⣿⣿⣷⣰⣶⣶⢰⣶⡶⢠⣶⢶⣦⢰⣶⣶⣶⣾⣷⠀⣶⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⠀⣿⣿⠀⢸⣿⢼⣿⣧⣿⡇⣿⣇⣛⣛⠀⠀⣿⣧⣿⡟⣿⣿⣿⣿⢿⣾⢿⡷⠸⣿⣬⣉⢸⣿⣥⡄⣿⡇⠀⣿⣿⣤⠘⠿⢿⣿⣿⠒⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡀⣿⣿⠀⣼⣿⢸⣿⢻⣿⡇⣿⡏⣿⣿⠀⢀⣿⡏⣿⡇⢸⣿⣿⣿⣾⣿⢺⣷⢰⣾⢹⣿⢸⣿⡛⠓⣿⣇⠀⣿⣿⠉⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠘⠛⠈⠛⠃⠙⠛⠛⠛⠀⠘⠛⠃⠛⠓⠚⠛⢻⡿⠛⠛⠘⠛⠈⠛⠟⠋⠘⠛⠛⠃⠛⠛⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣀⣀⣠⣄⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢀⡀⢀⣀⢀⣀⡀⣀⡀⢀⣀⣀⡀⠀⠀⣀⣀⣀⠀⣀⣀⣈⡁⢀⣀⣀⡀⣰⣶⣆⠀⣀⣀⣀⣀⣆⣀⢠⣄⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢠
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⢸⣿⣧⣿⡇⣾⣿⢹⣿⠀⠀⣿⡟⢻⣇⣿⣿⣿⣷⢸⣿⡟⢳⣿⡿⡿⡇⣿⣿⣿⣿⣿⣿⣾⣿⡟⠛⣿⣿⣼⣿⠛⣿⣿⡛⣿⡇⠀⢸
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢿⣿⣿⣸⣿⣿⣿⡇⣿⣿⢶⣶⠀⠀⣿⡿⠿⠋⣿⣿⢿⣯⢸⣿⠿⢇⣙⠿⣷⡆⣿⡟⢻⣿⢻⣿⡟⣿⡿⡿⣿⣿⣿⣿⣀⣿⣿⣆⣀⣀⣄⣸
⠀⠀⠀⢀⣀⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣟⣿⡇⠿⣿⡼⣿⠀⡄⣿⣿⡘⢿⣿⣿⣾⣿⢸⣿⣦⣜⢿⣧⣿⠇⣿⡇⢸⣿⣼⣿⢣⣿⣷⣾⣿⣿⢿⣿⠹⣿⣿⣿⣿⣿⣿⣿
⠀⢤⣶⣾⣿⣦⡄⠀⠠⠾⢿⣿⣿⡿⠿⠿⣿⠟⠛⠛⠛⠉⠻⠿⠟⠙⠛⣛⣛⣿⣿⡧⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠑⣮⣽⣤⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣿⣿⣾⣿⣿⣋⣙⢹
⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⣀⠀⠀⣀⡀⢤⣄⣀⣨⣿⣿⣿⡟⢠⣶⡿⠛⠀⠀⠀⠘⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⣿⣧⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣯⠍⠐⠈⣡⣴⣾⣿⣿⣿⣿⣿⡟⢡⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠲⡄⠀⠀⠀⠀⠈⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠹⣿⣿⡭⢭⣽⣿
⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠐⠛⠱⣾⣿⡿⠛⢿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣶⣶⣷⣷⣴⣮⣿⣻
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠈⢿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⢀⣸⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠘⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡤⡀⠀⠈⠉⠿⠿⠟⠉⢀⣴⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣶⣦⣤⣦⣤⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠞⠿⠶⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠠⠤⠼⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠉⠙⠓⠢⠴⠾⣿⣤⣀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⣿⣿⣿⣆⣀⣀⠀⠀⠀⠉⠉⠉⢩⣶⣀⣶⣶⠄⠀⠀⠀⣻⡿⢿⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠉⠛⢃⡀⠀⠘⠻⢿⠷⠀⢐⣒⣛⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⣿⣤⡖⠀⣤⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠛⠛⠂⢯⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣭⡍⠁⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⢀⡄⠠⠤⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐
⣀⠀⠀⢀⣀⣀⠀⠀⠀⡀⠀⠐⠖⠀⠀⠀⠐⠶⠶⠦⠄⠀⠀⠈⠉⠉⠻⠧⠔⠲⠄⠰⠶⠆⠀⠀⠀⠒⠾⠴⠂⠤⢤⣀⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠏⠈⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀
⡟⠛⠛⢛⣀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠘⠻⠀⠀⣘⡷⠤⠄⠀⠛⠻⠃⠀⠀⠀⠀⠀⠀⠒⠦⠄⠤⣼⠛⠃⠀⠐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡑⠦⠀⠘⡛⣿⣯⠥⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣤⠀⠀⠉⠘⠲⣶⣂⠀⠀⢠⣤⠀⢤⣤⠀⠀⠀⠀⠀⠀⢲⡦⠀⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀
⠁⠈⠉⠹⢹⡷⠿⠿⡿⠣⢻⣟⢿⣿⣷⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠿⠖⠉⠻⠟⠂⠈⠉⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠣⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠻⠿⠛⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⡍⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣯⡍⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠿⠿⢿⣿⣭⣭⣁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠀⠈⣻⣿⣿⣿⣧⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⣾⣿⣿⠉⠉⠁⠀
⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣷⣾⠚⢋⠀⣀⣀⠀
⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢥⡄⠞⠀⡛⠿⠀
⠀⠀⠀⠀⢀⣴⣿⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠉⠀⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⡉⢹⣿⣿⣇⠀⠤⢀⣿⣿⠓⠀⠀
⠀⠀⠤⠄⠈⣭⣤⣤⣬⣜⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠓⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⠇⢸⣿⡿⠃⠀⢠⣤⣥⣾⣥⠀⠀
⣾⣿⣶⣶⣶⣌⣉⠉⣙⣛⠛⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠶⠍⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣈⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡟⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠉⠿⠿⠇⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣉⣹⣿⣿⠋⠉⣿⣿⠾⠿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠋⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⢿⠉⠍⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣶⣤⣼⣦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⠶⠴⠶⣄⣼⣿⣿⣿⣿⣿⣄⡀⢀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠉⠛⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠟⢅⣻⣿⣿⣿⣿⠷⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠐⠒⠛⠛⠛⠂⠀⠀⠀⠀⢀⣿⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢹⣤⠀⠀⠂⣀⠀⠐⢻⣤⡀⠀⠛⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠻⢿⣿⢿⣶⣿⣿⣿⣿⣿⣷⣶⠀⣶⣶⠀⢰⣶⢰⣶⣿⣿⡆⣴⡶⣾⣏⠀⠀⣶⡆⣾⣿⣿⣷⣰⣶⣶⢰⣶⣶⢠⣶⢶⣦⢰⣶⣶⡾⣷⣾⣿⣶⣶⣶⠻⠀⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠤⠤⠤⠄⢠⠀⠀⠘⣧⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣇⣿⣿⠀⣿⣿⠀⢸⣿⢸⣿⣿⣿⡯⣿⣇⣻⣛⠀⠀⣿⣧⣿⡿⣿⣿⣿⣿⢿⣾⢿⣿⠸⣿⣬⣉⢸⣿⣧⡍⣿⡟⠁⣿⣿⡄⠀⠀⠻⣿⣿⣿⣷⠤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⠀⣾⣿⢸⣿⢻⣿⡇⣿⡏⣿⣿⠀⠰⣿⡏⣿⡷⣿⣿⣿⣿⣾⣿⢺⣷⢲⣾⢹⣿⢸⣿⡟⠓⣿⣷⠀⣿⣿⠁⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠘⠛⠘⠛⠃⠙⠛⠛⠛⠀⠀⠛⠃⠛⠛⠛⠛⢹⣿⠛⠛⠘⠛⠈⢛⣟⡋⠘⠛⠛⠃⠛⠛⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⣀⡀⠀⠀⣀⣀⣀⠀⣀⣀⣈⡃⢀⣀⣀⡀⣀⣉⣉⡁⣀⣀⣀⣀⣀⣠⢄⣀⣄⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⡀⠀⢀
⠀⠀⠀⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢸⣿⣧⣿⡇⣾⣿⢹⣿⠀⠀⣿⡟⢻⣷⣿⣿⣿⣿⢸⣿⡟⢳⣿⡏⠿⠇⣿⣿⣿⣿⢿⣿⡾⣿⡟⢻⣿⣿⣼⣿⣛⣿⣿⡟⣿⡇⠀⢸
⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⡇⣿⣿⢶⣶⠀⠀⣿⣿⠿⠏⣿⣿⢿⣯⢸⣿⠿⢇⣙⣿⣷⡄⣿⡇⢸⣿⢸⣿⡧⣿⡿⠿⣿⣿⣿⣿⣽⣿⣿⣇⣄⣀⣀⣸
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⢿⣿⡼⣿⠀⣠⣿⣏⠘⢿⣿⣿⣿⣿⢸⣿⣶⡞⢿⣧⣿⠇⣿⡇⢸⣿⣼⣿⠁⣿⣷⣶⣿⣿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⣤⣶⣶⣶⠄⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠉⠻⠿⠇⠘⠛⠛⠛⢻⣿⣿⣧⠀⠉⠁⠀⠀⣿⠇⠀⠀⠈⢿⣦⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣄⡀⠀⠀⠀⢀⢀⡀⠀⢀⣈⣿⣿⣿⣿⡟⢁⣤⠶⠀⠀⠀⠸⠀⠀⠀⠀⠀⠙⠛⢷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣯⣭⠄⠐⠈⣩⣴⣶⣿⣿⣿⣿⣿⡟⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠒⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⣿⡿⠛⢿⣿⣿⣿⣿⣿⠃⢠⡿⠿⠆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⣥⣄⡀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡋⠉⠉⢟⡿⠺⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠹⣿⣿⣷⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣶⡀⠀⠙⠿⢿⡿⠿⠟⢁⣰⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠓⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣶⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⠠⠤⠀⢺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠒⠒⠤⢄⠀⢶⣆⣀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠛⠛⢻⣤⣀⣀⣀⠀⠀⠀⠉⣿⢿⡦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠃⠀⠀⠐⠾⣿⣤⠀⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⢦⡄⠀⢠⣀⠀⠐⠀⠀⠀⠠⠄⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣷⣶⣼
⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣯⣭⠉⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠐
⣄⣀⠀⠀⠀⣀⣀⣀⠈⠉⢁⠀⠀⠰⠆⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠉⠛⢻⢿⡄⠀⠀⠀⠰⠦⠀⠀⠀⠰⠦⠀⠀⠀⠀⣀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠠⢭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠀⠀⠀⠀
⠀⠘⠛⠂⠐⣂⣀⣈⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠠⠤⠄⠀⠘⠿⠿⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⣠⡒⠀⠀⢙⣿⣿⡯⠀⠀⠈⠐⠂⠀⠀⠀⠒⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠤⠤⠀⠀⠀⠀⠀⠠⠀⠀⠐⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠿⠏⠹⢹⡟⠿⠿⠿⠻⠿⠟⣿⡿⣧⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠉⠺⢿⣿⣿⣿⣿⣿⡿⡁⠀⠸⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⣿⣿⣄⠀⢾⣿⣿⣿⣿⣟⢛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⢀⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⠛⠛⣿⣯⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠻⠿⠁⠈⠿⠿⢿⣿⣿⣸⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⣿⣿⡏⠹
⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣻⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⡟⠋⡀⢐
⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡧⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣿⣿⣿⣿⣿⣿⠈⠉⠤⠰⠃⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠘⠃⠸⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⣯⣿⣿⡆⠀⠂⣸⣿⢿
⠀⠀⠀⠀⢀⣀⠀⣩⣭⣥⣤⣀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏⠾⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡿⠘⣿⡿⠛⠁⠀⣤⣤⣀⣼
⠀⠀⣠⣶⣶⣦⣤⣀⠉⠙⢛⠿⠿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠱⠎⠉⠀⠀⠀⠀⠀⠀⠉⠉
⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣦⣈⣉⡛⠨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⣿⣿⣿⣽⣿⣿⣿⣷⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⣿⣾⣿⣿⣿⣿⣿⠿⠿⠿⠏⠀⠉⣶⣿⣷⠀⢀⡀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠀⠀⠈⣏⣉⣿⣿⠟⠉⢻⣿⠦⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢛⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠉⠀⠩⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⡸⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣦⣶⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠉⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⢤⣤⡀⣀⣿⢿⣿⣿⣿⣇⠀⠉⠻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⠿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠼⣿⣿⡇⣿⡄⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠒⠚⠛⠓⠀⠀⠀⣾⡇⠀⠘⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣧⡄⠀⠚⢀⡀⠀⢘⣧⣤⠀⠘⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢺⣾⢿⣷⣿⣶⣶⣾⣿⣿⣿⠀⣶⣶⠀⢰⣶⢰⣶⡀⣶⣾⣷⡶⣾⣏⠀⠰⣶⡿⣿⣿⣶⣶⢰⣶⣶⢰⣶⣶⢠⣶⢶⣦⢰⣶⣶⡆⣶⣾⠷⣶⣿⣷⠀⠰⣾⡇⢰⣿⣿⣿⣷⠀⠀⠀
⠀⢀⠀⠀⠀⠤⠤⠠⠀⠀⢻⠀⢸⣿⠸⢿⣇⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣸⣿⢸⣿⣧⣿⣿⣿⣇⣛⣟⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⠸⣿⣬⡉⢸⣿⣧⡄⣿⣿⠉⣿⣿⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⢰⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡀⣿⣿⢸⣿⢻⣿⡇⣿⡏⣿⣿⠀⠀⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⢺⣿⢲⣾⢽⣿⢸⣿⡋⠁⣿⣿⠒⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠘⠛⠘⠛⠃⠙⠟⠛⠛⠀⠀⠛⠃⠛⠛⠛⠛⢻⡿⠘⠻⠛⠛⠈⠛⠟⠋⠘⠛⠛⠃⠛⠛⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⢀⣀⡀⣀⡀⢀⣀⣀⡀⠀⠀⣀⣀⣀⠀⣀⣀⣘⡁⢀⣀⣀⡀⣀⣀⣀⠀⣀⡀⢀⣀⣀⡀⠀⣀⣀⣀⣤⣀⢀⣀⢀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⠀⡿⠛⣿⣿⠛⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣧⣿⡇⣾⣿⢹⣿⠀⠀⣿⡟⢻⣷⣿⣿⢻⣿⢸⣿⠛⢳⣿⡏⠿⠆⣿⡇⢸⣿⢹⣿⡀⣿⡟⠋⣿⣿⣸⣿⠛⣿⣿⠛⣿⡇⠀⢰
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⣿⣿⡇⣿⣿⢶⣶⠀⠀⣿⣿⢿⠏⣿⣿⣿⣯⢸⣿⡿⢇⣙⣿⣷⡄⣿⡇⢸⣿⢸⣿⡇⣿⡿⠇⣼⡿⣿⣿⠀⣿⣿⣧⣠⡜⡜⢸
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣼⣿⣿⣿⣷⣿⣿⡼⣿⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⢸⣿⣷⡞⢿⣧⣿⠇⣿⣧⣸⣿⣼⣿⠃⣿⣷⣦⣿⣇⢿⣿⠀⣿⣿⢿⣿⣿⣷⣼
⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⡇⠘⠛⠛⠋⠁⢸⣿⣯⡅⠀⠀⠀⣰⡀⠀⠀⣦⠀⠒⠶⢦⡄⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⠛⠋⠀⠉⠉⠀⠀⢀⡀⠀⣀⣲⣿⣾⣿⣿⠋⣠⡤⠄⠀⠸⠃⠀⠀⠘⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣾⣷⡶⠂⢀⠄⠒⠈⣡⣶⣾⣿⣿⣿⣿⣿⠋⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⣴⣾⣿⠟⠻⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⢻⣿⣿⠇⠀⠠⣾⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠃⠔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⢻⡏⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠉⠀⠠⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠀⠀⠈⠻⢿⣿⣿⠿⠟⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⣤⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠠⠄⣀⢰⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠄⠤⢄⢀⣀⣤⣄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣶⣾⣿⣷⡄⠀⠀⠀⠀⠀⠘⠿⠿⠷⣦⡀⣀⣀⡀⠀⠁⠈⢻⡷⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠘⠃⠻⠿⠿⠃⠀⠠⢤⣶⣷⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢒⣀⠠⠀⠀⠀⠀⠂⠀⠀⠠⣤⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠜⠛⢾
⠀⢀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠶⠄⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣭⠉⠁⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠈
⠀⠤⢤⣀⠀⠀⠀⢀⣀⣀⠀⠈⠁⣀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⡟⡀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢉⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠀⠰
⠀⠀⠀⠀⠛⠑⠀⠒⣀⣀⡙⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠿⠿⠂⠀⠀⠀⠀⠀⠀⠤⣄⠀⢀⡐⠶⠇⠀⠠⡄⠤⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀
⠀⠐⠒⢠⣄⠂⣤⠤⠙⣿⣯⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⢤⠄⠀⠀⠀⠀⠠⡄⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠿⠿⢻⡏⠿⠿⠯⠣⠸⠟⠿⠿⢏⡇⠀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠈⠐⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠙⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⠋⠈⢿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣷⣧⡀⠀⣿⣿⣿⣿⣿⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠰⢿⣿⡇⠀⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠿⠿⣿⣿
⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠷⠀⠸⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇⢸⢸⣿⣿⣿
⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣾⡗⠛⠉
⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⢿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⡏⠈⠫⣡⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠃⠸⠃⢿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡛⠹⣟⣿⣿⡀⠠⠄⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠛⡋⠁⠀⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡏⣾⣿⣿⣿⣿⣿⡿⠟⠛⠻⠿⠿⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⢸⣿⣿⠏⠁⠀⣠⣉⢸
⠀⠀⠀⢀⣴⣮⣍⣀⠈⠛⠻⠿⠿⠶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠡⠜⠋⠀⠀⠀⠀⠀⠀⠘
⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣦⣌⡛⠒⠠⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠣⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠉⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠛⣶⣿⣶⠔⢄⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠋⠉⢹⡋⣉⣿⣿⠿⠻⣿⣿⣭⠿⠿⠿⠿⠋⠉⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠘⠛⠙⢛⠋⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢸⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣿⣦⣤⡦⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠤⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣈⣉⣉⣑⣐⣂⣀⣀⢀⡟⣿⣿⣿⣿⡁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⢄⣵⣦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡿⣿⢿⣿⣿⡟⣿⣄⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⡡⠈⠘⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣧⠀⠀⠆⢀⠀⠀⢺⣥⣀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣶⢿⣿⡇⣿⣿⣿⣿⣶⣶⡆⣶⣶⠀⢶⣶⢰⣶⡀⣶⡆⣴⡾⣿⡆⠀⢸⣿⣿⣿⣷⣶⣶⢰⣶⣶⢰⣶⣶⢠⣶⢶⣦⢰⣶⣶⡆⣶⣶⠤⣷⣶⣿⠇⠀⠤⣼⡇⢰⣾⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣧⢸⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⣼⣿⢸⣿⣧⣿⣿⣿⣇⣻⣛⠀⠘⣿⣧⣿⣿⣿⣿⣼⣿⢿⣾⣿⣿⠸⣿⣬⣉⢸⣿⣤⡄⣿⣿⠈⣿⣿⡟⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡤⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣏⢸⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⠀⣿⣿⢸⣿⢻⣿⡏⣿⡏⣿⣿⠀⠀⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢰⣯⢹⣿⢸⣿⡏⠁⣿⣿⠄⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠘⠛⠈⠛⠃⠙⠛⠛⠛⠀⠀⠛⠃⠛⠛⠛⠛⢿⡿⠘⠛⢻⡟⠈⠛⠟⠋⠘⠛⠛⠃⠛⠛⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣁⢀⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⢀⣀⡀⣀⡀⢀⣀⣀⡀⠀⠀⣀⣀⣀⠀⣀⣀⣙⡁⢀⣀⣈⡀⢀⣀⣀⠀⣀⡀⢀⣀⣀⣀⠀⣀⣀⡀⢀⣄⢀⣀⢀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⠀⡿⠛⣿⣿⠛⣿⣿⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣧⣿⡇⣾⣿⢹⣷⠀⠀⣿⣿⣿⣷⣿⣿⢻⣿⢸⣿⠛⢳⣿⡏⠿⠇⣿⡇⢸⣿⢻⣿⣾⣿⡟⠃⣼⣿⣸⣿⠚⣿⣿⡟⣿⡇⠀⢠
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢸⣿⢹⣿⣿⣿⡇⣿⣿⢶⣶⠀⠀⣿⣿⠿⠇⣿⣿⣿⣯⢸⣿⡿⢇⣙⣿⣷⡄⣿⡇⢸⣿⣸⣿⡇⣿⡿⠗⣿⣿⣿⣿⠀⣿⣿⣇⢤⣤⣀⢸
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣼⣿⣿⣿⣿⣿⣿⡼⣿⠀⠀⣿⡿⠀⣀⣿⣿⣿⣿⢸⣿⣷⡞⢿⣧⣿⠇⣿⣇⢺⣿⣿⡿⠃⣿⣷⣦⣿⣿⢿⣿⠀⣿⣿⡷⢻⣿⣿⣽
⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣦⡄⠙⠛⠛⠉⠉⢹⣟⣃⠀⠀⠀⣴⠀⠀⠻⠀⠀⠈⠙⠓⠶⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⡦⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠸⠿⠿⠿⠿⠟⠛⠿⠋⠉⠙⠋⠀⠀⠀⡀⠀⢀⣶⣶⣴⣾⣿⠟⣀⠀⠀⠸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠱⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠈⠑⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⡤⠄⢀⡠⠀⠒⢨⣽⣶⣿⣿⣿⣿⣿⠋⢰⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠾⣃⣠⣶⣾⡿⢿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⠀⠀⣿⣿⣿⣿⣿⠋⠀⢿⣿⣿⡄⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠘⣿⠋⠀⠀⢸⣏⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⢀⠀⠈⠰⢶⣶⣾⣿⣿⠖⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣶⡶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⣀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠀⠄⢤⣀⡀⣠⣤⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣼⣿⣆⡀⠀⠀⠀⠀⠂⠿⠿⠷⠶⣀⡀⠀⠀⠈⠉⠉⠉⠻⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠰⠥⠷⢿⡿⠃⠀⠀⣤⣼⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠀⣄⠀⠀⠀⠠⠀⠀⠀⢠⡈⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠩⢹
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⡄⠉⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡛⠛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠉⠉⢀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠙⠿⠿⣟⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢰
⠀⠀⠀⠀⠉⠗⠢⠀⠂⣀⣉⠛⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠄⠀⠀⠠⣀⡀⠀⠘⢶⣦⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⣤⠤⠘⠛⣿⡓⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠈⡉⠀⠈⣤⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠁⠹⣿⡿⠿⠟⡯⠫⠹⠟⠿⠿⠏⠇⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⡥⠤⠀⠋⠄⠄⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⠋⠀⠀⠀⠀⠉⠁⠹⢿⣿⣿⣿⣿⣿⢟⣀⠀⠛⢿⣿⣿⣿⣿⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠑⣿⣿⡆⠀⣻⣿⣿⣿⣿⡍⣡⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣹⣿⣿⣿
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢄⣠⣿⣿⣅⠀⢿⣿⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⢰⣾⣿
⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⢛⣛⣿⣿⣷⢸⣿⣿⣯⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠇⣿⣸⡿⠿
⠙⠛⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣽⣿⣿⡎⣿⠸⢿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⢻⣿⣿⣿⣿⣿⡷⠙⠟⢁⢲
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⣿⠷⣿⣿⣿⣿⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣶⣿⠿⢻⠿⣻⣧⠀⢨⡍⣬
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠟⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠀⠙⣿⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢠⣿⣿⡟⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠠⠦⠁⠂⣄⣤⣤⣤⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠛⠉⠋⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⢏⠸⠿⠉⠀⠀⠀⠉⠉
⠀⠀⠀⢠⣴⣿⣿⣷⣷⣤⣀⣀⠨⢍⣙⡛⠿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣻⣿⣿⡄⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡌⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣬⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⣽⣿⣿⣿⣿⣿⣿⣿⣷⡍⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣋⣤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⡒⠛⢿⠿⢿⣿⣿⣿⢿⣿⣿⠖⣶⣿⣿⣿⠿⠿⠿⠷⠿⠿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣀⠸⢿⣿⣿⣿⣿⡛⠻⠛⠛⠛⠛⠀⠀⠛⠟⠃⠀⠤⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⠀⠀⠸⠷⢾⣿⠿⠃⠀⢿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠄⠘⢿⣿⡟⠉⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠸⠿⢇⠀⢀⡀⠀⠀⠰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠒⠓⠒⠲⠖⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣤⢦⣼⣤⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⣄⠀⠀⠀⢶⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣶⠀⣶⣶⣀⣶⣶⠀⢰⣶⢰⣶⡀⣶⡆⣼⣶⣶⣿⣿⣿⣿⣆⣶⡆⢰⣶⢰⣶⣶⢰⣶⣶⢠⣶⢶⣦⢰⣶⣶⡆⣶⣶⠀⣶⣷⣶⣿⡆⣀⣁⣸⡆⢠⣴⣿⣿⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⠀⢸⣿⢸⣿⣧⣿⣧⣿⣿⣛⣛⠈⢹⣿⣿⣿⣧⣼⣿⢸⣿⢿⣿⣿⣿⠸⣿⣬⡉⢸⣿⣤⡄⣿⣯⠀⣿⣿⡿⠿⠀⠀⠉⠛⠃⠸⣿⣿⣿⣿⣀
⠀⠀⠀⢴⠄⠰⠶⠖⠶⠲⠖⠀⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠀⣾⣿⢸⣿⢻⣿⡟⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣸⣿⢸⣿⢸⡿⢰⣮⢹⣿⢸⣿⡉⠁⣿⣿⡀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠠⠘⠛⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠘⠛⠈⠛⠃⠙⠿⠛⠛⠀⠐⠛⠃⠛⠻⠿⣿⣿⠛⠘⠛⠘⢻⠈⠛⠛⠋⠘⠛⠛⠃⠛⠛⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⣀⡀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⢀⣀⡀⣀⡀⠀⣀⣀⡀⠀⠀⣀⣀⣀⠀⣀⣺⣟⡀⢀⣀⣀⡀⣀⣀⣀⠠⣄⡀⢀⣀⣀⡀⠀⣀⣀⡀⣀⣀⢀⣀⢀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⠀⡿⠛⣿⣿⠛⣿⣯⢸⣿⢸⣿⡟⢃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣾⣿⣧⣿⡇⣼⣿⢹⣿⠀⠀⣿⣿⣿⡗⣿⣿⢻⣷⢸⣿⡟⢳⣿⡏⠿⠇⣿⡇⢸⣿⢹⣿⡄⣿⡟⠋⣿⣿⣸⣿⠚⣿⣿⠛⣿⡇⠀⢠
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣇⣿⣿⢶⣶⠀⠀⣿⣿⠿⠇⣿⣿⣿⣯⢸⣿⡿⢏⣙⡿⣷⡆⣿⡇⢸⣿⢸⣿⡇⣿⡿⠇⣿⡿⣿⣿⠀⣿⣿⡆⢠⣾⣾⣸
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣼⣿⡟⣿⡿⣿⣿⡼⣿⠀⠀⣿⣿⢀⡀⣿⣿⣿⣿⢸⣿⣷⡞⢿⣧⣿⠇⣿⡇⢸⣿⣼⣿⢃⣿⣷⡦⣿⡇⢿⣿⠀⣿⣿⣧⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢾⣶⠂⠉⢻⣶⡤⠀⠀⠙⠛⣂⠀⢠⣴⠀⠘⡧⠀⠀⠀⢀⠀⠀⠀⠦⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠤⣴⣶⣦⡄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠇⠀⠘⠛⠀⠀⠀⣠⣄⣀⣤⣼⣿⡀⢸⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠛⠁⠚⢶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠛⠋⠁⢀⣀⣉⠀⠀⠀⠀⢀⡠⠀⣲⣤⣴⣿⣿⣿⣿⣿⠟⠁⠈⠻⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠛⠙⠛⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⣀⠒⠈⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⣷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠿⠟⠃⠘⣿⣿⣿⣿⣿⣿⡇⠀⡿⠁⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣇⠀⡇⠀⠀⣀⣼⠛⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠻⣄⠀⠀⣀⣀⣼⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣈⠁⠀⠀⠈⠛⠛⠛⠛⠋⣀⣤⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣶⣶⣤⣴⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⢶⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠁⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢇⣀⣀⠀⠀⢀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢⠬⠉⠁⠐⠶⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣀⠀⠀⠀⠀⢀⡀⢰⣶⣦⣄⡀⠈⠉⠉⠓⠶⠾⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣧⣀⣀⡀⠀⠈⠀⠉⠉⠁⣿⣶⣄⣶⡤⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣀⡀⠉⠐⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠱⠦⠀⠀⠦⠄⠀⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘
⠀⠀⠀⡠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣶⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢰
⡀⠀⠀⠙⠛⠆⣤⠄⣀⣐⠒⠤⢤⠀⠰⠆⠀⠈⠁⠀⠀⠈⠀⠓⠐⠚⠒⠀⠀⠀⠀⠈⠉⠐⠀⠀⠀⠈⠛⠂⠀⡀⠈⠙⠀⠀⠀⠀⢤⣀⣓⡒⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢀⠒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣭⠠⠁⠠⣶⣶⣦⡀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠃⠀⡀⠈⠓⠒⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠌⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠰⠍⠹⢹⣷⡿⠿⡧⠣⠿⠿⠿⠿⣇⠇⠀⠁⠀⠀⠀⠈⠈⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠘⠭⠀⠀⠀⢄⠆⠀⠤⠠⠀⠀⠀⠐⠀⠀⠱⡆⠴⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠠⠀⠀⠀⡀⡀⠀⠀⠀⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠙⠛⠻⠟⣿⣿⣿⣿⣿⣿⡿⠃⠀⠻⣿⣿⣿⣿⣿⠷⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⢿⣵⣷⡆⠀⣾⣿⣿⣿⣿⡖⢊⣙⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿
⠀⠂⠀⠀⠀⠄⠀⠀⡀⢀⠀⠀⡀⠠⣿⣿⡏⠀⢸⣿⣿⣿⣿⣏⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢹⣿⣿
⣛⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠀⠘⠿⠿⢿⣾⣧⣸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⢸⣸⣿⠿
⠿⢿⠇⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣻⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡽⣷⠘⢿⠋⠳
⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⢸⡧⣾⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣿⣿⠿⣿⢿⣧⡀⢈⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠈⠁⠸⣿⣻⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣷⣿⣿⠃⠀⠁⠺
⠀⠀⠀⠀⠀⠀⠀⣀⠖⠉⣉⣉⣀⣈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠏⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡻⠏⠠⠿⠏⠁⠀⠀⠈⠛
⠀⠀⠀⠀⣠⣴⣶⣤⣤⣄⣉⠛⠛⣛⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣉⡑⠢⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⡼⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡦⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢄⡀⠀⠸⣭⣿⣿⣿⡿⢿⠿⠿⠿⠿⠀⠈⠻⣿⠿⠀⣀⡀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠃⠀⢸⣧⣤⣿⣿⡏⠀⣹⣿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡠⣽⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠉⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠁⠀⠘⣿⣇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣬⣭⣥⣭⣥⣤⣄⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢠⠀⠀⠀⢰⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠟⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⠝⣾⣷⣷⣦⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢸⣧⢀⠈⠀⣶⠀⣀⣿⣿⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⠀⠛⢿⣿⣿⣿⡀⢀⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡀⠈⠻⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠏⠀⠘⠛⠛⠀⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣄⡀⢠⣤⣤⣤⣤⡄⢙⡄⠀⠙⠛⣿⣿⣇⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠈⠉⠙⢙⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠉⢿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡢⠂⠀⠀⡠⠒⠷⣆⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⣪⠸⠅⢠⠊⣣⣟⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣂⣈⠋⠉⢳⣾⣷⣄⠀⠀⠀⠀⠃⠀⠀⠀⠐⠲⠶⠄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠍⠀⠈⣬⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣦⣤⠙⢻⣧⣄⠀⠙⠛⠛⡷⠀⣤⡄⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠰⡀⠈⠀⠀⠀⠛⠛⢋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡄⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣦⠀⠸⠿⠃⠀⠈⢉⣀⡠⣄⣸⣿⡏⣿⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠷⠘⠃⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠘⠛⠛⠛⠉⠉⠙⠁⠀⠀⠀⠀⠀⢀⠤⣤⣤⣽⣿⣿⣿⣿⣿⠃⢹⡇⠀⠀⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣷⠀⠠⠄⠊⢉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠧⢴⣾⣿⠿⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠿⠋⠀⠀⢈⣹⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⡀⠀⠁⠀⠀⠙⠻⠿⠿⠿⠟⠁⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠐⠢⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢶⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠟⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢸⣿⣀⣀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣒⠒⠠⠤⠘⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⣀⠆⣶⣦⣀⡀⠈⠛⠛⠳⠶⣼⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⢿⣿⣿⣧⣀⣀⠀⠈⠙⠂⠙⠛⠛⣻⢷⣤⣤⣤⠀⠀⠀⢸
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠊⠙⠛⠛⢋⠀⠀⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⣠⡐⠆⠀⣀⠀⠁⠀⠀⠐⠶⠤⠈⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐
⠀⠀⠀⢀⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡁⠁⠠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⢆⣀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠤⢤⠀⣐⠀⠀⠤⣀⣀⡀⠀⣤⠀⠀⠐⠂⠀⠀⠀⠀⠄⠀⠤⠄⠀⠀⠉⠉⠻⠃⠀⠀⠀⠀⠲⠆⠀⠀⠀⠐⠆⠀⠀⠀⠤⣀⣂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠐⠠⠀⠀⠀⠀⣼⠯⠛⠈⣠⣤⣬⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠢⠀⠀⠀⠒⠦⠄⠀⠙⠻⠏⠀⠀⠀⠀⠁⠀⠁⠦⡄⠀⢤⠳⠚⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠸⠯⠹⢺⡟⣿⡿⣧⠣⣻⡿⡿⡯⠇⠇⠀⠱⠀⠀⠀⠈⠀⠂⠀⠀⡄⠀⠀⠀⠀⠉⠁⠔⠐⣂⠀⠀⢀⢠⡀⠀⣀⡈⠁⠀⠀⠄⠀⠰⣦⡀⠤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠋⠀⠀⠀⠀⠈⠙⠙⢻⣿⣿⣿⣿⣟⣥⡄⠀⢹⣿⣿⣿⣿⣏⠽⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠙⣿⣿⣿
⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⢹⣿⣿⠀⢨⣿⣿⣿⣿⣿⠠⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⣯⣿
⠤⠤⠤⠀⠀⠈⠀⠀⠀⠐⠃⠀⠐⢠⣿⣿⣿⠄⠈⢿⣿⣿⣟⣿⡀⣿⣿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⠸⣇⣿⣿
⣴⣲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣽⣿⣿⣇⢿⡿⣿⣿⣻⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠘⣿⡟⢹
⠀⠉⠙⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⠘⣿⣻⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⣿⡿⣿⡷⣯⡀⠈⣃⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠟⠹⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⣫⣿⣿⡷⠀⠉⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠾⠿⠁⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢻⣿⢱⣿⣿⣿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠿⣏⠁⣿⡿⠋⠀⠀⠀⠶
⠀⠀⠀⠀⠀⢀⣠⣘⣂⡈⠹⠾⠿⠿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣆⠛⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣦⣤⠐⠒⠤⢍⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣿⣿⣿⣿⣿⣿⣿⣿⡑⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠛⠛⠋⠁⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣁⣸⣿⣿⣿⣿⣏⣿⣿⣿⣿⣆⣀⣸⣿⣿⣿⣿⣿⣿⣭⣽⣿⣷⣿⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠯⣼⣷⡆⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠁⠀⣿⣉⣹⣿⣿⠛⢛⣿⡧⠾⠿⠛⠛⠋⠀⠀⠀⠀⠈⠉⢉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⠛⣿⣿⣿⠿⠍⠉⠉⠉⠉⠁⠀⠠⠉⠉⠁⠐⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠙⡏⠉⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⣿⣿⡟⠀⠙⣿⣿⠀⠀⠀⠀⠀⢠⣶⣿⣷⣦⣀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠙⠋⠃⠀⠀⠘⠛⠆⠠⠀⠀⠀⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡿⠆⢿⣿⣿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⣶⠀⠈⠃⣴⡆⢀⣹⣷⣦⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠨⢿⣿⠃⣿⠀⢠⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⣬⡭⣽⣿⣶⣶⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣂⣾⣿⠃⠉⠛⠿⠃⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⢧⠀⠀⠀⠀⠰⠿⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠫⡃⠘⠛⠟⠛⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿
⠀⠀⠀⠀⠘⠛⠀⠈⠉⠙⠉⠉⠁⣾⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣴⣤⣢⡶⣤⠐⠆⣴⢀⣀⣰⣤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⢊⠑⠃⢐⠀⠀⠦⢰⣾⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⡀⠀⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠧⢅⠁⢐⡁⠰⠀⠀⠈⠈⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠚⣿⣤⠄⠙⠻⠟⠀⠀⠀⠀⣠⡄⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⢴⡬⠤⢦⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⠿⠃⠀⠀⠀⣿⣿⣿⡟⠛⠿⠿⠋⠉⠉⠁⠀⠈⠁⡀⠀⠀⠒⣶⣬⣯⡕⣿⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣄⠀⠀⡀⠴⠖⢈⣿⣶⣶⣿⣿⣿⣿⡇⢻⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠯⠬⣁⣠⣤⣶⡿⢿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⠋⠀⠈⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠉⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏⠀⠸⠏⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⣤⣤⣤⣴⣦⣤⣄⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⢶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⢰⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠑⠶⠶⠦⣄⣠⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣼⣿⣷⣄⠀⠀⠀⠘⠋⢘⠿⠿⠿⢷⣄⣀⣀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠠⠙⠚⠻⢿⡇⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠦⠄⢀⠀⠀⠀⠀⠆⠀⠀⠠⢄⡈⠙⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠉⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⠀⠄⠀⠀⠀⠠⠀⠛⠓⠂⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠘⠻⠿⠿⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣓⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠈
⠀⢠⠀⠀⠀⠉⣥⣴⠒⡤⠤⠉⠒⠲⠂⠘⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠈⠁⢨⣍⠀⠀⠈⠀⡄⠀⠀⠀⣄⡀⠈⠙⢷⣶⡤⠀⠀⠀⠐⠀⠀⢀⣄⠀⠀⠀⢤⣽⠀⠀⡀⠀⠠⠁⠀⠀⠁⠀⠀⠀
⠀⠸⠏⠹⢸⣧⠿⠿⡯⠣⠹⠿⢿⠿⠏⠇⠀⠁⣄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣹⣿⣿
⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿
⠿⠟⠀⠀⠀⠉⠙⠛⠛⣿⣿⣿⣿⣿⣿⢫⡀⠀⠛⣿⣿⣿⣿⣟⢩⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠛⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⠋⢛⣿⣿⠆⠘⣿⣿⣿⣿⣿⡆⣶⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡟⢹⣽
⣀⣈⣁⠀⠀⠘⠃⠀⠀⠄⠄⠀⠠⢄⣸⣿⣿⣄⠀⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣇⣹⣿
⣬⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⢩⣽⣿⣿⣇⢻⣿⣿⣾⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡆⢻⣿⢻
⠈⠛⠙⠁⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⡎⣿⣘⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣸⣿⣿⢿⡿⣾⣅⠀⢛⢛
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⣿⠛⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢨⣷⣿⣿⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠏⠉⢆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠿⣿⡏⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡹⣟⠋⢸⡿⠟⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠁⠲⠶⣶⣶⣦⣬⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣇⡘⠃⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣶⣿⣿⣿⣷⣦⣤⣤⠈⠭⣭⣝⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠉⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢡⣾⣿⣿⣿⣟⣻⣿⣿⣿⣷⣀⣈⣿⣿⣿⣿⣿⣿⣏⣭⣿⣿⣿⡉⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠿⣹⣦⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⢹⣏⣙⣿⣿⡟⠛⣿⣿⠴⠿⠟⠛⠋⠁⠀⠉⠉⠈⠉⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢤⣤⣤⡼⠻⣿⣿⣿⣿⠛⠛⠋⠋⠙⠀⠀⡙⠛⠃⠐⠒⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠛⠛⢛⠋⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡀⢸⣿⡿⠗⠘⢽⣿⠃⠀⠀⠀⠀⠀⣠⣶⣷⣄⡀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠘⠟⠃⠀⠀⠈⠻⠆⢀⡄⠀⠀⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀
⠛⠛⠛⠛⠛⠓⠛⠓⠒⠒⠒⠓⠒⢶⡆⢸⣿⣿⡟⣷⡄⠀⡀⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠀⣵⡆⠀⠙⢠⣆⠀⣈⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⢀⣿⣿⡇⢿⠀⢀⣿⣷⣤⣦⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠴⠶⡀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⣰⣿⡗⠈⠙⠻⠛⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠉⢁⣾⣄⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢾⡖⢻⣿⣶⣿⣷⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿
⠀⠀⠀⠀⠰⠶⠆⠰⠻⠿⠟⠛⠁⢰⠁⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠈⠹⠁⠀⠊⠙⠉⠉⠉⠋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠲⠞⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠠⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣴⣲⢴⡢⡀⠐⡂⣔⠠⣠⣴⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠾⠿⠿⠛⠗⠈⠠⠣⠀⠈⡼⣮⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⢡⣤⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⡬⠈⠁⡀⡀⠀⠀⠀⠀⠟⠻⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠹⢿⣆⡀⠻⠿⡷⠀⠀⠀⠀⣠⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢴⣤⠤⠤⣴⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⢷⠀⠀⠨⣿⣿⣿⣿⣿⢿⣿⣿⠛⠛⠗⠀⠈⠛⠁⠀⠀⢠⠤⣄⣀⠀⣾⣷⣶⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⠿⠿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⢁⣀⣀⣀⣀⠀⠀⢀⣀⠤⠄⣀⣴⣶⣶⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠤⠎⣁⣠⣤⣿⢻⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠋⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠉⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠀⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣤⣄⣀⢀⣠⣴⣶⣶⣾⣤⣄⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣷⣶⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠙⠷⠶⢶⣄⣀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠀⠉⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣿⣿⣆⡀⠀⠀⠘⠹⠇⠻⠿⠿⠿⣦⣀⣀⣀⡀⠈⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⢀⠫⠿⠿⣿⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⠃⢠⡈⠛⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠖⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⡀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⡇⠀⠈⠉⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡛⣓⡂⠀⠀⠐⠃⠀⠘⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠈⠉⣷⣶⡾⢤⣤⡖⠒⠂⡄⠀⠒⠀⠀⠈⠐⠀⠀⠌⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠁⠁⠀⢀⠀⠈⠉⠀⢠⠄⠀⠈⠀⠀⠀⠀⢰⣦⣭⠅⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⢠⣬⡍⠀⢀⠀⠀⠀⠀⠀⠈⠂⠀⠀
⠀⠈⠅⠹⢸⣇⡿⠿⣿⠣⠻⢿⢿⣿⡧⠇⠀⠙⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠈⠉⠁⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⡉⠉⠀⠀⢡⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢐⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡳⣼⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿
⣿⣿⠋⠉⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⡷⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣟⠛⢻⣿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⣷⣷⡄⠀⢾⣿⣿⣿⣿⡆⢁⣩⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣛
⠙⠁⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⡀⠀⣀⣿⡇⠀⢿⣿⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⡇⡤⢸⣿
⠒⢒⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠀⠈⠛⠓⢿⣾⣧⢸⣿⣽⣯⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡅⢲⣾⢻
⠛⠻⠿⡟⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⣛⣿⣿⡄⣿⡽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣘⣿⣿⣿⣿⡿⠃⠀⠻⠴
⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣇⢹⡇⣾⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡋⠉⣫⣼⣿⡄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠈⠁⠘⣿⣹⡿⣸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣿⠿⢸⣿⡿⠋⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠉⣉⣀⣀⣈⡓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠁⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣶⣴⣤⣤⠉⠉⠉⣛⠛⠋⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⣉⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠊⢁⣹⣿⣿⣿⢿⣿⣿⣿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡏⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⡟⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠔⠛⠛⡟⠛⣿⣿⡿⠿⠿⠿⠋⠾⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⣿⣿⣿⡟⠛⠿⠿⠟⠛⠃⠈⠙⠿⠿⠀⣤⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠟⢲⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣿⢿⡛⠅⠀⡿⠋⠉⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⠀⢿⡗⠅⠀⠀⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣌⠉⣿⣿⣿⣷⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢙⣄⠀⠐⠀⣀⠀⠀⢺⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⣿⡿⢰⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢠⣼⡿⠀⠀⠠⠟⠂⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢸⡇⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⡠⣶⠶⠶⠶⠀⡇⠀⠀⠀⠀⠀⢠⣸⣿⣿⣿⡿⠀⠀⠀⠀⠀⡀⣀⣤⣤⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣼⣿⣻⣿⣅⣤⡄⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⠃⠛⠛⣚⣳⣋⣻⣿⣾⣛⣛⣛⣓⡛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⣂⣠⣄⣤⠀⠀⢀⠀⠀⣠⣠⢰
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡤⠀⣤⣤⣼⡭⣿⣿⣿⣿⣽⣯⣭⡭⢥⣤⡤⢤⡤⣤⢠⣤⣄⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢸⣿⢿⢛⠛⠃⠙⠐⠂⠀⢈⠁⢷⣿⣾
⠀⣿⡟⢻⣯⣧⢸⡇⣿⡗⣽⣿⡇⢸⡇⠀⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⢿⡇⢸⡇⣿⢸⣿⣿⣿⣿⡇⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢨⡆⠈⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⢿
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⠃⠚⠃⣤⣛⣛⣭⣿⣯⣟⣿⣧⣿⣿⡛⠛⣛⡘⠃⠘⠃⠛⠊⠛⠃⠛⠙⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⣀⡤⠤⣀⣀⣀⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠉⠷⠄⠀⠀⠀⠀⠀⠀⠀⣾⣦⣀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡿⡿⠻⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⠛⠋⠁⠈⠉⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⣶⣾⡇⢸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⡿⠇⠠⠐⠊⣁⣤⡼⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠾⣿⠟⠁⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠈⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠿⠀⠀⠈⠁⠀⠀⠀⠸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⢀⣀⣄⣤⣔⣈⣿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣠⡄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠛⠁⠀⠂⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣶⣄⠀⠀⠀⠀⠀⢤⠰⣿⣷⣶⣤⡀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠈⠁⠀⠸⣻⣶⣵⡟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠠⠦⠉⠀⠰⠀⠀⠀⠀⠀⠈⠁⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣄⣀⡀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠄⠀⠀⠀⠀⠄⠂⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⣦⣤⣀⡂⠀⠠⣤⡀⠀⠀⢠⡄⠀⠀⠒⡀⠀⠀⠂⠒⠀⠐⠠⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠙⠀⠀⠀⠀⠠⣄⣐⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀
⠀⠰⠟⠹⢸⡇⠿⠛⡿⠣⠻⠏⣿⣿⡏⠇⠀⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠒⠲⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠐⠲⠄⠀⠄⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣖⢳⣸⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣇⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣸⣿⣿
⣿⣿⡟⠉⠛⠙⠻⠟⢻⣿⣿⣾⣿⣿⣿⣿⠋⠀⢹⣿⣿⣿⣿⣿⡇⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠌⢹⣿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⠿⣵⣶⣄⠀⢼⢿⣿⣿⣿⡆⢊⣙⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⠿⢹
⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⣀⣿⡏⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡇⢸⢠⢸
⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠛⠛⠛⠂⠈⠻⠏⢽⣾⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⢸⣶⣿
⠒⠿⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣟⣿⣿⣆⢿⣿⣿⣿⣽⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡙⣿⣿⣿⣿⣏⣛⠀⠙⠬
⠀⠀⠀⠀⠀⠀⠚⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⢸⡧⣾⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣻⣯⡟⠉⢟⣵⣿⡆⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠏⠈⠁⠘⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠇⣿⣿⠏⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠛⠁⣀⣀⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠁⠤⠙⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣶⣭⣥⣄⠀⠙⠛⠛⠓⠒⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣿⣿⣿⣿⣿⣿⡟⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⠿⣿⠗⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣌⣉⣁⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⣫⣻⣿⣿⠿⣿⣿⣿⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡿⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠛⡿⠻⣿⣿⡿⠿⠿⠿⠛⠰⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⠿⣿⡿⠿⠿⡇⠈⠑⣾⣿⣅⣀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣿⢶⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⠿⠂⢸⠟⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⣿⣿⡏⠀⠀⠘⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀
⣈⣀⣠⣤⣤⣤⣠⣀⣀⣀⣈⣀⣀⣀⣈⠉⣿⣿⣿⣿⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⣄⠀⠀⠆⢀⡀⠀⢺⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠘⣿⣿⠀⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠄⣤⣿⠄⠀⠤⠼⠇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠛⠛⠀⡇⢀⣴⣾⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠦⠀⠀⣱⠀⠀⠀⠀⠈⢙⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣬⣿⣻⣿⣏⣤⡄⣤⢠⡌⠛⠛⠋⠉⠀⢠⢤⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢸⣿⡇⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠍⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⠃⠛⠛⢚⣳⣋⣛⣷⣾⣛⣛⣛⡓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡤⠀⣤⣤⣿⡭⣽⣿⣿⣯⣽⣯⣭⡭⢤⣤⡤⢤⡤⣤⢠⣤⣄⣤⣠⡄⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢙⡗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸
⠀⣿⡟⢻⣯⣧⢸⡇⣿⡗⣼⣿⡇⢸⡇⠀⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⢿⡇⢸⡇⣿⢸⣿⣿⣿⣿⡇⠀⢰⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠞⢽
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⠃⠚⠃⣤⣛⣻⣭⣿⣯⣿⣿⣧⣿⣿⡛⠛⢛⠘⠃⠘⠃⠛⠊⠛⠃⠛⡙⠃⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡄⠀⠠⠤⠀⠀⠀⠀⠀⠀⢰⣧⣄⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠛⠛⠁⠀⠉⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⡿⠆⠀⠀⠚⣁⣠⡴⣿⣿⣿⣿⣶⣿⡆⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠶⣿⠟⠃⢹⣿⣿⣿⣿⣿⣿⡄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠈⠹⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠃⠀⠀⠁⠀⠀⠀⢸⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⣠⣤⣤⣼⣟⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠻⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡛⠂⠀⠤⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣤⡀⠀⠀⠀⠀⣠⠁⣿⣷⣾⣤⡀⠀⠀⠈⠑⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⣿⣿⣷⣄⣤⡀⠀⠀⠁⠈⠉⠁⠨⡛⣶⣶⡖⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠤⠐⠂⠠⠄⠀⠀⠀⠀⠈⠓⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣦⣤⠀⠀⠀⠀⣤⡀⠀⠉⠉⣁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠈⠉⠉⠛⠀⠄⠀⠠⠀⠒⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠽⠹⢸⡇⠿⠿⡿⠣⠻⠟⢿⣻⡏⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠨⠀⠀⠀⠒⠶⠄⠀⠈⠻⠋⠁⠀⠀⠀⠀⠀⠀⠶⠄⠀⠠⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣀⣀⣄⢸⣻⣿⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡒⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⡏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢹⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡞⢻⣿⣿
⣿⣿⠇⠀⠀⠀⠈⠉⠀⠈⢿⣿⣿⣿⣿⣏⣀⡀⠈⢛⣿⣻⣿⣿⡃⠹⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡄⢸⡿⢹
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠛⢿⣟⠀⢸⣼⣻⣿⣿⣷⠠⣦⣿⣿⣿⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⢸⠀⢸
⠀⣀⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣧⡄⠈⢿⡟⠛⣏⣽⠀⣿⢻⡷⣿⢛⣻⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠟⢸⣤⣸
⣀⣠⢤⣤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣌⣽⣿⡇⣿⡾⣿⣿⣻⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣟⡿⠀⠻⣺
⠀⠈⠛⠛⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⣺⣿⣿⢸⣇⣻⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣟⠿⠛⡿⣫⣷⡄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠘⠏⠙⣿⡿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡆⣾⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⡿⠸⠿⠿⠿⠿⠿⠟⠛⠉⠛⠛⠛⠛⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠓⠀⠛⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡐⠊⠀⠀⠴⣶⣶⣦⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⣭⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣶⣦⣀⡐⠶⠤⢈⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠛⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⣦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⠬⠾⣿⣿⣿⣧⣿⣿⣿⣿⡧⢠⣼⣿⣿⡿⠿⠿⠿⠶⠿⠿⠿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠫⣥⣶⡆⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⠀⠀⣿⠄⠙⠋⠉⠀⠈⠛⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣶⣶⣶⣾⡏⠉⣿⠿⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠁⠛⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡀⣾⣿⣿⡏⠀⠀⠋⠀⠀⠀⠀⠀⠀⣤⣶⣷⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠇⠙⠟⠛⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⠀⠀⡄⠀⠀⠀⢼⣀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠇⠸⣿⣿⡟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣀⣿⡆⠀⠀⢸⠇⢠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⣿⣿⠃⣷⠀⢠⣤⣴⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠟⠀⠀⠀⠀⠀⠘⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠧⠀⠀⠀⠀⠀⠛⠀⢿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠛⠋⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣤⣤⣻⣽⣿⣿⡇⣤⢠⡄⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⠁⠀⠀⠀⡊⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⠃⢛⣛⣞⣷⣋⣛⣣⣜⣛⡛⠛⠓⠛⠛⠃⠀⠀⠀⠀⠀⡟⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡤⠀⣬⣭⣿⡭⣽⣿⣿⣭⣽⣥⣤⡤⢤⣤⡤⢤⡤⣤⢠⣤⣄⣤⣠⡌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢸
⠀⣿⡟⢻⣯⣧⢸⡇⣿⡗⣼⣿⡇⢸⡇⠀⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⢿⡇⢸⡇⣿⢸⣿⣿⣿⣿⡇⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⣠⡴⣺
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⠃⠛⢃⣧⣛⣻⣭⣿⣯⣿⣿⣧⣿⣿⣿⣻⣟⠘⠃⠘⢃⠛⠊⠛⢃⠛⠙⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠙⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠃⠀⠀⠙⠂⠀⠠⣾⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠃⠀⠀⠀⠈⠙⠛⠋⠉⠉⠛⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠚⠹⣷⡶⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣶⡆⠀⠀⠤⠀⢀⣀⣤⣤⣤⣄⠀⠀⠸⡆⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⡤⣤⣶⣿⠇⠙⣿⣿⣿⡆⢐⣄⠀⢻⣿⣿⣇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⣿⣿⣷⣾⣿⡄⠀⠈⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠘⠃⠀⠀⠀⠨⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠹⣿⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠒⠓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⣶⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠷⣶⣶⡶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠀⣀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⡀⣤⣤⣤⣀⡀⠘⠛⠛⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣶⣿⣿⣷⡄⠀⠀⠀⠀⠁⠉⠛⠋⠉⡳⢦⠀⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⢂⡠⠄⠀⣀⠀⠐⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣠⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⠛⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⠇⠀⠀⠉⠀⢠⣄⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠨⠩⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠠⠁⡹⢸⡏⠿⠿⣷⡷⠿⠿⠿⠛⠧⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⡀⠀⠐⢶⡶⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠶⠖⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣥⠀⠀⡀⢿⢻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⠮⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢺⣿⣿
⣿⣿⡏⠀⠀⠀⠉⠙⠚⠻⣿⣿⣿⣿⣿⡿⣁⠀⠘⠿⣿⢿⣿⣿⡇⡩⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⡁⢸⣿⠻
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠚⢿⡧⠀⢛⣿⢿⣿⣿⣧⢠⣄⣻⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⡇⢸⢀⢰
⠀⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢀⣤⣾⣧⡀⠈⣿⡾⢿⡟⣿⠀⣿⢻⣿⣿⠛⢻⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⢸⣬⣾
⣀⣉⣭⣯⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⣍⣘⣻⣿⡄⣿⣼⣷⣿⢿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠻⣿⣿⣿⣿⡾⠿⠘⢿⣛
⠉⠉⠊⠻⠁⠀⢀⣁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢩⢻⣿⣷⢹⡏⢛⣿⣿⣿⣟⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⡟⣿⠛⣿⢻⣷⡄⠀⠽
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⠸⠏⠹⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡆⣾⣿⡿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢻⣿⢸⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠧⣀⠻⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⢀⣴⣴⣴⣬⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⣶⣦⣀⣀⠠⠥⠉⡙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣸⢾⣿⣿⣿⣭⣿⣿⣿⣿⡦⢀⣼⣿⣿⣿⠿⠿⠿⠴⠾⠿⠿⠗⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣹⣦⡄⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣪⠀⠀⣿⠅⠙⠛⠉⠉⠙⣿⡇⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢤⣄⣴⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣼⣾⠉⣽⣿⡉⠙⠉⠉⠉⠉⠀⠀⠙⠋⠑⠶⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠀⣾⣿⣿⣿⠂⠀⠻⠀⠀⠀⠀⠀⠀⣠⣤⣦⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠇⠻⠿⠿⠛⠀⠀⠀⠰⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠄⠀⠀⠀⢰⣀⠀
⠒⠒⠚⠛⠛⠛⠓⠚⠚⠓⠒⠛⠓⠒⠲⠆⠸⣿⣿⡟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡇⠀⣿⡆⠀⣀⢸⡆⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡆⠀⢀⣻⣿⠃⣿⠀⢀⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⠽⠿⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⠀⠛⠀⢾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠞⠋⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣤⣤⣩⣭⣟⣿⡅⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢸⣿⡇⣿⣾⡇⠀⠀⠺⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⢃⣛⣛⣟⣷⣋⣛⣶⣞⡛⠛⠛⠓⠛⠛⠃⠀⠀⠀⠀⡿⠿⢿⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠐⠂⠀⠀⠀⠀⢠
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⢤⣤⡤⢤⡤⠈⣭⣭⣿⡯⣽⣿⣻⣭⣥⣤⣤⡤⢤⣤⡤⢤⡤⣤⢠⣤⣄⣤⣡⡄⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡟⢻⣯⣧⢸⡇⣿⡗⣼⣿⡇⢸⡇⠀⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⢿⡇⢸⡇⣿⢸⣿⣿⣿⣿⡇⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢸
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⠃⠚⢣⣦⣛⣿⣭⣿⣯⣿⣿⣧⣿⣿⣿⣛⠛⠘⠃⠘⠃⠛⠊⠛⠃⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠻⠦⠀⢠⡄⠀⠀⠀⠚⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠀⠀⠀⠈⠻⠿⠟⠙⠛⠿⠿⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶⣤⣤⠀⠀⠠⠿⠃⢀⡀⣀⣀⣀⠀⠘⢿⣤⡀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⠉⠛⠐⢂⣤⣴⣾⡏⠸⣿⣿⣿⡄⠀⡈⠛⠃⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠹⣿⣿⣇⠀⢿⡄⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠃⠀⠀⠘⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⡇⠀⠀⠀⢲⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠒⠴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣷⣈⣀⣲⣴⣶⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣀⣄⠀⠐⠛⠘⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣶⣿⣿⣷⡄⠀⠀⠀⠈⠓⠙⠛⠛⠛⢳⣤⡠⢤⡤⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠁⠈⠛⠻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢄⡀⠀⠀⡀⠀⠐⠀⠀⠀⠤⠀⠈⠛⠛⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⡤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡇⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢉⣂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠁⠹⢨⡏⠿⠿⡷⡯⢻⣏⡿⠿⠇⡇⠀⠰⠆⠀⠈⠁⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⣶⣶⠤⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡛⠻⣽⣤⣿⡆⠀⠀⠀⠸⣿⣿⡇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣚⣆⢷⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⡧⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⢻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡯⠿⣿⣿⣿
⣿⣿⠏⠉⠉⠙⠿⠯⠻⢿⣿⣾⣿⣿⣿⡿⠁⠀⢿⣿⣿⣟⣿⡿⠸⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣌⠀⣿⡿⣿
⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠻⢼⣷⡀⠀⢼⣷⣿⣿⣿⡈⣀⠨⢽⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠀⡏⠀⢰
⠒⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠁⠀⢻⣯⣿⣿⠿⡇⢹⡾⣿⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠄⣇⣀⠚
⠀⠐⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠀⠈⠛⠂⠼⣾⣧⢸⣗⣿⣭⣷⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣛⣿⡿⢿⣿⣿⣿⣣⢿⠆⠹⠿⢀
⠒⢪⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣺⣿⣿⡌⣿⡸⠿⣷⣿⣿⢿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⣼⢿⡿⢻⡿⢻⣄⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡇⣿⡷⢿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢠⣾⣿⠿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈⠿⢸⡿⣾⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠿⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡻⠍⡸⠟⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠉⢁⣤⣄⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣷⣌⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣰⣶⣤⣤⣄⣈⠉⠉⣉⡉⠉⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⣿⣿⣿⣿⣿⣌⠁⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣈⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣠⣼⣬⣿⣿⣻⣿⣿⣿⣷⡄⢀⣼⣿⣿⣿⣿⣿⣯⣥⣽⣿⡿⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⡟⢡⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠈⠉⣏⠉⠻⠟⠛⠉⢻⣿⠀⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣷⣿⠿⢿⡿⠿⠿⠟⠿⠿⠇⠀⠉⠿⠿⠤⠄⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣻⣿⣿⢿⡟⠀⠈⠁⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡶⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⡀⠀⠀⠀⣢⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠀⢿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⣷⠀⢀⠀⣰⡀⢠⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠋⠀⠈⣿⣿⠀⡇⠀⠀⠀⣀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣰⣶⡿⠀⠀⠉⠉⠀⢾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣾⣿⣿⠀⠇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣤⣤⣤⣤⡝⣭⣅⢀⣤⣄⣤⣤⣩⣭⣿⣤⡄⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣽⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢸⣿⡇⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⠃⣛⢛⣚⡳⠋⠛⣢⡜⠛⠛⠛⠓⠛⠛⠃⠻⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠒⠀⠀⠀⠀⠀⢀
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⢤⣤⡤⢤⡤⠙⣯⣬⣯⡥⣄⣤⣩⣤⣄⣤⣤⡤⢤⣤⡤⢤⡤⣤⢨⣤⣄⣤⣠⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡟⢻⣯⣧⢸⡇⣿⡗⣸⣿⡇⢸⡇⡇⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⢿⡇⢸⡇⣿⢸⣿⣿⣿⣿⡇⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⢼
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⣃⣛⣃⣤⣛⣻⣭⣿⣯⣿⣿⣧⣿⣛⣛⡛⠛⢘⡃⠘⠃⢛⡊⠛⠃⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠙⣿⠀⠀⠀⠐⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠙⢿⣿⣿⠿⠿⠿⠿⠯⠛⠿⠇⠀⠀⠠⠤⠀⠀⢹⣧⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠈⠳⡄⢀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁⠤⣠⣤⣴⣾⡟⢭⣿⣶⣶⠀⠀⠙⠛⠙⢿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⢷⡀⠀⠀⠀⠀⠱⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣄⡀⠃⠀⠀⠀⡄⠀⠈⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⣠⡃⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⢶⣶⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠙⠙⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⣀⣄⣀⡀⠀⠐⠦⠰⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠀⠐⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⣦⠀⠀⠀⠀⠘⠂⠙⠿⠛⠛⢢⣄⠀⣠⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠑⠸⠷⠶⠀⠐
⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⢁⡀⠒⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⠀⠀⠀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠬⠉⠹⢸⡷⢿⣿⡧⠳⠺⠟⠿⣟⠏⠇⠀⣠⠀⠀⠐⠀⠀⠀⠀⠐⠂⠀⠐⠆⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣤⣀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠛⣿⣧⣸⣧⠄⠀⠀⠀⢸⣼⣿⡍⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⠰⡘⣿⣿⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣷⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣏⣿⢭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡟⢾⣿⣿⣛
⣿⣿⠛⠛⠛⠻⠿⠏⠿⣿⣷⣿⣿⣿⣿⡟⠁⠘⣿⣿⣿⣿⣿⡟⠸⠟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣭⣿⣿⣿⡷⣄⠀⣿⠟⣿
⠛⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⢻⣼⣦⡀⠠⠼⣾⣿⣿⣧⠘⡀⠭⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢧⣿⣿⣿⣿⣿⣿⣿⢀⡇⠀⢠
⠒⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠀⠀⣘⣿⠀⠀⣿⣿⣿⣿⣿⡅⣿⣶⣿⣿⢿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⡿⣿⣿⣿⣿⡿⣿⠸⣇⡀⠈
⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⠓⠀⠘⠻⠀⠧⣾⡆⢿⣧⣿⣽⣦⣶⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣷⡿⣿⣿⣿⣿⣧⠿⠄⠻⠏⡀
⠲⣿⢾⡆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠇⣾⣿⣷⡘⣿⣿⡿⣶⣿⣿⢿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓⣽⢿⡿⢻⡟⣧⡄⠀⠈⠁
⠀⠀⠁⠁⠀⠀⠶⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⡇⣿⠶⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢨⣾⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠘⠟⣽⡟⣿⣿⣯⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣜⡯⢍⠸⠟⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢀⣀⡈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣧⣌⠁⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣰⣶⣉⣀⡀⠈⠙⠛⣛⠋⠠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣻⣿⣿⣿⣿⣿⣿⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣿⣷⣦⣄⣈⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⣀⣯⣾⣿⣟⣻⣿⣿⣿⣧⠀⣀⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⠿⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⠗⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠉⢹⡏⠙⠿⠟⠛⠉⢿⣿⠐⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠿⠿⠿⡿⠿⠿⠿⠿⠿⠇⠀⠹⠿⠿⡄⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣿⣿⣿⡿⠁⡘⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡆⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀
⣉⣠⣥⣤⣤⣤⣤⣠⣤⠤⠤⢤⡄⢀⣤⠀⣿⣿⣿⠧⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣧⠀⠀⠀⢰⠀⣠⣼⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡟⠀⣿⣿⣿⢀⡇⠀⠀⠀⣀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣰⣷⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⠉⠙⠋⠠⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻
⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣤⣤⣫⣤⣽⣥⡄⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣻⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢸⣿⡇⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢙⣟⣃⠛⠛⠚⠳⠋⠛⣢⡜⠛⠛⠛⠓⠛⠛⠃⠺⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠀⠀⠀⠀⠀⢀
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡽⡿⣯⣬⣧⡤⣄⣤⣤⣤⣄⣤⣤⡤⢤⣤⡤⢤⡤⣤⢬⣤⣄⣤⣠⡄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣺⡟⢻⣯⣧⢸⡇⣿⡗⣾⣿⡇⢸⡇⡇⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⢿⡇⢸⡇⣿⢸⣿⣿⣿⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⢸
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⠃⠚⠃⣷⣿⣿⣭⣿⣯⣿⣿⣧⣟⣛⣛⠛⠛⠘⠃⠘⠃⢛⡊⠛⠃⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠁⠀⠀⠘⣧⠀⠀⠀⠘⠓⠒⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠖⠂⠀⠀⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠿⠿⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⡀⠸⠷⠤⠀⣀⣀⣀⣀⡀⠀⠉⠻⣦⣦⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠐⠢⠶⡶⠞⠿⠟⠛⣿⣿⣿⡄⠀⠈⠛⠛⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⢻⡀⠀⠀⠀⠈⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣀⠁⠀⠀⢠⡀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠲⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣤⣤⣾⡇⠀⠀⠀⢤⣤⣴⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⣶⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⢀⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⡀⠀⠐⠒⠰⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⣦⠀⠀⠀⠀⠀⠃⠙⠿⠛⠛⢢⣄⠠⢠⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠑⠚⠿⠶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡀⠒⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠂⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣷⡆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠉⠹⢸⡧⢿⣿⠧⠳⠸⠗⢿⣻⠏⠇⠀⣀⠀⠀⠐⠂⠀⠀⠀⠐⠆⠀⠀⠄⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣄⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣿⡛⢻⣽⣼⣿⡤⠀⠀⠀⢸⡷⣿⡇⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣰⣎⣷⣿⣧⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⢿⡿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣻⣧⣻⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡞⠓⣷⣿⣍⣹
⣿⡏⠉⠉⠙⠿⠟⠿⢿⣿⣾⣿⣿⣿⡟⠁⠀⢿⣿⣿⣿⣿⡿⠸⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣿⣟⣊⠀⣿⡏⢿⢰
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠿⠴⣷⡄⠀⢜⣿⣿⣭⣿⡀⣀⠨⢽⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⡄⡇⢀⢸⣼
⠢⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⣀⣿⡇⠀⢻⣷⣿⣿⠿⡇⢹⡗⣿⣽⡟⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⠇⣧⣬⠁⠉
⠠⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠈⢛⠀⠸⣾⣧⢸⣿⢼⣭⣷⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⡞⢿⣿⣿⣿⣳⣿⠇⠘⢟⣀⠀
⢪⡿⡗⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣸⣿⣿⡆⢻⡾⡿⣷⣿⣿⡿⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⠻⡿⠛⡿⢩⣤⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⡧⢸⡇⢿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢤⣿⣿⠟⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠻⢸⡿⢹⣿⣿⣿⣿⣿⣿⠿⠛⠿⠿⠿⠿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣻⠏⣀⠿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁⣀⣀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣻⣿⣤⠀⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣶⣦⣄⣄⣀⠉⠉⣙⣋⠓⠾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⣾⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣉⣑⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣰⣿⣿⣿⣿⣏⣿⣿⣿⣿⡤⢀⣸⣿⣿⣿⡿⠿⠿⠤⢾⣿⡿⠇⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⡿⢳⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠀⠈⣿⠉⠙⠛⠛⠉⠙⣿⡆⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣐⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣀⣹⢹⣿⠿⢿⡿⠿⠿⠿⠿⠗⠀⠈⠿⠿⣦⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⠠⡟⠃⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⣿⣿⣿⣿⡿⠀⠀⠁⡀⠀⠀⠀⠀⣿⢿⣿⣿⣧⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀
⣤⠤⠤⡤⠤⠤⡤⠤⠤⠤⠤⠤⠤⢤⡀⢸⣿⣿⡿⢤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡁⠀⢹⡀⠀⣀⣸⡇⢠⣼⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡘⠁⠈⣿⣿⡇⣾⠀⠀⢀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠥⢼⣿⠀⠀⠈⠀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠉⠙⢁⢿⡄⢼⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠤⠀⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣤⣬⣣⣬⣿⣤⡄⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⣃⡛⠛⠚⠳⠋⠛⢢⡘⠛⠛⠛⠓⠛⠛⠃⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡬⠛⣧⣤⣤⡤⣄⣤⣠⣤⣄⣤⣤⡤⢤⣤⡤⢤⡤⣤⢠⣤⣄⣤⣠⡄⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠀⣹⡟⢻⣯⣧⢸⡇⣿⡗⢽⣿⡇⢸⡇⡆⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⢿⡇⢸⡇⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠂⢸
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⠃⠚⠃⣱⣿⣿⣭⣿⣯⣿⣽⣇⣛⣛⠛⠛⠟⣜⠃⠘⠃⣛⠊⠛⠃⢛⣙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠣⠀⠉⡁⠀⠀⢿⣄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠛⠿⠿⠛⠛⠛⠀⠀⠀⠒⠀⠀⠀⠈⠛⠷⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠟⠛⠃⠀⠀⠀⠀⠀⢠⣴⣶⣷⣦⡤⠀⠀⢒⣀⣠⣤⡤⣤⣤⣤⣤⠀⠈⠻⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠑⠚⠛⠛⠛⠋⠁⠙⣿⣿⣿⡆⢸⣶⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣷⡀⠙⠀⠀⠀⠀⠑⢶⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⣀⣠⡇⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⢹⣿⣿⣿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠐⠢⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠶⣶⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠠⢄⣤⣄⣠⠀⠀⠛⠛⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣼⣿⣷⣤⠀⠀⠀⠀⠈⠀⠛⠛⠛⢙⣦⡄⠀⡤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣾⣿⡶⠀⠀⠀⠀⠀⠀⠌⠀⠉⠛⠇⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠄⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠀⠀⠀⡀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡶⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠹⢸⡿⢿⣏⡧⠣⠸⠟⣿⡛⠏⠇⠀⡀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡬⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣬⣷⣿⣾⣿⣄⠀⠀⠀⢸⡿⣿⡾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⡎⢷⣿⡇⣾⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⢿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⡿⣿⡇⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡽⣧⢿⣷⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⡜⢋⠙⣿⣿⣦⢺
⣿⠁⠉⠉⠉⠛⠋⠛⢿⣿⣿⣿⣿⣿⢏⠀⠀⠻⢿⠿⣿⣿⣟⢈⠅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⠀⡿⠋⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠟⠱⢻⣿⠄⠘⣟⡿⣿⣿⣿⠀⣄⢘⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣽⠀⡇⣠⡸⢼
⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣼⣿⡀⠀⢻⣷⠿⣟⢻⡂⢻⡟⣿⣿⡟⠛⣿⣿⣿⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢯⣿⣿⣿⣿⡟⣛⡀⣷⣾⠀⠀
⣚⣛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠀⠀⢙⣁⢛⣿⣧⢸⣧⢿⣾⡿⣿⣿⣿⡿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣟⢻⣿⣿⣿⣿⣙⠃⠘⠫⠤⠀
⠻⡿⠏⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠼⢿⣿⡎⣿⡜⣻⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣾⣛⠋⠹⣟⣴⣦⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⢿⠏⢿⣿⢹⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⢰⣿⡿⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠛⣼⡇⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠃⠌⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⢀⣄⣤⣤⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣭⣽⣿⡖⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣶⣿⣶⣶⣦⣀⣈⠉⠭⢉⣀⠻⠷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠉⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣏⡿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⠬⢿⣽⣾⣿⣤⣿⣿⣿⣿⠆⣠⣼⣿⣿⠿⠿⠿⠿⠾⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠹⣏⣡⣤⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⡯⠀⠙⠋⠉⠀⠘⣿⡄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣀⣷⣻⣿⠿⢻⣟⠛⠋⠉⠋⠁⠀⠀⠙⠛⠶⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠄⠿⠿⠿⠿⠫⠀⠀⠀⠄⠀⠀⠀⠸⡿⢻⣿⣿⣷⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣄⠀⠀⠆⢀⠀⠀⢿⣀⡀⠀
⠤⠴⠶⠶⠶⠶⠦⠴⠶⠶⠶⠆⠖⣶⠄⢸⣿⣿⡟⣦⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢀⣀⣻⠄⠀⠤⠼⠇⢰⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⠀⢸⣿⣿⠁⣿⠀⢀⣤⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠛⠛⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠉⠠⠿⠤⠺⣿⡟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠤⠤⠀⠠⠄⠀⣤⣤⣬⣤⡄⣤⣄⢀⣤⣄⣤⣭⣡⣬⢿⣤⡄⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⢚⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⠃⠛⠛⠚⠳⠋⢛⠃⠘⠛⠛⠛⠓⠛⠛⠃⠀⣿⡿⠿⣆⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⣀⣀⠀⠁⠀⠀⡀⣀⣀⢰
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡤⠀⣤⣤⣤⡤⣤⣤⣤⣤⣄⣤⣤⡤⢤⣤⡤⢤⡤⣤⢤⣤⣄⣤⣠⡄⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⡊⡰⠠⠀⠀⠀⠁⠘⠸⠋⠳⠁⢸
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⢾⡇⡄⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣾⡗⢸⢿⡇⢸⡇⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠈⠘⡁⠀⠀⠀⠀⠀⠀⠞⠀⢶⢿⠃⢸
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⢘⣃⣛⠃⣻⣿⣿⣭⣿⣯⣿⣿⣧⣟⣛⠛⢛⠛⠼⣃⠘⠃⢛⠋⠛⠃⠻⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠛⠛⠛⠃⠒⠀⣀⠀⠀⠀⢀⠀⠠⢄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⡐⠀⠀⠀⠙⣷⣤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠂⠉⢙⠙⠗⠊⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠘⠿⠛⠛⠉⠉⢙⠋⠉⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠈⠘⢳⣒⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⢆⣀⣀⣉⣤⣤⣶⠶⣶⣶⣶⣦⡀⢀⣙⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢈⢿⣿⣿⣄⠘⠛⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣄⡈⠀⠀⠀⡀⠈⠹⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣤⣤⣴⣃⠀⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇⣬⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢅⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⣀⢢⣶⣦⣤⣀⠀⠈⠈⠉⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⣾⣿⣿⣦⠀⡀⠀⠀⠈⠀⠉⠉⠉⢹⠲⣤⣒⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⣀⠤⠀⢀⡀⠀⠂⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⢀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠈⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⠿⣿⠀⠀⠉⠁⠀⣀⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠘⠉⠹⢸⡿⠿⡧⣧⡣⠺⠟⠿⠯⢏⠇⠀⠆⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⡁⠀⠀⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠰⣶⡶⠂⠀⠀⠀⠀⠀⠀⠤⡄⠀⣀⠁⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⡄⢧⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⡏⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣹⣿⢹⣿⣿⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡽⢿⣿⣿⣛⢛
⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢻⣿⣿⣿⢿⣿⡇⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⡁⢸⣿⣿⣿⢸
⠋⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⡿⣏⣦⡀⠈⣉⣯⣿⣿⣿⡄⠏⠸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢨⠉⠐⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⣉⣿⡟⠀⢸⣾⣻⣿⣿⣿⢸⣗⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣀⣺⠈⠛
⣭⣍⠀⠀⠈⠀⠀⠐⠐⠂⠀⠀⢠⠾⠿⣷⠄⠈⠻⣯⢻⣧⣿⠀⣿⣼⣟⣻⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢻⣿⡿⣿⣿⣿⣿⣵⢷⠈⢿⠟⠐⠀
⣤⣤⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠦⣾⣿⣇⢻⣟⣿⣿⣽⣿⣿⡿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣽⣿⡿⢿⡿⣣⡀⠀⠙⠃⢠
⠓⠛⠀⠀⢠⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⣿⢸⣿⣽⣿⣿⣿⣿⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣨⣶⣿⠷⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠈⠋⠀⢿⡿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⢿⠉⠹⡿⠁⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠛⠀⠀⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠘⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣧⡈⠁⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣔⠒⠀⠐⠺⠷⣿⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠉⠁⠙⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣶⣤⣀⠒⠖⠦⢉⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣸⣿⣿⣿⣿⢿⣿⣿⣷⣆⡀⠈⣿⣿⣿⣿⣿⣿⣏⣩⣿⣿⣾⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠛⢻⡿⠛⣿⣿⡟⠛⢿⣿⠠⠿⠟⠛⠛⠋⠈⠀⠈⠀⠀⠈⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢲⣿⣗⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠃⠀⠙⠋⠁⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣤⣶⣶⣷⣿⡿⠉⠹⠏⠉⠈⠈⠀⠀⣀⠄⠀⠉⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⠃⠁⠁⠀⠀⠀⠀⢠⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⠀
⠸⠿⠿⠻⠟⠛⠀⠀⠀⠒⠀⠀⠀⡘⠉⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠀⠈⣷⠀⠀⠀⣰⡆⣀⣿⣷⣆⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⠉⠉⢙⠟⠀⣻⣿⣿⢹⡇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⣛⣒⣶⣿⠁⠀⠉⠈⠁⢾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢸⠀⠀⠘⢿⡿⢀⣧⡀⢰⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢆⠀⠀⠀⠀⠈⠉⠀⢸⣿⠇⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠰⠚⠛⠃⠀⠙⠁⠀⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣤⣽⣠⣤⣭⣥⡄⣤⢤⡄⢴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠑⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⠃⠛⠛⠚⠳⠋⣛⡃⠘⠛⠛⠛⠓⠛⠛⠃⠐⣿⡏⠀⢿⣇⠀⠀⠀⢀⣁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⣖⡂⡁⢐⠐⠌⠀⠀⠀⢂⢰⢶⠔⢸
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡤⠀⣤⣤⣤⡤⣬⣯⣥⣤⣤⣤⣤⡤⢤⣤⡤⢤⡤⣤⣤⣤⣄⣤⣠⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠸⠻⡟⠇⠁⠀⠀⠀⠀⠀⠀⢘⣦⣭⠄⢸
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⣿⡇⠀⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⣿⡇⢸⡇⣿⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣠⣤⣤⠤⢤⢄⡨⠀⠀⠠⠂⠀⠀⠙⠙⠀⢸
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⣃⣛⢃⣤⣿⣿⣽⣿⣯⣿⣿⣧⣟⣛⣛⠛⣛⡾⠧⠘⠃⢛⣋⠛⠃⠛⠙⠃⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠠⠀⡀⡤⠀⠀⠀⠄⢰⣶⢛⠷⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠛⣷⡆⠀⠀⠘⠻⣷⡄⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠈⠃⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⡾⠶⠆⠀⠀⠈⠉⠉⢁⣀⣀⣈⡁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⢄⣠⣤⣤⣾⠿⠿⣿⣿⣿⣿⡄⢠⣌⠉⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⣿⣿⣿⣷⠈⠉⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⢠⠁⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⢰⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⣾⣿⣷⣄⣿⣿⣶⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⣠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠉⠰⠶⠶⠄⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⠀⠤⠄⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣦⡀⠀⠀⠀⠐⠷⠘⠿⠿⠿⢦⣀⠀⣀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣷⣴⣦⡄⠀⠀⠀⠀⠀⢠⠉⠙⠳⢾⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠙⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠤⠙⠀⠰⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠰⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣭⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀
⠀⠤⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠠⠓⠒⠀⠀⠀⡤⠀⠀⠀⠠⣤⠀⠀⣄⠀⠀⠈⠉⠉⡛⠠⠀⠀⠄⠐⠒⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⣀⣒⠂⠀⠀⢀⠀⠀⠀⠀⠈⢀⠀⣄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⠁⠀⢩⠹⢨⡏⠿⠷⣷⠧⠿⠟⠿⠻⠷⠇⠀⢁⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠭⠀⠀⠀⠒⠒⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⢠⡸⣿⣿⡏⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣹⣿⣹⣗⣿⣿⣿⡿⢽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠿⡛⢿⣿⣿⣥⢸
⣿⠿⠿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠋⠈⣿⣿⣿⣿⣿⣿⠺⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣒⡅⢸⣿⢻⣿⢸
⠁⠀⠀⠀⠈⠁⠉⢹⣿⣿⣿⣿⡿⣣⣦⡀⠈⣩⣿⣿⣿⣷⡐⢉⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⡇⢸⠀⡌⡷⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⢨⡁⣿⡇⠀⣷⣟⣿⣿⣿⡇⢻⡷⣾⣻⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⢿⡇⢸⣬⡝⠀⠉
⣥⡁⠀⠀⠁⠀⠀⠐⠐⠀⠈⠂⢰⠿⠿⡷⠀⠘⢻⡯⣿⣷⣧⢸⣷⣽⣭⣷⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣞⡿⠀⠻⣃⡌⠀
⣤⣤⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢲⢰⣿⣿⡌⢿⡟⣿⣧⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣣⣿⠿⠟⣿⣟⣧⡄⠀⠀⠀⢰
⠛⠓⠀⠀⣽⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⣿⣿⢸⡿⣷⣿⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣼⣿⡿⠓⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠘⠁⠈⢿⢏⣿⢷⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣜⠿⢁⠿⠏⠁⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⠀⠀⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠘⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣛⣿⣧⡄⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡔⠂⠀⠐⠾⠶⣾⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣿⣿⣿⣿⣿⣿⣯⠉⠀⠙⢿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣶⣿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⣶⣄⣐⠒⠲⠮⢉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢡⣾⣿⣿⣿⣟⣿⣿⣿⣿⣆⡀⢀⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠉⢻⡟⠻⣿⣿⡟⠛⣿⣿⠠⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠛⢲⣿⡇⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠀⠛⠛⠁⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣶⣾⣿⣿⣿⠉⠹⠏⠉⠉⠀⠀⠀⢀⠀⠈⠉⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⠃⠉⠉⠀⠀⠀⠀⢠⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠠⠄⠀⠀⢰⡆⠀⠀⠀
⠸⠿⠿⠿⠿⠛⠀⠀⠈⠑⠂⠀⠀⠻⠋⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⠀⠸⣷⠀⢀⣀⣿⡄⣤⣿⣿⣦⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⢹⠟⠀⢿⣿⣇⠘⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠿⠿⠀⠀⠀⠀⠀⠿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢸⠀⠀⠛⢿⡿⠀⣿⠀⢰⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⡄⠀⠀⠀⠀⠈⢙⠂⢸⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠰⠛⠛⠃⠀⠛⠃⠀⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣤⣽⣠⣤⣨⣧⡄⣤⢤⡤⢴⣷⣶⣤⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⢸⣿⣿⠿⣷⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⠃⠛⠛⠛⠳⢋⣛⣃⠘⠛⠛⠛⠓⠛⠛⠃⠘⣽⣿⠀⠹⣷⠀⠀⠀⢀⣁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⣰⣷⣗⣪⢄⡄⠀⠈⠀⠀⠰⣾⣾⠧⣏⢿
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡤⠀⣤⣤⣤⡤⣬⣭⣥⣤⣤⣤⣤⡤⢤⣤⡤⢤⡤⣤⣤⣤⣄⣤⣠⡄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⣪⠐⠁⠀⠘⠙⠻⠇⠈⣁⢀⠀⠀⠀⠠⠰⢷⣵⣿⠾⢻
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⢿⡇⡇⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⣿⡇⢸⡇⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠃⠀⠀⠢⣠⠤⠴⠔⠲⢤⡤⠤⠄⠀⠀⠀⠀⠀⠉⠙⢁⢸
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⠘⣃⣛⣣⣷⣿⣿⣽⣿⣯⣿⣿⣧⣿⣛⣛⢛⣻⣾⡧⠘⠃⢛⣋⠛⠋⠛⠙⠃⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠊⠀⠀⢠⠴⠤⠦⠴⠅⠬⠖⠒⢿⡿⢿⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⡆⠀⠀⠘⢻⣷⡄⠀⠂⠀⠀⠉⠉⠙⠃⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠁⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠶⡶⠿⠷⠄⠀⠀⠈⠉⠉⠉⣁⣈⣉⣉⠀⠀⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠉⠻⣦⣶⡆⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⠿⣀⣀⣠⣤⣴⡿⢿⣶⣶⣶⣷⡄⢠⣈⠉⠃⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⢀⠀⡀⠀⠀⠀⠀⡀⠀⠲⠄⠠⠤⠀⠸⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠋⠉⠉⠀⠈⢻⣿⣿⣿⣧⠀⠁⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠤⠤⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⣰⠁⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡂⠰⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⣼⣿⣿⣾⣿⣿⣶⣶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠤⠀⠀⠂⠠⠷⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣂⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⠿⠿⠿⠿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⢀⣄⣀⣀⠉⠙⠛⠙⠆⠠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢘⠋⠀⠠⠄⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣿⣧⡀⠀⠀⠀⠈⠛⠘⠛⠛⠛⣷⢤⣀⠤⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠙⠚⠛⠻⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠒⠈⣀⠒⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⡀⠀⠀⠀⢀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⡰⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣧⠀⠀⠠⠄⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⣓⡂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠤⠄⠀⠀⠀⣤⠤⠀⡀⠀⠀⠀⠠⠶⠚⠒⠂⠀⠀⡤⠀⠀⠁⠤⢤⡄⠠⢤⠀⠀⠈⠉⠉⡛⠠⠄⠀⠠⠀⠒⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣬⣭⡄⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠤⣼⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀
⡉⠨⢍⠹⢸⡏⠿⠿⣷⠷⡿⠿⠿⠻⠷⠇⠈⢉⡀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠳⠀⢀⡀⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠅⠰
⣿⣤⣿⣿⣿⣿⣧⠀⠀⢀⢻⣸⣿⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡂⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡟⠉⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣷⡿⡗⣿⢿⣿⡯⠆⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠷⡓⢿⣿⣧⡅⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⢸⣿⢻⡷⠀⣤
⠁⠀⠈⠹⠻⠛⢻⣿⣿⣿⣿⣿⢏⣀⠀⠘⣛⣟⣿⣿⣿⡠⠗⢺⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⢸⠀⡄⡇⡆⠉
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⢁⠛⢿⡇⠀⢹⣽⣿⣿⣿⡇⢸⣤⣽⢿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣻⣿⣿⣿⣿⢿⡟⢸⣤⡍⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⠀⢨⣶⣾⣧⡄⠘⢿⣟⢻⣭⣧⢸⣯⢹⣛⣷⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠛⣿⣿⣿⣯⣾⡟⠀⠛⣥⡄⠀⠀
⣃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢤⡌⣽⣿⣆⢿⡟⣿⣿⣽⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣟⡿⠟⡻⣏⣷⡄⠀⠀⢀⠸⢦
⠯⠀⠀⢰⣇⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣿⣿⣿⢸⣷⣽⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣼⣿⡿⠓⠀⠀⣀⠀⠈
⠀⠀⠀⠉⠙⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠈⠏⠈⣿⡇⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣎⡻⢀⡺⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠀⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠐⠿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣻⣿⣷⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠤⠁⠀⣴⣶⣶⣦⣬⡁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣯⡉⠁⠘⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢳⣿⠏⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣾⣿⣷⣶⣶⣤⣀⠀⠦⠤⢉⡛⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢉⣾⣿⣿⣿⣿⢿⣿⣿⣿⣦⡀⠀⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣶⣤⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠛⢻⡿⠛⣿⣿⡟⠛⢿⣿⠤⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣭⣷⣶⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠘⠓⠑⢛⠛⠁⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣠⣿⣿⣿⣿⠛⢿⠛⠉⠉⠉⠁⠀⢀⡉⠙⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠛⠒⠃⠀⠀⠀⠀⣠⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠘⠀⠀⠸⣇⡀⠀⠀⠀
⣿⣿⣿⠿⠟⠻⠀⠀⠐⠦⠀⠀⠰⡿⠿⣷⣾⣇⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⣿⡆⠀⠀⠔⠃⣰⣿⣿⣷⡀⠀
⠤⠴⠶⠶⠶⠶⠶⠒⠒⠒⠒⠚⡶⠄⢸⣿⣿⠇⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⠿⠿⠇⠀⠀⠀⠀⠙⣿⣿⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣿⣿⡆⢰⠀⠀⣴⣶⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠚⠆⠀⣿⣿⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠐⠀⡤⠴⠤⠄⠀⠐⠂⠀⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣬⣯⣠⣤⣭⣧⡄⣤⢤⡤⣤⣤⣤⣤⡀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⣃⠛⠛⠚⠳⢋⣛⣃⠘⠛⠛⠛⠓⠛⠛⠃⠀⣻⣿⠀⠈⠿⠆⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣞⣕⡄⠀⠀⠠⠀⠄⠀⠤⡥⢾⠞⠍⢸
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡽⡿⣯⣭⣧⡤⣬⣯⣥⣤⣤⣤⣤⡤⢤⣤⡤⢤⡤⣤⣤⣤⣄⣤⣠⡄⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢒⠀⠀⠀⠀⠂⠛⠛⠇⠀⠀⠀⠀⠀⠀⠴⠍⢿⣾⣖⠀⢸
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⣺⡇⡇⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⣿⡇⢸⡇⣿⣺⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠄⠒⠒⠢⠦⠠⠂⠀⠀⠀⠀⢀⣈⣈⠁⠀⢸
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⣘⣃⣛⣷⣿⣿⣿⣽⣿⣯⣿⣿⣧⣿⣛⣛⣛⣿⣼⣧⠚⢃⣛⡋⠛⠋⠛⠙⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠂⠀⠀⠀⠀⠠⠄⠘⠇⠀⠀⠋⠹⡿⡏⡱⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣯⠉⠀⠛⣿⣯⠀⠀⢠⠀⠁⠀⠀⠀⠀⠉⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡆⠀⠀⠙⠿⠿⠿⠟⠙⠻⠟⠉⠉⠉⠁⠀⠀⠘⠉⠀⠀⠀⠈⠙⢷⣆⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⡂⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⠀⠹⠿⠿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠒⠀⠒⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠾⠿⠛⠋⠉⢻⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⡀⠀⠀⠀⣶⡀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣤⣀⣠⣿⣯⣀⠀⠀⣀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣀⡀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠿⠿⠿⣿⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⣤⣦⣀⣄⠀⠈⠉⠙⠢⠆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡚⠃⠀⠤⠌⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⣦⡀⠀⠀⠀⠈⠃⠙⠛⠛⢋⡷⣦⣐⡴⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣷⣾⣷⡆⠀⠀⠀⠀⠀⠐⠉⠉⠉⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠂⠈⣀⠛⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠈⠀⠀⠀⣠⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣭⠀⠀⠤⠄⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠉⠙⠛⡛⠠⠀⠀⠀⠀⠒⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣬⣭⡄⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠒⠼⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀
⠂⠈⠋⠹⢸⡟⠿⠿⣷⡣⣺⣟⠿⠿⠯⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⣧⣼⣿⣿⣿⣿⣆⢀⡀⡄⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡏⠁⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣷⠿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣿⡿⣿⣿⣿⠯⠇⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠧⠃⣿⣿⣷⡇⠀⠐
⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⣿⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣥⡀⢿⡟⢻⠗⠠⡄
⠀⠀⠈⠛⠙⠋⢿⣿⣿⣿⣿⣿⣣⣀⠀⢙⣻⣻⣿⡿⣧⠸⠃⢾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣻⡇⣆⢠⡸⢷⡆⠈
⠀⠀⠀⠄⠀⠀⠈⠙⠛⠿⠋⡘⠛⣿⡃⠀⣷⣿⣿⣿⣿⡇⣿⣠⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⢻⡃⢧⣴⡇⠀⠀⠀
⠂⠀⠀⠂⠀⠀⠄⠤⠀⠐⠀⣤⣶⣿⣦⠀⠹⣿⡟⣿⣽⡇⢸⣧⣿⣛⣧⣭⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡹⣿⣿⣿⣿⣯⡃⠈⠫⢵⠄⠀⠀
⣃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠠⣿⣿⡘⣿⣻⣿⣯⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⠿⠛⣿⣣⣷⡄⠀⠀⢠⠿⢓
⠏⠀⠀⢸⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣽⣿⣷⢸⡏⣿⣿⣿⣿⡷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡖⣾⣿⠏⠁⠀⠀⣤⠀⢠
⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠏⠘⠃⠘⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡓⢀⠙⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠘⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⡷⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⠌⠁⠠⣶⣶⣶⣦⣭⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣯⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣿⣿⣷⣶⣶⣄⣀⠰⠶⠤⢍⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡁⣿⣿⣿⣿⣿⣻⣿⣿⣿⣦⡀⣀⣿⣿⣿⣿⡿⠿⠷⠶⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣶⣬⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡟⠙⢻⡟⠛⣿⣟⡟⠛⣿⣿⠐⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣭⣶⡖⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠓⠒⠙⠛⠁⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣼⣿⣿⣿⣿⠋⠿⠋⠉⠉⠉⠁⠀⢀⡍⠉⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠑⠃⠀⠀⠀⠀⣠⣼⡿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢃⡄⠀⠀⠉⠀⠀⠸⣥⡀⠀⠀⠀
⣿⣿⡿⠿⠏⠹⠄⠀⠰⠦⠀⠀⠸⠿⠿⣷⣾⡇⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⡀⣀⣿⡀⠀⠀⠀⢁⣶⣿⣿⣷⡀⠀
⠶⠶⠶⠶⠖⠲⠒⠒⠛⠓⠒⠚⡷⠄⢸⣿⣿⡁⠀⠸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠿⠿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⡄⠀⢸⣿⣿⡄⢰⠀⠀⣶⣶⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠚⠄⢠⣿⡿⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠂⠀⡤⠤⠤⠄⠀⠘⠂⠈⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣭⣧⣠⣤⣬⣭⡄⣤⢤⡤⣤⣤⣤⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⡿⢻⡷⢼⣿⡇⣿⣾⡇⢸⢿⣿⣿⣿⣦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢀⡀⠀⠉⠁⠀⢀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠟⠃⠛⠛⠚⠳⣋⣛⣂⠘⠛⠛⠛⠓⠛⠛⠃⠈⠱⣿⠇⠀⠙⠗⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠀⠀⢀⠀⠐⢀⡄⣾⣿⣝⢺⠀⠃⠈⠁⠄⠐⠐⡗⡮⢒⠕⢻
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⣤⡤⡟⣥⣤⣾⡭⣽⣿⣥⣤⣤⣬⣤⡤⢤⣤⡤⢤⡤⣬⣤⣤⣄⣤⣠⡄⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡛⡛⠓⠨⡒⠔⠉⠙⠛⠛⠷⠡⠤⠀⠀⠀⠀⠸⠂⢿⣿⠋⠑⢼
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⣿⡇⡃⣿⣭⣽⡇⣿⣿⣿⡏⣿⣿⣿⡗⢸⣿⡇⢸⡇⣿⣸⣿⣿⣿⣿⡇⢈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⣠⣠⡠⠤⠖⠲⠚⠃⠖⠂⠂⠀⠀⠀⢀⣠⣤⣤⣀⠀⢺
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⣘⣃⣛⣃⣿⣿⣿⣽⣿⣯⣿⣿⣧⣿⣛⣛⣻⣿⣾⣇⠘⢃⣛⡋⠛⠋⠛⠙⡃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⢀⢀⠀⠐⠄⠠⠼⠃⠀⠈⠉⢽⠿⡿⠿⡃⠠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣭⠉⠁⠻⣿⣮⠀⠀⢠⡀⠁⠀⠀⠀⠀⠈⠙⠒⢠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⡂⠀⠈⠙⠿⠿⠟⠋⠉⠛⠟⠉⠉⠈⠁⠀⠀⠘⠉⠀⠀⠀⠈⠙⢷⣂⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣶⣀⠀⠀⣀⣠⣠⣤⣤⣤⣤⣤⡀⠀⠻⠿⠿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠙⠀⠛⠀⠂⠉⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠻⠛⠛⠋⠉⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠐⠒⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⢰⣶⡀⠈⠐⠒⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⣀⣀⣸⣿⣧⡀⠀⠀⢀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠠⠘⠁⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠘⠋⣠⡀⣀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⠿⣿⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡒⣶⣶⣤⣆⡀⠈⠉⠉⠁⠂⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣀⡚⠃⠀⠤⠌⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣴⣿⣿⣧⡀⠀⠀⠀⠈⠁⠈⠛⠋⠉⡿⣧⣔⣲⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣿⣷⠆⠀⠀⠀⠀⠀⠐⠈⠉⠉⠉⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢀⡀⠀⣀⠀⠀⠀⠰⠀⠀⠀⠠⣀⡉⠉⠉⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠃⠀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠈⠀⠀⠀⣠⠁⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⣀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣥⠀⠀⠠⠄⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⠀⠠⣀⠀⠀⠉⠉⠙⡛⠠⠀⠀⠀⠀⠒⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣤⣭⠄⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠒⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀
⠂⠈⠏⠹⢸⡿⠿⠿⣷⣧⣻⣟⠿⠿⠯⠇⠐⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠒⠀⠀⠀⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈
⣷⣾⣿⣿⣿⣿⣅⣀⡠⡜⣇⣿⣧⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢸⣿⣿⣿⢉⠁⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡏⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⢺⣿⣿⡿⠞⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡻⢜⢸⣿⣿⣶⡀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢻⣿⣿⣿⣿⣿⡇⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣯⣤⠸⡿⠋⡿⠗⢠⠀
⠀⠀⠈⠛⠉⠙⣿⣟⣿⣿⣿⣟⣡⡀⠀⢉⣿⣽⣿⣿⣅⠚⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣆⢠⠿⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠙⠿⠟⠁⡛⢹⣿⠀⢨⣶⣻⣿⣿⣿⡘⣷⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⣟⠘⣷⣾⠀⠀⠀⢠
⠂⠀⠐⠀⠀⠀⠀⠄⠀⠐⢀⣿⣾⣿⡤⠀⠻⣿⣛⣿⣽⡄⣿⣮⣿⣻⣬⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣏⢿⣿⣿⣿⣿⣿⠃⠙⠫⡤⠐⠀⠈
⡀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⢴⣿⣇⠸⣿⢻⣿⣯⣿⣿⣿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡻⠟⠹⣟⣼⣧⠀⠀⠀⠸⠿⢀
⠁⠀⠈⣿⣄⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⢯⣿⣿⡇⣿⣮⣿⣿⣿⣿⡞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⣿⣷⢰⣿⣿⠉⠁⠀⢠⡄⠀⣴
⠀⠀⠈⠉⠁⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠃⠛⠁⠹⣿⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⠂⣌⠛⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠤⠾⠇⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⡦⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⠈⠀⠴⢶⣶⣶⣦⣍⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣏⠈⠀⠛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⡿⠟⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣾⣿⣿⣿⣷⣶⣤⣀⠲⠶⠤⢍⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⣡⣿⣿⣿⣿⣏⣿⣿⣿⣷⣄⠀⣸⣿⣿⣿⣿⠿⠿⠴⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣦⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠛⠛⢻⣛⢻⣿⣿⠋⢻⣿⡇⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠤⠄⠴⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠯⣽⣶⡆⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠘⠑⠊⡟⠋⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣿⣿⣿⣿⣿⠋⠿⠋⠉⠉⠉⠁⠀⢠⠍⠁⠀⠀⠀⠀⠀⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠛⠛⡃⠀⠀⠀⠀⣤⣼⣷⣄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⣄⠀⠀⠀⠃⢀⠐⣧⣀⠀⠀⠀⠀
⣿⣿⡿⠿⠿⠟⠄⠀⠀⠀⠀⠀⠸⢿⣿⣿⢛⡇⠈⢰⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣇⢀⣹⣇⠀⠀⠀⠈⣴⣿⣿⣷⡄⠀⠀
⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⢻⠷⠀⢠⣿⣿⡇⠀⢿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⠿⠇⠀⠀⠀⠀⠘⢿⣿⣿⣿⡶⠶
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠼⢿⣿⡷⠀⠀⠀⣰⣶⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⠁⠹⣿⣇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠂⠠⠴⠶⠶⠆⠀⠐⠂⠈⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣬⣧⣠⣤⣬⣭⡄⣤⣤⡄⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⢹⣿⣿⣿⣷⣆⠀⠀⢀⡔⠂⠀⠀⠀⠀⠀⠀⡞⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⣟⣃⣛⣛⣛⣳⣋⣛⣧⣘⠛⠛⠛⠓⠛⠛⠃⠀⠹⣿⣿⠛⠻⣷⡀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⡀⠀⠀⢀⢀⣀⣴⣼⣿⣾⣿⣿⡾⠻⠿⠷⠳⠿⣿⣿⣿⣿⣿⢹
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⢤⡬⡿⣿⣽⣿⡯⣿⣿⣭⣤⣤⣤⣤⡤⢤⣤⡤⢤⡤⣤⣥⣤⣄⣤⣠⡄⠀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⣛⠃⣾⡙⠊⠛⠻⠿⠿⠿⠳⡆⠀⠀⡤⠾⠟⢿⣿⣿⣿⢿⢾
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⢿⡇⡇⣿⣭⣽⡇⣿⣿⣿⡇⣿⣿⣿⡗⢸⣿⡇⢸⡇⣿⣸⣿⣿⣿⣿⡇⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣁⣹⣨⠶⠖⠚⠛⠻⠶⠖⢓⠠⠗⡃⢀⣤⣤⣤⣭⣅⣶⢿
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⠛⣘⣃⣛⣣⣿⣿⣿⣽⣿⣯⣿⣿⣧⣟⣛⣛⣛⣿⣾⣇⠘⣃⣛⠋⠛⠋⠛⠙⠃⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠃⠀⠀⠄⠝⠶⠟⠿⠋⠒⠽⠍⣿⣿⠿⠟⡿⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣍⠉⠈⣿⣧⡄⠀⠀⡀⠀⠁⠀⠀⠀⠀⠙⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣷⣶⠀⠀⠈⠙⠛⠛⠋⠉⢉⣙⡁⠀⠀⠈⠀⠀⠀⠹⠉⠀⠀⠀⠙⠿⣆⣰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣧⡀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣄⠀⢙⣿⢿⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⡀⠀⠀⠀⠰⠂⠀⠈⠉⠈⠃⠀⠓⠉⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠘⢿⣿⣿⣿⠀⡂⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⣿⣦⠀⠁⠒⠆⠀⠀⠀⠀⠀⠀⠁⠀⠄⠸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⢀⣿⣿⣆⡀⠀⠀⠀⢀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠁⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⢿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠁⠿⢡⣤⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠿⠿⡿⡿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣐⢲⣶⣦⣶⣀⠀⠉⠉⠉⠚⠚⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠛⠂⠠⠄⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣴⣾⣿⣿⣄⠀⡀⠀⠀⠈⠀⠉⠉⠡⢼⣿⣼⣛⡛⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠉⠉⠉⢣⡀⠀⠈
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⡄⠄⢀⡀⠀⠀⠀⠆⠀⠀⠰⠄⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠂⢤⠘⠋⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠉⠀⠀⢀⠎⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠂⣀⣀⣀⠀⠀⣠⡐⠂⠦⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠈⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣧⡄⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠤⡄⠀⠀⠀⠄⠠⠄⠀⠢⡄⠀⠀
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⣰⡒⠒⠀⠀⠀⢠⠄⠀⠀⠠⢤⡄⠀⢤⡀⠀⠈⠉⠉⢙⠁⠄⠀⠀⠀⠐⠒⠀⣀⠀⠈⠉⠀⠀⠈⠀⠠⣤⣬⠥⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀⠒⠒⠃⠀⠒⠄⠀⠀⠀⠀⠀⡄⠀⠀
⠀⠸⠿⠹⢹⡿⠿⢶⡿⣧⣹⡟⠿⠿⠏⠇⢙⡀⠀⠄⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠑⠀⠀⠀⠈⠉⠑⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠲⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠁⠀⠀
⣤⣿⣿⣿⣿⣧⣁⢀⢄⢹⣻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠿⣿⣷⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⠛⠉⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⠹⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣼⣿⣿⣿⣿⡷⠷⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣾⡷⡛⢿⣿⣯⡦⠀⠀⣸
⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⡅⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣗⡅⢸⣿⢻⣿⢆⣤⢈
⠀⠀⠝⠋⠙⠻⣿⣿⣿⣿⣿⢟⣄⠀⠈⣛⣽⣻⣾⣿⡀⡗⠰⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢰⠀⡈⡗⡇⠈⠈
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠁⡟⢻⣷⠀⢹⣼⣿⣿⣿⣇⢸⣆⣽⢿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣿⡿⡿⢸⣬⣝⠀⠁⠀⢀
⠀⠀⠒⠀⠀⠠⠠⠀⠀⠂⢀⣷⣾⣿⡄⠘⢿⣟⢻⣏⣯⢸⣿⢹⡟⣻⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⣿⣿⣿⣿⣞⡿⠀⠻⣉⡄⠐⠀⠘
⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢤⡌⣽⣿⡇⢿⡞⣿⣿⣿⣿⣿⡿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣟⡿⠟⢻⢏⣷⡄⠀⠠⠀⡸⠷⠀
⠁⠀⢙⣏⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⣞⣿⣿⠈⣿⢹⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⢰⣿⣿⠛⠀⠀⣀⠀⠀⣨
⠀⠀⠉⠙⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠟⠈⣿⡿⣿⡿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢃⡚⠏⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣤⠿⠇⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠁⠿⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣛⣿⣷⡤⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⠁⠀⣤⣶⣶⣦⣬⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡍⠁⠘⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢶⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣿⣿⣷⣶⣶⣤⣀⡀⠤⠭⢉⡛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣵⣿⣿⣿⣿⢿⣿⣿⣿⣦⣀⠀⣹⣿⣿⣿⣿⣿⣿⣹⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣶⣤⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠛⠛⡿⠛⢿⣿⣻⠛⢻⣿⡅⠼⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠘⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣯⣵⣶⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠛⠉⢚⠛⠛⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣯⣿⣿⣿⡿⠋⡿⠋⠉⠉⠉⠀⠀⣈⠉⠀⠀⠀⠀⠀⠀⡏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠛⠚⠅⠀⠀⠀⠀⣠⣾⣧⡀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠃⠀⢼⣄⠀⠀⠀⠀⠘
⣿⣿⡿⠿⠫⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢿⠀⠿⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⢿⡆⠀⠀⠀⢁⣾⣿⣿⣦⠀⠀⠀
⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⡶⠦⠀⢱⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⠿⠇⠀⠀⠀⠀⠻⣿⣿⣿⣧⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣽⣿⣿⡆⠀⠀⠀⣶⣶⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣⠓⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⠉⠀⠂⠀⠀⣿⣿⠋⢻⣿⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡤⠤⠤⠤⠖⠀⠀⠀⠁⣤⣤⣤⣤⡄⣤⣄⢀⣤⣄⣽⣥⣠⣤⣭⣧⡄⣤⢠⡄⠀⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⠿⢻⡷⢼⣿⡇⣿⣾⡇⢺⣿⣿⣿⣶⡄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢙⣿⣃⣛⣛⡛⢳⣋⣛⣷⣜⠛⠛⠛⠓⠛⠛⠃⠘⠿⣿⣿⠿⣿⣦⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣿⡷⢧⢦⠖⠶⠴⠁⠤⠒⣠⣆⠺⢖⠔⢹
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⣤⡽⡿⣯⣽⣿⡭⣽⣿⣭⣤⣤⣤⣤⡤⢤⣤⡤⢤⡤⣤⣥⣤⣄⣬⣠⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠶⠒⠀⠐⠀⠚⠺⠿⠿⠭⠃⠄⠀⠀⠀⠀⠤⠶⣿⣷⡿⠺⠀⢸
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⣸⡇⠃⣿⣭⣽⡇⣿⣿⣿⡏⣿⣿⣿⡗⢸⣿⡇⢸⡇⣿⢿⣿⣿⣿⣿⡇⠠⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢀⠠⠤⠔⠒⠒⠢⢶⠰⠆⠀⠀⠀⠀⠀⣠⣄⡀⠀⠠⢼
⠀⠛⠃⠘⠃⠛⠘⠃⠛⠛⣛⣘⣃⣛⣣⣤⣿⣿⣽⣿⣯⣿⣿⣧⣛⣛⣛⣻⣿⣜⡃⠘⢃⡛⠋⢛⡋⠛⠙⠃⠒⠒⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠒⠀⠀⠀⠀⠤⠄⠰⠾⠄⠄⠟⠛⢿⠿⠿⠺⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣿⣿⠉⠁⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⢠⣼⣶⣶⡄⠀⠀⠉⠻⠿⠿⠛⠉⠙⠟⠁⠉⠉⠁⠀⠀⠈⠿⠇⠀⠀⠈⠻⢷⣀⣠⣥⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣶⡀⠀⠀⣈⣁⣠⣤⣤⣤⣤⣄⡀⠀⢻⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠒⠂⠒⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠺⠿⠛⠋⠉⠹⣿⣿⣿⣧⣴⡎⠁⠀⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠐⠒⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡯⠀⠀⠐⣶⡀⠀⠐⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠐⠒⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠻⠿⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣀⡀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⠿⣷⡶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠲⣰⣶⣀⣄⡀⠈⠁⠉⠀⠐⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣘⠃⠀⠤⠌⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⣦⡀⠀⠀⠀⠀⠃⠘⠛⠋⢉⡷⣦⣐⡶⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣷⣿⣷⠆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⢀⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠃⠈⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣅⠀⠀⠤⠄⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠉⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⢀⣀⠀⠀⠉⠛⠛⡋⠠⠀⠠⠄⠀⠒⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣤⣬⣭⠀⠀⠀⠐⠀⠀⢠⣀⠀⠀⠐⠒⠼⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀
⠀⠸⠏⠹⢻⡿⠿⣿⡷⣣⡹⠿⠿⢿⠏⠗⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠂⠀⣀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣆⡀⡀⡀⣟⣿⣿⠛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⠸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠟⠋⠙⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣧⣿⣷⣿⣿⡿⢷⡆⠀⡄⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣧⡿⠟⠇⣿⣿⣽⡄⠀⢀⡁⠀
⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣟⣂⠀⣿⡟⢻⡧⢁⡈⠁⠀
⠈⠻⠚⠛⣿⣿⣿⣿⣿⡿⢃⡀⠀⢙⣫⣛⣿⣿⣇⢸⠂⢾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡌⢀⣸⣶⡎⠁⠁⠀
⠀⠀⠀⠀⠘⠛⠻⠿⠋⡸⠛⣿⡆⠈⣯⣿⣿⣿⣿⡆⣷⣨⣿⢿⣷⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢿⠇⣿⣭⡇⠈⠁⠀⣀⠀
⠐⠂⠀⠀⠀⡄⠀⠐⠀⣸⣶⣿⣧⠀⠻⣿⡟⣿⣽⡇⢹⣯⣿⡛⣯⣭⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢻⣿⣿⣿⣿⡾⡇⠘⠟⣣⠀⠃⠀⠛⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⢤⠨⣽⣿⡸⣿⣿⣿⣿⣿⣿⣿⡿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢣⡿⣿⠟⣿⢛⣧⡀⠀⠀⢀⣶⡆⠀⠀
⠈⣻⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢰⣿⣿⣷⢸⡧⣭⣿⣿⣿⣿⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⡆⣵⣿⡟⠓⠀⠀⡈⠀⠀⣀⠀
⠈⠙⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠸⠇⠙⣿⡟⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣜⠿⢁⠿⠏⠀⠀⠀⠀⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣠⡴⠿⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠟⠸⠿⠟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣿⣧⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢤⠄⠀⢠⣶⣶⣶⣤⣍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣯⠉⠁⠙⢿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⢰⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣷⣶⣶⣦⣄⡀⠠⠭⠍⣙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⣼⣿⣿⣿⣿⢿⣿⣿⣿⣆⡀⠀⣹⣿⣿⣿⣿⣿⣯⣽⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠻⡿⠻⣿⣿⡛⠛⢻⣿⠄⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀
⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢻⣭⣷⡆⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠃⠀⠻⠿⠃⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣿⣿⣿⣟⠋⠿⠋⠉⠉⠉⠘⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⣿⣿⣿⣿⠏⠀⠀⠃⠀⠀⠀⠀⣠⣾⣦⣰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢸⠀⠨⣇⠀⠀⠀⠀⠀⠘⠀
⣿⡿⠿⠝⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⣷⡀⠀⠀⠀⣰⣿⣿⣶⡀⠀⠀⠀⠀
⠤⠦⠤⠤⠤⠶⠖⠶⠒⢲⣶⠶⠀⢀⣤⣼⡶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠿⠿⠀⠀⠀⠀⠘⢻⣿⣿⣿⣦⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣛⣿⣿⡇⠉⠁⠀⢰⣶⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠘⣻⠚⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⣿⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⡤⠤⠴⠤⠔⠀⠐⠀⡈⣥⣤⣤⣤⡄⣤⣄⢀⣤⣄⣽⣥⣠⣽⣄⣤⡄⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⡷⣿⣿⡇⣿⣿⢸⡇⣿⣿⡿⢻⡷⢼⣿⡇⣿⣾⡇⣤⣤⣤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⠀⠀⠀⠒⠃⢀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣛⣛⣛⣿⣳⣛⣛⣿⣷⣯⣿⣷⣜⠛⠛⠛⠓⠛⠛⠃⠽⣿⣿⣿⣷⣄⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⢰⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣲⣿⣿⣿⣿⣿⣿⣿⣿⠷⢿⣿⣿⣿⣿⣿⣏⢈⢸
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡬⣭⡽⡿⣿⣿⣿⡯⣿⣿⣭⣤⣤⣤⣤⡤⢤⣤⡤⢤⡤⣤⣭⣤⣍⣤⣠⡅⠀⠀⠀⠀⠀⠀⠀⠇⠌⠀⠀⠀⠴⠶⠖⢀⡋⠻⠻⠿⠿⠿⣿⢿⣦⡀⣠⣀⣯⡿⠿⣿⣿⣿⡿⣿⡿⣾
⠀⣿⡟⢻⣯⣗⢸⡇⣿⡗⣿⣿⡇⣿⡇⡁⣿⣭⣽⡇⣿⣿⣿⡏⣿⣿⣿⡗⢸⣿⡇⢸⡇⣿⢽⣿⣿⣿⣿⡇⣠⣤⡚⠐⠒⠀⠀⠀⠀⠀⠀⢘⠘⠛⠛⠙⣆⢤⣤⠖⠶⠒⣷⡶⠾⠔⢾⠞⠃⢠⣤⣬⣭⣥⣶⣿⣾⣻
⠀⠛⠃⠘⠃⠛⠘⠃⠛⣛⣛⣘⣃⣛⣧⣿⣿⣿⣽⣿⣿⣿⣿⣃⣛⣛⣛⣛⣛⠘⠃⣘⣃⠛⣋⡛⠋⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠒⠀⠀⢠⠰⠦⠿⠾⠿⠥⠼⠋⣻⣿⣿⣿⠿⠋⠛⢛⣹
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⠛⠃⢹⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣀⣴⣶⣶⠀⠀⠈⠻⠿⠿⠿⠿⠛⠿⠿⠋⠉⠉⠉⠀⠀⠛⣷⡆⠀⠈⠙⢿⣦⣀⣨⣆⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣀⣀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣤⡀⠀⠀⠒⣀⣀⣀⣀⣀⣀⡀⠀⠙⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⢀⠀⠀⠀⠀⠄⠀⠈⠒⠀⠓⠀⠈⠁⠁⠁⢠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠶⣶⣾⡿⠟⠋⢻⣿⣿⣷⣶⣾⣿⡿⠉⠙⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠐⠒⠠⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦⡀⢀⣧⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠀⠠⠐⠐⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣾⣿⣿⣶⣦⣦⣶⣶⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠌⠀⠺⢋⣠⣀⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⡶⢶⣶⡶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠒⣶⣦⣴⣄⡀⠉⠉⠉⠒⠒⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣀⠒⠂⠤⠤⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⣿⣦⠀⠀⠀⠀⠘⠃⠝⠛⠉⢭⣿⣦⣷⡾⠂⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⢓⣀⡀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠄⣀⠉⠉⠉⠉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢰
⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠜⠂⢉⣈⠓⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡐⢠⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠀⠀⠰⠀⣀⠀⠀⠀⢀⣀⡠⠤⠄⠀⠀⠀⠀⠀⢰
⠀⠄⠈⠑⠂⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣅⠀⠀⠤⠄⠀⠀⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠩⣥⠀⠈⠀⠤⠀⠄⠀⠠⣀⠀⠀⠀⢸
⠀⠠⠀⠀⠀⠀⣤⠤⠀⠁⠀⠀⡤⠤⠤⠀⠀⠀⡀⠀⠁⠂⣀⣀⣀⣀⡀⠀⠀⠙⠛⠛⡋⢤⠀⠤⠄⠐⠒⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣤⣭⣭⠀⠀⠀⠐⠀⠀⢠⣄⠀⢀⡐⠲⠾⠀⠐⠢⠄⠂⠀⠀⠀⢠⠀⠀⠀⠀
⠀⠸⠿⠿⣿⡇⣿⠿⡿⠳⠿⠟⡿⠿⠷⠇⠀⠈⠑⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠂⠀⠀⠀⠘⠇⠀⣀⠈⠉⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠰⠄⢀⠀⠀⠠⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀
⣿⣿⣿⣆⣄⡄⡌⣧⣿⣷⢛⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⠉⠈⠿⣇⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣷⣿⡷⡿⢿⣿⠟⠧⢠⡆⠈⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠧⠃⣿⣿⣦⡇⢀⠀⡄⠀⢸
⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠃⠸⣿⣿⣿⣿⣿⣿⢸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣿⡟⢻⡗⣎⡄⠁⠀⠙
⠉⠉⠉⣻⣿⣿⣿⣿⡿⣡⣄⠀⢉⣹⣽⣿⡿⣧⠸⠁⢚⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⡇⡄⢐⡸⣷⡆⠁⠀⠀⠀
⠀⠀⠀⠈⠙⠻⠟⠋⢘⠋⣿⡃⠀⣷⣟⣿⣿⣿⡇⢿⡠⣾⣿⣻⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣻⣿⣿⣿⣿⢿⡇⢣⣤⡄⠀⠀⠀⣀⠀⠀
⠂⠀⠀⠀⠖⠀⠐⠂⣼⠷⢿⡦⠀⠘⢿⡟⣿⣽⣇⢸⣷⣽⣟⣧⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡽⣷⡛⣿⣿⣿⣿⣎⡟⠈⠛⢥⡆⠀⡀⠙⠂⠀
⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢢⠠⣾⣿⡀⢿⡿⣿⣿⣽⣿⣿⡿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢳⣟⡿⠛⠿⣋⣷⡄⠀⠀⢀⠿⠇⠀⠀⠀
⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢽⣿⣿⢸⡏⣽⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡖⣾⣿⡿⠁⠀⠀⣤⠀⢀⣤⡄⠀
⠉⠁⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠘⠃⠈⢿⣏⣿⠇⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡳⢀⡘⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⡠⠾⠟⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠘⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣿⣿⣷⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠠⠈⠀⠠⢶⣶⣶⣶⣬⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡍⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡿⠋⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣶⣦⣀⡐⠶⠦⠬⡙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠩⣼⣿⣿⣿⣿⣻⣿⣿⣿⣶⡄⢀⣽⣿⣿⣿⣿⣿⣿⡴⢿⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⡤⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠙⠛⣟⡛⢿⣿⣛⠋⢻⣿⡄⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣻⣭⣵⣶⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠓⠒⢻⠛⠋⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣟⠉⠹⠋⠉⠉⠉⠉⠁⢀⡌⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⡀⠀⠀⢠⡇⠀⢧⣄⠀⠀⠀⠀⠈⠀⠀
⠿⠫⠪⠠⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠛⣉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡀⢀⢻⡆⠀⠀⠀⣰⣿⣿⣷⣆⠀⠀⠀⠀⠀
⠶⠶⠷⠒⠒⠛⠛⠛⠛⠿⠷⠄⢰⣶⣴⡸⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠿⠿⠧⠀⠀⠀⠀⠉⣿⣿⣿⣷⠤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠽⢿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀
⠤⠴⠤⠾⠷⠟⠁⠀⠁⡀⠀⣤⣤⣤⣤⡄⣤⣬⢉⣭⣍⣽⣤⣩⣥⣄⣤⡄⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡄⣿⡷⣿⣿⡇⣿⣿⣸⡇⣿⣿⡿⢻⡷⢸⣿⡇⣿⣾⡇⣀⣀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⢀⣄⣀⠀⠀⣀⢈⣁⣀⢀⠀⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣛⣛⣛⣿⣷⣛⣻⣿⣷⣯⣟⣷⠘⠛⠛⠛⠓⠛⠛⠃⢻⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣽⣿⣿⣿⣿⡿⠿⠿⣿⠿⠻⣿⣿⣿⣿⣿⣷⣧⣴⢸
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣬⡥⣭⡿⡿⣿⣿⣿⡯⣿⣯⣤⣤⣤⣤⣤⡤⢤⣤⡤⢤⡤⣤⣭⣥⣄⣤⣠⡍⠑⠀⠀⠀⠀⠀⡼⠡⠃⠀⠀⠀⠀⠂⣀⣈⡉⠛⠛⠻⠿⠿⠿⠷⠄⠄⣠⡼⠿⠻⠿⢿⣿⢿⣿⣿⣿⣾
⠀⣿⡟⢻⣯⣗⢸⡇⣿⡗⣿⣿⡇⣿⣧⡇⣿⣭⣽⡇⣿⣿⣿⡏⣿⣿⣿⡗⢸⣿⡇⢸⡇⣿⣾⣿⣿⣿⣿⡇⠀⢠⣄⣤⡤⠄⠉⠀⠀⠀⠀⣤⠙⠃⣉⣼⡓⠶⠒⠛⠛⠻⡖⠚⣊⡱⣟⣁⣠⣦⣤⣤⣼⣸⣾⣿⣿⣿
⠀⠛⠃⠘⠃⠛⠘⠃⢛⣛⣛⣘⣧⣿⣿⣿⣿⣿⣽⣿⣿⣿⣙⣃⣛⣛⠛⣛⡛⢘⣃⣚⡣⢛⣋⠛⠋⢛⠙⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠁⠀⠠⠺⠳⠎⠺⠿⠆⠟⠍⣹⣿⡿⡿⣿⠘⡹⠻⢿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⡖⠉⠉⢿⣿⣿⠃⠈⠉⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢤⣷⢿⣿⠀⠀⠀⠙⠿⠿⠻⠛⠉⠛⠟⠃⠉⠉⠉⠀⠀⠘⢿⠶⠀⠈⠙⠻⣷⣆⣠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⣤⣤⡄⠀⢠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣶⣀⠀⠐⠛⣀⣀⣠⣤⣤⣠⡀⠀⠈⣹⣿⣿⣷⣀⠀⠀⠘⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠉⠀⠙⠈⠐⠉⠀⠁⢸⢾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠉⠉⠛⠳⠶⣿⠿⠛⠋⠹⣿⣿⣿⣶⣾⣿⣿⠋⠉⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⠐⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⡀⣿⣦⡀⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠈⠀⠛⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠠⠀⠀⡀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠿⠿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠇⢤⣤⣤⡀⠀⣀⣀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⠿⣿⡿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡄⣾⣷⣶⣶⡀⠀⠀⠈⠉⠉⠉⠁⠑⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡀⢘⠃⠀⠠⠄⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⢶⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠁⠀⠠⣟⣷⣼⣿⠃⠀⠀⢀⣴⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠥⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡤⠀⣀⠀⠀⠀⠐⠀⠀⠀⠐⠠⠀⠉⠁⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠸
⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠈⠛⠀⠄⠙⠁⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠑⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣠⢀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⣀⣀⣀⡀⠠⠤⠆⠐⠂⠀⠀⠀⠀⠀⢀⢸
⠠⠈⠁⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣥⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠁⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠘⠘
⠀⠠⠀⠀⠀⠀⣤⠤⠁⠀⠠⡔⠒⠀⠀⠀⠀⣠⠀⠀⠀⣠⣤⠄⢠⣄⠀⠀⠈⠉⠉⠟⠀⠄⠀⠀⠈⠑⠀⢀⣀⠀⠈⠁⠀⠀⠀⠀⢰⣶⡖⠀⠀⠀⠀⠀⠈⠠⢤⡄⠀⡌⠉⠛⠀⠀⠚⠀⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀
⠀⠺⠿⢿⢿⣿⡿⣿⡿⠷⠽⣿⠿⠿⣏⠇⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠑⠀⠠⠀⠉⠉⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠂⠀⠀⠀⠐⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣏⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣏⠛⢻
⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⣿⣿⣿⠿⠛⢛⣿⡇⡤⣸
⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⣯⣻⡧⣿⣿⣿⣦⡆⢨⡍⠱⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣿⡏⠇⣷⣾⣝⡂⠉⠈⡋⠀⠸⣼
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢻⣿⣿⣿⣿⣿⣯⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢜⠀⣿⡿⢿⣯⣗⡀⠃⠀⠺⠿
⠛⠛⣿⣟⣿⣿⣿⣿⣁⠀⠈⠛⢫⣻⣿⣿⣏⢸⠃⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡆⡍⢁⢸⣟⡏⠃⠀⠀⠀⠀
⠀⠀⠙⠻⢿⠿⠋⠸⢻⣷⠀⠈⣯⡿⣿⣿⣿⠀⣶⣈⣿⣿⢷⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⡇⣿⣘⡣⠉⠃⠀⠀⠀⠀⢀
⠀⠀⠀⡌⠀⠢⢄⣠⣤⣿⣄⠀⠻⣿⡿⢿⣻⡇⢸⣧⣿⡿⣏⣻⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⣿⣿⣿⣿⣼⡷⠹⠿⢃⡃⡀⠀⠻⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠨⣥⢩⣽⣿⠸⣿⢿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢆⡿⣿⡟⣿⣟⣧⡀⠂⣩⠀⣴⡍⠂⠀⠀⢸
⣀⢀⠁⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠈⠛⢐⣻⣿⣧⢸⣟⣿⣿⣿⣿⣯⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣵⣿⣿⠧⠀⠀⠘⠁⠑⣀⡀⠀⠀
⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢹⣿⡟⠸⡏⢹⣿⡿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⢯⠁⢿⡟⠉⠀⠀⠀⠉⠀⠐⠛⠃⠀⠀
⠀⠀⠀⣀⣴⣿⠉⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠸⡿⠸⡿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠉⠉⠉⣁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣇⡈⠁⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⣀⡘⠩⣤⣤⣤⣤⣌⣓⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡛⠋⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣦⣬⣉⠉⢭⣍⣉⡛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣫⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣬⡐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣾⠿⢿⣿⠿⣿⣾⢿⠿⢿⣿⡋⣰⠿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢿⣊⣧⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠀⠀⠷⢶⢾⠿⠿⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠟⢻⡟⠛⠛⠚⠻⡿⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡯⠉⠀⠾⡁⠀⠀⠀⠀⣠⣶⣿⣄⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⢰⡆⠈⣆⠀⠀⠀⠀⠀⠸⠀⠀⠀
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⠷⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢿⣦⡄⠀⠈⠃⢠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⣭⣭⣭⣤⠤⠤⠤⢴⣦⣤⡄⢀⣽⣩⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣒⣶⣿⡇⠀⠀⠈⠋⠉⣿⣿⣿⣦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠈⢼⣿⣿⡟⠛⠀⠀⠀⢾⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⢰⣿⠯⡇⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠛⣡⡄⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣬⠤⠠⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⢤⠤⠤⠤⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀
⣀⣀⣴⣶⣶⠆⢰⣤⣷⣞⠀⢀⣀⣀⣹⣿⣀⠀⠀⠀⣼⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠈⠋⠁⢻⣿⣿⡿⠟⣯⣭⣿⣿⡟⣿⣿⢈⣭⣟⣯⣽⣻⣥⣄⣤⡄⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋⠀⠀⠀⠤⠖⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⣿⡆⠀⣿⡷⣿⣿⡇⣿⣿⣹⡇⣿⣿⡿⢻⡷⢾⣿⡇⣿⣾⡷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⢠⣦⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣿⣦⣾⣿⣶⣖⣰⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⠄⠛⣛⣿⣿⣷⣟⣿⣿⣷⣋⣛⣣⡘⠛⠛⠛⠓⠛⠛⠃⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠩⣿⣧⣥⠤⢶⢲⠾⠿⣿⣿⣿⣿⡿⣝⠀⠈⠉⢱⣶⣾⣧⣿⣿⣿⣿⣿⣷⣶⢸
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡬⣭⡿⡿⣿⣿⣿⡯⣭⣥⣤⣤⣤⣤⣤⡤⣤⣤⡤⢤⡤⣭⣥⣤⣄⣤⣠⡄⠉⠉⠀⠀⠄⣧⣤⡤⢄⠐⡷⠤⠯⠛⠓⡤⣀⣤⢤⢤⣍⣤⢭⣉⡬⣿⠏⢀⣀⣙⣛⣩⣩⣿⣽⣿⡿⢽
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⣽⣷⡇⣿⣭⣽⡇⣿⣿⣿⡏⣿⣿⣿⡗⣿⣿⡇⢸⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣄⠐⠠⠋⠀⠑⠚⠀⠀⠐⠚⠛⠩⠉⠁⠀⠠⣭⡟⢲⣶⡦⣵⡖⢺⣿⣿⣿⣿⡿⣿⡿⠟⠖⢸
⠀⠛⠃⠘⠃⠛⠘⠃⠛⣛⣛⣜⣣⣾⣿⣿⣿⣿⣽⣿⣯⣟⡙⣃⣛⣛⠛⠛⣛⣘⣣⠛⠃⠛⠋⠛⠋⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠙⠀⠀⠀⠀⠉⠈⠽⠃⢸
⠀⠀⢀⣀⣬⣷⣷⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠛⠁⠈⢹⣷⣤⠀⢻⣿⣿⣤⡀⠀⣠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣦⣄⡀⠀⢠⡤⠆⠀⠈⠂⠀⠀⠀⠈⠛⢿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⢀⠀⠀⠢⠀⠶⠀⠹⠮⠋⠋⢐⣿⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⢷⣆⣠⣤⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠘⠛⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠍⠁⠀⠉⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠠⢄⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⠀⢀⠠⠰⠦⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣷⣿⣿⣷⣤⣤⣤⣤⣤⣶⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡄⠀⠀⠁⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⡐⠂⢰⡖⣀⡀⡈⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢶⣦⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠄⣤⣤⣠⣄⠀⡙⠋⠛⠀⠶⠟⠓⠤⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠉⠉⠀⠠⠀⠀⠀⢠⠄⣀⣀⡐⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣷⣄⠀⠀⠀⠀⠚⠇⡹⠟⠛⢹⡶⣆⣦⠶⠆⠀⠀⠀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⣿⣿⣷⣾⣦⠀⠀⠀⠀⠀⠄⠀⠛⠛⠛⠣⡀⠀⠈⠘⠛⣛⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠈⠙⠛⠛⠋⠀⠀⢀⢀⡀⠀⠄⠀⠀⠀⢠⠉⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠈⡱⠆⠁⠀⠶⠂⠀⠀⠀⠀⠀⠉⠡⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡁⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠀⠓⠂⡀⢠⠀⠀⠀⠀⠈⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⠀⡒⢠
⠰⠋⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠛⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⢈⢉⣋⠁⠁⠈⠁⠀⡈⠀⠰⡀⠀⠀⠈⢳⠀⢸
⠀⠀⠂⠀⠀⠘⠀⠂⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⣀⠀⢀⣀⠠⠤⠀⠀⠀⠀⠓⠂⠀⠁⠀⠀⣀⣀⣉⡀⠀⠀⠤⠀⠀⣀⣀⠀⢀⡠⠤⠭⠀⠠⢀⠀⠒⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈
⣀⣤⡀⠀⠀⠀⣤⣤⣀⠊⠁⢠⢠⡄⠀⠐⠊⠀⠀⠀⠈⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠄⠀⠀⠀⠰⡦⠀⠀⠐⠒⠒⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⢨⠉⠁⠈⢱⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀
⠀⠸⠿⠹⣿⣿⠿⠿⣿⣣⡻⠟⠿⠿⡏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⣀⠡⠄⠀⠀⠀⣀⠀⢀⢀⠉⠀⠀⠐⠂⠀⠐⠶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠈⢹
⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⣿⣿⣿⡟⡓⠨⣿⣇⠾⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⠙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣽⡗⣿⣿⣿⠳⣷⠀⣦⠘⢀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢇⠃⣿⣿⣮⡏⠈⠀⣅⠀⢀⣾
⣿⣿⣿⣧⣿⣿⣿⣿⡟⠁⠘⣿⣿⣿⣿⣿⣿⠸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣃⡀⣿⡿⢻⡿⣌⡀⠉⠀⠘⠛
⠉⠀⣿⣿⣿⣿⣿⢟⣴⣤⠀⢨⡵⣾⣿⣿⣷⠘⠁⢸⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣮⢀⡜⣾⡇⠁⠁⠀⠀⠀
⠀⠀⠀⠈⠙⡋⠀⠈⠐⣿⡅⠀⢿⣯⣿⣿⣿⡇⢹⡷⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠷⣹⣨⡍⠈⠁⠀⣀⠀⠰⢀
⠀⠀⠂⠃⠀⠈⠃⠴⠿⠿⡷⠀⠘⠻⠯⠻⣶⣧⡸⣿⢽⣿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡛⣿⣿⣿⣿⣞⣿⠘⠿⢋⡆⠔⣀⠙⠥⠀⢸
⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢶⢐⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣣⣟⢿⠟⣿⢏⣿⡆⠀⠰⢀⣶⡎⠁⠀⠀⠸
⡤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⣿⣿⢸⣿⢼⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⠛⠀⠀⣀⠀⠀⣀⡀⠀⠀
⠁⠀⠀⠀⠀⣤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠈⠋⠘⢿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢁⡙⠏⠁⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀
⠀⠀⢀⠰⠿⠟⠀⠨⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠛⠙⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣷⡄⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣒⣀⠘⠳⠿⠿⠿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣍⠁⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣦⣤⡐⠒⠒⠭⡙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠫⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⣄⠀⣸⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⠦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠋⠹⡿⠛⢿⣿⣻⠋⢻⣿⡇⠾⠟⠋⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣤⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠀⠀⠗⠲⢿⠿⠛⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠍⢙⡟⠉⠉⠉⠙⠛⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠀⠀⠘⢂⠀⠀⠀⠀⣴⣶⣿⣷⡆⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣀⠀⠀⠀⣸⡃⠀⣧⣄⠀⠀⠀⠀⠙⠀⠀⠀
⠿⢿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠂⠀⠀⠠⠀⠀⠀⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠛⣷⡄⠀⠀⢀⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠋⢹⠿⠿⠇⢰⣶⣶⣿⣿⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠁⠁⠉⠀⠀⣀⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⡁⠀⠀⠈⠀⠀⢼⣿⣿⣷⡤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⢾⣿⣿⠇⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⢷⠟⠇⠀⠒⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⣬⣭⣽⣶⣤⡀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠠⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠿⢿⣿⡇⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⣿⣿⣿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢿⣯⣝⣯⣭⣻⣥⣤⣤⡄⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣈⣀⣀⣁⠀⣀⢀⡚⣃⣀⠀⡀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢾⢻⠋⣿⡷⣿⣿⡇⣿⣿⣹⡇⣿⣿⡿⢻⡷⢾⣿⡇⣿⣾⡇⣿⣿⣷⣦⡀⠀⠀⠀⠠⣤⢤⡠⣀⣠⠀⡀⣀⣠⣤⣦⡤⠄⠀⠀⠀⢢⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⢷⣿⣶⣿⣿⣿⣿⡻⡅⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⡛⣛⣛⣿⣷⣟⣻⣿⣷⣋⣛⣃⣘⠛⠛⠛⠓⠛⠛⠃⣾⣿⣿⣿⣷⠀⠀⠀⠀⠁⠈⠈⠀⠉⡂⡀⢺⢘⢿⣿⢶⣾⣿⠙⠿⠿⠿⢿⣿⣿⣿⣇⡀⠀⣀⣸⣶⢟⣷⣿⣿⣿⣿⣿⣷⣷⣾
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣤⡤⣭⡿⡿⣿⣿⣿⡯⣭⣯⣥⣤⣤⣤⣤⡤⣤⣤⡤⢤⡤⣤⣤⣥⣄⣤⣠⡄⠠⠤⠤⠤⣤⠀⠁⠻⣾⡿⠿⠗⠛⣉⠻⠣⣤⠤⠶⠶⣧⡤⠴⠤⣤⡿⠇⣀⣀⣀⣉⣠⣤⣿⣿⣿⠿⢻
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⣿⣷⡇⣿⣭⣽⡇⣿⣿⣿⡏⣿⣿⣿⡗⢿⣿⡇⢸⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠦⠒⡀⠁⠑⠁⠐⠚⠛⠛⠒⠀⠀⢠⣴⣤⣝⢲⡿⠈⡿⠋⣻⣿⣿⣿⢿⠻⡿⣛⣛⡛⢿
⠀⠛⠃⠘⠃⠛⡘⠃⠛⢛⣛⣘⣣⣟⣻⣿⣿⣿⣽⣿⣯⣛⠙⠃⢛⡛⠛⠛⣛⣼⣇⠚⠃⠛⠋⠛⠋⠛⠙⠃⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠂⠂⠀⢀⠂⠀⠈⠁⢸
⠀⠀⠀⠶⣾⣿⣿⠂⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠃⠉⠙⠉⠀⠀⠘⢿⠒⠄⠛⠛⢿⣷⣶⣤⣼⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠴⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⣀⠀⠀⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣶⣆⠀⠰⠞⢁⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⡿⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⣀⣀⢀⣈⢂⣈⠀⠀⠠⠀⠷⠄⠈⠂⠀⠓⠀⠘⠛⠉⠁⣴⣶⠷⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⠷⢶⣿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠒⠢⠄⠀⠀⠀⠀⠀⠉⠈⠈⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⣐⠐⠖⠚⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠖⠀⠄⠀⠐⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠿⠿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠠⠀⠿⢁⣄⣠⡀⠀⠀⣀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⢿⣿⡿⢶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⣐⢢⣶⣦⣶⣄⠀⠈⠀⠉⠛⠚⠛⠓⠲⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠐⢀⡀⠶⠒⠤⠤⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣬⣾⣿⣷⣄⠀⠀⠀⠀⠉⠨⠉⠉⠉⣹⣷⣄⣶⠟⠀⠀⠀⣀⣀⡈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡷⠀⠀⠀⠀⠐⠀⠃⠀⠉⠙⢒⣀⠀⠀⠙⠛⡛⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⣥⠀⢀⡀⠀⠂⠀⠢⠀⠀⠠⢤⣬⠉⠉⠉⠁⠠⣀⠄⠠⠄⠒⠀⠀⠀⠀⠤⠀⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠘⠂⢁⡈⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢠⡔⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣤⣠⣼⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⢄⡆⢀⡀⣀⠀⠀⣤⡴⠀⡄⠀⠀⠀⠀⠀⣀⠬⠐⢲
⠈⠒⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣭⡍⠉⠠⠤⠀⠀⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠄⢽⡄⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠈⠇⠀⠘
⠀⠀⠀⠀⠀⡀⠈⠁⠀⣠⠴⠤⠅⠀⠀⢀⡀⠀⠐⠀⢀⣠⠀⢀⡀⠀⠀⠙⠛⠛⠃⠤⠀⠠⠄⠘⠒⠀⣀⡀⠀⠉⠀⠀⠀⠀⠠⣤⣤⠤⠀⠀⠐⠃⠈⠁⠤⣄⠀⣆⡛⠳⠇⠀⠲⠀⠈⠁⠀⠀⢠⠄⠀⠀⠀⠀⠀⠐
⠒⢶⣤⠤⣼⣄⣤⠶⠮⢤⡄⠂⠐⠀⠀⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠒⠂⠀⠀⠀⠙⠂⠀⣤⠈⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠱⠀⠀⠀⠀⠈⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠼⠟⢹⢿⡿⠿⠿⣿⣷⣾⠟⠿⠻⢏⡇⠂⠀⠀⠄⢀⠀⠀⢀⠀⠀⡀⠀⠈⠁⠠⡆⣒⠀⠀⠀⡀⢆⠐⠆⠴⠀⠀⠀⠈⠀⠀⠭⠇⠉⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢸⣿⣿⣿⡿⠛⢻⣿⢫
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣸⣿⣿⣧⣤⠀⣙⠛⠞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣽⣿⢿⢸⣯⣟⢫⠙⠀⠛⠃⠰
⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠃⢿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣎⠆⢸⣿⢿⣿⣲⠆⠺⠀⠸
⠛⠛⠻⣿⣿⣿⣿⣿⡿⣣⡀⠀⢛⣫⣻⣿⣿⣏⢸⠆⢼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⠛⠼⣿⣿⠻⠀⠂⠀
⠀⠀⠀⠉⠛⢿⡟⠋⠘⢻⣿⠀⠈⣯⣿⣿⣿⣿⡆⣶⢨⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣷⢸⠐⠿⠃⠛⠀⠀⠀⠀
⠀⠀⠠⠄⠆⠀⠲⠄⣠⣶⣿⣤⠀⠻⣿⡿⣿⣹⡇⢸⣯⣻⠿⣟⣻⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣻⣿⠸⣿⡷⡸⠠⠀⢰⡦⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠠⣅⢩⣿⣿⡈⣿⣽⣿⣟⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡦⣻⣿⡿⢿⡿⣟⡀⠉⢒⠃⢈⣐⠆⡘⠀
⣛⣀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⣶⣻⣿⣷⢹⡟⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣯⣅⢸⣷⣿⣷⠀⠈⠐⠚⠛⡀⠀⠀
⠛⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠸⡇⢻⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⠟⢺⣿⠟⠀⠀⠀⠲⠀⠀⠶⠦⠀
⠀⠀⠀⠀⣠⣶⡯⠉⢂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠙⢹⣿⢸⣿⣿⠿⠿⠿⠟⠛⠉⠉⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣮⠐⠪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⡘⠹⣤⣦⣴⣶⣌⣑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⡶⠿⠿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣶⣶⣦⣤⣀⠉⠭⢍⣛⡻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣻⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢻⣿⣿⣿⣿⣿⣿⢟⣿⣿⣽⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣭⡐⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡗⣠⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣋⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣧⣦⣿⣿⡆⠀⢸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⣿⣿⣿⣿⣿⠿⢻⣿⠛⠛⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠏⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⣦⡆⠀⠀⠀⠀⢠⠀⠀
⣿⣿⣿⣄⠀⠀⠀⠘⠀⠀⠀⠀⢰⣿⣿⣿⣇⣀⡀⠠⠆⠀⠺⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⢰⣶⣄⠀⠀⠙⢀⣤⣿⣿⣶⣄⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣽⣣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢬⣽⣿⠀⠀⠀⠈⠀⠙⢻⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠉⠉⢀⢠⣿⣿⡟⠁⠀⠀⠀⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠋⠀⠀⠀⠀⠐⠂⠀⠉⠉⠹⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⣈⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣴⠆⠙⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⣤⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⢉⠛⠀⠀⢿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠰⠆⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠐⣈⠀⠀⠀⢺⡟⠛⣭⣬⣿⣿⡿⣿⣿⢿⣿⣝⣭⣭⣩⣭⣩⣬⡍⣭⣭⡝⢿⣿⣦⣤⡀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⣔⣤⣤⣤⣤⣤⣴⣿⣾⣮⣦⣤⣦⣤⣤⣴⣤⣤⣤⣄⢸
⠀⠀⠀⠈⢇⢉⠀⠀⠀⣛⡀⣿⡷⣿⣿⡇⣿⣿⣹⡇⣿⣿⡿⢻⡷⢾⣿⡇⣿⣾⡇⢸⣿⣿⣿⣿⡆⠀⢠⢰⣾⣾⣇⣏⣾⢼⣷⣾⣷⣿⣿⣻⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣼
⠀⠀⠀⠀⡜⠵⢶⣿⣾⣿⣧⣛⣛⣛⣿⣷⣟⣿⣿⣷⣯⣿⣿⣜⡛⠛⠛⠓⠛⢛⣣⣾⣿⣿⠿⢿⡇⠀⠀⠈⠛⠺⠥⢷⢝⡝⡿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣍⠙⣙⣉⣻⣟⠛⣿⠶⣿⣿⡿⢟⡹⠿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⣤⣄⣤⡄⢤⡤⣤⡤⣤⣬⡥⣤⡽⡿⣿⣿⣿⡿⣿⣿⣿⣭⣤⣤⣤⡤⣤⣤⡤⢤⡬⣥⣤⣤⣄⣤⣠⡄⠀⠀⠘⠓⠀⠀⠵⢹⢛⡟⣻⣙⣁⣤⡶⣿⣛⠛⠋⣛⣻⣿⣟⣻⣿⣿⣿⢥⣿⣿⣶⣾⣿⣿⣿⣿⣿⣽
⠀⣿⡟⢻⣯⣷⢸⡇⣿⡗⣿⣿⡇⣽⡗⡇⣿⣭⣽⡇⣿⣿⣿⡏⣿⣿⣿⡗⣿⣿⡇⣼⡇⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠁⠰⠤⠞⠛⠛⠚⠛⠛⠛⢻⣶⣿⣿⣿⡟⣿⣿⡿⡻⢿⢹
⠀⠛⠃⣘⣃⣛⣘⡃⠛⠛⠛⣘⣣⣿⣣⠤⢻⣿⡍⠛⠫⠿⠙⠃⠛⠛⢛⡛⠛⠘⠃⠛⠃⣛⣋⣛⣋⣛⣙⡃⠠⢄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡚⠂⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸
⠀⠀⠀⠉⠍⠛⠛⠋⠀⠐⠀⠀⠀⠀⣤⣤⣤⣤⣄⡀⠀⠀⣦⠤⠀⠀⠈⠁⠀⠀⠀⣠⣴⣿⣿⣿⠟⠿⠋⠉⠀⠀⠉⠁⠀⠀⠈⣧⠀⠀⠀⠀⠈⠁⠐⠀⠀⣄⠀⠲⠀⠀⠀⠀⠀⣀⣀⡀⣠⡔⣲⣶⣶⣶⣦⣴⣶⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣶⣈⣠⣴⣾⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠂⠒⠒⠢⠖⠀⠀⠈⠘⠉⠁⢀⣀⠉⠉⠉⢉⡉⠉⣽⣿⠿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠉⠛⠟⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣇⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠙⠂⠀⠉⠈⠀⠘⠋⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀⣤⣴⣶⣶⣦⣄⣀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠈⠀⠀⠀⢁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠠⣤⡀⡀⢀⣀⢨⣥⠀⠀⢀⠀⠀⠀⠐⠢⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢶⣶⣦⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠀⡀⢈⣁⢂⡈⠳⠷⡦⠷⣀⣀⣶⣶⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠙⠡⠠⠀⠀⠀⢠⡄⢀⣀⡀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⣀⠀⠀⠀⠀⠤⢆⠿⠿⠿⠿⣇⡂⣀⣀⡈⠀⠀⠈⠛⡻⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠒⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠘⠛⠻⠿⣿⣿⣿⣆⣤⣄⠀⠀⠀⠁⠀⡀⡘⠿⠿⢿⣟⠁⠀⠤⢶⣾⣶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠀⠀⠀⠀⠀⢀⡀⣐⠀⣀⠈⠴⠄⠀⠀⠜⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡚⠘⣠⡔⠲⠀⣤⡄⠈⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠒⠂⠀⠀⠀⠁⠁⠀⠉⠙⠀⠀⠀⠀⠈⠀⢸
⡁⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠖⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⣀⢄⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠚⠀⠀⠠⠠⠤⠀⠀⢀⠀⠀⠀⠈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢘
⠐⠫⠌⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⣼⠾⠟⠛⠊⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠐⠶⠔⠀⠰⠒⠚⠋⠙⠀⢀⠀⠀⠈⠺⡔⠂⢸
⠀⠀⠁⠀⠀⠈⠁⠖⠀⢀⣀⣀⣨⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⢿⡿⠀⠀⠈⠁⠀⣀⡀⠈⠁⠀⠶⠄⠠⠄⠀⠀⢀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠀⠉⡀⢌⣉⣇⢀⣀⡄⢩⡈⠁⠀⠈⠂⠀⠠⠀⠉⠀⠸
⠠⣤⣄⡀⢀⣔⠂⢠⣄⣘⣛⠠⠠⢄⡀⠐⠋⠄⠄⢒⠘⠛⠉⠙⠒⠀⡀⠀⠀⠀⠃⠙⠀⢁⠉⠀⠀⠀⢴⣆⠀⠀⠠⠤⠤⠀⠀⠛⠻⠉⠀⠀⠀⠀⠀⠀⠛⠛⠀⠚⢆⠈⠁⠀⠈⠹⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀
⡄⠨⠉⠹⡟⢹⣾⠶⣤⣴⡍⠀⠀⠒⡅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⣠⣤⡄⠀⠀⠀⡀⠀⠀⠀⠂⠈⠁⠠⢅⠀⢰⣆⢤⠂⠀⠀⠀⠀⠀⠉⢰⠂⠀⠈⠀⠐⠂⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠿⢻⣿⡿⡿⢿⣿⢿⡻⡿⠿⢿⠏⠇⠀⠀⠀⠈⠈⠀⠀⠐⠆⠀⠒⠀⠀⠀⠀⠉⠱⠧⢀⠀⠱⣏⠤⠌⠈⠢⠤⠀⠀⠀⠀⠈⠁⢀⠀⡀⠀⡀⢀⡑⢖⡀⠀⢀⡀⠀⣀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸

                    ䷩ 𝚕𝚒𝚗𝚎 4079

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

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    Gemini version at gemini://gemini.techrights.org/2022/06/22/at-the-epo-bringing-teams-together-or-new-management-of-office-space-is-another-step-towards-epo-outsourcing/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ At_the_EPO,_“Bringing_Teams_Together”_or_“New_Management_of_Office_Space”_is
Another_Step_Towards_EPO_Outsourcing⠀✐


Posted in Europe, Patents at 4:03 pm by Dr. Roy Schestowitz


Monopoly Tony (or Campinos the Pretender, who pretends_to_support_Ukraine_while
sending_EPO_money_to_Belarus) is trying to kill both the EPC and the EPO [1, 2]
after giving_a_similar_"departure_gift"_to_the_EUIPO


                 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Serco EPO deal censored⦈
     Campinos isn’t even pretending anymore; it’s just another Battistelli


Summary: The Local Staff Committee Munich (LSC Munich/LSCMN) and Central Staff
Committee (CSC) raise awareness of a scheme that may result in only “33% of
staff (at best) [having] a permanently allocated desk.” Shades of what the
Office dictator Benoît_Battistelli did to Judge Corcoran after he repeatedly
won in court and his reinstatement was forced, whereupon he found himself back
but without a desk


ALARMED by unprecedented and very likely illegal actions by EPO President
(saboteur) António_Campinos, LSCMN [PDF] and the_CSC [PDF] wrote to staff and
to Campinos.


“The EPO is run by a Mafia; the only solution is for this Mafia to be removed
entirely.”Earlier today LSCMN told staff (whom it calls “colleagues”): “The May
MAC report announced on 2 June 2022 the project “Bringing Teams Together” which
foresees a new management of office space allegedly “to ensure that teams
cluster in our buildings when working on site”. Staff is now asked to make use
of the New Ways of Working (NWoW) Planning Tool to reveal their (tele)working
arrangements for the next two years. However, the planned closure of PH1-4 will
obviously set physical limits to flexibility. According to our estimates, 33%
of staff (at best) may have a permanently allocated desk. This paper explains
the details.”


We’ve included a_sanitised_PDF [PDF] as it contains tables and formulas.


The LSCMN committee isn’t alone. On the same day the Central Staff Committee
(CSC), i.e. elected staff representatives (not the union), wrote to the
dictator:


     Reference: sc22076cl
     Date: 14/06/2022


     European Patent Office | 80298 MUNICH | GERMANY


     Mr António Campinos
     President of the EPO


     By email


     § OPEN LETTER⠀➾


     § Consultation on “New management of office space” et al.⠀➾


     Dear Mr President,


     The May MAC report of 2 June 2022 mentions the project “Bringing
     Teams Together” which foresees a new management of office space
     allegedly “to ensure that teams cluster in our buildings when working
     onsite”.


     Meetings have already taken place during which the project has
     already presented to staff, including the new management of office
     space. Many staff have expressed their concerns about a new way of
     working, which will concretely shape their daily work on site and
     make it more cumbersome. Indeed, this project introduces very deep
     changes in their working conditions. This new management was not
     addressed at all when Circular No.419 was consulted on. Thus,
     consultation is not optional prior to its entry into force.


     Furthermore, this “new management” definitely requires a consistent
     approach in all places of employment, with a sound legal basis and a
     formal decision with an identifiable signatory. None of these basic
     requirements have been met so far.


     In conclusion, the CSC urgently demands that:


     • The “new management of office space”, and any other project
     implementing Circular No.419 that management might have up its
     sleeve, be discussed with the Staff Representation;
     • Prior to entry into force, statutory consultation take place in the
     GCC and in the COHSEC, in accordance with Articles 38 and 38a
     ServRegs.


     Alain Dumont
     Chairman of the Central Staff Committee


The key part is this: “this “new management” definitely requires a consistent
approach in all places of employment, with a sound legal basis and a formal
decision with an identifiable signatory. None of these basic requirements have
been met so far.”


They’re doing the same with the UPC, trying to construct a totally illegal and
unconstitutional court system by cheating, lying, and attacking reasonable
people. The EPO is run by a Mafia; the only solution is for this Mafia to be
removed entirely. █


⣿⡿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣼⣿⡉⠟⠛⢛⠛⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠹⣿⣿⠫⢙⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣜⠿⣶⣷⣶⣶⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡷⠿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠩⢻⠟⠛⣽⣿⡏⠉⡟⠻⠛⠛⢻⣿⣿⠉⢹⠛⠻⠻⠛⠟⣿⣿⡿⠉⡿⠛⠛⠟⠛⠛⠟⣿⣿⡏⠍⢩⠛⠻⠻⢻⣿⣿⣿⡟⠛⠟⠻⣿⣿⣿⠛⠛⢻⠛⠛⢻⣿⣿⡛⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠿⢿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣶⣾⣷⣿⣿⣿⣾⣿⣶⣾⣿⣾⣾⣷⣿⣿⣷⣶⣾⣷⣷⣾⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣾⣶⣾⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠻⠿⠿⢿⠿⢿⡿⠿⠿⡿⠿⠿⠟⠿⢿⠻⢿⢿⢿⠿⢿⠿⠿⠿⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣾⣶⣮⣶⣶⣶⣷⣶⣶⣶⣶⣾⣴⣾⣶⣾⣶⣶⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⣿⢿⢿⢿⣿⢿⢟⢿⢿⡿⠿⡿⡿⢿⠿⣿⣿⡿⠿⣿⢿⡿⠟⣻⡿⡿⣿⣿⢿⢿⡿⣿⠿⠿⡿⢿⢿⢿⠿⡿⠿⡿⠟⠿⣿⢿⡿⡿⣿⡿⣿⠿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣄⣀⣆⣠⣠⣇⣠⣀⣠⣠⣀⣀⣀⣄⣸⣀⣄⣸⣇⣐⣠⣠⣇⣒⣀⣐⣄⣄⣠⣠⣀⣤⣸⣰⣆⢠⣂⣀⣀⣔⣧⣁⣄⣸⣄⣠⣠⣅⣀⣼⣀⣀⣆⣰⣰⣀⣠⣀⣿⡉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠈⡈⠍⡉⡉⠈⢉⡉⣉⠙⠉⠈⠉⡈⠉⠃⠉⠀⢉⡏⣻⠉⠉⣉⡁⣸⣹⠉⣉⢉⢁⡉⣛⣉⠁⡉⠉⠉⠉⠉⣏⡏⠉⠉⡨⡈⣋⢉⢁⡉⡉⡈⢉⠁⡃⠉⢙⡨⡈⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⡾⡿⠿⠿⠿⠿⠿⢿⣿⠿⢿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⡿⠿⠿⠿⠿⢿⠿⡿⠿⠿⠿⠿⢿⠿⢿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣷⡤⢤⢬⣤⣬⣤⡼⡾⣼⡤⠤⠤⢾⣤⣤⣤⡄⣦⣤⣤⣤⡤⣤⢧⢤⠤⣧⣼⢬⡬⡠⢴⡴⣤⣤⣤⣤⣬⡼⣤⢼⣤⡤⢼⣤⣬⣤⡤⣬⣠⣤⣤⣤⣤⣴⣦⣤⣤⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣼⣤⣜⣴⣤⣤⣰⣤⣧⣤⣦⣴⣧⣤⣆⣤⣤⣠⣤⣄⣧⣬⣤⣼⣤⣤⣾⣠⣥⣤⣤⣤⣤⣤⣤⣤⣵⣤⣴⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠩⠛⠛⡛⡛⡛⡟⡭⢛⢛⠛⠛⠛⡏⠝⠙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢖⢶⣶⣷⣶⠶⣷⣴⣾⣶⣶⣦⣶⣷⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣄⣤⣤⣀⣤⣤⣤⣠⣤⣤⣤⣤⣤⣥⣤⣤⣤⣧⣼⣠⣤⣤⣤⣼⣼⣤⣤⣤⣤⣤⣯⣤⣤⣤⣤⣤⣤⣤⣧⣧⣤⣄⣤⣤⣅⣤⣤⣤⣤⣤⣤⣤⣤⣭⢬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣉⣁⣀⣈⢉⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣻⣛⡟⠛⠻⡟⠛⢛⠛⢻⢿⣿⡟⠛⡟⣛⠛⡟⠛⠛⠛⠛⢟⠛⢛⠛⢻⠛⢛⠛⠛⢻⠛⠙⠛⠛⠋⠙⠛⠛⠛⠛⡟⠛⠛⠛⢛⡻⠙⠛⠛⠛⢙⠛⠋⡟⠛⡟⢻⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠛⠿⠿⡟⠿⠿⠿⠿⠿⠿⠿⠻⢿⢻⠛⠟⡛⠛⡿⠿⠿⢻⠟⠿⠿⠻⠿⠿⠿⠿⠿⢿⠟⠿⠻⠿⠟⡟⠛⠛⠿⠿⠺⠛⠛⠛⢻⠻⢿⢻⠻⠻⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣶⣷⣷⣶⣶⣶⣶⣶⣶⣷⣷⣾⣶⣶⣾⣷⣶⣷⣶⣶⣾⣾⣶⣾⣶⣶⣶⣶⣶⣶⣷⣾⣶⣶⣾⣶⣷⣶⣶⣶⣶⣿⣶⣿⣶⣾⣶⣾⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⡆⢉⠉⣇⠒⠉⡉⢩⠙⠉⢁⢸⡀⠄⢤⠰⣸⢃⠉⢍⠉⡋⠉⡍⠉⡍⠨⠈⣹⡇⠀⠈⠀⠉⠉⣽⠀⠍⢹⠠⠈⠩⠉⢉⠉⣇⠒⡉⢁⠍⢉⢍⠉⢩⠉⠈⡍⠉⢹⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠻⡋⠛⡛⠛⠙⠛⢻⠙⠋⡛⡟⣟⠛⡛⠛⠛⠛⠘⠓⠚⠛⢛⢿⠛⠛⠖⠿⠺⠛⠛⠙⠛⠛⢛⠙⠻⠻⠛⠛⠟⠛⠛⢛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢶⡾⠶⡶⡷⠤⠶⣶⣶⠶⠾⠴⣷⠷⠶⠾⠶⠶⠶⡶⠶⠶⣷⠾⠿⢶⠴⠶⠿⢶⢶⠶⡶⢶⠶⠶⣶⠷⠼⢷⠶⠷⠶⢶⠷⠶⢿⠾⠿⠿⡿⠿⠿⠿⠻⠿⠿⡿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠭⣧⣤⣤⣧⣤⣤⣶⣦⣦⣤⣤⣼⢤⠤⣴⣥⣼⣤⣧⣦⣤⢼⣤⢴⠼⣤⣤⢤⣴⣼⣤⣤⣤⣤⡤⣴⢧⣴⣶⡴⠤⠤⣶⣤⡶⠼⢤⠤⠤⣧⣤⣬⣦⣤⣦⣤⣷⣧⣴⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣥⣤⣴⣌⣧⣤⣤⣰⣤⣼⣤⣼⣤⣦⣼⣤⣤⣨⣤⣤⣴⣤⣾⣤⣤⣴⣴⣤⣤⣠⣤⣤⣾⣴⣤⣤⣤⣤⣧⣤⣤⣤⣴⣧⣤⣶⣤⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢩⡉⠉⡍⢿⢛⠟⠛⡋⠛⠛⠛⠛⠛⡟⠛⢙⠉⡛⣕⠍⠛⠟⢛⢛⢻⢋⠍⠛⢛⠛⡛⠛⠟⠛⠟⡇⡙⠛⣻⢛⠛⢛⠛⠛⠛⢋⣿⣿⣿⠿⣿⠉⠉⠍⠛⡛⡏⠙⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣷⣶⡿⣴⣶⣶⣷⣶⣶⣶⣶⣶⡷⣦⣾⣶⣶⣶⣶⣶⣷⢶⣶⣾⣷⣶⣦⣶⣶⣦⡶⢶⣮⣼⣷⡷⣴⣿⣴⣶⣼⡶⣶⣶⡶⣿⢶⡾⡿⡿⣶⣷⣿⣾⣶⣷⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣴⣤⣥⢠⢠⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣥⣤⣤⣤⣧⣾⣄⣄⣤⣤⣴⣤⣤⣀⣤⣤⣤⡤⡤⣤⣤⣤⣤⣧⣇⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣇⣉⡍⣙⣀⣐⣀⣸⣽⣲⣉⣉⣀⣉⣉⡉⣉⣉⣩⣇⣌⣉⣉⣍⣸⣂⣀⣈⣉⣇⣀⣀⣁⡀⣇⣉⣉⡏⣉⣉⣈⣉⣉⣉⣁⣍⣁⣀⣹⣀⣉⣩⣉⣹⣀⣉⣩⣉⣉⣉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣉⣹⣁⣉⣋⣁⡉⢉⣉⣉⣉⣙⣉⣉⣿⣉⣉⣉⣉⡉⢩⣉⣩⣉⣉⣉⣁⣉⣉⡉⣌⣉⣉⣉⣩⣋⣉⢉⣸⢉⣉⣉⣉⣉⣁⣉⣉⡉⣉⢉⣏⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢛⡛⠻⠛⣿⠿⡿⠿⠏⠿⠿⠿⠿⠿⡿⠿⠛⠟⠿⡿⠛⠿⡿⠿⡿⢿⠟⠛⠿⠿⠿⠿⠿⡿⠿⡿⡏⠻⠿⢿⠿⠿⠯⠿⠿⠿⠿⣿⠿⠻⠿⠿⠿⠛⢻⠿⠿⠽⠫⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣦⣥⣿⣠⣄⣤⣧⣤⣤⣤⣤⣤⣦⣀⣤⣤⣥⣧⣤⣤⣤⣬⣌⣼⣦⣤⣄⣬⣤⣧⣤⣤⣄⣰⣧⣧⣠⣿⣠⣤⣴⣤⣤⣤⣤⣧⣥⣄⣤⣤⣤⣠⣴⣬⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣉⣉⣩⣉⣃⢈⢉⣉⣉⣉⣉⡉⢉⣉⣁⣉⣉⣋⣉⣉⣉⣏⣹⡈⡉⣉⣉⣩⣉⣉⠉⣉⣁⣈⣉⣉⣉⣉⣉⣉⣏⣏⣉⣉⣈⣁⣉⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠉⢉⢛⢻⠙⠘⠚⠛⠛⠛⠛⡏⠛⠛⡛⢻⠛⠛⡋⠛⡏⠛⠛⠛⠃⠛⢻⠛⠛⠋⠙⠛⠛⠙⠛⡏⠙⢛⠉⠛⠛⡟⠛⠛⠛⢿⠛⠙⠛⠛⢻⠛⠛⢹⠛⠛⢙⠛⠛⢻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⠛⠛⡛⠇⠛⡟⠛⠛⠛⠛⠛⠛⡛⠒⠛⠛⢿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣶⣾⣶⣶⣦⣴⣷⣶⣷⣶⣶⣶⣾⣷⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⡈⠉⡅⢉⢉⡇⠤⠈⣉⡁⡉⢈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠙⠛⡛⠛⠛⠙⠛⠛⠙⠻⠛⠛⠛⠙⠛⠟⠋⢻⠻⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠒⠶⠶⠶⢷⠲⠾⢷⠚⢒⢲⢲⡖⠖⠖⡖⠶⠶⠿⠷⠶⠿⠿⠿⠟⡿⠿⠿⠟⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⢻⠿⠿⠿⠿⠿⠿⠿⠿⢿⠋⠿⢿⠿⠿⠟⠛⠿⡿⠿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠶⢶⠶⠶⠾⣶⠾⠾⡾⠾⠶⡶⢷⠶⠶⡷⠶⠶⡾⠶⢶⠶⠶⠶⡶⢷⢶⢶⡶⡶⠾⠶⡶⢾⠴⢶⢶⢼⠷⠾⠶⠶⠶⠦⠶⠶⠾⢶⢶⠶⠶⠾⡦⠶⢶⣶⣴⣶⣾⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⢉⡙⠛⡛⠛⠛⠛⠛⠛⡛⣏⣉⠛⢙⠛⠛⠋⢛⠩⠙⠉⠙⠛⠛⢿⠘⠛⠙⠛⣿⠛⢙⡏⡉⠛⠛⢛⠛⢻⡏⡏⣉⢹⠉⠉⠉⠋⠭⢩⢀⠋⣿⠙⠋⠛⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠲⠶⠶⠷⡾⠶⠷⠖⠶⢷⠷⠾⠶⢷⠶⠶⡶⡾⡶⡾⠶⡾⡶⡶⠻⣶⣾⠶⠶⠿⢦⢷⢿⢶⠶⡷⠷⠧⠾⡧⡷⣶⠶⠒⠷⡾⣖⠲⡞⠾⢼⠗⠴⠶⠶⡶⠷⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣀⣀⣠⣠⣸⣄⣀⣠⣁⣸⣀⣭⣂⣀⣠⣀⣀⣀⣬⢀⣠⣀⡄⣀⣘⣀⣘⣦⣀⣀⣨⣀⣄⣂⡀⣈⣸⣑⣀⣄⣅⣰⣅⣀⣀⣀⣀⣀⣀⡀⣀⣀⣇⣀⣸⣨⢀⡀⣀⣨⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣉⡹⣛⢗⣀⡁⣈⣉⡿⣉⣉⣀⣈⣁⣉⣋⣉⣀⣇⣉⣹⣈⣉⣉⣉⣐⢁⣩⣩⣉⣅⣸⣨⣀⠍⣉⣉⣩⡉⣉⣉⢇⣉⣇⣈⣉⣀⣀⣝⣏⣈⣉⣉⣅⡉⡉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣬⣥⣶⣥⣿⣠⣤⡠⣧⣴⣤⣤⣬⣤⣧⣤⣼⣠⣧⣧⢤⣤⣦⣬⣮⡼⢦⣤⣄⣼⣠⣥⣠⣤⣜⣸⣧⣥⣤⣿⣨⣤⣬⣤⣤⣤⣬⣕⣭⣤⣈⣤⣤⣤⣼⣬⣤⣥⣤⣥⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣉⣉⣩⣉⣃⢉⣉⣁⣉⣨⢉⣉⣉⣉⣹⣩⣏⣉⣀⣉⣈⣹⣫⣇⣉⣁⣉⣉⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠉⣏⠛⡋⠫⠙⠩⠉⢹⣻⢩⠙⠙⠉⠙⠛⠋⠉⠉⢛⡏⡉⠫⠛⡻⢹⠉⠉⠉⠋⡏⠉⢉⡉⠉⡏⠋⠋⡟⠉⠋⠙⠋⠉⠙⠋⡟⠋⠉⢻⠉⠛⠻⠙⢻⠉⡋⠹⡙⠛⠙⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠙⢻⠋⠛⠛⠋⠛⠛⠛⠛⠛⠋⠙⠛⣿⡛⠑⠋⠙⠛⢛⠙⢛⠋⠛⡛⠋⠛⠛⠛⡙⠛⠋⠙⢛⠟⠓⠛⢹⠛⠛⠑⠛⠛⠉⠙⠋⠉⠛⠛⡟⢋⡿⢿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4278

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/22/bullying-epo-staff/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/22/bullying-epo-staff/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO_Management_Severely_Harms_the_Health_of_Staff_by_Bullying_Them⠀✐


Posted in Europe, Patents at 4:39 pm by Dr. Roy Schestowitz


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DG1: close target monitoring revived: a supporting or an
                            oppressive exercise?⦈
          Campinos bought no social peace; he did the exact opposite!


Summary: EPO management that breaks the law wants the staff to blindly
cooperate; failing to achieve full cooperation (in crimes), the managers are
increasingly bullying the workers, causing some of them to get ill (in the past
this led to a lot of suicides)


THE [firing] line managers at the EPO are dialling up the pressure to
demonstrate their loyalty to their “f***cking president” (what António_Campinos
is calling himself) and the Dutch branch of the EPO spoke_about_it_this_week.
We’re back to the Benoît_Battistelli era, even more formally. The management
tries to find new and still-dubious or still-unlawful ways to ‘motivate’
(intimidate) staff. See or recall what_happened_in_France_Télécom. There was a
prison sentence for (mis)management.


“The management tries to find new and still-dubious or still-unlawful ways to
‘motivate’ (intimidate) staff.”The Central Staff Committee (CSC) of the EPO,
i.e. elected representatives, issued a publication, which is still circulating
among staff (we too got a copy; anyone who receives a copy can leak it to us!)
and here’s what it says. “This publication provides recommendations on how to
react to the pressurising practices,” says the CSC.


     Munich,09/06/2022
     sc22074cp


     § DG1: close target monitoring revived:⠀➾


     § a supporting or an oppressive exercise ?⠀➾


     Dear Colleagues,


     We have been contacted by a number of colleagues reporting an
     increase in the degree of micromanagement they are facing in recent
     months. These micromanaging measures include, inter alia, a weekly
     monitoring of their targets, daily calls from their team manager, and
     excessive scrutiny of search strategies, communications or FO
     mailboxes. Although the purported intention of the intervention of
     the managers is to support the staff members, it is often experienced
     as oppressive and leaves colleagues feeling overwhelmed. Being in
     such a situation may seriously affect their health, and result in
     them needing to take sick leave.


     The background: “Challenging people” doctrine, excessively long
     target monitoring


     This behaviour is, unfortunately, not a new approach. In 2014, the
     Office management drafted a document titled “Challenging people”1, in
     which proposals were presented how to better control staff members
     not fulfilling the expectations of the Office management. When Mr
     Campinos arrived in the Office in 2018, he dissociated himself from
     the challenging people doctrine during a meeting with the CSC, which
     was appreciated by staff representation. Regretfully, some DG1 line
     managers continued to impose weekly recording of activities on some
     allegedly low-performing DG1 staff members over an excessively long
     period of time. Although we felt, due to this special program named
     the weekly target monitoring program (WTMP), that the challenging
     people doctrine continued to prevail within the Office, the practice
     seemed to subsequently “dry out”, which reassured us again.


     Were we too optimistic?


     _____________
     1 Presentation titled “DG1 Teaming Up, Challenging People”, authored
     by A. Bailas, Y. Chabod


     =====================================================================
     A disguised reactivation of poor practices?


     Sadly, it has recently come to our knowledge that in some DG1 teams,
     which apparently foster quantity above quality, micromanagement
     intensity has again increased, this time, for example, in the form of
     weekly and individual meetings between the team manager and team
     members.


     This is surprising because these micromanaging activities have
     resulted in the recent past in the filing of internal appeals and
     subsequent complaints with ILOAT, which is known to the upper
     management of the Office. We are also surprised because we thought
     that the entire Office management would have drawn the right
     conclusions from the events of the past. Apparently, at least some
     management members did not.


     How to react to the pressurizing practices?


     To overcome the oppressive situation as quickly as possible, we
     recommend the staff member concerned to communicate to their line
     manager in writing that they are not feeling supported by the
     measures being used, and that they are harming rather than helping.
     It may also be useful to request the legal basis for being exposed to
     the relevant measure. Liaising with trusted colleagues to find any
     common experiences to prevent feeling isolated with the problem is
     also recommended.


     We also recommend those DG1 staff members concerned to draft minutes
     of all meetings with the line manager that have been convened to
     check their progress, which could be used later to demonstrate the
     overbearing micromanagement. You can also contact your staff
     representatives who can assist you in the meetings with your line
     manager.


     Finally, should you wish to legally challenge the unlawful measures
     you are subjected to, you may contact your staff representation who
     will assist you in drafting a request for review and subsequently an
     internal appeal to defend yourself.


     The Central Staff Committee


Where is the oversight? Where are the national delegates? Are they consenting
to a regime of terror, wherein workers are pressured to act in violation of the
EPC? █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⢭⣃⠥⣣⣦⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠘⣿⣧⡀⠀⠀⣠⣿⡟⠀⣼⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠻⣷⠈⢿⣦⣀⣀⣠⣾⠏⣰⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 4460

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/22/epo-abolishing-rights/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/22/epo-abolishing-rights/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO_Abolishing_Workers’_Rights_and_Creating_Second-Class_Workers_in_Direct
Violation_of_the_European_Patent_Convention_(EPC)⠀✐


Posted in Europe, Patents at 5:18 pm by Dr. Roy Schestowitz


Video to come shortly


              🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Technologia Staff Survey 2022⦈
                               Coming soon, too…


Summary: The EPO‘s presidents Benoît_Battistelli and António_Campinos have
demolished any remnant of EPC compliance; this institution must be reobooted
immediately and all the managers sacked if not prosecuted


THE Central Staff Committee (CSC) of the EPO has released or circulated this
long_document_with_annex. I intend to make a video about it shortly
(separately, too). It proves that the suspicions and concerns were very much
justified all along.


“Anyone who authorises such an agenda — including national delegates — is
breaking the law.”“Dear colleagues,” the CSC wrote. “In a previous GCC meeting,
the CSC members of the GCC gave a negative opinion on the new package on
mobility corresponding to document CA/32/22. In the GCC meeting on 2 June, the
President submitted document GCC/DOC 9/2022 aiming at the implementation of the
mobility package. In particular, the CSC members of the GCC had to give their
opinion on: [a] A new Circular on “Young Professionals”; [b] A new Circular on
(outbound) secondment and on leave on personal grounds (aka unpaid leave); [c]]
Changes to Circular No. 364 lowering qualifications for external recruitment.


“The circulars give us the occasion to revisit the buzzwords used by the
Administration to make the package palatable to the Administrative Council (and
maybe to some staff). They confirm that buzzwords are just that: empty words,
and that we were right in our strong reservations against the package presented
in CA/32/22 as it calls centralisation into question and establishes a separate
set of Service Regulations for a category of low-cost staff with fewer rights.”


Such “low-cost staff [examiners] with fewer rights” aren’t legal. Moreover,
Campinos_did_something_similar_at_EUIPO_just_months_before_he_left.


So not only does the EPO grant loads of fake patents (including European
software_patents which ought not exist!). It also tries to replace competent
patent examiners with rubber-stampers. Anyone who authorises such an agenda —
including national delegates — is breaking the law.


Fake patents, fake examiners (scabs), fake courts (UPC)? Whose agenda is this?
Cui bono? █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢰⣦⣤⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⠀⣬⣯⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⢹⡏⠀⢸⣀⠋⡛⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠛⣛⣻⣵⣧⡟⠁⢠⢿⣯⡻⣿⣻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠏⠀⠀⡘⣿⣿⠷⡏⠿⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⣀⣀⢈⣿⠁⠴⡌⢝⢿⡛⡻⣿⡿⡿⢿⣿⣿⣿⣿⢿⢿⣿⢿⣿⡿⣿⡇⢀⣼⣿⣿⠁⠀⠀⠀⠀⣴⣛⠣⢟⣷⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣈⣻⣿⠿⢿⣿⠰⣽⡃⠃⣨⣇⣌⣡⣘⣃⣷⣇⣇⣜⣣⣀⣛⣅⣓⣿⣚⣺⡇⣾⣿⣿⡟⡀⠀⠀⠀⠀⠘⠉⠴⠟⣿⡿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢘⣻⡿⣷⡄⣾⣿⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠟⠿⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡡⠀⣁⣡⣑⡰⡮⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢰⡆⠾⠑⢊⠈⡤⢰⠠⠄⢿⣿⣿⣿⣿⣿⣿⣿⡿⣰⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣤⠀⠐⠡⠃⢈⣈⡄⣴⢢⣿⣿⣿⣿⣿⣿⣿⠏⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⠠⣤⢲⠽⠭⢊⠀⢊⣾⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣌⣃⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⢿⣿⣿⠛⡿⢿⠟⢿⡿⠿⡿⣿⡿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠀⠀⠀⢁⣾⣿⣏⣈⣇⣾⣘⣼⣇⣑⣐⣀⣃⣆⣾⣇⣑⣈⣀⣦⣰⣀⡎⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⢠⣶⣿⣿⣿⣿⣿⠿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢻⠿⢻⣿⣿⣿⣀⣂⣃⣋⣚⣀⣊⣿⣇⣨⣀⣁⢠⣿⣐⣠⣰⣀⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⠿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣇⣄⣅⣈⣀⣠⣂⣰⣏⣀⣰⣰⣰⣸⣿⣿⣿⣿⡏⠉⠻⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢈⣭⣹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4558

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/22/epo-dumpster-fire/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/22/epo-dumpster-fire/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Battistelli_the_Second_(Battistelli_II)⠀✐


Posted in Europe, Fraud, Patents at 3:24 pm by Dr. Roy Schestowitz


                🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I am the f***ing president⦈
 Don’t worry. The EPO is doing great, according to corrupt EPO management with
                         its pamphlets and buzzwords.


Summary: Benoît_Battistelli‘s French buddy António_Campinos is destroying
what’s left of the EPO; as the 50th anniversary approaches it’s not clear if
the EPO has any future at all (laws aren’t obeyed and new hires aren’t
examiners but a disposable workforce, akin to scabs, that doesn’t meet the
requirements explicitly specified in the EPC)


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢻⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⢘⡟⣿⡻⣟⣻⠛⣟⢣⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣦⣤⣤⣄⣀⣀⣀⠒⠲⠆⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠋⠘⠀⠋⠙⠁⠉⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⣽⣿⣿⣧⡄⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣶⣦⡄⠀⠀⠊⠁⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣹⣖⣒⣒⣶⡿⠿⠿⠿⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣿⣿⣿⡏⣴⡤⣄⣀⣈⠁⠀⠀⠀⠈⠑⠳⣶⡄⣐⣒⣲⣤⣀⣂⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣼⡿⣿⣿⣷⡦⣾⣛⠓⠓⠛⠐⠂⠀⠀⠀⢸⡇⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⣯⣼⣿⣿⣻⡶⠤⠀⠐⠂⠀⠠⢤⡄⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠽⠚⢱⣷⢶⠖⠪⠯⣯⣬⢡⠝⠛⠐⠀⠀⠘⢃⣭⣿⣿⣯⣹⣽⣛⡒⠒⠀⠐⠒⠂⠈⠁⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⠛⡒⠒⠂⠀⠠⠠⠤⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣶⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣶⣶⣤
⢛⣛⣿⣻⣿⣿⣿⣿⣿⣁⣨⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⡿⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⣿⣿⣿⣿⣿⣇⣈⣙⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠂⠲⣶⠿⢿⢿⣾⣿⣿⣿⣏⣙⣿⣯⣽⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡦⣡⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢛⢻⡟⣿⢻⣟⣿⢛⣇⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⣽⣦⣤⣤⣄⣀⣀⣀⠐⠦⠆⣠⣄⣄⣄⡀⢠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠸⠘⠋⠙⠀⠋⠹⠁⠉⠈⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣼⣿⣯⣤⣄⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣴⣶⡆⠀⠀⠊⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣟⣿⣿⣿⣿⣿⣿⡃⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⣽⣖⣒⣒⣶⡿⠿⠿⠿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣾⣿⣿⣿⣧⣠⡤⣄⣀⣈⠁⠀⠀⠀⠈⠓⢲⡄⣂⣐⣢⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣼⣿⣿⣿⣷⣶⢾⣛⠓⠓⠛⠐⠂⠀⠀⠀⢰⡆⣿⣿⣿⡿⢿⡿⠿⣿⣶⣶⣶⣿⣿⣿⡒⠠⠀⠀⠀⠀⠠⢤⡀⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⠭⠽⠚⢳⣷⣶⠖⠪⠯⣯⣬⢡⠝⠛⠐⠀⠀⠘⣁⣽⣿⣭⣉⣉⣙⣑⠂⠀⠀⠒⠒⠈⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⡻⠒⠒⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣦⣤⣤
⣟⣿⣻⣻⣿⣿⣿⣿⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⠿⣾⡋⠙⢿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣿⣿⢿⣿⣶⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⢛⢻⡿⣿⢻⡟⣿⢓⡄⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣄⣠⣄⣀⣀⣀⠠⠠⠤⢀⣤⣤⣤⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠘⠘⠉⠙⠈⠏⢹⠁⠋⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣿⣿⣿⣧⣄⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣦⣴⣶⠆⠀⠀⠊⠀⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣿⣿⣿⣿⣿⣿⠋⢺⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⣽⣒⣒⣒⣶⡿⠿⠿⠷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣾⣿⣿⣿⡧⣣⡤⣄⣀⣈⠁⠀⠀⠀⠈⠓⠤⣀⣐⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣷⣶⢾⣛⠓⠓⠛⠐⠂⠀⠀⠀⣶⠈⣿⣿⣿⣿⣿⡿⣿⣿⣿⣵⣿⣶⣖⡒⠠⠤⠀⠀⠀⠤⣄⠠⣤⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠽⠚⢳⣷⢶⡖⠺⠩⣿⣬⢡⠝⠛⠐⠀⠀⠘⣠⣭⣭⣉⡉⢉⣉⣂⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠲⠖⠒⠠⠄⠤⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣦⣤⣤⣤⣤⣄⣀⣀
⣛⣛⣻⣿⣿⣿⣿⣃⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⠯⣄⣉⣙⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠿⣿⠿⢿⢷⣼⣿⣿⣿⣯⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣶⡦⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠛⠛⢻⡟⣿⢿⣟⣷⢀⡄⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⣤⣀⣀⣂⡀⠲⠦⢄⣤⣤⣤⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⠘⠋⠹⠁⠏⠻⠁⠋⠈⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣧⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣵⣿⣦⣶⣤⡇⠀⠀⠀⠊⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣏⢘⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣽⣖⣒⣒⣶⡿⠿⠿⠿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣾⣿⣿⣿⣯⣰⡤⣄⣀⣈⠁⠀⠀⠀⠈⠓⠄⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣷⣶⣾⣟⠓⠓⠛⠑⠂⠀⠀⠀⢲⡆⣿⣿⡿⢿⣿⠿⣿⣿⣿⣾⣿⣿⡷⠶⠤⠄⠀⠀⡤⣄⢠⣤⠤⠤⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠭⠽⠚⢳⣷⣷⡗⠺⠯⣿⣬⢩⠝⠛⠐⠀⠀⠘⣁⣭⣭⣙⣉⣙⣀⣐⣀⠀⠀⢀⡠⠥⠉⠉⠉⠉⠉⠁⠒⠒⠒⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣻⣿⣛⣿⣿⣿⣿⡶⠶⠶⠖⠒⠠⠤⠤⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣦⣤⣤⣤⣤⣀⣀⣀
⣛⣛⣿⣿⣿⣿⣏⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⡿⢧⣤⡸⠿⣿⣿⣿⣿⣿⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣦⣾⣦⠘⠊⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣼⣿⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠛⠛⠛⡟⣟⢿⡻⣟⣢⡄⡄⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣤⣄⣀⣀⡀⠢⠶⠄⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡄⠀⠀⠀⠀⠀⠀⠀⠉⠋⠹⠁⠟⠹⠉⠹⠈⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢻⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣿⣷⣿⣧⣴⣤⣷⠀⠀⠀⠊⠁⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⣤⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣖⣒⣒⣶⡿⠿⠿⠿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⡤⣤⣀⣈⠁⠀⠀⠀⠈⠑⠠⣄⡤⢀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⠛⠓⠛⠓⠂⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠶⠂⠀⠀⠀⡤⣄⢤⣤⠤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣻⣿⣿⣿⡗⢻⠯⣿⣬⢫⠝⠛⠘⠀⠀⠘⢃⣽⣽⣛⣓⣒⣒⣒⣂⠀⠀⠠⠤⠍⠉⠉⠉⠉⠉⠑⠒⠒⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⡶⠶⠶⠖⠒⠒⠤⠤⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⣀⣀⣀
⣛⣿⣿⣿⣿⣟⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣭⣀⣈⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣦⣴⣯⠷⠗⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠟⠻⠛⠛⠛⡿⣿⢿⡟⣆⢀⡄⣠⢠⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣄⣀⣀⣀⠀⠴⠤⣠⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡇⠿⠙⠏⠹⠛⡏⠙⠁⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣷⠀⢂⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣥⡄⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣷⣿⣧⣴⣤⣶⠀⠀⠀⠐⠁⠈⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣀⣀⣠⣄⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣖⣒⣒⣶⡾⠿⠿⠿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡤⣤⣀⣈⠁⠀⠀⠀⠈⠙⠠⠤⢠⣀⣀⡀⣀⣀⡀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⠛⠛⠛⠓⠂⠀⠀⠀⠰⡇⢺⣿⣶⣶⣿⣿⣿⣿⣿⣿⣟⡓⠒⠤⠀⠀⠠⡬⢤⣤⠤⢤⣤⠤⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣾⣿⣿⣿⣻⣿⣿⣿⡗⠿⠽⣿⣬⢫⠝⠛⠘⠀⠀⠈⢃⣼⣋⣋⣀⠀⢐⣒⣒⠒⠦⠤⠌⠉⠉⠉⠉⠛⠛⠒⠒⠒⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣷⠶⠶⠶⠶⠒⠂⠀⠠⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣀⣀⣀⣀⣀
⣻⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⡿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢴⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠿⠟⠛⠛⢻⢻⡻⣇⢠⡀⣤⢠⡄⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⣀⣀⡀⠢⠦⠄⣀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠉⠟⠹⠛⢛⠙⠏⢹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣧⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣽⣿⣿⣧⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢠⣿⣿⣿⣿⣿⣶⣤⣶⠂⠀⠀⠐⠉⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠿⠿⠿⠿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⢠⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣒⣒⣶⡲⠿⠿⠾⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⡧⣤⣀⣈⠁⠀⠀⠀⠀⠉⠀⢤⣄⣀⣀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣿⠛⠓⠛⠓⠂⠀⠀⠀⠀⣿⢸⣿⡿⣾⣿⣿⣿⣿⣿⣟⣛⡓⠢⠄⠀⠀⣤⢥⣤⢴⣤⣤⠤⠤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⡷⠿⠻⣿⣬⢥⠝⠛⠘⠀⠀⠀⠛⣨⣍⣁⣀⡀⡒⡒⣂⠒⠦⠄⠉⠉⠉⠉⠉⠛⠓⠒⠒⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣾⣷⡶⠶⠶⠦⠶⠒⠀⠠⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣏⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣦⣼⣿⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠛⠛⢻⢟⡟⣤⢠⡄⣠⢀⡄⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣔⣀⣀⣠⠠⠤⠄⣠⣤⣤⣤⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠏⠹⠉⡟⢻⠁⠋⢸⡇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠈⣼⣷⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣿⣿⣿⣤⡌⣺⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⣿⣿⣿⣿⣿⣶⣦⣶⡅⠀⠀⠀⠊⠀⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⢽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠿⠿⠿⠿⢿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣖⣒⣶⡲⠿⠿⠿⠿⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠗⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡥⣤⣀⣈⠁⠀⠀⠀⠀⠈⠁⢄⣀⣀⣀⢀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣿⠛⠓⠛⠑⠂⠀⠀⠀⠀⠿⠂⣿⠿⣿⠿⣿⣦⣿⣿⣋⡓⠒⠂⠀⠀⢤⣶⡤⣶⣤⣤⣤⣤⡤⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠇⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⡷⠿⢯⣿⣬⢣⠝⠛⠘⠀⠀⠀⠘⣁⣁⣀⣐⣂⡒⣒⣒⠂⠀⠀⠉⠉⠉⠙⠋⠛⠓⠒⠒⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⣿⣿⣾⣿⣿⣟⣗⣲⣶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣇⣀⣤⣄⣀⣀
⣿⣿⣿⣟⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⡝⠩⢽⣿⣽⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣙⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣤⡷⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠛⠛⠟⡆⢠⢠⣄⣠⢄⣄⢠⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⠀⠰⠤⢀⣠⣤⣤⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠹⠉⠟⠻⠁⠟⠘⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠅⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣾⣷⣹⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣭⣿⣤⡄⢰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⡆⠀⣿⣿⣿⣿⣿⣷⣶⣶⡇⠀⠀⠀⠊⠁⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠾⠿⠿⠿⢿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⢄⠀⠀⠀⠀⠀⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣆⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣖⣒⣶⡲⠿⠿⠿⠿⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠃⠀⣿⡿⣾⣿⣿⣿⣿⣿⡟⢯⡼⣤⣀⣈⠁⠀⠀⠀⠀⠈⠁⢀⣀⡀⢀⣀⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⡷⣿⣿⠟⠓⠛⠒⠂⠀⠀⠀⠀⢸⡇⡿⠿⠿⣿⣿⣽⣿⣏⡛⠒⠓⠀⠀⢁⣠⣴⡶⣤⣤⣤⣤⢴⣤⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⡷⠿⠯⣿⣬⢭⠝⠛⠘⠀⠀⠀⠘⣁⣉⣉⣛⣓⠀⣒⠒⠀⠀⠠⠀⠉⠉⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣷⣲⣟⣛⣛⣒⣉⣛⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀
⣿⣿⣿⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⠤⠩⢭⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣤⣮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢼⣿⡿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⠛⡂⣤⢠⡀⣄⢠⡄⣤⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⡀⠀⠤⢀⣤⣤⣤⣤⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⠹⠉⠟⠙⠉⠻⠈⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣀⣀⠀⠀⢠⣀⣠⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⣥⡤⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣾⡆⠀⢸⣿⣿⣿⣿⣿⣷⣾⡀⠀⠀⠀⠈⠁⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣇⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⢄⠀⠀⠀⠀⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⣤⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣒⣶⡲⠿⠿⠿⠿⢀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠃⠀⣿⣯⣫⣿⣿⣿⣿⣿⡟⢿⡾⣤⣀⣈⠁⠀⠀⠀⠀⠈⠁⠈⢀⣐⣀⡠⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⢛⠛⠛⠐⠂⠀⠀⠀⠀⠸⠇⢿⡿⠿⢯⣭⣭⣭⣙⡉⠛⠒⠀⠀⢄⣴⡶⡶⠶⠶⠶⢶⣤⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠿⣿⣬⢣⠝⠛⠘⠀⠀⠀⠈⣁⣁⡈⣉⣀⣀⣐⠀⠐⠀⠀⠈⠉⠉⠛⠋⠉⠙⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣶⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣽⣿⣿⣷⣶⣚⣛⣓⣉⣉⠩⠵⠴⠖⠂⠂⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣷⣿⣿⣷⣶⣦⣤⣀⣀⣀⣀
⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢲⡿⢭⣽⣟⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⠛⠀⡀⣄⢠⣠⣄⣠⠄⣄⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠦⠄⣠⣤⣤⣤⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠹⠉⠟⠹⠉⠋⠈⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣥⣴⣄⠀⠀⢠⣤⣶⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣧⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣾⣿⡆⠀⢸⣿⣿⣿⣿⣿⣷⣟⠀⠀⠀⠀⠊⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⠇⠰⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣇⣤⡤⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⢄⠀⠀⠀⠀⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣧⣤⣥⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣗⣒⣶⡲⠿⠿⠿⠿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡾⣤⣀⣈⠁⠀⠀⠀⠀⠈⠁⠀⣂⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣟⢛⠛⠛⠓⠂⠀⠀⠀⠀⠸⠇⣿⡿⠿⢽⣭⣍⣉⡉⠛⠒⠒⠂⣠⣶⡾⠶⠶⠶⠶⢶⣴⣤⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠭⣿⣬⢣⠝⠛⠘⠀⠀⠀⠈⣁⣀⣉⣀⣀⡀⠀⠐⠂⠀⠀⠀⠉⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣭⣭⣿⣿⣷⣶⣾⣛⣛⣂⣛⡭⠥⠴⠖⠒⠒⠂⠀⠀⠀⠀⠀
⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣄⣀⣀⣀⣀
⣿⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣤⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠟⠛⠀⠀⢀⡄⣄⢠⡄⣠⢀⡄⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠠⠀⣠⣤⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠏⢹⠉⡟⢻⠁⠋⠘⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣭⣿⣦⡄⠀⠀⣤⣶⣧⣴⣶⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⡄⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣟⣫⣤⡄⠀⣹⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⠊⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠇⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣀⣠⣤⡄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣧⣬⣤⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣖⣒⣶⡶⠿⠿⠿⠿⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠗⠃⠀⣿⣾⣿⣿⣿⣿⣿⣿⡟⣿⡵⣤⣀⣈⠁⠀⠀⠀⠀⠉⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢳⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣟⢛⠓⠛⠐⠂⠀⠀⠀⠀⠶⠈⡿⠿⣿⣟⣍⠙⠘⠓⠒⠲⠾⢴⣶⡿⠶⠶⠶⠶⢦⣶⣴⣿⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡼⠷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠯⣿⣬⢯⠝⠛⠘⠀⠀⠀⠀⣀⣈⣁⣀⣀⠀⠐⠀⠀⠀⠀⠀⠛⠛⠓⠋⠙⠙⠓⠒⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⣿⣶⣶⣀⣐⣛⣛⣏⣛⡿⠧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣥⣶⣤⣤⣤⣤⣀⣀⣀⣀
⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠩⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠛⠀⠀⢀⢠⡀⣄⢠⡀⣤⢠⡄⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⣀⣠⣠⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢹⠉⠿⠹⠋⠛⠙⡏⢻⠸⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣽⣿⣿⡆⠀⠀⠀⢿⣿⣿⣧⣤⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣟⣧⣤⣶⠀⠀⣾⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠐⠉⠀⠁⠈⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠒⠆⠘⠿⠿⢿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣠⣤⣤⡀⠄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡀⠀⠀⠀⠀⢠⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣬⣤⣶⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣶⡾⢿⠿⠿⠇⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡧⣤⣀⣈⠁⠀⠀⠀⠀⠉⠀⢠⡀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢰⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣟⡟⠛⠛⠓⠆⠀⠀⠀⠀⠿⠸⠿⡿⣏⣉⡓⠒⠒⠛⠷⠶⣷⣾⡷⠶⠦⠴⠶⠶⠶⣿⣷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡸⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠿⣿⣼⢯⡝⠛⠚⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠛⠛⠉⠛⠒⠒⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣯⣭⣤⣤⣀⣒⣛⣛⣓⣊⠻⠧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀
⣄⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⠀⠀⠀⣠⢠⡀⣄⢀⡄⣠⢠⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣠⣀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⡇⡿⠙⡏⢹⠛⡏⠹⠉⡏⠑⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠴⠀⠀⠀⠀⣿⣿⣇⢀⣴⣆⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣧⣴⣶⣦⠀⢀⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠐⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠒⠺⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣠⣤⣤⠠⢤⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⠀⠀⢰⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣦⣭⣶⣶⣶⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣒⣒⣶⡿⠿⠿⠿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡧⣤⣀⣈⠁⠀⠀⠀⠈⠁⠀⣀⡀⠀⠀⠠⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣛⡛⠛⠛⠑⠂⠀⠀⠀⠸⠇⠽⢿⣭⣉⡛⠒⠒⠿⣶⡾⢶⣿⣿⡶⠶⠶⠶⠶⠾⣿⣦⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠽⣿⣼⢫⠝⠛⠚⠀⠀⠀⢀⣀⣁⡀⣀⢠⠀⠀⠀⠈⠀⠐⠒⠚⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣯⣤⣐⣒⣚⣛⣛⣖⣐⠀⠄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣦⣤⣤⣤⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⣀⢀⡀⣀⢀⡄⣠⢠⡄⡄⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣠⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⡏⣿⠙⡏⢻⠛⡏⢻⠉⡏⠁⠀⠀⠀⠀⠀⢘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣴⠀⠀⠀⠀⣿⣿⠀⢀⣴⡆⠀⠀⠀⠃⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣟⣷⣴⣾⣦⣤⠀⢠⣿⣿⣿⣿⣿⣿⣤⣤⠀⠀⠀⠐⠁⠈⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠐⠒⠒⠸⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⣠⣤⣤⠠⡤⠤⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⠀⠀⠀⢠⣶⣶⣶⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣭⣶⣶⣶⣶⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣲⣶⡿⠿⠿⠿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣀⣈⠃⠀⠀⠀⠈⠁⠀⣀⡀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡟⠛⠛⠳⠆⠀⠀⠀⠸⡇⢿⣯⣿⡛⢒⣲⡿⠿⣿⣿⣿⣿⣶⠶⠷⢶⣶⡿⣿⣇⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠽⣿⣼⢯⡟⠛⠻⠀⠀⠀⢀⣀⣀⠀⠁⠀⠈⠁⠀⠉⠉⠙⠒⠛⠛⠛⠛⠓⠚⠛⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣿⣯⣽⣟⣲⣾⣿⣶⣂⣀⠦⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢠⢀⢀⠀⠀⠀⠀⠀⠈⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠘⠘⢀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢰⢠⠘⠛⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⢀⢀⡀⣀⢀⡄⣠⢠⡄⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣄⣠⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣎⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠘⢿⠉⡏⢹⠛⡏⢹⠉⣿⠱⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⠆⡆⠀⠀⠀⣿⣿⣆⣤⣼⣇⠀⠀⠀⠀⠈⠀⠁⠀⠀⠃⠈⠀⠈⠈⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣟⣷⣤⣾⣦⣥⣤⠀⠀⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠐⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠐⠒⠓⠀⠀⠀⠸⠿⠿⠿⠿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣠⣤⣤⡠⡤⠤⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⡀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣭⣽⣶⣿⣶⣶⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣺⣶⡾⢿⠿⠿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣦⣀⣈⠁⠀⠀⠀⠀⠁⠀⡀⠀⠄⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡟⠛⠛⠓⠆⠀⠀⠀⠸⠇⠸⣿⣋⡐⣶⣾⣿⣿⣿⡿⣿⣿⣷⠿⠷⠿⠿⣿⣧⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠇⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⡷⠿⢽⣿⣼⣿⡟⠛⠛⠀⠀⠀⢁⣀⣀⣀⠀⠀⠉⠉⠙⠉⠋⠙⠓⠓⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣿⣽⣷⣾⣾⣿⣛⣶⣶⣿⣓⣒⣐⣒⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⣀⣀⣀⠀⣀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢰⢠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⠘⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⢸⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⢀⡀⣠⢠⡄⡄⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣠⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣾⣿⡄⡀⠀⠀⠀⠀⢀⣄⠀⠀⢀⡀⠀⠀⠀⠘⢿⠉⡏⢹⠛⡏⠹⠉⣿⠱⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⡗⣿⠆⠀⠀⠈⣿⣿⣶⣶⣾⣧⠀⠀⠀⠀⠈⠀⠁⠀⠀⠃⠀⠀⠀⠈⠃⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣟⣷⣤⣾⣦⣧⣤⣤⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠐⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠐⠒⠓⠀⠀⢸⠀⠰⡿⠿⢿⡿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⢠⣤⣤⠤⡤⠤⠀⠼⡄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣭⣵⣶⣿⣶⣶⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣺⣶⡿⢿⠿⠿⠇⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡷⣦⣐⣬⠓⠀⠁⠀⠀⠁⠀⡀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡛⠛⠛⠓⡆⢰⠀⠀⠈⠃⢹⣛⣙⢛⡲⢿⣿⣿⣿⣿⣿⣷⣿⠾⠾⠿⣿⣧⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⢽⣿⣼⢯⡟⠛⠛⠃⠀⠀⢀⣀⣠⣀⡀⠉⠉⠉⠉⠙⠙⠉⠚⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⣿⣿⣽⣿⣷⣖⣿⣷⣶⣶⣾⣓⣶⣂⡒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠶⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢹⢼⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢻⢈⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣼⣼⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⣀⢀⣀⢠⢀⡄⡄⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⡀⠀⠀⠀⢀⣠⣤⠀⠀⢀⡀⠀⠀⠀⠸⢻⠉⡟⢹⠛⡏⠹⡏⣿⢹⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡟⣿⣿⠆⠀⠀⠀⣿⣿⣶⣾⣸⣷⠀⠀⠀⠀⠘⠐⠁⠀⠀⠁⠈⠀⠀⠀⠂⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣟⣿⣤⣾⣧⣯⣤⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠐⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠐⠒⠓⠀⠀⢸⡇⠇⠀⡿⡿⢿⡿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣠⣤⣤⡤⡤⠤⠀⠼⠷⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⡀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣮⣷⣶⣿⣶⣶⣾⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣺⣶⡿⢿⡿⠿⠇⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣦⣀⣈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡛⠛⠛⠓⠆⠀⠀⠀⠀⡋⢘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣆⣀⡀⠀⢀⣀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠿⣿⣼⣿⡟⠛⠛⠀⠀⠀⢀⣀⣀⣀⣉⠉⠉⠛⠋⠙⠙⠛⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠈⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣽⣽⣿⣿⣤⣽⣿⣶⣶⣶⣟⣳⣖⡂⡢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣄⣀⣀⣀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣬⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡆⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⡇⡇⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⢀⡀⣀⢀⡀⣄⢀⠀⠀⠅⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣷⣇⣿⣿⡀⠀⠀⠀⢠⡄⣀⣀⡀⠀⣐⠀⠀⠀⢸⢻⡟⢻⠙⡟⢿⠙⡏⢻⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡿⣿⣿⣷⠄⠀⠀⠈⣿⣟⣿⣿⠀⡋⠀⠀⠀⠘⠸⠐⠀⠀⠀⠈⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣾⣿⣦⣾⣷⣭⣤⣶⣷⠄⠀⠀⢹⣿⣿⣿⣿⣿⣦⣹⡇⠀⠀⠀⠊⠀⠁⠈⠂⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠐⠒⠛⠀⠀⢸⣇⠀⠀⠀⠼⠿⡿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡧⣤⣤⠄⠤⠤⠀⠸⡿⠒⠂⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⡀⠀⠀⠀⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣼⣿⣿⣿⣶⣶⣾⣿⣶⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣲⣶⡿⠿⠿⠿⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣯⣀⣨⢁⠀⡀⡀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⠛⠛⡓⠮⠀⠀⠀⠀⣋⢘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⢀⣀⣀⠀⠀⠀
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⡷⠿⢿⣿⣼⢯⡟⠟⠛⠀⠀⠀⢀⣀⣀⣈⣉⠉⠉⠋⠋⠉⠛⠙⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣯⣥⣅⣒⣒⣲⣿⣶⣶⣂⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⣀⣀⣀⠀⠀
⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⠀⠰⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⡇⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⡇⣿⣷⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⢀⡀⣀⡀⡀⣠⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡄⠀⠀⠀⢶⡄⡤⢴⣤⡀⢀⠀⠀⠀⠀⠟⡟⢻⠍⡟⠻⠉⣿⠹⡏⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⡦⠀⠀⠀⢻⣧⢈⣿⢃⣀⠀⠀⡀⠀⠀⠇⠊⠐⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣾⣿⣧⣴⣿⣬⣥⣴⣿⠷⠀⠀⠀⠰⣿⣿⣿⣼⣿⣿⣠⣷⠀⠀⠀⠀⠁⠘⠀⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠒⠛⠃⠀⠀⣿⠀⠀⢸⠀⢸⠿⢿⠿⠿⡿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡇⣤⣤⠤⠤⠤⠀⠠⠿⠖⠒⣶⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⣤⣴⣶⣦⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣤⣿⣿⣿⣷⣶⣾⣿⣶⣖⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣒⣶⡶⠿⣿⠿⠿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠚⠀⣿⣿⢿⣿⣿⣿⣿⣿⣟⢿⣿⣵⣀⣈⠁⠀⠀⠀⠀⠈⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⠛⠛⠓⠆⠀⠀⠀⠀⢉⠀⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⣀⣀⡀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠿⣿⣽⢯⠟⠛⠚⠀⠀⠀⠀⣀⣀⣀⣉⡉⠉⠉⠉⠉⠉⠉⠋⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣭⣽⣽⣿⣿⣽⣆⣒⣲⣒⣒⣒⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣤⣐⣀⣀⣀⣀⣀⡀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣽⣿⢹⣿⣿⠾⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢼⣼⢸⣿⣿⣿⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⢀⡀⣀⢀⡀⡘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠺⡀⠀⠸⣶⡤⠀⠀⠀⠀⠀⠘⢿⠙⡏⢹⠛⡟⢹⠋⣿⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⠧⠀⠀⠀⢻⣿⣀⣘⠃⣠⡀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣶⣿⣷⣤⣾⣦⣥⣤⣾⣿⠆⠄⠀⠀⠀⣻⣿⣿⣷⣿⣿⣦⣼⡀⠀⠀⠠⠂⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠒⠓⠀⠀⢸⡇⠀⠀⠈⡇⠠⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⢤⣤⣤⠄⠤⠄⠀⠼⠧⠒⢲⣶⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣯⣭⣿⣾⣷⣶⣶⣿⣷⣶⣲⣶⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣶⡷⢾⣿⡿⠿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠂⣿⣿⢯⣿⣿⣿⣿⣿⣯⣻⣿⣧⣁⣈⠁⠀⠀⠀⠀⠈⠁⠀⢀⢀⡀⠀⠀⠀⠀⠀⡀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⡛⠛⠓⠆⠀⠀⠀⠀⢘⡃⢚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⡀⠀⣀⣀⡀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⢿⣿⣽⢯⡟⠛⠛⠀⠀⠀⠀⠀⠈⣉⡉⠉⠉⠉⠙⠙⠛⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⣿⣿⣿⣿⣡⣤⣶⣶⣖⡶⠂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣦⣀⣐⣀⣂⣀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⣶⠀⠐⠄⠠⠠⠔⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡇⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⢀⡀⣀⢀⡀⣘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣿⣷⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⢸⢻⡟⢻⠙⡟⢿⠛⡟⢻⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠈⣙⣇⣠⣄⠿⣆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣾⣿⣤⣾⣷⣭⣤⣾⡿⠏⠄⠀⠄⠀⠀⢹⣿⣿⣿⣿⣿⣷⣦⣦⠀⠀⠀⠘⠀⠓⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠘⠚⠛⠀⠀⢸⣇⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⡧⣤⡤⠄⠤⠤⠀⠺⡿⠒⠒⣶⣆⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀⡀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣷⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡷⠾⣿⡿⠿⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⣈⠁⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⢀⠀⠀⢀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡿⢟⠛⠓⠆⠀⠀⠀⠀⠀⣗⢘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⢿⣿⣿⣯⠟⠛⠛⠀⠀⠀⠀⠀⠈⠉⢉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣽⣿⣿⣾⣿⣿⣤⣄⣐⣒⣶⡂⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣥⣍⡀⢀⣀⡀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠰⣶⠀⠰⠄⠠⠠⠔⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣼⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡯⣿⡇⣿⣿⠿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣿⡇⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⡀⣀⢀⢀⡀⢀⡀⡀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⢀⠀⠀⠀⠹⣤⡀⠀⠀⠀⠀⠟⡟⢺⠏⡿⢻⠋⣿⢹⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⣈⡀⣀⣶⣍⡁⠀⠀⠀⠀⠄⠃⠘⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣾⣿⣧⣴⣿⣬⣥⣼⣿⠿⠹⠀⠰⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠔⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠚⠛⠃⠀⠀⣿⠀⠀⠀⠀⠀⠰⠀⡾⢿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣧⣤⡤⠤⠠⠤⠀⠲⢿⠒⠒⣶⣦⣄⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⣙⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠦⢿⡿⠿⠿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣓⣉⠁⠄⠀⠀⠀⠀⠈⠀⢀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣟⠛⠓⠆⡀⠂⠀⠀⠀⣲⠘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⢀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢿⣿⣿⣯⡟⢛⠛⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⣿⣷⣶⣿⣿⣧⣀⣰⡶⠒⡂⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣽⣤⣀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠆⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣯⣿⣿⢿⣿⣿⣿⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⣀⢀⡀⣇⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⡇⠀⠀⠀⠀⡟⣿⠛⡟⢻⠻⡟⢻⠛⡏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⠿⠯⡅⠀⠀⠀⠀⠀⠀⣀⣴⣦⣀⡀⠀⠀⠀⠣⠘⠀⠀⢀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣿⣧⣴⣿⣮⠭⠽⣿⠿⠹⠁⠠⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠠⠂⠘⠂⠓⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠒⠛⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⣻⣤⣤⠤⠠⠤⠔⠒⣿⠒⠒⢲⣶⣄⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⢀⡀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣘⡄⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⡷⠦⢽⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣈⠁⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⢿⡛⠓⠆⠀⠀⠀⠀⠀⢰⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⡄⠀⡀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⣿⣿⣿⣿⣻⣿⣿⣿⡷⠿⢿⣿⣿⣿⠟⠛⠛⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠛⠙⠛⠛⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣽⣿⣶⣺⣖⣇⣀⣀⣒⢒⡀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣝⣛⣩⣅⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⣶⠀⠠⠄⠠⠰⠶⠆⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣹⣿⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⢀⢀⠀⡀⣀⠀⡇⢀⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⢸⢾⠓⡿⢺⠿⡟⢻⡏⣷⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⠿⠿⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣠⣀⡀⠀⠈⠌⠀⠀⠈⠀⠁⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣿⣿⣤⣿⣦⣭⣤⣿⡿⠯⠏⠀⠄⡆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠠⠒⠀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠐⠚⠛⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⠀⡇⣼⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣠⣤⠤⠄⠤⠄⠀⢾⠗⠒⢲⣶⣠⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⡀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣋⣹⡇⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⢉⠎⠝⠃⠀⠀⠈⠃⠀⠀⠀⠀⣀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡆⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣻⢓⢗⢪⡀⠀⠀⠀⢰⡆⢻⣿⣿⣿⣿⣿⣿⣿⣷⣤⢀⢀⡀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠇⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⢟⢻⠄⠀⠀⠀⠈⠁⠉⠉⠙⢹⡿⡿⡟⠛⠋⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠀⠉⠁⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣷⣿⣿⣗⣣⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣭⣿⣿⣟⣋⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠶⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣹⣿⢹⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⡀⠀⢀⡇⢀⢄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⢸⡗⢻⠚⠷⢿⠺⡗⢿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠒⢄⣤⣦⣷⣶⣤⣄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣦⣾⣧⣭⣤⣾⡿⠏⠏⠁⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠔⠀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠚⠛⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⡠⣤⠤⠄⠤⠄⠂⠾⠗⠒⠲⣶⣠⣀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣾⣿⣿⣿⣷⣿⣿⣿⣷⣿⣏⣛⢉⢉⠙⣡⠘⠣⢂⠠⣿⣿⣷⡨⡟⣾⣿⣷⣾⣶⡷⠦⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⡟⢹⡶⣿⣿⣿⣿⠋⣿⣿⣿⣏⣩⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⢷⡆⠃⣷⣺⣿⣿⣿⣿⠻⠷⣿⣿⣿⠿⡛⠓⠆⠀⠀⠀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡿⣿⣧⣤⢀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠇⠀⣿⡿⠿⡛⢁⡥⠀⣷⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⠀⠀⠀⠁⢘⠛⠛⠉⠙⠋⠻⠿⠯⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣗⣒⣶⣖⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣿⣯⣍⣛⣋⣷⣤⣤⠄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⢶⠀⠰⠄⠠⠴⠶⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣹⣿⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⠀⠀⠀⠀⠀⢸⢸⡗⢿⠺⡷⢿⠺⡇⢿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⣰⣿⣷⣦⣄⠀⠈⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣿⣿⣤⣾⣧⣭⣤⣾⡿⠏⠏⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠔⠀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠐⠛⠚⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣟⡠⣤⠤⠄⠤⠄⠢⠾⠗⠒⠲⣶⣄⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣾⣿⣿⣿⣶⣿⣿⣿⣷⣿⣏⣙⣁⡁⠈⡉⠡⠀⠀⠀⠀⣻⣿⣷⠈⡖⣾⣾⣷⣶⣶⡶⠢⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⢠⡶⣾⣿⣿⣿⠛⣿⣿⣿⣏⣈⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⢀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢷⡆⠀⢀⣸⣾⣿⣿⣿⠛⠶⣿⣿⣿⠿⡛⠓⠆⠀⠀⠀⠀⠀⠀⡆⢹⡿⢿⠿⠿⣿⡦⠤⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠇⠀⠾⠿⠽⠚⠁⠁⠀⢶⣿⣿⣿⣿⣯⠟⠛⠞⠀⠀⠀⠀⠈⠁⠈⠋⠋⠁⠉⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣗⣂⣀⣐⣂⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣏⣡⣈⣈⣷⣤⠤⢤⣀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⣦⠀⠰⠄⠰⠴⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⠑⡗⢺⠿⡗⢻⠊⣷⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣤⣾⣿⣴⣆⠀⠠⠘⠀⠁⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣷⣴⣾⣮⣥⣴⣾⡿⠹⠉⠨⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠒⠛⠓⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣛⠤⡤⠤⠠⠤⠔⠲⠿⠗⠒⢶⣶⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣉⣛⣉⡁⣉⡉⠁⡀⣿⣿⣿⣿⣿⣿⣿⢿⣟⣾⣿⣷⣿⣶⡷⠢⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠇⣿⣿⣿⡿⣾⣿⣿⣿⡿⣻⣿⣿⣇⣉⠁⠀⠀⠀⠀⠀⠘⠃⠀⢀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡆⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⠿⡟⠓⠆⠀⠀⠀⠀⠀⢰⠂⣻⣿⠿⢿⣿⠤⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠇⣿⣿⣿⢿⡻⣯⣿⣿⣷⣿⣿⣿⣿⣯⠟⠛⠚⠀⠀⠀⠀⠈⠁⠉⠛⠁⠈⠹⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣩⣂⣐⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⣭⣥⣄⣀⣐⣂⡴⠦⠤⢤⣤⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣤⣤⣤⣴⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⢶⠀⢰⠄⠰⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠺⡗⢿⠾⡗⡷⠸⡎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⡿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣤⡀⣧⣤⣾⡆⠀⠅⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣾⣿⣦⣶⣷⣬⣤⣶⣿⠏⠍⠁⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠠⠂⠐⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠒⠛⠂⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢜⡣⠤⠤⠤⠠⠤⠒⠶⡿⠒⠒⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣟⣛⣉⡉⢉⣉⡉⠀⠒⡆⠀⠁⠀⠀⣻⣿⣷⢨⣞⣿⣿⣶⣾⣶⡶⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⡶⠟⠀⠀⢠⡶⣾⣿⣿⣟⣗⣿⣿⣿⣅⣈⠁⠀⠀⠀⠀⠀⠘⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣶⠀⠀⢀⣸⣾⣿⣿⣿⠿⠷⣿⣿⡿⠟⠛⠓⠆⠀⠀⠀⠀⠀⢒⠘⣿⠿⠿⣧⡤⠄⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠀⠀⡾⠿⠿⠛⠁⠁⢰⣷⣿⣿⣿⣾⢯⠟⠛⠚⠀⠀⠀⠀⠉⠈⠉⠀⠈⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣀⣀⣀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣾⣶⣶⣶⣶⣴⣶⣴⣶⣶⣶⣶⣤⣽⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣭⣅⣀⣀⡠⣤⠴⣤⣤⣤⣤⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⣶⠀⢶⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⣿⣹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⢸⡗⢿⠺⡷⢿⠾⡇⢷⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⢠⣆⠐⣀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣷⣶⣿⣷⣤⣾⣦⣥⣴⣾⡿⠩⠉⠨⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠔⠀⠂⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠐⠚⠓⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠤⣛⠤⠤⠤⠄⠤⠔⠒⢾⠗⠒⢲⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣟⣋⣉⣍⣉⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⣻⣿⣷⣴⡿⣾⣷⣶⣲⣶⡶⢺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣿⣷⣶⠾⠃⠀⠀⢠⡶⣾⣿⣿⣿⡿⣿⣿⣯⣄⣈⠁⠀⠀⠀⠀⠀⠃⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡛⢛⢳⡆⠀⠀⢀⣸⣾⣿⣿⣿⠷⣯⣿⣿⠿⠛⠛⠓⠂⠀⠀⠀⠀⠐⠂⢻⢿⣿⣤⠄⠀⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠿⠀⢀⡺⠯⠿⠚⠁⠁⣶⣷⡿⣿⣿⣽⢫⠝⠛⠚⠀⠀⠀⠈⠁⠉⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⣀⣀⣀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣶⣶⣶⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣉⣁⣒⣒⣢⣴⣶⣤⣤⣤⣤⣤⣀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣽⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⣶⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠺⠂⠷⢾⠒⡷⠹⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⣀⠀⠀⣱⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣶⣾⣯⣤⣾⣷⡬⠤⣾⡿⠏⠏⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣾⣿⠁⠀⠀⠀⠠⠂⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⡆⠀⠐⠚⠛⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⢜⡣⠤⠤⠄⠴⠶⠒⢺⡗⠒⠐⣶⣦⣄⡄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣾⣿⣿⣭⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣉⣀⣤⣭⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣻⣿⣷⣶⣿⣿⣶⣖⣒⣶⡲⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣶⣶⡶⠟⠀⠀⠀⢠⡶⣾⣿⣿⣿⣿⣿⣽⣤⣀⣈⠁⠀⠀⠀⠀⠚⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⡿⡛⢛⣛⣔⠀⠀⠀⢀⣸⣾⣿⣿⣿⢿⣧⣿⣿⠟⠓⠛⠓⠂⠀⠀⠀⠀⠂⠘⣿⣦⠤⠀⠀⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⠀⠀⠀⠺⠭⠽⠚⠁⢱⣷⣷⠿⣿⣿⣬⢫⠝⠛⠐⠀⠀⠀⠁⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣁⣀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣦⣦⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⣋⣁⣙⣒⣒⣠⣶⢶⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠚⡗⢻⠾⡗⢻⠚⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⠀⣠⣄⠀⢀⡄⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣶⣾⣭⣤⣶⣷⡬⠭⠿⡿⠯⠍⠁⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⡁⠀⠀⠀⠠⠂⠀⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡆⠀⠀⠚⠛⠃⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠤⢜⡃⠤⠤⠄⠰⠶⠒⠒⣛⠀⠐⣾⣧⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣍⣠⣤⣬⠍⠁⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⠀⠀⣻⣿⣷⣿⣿⣿⣶⣒⣒⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⡶⠗⠃⠀⠀⠀⢠⡶⣾⣿⣿⣿⣿⢯⡥⣤⣀⣈⠁⠀⠀⠀⠘⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⡿⢿⣿⠟⣛⣀⡂⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⣷⣯⣟⠛⠛⠛⠑⠂⠀⠀⠀⠐⠈⣧⠤⠀⠀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠇⠀⠀⠀⠺⠭⠽⠚⢁⣿⣷⣶⣿⡿⣿⣼⢯⠝⠛⠚⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⣀⡀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣶⣿⣾⣶⣶⣶⣶⣴⣶⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣽⣭⣿⣯⣚⣉⣉⣛⣒⣂⣴⣶⣶⣦⣤⣤⣤⣀⣀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⡗⢻⠚⡷⢿⠺⡇⢷⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⣤⣀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢘⣷⣶⣯⣥⣴⣾⣦⠭⠽⡿⠿⠽⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠔⠀⠦⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣷⠀⠀⠒⠛⠃⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠤⣛⠠⠤⠤⠰⠶⠒⠒⣛⡃⠀⢲⣓⣠⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣽⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣏⣁⣤⢭⡬⠀⠀⠀⠂⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡿⣾⣖⣒⣒⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣦⠼⠂⠀⠀⠀⠀⢀⡶⣾⣿⣿⣿⡿⣫⡤⣤⣀⣈⠁⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⠿⢿⣿⣛⣛⣃⣠⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⣮⣽⣛⠛⠛⠛⠑⠂⠀⠀⠀⠂⠠⠄⠀⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⡍⠺⠀⠀⠀⠀⠺⠭⠽⠚⢽⣿⣶⣶⣻⠭⣿⣬⢯⠝⠛⠚⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣤⣶⣦⣤⣤⣔⣦⣾⣿⣿⣿⣿⣿⣯⣭⣭⣭⣽⣃⣊⣉⣽⡛⣶⣒⣴⣶⣤⣤⣤⣤⣀⣀⣀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠿⠺⡗⢿⢾⠗⢷⠹⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⡿⣿⣿⢿⣿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⣦⡀⣀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣶⣾⣭⣤⣾⣷⠭⠭⢿⠿⠯⠏⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣈⣿⣿⣿⣾⣿⠀⠀⠀⠀⠠⠂⠰⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⡄⠀⠐⠚⠛⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⣟⡃⠤⠤⠄⠶⠖⠒⢚⣓⠀⠐⣟⣢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣯⣉⣥⠬⣭⣉⠁⠀⠈⠀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣖⣾⣒⣒⣒⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣶⣶⣦⡤⡬⠗⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣟⢡⡤⣤⣀⣈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⠿⣿⣟⡛⣓⣚⣐⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⡧⣍⣛⠛⠓⠛⠑⠂⠀⠀⠀⠀⠀⠠⠤⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣥⣤⣭⠹⠇⠀⠀⠀⠀⠺⠭⠽⢺⣿⣿⣿⣗⡻⠩⣿⣬⢯⠝⠛⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣦⣤⣤⣶⣴⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣒⣚⣹⡿⠿⠶⢖⣴⣦⣤⣤⣤⣀⣀⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡗⢻⠚⡷⢿⠚⠗⢻⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⠿⣿⠿⢿⣿⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡃⣸⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣯⣥⣴⣿⣦⠭⠽⢿⠿⠭⠉⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠐⠛⠃⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⠠⠤⠤⠔⠶⠖⠒⣚⡃⠀⠒⣛⣤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣯⣉⠥⡭⢍⡉⠉⠀⠁⠀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣞⣼⣒⣒⣒⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣖⣲⠤⢶⣶⡶⠤⢤⡼⠘⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣯⢡⡤⣤⣀⣈⠉⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠓⠒⠊⣠⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⡧⣍⣛⠛⠛⠛⠑⠂⠀⠀⠄⢀⠠⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣯⣤⡤⡆⠹⠀⠀⠀⠀⠀⠺⠿⠿⢻⣿⣿⣿⣗⡻⠭⣿⣼⢯⠟⠛⠐⠀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣦⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣖⣶⣿⠿⠶⠶⢆⣠⣤⣤⣤⣄⣀⣀⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⢀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⠀⠀⠀⠅⠟⠺⠓⠿⢿⠚⣷⠹⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⢿⡟⣿⠿⢿⣿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⢀⡄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡮⠭⢤⠿⠷⠾⠷⢿⡿⠯⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣷⠀⠀⠀⠀⠠⠂⠐⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⣷⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⠶⠶⠆⠒⠒⠀⢚⣛⠀⣙⣿⣧⣄⡀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢥⣬⡭⢉⠀⢄⠀⠀⠀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⢾⣒⣒⣒⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⣲⡮⠵⢒⣶⡶⠶⠤⡼⠗⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣟⢡⡤⣤⣀⣈⠁⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⠿⠟⠛⠛⠒⠛⢐⠄⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⡧⢾⣛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣛⣛⣛⣂⣠⣤⣤⣤⣤⣤⠸⠇⠀⠀⠀⠀⠾⠿⠿⢻⣿⣿⣿⣗⡻⠭⣿⣼⢯⠟⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣟⣓⣲⣿⣶⠶⠖⠤⢠⣤⣄⣀⣀⣀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⢻⠚⠗⢻⠾⡗⠿⠘⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⢿⡿⢿⠿⠿⣿⠿⠿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡭⢤⡾⠷⠾⠿⠿⡿⠯⠍⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⣿⠀⠀⠀⠀⠀⠄⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠁⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠶⠆⠲⠒⠒⠒⣛⠀⠐⢻⣣⣆⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⢀⡀⢀⡀⣀⣁⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣭⡭⣬⢭⣭⣅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡟⣾⣒⣒⣒⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⡯⠵⢶⣶⣤⠤⠤⡤⢼⡧⠂⠀⠀⠀⠀⢠⡶⣿⣿⣿⣿⣏⣯⡤⣄⣀⣈⠉⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠿⠿⠿⠟⠛⠻⠿⠴⠛⠃⡄⠀⠀⠀⢀⢀⣸⣾⣿⣿⣿⣿⣏⣭⣛⠛⠛⠛⠑⠂⠀⠀⢀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣃⣈⣠⣀⡤⣬⣤⣤⣴⠊⠇⠀⠀⠀⠀⠾⠿⠿⢚⣿⣿⣿⣷⣻⠭⣿⣼⢫⠝⠛⠚⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣶⣒⣶⣶⣶⠶⠦⠤⠄⠀⣀⣀⣀⣀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣷⣾⣿⣿⣷⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠓⠸⠾⠗⢹⠊⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠻⣿⢻⡿⠿⣿⡿⠿⢿⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⡼⠿⠾⠿⠾⣿⠿⠝⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠤⠀⠤⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣶⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠆⠐⠒⠀⠐⣛⠀⢉⣻⣷⣖⡀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣭⣬⢤⣭⣁⡁⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣝⣫⣿⣿⣿⣿⣟⣾⣞⣒⣒⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣼⣿⢶⣶⣦⠤⣤⠤⢤⡿⠂⠀⠀⣯⡿⣼⣿⣿⣿⣿⣿⣟⣯⡤⣤⣀⣨⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠿⣿⣿⠿⠟⠛⠛⠛⠦⠜⠃⢋⣠⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⣿⣯⣭⣛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣺⣿⣛⣟⣳⣆⣀⠠⢤⣤⣤⣤⠎⠏⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⠭⣿⣬⢯⠝⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣶⣶⣶⣶⣶⣤⣤⠤⠤⠄⠀⢀⣀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⢿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡗⠛⠚⡷⢿⠺⠂⠳⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣿⢻⡿⠿⣿⡿⠿⢿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢀⣄⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠼⠿⠶⠿⠾⣿⠿⠽⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢐⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣶⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠐⡒⠂⠀⣛⡃⢉⣻⣿⣴⡤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣧⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⣀⢠⣤⣍⣀⢤⣉⠀⠀⡀⠀⠀⠸⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣖⣒⣲⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣿⠶⢶⣦⡤⠤⠤⠄⢀⡿⠒⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡥⣤⣀⣈⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠟⣿⠿⠿⠟⠛⠛⠛⠢⠬⠋⠋⣠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣟⠛⠛⠛⠓⠆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣗⣾⣞⣲⣤⡀⠠⣬⣤⠤⠤⡆⠿⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣼⢯⠟⠛⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣖⣲⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣦⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⡤⠤⠄⠀⠀⠀⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣽⣿⣿⣭⣿⠷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠂⠗⠸⠾⠗⠹⠊⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢻⠿⠿⣿⣿⣟⣿⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⣤⣄⣦⠀⠀⢰⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠾⠿⠿⡿⠏⠀⠀⠘⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠔⠀⠤⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣒⠒⠀⢘⣛⠉⢙⣻⣷⣦⣤⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⣇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣤⣀⡀⡌⢉⡀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⢗⣿⣿⣿⣿⣿⣿⣟⣾⣗⣒⣒⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⡷⠶⢶⣦⣤⠤⣤⠖⠀⢤⡿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⣤⣀⣈⠉⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠻⠳⠬⠍⠀⡏⡆⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⠛⠛⠛⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀⢠⣤⣤⠤⠤⠗⠇⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣷⣻⡿⣿⣼⢯⠟⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣒⣒⣲⣶⣶⣶⣶⣶⣶⣶⣤⣤⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣶⣶⣦⣤⣤⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣖⣺⣿⡿⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⡀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⠊⠗⢻⠾⠗⠻⠘⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⢿⣿⣛⣛⠿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⢿⡟⠃⠃⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣼⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠐⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠉⣻⣏⢉⣉⣿⣶⣤⣤⡀⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡠⣤⣠⣀⠈⢉⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣖⣒⣒⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣤⣬⡿⠶⠶⢦⣤⠤⠤⠶⠤⢀⣸⠗⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⡤⣤⣀⣈⠉⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⠛⠛⠛⠿⠿⠿⠿⠯⠅⠀⠈⢱⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣶⣶⣢⣤⣀⡠⢤⣦⠵⠦⠤⠘⠇⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣷⣻⠿⣿⣼⢯⠝⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠒⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣄⡀⠀⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣖⣺⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⢀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠓⠚⠂⠻⠿⠎⢗⠹⠎⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣟⣛⡻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⣿⠛⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⡀⠀⠀⠠⠂⠀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⢰⣾⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢉⣿⣉⣉⣹⣷⡤⣤⡄⠀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⣤⣀⢤⣤⣄⠀⠈⣉⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣖⣒⣲⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣭⣿⣿⡿⠶⠶⢶⣤⠤⠴⠶⠄⣀⣤⡿⠗⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⡤⣤⣀⣈⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣟⡛⠛⠻⠿⠿⠿⠿⠯⠀⠀⠀⢸⣲⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⣯⣛⠛⠛⠛⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣶⣖⣒⣂⣠⣄⣀⠦⢮⡧⠶⠤⠼⠻⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣻⠽⣿⣼⢯⡟⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠒⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣦⣤⣤⣀⣤⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣦⣶⣺⣟⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣻⣛⣻⢿⣻⣻⣿⣿⢻⢻⣻⢛⣟⢿⣿⣿⣿⣆⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣾⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⢀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢾⡷⣿⣿⡿⣿⣾⡾⣾⣽⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠈⠓⠙⠊⠓⠻⠊⠃⠙⠘⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⣿⣛⣛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⣤⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⡛⠓⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣆⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⡀⠀⠀⠠⠂⠐⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠂⢰⣾⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣀⠉⠉⠡⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣠⣄⣠⠄⢤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣗⣾⣒⣒⣒⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠿⣷⣿⣿⣿⡿⣭⣽⡷⠶⠶⠶⠤⠤⠴⠦⠄⣀⣐⡅⡿⠛⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣏⢡⡤⣄⣀⣈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣶⣾⠯⢟⣛⡛⠻⠿⠿⠟⠒⠆⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⡧⢎⣛⠓⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣶⣶⣒⣒⣒⣒⣀⣀⠠⠤⠀⣠⠤⠤⠤⠄⠻⠀⠀⠀⠀⠀⠺⠭⠽⢺⣿⣷⣷⡖⡺⠩⣿⣬⢩⠝⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡭⠤⠤⣒⣒⣊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣻⣛⣻⢿⣻⣻⣿⣿⢻⢻⣻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣮⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⢀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢾⡷⣿⣿⡿⣿⣾⡾⣾⣽⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠓⠙⠊⠷⠻⠊⠃⠙⠘⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⣛⡛⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⣦⣤⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠒⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣦⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⡄⠀⠀⠠⠂⠐⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠉⠉⠀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣷⣦⠀⢠⣤⡠⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⣿⣶⣾⣒⣒⣒⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣿⢿⡽⢯⠿⣾⣿⡷⠶⠶⠶⠤⠤⠶⠤⠄⢈⣙⠅⢀⡿⠛⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣏⢡⡤⣤⣀⣈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⠟⢛⣛⣛⠻⠻⠛⠛⠉⠀⠀⠀⠀⠀⡋⣶⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⡧⢎⣛⠓⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣖⣒⣒⣒⣒⣒⣒⣀⣠⠀⠄⠀⣤⠤⠀⠀⠆⠋⠀⠀⠀⠀⠀⠺⠭⠽⠺⣿⣿⣿⡖⡺⠩⣿⣬⢩⠝⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣒⠶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⣀⠀⣀⣀⣀⣀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠭⠭⠅⢒⣒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣻⣛⣻⢿⣻⣻⣿⣿⢻⢻⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣮⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⡀⣀⢀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢾⡷⣿⣿⡿⣿⣾⣾⣾⣽⣿⣿⣿⣿⣿⠇⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠊⠗⠻⠊⠓⠙⠘⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⡛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡀⣠⣶⣄⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣦⠀⠀⠘⣿⣿⣿⣿⣿⡇⢠⣆⠀⠀⠠⠂⠐⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣤⠠⠤⠐⡤⢄⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣗⢾⣒⣒⣒⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⠿⡿⠿⣿⣿⣿⠮⡍⠓⠲⠶⠶⡶⢦⠤⠤⠀⠨⠝⠣⠠⢰⡿⠛⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣏⢡⡤⣄⣀⣈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣥⣤⣤⣤⣶⣶⢖⡛⠛⢛⣛⣛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢉⣶⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⡧⢎⣛⠓⠒⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⣿⣶⣿⣿⣶⣿⣷⣖⣒⣒⣒⣒⣒⣒⣂⣀⣀⡀⠀⠤⠤⠀⠀⠎⠛⠀⠀⠀⠀⠀⠺⠭⠽⠺⣿⣿⣿⡖⡻⠩⣿⣬⢡⠝⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡲⣲⣶⣶⣶⣶⣶⣦⠤⢤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⡀⣀⣀⣀⠀⢀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡬⠉⠩⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣻⣛⣻⣻⢿⣛⣻⣻⣻⢻⢻⣻⢛⣟⢿⣿⣿⣿⣆⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣾⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⢀⠀⡀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣿⢾⡷⣿⣿⡿⣿⣾⣾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠂⠳⠛⠊⠓⠙⠈⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⣤⣄⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣶⠀⢀⣸⣿⣿⣿⣿⣿⣧⢀⣦⠀⠀⠠⠂⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⠤⣄⠰⠤⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⢾⣒⣒⣒⣾⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⠿⠿⠿⣿⣽⣿⠯⢭⠒⠒⠒⠶⣶⣷⠤⠴⠆⠈⠙⠇⢀⡢⣄⡿⠇⠁⠀⠀⠀⠀⢀⡶⣾⣿⣿⣿⣏⢥⡤⣄⣀⣈⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣭⣿⣿⠷⢤⡤⠤⣤⣲⢖⡛⠚⠛⣛⣙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⡇⢮⣛⠓⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣶⣶⣖⣒⣒⣒⣒⣂⣀⣀⡀⠀⠠⠀⠄⠀⢚⠛⠀⠀⠀⠀⠀⠺⠭⠽⠚⣿⣿⣿⡖⠻⠩⣿⣬⢩⠝⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠉⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡖⣶⣶⣶⣶⣶⣦⡤⢤⣤⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⢿⣷⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡭⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣻⣻⣛⣻⢿⣛⣻⣿⣿⢻⢻⣻⢛⣟⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣿⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⢀⠀⡀⣀⢀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣿⢿⡷⣿⣿⡿⣿⣾⣾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠈⠃⠻⠚⠂⠳⠘⠎⠄⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣀⣠⣶⣆⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣿⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣶⡄⠠⣬⣿⣿⣿⣿⣿⣿⣀⣴⡄⠀⠀⠔⠀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠇⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡿⣾⣒⣒⣒⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⠿⠿⠿⠿⠿⠿⢿⠿⠍⡽⠞⠳⠶⠶⠿⠶⠤⠄⠀⠘⠧⢔⣒⢤⣄⡿⠟⠃⠀⠀⠀⠀⢠⡶⣿⣿⣿⣿⡧⣯⡤⣄⣀⣈⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣿⣿⣳⠶⠶⠶⠦⣤⡄⢁⣀⠈⠉⣙⣛⣛⠛⠢⠤⠤⠄⠀⠀⠀⠀⢸⣲⡀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⣧⢾⣛⠓⠓⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣖⣒⣒⣒⣀⣀⣀⡀⠀⠀⠀⠀⠀⠸⡛⠀⠀⠀⠀⠀⠺⠿⠿⠚⣿⣿⣾⣗⣻⠩⣿⣬⢣⠝⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠉⠀⡒⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⣤⡤⣤⣤⣄⣀⣠⣀⣸⣿⣿⣿⣿⣿⡿⢶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⡀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣻⣻⣻⣻⢿⣻⣻⣿⣻⢻⢻⣻⢛⣟⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣿⢸⢸⣿⢸⣿⣹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⣀⢀⡀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢾⡷⣿⣿⡿⣿⣾⣾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠃⠛⠛⠂⠓⠘⠊⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⣹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡀⠀⣤⣽⣿⣿⣿⣿⣿⣤⣾⠆⠀⠀⠐⠀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⠇⠸⠿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⢾⣒⣒⣒⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⢓⠒⠾⡿⡶⠦⠤⠀⠀⠤⣔⢦⣦⣤⣼⡸⠃⠁⠀⠀⠀⠀⢀⡶⣾⣿⣿⣿⣇⣧⡤⣄⣀⣈⠁⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣓⠲⠿⠶⠶⠦⣀⡀⠀⣈⠉⠉⣙⣛⠛⠂⠀⠄⠀⠀⠀⠀⠀⠉⢹⢲⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⡧⢾⣛⠓⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣾⣿⣿⣷⣶⣖⣒⣒⣒⣶⣖⣒⣒⣐⣀⣀⣀⢀⠀⠀⠠⠤⠤⢼⡚⠀⠀⠀⠀⠀⠺⠭⠽⠚⢿⢿⠿⡗⢹⠩⣿⣬⢡⠝⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠤⠤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⠠⣤⣤⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⠶⠶⡶⣦⣤⣤⣤⣄⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⡀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣛⣻⣻⣻⣻⢿⣛⣻⣿⣿⢻⢻⣻⢛⣟⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿⢸⣿⣿⣗⢸⡷⣽⣿⣿⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⣀⢀⡀⣀⢀⢀⡀⡀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣿⢿⡷⣿⣿⡿⣿⣾⣾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠈⠃⠉⠈⠛⠻⠈⠃⠉⠐⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⣤⣄⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣿⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣼⣿⣿⣿⣿⣿⣿⣤⣿⠁⠀⠠⠂⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⢀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⣾⣒⣒⣒⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠷⠾⠷⠶⢶⡗⠟⢙⡛⠟⡷⠶⠤⡤⠀⠀⠉⣿⣶⣦⣤⣤⣧⠟⠋⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣏⢠⡤⣄⣀⣈⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⠛⠒⠒⠒⠀⠀⠀⡀⠀⢀⣀⠀⠉⠍⠁⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠟⣦⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣿⡇⢏⣛⠓⠓⠛⠐⠂⠀⠀⠀⠀⠀⠠⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣮⣿⣿⣿⣿⣷⣒⣒⣀⣒⣖⣒⣒⣒⡒⢀⠀⠀⠀⠀⠀⠠⠤⠄⣦⡃⠀⠀⠀⠀⠀⠺⠭⠽⠺⣿⣿⠿⠇⠿⠭⣿⣬⢫⠝⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠦⠤⠴⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⡄⣤⣤⣄⣀⣀⣻⣿⣿⣿⣿⣾⣷⡶⠶⡶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣍
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⠭⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣛⣻⣻⣛⣻⢿⣻⣻⣿⣿⢻⢻⣻⢛⣟⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿⢸⣿⣿⣗⢸⡷⣽⣿⣿⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢠⠠⡄⣠⠀⡄⣄⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢿⡿⣿⣿⡿⣿⣾⡾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠁⠉⠀⠁⠘⠉⠃⠙⠈⠃⠂⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣰⣶⣿⣷⣶⣴⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣿⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣰⣿⣿⣿⣿⣿⣿⣷⣼⡇⠀⠀⠊⠀⠁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⠀⢀⣒⣂⣀⣀⠀⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⢼⣒⣒⣒⣿⡿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠟⠲⠶⠾⠗⡶⡟⠛⣙⠛⢛⣶⠖⠷⠄⠐⠊⠽⣷⠶⡦⠶⢦⣼⡼⠛⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⢠⡤⣤⣀⣈⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣁⠀⠀⠀⠁⠀⠀⠠⠀⠀⢀⢉⠈⠁⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠉⢹⢻⠄⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⡗⣋⣛⠛⠓⠛⠑⠂⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣭⣭⣿⣿⣿⣿⣯⣉⣀⣀⣶⣶⣖⣀⡐⣂⣀⡀⠀⢀⣀⠀⢠⣤⣼⣌⠀⠀⠀⠀⠀⠀⠺⠿⠽⣿⢿⠿⠿⠧⠩⠩⣿⣬⢩⠝⠛⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠍⠉⠉⠭⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣾⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀⣈⣿⣿⣿⣿⣿⣷⣾⣷⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣤⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣯⠉⣩⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣛⣛⣛⣛⣻⢿⣻⣻⣿⣿⣻⢻⣻⢛⣟⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣽⣿⣾⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡠⣄⢤⢠⡄⢠⢠⡄⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣿⢿⡷⣿⣿⡿⣿⣾⣾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠁⠈⠀⠋⠙⠈⠃⠉⠐⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⣄⣿⣇⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣰⠂⠀⠐⠁⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⣲⣒⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢘⣒⣒⣺⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠓⠒⠶⠶⠒⠶⣟⠛⠛⠛⢓⡒⠒⠶⠀⣐⠚⠿⢶⠶⠶⠶⣶⣶⣧⠟⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠆⢠⡤⣤⣀⣈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠈⠉⠉⠀⠀⠀⠄⠀⢀⠈⠉⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠉⠉⡟⡧⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⡇⢈⣛⠛⠓⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣽⣭⣿⣿⣿⣝⣉⣉⣉⣀⣦⣄⣀⣀⣀⣀⣀⡀⡀⣀⣀⣀⣠⣰⣇⡁⠀⠀⠀⠀⠀⠀⠺⠿⠽⢿⠿⠿⠿⠥⠩⠩⣿⣬⢩⠝⠛⠐⠀⠠⠄⠀⠄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠁⠀⠉⠤⠍⠉⠙⠲⠖⠖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣙⣻⣿⣟⣿⣿⣶⣶⢶⣶⣶⣦⣤⣤⣤⣤⣀⣤⣄⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣷⣿⣭⣽⣿⣗⣿⣿⣿⣿⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣛⣿⣿⣿⢿⣿⣋⡉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣛⣻⣻⣻⣻⣿⣛⣻⣿⣿⢻⢻⣻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣽⣿⣾⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⡄⢤⡠⡄⣤⠠⡄⣄⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣿⢿⡷⣿⣿⡿⣿⣾⡾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⣀⡀⠀⠀⠀⠁⠀⠁⠉⠉⠁⠉⠈⠀⠂⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣤⣼⣿⢀⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣰⣿⣿⣿⣼⣿⣿⣿⣇⡎⠀⠀⠊⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠟⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⣴⣤⣤⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣲⣦⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⣧⡀⠀⠀⠀⠀⠀⠐⠀⣾⣿⣿⣿⣿⠆⢘⣒⣒⣿⣿⡿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠚⠛⠛⠓⣒⣛⠛⠛⠛⠛⠒⠒⠒⠀⠐⡻⠿⠶⠾⢷⣾⣿⣷⣯⠞⠋⠁⠀⠀⠀⠀⠀⠅⢼⣿⣿⣿⣿⡿⡂⢠⡤⣤⣀⣈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡈⡉⠙⠂⠀⠀⠀⠤⠂⠨⠉⠁⠀⠠⠄⠒⠂⠀⠀⠀⠀⠀⠀⠈⢸⢿⠀⠀⠀⠀⠀⠀⠀⢅⣸⣿⣿⣿⣿⣿⡂⢈⣛⠛⠓⠛⠐⠂⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⣉⣉⣍⣉⣠⣄⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣰⣿⣌⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠁⠩⠩⣿⣬⢭⠝⠛⠐⠀⠤⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠉⠀⠀⠉⠹⠟⠛⠛⠛⠒⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣈⣛⣿⣿⣿⣟⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣄⣀⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣟⣚⣿⣿⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠿⠿⠿⣻⡟⠉⠩⠭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣛⣻⣻⣻⣻⢿⣛⣻⣿⣿⢻⢻⣻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣽⣾⣾⢸⢸⣿⢸⣿⣽⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢰⡀⣄⢤⣠⣄⢤⡰⡄⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣿⢿⡿⣿⣿⡿⣿⣾⡾⣮⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣶⡄⠀⠀⠀⠀⠀⠀⠉⠈⠀⠃⠀⠈⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢺⣿⣿⡇⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢠⣿⣿⣿⣷⣿⣿⣿⣭⣰⠀⠀⠐⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠘⠛⠛⠛⠛⠛⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣀⣀⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡠⠤⡤⠀⢀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⢘⣒⣺⣿⣷⡿⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠙⠉⠉⠉⠁⠀⠐⠂⠈⠉⢿⡿⠷⠿⣿⣿⣿⣿⣿⣾⠛⠁⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠀⢠⡤⣤⣀⣈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⠀⠀⠀⠠⠤⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⡄⢈⣛⠓⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣯⣯⣭⣭⣥⣍⣭⣉⣀⣀⣀⣀⣤⣤⣤⣀⣀⣰⣾⣧⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⠻⠻⠟⢛⡀⠨⠩⣿⣬⢡⠝⠓⠐⠀⠐⠒⠀⠐⠂⠀⠠⠤⠤⠄⠀⠀⠀⣀⣤⡄⠀⣀⣀⠀⢀⣀⢀⣀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠒⠈⠛⠀⠀⠀⠒⠛⠒⠈⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣬⣻⣿⣿⣿⣿⣛⣻⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣯⣽⣟⣐⣶⣮⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣛⣏⣉⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣛⣻⣻⣻⣻⢿⣛⣻⣿⣿⢻⢻⣻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣿⣾⢸⢸⣿⢸⣿⢽⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⣆⢦⣰⣆⢦⡰⡔⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢿⡷⣿⣿⡿⣿⣾⣾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢲⣦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⣠⣿⣟⡰⣆⣾⣿⣿⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣖⣄⣀⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠀⢀⣀⣀⣀⠤⠄⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⣀⠀⠀⠀⠈⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠁⢘⣒⣚⣻⣿⡿⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⠛⠉⠉⠛⠉⠉⠉⠀⠀⠀⠈⠉⢻⣻⠟⡻⠿⢿⣿⣿⣿⣿⣾⡋⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡗⠀⢠⡤⣤⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⡅⢈⣛⠛⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣬⣭⣽⣶⣤⣤⣤⣤⣭⣀⣁⣤⣀⣄⣤⣤⣤⣤⣤⣴⣾⣧⢄⠀⠀⠀⠀⠀⠀⠀⠺⠽⠿⠛⠛⠛⠓⠀⠨⠩⣿⣬⢩⠝⠛⠐⠀⠒⠒⠁⠀⠂⠀⠠⠄⠐⠀⠀⠀⢀⣀⣤⣤⣄⠀⣀⣀⣀⣀⡀⣀⣀⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠛⠋⠉⠀⠀⠘⠛⠋⠉⠛⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣆⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣟⣛⣷⣶⣶⣒⣒⣶⣶⣶⣶⣤⣤⣤⣤⣤⠤⣤⣤⣴⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣐⣮⣵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⣛⣿⣿⣙⣛⣻⣭⠍⢹⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣻⣻⣻⣻⢿⣛⣻⣿⣿⢻⢻⣻⢛⣟⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣾⢸⢸⣿⢸⣿⢽⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠲⠐⡦⢲⣰⡆⢶⠰⡔⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣿⢿⡷⣿⣿⡿⣿⣾⡾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⢘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⢀⣴⣿⣧⣘⣷⣿⣿⣛⣠⠀⠀⠀⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣖⣀⣀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⡶⠀⢤⣀⣀⣤⣄⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⡄⣿⡧⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⡿⠀⢘⣒⣚⣛⣿⡻⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠛⠻⠿⣿⢿⠿⠿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⣿⣿⣿⣿⠀⢠⡤⣤⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣐⣒⡀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢳⡇⠃⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣻⠆⢈⣛⠓⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣶⣶⣴⣴⣶⣦⣤⣼⣹⣷⣤⣤⣤⣦⣤⣤⣤⣴⣿⡷⢄⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠛⠛⠛⠓⠀⠨⠩⣿⣬⢩⠝⠓⠐⠀⠒⠋⠁⠀⠀⠀⠐⠒⠒⠂⠀⠀⠠⠤⣴⣤⢄⣀⣠⣤⣀⣠⣄⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣒⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣿⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣭⣵⣿⣿⣶⣿⣿⣯⣷⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⠟⢻⣭⣛⣛⣿⣿⡯⣷⣶⣲⣒⣛⣛⣿⣓⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣻⣻⣛⣻⢿⣛⣻⣻⣻⢻⢻⣻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣮⢸⢸⣿⢸⣿⢹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠳⠘⠮⠳⣼⡆⢳⠙⠄⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣿⢿⡷⣿⣿⡿⣿⣾⡾⣮⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢤⡄⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⢠⣤⣿⣷⣮⣧⣾⣿⢉⡀⠀⠀⢀⠄⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣷⡁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣿⣤⣄⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣀⣤⣀⣀⣐⣀⣀⡈⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣤⣄⡇⣿⡧⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡟⠀⢘⣒⣚⣛⣿⡛⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⣭⠉⠙⠛⣿⡿⢻⠟⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⢠⡤⣤⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠤⠀⠀⣀⣀⠐⠒⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣳⡇⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⢷⠆⢈⣛⠛⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣷⣤⣤⣤⣶⣦⣴⣶⣶⣿⣷⢤⠀⠀⠀⠀⠀⠀⠀⠺⠭⠿⠛⠉⠙⠉⠀⠨⠩⣿⣬⢡⠝⠛⠐⠀⠀⠉⠀⠈⠁⠀⠀⠒⠐⠁⠀⠀⠠⠤⢰⣤⣤⣀⣤⣤⣤⣀⣤⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣤⣄⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣺⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⡶⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣯⣭⣿⣿⣷⣾⣿⣭⣬⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣭⣭⣭⣭⣉⣉⣉⣑⣚⣛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣻⣻⣛⣻⢿⣛⣻⣻⣻⢻⢻⣻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣮⢸⢸⣿⢸⣿⣹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡅⠹⠈⠦⠱⡼⠧⠳⠜⠆⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢿⡷⣿⣿⡿⣿⣾⡾⣾⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡘⠃⠀⣼⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⠀⢠⣤⣾⣿⣇⣀⣼⣿⣀⡀⠀⠀⢀⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣿⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣯⣦⣄⡀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣀⣐⣒⣠⣈⠰⣀⣀⣀⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⣆⣧⣿⡧⠆⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⣿⣿⠃⢘⣒⣚⣛⣿⡛⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠩⠍⠉⠉⡟⢛⠛⢻⢿⠃⣿⠅⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣟⠀⢠⡤⣄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠀⣤⣀⠀⠀⢐⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⡟⡍⠅⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠷⠆⢈⣛⠓⠓⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣦⣤⣤⣴⣶⣦⣴⣶⣶⣿⣯⣦⠀⠀⠀⠀⠀⠀⠀⠺⠭⠿⠛⠉⠉⠉⠀⠨⠩⣿⣬⢡⠝⠓⠐⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣦⣄⣤⣤⣤⣤⣄⣄⣀⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣧⣤⣤⣄⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⣀⣄⣀⣤⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠈⠉⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣷⣶⣾⣶⣿⣶⣶⣶⣶⣶⣾⣷⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣭⣭⣴⣶⣾⣿⣥⣥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣉⣉⣭⣭⣽⣿⣿⣋⣉⣉⣉⣉⣭⣭
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣻⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣻⣻⣻⢻⢻⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣮⢸⢸⣿⢸⣿⢹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡧⠙⠈⠧⠹⠼⠧⠳⠜⠎⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢾⡷⣿⣿⡿⣾⣾⡾⣮⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⠀⠀⣠⣾⣷⣆⣤⣾⣿⣀⡀⠀⠀⢀⠄⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⣿⡄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡚⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⣿⣧⣤⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠀⣐⣒⢂⣀⣰⣄⠀⣠⣤⣤⣄⣀⣀⣀⣤⣤⣴⣶⣶⣆⢠⣇⣿⠇⠂⠀⠀⠀⠀⠀⠀⡴⢿⣿⣿⣿⣿⠀⢘⣐⣚⣛⣿⡛⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠩⠅⠉⠹⠛⢿⢛⣙⣿⣿⡂⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⣿⣿⣧⠀⢠⡤⣄⣀⣈⠁⠀⠀⠀⠀⠀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⣀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⡟⡇⠅⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⠷⠃⢈⣛⠓⠒⠛⠐⠂⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣶⣶⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠲⠭⠿⠛⠉⠉⠁⠀⠨⠩⣿⣬⢡⠝⠓⠐⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠨⢀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣖⣾⣿
⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣧⣶⣶⣾⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠿⢿⡛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣯⣭⣭⣭⣭⣿⣿⣿⣯⣭⣭⣽⣯⣭⣭⣭
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣛⣻⣻⢛⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠙⠊⠳⠙⠮⢧⠙⠎⠣⠢⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢿⣽⢾⡷⣿⣿⡿⣿⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⣠⣾⣿⣶⣴⣾⣿⣦⡀⠀⠀⠀⠠⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠂⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣄⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣙⣧⣤⡀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣂⠀⢐⠒⢒⣠⣤⣀⣠⣤⣤⣤⣤⣤⣀⣤⣤⣶⣶⣶⣦⠀⠀⣶⣼⡿⠂⠀⠀⠀⠀⠀⠀⡠⢿⣿⣿⣿⣟⠁⢘⣐⣒⣛⣿⡛⠃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠙⠛⠉⠙⣿⣿⣧⡀⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣷⠁⢠⡤⣄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⡀⠄⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⢧⠂⢈⣛⠓⠒⠛⠐⠂⠀⠀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⡷⡄⠀⠀⠀⠀⠀⠀⠲⠭⠽⠛⠉⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⢤⢴⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⢰⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣨⢅⣀⠀⠀⠉⠈⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⡿⣿⣿⣷⣾⣶⣶⣿
⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣶⣬⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣭⣭⣭⣽⣿⣿⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣛⣻⣻⢻⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠂⠱⠙⠮⠳⠙⠎⠣⠡⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢯⣽⢾⡷⣿⣿⡿⣿⣾⡾⣮⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣀⣮⣿⣿⣶⣿⣿⣿⣄⠀⠀⠀⠠⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣯⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠃⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣙⣗⣢⡀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣒⡂⠌⠁⢒⣀⣀⣀⣤⣦⣴⣤⣤⣤⣤⣤⣶⣶⣶⣶⣦⠀⠀⠀⣷⣼⠿⠂⠀⠀⠀⠀⠀⠀⢰⠾⣿⣿⣿⣯⠁⢐⣐⣒⣚⣿⡛⠃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠈⠉⠋⠉⣉⢿⣿⣿⠀⠀⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣿⣧⠄⢠⡤⣄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⡀⠀⣀⠄⠠⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣷⠆⢈⣛⠓⠒⠛⠐⠂⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣿⣶⣷⡄⠀⠀⠀⠀⠀⠀⠲⠭⠽⠛⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠉⠉⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠶⠒⠚⠶⡶⢲⣶⣶⣦⣤⣤⣤⣤⣤⣄⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠐⠀⢰⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣈⣉⣍⣀⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡻⠿⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣯⣽⣿⣿⣿⣿⡿⠶⠿⣿⡷⠶⠶
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣛⣻⣻⢛⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢸⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠙⠺⠳⠙⠎⠃⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢯⣽⢾⡷⣿⣿⡿⣯⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⠀⠀⣤⢋⣸⣿⣶⣾⣿⣿⣤⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣯⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⠃⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣙⣗⣢⡀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠈⠉⠀⠀⣀⠠⢤⣦⣴⣤⣤⣴⣦⣤⣶⣶⣶⣶⣆⠀⠀⠀⠠⢸⣼⠟⠃⠀⠀⠀⠀⠀⠀⣰⡾⣿⣿⣿⣿⠀⢐⣐⣒⣚⣶⡓⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠉⠉⣍⣭⡉⠉⠀⢀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣧⠀⢠⡤⣄⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⡀⣀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣳⠂⢈⣛⠓⠒⠛⠐⠂⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣶⣷⣶⣾⣷⣶⣿⣶⣶⣶⣾⣦⣷⡄⠀⠀⠀⠀⠀⠀⠲⠭⠽⠛⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠀⠀⠀⠉⠉⠀⠀⠐⠒⠒⠒⠲⠒⠒⠛⠳⢶⢶⣶⣤⣴⣶⣦⣤⣤⣤⣄⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠐⠀⢰⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣈⣉⣁⣀⡈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣾⣶⣶⣾⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿⡿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣓⣿⣿⣿⣭⣿⣦⣤⣭⣿⣿⣭⣥⣤⡽⠿⠾⠿⠷⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣛⣻⣻⢻⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⠈⠓⠙⠺⠃⠙⠌⠂⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⢯⣽⢾⡷⣿⣿⡿⣿⣾⡾⣮⣽⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⠀⢀⠾⣽⣏⣿⣷⣾⣿⣿⣷⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠸⠂⠸⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣬⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣝⣗⣲⡀⠀⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠫⠁⠐⠀⠀⠀⠰⢦⣴⣤⣥⣶⣦⣤⣴⣾⣶⣶⣆⠀⠀⠀⠀⠀⣸⣼⠗⠃⠀⠀⠀⠀⠀⠀⣔⢿⣿⣿⣿⡟⠀⢐⣐⣒⣒⣶⡓⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠩⠉⢝⢿⠭⠉⠀⠈⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⠀⢠⡤⣄⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣻⠃⢈⣛⠓⠒⠛⠐⠂⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣾⣶⣶⣶⣿⣶⡷⠄⠀⠀⠀⠀⠀⠀⠲⠭⠽⠛⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠒⠒⠖⠒⠶⠺⠻⢶⡶⢶⣤⣶⣶⣶⣶⣶⣦⣤⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠀⢰⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣈⣉⠀⠈⠉⠉⠉⠉⠉⠉⠭⠭⠉⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⡿⡟⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢛⣲⣾⣿⣯⣽⣷⣶⣿⣿⣭⣵⣿⣶⡿⠿⠷⠿⠷⠶⠖⠶⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣛⣻⣻⢛⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠈⠃⠑⠚⠂⠱⠈⠈⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣯⢯⣽⢾⡷⣿⣿⡿⣿⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣀⣀⡂⢀⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣆⠀⠀⠻⣾⣡⣿⣿⣿⣿⣿⡟⠀⠀⠠⠂⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣾⣯⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠚⠀⢸⢷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣐⣞⣶⣓⣢⠀⠀⠀⢸⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠐⠀⠀⠐⠶⠶⣦⣬⣽⣶⣦⣴⣶⣶⣶⣾⣆⠀⠀⠀⠀⠀⡀⣲⡿⠇⠃⠀⠀⠀⠀⠀⠀⡖⢿⣿⣿⣿⡏⠀⢐⣐⣒⣒⣶⡒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠍⣿⣯⡉⠉⠁⠉⠉⠍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⡧⠀⢠⡤⣄⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡆⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣓⠃⢈⣛⠓⠒⠛⠐⠂⠀⢀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠲⠭⠽⠚⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠐⠾⢷⣶⠶⢾⡷⢶⣶⣴⣶⣶⣶⣶⣶⣦⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠀⢰⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣁⣀⠤⢀⠩⠉⠉⠉⢉⣩⢭⠭⠉⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⣻⣿⣿⣛⣿⣛⣛⣛⣛⣿⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡋⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣿⡿⠿⠟⠓⠶⠶⠖⠒⠒⠂⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢟⣛⣛⣻⣻⢛⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⠀⡀⢀⢀⡀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢸⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠊⠓⠛⠈⠣⠑⠐⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣭⢭⣽⢾⡷⣿⣿⡿⣿⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣧⣀⣀⡀⣠⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠄⠀⢀⠂⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠠⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣯⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠜⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣮⣿⣒⣆⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠒⠶⢤⣤⡭⠽⠶⠦⢴⣶⣶⣾⣷⣦⠀⠀⠀⠀⠀⢘⢀⣷⡶⠛⠀⠀⠀⠀⠀⠀⢐⡓⢿⣿⣿⣿⠇⠀⢐⣐⣒⣒⣶⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠏⠭⠍⠉⠉⠹⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣿⣿⣿⡇⠀⠠⡄⣄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⡛⠀⢈⣛⠓⠒⠛⠐⠂⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⡎⠀⠀⠀⠀⠀⠀⠀⠀⠲⠭⠽⠚⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠀⠈⠈⠉⠀⠀⠀⢀⠐⠚⠛⠙⢟⣶⣶⠶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣂⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡈⠀⢭⠉⠉⢉⣉⣩⣭⡭⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⡿⢿⠿⣿⢿⣟⣻⣿⢿⣿⣛⣛⣛⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣾⣶⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣛⠋⠉⠭⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⠉⠓⠛⠿⠟⠓⠒⠂⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣛⣻⣻⢛⢛⢛⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⡀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢸⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠈⠀⠑⠈⠚⠓⠉⠊⠃⠠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣯⢭⣽⢾⡷⣿⣿⡿⣿⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢿⣦⣠⣀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠐⡀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣾⣯⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠁⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣹⣞⣒⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠒⢶⣤⣼⡯⠵⠶⠦⠶⣶⣾⣿⣷⣄⣀⠀⠀⠀⠀⠀⡇⢰⣶⠾⠈⠀⠀⠀⠀⠀⠀⣰⠚⣿⣿⣿⣿⠁⠀⢐⣐⣒⣒⣶⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⠛⠯⠤⠤⠉⠉⠉⠧⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣿⣿⣿⣿⡇⠀⢠⡤⣄⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⢀⣀⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡃⠀⢈⣛⠓⠒⠛⠐⠂⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠲⠭⠽⠚⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠈⠉⠉⠀⠀⠀⠀⠀⠀⣐⠒⠛⠛⠻⣻⣷⡶⣖⣒⣶⣦⣤⣶⣶⣶⣖⣂⣠⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠐⠂⠐⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣁⡉⠭⠨⣭⡉⢉⣭⣙⣩⣭⡭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⢿⣛⣛⣛⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠛⢛⣛⣛⣛⣛⡛⠻⠿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣛⣿⡿⠿⣿⣿⡷⢶⣾⣿⣭⣭⣽⡟⠛⠚⢻⣿⣟⣶⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢟⣛⣛⣻⣻⢛⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢸⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⣰⡄⠈⠀⠃⠙⠚⠃⠙⠈⠂⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣭⢯⣽⢾⡷⣿⣿⡿⣿⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢨⣿⡄⣼⣶⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠢⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣾⣯⣿⣿⣽⣯⣿⣽⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠁⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣬⣷⣶⡀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠂⠴⠶⠿⠽⠶⠶⠿⠿⠿⣿⣿⣄⠀⣀⠀⢀⣀⡀⠀⠀⣸⡾⠟⠁⠀⠀⠀⠀⠀⠀⣶⠿⣿⣿⣿⣿⠀⠀⢐⣐⣒⣒⣶⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠐⠂⠀⠀⠤⠄⠀⠉⠩⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⠠⡤⣄⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⣀⣀⡀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⢈⣛⠓⠒⠛⠐⠂⠀⠀⣀⡀⡀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠽⠚⠁⠁⠀⠀⠨⠩⣭⡬⢡⠙⠓⠐⠈⠉⠀⠀⠀⠐⠂⠁⠀⢀⡉⠽⡟⠛⣟⣿⣿⣷⣾⣷⣶⣶⣾⣷⣶⣶⣶⣂⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠐⠀⠰⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣐⣒⣀⣀⣤⣄⣠⣥⣬⣥⣬⢭⣿⣿⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣙⣟⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⡿⣟⣛⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣭⣽⣛⣿⣿⣛⣉⣛⣉⣭⣯⣥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠚⣛⢛⣛⣛⣛⣿⡖⠂⠀⠒⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢟⣛⣛⣻⣻⢛⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⣀⢀⡀⣀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢸⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣶⡇⠈⠀⠁⠉⠚⠃⠙⠈⠃⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣭⢯⣽⢾⡷⣿⣿⡿⣯⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡄⣸⣿⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢠⣦⣸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⠀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣾⣯⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠁⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣽⣿⣶⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠂⠐⠶⠶⠿⠶⠶⠶⠶⠿⠿⣿⡆⠀⠀⠀⣀⣀⣀⠀⠀⠀⣸⡾⠟⠁⠀⠀⠀⠀⠀⠀⣸⣻⣿⣿⣿⣿⠁⠀⢐⣐⣒⣒⣶⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠩⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⡇⠀⠠⡄⣄⣀⣈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠠⠤⠤⢄⢀⣀⣀⣀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣾⣿⣿⣿⡃⠀⢈⣛⠓⠓⠛⠐⠂⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠺⠽⠽⠚⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⣀⣩⢿⡟⢻⣛⣿⣿⣷⣼⣶⣴⣶⣯⣶⣶⣶⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠂⠐⣶⣾⣶⣶⣶⣶⣶⣴⣶⣦⣤⣤⣤⣄⣀⣒⣒⣐⣀⣤⣬⣭⣿⣯⣭⣭⣭⣻⣷⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣙⣛⣛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣛⣻⣿⢛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣭⣻⡩⠭⠿⠭⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣷⣶⣶⣶⣿⠿⠿⠿⣿⣿⣶⣖⣚⣛⡛⠛⠛⠛⡚⠒⠒⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣻⣻⣻⢛⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢀⢀⡀⣀⢀⡀⡀⢀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣼⣾⣮⢸⢸⣿⢸⣿⢸⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⣹⣇⠈⠃⠉⠈⠚⠃⠈⠂⠓⠡⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣭⢭⣽⢾⡷⣿⣿⡿⣯⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣥⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⡀⢠⣷⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠔⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣯⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⢀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣽⣶⣆⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠀⠶⠶⠿⠷⠶⠶⠷⠿⣿⣿⣧⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣰⣾⠗⠈⠀⠀⠀⠀⠀⠀⢰⡛⣿⣿⣿⣿⠃⠀⢐⣐⣒⣒⣶⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠨⠦⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣇⠀⢠⡄⣄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠠⠀⠠⠄⠤⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠏⠀⢈⣛⠓⠒⠛⠐⠂⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠽⠚⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠓⣬⣽⣿⣿⣟⣿⣿⣿⣷⣤⣧⣴⣶⣤⣶⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠐⠀⣷⣾⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣲⣐⣒⣤⣼⣭⢽⣯⣭⣭⣵⣞⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣯⣭⠿⠿⠿⠶⢶⣶⣶⣶⣖⣒⡛⠛⠛⠛⠛⠛⠐⠒⠒⠒⠒⠶⣖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣛⣻⣻⢛⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⢤⠠⡀⣄⢀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡗⣸⣾⣮⢸⢸⣿⢸⣿⢸⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢸⣧⠀⠁⠈⠈⠛⠉⠈⠃⠑⠑⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣽⢯⣽⢾⡷⣿⣿⡿⣯⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣀⣤⣀⣸⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢠⣿⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠐⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣾⣯⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠐⣀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣽⣭⡆⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠳⠶⠮⠷⠖⠒⠒⠿⠿⢿⣷⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⣰⣾⠟⠈⠀⠀⠀⠀⠀⠀⢠⡭⢿⣿⣿⣿⠇⠀⢐⣐⣒⣒⣶⡒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣧⠀⢠⡤⣄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⡄⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡏⠀⢈⣛⠓⠒⠛⠐⠂⠀⠠⢄⠀⣀⠀⢀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣶⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠲⠭⠽⠚⠁⠁⠀⠀⠨⠩⣯⡬⢡⠝⠓⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⣯⢽⣿⣿⡿⣿⣷⣶⣶⣤⣧⣤⣴⣦⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠐⠀⣶⣾⣷⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣒⣀⣒⣲⣶⣦⣿⣭⣿⣿⣭⣭⣥⣞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢟⣛⡛
⣿⣿⣿⣿⣿⣟⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡽⡿⠿⠿⢿⣯⠿⠭⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⢛⠛⠛⢉⣉⣓⡒⠒⠒⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢺⡟⣹⡏⣿⣹⡟⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣛⣛⣛⣻⢿⣛⣻⣻⣻⢻⢛⢻⢛⣛⢿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⢤⠠⡀⣄⢠⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢸⣿⣿⣗⢸⡷⣼⣾⣮⢸⢸⣿⢸⣿⢹⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠈⠁⠙⠈⠛⠛⠈⠃⠑⠑⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣽⢯⣽⢾⡷⣿⣿⡿⣿⣾⡾⣮⣭⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣠⣀⣶⣆⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⡯⣻⣏⣿⣿⣿⣿⢽⣿⡏⣿⢹⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣽⣯⣿⣿⣯⣿⣯⣯⣧⣿⣾⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠁⠘⠛⠛⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡗⢝⣂⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣿⣭⣆⠀⠀⠀⢽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠶⠾⠷⠒⠶⠺⠻⠿⢿⣿⡄⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⢐⣐⣒⣒⣶⡒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣇⠂⢠⡄⣄⣀⣈⠁⠀⠀⠀⠀⠐⠒⠒⠀⠠⠤⠤⠤⠤⠤⢤⡤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠯⠀⢈⣛⠓⠒⠛⠐⠂⠀⢠⣄⢀⣀⣀⠀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣾⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠺⠭⠿⠚⠁⠁⠀⠀⠨⠩⣿⣬⢡⠝⠓⠐⠀⠀⠀⠀⠀⠈⠁⠈⠭⠭⠭⠽⠿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣦⣤⣴⣦⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⢀⠀⠀⠀⠐⠀⣶⣾⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣼⣷⣀⣒⣒⣶⣶⣿⣿⣿⣿⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⣭⣭⣿⣿⣿⣿⣿⣿⣭⠭⠭⠭⠤⠤⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⠛⣛⣀⣠⡤⠐⠒⠶⢤⣤⣤⣀

                    ䷩ 𝚕𝚒𝚗𝚎 6130

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/22/executing-epc/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/22/executing-epc/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Executing_the_EPC_(as_in_Killing_It,_Not_Following_It)⠀✐


Posted in Europe, Patents at 4:16 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Executing_EPC:_EPO_President_and_VP1_VP2_VP3_VP4_VP5_vs.
EPC⦈_


Summary: Vichy_Battistelli and his French_friend have basically killed the EPC,
i.e. they committed crimes to turn the EPO into a private bank instead of a
patent office; who will hold them accountable and when?


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⡟⠋⠉⠁⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⢸⢸⠀⡀⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⣿⣿⣧⢀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⠀⡆⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⣿⣷⣶⢰⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⠀⡇⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⢸⣿⣿⣿⣿⣿⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢸⠸⠀⡇⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢸⣿⣿⣿⣿⣿⢹⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⢘⠘⠀⡃⡓⡃⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢠⣀⠀⠀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⣧⣸⣿⣿⣿⣿⣛⢚⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⠰⠀⡇⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⣄⢤⠦⠠⠦⢤⠄⠲⣿⣿⣿⣿⣿⣗⡀⠀⢀⣠⣤⣤⣊⣀⡔⣟⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⢘⠀⡂⡃⡓⡃⡃
⠀⠀⠀⠀⠀⡀⠀⠄⡀⠃⠁⢡⣾⣿⢛⣴⠰⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠟⢻⣶⣶⣶⣶⣶⣶⣷
⠀⠀⠀⠀⠀⠀⠀⢀⢟⣄⠀⢼⣿⡇⣞⣷⠶⢰⡶⡌⣽⢾⣽⣿⣿⣿⣿⣿⡟⠋⠿⠿⠟⢛⣿⡤⠖⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⢹⡿⣿⣿⣯⠁⢀⣿⣿⣿⣿⡿⢿⠿⢿⠍⠀⢸⡿⢿⢿⠇⡀⠸⢿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⣠⣴⡄⣀⠸⡿⠁⠀⠈⠃⠀⠀⣿⠛⢸⡟⡃⣿⢨⡽⣿⣿⣿⣿⠛⠀⡀⠀⠀⠀⠀⣞⡡⠀⠀⠀⠀⠈⠲⣦⣵⠍⠀⠐⠻⠿⣿⡼⠧⠒⠈⠙⠿⣿⣿⣿⣿⡟⠃⠀⠀⠉⠛⢿⠋⠉⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⢫⢾⠅⠆⡀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠙⠋⠁⠀⠀⢼⡟⠞⠁⠀⠀⠀⠀⣤⣋⣤⣤⣄⡀⣠⠀⢠⡜⣥⢠⣤⡀⣠⣄⢈⢤⡄⣤⣤⣤⣀⣼⣟⢿⢥⡇⣤⣤⣄⡰⢢⣼⠀⣤⢀⡤⣬⣟⢻⣿⣿⣿⣿
⠓⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⠼⠏⣿⠀⢸⣧⣿⢸⡿⠇⢩⡿⣼⢸⣿⡏⣿⠼⢯⡡⣿⢸⣸⣷⡟⣿⠼⢇⡏⣿⠀⢹⣿⡇⣿⠼⢻⡗⣷⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣃⠻⠀⠀⠛⠀⠀⠛⠇⠸⠃⠀⠿⠶⢘⠘⠿⡇⠻⠀⣿⣷⣟⣼⡟⡿⠃⠻⠀⠈⣍⣟⠀⠘⠛⠃⠻⣸⣟⣷⣟⣼⣿
⠀⠀⠀⠀⠀⠠⣤⣤⣤⣇⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠼⠇⠇⠀⠀⢀⠀⣀⣀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠿⢿⠿⡿⡗⠕⠀⠀⠀⢘⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣶⣶⣿⣷⣤⣤⣼⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡁⣿⣹⣶⡏⣿⢹⣿⡀⠀⠀⠀⢸⣿⣶⣶⡶⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡄⣿⠉⠸⣇⡿⣸⣿⡇⠀⠀⢠⣿⣿⣿⣿⣷⠀⢀⡀⠀⣻⣿⣿⡇⠀⡄⠀⣾⣿⣿⣷⣶⡆⢀⣄⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠿⠙⠟⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣟⡻⣿⣿⣳⣤⡐⣤⢸⣷⣚⢻⣿⢡⡘⣄⣼⣿⣿⣿⣿⣿⡇⢸⠇⢸⣿⣿⣿⡇⢰⡇⠀⣿⣿⣿⣿⣿⠀⣼⣿⡇⠀⣿⣶⣎⢀⣤⠀⢀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣤⣬⣽⣿⣿⣿⣿⣧⠿⢸⣿⡇⣿⠤⠻⣮⡁⣿⢸⡇⣿⢸⡧⢸⣷⣿⣾⣿⣾⣿⣿⣿⡇⢸⠄⣼⣿⣿⣿⣷⠸⡇⢠⣿⣿⣿⣿⣿⠀⣿⣿⡇⢨⣿⣿⡛⠸⠛⠀⠿⠿⢿⣶⣶⣦⣤⣄
⣿⣿⣿⣿⣿⡿⠛⠉⢀⣨⣴⣾⣿⣤⡈⠙⢿⣿⣇⣿⣼⣿⣇⣿⣶⡻⠾⢃⠿⠸⢷⣟⣸⣷⣸⡟⠿⠹⠿⣿⣿⣿⣯⣥⣈⠀⠙⠻⢿⣿⣯⣄⡀⠈⠛⠻⠿⠿⢧⣄⣙⣛⡃⠀⠙⠻⠧⣤⢄⠀⠀⠐⠶⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡀⣼⣿⣿⣿⣿⣿⣿⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣭⣛⣛⣛⠛⠿⠿⠶⢿⣷⣶⣤⣭⣭⣍⣉⣒⣚⣓⠀⠤⠌⠉⠉⠉⣑⣒⠒⠀⠠⠀⠭⠍⢉⣛⣒⠒⠒⠂⠀⠬⠭⠤⢉⣐⣶⣶
⣿⣿⣿⣿⣿⡇⠀⠀⠟⠛⠿⣿⡿⠛⠛⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⣈⣉⣉⡉⠉⠉⠉⠓⠶⠶⣀⡀⠀⢄⣁⣀⣀⠐⠒⠀⠀⠀⠠⣀⣉⣀⣀⣤⠶⠟⠛⠉⠀
⣿⣿⣿⣿⣿⣃⠀⢠⣄⣴⣶⢽⣿⣦⣦⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣬⣍⣉⣛⣳⣶⣶⣶⣶⠾⠛⠉⠁⠀⣀⣠⣴⣶
⣿⣿⣿⣿⣿⣟⠀⠸⣿⣿⣟⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠀⠀⠠⠴⠶⠿⠿⠿⠿⠿
⣿⣿⡿⣿⣿⡿⣦⠀⣿⣿⣛⣛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣄⡀⣀⢀⡀⣀⢀⢠⣀⢀⢠⡀⣀⡀⠀
⡇⠀⠀⠽⠿⠏⠋⣄⠈⠛⢿⣿⣿⡿⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣁⠉⢉⠈⠁⠋⡉⠈⠈⠈⢈⠁⠁⠈⠀
⣧⣤⣤⣤⠄⠀⠀⠹⣷⣤⣠⣤⣴⡆⣧⠀⠀⠀⠤⠤⣤⣤⣼⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠋⠚⠘⠘⠛⠘⠃⠚⠘⠃⠘⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 6185

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/22/irc-log-210622/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/22/irc-log-210622/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Tuesday,_June_21,_2022⠀✐


Posted in IRC_Logs at 2:20 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-210622.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-210622.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-210622.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-210622.gmi
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 Qman3pjLziSjD5jVqDjotncDCs1UQKkV42PMguw72eX9qL #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
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                                                 as plain/ASCII
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                                                 IRC log for
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                                                 IRC log for
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                                                 (full IRC log
                                                 as plain/ASCII
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                                                 IRC log for
 QmeGH2vjRYiGCQRNC6Jmuk7zZKtNwQ72f3tuzQiW9tS8Em #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
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                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmbutb4kju2tYUqTCQVqyHhuvGEihGDQCdb3LwEGNMWXpP #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
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 QmPQ1ggEyxTknkbyTKjgSPa97HrCnqrRxMJbRTaZ48BDwj (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


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§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmfEjig2FSS7dnn2KEr26v5JW9wSenfByFz7Kpont5s6p2



                    ䷩ 𝚕𝚒𝚗𝚎 6312

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/22/phoronix-amd/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/22/phoronix-amd/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ So_Far_Today_67%_of_Phoronix_Articles_Are_About_AMD⠀✐


Posted in Hardware, Marketing at 10:05 am by Dr. Roy Schestowitz


Context: Phoronix:_Microsoft_and_Phoronix_Sponsor_(and_Close_Microsoft_Partner)
AMD_All_Over_the_Place | Phoronix_Turned_18_This_Past_Weekend,_Asked_Readers
for_Money,_and_This_Monday_It_Shows_Off_Hugely_Expensive_AMD_‘Gifts’_(Again) |
When_Blogs_Become_Marketing_and_Benchmarks_Become_Product_Promotions | Peak_AMD
| Phoronix_Editorial_Control


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇amd-photonix-today⦈_


Summary: Little AMD (in relative terms it’s a small company) getting its
money’s worth?


⡟⠋⠹⣿⣿⡿⢻⣿⣿⣿⡻⣿⣿⣿⢟⣛⣿⣿⡿⣛⣻⣿⢻⣿⠿⠿⢿⣿⠿⣿⣿⠫⠙⢿⡏⣶⠲⠶⠶⠶⠶⢶⠶⡶⢶⠶⢶⠶⠲⡶⡶⠶⠶⠶⣶⡶⠶⠶⢶⠶⠶⡶⡶⣶⠶⠶⠶⠶⠶⡶⡶⡶⡶⠶⡶⣶⡖⢒
⣇⣀⣰⣿⣿⣷⣽⣿⣿⣿⣯⣿⣿⣿⣜⣹⣿⣿⣯⣒⣿⣿⣼⣿⣦⣴⣾⣿⣶⣿⣿⣄⣀⣸⣿⢿⣤⣤⣅⣤⣬⣦⣦⣤⣦⣴⣬⣠⣤⣮⣼⣤⣴⣬⣬⣬⣤⣴⣯⣦⣬⣥⣼⣬⣤⣤⣨⣷⣠⣤⣈⣦⣶⣾⣤⣿⣇⣀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⢀⠀⡧⠤⠤⠀⡀⠀⡀⠠⠤⢀⡀⢀⠀⠀⣀⠠⠤⠀⡀⢀⡀⠤⠄⢀⠀⣀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⡇⠀⠀⠀⣿⢸⡇⠀⠀⠀⡇⣿⠀⠀⡇⠀⠀⠀⡷⢸⠀⠀⠀⢸⡇⣿⠀⢈⠵⠮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠉⠉⠉⠀⠁⠀⠀⠀⠉⠀⠉⠉⠉⠉⠀⠉⠀⠀⠉⠉⠉⠉⠁⠈⠀⠀⠀⠈⠁⠉⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠚⠃⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣴⣶⣶⣿⣷⣶⣶⣭⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⠏⠹⣏⢏⢹⢨⠝⣿⢐⡛⡟⡇⡟⠛⠉⢸⢹⠻⢻⢐⣯⠉⣿⣏⡪⡟⡟⡟⡛⠛⠛⢛⣿⡇⢉⠟⠛⠻⠛⡛⠇⣿⡟⢉⡗⢛⡻⢛⢻⣿⡅⣹⡏⣬⢻⣏⡪⡟⡛⣿⡟⢛⡟⣿⠻⢻⡟⣵⣽⣛⠛⣛⡟⠛⣿⣿⡇
⠻⠾⠷⠿⠾⠾⠖⣚⣥⣾⣷⣷⣶⣷⣶⣶⣾⣶⣣⣿⣾⣷⣷⣾⣷⣶⣷⣶⣧⣶⣶⣾⣾⣿⣿⣷⣷⣶⣶⣶⣶⣷⣷⣶⣷⣷⣶⣾⣾⣾⣿⣶⣾⣾⣶⣿⣷⣶⣷⣶⣷⣶⣾⣷⣶⣶⣾⣿⣶⣾⣶⣶⣶⣷⣶⣿⣿⡇
⣿⠟⠶⣶⣶⠻⣿⡟⣿⣿⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣠⣴⣘⣸⣘⣸⣇⣇⣸⣸⣨⣀⣀⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣆⣇⣃⣸⣇⣁⡏⠏⠙⠘⠉⢍⣿⣀⡙⢉⣹⣿⣟⣈⣈⣸⣒⣿⣿⣧⣄⣁⣉⣁⣀⡏⣅⣔⣕⣇⣐⣉⢙⣉⣉⣿⣠⣋⣉⣉⣋⣈⣁⣁⣉⣩⣹⣿⣏⣸⣇⣒⣉⣩⣍⣉⣏⣉⣹⣁⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡿⡿⠻⡿⢿⢡⣶⢿⠿⠿⠿⢦⡹⢿⡿⣿⢿⡿⣿⣿⡿⡿⣿⢿⡿⣿⡿⠿⡿⢿⢿⢿⡿⣿⡿⠿⢿⢿⡿⢿⣿⡿⣿⢿⡿⣿⠿⣿⢿⢿⡿⡿⣿⡿⠿⡿⣿⢿⣿⠿⣿⠿⣿⠿⣿⢿⡿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇
⣿⣠⣰⣆⣁⣠⣜⠇⢄⣠⣄⡘⠔⣀⣂⣰⣇⣦⣀⣌⣸⣦⣄⣢⣀⣀⣿⣷⣆⣔⣠⣀⣸⣇⡎⣄⣶⣡⣹⣗⣠⣃⣀⣠⣀⣰⣿⣦⣁⣰⣀⣔⣄⣜⣠⣃⣔⣄⣆⣿⣑⣿⣈⣼⣐⣀⣂⣜⣧⣸⣇⣰⣸⣿⣿⣿⣿⡇
⣿⠛⠛⠿⠿⠿⠿⠷⣶⣶⠶⠶⣿⠿⠟⣻⠻⠿⡿⢻⠿⢿⢿⠿⠿⠿⠿⢿⢿⡿⢿⠿⢿⠿⢿⡿⠿⢿⠿⡿⢻⠿⣿⠿⠿⢿⠿⠿⢻⡿⢿⠿⣿⠻⠻⡿⢿⠻⢿⠿⠿⠿⠿⠿⠟⡟⠿⠿⡿⠿⠿⠿⠿⠿⢿⣿⣿⡇
⣿⣴⣦⣤⣤⣧⣭⣧⣿⣧⣤⣤⣿⣬⣦⣿⣬⣥⣮⣤⣤⣃⣾⣯⣽⣤⣤⣂⣿⣿⣤⣤⣦⣧⣴⣧⣧⣼⣤⣮⣴⣤⣿⣈⣬⣴⣥⣮⣼⣧⣵⣤⣿⣬⣼⣧⣴⣤⣿⣧⣴⣬⣦⣧⣥⣧⣥⣥⣷⣥⣨⣤⣤⣼⣴⣿⣿⡇
⣿⠛⢟⠛⡟⢛⢛⡟⢻⡏⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣶⣶⣾⣶⣾⣶⣷⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣷⣷⣷⣷⣷⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣾⣾⣾⣾⣾⣾⣾⣾⣾⣾⣾⣾⣾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣷⣶⣶⣷⣷⣷⣷⣷⣷⣷⣷⣷⣷⣷⣷⣷⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣾⣾⣾⣾⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣩⣭⣤⣴⣶⣶⣶⣤⣬⣍⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢛⠻⡿⢿⢿⢿⡿⠿⡟⠟⢿⠿⠿⠿⣿⡟⢻⢻⡟⡛⣿⡿⣛⡻⠿⡿⠟⡿⠿⣿⡟⢻⠿⢿⠿⣿⢛⡛⡟⠡⢺⣿⢛⢻⠿⢿⠿⢻⠿⡿⠿⡿⠿⣿⡆⠛⡛⡿⠛⡟⡛⡟⡛⡟⢻⡟⣿⣿⠿⢿⢿⢿⠿⢿⣿⣿⡇
⣿⣴⣮⣤⣲⣤⣦⣧⣿⣧⣧⣽⣔⣤⣿⣼⣧⣧⣼⣧⣶⣽⣧⣝⣥⣩⣤⣣⣧⣢⣿⣷⣿⣜⣼⣼⣿⣜⣥⣧⣌⠸⢿⣴⣼⣔⣴⣭⣤⣔⣦⣣⣧⣧⠿⣣⣦⣶⣥⣁⣤⣫⣧⣣⣿⣿⣧⣭⣿⣼⣼⣜⣼⣥⣽⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣍⣉⣛⣛⣋⣉⣭⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⠰⠆⡏⡍⣏⢏⠋⣉⢩⣿⡇⢩⢩⢹⢩⢹⢩⢩⢹⠹⡙⢉⡉⡩⣿⢐⣸⢉⠉⣭⢨⢩⢹⢩⢩⢩⢹⠉⠉⣩⠉⠭⠋⣉⣿⢸⢩⢹⣿⠆⡅⠶⡱⠢⡷⠢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣴⣿⣿⣷⣿⣿⣿⣷⣿⣾⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡉⣿⢙⠙⠛⡟⢛⢻⡟⠙⡛⠛⣿⢿⢉⠛⠻⡋⢛⢟⠛⢻⡿⡏⡉⠙⠉⣿⡉⠟⠟⡋⠛⣻⠛⠛⣿⠉⡟⡛⠛⢛⠉⡟⣻⣿⣏⢹⡏⡽⠛⢛⡛⠛⡛⢛⢛⠋⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡆⡆⡍⠉⣿⠩⡉⢍⠉⠉⣝⡫⢉⠉⡋⢹⣍⠭⠉⢹⢀⡁⡉⠩⢙⠉⣿⣤⢠⢈⠄⡰⢀⢆⣤⣿⠰⠈⠉⢀⡇⠹⡏⣭⠹⠄⡷⢎⣏⠅⣯⢨⢋⡉⠉⣽⡅⠩⡉⣽⠍⡋⢻⠩⡋⢙⠉⢩⡨⢸⡍⡩⢹⣿⣿⣿⡇
⣭⡴⡶⢶⠶⠦⣭⣑⢻⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⡿⡿⠿⢿⡿⠿⡿⣿⢿⠿⣾⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇
⢿⣡⣀⣤⣀⣓⡼⠑⢀⣆⣈⢐⣀⣎⣀⣒⣀⣿⣂⣵⣐⣀⣒⣀⣁⣀⣈⣂⣰⣀⣿⢐⣀⣆⣐⣀⣾⣐⣐⣸⣆⣰⣀⣀⣿⣠⣃⣨⣂⣅⣨⣂⣰⣸⣇⣅⣘⣢⣿⣱⣘⣀⣃⣘⣸⣀⣀⣈⣰⣅⣈⣀⢻⣇⣈⣿⣿⡇
⣷⠶⡶⡶⢶⡶⠾⠿⢿⠿⠿⢿⡟⡿⢿⠻⣿⠻⠿⢿⡿⢿⢿⡿⢿⠿⡿⢿⡟⢿⠿⡿⢿⡟⢿⠿⡿⠿⠿⣿⠿⡿⣿⠿⣿⠻⢿⠿⡿⢿⠟⣿⠿⠿⡿⠿⢿⡿⢿⠿⡿⣿⠿⢻⠿⡿⣿⠻⢿⢿⠿⠿⠿⡿⣿⣿⣿⡇
⣿⣼⣴⣤⣤⣧⣧⣼⣼⣤⣼⣼⣧⣤⣼⣤⣿⣬⣤⣤⣼⣥⣵⣦⣶⣴⣤⣼⣧⣧⣤⣴⣽⣧⣥⣴⣦⣤⣧⣿⣨⣤⣼⣤⣾⣤⣬⣦⣤⣤⣥⣿⣼⣤⣥⣼⣽⣧⣦⣤⣵⣼⣧⣤⣤⣴⣽⣬⣤⣦⣼⣼⣴⣴⣿⣿⣿⡇
⣿⠿⠿⠿⠿⠻⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠟⣿⠿⡿⠿⠿⠿⠿⠿⢿⡟⠛⠛⠛⡿⢻⡿⡿⠿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣨⣦⣤⣼⣴⣥⣼⣼⣼⣧⣴⣧⣮⣥⣤⣷⣤⣼⣤⣥⣿⣤⣾⣮⣄⣥⣦⣤⣿⣿⣧⣿⣬⣶⣴⣧⣥⣤⣦⣴⣡⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣡⡖⢺⡟⡟⢻⢒⢨⠻⢛⢻⠿⡿⠿⠻⡿⢿⣿⢛⠿⠿⡟⢿⠿⡿⢿⣿⢛⣻⠿⢿⠿⡟⠿⡟⡟⠿⢿⡿⢿⣿⢻⢟⡿⢿⠿⢿⠿⣿⣿⠻⡟⡛⠟⡟⣿⠻⣛⣻⢛⠟⣿⢻⡿⣛⡻⡿⡿⠿⡿⠿⡿⢿⠿⠟⢿⣿⡇
⠻⢡⣌⣳⣴⣸⣘⠱⣡⣰⣦⣚⣔⣉⣜⣂⣹⣿⣰⣎⣂⣇⣃⣛⣷⣇⣿⣐⣺⣸⣸⣑⣀⣛⣄⣇⣰⣇⠜⢸⣿⣎⣼⣈⣸⠘⢈⣂⣿⣇⣥⣃⣶⣇⣃⣇⣧⣓⣸⣰⣦⣛⣸⣟⣒⣁⣃⡇⣃⡇⣃⣔⣣⣸⣇⣻⣿⡇
⣿⣶⣤⣭⣭⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢐⣺⢩⠋⣭⣿⢐⢸⠘⢉⡋⡍⡏⡅⠏⣝⢩⣥⡋⢽⡇⣛⢸⢸⢐⣸⡇⣂⠯⡉⡏⣭⠘⣽⢩⡋⡍⡏⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣾⣿⣶⣷⣿⣿⣶⣾⣾⣶⣶⣷⣷⣶⣷⣶⣾⣿⣶⣾⣷⣿⣾⣾⣾⣿⣷⣶⣷⣶⣷⣶⣾⣾⣶⣶⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡛⣿⠻⠛⠛⡿⢛⢻⡟⠻⠛⠛⣛⢛⠛⠛⠻⡛⠛⢟⠟⢻⡿⣟⠟⠛⢟⠛⢻⡟⠟⠛⢻⣟⠟⣻⡟⢻⠟⠛⡻⡋⠟⢟⡿⢿⡟⣿⢫⣟⠛⣛⠟⣛⠟⠛⡻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣶⣿⣾⣶⣶⣶⣶⣾⡟⣱⣴⣶⣿⣿⣾⣶⣶⡄⣶⣷⣶⣾⣿⣿⣾⣶⣧⣶⣾⣷⣷⣶⣿⣷⣶⣿⣷⣾⣷⣶⣿⣶⣶⣿⣿⣿⣷⣿⣶⣶⣶⣿⣶⣿⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡘⡘⡄⠨⢨⣿⠨⢨⠃⠙⡟⠈⢁⠁⡇⠌⡏⠂⠏⢙⠅⠋⠙⠍⢩⢹⣧⡇⡃⠈⢀⣥⣿⠉⡏⠝⠭⠉⡃⠉⠋⡍⢩⠅⡫⢹⡍⣿⠈⡍⣿⠀⠃⠉⠋⡝⠩⡏⢙⢩⡷⠊⠿⠊⣿⠉⢫⡇⠅⢹⡇⠅⣽⠉⣻⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⡍⣉⣩⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡰⢢⢣⡱⣇⠁⡅⢸⡇⢘⠈⡡⠇⣹⣉⠈⢰⢉⠄⢻⡇⢸⢠⣿⡹⠈⡌⢠⠀⣉⡄⡹⠈⡌⠁⡁⠎⢨⣏⠈⠀⡇⡆⡉⣿⢸⡏⣤⢁⡄⡣⢁⠆⡡⡉⡌⣿⡡⢸⡇⣤⢘⠌⡰⣿⢀⡌⣸⠐⣿⡁⢸⣿⣿⣿⣿⡇
⣿⢿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⢿⣿⠿⡿⡿⡿⠿⣿⠿⡿⠿⡿⡿⡿⡿⠿⣿⢿⠿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢾⢿⢿⡿⢿⠿⠿⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣸⣇⣶⣀⣖⣀⣀⣂⣷⣢⣂⡿⣀⣃⣀⣐⣟⣤⣁⣄⣄⣃⣿⣠⣃⣃⣴⣀⣠⣘⣑⣿⣸⣄⣇⣨⣂⣄⣀⣂⣰⣸⣧⣜⣠⣻⣔⣠⣃⣜⣀⣃⣿⣀⣀⣀⣆⣀⣀⣸⣸⡕⢸⣠⣀⢐⣀⣆⣨⣒⣀⣿⣿⣿⣿⣿⡇
⣿⠿⠿⠿⢿⠿⡿⠿⢿⠿⠿⡿⠿⢿⢿⠿⠻⠟⣿⠿⣿⠿⠿⠟⡿⠿⢿⡿⢿⠿⡿⢿⠿⠿⠿⡟⠟⠿⡿⢿⡟⡻⣟⡻⠻⢻⠻⡟⣿⡿⣛⡟⠻⣿⠿⢿⡟⢿⠿⢿⠿⠿⣿⠻⠿⢿⠿⡿⠿⢿⡿⡿⠟⠿⠻⢿⣿⡇
⣿⣨⣤⣧⣥⣬⣤⣤⣬⣤⣬⣤⣧⣼⣧⣦⣼⣤⣷⣤⣿⣨⣤⣧⣬⣤⣿⣏⣸⣤⣾⣤⣤⣼⣤⣤⣥⣬⣤⣧⣧⣦⣯⣥⣴⣬⣦⣭⣽⣧⣥⣤⣶⣭⣦⣼⣧⣯⣤⣧⣦⣤⣿⣤⣤⣬⣤⣦⣤⣬⣷⣤⣦⣬⣼⣼⣿⡇
⣿⠟⠟⢻⠻⠻⠛⣿⢛⠟⠟⢟⠻⡟⢛⠟⠟⢻⡏⢹⠟⠟⢿⠛⠛⠿⡻⠟⠟⢻⡟⣿⢛⠟⠿⡛⡿⡟⢻⡟⡋⡻⠟⣿⢙⠿⠻⢛⠿⡛⠛⡟⠟⠟⢻⢛⠛⠟⣿⣿⣛⡛⠻⡟⣻⡿⠻⠟⠿⠻⠹⣻⣿⣿⣿⣿⣿⡇
⣿⣥⣦⣼⣧⣷⣬⣿⣮⣮⣶⣾⣴⣥⣾⣮⣮⣼⣧⣾⣦⣦⣾⣧⣾⣴⣵⣥⣦⣼⣧⣼⣥⣮⣶⣵⣷⣷⣾⣷⣥⣷⣮⣿⣮⣶⣵⣼⣶⣵⣷⣿⣼⣦⣼⣾⣶⣧⣦⣿⣿⣿⣶⣯⣾⣧⣶⣦⣴⣤⣴⣿⣿⣿⣿⣿⣿⡇
⣿⢙⢙⡟⡻⠻⠟⠛⡛⣿⠋⠏⠉⠉⡍⢻⢛⠉⢛⢹⡟⡛⡛⡛⠋⣻⠛⢻⡟⠛⠛⠛⠛⣿⢛⠟⠋⡛⣛⠙⣿⢉⡛⢟⣻⢉⠉⠛⠛⡛⢛⠙⠛⢛⡿⠛⢛⠛⠛⢙⠋⣿⡛⢛⢻⡏⡋⢹⠉⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣶⣾⣷⣾⣶⣧⣼⣷⣿⣾⣶⣿⣶⣶⣿⣶⣶⣷⣾⣧⣾⣶⣷⣶⣾⣶⣾⣷⣾⣶⣷⣾⣿⣴⣷⣾⣶⣶⣶⣿⣾⣶⣿⣿⣶⣶⣷⣶⣷⣶⣶⣶⣾⣿⣶⣾⣶⣶⣶⣶⣿⣷⣧⣼⣷⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⠉⠹⢹⠍⡫⠙⠍⢩⠨⡟⠍⢩⢹⡎⡈⡄⢩⠙⠅⠩⠉⠙⡉⢹⡏⠙⠉⡫⢸⡇⠿⠈⡝⠹⡏⢹⡇⡨⠉⣽⣏⢣⠉⠋⠍⠉⢇⠱⢺⢐⠎⢸⠀⣿⠩⠉⡍⢹⠩⡇⣽⠈⠍⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠿⠿⠿⠿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⠿⠿⠿⠿⠿⠿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠿⠿⠿⠿⢿⢿⢿⢿⢿⢿⢿⢿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢉⠋⡟⠛⡻⠻⢻⡏⠍⡟⡛⡛⡟⡛⡟⡛⠛⡟⢻⠛⣿⡏⡉⡟⠛⡟⢛⣻⢛⢻⣿⠙⠋⡟⠛⢟⡃⠛⢻⣿⢩⡍⣟⡻⣿⢩⡍⡟⠛⠛⠛⢛⢻⣿⢩⣽⢛⢻⠙⣛⡟⣻⣏⡩⠟⡟⡟⡛⣟⡛⢛⣻⢛⢙⣿⣿⡇
⣿⣾⣶⣷⣷⣷⣷⣿⣷⣿⣷⣷⣷⣗⣢⣷⣷⣶⣿⣾⣶⣿⣷⣶⣷⣷⣷⣾⣿⣖⣼⣿⣾⣷⣷⣶⣶⣶⣶⣾⣿⣶⣶⣿⣷⣿⣶⣶⣷⣷⣶⣿⣰⣾⣿⣶⣾⣾⣾⣶⣷⣷⣿⣷⣷⣶⣷⣇⣷⣧⣷⣶⣾⣾⣷⣿⣿⡇
⣿⠿⢿⣿⣿⣿⣿⢟⠿⡿⡿⡿⡻⢿⢿⠿⡿⢿⣿⢿⠿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⢟⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣰⣾⣐⣀⣾⣿⣘⣉⣷⣀⣇⣛⣸⣀⣄⣇⣒⣿⣎⣄⣸⣠⣸⠈⣆⣇⣀⣇⣆⣐⣺⣿⣒⣹⣠⣐⣄⣢⣸⣀⣒⣇⣆⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣀⣿⣨⣈⣉⣏⣩⣹⣇⣈⠍⣉⣿⣿⣑⣸⣄⣑⣪⣈⣀⣼⣿⣏⣂⣠⣈⣒⣁⣁⣠⣿⣐⣉⣍⣭⢉⣯⣲⣩⣁⣉⣩⣿⣿⣁⣿⣲⣩⣉⣩⣩⣩⣉⣍⣍⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⠿⢿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⢿⣿⣿⢿⣿⣿⠿⣿⣿⣿⡿⠿⠿⢿⠿⠿⢿⠿⠿⣿⠿⠿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⣿⣜⣡⣰⣄⣸⣇⣢⣸⣇⣃⣼⣀⣿⣰⣀⣟⣠⣇⣣⣵⢠⣄⣀⣀⣰⣧⣀⣰⣠⣂⣰⣐⣀⣿⣀⣆⣿⣀⣆⣄⣸⣎⣂⣰⣰⣙⣤⣤⣀⣐⣿⣠⣠⣀⡰⣱⣀⣀⣰⣀⣂⣧⣒⣀⣇⣰⡀⣂⣿⣆⣇⣐⣨⣿⣿⣿⡇
⣿⠻⠿⠿⠿⡿⢿⡿⠿⠿⣿⠿⠻⠿⠿⠿⠿⣿⠿⠿⡟⠿⠿⢿⠿⠿⡿⠿⡿⢿⠿⡿⠻⣿⠿⡿⠿⠟⣿⠛⠟⠿⣿⠻⠿⢿⠿⡿⢿⡿⠿⠛⡟⠿⠟⠿⠿⠿⠿⡿⠟⢿⠻⠿⢿⢻⡟⠻⣿⢿⠿⠿⢿⢿⣿⣿⣿⡇
⣿⣬⣤⣤⣤⣦⣿⣧⣥⣼⣼⣮⣤⣤⣤⣄⣵⣷⣭⣬⣦⣬⣤⣿⣤⣤⣤⣨⣆⣵⣥⣾⣬⣿⣤⣿⣤⣥⣿⣤⣽⣤⣿⣬⣦⣴⣤⣼⣼⣧⣵⣼⣧⣼⣤⣥⣤⣼⣤⣥⣤⣽⣬⣬⣼⣦⣵⣬⣧⣼⣧⣯⣬⣼⣿⣿⣿⡇
⣿⢛⠙⠻⠻⠟⠻⡟⣻⢛⠟⠛⡛⢻⡟⠻⢛⠛⢟⠛⡛⢟⢻⡟⠛⣛⡛⠟⠛⣻⡟⢻⠛⣟⢛⠹⠛⠛⣿⣿⠙⡋⢙⠛⠟⣻⢛⠻⡛⢛⣿⡛⠟⠛⠻⢛⠙⡛⢛⢻⡟⢻⡛⢟⠛⡟⢛⣿⠛⢛⠛⢟⣿⣿⣿⣿⣿⡇
⣿⣶⣶⣶⣶⣷⣶⣷⣾⣴⣶⣶⣷⣶⣷⣶⣾⣷⣶⣶⣷⣦⣼⣷⣾⣶⣷⣶⣶⣿⣧⣶⣶⣿⣶⣶⣶⣶⣷⣷⣶⣶⣶⣶⣶⣿⣾⣶⣶⣶⣿⣷⣶⣶⣶⣾⣶⣷⣤⣼⣷⣾⣶⣶⣶⣶⣶⣷⣶⣾⣮⣼⣿⣿⣿⣿⣿⡇
⣿⢋⠛⡙⠙⠛⡟⡛⢛⠹⠉⣿⠛⡟⢻⡏⡍⣏⠋⢩⠝⠙⠉⢉⣿⠙⠙⡍⢻⠛⠹⠙⣟⠛⡉⣿⠋⡟⠛⠙⢋⢻⡟⡙⡙⠙⡙⢋⣿⠙⢻⠛⡙⢋⠛⠹⢋⢹⡏⢋⢻⡏⢻⡟⠛⡏⢹⠉⠋⢻⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣴⣷⣷⣾⣤⣷⣷⣶⣾⣶⣿⣶⣿⣾⣿⣶⣿⣷⣷⣾⣾⣿⣶⣿⣷⣷⣷⣾⣼⣾⣶⣿⣾⣶⣿⣶⣷⣾⣶⣶⣾⣷⣾⣾⣾⣶⣾⣿⣶⣶⣦⣾⣴⣷⣾⣾⣾⣷⣾⣾⣷⣾⣷⣷⣷⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇
⣿⠉⡫⢙⡍⡝⠉⣿⠩⠉⡍⢍⠉⡏⡍⠩⠙⠉⣿⠈⢹⡏⡍⠩⡉⡉⣿⠨⠉⠉⠈⡍⠩⢹⣯⢩⠉⢹⠉⡏⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢹⣿⠚⣋⡏⡟⡟⢫⣿⣑⢺⣿⡅⣿⠰⢹⡏⡸⡁⠯⢹⠘⡹⠫⢛⠽⣿⢹⢩⡫⢿⣏⡒⠇⡟⡍⡟⡝⠯⢻⢩⢻⣿⢩⠟⠝⣿⡸⢣⠫⢻⢩⢺⢠⢸⢫⡿⠝⡏⡇⣏⡙⢛⢹⣿⢱⣮⢫⢻⣫⠸⠩⢻⣿⣿⣿⡇
⣿⣶⣾⣶⣿⣷⣶⣷⣷⣿⣶⣾⣾⣶⣾⣶⣾⣷⣿⣷⣶⣾⣾⣾⣶⣶⣶⣿⣾⣶⣶⣾⣷⣶⣷⣧⣤⣷⣷⣶⣾⣶⣷⣾⣾⣷⣶⣿⣷⣾⣶⣾⣾⣾⣾⣾⣶⣷⣶⣷⣶⣷⣶⣾⣾⣿⣶⣶⣶⣾⣶⣾⣶⣾⣿⣿⣿⡇
⣿⠟⣻⢻⠛⠿⣛⣿⡿⣛⣿⢿⣿⢿⢿⡿⢿⢻⢻⠿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣰⣾⣸⣰⣖⣂⣿⣇⣛⣇⣃⣀⣆⣇⢐⣺⣸⣈⣁⣇⣇⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣀⣿⣨⣀⣉⣋⣉⣸⣇⣈⠊⣉⣿⣽⣘⣿⣌⣙⣋⣹⣂⣉⣉⣊⣋⣱⣁⠍⣿⣽⣧⣄⣠⣆⣸⣐⣊⣉⣎⡉⣊⣇⣈⣱⣁⣿⣀⣈⠊⣁⣃⣁⣙⣉⣅⣹⣞⣌⣈⣆⣰⣗⣃⣁⣂⣉⣱⣿⣽⣇⣈⣂⣁⣿⣿⣿⡇
⣿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣤⣽⣜⣧⣤⣶⣤⣶⣤⣢⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⠛⠛⠿⠿⠿⢿⠿⡿⢿⡿⡿⠿⡿⠟⠿⢿⠿⠟⡿⠿⡿⣿⡿⠿⠻⠿⣿⢻⣿⠿⡿⣿⠿⣿⠛⣿⡛⡟⡛⣿⠿⠿⣿⡿⢿⡿⢿⠿⠿⠟⢿⠿⠿⡿⠿⠿⠿⠿⢿⡿⠿⣿⠿⡿⢻⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣴⣦⣤⣤⣇⣹⣤⣮⣼⣗⣼⣤⣧⣤⣥⣴⣼⣥⣧⣜⣰⣿⣧⣿⣬⣥⣿⣬⣽⣼⣧⣽⣤⣿⣭⣮⣧⣭⣤⣿⣤⣥⣼⣦⣼⣇⣵⣥⣥⣤⣽⣼⣼⣦⣴⣼⣁⣦⣼⣧⣦⣾⣼⣦⣼⣤⣧⣦⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢛⡋⢻⠛⣟⠻⡛⠟⢻⡏⠛⣿⠛⡛⠛⠏⢛⠙⡻⢛⢻⣛⢙⠛⠛⣿⢛⠛⠛⡛⡻⠛⠏⡙⢻⡟⢻⠙⡛⢛⠟⢛⡛⡟⢛⠛⢻⡻⠛⠛⢛⢙⡉⢛⡛⢻⢙⠟⡻⠛⣿⢛⢟⠻⡋⠛⢻⡏⠍⡏⢙⠩⣿⣿⣿⣿⡇
⣿⣶⣶⣶⣶⣿⣶⣤⣶⣾⣷⣶⣿⣶⣷⣶⣶⣶⣶⣷⣤⣾⣷⣾⣶⣶⣿⣶⣶⣶⣷⣷⣶⣷⣷⣶⣷⣾⣦⣴⣾⣶⣾⣶⣶⣾⣶⣾⣷⣷⣶⣾⣾⣷⣶⣶⣾⣶⣷⣶⣷⣿⣶⣷⣶⣶⣶⣾⣿⣷⣷⣷⣶⣿⣿⣿⣿⡇
⣿⢫⠋⠙⡉⡝⢩⠃⠸⡉⢩⠉⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣷⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠿⠿⠿⠿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⠿⠿⠿⠿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠿⠿⠿⠿⢿⢿⢿⢿⢿⢿⢿⢿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡿⢟⣋⣭⣭⣥⣴⣶⣶⣤⣭⣭⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣾⠏⠹⣏⠏⢹⢩⡙⡹⢫⢹⣿⠙⣽⣧⡌⠋⡍⣯⢍⣯⢍⣿⢫⣍⢫⠍⣿⣯⠍⣿⡹⢏⣿⡟⢹⠹⣛⠛⡟⡛⣿⡏⣭⠛⣛⢙⠿⡛⠛⡟⣻⡏⠍⡟⠛⡏⠟⠻⠛⢻⠛⡟⠛⢟⡋⣿⢹⡙⢫⢙⢙⢙⢻⣿⣿⣿⡇
⠻⣴⣦⣿⣾⣼⣬⣾⣧⣾⣬⣽⣶⣼⡯⢈⣴⣵⣧⣭⣧⣭⣿⣦⣥⣧⣬⣧⣯⣵⣿⣷⣼⣯⣤⣼⣴⣵⣥⣧⣧⣿⣧⣵⣦⣿⣼⣴⣷⣭⣿⣿⣧⣷⣵⣭⣧⣮⣽⣬⣼⣥⣧⣭⣮⣴⣿⣧⣷⣼⣼⣬⣼⣼⣿⣿⣿⡇
⣷⠶⢬⣍⣛⣛⣛⣛⣛⣛⡛⠉⣭⣴⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⠮⢙⡰⣸⢰⢰⢈⠠⣽⡇⣥⡅⠤⢰⡆⡆⢆⣷⡆⡆⡆⡇⠄⣰⣎⡰⢎⠠⣽⣇⠿⣸⠰⣰⢾⢀⣰⣰⠀⡗⠴⠠⢰⠰⢸⠰⣀⣶⡧⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣆⣿⢨⡉⢉⢏⡩⢹⣏⣙⠍⠉⣿⣻⣰⠉⢙⠅⠉⡫⡉⣹⣟⡟⡈⢈⣸⠖⣌⣁⠿⡑⣿⠪⠐⡗⠕⢸⡇⢎⠢⣿⠄⣟⣻⠆⣿⡱⡏⠉⣭⠉⣭⠉⠉⣍⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢛⡩⡥⢴⠶⠤⣭⡛⢿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⠿⡿⡿⡿⠿⢿⠿⣿⢿⢿⣿⢿⢿⣿⣿⢿⣿⣿⡿⠿⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⢿⣡⣀⣤⣀⣛⣼⡖⢐⣀⣂⣀⡇⣸⣇⣆⣈⣇⣈⣀⣇⣀⣀⣐⣿⣀⣸⣇⣨⣀⣄⣀⣿⣘⡇⣺⣂⣁⣀⣂⣀⣷⣂⣂⣟⣤⣃⣤⣇⣃⣎⣴⣛⣠⡛⣿⣐⣰⣁⣸⣀⣾⣐⣀⣆⣸⣐⣸⣀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⣶⠭⡉⢛⠛⡉⢭⡴⢿⠿⣿⢿⠿⠿⠿⣿⢛⢿⠿⡿⢻⠿⠿⡿⢿⡟⡿⢿⢿⡟⢿⠿⡿⢿⡿⢿⠿⡿⣿⠿⠿⣿⢻⠿⠿⣿⢻⢻⠿⢿⠿⡿⣿⠿⢿⠿⠿⠿⢿⠿⠿⠿⣿⠿⠻⡿⢿⠿⡟⠿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣬⣄⣥⣤⣦⣷⣦⣬⣤⣧⣤⣦⣭⣤⣼⣴⣬⣤⣬⣤⣤⣬⣤⣿⣿⣤⣯⣼⣧⣬⣤⣿⣼⣧⣼⣤⣧⣴⣤⣼⣿⣤⣥⣼⣿⣬⣼⣧⣮⣬⣬⣿⣬⣀⣧⣤⣥⣴⣼⣧⣤⣽⣬⣼⣤⣤⣼⣧⣤⣿⣿⣿⣿⣿⣿⣿⡇
⣿⠟⠻⠻⢟⠻⡿⠟⡟⢻⡟⡹⠟⠿⠿⠻⡟⠛⠻⠟⠟⠟⣿⠛⠻⢻⠟⠿⠟⢿⠻⢻⡟⡟⢿⠛⠻⠻⠻⠟⢿⠟⠻⠛⢿⠻⠻⠛⡿⢻⠟⢿⢿⠿⠛⠟⠟⢻⡿⠻⠛⢻⡟⠟⢿⠟⠟⡿⢿⠿⠻⠛⠿⠻⠟⣿⣿⡇
⣿⣮⣴⣴⣼⣴⣼⣤⣧⣼⣧⣷⣦⣴⣧⣧⣷⣥⣧⣦⣤⣼⣿⣦⣧⣬⣤⣾⣿⣴⣤⣼⣿⣼⣮⣤⣶⣤⣴⣼⣾⣮⣤⣧⣧⣷⣤⣼⣯⣴⣤⣦⣼⣾⣬⣦⣦⣼⣧⣦⣿⣼⣧⣦⣼⣬⣤⣧⣼⣧⣧⣬⣦⣼⣤⣿⣿⡇
⣿⢙⢛⢿⢻⠛⠻⠛⣿⢙⠙⠟⢻⡟⡻⢛⡟⠻⡛⠿⠛⢟⠛⡟⢛⢛⡛⢻⡏⣿⢹⡹⢋⠙⢹⡟⠹⠙⠉⢩⠙⢩⠍⢍⢹⢹⡟⠋⡛⠛⠛⡋⠛⠛⣻⢛⡛⡻⢛⡛⢛⠋⢹⠛⢛⣿⢙⠛⢻⣛⠙⡻⣿⣿⣿⣿⣿⡇
⣿⣶⣶⣿⣶⣶⣾⣶⣿⣶⣶⣷⣾⣷⣾⣴⣷⣾⣷⣿⣶⣷⣾⣶⣾⣶⣶⣾⣷⣶⣶⣷⣿⣿⣾⣷⣷⣾⣷⣶⣾⣶⣶⣿⣶⣾⣷⣶⣷⣶⣶⣶⣶⣶⣿⣶⣶⣾⣾⣷⣴⣶⣾⣶⣾⣿⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⡇
⣿⠉⠉⡝⠩⡿⣿⢐⡯⢹⣽⡇⠇⢫⢉⠏⠝⢽⡫⠹⠉⢩⢩⠋⢹⢩⠉⣯⠭⡍⠘⠉⡟⠅⣯⣭⠋⠋⠉⣽⡫⠘⠍⠋⠉⠹⡍⣯⢸⡏⡍⠙⢩⡍⠉⠁⣯⢹⡏⢹⠉⣿⠉⠫⠉⠍⠹⠁⠏⠉⣽⡏⠙⠉⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢀⡀⡁⡡⢘⠌⣾⢘⣿⣄⢃⡘⠐⣠⢁⣿⠠⡁⢫⢸⣇⠆⣌⠁⣿⡸⠀⢎⡡⡀⢈⢈⠀⣿⠰⠀⡁⢘⠈⡜⣼⡇⢸⠀⡁⠩⢸⣏⢄⡁⡁⣨⢁⡁⠁⣾⡡⣹⡌⣿⠐⡱⡁⣄⢈⠈⣿⠀⡇⢸⡄⡎⡁⣽⣿⣿⡇
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⡿⣿⣿⡿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢐⣀⣀⣰⣠⣂⣰⣰⣰⣇⣀⣆⣔⣂⣀⣧⣂⢐⣀⣂⣰⣰⣁⣀⣀⣀⣂⣔⣀⣆⣀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

                    ䷩ 𝚕𝚒𝚗𝚎 6472

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    Gemini version at gemini://gemini.techrights.org/2022/06/22/school-spyware/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ New_Article_by_Richard_Stallman:_Many_Governments_Encourage_Schools_to_Let
Companies_Snoop_on_Students⠀✐


Posted in Free/Libre_Software, GNU/Linux at 11:28 am by Guest Editorial Team


Human Rights Watch studied 164 software programs and web sites recommended by
various governments for schools to make students use. It found that 146 of them
gave_data_to_advertising_and_tracking_companies.


The researchers were thorough and checked for various snooping methods,
including fingerprinting of devices to identify users. The targets of the
investigation were not limited to programs and sites specifically “for
education;” they included, for instance, Zoom and Microsoft Teams.


I expect that each program collected personal data for its developer. I’m not
sure whether the results counted that, but they should. Once the developer
company gets personal data, it can provide that data to advertising profilers,
as well as to other companies and governments, and it can engage directly in
manipulation of students and teachers.


The recommendations Human Rights Watch makes follow the usual approach of
regulating the use of data once collected. This is fundamentally inadequate;
personal_data,_once_collected,_will_surely_be_misused.


The only approach that makes it possible to end massive surveillance starts
with demanding that the software be free. Then users will be able to modify the
software to avoid giving real data to companies. █


The original_here.



                    ䷩ 𝚕𝚒𝚗𝚎 6524

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

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✐ The_Future_of_the_EPO’s_Work-to-Rule_Industrial_Action_(Examiners_Following
the_Law_Rather_Than_Unlawful_Instructions_From_Management)⠀✐


Posted in Europe, Law, Patents at 3:10 pm by Dr. Roy Schestowitz


               🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇A hardcore António Campinos⦈
                “Do what I say!! I’m the f***ing president!!!”


Summary: The sort of atmosphere that has already led to a ‘suicide wave’ at the
EPO is being reproduced by António Campinos (Monopoly Tony) less than 4 years
after he came, just like Benoît Battistelli around 2014


THE EPO situation isn’t improving ahead of next week’s meeting. Benoît
Battistelli and António_Campinos are both corrupt dictators, who do anything
within their power and even illegal things to suppress the staff and pretend
all is well.


In a saner world, Battistelli and Campinos would both be detained, arrested,
prosecuted, and left behind bars for more years than Blatter. It’s a tragedy
and a stain on Europe’s reputation that this has not happened.


“Benoît Battistelli and António Campinos are both corrupt dictators, who do
anything within their power and even illegal things to suppress the staff and
pretend all is well.”Earlier this year the staff voted in favour of industrial
action, lessening the grants of bogus patents (such as software_patents) by_a
considerable_level. There is currently another ballot, this one “on extension
of the Work-to-Rule actions until 30 September 2022″ (the next big meeting) and
this “ballot will run until Thursday 23 June at 12:00 (noon).”


That’s tomorrow.


“…not only does EPO management break the law; it’s trying to break the staff
too.”Dutch or Netherlands-based (mostly the latter, not the former) union
leaders say there are efforts to break the staff. The issues spill_over_to
blogs (see comments) and the union has taken_note. “Translations are available
in German, French and Dutch,” it says, having produced these in recent days.
Where is the media? Where are national broadcasters? Complicity by silence?


The SUEPO (in The Hague) committee has meanwhile issued the following guidance
to staff:


     21 June 2022
     su22016hp – 0.2.1


     § Production pressure and staff reporting for 2022 – What to do?⠀➾


     Holistic_Approach
     With the introduction of the Holistic approach (link to intranet
     page) most of the time deductions that were accounted for in MUSE
     have been replaced by a common pre-determined fixed value.
     As a consequence, this change can affect your productivity
     considerably if your actual time deductions are above the pre-
     determined fixed value. Also, concrete individual production targets
     were replaced with a production range (individually and/or at team
     level). This fits with the business goal of supporting your team.
     Other goals like Quality, Collaboration and Development are also part
     of your evaluation.


     Evaluation_in_your_Staff_Report


     According to Circular 366 that regulates our staff reporting
     procedures, staff members are responsible for “meeting the
     expectations discussed with their manager” and are expected “to
     review their progress regularly and to actively report to their
     manager on their progress as well as on potential difficulties”. This
     means that any foreseeable impact on the productivity expectations or
     production should be communicated to your manager. Also, it is
     important to leave a periodic registration of the actual time
     deductions (on the successfactors or by email to your manager), so
     that a realistic assessment of the productivity can be made.


     Working_under_exceptional_circumstances_–_impact_on_staff’s_health


     From March 2020 until the present-day EPO staff continues to work
     under exceptional circumstances due to the pandemic. There is still a
     limitation to work at the EPO premises and staff members and their
     family are still struggling to cope with the effects of the pandemic.
     The recent statistics on sick leave at the EPO illustrate the impact
     that the pandemic has on staff members. In view of this, it is
     important for staff members to look after their health and leave a
     written record of the impact their health state is having on their
     performance. As the statistics have shown, while some of us have
     managed to cope with the extraordinary situation there are those that
     have seen their health take a toll.


     Production_Pressure


     At a recent meeting with the LSCTH, the VP1 stated that “examiners
     can only do what they can do. Colleagues put themselves under
     pressure because they want to give a good service.” and that “…TMs
     which have only a certain capacity should not try to do more.
     Whatever workload is unable to be dealt with is the problem of upper
     management, and not the responsibility of the individual staff
     members”. These statements confirm the advice to staff that they
     should not put their health in danger and that undue production
     pressure should not be put onto staff’s shoulders.


     What_to_do?


     In view of the above it is important to follow these points:


     - Take care of your health. If you feel tired or exhausted, please
     consult your doctor and report it to your manager and H&S.


     - Keep a written record of your actual time deductions and share them
     with your manager regularly.


     - In the intermediate reviews, call your manager’s attention to the
     actual productivity that you would get if these time deductions were
     accounted for. Leave a written record of your assessment of your
     situation.


     - Leave a written record of the impact on your performance caused by
     the extraordinary circumstances we’re experiencing.


     - If you find yourself being put under production pressure by your TM
     please seek advice and get in contact with either the staff
     representation or the union.


     If these steps are taken, when the final review meeting takes place
     the staff member will be better prepared to argue and defend the
     final evaluation in their staff report.


As can be seen from the above, not only does EPO management break the law; it’s
trying to break the staff too. █


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                    ䷩ 𝚕𝚒𝚗𝚎 6720

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

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Gemini_version_available_♊︎


✐ Links_22/06/2022:_Clonezilla_Live_3.0.1⠀✐


Posted in News_Roundup at 9:02 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Applications
    * Distributions_and_Operating_Systems
          o Debian_Family
          o Devices/Embedded
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
    * Leftovers
          o Hardware
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Copyrights
    * § GNU/Linux⠀➾


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Chafa_–_terminal_graphics_image_viewer⠀⇛


                       
                       We’ve recently reviewed two terminal-based image
                       viewers, viu and timg, that support the Kitty
                       Graphics Protocol. These image viewers let you view
                       high resolution images direct in a terminal.


                       This review looks at a third terminal-based image
                       viewer that supports the Kitty Graphics Protocol.
                       It’s named Chafa, shorthand for Character Art
                       Facsimile. This is an image-to-text converter. It’s
                       free and open source software written in the C
                       programming language.


                       Chafa lets you view images as well as animated
                       GIFs. Its core functionality is provided with a C
                       library.


                # ⚓ Its FOSS ☛ Rocket.Chat_Aims_to_Replace_Skype_for_Business
                  by_Collaborating_with_Pexip⠀⇛


                       
                       Rocket.Chat is making headlines this year, and for
                       all the good reasons.


                       To start with, they collaborated with Nextcloud to
                       offer an open-source Microsoft 365 alternative,
                       then joined forces with Matrix, and now they have
                       announced another partnership to tackle the likes
                       of “Skype for Business” and Microsoft Teams.


                       So, what is it about? Let us get to know more here.


    * § Distributions and Operating Systems⠀➾


          o § Debian Family⠀➾


                # ⚓ 9to5Linux ☛ Debian-Based_Clonezilla_Live_3.0.1_Disk
                  Imaging/Cloning_Tool_Released_with_Linux_5.18⠀⇛


                       
                       Synced with the Debian Sid repository as of June
                       12th, 2022, the Clonezilla Live 3.0.1 release is
                       the first minor update to the Clonezilla Live 3.0
                       series launched at the end of May 2022 with APFS
                       and LUKS support, as well as numerous other
                       improvements.


                       Clonezilla Live 3.0.1 is powered by the latest and
                       greatest Linux 5.18.5 kernel to provide users with
                       better hardware support, and introduces several new
                       packages to the live system.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Arm_Linux_IoT_gateway_ships_with_up_to_8GB
                  RAM,_offers_dual_GbE,_4G_LTE,_WiFi_6,_BLE_5.3,_GNSS
                  connectivity⠀⇛


                       
                       Compulab IOT-GATE-IMX8PLUS is a new Arm Linux IoT
                       gateway powered by NXP i.MX 8M Plus SoC with up to
                       8GB RAM, 128GB storage, and plenty of connectivity
                       options with dual Gigabit Ethernet, WiFi 6,
                       Bluetooth 5.3 LE, and 4G LTE connectivity, as well
                       as GNNS support and RS485/RS232 interfaces.


                       The new IoT gateway builds upon theArm SystemReady
                       IR certified IOT-GATE-IMX8 industrial gateway, but
                       offers more RAM and storage, a 2.8 TOPS AI
                       accelerator (in the NXP processor), improved
                       connectivity, as well as a DVI-D port for video
                       output.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ 9 to 5 Toys ☛ Lenovo_Tab_P11_Plus_runs_Android_11_with_a
                  detachable_keyboard_at_$250_(Save_$100)_–_9to5Toys⠀⇛


                # ⚓ XDA ☛ OnePlus_Nord_2_receives_another_Android_12_update,
                  but_still_no_June_2022_patches⠀⇛


                # ⚓ Phone Arena ☛ Android_13_could_have_a_separate_button_in
                  its_clipboard_overlay_for_Nearby_Share_–_PhoneArena⠀⇛


                # ⚓ Computer World ☛ 14_ways_Google_Lens_can_save_you_time_on
                  Android_|_Computerworld⠀⇛


                # ⚓ Android Police ☛ 8_of_the_best_web_games_to_play_on
                  Android⠀⇛


                # ⚓ CNX Software ☛ Orbbec_Femto_ToF_camera_enables_accurate_3D
                  object_and_scene_capture_–_CNX_Software⠀⇛


                # ⚓ Make Use Of ☛ What_Is_High-Performance_Mode_on_Android?⠀⇛


                # ⚓ Android Authority ☛ The_end_of_the_road_for_Android_Auto_on
                  phones;_only_available_for_car_screens_–_Android_Authority⠀⇛


                # ⚓ Android Police ☛ Android_13_will_make_it_easier_for_more
                  phones_and_ROMs_to_support_Material_You⠀⇛


                # ⚓ Android Police ☛ Tell_Google_exactly_what_you_think_about
                  Android_13′s_home_screen_search_bar⠀⇛


                # ⚓ Make Use Of ☛ How_to_Add_App_Shortcuts_to_the_Android_Quick
                  Settings_Panel⠀⇛


                # ⚓ Hindustan Times ☛ Tired_of_getting_spam_calls_on_Android
                  phones?_Know_how_to_identify_and_stop_them_|_How-to⠀⇛


                # ⚓ Android Central ☛ Google_Password_Manager_now_has_an
                  Android_home_screen_shortcut_|_Android_Central⠀⇛


                # ⚓ Android Headlines ☛ Best_Payment_Apps_Compatible_With
                  Android_Casinos⠀⇛


    * § Free, Libre, and Open Source Software⠀➾


          o § Programming/Development⠀➾


                # ⚓ Taking_A_Blog_Break⠀⇛


                       After the log mentioning my playing with CGI
                       scripts, Acidus was nice enough to send me an email
                       with some helpful tips. The jist of it was renaming
                       the script files extention to .cgi and running the
                       command ‘chmod 755 script.cgi’ to make it
                       executible. I tried the chmod thing but didn’t know
                       about the 755 part. Its simple things to mess up
                       that are easily avoided once you know about them.


                # ⚓ Removing_the_“packaging_cruft”_from_the_web._Or_buying
                  without_packaging_with_Gemini.⠀⇛


                       Have you ever received a parcel or bought an item
                       to realise, once unpacked, that the room was mostly
                       full of packaging? Holding the item in your hand,
                       you thought : “all this crap only for this thing in
                       my hand”. Isn’t that feeling similar to reading
                       most modern webpage?


                       After releasing Offpunk 1.0 and announcing it on my
                       blog, I started to fear having released it with a
                       huge bug that would prevent first-time users to
                       even start the software. Breaking my disconnection
                       rule, I started to watch my inbox several times
                       during that day.


                       There was two crashes reported but also a few
                       strange feedback from people which were obviously
                       not Gemininauts. Intrigued, I connected my laptop
                       and did a Google search for “offpunk gemini”.
                       I don’t like Google but I know it has a recency
                       bias which allow spotting very recent webpages.


                # ⚓ dwim-sort⠀⇛


                       The dwimmiest sort of all time!


    * § Leftovers⠀➾


          o ⚓ Counter Punch ☛ Hire_Rosa?_R.I.P._Charlie_Kernaghan⠀⇛


                 – Toots and the Maytals


                 I went to a planning board meeting last night. Since we
                 shed the reeking regional incinerator that occupied
                 downtown for nearly 30 years, the city’s political class
                 has been giddy over the wave of gentrification and sprawl
                 that’s ensued. Concerns about working farm and forest
                 land are easily swept aside in pursuit of “development.”
                 The policy is often justified by a lack of housing that’s
                 “affordable.”


          o ⚓ Counter Punch ☛ Sparks⠀⇛


                 Will there be a spark initiating a cascade, a rebellion,
                 a realignment?  Will it even matter?  A Fluxus of
                 purgation? Can weak minded pseudo- lefties ever get it
                 straight? Can right winglets out to blindly wreck the
                 world in their own image, with the sauce of your apathy,
                 make it a better place? You won’t stop them with puny
                 little protests in the streets (not to say you shouldn’t
                 try, but that’s not the half of what’s required) You
                 won’t stop them with litters to the editor You won’t stop
                 them with shouts and incantations or especially, even
                 better ideas They have guns.  They will use them.
                 Bullshit gerrymandered politicians elected by misled
                 fearful masses will be ready to roll over you and you and
                 you and all you love and all the order you think you love
                 BTW, cops won’t be there to save you.  They will be too
                 busy bustin’ heads, like they’re programmed to do, all
                 according to your governments business model


                 How can a house built to be divided stand?


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ The_Sub-$100_Easythreed_X1_3D_Printer,_Is_It
                  More_Than_A_Novelty?⠀⇛


                       There was a time when a cheap 3D printer meant an
                       extremely dubious “Prusa i3” clone as a kit of
                       parts, with the cheapest possible components which,
                       when assembled, would deliver a distinctly
                       underwhelming experience. Most hackerspaces have
                       one of these cheap printers gathering dust
                       somewhere, usually with a rats-nest of wires
                       hanging out of one side of it. But those awful kits
                       have been displaced by sub-$200 printers that are
                       now rather good, so what’s the current lowest end
                       of the market? The answer lies in printers such as
                       the sub-$100 Easythreed X1, which All3DP have given
                       a review. We’ve been curious about this printer for
                       a while, but $100 is a bit much to spend on a toy,
                       so  it’s interesting to see their take on it.


                # ⚓ Hackaday ☛ Casting_Parts_In_Urethane:_Tips_From_A_Master⠀⇛


                       When you want a couple copies of a thing, you can
                       3D print ’em. When you want a ton of them, you
                       might consider making a mold. If those are the
                       shoes you’re in, you should check out this video
                       from [Robert Tolone] (embedded below). Or heck,
                       just check out all of his videos.


                # ⚓ Hackaday ☛ Teensy_Spectrum_Analyzer_Has_170_Channels⠀⇛


                       While high-fidelity audio has come a long way in
                       the past several decades, a lot of modern stereo
                       equipment is still missing out on some of the old
                       analog meters that were common on amplifiers and
                       receivers of the 60s through the 80s. Things like
                       VU meters don’t tend to be common anymore, but it
                       is possible to build them back in to your sound
                       system with the help of some microcontrollers.
                       [Mark] shows us exactly how to reclaim some of the
                       old-school functionality with this twin audio
                       visualizer display.


                # ⚓ Hackaday ☛ Inside_3D_Printing_Shoes⠀⇛


                       If you’ve ever thought about 3D printing shoes,
                       you’ll enjoy watching the video below about a
                       Portland-based company that creates shoes on demand
                       using an HP MJF 5200 3D printer. Granted, this
                       isn’t a printer you likely have in your basement.
                       The one-ton printer costs up to a half-million
                       dollars but watching it do its thing is pretty
                       interesting.


                # ⚓ Hackaday ☛ Plastic_CPUs_Will_Bend_To_Your_Will⠀⇛


                       As microcontroller prices drop, they appear in more
                       things. Today you will find microcontrollers in
                       your car, your household appliances, and even kid’s
                       toys. But you don’t see them often embedded in
                       things that are either super cheap or have to flex,
                       such as for example a bandage. Part of the reason
                       is the cost of silicon chips and part of the reason
                       is that silicon chips don’t appreciate bending.
                       What if you could make CPUs for less than a penny
                       out of flexible plastic? What applications would
                       that open up? PragmatIC — a company working to make
                       this possible — thinks it would open up a whole new
                       world of smart items that would be unthinkable
                       today. They worked with a team at the University of
                       Illinois Urbana-Champaign to create prototype
                       plastic CPUs with interesting results.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ PIA ☛ Interview_With_Michał_Kasprzak_–_TraceRoute42⠀⇛


                             Michał Kasprzak: TraceRoute42 is a technology
                             consultancy firm with a vast expertise in
                             infrastructure architecture, design &
                             maintenance. We help startups and enterprises
                             create bulletproof architectures and choose
                             an optimal solution during the concept phase
                             or implementation of major functional
                             changes. We advise on how to prepare for
                             changing factors and parameters of system
                             load, security breaches, unexpected emergency
                             situations, and their impact on project
                             resources.We are a team of Linux
                             Administrators who have once decided to move
                             over to Kubernetes. Currently we are working
                             on automation of creation and updates of
                             various k8s environments, and we assist
                             projects in their sysadmin, devops, and
                             database related issues.


                      # ⚓ EFF ☛ Pass_the_“My_Body,_My_Data”_Act⠀⇛


                             Privacy fears should never stand in the way
                             of healthcare. That’s why this common-sense
                             bill will require businesses and non-
                             governmental organizations to act responsibly
                             with personal information concerning
                             reproductive health care. Specifically, it
                             restricts them from collecting, using,
                             retaining, or disclosing reproductive health
                             information that isn’t essential to providing
                             the service someone asks them for.


                             These restrictions apply to companies that
                             collect personal information related to a
                             person’s reproductive or sexual health. That
                             includes information such as data related to
                             pregnancy, menstruation, surgery, termination
                             of pregnancy, contraception, basal body
                             temperature or diagnoses. The bill would
                             protect people who, for example, use
                             fertility or period-tracking apps or are
                             seeking information about reproductive health
                             services. 


                             We are proud to join Planned Parenthood,
                             NARAL, National Abortion Federation, URGE,
                             National Partnership for Women & Families,
                             and Feminist Majority in support of the bill.


                      # ⚓ EFF ☛ Daycare_Apps_Are_Dangerously_Insecure⠀⇛


                             As is the case with so many of these
                             services, there are a few apps that are more
                             popular than others. While we started with
                             the one we were being asked to use, this
                             prompted us to look closer at the entire
                             industry.


                             These days, offering two-factor
                             authentication (2FA), where two different
                             methods are used to verify a user’s login, is
                             fairly standard. EFF has frequently asserted
                             that it is one of the easiest ways to
                             increase your security. Therefore, it seemed
                             like a basic first step for daycare apps.


                             In October 2021, we tried to reach out to one
                             of the most popular daycare services,
                             Brightwheel, about the lack of two-factor
                             authentication on their mobile app. We
                             searched around on the site for an email to
                             report security concerns and issues, but we
                             could not find one.


          o § Defence/Aggression⠀➾


                # ⚓ Counter Punch ☛ Embracing_the_Complexity_of_Peace⠀⇛


                       Just imagine! The words are those of Robert
                       Weissman, president of the organization Public
                       Citizen, in response to the legislative efforts of
                       Reps. Barbara Lee and Mark Pocan, who are the co-
                       chairs of — glory hallelujah! — the Defense
                       Spending Reduction Caucus. They recently introduced
                       legislation that would cut Pentagon spending by
                       $100 billion and divert the money to programs that
                       actually helped the country . . . e.g., universal
                       health care, ending child poverty, saving the
                       environment.


                       Yeah, just imagine. One can also quickly,
                       unavoidably imagine the cynicism that rushes in
                       whenever someone tosses out the word “peace.” Then
                       it’s all pushed to the margins, both political and
                       social, as America continues its business as usual,
                       which is all about protecting itself from enemies
                       (most of whom it creates). The sales pitch is fear.
                       The motive, hidden in the shadows, is extraordinary
                       profit for some.


                # ⚓ Scheerpost ☛ ‘Totally_Unacceptable’:_US_Rejecting_90%_of
                  Afghans_Seeking_Asylum_Under_Humanitarian_Program⠀⇛


                       “We don’t feel safe,” lamented one Afghan asylum-
                       seeker whose brothers translated for U.S. invasion
                       forces. “We don’t know what will happen in an hour.
                       We don’t …


                # ⚓ Common Dreams ☛ Opinion_|_Amid_New_Cold_War,_US_Playing
                  With_Fire_in_Ukraine⠀⇛


                       From his first days in office, Joe Biden and his
                       national security advisers seemed determined to
                       revive America’s fading global leadership via the
                       strategy they knew best—challenging the
                       “revisionist powers” Russia and China with a Cold
                       War-style aggressiveness. When it came to Beijing,
                       the president combined the policy initiatives of
                       his predecessors, pursuing Barack Obama’s
                       “strategic pivot” from the Middle East to Asia,
                       while continuing Donald Trump’s trade war with
                       China. In the process, Biden revived the kind of
                       bipartisan foreign policy not seen in Washington
                       since the Soviet Union collapsed in 1991.


                # ⚓ Common Dreams ☛ Demanding_Prosecution,_Legal_Experts_Say
                  This_Is_the_‘Smoking_Gun’_to_Nail_Trump⠀⇛


                       As a key witness prepared to testify Tuesday before
                       the congressional committee investigating the
                       January 6, 2021 attack on the United States
                       Capitol, a growing number of U.S. legal experts
                       argued that one of Donald Trump’s recorded phone
                       calls offers ample grounds for the former
                       president’s prosecution.


                       “The tape should provide a simple case for criminal
                       prosecutors to bring against Trump after the
                       hearings.”


                # ⚓ TruthOut ☛ Trump_Claims_His_Mob_That_Attacked_Capitol_Was
                  “Well_Behaved”⠀⇛


                # ⚓ Counter Punch ☛ Co-opted:_The_UN’s_Misguided_Mission_to
                  Xinjiang⠀⇛


                       It was a thoroughly misguided mission.


                       Call it a cultural genocide, a crime against
                       humanity, or (as I prefer) a genocide, the
                       repression in Xinjiang Province is a well-
                       documented Chinese government policy authorized by
                       the specific order of President and communist party
                       leader Xi Jinping.


                # ⚓ TruthOut ☛ Mayor_Eric_Adams_Is_Siphoning_Funds_From_Public
                  Schools_to_Fortify_NYPD⠀⇛


                # ⚓ Scheerpost ☛ We’re_Playing_With_Fire_in_Ukraine⠀⇛


                       Alfred McCoy takes you to a planet where things are
                       only getting hotter in so many ways, not just
                       nuclear.


                # ⚓ Common Dreams ☛ As_Biden_Reverses_Trump_Land_Mine_Policy,
                  US_Urged_to_Join_Global_Ban_Treaty⠀⇛


                       Campaigners on Tuesday welcomed an announcement
                       that the United States military would end anti-
                       personnel land mine use in most of the world, while
                       pushing the Biden administration to go further and
                       join the international treaty prohibiting the
                       deployment of weapons that kill and maim thousands
                       of people every year.


                       “Inherently indiscriminate weapons that
                       disproportionately harm civilians have no place in
                       the 21st century.”


                # ⚓ Meduza ☛ ‘We’ll_fight_for_them_everywhere_and_always’:_The
                  Azovstal_defenders_currently_in_Russian_captivity_—_and_the
                  women_advocating_for_their_release⠀⇛


                       In mid-May, the Azovstal steel plant became the
                       last bulwark of Ukrainian resistance in Mariupol as
                       Ukrainian troops, including from the Azov regiment,
                       sheltered there. On May 16, Azovstal’s defenders
                       started leaving the complex in surrender, and on
                       May 20, the Russian Defense ministry reported that
                       the Azovstal plant had been “completely liberated.”
                       According to Ukrainian President Volodymyr
                       Zelensky, over 2,500 soldiers surrendered. A
                       portion of them are currently being held on the
                       territory of the self-proclaimed “Donetsk People’s
                       Republic”; others are in Moscow’s Lefortovo remand
                       prison. In an effort to rescue their loved ones,
                       relatives of the captured soldiers have created the
                       Association of Azovstal Defenders’ Families. Meduza
                       spoke to its deputy head, Yulia Fedosyuk, wife of
                       Azov fighter Arseniy Fedosyuk, about the ongoing
                       fight to free the soldiers.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Techdirt ☛ Appeals_Court_Tells_Police_Union_Its_Contract
                  Doesn’t_Supersede_State_Public_Records_Laws⠀⇛


                       Cops love secrecy. When a citizen does something
                       wrong, it’s a public record. When cops do the wrong
                       thing, union contracts, internal policies, and
                       multiple public records exemptions often allow law
                       enforcement agencies to keep the public from
                       learning about misconduct.


          o § Environment⠀➾


                # ⚓ Common Dreams ☛ Young_Europeans_Sue_to_Stop_Treaty_That
                  Fossil_Fuel_Giants_Use_to_Foil_Climate_Action⠀⇛


                       Several young victims of the climate emergency plan
                       to file a lawsuit Tuesday in Europe’s top human
                       rights court, where they will challenge an arcane
                       energy treaty that protects fossil fuel investors
                       at the expense of securing a livable planet.


                       “It’s hard to think of an international treaty that
                       is more out-of-date and out-of-time.”


                # § Energy⠀➾


                      # ⚓ Common Dreams ☛ African_Climate_Campaigners_Demand
                        Clean_Energy_Revolution,_Not_IEA’s_Fossil_Fuel_Push⠀⇛


                             Climate justice campaigners in Africa on
                             Tuesday rebuked the International Energy
                             Agency over a new report that urges nations
                             across the continent to quickly extract and
                             export their natural gas reserves before the
                             world shifts to renewable energy sources.


                             The IEA’s new Africa Energy Outlook 2022,
                             released Monday, notes that countries around
                             the world are gradually shifting toward
                             alternatives to fossil fuels and called on
                             the continent to profit from the 90 billion
                             cubic meters (bcm) of gas that it could
                             potentially produce per year until 2030. The
                             report says a full third of that production
                             should be exported to overseas markets.


                # § Wildlife/Nature⠀➾


                      # ⚓ Counter Punch ☛ Cultivated_meat_will_Inevitably_be
                        Drawn_into_the_Culture_War⠀⇛


                             “You have to accept the fact that the
                             government totally wants to provide
                             surveillance on every part of your life,” she
                             said. “They want to know if you’re eating a
                             cheeseburger, which is very bad because Bill
                             Gates wants you to eat his fake meat that
                             grows in a peach tree dish [sic].” The
                             fascist went on, saying the government would
                             punish those who didn’t comply.


                             “So you’ll probably get a little zap inside
                             your body that’s saying, ‘No no don’t eat a
                             real cheeseburger; you need to eat the fake
                             burger,’ the fake meat from Bill Gates,” she
                             said, in characteristically bizarre fashion.
                             “They probably also want to know when you go
                             to the bathroom and if your bowel movements
                             are on time or consistent.”


                      # ⚓ Counter Punch ☛ The_Rare_Earth_Dilemma⠀⇛


                             By 2002, according to Defense News:


                             But buyer’s remorse set in quickly. As the
                             U.S.-China relationship—never entirely
                             smooth—soured in the twenty-first century,
                             the realization that our entire tech industry
                             was at the mercy of an authoritarian and
                             sometimes capricious government set off
                             reactions ranging from fear to anger. Since
                             2010, the United States and other countries
                             have been searching for a way to replace
                             these critically sourced strategic materials.


                      # ⚓ Counter Punch ☛ Wild_Green_Washing_Machines⠀⇛


                             These groups preach protection for WSAs but
                             in practice they are actually part of the
                             “measly 6%.” They justify this by saying it’s
                             okay to drop protections for some of
                             “Montana’s wildest places” as long as it’s
                             done by “locally-driven collaborative
                             process.” They are wrong. These National
                             Public Lands belong to all Americans and not
                             just a few self-appointed collaborators using
                             a top-down approach embodied in legislation.


                             Wild Montana’s history on WSA protection
                             represents the measly 6%. They supported the
                             Rocky Mountain Front Heritage Act, which
                             ended WSA status for the Zook Creek and
                             Buffalo Creek WSAs on Bureau of Land
                             Management (BLM) lands in eastern Montana and
                             forced the BLM to assess the oil potential in
                             other WSAs, angering conservationists. They
                             supported Jon Tester’s Forest Jobs and
                             Recreation Act agreeing to remove protections
                             from the entire 151,000 acre West Pioneer
                             WSA, the second largest in Montana, removing
                             part of the Sapphire WSA and releasing 68,000
                             acres in seven BLM WSAs. They supported
                             Wilderness designation for just 29% of the
                             400,000 acres of WSAs considered. More
                             recently, on the EIS for BLM WSAs in Montana
                             they recommended that several of these be
                             opened to other uses and their status as WSAs
                             ended.


                      # ⚓ Common Dreams ☛ Opinion_|_The_Alliance_for_a_Green
                        Revolution_in_Africa_Is_Hurting_Farmers,_Not_Helping⠀⇛


                             In March, the Southern African Faith
                             Communities’ Environment Institute (SAFCEI)
                             sent letters to the U.S. Agency for
                             International Development (USAID) and other
                             donors calling on them to stop funding the
                             Alliance for a Green Revolution in Africa
                             (AGRA). Evidence from a donor-commissioned
                             evaluation, released in February, confirmed
                             the findings of an independent academic
                             assessment that the billion-dollar program
                             was failing to significantly improve yields,
                             incomes or food security for Africa’s small-
                             scale farming households. 


                      # ⚓ Common Dreams ☛ Global_Summit_to_Halt_Extinction
                        Crisis_Moved_to_Montreal⠀⇛


                             The United Nations announced Tuesday that it
                             is moving the conclusion of its pivotal
                             global biodiversity conference from Kunming,
                             China to Montreal, Canada after several
                             coronavirus-related delays.


                             “We don’t have a moment to waste.”


                      # ⚓ Common Dreams ☛ Opinion_|_The_Right-Wing_Supreme
                        Court_Readies_to_Help_Destroy_the_Planet⠀⇛


                             It appears that Republicans on the Supreme
                             Court are preparing to light our planet on
                             fire.


                      # ⚓ Counter Punch ☛ The_Critical_Theory_of_Pope_Francis
                        III:_The_Human_Roots_of_the_Ecological_Crisis_(Laudato
                        Si)⠀⇛


                             Technology: creativity and power


                             Humanity’s considerable technical prowess
                             over the last two centuries – stream engines,
                             railways, the telegraph, electricity,
                             automobiles, airplanes, chemical industries,
                             modern medicine, information technology and,
                             more recently, the digital revolution and
                             robotics, biotechnologies,
                             nanotechnologies—has provided humanity with
                             enormous benefits. We are right to rejoice:
                             Pope John Paul II exclaimed that “science and
                             technology are wonderful products of a God-
                             given human creativity” (p. 79). Pope Francis
                             adds his praise: “How can we not feel
                             gratitude and appreciation for this progress,
                             especially in the fields of medicine,
                             engineering and communications? How could we
                             not acknowledge the work of many scientists
                             and engineers who have provided alternatives
                             to make development sustainable?” (ibid.).
                             Humanity, it appears, has a relentless
                             impulse to overcome all material limitations.


          o § Finance⠀➾


                # ⚓ Common Dreams ☛ Free_School_Meal_Waivers_Set_to_Expire_as
                  Senate_Pushes_$857_Billion_Military_Budget⠀⇛


                       Federal free school meal waivers that would cost
                       just $11 billion to extend for another year are set
                       to lapse at the end of the month due to GOP
                       obstruction as the Senate simultaneously
                       advances—on a bipartisan basis—an $857 billion
                       military budget, a $45 billion increase over
                       President Joe Biden’s latest request.


                       “Universal school lunches have been a lifeline for
                       families, especially as corporations price-gouge at
                       the grocery store.”


                # ⚓ Common Dreams ☛ Study_Shows_Excess_Corporate_Profits_in_the
                  US_Have_Become_‘Widespread’⠀⇛


                       A new paper published Tuesday shows that U.S.
                       corporate price markups and profits surged to their
                       highest levels since the 1950s last year,
                       bolstering arguments for an excess profits tax as a
                       way to rein in sky-high inflation.


                       Authored by Mike Konczal and Niko Lusiani of the
                       Roosevelt Institute, the analysis finds that
                       markups—the difference between the actual cost of a
                       good or service and the selling price—”were both
                       the highest level on record and the largest one-
                       year increase” in 2021.


                # ⚓ TruthOut ☛ Don’t_Let_Corporations_Profit_From_Our_Inflation
                  Pain⠀⇛


                # ⚓ TruthOut ☛ A_TikTok_Investor_Has_Avoided_$1_Billion_in
                  Taxes._Now_He’s_a_GOP_Megadonor.⠀⇛


                # ⚓ TruthOut ☛ Corporate_Profits_Soared_to_Highest_Levels_in_7
                  Decades_Last_Year⠀⇛


                # ⚓ Scheerpost ☛ Taxing_the_Rich_to_Boost_Social_Security⠀⇛


                       Instead of growing financial security, Sam
                       Pizzigati says the current retirement system in the
                       U.S. is growing greater overall economic
                       inequality.


                # ⚓ Scheerpost ☛ “Fight_Poverty,_Not_the_Poor!”:_Thousands
                  Rally_in_Washington_DC⠀⇛


                       Labor unions, civil society and religious groups
                       joined the Poor People’s Campaign on June 18 to
                       demand justice and redressal for the 140 million
                       people in the US facing poverty and growing
                       insecur…


                # ⚓ Common Dreams ☛ Opinion_|_Poor_People’s_March:_Organizing
                  for_Peace,_Justice,_and_Equality⠀⇛


                       After her niece, a low-income mother of three, was
                       murdered several years ago, Wel’ega Ma’Shak of
                       Galt, California, joined Missing and Murdered
                       Indigenous Women (MMIW) to feel less alone in her
                       grief. She also joined the state chapter of the
                       Poor People’s Campaign (PPC), and on Saturday, June
                       18, she stood with tens of thousands of people in
                       Washington, D.C.—representing MMIW—to condemn
                       government policies that elevate militarism over
                       human needs and to denounce religious bigotry and
                       legislation that allows racism, sexism, classism,
                       and homophobia to persist.


                # ⚓ Common Dreams ☛ ‘Moral_Failure’:_California_Dem_Pulls_Plug
                  on_Fossil_Fuel_Divestment_Legislation⠀⇛


                       Climate, environmental, and social justice
                       advocates on Tuesday condemned the decision by a
                       Democratic California lawmaker to kill proposed
                       legislation that would require two of the state’s
                       leading pension funds to divest from the fossil
                       fuel industry. 


                       “Teachers and state employees whose retirement
                       futures are invested by our state’s pension funds
                       have long demanded that CalPERS and CalSTRS cease
                       investing their money in fossil fuel companies.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Counter Punch ☛ Ranchos_Deluxe⠀⇛


                       The California-born governor of Montana sports a
                       modified version of western wear with Levi and
                       Carhart clothing and the ever-present over-sized,
                       somewhat Freudian compensation, belt buckle with
                       his ranch brand, implying good-old-boy Lyndon
                       Johnson type power, including body-slamming
                       reporters half his size. A candidate for a Montana
                       U.S House seat, when he isn’t   Nav cribbing a
                       travel invoice, is often seen during election times
                       clad in cowboy attire with a black hat and riding a
                       paint horse like Monte Montana.  While the governor
                       tries to pass as one of the common people
                       (excluding reporters) the potential House Seat
                       politico tries to portray a John Wayne image, but
                       resembles a goofy ex-jock variety of Don Knotts,
                       with the ethics of Richard Nixon.


                       The new women of the west sport over-sized belt
                       buckles, sequin-laden clothing, pink ropes,
                       intentionally shredded Levis and New Mexico
                       buckaroo hats, with silk scarfs, spurs and chinks
                       that make a statement – apparently with a
                       subliminal desire to look like a hybrid Dolly
                       Parton and Dale Evans – while going to the post
                       office in their RAM 3500, dually, diesel pickup.
                       Meanwhile, back at the ranch, the chore person will
                       deliver the bedecked lady rider in a side-by-side
                       to a saddled, trusty steed. This modern-day cowgirl
                       will then transport the trusty steed in a $50,000
                       plus, truck and trailer, to a place to ride in
                       circles in a large barn.


                # ⚓ Democracy Now ☛ Colombia’s_Incoming_VP_Francia_Márquez_in
                  Her_Own_Words:_“A_New_Form_of_Government_Is_Possible”⠀⇛


                       Following the historic victory in Colombia’s
                       presidential election of former guerrilla member,
                       former senator and former mayor of Bogotá Gustavo
                       Petro and his running mate, the Afro-Colombian
                       environmentalist Francia Márquez Mina, we feature
                       interviews with each of the candidates on Democracy
                       Now! Francia Márquez Mina is set to become
                       Colombia’s first Black vice president. We spoke to
                       her in March, when she was running for president.
                       She later lost in the primary to Petro, who went on
                       to choose her as his running mate. “We are giving
                       impetus to the idea that in Colombia a new form of
                       government is possible, governance that is built up
                       from the Black, Indigenous and peasant peoples from
                       the very different sectors of the community,
                       LGBTIQ+, from the youth, from the women, from the
                       small farmers of Colombia, those who have been no
                       one — that is to say, who have never had a voice in
                       the government,” says Márquez Mina.


                # ⚓ Democracy Now ☛ Gustavo_Petro_Promised_a_“New
                  Progressivism.”_Now_He’s_Set_to_Be_Colombia’s_First_Leftist
                  President⠀⇛


                       Colombian President-elect Gustavo Petro spoke to
                       Democracy Now! in 2018 about his vision for the
                       country after he placed second in the presidential
                       election, losing to right-wing politician Iván
                       Duque. Petro is a former M-19 guerrilla and the
                       former mayor of Bogotá. “A new progressivism is
                       emerging,” explained Petro. On Sunday, he succeeded
                       in his new attempt at the presidency, becoming the
                       first leftist president in Colombia, long a
                       conservative stronghold in Latin America. He has
                       vowed to fight worsening climate change, poverty
                       and inequality in Colombia by raising taxes on the
                       rich and expanding social programs, as well as
                       access to education and healthcare.


                # ⚓ Counter Punch ☛ Electoral_Victory_of_Colombians_Petro_and
                  Marquez_is_Unprecedented⠀⇛


                       The Historical Pact coalition they represent had
                       gained 50.5 percent of the votes cast in a second
                       round of elections. The loose-lipped, right-wing
                       construction and real estate mogul Rodolfo
                       Hernández, candidate of the recently-devised League
                       of Anti-Corruption Governors Party, accounted for
                       47.2 percent.


                       This was the third presidential campaign for Petro,
                       senator, former urban guerrilla and former Bogota
                       mayor, who won 40.3 percent of the votes in first-
                       round voting on May 29. He and Vice President-elect
                       Francia Marquez take office on August 7.


                # ⚓ Meduza ☛ ‘My_neighbors_fully_support_me’_:The_Russian_man
                  using_the_front_of_his_shop_to_protest_against_the_war⠀⇛


                       47-year-old Dmitry Skurikhin, a small business
                       owner from the village of Rusko-Visotskoye in
                       Russia’s Leningrad region, has a “No to War” bumper
                       sticker, refuses to shave his beard as long as
                       Putin is in power, and keeps the front of his shop
                       covered in political and anti-war graffiti and
                       posters. He spoke to the Russian outlet The Village
                       about his small acts of protest, the reactions he
                       gets from his neighbors, and whether he’s afraid
                       there might be criminal prosecution in his future.


                # ⚓ Meduza ☛ ‘What_I_want_is_a_secular_Chechnya’:_More_women
                  are_trying_to_escape_violence_and_persecution_in_Chechnya.
                  But_fleeing_to_Moscow_is_no_longer_enough_to_ensure_their
                  safety.⠀⇛


                       In 2017, thanks to an investigation by independent
                       Russian newspaper Novaya Gazeta, the world learned
                       about the repressions queer people face in the
                       North Caucasus. Stories of torture and kidnappings
                       appeared on the homepage of the New York Times, and
                       Vladimir Putin had no choice but to comment. Soon,
                       people began evacuating from Chechnya. The majority
                       of evacuees in the first wave were men, but human
                       rights advocates have since seen an increase in the
                       number of requests from women, not all of them
                       LGBT+. To learn more about the threats women face
                       in Chechnya, Meduza spoke to two human rights
                       advocates and two Chechen women who managed to
                       escape.


                # ⚓ Common Dreams ☛ Filmmaker_Has_‘Fully_Complied’_With
                  Subpoena_of_Secret_Trump_Tapes⠀⇛


                       A documentary filmmaker who filmed extensively with
                       former President Donald Trump and his top advisers
                       in the run-up to the 2020 election and the January
                       6 attack on the U.S. Capitol has “fully complied”
                       with a subpoena of his footage and is expected
                       speak to the House Committee investigating the
                       insurrection on Thursday.


                       “A very small group of people had knowledge of this
                       documentary project, and a lot of Trump advisers
                       were surprised to see it existed.”


                # ⚓ Common Dreams ☛ Opinion_|_Trump_and_His_Allies_Are_‘A_Clear
                  and_Present_Danger_to_American_Democracy’⠀⇛


                       On Thursday, June 16, a conservative icon issued an
                       ominous warning about the most influential
                       Republican in the country. Former federal appellate
                       judge J. Michael Luttig concluded his testimony
                       before the House Select Committee to Investigate
                       the January 6th Attack on the U.S. Capitol with
                       these words:


                # ⚓ Scheerpost ☛ Neoliberal_Macron_Loses_Parliamentary_Majority
                  as_Mélenchon-Led_Left_Surges_in_France⠀⇛


                       The president of far-right National Rally,
                       meanwhile, celebrated a “historic breakthrough” as
                       Le Pen’s xenophobic party won a record 89 seats.


                # ⚓ TruthOut ☛ Colombia’s_First_Leftist_President_Will_Face
                  Hurdle_of_Conservative_Congress⠀⇛


                # ⚓ Common Dreams ☛ WATCH_LIVE:_Jan._6_Hearing_Highlights_Trump
                  Role_in_Fake_Elector_Scheme⠀⇛


                       Former President Donald Trump’s role in concocting
                       a fake electors scheme with the goal of overturning
                       the 2020 election is set to be a major focus of the
                       House January 6 committee’s latest public hearing
                       Tuesday on the origins of last year’s violent
                       assault on the U.S. Capitol.


                       As The Guardian explains, the fake electors ploy
                       was “conceived in an effort to create ‘dueling’
                       slates of electors” that Vice President Mike Pence
                       “could use to pretend the election was in doubt.”


                # ⚓ Common Dreams ☛ ‘He_Must_Resign’:_Staff_Texts_Over_Fake
                  Elector_Slates_Implicate_Ron_Johnson⠀⇛


                       Wisconsin Democrats on Tuesday led calls for U.S.
                       Sen. Ron Johnson’s resignation after the House
                       January 6 committee revealed texts indicating that
                       the Republican’s office wanted to hand-deliver
                       certificates of fake electors to then-Vice
                       President Mike Pence in service of former President
                       Donald Trump’s attempt to overturn the results of
                       the 2020 presidential election.


                       “Ron Johnson actively tried to undermine this
                       democracy. He literally tried to hand Mike Pence
                       fake ballots.”


                # ⚓ Common Dreams ☛ Opinion_|_Why_Merrick_Garland_Must
                  Prosecute_Donald_Trump_for_Insurrectionist_Plot⠀⇛


                       Will Donald Trump be held accountable for the
                       attack on the U.S. Capitol on Jan. 6, 2021 and what
                       was a multi-layered conspiracy to overturn the
                       results of the presidential election?


          o § Censorship/Free Speech⠀➾


                # ⚓ Techdirt ☛ Giant_Private_Prison_Company_Goes_To_Court_To
                  Try_To_Get_Lawyer_To_Stop_Tweeting_About_Them⠀⇛


                       CoreCivic is one of the nation’s largest private
                       prison companies. And while it should already be
                       concerning that we even have private prison
                       companies, CoreCivic appears to be particularly
                       awful. Just last week, CoreCivic was in the 9th
                       Circuit appeals court trying to overturn a
                       dismissal of its SLAPP lawsuit that it filed
                       against investment firm Candide Group and a Forbes
                       writer, Morgan Simon, for making claims about the
                       company that turned out to be pretty accurate. In
                       the process, CoreCivic is trying to undermine
                       California’s useful anti-SLAPP law by saying it
                       can’t be used in federal court (something the 9th
                       Circuit has already allowed in other cases).


                # ⚓ Techdirt ☛ Impossibility_Theorem_Strikes_Again:_YouTube
                  Deletes_January_6th_Committee_Video⠀⇛


                       Content moderation at scale is impossible to do
                       well says my impossibility theorem. And, basically
                       every day we see more examples of this in action.
                       The latest is that the NY Times reports how YouTube
                       took down a video that the January 6th House Select
                       Committee had posted to the site, detailing many of
                       the lies Donald Trump made about the 2020 election.


          o § Freedom of Information / Freedom of the Press⠀➾


                # ⚓ Counter Punch ☛ Free_Assange?_Yes,_But_That’s_Not_Nearly
                  Enough⠀⇛


                       His final recourse is an appeal to the High Court
                       of Justice where, if the history of his case is any
                       indication, he’ll be told that they’re all out of
                       justice and have none for him.


                       If justice had anything to do with it, previous
                       courts would have thrown out the US extradition
                       request on grounds of both jurisdiction and treaty
                       language. The “crimes” of which Assange is accused
                       were not committed on US soil. And Article 4 of the
                       US-UK extradition treaty forbids extradition for
                       political offenses.


          o § Civil Rights/Policing⠀➾


                # ⚓ TruthOut ☛ Warren_Unveils_Bill_to_Ban_Sales_of_Health_Data
                  With_“Roe”_Overturn_Looming⠀⇛


                # ⚓ Common Dreams ☛ Supreme_Court_Ruling_Turns_Separation_of
                  Church_and_State_Into_‘Constitutional_Violation,’_Warns
                  Sotomayor⠀⇛


                       U.S. Supreme Court Justice Sonia Sotomayor on
                       Tuesday warned that the court’s right-wing majority
                       had further eroded the nation’s bedrock laws
                       separating church and government when it ruled that
                       Maine must include religious schools in a state-run
                       tuition program.


                       “Today, the court leads us to a place where
                       separation of church and state becomes a
                       constitutional violation,” wrote Sotomayor in the
                       minority’s dissent of the 6-3 decision.


                # ⚓ The Gray Zone ☛ British_security_state_collaborator_Paul
                  Mason’s_war_on_‘rogue_academics’_exposed⠀⇛


                # ⚓ The Gray Zone ☛ British_‘watchdog’_journalists_Mason_and
                  Cadwalladr_unmasked_as_security_state_lapdogs⠀⇛


                # ⚓ Counter Punch ☛ The_Southern_Baptists’_Changing_Positions
                  on_Abortion⠀⇛


                       The resolution, “On Anticipation of a Historic
                       Moment in the Pro-Life Movement,” was not without
                       controversy, however. A faction of Southern
                       Baptists who consider themselves “abortion
                       abolitionists” argued the Convention should also
                       call for the criminalizing of people who have
                       abortions as murderers. Instead, the resolution
                       calls on Southern Baptists to stand with and pray
                       for “abortion-vulnerable women.”


                       The Southern Baptist Convention, the largest
                       Protestant denomination in the U.S., and often
                       referred to as the “bellwether for conservative
                       Christianity,” has long voiced opposition to
                       abortion. A Pew survey in 2014 found that two-
                       thirds of Southern Baptists believed abortion
                       should be illegal in most or all cases. In 2021,
                       the Convention passed a resolutionstating
                       “unequivocally that abortion is murder” and calling
                       for “abolishing abortion immediately, without
                       exception or compromise.”


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Techdirt ☛ Dish’s_New_5G_Network,_Created_By_Trump
                  Regulators_To_Justify_Rubber_Stamping_T-Mobile_Merger,_Looks
                  Like_A_Silly_Dud⠀⇛


                       A few years ago the Trump DOJ and FCC rubber-
                       stamped the Sprint T-Mobile merger without heeding
                       expert warnings that it would stifle competition,
                       kill jobs and slowly raise rates. Working closely
                       with T-Mobile and Dish, the FCC and DOJ “antitrust
                       enforcers” unveiled what they claimed was a “fix”
                       for these problems: they’d cobble together a fourth
                       major replacement wireless carrier in Dish Network.


          o § Monopolies⠀➾


                # ⚓ Techdirt ☛ Senators_Ask_Amy_Klobuchar_To_Fix_The_Content
                  Moderation_Loophole_In_Her_Antitrust_Bill⠀⇛


                       We’ve been pointing out for a long time now that
                       the main antitrust bill making its way through the
                       Senate has a hidden content moderation trojan horse
                       in it. Indeed, it seems likely the main reason the
                       bill has significant Republican support is that
                       they know the bill will be abused to file vexatious
                       lawsuits over content moderation decisions,
                       attempting to get around Section 230 by claiming
                       the decisions were actually anti-competitive.
                       Senator Ted Cruz has admitted he supports the bill
                       because it will “unleash the trial lawyers” to file
                       lawsuits about content moderation against internet
                       companies.


                # ⚓ Counter Punch ☛ How_Corporate_Food_Monopolies_Caused_the
                  Baby_Formula_Scandal⠀⇛


                       The formula scarcity began when the COVID-19
                       pandemic led to a disruption of ingredient supply
                       chains and transportation delays. Then, this past
                       February, the Food and Drug Administration found
                       that several leading brands produced by Abbott
                       Laboratories were contaminated with dangerous
                       bacteria leading to a recall and a temporary
                       closure of Abbott’s main Michigan factory where
                       government inspectors found “shocking” conditions.
                       Then, just as the Michigan plant reopened,
                       torrential flooding forced it to shut down again.


                       There is nothing more important to a parent than
                       providing for their child, especially during the
                       most vulnerable, early years of their child’s life.
                       As a mother who was unable to breastfeed when my
                       children were newborns, I relied on formula and
                       remember once having to drive quite far to a store
                       in a neighboring town because my local store was
                       out of the brand I relied on and that my child was
                       used to. It was a stressful experience, one that is
                       a mild example of what millions of parents are
                       feeling right now as they face store shelves
                       emptied of formula.


                # § Copyrights⠀➾


                      # ⚓ Techdirt ☛ Twitter_Successfully_Quashes_Sketchy
                        Copyright_Subpoena_Over_Billionaire’s_Critic_On
                        Twitter⠀⇛


                             You may recall that, last fall, we wrote
                             about a truly bizarre legal fight, in which a
                             little-followed pseudonymous Twitter account
                             @CallMeMoneyBags had tweeted out some images
                             of a woman, suggesting a few times that the
                             woman was the mistress of billionaire Brian
                             Sheth. The account put out lots of tweets
                             generally mocking people in the private
                             equity space, including Sheth. Sometime after
                             the tweets including those photos, Twitter
                             received a DMCA subpoena from a company
                             called Bayside Advisory, which had basically
                             no presence online, claiming it held the
                             copyrights in those photos and demanding
                             identifying information on Money Bags.



                    ䷩ 𝚕𝚒𝚗𝚎 8123

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Gemini_version_available_♊︎


✐ Links_22/06/2022:_Flameshot_12.0.0_and_KaOS_2022.06⠀✐


Posted in News_Roundup at 2:22 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o New_Releases
          o BSD
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Events
          o Web_Browsers
                # Chromium
          o Programming/Development
    * Leftovers
          o Hardware
          o Linux_Foundation
          o Security
                # Fear,_Uncertainty,
                  Doubt/Fear-mongering/Dramatisation
                # Privacy/Surveillance
          o Finance
          o Censorship/Free_Speech
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ Apache Blog ☛ The_Apache_Software_Foundation_Announces
                  Apache_InLong_as_a_Top-Level_Project⠀⇛


                       The Apache Software Foundation (ASF), the all-
                       volunteer developers, stewards, and incubators of
                       more than 350 open source projects and initiatives,
                       announced today Apache® InLong™ as a Top-Level
                       Project (TLP).


                       Apache InLong is a one-stop integration framework
                       for massive data that provides automatic, secure,
                       and reliable data transmission capabilities. The
                       project was originally developed at Tencent in June
                       2013 and entered the Apache Incubator in November
                       2019.


                # ⚓ Help Net Security ☛ How_to_properly_adopt_and_manage
                  Kubernetes_in_production⠀⇛


                       Kubernetes is a very important technology in the
                       marketplace because vendors, ISVs, end users and
                       enterprises are all able to come together and use
                       this common infrastructure substrate to build their
                       product on.


                       In this video for Help Net Security, Alex Jones,
                       Director of Kubernetes Engineering at Canonical,
                       talks about properly adopting and managing
                       Kubernetes in production.


                # ⚓ Big_Data_on_Kubernetes:_The_End_For_Hadoop?⠀⇛


                       When data sets are too large and/or too complex for
                       traditional software to deal with, we refer to them
                       as ‘big data.’ Organizations and businesses around
                       the world need to use big data to work on projects
                       that influence the way we live now and in the
                       future.


                       Conversational AI companies want their bots to seem
                       as natural as possible. To achieve this, they must
                       process massive amounts of data in the most
                       efficient and cost-effective way possible. That’s
                       where open source ecosystems like Hadoop come in.


                # ⚓ Traefik_Labs_Adds_Hub_to_Simplify_Container_Networking_–
                  Container_Journal⠀⇛


                       Traefik Labs today unveiled a cloud service that
                       leverages agent software to simplify the
                       provisioning of network services for containers.


                       Manuel Zapf, a product manager for Traefik Labs,
                       says Traefik Hub is a software-as-a-service (SaaS)
                       platform that adds an agent to the open source
                       Traefik Proxy software. That agent makes it
                       possible to instantly authorize access to
                       containers from a single dashboard. That capability
                       eliminates the need to manually configure domain
                       name system (DNS) addresses, routing rules, access
                       control and network access translation to gain
                       access to the internet, he adds.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ How_to_install_Manjaro_21.3.0_–_Invidious⠀⇛


                       In this video, I am going to show how to install
                       Manjaro 21.3.0.


                # ⚓ Video ☛ Ubuntu_22.04_LTS_Vs_Fedora_36_|_The_BEST_Linux_OS
                  of_2022!_–_Invidious⠀⇛


                       Fedora 36 and Ubuntu 22.04 LTS, both released back
                       to back pretty at the same time. Both of these
                       distros are one of the biggest names in the Linux
                       scene. At the same time, they are radically
                       different from each other. But which among them is
                       the best? How they compare against each other?


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Linux_5.18.6⠀⇛


                       I'm announcing the release of the 5.18.6 kernel.

                       All users of the 5.18 kernel series must upgrade.

                       The updated 5.18.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.18.y
                       and can be browsed at the normal kernel.org git web
                       browser:

                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s...

                       thanks,

                       greg k-h
                # ⚓ LWN ☛ Linux_5.15.49⠀⇛


                # ⚓ LWN ☛ Linux_5.10.124⠀⇛


                # ⚓ LWN ☛ Linux_5.4.200⠀⇛


                # ⚓ ZDNet ☛ At_Open_Source_Summit,_Linus_Torvalds_hosts_another
                  fireside_chat_|_ZDNet⠀⇛


                       Once more, at The Linux Foundation’s Open Source
                       Summit, Cardano’s chief open source officer Dirk
                       Hohndel and Linux creator Linus Torvalds had a
                       wide-ranging conversation about Linux development
                       and related issues.


                       Torvalds, who hates public speaking, said that he
                       always does these presentations as interviews
                       because, “I do software. I don’t do public
                       speaking.” The hindrance being, he explained, “I
                       don’t know what people are interested in. So, Dirk
                       asks the questions and, hopefully, if he asks bad
                       questions, it’s not my fault.”


          o § Graphics Stack⠀➾


                # ⚓ The Register UK ☛ Graphical_desktop_system_X_Window_turns
                  38_•_The_Register⠀⇛


                       The X window system turned 38 years old this week,
                       and although it has more rivals than ever, it is
                       still the go-to for a graphical desktop on Unix.


                       The first public release of the X window system,
                       according to Robert W. Scheifler’s announcement,
                       was 19 June 1984.


                       X itself was a rewrite of an older windowing system
                       called W, which ran on a research microkernel OS
                       called the V-System (V→W→X, you see.) Both the V-
                       System and the W window system seem to have now
                       been lost, although Bryan Lunduke has an
                       interesting history.


                       About the only relic that you can see today, if
                       you’re curious, is the V-System manual [PDF].


                       Just two years after launch, X had already reached
                       version 10 – the oldest point release showing in
                       the release history on the X.org Foundation web
                       page. X11R1 was introduced in 1987, and with some
                       modifications, that’s what the world is still using
                       today.


                       That is quite a feat of longevity, considering that
                       that’s the same year as OS/2 1.0 came out, as well
                       as Acorn’s Archimedes range.


          o § Applications⠀➾


                # ⚓ DebugPoint ☛ Flameshot_12.0.0_Released_with_Movable_Layer,
                  New_Magnifier_and_20+_Bug_Fixes⠀⇛


                       The fantastic Flameshot screenshot tool released
                       its latest version, 12.0.0, today with many
                       exciting changes. We round up the release in this
                       post.


                # ⚓ Ubuntubuzz ☛ Video_Editors_on_Ubuntu,_FLOSS_Alternatives_to
                  Premiere_and_Movie_Maker⠀⇛


                       This is for multimedia and video editing people who
                       work with Ubuntu and seeking for free libre open
                       source software alternatives to Adobe Premiere or
                       Windows Movie Maker alike. In order to write this
                       overview article, we installed all programs on
                       Ubuntu 22.04 to show you what you can do with them.
                       We use Mandalika and Bunaken from Wonderful
                       Indonesia as video materials. Happy editing!


                # ⚓ Dedoimedo ☛ XnView_–_Small,_feisty_and_powerful⠀⇛


                       XnView is a fantastic program, overall. There are
                       some bugs and problems, of course. In my Plasma
                       desktop, the UI didn’t render perfectly – some
                       icons were low-res, some buttons didn’t have all
                       the border lines and such. The installation comes
                       with a bogus dependency warning, and the program
                       can be overwhelming to new users, due to its myriad
                       options and settings and somewhat confusing Browser
                       mode.


                       That said, once you settle in, and you invest a
                       little bit of time taming the tool, XnView can look
                       and behave the part. You can also adjust its
                       shortcuts for a much more efficient work session,
                       you have tons of filters and effects, plus you can
                       work with image metadata, and there’s a tabbed
                       interface to boot. ‘Tis a pretty solid program,
                       with lots of great features. I still do find some
                       elements a bit clunky, or not as fast or efficient
                       as I’d like them. That said, IrfanView aside, this
                       is one of the more capable and useful image viewers
                       out there. You should definitely check it out. And
                       with that, I bid you farewell.


          o § Instructionals/Technical⠀➾


                # ⚓ MakeTech Easier ☛ How_to_Fix_Ubuntu_Can’t_Open_the_Terminal
                  Issue_–_Make_Tech_Easier⠀⇛


                       You can’t get the terminal in your Ubuntu machine
                       to open. What can you do? While this issue seldom
                       happens, it is a fact that the problem exists and
                       can happen to you at anytime. Read on to learn what
                       to do when your Ubuntu machine can’t open its
                       terminal.


                # ⚓ Tips On UNIX ☛ Install_Rhythmbox_On_Ubuntu_/_Alma_Linux_&
                  Fedora_|_Tips_On_UNIX⠀⇛


                       This tutorial will be helpful for beginners to
                       Install Rhythmbox on Ubuntu 22.04 LTS, Ubuntu 20.04
                       LTS, Linux Mint 20.3, AlmaLinux 9, Rocky Linux 8,
                       and Fedora 36.


                # ⚓ H2S Media ☛ How_to_install_Apache_Tomcat_10_on_Ubuntu_22.04
                  LTS_–_Linux_Shout⠀⇛


                       Learn the steps and commands to install the latest
                       version of Apache Tomcat on Ubuntu 22.04 LTS Jammy
                       JellyFish Linux to test various Java-based
                       applications…


                       Apache Tomcat is an open-source web server that
                       allows you to run web applications written in Java.
                       Tomcat is developed and maintained by a free
                       community of developers and our Apache license is
                       published as open-source software.


                       Well, Tomcat is significantly different from the
                       Apache web server, it was developed to primarily
                       focus on Web applications. Tomcat does not
                       understand URLs as a file specification, but as a
                       notification of a user action. This is comparable
                       to event-driven programming in classic GUI
                       programming: a click on a button generates an event
                       that the window manager reports to the program.
                       Calling up a URL is analogous, be it in the form of
                       a link or a form called.


                # ⚓ Make Use Of ☛ How_to_Fix_a_Corrupted_Windows_NTFS
                  Filesystem_With_Ubuntu⠀⇛


                       How many of you have had that sinking feeling as
                       your PC boots up? You know, a slight niggle in the
                       back of your mind that says “this is taking longer
                       than usual” before Windows drops dead in front of
                       you, and refuses to play ball.


                       When it comes to fixing your broken Windows
                       install, Ubuntu has its uses there too. If you
                       happen to break your filesystem or master boot
                       record on Windows, then fear not, all is not lost.
                       You can use Ubuntu to fix issues related to the
                       Windows operating system. This technique should
                       work on any Ubuntu-based Linux distribution.


                # ⚓ RoseHosting ☛ How_to_Install_and_Secure_Tomcat_10_on
                  AlmaLinux_–_RoseHosting⠀⇛


                       In this tutorial, we are going to install Tomcat 10
                       and secure it with an SSL certificate on AlmaLinux
                       OS.


                       Tomcat is an open-source application written in
                       Java program language used for rendering Java web
                       pages and executing Java servlets. Tomcat is also
                       known as Apache Tomcat and it can be installed on
                       many Linux distributions such as Debian, Ubuntu,
                       CentOS, and of course AlmaLinux. In this tutorial,
                       we are going to install Tomcat 10 and set up a
                       reverse proxy with Apache configuration so we can
                       secure the domain with an SSL certificate.


                       Installing Tomcat 10 on AlmaLinux with Apache as a
                       reverse proxy can take up to 15 minutes. Let’s get
                       started!


                # ⚓ Ubuntu Handbook ☛ How_to_Install_The_Latest_Krita_5.0.8_in
                  Ubuntu_22.04_via_PPA_|_UbuntuHandbook⠀⇛


                       For those prefer the classic .deb package, the
                       Krita digital painting software finally available
                       to install / update through PPA for Ubuntu 22.04
                       LTS.


                       Krita has reached version 5.0.8 and being in
                       development of the next 5.1 release (in beta now).
                       For those do not like the Flatpak and AppImage that
                       run in sandbox, the .deb package has now been made
                       into the official Krita Lime PPA.


                # ⚓ TecAdmin ☛ How_to_Install_Composer_on_Ubuntu_22.04_–
                  TecAdmin⠀⇛


                       If you’re using PHP on your Ubuntu 22.04 system,
                       you may need to install Composer at some point.
                       Composer is a PHP dependency manager that can help
                       you manage your project’s dependencies in an easy
                       and efficient way. In this guide, we’ll show you
                       how to install Composer on your Ubuntu system.


                # ⚓ ID Root ☛ How_To_Install_FFmpeg_on_Fedora_36_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       FFmpeg on Fedora 36. For those of you who didn’t
                       know, FFmpeg is open-source and free software for
                       managing video, audio, and other multimedia files
                       and streams. FFmpeg compiles and runs on Linux,
                       macOS, Microsoft Windows, BSD systems, and Solaris.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the FFmpeg on a Fedora 36.


                # ⚓ Installing_MetaTrader_4_on_Linux⠀⇛


                       Installing MetaTrader 4 on a Windows system is
                       relatively easy. It is not surprising considering
                       that the desktop application was designed
                       specifically for Windows. But that makes installing
                       the application on a Linux system relatively
                       complicated. This guide explains different ways you
                       can install MetaTrader 4 on Linux.


                       The guide uses Ubuntu 22.04 LTS as an example of a
                       Linux system.


                # ⚓ News Update ☛ How_To_Install_The_Etherpad_Collaborative
                  Note-Taking_Platform_On_Linux⠀⇛


                       In these wild times, collaboration has become an
                       absolute necessity. Thankfully, there are so many
                       ways to collaborate: Every platform offers the
                       means to work together, whether it’s a desktop,
                       server, mobile or container deployment, you name it
                       and you can collaborate with it. Some of those
                       collaborative tools offer a ton of features, but
                       sometimes you want something simple — just the
                       ability to collaborate on, say, notes.


                # ⚓ TecAdmin ☛ How_to_Create_DMARC_Record_For_Your_Domain_–
                  TecAdmin⠀⇛


                       Domain-based Message Authentication, Reporting, and
                       Conformance (DMARC) is a technical specification
                       for email authentication that was developed jointly
                       by the Internet Engineering Task Force (IETF) and
                       DMARC.org. DMARC allows email senders to create
                       DMARC records in DNS that tell receivers what to do
                       if the email being sent doesn’t pass either SPF or
                       DKIM authentication checks.


                       In this blog post, we will show you how to create
                       DMARC records for your domain using DMARC.org’s
                       free DMARC reporting tool.


                # ⚓ Linux Shell Tips ☛ How_to_Change_File_Permissions_in_Linux
                  Systems⠀⇛


                       Being an expert user or administrator of a Linux
                       operating system environment requires us to have a
                       mastery of Linux file management. Everything under
                       the Linux operating system environment is regarded
                       as a file, from created or existing files and
                       folders to internal or external hardware devices
                       like USB devices.


                       Linux file management accounts for a larger
                       proportion of the Linux OS operations and starts at
                       a folder/directory level. Linux adheres to a tree-
                       like structure with a base directory that leads to
                       other sub-directories or sub-folders used to
                       maintain created or already-existing files.


                # ⚓ ID Root ☛ How_To_Install_XAMPP_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       XAMPP on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, XAMPP is a cross-platform development
                       environment consisting of Apache, MariaDB, and PHP.
                       These are all common components used in web
                       hosting, and combining them into a single
                       installation makes the initial setup less
                       complicated.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the XAMPP on Ubuntu 22.04 (Jammy
                       Jellyfish). You can follow the same instructions
                       for Ubuntu 18.04, 16.04, and any other Debian-based
                       distribution like Linux Mint.


                # ⚓ H2S Media ☛ How_to_increase_Swap_Space_in_Ubuntu_22.04_LTS
                  Jammy_–_Linux_Shout⠀⇛


                       Add the required Swap Space in Ubuntu 22.04 LTS
                       Jammy JellyFish Linux, if you think the existing
                       one is not enough on your Server or Desktop system.
                       Users can also follow this tutorial for Ubuntu
                       20.04 LTS as well.


                       Linux (like almost all other operating systems)
                       tries to keep the operating system components,
                       currently required program data, etc. in RAM (main
                       memory), since the access to the RAM is much faster
                       than to data carriers such as hard disk, CD, or USB
                       stick.


                       However, RAM has its limit of volatile space, if
                       your system has 4GB of memory then it can happen
                       many times your RAM space is allocated completely
                       when we run many programs simultaneously. At this
                       point, the Linux kernel begins to free up RAM by
                       writing parts of the data stored in RAM to the hard
                       disk, the portion of the hard disk that is
                       dedicated to this is called “Swap” memory. If the
                       data is needed again, it is loaded back into RAM
                       and other data that is not needed at the moment is
                       written to the swap. In such a case, it is also
                       said: that “the system swaps”.


                # ⚓ Red Hat Official ☛ How_to_create_a_Rust_application_on
                  OpenShift_|_Enable_Sysadmin⠀⇛


                       With the help of a container and OpenShift’s
                       “import from Git” functionality, you can onboard a
                       Rust application onto OpenShift quickly.


                # ⚓ Own HowTo ☛ How_to_Enable_Gzip_Compression_on_Nginx⠀⇛


                       In this tutorial you will learn how to enable Gzip
                       compression on Nginx.


                       Enabling gzip compression is a must because it will
                       not only make your site faster, but it will also
                       save your server’s bandwidth from getting used to
                       serve uncompressed content, this means less
                       bandwidth and a faster site served to your
                       visitors.


                # ⚓ Fedora Magazaine ☛ Using_Linux_System_Roles_to_implement
                  Clevis_and_Tang_for_automated_LUKS_volume_unlocking_–_Fedora
                  Magazine⠀⇛


                       One of the key aspects of system security is
                       encrypting storage at rest. Without encrypted
                       storage, any time a storage device leaves your
                       presence it can be at risk. The most obvious
                       scenario where this can happen is if a storage
                       device (either just the storage device or the
                       entire system, server, or laptop) is lost or
                       stolen.


                       However, there are other scenarios that are a
                       concern as well: perhaps you have a storage device
                       fail, and it is replaced under warranty — many
                       times the vendor will ask you to return the
                       original device. If the device was encrypted, it is
                       much less of a concern to return it back to the
                       hardware vendor.


                       Another concern is anytime your storage device is
                       out of sight there is a risk that the data is
                       copied or cloned off of the device without you even
                       being aware. Again, if the device is encrypted,
                       this is much less of a concern.


                       Fedora (and other Linux distributions) include the
                       Linux Unified Key Setup (LUKS) functionality to
                       support disk encryption. LUKS is easy to use, and
                       is even integrated as an option in the Fedora
                       Anaconda installer.


                # ⚓ Barry Kauler ☛ Complete_separation_between_boot-manager_and
                  EasyOS⠀⇛


                       The separation means that it looks exactly like a
                       frugal install in the image file. This makes it
                       conceptually very simple for someone to see how to
                       do a frugal install into an internal drive.
                       EasyOS no longer knows anything about the boot
                       manager or bootloader that caused it to boot. The
                       boot-partition variables BOOT_UUID, BOOT_DEV and
                       BOOT_DIR are no longer in EasyOS. All that Easy
                       knows about is where it is installed, in the
                       working-partition, variables WKG_UUID, WKG_DEV and
                       WKG_DIR.


                # ⚓ Vitux ☛ Save_Output_Of_A_Command_From_the_Debian_Terminal
                  To_A_File_–_VITUX⠀⇛


                       We all know how running a command in the Debian
                       command line, the Terminal, results in the
                       execution of the command and printing of the
                       results, if any, in the Terminal itself. Sometimes,
                       this immediate display of output is not enough,
                       especially if we want to save the output for later
                       use. Fortunately, the Linux bash and all operating
                       system bash, for that matter, is equipped with the
                       ability to print the output of a command to a
                       specified file. In this article, we will work on
                       the following two scenarios…


                # ⚓ Why_is_my_syslog-ng_disk-buffer_file_so_huge_even_when_it
                  is_empty?_–_Blog_–_syslog-ng_Community_–_syslog-ng
                  Community⠀⇛


                       Most people expect to see how many log messages are
                       waiting in the disk-buffer from the size of the
                       syslog-ng disk-buffer file.. While it was mostly
                       true for earlier syslog-ng releases, for recent
                       syslog-ng releases (3.34+) the disk-buffer file can
                       stay large even when it is empty. This is a side
                       effect of a recent syslog-ng performance tuning.


                # ⚓ Red Hat ☛ Measuring_BPF_performance:_Tips,_tricks,_and_best
                  practices_|_Red_Hat_Developer⠀⇛


                       Measuring stuff is harder than you may think. Even
                       in math, there is such a thing as non-measurable
                       sets and Banach-Tarski paradox, which shows that a
                       three-dimensional ball of radius 1 can be dissected
                       into 5 parts, which can be magically reassembled to
                       form two balls of radius 1. Now imagine what kind
                       of mess we’ve got in software engineering.


                       This may sound somewhat philosophical, so let’s get
                       down to earth and talk about BPF programs. BPF,
                       which originally stood for Berkeley Packet Filter,
                       is a general-purpose execution engine that can be
                       used for a variety of purposes, including
                       networking, observability, and security. What we’ll
                       be discussing in this article was initially called
                       extended BPF (eBPF) to differentiate from the
                       classic BPF, but now this technology is often
                       referred to as just BPF, and that’s what we’ll call
                       it here.


                       Having full visibility throughout the systems we
                       build is a well established best practice. Usually,
                       one knows which metrics to collect, and how and
                       what to profile or instrument to understand why the
                       system exhibits certain levels of performance. But
                       all of this becomes more challenging as soon as the
                       BPF layer is included. Despite years of
                       development, it is still a black box in many ways.


                       But do not despair: this article will show, with
                       some amount of creativity, that one can reveal what
                       is going on under the hood. The article will begin
                       with a userspace service that uses BPF programs
                       attached to various syscalls to inspect system
                       activity. It does the job, but what we really want
                       is to understand the overhead of the BPF programs
                       themselves. How do you look inside? That’s the
                       problem that we will ultimately tackle.


          o § Games⠀➾


                # ⚓ Boiling Steam ☛ 3500_Games_Now_On_The_Steam_Deck_with_Kao
                  the_Kangaroo_(2022)_and_Moonlighter_Verified⠀⇛


                       We are still observing a relatively low rate of
                       addition of verified/playable games for the Steam
                       Deck. We are now more than 3500 games validated
                       (3510 games to be precise at the time of
                       publication) on the Steam Deck – in two categories…


    * § Distributions and Operating Systems⠀➾


          o § New Releases⠀➾


                # ⚓ The Register UK ☛ 21.3_of_Arch_Linux_derivative_Manjaro
                  released_•_The_Register⠀⇛


                       Version 21.3 of Manjaro – codenamed “Ruah” – is
                       here, with kernel 5.15, but don’t let its beginner-
                       friendly billing fool you: you will need a clue
                       with this one.


                       Manjaro Linux is one of the more popular Arch Linux
                       derivatives, and the new version 21.3 is the latest
                       update to version 21, released in 2021. There are
                       three official variants, with GNOME 42.2, KDE
                       5.24.5 or Xfce 4.16 desktops, plus community builds
                       with Budgie, Cinnamon, MATE, a choice of tiling
                       window managers (i3 or Sway), plus a Docker image.


                       The Reg took its latest look at Arch Linux a few
                       months ago. Arch is one of the older rolling-
                       release distros, and it’s also famously rather
                       minimal. The installation process isn’t trivial:
                       it’s driven from the command line, and the user
                       does a lot of the hard work, manually partitioning
                       disks and so on.


                # ⚓ KaOS_2022.06⠀⇛


                       It is with great pleasure to present to you the
                       June release of a new stable ISO.


                       Changes were numerous and all over the place, the
                       base of the system for example, was built on a new
                       Glibc 2.35, GCC 11.3.0, and Binutils 2.38 based
                       Toolchain. Further updates in Core included DBus
                       1.14.0, Systemd 250.7, Nettle 3.8 and the kernel
                       moved to 5.17.15.
                       Midna, the Plasma theme used in KaOS received some
                       changes (partly to get ready for Plasma 5.25),
                       visual biggest change is the addition of a well-
                       integrated virtual keyboard in the login & lock
                       screen.


                # ⚓ Linuxiac ☛ KDE-Focused_KaOS_Linux_2022.06_Is_Here_with_the
                  Latest_Plasma_5.25⠀⇛


                       KaOS 2022.06 comes with the latest Plasma 5.25, the
                       latest KDE Frameworks 5.95, and the newest app set
                       provided by KDE Gear 22.04.


                       KaOS is an independent rolling-release distribution
                       inspired by Arch Linux that includes the latest KDE
                       Plasma Desktop and related Qt Toolkit-based
                       software.


                       Unlike most other Linux distros, KaOS does not
                       provide various installation images with GNOME,
                       Xfce, LXQt, or any other desktop. In other words,
                       the distro is solely dedicated to the KDE Plasma
                       desktop.


                       The distro uses Pacman as its package manager but
                       does not rely on software repositories developed
                       and maintained by Arch Linux. Instead, the software
                       is available from in-house repositories and is
                       built exclusively for 64-bit machines.


          o § BSD⠀➾


                # ⚓ TrueNAS ☛ TrueNAS_SCALE_adds_SMB_Clustering_and_HA_in_2nd
                  Major_Update_–_TrueNAS_Open_Storage_|_ZFS_for_the_Home_to_the
                  Data_Center⠀⇛


                       TrueNAS SCALE 22.02.2 (“Angelfish”) was released
                       today after the previous versions were deployed on
                       over 20,000 active systems. TrueNAS SCALE 22.02.2
                       includes the completion of SMB clustering and the
                       delivery of High Availability (HA) on TrueNAS M-
                       Series systems. This release is complemented by the
                       new functionality in TrueCommand that provides
                       wizards for creating SMB clusters.


                       TrueNAS SCALE continues with system count growth at
                       over 100% per quarter since the start of the BETA
                       process in mid 2021. There is widespread adoption
                       by Linux admins and great feedback as TrueNAS SCALE
                       matures.


                # ⚓ How_I_would_sell_OpenBSD_as_a_salesperson⠀⇛


                       Let’s have fun today. I always wondered how I would
                       sell OpenBSD licences to customers if I was a
                       salesperson.


                       This text is pure fiction and fun. The OpenBSD
                       project is free of charge and under a libre
                       software licence.


          o § SUSE/OpenSUSE⠀➾


                # ⚓ CubicleNate ☛ All-in_on_PipeWire_for_openSUSE_Tumbleweed_–
                  CubicleNate’s_Techpad⠀⇛


                       I have written about using PipeWire previously
                       where I did have a very positive experience with
                       it. Unfortunately, I did have some irritating
                       quarks with it that ultimately resulted in my going
                       back to using PulseAudio on my openSUSE Tumbleweed
                       machines. They were little things needing to
                       refresh the browser after a Bluetooth device
                       changed status. I decided it was time to try
                       PipeWire again when PulseAudio started to give me
                       random Bluetooth audio device issues where the
                       device, after connecting, would not become
                       available.


                       I have heard about many of the improvements that
                       had come to PipeWire and decided that now was the
                       time to try it out again. I revisited the
                       directions I had previously put together on the
                       installation process and sure enough it worked. I
                       did have to make one modification to it. I added a
                       now new module called pipewire-aptx which is the
                       Bluetooth aptX codec plugin.


                       If you have an installation of openSUSE Tumbleweed
                       that is using the PulseAudio sound server, the
                       command is quite simple to execute in the terminal
                       to switch you over. I have tested and verified this
                       on multiple machines with success.


          o § Fedora Family / IBM⠀➾


                # ⚓ Red Hat Official ☛ Using_convert2rhel_with_Red_Hat
                  Satellite:_walking_through_a_migration⠀⇛


                       The convert2rhel tool makes it possible to convert
                       an operating system that is CentOS or Oracle Linux
                       to Red Hat Enterprise Linux (RHEL).


                       For converting from these operating systems, the
                       supported source version is the latest one, at the
                       time of this writing it was 7.9 or 8.5.


                       For Oracle Linux there are some particularities,
                       and the kernel to be used must be the Red Hat
                       Compatible Kernel (RHCK) and not the Unbreakable
                       Enterprise Kernel (UEK) which is the default kernel
                       for all Oracle Linux.. Also Oracle marked the
                       subscription-manager package as deprecated for the
                       rhn-client-tools package in version 7.x.


                # ⚓ OpenSource.com ☛ A_site_reliability_engineer’s_guide_to
                  change_management⠀⇛


                       Infrastructure and platforms are rapidly evolving.
                       Not so long ago, infrastructure was not as complex,
                       and it was easy to manage.


                # ⚓ Enterprisers Project ☛ How_to_create_a_return-to-office
                  playbook_for_your_IT_team [Ed: Red Hat is modeling itself
                  like Microsoft?]⠀⇛


                       In February, Microsoft revealed its hybrid working
                       strategy, and last month, IBM shared its Return to
                       Workplace Playbook – a global set of standards
                       containing guidance, policies, and procedures to
                       ensure that employees can head back to the office
                       as safely and seamlessly as possible.


                # ⚓ Enterprisers Project ☛ 4_ways_digital_transformation_has
                  changed_how_business_is_done⠀⇛


                       Understanding how digital transformation has
                       changed companies both culturally and
                       technologically is allowing business leaders to
                       reevaluate their current processes and implement
                       more digital and virtual operations across HR,
                       product development, marketing, sales, and customer
                       experience.


                       Here are four things that digital transformation
                       has forever changed about the way companies
                       operate.


                # ⚓ Red Hat Official ☛ Ericsson_and_Red_Hat_empower_service
                  providers_to_build_multi-vendor_networks⠀⇛


                       Service providers are uniquely positioned to serve
                       up a new generation of immersive, personalized,
                       ultra-reliable experiences, applications and
                       solutions. Ericsson and Red Hat are expanding their
                       collaboration for validation of network functions
                       and platforms to enable service providers to bring
                       their next generation services to market faster in
                       a multi-vendor scenario.


                       Read on to find out how far we’ve come in de-
                       risking service providers’ expansion projects
                       through our technical collaborations for validation
                       of Red Hat’s platforms for Ericsson’s network
                       functions.


          o § Debian Family⠀➾


                # ⚓ Daniel Pocock ☛ Daniel_Pocock:_Using_the_Debian_trademark
                  for_good⠀⇛


                       At the Software Freedom Institute, we were a little
                       bit shocked to receive the trademark so quickly, it
                       almost caught us off guard.


                       Nonetheless, after a few days careful
                       contemplation, it became clear in my mind how I
                       should use the powers that come with the trademark.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ 9to5Linux ☛ Ubuntu_Touch_OTA-23_Is_Coming_on_June_28th_with
                  FM_Radio_Expansion,_Lomiri_Fixes⠀⇛


                       
                       Scheduled for release next week on June 28th, 2022,
                       the Ubuntu Touch OTA-23 software update will still
                       be based on the Ubuntu 16.04 (Xenial Xerus)
                       operating system series and promises FM Radio
                       expansion on most BQ devices and the Poco X3 NFC
                       smartphone, improved sound playback during device
                       sleep, as well as wireless display support for
                       Halium 9 and later devices.


                # ⚓ Linux_Lite_6.0_Based_On_Ubuntu_22.04_LTS_Released_|
                  Itsubuntu.com⠀⇛


                       The latest version of Linux Lite 6.0 which is based
                       on Ubuntu 22.04 LTS is now available for download.
                       Linux Lite 6.0 is powered by Linux kernel 5.15, and
                       you will find the Xfce 4.16 desktop environment.
                       Google Chrome is now the default web browser in
                       Linux Lite 6.0.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Orbbec_Femto_ToF_camera_enables_accurate_3D
                  object_and_scene_capture⠀⇛


                       The camera supports the same Orbbec SDK as used
                       with earlier models such as the Persee+ 3D AI
                       camera and that works with hosts running Android,
                       Linux, or Windows. Femto 3D cameras should offer
                       higher accuracy and lower latency than earlier
                       structured light cameras from the company, and be
                       especially useful to track human forms, measure
                       small live objects, and implement obstacle
                       avoidance and/or gesture recognition algorithms.


          o § Open Hardware/Modding⠀➾


                # ⚓ CNX Software ☛ Imagination_unveils_IMG_RTXM-2200_32-bit
                  RISC-V_real-time_“Catapult”_CPU_–_CNX_Software⠀⇛


                       Imagination IMG RTXM-2200 32-bit RISC-V real-time
                       CPU core is the first member of the company’s
                       Catapult family comprised of four distinct RISC-
                       V families for dynamic microcontrollers, real-time
                       embedded CPUs, high-performance application CPUs,
                       and functionally safe automotive CPUs.


                       The company says it’s a highly scalable real-time,
                       deterministic, 32-bit embedded CPU, that is
                       feature-rich and flexible in design for mainstream
                       devices, but, excuse the pun, leaves most of the
                       details to your imagination…


                # ⚓ Arduino ☛ Monitoring_IV_fluid_bag_levels_with_the_Arduino
                  Portenta_H7_and_Vision_Shield⠀⇛


                       When a patient is receiving intravenous (IV)
                       fluids, it is vital that air is not introduced into
                       the line, as its presence can create issues such as
                       excessive pressure or even embolisms that can be
                       life-threatening. Normally, the level of fluids
                       remaining within the bag is periodically checked by
                       a nurse, but due to challenges related to staffing,
                       this might not be enough. Therefore, Manivannan
                       Sivan devised an automated monitoring system that
                       uses computer vision along with machine learning to
                       do this repetitive task instead of a person.


                       To begin the project, Sivan gathered a series of
                       images that spanned three categories with an
                       Arduino Portenta H7 and Vision Shield. Within each
                       picture, the IV fluid bag is 15cm away and contains
                       either an adequate, less than 50%, or low level of
                       fluid remaining. Once trained, his model was able
                       to successfully recognize the correct level around
                       96% of the time, although additional images taken
                       at different light levels would help improve the
                       accuracy even more.


                # ⚓ CNX Software ☛ ESP32-C5_RISC-V_IoT_MCU_supports_dual-band
                  WiFi_6,_Bluetooth_5.0_LE_–_CNX_Software⠀⇛


                       Espressif Systems ESP32-C5 is an upcoming wireless
                       RISC-V microcontroller for IoT applications that
                       supports dual-band (2.4 & 5.0 GHz) WiFi 6
                       connectivity as well as Bluetooth 5.0 LE.


                       It is the first dual-band processor from Espressif,
                       as while the Shanghai-based company previously
                       announced the ESP32-C6 WiFi 6 and Bluetooth 5 LE
                       RISC-V SoC last year, it only supports 2.4 GHz
                       frequency. Note it’s not the first dual-band WiFi 6
                       IoT chip on the market as NXP introduced the IW612
                       Wi-Fi 6, Bluetooth 5.2, 802.15.4 tri-radio solution
                       last January, but ESP32-C5 should target different
                       use cases.


                # ⚓ peppe8o ☛ SG90_Servo_Motor_Interfacing_with_Arduino_Uno⠀⇛


                       To control a motion within specified degrees, such
                       as turning a robot, the SG90 servo motor is a
                       widely used device with Arduino, as this motor can
                       rotate up to 180 degrees


                       In this tutorial, we’ll connect and use an SG90
                       servo motor with Arduino Uno. This tutorial
                       provides the coding, wiring diagram and component
                       list. We’ll learn how to use the servo motor to
                       perform 0 to 180 degrees movement by using Arduino
                       programming.


    * § Free, Libre, and Open Source Software⠀➾


          o § Events⠀➾


                # ⚓ Hack_Week_starts_Hacking_for_Humanity_next_week⠀⇛


                       The coveted Hack Week 21 runs from June 27 to July
                       1 and has both virtual and physical participation
                       elements. Hack Week is put on for openSUSE
                       contributions and gives any open-source contributor
                       and SUSE employees a playground to experiment,
                       innovate, collaborate and learn for an entire week.


                       People all over the world can create, view or join
                       projects on hackweek.opensuse.org. The projects
                       range from the packaging of freeware games to
                       improving full-disk encryption and from learning
                       network related knowledge to writing a
                       software.opensuse.org replacement. There is even a
                       project using solar panels to regulate water
                       heating. There are more than 80 projects for this
                       year’s Hack Week.


          o § Web Browsers⠀➾


                # § Chromium⠀➾


                      # ⚓ CISA ☛ Google_Releases_Security_Updates_for_Chrome_|
                        CISA⠀⇛


                             Google has released Chrome version
                             103.0.5060.53 for Windows, Mac, and Linux.
                             This version addresses vulnerabilities that
                             an attacker could exploit to take control of
                             an affected system.


          o § Programming/Development⠀➾


                # ⚓ Better_diagnostics_with_Performance_Co-Pilot⠀⇛


                       This article is intended to help Oracle Linux users
                       get a basic understanding of Performance Co-Pilot
                       (PCP) and it’s commands and architecture. PCP will
                       be replacing the legacy tool OSWatcher as Oracle’s
                       recommended tool for diagnosing and tuning Oracle
                       Linux systems.


                # ⚓ Sourceware_–_GNU_Toolchain_Infrastructure_roadmap⠀⇛


                       Sourceware, https://sourceware.org/, is community
                       run infrastructure, mailinglists, git, bug
                       trackers, wikis, etc. hosted in the Red Hat Open
                       Source Community Infrastructure Community Cage
                       together with servers from e.g. Ceph, CentOS,
                       Fedora and Gnome.


                       Sourceware is mainly known for hosting the GNU
                       Toolchain projects, like gcc at https://
                       gcc.gnu.org/, glibc, binutils and gdb. But also
                       hosts projects like annobin, bunsen, bzip2, cgen,
                       cygwin at https://cygwin.org/, debugedit, dwz,
                       elfutils at http://elfutils.org, gccrs, gnu-abi,
                       insight, kawa, libffi, libabigail, mauve, newlib,
                       systemtap and valgrind at https://valgrind.org/.


                       A longer list of Sourceware projects, those without
                       their own domain name, including several dormant
                       projects, can be found here: https://
                       sourceware.org/mailman/listinfo.


                       Most of these projects use a email/git based
                       workflow using mailinglists for discussing patches
                       in preference to web based “forges”.


                # ⚓ LinuxSecurity ☛ Web_App_Vs._Progressive_Web_App:_How_Are
                  They_Different?⠀⇛


                       Wondering what is the difference between regular
                       web apps and progressive ones? Hopefully, this
                       article shed more light on the features they come
                       with. Progressive web apps or PWAs are developed
                       using the same technology stack. You need both
                       front-end and back-end technologies to build it,
                       but also a few frameworks. But the differences are
                       immense.


    * § Leftovers⠀➾


          o ⚓ Tedium ☛ 10_Social_Networks_That_Didn’t_Make_It⠀⇛


                 The website Orkut.com is a site you’ve probably visited
                 even if it feels like a vague memory today. It is
                 Google’s first attempt at a social network, and one that
                 became a success largely by chance; it started with
                 modest goals and grew pretty quickly, although it never
                 reached Facebook scale. Named for its creator, Orkut
                 Büyükkökten, the network surged for a time, but
                 eventually fell into decay, eventually going offline in
                 2014. After a few years of attempting to build a follow-
                 up network, Orkut is back on that original domain,
                 promising a follow-up. “I’ve always believed that a
                 friendship is more than a friend request, and I have
                 dedicated my life to helping millions of you build
                 authentic connections with your neighbors, family
                 members, employees and the beautiful strangers who come
                 into your lives,” he wrote. You kind of want to root for
                 Orkut Büyükkökten, knowing that the odds are against him
                 in reviving this old social network in a new way. But
                 it’s in his spirit that I shine the “didn’t make it” list
                 on social media. Even if the community is dead, the
                 people that made it are still worth discussing.


          o ⚓ On_Hork-Bajir_language⠀⇛


                 Someone whose blog I follow has been posting about how
                 the portrayal of the Hork-Bajir in Animorphs isn’t really
                 internally consistent. If you’re unfamiliar, they’re
                 these huge biped dinosaur-bird guys. No feathers, but
                 they have horns on their heads and blades growing out of
                 their arms and legs.


                 (They’re pacifist herbivores. The blades are for
                 stripping bark from trees to eat.)


                 And they’re portrayed as this kind of stupid, noble-
                 savage stereotype. Except for the once-in-a-generation
                 mutation they call “seers”, who have intelligence on par
                 with the ~smart~ species in the series. One weird moment
                 in “The Hork-Bajir Chronicles” is when the seer Dak Hamee
                 is making little stick-drawings in the ground and tells
                 his friend Jagil Hullan “hey look it’s you” and Jagil is
                 like “what no that’s not me, I’M me”. The whole conceit
                 of the book is that a Hork-Bajir is telling this story to
                 one of the Animorphs! Can they or can they not recognize
                 representations?


          o § Hardware⠀➾


                # ⚓ The New Stack ☛ Chip_Maker_CEOs_Frustrated_as_$52_Billion
                  Chip_Bill_Stalls_–_The_New_Stack⠀⇛


                       It has been a little more than two years since the
                       CHIPS for America Act , which would strengthen the
                       U.S. semiconductor industry act, was proposed, but
                       it has now stalled, and the top chipmakers are
                       getting frustrated.


                       The bill would open up $52 billion in funding to
                       bolster the chip manufacturing, supply chain, and
                       research and development infrastructure in the
                       United States. The bill was introduced in response
                       to chip shortages, with some car makers shutting
                       down assembly plants due lack of components or
                       halting production of specific models.


          o § Linux Foundation⠀➾


                # ⚓ FOSSLife ☛ Open_Programmable_Infrastructure_Project
                  Announced [Ed: OPI outsourced to Microsoft proprietary
                  software of course...]⠀⇛


                       The Linux Foundation has announced the Open
                       Programmable Infrastructure (OPI) Project, which
                       will work to foster an open, standards-based
                       ecosystem for architectures and frameworks based on
                       data processing unit (DPU) and information
                       processing unit (IPU) technologies.


                # ⚓ LinuxInsider ☛ Open-Source_Technologies,_Issues_on_Display
                  at_Linux_Foundation_Summit_|_LinuxInsider⠀⇛


                       The Linux Foundation is holding one of its most
                       expansive physical and virtual showcases this week
                       at its Open Source Summit North America 2022 in
                       Austin, Texas.


                       The event is a staging ground for some of the most
                       important announcements and cutting-edge topics
                       touching open source today.


                       LF built the Summit as an umbrella for the open-
                       source projects and technologies that are
                       fundamental across software and other industries.
                       It highlighted those that are poised for growth and
                       widespread use.


                # ⚓ FOSSLife ☛ How_to_Develop_an_Open_Source_Strategy [Ed:
                  We’re meant to think Microsoft-funded_anti-FOSS_shills are
                  those who should be lecturing us. That’s the “Linux
                  Foundation club”… since when is Forrester an expert in “Open
                  Source”?]⠀⇛


                       When setting goals and shaping your plan, you also
                       need to set up your organization for success.


                # ⚓ Linux Foundation’s Site/Blog ☛ Open_Source_Technology
                  Careers_Become_More_Lucrative_as_Open_Source_Software_Becomes
                  Dominant_and_Talent_Gaps_Persist [Ed: Pushing the “talent
                  gap” with edX 1, 2]; edX should rebrand, maybe adX. The
                  employment crisis isn’t a “skills shortage” or “labour
                  shortage” crisis but a crisis of underpaid workers whose
                  skills are lied about to lower the salaries further, then
                  laying them off and blaming it on them (“Great Resignation”).
                  In some countries real unemployment rate is about 50%. Linux
                  Foundation is a front_group_for_billionaires, oppressing the
                  community that did all the work free of charge. Linux
                  Foundation is led by chronic liars who forge/fabricate their
                  qualifications. It’s the LIE-NOX Foundation.]⠀⇛


          o § Security⠀➾


                # ⚓ LWN ☛ Security_updates_for_Wednesday_[LWN.net]⠀⇛


                       Security updates have been issued by Debian (exo
                       and ntfs-3g), Fedora (collectd, golang-github-cli-
                       gh, grub2, qemu, and xen), Red Hat (httpd:2.4,
                       kernel, and postgresql), SUSE (drbd, fwupdate,
                       neomutt, and trivy), and Ubuntu (apache2, openssl,
                       openssl1.0, and qemu).


                # ⚓ USCERT ☛ CISA_Releases_Security_Advisories_Related_to_OT:
                  ICEFALL_(Insecure_by_Design)_Report⠀⇛


                       CISA is aware that Forescout researchers have
                       released OT:ICEFALL, a report on 56 vulnerabilities
                       caused by insecure-by-design practices in
                       operational technology across multiple vendors. The
                       vulnerabilities are divided into four main
                       categories: insecure engineering protocols, weak
                       cryptography or broken authentication schemes,
                       insecure firmware updates and remote code execution
                       via native functionality.


                # ⚓ Useful_web_hosting_tips_that_can_help_secure_your_site⠀⇛


                       Website security is about preparing for the worst
                       if applied security mechanisms fail. After all,
                       protecting your site from every threat on the book
                       can be laborious. However, it does not mean website
                       owners should not try. It simply refers to the two
                       sides of the coin: preventing attacks or other
                       interruptions and mitigating successful ones.


                       Thus, it might be an excellent idea to review the
                       security of your business website to ensure you
                       don’t end up a victim of vicious attacks.
                       Considering that, here are the top 7 definitive web
                       hosting tips to help secure your site for the
                       foreseeable future.


                # ⚓ Linux Foundation’s Site/Blog ☛ Free_Training_Course_Teaches
                  How_to_Secure_a_Software_Supply_Chain_with_Sigstore [Ed:
                  OpenSSF (former_Microsoft) telling you to deny people who
                  want to run applications of their choice; they call that
                  “security”]⠀⇛


                # ⚓ Linux Foundation’s Site/Blog ☛ Learn_the_Principles_of
                  DevSecOps_in_New,_Free_Training_Course [Ed: This is what
                  Zemlin et al are 'teaching']⠀⇛


                       At the most basic level, there is nothing
                       separating DevSecOps from the DevOps model.
                       However, security, and a culture designed to put
                       security at the forefront has often been an
                       afterthought for many organizations. But in a
                       modern world, as costs and concerns mount from
                       increased security attacks, it must become more
                       prominent. It is possible to provide continuous
                       delivery, in a secure fashion. In fact, CD enhances
                       the security profile. Getting there takes a
                       dedication to people, culture, process, and lastly
                       technology, breaking down silos and unifying multi-
                       disciplinary skill sets. Organizations can optimize
                       and align their value streams towards continuous
                       improvement across the entire organization.


                # ⚓ USCERT ☛ Keeping_PowerShell:_Measures_to_Use_and_Embrace
                  [Ed: Has CISA become a "damage control" or PR department of
                  Microsoft?]⠀⇛


                       Cybersecurity authorities from the United States,
                       New Zealand, and the United Kingdom have released a
                       joint Cybersecurity Information Sheet (CIS) on
                       PowerShell. The CIS provides recommendations for
                       proper configuration and monitoring of PowerShell,
                       as opposed to removing or disabling it entirely due
                       to its use by malicious actors after gaining access
                       into victim networks. These recommendations will
                       help defenders detect and prevent abuse by
                       malicious cyber actors, while enabling legitimate
                       use by administrators and defenders.


                # ⚓ The Register UK ☛ For_a_few_days_earlier_this_year,_rogue
                  GitHub_apps_could_have_hijacked_countless_repos⠀⇛


                       A GitHub bug could have been exploited earlier this
                       year by connected third-party apps to hijack
                       victims’ source-code repositories.


                       For almost a week in late February and early March,
                       rogue applications could have generated scoped
                       installation tokens with elevated permissions,
                       allowing them to gain otherwise unauthorized write
                       or administrative access to developers’ repos. For
                       example, if an app was granted read-only access to
                       an organization or individual’s code repo, the app
                       could effortlessly escalate that to read-write
                       access.


                       This security blunder has since been addressed and
                       before any miscreants abused the flaw to, for
                       instance, alter code and steal secrets and
                       credentials, according to Microsoft’s GitHub, which
                       assured The Register it’s “committed to
                       investigating reported security issues.”


                       This is good news, because according to Aqua
                       Security researchers, exploitation would have had a
                       massive impact on “basically everyone.” In effect,
                       this is a near hit for the industry as miscreants
                       could have exploited the hole to exfiltrate cloud
                       credentials from private repos or potentially
                       tamper with software projects.


                # § Fear, Uncertainty,
                  Doubt/Fear-mongering/Dramatisation⠀➾


                      # ⚓ Bruce Schneier ☛ Symbiote_Backdoor_in_Linux [Ed:
                        Bruce Schneier continues to repeat talking points and
                        misuse the term "backdoor" (it's not a back door, it is
                        malware)]⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ Euractive ☛ EU_court_limits_air_travel_surveillance
                        to_the_‘strictly_necessary’_–_EURACTIV.com⠀⇛


                             The European Court of Justice ruled on
                             Tuesday (21 June) that the EU’s Passenger
                             Name Record (PNR) directive must be curtailed
                             to be compatible with fundamental rights.


                             The PNR directive was adopted in 2016,
                             introducing a mechanism whereby airlines had
                             to hand to national authorities the data of
                             all the passengers that enter or exit the
                             European Union with the aim of preventing,
                             detecting or investigating terrorist
                             activities and serious crimes.


                             The directive allows member states to extend
                             the same screening procedures also to flights
                             from other EU countries, provided that they
                             inform the European Commission. All EU
                             countries except Austria and Ireland notified
                             the Commission of their intention to do that.


                             In Belgium, the transposition of the
                             directive into national law was contested by
                             the Ligue des droits humains, which filed an
                             action for annulment before the Belgian
                             Constitutional Court in July 2017. The NGO
                             accused the legislation of introducing
                             generalised surveillance that infringes on
                             the fundamental rights to privacy and data
                             protection.


          o § Finance⠀➾


                # ⚓ The_Coming_Recession_and_Twitch⠀⇛


                       With all of this inflation that the world has been
                       seeing the last while, it has resulted in various
                       central banks tightening policy in order to stamp
                       it out. The Federal Reserve in America appears to
                       be getting particularly aggressive with this. Now
                       economists are predicting a recession is likely on
                       the horizon as a result of all this. The Fed seems
                       willing to go to great lengths to create demand
                       destruction and stamp out inflation. This got me
                       wondering about just how the Web will weather such
                       a recession. Looking back on history, such economic
                       downturns have not been kind to the Web. The
                       fallout of the Dot Com crash was very painful. What
                       happened in the wake of the 2008 recession saw a
                       pretty big changing of the guard in terms of what
                       the dominant sites on the Web were. Even smaller
                       events like the “Ad-pocolypse” on YouTube caused
                       significant pain for people who post videos there.
                       Now we’re back to a possible large scale, system-
                       wide economic slowdown, and it’s not hard to
                       imagine that the Web will be in for quite the
                       enema.


                       This brings me to how Twitch in particular will or
                       won’t get by. Over the last year or so, it has
                       become obvious that their corporate overlords at
                       Amazon want Twitch to get serious about making a
                       profit.


          o § Censorship/Free Speech⠀➾


                # ⚓ Video ☛ How_to_Bypass_Internet_Censorship_–_Invidious⠀⇛



                    ䷩ 𝚕𝚒𝚗𝚎 9756

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Gemini_version_available_♊︎


✐ Links_22/06/2022:_Microsoft’s_Very_Long_Downtimes_and_Games_Ported_to_GNU/
Linux⠀✐


Posted in News_Roundup at 3:54 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
          o Programming/Development
                # Shell/Bash/Zsh/Ksh
    * Leftovers
          o Hardware
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Monopolies
                # Copyrights
    * § GNU/Linux⠀➾


          o § Instructionals/Technical⠀➾


                # ⚓ TecMint ☛ How_to_Install_Software_Packages_via_YUM/DNF
                  Using_RHEL_9_DVD⠀⇛


                       Linux has always been known for its flexibility and
                       installing packages from ISO is one of them. There
                       are many use cases when a user wants to use ISO/DVD
                       for downloading packages.


                       In this guide, we are not just going to show you
                       how you can set up ISO for downloading packages but
                       also what are those scenarios when installing
                       packages from ISO can be quite helpful.


                # ⚓ TecMint ☛ How_to_Install_MySQL_8_in_Fedora_36_Linux⠀⇛


                       MySQL is one of the oldest and most reliable open-
                       source relational database management systems which
                       is trusted and used by millions of users on daily
                       basis. Since Fedora has recently announced their
                       new version of the flagship distribution, we are
                       going to cover how you can easily install MySQL 8
                       in Fedora 36.


                       Throughout this tutorial, we are going to utilize
                       the default Fedora repositories so we can make this
                       installation process as simple as it can be.


                # ⚓ Rachel ☛ More_on_geo-tagging_photos_with_a_time_element⠀⇛


                       Some readers have written in with questions about
                       my photo geotagging post from last week. One common
                       question is whether the place name has ended up in
                       the file’s metadata somehow. The answer is: I don’t
                       think so. I did an “export as original” on the
                       photo in question and ran it through a bunch of
                       exif dumper tools and didn’t find anything that
                       suggested a name like that.


                # ⚓ Trend Oceans ☛ shred_command:_makes_files_unrecoverable_in
                  Linux_–_TREND_OCEANS⠀⇛


                       Are you still removing your files containing
                       sensitive information (ssh keys, account password,
                       auth file, etc) using the standard way?


                # ⚓ LinuxConfig ☛ How_to_install_Monero_Wallet_on_Linux_(GUI_&
                  CLI)⠀⇛


                       Monero is a cryptocurrency that is decentralized
                       and has a primary focus on user privacy. To get
                       started using Monero, you will first need a Monero
                       Wallet. The Monero Wallet is available for Linux
                       systems, whether you are running a GUI or just
                       command line only. It is open source and free to
                       use.


                       In this tutorial, we will go through the step by
                       step instructions of downloading Monero Wallet
                       (both the GUI and CLI versions), verifying the
                       download, and installing the Monero Wallet
                       application on all major Linux distros.


                # ⚓ Techtown ☛ How_to_install_CakePHP_on_Rocky_Linux_8_/_Alma
                  Linux_8⠀⇛


                # ⚓ LinuxConfig ☛ GNOME_login_as_root⠀⇛


                       In this tutorial, you will see how to enable root
                       login for the GNOME desktop environment on a Linux
                       system. By default, users are expected to log in to
                       the GNOME desktop environment using a normal
                       account. This is a recommended practice due to
                       security concerns. If you wish to ignore this
                       recommendation and log in to GNOME with the root
                       account, keep reading below.


                # ⚓ LinuxConfig ☛ Check_GNOME_version⠀⇛


                       The GNOME desktop environment is one of the most
                       well known and popular GUIs for Linux systems. Many
                       Linux distributions such as Ubuntu and Fedora even
                       have it preinstalled on their default downloads. In
                       this tutorial, you will learn how to check the
                       installed version of GNOME desktop environment via
                       command line and GUI on any Linux system.


                # ⚓ LinuxConfig ☛ How_to_check_battery_life_on_Ubuntu⠀⇛


                       If you are running Ubuntu Linux on a laptop, there
                       are a few different ways that you can monitor the
                       battery life of your system. Ubuntu makes this easy
                       to do in the default GNOME desktop environment, but
                       it is also possible to check the battery life from
                       command line. In this tutorial, you will learn
                       several methods to check the battery life on
                       Ubuntu.


                # ⚓ Linux Shell Tips ☛ How_to_Find_User’s_Home_Directory_in
                  Linux_or_Unix⠀⇛


                       Under a Linux operating system distribution
                       environment, a created/existing system user is
                       associated with a Home directory. The configuration
                       of the Home directory ensures that the files
                       belonging to the currently active Linux user are
                       only accessible to that user unless this user
                       switches to another user account where they will
                       access the Home directory of that switched user.


                       The files under a Linux Home user directory are
                       specific to the currently active users. The base
                       directory of the Linux operating system is the root
                       (/) directory.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Despot’s_Game:_Dystopian_Army_Builder_to
                  leave_Early_Access_this_‘Summer’⠀⇛


                       Despot’s Game: Dystopian Army Builder is a great
                       little auto-battler with dungeon crawling that
                       allows you to build up a truly ridiculous
                       combination of characters and it’s getting ready to
                       leave Early Access. Sent out today was word that
                       the 1.0 release is fast approaching, with an expect
                       release “this summer”.


                # ⚓ GamingOnLinux ☛ Horror_mystery_visual_novel_Five_Stages_of
                  Pink_now_supported_on_Linux⠀⇛


                       Five Stages of Pink is a horror mystery adventure
                       presented in a visual novel / interactive fiction
                       form and it actually looks pretty great. The
                       developer also just put up a Native Linux version
                       if that interests you. The first part is also free,
                       with another part due out sometime soon.


                # ⚓ GamingOnLinux ☛ FOUNTAINS_is_a_promising_looking
                  metroidvania_action-RPG_with_a_demo_up⠀⇛


                       Featuring some pretty great looking pixel-art, the
                       in-development action-RPG metroidvania FOUNTAINS
                       has a demo available with Native Linux support you
                       can try right now.


                # ⚓ GamingOnLinux ☛ Erannorth_Chronicles_gets_fixed_up_for
                  Steam_Deck⠀⇛


                       Erannorth Chronicles, what the developer says
                       blends together an old-school card game with
                       tabletop RPG-like progression recently had an
                       upgrade to make it work nicely on the Steam Deck.


                # ⚓ GamingOnLinux ☛ Comedy_point_and_click_adventure_A_Twisted
                  Tale_has_a_demo_and_Kickstarter_live⠀⇛


                       Full of loony characters, unexpected twists and
                       challenging riddles A Twisted Tale looks like
                       another interesting point and click adventure
                       coming with Native Linux support.


                # ⚓ GamingOnLinux ☛ Missed_your_Steam_Deck_email?_Valve
                  confirms_a_grace_period_to_still_get_one⠀⇛


                       Given how busy some of us are, it can still be
                       quite easy to miss that Steam Deck email coming in
                       to make your purchase through the reservation
                       system. The good news is, you do actually have a
                       few extra days after the timer is up.


    * § Distributions and Operating Systems⠀➾


          o § Open Hardware/Modding⠀➾


                # ⚓ Hackaday ☛ A_Simple_RP2040-Based_Audio_DSP_Board⠀⇛


                       If you’re one of those people who got into building
                       electronics for the purpose of making music, then
                       this Raspberry Pi RP2040-based audio DSP project by
                       [DatanoiseTV] might be of interest. Provided is a
                       FreeRTOS template application for creating Eurorack
                       compatible synthesizers, effects processors, and
                       similar DSP-based audio widgets.


    * § Free, Libre, and Open Source Software⠀➾


          o § Web Browsers⠀➾


                # ⚓ Seth Michael Larson ☛ Get_paid_to_contribute_to_urllib3⠀⇛


                       Spotify announced the recipients of the 2022
                       Spotify FOSS Fund and urllib3 was among the 8
                       projects receiving funding. urllib3 was awarded
                       €13,000 from the total fund of €100,000. In the
                       announcement post it was noted that Spotify had
                       over 2400 dependencies and 59 nominations from
                       staff which were narrowed down to 18 which met
                       eligibility criteria and finally 8 projects which
                       received funding.


          o § Programming/Development⠀➾


                # ⚓ Steve Kemp ☛ Writing_a_simple_TCL_interpreter_in_golang⠀⇛


                       Recently I was reading Antirez’s piece TCL the
                       Misunderstood again, which is a nice defense of the
                       utility and value of the TCL language.


                       TCL is one of those scripting languages which used
                       to be used a hell of a lot in the past, for
                       scripting routers, creating GUIs, and more. These
                       days it quietly lives on, but doesn’t get much
                       love. That said it’s a remarkably simple language
                       to learn, and experiment with.


                       Using TCL always reminds me of FORTH, in the sense
                       that the syntax consists of “words” with
                       “arguments”, and everything is a string (well, not
                       really, but almost. Some things are lists too of
                       course).


                # ⚓ Ruben Schade ☛ Web_design_101:_field_order_matters⠀⇛


                       The modern web is replete with such examples, where
                       convention is discarded for stylistic reasons, or
                       through insufficient user testing. We wouldn’t
                       fault someone for being confused by a screwdriver
                       with a bit on the same end as the handle, yet such
                       inaccessible design passes muster on the web.


                # § Shell/Bash/Zsh/Ksh⠀➾


                      # ⚓ Been_there,_done_that⠀⇛


                             Yet, I’d like yet another layer: semantic
                             “bookmarking” of history entries, so that I
                             can memorize an important command for later.
                             What is particularly important, I want to be
                             able to “tag” it with something concise,
                             instead of having to rely on a fuzzy match of
                             a part of the command to find it.


    * § Leftovers⠀➾


          o ⚓ Telex (Hungary) ☛ The_German_ultra-hiker_whose_favourite_trail_is
            in_Hungary⠀⇛


                 Christine Thürmer is probably the woman who has walked
                 the most kilometres around the world. The former manager
                 has spent most of the last few years sleeping in tents,
                 washing in cold streams and making rain pants out of bin
                 bags. We asked her about her favourite European hiking
                 trail, the National Blue Trail in Hungary but then a lot
                 of other things came up as well.


          o ⚓ The Nation ☛ Rainbow_Sleeves⠀⇛


          o ⚓ The Nation ☛ The_World-Making_Aesthetic_of_Hong_Sangsoo⠀⇛


                 Few contemporary filmmakers have been as prolific as the
                 Korean director Hong Sangsoo, who has produced an average
                 of one film per year for the past 26 years, since his
                 volcanic debut, The Day a Pig Fell Into the Well, in
                 1996. On their surface, Hong’s films appear like chamber
                 plays, centering on the cultural class of South Korea and
                 skewering the whims, hypocrisies, desires, and anxieties
                 of urbane artists and intellectuals as they frequent
                 cafés, bars, restaurants, and hotels. Yet in Hong’s
                 peculiar and distinctive treatment, these mundane-seeming
                 dramas are continuously bifurcated and atomized, often
                 stopping and starting up again with only the slightest
                 variations between sequences: a spoon instead of a fork
                 dropped at a restaurant, or even a repeated gesture or
                 tone uttered with slight differences. Episodic and
                 elliptical, Hong’s films more closely resemble paper
                 cuttings, whereby an image comes into shape only through
                 the removal of interstitial space.


          o ⚓ Hackaday ☛ Edging_Ahead_When_Learning_On_The_Edge⠀⇛


                 “With the power of edge AI in the palm of your hand, your
                 business will be unstoppable.”


          o § Hardware⠀➾


                # ⚓ GamingOnLinux ☛ Looks_like_Valve_are_gearing_up_for_a_new
                  ‘Deckard’_VR_Headset⠀⇛


                       We’ve sort-of known for a while that Valve were
                       working towards a next-generation VR headset to
                       succeed the Valve Index and we’ve now seen a lot
                       more supporting evidence that it’s getting closer.


                # ⚓ uni Toronto ☛ Modern_HDDs_have_gotten_somewhat_better_than
                  they_used_to_be⠀⇛


                       Recently we got some 20 TB HDDs to become the
                       future data storage for our Prometheus metrics
                       system, which is outgrowing its current mirrored
                       pair of 4 TB HDDs. For reasons somewhat beyond the
                       scope of this entry, I’m not doing an in-place
                       storage upgrade; instead I put the 20 TBs into the
                       new Ubuntu 22.04 server that will take over as our
                       Prometheus server and built a Linux software RAID
                       mirror. When you build new Linux software RAID
                       mirrors, they need to resync. I was curious to how
                       long this would take, so I looked at /proc/mdstat,
                       which gave me both an estimated time (which
                       amounted to about 24 hours) and a current data
                       rate, which it said was around 220,000K/sec.


          o § Proprietary⠀➾


                # ⚓ Computer World ☛ Cloudflare_outage_brings_hundreds_of
                  sites,_services_temporarily_offline⠀⇛


                       The company faced similar issues last week when an
                       outage in the India region caused several services
                       including Discord, Shopify, Canva and GitLab to
                       suffer from network performance issues across
                       India, Indonesia and Eastern Europe.


                # ⚓ The Independent UK ☛ Microsoft’s_Outlook_email_taken_down
                  by_global_internet_outage⠀⇛


                       According to website monitoring service Down
                       Detector, affected users are seeing messages
                       telling them they have been unable to connect to a
                       server, and are struggling to connect to the
                       service from across a range of devices.


                       The monitoring service showed it began receiving
                       reports of problems at around 9am on Tuesday.


                # ⚓ The Scotsman ☛ Microsoft_Outlook_outage:_Email_service_down
                  with_company_working_on_fix_after_service_inaccessible⠀⇛


                       However, the outage appears to be unrelated to an
                       issue at web infrastructure firm Cloudflare which
                       took a large number of popular websites offline
                       earlier on Tuesday morning.


                # ⚓ The Hill ☛ Former_NSA_chief_warns_of_Russian_cyberattacks
                  against_US_financial_sector⠀⇛


                       Alexander made his remarks during a cyber webinar
                       hosted by IronNet, a cybersecurity firm founded and
                       led by the retired general. Alexander was joined by
                       other panelists who discussed several key issues,
                       including how nation-state threat actors such as
                       Russia will use cyber as a weapon to target banks
                       and other financial institutions.


                       Following the invasion of Ukraine, the U.S. and
                       Western Europe imposed crippling economic sanctions
                       against Russia, including cutting the country off
                       from roughly $600 billion in reserves held by the
                       Central Bank of Russia, suspending its access to
                       the U.S. dollar and banning the state banks from
                       using SWIFT, a messaging system used by banks to
                       conduct international transactions.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Papers Please ☛ European_Court_ruling_on_air_travel
                        surveillance⠀⇛


                             The highest court of the European Union ruled
                             today that an EU mandate for dragnet
                             surveillance of travelers through government
                             access to airline reservations might be
                             permissible under EU law — but only under
                             conditions that governments of EU member
                             countries, and the US government, may be
                             unable or unwilling to meet.


                             In 2016, the EU enacted a directive requiring
                             each EU member state to enact a law requiring
                             airlines to hand over copies of passenger
                             name records (PNRs) to the government, and
                             establish a new surveillance agency to
                             profile travelers based on this PNR data. 
                             This EU PNR Directive was modeled on US law
                             and on the extrajudicial practices — never
                             tested against the provisions of
                             international human rights treaties, which
                             generally can’t be invoked in US courts — of
                             the US Department of Homeland Security.


                             The Belgian “Ligue des droits humains” (LDH)
                             filed a lawsuit in the Belgian Constitutional
                             Court challenging the law enacted in Belgium
                             to implement the EU PNR Directive as contrary
                             to multiple provisions of Belgian and EU law.


                      # ⚓ The Economist ☛ Alphabet_is_spending_billions_to
                        become_a_force_in_health_care⠀⇛


                             Yet it is Alphabet, Google’s corporate
                             parent, whose health-care ambitions seem to
                             be the most vaulting. Between 2019 and 2021
                             Alphabet’s venture-capital arms, Google
                             Ventures and Gradient Ventures, and its
                             private-equity unit, CapitalG, made about 100
                             deals, a quarter of Alphabet’s combined
                             total, in life sciences and health care. So
                             far this year it has injected $1.7bn into
                             futuristic health ideas, according to cb
                             Insights, a data provider, leaving its fellow
                             tech giants, which spent around $100m all
                             told, in the dust. Alphabet is the fifth-
                             highest-ranking business in the Nature Index,
                             which measures the impact of scientific
                             papers, in the area of life sciences, behind
                             four giant drugmakers and 20 spots ahead of
                             Microsoft, the only other tech giant in the
                             running. The company has hired former senior
                             health regulators to help it navigate
                             America’s health-care bureaucracy.


                      # ⚓ Gregory Hammond ☛ Is_Privacy_Dead⠀⇛


                             What I want you to do after you finish
                             reading this, is email me every single login
                             you have. Not just the nice and respectable
                             ones, but all of them. Because I want to be
                             able to go through them, read what I want to
                             read and publish whatever I find interesting.
                             After all, if you’re not a bad person, if
                             you’re doing nothing wrong, you should have
                             nothing to hide.


                      # ⚓ The Hill ☛ Democrats_introduce_bill_to_ban_collection
                        of_reproductive_health_data⠀⇛


                             The legislation was drafted in response to a
                             Supreme Court draft leaked in May that showed
                             the court was prepared to overturn Roe v.
                             Wade, a decision that would trigger abortion
                             bans or severe restrictions in a number of
                             U.S. states.


          o § Defence/Aggression⠀➾


                # ⚓ NPR ☛ Trump_team_didn’t_have_the_evidence_and_4_other
                  takeaways_from_the_Jan._6_hearing⠀⇛


                       That was one of the eye-opening findings of the
                       Jan. 6 committee’s fourth hearing that showed the
                       depth and breadth of Trump and his allies’ pressure
                       on local and state officials. But there was more.


                # ⚓ The Times Of Israel ☛ US_Navy_reports_‘unsafe’_encounter
                  with_Iran’s_Guards_in_Strait_of_Hormuz⠀⇛


                       In a video released by the Navy’s Bahrain-based 5th
                       Fleet, a high-speed Guard Boghammar is seen turning
                       head-on toward the Sirocco. The Sirocco repeatedly
                       blows its horn at the Boghammar, which turns away
                       as it closes in. The flare shot can be heard, but
                       not seen, as the Boghammar passes the Sirocco with
                       the Iranian flag flying above it.


                       The Navy said the Boghammar came within 50 yards
                       (45 meters) of the Sirocco, raising the risk of the
                       vessels running into each other. The overall
                       encounter lasted about an hour, the Navy said.


                # ⚓ VOA News ☛ Suspected_Islamist_Militants_Kill_132_Civilians
                  in_Central_Mali⠀⇛


                       She says the government condemns with the utmost
                       rigor the attacks and abuses perpetrated against
                       peaceful populations. Kone says the government
                       reassures that all measures will be taken to find
                       and bring the perpetrators of these criminal acts
                       before the court.


                       The attack in Mopti is the latest in a wave of
                       attacks on civilians in Mali and neighboring
                       Burkina Faso.


                # ⚓ Rolling Stone ☛ Election_Worker_Gives_Emotional_Account_of
                  How_Trump’s_Election_Lies_Ravaged_Her_Life⠀⇛


                       Before the committee Moss discussed the cataclysmic
                       effects the conspiracy theories Trump leveraged
                       against her had on her life. “It has turned my life
                       upside down.” Moss testified, “I don’t want anyone
                       knowing my name […] I just don’t do nothing
                       anymore, I don’t want to go anywhere. I second
                       guess everything that I do. It’s affected my life
                       in a major way, in every way. All because of lies.”


                # ⚓ The Nation ☛ The_Pentagon_Gets_More_Money,_and_Americans
                  Pay_the_Price⠀⇛


                       Bipartisanship is a rare and endangered species in
                       today’s bitterly divided Washington. Except when it
                       comes to one thing: the Pentagon budget.


                # ⚓ Counter Punch ☛ An_Open_Letter_to_Prime_Minister_Justin
                  Trudeau_on_Behalf_of_Science_for_Peace⠀⇛


                       All of this was before Russia invaded Ukraine,
                       raising tensions between the two largest nuclear
                       powers on the planet to unprecedented levels. With
                       president Putin warning of “consequences the likes
                       of which have never been seen” for any country
                       doing what NATO is currently doing: arming Ukraine,
                       how long until a tactical nuclear weapon is
                       deployed or a NATO country supplying arms is
                       attacked, leading to a tit for tat escalation to a
                       full nuclear exchange? We are in fact already in a
                       nuclear war if we accept that the mere threat of
                       nuclear attack (implicit in Putin’s warning) is use
                       of nuclear weapons. We would argue that a state’s
                       mere possession of nuclear weapons is an implicit
                       threat to use them. Neither the use, threat or
                       possession of nuclear weapons are in keeping with
                       existing international humanitarian law or basic
                       morality. International law unambiguously outlaws
                       the targeting of civilian populations. Clearly
                       nuclear weapons, by the scale of their destructive
                       powers are contrary to this prohibition, quite
                       independently from the TPNW.


                       If ever the precautionary principle was
                       appropriate, this would seem to be the time: it
                       advises that in the context of a potentially
                       catastrophic risk, reducing that risk must take
                       precedence over all secondary considerations. It is
                       this concern, in particular the call of
                       humanitarian empathy, that prompted the
                       international community to negotiate the Treaty on
                       the Prohibition of Nuclear Weapons. The Nuclear
                       Non-Proliferation Treaty, while having slowed the
                       spread of nuclear weapons, has clearly failed in
                       getting the existing nuclear powers to live up to
                       their commitment to work toward the elimination of
                       their stockpiles. While the TPNW is unlikely to
                       compel nuclear states to surrender their arsenals,
                       it is an important step in delegitimizing nuclear
                       weapons as a tool of statecraft and making those
                       holdout states pariahs.


                # ⚓ Scheerpost ☛ A_Trail_of_Tears:_How_Veterans_Return_From
                  America’s_Wars⠀⇛


                # ⚓ Scheerpost ☛ VIDEO:_Ecuador’s_Indigenous_Revolt_Against
                  Their_Neoliberal_President⠀⇛


                       The Grayzone spoke with leaders of Ecuador’s
                       indigenous movements, now engaged in ferocious
                       street protests against the privatization policies
                       of President Guillermo Lasso, a billio…


          o § Environment⠀➾


                # ⚓ The Nation ☛ Why_This_N.Y._Socialist_Is_Running_on
                  Climate⠀⇛


                       Sarahana Shrestha is a climate activist running to
                       represent New York’s 103rd Congressional District
                       in the state Assembly as part of New York City
                       Democratic Socialists of America’s slate of 13
                       candidates, many of whom are putting the climate
                       crisis at the center of their campaigns. With the
                       ultimate goal of providing all energy through the
                       public sector, Shrestha and other DSA candidates
                       have been pushing an incremental step: the Build
                       Public Renewables Act, which Democratic leadership
                       in the Assembly failed to even introduce despite
                       having the votes to pass it. (The bill did pass the
                       state Senate.)1


                # § Energy⠀➾


                      # ⚓ The Nation ☛ Stanford’s_New_School_of_Sustainability
                        Is_a_Gift_to_Fossil_Fuel_Companies⠀⇛


                             The Doerr School will incorporate over a
                             dozen fossil fuel-funded affiliate programs
                             researching deep-sea oil exploration,
                             hydraulic fracturing, and other methods of
                             expanding oil reserves. One product of these
                             programs: BP recently discovered a new cache
                             containing 200 million barrels of oil using
                             an algorithm developed by an alum of one of
                             these programs, the Stanford Exploration
                             Project. Another industry-funded program is
                             the Stanford Natural Gas initiative, which
                             gives its “sustaining members” (donors at a
                             $250,000 per year level) seats on the
                             governance board that has significant
                             leverage to dictate research priorities.


                             Fossil fuel companies can also buy lobbying
                             time hidden within the ivory tower. At the
                             neutral sounding Energy Modeling Forum, an
                             “affiliate” program allows corporations
                             “closer professional interactions” with
                             Stanford’s modelers as well as interaction
                             with government agencies through the program
                             for $20,000 annually. Past affiliates through
                             the program include the American Petroleum
                             Institute, BP, Chevron, Exxon and
                             Schlumberger.


                             Then there’s the research itself. These
                             centers produce complex scientific and
                             economic research that is hard for non-
                             academics to review critically. Stanford’s
                             research ethics training, which is required
                             for studies with human participants, warns
                             that studies have shown that industry-
                             sponsored research is much more likely to
                             report positive outcomes than those funded
                             with federal money. As Stanford PhD Ben
                             Franta has noted, the fossil fuel industry
                             has made a clear progression from spreading
                             climate denial with bad science to spreading
                             climate delay with economic policy modeling
                             laden with variables designed for industry
                             self-preservation.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Set_It_Back:_Moving_Levees_to_Benefit
                        Rivers,_Wildlife_and_Communities⠀⇛


          o § Finance⠀➾


                # ⚓ Pro Publica ☛ Jeff_Yass:_The_Billionaire_GOP_Mega-Donor
                  Gaming_the_Tax_System⠀⇛


                       One day in July 1985, three young men from
                       Philadelphia, their lawyer and a burly Pinkerton
                       guard arrived at a horse track outside Chicago
                       carrying a briefcase with $250,000 in cash.


                       Running the numbers on a Compaq computer the size
                       of a small refrigerator, Jeffrey Yass and his
                       friends had found a way to outwit the track’s
                       bookies, according to interviews, records and news
                       accounts. A few months earlier, they’d wagered
                       $160,000, gambling that, with tens of thousands of
                       bets, they could nail the exact order of seven
                       horses in three different races. It was a
                       sophisticated theory of the racing odds, honed with
                       help from a Ph.D. statistician who’d worked for
                       NASA on the moon landing, and it proved right. They
                       bagged $760,000, then the richest payoff in
                       American racing history.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ EFF ☛ Victory!_Court_Rules_That_DMCA_Does_Not_Override
                  First_Amendment’s_Anonymous_Speech_Protections⠀⇛


                       The decision by a judge in the United States
                       District Court for the Northern District of
                       California confirms that copyright holders issuing
                       subpoenas under the Digital Millennium Copyright
                       Act must still meet the Constitution’s test before
                       identifying anonymous speakers.


                       The case is an effort to unmask an anonymous
                       Twitter user (@CallMeMoneyBags) who posted photos
                       and content that implied a private equity
                       billionaire named Brian Sheth was romantically
                       involved with the woman who appeared in the
                       photographs. Bayside Advisory LLC holds the
                       copyright on those images, and used the DMCA to
                       demand that Twitter take down the photos, which it
                       did.


                       Bayside also sent Twitter a DMCA subpoena to
                       identify the user. Twitter refused and asked a
                       federal magistrate judge to quash Bayside’s
                       subpoena. The magistrate ruled late last year that
                       Twitter must disclose the identity of the user
                       because the user failed to show up in court to
                       argue that they were engaged in fair use when they
                       tweeted Bayside’s photos.


                # ⚓ EFF ☛ When_“Jawboning”_Creates_Private_Liability⠀⇛


                       Among the state actor theories presented is one
                       based on collaboration with the government on
                       content moderation. “Jawboning”—or when government
                       authorities influence companies’ social media
                       policies—is extremely common. At what point, if
                       any, does a private company become a state actor
                       when they act according to it?


                       Deleting posts or cancelling accounts because a
                       government official or agency requested or required
                       it—just like spying on people’s communications on
                       behalf of the government—raises serious human
                       rights concerns. The newly revised Santa Clara
                       Principles, which outline standards that tech
                       platforms must consider to make sure they provide
                       adequate transparency and accountability,
                       specifically scrutinize “State Involvement in
                       Content Moderation.” As set forth in the
                       Principles: “Companies should recognise the
                       particular risks to users’ rights that result from
                       state involvement in content moderation processes.
                       This includes a state’s involvement in the
                       development and enforcement of the company’s rules
                       and policies, either to comply with local law or
                       serve other state interests. Special concerns are
                       raised by demands and requests from state actors
                       (including government bodies, regulatory
                       authorities, law enforcement agencies and courts)
                       for the removal of content or the suspension of
                       accounts.”


                       So, it is important that there be a defined, though
                       narrow, avenue for holding social media companies
                       liable for certain censorial collaborations with
                       the government. But the bar for holding platforms
                       accountable for such conduct must be high to
                       preserve their First Amendment rights to edit and
                       curate their sites. 


                # ⚓ Salon ☛ “Big_Lie”_vigilantes_publish_targets_online_—_but
                  Facebook_and_Twitter_are_asleep_at_the_wheel⠀⇛


                       Promoting such false information violates the
                       policies of Facebook, Twitter and TikTok.
                       Facebook’s “Community Standards” says its policy is
                       to remove content that incites harassment or
                       violence or impersonates government officials.
                       Twitter and TikTok have similar rules and
                       guidelines for what can and can’t appear on their
                       platforms.


                       ProPublica identified at least a dozen additional
                       posts on Twitter, Facebook and TikTok that accuse
                       unnamed individuals of being “ballot mules” and
                       engaging in allegedly illegal activity. Some of
                       these posts echo the “WANTED”-style language seen
                       in the Gwinnett County meme, while others include
                       similar calls to action to identify the
                       individuals.


                       None of the posts reviewed by ProPublica include
                       evidence that any of the people depicted in the
                       posters engaged in illegal activity. Yet the social
                       media companies have reacted slowly or not at all
                       to such posts, some of which clearly violate their
                       policies, experts say.


                # ⚓ Tutao GmbH ☛ Leaked_‘chat_control’_document:_Will_Germany
                  fight_for_privacy?⠀⇛


                       In a leaked internal statement to the EU
                       Commission, the German government demands that the
                       draft law must be brought in line with
                       “constitutional standards for the protection of
                       private and confidential communications”. The
                       statement positions itself against “general
                       surveillance and private communications scanning
                       measures”.


                       According to the leak, the German government asks
                       61 questions, which in part are very tough and will
                       pose serious problems for the EU Commission to
                       answer.


                # ⚓ Rolling Stone ☛ ‘What_the_F-ck_Is_This?’:_Team_Trump
                  Blindsided_by_Jan._6_Committee_Getting_Doc_Footage⠀⇛


                       In other words: many of the people actually running
                       Trump’s reelection operation are now saying they
                       somehow had zero clue that an entire documentary
                       was being filmed largely about Trump and his
                       reelection campaign. And now the fruits of that doc
                       are being mined for evidence by the congressional
                       committee investigating Trump and his multi-pronged
                       efforts to shred the American democratic order.


                # ⚓ The Hill ☛ Biden_signs_cyber_bills_into_law⠀⇛


                       The second bill, called the State and Local
                       Government Cybersecurity Act, aims to improve
                       coordination between the Department of Homeland
                       Security and state and local governments on
                       cybersecurity.


                # ⚓ Democracy Now ☛ Colombia_Elects_1st_Leftist_President
                  Gustavo_Petro_&_1st_Black_VP_Francia_Márquez._Can_They
                  Deliver?⠀⇛


                       Colombia made history Sunday as voters elected
                       former guerrilla member Gustavo Petro as the
                       country’s first leftist president and environmental
                       activist Francia Márquez Mina as the country’s
                       first Black vice president. The pair, gaining over
                       50% of the vote, defeated right-wing real estate
                       millionaire Rodolfo Hernández but will now face a
                       major challenge to pass legislation in the
                       conservative Congress, where they lack a majority.
                       “The hurdle has been overcome by winning the
                       election, but the main hurdle, the establishment,
                       cannot be changed by the government; it has to be
                       changed from the people, by the people,” says
                       Manuel Rozental, Colombian physician, activist and
                       grassroots organizer. We also speak with Colombia-
                       based journalist Simone Bruno, who says Petro’s
                       election could transform the politics and economy
                       of Latin America.


                # ⚓ The Nation ☛ The_Tragic_Absurdity_of_Qatar’s_World_Cup
                  Sportswashing⠀⇛


                       Were there not so much suffering involved, the
                       Qatar 2022 World Cup would be an absurdist parody
                       of sportswashing. The extraordinarily popular event
                       is meant to put a happy gloss on both the brutal
                       kingdom of Qatar and soccer’s governing body—that
                       infamous organization of finely tuned corruption:
                       FIFA.


                # ⚓ The Nation ☛ Why_the_Poor_People’s_Campaign_2022_Matters⠀⇛


                       Today, on this land where our First Nation brothers
                       and sisters first lived free, we are gathered
                       because there are unnecessarily 140 million poor
                       and low wealth people in this country. That’s 43
                       percent of the nation, 52 percent of our children,
                       66 million white people, 26 million black people,
                       68 percent of Latinos and Natives, and more than 60
                       percent of Asians who are entangled in the unjust
                       weeds of poverty and bound up by the interlocking
                       realities of systemic racism, refusal to pay a
                       living minimum wage, bad tax policy, ecological
                       devastation, denial of health care, the war economy
                       and the false moral narrative of religious
                       nationalism and white supremacy. This level of
                       poverty in this nation—the richest nation in the
                       history of the world—constitutes a moral crisis and
                       a fundamental failure of the polices of greed.


                # ⚓ Counter Punch ☛ The_Age_of_Stupidity:_From_Johnson_and
                  Biden_to_Putin_and_Xi_Jinping⠀⇛


                       This is surely a mistake. “Never lose your sense of
                       the superficial,” said the newspaper publisher Lord
                       Northcliffe and his advice applies as much to
                       historic trends as it does to daily news. Yet
                       pundits like to feel that they are digging deeper
                       than a personal failing, and seldom focus on plain
                       and simple stupidity as the reason why leaders make
                       unforced errors.


                       This kind of individual inadequacy is not equally
                       present in all periods and it may be that in some
                       eras the scope for chronic blunderers to do damage
                       is higher than in others. It was certainly high in
                       1914, for instance, when dim-witted leaders such as
                       Kaiser Wilhelm 11 in Germany, Tsar Nicholas 11 in
                       Russia and the Austro-Hungarian monarchy were
                       making the decisive moves leading to a European war
                       that more intelligent leaders might have avoided as
                       being much against their interests and putting at
                       risk the future of their regimes.


                # § Misinformation/Disinformation⠀➾


                      # ⚓ NPR ☛ Here’s_how_Stephen_Colbert_says_his_staff
                        members_got_arrested_on_Capitol_Hill⠀⇛


                             The “TV people” that Colbert referenced
                             included Fox News host Tucker Carlson, who
                             called the CBS team “saboteurs” and falsely
                             said that they breached the Capitol.


                             [...]


                             “They want to talk about something other than
                             the Jan. 6th hearings on the actual
                             seditionist insurrection that led to the
                             deaths of multiple people, and the injury of
                             over 140 police officers,” Colbert said. “But
                             drawing any equivalence between rioters
                             storming our Capitol to prevent the counting
                             of electoral ballots and a cigar-chomping toy
                             dog, is a shameful and grotesque insult to
                             the memory of everyone who died. And it
                             obscenely trivializes the service and the
                             courage the Capitol Police showed on that
                             terrible day.”


                      # ⚓ Free Press Journal ☛ Johnny_Depp_warns_fans_of_fake
                        accounts_pretending_to_be_him_on_social_media⠀⇛


                             Fresh off his legal battle with his ex-wife
                             Amber Heard, Johnny Depp took to his social
                             media and warned fans of fake accounts made
                             in his name.


                      # ⚓ People Magazine ☛ Johnny_Depp_Urges_Fans_to_‘Remain
                        Cautious’_as_His_Team_Works_to_‘Combat’_Fake_Social
                        Media_Accounts⠀⇛


                             “I ask that you remain cautious as it seems
                             these fake accounts can be relentless. My
                             team is working to combat the problem. Thank
                             you for your continued support and for making
                             me aware of this issue!” Depp continued,
                             signing off the note, “Love & respect, JD X.”


                      # ⚓ India Times ☛ ‘I_do_not_have_any_private_or_side
                        accounts’._Johnny_Depp_warns_fans_of_impostors,_shares
                        list_of_verified_profiles⠀⇛


                             In a note shared on Instagram Story, the 59-
                             year-old said that he was informed that some
                             ‘fake’ social media accounts were
                             ‘pretending’ to be him or claiming that they
                             work with him.


                             Clarifying further on Sunday, the ‘Pirates of
                             the Caribbean’ star informed his nearly 26
                             million Instagram followers that he does not
                             have any ‘private or side accounts’ on any
                             social media platforms.


                             “I’ve been made aware that there are fake
                             accounts pretending to be me or people
                             working with me. I do not have any private or
                             side accounts on any platforms,” his
                             statement read.


                      # ⚓ NPR ☛ No,_this_7-Eleven_isn’t_charging_$7.11_for_gas,
                        even_if_the_internet_says_so⠀⇛


                             The photo was taken by Matt Beemsterboer, 34,
                             who was surprised to see the likes of Elon
                             Musk share it Tuesday, considering the price
                             depicted wasn’t accurate, nor was the photo
                             taken this year.


          o § Censorship/Free Speech⠀➾


                # ⚓ New York Times ☛ If_I_Get_Canceled,_Let_Them_Eat_Me_Alive⠀⇛


                       My brief tangle with the mob taught me that it is
                       not when I am most embattled that I see most
                       clearly. Hence I, like Odysseus, am tying myself to
                       the mast in advance. I commit now, publicly, in
                       print: please don’t fight on my behalf. Don’t stand
                       up for me. Don’t rescue my good name. Let it be
                       tarnished. Let my reputation die.


          o § Freedom of Information / Freedom of the Press⠀➾


                # ⚓ Michael West Media ☛ Time_to_act_Anthony_Albanese,_the
                  Assange_persecution_cannot_be_allowed_to_go_on⠀⇛


                       Now is the time to end the dangerous threat to
                       basic freedoms and the rule of law that the Julian
                       Assange persecution represents. The Albanese
                       government has a critical role to play to do
                       everything in its power to stop the extradition and
                       end his punishment, Greg Barns writes.


                # ⚓ TruthOut ☛ Julian_Assange_Is_Enduring_Unbearable
                  Persecution_for_Exposing_US_War_Crimes⠀⇛


                # ⚓ Techdirt ☛ UK_Approves_Extradition_Of_Julian_Assange,
                  Allowing_The_US_Government_To_Continue_Criminalizing
                  Journalism⠀⇛


                       It appears all but inevitable that Julian Assange
                       will be receiving an all-expenses-paid (except for
                       his defense!) one-way trip to the United States to
                       face espionage charges for, mostly, performing acts
                       of journalism.


                # ⚓ Eesti Rahvusringhääling ☛ Family_values_group_head_fined
                  over_journalist_ejection_from_public_protest⠀⇛


                       “The person named in the proceedings at no point
                       intervened or called over those participants in the
                       demonstration who surrounded a journalist and
                       attacked their security via hostile behavior, but
                       rather restated alongside the participants at the
                       demonstration that he, Sander Punamäe, should
                       disappear, get out of there, leave, and be
                       ashamed.”


                       Punamäe at the time worked for daily Postimees.


                       The PPA imposed a fine of €320 on Vooglaid in
                       respect of the incident and the misdemeanor
                       proceedings.


          o § Civil Rights/Policing⠀➾


                # ⚓ Craig Murray ☛ Your_Man_in_Saughton_Jail_Part_2⠀⇛


                       I was walking down that improbably long central
                       corridor in a group of about eight mainstream
                       prisoners heading for legal visits, when panic
                       broke out among the escorting guards. About a
                       hundred yards further down, and coming towards us,
                       was an overweight and bearded old man walking with
                       a zimmer frame and wearing the maroon shirt of a
                       protected prisoner.


                # ⚓ Exclusive:_Officers_arrived_at_Uvalde_school_with_rifles,
                  ballistic_shield_19_minutes_after_gunman⠀⇛


                       Even as officers with high-powered weapons and
                       ballistic shields massed inside the blue and green
                       hallway, the gunman could be heard firing rounds —
                       including at 12:21 p.m., 29 minutes before officers
                       entered the classroom and killed him, the documents
                       show.


                       Investigators say the latest information indicates
                       officers had more than enough firepower and
                       protection to take down the gunman long before they
                       finally did.


                # ⚓ NPR ☛ Police_could_have_stopped_Uvalde_shooting_within_3
                  minutes,_a_Texas_official_says⠀⇛


                       A top Texas law enforcement official said that
                       there were enough armed police officers wearing
                       body armor to stop the late May shooting at Robb
                       Elementary School in Uvalde, Texas three minutes
                       after it began.


                       But instead, it took about an hour and 14 minutes
                       from when officers arrived at the school to when
                       they breached the door and ended the standoff with
                       the gunman.


                # ⚓ Christian Post ☛ Surging_violence_against_Nigeria’s
                  Christians_demands_White_House_action⠀⇛


                       The early casualty estimates all proved to be low.
                       On June 8, “An ABC news source with direct
                       knowledge of the investigation said the bodies of
                       82 victims were in a local morgue. Another source
                       briefed on the latest U.S. intelligence assessment
                       said the estimate was over 80. Both sources spoke
                       on the condition of anonymity because they didn’t
                       have the authorization to speak to the press about
                       the ongoing probe.”


                # ⚓ Medforth ☛ France:_A_headmistress_of_a_high_school_was
                  threatened_with_death_after_she_asked_a_pupil_to_take_off_her
                  Muslim_headscarf⠀⇛


                       On Thursday June 16, a girl from a Parisian high
                       school went to the Lycée Charlemagne for the French
                       baccalaureate exam. She allegedly refused to remove
                       her headscarf, thus preventing the identity check
                       that is usually carried out before candidates enter
                       the examination room. She insisted on wearing her
                       headscarf “despite several reminders of the law (of
                       2004 on the wearing of religious symbols at school,
                       ed.) by the staff of the education office who were
                       present at the reception of the examination”, as
                       reported by Le Figaro. The pupil is said to have
                       finally given in after what was perceived as a
                       “tense” exchange with the CPE.


                # ⚓ Muslims_slam_young_LADY_because_of_her_dressing!_LOOK⠀⇛


                       Photos of the lady were posted on a Twitter account
                       (Hafsa @wy_dee) on Saturday, June 18, however, it
                       cannot be ascertained if she is the owner of the
                       account or a catfish.


                       Reacting to the post, some Muslims criticised the
                       lady for wearing ‘such a dress,’ saying that it’s
                       against the teaching of Qur’an.


          o § Monopolies⠀➾


                # ⚓ RTL ☛ Germany_opens_anti-cartel_probe_into_Google_Maps⠀⇛


                       The move comes after the Federal Cartel Office in
                       January classified Google as a company of
                       “paramount significance across markets”, paving the
                       way for the authorities to clamp down on any
                       potentially anti-competitive activities.


                       Parallel proceedings are already ongoing to examine
                       Google’s terms and conditions for data processing
                       and its news offer Google News Showcase.


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ Paris_Hilton_is_One_of_the_First
                        Defendants_at_the_‘Small’_Copyright_Claims_Board⠀⇛


                             The U.S. Copyright Claims Board has been live
                             for a few days and thus far 19 cases have
                             been filed. This doesn’t include any file-
                             sharing piracy claims. Most cases are filed
                             by smaller creators, including an artist who
                             accuses Paris Hilton of repeatedly sharing
                             photos on social media that infringe on her
                             fairy wing design.


                      # ⚓ Torrent Freak ☛ MANGA_Plus_Invites_Users_to_Confess
                        Piracy_&_Name_Most-Used_Pirate_Sites⠀⇛


                             Manga publisher Shueisha is running a survey
                             on its MANGA Plus service. Many of the
                             questions seek information to help improve
                             the platform but others raise a few concerns.
                             Users are invited to confess to being
                             pirates, say whether they are heavy users of
                             pirate sites, and then name the pirate sites
                             they use the most. Savvy business move or
                             something more sinister?



                    ䷩ 𝚕𝚒𝚗𝚎 11144

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_22/06/2022:_Turkey’s_GNU/Linux_Stories_and_Giving_up_on_GNOME_To_Do⠀✐


Posted in News_Roundup at 2:35 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Chromium
          o Programming/Development
                # Perl_/_Raku
                # Python
                # Rust
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Environment
                # Energy
          o Finance
          o Civil_Rights/Policing
          o Monopolies
                # Patents
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ FSF ☛ How_the_Eyüpsultan_district_of_Turkey_uses_GNU/Linux
                  —_Free_Software_Foundation⠀⇛


                       Eyüpsultan is a district located on the European
                       side of Istanbul. The area of Eyüpsultan district
                       is 242 km². According to 2018 census data, the
                       Eyüpsultan district, with its twenty-one
                       neighborhoods and seven villages, has a population
                       of 383,909. In this article, Pardus project leader,
                       Hüseyin GÜÇ, explains why Eyüpsultan chose free
                       software.


                       What is Pardus?


                       Pardus is a distribution of the GNU/Linux operating
                       system whose development began in 2003. It is
                       developed by Ulakbim, which is a government
                       research institute subsidiary of the Scientific and
                       Technological Research Council of Turkey, called
                       Tübitak. Pardus GNU/Linux is based on Debian GNU/
                       Linux, but it is redesigned to be used in
                       accordance with the practices and habits of users
                       in Turkey.


                       LibreOffice, GIMP, VLC, and other free software
                       programs are the default applications for use in
                       the Pardus GNU/Linux operating system.


                       Additionally, with customizations implemented by us
                       at the Eyüpsultan IT department, Pardus has a theme
                       resembling Microsoft Windows and other common
                       proprietary software that people are commonly
                       familiar with. This choice of theme was made
                       because it was expected that users would be able to
                       more easily adopt the change.


          o § Kernel Space⠀➾


                # ⚓ Linux Plumbers Conference (LPC) ☛ Linux_Plumbers
                  Conference:_Microconferences_at_Linux_Plumbers_Conference:
                  CPU_Isolation⠀⇛


                       Linux Plumbers Conference 2022 is pleased to host
                       the CPU Isolation Microconference


                       CPU Isolation is an ability to shield workloads
                       with extreme latency or performance requirements
                       from interruptions (also known as Operating System
                       noise) provided by a close combination of several
                       kernel and userspace components. An example of such
                       workloads are DPDK use cases in Telco/5G where even
                       the shortest interruption can cause packet losses,
                       eventually leading to exceeding QoS requirements.


                # ⚓ Linux Plumbers Conference (LPC) ☛ Registration_Still_Sold
                  Out,_But_There_is_Now_a_Waitlist⠀⇛


                       Because we ran out of places so fast, we are
                       setting up a waitlist for in-person registration
                       (virtual attendee places are still available).
                       Please fill in this form and try to be clear about
                       your reasons for wanting to attend. This year we’re
                       giving waitlist priority to new attendees and
                       people expected to contribute content. We expect to
                       be able to accept our first group of attendees from
                       the waitlist in mid July.


          o § Applications⠀➾


                # ⚓ 9to5Linux ☛ Mixxx_2.3.3_DJ_Software_Brings_Improvements_for
                  Pioneer_DDJ-SB3_and_Traktor_S3_Controllers⠀⇛


                       Mixxx 2.3.3 comes almost five months after Mixxx
                       2.3.2 and it’s here to further improve support for
                       several DJ controllers and mixers. For example, it
                       improves the stability of the Behringer DDM4000
                       mixer, which also received soft-takeover for
                       encoder knobs in this release.


                       The Pioneer DDJ-SB3 DJ controller received a fix
                       for the broken controller issue that occurred when
                       releasing the shift button, the Traktor S3 DJ
                       controller gets better deck cloning, and the Denon
                       MC7000 DJ controller gets a fix for the ‘inverted
                       shift’ bug in the controller mapping.


                # ⚓ Meet_Chris_Hildenbrand,_the_artist_behind_the_winning
                  Inkscape_1.2_About_Screen_|_Inkscape⠀⇛


                       Congratulations to Chris Hildenbrand, the winner of
                       the Inkscape 1.2 About Screen Contest, held this
                       year, 2022.


                       We recently caught up with Chris to ask a few
                       questions about himself and his use of Inkscape.


                       Inkscape: Please introduce yourself to the Inkscape
                       Community. Who is Chris and where in the world do
                       you live?


                       Chris Hildenbrand (Chris): I grew up in Germany but
                       was lucky enough to end up in tropical far North
                       Queensland in Australia. I am calling Cairns home
                       now – where the reef meets the rain-forest.


                # ⚓ 10_Best_Kali_Linux_Tools_for_Hackers_–_Hack_Ware_News⠀⇛


                       Kali Linux is arguably one of the best Linux
                       distros used by hackers of the whole color
                       spectrum, thanks to its hundreds of built-in
                       hacking, security, and pen-testing tools. That’s a
                       lot but not all of them will be used given that
                       many of those tools are already multi-purpose,
                       encapsulating the other tools in Kali’s arsenal.


                       They’re all included for a purpose to be used by
                       seasoned users but for beginners, it would be nice
                       to narrow things down a bit and list down the 10
                       Best Kali Linux Tools for Hackers.


                       And since hackers are a very diverse lot,
                       preferences can be quite relative. This listing of
                       10 Best Kali Linux Tools for Hackers therefore
                       won’t be in any particular order nor would reflect
                       the actual preferences of absolutely everyone.


          o § Instructionals/Technical⠀➾


                # ⚓ UNIX Cop ☛ Install_Icecast_on_Ubuntu_20.04⠀⇛


                       Hello, friends. In this post, you will learn how to
                       install Icecast on Ubuntu 20.04. The procedure is
                       simple and thanks to our tutorial you will have no
                       problems.


                # ⚓ Eerie Linux ☛ Legends_start_at_1.0!_–_FreeBSD_in_1993_(pt.
                  2)⠀⇛


                       In part one I covered a little bit of general
                       information and preparation work before detailing
                       the first part of the installation of FreeBSD 1.0
                       on real hardware. We stopped with having
                       transferred a rump root filesystem and the kernel
                       from two diskettes onto the hard drive.


                       Part two covers the rest of the installation. We’re
                       going to continue right where we left off.


                       In case you want to play with FreeBSD 1.0 yourself
                       – I’ve made an image of the drive and zstd-
                       compressed it to make it as small as possible. It
                       contains a bootable 1.0 system with bindist
                       installed and both srcdist and xfree86 sources
                       available, too. Download it here (60 MB compressed,
                       20 GB uncompressed) and play with it if you like.


                # ⚓ Bryan Lunduke ☛ TUIFI_Manager:_A_file_manager,_in_the
                  terminal,_with_file_icons_made_out_of_ascii_characters.⠀⇛


                       That, right there, is a file manager for the
                       terminal. Written in Python (using an NCurses
                       wrapper). That runs on Linux, Windows, & Mac.


                       … and, perhaps most interestingly, it displays
                       icons for files and folders… built entirely out of
                       ASCII characters.


                # ⚓ Frederic Cambus ☛ Differences_between_base_and_ports_LLVM
                  in_OpenBSD⠀⇛


                       LLVM was imported in the OpenBSD ports tree back in
                       2008, and happily lived there for a long while
                       before being imported in the source tree at the
                       g2k16 hackathon in 2016. I previously wrote about
                       this in “The state of toolchains in OpenBSD” last
                       year.


                       As mentioned in my previous article, we do not use
                       upstream build system to build LLVM in the base
                       system, but hand-writen BSD Makefiles. Importing
                       CMake into the base system was not an option,
                       because of the size of the project and the large
                       dependency chain it requires for building. As a
                       drawback, the build is slower than it could be,
                       were we able to take advantage of a more modern
                       build system.


                       Nowadays, Clang is the default compiler on the
                       amd64, arm64, armv7, i386, macppc, octeon,
                       powerpc64, and riscv64 platforms. It is also
                       available in the sparc64 base system.


                # ⚓ Michael Stapelberg ☛ rsync:_Series_Overview⠀⇛


                       For many years, I was only a casual user of rsync
                       and used it mostly for one-off file transfers.


                       Over time, I found rsync useful in more and more
                       cases, and would recommend every computer user put
                       this great tool into their toolbox!


                # ⚓ HowTo Forge ☛ How_to_Install_a_Debian_11_(Bullseye)_Minimal
                  Server⠀⇛


                       This tutorial shows how to install a Debian 11
                       (Bullseye) minimal server in detail with many
                       screenshots. The purpose of this guide is to
                       provide a minimal setup that can be used as the
                       basis for our other Debian 11 tutorials here at
                       howtoforge.com.


                # ⚓ ZDNet ☛ How_to_install_Linux_applications_from_the_command
                  line_|_ZDNet⠀⇛


                       Jack Wallen demonstrates how to install software
                       from the command line on Ubuntu, AlmaLinux, Arch
                       Linux, and openSUSE.


                # ⚓ Video ☛ How_to_install_Skype_on_Pop!_OS_22.04_–_Invidious
                  [Ed: Better use something that is not Microsoft spyware
                  though]⠀⇛


                # ⚓ ByteXD ☛ How_to_Check_Your_Ubuntu_Version_(Command-line_&
                  GUI)_–_ByteXD⠀⇛


                       The Ubuntu Linux distribution from Canonical is an
                       always evolving operating systems. Ubuntu gets
                       updated once per year with a new release. On every
                       second year that release is a Long Term Support, or
                       better known as LTS, release. It is constantly
                       being developed with new features and hardened with
                       security patches.


                       As such, it’s important for us to know what version
                       of Ubuntu we are running on. Like that we know when
                       to do upgrades to our system. Below we will show
                       you some examples on how to check your Ubuntu
                       version using the desktop or the command line
                       terminal.


                # ⚓ OSTechNix ☛ How_To_View_Directory_Tree_Structure_In_Linux_–
                  OSTechNix⠀⇛


                       Today, we are going to learn how to view directory
                       structure using Tree command. As the name says, the
                       tree command will display the contents of a
                       directory in a tree-like format in Linux and Unix-
                       like operating systems.


                       You might wonder why would someone use this command
                       while we already have ls command to list the
                       contents of a directory.


                # ⚓ HowTo Forge ☛ How_to_Install_SuiteCRM_with_Nginx_and_Free
                  Let’s_Encrypt_SSL_on_Ubuntu_22.04⠀⇛


                       SuiteCRM is an open-source customer relationship
                       management solution written in PHP. It’s a fork of
                       the popular SugarCRM software after SugarCRM
                       stopped releasing its community edition. In this
                       post, you will learn how to install SuiteCRM using
                       the Nginx web server and Let’s Encrypt SSL on
                       Ubuntu 22.04.


                # ⚓ How_to_troubleshoot_deferred_probe_issues_in_Linux_|_Blog_|
                  Javier_Martinez_Canillas⠀⇛


                       When working on the retro handheld console
                       mentioned in a previous post, I had an issue where
                       the LCD driver was not probed when booting a custom
                       Linux kernel image built.


                       To understand the problem, first some knowledge is
                       needed about how devices and drivers are registered
                       in the Linux kernel, how these two sets are matched
                       (bound) and what is a probe deferral.


                       If you are not familiar with these concepts, please
                       read this post where are explained in detail.


                # ⚓ Citizix ☛ How_to_run_Grafana_Loki_with_Helm_and_kustomize
                  in_kubernetes⠀⇛


                       In this guide we will set up grafana loki for log
                       aggregation on kubernetes using helm chart.


                       Loki is a Prometheus-inspired logging service for
                       cloud native infrastructure. It is a logging
                       backend optimized for users running Prometheus and
                       Kubernetes with great logs search and
                       visualization. It is designed to be very cost
                       effective and easy to operate. It does not index
                       the contents of the logs, but rather a set of
                       labels for each log stream.


                       Unlike other logging systems, Loki is built around
                       the idea of only indexing metadata about your logs:
                       labels (just like Prometheus labels). Log data
                       itself is then compressed and stored in chunks in
                       object stores such as S3 or GCS, or even locally on
                       the filesystem. A small index and highly compressed
                       chunks simplifies the operation and significantly
                       lowers the cost of Loki.


                # ⚓ Linux Hint ☛ How_To_Configure_Synology_NAS_to_PXE_Boot
                  Linux_Installation_Images_With_iPXE_(BIOS_and_UEFI
                  versions)⠀⇛


                       iPXE is a modern PXE firmware that works for the
                       BIOS and UEFI motherboards. It can download the
                       required boot files using many protocols, such as
                       TFTP, FTP, HTTP, HTTPS, and NFS. Also, iPXE can
                       boot from iSCSI SAN (Storage Area Network), Fibre
                       Channel SAN via FCoE, and AoE SAN. iPXE can boot
                       operating system installer images and full
                       operating systems without requiring any HDD/SSD
                       installed on the host (iSCSI SAN boot). Diskless
                       booting with iPXE is very easy to configure.In
                       addition, iPXE supports scripting. You can control
                       the boot process with iPXE scripts stored on a
                       remote server. Thus, iPXE script is a very powerful
                       tool for dynamic boot management with iPXE.


                # ⚓ ByteXD ☛ Install_AnyDesk_on_Ubuntu_22.04_or_20.04_–
                  ByteXD⠀⇛


                       Now a days we are more and more depending on mobile
                       smartphones for work and our computing needs. Yet a
                       desktop computer is still indispensable for our
                       professional needs.


                       There are times that we can’t have access to our
                       desktop, for example when traveling on vacation.
                       For this situations there are a myriad of remote
                       desktop software, but one of the best is the
                       AnyDesk suite of remote desktop utilities.


                       Remote desktop software are applications that are
                       used to access a desktop or desktop interface of a
                       remote computer locally through a software client.


                # ⚓ ByteXD ☛ How_to_Install_Sublime_Text_on_Ubuntu_22.04_or
                  20.04⠀⇛


                       It’s no secret that Ubuntu is a great operating
                       system for software development. While programmers
                       have ample choices as to what code editor or IDE to
                       use, one of the most beloved ones is Sublime Text.


                       In this tutorial we will learn how to install
                       Sublime Text on our Ubuntu Desktop computer.


                # ⚓ Linux Made Simple ☛ How_to_install_Funkin’_Chromatic_Scale
                  Generator_on_a_Chromebook⠀⇛


                       Today we are looking at how to install Funkin’
                       Chromatic Scale Generator on a Chromebook. Please
                       follow the video/audio guide as a tutorial where we
                       explain the process step by step and use the
                       commands below.


                       This tutorial will only work on Chromebooks with an
                       Intel or AMD CPU (with Linux Apps Support) and not
                       those with an ARM64 architecture CPU.


                # ⚓ Converting_an_OpenGL_project_to_use_Autotools_|_Adam
                  Young’s_Web_Log⠀⇛


                       In a science fiction game I play, we often find
                       ourselves asking “which side of the Sun is Mars
                       from the Earth right now?” Since this is for a
                       game, the exact distance is not important, just
                       “same side” or “90 degrees ahead” is a sufficient
                       answer. But “right now” actually means a couple
                       hundred years in the future.


                # ⚓ Use_a_gamepad_to_control_mpv_video_playback⠀⇛


                       This is certainly not a common setup, but I have a
                       laptop plugged on my TV through an external GPU,
                       and it always has a gamepad connected to it. I was
                       curious to see if I could use the gamepad to
                       control mpv when watching videos; it turns out it’s
                       possible.


                       In this text, you will learn how to control mpv
                       using a gamepad / game controller by configuring
                       mpv.


                # ⚓ Manipulating_the_display_backlight_from_the_shell⠀⇛


                       I wrote a simple Bash script to more easily change
                       the screen brightness on systems where that’s
                       possible. Normally you have to guess at how much to
                       change it by, since as far as I can tell, every
                       backlight has a different scale (for example, my
                       main laptop goes up to 120000 but another goes up
                       to only a couple thousand); with this script you
                       can work with a consistent percentage scale on all
                       systems.


                # ⚓ Todo_lists_in_Vim,_syntax_highlighting⠀⇛


                       I keep a todo list on my computer, which contains
                       tasks for work and home. It also contains items
                       where I’m waiting for someone to do something, and
                       I use it as a scratchpad for bits of pertinent
                       information that might be useful in the near
                       future. The file is written in Markdown[1]. Items
                       in the list are written as bullet points (-), and
                       sometimes I group items together under headers (#).
                       Sometimes I have headers for each day of the week,
                       and sometimes for a particular project I’m working
                       on. The bullet point list of tasks is sometimes
                       nested to include extra information about each
                       task, or to add subtasks below a main task.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Giving_up_on_GNOME_To_Do_–_Georges_Stavracas⠀⇛


                             Seven years ago, back when I was a university
                             student living with my parents and with lots
                             of free time in my hands, I created GNOME To
                             Do to help me organize my Google Summer of
                             Code tasks. It was a fantastic time of my
                             life, and I had the privilege of having time
                             to procrastinate on writing productivity
                             tools without earning a single coin on it.


                             Over the years, however, things changes. I
                             married, moved to a new home with my partner,
                             adopted a lovely dogga. Had to deal with the
                             sucky parts of life like paying bills,
                             planning meals, doing groceries, therapy,
                             relearning how to live and operate under
                             ADHD, taking care of myself and people around
                             me.


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ DRV_Brings_More_Automation_to_IBM_i_Message_Monitoring_–_IT
                  Jungle⠀⇛


                       Automation is the name of the game in IT today,
                       particularly with the talent shortage gripping the
                       industry and remote work becoming the norm. To that
                       end, a new release of a message management solution
                       from DRV Technologies that will enable IBM i shops
                       to automate their responses to IBM i messages will
                       likely be well received.


                       DRV Technologies develops a series of handy
                       utilities for the IBM i server, including spool
                       management and distribution (SpoolFlex), a forms
                       management tool (FormFlex), secure MICR check
                       printing (SecureChex), a database query and report
                       writing tool (DBXFlex), and MessageFlex, a message
                       monitoring solution.


                # ⚓ Managed_Cloud_Saves_Money_By_Cutting_System_And_People
                  Overprovisioning_–_IT_Jungle⠀⇛


                       For most IBM i shops in the world, a unit of
                       compute, storage, or networking on a cloud or a
                       unit of time for a skilled IT specialist is always
                       going to cost more than what it costs to have such
                       talent in house. And so, you would think, putting
                       an IBM i system in the cloud and managing all
                       aspects of that system will always cost companies
                       more money, right?


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Linuxiac ☛ Why_Ubuntu_Isn’t_a_Flagship_Linux_Desktop
                  Distribution_Anymore⠀⇛


                       Although Ubuntu has been an enormous success,
                       controversial decisions will prevent it from being
                       named the best Linux desktop distribution in the
                       future.


                       I’m aware that this article’s headlines are not
                       among the most popular of the day. On the other
                       side, the Internet is overflowing with articles
                       like “Why Ubuntu is the best distribution for…,”
                       which are not valid for one reason. In Linux, there
                       is no such thing as “best.”


                       But before we go any further, it is essential to
                       note that this post only covers the desktop
                       editions of Ubuntu. The server side of things is an
                       entirely different story that is outside the scope
                       of this article.


                       So we will start with the following maxim – Ubuntu
                       is a phenomenon. The distribution has risen from 0
                       to 100 at a rate that no other Linux distribution
                       has ever matched.


                       Only a few years after its initial version 4.10,
                       “Warty Warthog,” in 2004, Ubuntu rose to the top of
                       the desktop Linux rankings.


                       In the years that followed, Ubuntu evolved to the
                       point where, to the uninitiated, the terms Linux
                       and Ubuntu meant the same thing. In other words,
                       the distro became synonymous with Linux for a good
                       reason.


                # ⚓ OMG Ubuntu ☛ Linux_Lite_6.0_Released,_Based_on_Ubuntu_22.04
                  LTS_–_OMG!_Ubuntu!⠀⇛


                       A new version of Linux Lite, a lightweight Linux
                       distro based on Ubuntu, is available to download.


                       Linux Lite 6.0 uses the latest Ubuntu 22.04 LTS as
                       its foundation, paired with Linux kernel 5.15, and
                       the nimble Xfce 4.16 desktop environment. Although
                       it runs fine on modern machines Linux Lite is
                       tailored towards use on older and/or resource-
                       limited hardware.


                       In this post I whizz through what’s new in Linux
                       Lite 6.0, and point you in the direction of the
                       official download so you can grab a copy, boot it
                       up, and try it out for yourself.


                       Let’s dive in!


                # ⚓ InfoQ ☛ Ubuntu_Core_22_Brings_Real-time_Compute_Support_for
                  IoT_Industrial_Applications⠀⇛


                       The latest version of Canonical OS for IoT and
                       embedded systems, Ubuntu Core 22, introduces real-
                       time support for applications in robotics and
                       industry.
                       With a 10y LTS and a special focus on security,
                       Ubuntu Core is a containerized version of Canonical
                       Linux-based OS specifically crafted for IoT devices
                       and embedded systems.
                       Ubuntu Core leverage containerization to enforce a
                       clean separation the kernel, OS image and
                       applications. Additionally, it supports “on the air
                       updates” to make it easier for customers to update
                       their app in a transactional way and reducing
                       network traffic by only transmitting diffs. Devices
                       running Ubuntu Core can also have their dedicated
                       IoT App Store which allows to control which apps
                       can be installed.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ SolidRun_RZ/G2LC_SOM_is_powered_by_Renesas
                  RZ/G2LC_processor_for_AI-enhanced_HMI_applications_–_CNX
                  Software⠀⇛


                       SolidRun RZ/G2LC SOM is a system-on-module based on
                       Renesas RZ/G2LC single or dual-core Cortex-A55/M33
                       processor and designed for AI-enhanced human-
                       machine-interface (HMI) applications, industrial
                       and building automation, video surveillance, IoT,
                       etc…


                       The module is also equipped with 1GB DDR4 RAM, 8GB
                       eMMC flash, and a wireless module with dual-band
                       WiFi 4 and with Bluetooth 4.2 all packed into a
                       tiny footprint measuring just 47 x 30mm that makes
                       it suitable for space-constrained devices such as
                       video doorbells and compact IP cameras.


          o § Open Hardware/Modding⠀➾


                # ⚓ Tom’s Hardware ☛ Clockwork’s_DevTerm_Teases_Raspberry_Pi
                  Compute_Module_4_Compatibility_(Updated)_|_Tom’s_Hardware⠀⇛


                       The DevTerm modular computer from Clockwork has a
                       hint of a significant upgrade, after its creator
                       posted on Twitter to show an adapter to fit a
                       Raspberry Pi Compute Module 4 board into the slot
                       previously occupied by a Compute Module 3.


                       With a simple adapter board, we can make the
                       #DevTerm immediately compatible with the #CM4. CM4
                       is so GREAT, for me it’s not much different from a
                       desktop PC already.


                # ⚓ Gizmodo ☛ Raspberry_Pi_Retro_Black_and_White_TV_Hack⠀⇛


                       Before you complain about there being nothing to
                       watch on Netflix, check out Rodrigo Feliciano’s
                       potent reminder of just how awful watching
                       broadcast TV once was. Using a Raspberry Pi, this
                       hacked black-and-white set simulates the classic TV
                       experience using modern content.


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_3A+_Mod_Brings_Double_the_RAM
                  |_Tom’s_Hardware⠀⇛


                       Finding a Raspberry Pi right now is harder than
                       ever with many vendors selling out almost as soon
                       as they’re restocked. But if you’re like maker and
                       developer Pi800, you can always splice together a
                       mod using an old Pi to create a faster, more
                       efficient model that would be otherwise impossible
                       to find on the market. In this project, Pi800 has
                       updated a Raspberry Pi 3A+ to use a 1GB RAM chip
                       harvested from a broken Pi.


                       This mod makes the 3A+ a more viable contender for
                       projects by doubling the RAM from it’s usual 512MB
                       to 1GB. According to Pi800, this mod uses a chip
                       from an old Raspberry Pi 3B+. so recreating it will
                       require either sacrificing a Pi or using components
                       from an out-of-commission module.


    * § Free, Libre, and Open Source Software⠀➾


          o § Web Browsers⠀➾


                # § Chromium⠀➾


                      # ⚓ TechRadar ☛ Wait,_is_Microsoft_tempting_kids_away
                        from_Chrome_with_Minecraft_money?⠀⇛


                      # ⚓ Stable_Channel_Update_for_Desktop⠀⇛


                             The Chrome team is delighted to announce the
                             promotion of Chrome 103 to the stable channel
                             for Windows,Mac and Linux.This will roll out
                             over the coming days/weeks.


                             Chrome 103.0.5060.53 contains a number of
                             fixes and improvements — a list of changes is
                             available in the log. Watch out for upcoming
                             Chrome and Chromium blog posts about new
                             features and big efforts delivered in 103.


          o § Programming/Development⠀➾


                # ⚓ Earthly ☛ Comparing_Local_Kubernetes_Development_Solutions
                  –_Earthly_Blog⠀⇛


                       Once you’ve determined that you want to use
                       Kubernetes as your base for developing applications
                       locally, it’s time to figure out which development
                       solution is the best. There are many different
                       options out there, but a few select reign over the
                       others as the most common, including minikube,
                       kind, K3s, kubeadm, Docker Desktop, and MicroK8s.


                       In this article, you’ll take a more in-depth look
                       at these six tools, and by the end, you should have
                       an easier time picking out the one that works best
                       for you. These options will be compared based on
                       what platforms they support, what the complexity of
                       the setup is, how flexible they are, and what kind
                       of support they provide.


                # ⚓ Dirk Eddelbuettel ☛ #38:_Faster_Feedback_Systems⠀⇛


                       Engineers build systems. Good engineers always
                       stress and focus efficiency of these systems.


                       Two recent examples of engineering thinking follow.
                       One was in a video / podcast interview with Martin
                       Thompson (who is a noted high-performance code
                       expert) I came across recently. The overall focus
                       of the hour-long interview is on ‘managing software
                       complexity’. Around minute twenty-two, the
                       conversation turns to feedback loops and systems,
                       and a strong preference for simple and fast systems
                       for more immediate feedback. An important topic
                       indeed.


                # ⚓ Collabora ☛ Adding_even_more_heads_for_the_group_picture⠀⇛


                       Part steadfast approach – part welcoming spirirt;
                       Collabora continues to successfully expand with new
                       talent amply on deck. Well ahead of the remote work
                       curve, our new joiners have settled into their
                       roles from their respective corners of the planet.


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ Trying_to_contact_Francis_van_Dun_(FVANDUN)_|
                        dean_[blogs.perl.org]⠀⇛


                             I am trying to contact Francis van Dun
                             (FVANDUN on cpan) for permission to relicense
                             Net::DHCP to the MIT license.


                # § Python⠀➾


                      # ⚓ Didier Stevens ☛ New_Tool:_sortcanon.py⠀⇛


                             sortcanon.py is a tool to sort text files
                             according to some canonicalization function.
                             For example, sorting domains or ipv4
                             addresses.


                             This is actually an old tool, that I still
                             had to publish. I just updated it to Python
                             3.


                # § Rust⠀➾


                      # ⚓ OpenSource.com ☛ Manage_your_Rust_toolchain_using
                        rustup_|_Opensource.com⠀⇛


                             The Rust programming language is becoming
                             increasingly popular these days, used and
                             loved by hobbyists and corporations alike.
                             One of the reasons for its popularity is the
                             amazing tooling that Rust provides making it
                             a joy to use for developers. Rustup is the
                             official tool used to manage Rust tooling.
                             Not only can it be used to install Rust and
                             keep it updated, it also allows you to
                             seamlessly switch between the stable, beta,
                             and nightly Rust compilers and tooling. This
                             article will introduce you to rustup and some
                             common commands to use.


    * § Leftovers⠀➾


          o ⚓ K-punk_haunts_gemini_21-06-2022⠀⇛


                 Last night I started on a journey: re-reading some of the
                 early writings by k-punk, the blogging alias of music
                 writer and cultural theorist Mark Fisher. Mark was
                 possibly most famous for his short essay ‘Capitalist
                 Realism’, and for those who haven’t yet come across the
                 writings or experienced the influence of his work, I
                 think you’re missing out, and I’d encourage you to dive
                 in to *some* – the vast majority – of what you’re missing
                 out on. Mark’s writing can have a raw energy that rebels
                 against the sober tendencies of academic theory, whilst
                 itself drawing heavily on theoretical substance/concept
                 in an approachable and creative way, and also heightens
                 ‘everyday text’ like music journalism.


                 The writers in the foreword and introduction to The
                 Collected and Unpublished Writings of Mark Fisher[1],
                 Simon Reynolds and Darren Ambrose, capture and frame this
                 sense of Mark’s work better than I can, but for me I’ve
                 always thought that what was great about Mark’s approach
                 is how it acknowledges our ‘media landscapes’ as
                 something in common; something that we can point to,
                 identify, find, critique and navigate through (or
                 escape), together – by acknowledging and drawing in all
                 of the shared experience of theory, concept, television,
                 film, music, art, etc. And in this approach, Mark would
                 avoid the stale or rigid somnambulist culture of academic
                 text, whilst also steering clear the emptiness of anti-
                 intellectual trends in discourse that could be found in
                 much of the popular UK broadcast and mainstream media
                 that had surrounded his experience in his formitive years
                 and the time of his writing (1980s-90s).


          o ⚓ The_Impermanence_Of_Architecture⠀⇛


          o ⚓ Canadaian_GP_warmed_up_at_the_end⠀⇛


                 A fast circuit with long straights and heavy braking is
                 usually a recipe for some overtaking. This one has walls
                 that break cars that go off and bring out saftey cars to
                 mix things up. Despite all that, most of this race wasn’t
                 that interesting. But then at the end, Sainz was right
                 behind, and Verstappen had to work for it. It seemed as
                 though Sainz had a chance of a win, but it’s Verstappen’s
                 year.


          o ⚓ Ruben Schade ☛ Happy_80th,_Paul_McCartney!⠀⇛


                 Clara and I have been diving headfirst into Paul’s
                 discography of late, and now I learn the chap just hit
                 the big 80 yesterday.


          o § Science⠀➾


                # ⚓ ACM ☛ 3D-Printed_Acoustic_Holograms_Against_Alzheimer’s_or
                  Parkinson’s⠀⇛


                       A team of researchers at Spain’s Universitat
                       Politècnica de València (UPV), the Spanish National
                       Research Council, and Columbia University has
                       created customizable, three-dimensionally-printed
                       acoustic holograms that could be used to treat
                       diseases like Alzheimer’s and Parkinson’s.


                       The holograms focus ultrasound to open the blood-
                       brain barrier in a controlled manner, so drugs that
                       target central nervous system-affecting pathologies
                       can pass through.


                       They also correct for skull-induced aberrations,
                       and can produce an ultrasonic multi-focal beam in
                       critical brain structures.


                # ⚓ IDA ☛ The_Historic_Keweenaw_Mountain_Lodge_Designated_as
                  Michigan’s_Third_International_Dark_Sky_Park_–_International
                  Dark-Sky_Association⠀⇛


                       The International Dark-Sky Association (IDA) has
                       named Keweenaw Dark Sky Park the newest addition to
                       the International Dark Sky Places Program. The
                       headquarters for the Dark Sky Park is located at
                       the Keweenaw Mountain Lodge (KML). Here, visitors
                       and supportive community members can meet, learn,
                       and look “U.P.” to the stars for inspiration and
                       embrace nature while traveling around the top of
                       the Keweenaw Peninsula. The park becomes the 3rd
                       IDA-certified Dark Sky Park in the State of
                       Michigan, joining the Headlands International Dark
                       Sky Park and the Dr. T.K. Lawless International
                       Dark Sky Park, and is the first International Dark
                       Sky Park in the Upper Peninsula of Michigan.


                # ⚓ Ben Congdon ☛ You_Need_to_be_Wrong_(Sometimes)⠀⇛


                       “Well-calibrated” means that if you predict
                       something occurs with X% probability, then that
                       event actually occurs X% of the time. Since
                       predictions are often made on one-off events,
                       another way of expressing calibration is that X% of
                       predictions that you made with X% confidence should
                       resolve in your favor. For example, if you make 100
                       predictions of 100 independent events, each with
                       probability 75%, then you’d expect that (roughly)
                       75 of your predictions would be “correct”.


                       The corollary to this is that, in the same example,
                       you’d expect that 25 of your predictions would be
                       “wrong”. And this is a good thing. If you instead
                       observed that only 5 of your predictions were
                       “wrong”, then you would not be well-calibrated.
                       Rather, you’d be significantly underconfident in
                       your predictions.


          o § Education⠀➾


                # ⚓ Michael West Media ☛ The_great_Sydney_University_grant
                  swindle⠀⇛


                       Australia’s universities have been corporatised and
                       compromised, and business schools are at the
                       vanguard of academic capture. Jeanne Ryckmans
                       investigates the rise and fall of the five-star
                       travelling former professor who led the high-life
                       on public grants.


                       The University of Sydney Business School website
                       trumpets “Business not as usual!”. Its mission? To
                       “develop students into future business leaders”
                       using an “innovative approach to our teaching and
                       learning”. True to its word, in 2021, the school
                       promoted on LinkedIn a free online “Masterclass in
                       leadership” that promised to give “a taste of what
                       it’s like to study at Sydney: Discover how so-
                       called ‘dark side’ personality characteristics,
                       such as narcissism and psychopathy, play a part in
                       effective leadership.”


                       Established in 1920, the University of Sydney
                       Business School claims to be the oldest business
                       faculty in Australia. Its $250 million state-of-
                       the-art Abercrombie Building, a high-tech 376,740
                       square feet facility in Sydney’s Inner West is the
                       “physical manifestation of the school’s ‘Business
                       Not as Usual’ vision for the future” where
                       “academics will solve poverty through
                       profitability”. It boasts of all things, a
                       “Sandpit”.


          o § Hardware⠀➾


                # ⚓ Ruben Schade ☛ Cathode_Ray_Dude_on_retro_hardware
                  collecting⠀⇛


                       I’ve felt that for a few pieces of kit lately. I
                       keep it around in the hopes that one day I’ll skill
                       up enough to work on them.


                       This has worked out in a few cases. I was ready to
                       throw away a tape drive years ago, then I learned
                       about belts and how to replace them. A set of DIMMs
                       in my Pentium 1 tower suddenly worked when I
                       learned about timings and voltages. Heck, I even
                       learned recently that a beloved childhood toy has a
                       glorified Z80 in it, which gets me a step closer to
                       figuring out how to bring it back to life one day.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ I’m_Not_Dead!⠀⇛


                       In other news, my parents flew in last night only
                       to find out when they arrived that they have COVID.
                       We wore masks in the car and they are isolating in
                       their room, so hopefully I will avoid catching it.


          o § Proprietary⠀➾


                # ⚓ The Record ☛ Microsoft_365,_Cloudflare_say_service_restored
                  after_outages⠀⇛


                       Microsoft said a day-long service outage affecting
                       the Exchange Online service has ended following
                       hours of complaints from users about connection
                       issues.


                       On Monday evening, Microsoft explained that it was
                       investigating problems with the service after users
                       said they were “experiencing delays or connection
                       issues when accessing the Exchange Online service.”


                       Two hours later, the company said its traffic
                       management infrastructure was not working and
                       attempted to reroute traffic in an effort to end
                       the outage.


                       It took another nine hours before service was fully
                       back to normal.


          o § Security⠀➾


                # ⚓ Help Net Security ☛ Researchers_disclose_56_vulnerabilities
                  impacting_thousands_of_OT_devices_–_Help_Net_Security⠀⇛


                       Forescout’s Vedere Labs disclosed OT:ICEFALL, 56
                       vulnerabilities affecting devices from 10
                       operational technology (OT) vendors. This is one of
                       the single largest vulnerability disclosures that
                       impact OT devices and directly addresses insecure-
                       by-design vulnerabilities.


                       In this video for Help Net Security, Daniel dos
                       Santos, Head of Security Research, Forescout, talks
                       about the 56 vulnerabilities, which impact ten
                       vendors, including Bently Nevada, Emerson,
                       Honeywell, JTEKT, Motorola, Omron, Phoenix Contact,
                       Siemens, and Yokogawa.


                # ⚓ Threat Post ☛ Voicemail_Scam_Steals_Microsoft_Credentials⠀⇛


                       Attackers are targeting a number of key vertical
                       markets in the U.S. with the active campaign, which
                       impersonates the organization and Microsoft to lift
                       Office365 and Outlook log-in details.


                # ⚓ IBM_i_PTF_Guide,_Volume_24,_Number_25_–_IT_Jungle⠀⇛


                       While the number of new security bulletins for IBM
                       i is nowhere near what we see with Windows Server
                       and Linux platforms, it has become a constant game
                       of Whack-a-mole.


                # ⚓ Multiple_Security_Vulnerabilities_Patched_on_IBM_i_–_IT
                  Jungle⠀⇛


                       In recent weeks, IBM has disclosed a handful of
                       vulnerabilities in its IBM i operating system and
                       related IBM i products, including Db2 Mirror,
                       WebSphere, Navigator for i, the Java development
                       and runtime tools, and OmniFind Text Search Server.
                       IBM has shipped PTFs for the security problems,
                       which range in severity from medium to high.


                # ⚓ Threat Post ☛ Office_365_Config_Loophole_Opens_OneDrive,
                  SharePoint_Data_to_Ransomware_Attack⠀⇛


                       A reported a “potentially dangerous piece of
                       functionality” allows an attacker to launch an
                       attack on cloud infrastructure and ransom files
                       stored in SharePoint and OneDrive.


                       Researchers are warning attackers can abuse
                       Microsoft Office 365 functionality to target files
                       stored on SharePoint and OneDrive in ransomware
                       attacks.


                       Those files, stored via “auto-save” and backed-up
                       in the cloud, typically leave end users with the
                       impression data is shielded from a ransomware
                       attack. However, researchers say that is not always
                       the case and files stored on SharePoint and
                       OneDrive can be vulnerable to a ransomware attack.


                # § Privacy/Surveillance⠀➾


                      # ⚓ PIA ☛ 8_Ways_to_Prevent_Replay_Attacks_—_How_to_Stop
                        the_Interception_and_Retransmission_of_Data⠀⇛


                             Around 16% of all global companies work
                             remotely, with no indication the trend will
                             slow anytime soon. While remote working can
                             save companies money in the long run, the
                             lack of digital security used to secure
                             remote networks creates an issue that’s
                             incredibly costly.


                             A rise in remote working means many companies
                             face increased cyber threats and attacks.
                             Unsecured public networks, weak security
                             measures, and use of personal devices for
                             remote access create vulnerabilities.
                             Cybercriminals use replay attacks to exploit
                             these security holes, intercepting traffic to
                             steal important company data.


          o § Environment⠀➾


                # ⚓ Idiomdrottning ☛ Discourses_of_climate_delay⠀⇛


                       Skeptical Science is a good collection of arguments
                       against many common myths among climate change
                       deniers. Those same old climate change denial myths
                       are still going strong and unfortunately still need
                       to be debunked again and again.


                       These days, there’s a new category of debunking
                       that we need to do even as people are realizing the
                       gravity of the situation. This isn’t meant to be
                       doomy but it’s so we can recognize common arguments
                       when they show up again and again and figure out a
                       way to address them (or ignore them). I feel like
                       some of these arguments do have a kernel of merit.


                # § Energy⠀➾


                      # ⚓ New York Times ☛ How_‘Trustless’_Is_Bitcoin,
                        Really?⠀⇛


                             Alyssa Blackburn, a data scientist at Rice
                             University and Baylor College of Medicine in
                             Houston, has spent several years performing
                             digital detective work with her trusty lab
                             assistant, Hail Mary, a shiny black computer
                             with orange trim. She has been collecting and
                             analyzing leaks from the Bitcoin blockchain,
                             the immutable public ledger that has recorded
                             all transactions since the cryptocurrency’s
                             launch in January 2009.


                             Bitcoin represents a techno-utopian dream.
                             Satoshi Nakamoto, its pseudonymous inventor,
                             proposed that the world run not on
                             centralized financial institutions but on an
                             egalitarian, math-based electronic money
                             system distributed through a computer
                             network. And the system would be “trustless”
                             — that is, it would not rely on a trusted
                             party, such as a bank or government, to
                             arbitrate transactions. Rather, as Satoshi
                             Nakamoto wrote in a 2008 white paper, the
                             system would be anchored in “cryptographic
                             proof instead of trust.” Or, as T-shirts
                             proclaim: “In Code We Trust.”


                      # ⚓ Ruben Schade ☛ Rubenerd:_Cryptocurrency_waste,_in_all
                        senses_of_the_word⠀⇛


                             Cryptocurrencies continue their precipitous
                             free fall, assuming they were even worth
                             something in the first place. The bandits and
                             whales are long out, and the marks have
                             switched from arguing about utility to
                             claiming that w-well everything else is a
                             Ponzi scheme too in a desperate attempt to
                             shore up their positions and retain what
                             little credibility they can.


                             I see some people revelling in the crumbling
                             of this smoke-belching edifice, citing how
                             nauseating some of the conduct of these
                             crypto bros have been. “Have fun being poor”
                             is the quote most often thrown back at them.


          o § Finance⠀➾


                # ⚓ RetailWire ☛ Retailers_applaud_as_Ocean_Shipping_Reform_Act
                  sails_through_Congress_–_RetailWire⠀⇛


                       The House of Representatives on Monday, following
                       an earlier vote by the Senate, approved legislation
                       that retailers believe will help reign in ocean
                       carriers who have used the coronavirus pandemic as
                       a rational to jack up rates to transport goods to
                       the U.S.


                       The bill, known as the Ocean Shipping Reform Act of
                       2022 (OSRA), passed in a vote of 369 to 42. It
                       seeks to improve oversight of ocean shipping
                       practices by granting more investigative authority
                       to the Federal Maritime Commission (FMC), providing
                       greater clarity on prohibited business practices
                       and giving the FMC the authority to order refunds.


          o § Civil Rights/Policing⠀➾


                # ⚓ EDRI ☛ New_Technologies_and_Fundamental_Rights_–_Monsters
                  of_Law_event_–_European_Digital_Rights_(EDRi)⠀⇛


                       Wikimedia Movement and the Free Knowledge Advocacy
                       Group EU have the pleasure to invite you to a
                       Monsters of Law event featuring First Advocate
                       General of the Court of Justice of the European
                       Union, Maciej Szpunar titled: New Technologies and
                       Fundamental Rights.


                # ⚓ New York Times ☛ Apple_Workers_at_Maryland_Store_Vote_to
                  Unionize,_a_First_in_the_U.S.⠀⇛


                       Apple employees at a Baltimore-area store have
                       voted to unionize, making it the first of the
                       company’s 270-plus stores in the United States to
                       join a trend in labor organizing sweeping through
                       retailers, restaurants and tech companies.


                       The result, announced on Saturday by the National
                       Labor Relations Board, provides a foothold for a
                       budding movement among Apple retail employees who
                       want a greater voice over wages and Covid-19
                       policies. Employees of more than two dozen Apple
                       stores have expressed interest in unionizing in
                       recent months, union leaders say.
                       In the election, 65 employees at Apple’s store in
                       Towson, Md., voted in favor of being represented by
                       the union, known as the Apple Coalition of
                       Organized Retail Employees, while 33 voted against.
                       It will be part of the International Association of
                       Machinists and Aerospace Workers, an industrial
                       trade union that represents over 300,000 employees.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Kluwer Patent Blog ☛ Petition_for_ministerial
                        conference_on_European_Patent_Organisation
                        ⠀⇛


                             Ahead of their meeting late June, a petition
                             calling for a conference of ministers of
                             contracting states under Article 4a EPC has
                             been sent to the members of the
                             Administrative Council of the EPO.


                             The petition is an initiative of the EPO’s
                             trade union SUEPO, which has invited all
                             staff members to sign it.


                             According to the petition: ‘the development
                             of the European Patent Organization (…) has
                             increasingly departed from the structure and
                             its mission as foreseen under the EPC and it
                             appears that no appropriate countermeasures
                             will be taken.


                             Therefore, we consider an external review of
                             the EPO’s situation by a Conference of
                             Ministers of the Contracting States under
                             Article 4a EPC to be expedient; such a
                             Conference is anyway long overdue in view of
                             Article 4a EPC.


                             [...]


                             Backlogs in examination and search are
                             increasing and it appears that for tackling
                             the problems the current line management is
                             tempted to return to outdated management
                             approaches like “challenging people” measures
                             and management “by fear”, which are unworthy
                             of a modern organization like the EPO with
                             highly qualified personnel. At the same time
                             the EPO plans to reduce the staffing level in
                             core tasks even further. This adds to current
                             plans squaring with a large-scale
                             decentralization of EPO tasks, including
                             transfer of tasks to NPOs. Such significant
                             amendments of the Organization’s structure
                             fall outside the prerogatives of the
                             President or the Administrative Council as
                             defined in Articles 10 and 33 EPC.
                             Furthermore, such a decentralization of EPO
                             tasks would also affect the legal certainties
                             of the validity of the patents granted by the
                             EPO.


                             [...]


                             According to the European Patent Convention,
                             meetings under Article 4a are due to be held
                             ‘at least every five years’ but since 2000,
                             when the article was introduced, such
                             conference has never been held.


                             The AC meeting of 29 and 30 June 2022 is
                             especially interesting as a decision will be
                             made about the re-appointment of president
                             António Campinos, who started in office in
                             2018, for a second five-year term.


                             [...]


                             It remains to be seen what the AC’s reaction
                             will be to the petition, which is a sign of
                             the troubled relations at the EPO as well.
                             Kluwer IP Law contacted several members of
                             the Administrative Council about the
                             performance of Antonio Campinos during his
                             first term, but non of them wanted to
                             comment.


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