𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Sunday, February 27, 2022
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Generated Mon 28 Feb 02:40:32 GMT 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/02/27/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
  Previous bulletins in IPFS (past 21 days, in chronological order):

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Qmae8sev1AAiuQdXEbMcdP8Nmxxz3DL81fAkGoiVLghjbB
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QmfSu9XMsGzj9YkPDP79UmwB6R9G9p3HQjsSCvUovR8y4o
QmeC7QgpY53w9VR36JGVyYSzhMZkHLkGiYWgd57Dskr9pH
QmZHDDpdkiKdpvVjLb94b8X2LhPVMcNQweiDqukj1DyKVT
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QmXBF3kDxFdmKcnVa7vYpbU6MyXrd1r3Y1NNrKZ3hrTTFa
QmbGvonNbAJzqBpoefSxdJSBAiUubKnrKDWzMQhqE8sKy9
QmNyjuGQ9G6aZFzvjbDENKmySNxf1JG2psBTi252HdEGHE
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QmcEFBoREHvxtA22UaNuV5Mx1EPRF8ANqTeNuB9Sx6DA3x
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ Free Software at Times of War (Versus Microsoft Graft) | Techrights

⦿ Gemini Will be Okay, Even If Some People Try to ’Extend’ It | Techrights

⦿ It’s Too Late to Change All the Infrastructure When War Erupts or Escalates | Techrights

⦿ IRC Proceedings: Saturday, February 26, 2022 | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/02/27/freesw-times-of-war/#comments
		http://techrights.org/2022/02/27/gemini-will-be-okay/#comments
		http://techrights.org/2022/02/27/infrastructure-consolidation-and-centralisation/#comments
		http://techrights.org/2022/02/27/irc-log-260222/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/02/27/gnunet-0-16-0/#comments
		http://techrights.org/2022/02/27/tech-in-russia-and-ukraine/#comments
		http://techrights.org/2022/02/27/texworks-0-6-7/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 58

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/27/freesw-times-of-war/#comments
    Gemini version at gemini://gemini.techrights.org/2022/02/27/freesw-times-of-war/

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Gemini_version_available_♊︎


✐ Free_Software_at_Times_of_War_(Versus_Microsoft_Graft)⠀✐


Posted in Finance, Free/Libre_Software, Microsoft at 8:39 pm by Dr. Roy
Schestowitz


Related: The_United_States_Government_Should_Quit_Bailing_Out_Microsoft_at
Taxpayers’_Expense


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Joe_Biden_gave_Microsoft_$22,000,000,000?_A_useless
             proprietary_helmet_contract_at_taxpayers'_expense?⦈_


Summary: Microsoft uses_militarism to receive_bailouts and it hopes to make the
military dependent on Microsoft (so that it becomes “too big to jail/fail”);
but recent events have shown that from a military perspective Microsoft
software and other proprietary software are an unacceptable risk


The one angle that interests us most (not_because_other_things_aren't
important) is how infrastructure_can_be_turned_off,_cracked,_undermined,_or
kept_online_only_to_target_users (e.g. marking them for arrest/assassination).
Centralisation contributes to this. For instance, you can “mute” millions of
people in one fell swoop by blocking Twitter and/or Facebook.


“Had more nations grasped the risk of proprietary software, social control
media (disinformation), and clown computing (outsourcing to foreign nations),
Free software would be more widely adopted.”Our hope is that there will be
peace, humanity will prevail, but also that more people will take note of this
past week’s events, perhaps using them as a lesson_on_the_importance_of
Software_Freedom.


We don’t mean to sound blunt, insensitive and uncaring. We very much care for
all human life, yet we try to highlight aspects of Free software by showing
what happens at times of war. Had more nations grasped the risk of proprietary
software, social control media (disinformation), and clown computing
(outsourcing to foreign nations), Free software would be more widely adopted.


So be that as it may, this is likely to be a recurring theme in our imminent
coverage. █


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⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⢹⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠄⠨⠏⠴⢿⣿⣿⣇⠭⡙⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠻⠿⣿⣿⣿⣿⣿⠛⡀⠀⠀⠀⠂⠀⢀⠀⠈⢠⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠠⠀⢰⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⣄⣀⣾⣶⣶⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣤⣤⣀⣼⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣟⠙⣽⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⠟⠋⣉⣛⣿⣿⠇⠀⣿⣿⣿⣿⡿⢟⣿⠿⢿⠃⠀⠀⠹⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡈⠛⠘⣥⣬⣿⡿⠏⠀⠀⠀⣴⣿⠃⠞⠉⠀⠀⠚⠂⠀⠀⠀⠙⠻⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡏⠸⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡍⠁⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢫⠉⣀⣈⣽⠿⠛⠛⠋⠉
⣿⣿⣿⣀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣾⡇⠀⠀⠀⠀⠀⠈⣿⣿⡀⠈⢀⣼⣏⢿⠰⣶⡿⠛⠛
⣿⣿⣿⣿⠷⢤⣾⣿⣿⣿⠏⠀⢙⣿⣿⣿⣿⣿⣿⠟⡻⠿⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢤⣐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠠⣰⡿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠄⢸⣿⣿⢸⣄⢁⠀⠴⠒
⢛⣿⣛⣋⠀⠀⠉⠻⢷⠗⠲⡀⠈⠛⠉⠉⠙⠛⠁⠈⠁⠀⣀⢚⣛⠛⣛⡛⠟⣛⣛⢋⣉⡛⣫⣍⢋⣩⡁⣤⣤⢨⡍⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⣧⣿⢸⡃⠈⠀⠂⢀
⢀⠴⠛⠟⠀⠀⠀⠀⠀⣰⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⢻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠀⣂⣿⢸⠓⠟⠿⠓⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⡛⠛⣘⡃⡄⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢉⣈⡈⢶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠐⠀⣀⠀⣀⢀⢂⣐⡒⣂⣒⢀⣀⠀⣠⣄⣨⣭⡝⢫⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠛⠉⣹⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⢹⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠨⠏⠴⢿⣿⣿⣇⠩⡙⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡅⠈⠻⠿⣿⣿⣿⣿⣿⠛⡂⠀⠀⠀⠂⠀⢀⠀⠈⢠⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠠⠀⢰⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⣄⣀⣾⣶⣶⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣤⣤⣀⣼⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣟⠙⣽⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⠟⠋⣉⣛⣿⣿⠇⠀⣿⣿⣿⣿⡿⢟⣿⠻⢿⠃⠀⠀⠹⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡈⠛⠘⣥⣬⣽⡿⠏⠀⠀⠀⣴⣿⠃⠞⠉⠀⠀⠚⠂⠀⠀⠀⠙⠻⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡏⠸⠋⠉⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⡍⠁⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢫⠉⣀⣈⣽⠿⠛⠛⠋⠉
⣿⣿⣿⣀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣾⡇⠀⠀⠀⠀⠀⠈⣿⣿⡀⠈⢀⣼⣏⢿⠰⣶⡟⠛⠛
⣿⣿⣿⣿⠷⢤⣼⣿⣿⣿⠏⠀⢙⣿⣿⣿⣿⣿⣿⠟⡻⠿⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⣐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠠⣰⡿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠄⠸⣿⣿⢸⣄⢁⠀⠴⠒
⢛⣿⣛⣋⠀⠀⠉⠻⢿⠗⠒⡀⠈⠛⠉⠉⠙⠛⠁⠈⠁⠀⣀⢚⣛⠛⣛⡛⠟⣛⣛⢋⣉⡛⣫⣍⢋⣩⡁⣤⣤⢨⡍⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⣧⣿⢸⡃⠈⠀⠂⢀
⢀⠴⠛⠟⠀⠀⠀⠀⠀⣰⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⢻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠀⣊⣿⢸⠓⠟⠿⠓⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⡛⠛⣘⡃⡄⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢉⣈⡈⢶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠐⠀⣀⠀⣀⢀⢒⣒⣒⣀⣒⢀⣀⠀⣠⣄⣨⣭⡝⢫⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠛⠉⣹⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⢹⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠠⠏⠴⢿⣿⣿⣇⠩⡙⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡅⠈⠻⠿⣿⣿⣿⣿⣿⠛⡂⠀⠀⠀⠂⠀⢀⠀⠈⢠⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠠⠀⢰⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⣄⣀⣾⣦⣶⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣤⣤⣀⣼⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣟⠙⣽⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⠟⠋⣉⣛⣿⣿⠇⠀⣿⣿⣿⣿⡿⢟⡿⠿⢿⠃⠀⠀⠹⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡈⠻⠘⣥⣬⣿⡿⠏⠀⠀⠀⣴⣿⠃⠞⠉⠀⠀⠚⠂⠀⠀⠀⠙⠻⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡏⠸⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡍⠁⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢫⠉⣀⣈⣽⠿⠛⠛⠋⠉
⣿⣿⣿⣀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⠀⠀⠀⠀⠀⠈⣿⣿⡀⠈⢀⣼⣏⢿⠰⣶⡟⠛⠚
⣿⣿⣿⣿⠷⢤⣼⣿⣿⣿⠏⠀⢙⣿⣿⣿⣿⣿⣿⠟⡻⠿⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⣔⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠠⣰⡿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠄⢸⣿⣿⢸⡄⢁⠀⠴⠒
⢛⣿⣛⣋⠀⠀⠉⠻⢿⠗⠶⡀⠈⠛⠉⠉⠙⠛⠁⠈⠁⠀⣀⢚⣛⠛⣛⡛⠟⣛⣛⢋⣉⡛⣫⣍⢋⣩⡁⣤⣤⢨⡍⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⣧⣿⢸⡃⠈⠀⠂⢀
⢀⠴⠛⠟⠀⠀⠀⠀⠀⣰⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⢻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠀⣊⣿⢸⠓⠟⠿⠓⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⡛⠛⣘⡃⡄⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢉⣈⡈⢶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠐⠀⣀⠀⣀⢀⢒⣒⣒⣀⣒⢀⣀⠀⣠⣄⣨⣭⡝⢫⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠛⠉⣹⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠀⠠⠀⢣⠌⣿⣿⣿⣿⢛⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⠏⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠠⠈⠀⠛⠛⠛⠃⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠉⣙⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⢠⣦⣀⣤⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠉⠀⠚⣿⣿⣿⣿⣿⣆⠀⠀⣶⣿⣷⠾⠿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡾⣿⣿⣿⣿⣿⣿⡀⠀⢻⣿⣿⡷⠾⢿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠁⠹⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣄⡜⡿⡏⠤⠒⣲⣿⣿⠇⠀⠉⢉⣽⡿⣭⠿⠋⠁⠹⡅⠀⠀⠀⠹⢿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⡿⠻⠛⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⢚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠍⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠆⠀⢑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡼⠀⠀⠀⠀⠀⠀⣶⣤⡄⠈⠇⢸⣟⢿⠛⢉⣉⣁⣀
⣿⣿⣿⣿⣦⣄⣈⣿⣿⣿⣿⡿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠘⣿⣷⢀⠘⣿⣿⡜⡇⠿⠿⠋⠉
⢿⣿⣿⣿⣿⠋⠉⠙⠏⠙⡹⢥⣦⠀⠉⠉⠀⢻⣿⠟⠁⠖⠩⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⢠⣸⠱⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⡆⣿⣿⡇⡷⠀⡤⢘⠋
⠀⠓⠚⢣⣶⡆⠀⠀⠀⠈⠃⠀⠉⠾⠠⠶⠀⠀⠛⠆⠀⠀⣀⢀⣈⠙⣛⡛⠟⣛⣛⢋⣉⡛⣫⣍⢋⣭⡙⣭⣤⢠⡍⣭⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⡩⢻⡇⡷⣀⣀⣈⡀
⠀⠀⠞⠃⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣏⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠀⢻⠺⠇⢉⣉⢙⣃⣥
⠈⠁⠂⠀⠀⠀⠀⢀⡆⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⡛⠛⣘⡃⣄⠛⠘⠘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢀⣀⡀⢿⠟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⠀⣀⢀⢀⣀⡐⣒⣂⢀⣐⠀⣠⣄⣠⣤⡜⢫⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠄⢀⣾⣿⠿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠲⣶⠀⠴⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠀⠠⠀⢣⠌⣿⣿⣿⣿⢛⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⠏⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠠⠈⠀⠛⠛⠛⠃⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠉⣙⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⢠⣦⣀⣤⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠁⠀⠚⣿⣿⣿⣿⣿⣆⠀⠀⣶⣿⣷⠾⡿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡾⣿⣿⣿⣿⣿⣿⡀⠀⢻⣿⣿⡷⠾⢿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⠹⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⣿⣷⣄⡜⣿⡏⠤⠒⣲⣿⣿⠇⠀⠉⢉⣽⡿⣯⠿⠋⠁⠹⡅⠀⠀⠀⠹⢿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⡿⠻⠛⠀⠀⠚⠛⠛⠛⠁⠀⠀⠀⢚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠍⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠆⠀⢑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡼⠀⠀⠀⠀⠀⠀⣶⣤⡄⠈⠇⢸⣟⢿⠛⣉⣉⣁⣀
⣿⣿⣿⣿⣦⣄⣈⣿⣿⣿⣿⡿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠘⣿⣷⢀⠘⣿⣿⡜⡇⠿⠿⠋⠉
⢿⣿⣿⣿⣿⠋⠉⠙⠏⠙⡹⢥⣦⠀⠉⠉⠀⢻⣿⠟⠁⠒⠩⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⢠⣸⠱⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠞⡆⣿⣿⡇⡷⠀⡤⠘⠋
⠀⠓⠚⢳⣶⡆⠀⠀⠀⠈⠃⠀⠉⠾⠠⠶⠀⠀⠛⠆⠀⠀⣀⢀⣈⠙⣛⡛⠟⣛⣛⢋⣉⡛⣫⣍⢋⣩⡙⣭⣤⢠⡍⣭⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⡩⢻⡇⡷⣀⣀⣈⠀
⠀⠀⠞⠃⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣏⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠀⠻⠺⠇⢉⣉⢙⣃⣥
⠈⠁⠀⠀⠀⠀⠀⢀⡆⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⣛⠛⣘⡃⣆⠛⠘⠘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢀⣀⡀⢾⠟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⠀⣀⢀⢀⣀⡐⣒⣂⢀⣐⠀⣠⣄⣠⣤⡜⢫⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠄⢀⢾⣿⠿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠀⠠⠀⢣⠌⣿⣿⣿⣿⢛⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⠏⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠠⠈⠀⠛⠛⠛⠃⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠉⣙⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⢠⣦⣀⣤⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠁⠀⠚⣿⣿⣿⣿⣿⣆⠀⠀⣶⣿⣷⠾⠿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠾⣿⣿⣿⣿⣿⣿⡀⠀⢻⣿⣿⡷⠾⢿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠁⠹⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⣿⣷⣄⡜⣿⡏⠤⠒⣲⣿⣿⠇⠀⠉⢉⣽⡿⣫⠿⠋⠁⠹⡅⠀⠀⠀⠹⢿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠻⡿⠻⠛⠀⠀⠘⠛⠛⠛⠁⠀⠀⠀⢚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠍⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠆⠀⢑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡼⠀⠀⠀⠀⠀⠀⣶⣤⡄⠈⠇⢸⣟⢿⠛⣉⣉⣁⣀
⣿⣿⣿⣿⣦⣄⣈⣿⣿⣿⣿⡿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠙⣿⣷⢀⠘⣿⣿⡜⡇⠿⠿⠉⠉
⢿⣿⣿⣿⣿⠋⠉⠛⠏⠙⡹⢥⣦⠀⠉⠉⠀⢻⣿⠟⠁⠒⠩⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⢠⣸⠱⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠞⡆⣿⣿⡇⡷⠀⠤⢘⠋
⠀⠓⠚⢳⣶⡆⠀⠀⠀⠈⠃⠀⠉⠾⢠⠶⠀⠀⠛⠆⠀⠀⣀⢀⣈⠙⣛⡛⠟⣛⣛⢋⣉⡛⣫⣍⢋⣭⡙⣭⣤⢠⡍⣭⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⡩⢻⡇⡷⣀⣀⣈⡀
⠀⠀⠞⠃⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣏⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠀⠻⠺⠇⢉⣉⢙⣃⣥
⠈⠁⠀⠀⠀⠀⠀⢀⡆⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⣛⠛⣘⡃⣄⠛⠘⠘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢀⣀⡀⢿⠟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⠀⣀⢀⢀⣀⡐⣒⣂⢀⣐⠀⣠⣄⣠⣤⡜⢫⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠄⢀⢾⣿⠿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠲⣶⠀⠴⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠉⠀⠈⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⠀⠼⠱⠿⣿⣿⣿⡺⠁⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⠈⠿⢿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠐⠀⠈⡀⠀⠠⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⠤⢀⣲⣿⣿⣿⣿⣆⠀⠀⠀⣄⣤⣀⣼⣷⣶⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣤⣦⢀⣠⣿⣿⣿⣿⣿⣇⠀⠘⣿⣿⣿⡉⣭⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⠛⠿⢿⣿⣿⡀⠀⣻⣿⡟⢋⣉⣙⣿⣿⡇⠀⠿⠿⣿⣿⢿⣿⠭⠛⠿⠇⠀⠁⠹⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣾⡿⠛⠉⣥⣴⣿⣿⠟⠀⠀⠀⣶⣿⠓⠟⠁⠀⠠⠉⠠⠀⠀⠀⢉⡻⡟⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⠁⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⡈⠀⠀⠀⠀⠀⢀⣀⠀⠀⢥⢈⣤⣬⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣄⡀⠸⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣾⡇⠀⠀⠀⠀⠀⠘⣿⣿⡄⠈⣤⣾⣆⣷⢉⣉⣥⣀⣄
⣿⣿⣿⣿⣿⣿⠾⢿⢿⡿⠿⣿⣡⣤⠘⠋⠁⠀⠹⣿⡿⠟⣛⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣐⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢠⣴⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣦⢸⣿⣿⢸⡿⠿⢿⡋⢁
⠿⢻⣿⣍⡛⣛⠀⠀⠀⠁⢀⠀⠈⠹⢾⢀⣔⢶⠒⢿⡀⠀⠉⠃⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⢒⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠹⠞⢿⣿⢸⠗⠒⠶⣻⠉
⠀⠀⠀⣀⣞⠻⠃⠘⠀⠀⠈⠃⠀⠉⠀⠈⠉⠐⠂⠾⠣⠀⣀⢀⣀⠙⣛⡛⠟⣛⣛⢋⣉⡛⣫⣍⢫⣭⡛⣤⣤⢨⡍⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⣶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⣭⣿⢸⣿⣠⣄⣅⢠
⠀⢀⣀⢣⠛⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡻⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⠀⠁⡉⣀⣲⣏⣈⣠⣵
⠀⠀⠀⠉⠀⠀⠀⠀⠂⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⡀⠿⢠⣸⢟⠃⣛⢛⣘⣃⡄⠛⠘⠘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢚⣍⡊⠛⢀⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣀⢂⢀⣀⡀⣐⣐⢒⣀⠀⣠⣄⣬⣤⡌⢩⣭⡭⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⣯⢨⣽⡇⣀⢟⣿⣿⠿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠈⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠜⠀⠼⠱⠿⣿⣿⣿⡺⠁⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⠉⠿⢿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠐⠀⠈⡀⠀⠠⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⢤⢀⣶⣿⣿⣿⣿⣆⠀⠀⠀⣤⣤⣄⣼⣷⣶⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣤⣦⢀⣠⣿⣿⣿⣿⣿⣇⠀⠘⣿⣿⣿⡉⣭⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣩⡿⠛⠿⣿⣿⣿⡀⠀⣻⣿⡟⢋⣉⣙⣿⣿⡇⠀⠿⠿⣿⣿⢿⣿⠯⠛⠿⠇⠀⠁⠹⣿⣦⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣾⡿⠛⠉⣭⣴⣿⣿⠟⠀⠀⠀⣶⣿⠓⠟⠁⠀⠠⠉⠠⠀⠀⠀⢉⡻⡟⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⠁⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠁⡈⠀⠀⠀⠀⠀⢀⣀⠀⠀⢥⢈⣤⣬⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⡀⠹⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣾⡇⠀⠀⠀⠀⠀⠘⣿⣿⡄⠈⣤⣾⣎⣷⢉⣉⣥⣀⣄
⣿⣿⣿⣿⣿⣿⠾⠻⢿⡿⠿⣿⣡⣤⠘⠋⠁⠀⠹⣿⡿⠟⣛⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣐⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢠⣴⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣦⢸⣿⣿⢸⡿⠿⢿⡋⢁
⠻⢻⣿⣝⡛⣛⠀⠀⠈⠁⢀⠀⠈⠹⢾⢀⣔⢶⠒⢿⡀⠀⠉⠃⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⢒⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠹⠾⢿⣿⢸⠗⠒⠶⣻⠉
⠀⠀⠀⣀⣞⠻⠃⠘⠁⠀⠈⠃⠀⠉⠀⠈⠉⠑⠂⠾⠣⢀⣀⢀⣀⠙⣛⡛⠟⣛⣛⢛⣉⡛⣫⣍⢫⣭⡙⣤⣤⢨⡍⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⣭⣿⢸⣿⣠⣄⣅⢠
⠀⢀⣀⢣⠛⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡻⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⠀⠁⡉⣀⣲⣏⣈⣠⣵
⠀⠀⠀⠉⠀⠀⠄⠀⠂⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⡀⠿⢠⣸⢟⠃⣛⢛⣘⣃⡄⠛⠘⠘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢚⣉⡊⠛⢀⣿⣿⣿
⠉⠀⠀⠀⠀⡀⠀⠀⠀⣀⠲⣀⢂⢀⣀⣀⣐⣐⢒⣀⠀⣠⣄⣬⣤⡌⢩⣭⡭⣬⣥⠨⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⣯⢨⣽⡇⣀⢟⣿⣿⠿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠀⠈⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡀⠰⠀⠱⢇⣿⣿⣿⣿⡩⡋⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠁⠻⡿⣿⣿⣿⣿⡟⠃⠀⠀⠄⠠⠀⠒⠀⠈⠉⣉⠉⠁⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⡄⠀⣾⣿⣿⣿⣇⠉⠀⠀⣀⣀⡀⢰⣷⣤⣶⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣠⣄⡀⠀⣹⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⠛⢟⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣹⠿⠻⣿⣿⣿⡀⠀⢻⣿⡿⠛⠛⠻⣿⣿⡇⠀⣶⣿⣿⣿⡿⣿⡛⠻⢿⠇⠀⠀⢻⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⣠⣿⣿⣷⣴⣯⠟⠓⣋⣭⣽⣿⡿⠁⠀⠀⣴⣿⠛⠞⠉⠀⠀⠓⠠⠀⠀⠀⠙⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠃⢹⠋⠋⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⡉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣯⢁⣤⣬⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣄⠀⢻⣿⣿⣿⣿⣿⡿⠛⠻⣿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣼⡇⠀⠀⠀⠀⠀⠈⣿⣿⡀⠈⣠⣾⡎⣧⢻⠿⠛⡛⠛⠋
⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠻⢻⡧⣤⡄⠃⠀⢀⢀⣉⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⠠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⢀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣧⣆⢸⣿⣿⢸⣾⣶⣿⡿⠟⣚
⠘⠛⡿⡉⠉⠛⠂⠀⠁⠙⠀⠀⠀⢙⠿⡦⢰⡟⠛⠻⠁⠀⠰⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⢽⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⠚⢿⣿⢸⣯⣈⣉⡰⡴⠖
⠀⠀⠈⠉⢹⠿⡆⠀⠃⠀⠰⡆⠀⠀⠁⠀⠀⠈⠃⠾⠇⢀⣀⢀⣀⠛⣛⡛⠟⣛⣛⢋⣙⡛⣫⣝⢫⣭⡀⣤⣬⢩⡌⣬⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠈⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣀⣿⢸⣶⡀⠈⠐⠃⡀
⠀⠐⠀⠺⡹⠇⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⠉⠙⣈⢿⣾⠟⠞⢓⣁
⠀⠀⠀⠒⠦⠀⡀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⢟⠃⣛⢛⣘⡃⠀⠛⠘⠘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣘⢁⣈⡛⠉⣶⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣒⢐⢀⣂⣀⣀⣒⢂⣒⠂⣠⣄⣠⣤⡌⢩⣭⡭⣬⣥⠨⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⡄⠸⡬⣹⣿⣿⣿⣟⡟⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣙⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡁⠈⠅⠩⠙⠛⠛⠓⠁⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⢉⣹⣿⣿⣏⠰⠀⠀⠀⠀⠀⠀⣴⣀⣠⣽⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⢀⠀⠁⠐⢻⣿⣿⣿⣦⠀⠀⣴⣾⣷⡶⠿⢿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠐⢻⣿⣿⣿⣿⡄⠀⢸⣿⣿⣷⠴⢿⣿⣿⣿⠀⢠⣼⣿⣿⣿⡿⣿⠿⣿⡇⠀⠂⠹⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⠈⢙⣿⣷⡄⡠⢿⠿⡤⠐⢲⣾⣿⡟⠀⠈⢉⣽⡟⣭⠞⠁⠀⠴⠇⠀⠀⠀⠙⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⡟⠹⡟⠿⠛⠁⠀⠘⠛⠛⠛⠋⠀⠀⠀⠺⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠑⢀⣐⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡾⠀⠀⠀⠀⠀⠀⣿⣶⡆⠈⢃⣹⣯⢻⣹⣿⣿⣿⡿⠿⠿
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⢁⡀⢸⠀⠀⢀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠘⢿⣿⣠⠈⣿⣿⡎⣿⣩⣄⣴⣦⣤⣤
⠿⠿⢿⡟⠛⠛⠏⠀⠐⠙⠏⠁⠉⠙⢿⡦⣤⢾⡿⢿⡟⠛⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣦⣽⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢣⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠇⠛⢻⡇⡟⠛⠛⠛⢃⣀⡂
⠀⠀⠘⠲⢶⣶⣦⠀⠠⠂⠀⠀⠀⠀⠒⠈⠀⠁⠐⠠⠥⢀⣀⢈⣙⠛⣛⡛⠟⣛⣛⢋⣙⡛⣫⣝⢫⣥⡀⣬⣭⢩⡅⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠈⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢸⡇⣟⢓⠒⡖⣪⠁⠀
⠀⠀⠄⠀⡀⣯⡛⠐⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⣿⣯⢿⣝⡻⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⠘⠃⢿⣿⣤⣤⢦⡠⠆
⠀⠀⠀⠀⠁⠈⠃⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⣛⢛⡘⠃⠀⠛⠘⠘⡃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡂⣀⣀⢀⣂⢉⣋⡙⢁⣨⣥⣶⣶
⠰⠂⠀⠀⠈⠙⠒⠀⠀⣀⠲⣀⢀⢀⣀⡂⣀⣀⢒⣒⠒⣫⣄⣠⣤⡌⢩⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠄⠸⡬⣹⣿⣿⣿⣟⡿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣙⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡁⠈⠅⠩⠙⠛⠛⠓⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⢉⣹⣿⣿⣏⠰⠀⠀⠀⠀⠀⠀⣴⣀⣠⣽⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠀⠁⠐⢻⣿⣿⣿⣦⠀⠀⣴⣾⣷⡾⠿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⠐⢻⣿⣿⣿⣿⡆⠀⢸⣿⣿⣷⠼⢿⣿⣿⣿⠀⢠⣸⣿⣿⣿⣿⣿⠿⣿⡇⠀⠂⠹⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⠈⢙⣿⣷⡄⡠⢿⡿⣤⠔⢲⣾⣿⡟⠀⠈⢉⣽⡟⣵⠞⠁⠀⠴⠇⠀⠀⠀⠙⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣯⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⡟⠹⡟⠿⠛⠁⠀⠘⠛⠻⠛⠋⠀⠀⠀⠺⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠑⢂⣐⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡼⠀⠀⠀⠀⠀⠀⣿⣶⡆⠈⢃⣹⣯⢻⣹⣿⣿⣿⡿⠿⠿
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⢁⡀⢸⠀⠀⢀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠘⢿⣿⣠⠈⣿⣿⡎⣿⣉⣠⣴⣦⣤⣤
⠿⠿⢿⡟⠛⠛⠏⠀⠐⠙⠏⠁⠉⠙⢿⡦⣤⢾⡿⢿⡟⠛⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣦⣽⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢣⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠇⠛⢿⡇⡟⡛⠛⠛⣃⣀⡒
⠀⠀⠘⠶⢶⣶⣦⠀⠠⠂⠀⠀⠀⠀⠒⠈⠀⠁⠐⠠⠥⠀⣀⢈⣙⠛⣛⡛⠟⣛⣛⢋⣉⡛⣫⣝⢻⣥⡀⣬⣭⢩⡅⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠈⣶⢰⣶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢸⡇⡟⢓⠒⡒⢚⠁⠀
⠀⠀⠄⠀⡀⣯⡛⠐⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡻⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⠘⠃⢷⣿⣤⣤⢦⡠⠆
⠀⠀⠀⠀⠁⠘⠃⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⢟⠃⣛⢛⡘⠃⠀⠛⠘⠘⡃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡂⣀⣀⢀⣂⢉⣉⡙⢁⣨⣥⣶⣾
⠰⠂⠀⠀⠈⠙⠒⠀⠀⣀⠲⣀⢀⢀⣀⣂⣀⣀⢒⣒⠒⣫⣄⣠⣤⡌⢩⣭⡭⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⠀⣏⡻⣿⣿⣿⣿⠿⠿⠛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⠛⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠄⠒⠀⢚⠘⠙⠿⠿⠿⠌⠂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠛⢻⣿⣿⠋⡀⠀⠐⠀⠈⠀⢀⡄⠀⣐⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⠂⠈⢿⣿⣿⣄⠀⠀⢀⣤⣴⣤⣼⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣆⡀⠠⢾⣿⣿⣿⣇⠀⠈⣿⣿⣿⣄⣵⣿⣿⣿⡇⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠰⠈⢿⣯⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡌⠉⠙⠻⣿⡄⠀⢹⣿⣏⡁⠤⣬⣽⣿⡇⠀⠛⢛⣿⣟⣭⠟⠉⠀⠥⠀⠀⠀⠈⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠴⡟⢿⡿⠴⠂⠉⠀⠴⠾⠿⠿⠋⠀⠀⠠⠿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣒⠊⣁⣘⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⡆⠀⠀⠀⠀⠀⢸⣶⣶⠀⠑⣈⣽⡍⣿⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⣿⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣇⡀⢹⡿⣿⢸⣼⣛⣉⣩⣄⣀⣀
⣻⣿⣿⣿⡿⠿⢿⡟⠉⠻⢿⡿⠩⠶⢶⢆⣈⣠⣴⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣤⣘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠰⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠼⠈⠃⣿⢸⡿⠿⠿⠿⠋⠉⠭
⠀⠀⠀⢋⣡⡤⣤⡀⠀⠠⠀⠁⠠⠀⠨⠛⠉⠘⠋⠉⠙⢀⣀⢀⣐⠛⣛⡛⠟⣛⣛⢋⣉⡛⣫⣝⢻⣡⡀⣬⣭⢩⡌⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠉⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢸⣼⡷⠷⠄⠢⠞⠋⠁
⡀⠀⠀⠀⠈⠹⠿⡆⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡄⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠘⠋⣿⣿⣀⣄⣁⡀⡄
⡇⠀⠀⠀⠀⠀⠳⠆⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⣛⢛⡘⠃⠀⠛⠘⢘⢃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢐⡀⣀⣀⢐⣀⢛⣈⡙⠈⢉⣁⣥⣶
⡇⣴⠄⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⢀⣀⣀⣀⣐⢒⣒⠒⣢⣌⣠⣤⡍⢩⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠲⣶⠀⠲⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⠀⣏⡻⣿⣿⣿⣿⠿⠿⠛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⠛⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠄⠚⠀⢚⠘⠙⠿⠿⠿⠌⠂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠛⢻⣿⣿⠋⡀⠀⠐⠀⠈⠀⢀⡄⠀⣐⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⠂⠈⢿⣿⣿⣄⠀⠀⢀⣤⣴⣤⣼⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣆⡀⠠⢾⣿⣿⣿⣇⠀⠈⣿⣿⣿⣄⣵⣿⣿⣿⡇⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠰⠈⢿⣯⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡌⠉⠙⠻⣿⡄⠀⢹⣿⣏⡁⠤⣬⣽⣿⡇⠀⠛⢛⣿⣟⣭⠞⠉⠀⠥⠀⠀⠀⠈⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠴⡟⢿⡿⠴⠂⠉⠀⠴⠾⠿⠿⠋⠀⠀⠠⠿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣚⠂⣁⣘⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⡆⠀⠀⠀⠀⠀⢸⣶⣶⠀⠑⣈⣽⡍⣿⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣇⡀⢹⣿⣿⢸⣜⣛⣉⣉⣄⣀⣀
⣻⣿⣿⣿⡿⠿⢿⡟⠉⠻⢿⡿⠩⠶⢶⣆⣈⣠⣴⣿⣿⡿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣤⣘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠰⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠼⠈⠃⣿⢸⡿⠿⠿⠿⡋⠉⠍
⠀⠀⠀⢋⣡⡤⣤⡀⠀⠠⠀⠁⠠⠀⠨⠛⠉⠙⠋⠉⠙⠀⣀⢀⣘⠛⣛⡛⠟⣛⣛⢋⣉⡛⣫⣝⢻⣡⡀⣬⣭⢩⡌⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠉⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢸⣾⡷⠷⠆⠦⢜⠋⠁
⡀⠀⠀⠀⠈⠹⠿⡆⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡄⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠘⠋⣿⣿⣀⣄⣁⡀⡄
⡇⠀⠀⠀⠀⠀⠓⠆⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⢟⠃⣛⢛⡘⠃⠀⠛⠘⢘⢃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢐⡀⣀⣀⢐⣀⢛⣈⡙⠈⢉⣁⣥⣶
⡇⣴⠄⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⢀⣀⣀⣀⣐⢒⣒⠒⣢⣌⣠⣤⡍⢩⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⠀⢏⡻⣿⣿⣿⣿⠿⠿⠛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⡛⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠄⠒⠀⢚⠘⠙⠿⠿⠿⠌⠂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠛⢻⣿⣿⠋⡀⠀⠐⠀⠈⠀⢀⡄⠀⣐⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⠂⠈⢿⣿⣿⣄⠀⠀⢀⣤⣴⣤⣼⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣆⡀⠠⢾⣿⣿⣿⣇⠀⠈⣿⣿⣿⣄⣵⣿⣿⣿⡇⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠰⠈⢿⣯⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡌⠉⠙⠻⣿⡄⠀⢹⣿⣏⡁⠤⣬⣽⣿⡇⠀⠛⢛⣿⣟⣭⠟⠉⠀⠥⠀⠀⠀⠈⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠴⡟⢿⡿⠴⠂⠉⠀⠴⠶⠿⠿⠋⠀⠀⠠⠿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣚⠂⣁⣘⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⡆⠀⠀⠀⠀⠀⢸⣶⣶⠀⠑⢈⣽⡍⣿⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣄⣽⣿⣿⣿⣿⣿⣿⣿⠋⠈⣿⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣇⡀⢹⡿⣿⢸⣼⣛⣉⣩⣄⣀⣀
⣻⡿⣿⣿⡿⠿⢿⡟⠉⠻⢿⡿⠩⠴⢶⣆⣈⣠⣴⣿⣿⡿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣤⣘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠰⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠼⠈⠃⣿⢸⡿⠿⠿⠿⡋⠉⠍
⠀⠀⠀⢋⣡⡤⣤⡀⠀⠠⠀⠁⠠⠀⠨⠛⠉⠙⠋⠉⠙⠀⣀⢀⣘⠛⣛⡛⠟⣛⣛⢋⣉⡛⣫⣝⢻⣡⡀⣬⣭⢩⡌⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠉⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢸⣼⡷⠷⠄⠢⠜⠋⠁
⡀⠀⠀⠀⠈⠹⠿⡆⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡄⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠘⠋⣿⣿⣀⣄⣁⡀⡄
⡇⠀⠀⠀⠀⠀⠳⠆⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⢟⠃⣛⢛⡘⠃⠀⠛⠘⢘⢃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢐⡀⣀⣀⢐⣀⢛⣈⡙⠈⢉⣁⣥⣶
⡇⣴⠄⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⢀⣀⣀⣀⣐⢒⣒⠒⣢⣌⣠⣤⡍⢩⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢸⣙⢻⣿⣿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠁⠀⠠⠀⠃⠐⡋⠛⡻⠿⠿⠿⠁⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣯⠀⠙⠿⢿⣿⣿⢛⠀⠀⠐⠀⠀⠈⢠⠀⠀⣲⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠁⠄⠐⣾⣿⣷⠀⠀⠀⢀⣠⣤⣤⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡄⠀⢀⣼⣿⣿⣷⡄⠀⢸⣿⣿⣿⣈⣾⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠹⣿⣏⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣠⠘⠛⠻⢿⣧⠀⠀⣿⣿⡏⣉⣩⣭⣿⣿⠇⠸⠿⠿⣿⢟⣫⠷⠒⠉⣟⠀⠀⠀⠙⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡝⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣤⡶⣿⣦⣠⠉⠉⠈⣴⠶⣾⠿⠋⠀⠀⢰⣿⠏⠘⠁⠀⠀⠀⠉⠁⠀⠀⢠⠔⠝⠀⠽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⠛⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢠⠀⠀⠀⠀⠀⠀⢶⣤⣄⠀⠇⠐⣟⡻⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⠋⠁⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⢿⣿⣧⢻⡈⠻⠛⠉⣍⢉
⡿⢿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠿⣿⣿⣟⣫⡤⠀⠙⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠧⠘⢸⣿⢸⣧⣿⡿⢿⠿⠋
⠀⠈⠉⠉⠉⠛⣃⡀⠉⠁⠀⠀⠈⠁⠈⠉⠉⠆⠙⠛⠻⢛⣛⢉⣁⠀⣉⡛⠟⣛⣛⢛⣉⡛⣫⣝⢋⣭⡃⣤⣭⢡⡅⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠈⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠈⣿⢸⣿⡶⠤⢠⠌⠒
⣤⣄⠀⠀⠀⠐⠲⢭⡍⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡄⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠶⠿⢸⣿⣶⣄⣀⢀⡀
⠿⣿⡆⠀⠀⠀⠀⠈⠅⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⢠⡸⠟⠃⣛⢛⣘⡃⠀⠛⠘⠘⠃⠛⡃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡂⣀⣀⢀⣀⢀⣀⡙⠏⠉⠉⣃⣁
⣾⣿⡇⣄⡀⠀⠀⠀⠀⣀⠀⣀⢂⢀⣀⡀⣀⣒⢂⣀⠒⣠⣌⣩⣥⡄⢠⣤⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠲⣶⠀⠲⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⢽⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠅⠀⠿⠰⢿⣿⣿⣿⠪⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⣙⣿⠟⠹⢿⣿⣿⣿⠿⠀⠀⠠⠄⠐⠀⢉⠀⠀⢤⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢀⠀⢉⣿⣿⠈⠁⠀⠀⣀⣀⣀⣿⣶⣶⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠀⠘⣿⣿⣶⡀⠀⢸⣿⣿⣏⠙⣽⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣻⣿⣿⡿⠻⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣄⡀⠚⣿⣿⣿⡇⠀⠘⣿⣿⡟⠛⢉⣛⣿⣿⡇⢠⣶⣿⣿⣿⠿⣛⣛⡻⢿⡇⠀⠁⠘⣿⣷⣙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣇⡀⠀⢸⣿⣄⢀⠛⠟⠐⣩⣭⣽⣿⠿⠁⠀⢠⣶⡟⠰⠟⠉⠀⠀⠠⠧⠀⠀⠀⢈⣙⠟⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣨⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⠿⠛⠿⠿⠂⠀⠀⠉⠀⠉⠁⠀⠀⠀⢠⠍⢀⡀⠀⠀⠀⠀⠀⢠⣀⠀⠀⢡⠀⢥⣬⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠛⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⣾⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⢠⣼⣶⢹⣧⠹⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠸⡦⠀⢠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⠿⠧⠀⠈⡏⣿⡇⣿⠀⣰⣶⣦
⠛⠛⠛⠛⠹⠛⡿⢿⣿⠛⠳⠎⠉⠉⠙⠛⠛⠒⠛⠁⠀⠀⣒⢛⣛⠛⣋⡛⠉⣙⣛⢛⣛⡛⣫⣍⢋⣩⡉⣭⣤⢠⡄⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⡀⠷⣿⣧⠏⢠⣍⡉⠉
⣄⠀⠀⠀⡀⠀⠀⠀⡀⣰⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠀⣄⣹⡧⠅⣸⣭⠉⠀
⠀⠀⠀⠚⠂⠀⠀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⡛⠚⣘⡃⢄⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣂⣀⢀⣀⢉⣈⡁⣳⣿⠛⠳⠗
⣠⣤⣤⣾⡇⠀⠀⠀⠀⣀⠀⣀⢀⢀⣀⡐⣀⣀⢀⣀⠀⣠⣄⣡⣤⡝⢢⣤⡤⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠑⢁⣤⣤⣴
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⢸⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⠂⠐⠃⢛⣻⣿⣿⣷⠫⡈⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡙⠻⢿⠿⢿⣿⣿⣿⢃⠀⠀⠂⠀⠁⠈⡀⠀⠠⢤⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡆⠀⠙⠛⣇⠈⠀⠀⢀⣠⣄⣰⣿⣶⣾⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠒⠀⠹⣿⣷⠀⠀⢿⣿⣿⣏⢩⣽⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣆⠀⠀⠴⣿⣿⡆⠀⠸⣿⣿⠟⠉⣙⣻⣿⣿⡇⠀⣴⣿⣿⣿⠿⣟⣛⡿⢿⡇⠀⠁⠘⣿⣷⣞⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡄⠉⠉⢳⣀⣐⠛⠋⢉⣩⣭⣽⣿⠟⠀⠀⢡⣶⡟⠱⠟⠋⠉⠉⠀⢩⡀⠀⠀⠈⣙⢿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣌⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⡾⡿⠿⠄⠀⠈⠉⠈⠉⠀⠀⠀⠀⢨⠉⢀⡀⠀⠀⠀⠀⠈⢀⡀⠀⠀⢫⠌⣁⣀⣉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⢀⡴⣿⡝⣿⡙⣿⣿
⠿⢿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡄⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⢀⠈⣿⣿⡇⣿⠃⠈⣧
⠀⠀⠹⠿⠿⠛⢛⢿⡿⠿⠿⣿⠯⠍⠋⠙⠛⠟⠛⠋⠰⠒⣀⢀⣀⠐⣛⡛⠟⣋⣉⢉⣉⡛⣫⣍⢋⣩⡉⣭⣭⢡⡌⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣸⡆⣯⣿⣇⡟⠈⢀⡏
⠀⣘⡉⠀⠀⠀⠀⠀⠁⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣏⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠀⠁⣐⢹⡇⣷⠆⣹⣯
⠀⠉⠁⠀⠀⠀⠐⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⡀⠿⠀⠸⠟⠃⠛⠚⠘⠃⢄⢛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢀⣉⡉⢁⢿⣤⡟⠛
⠀⢀⣀⣠⣤⣤⠶⠂⠀⣀⠀⣀⢀⢀⣀⡀⣀⣐⢂⣀⠀⣠⣄⣠⣤⡌⢣⣬⡥⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⡙⠷⠉⣱⣤
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠸⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⢸⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⠂⠐⠃⢛⣻⣿⣿⣧⠫⡈⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡙⠻⢿⠿⢻⣿⣿⣿⢇⠀⠀⠂⠀⠁⠈⡀⠀⠠⢤⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠙⢛⣇⠈⠀⠀⢀⣠⣄⣰⣿⣶⣾⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠐⠀⠹⣿⣷⠀⠀⢿⣿⣿⣏⣩⣽⣿⣿⣿⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣆⡀⠀⠶⣿⣿⡄⠀⠸⣿⣿⠟⠉⣙⣻⣿⣿⡇⠀⣴⣿⣿⣿⠿⣟⣛⡿⢿⡇⠀⠁⠘⣿⣷⣞⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡄⠉⠉⢳⣀⣐⠛⠋⢉⣩⣭⣽⣿⠟⠀⠀⢡⣶⡟⠱⠟⠋⠉⠉⠀⢩⡀⠀⠀⠈⣙⢿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣍⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⡶⡿⠿⠄⠀⠈⠉⠈⠉⠀⠈⠀⠀⢨⠉⢀⡀⠀⠀⠀⠀⠈⢀⡀⠀⠀⢫⠈⣁⣀⣋⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⢀⡴⣿⡽⣿⡙⣿⣿
⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡄⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣨⠂⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢀⠈⣿⣿⡇⣿⠃⠈⣧
⠀⠀⠹⠿⠿⠛⠻⢿⡿⠿⠿⣿⠯⠍⠉⠙⠛⠟⠛⠋⠰⠒⣀⢀⣀⠐⣛⡛⠟⣉⣉⢉⣉⡛⣫⣍⢋⣩⡉⣭⣭⢡⡌⣤⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣸⡆⣿⣿⡇⡟⠈⢀⡏
⠀⣘⡉⠀⠀⠀⠀⠀⠁⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣏⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣅⢸⡇⠀⠁⣔⢹⡇⣷⠆⣹⣍
⠀⠉⠁⠀⠀⠀⠐⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⡀⠿⠀⠸⠛⠃⠛⠚⠘⠃⢄⢛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⠀⣀⢀⢀⡀⣀⣀⢀⣀⢀⣉⡉⢁⢿⣤⡟⠛
⠀⢀⣀⣠⣤⣤⠖⠂⠀⣀⠀⣀⢀⢀⣀⡀⣀⣐⢂⣀⠀⣠⣄⣠⣤⡌⢣⣬⡥⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⡙⠷⠉⣱⣤
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢠⠀⣳⢂⣽⣿⣿⣿⡟⡻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡿⠀⢀⠀⠀⠀⠤⠈⠐⠛⠛⠛⠓⠈⠂⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠛⠛⢿⡟⠱⠀⠀⠀⠀⠀⢠⣦⣀⣠⣽⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⢀⠈⢥⡀⠀⠀⣴⣾⣶⡾⡿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠈⠀⠻⣿⠀⠀⢹⣿⣿⣶⠾⢿⣿⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⢻⣿⣿⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣄⠀⠙⢿⡇⠀⠈⣿⡿⡡⠤⠶⣾⣿⣿⠃⠀⠼⠿⣿⡟⣻⣭⠭⠭⠙⢧⠀⠀⠀⠻⣿⣿⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠈⢢⣴⠈⠁⠴⠾⠿⠿⠛⠡⠀⠀⠰⠿⠏⠈⠋⠀⠀⠀⢀⡐⠀⠀⠀⣀⠬⡻⠋⢻⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣌⣽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠟⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢀⢠⠂⠀⠀⠀⠀⠀⢠⣤⣀⡀⠰⡆⠤⡤⣬⣼⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠟⠉⠀⠀⣀⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⢠⣾⣿⡆⣿⣇⡘⢿
⣿⡟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣀⠀⠻⠂⢀⣤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⡰⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢠⠀⣿⣿⡿⣸⠃⠀⠘
⠙⠷⠀⢠⡤⠋⠉⠐⠛⠛⠟⠟⠻⠛⠒⠂⠀⠀⠙⠿⠉⠉⣉⢁⣀⠀⣚⡛⠟⣛⣉⢁⣀⡀⣩⣍⢋⣩⡉⣭⣭⢡⡍⣥⡥⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠈⡆⠿⣿⡧⡏⠁⠀⣼
⡼⠀⠀⠆⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢻⣯⢿⣝⡛⢯⣟⠂⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠀⠀⣏⣹⡇⣷⠀⠘⢿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⡀⠿⠀⠸⠟⠃⠛⠛⣘⡃⢀⣛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢀⣉⡈⣐⡻⣧⡘⠎
⠀⠀⠀⣶⣿⣿⠿⠿⠗⣀⠀⣀⢀⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⡈⠓⠁⣽⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠲⣶⠀⠰⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢠⠀⣣⢂⣽⣿⣿⣿⡟⡻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡿⠀⢀⠀⠀⠀⠤⠈⠐⠛⠛⠛⠓⠈⠂⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠛⠛⢿⡟⠱⠀⠀⠀⠀⠀⢀⣦⣀⣠⣽⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⢀⠈⢡⡀⠀⠀⣴⣾⣶⡾⠿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠈⠀⠻⣿⠀⠀⢹⣿⣿⣶⠾⢿⣿⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⢻⣿⣿⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⠙⢿⡇⠀⠈⣿⡿⡡⠤⠶⣾⣿⣿⠃⠀⠼⢿⣿⡟⣻⣭⠭⠭⠙⢧⠀⠀⠀⠻⣿⣿⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⢢⣴⠈⠁⠴⠾⠿⠿⠛⠡⠀⠀⠰⠿⠏⠈⠋⠀⠀⠀⢀⡐⠀⠀⠀⣀⠬⡻⠋⢻⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣌⣽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠟⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⢠⠂⠀⠀⠀⠀⠀⢠⣤⣀⡀⠰⡆⠤⡤⣬⣼⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠟⠉⠀⠀⣀⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⢰⣾⣿⡆⣿⣇⡘⢿
⣿⡟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣀⠀⠻⠂⢀⣤⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⡰⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢠⠀⣿⣿⡿⣸⠃⠀⠘
⠙⠷⠀⢠⡤⠛⠉⠐⠚⠛⠻⠟⠻⠛⠒⠊⠀⠀⠛⠿⠉⠉⣉⢁⣀⠀⣚⡛⠟⣋⣉⢁⣀⡀⣩⣍⢋⣩⡉⣭⣭⢡⡍⣥⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠈⡆⠿⣿⡇⡏⠁⠀⣼
⡼⠀⠀⠆⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣟⠂⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠀⠀⣏⣹⡇⣷⠀⠘⢿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⡀⠿⠀⠸⠟⠃⠛⠛⣘⡃⢄⣛⠘⠘⠃⢛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢀⣉⡈⣔⡻⣧⡸⠊
⠀⠀⠀⣶⣿⣿⠿⠿⠗⣀⠀⣀⢀⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⡈⠓⠁⣽⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠲⣶⠀⠲⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢠⠀⣣⢂⣽⣿⣿⣿⡟⡻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡿⠀⢀⠀⠀⠀⠤⠈⠐⠛⠛⠛⠓⠈⠂⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠛⠛⢿⡟⠱⠀⠀⠀⠀⠀⢀⣦⣀⣠⣽⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⢀⠈⢡⡀⠀⠀⣴⣾⣶⡾⠿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠈⠀⠻⣿⠀⠀⢹⣿⣿⣶⠾⢿⣿⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⢻⣿⣿⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⠙⢿⡇⠀⠈⣿⡿⡡⠤⠶⣾⣿⣿⠃⠀⠼⢿⣿⡟⣻⣭⠭⠭⠙⢧⠀⠀⠀⠻⣿⣿⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠈⠢⣴⠈⠁⠴⠾⠿⠿⠛⠡⠀⠀⠰⠿⠏⠈⠋⠀⠀⠀⢀⡐⠀⠀⠀⣀⠬⡻⠋⢻⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣄⣽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠟⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⢠⠂⠀⠀⠀⠀⠀⢠⣤⣀⡀⠰⡆⠤⡤⣬⣼⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠟⠉⠀⠀⣀⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⢰⣾⣿⡆⣿⣇⡘⢿
⣿⡟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣀⠀⠻⠂⢀⣤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⡰⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢠⠀⣿⣿⡿⣸⠃⠀⠘
⠙⠷⠀⢠⡤⠛⠉⠴⠚⠛⠻⠛⠻⠛⠒⠚⠀⠈⠛⠿⠉⠉⣉⢁⣀⠀⣚⡛⠟⣛⣉⢁⣀⡀⣩⣍⢋⣩⡉⣭⣭⢡⡍⣥⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠈⡆⠿⣿⡇⡏⠁⠀⣼
⡼⠀⠀⠆⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣟⠂⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠀⠀⣏⣹⡇⣷⠀⠘⣿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⡀⠿⠀⠸⠟⠃⠛⠛⣘⡃⢄⣛⠘⠘⠃⢛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣀⢀⣉⡈⣔⡻⣧⡸⠊
⠀⠀⠀⣶⣿⣿⠿⠿⠗⣀⠀⣀⢀⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣭⡭⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⡈⠓⠁⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠲⣶⠀⠲⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣄⠀⣣⢈⣿⣿⣿⣿⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⣀⠀⠄⠈⠈⠛⠛⠛⠓⠙⠀⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠉⠗⠀⠀⠀⠀⠀⢠⣆⠀⣈⣻⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⡀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠀⠀⢿⣿⣿⣤⣶⣿⣿⣿⣿⡆⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠸⣿⡟⣁⠤⢬⣽⣿⣿⠃⠀⣠⣿⣿⣿⣿⠿⠿⠿⠿⣿⠀⠐⠈⢿⣿⣯⡹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣀⣠⠙⠁⣴⡶⣶⡿⠟⢃⠀⠀⢉⣴⡾⠫⡶⠛⠋⠉⠁⢀⡀⠀⠀⠈⠻⣿⣷⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⠟⠟⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⡚⠮⠁⠸⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣻⠏⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⡏⠰⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡞⠀⠀⠀⠀⠀⠀⢸⣷⣶⡆⠈⠓⣘⣟⡺⣾⣏⠉⢶⡮
⣿⣿⣿⣿⣿⠋⠉⠉⢻⣿⣿⣿⣿⣶⣾⣿⠿⠿⡿⠿⢿⣿⣿⣿⣿⢿⣀⠀⠺⠃⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⢸⣿⣿⣧⢻⡏⠐⠘⠃
⠄⠀⠀⠈⠻⡷⠀⣰⠄⠁⠉⠙⠛⠉⠋⠙⠉⠉⠁⠀⠀⠉⣛⢉⣀⠀⣀⡈⠀⣋⣛⢛⣉⡉⣡⣍⢈⣩⡉⣭⣭⢩⡍⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢠⣿⣿⡏⣾⡇⠀⠀⠀
⡉⠀⠀⢠⡶⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣏⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠘⣻⣿⡇⡏⠀⠀⠀⠀
⣤⡄⠀⠀⠀⠀⠀⠉⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⠀⠿⢀⡸⠟⠃⠛⠛⡘⠃⠀⠛⠘⠘⢃⡛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠇⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣈⢀⣉⡁⣧⠀⠀⣶⣦
⠈⠁⠀⠀⠀⡀⠙⠻⠷⣂⠀⣀⢀⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⢿⣥⡀⠀⠁
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣄⠀⣣⢈⣿⣿⣿⣿⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⣀⠀⠄⠈⠈⠛⠛⠛⠓⠙⠄⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠉⠗⠀⠀⠀⠀⠀⢠⣆⠀⣈⣻⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⡀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠀⠀⢿⣿⣿⣤⣶⣿⣿⣿⣿⡆⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠸⣿⡟⣁⠤⢬⣽⣿⣿⠃⠀⣠⣿⣿⣿⡿⠿⢿⠿⠿⣿⠀⠐⠈⢿⣿⣯⡹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣀⣠⠙⠁⣴⡶⣶⣿⠿⢃⠀⠀⢉⣴⡾⠫⡶⠛⠋⠉⠁⢀⡀⠀⠀⠈⠻⣿⣷⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⠟⠟⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⡚⠮⠁⠸⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣻⠏⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⡏⠰⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡞⠀⠀⠀⠀⠀⠀⢸⣷⣶⡆⠈⠓⢸⣟⡺⣿⣏⠉⢶⡮
⣿⣿⣿⣿⣿⠋⠉⠉⢻⣿⣿⣿⣿⣶⣾⣿⠿⠿⣿⠿⢿⣿⣿⣿⣿⢿⣀⠀⠸⠃⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⢸⣿⣿⣧⢻⡏⠀⠘⠃
⠄⠀⠀⠈⠻⡷⠀⣰⠄⠁⠙⠁⠙⠹⠏⠙⠉⠉⠁⠀⠀⠉⣛⢉⣀⠀⣀⡈⠐⣋⣛⢛⣉⡉⣡⣍⢈⣩⡉⣭⣭⢩⡍⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢀⣿⣿⡏⣾⡇⠀⠀⠀
⡉⠀⠀⢠⡶⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⠘⣻⣿⡇⡏⠀⠀⠀⠀
⣤⡄⠀⠀⠀⠀⠀⠉⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⢀⡸⠟⠃⠛⠛⡘⠃⠀⠛⠘⠘⢃⡛⠃⠘⠁⠉⠈⠉⠁⠉⠈⠁⠇⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣈⢀⣉⡁⣧⠀⠀⣶⣦
⠈⠁⠀⠀⠀⡀⠙⠻⠷⣂⠀⣀⢀⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⢿⣥⡀⠀⠁
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⢀⠀⢏⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠇⠀⠀⠈⠀⣉⠐⠫⠿⠿⠿⠿⠖⠀⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⠀⠉⠀⠉⠀⢀⡄⠀⠐⣲⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣠⣤⣤⣾⣿⣶⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣉⣭⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠸⣿⡿⠋⣉⣙⣻⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⠻⢋⣩⣤⣬⣿⣿⠏⠀⠀⠙⣉⣹⠟⣋⡵⠶⠒⠂⠉⠀⠀⠀⢻⣿⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡻⣿⣿⣿⣿⡿⠛⠋⠛⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠾⠿⠃⠈⠉⠀⠀⠀⠀⠤⠁⠀⠀⢀⣬⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⡁⠀⠀⣀⣘⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣤⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⡂⢤⣤⣬⣥⣌⠛⠿⢿⣉⣈
⣿⠻⠻⠿⢿⣿⡏⠉⠉⠻⣿⣿⣿⣿⣿⣿⣟⣻⣿⡟⠛⢿⣿⣿⣿⡿⢻⣄⠀⠘⢃⣴⣾⣿⣿⣿⣿⣿⣿⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⠀⠾⣷⣶⣿⡟⠁⠀⠀⢠⢹
⣭⣇⠀⠑⠀⠙⠟⠀⢠⠆⠀⠀⠀⠀⠓⠁⠚⠀⠉⠀⠀⠀⣈⢙⣉⠀⣀⡐⠀⣀⣛⢛⣉⡉⣩⣍⢁⣩⡉⣥⣬⢩⡄⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠁⣶⢰⡶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⣼⣿⣿⡇⠀⠀⠀⠀⠀
⣶⣆⠀⠀⠀⠟⠀⠀⠂⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣿⣿⠟⠃⠀⠀⠀⠀⠀
⠀⠰⣿⠀⠀⠀⠀⠠⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⡛⠛⠘⠃⠀⠛⠘⡘⠃⠛⠃⠘⠁⠉⠈⠉⠁⠉⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢘⣛⢋⣀⡀⠀⠀⠀⠀⣤
⠀⠀⠀⢀⣄⡀⠀⠒⠀⣀⠀⣒⢃⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠀⣸⣦⡀⠈
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⢀⠀⢏⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠇⠀⠀⠈⠀⣉⠐⠉⠿⠿⠿⠿⠖⠄⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⠀⠉⠀⠉⠀⢀⡄⠀⠐⣲⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣠⣤⣤⣾⣿⣶⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣉⣭⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠸⣿⡿⠋⣉⣙⣻⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⠻⢋⣩⣤⣬⣿⣿⠏⠀⠈⠙⣉⣹⠟⣫⡵⠶⠒⠂⠉⠀⠀⠀⢻⣿⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡻⣿⣿⣿⣿⡿⠛⠋⠛⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠾⠿⠃⠈⠉⠀⠀⠀⠀⠤⠁⠀⠀⢀⣤⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⡁⠀⠀⣀⣘⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡤⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⡂⢤⣤⣬⣥⣌⠛⠿⢿⣉⣈
⣿⠻⠻⠿⢿⣿⡏⠉⠉⢻⣿⣿⣿⣿⣿⣿⣛⣻⣿⡟⠛⢿⣿⣿⣿⡿⢻⣄⠀⠘⢃⣴⣾⣿⣿⣿⣿⣿⣿⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⠀⠾⣷⣶⣿⡟⠁⠀⠀⢠⢹
⣭⣇⠀⠑⠀⠙⠟⠀⢠⠆⠀⠀⠀⠀⠛⠃⠚⠀⠉⠀⠀⠀⣈⢙⣉⠀⣀⡐⠀⣀⣛⢛⣉⡉⣩⣍⢁⣩⡉⣥⣬⢩⡄⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠁⣶⢰⡶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⣼⣿⣿⡇⠀⠀⠀⠀⠀
⣲⣆⠀⠀⠀⠟⠀⠀⠂⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⣿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣿⣿⠟⠃⠀⠀⠀⠀⠀
⠀⠰⣿⠀⠀⠀⠀⠠⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⡛⠛⠘⠃⠀⠛⠘⡘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢘⣛⢋⣀⡀⠀⠀⠀⠀⣤
⠀⠀⠀⢀⣄⡀⠀⠒⠀⣀⠀⣒⢃⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠀⣸⣦⡀⠈
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⠁⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⢀⠀⢬⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠀⣉⠑⠋⠿⠿⠿⠿⠗⢆⢁⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠀⠉⠀⢀⡄⠀⠀⢲⣄⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣠⣤⣤⣾⣿⣶⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢿⣿⣿⣉⣭⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⠉⣉⣙⣻⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⠻⣛⣭⣤⣭⣿⣿⠟⠀⠀⠙⢛⣻⠿⣛⣭⠽⠮⠉⠉⠀⠀⠘⣿⣿⣿⣞⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠙⢿⣿⡿⠉⠉⠙⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣾⡿⠁⠘⠋⠀⠀⠀⠀⢄⠀⠀⠀⢈⣙⢿⠿⢿⡿⢶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠻⡿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠟⠀⢰⡆⢀⣀⣠⣮⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⡀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢩⢉⣁⣀⣘⣋⡄⠹⣿⡿⠿⠿⣿⣋
⣉⣽⣯⡀⠀⠀⠙⡿⠂⠀⣈⠋⠙⠉⠛⢛⡛⡿⠛⢛⠀⠀⠘⠛⣻⡿⠛⠂⠓⠂⠀⣾⣿⣿⣿⣿⣯⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠁⠀⠀⠀⠀⠀⢸⣿⡿⠿⠀⠈⠠⠿⠭⠽⣿⠃⠹⡌⠀⠀⠀⠀⠉
⠋⠹⣿⡧⢀⠀⣼⡃⠀⠠⠷⣶⠀⠤⠀⠀⠀⠀⠐⠛⠛⢖⣒⢟⣓⠀⣀⡀⠛⣁⣀⢙⣛⡛⣩⣍⢋⣩⡉⣭⣤⢠⡄⣤⡤⣤⡤⣤⣤⢰⣶⡆⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⣼⠀⠀⢇⠀⠀⠀⠀⠀
⠀⠀⠀⠰⣿⠖⠛⠁⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣱⠔⠁⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣒⣒⢀⣂⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠒⣂⠀⣐⢓⢒⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠀⠀⣰⣄⠀
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⠁⠀⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⢀⠀⢬⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠀⣉⠑⠋⠿⠿⠿⠿⠕⢆⢁⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠀⠉⠀⢀⡄⠀⠀⢲⣄⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣠⣤⣤⣾⣿⣶⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢿⣿⣿⣉⣭⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⠉⣉⣙⣻⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⠻⣛⣭⣤⣭⣿⣿⠟⠀⠀⠙⢛⣻⠿⣛⣭⠽⠮⠉⠉⠀⠀⠘⣿⣿⣿⣞⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠙⢿⣿⡿⠉⠉⠙⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣾⡿⠁⠘⠋⠀⠀⠀⠀⢄⠀⠀⠀⢈⣙⢿⠿⢿⡿⢶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠻⡿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠀⢸⡆⢀⣀⣠⣮⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⡄⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢩⢉⣁⣀⣘⣋⡄⠹⣿⡿⠿⠿⣿⣋
⣉⣽⣿⡀⠀⠀⠙⡿⠂⠀⣈⠛⠛⠉⠙⢛⡛⡿⠛⢛⠀⠀⠈⠛⣻⡿⠛⠂⠓⠂⠀⣾⣿⣿⣿⣿⣿⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠁⠀⠀⠀⠀⠀⢸⣿⡿⠿⠀⠈⠠⠿⠭⠽⣿⠇⠻⡌⠀⠀⠀⠀⠉
⠋⢹⣿⡧⢀⠀⣼⡃⠀⠠⠷⣶⠀⠤⠀⠀⠀⠀⠐⠛⠛⢒⣒⢟⣓⠀⣀⡀⠛⣁⣀⢙⣛⡛⣩⣍⢋⣩⡉⣭⣤⢠⡄⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⣼⠀⠀⢇⠀⠀⠀⠀⠀
⠀⠀⠀⠰⣿⠖⠛⠁⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣱⠔⠁⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣒⣒⢀⣂⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠒⣂⠀⣐⢓⢒⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠀⠀⣰⣄⠈
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠙⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⢿⣿⣿⡭⠉⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⠀⢪⡄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣈⠀⣀⣀⠨⠈⠩⠿⠿⠿⠿⠗⢆⡙⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣄⠀⠐⡲⣄⠀⠀⠀⢀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣴⣶⣦⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣼⣮⣿⣿⣿⣿⡇⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⣉⣉⣙⣿⣿⣿⡇⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢻⣿⣭⣬⣽⣿⣿⠟⠀⠀⠀⠛⣻⡿⠛⣩⣭⠭⠍⠋⠀⠈⠈⣿⣿⣇⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⠛⠋⢽⢟⠋⠘⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⣾⡿⠋⠸⠋⠁⠀⠀⠀⢀⡀⠀⠀⠘⠻⣿⣿⣿⣿⢢⠽⠿⢿⣿⣿⣿⣿⣿
⢿⣿⣟⣛⣿⣟⡁⠀⠉⠿⠿⠁⠀⠹⠿⠿⠿⠿⢿⣿⣿⣿⠟⠉⠻⢿⣿⣿⣿⣛⢍⣀⡀⢀⣤⣤⠄⠘⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣚⠓⠌⠀⠸⠟⡀⠁⣤⣤⣿⣿⣿⠿⠻
⠈⠉⠉⠛⠙⣿⣿⡆⣠⣶⡄⠀⢰⡦⠀⣀⣤⠂⠀⠈⠀⠰⠦⢤⣤⣤⣚⡋⠁⠀⠠⣭⠄⠹⣿⣿⡀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⠁⠀⠀⠀⠀⠀⢸⣿⣶⡶⠀⠝⠒⠿⠛⠻⠿⠇⢰⡌⢻⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⠦⠀⠀⠉⠁⠙⠛⠃⠀⠀⠀⠀⠀⣀⢘⣛⠋⣉⡁⠀⣀⣀⢂⣀⡀⣩⣍⢋⣭⡉⣤⣤⢠⡄⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⣶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⠈⠘⠀⢿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡻⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠙⠃⠀⠛⠘⠘⠃⠛⣃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠒⢒⣀⢀⢂⡒⣂⣀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⢀⣀⣀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢢⣤⡭⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠛⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠙⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⢿⣿⣿⡭⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⠀⢪⡄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣈⠀⣀⣀⠨⠈⠩⠿⠿⠿⠿⠝⢆⡙⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣄⠀⠐⡲⣄⠀⠀⠀⢀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣴⣶⣦⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣼⣮⣿⣿⣿⣿⡇⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⣉⣉⣙⣿⣿⣿⡇⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢻⣿⣭⣬⣽⣿⣿⠟⠀⠀⠀⠛⣻⡿⠛⣩⣭⠭⠍⠋⠀⠈⠈⣿⣿⣇⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⠛⠋⢽⢏⠋⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⣾⡿⠋⠸⠋⠁⠀⠀⠀⢀⡀⠀⠀⠘⠻⣿⣿⣿⣿⢢⠽⠿⢿⣿⣿⣿⣿⣿
⢿⣿⣟⣛⣿⣟⡁⠀⠉⠿⠿⠁⠀⠹⠿⠿⠿⠿⢿⣿⣿⣿⠟⠉⠻⢿⣿⣿⣿⣛⢍⣀⡀⢈⣤⣤⠄⠈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣞⠓⠌⠀⠸⠟⡀⠁⣤⣤⣿⣿⣿⠿⠻
⠈⠉⠉⠛⠙⣿⣿⡆⣠⣶⡄⠀⢰⡦⠀⣀⣤⠀⠀⠈⠀⠰⠦⢤⣤⣤⣚⡋⠁⠀⠠⣬⠄⠹⣿⣿⡀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⠁⠀⠀⠀⠀⠀⢸⣿⣶⡶⠀⠟⠒⠿⠛⠻⠿⠇⢲⡌⢻⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣿⠦⠀⠀⠉⠁⠙⠛⠃⠀⠀⠀⠀⠀⣀⢘⣛⠋⣉⡁⠀⣀⣀⢂⣀⡀⣩⣍⢫⣭⡉⣤⣤⢠⡄⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⣶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⠀⠈⠘⠀⢿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡻⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠙⠃⠀⠛⠘⠘⠃⠛⣃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠒⢒⣀⢀⢂⡒⣂⣀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⢀⣀⣀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢢⣤⡭⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠛⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠙⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣋⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠠⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣦⠀⢣⠌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡈⠀⣁⣈⡉⠈⠫⠿⠿⠿⣿⠔⢇⠛⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠀⠀⢠⡄⠀⠐⢶⣄⠀⠀⠀⢀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣴⣶⣦⣿⣿⣶⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣯⣹⣽⣿⣿⣿⣿⡇⠀⠀⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⠉⠙⠻⣿⣿⣿⠁⠀⠀⠙⠁⢹⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢿⣿⣫⣩⣿⣿⣿⠟⠀⠀⠁⠂⢀⣽⠿⠛⣻⣯⡙⠛⠃⠀⠂⢿⣿⣿⢍⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⡟⡿⠁⠀⠙⠛⠛⠛⠉⠀⠂⠀⠀⣴⣿⠏⠰⠟⠉⠁⠀⠀⢀⠀⠀⠐⠘⢿⡿⣷⣾⣿⣏⣙⣿⣿⣿⠿⠿⣿⣿
⠉⠉⠀⠚⠿⢿⠭⠭⢿⣥⣤⣀⣈⠛⠋⠀⠀⠙⠛⠛⠛⢿⣿⡿⡿⠿⠋⠈⠛⠿⣿⣿⠿⠶⠤⣴⡄⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠁⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⠴⣝⠋⠙⣿⠇⠙⣿⣿⣿⣀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⡥⠀⣘⣇⣤⣶⠛⠉⠁⠀⠀⠙⠓⣶⣶⣭⣽⠃⠀⠀⠰⠶⣄⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⠃⠀⠀⠀⠀⠀⠀⣷⣦⡤⠀⠰⠤⠬⠧⠤⠥⣼⢠⡌⠁⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠽⠇⠤⠀⠀⠀⠀⠉⠀⢀⣀⢀⣀⠀⣀⡀⠚⣀⣁⢀⣀⡀⣠⣌⢫⣬⡉⣤⣤⢠⡄⣤⡤⣤⡤⣤⣤⢰⣶⡆⣦⣶⠀⣶⢰⣶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⡄⠀⠋⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠙⠃⠀⠛⠘⠘⠃⠛⣃⠘⠃⠉⠈⠉⠁⠉⠈⠁⠀⠉⠈⠁⠉⠁⠶⢖⣀⢀⢀⡒⣒⣐⢊⣀⢀⣀⡀⠀⠀⠀⠀⠀
⣤⣤⡀⠈⠁⠀⠀⠀⠀⣀⠀⣀⢀⢀⣀⣀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⣯⢨⣽⡇⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠛⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⡿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣭⣽⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠃⢀⠀⢼⡁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠚⠁⢛⣻⣿⣿⣿⣟⠭⠙⡃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠐⠒⠈⠉⠁⣀⠀⠀⠤⣄⠀⠀⠀⠀⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣤⣤⣴⣿⣦⣶⣾⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢸⣿⣿⡛⣙⣿⣿⣿⣿⣿⠀⠀⢸⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⠟⠛⠿⣿⣿⣿⣿⠀⠀⠈⠋⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠸⣿⠖⣚⣻⣿⣿⡿⠃⠀⠀⠰⠀⢀⣤⠶⠒⢒⣒⡚⠻⠏⠀⠀⢿⣿⣿⡙⢿⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠉⠻⠿⠿⠟⠋⠁⠀⠀⢀⣶⣾⠋⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣼⣿⣟⢛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠟⠛⠁⠸⢿⣿⣿⠿⠯⢥⣴⣦⡛⠛⠋⠀⠀⠛⠛⠛⠋⢶⣧⣽⣿⣿⠏⠹⠿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠁⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣈⡙⠟⠻⣿⠟⠙⠿⠿⢿⣿⣿
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡯⠥⢀⣀⣀⣶⣾⠛⠉⠉⠉⠁⠒⠲⣶⣶⣾⡿⠁⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠁⠀⠀⠀⠀⠀⠠⡤⠄⠀⠀⠨⠀⠉⠀⣀⣈⣤⠀⠀⠀⠀⠀⠀
⢿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠈⠉⣛⢛⣋⠀⣀⡀⠀⣀⣀⢀⣀⡉⣩⣍⢀⣤⡁⣭⣭⢠⡄⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⣬⣿⡟⠀⠀⠀⠀⠀⠀
⢀⣀⣯⣣⡀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣀⣙⣉⣉⣃⣀⡀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠛⠃⡛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠥⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣒⢒⢀⡀⣀⣒⢚⣉⢛⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣭⣭⣭⠀⠀⠀⣀⠀⣀⢀⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡠⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⢿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣭⣽⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠃⢀⠀⢼⡁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠚⠁⢛⣻⣿⣿⣿⣿⠭⠙⡃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠐⠒⠈⠉⠁⣀⠀⠀⠤⣄⠀⠀⠀⠀⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣤⣤⣴⣿⣦⣶⣾⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡛⣙⣿⣿⣿⣿⣿⠀⠀⢸⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⠟⠛⠿⣿⣿⣿⣿⠀⠀⠈⠋⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠸⣿⢖⣚⣻⣿⣿⡿⠃⠀⠀⠰⠀⢀⣤⠶⠒⢒⣒⡚⠻⠏⠀⠀⢿⣿⣿⡙⢿⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠉⠻⠿⠿⠟⠋⠁⠀⠀⢀⣶⣾⠋⠰⠞⠋⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣼⣿⣟⢛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠟⠛⠁⠸⢿⣿⣿⠿⠯⢥⣤⣦⡛⠛⠋⠀⠀⠛⠛⠟⠻⢶⣦⣽⣿⣿⠏⠹⠿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠁⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣈⡙⠟⠻⣿⠟⠙⠿⠿⢿⣿⣿
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡯⠥⠀⣀⣀⣶⣾⠛⠉⠉⠉⠁⠓⠲⣶⣶⣾⡿⠃⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠁⠀⠀⠀⠀⠀⠠⡤⠄⠀⠀⠨⠀⠉⠀⣀⣈⣤⠀⠀⠀⠀⠀⠀
⢿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠈⠉⣛⢛⣋⠀⣀⡀⠀⣀⣀⢀⣀⡉⣩⣍⢀⣤⡁⣭⣭⢠⡄⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⣬⣿⡟⠀⠀⠀⠀⠀⠀
⢀⣀⣿⣥⡀⠀⠀⠀⠀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀
⣈⣙⣉⣉⣁⣀⡀⠀⠀⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠛⠃⡛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠥⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣒⢒⢂⡀⣀⣒⢚⣉⢛⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣯⣭⣭⣭⠀⠀⠀⣀⠀⣀⢀⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡠⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣤⣄⣀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠀⠀⠀⢸⣿⣟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⠿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⠋⠀⢠⠀⢣⠄⣻⣿⣿⣿⣿⡿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢁⢀⡉⠈⠡⠽⠿⠿⠿⠏⠃⠈⡆⣀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠈⠀⠀⢀⣤⠀⠀⣲⣦⠀⠀⠀⢠⣶⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣶⣦⣾⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣍⣽⣿⣿⣿⣿⣿⠀⠀⢸⣿⠏⠁⠘⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⡟⠉⢉⣛⣿⣿⣿⡟⠀⠀⢀⣿⠄⠀⠀⣀⣀⣀⡛⠿⠻⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢘⣿⣫⣭⣿⣿⣿⡟⠀⠀⠀⢈⣉⡽⢚⣋⣭⠿⠿⠉⠉⠀⠈⠀⣿⣿⣿⣌⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠛⠻⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠃⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠴⠿⠏⠀⠛⠁⠀⠀⠀⠀⢠⡀⠀⠀⠸⠿⣿⣿⣿⣿⡧⣨⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠠⠞⢛⣿⡿⠿⠶⢶⣶⣶⡛⠛⠁⠀⢠⡜⠛⣛⣻⣷⣾⣿⠿⣃⠈⠛⠿⣿⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠲⠌⠉⠈⠿⠁⠈⠿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡟⠋⠁⢢⣤⣾⣿⣿⠉⠀⠀⠀⠉⠉⠻⣿⣿⣿⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠸⡿⠶⠶⠀⠘⠀⢶⡶⡶⣶⡿⠀⢦⡀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣀⢀⣀⠀⣀⡉⠛⣁⣀⢀⣀⡀⣠⣄⢈⣭⡉⣭⣭⢩⡅⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠉⣶⢰⡶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⣸⣿⡇⣿⡇⠀⠀⣇⠀
⣼⣿⣿⣿⡏⢀⣸⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣿⣿⠇⣿⠀⠀⠀⠈⣀
⣿⣿⣿⣿⣿⣯⣥⣤⡄⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⡧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⠘⡘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢒⡒⣀⣀⢂⣛⢛⣈⡋⠀⠠⡶⠸⠁
⣿⣿⣿⣿⣿⣿⠟⠩⠦⣀⠠⣀⢀⢀⣀⣀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠚⡻⠃⣴⡤
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠋⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣤⣄⣀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠀⠀⠀⢸⣿⣟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⠿⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⠋⠀⠠⠀⢣⠄⣻⣿⣿⣿⣿⡿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢁⢀⡉⠈⠡⠽⠿⠿⠿⠏⠃⠈⡆⣀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠈⠀⠀⢀⣤⠀⠀⣲⣦⠀⠀⠀⢠⣶⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣶⣦⣾⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣍⣽⣿⣿⣿⣿⣿⠀⠀⢸⣿⠏⠁⠘⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⡟⠉⢉⣛⣿⣿⣿⡟⠀⠀⢀⣿⠄⠀⠀⣀⣀⣀⡛⠿⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢘⣿⣯⣭⣿⣿⣿⠟⠀⠀⠀⢈⣉⡽⢛⣋⣽⠿⠞⠋⠉⠀⠈⠀⣿⣿⣿⣨⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠃⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠴⠿⠏⠀⠛⠁⠀⠀⠀⠀⢀⡀⠀⠀⠸⠿⣿⣿⣿⣿⡧⣨⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠠⠞⢻⣿⡿⠿⠷⢶⣶⣶⡛⠛⠁⠀⢀⡝⠙⣛⣻⣷⣾⣿⠿⣃⡈⠛⠿⣿⠁⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠲⠌⠉⠈⠿⠁⠈⠻⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠋⠁⢢⣤⣾⣿⣿⠉⠀⠀⠀⠈⠉⠻⣿⣿⣿⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠸⡿⠶⠶⠀⠘⠀⢶⣶⡶⣶⡿⠀⢦⡀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣀⢀⣀⠀⣀⡉⠛⣁⣀⢀⣀⡀⣠⣄⢈⣭⡉⣭⣭⢡⡅⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠉⣶⢰⡶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⣸⣿⡇⣿⡇⠀⠀⣇⠀
⣼⣿⣿⣿⡇⣀⣸⣿⡄⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣿⣿⠇⣿⠀⠀⠀⠈⣀
⣿⣿⣿⣿⣿⣯⣬⣤⡄⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⠘⣘⠃⠛⠃⠘⠃⠉⠈⠉⠁⠉⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢒⡒⣀⣀⢂⣛⢛⣈⡋⠀⠠⡶⠸⠁
⣿⣿⣿⣿⣿⣿⠟⠻⠤⣀⠠⣀⢀⢀⣀⡀⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠘⡻⠃⣴⡤
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠋⠙⠁⠙⠋⠙⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣦⣤⣤⣤⣤⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣥⣾⠀⣉⣉⣀⡀⠀⠁⢀⣸⣿⢍⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢸⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠸⠅⠬⠏⠴⠿⣿⣿⣿⣿⢯⡙⢏⠉⠻⡀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠄⠤⠂⠒⠀⠀⠉⣉⣉⠉⠉⠀⠈⢘⣡⠛⢳⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⢀⡀⢀⣾⣆⣠⣴⣽⣧⠀⠀⠀⣿⣿⡦⠤⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠠⣿⣿⡿⡿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠻⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣷⠾⢿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⢩⢿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⣤⠤⢤⣼⣿⣿⡿⠀⠀⠀⠜⠛⣛⡷⠴⣦⣒⡀⠤⠀⠰⠈⣿⣿⣯⢍⢳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠂⠝⢷⣾⣿⣿⠿⠛⠀⠀⠀⣰⣶⠞⢡⠶⠚⠋⠁⠀⠀⠀⠀⠄⠹⢿⣿⣾⣾⣿⣟⣛⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣽⣿⣿⣿⠿⠋⣿⠿⢿⣿⡏⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡝⠋⠀⠄⠀⠀⠀⠀⠀⠈⠂⠀⠀⣨⠤⡙⠋⠙⣿⡇⠙⢿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠈⠉⠉⢽⡿⠛⠙⠛⢻⡿⢯⠉⠿⣦⣴⣋⣨⣭⡿⠛⠛⠛⠫⠶⢤⡄⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣰⠋⠀⠀⠀⠀⠀⢠⣦⣄⣠⠀⢰⡄⢬⣦⣤⣤⣾⠀⢀⠙⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡻⠟⠀⠀⠈⠹⠿⣿⣿⠀⠀⣠⡀⠀⢀⣴⣯⣽⣻⠁⠀⠀⠀⠀⠀⠀⢀⡠⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠄⠀⠤⢺⣶⡆⢹⡏⠀⠸⢱⡘
⣭⣽⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⢀⣀⠀⣀⡀⠀⣀⣀⢋⣉⡀⣠⣍⢁⣤⡀⣭⣭⢩⡌⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠁⣶⢰⣶⣶⠒⣶⢸⣿⣾⡇⣿⡛⢻⡟⢸⣿⡟⣸⡇⠀⠀⠀⠃
⢸⣿⣿⣿⣿⣿⣿⣅⡀⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣟⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣸⣿⡇⣿⠁⠀⢀⢀⣼
⣾⣿⣿⣿⣿⣿⣿⣿⡆⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⣘⣚⡃⠛⠃⠘⠃⠉⠌⠉⠁⠭⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣛⢛⣈⡸⣀⣠⣼⢠⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠷⣒⠶⣒⢒⣒⣒⣂⣀⣀⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⣤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⣯⢨⣽⡇⠈⠐⣃⣼⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠛⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠋⠙⠁⠙⠋⠙⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣥⣤⣤⣤⣤⡤⠄⠀⠀⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣭⡏⠉⢉⣉⣉⠀⠈⠁⢠⣻⡯⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⣸⠛⢿⣿⣿⣿⣿⣿⣿⣷⠂⠻⠿⢿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⠨⠂⠼⠋⠶⢿⣿⣿⣿⡏⢭⠙⢇⠀⢳⣶⣄⡀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠤⠤⠔⠐⠒⠀⠈⠉⣉⣉⠉⠁⠀⠉⢘⣤⠋⠁⠀⠻⠷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⣀⡀⢠⣿⣆⣤⣴⣿⣇⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢰⣿⣿⠿⡿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⢹⣿⡆⠀⠀⠀⠙⠉⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡷⠾⢿⣿⣿⣿⣿⠀⠀⠀⠛⡽⣿⣿⣿⡄⠀⠀⠀⡴⠾⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⣤⠤⢶⣾⣿⣿⡟⠀⠀⠀⠬⠁⣠⡴⢖⣛⣒⣒⠀⠀⠈⠘⣿⣿⣗⢮⢻⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠂⠟⢷⣾⣿⣿⠿⠛⠀⠀⠀⣴⣶⠟⢡⠶⠛⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣿⡯⣉⣽⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣈⣿⣿⣿⣻⠛⠉⣿⣿⣿⣿⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⠉⢀⠄⠀⠀⠀⠀⠀⠀⠑⠀⠀⠴⠳⢌⡁⠈⠿⢃⡙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠈⠀⠨⢿⡾⠛⠉⠛⢿⡿⢏⠉⠛⢻⣿⣴⣾⠟⠛⠋⠉⠉⠓⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣰⠋⠀⠀⠀⠀⠀⢸⣷⣦⣤⠀⠸⠀⢲⠶⠶⣶⡿⠀⣀⠙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠛⠛⠀⠀⠀⠚⢿⣿⣷⠀⢠⣦⠀⣶⣽⣻⠃⠀⠀⠀⠀⠀⠀⠀⡤⢀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠆⠀⠾⢿⣿⣇⢸⡇⠀⠸⠱⠘
⣿⣿⣯⣯⣻⣿⣿⣿⣿⠿⠛⠿⠿⠿⠛⠀⠀⠀⠀⠀⠐⢂⣀⢀⣀⠀⣀⡀⠀⣀⣀⢀⣀⡀⣩⣄⢀⣭⡁⣬⣭⢩⡌⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠁⣶⢰⣶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢸⣿⡏⣼⡇⠀⠀⠀⢀
⠿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⣿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⢸⣿⣇⢿⠁⠀⢀⢠⣾
⣠⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⢘⣚⡃⠛⠃⠘⠃⠉⠌⠉⠁⠩⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢂⣙⢛⣈⡸⣀⣤⣼⢸⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⣖⠶⣒⢒⣒⣒⣒⣒⣂⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⣯⢨⣽⡇⠀⠐⣡⣾⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠛⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢻⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠙⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣥⣤⣤⣤⣤⡤⠄⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣭⡏⠉⢉⣉⣉⠀⠈⠁⢠⣻⡯⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠁⠀⣸⠛⢿⣿⣿⣿⣿⣿⣿⣷⠂⠛⠿⢿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⠨⠂⠼⠃⠶⢿⣿⣿⣿⡏⣭⠙⢇⠀⢳⣶⣄⡀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠤⠤⠔⠐⠒⠀⠈⠉⣉⣉⠉⠁⠀⠉⢘⣤⠋⠁⠀⠻⠷⡾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⣀⡀⢠⣿⣆⣤⣴⣿⣇⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢰⣿⣿⠿⡿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⢻⣿⡆⠀⠀⠀⠙⠉⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡷⠾⢿⣿⣿⣿⣿⠀⠀⠀⠛⡽⣿⣿⣿⡄⠀⠀⠀⡴⠾⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⣤⠤⢶⣾⣿⣿⡟⠀⠀⠀⠬⠁⣠⡴⢖⣛⣒⣒⠀⠀⠈⠘⣿⣿⣇⢮⢻⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠂⠛⢷⣾⣿⣿⠿⠛⠀⠀⠀⣴⣶⠟⢡⠶⠛⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣿⡯⣉⣽⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣈⣿⣿⣿⣻⠛⠉⣿⣿⣿⣿⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⠉⢀⠄⠀⠀⠀⠀⠀⠀⠑⠀⠀⠴⠳⢌⡁⠈⠿⢃⡙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠈⠀⠨⢽⡶⠛⠉⠛⢿⡿⣏⠉⠛⢻⣿⣴⣶⠟⠛⠋⠉⠉⠓⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣰⠋⠀⠀⠀⠀⠀⢸⣷⣦⣤⠀⠸⠐⢲⠶⠶⣶⡿⠀⣀⠙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠛⠛⠀⠀⠀⠚⢿⣿⣷⠀⢠⣦⠀⣶⣽⣻⠃⠀⠀⠀⠀⠀⠀⠀⡤⢀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠆⠀⠶⢿⣿⣇⢸⡇⠀⠸⠱⠘
⣿⣿⣯⣭⣻⣿⣿⣿⣿⠿⠛⠿⠿⠿⠛⠀⠀⠀⠀⠀⠐⢂⣀⢀⣀⠀⣀⡀⠀⣀⣀⢀⣀⡀⣩⣄⢀⣭⡁⣬⣭⢩⡌⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠁⣶⢰⣶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢸⣿⡏⣼⡇⠀⠀⠀⢀
⢻⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⣿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⢸⣿⣇⢿⠁⠀⢀⢠⣾
⣠⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⢘⣚⡃⠛⠃⠘⠃⠉⠌⠉⠁⠩⠌⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢂⣙⢛⣈⡸⣀⣤⣼⢸⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⣖⠶⣒⢒⣒⣒⣒⣒⣂⢀⣀⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⣯⢨⣽⡇⠀⠐⣡⣾⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠛⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠙⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⡤⠀⠀⢸⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⢽⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣍⣹⠉⠉⠉⠉⠉⠀⠉⠠⣘⣿⠭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠘⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡀⠸⠀⢵⠂⣴⣿⣿⣿⣿⡟⣛⠻⠏⠉⢻⣿⡿⠧⢄⣄⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⢀⠠⠠⠐⠀⠐⠚⢛⡉⠉⠁⠀⠑⠘⣂⢾⠁⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣾⣄⣀⣬⣿⣆⠀⠀⠀⣿⣿⡟⣶⣄⣀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠠⣿⣿⡿⡿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣷⣽⣾⣿⣿⣿⣿⠀⠀⠀⠿⣻⡎⠙⠿⠿⢿⣤⡄⢠⠶⠻⣿⣿⣿⣷⣄⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠘⢿⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⣁⡤⣤⣭⣿⣿⡿⠀⠀⠀⠸⠿⣥⣤⠶⣒⣚⣛⡛⠂⠀⠁⢻⣿⣿⡢⡹⣷⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⡿⢻⠂⠹⢵⣶⣶⣿⡿⠟⠁⠀⠀⢠⣶⡾⠋⡶⠚⠉⠁⠀⠀⠈⠀⠈⠈⠻⢿⣿⣷⣿⣯⢌⣽⣿⣿
⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣨⣽⣿⣿⣿⡟⢻⣿⣿⣿⣏⠀⠀⠻⣷⣯⣽⣿⣿⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠉⠁⡠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠞⠢⣙⠀⠹⠇⡈⠻⣿⣿
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠙⢿⠟⠛⠉⠉⣿⡿⠏⠉⠉⠻⣿⣿⡟⠉⠉⠁⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⡞⠀⠀⠀⠀⠀⠀⣿⣶⣤⡄⠀⠗⠐⡾⠶⢶⣾⠅⢠⡙⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⠙⠃⠀⠀⠀⠻⣿⡿⠀⢀⣶⣴⡻⡇⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠷⠀⠰⢿⣿⣿⡈⣿⠀⠘⠚⡌
⣿⣿⣿⣿⣿⣿⣛⣿⣿⠿⠿⠿⠛⠻⠿⠟⠛⠛⠀⠀⠀⢀⣀⢘⣂⠀⣀⡀⠀⣀⣀⢀⣀⡀⣠⣄⢀⣠⡀⣬⣭⢩⡅⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠉⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣨⣿⣿⢱⣿⠀⠀⠀⢁
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣼⣿⣿⡸⡇⠀⢀⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⢘⣚⣃⠛⠃⠘⠁⠩⠬⠍⡁⠉⠬⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣉⢛⣁⡃⣧⡴⣼⢠⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⣖⠶⣾⢗⢀⣒⣒⣒⣒⢒⣂⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠀⠀⣡⣾⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠛⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡷⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡷⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠙⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⡤⠀⠀⢸⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⢽⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣍⣹⠉⠉⠉⠉⠁⠀⠉⠠⣘⣿⠭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠘⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡀⡸⠀⢵⠊⣴⣿⣿⣿⣿⡟⣛⠻⠏⠉⢻⣿⡿⠧⢀⣄⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⢀⠠⠤⠐⠀⠐⠚⢛⡉⠉⠁⠀⠑⠘⣂⢾⠁⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣾⣄⣀⣬⣿⣆⠀⠀⠀⣿⣿⡟⣶⣄⣀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠠⣿⣿⡿⡿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠛⣿⣿⣿⡀⠀⠀⠀⠀⠀⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣷⣽⣾⣿⣿⣿⣿⠀⠀⠀⠿⣻⠎⠙⠿⠿⢿⣤⡄⢠⠶⠻⣿⣿⣿⣷⣄⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠘⢿⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⣁⡤⣤⣭⣿⣿⡿⠀⠀⠀⠸⠿⣥⣤⠶⣒⣚⣛⡛⠂⠀⠁⢻⣿⣿⡢⡹⣷⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⠻⠂⠹⢽⣶⣶⣿⡿⠟⠁⠀⠀⢠⣶⡾⠋⡶⠚⠉⠁⠀⠀⠈⠀⠈⠈⠻⢿⣿⣷⣿⣯⢌⣽⣿⣿
⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣨⣿⣿⣿⣿⣟⢻⣿⣿⣿⣏⠀⠈⠻⣷⣧⣽⣿⣿⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠉⠁⡠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠞⠢⣙⠀⠹⠇⡈⠻⣿⣿
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠝⢿⠟⠛⠉⠉⣿⡿⠏⠉⠉⠻⣿⣿⡟⠉⠉⠁⠀⣰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⡞⠀⠀⠀⠀⠀⠀⣿⣶⣤⡆⠀⠗⠐⡾⠶⢶⣾⠅⢠⡙⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⠙⠃⠀⠀⠀⠻⣿⡿⠀⢀⣶⣴⡻⡇⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠷⠀⠰⢿⣿⣿⡈⣿⠀⠘⠞⡌
⣿⣿⣿⣿⣿⣿⣛⣿⣿⠿⠿⠿⠟⠻⠿⠟⠛⠛⠀⠀⠀⢀⣀⢘⣂⠀⣀⡀⠀⣀⣀⢀⣀⡀⣠⣄⢀⣠⡀⣬⣭⢩⡅⣤⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠉⣶⢰⣶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣨⣿⣿⢱⣿⠀⠀⠀⢁
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⠀⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣾⣿⣿⡸⡇⠀⢀⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⢘⣚⣃⠛⠃⠘⠁⠩⠨⠍⡁⠉⠬⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣉⢛⣁⡃⣧⡴⣼⢠⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⣖⠶⣾⢗⢐⣒⣒⣒⣒⢖⣂⠀⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣶⡆⣶⠂⣾⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠀⠀⣡⣾⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠛⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡧⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣏⣁⣉⣉⣉⣉⠀⠀⠘⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⠛⡟⠛⠛⠛⠛⠁⠐⠀⡀⢿⣃⣉⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣀⣀⣀⣀⠀⠀⠀⠀⠶⡈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣴⢶⣶⣶⣖⣶⣶⣾⣿⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢠⠀⢼⡈⢙⣿⣿⣿⣿⣿⢿⢿⣿⠿⣿⣿⣿⣿⠿⠷⣄⡀⢀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠂⠈⠀⢉⠀⠋⢹⠿⠿⠿⠧⠙⠌⢱⠀⣼⣿⠋⠀⠀⠀⠉⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠀⠈⠀⠀⣠⠀⠀⢐⢦⡄⠀⠀⠀⣠⣾⡾⣿⣦⡄⢀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣤⣤⣴⣿⣷⣾⣿⣿⣿⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣏⣫⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣧⠟⠛⠻⢿⠿⣆⡀⣀⣴⣾⣯⣶⣬⡉⠁⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠻⣿⣿⣿⣿⣿⡇⠀⢹⣿⠟⠛⠛⢿⣿⣿⣿⠄⠀⠀⢨⣿⢿⣄⣀⣠⣤⣤⣿⡟⠉⠅⢹⣿⣿⡍⠻⣦⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣦⡀⢻⢾⣋⣙⣿⣿⣿⠏⠀⠀⠀⣨⣡⡾⣋⣭⠼⠛⠓⠂⠀⠀⠀⠀⢻⣿⣷⣧⣽⣿⠻⢿⣿⣿
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣯⣙⣿⠏⡌⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣌⠻⠛⢻⣿⠸⣿⣿⣿
⣿⣷⣤⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠻⠫⣿⠟⠋⠉⢹⣿⢿⡛⠓⠲⣶⣿⡿⠇⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢤⠆⠀⠀⠀⠀⠀⢠⣤⣀⣀⠀⢵⡀⣱⣤⣨⣥⡧⠈⠻⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⢻⣶⠀⠀⠠⠹⣿⡿⣀⠠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡏⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠈⢠⢾⣽⡍⣿⠇⠸⢣⠘
⣿⣿⣿⣿⠿⣿⣿⡿⠿⠿⠿⣿⠿⠿⠿⠟⠿⠟⠛⠛⠂⠀⣀⢀⣀⠀⣀⡀⠀⣀⣀⢀⣀⡀⣠⣄⢀⣠⡉⣤⣭⢡⡄⣥⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠈⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣸⣾⣿⡇⣿⠀⠀⠘⠇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡻⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣹⣿⣿⢇⡿⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠄⠛⠘⢘⣃⠛⠃⠘⠃⠉⠈⠭⠅⠉⠈⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣉⢛⣉⡘⡇⣀⣾⠀⣿
⠙⣿⣿⣿⣿⣿⠿⠿⠷⣒⠶⣾⢗⢂⣀⣀⣀⣐⢂⣀⠒⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⣯⢨⣽⡇⠋⠡⢋⣼⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⢀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡧⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡯⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣏⣁⣈⣉⣁⣉⠀⠀⠘⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⠛⡟⠛⠛⠛⠛⠁⠐⠀⣀⢿⣋⣉⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⠀⠀⠀⠀⠶⡈⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣴⢶⣶⣶⣖⣶⣶⣾⣿⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢠⠀⢼⡈⢙⣿⣿⣿⣿⣿⢿⢿⣿⠿⣿⣿⣿⣿⠿⠷⣄⡀⢀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠂⠈⠀⢙⠀⠋⢹⠿⠿⠿⠧⠙⠌⢱⠀⣼⣿⠋⠀⠀⠀⠉⠛⠟⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠀⠈⠀⠀⣠⠀⠀⢐⢦⡄⠀⠀⠀⣠⣾⡾⣿⣦⡄⢀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣤⣤⣴⣿⣷⣾⣿⣿⣿⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣏⣫⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣧⠟⠉⠻⢿⠿⣆⡀⣀⣴⣾⣭⣶⣬⡉⠁⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢻⣿⣿⣿⣿⣿⡇⠀⢹⣿⠟⠛⠛⢿⣿⣿⣿⠄⠀⠀⢨⣿⢷⣄⣀⣀⣠⣤⣿⡟⠁⠥⢹⣿⣿⡍⠻⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣦⡀⢻⢿⣋⣙⣿⣿⣿⠏⠀⠀⠀⣨⣡⡾⣋⣭⠴⠛⠓⠂⠀⠀⠀⠀⢿⣿⣷⣧⣽⣿⠻⢿⣿⣿
⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢻⣯⣙⣿⠏⡌⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣌⠻⠛⢻⣿⠸⣿⣿⣿
⣿⣿⣄⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠻⠫⣿⠟⠋⠉⢹⣿⢿⠛⠓⠲⣶⣿⣿⠇⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢠⠆⠀⠀⠀⠀⠀⢠⣤⣀⣀⠀⢵⡀⣱⣤⣨⣥⡷⠈⠻⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⢻⣶⠀⠀⠠⠹⣿⡷⣀⠠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡏⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠈⢠⢾⣽⡍⣿⠇⠸⢣⠘
⣿⣿⣿⣿⠿⣿⣿⡿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠂⠀⣀⢀⣀⠀⣀⡀⠀⣀⣀⢀⣀⡀⣠⣄⢀⣠⡉⣤⣭⢡⡄⣥⡤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠈⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣸⣾⣿⡇⣿⠀⠀⠘⠇
⣿⣿⣿⣿⣿⣿⣿⣽⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣽⣿⣿⢇⡿⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢺⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠄⠛⠘⢘⣃⠛⠃⠘⠃⠉⠈⠭⠅⠉⠨⠁⠀⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡀⣀⣀⢀⣉⢛⣉⡘⡇⣀⣼⠀⣿
⠙⣿⣿⣿⣿⣿⠿⠿⠷⣒⠶⣾⢗⢂⣀⣀⣀⣒⢂⣀⠒⣠⣄⣠⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣶⢰⣶⡆⣶⣶⢰⣶⡰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⠋⠡⢋⣼⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡿⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⡰⣟⡷⠀⠸⣿⣴⡟⣧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠿⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠋⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⠿⠿⠟⠁⠄⠀⢸⡿⠙⠻⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠙⠙⠋⢉⣉⠉⠉⠁⠉⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣾⣀⣤⣤⣤⣤⣤⣤⣬⣶⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠉⠀⢤⣤⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠨⠆⡤⢟⣿⣿⣿⡿⢝⠻⠟⠉⠹⣿⣿⡿⠛⠉⠀⠙⠷⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⠀⠠⠠⠀⠀⠐⠚⠛⠛⠉⠉⠀⠑⠘⢃⣺⣿⣿⣇⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣾⣄⣀⣠⣽⣧⠀⠀⠀⣼⣿⡏⢻⣿⣿⣿⣶⡆⠀⠀⠀⠘⠛⠙⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⢻⣿⣿⣿⣿⣿⣿⣷⡄⠀⣿⣿⡾⡿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡇⣾⡿⠻⢿⣿⣿⣄⠀⠀⢀⣀⣀⠀⠘⠻⠟⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⣿⣿⣿⣿⡇⠀⢻⣿⣷⣽⣾⣿⣿⣿⣿⡆⠀⠀⠻⣿⣿⣭⠁⠀⠀⠉⠁⢹⡶⠺⢻⣷⣿⣷⣦⣀⣀⣀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣷⣦⡀⢙⣿⣿⣿⣧⡀⠘⣿⣁⣠⣤⣭⣿⣿⣿⠃⠀⠀⠰⠿⢿⣿⠿⠗⣒⣒⡒⠷⠀⠘⠈⣿⣿⣇⢌⢿⣿⣿⣶⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⢟⣻⣿⣿⡿⠿⢿⡿⡿⠻⠂⠸⢭⣶⣶⣿⡿⠟⡁⠀⠀⢀⣴⣶⠋⠰⠞⠋⠁⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣾⣿⢍⣩⣿⣿
⣿⣿⣿⣄⠀⣿⣯⢻⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣈⣿⣿⣿⡿⠟⠛⠛⠲⠞⠻⢓⡿⠾⠉⢹⣿⣿⡿⠟⣀⣬⡟⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠍⠁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠲⢌⠃⠈⡿⡈⠻⣿⣿
⠛⢿⣿⣿⡄⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠊⠙⣿⣤⠤⠀⠈⠿⡇⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣴⠃⠀⠀⠀⠀⠀⠀⠷⠦⠤⠀⠸⠁⢲⠶⠶⣶⡏⢠⡙⢿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⠿⠿⠛⠿⠿⠛⠛⠛⢛⣃⢀⣀⠀⣀⡀⠀⣀⣀⢀⣀⡀⣨⣍⢀⣠⡀⣤⣥⢠⡍⣥⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢰⣾⣿⡇⣿⡇⠈⢹⡌
⠙⢛⣿⣿⣿⣷⣶⣾⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⢸⣿⣿⡇⣾⠇⠀⠨⢁
⣀⣬⣿⣿⣿⣿⣿⣿⡃⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠡⠉⠈⠵⠇⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡐⣒⣂⢀⣈⢘⣉⡃⠛⠀⣀⠀⣿
⠀⠙⢿⣿⣿⡿⠛⠛⠗⣀⠢⣐⢓⢒⣒⣒⣒⣒⢒⣀⠚⣩⣍⣠⣤⡄⢠⣤⡠⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⣤⠦⡿⢰⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣟⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠲⣶⠀⠴⠄⠠⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠋⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⠿⠿⠟⠁⠄⠀⢸⡿⠛⠻⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠙⠙⠋⢉⣍⠉⠉⠁⠉⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣾⣀⣤⣤⣤⣤⣤⣤⣬⣶⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠉⠀⢤⣤⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠂⠨⠆⡠⢟⣿⣿⣿⣿⢝⠻⠟⠉⠹⣿⣿⡿⠛⠉⠀⠙⢶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⠀⠠⠠⠄⠀⠐⠚⠛⠛⠉⠉⠀⠑⠘⢃⣺⣿⣿⣇⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣾⣄⣀⣨⣽⣧⠀⠀⠀⣼⣿⡏⢻⣿⣿⣿⣶⡆⠀⠀⠀⠘⠛⠙⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⢻⣿⣿⣿⣿⣿⣿⣷⡄⠀⣿⣿⡾⡿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡇⣾⡿⠻⢿⣿⣿⣄⠀⠀⢀⣀⣀⠀⠘⠻⠟⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢿⣿⣿⣿⣿⡇⠀⢻⣿⣷⣽⣾⣿⣿⣿⣿⡆⠀⠀⠻⣿⣿⣭⠁⠀⠀⠉⠁⢹⡶⠺⢻⣷⣿⣷⣦⣀⣀⣀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣛⣛⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢙⣿⣿⣿⣧⡀⠘⣿⣁⣠⣤⣭⣿⣿⣿⠃⠀⠀⠰⠿⢿⣿⠿⠗⣒⣒⡒⠿⠀⠘⠀⣿⣿⣇⢌⢿⣿⣿⣶⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⢟⣻⣿⣿⡿⠿⢿⠻⡿⠻⠂⠸⢽⣶⣶⣿⡿⠟⡁⠀⠀⢀⣴⣶⠋⠰⠞⠋⠁⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣾⣿⢍⣹⣿⣿
⣿⣿⣿⣆⠀⣿⣯⢻⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣈⣿⣿⣿⡿⠟⠛⠛⠲⠞⠻⢟⡿⠾⠉⢹⣿⣿⡿⠟⣀⣬⡟⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠍⠁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠲⢌⠋⠈⡿⡈⠻⣿⣿
⠛⢿⣿⣿⡄⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠊⠙⣿⣤⠤⠀⠈⠿⡇⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣴⠃⠀⠀⠀⠀⠀⠀⠷⠦⠤⠀⠸⠅⢲⠶⠶⣶⡏⢠⡘⢿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⠿⠿⠹⠿⠿⠛⠛⠻⢛⣃⢀⣀⠀⣀⡀⠀⣀⣀⢀⣀⡀⣨⣍⢀⣠⡀⣤⣥⢠⡍⣥⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⢰⣾⣿⡇⣿⡇⠈⢹⡌
⠙⢛⣿⣿⣿⣷⣶⣾⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⢸⣿⣿⡇⣾⠇⠀⠨⢁
⣀⣬⣿⣿⣿⣿⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠟⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠡⠉⠈⠵⠇⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡐⣒⣂⢀⣈⢘⣉⡃⠛⠀⣀⠀⣿
⠀⠙⢿⣿⣿⡿⠛⠛⠗⣀⠢⣐⢓⢒⣒⣒⣒⣒⢒⣀⠚⣩⣍⣠⣤⡄⢠⣤⡠⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⣤⠦⡿⢰⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣟⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠲⣶⠀⠴⠄⠠⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⠙⠛⠛⠛⠛⠉⠉⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠉⠠⠀⠸⣿⠟⠻⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⢉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣇⣠⣤⣤⣤⣤⣤⣤⣷⣾⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣹⠛⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣯⣍⣑⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⠀⣱⠂⡬⢻⣿⣿⣿⡟⣛⠻⠟⠉⠹⣿⣿⣿⣿⢟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡏⢀⢀⠠⠠⠄⠀⠀⠚⠚⠛⠋⠃⠀⠐⠘⣂⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣯⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣶⣀⣀⣬⣿⡆⠀⠀⠀⣾⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⢻⣿⣿⣿⣿⣿⣷⡄⠀⣿⣷⣾⠿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠻⣿⣿⣿⡇⠀⣿⣿⣦⣷⣿⣿⣿⣿⣿⠀⠀⠀⠿⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣛⣛⣟⣛⣿⣟⣿⣿⣿⣻⣟⣛⣻⣿⣟⣛⣛⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣦⣀⣈⣿⣿⣧⡀⠸⣿⣁⣠⣬⣽⣿⣿⡿⠀⠀⠀⠰⠿⢿⣿⠿⢟⣛⣛⠻⠏⠁⠻⠻⣿⣿⣷⠝⣿⣿⣿⣿⣿⣿
⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⡿⣿⢿⣿⡿⢿⣿⣿⠿⠿⠂⠹⢩⣶⣾⣿⡿⠟⠁⠀⠀⢀⣴⣶⠋⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⢙⢿⣿⣷⣾⣿⢙⣻⣿⣿
⣿⣿⣿⣭⣿⠀⢹⣿⣭⣭⣿⣿⢟⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⡿⠟⠛⠛⠲⠆⠻⠟⣷⠖⠉⢉⣿⡿⠟⠛⡋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⠁⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡤⠴⢝⠋⢙⡿⡘⢿⣿⣿
⠛⠛⠻⣿⣿⣷⠈⠹⣿⣾⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠈⢿⣦⡀⠂⠐⠀⣰⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⡰⠁⠀⠀⠀⠀⠀⠀⠶⠤⠤⠀⠸⠄⢴⠶⠶⣶⡏⣠⠙⣿
⢰⣶⣶⣶⣿⣿⣷⣾⣿⠿⠷⣾⠿⠿⠿⠿⠋⠙⠛⠛⠿⢛⣛⢛⣃⠀⣀⡀⠀⣀⣀⢀⣀⡀⣠⣌⢀⣠⡀⣤⣤⢠⡍⣥⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣰⣼⣿⡇⣿⠃⠈⢳⠘
⠀⠉⠙⠻⣯⣿⡶⢦⡆⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣏⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⢻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⣸⢿⣿⡇⣿⠀⠀⠸⢀
⠀⠀⠀⣨⣿⣿⣿⣿⡅⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⠸⠛⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠡⠉⠈⠵⠇⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡒⣒⣂⢀⣉⢘⣉⡁⠛⠀⣀⢠⣾
⠀⠀⠈⠻⣿⡿⠟⠛⠓⣀⠰⣐⢒⢒⣒⡒⣒⣒⢒⣀⠒⣩⣍⣩⣥⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⣠⣤⡿⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣯⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠲⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠯⠉⠉⠉⠉⠉⠉⠉⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣟⠛⠛⠛⠛⠋⠀⠀⠀⢿⡟⠙⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⣶⣶⣶⣶⣶⣾⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⡟⠽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣅⣙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠬⠠⠕⠠⠞⣿⣿⣿⣿⡯⠍⠻⡍⠁⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠄⠀⠄⠐⠂⠀⠀⠉⣉⡉⠉⠁⠀⠁⢉⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⡀⠀⠀⢀⠀⣰⣷⣄⣤⣮⣿⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣙⣿⣿⣿⣿⣷⡄⢰⣿⣿⢿⠿⣿⣿⣿⣿⣷⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢿⣿⡇⠀⣿⣿⣶⢿⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣷⣆⣀⣿⣧⡀⠸⣯⡤⠤⣤⣾⣿⣿⠟⠀⠀⠀⠼⠿⣿⡿⢿⣿⣿⣟⡛⠏⠉⢻⠻⣿⣿⣗⡝⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⡇⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣛⠿⢟⠁⠭⢷⣶⣿⡿⠿⠋⠀⠀⠀⣠⣾⡿⠁⠾⠋⠉⠀⠀⠀⠀⠀⠈⠁⠙⢿⣻⣷⣿⣿⣍⣿⣿⣿
⠩⠝⢿⣿⣷⣶⣿⠀⢸⣿⣶⢤⣶⣿⣫⣿⣿⣿⣿⣿⣻⣷⣼⣿⣿⣿⡿⠟⠉⠓⠒⠶⠘⠛⢿⠟⠋⣀⣼⡿⠏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠓⢍⠀⠸⠇⡙⢿⣿⣿
⠀⠒⠞⠛⠻⢿⣿⣷⡄⢹⣿⣶⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠿⠿⠂⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡟⠀⠀⠀⠀⠀⠀⠸⠷⠦⠦⠀⠛⠒⣺⠷⠾⣾⠏⣤⡙⣿
⠄⠀⢰⣾⣿⣿⣿⣿⣿⠿⠿⠿⠷⠾⠿⠿⠿⠟⠉⠙⠻⢛⣛⢛⣛⠛⣋⡀⠀⣀⣀⢀⣀⡀⣠⣄⢀⣠⡁⣤⣤⢨⡍⣥⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠈⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣸⢹⣿⡇⣿⠀⠀⢳⠘
⠀⠀⠈⠙⠻⣿⣧⣶⠇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣯⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣿⢹⣿⠇⣿⠀⠀⠘⢠
⠀⠀⠀⠀⠀⢨⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⡸⠛⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠡⠉⠈⠵⠁⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡐⣒⣀⢀⣉⢘⣉⡘⠉⠀⣀⢰⣿
⠀⠀⠀⠀⠀⠻⠟⠻⠗⣀⠀⣐⢒⢒⣒⡒⣒⣂⢂⣀⠐⣠⣍⣩⣤⡄⢠⣤⡠⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⡤⢶⡏⣸⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣾⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠉⠁⠀⠀
⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠯⠉⠉⠉⠉⠉⠉⠉⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣟⠛⠛⠛⠛⠋⠀⠀⠀⢿⡟⠙⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⣶⣶⣶⣶⣶⣾⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣍⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠬⠠⠕⠠⠞⣿⣿⣿⣿⡯⠍⠻⡍⠁⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠄⠀⠄⠐⠂⠀⠀⠉⣉⡉⠉⠁⠀⠁⢉⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⡀⠀⠀⢀⠀⣰⣷⣄⣤⣮⣿⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣿⣷⡄⢰⣿⣿⢿⠿⣿⣿⣿⣿⣷⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⢿⣿⡇⠀⣿⣿⣶⢿⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣆⣀⣿⣧⡀⠸⣯⡤⠤⣤⣾⣿⣿⠟⠀⠀⠀⠼⠟⣿⡿⢿⣿⣿⣟⡛⠏⠉⢻⢻⣿⣿⣗⡝⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡇⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣟⣛⠿⢟⠁⠽⢷⣶⣿⡿⠿⠋⠀⠀⠀⢠⣾⡿⠁⠾⠋⠉⠀⠀⠀⠀⠀⠈⠁⠝⢿⣿⣷⣿⣿⣍⣿⣿⣿
⠩⠝⢿⣿⣷⣶⣿⠂⢸⣿⣶⢤⣾⣿⣫⣿⣿⣿⣿⣿⣻⣧⣼⣿⣿⣿⡿⠟⠉⠓⠒⠶⠘⠛⢿⠟⠋⣀⣼⡿⠏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠓⢍⠀⠸⠇⡙⢿⣿⣿
⠀⠒⠞⠛⠻⢿⣿⣷⡄⢹⣿⣶⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠿⠿⠂⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡟⠀⠀⠀⠀⠀⠀⠸⠷⠦⠦⠀⠛⠒⣺⠷⠾⣾⠏⣤⡙⣿
⠄⠀⢰⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠾⠿⠿⠿⠟⠉⠘⠻⢛⣛⢛⣛⠛⣋⡀⠀⣀⣀⢀⣀⡀⣠⣄⢀⣠⡁⣤⣤⢨⡍⣥⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠈⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣰⢹⣿⡇⣿⠀⠀⢳⠘
⠀⠀⠈⠉⠻⣿⣧⣶⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢿⣏⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⣇⣿⣥⢸⡇⣿⢿⣿⠇⣿⠀⠀⠘⢠
⠀⠀⠀⠀⠀⢨⣿⣿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⠀⠿⠀⡸⠛⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠡⠉⠈⠵⠁⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡐⣒⣀⢀⣉⢘⣉⡘⠉⠀⣀⢰⣿
⠀⠀⠀⠀⠀⠻⠟⠻⠗⣀⠀⣐⢒⢒⣒⡒⣒⣂⢂⣀⠐⣠⣌⣩⣤⡄⢠⣤⡤⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⡠⢶⡏⣸⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠲⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠉⠉⠉⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⡿⠿⠿⠿⠟⠋⠡⠀⠀⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣠⣤⣤⣤⣦⣤⣶⣾⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⡟⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⠉⠉⠉⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⠀⠵⢠⠜⣛⣿⣿⣿⡯⡛⠿⠍⠉⠹⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠛⢷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡄⡀⠄⠄⠂⠀⠒⠛⣉⠉⠉⠁⠈⠀⠙⣀⣺⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿⡁⠀⠀⠀⠀⢠⣧⣀⣀⣬⣿⡄⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢛⣿⣿⣿⡄⠀⣿⣿⢿⢿⣿⣿⣿⣿⣷⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣾⣷⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣛⣛⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠸⣿⣤⠤⣬⣽⣿⣿⡿⠀⠀⠠⠼⠿⣿⣿⢿⣿⣟⣛⡛⠇⠀⠋⠘⣿⣿⣖⠜⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠀⢀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣁⣀⣈⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⡿⣿⠃⠩⢷⣶⣾⣿⠿⢋⠀⠀⠀⢠⣶⡾⠋⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣻⣷⣿⣿⢌⣽⣿⣿
⠐⠛⠛⠻⢿⣿⣷⣶⣾⠀⠈⣿⣯⡉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⡿⠛⠫⠥⢤⡄⠘⠻⣿⡿⠟⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠴⠳⢍⠀⠸⠟⡘⢿⣿⣿
⣠⣤⠀⠠⠦⡭⠿⢿⣿⣷⡄⠘⣿⣧⡈⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣛⣉⠁⠀⠀⠀⠤⠒⠀⠀⠈⠀⠈⠗⠀⣰⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⣤⡞⠀⠀⠀⠀⠀⠀⠰⠷⠦⠤⠀⠙⠀⢲⠷⠶⣾⡏⢤⡙⢿
⠸⠿⠄⠀⠀⣿⣶⣾⣿⠿⠷⣶⠿⠿⠷⠀⠻⠟⠛⠛⠋⠉⣛⢛⣛⠛⣉⡙⠟⣁⣀⢀⣀⡀⣠⣄⢀⣠⡀⣤⣤⢠⡍⣥⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣰⣾⣿⡇⣿⠃⠐⢱⠈
⠀⠀⠀⠀⠀⢿⣿⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢻⣏⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⢹⢹⣿⡇⣿⠁⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠘⢿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⠀⠸⠛⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠡⠉⠈⠵⠃⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡐⣒⣂⢀⣉⢘⣉⡁⠏⠀⣀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠲⠷⣂⠒⣒⢂⢀⣒⡒⣒⣒⢖⣀⠐⣩⣍⣩⣭⡍⢩⣭⡥⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⣤⡦⡿⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠉⠉⠉⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⡿⠿⠿⠿⠟⠋⠡⠀⠀⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣠⣤⣤⣤⣦⣤⣶⣾⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⡟⠽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⢉⠉⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⠀⠵⢠⠼⣻⣿⣿⣿⡯⡋⠿⠍⠉⠹⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠛⢷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡏⡄⡀⠤⠄⠂⠀⠒⠛⣉⠉⠉⠁⠈⠀⠙⣀⣺⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⡁⠀⠀⠀⠀⢠⣧⣄⣀⣮⣿⡄⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢛⣿⣿⣿⡄⠀⣿⣿⢿⢿⣿⣿⣿⣿⣷⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣾⣷⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣛⣛⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠸⣿⣤⠤⣬⣽⣿⣿⡿⠀⠀⠠⠼⠿⣿⣿⢿⣿⣟⣛⡛⠇⠀⠋⠘⣿⣿⣖⠜⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠀⢀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣉⣍⣈⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⡿⣿⠃⠩⢷⣶⣾⣿⠿⢋⠀⠀⠀⢠⣶⡾⠋⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣻⣷⣿⣿⢌⣽⣿⣿
⠐⠛⠛⠻⢿⣿⣷⣶⣾⠀⠈⣿⣯⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⡿⠛⠫⠥⢤⡄⠘⠿⣿⡿⠟⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠔⠲⢍⠀⠸⠟⡘⢿⣿⣿
⣠⣤⠀⠠⠦⡭⠿⢿⣿⣷⡄⠘⣿⣧⡈⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣛⣉⠁⠀⠀⠀⠤⠒⠀⠀⠈⠀⠈⠗⠀⣰⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⣤⡞⠀⠀⠀⠀⠀⠀⠰⠷⠦⠤⠀⠙⠀⢲⠷⠶⣾⡏⣤⡙⢿
⠸⠿⠄⠀⠀⣿⣶⣾⣿⠿⠷⣶⠿⠿⠷⠄⠻⠟⠛⠛⠋⠉⣛⢛⣛⠛⣉⡛⠟⣁⣀⢀⣀⡀⣠⣄⢀⣠⡀⣤⣤⢠⡍⣥⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣰⣾⣿⡇⣿⠁⠐⢱⠈
⠀⠀⠀⠀⠀⣿⣿⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢻⣏⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⢹⣽⣿⡇⣿⠁⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠘⢿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⠀⠸⠛⠃⠛⠚⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠡⠉⠈⠵⠃⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡐⣒⣂⢀⣉⢘⣉⡁⠏⠀⣀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠲⠷⣒⠒⣒⢂⢀⣒⡒⣒⣒⢖⣀⠐⣩⣍⣩⣭⡍⢩⣭⡥⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⣤⡦⡿⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⣀⡀⣀⡀⢀⣀⡀⡀⣀⣀⣀⡀⣀⣀⠀⣀⡀⢀⣀⣀⢀⣀⣀⠀⣀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⡀⢀⣄⢀⣀⣀⣀⡀⢀⣀⠀⣀⡀⣀⡀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⢀⣀⢀⣀⡀⣀⡀⠀
⠀⢸⡇⡇⣿⣿⠆⢸⣿⡇⡇⣿⣿⣿⠆⣿⣿⠀⣿⣭⣾⣿⢹⣿⢹⡷⠀⣿⣿⣿⡇⣿⣛⣿⣿⢸⣿⣟⡳⡅⡇⣿⣿⠆⣿⠀⢘⢾⡍⣽⠋⣽⠃⢸⣿⣿⡇⡇⡇⣿⢸⡇⡇⣿⣿⣿⣿⠀⣿⣿⣾⢸⣿⣿⡏⣭⠇⠀
⠀⠈⠁⠙⠁⠉⠁⠈⠉⠁⠁⠉⠉⠉⠁⠁⠉⠀⠙⠉⠉⠉⠈⠉⠈⠉⠀⠉⠉⠉⠁⠙⠋⠉⠉⠈⠛⠉⠙⠁⠙⠉⠉⠀⠉⠀⠈⠋⠉⠉⠉⠉⠙⠉⠛⠉⠙⠁⠙⠉⠃⠙⠁⠙⠋⠉⠋⠙⠙⠋⠈⠋⠈⠛⠁⠁⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⠀⠵⢠⠼⣻⣿⣿⣿⡯⡋⠿⠍⠉⠹⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠛⢷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡏⡄⡀⠤⠄⠂⠀⠒⠛⣉⠉⠉⠁⠈⠀⠙⣀⣺⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⡁⠀⠀⠀⠀⢠⣧⣀⣀⣬⣿⡄⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣛⣿⣿⣿⡄⠀⣿⣷⢿⢿⣿⣿⣿⣿⣷⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣾⣷⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣛⣛⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠸⣿⣤⠤⣬⣽⣿⣿⡿⠀⠀⠠⠼⠿⣿⣿⢿⣿⣟⣛⡛⠇⠀⠛⠘⣿⣿⣖⠜⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠀⢀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣉⣁⣈⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⡿⣿⠃⠹⢵⣶⣾⣿⠿⢋⠀⠀⠀⢠⣶⡾⠋⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣻⣷⣿⣿⢌⣽⣿⣿
⠐⠛⠛⠻⢿⣿⣷⣶⣾⠀⠈⣿⣧⣉⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⡿⠛⠫⠥⢤⡄⠘⠿⣿⡿⠟⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠴⠳⢍⠀⠸⠟⡘⢿⣿⣿
⣠⣤⠀⠠⠦⡭⠿⢿⣿⣷⡄⠘⣿⣇⡈⢹⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣛⣉⠁⠀⠀⠀⠤⠒⠀⠀⠈⠀⠈⠗⠀⣰⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⣤⡞⠀⠀⠀⠀⠀⠀⠰⠷⠦⠤⠀⠙⠀⢲⠷⠶⣾⡏⢤⡙⢿
⠸⠿⠄⠀⠀⣿⣶⣾⣿⠿⠷⣶⠿⠿⠷⠄⠻⠟⠛⠛⠋⠉⣛⢛⣛⠛⣉⡛⠟⣁⣀⢀⣀⡀⣠⣄⢀⣠⡀⣤⣤⢠⡍⣥⠤⣤⡤⣤⣤⢰⣶⡄⣦⣶⠀⣶⢰⡶⣶⠒⣶⢸⣷⣾⡇⣿⡛⢻⡟⣰⣿⣿⡇⣿⠁⠀⢱⠈
⠀⠀⠀⠀⠀⣿⣿⣿⡇⣸⣿⠀⢸⣿⡇⣿⡛⢸⣟⢸⡇⢻⣏⢿⣝⡛⢯⣏⠀⣿⡽⢸⣿⡇⣿⣿⣸⡷⠟⣿⢿⢸⡇⣿⠂⢸⡇⣿⣿⣸⡟⣧⢹⡇⡆⣿⣻⡇⣿⡁⣿⣸⡿⣿⡇⣿⣥⢸⡇⢹⢹⣿⡇⣿⠁⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠘⢿⡇⣿⢿⡆⢸⣿⡇⢾⣿⢸⣧⢼⣧⠼⠧⠻⠼⠏⠷⠟⣀⠿⠀⠸⠛⠃⠛⠛⠘⠃⠀⠛⠘⠘⠃⠛⠃⠘⠁⠉⠈⠉⠡⠉⠈⠵⠃⠉⠈⠁⠉⠁⠀⢀⣀⢀⢀⡐⣒⣂⢀⣉⢘⣉⡁⠏⠀⣀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠲⠷⣒⠒⣒⢂⢀⣒⡒⣒⣒⢖⣀⠐⣩⣍⣩⣭⡍⢩⣭⡥⣬⣥⠠⢤⡴⢰⣦⢰⣶⡆⣶⣶⢰⣶⠰⣦⡆⣶⠂⣶⣶⢸⣿⠇⠇⢸⣟⡙⣿⡇⣿⣿⢸⣯⢸⣿⡇⢿⣍⢸⡯⢨⣽⡇⣤⡦⡿⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠿⢸⡟⣷⣿⣾⡏⣿⠁⣿⣿⢸⣿⡇⣿⣛⠀⣿⠀⢸⣿⡇⢸⡇⠀⢸⡇⣿⣽⣼⣿⣇⣿⠋⣼⣽⡇⣿⠁⣿⣁⣿⣿⠰⣏⡷⠀⠸⣿⣴⡟⡧⠿⠀⠸⠷⠼⠿⠇⠻⠿⠸⠷⠸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡿⠸⠧⠟⠿⠻⠇⠿⠀⠿⠻⠸⠛⠓⠛⠛⠀⠛⠀⠘⠋⠛⠘⠃⠀⠈⠁⠉⠈⠉⠁⠉⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1219

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/27/gemini-will-be-okay/#comments
    Gemini version at gemini://gemini.techrights.org/2022/02/27/gemini-will-be-okay/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Gemini_Will_be_Okay,_Even_If_Some_People_Try_to_‘Extend’_It⠀✐


Posted in Free/Libre_Software, Microsoft at 6:24 am by Dr. Roy Schestowitz


Video_download_link | md5sum 55cf89b366e25460f7932d57f74c917a
Threats to Spirit of Gemini
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/gemini-fears.webm


Summary: FUD, harassment/trolling and infiltration tactics may sooner or later
be leveraged to discourage Gemini’s growth (The Register dished_out some FUD
last month, obviously with an “ethical” angle, concern-trolling_with_pseudo-
ethics), but this is what always happens when popular movements gain ground and
catch momentum/inertia (like proprietary software companies calling themselves
“Linux_Foundation” while trying to take over the whole thing, GNU included)


THE mental fatigue associated with dissent (usually against bloat and
complexity; sometimes the opposite) is what led Amfora to a removal of a
feature and maybe had Gemini Protocol’s originator on_hiatus_for_a_year.
Similar things happened in Diaspora. People are very passionate and that’s
understandable; at one point moderation (censorship) was added to the mailing
list to reduce abusive messaging/trolling/noise (some_of_it_came_from
Microsoft).


We’ve already taken note of downtime in the main site and capsule for Gemini
(for at least a day until yesterday), leading to some confidence issues. That
has thankfully been resolved since (unlike the mailing list), but right now the
developer_of_Lagrange says people_are_“Fearing_for_Gemini”_and_writing_to_him,
expressing concern not about the future of the specifications but their
expansion or de facto extensions.


About a year ago we wrote a list of FUD tactics that can be leveraged or would
be used against Gemini if it grew a lot bigger. This is one of them (see
“Microsoft Staff Trying to Subvert the Freedom of Gemini (Without Disclosure of
the Paymaster)”) and it’s likely a sign of growth. Let’s not allow the
disruptors to put us down and lower morale. In the words of Lagrange’s
developer: “Could a tech giant swoop in and stake Gemini for themselves? Out of
the big players, I think Microsoft today is the most dangerous in this regard.
They seem to be on a quest to own the hearts and minds of developers and
technology-minded people…”


He later explains in a reasonable fashion why that’s unlikely to happen, but in
theory it is not impossible that a Microsoft takeover/infiltration would be
intended to just destroy the project. As former or present Nokia employee, he
too should know that. █


“I’ve killed at least two Mac conferences. [...] by injecting Microsoft content
into the conference, the conference got shut down. The guy who ran it said, why
am I doing this?”


                                                  –Microsoft's_chief_evangelist



                    ䷩ 𝚕𝚒𝚗𝚎 1297

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/27/infrastructure-consolidation-and-centralisation/#comments
    Gemini version at gemini://gemini.techrights.org/2022/02/27/infrastructure-consolidation-and-centralisation/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ It’s_Too_Late_to_Change_All_the_Infrastructure_When_War_Erupts_or_Escalates⠀✐


Posted in Free/Libre_Software at 6:52 am by Dr. Roy Schestowitz


Video_download_link | md5sum 8fce0e9e690cdc94b2801d21f8aef156
Technology and Net at Times of War
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/ukraine-tech-side.webm


Summary: Too much consolidation and centralisation have taken their toll on
countries’ ability to operate and communicate; technology has, in effect, been
profoundly weaponised


IN our Daily_Links_of_earlier_today_(just_minutes_ago) we included a lot of
stuff about the technical_aspects_of_the_invasion_in_Ukraine (not_political
aspects), continuing our thoughts about the need to think in advance about
one’s choice of technology and the topology of infrastructure (clown computing
was always a bad idea). As it turns out, the US controls a lot of the important
communication channels globally and that extends to banking among other things,
as noted in the video above. █



                    ䷩ 𝚕𝚒𝚗𝚎 1339

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/27/irc-log-260222/#comments
    Gemini version at gemini://gemini.techrights.org/2022/02/27/irc-log-260222/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Saturday,_February_26,_2022⠀✐


Posted in IRC_Logs at 2:42 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-260222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-260222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-260222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-260222.gmi
Over HTTP:


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                                         #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
 QmNd2JMuuGuiso3jUJbnYp1s1SiWG2N8tD2rFm53xpc4EY #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmRNnYDWMqLv69qdM1yD1unfFZ1YnCvmNaSMfeSKseNGsH (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmNjF5da54pThQHhS2oqk8Uky3v5hNfyxTbBqvVqBc9dfD social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 Qme3nCaR5L93sGN8haNRru8fw1u46H7ifjp63CiNU7jFa2 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmSjKD3aHmWVFPrnTkRjA5hGjVatDwPqrXPxZKwNxGA8Ku #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmS3q59fnHnaPH3m6RdH3tyim2v6K3RWEHuWkkQXX3KqS4 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmeoM7eEp6oGhpMrQhGP4H1j1EQo55QHssXnP7ujotCctd #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmXA3hZpANRfZSLfQDoJvFFRJhfmjgUBqGS156xPZydJWx (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmUWSqFs7G64P11sRgFghydAWm5vaGowUWhjb5bQ6WVLjv



                    ䷩ 𝚕𝚒𝚗𝚎 1466

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_27/2/2022:_Coreboot_4.16_and_GNUnet_0.16.0⠀✐


Posted in News_Roundup at 12:00 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Dmitry Medvedev and Bill Gates⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ The_4_Best_ARM_Linux_Laptops_You_Can_Buy_Now⠀⇛


                       With transistors already nearing their physical
                       size limits, many would agree that ARM-based CPUs
                       will supersede x86-based CPUs soon. For this
                       reason, veteran laptop manufacturers and startup
                       companies have begun the race to develop and
                       produce quality ARM laptops for the new market.


                       And with efficiency being an ARM-based laptop’s
                       main advantage, pairing such an efficient CPU with
                       an efficient operating system, such as Linux, is a
                       dream come true for many tech enthusiasts.


                       If you’re in the market for the best Linux laptop
                       that utilizes a highly efficient SoC (System on
                       Chip), keep reading below for a list of the best
                       ARM Linux laptops you can buy today.


          o § Server⠀➾


                # ⚓ AlmaLinux_OS_8.5_for_PowerPC_Now_Available,_Distribution
                  Inches_Closer_to_Parity_with_Red_Hat_Enterprise_Linux⠀⇛


                       The AlmaLinux OS Foundation, the nonprofit that
                       stewards the only community owned and governed open
                       source CentOS alternative, today announced a new
                       stable release with support for the PowerPC
                       architecture and IBM Power Systems, inching closer
                       to parity with Red Hat Enterprise Linux (RHEL) and
                       CentOS.


          o § Audiocasts/Shows⠀➾


                # ⚓ 187:_Steam_Deck_Reviews,_Ubuntu_Snap_Vulnerability,_Intel
                  Buys_Linutronix_and_more_Linux_news_–_TuxDigital⠀⇛


                       On this episode of This Week in Linux: Steam Deck
                       Officially Launched, Intel Acquires Linutronix,
                       Podman 4.0, MythTV 32, PeerTube 4.1, Planner 3.0,
                       Vulnerability Found In Ubuntu’s Snaps, Mir 2.7,
                       GIMP 2.99.10, Libinput 1.20, NetworkManager 1.36,
                       Slax 11.2. All that and much more on Your Weekly
                       Source for Linux GNews!


                # ⚓ Onefetch:_Useless_Neofetch_Like_Stats_For_Git_Repos_–
                  Invidious⠀⇛


                       Every fetch application is the same or so I thought
                       until I found this one shining light in the dark,
                       Onefetch which is basically neofetch but for git
                       repos instead of your system.


          o § Applications⠀➾


                # ⚓ 4_Best_Free_and_Open_Source_Sound_Systems⠀⇛


                       
                       A sound system is software that manages the use of
                       and access to audio devices (usually a sound card).
                       It commonly runs as a background process.


                       To provide an insight into the quality of software
                       that is available, we have compiled a list of 4
                       high quality free and open source sound systems.


                       Here’s our verdict captured in a legendary
                       LinuxLinks chart. We only feature open source
                       goodness.


                # ⚓ Strimio:_A_Collection_of_Best_Radio_Streaming_Stations_for
                  Linux⠀⇛


                       It is true that modern music streaming tools are
                       quite flexible and let you enjoy just technically
                       any song you like. But still, people like me are
                       there who love the old fashion radio streaming
                       functions. I called this radio streaming system an
                       old-fashioned one because you don’t control what
                       program is running on it. So, everything is just
                       like a surprise here. However, if you love to enjoy
                       a radio streaming tool on Linux, this is where you
                       should be right now. We will here discuss one of
                       the best radio streaming apps, Strimio.


                       [...]


                       Strimio is one of the most popular radio streaming
                       apps for Linux. And it’s completely free.
                       Furthermore, the installation process is easier
                       too. So, why don’t you give it a try? This
                       beautiful app requires nothing but a few minutes to
                       spare to install. In exchange, it offers you hours
                       of exciting radio streaming experience.


                       Here, we take our leave and promise to come back
                       with something new. So, if you are already
                       impressed, just follow the installation process
                       mentioned above to enjoy unlimited streaming fun
                       with Strimio. Till then, stay tuned with Strimio.
                       Thank you.


                # ⚓ NewPipe_Is_Your_Alternative_YouTube_Client_For_Android⠀⇛


                       The official YouTube client for android is full of
                       ads and other tracking scripts. If you use it, then
                       you will be forced to watch tens of intrusive ads
                       from video to video, and your privacy will be under
                       attack because of Google’s tracking activities.


                       Luckily, you don’t have to go through all this. You
                       can use an alternative YouTube client app for
                       android in order to avoid this situation.


                       NewPipe is an open source YouTube client for
                       android, which also happens to be completely free
                       of charge. It allows you to watch and browse any
                       content on YouTube without having to use the
                       official YouTube app from Google. In this way, you
                       won’t see any ads and you will never be tracked by
                       Google.


          o § Instructionals/Technical⠀➾


                # ⚓ How_To_Install_Timeshift_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Timeshift on Debian 11. For those of you who didn’t
                       know, Timeshift is a powerful open-source tool that
                       can help you protect your data. Timeshift protects
                       your system by taking incremental snapshots of the
                       file system at regular intervals. These snapshots
                       can be restored at a later date to undo all changes
                       to the system.


                       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 through the step-by-
                       step installation of the Timeshift open-source tool
                       back up and restore file snapshots on a Debian 11
                       (Bullseye).


                # ⚓ How_to_Show_Line_Numbers_in_Vim⠀⇛


                       Vim is a remarkable editor that most Linux/UNIX
                       sysadmins have come to love and use every day.


                       You might think, “I would switch to Vim immediately
                       if Vim could show me line numbers”. Well, consider
                       that done.


                # ⚓ Install_Google_Cloud_SQL_Proxy_on_Ubuntu_22.04_|_20.04_–
                  Linux_Shout⠀⇛


                       The Cloud SQL Auth proxy works by having a local
                       client running in the local environment. Your
                       application communicates with the Cloud SQL Auth
                       proxy with the standard database protocol used by
                       your database.


                       It uses a secure tunnel to communicate with its
                       companion process running on the server. Each
                       connection established through the Cloud SQL Auth
                       proxy creates one connection to the Cloud SQL
                       instance.


                # ⚓ How_To_Install_Nmap_on_AlmaLinux_8_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Nmap on AlmaLinux 8. For those of you who didn’t
                       know, Nmap is an open-source network scanner and
                       security auditing utility. Nmap allows finding
                       devices running on their network and discovering
                       open ports and services that, if not secure or
                       hardened, can lead to potential exploiting known
                       vulnerabilities security risks. Nmap support is
                       available for Linux, Windows, UNIX, FreeBSD, etc.


                       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 through the step-by-
                       step installation of the Nmap network scanner on an
                       AlmaLinux 8. You can follow the same instructions
                       for CentOS and Rocky Linux.


                # ⚓ How_To_Install_MyPaint_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       MyPaint on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, MyPaint is an easy-to-use painting
                       program that works well with Wacom graphics tablets
                       and other similar devices. MyPaint takes quite a
                       little memory and has a smaller footprint on the
                       disk. It is super fast and does a marvelous job to
                       get bitmap images done just like MS Paint. It’s a
                       cross-platform application available for Microsoft
                       Windows, macOS, Linux, and Unix-like operating
                       systems.


                       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 MyPaint simple painting tool on
                       Ubuntu 20.04 (Focal Fossa). You can follow the same
                       instructions for Ubuntu 18.04, 16.04, and any other
                       Debian-based distribution like Linux Mint.


                # ⚓ How_to_Add_a_Directory_to_PATH_in_Linux_[With_Examples]⠀⇛


                       This article discusses an important Linux shell
                       environment variable called PATH and how you can
                       add a directory to this variable.


                       In general, most programs you’ll ever run on your
                       Linux system will work flawlessly, and your shell
                       will not present any errors at the time of their
                       execution. However, there may be times when you
                       might want to quickly run custom scripts or
                       programs from non-standard directories on your
                       Linux system.


                       In such cases, you need to add their source
                       directory to your shell’s PATH variable so that it
                       knows where to find them.


                # ⚓ How_to_Install_Google_Chrome_on_Manjaro_21_Linux_–
                  LinuxCapable⠀⇛


                       Most web users need no introduction to Google
                       Chrome as it is the most used Internet Browser
                       software globally, with a recent update in 2022
                       that Chrome is currently the primary browser of
                       more than 2.65 billion internet users and is why
                       most websites’ code now target it first before any
                       other browser.


                       Chrome is designed to be sleek and clean in its
                       looks and features and especially at loading
                       website pages as it used to claim to be the fastest
                       of all the browsers, but that is now a considerable
                       debate with Edge leading the charge and many others
                       have caught up, the browser competition has
                       increased recently.


                       The tutorial will use the yay AUR helper, ideally
                       most users may be using some wrapper for Pacman,
                       for new users, it is essential to install one to
                       keep your packages up-to-date while you learn Arch/
                       Manjaro.


                       In the following tutorial, you will learn how to
                       install Google Chrome on Manjaro 21 Linux by
                       installing either stable, beta, unstable (nightly
                       build), or a combination of the browsers.


                # ⚓ How_to_install_Python_on_Linux_Mint_20⠀⇛


                       If we discuss very popular programming languages,
                       we have to discuss Python. This programming
                       language is present in many technologies that are
                       part of our days. And Python is also a fundamental
                       component of many Linux distributions. So, in this
                       post, you will learn how to install Python on Linux
                       Mint.


                # ⚓ How_To_Make_SLAX_Bootable_USB_Stick⠀⇛


                       SLAX is a portable desktop operating system
                       designed to run on removable media like USB stick.
                       We covered it yesterday in a short review. However,
                       we didn’t make it clear how to make its bootable
                       media. It’s different to Ubuntu and another
                       standard GNU/Linux distros in the making of its
                       bootable as we cannot use image writing utilities
                       like Rufus or Unetbootin. For that purpose, now we
                       share with you how to make it from start to finish.


          o § Games⠀➾


                # ⚓ Proton_Experimental_Beta_gets_Steam_Deck_performance_fix
                  for_ELDEN_RING_|_GamingOnLinux⠀⇛


                       Are you finding that ELDEN RING has some mad
                       stuttering when loading things in the background?
                       Valve has released an update for Proton
                       Experimental in the bleeding-edge Beta to help.


                # ⚓ Godot_Engine_–_Godot_XR_Update_Feb_2022⠀⇛


                       At the end of last year we had rounded off most of
                       the core changes in Godot 4 to support XR, had XR
                       fully working through OpenVR/SteamVR and except for
                       a pesky timing issue had OpenXR up and running.


                       It initially seemed the timing issue was related to
                       issues with the original Vulkan implementation on
                       OpenXR, OpenXR had already moved to a new approach
                       where OpenXR takes over managing the Vulkan
                       instance. Switching to this new approach however
                       required embedding OpenXR support into the core of
                       Godot. With the Meta grant securing the funding to
                       switch to the new approach the whole implementation
                       was ported to the core.


                       While we would later discover the cause of the
                       timing issue was fixable in the plugin the new
                       approach is far more future proof and will make it
                       much easier to implement various XR features
                       including the editor features we have on the
                       roadmap.


                       The initial version of this work was merged this
                       week, for details check the Core OpenXR PR.
                       Currently only desktop VR is supported as we are
                       waiting on Meta to adopt the official Khronos
                       OpenXR loader.


          o § Distributions⠀➾


                # § EasyOS⠀➾


                      # ⚓ Take_a_Shot_fixed_and_version_bump⠀⇛


                             EasyOS has three screen-shot apps: Take a
                             Shot! (TAS), Screeny and the full-screen
                             capture feature of mtPaint. These are to be
                             found in the Graphic menu.


                             Screeny is builtin to woofQ and is in all
                             releases of EasyOS, it is not a PET. The
                             author is 01micko.


                      # ⚓ EasyApps_fixes_and_improvements⠀⇛


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ IBM_Emeritus_Irving_Wladawsky-Berger:_How_Do_Digital
                        Infrastructures_Increase_a_Firm’s_Value?⠀⇛


                             “In the information age, the value of a firm
                             rests fundamentally on how it stores, shares
                             and processes information,” wrote Seth
                             Benzell, Jonathan Hersh, and Marshall Van
                             Alstyne in a recent paper, How APIs Create
                             Growth by Inverting the Firm. “Digital
                             infrastructure is therefore central to a
                             firm’s success.”


                             But, how do digital infrastructures increase
                             a firm’s value? One method is to make more
                             efficient use of the firms internal capital
                             by modularizing, reconfiguring and reusing
                             the firms IT resources. A second method, used
                             in platform businesses, is to leverage
                             external capital by giving access to the
                             firm’s resources to third parties, and
                             capturing a share of the resulting surplus.
                             Both methods require the implementation of
                             Application Programming Interfaces (APIs),
                             whether for only for internal use by the
                             firm’s developers or exposed externally to
                             the firm’s platform partners. Both methods
                             also feature a modular architecture of
                             remixable resources. “Modularity combines the
                             advantages of standardization typically
                             associated with high volume processes
                             together with the advantages of customization
                             typically associated with bespoke processes.”


                             “An API is a set of routines, protocols, and
                             tools that standardizes building software
                             applications compatible with an associated
                             program or database. APIs fundamentally are
                             code that control access to information. …
                             They govern the type and format of calls or
                             communications that any application can make
                             of another associated program. The answering
                             program is agnostic about the source of the
                             call, yet can require access permission, and
                             the calling program need not know anything
                             about the internal workings of the answering
                             program. … When designing an API, the
                             architect decides how much of the computer
                             system or data to expose to which users.
                             Being accessible on the web, these API
                             endpoints act as a constant conduit to
                             business processes that the firm itself
                             specifies.”


                             The authors developed a novel method to
                             quantify the changes in a firm’s valuation
                             based on its adoption of APIs by analyzing
                             four unique data sets. They then applied
                             their methods to systematically evaluate
                             several different hypotheses on the potential
                             impact of APIs on firms. Let me summarize
                             their evaluation of four of these hypotheses.


                # § Debian Family⠀➾


                      # ⚓ Daniel_Silverstone:_Subplot_and_FOSDEM_2022_talk⠀⇛


                             At the start of February we had FOSDEM which
                             was once again online, and I decided to give
                             a talk in the Safety and open source devroom
                             to introduce the concepts of safety
                             argumentation and to bring some attention to
                             how I feel that Subplot could be used in that
                             arena. You can view the talk on the FOSDEM
                             website at some point in the future when they
                             manage to finish transcoding all the amazing
                             talks from the weekend, or if you are more
                             impatient, on Youtube, whichever you prefer.


          o § Devices/Embedded⠀➾


                # ⚓ Add-on_card_lets_you_run_Raspberry_Pi_HATs_on_a
                  BeagleBone⠀⇛


                       Sequent Microsystems has gone to Kickstarter to
                       launch an $18 “Beagle-Pi” emulator board that
                       enables HATs for the hard-to-find Raspberry Pi to
                       run on the Cape expansion interface for the more
                       widely available BeagleBone Black.


                       When we checked prices for the Raspberry Pi back in
                       late December for our annual catalog of Linux
                       hacker boards, we found most Raspberry Pi’s
                       available at the usual price, but only from
                       selected vendors in selected configurations with
                       limited quantities and wait times stretching to two
                       months. Since then, the situation has grown worse,
                       as chip shortages have pushed wait times up to a
                       year or more. In Europe, prices have skyrocketed.
                       Raspberry Pi HAT vendor Sequent Microsystems
                       noticed that the venerable BeagleBone Black is
                       still widely available and developed a Beagle-Pi
                       emulator board in the BeagleBone Cape add-on form-
                       factor that enables the BB Black to use Raspberry
                       Pi HATs.


                # ⚓ Weekly_Update_(8/2022):_Phosh_0.16.0,_Nemo_Mobile’s
                  February_Report_and_adding_Kodi_to_Megi’s_multi_boot_image⠀⇛


                       Another boring week with just a few releases, I
                       even had to reach for Steam Deck content to fill
                       this one up.


                # ⚓ Solving_Wordle_By_Adding_Machine_Vision_To_A_3D_Printer_|
                  Hackaday⠀⇛


                       Truth be told, we haven’t jumped on the Wordle
                       bandwagon yet, mainly because we don’t need to be
                       provided with yet another diversion — we’re more
                       than capable of finding our own rabbit holes to
                       fall down, thank you very much. But the word puzzle
                       does look intriguing, and since the rules and the
                       interface are pretty simple, it’s no wonder we’ve
                       seen a few efforts like this automated Wordle
                       solver crop up lately.


                # § Open Hardware/Modding⠀➾


                      # ⚓ $60_PC_Oscilloscope_Review_|_Hackaday⠀⇛


                             Owning an oscilloscope is a real gamechanger
                             and these days, scopes are more capable and
                             less expensive than ever before. However,
                             there is a big difference between scopes that
                             cost several hundred dollars which are
                             usually quite good and many of the very
                             inexpensive — below $100 — instruments that
                             are often — but not always — little more than
                             toys. [Adrian] looks at a PC-based scope from
                             Hantek that costs about $60. Is it a toy? Or
                             a useful tool? He answers the question in the
                             video below.


                             The Hantek 6022BE sports two channels with a
                             20 MHz bandwidth and 48 million samples per
                             second. The device included probes, too. Of
                             course, you also need a PC, although there is
                             apparently third-party software for Android
                             if you don’t want to lug a laptop around.


                      # ⚓ 3D_Printed_Mechanical_Contraption_Shows_Live_Weather
                        Forecast⠀⇛


                             “What’s the weather going to be like today?”
                             is a question that’s near-permanently on the
                             mind of those living in places like Britain,
                             where brilliant sunshine can follow thick
                             clouds, only to turn into drizzle an hour
                             later. Nowadays you simply need to glance at
                             your phone to know whether you need to pack
                             an umbrella, but where’s the fun in that? Why
                             not have a huge mechanical display to show
                             you a summary of today’s weather?


                      # ⚓ Codasip_L31_and_L11_RISC-V_cores_for_AI/ML_support
                        TFLite_Micro,_customizations_–_CNX_Software⠀⇛


                             Codasip has announced the L31 and L11 low-
                             power embedded RISC-V processor cores
                             optimized for customization of AI/ML IoT edge
                             applications with power and size constraints.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ The_Best_New_Games_for_Android_This_Week_–_Night
                        Skate,_Unheard_and_More_–_Droid_Gamers⠀⇛


                      # ⚓ Samsung_Galaxy_Tab_S8_Plus_review:_A_multitasking
                        powerhouse_|_Android_Central⠀⇛


                      # ⚓ The_7_Best_Android_Apps_to_Practice_Calligraphy_and
                        Improve_Your_Handwriting⠀⇛


                      # ⚓ 5_Android_apps_you_shouldn’t_miss_this_week_–_Android
                        Apps_Weekly⠀⇛


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


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Intuit
                  Quickbooks⠀⇛


                       
                       Intuit Inc. is an American corporation that
                       specializes in financial software. Specfically, the
                       company develops personal finance, accounting, and
                       tax return software.


                       The company is headquartered in Mountain View,
                       California. It has more than 10,000 employees.


                       While Intuit has a GitHub presence with over 100
                       repositories for numerous open source projects,
                       none of these repositories offer any substantial
                       desktop software. Instead, the repositories focus
                       on tools and libraries for the developer community.
                       None of these projects have attracted significant
                       interest from the open source community.


                # ⚓ Announcing_coreboot_4.16_–_coreboot⠀⇛


                       coreboot 4.16 release


                       coreboot’s first quarterly release in a number of
                       years, version 4.16 was tagged on February 25th,
                       2022.


                       Since 4.15 there have been more than 1770 new
                       commits by more than 170
                       developers. Of these, more than 35 contributed to
                       coreboot for the
                       first time.


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ GNUnet_0.16.0_released⠀⇛


                                   We are pleased to announce the release
                                   of GNUnet 0.16.0.
                                   This is a new major release. It breaks
                                   protocol compatibility with the 0.15.x
                                   versions. Please be aware that Git
                                   master is thus henceforth (and has been
                                   for a while) INCOMPATIBLE with the
                                   0.15.x GNUnet network, and interactions
                                   between old and new peers will result
                                   in issues. 0.15.x peers will be able to
                                   communicate with Git master or 0.16.x
                                   peers, but some services – in
                                   particular GNS – will not be
                                   compatible.
                                   In terms of usability, users should be
                                   aware that there are still a number of
                                   known open issues in particular with
                                   respect to ease of use, but also some
                                   critical privacy issues especially for
                                   mobile users. Also, the nascent network
                                   is tiny and thus unlikely to provide
                                   good anonymity or extensive amounts of
                                   interesting information. As a result,
                                   the 0.16.0 release is still only
                                   suitable for early adopters with some
                                   reasonable pain tolerance.


                                   [...]


                                   This release was the work of many
                                   people. The following people
                                   contributed code and were thus easily
                                   identified: Christian Grothoff, Tristan
                                   Schwieren, Alessio Vanni, Florian Dold,
                                   Thien-Thi Nguyen, t3sserakt, Lucien
                                   Heuzeveldt, Gian Demarmels, madmurphy,
                                   TheJackiMonster and Martin
                                   Schanzenbach.


                # § Programming/Development⠀➾


                      # ⚓ 9_Top_Free_and_Open_Source_C++_Web_Frameworks⠀⇛


                             One of the types of software that’s important
                             for a web developer is the web framework. A
                             framework “is a code library that makes a
                             developer’s life easier when building
                             reliable, scalable, and maintainable web
                             applications” by providing reusable code or
                             extensions for common operations. By saving
                             development time, developers can concentrate
                             on application logic rather than mundane
                             elements.


                             A web framework offers the developer a choice
                             about how to solve a specific problem. By
                             using a framework, a developer lets the
                             framework control portions of their
                             application. While it’s perfectly possible to
                             code a web application without using a
                             framework, it’s more practical to use one.


                      # ⚓ Russ_Allbery:_INN_2.6.5⠀⇛


                             This is a bit of a sneak preview announcement
                             since I’m waiting for the ISC mirror to
                             update before sending the official
                             announcement to the normal channels, but INN
                             2.6.5 has been released. (The release was
                             finalized a few days ago, and I’m a bit
                             behind in posting it.)


                             This is a bug fix and minor feature release
                             over INN 2.6.4, and the upgrade should be
                             painless. You can download the new release
                             from ftp.isc.org (once it updates) or my
                             personal INN pages. The latter also has links
                             to the full changelog and the other INN
                             documentation.


                      # ⚓ Linux_applications_with_Python_and_QML_–_dimitris.cc
                        –_Notes_on_technology_and_freedom⠀⇛


                             Linux applications with QML and Python? Why
                             not? Python is a popular programming
                             language. QML offers an intuitive way to
                             create user interfaces. Kirigami provides
                             useful UI components and implements UI/UX
                             patterns for mobile and desktop. Let’s fit
                             these technologies together and create a
                             simple application.


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ ML_system_proves_adept_at_pinpointing_power_grid_problems_•
                  The_Register⠀⇛


                       Machine learning could one day help energy
                       providers better pinpoint failing or compromised
                       components in power grids, or better identify
                       traffic congestion for local authorities, according
                       to a study.


                       A research project led by MIT describes a technique
                       capable of modelling complex interconnected systems
                       made up of numerous variables that change value
                       over time. By mapping connections in these so-
                       called multiple time series, a Bayesian network can
                       learn to identify anomalies in the data.


                # ⚓ 3D_Printed_CPU_Bracket_Reduces_Temperatures_|_Hackaday⠀⇛


                       What do you do when your motherboard bends your
                       CPU? If you’re [Karta] or [Luumi], you 3D print a
                       new retaining bracket to fix the problem. [Karta]
                       originated the design, and [Luumi] also tried it
                       and produced the video you can see below.


                       We think we find flat surfaces all the time, but it
                       is actually very difficult to create something
                       truly flat. You usually learn this when you try to
                       maximize heat transfer between two surfaces.
                       Getting two supposedly flat surfaces to touch is
                       quite hard. CPU brackets use a combination of
                       pressure and some sort of thermal media or paste to
                       fill in any gaps between the CPU case and the heat
                       sink. Intel’s LGA1700 bracket is an example, but
                       there’s been a problem. Apparently, with recent
                       CPUs, the bracket is a little too tight, and it
                       bends the CPU’s case. It doesn’t hurt the CPU, but
                       it does inhibit thermal transfer.


                       Others have “fixed” this problem by adding some
                       washers to slightly raise the bracket. In both
                       cases, there has been some very small improvement
                       in CPU temperatures. [Luumi] says part of the
                       problem is his water cooling block is not
                       completely flat and needs to be lapped. [Karta],
                       however, reported a 7 degree drop in temperatures,
                       which is pretty significant.


          o § Hardware⠀➾


                # ⚓ 3D_Printed_Climbing_Holds,_Now_With_Texture_|_Hackaday⠀⇛


                       Technology enables all kinds of possibilities to
                       mold our environments in the way we best see fit.
                       Plenty of ski resorts use snowmaking to extend
                       their seasons, there are wave pools for surfing
                       hundreds of miles away from oceans, and if you
                       don’t live near any mountains you can build your
                       own climbing wall as well. For the latter, many
                       have turned to 3D printers to create more rock-like
                       climbing grips but plastic doesn’t tend to behave
                       the same as rock unless you do what [Giles Barton-
                       Owen] did and incorporate salt into the prints.


                # ⚓ Here’s_How_Those_Battery-Free_Flashing_Phone_Stickers
                  Worked_|_Hackaday⠀⇛


                       The late 90s and early 2000s were a breakout time
                       for mobile phones, with cheap GSM handsets ushering
                       in the era in which pretty much everybody had a
                       phone. Back then, a popular way to customize one’s
                       phone was to install a sticker that would flash
                       when the phone rang. These required no batteries or
                       any other connection to the phone, and [Big Clive]
                       has dived in to explain how they worked.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ CISA_Releases_Advisory_on_Destructive_Malware
                              Targeting_Organizations_in_Ukraine⠀⇛


                                   CISA and the Federal Bureau of
                                   Investigation have released an advisory
                                   on destructive malware targeting
                                   organizations in Ukraine. The advisory
                                   also provides recommendations and
                                   strategies to prepare for and respond
                                   to destructive malware.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ 12_Simple_Tools_to_Protect_Your_Privacy⠀⇛


                                         
                                         Data is one of the most valuable
                                         assets available.


                                         For better or worse, data
                                         collection techniques aren’t
                                         going anywhere. To be practical,
                                         we need all sorts of data to
                                         analyze, study, and learn about
                                         things.


                                         Of course, it also brings in the
                                         risk of exploiting the data
                                         collected, such as malicious
                                         agencies getting hold of your
                                         browsing data (or internet
                                         activity).


                                  # ⚓ You_Break_It,_We_Fix_It⠀⇛


                                         Apple’s AirTags have caused a
                                         stir, but for all the wrong
                                         reasons. First, they turn all
                                         iPhones into Bluetooth LE beacon
                                         repeaters, without the owner’s
                                         permission. The phones listen for
                                         the AirTags, encrypt their
                                         location, and send the data on to
                                         the iCloud, where the tag’s owner
                                         can decrypt the location and
                                         track it down. Bad people have
                                         figured out that this lets them
                                         track their targets without their
                                         knowledge, turning all iPhone
                                         users into potential accomplices
                                         to stalkings, or worse.


                                         Naturally, Apple has tried to
                                         respond by implementing some
                                         privacy-protecting features. But
                                         they’re imperfect to the point of
                                         being almost useless. For
                                         instance, AirTags now beep once
                                         they’ve been out of range of
                                         their owner’s phone for a while,
                                         which would surely alert the
                                         target that they’re being
                                         tracked, right? Well, unless the
                                         evil-doer took the speaker out,
                                         or bought one with the speaker
                                         already removed — and there’s a
                                         surprising market for these
                                         online.


          o § Defence/Aggression⠀➾


                # ⚓ NATO_Puts_Response_Force_on_Stand-by_After_Russia’s
                  Aggressive_Invasion_of_Ukraine⠀⇛


                       As Russia moves aggressively on its objective to
                       invade Ukraine, other countries, especially Sweden
                       and Finland, are concerned. NATO’s reaction force
                       has been launched for the first time in response to
                       Russia’s invasion of Ukraine.


                       To protect its partners, NATO Supreme Allied
                       Commander Gen. Tod Wolters ordered the response
                       force. This activation of the response force means
                       that any attack on a NATO member will be met with
                       resistance from this multinational force. The
                       mobilisation of this multinational force does not
                       imply that NATO forces will enter Ukraine to defend
                       it against invasion.


                       The US president, Joe Biden, has made it clear that
                       the US will not enter Ukraine to confront Russia.


          o § Finance⠀➾


                # ⚓ all_money_is_fake⠀⇛


                       “American money stopped being real when the gold
                       standard was abandoned, but Bitcoin is definitely
                       real money because we say so” is certainly a take.


                       Gold was “real money” when we used it, because we
                       all agreed that it was.


                       If people agree that Bitcoin is “real money” then
                       sure, it’s real money.


                       And yet somehow paper money isn’t “real money” even
                       though everyone agrees that it is? Money doesn’t
                       have to be backed by anything but public opinion.
                       That’s what money IS.


          o § Censorship/Free Speech⠀➾


                # ⚓ Russia_Blocked_Twitter⠀⇛


                       Russia has blocked Twitter as it continues its
                       invasion of Ukraine. In Russia, Twitter has the
                       most users (31.1 million messages per month),
                       followed by Odnoklassniki (88.5 million m/month),
                       Instagram (135.1 million m/month), and Vkontakte
                       (408.8 million m/month).


                       Today, February 26, NetBlocks, a global internet
                       monitoring service, verifies that Russia began
                       restricting Twitter access on the morning of
                       February 26th, 2022. “The bans apply to numerous
                       providers and come as Russian authorities and
                       social media sites dispute over platform rules
                       related to the crisis with Ukraine,” NetBlocks
                       stated in an article.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Corona_Plandemic [Ed: I don't agree with the points about
                  it being faked as a crisis]⠀⇛


                       The internet in its current state is an instrument
                       of control and suppression. This becomes especially
                       obvious in the increase in censorship and the
                       introduction of vaccine-passports which are planned
                       to become universal passports for all aspects of
                       our life.


                # ⚓ A_flawed_idea_of_InDEA!⠀⇛


                       IFF submitted comments in the ongoing consultation
                       for India Digital Ecosystem Architecture (InDEA)
                       2.0 released by the Ministry of Electronics and
                       Information Technology in January 2022. Our core
                       approach is towards ensuring that the rollout of
                       the architecture happens in a manner that
                       safeguards the rights of the user. In our response,
                       we focus on four core data rights-centric issues
                       that we feel are of extreme significance. Comments
                       on this paper have been invited by the Ministry
                       from the public and other stakeholders latest by
                       February 27, 2022.



                    ䷩ 𝚕𝚒𝚗𝚎 2580

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_27/2/2022:_Lots_About_Tech_in_Russia_and_Ukraine⠀✐


Posted in News_Roundup at 6:42 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Why_30fps_Is_GREAT_On_Steam_Deck_–_Invidious⠀⇛


                       Valve’s Steam Deck has a wonderful 30fps frame
                       limiter, and it proves that smooth frame pacing is
                       always better than higher framerates. I tested
                       Cyberpunk 2077 and Borderlands 3 to show you the
                       difference.


                # ⚓ People_That_Say_“Linux_Is_Hard”_Make_Me_Laugh_–_Invidious⠀⇛


                       I see it all over the Internet…people telling
                       potential new Linux users to not bother trying
                       Linux because “Linux is hard” or “Linux is not for
                       beginners.” And I can’t help but laugh every time I
                       see such nonsense.


          o § Kernel Space⠀➾


                # ⚓ Intel_Purchases_Linutronix_To_Revive_It’s_Real_Time_Linux
                  Kernel⠀⇛


                       Over the years the maintenance and development of
                       PREEMPT_R has languished as people moved on to
                       other projects, but will now have the backing of
                       Intel. They also get another benefit, in the form
                       of Linutronix’s CTO Thomas Gleixner who has been a
                       major driver in developing security mitigations for
                       the Linux kernel’s x86 codebase.


          o § Instructionals/Technical⠀➾


                # ⚓ Math_is_fun_with_this_Linux_graphing_calculator_|
                  Opensource.com⠀⇛


                       If you spent your high school years gazing at TI-80
                       series calculators but lost track of the device
                       somewhere along the way, then you might sometimes
                       yearn to relive those thrilling years of algebra
                       and calculus. Somebody on the Linux KDE project
                       must have felt that way, too, because one of the
                       KDE Framework libraries, Analitza, provides syntax
                       and widgets to enable you to perform advanced math
                       functions with K apps like the graphing calculator
                       KAlgebra.


                # ⚓ How_to_Install_Brave_Browser_on_Manjaro_21_Linux_–
                  LinuxCapable⠀⇛


                       Brave is a free and open-source web browser
                       developed by Brave Software, Inc. based on the
                       Chromium web browser. Brave is a privacy-focused
                       internet browser that sets itself apart from other
                       browsers by automatically blocking online
                       advertisements and website trackers in its default
                       settings.


                       Brave claims that its browser puts less strain on
                       your computer’s performance than Google Chrome.
                       Even with multiple tabs open at once, the new Brave
                       Software uses 66% less memory and has 50 million
                       more active users than before – a growth of 2X in 5
                       years!


                       The tutorial will use the yay AUR helper, ideally
                       most users may be using some wrapper for Pacman,
                       for new users, it is essential to install one to
                       keep your packages up-to-date while you learn Arch/
                       Manjaro.


                       In the following tutorial, you will learn how to
                       install Brave Browser on Manjaro 21 Linux by
                       installing the stable, beta, or nightly browser
                       build.


                # ⚓ 2_ways_to_Install_MyPaint_on_Ubuntu_22.04_|_20.04_LTS_Linux
                  –_Linux_Shout⠀⇛


                       Create beautiful freehand pictures on your PC by
                       installing MyPaint on Ubuntu 22.04 Jammy JellyFish
                       or Ubuntu 20.04 Focal Fossa using the command
                       terminal.


                # ⚓ How_To_Install_Tor_Browser_on_AlmaLinux_8_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Tor Browser on AlmaLinux 8. For those of you who
                       didn’t know, Tor browser is an open-source browser
                       that anonymizes your browsing activity and gives
                       you an unparalleled level of privacy over the
                       internet. Tor will come in handy by hiding your
                       public IP which typically identifies your
                       geographical location over the internet. It
                       redirects your traffic through multiple layers of
                       encryption and nodes, thereby hiding your identity
                       from prying eyes.


                       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 through the step-by-
                       step installation of the Tor Browser on an
                       AlmaLinux 8. You can follow the same instructions
                       for CentOS and Rocky Linux.


          o § Desktop Environments/WMs⠀➾


                # ⚓ 10_reasons_to_use_Pantheon_as_your_desktop_environment⠀⇛


                       Pantheon is a great desktop environment for those
                       who prefer a simple, fast, and light desktop
                       experience. It boasts a desktop design similar to
                       mac OS, naturally making it easy for mac users to
                       get accustomed to it fairly quickly.


                       Pantheon comes as the default desktop environment
                       with elementary OS, a beautiful and intuitive Linux
                       distro. Still, if you want to install it on your
                       Ubuntu installation as an additional DE, you can
                       also do that with only a few commands. Either way,
                       you can check out some valuable things we listed
                       hereafter installing it on your system.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Flatpak_App_of_the_Week:_Foliate_–_Simple_and_Modern
                        eBook_Viewer⠀⇛


                             Written in GTK, Foliate is a great ebook
                             viewer/reader software with lots of cool
                             features. While its interface may look
                             simple, don’t be fooled because Foliate comes
                             with numerous options and nifty tools that go
                             beyond just reading ebooks.


                             Foliate’s user interface has two main views,
                             Library and Catalogs. While in the Catalogs
                             section you’ll be able to browse and download
                             free ebooks from some well-known sources, the
                             Library view is the place you’ll find every
                             ebook that you’ve downloaded through the app
                             or manually opened with reading progress
                             information.


                      # ⚓ Fedora_36_–_Top_New_Features_&_Release_Details⠀⇛


                             This article summarises significant new
                             features and releases information about
                             Fedora 36 release (upcoming).


          o § Devices/Embedded⠀➾


                # ⚓ Beagle-Pi_Emulator_is_a_Raspberry_Pi_HAT_adapter_for
                  BeagleBone_Black_(Crowdfunding)_–_CNX_Software⠀⇛


                       We recently reported the Raspberry Pi boards were
                       getting really expensive due to a lack of supply,
                       and the problem has gone on for while without a
                       clear idea when the issue will be resolved. This
                       does not help Raspberry Pi HAT manufacturers, and
                       for instance, Sequent Microsystems has made
                       Raspberry Pi HATs over the years most models with
                       multiple relays, but also others for temperature
                       sensors, and others automation applications.


                       One solution would be to use compatible boards like
                       ODROID-C4 or Rock64, but Sequent Microsystems found
                       out the BeagleBone Black Industrial was well-
                       stocked by various distributors, and instead, they
                       designed the “Beagle-Pi Emulator” adapter to use
                       Raspberry Pi HAT on the Texas Instruments Sitara
                       AM3358 board.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ How_Google_Plans_to_Fix_Android’s_Targeted
                        Advertising⠀⇛


                      # ⚓ Is_Spam_App_Social_Media_On_Android?_Here’s_What_We
                        Know⠀⇛


                      # ⚓ Update_to_Android_12_dialer_is_hidden_in_Google_Phone
                        app_–_PhoneArena⠀⇛


                      # ⚓ How_to_Schedule_Text_Messages_on_Android_Using_Google
                        Messages_–_TechPP⠀⇛


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


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Google_Chat⠀⇛


                       Google has a firm grip on the desktop. Their
                       products and services are ubiquitous. Don’t get us
                       wrong, we’re long-standing admirers of many of
                       Google’s products and services. They are often high
                       quality, easy to use, and ‘free’, but there can be
                       downsides of over-reliance on a specific company.
                       For example, there are concerns about their privacy
                       policies, business practices, and an almost
                       insatiable desire to control all of our data, all
                       of the time.


                       What if you are looking to move away from Google
                       and embark on a new world of online freedom, where
                       you are not constantly tracked, monetised and
                       attached to Google’s ecosystem.


                # § FSF⠀➾


                      # ⚓ I’m_developing_a_rather_intense_dislike_of_Richard
                        Stallman._He_went_on_Russian_state_television_numerous
                        times_after_knowing_what_their_plans_were_for_the
                        region. [Ed: RMS has repeatedly spoken about abuses in
                        Russia, inc. in Russian TV, so this is based on a false
                        premise.]⠀⇛


                             I’ll avoid linking to the podcasts where
                             Stallman was featured, however many of them
                             were published less than a year ago, and he’s
                             made numerous appearances on RT in the past
                             decade, completely ignoring Putin’s invasions
                             of Georgia and Ukraine while doing so, and
                             they were very happy to have him speaking out
                             against the United States government. Which,
                             admittedly, is far from perfect, but it’s no
                             Russia either.


    * § Leftovers⠀➾


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ I_used_Apple’s_AirTag_to_track_my_wife_and_kids.
                        Here’s_what_I_learned⠀⇛


                             Actively tracking you at freeways speeds is
                             pointless but if the only thing someone wants
                             to know is where you live, Apple’s AirTag is
                             scary effective. But indeed, so is the Tile
                             Pro. Again, my experience with my Tile Pros
                             have been pretty much hit or miss for finding
                             lost stuff in my home. So I was quite
                             surprised to see the Tile Pro work reasonably
                             well as a tracking device.


                      # ⚓ Ukraine:_Can_Apple_solve_this_new_supply_chain
                        challenge?⠀⇛


                             But, it’s not just development (and also
                             wheat) that comes from Ukraine; the nation is
                             also rich in hard-to-find raw materials used
                             in silicon chips and advanced sensors. This
                             includes the neon gas used by chip-making
                             lasers, palladium, and around 90% of US
                             semiconductor-grade neon. Citing US-based
                             advisory firm, Techcet, Reuters is warning
                             that if the conflict escalates, some of the
                             world’s biggest chipmakers may be impacted.
                             Intel, for example, gets half its neon from
                             Eastern Europe.


                      # ⚓ Cyber_officials_urge_federal_agencies_to_armor_up_for
                        potential_Russian_attacks [iophk: Windows TCO]⠀⇛


                             The specter of broad cyber warfare has
                             increased following Russia’s invasion this
                             week, with experts warning that Moscow could
                             respond to retaliatory sanctions over the
                             incursion with additional cyberattacks
                             against the West.


                      # ⚓ Conti_ransomware_gang:_You_attack_Russia,_we’ll_
                        [crack]_you_back [iophk: Windows TCO]⠀⇛


                             The Conti ransomware gang says that it
                             supports the Russian government’s invasion of
                             Ukraine… and if anyone launches a retaliatory
                             cyber attack against Russia, they will hit
                             back hard.


                      # ⚓ ACSC_calls_on_Australian_organisations_to_urgently
                        adopt_an_enhanced_cyber_security_posture [iophk:
                        Windows TCO]⠀⇛


                             The ACSC also links to similar information
                             from the US, UK, NZ and Canada, to prepare
                             for and better defend against threat actors
                             in any country, whether small, large or
                             nation state, because the cyber cold war has
                             already been happening for years, and all the
                             chaos in the world is digitally accelerating
                             cyber attacks, too.


                      # ⚓ Outlook_bad_for_Starbucks’_anti-union_lawyers⠀⇛


                             The firm Littler Mendelson, who has been
                             representing Starbucks’ anti-union efforts,
                             failed to submit a dispute with the National
                             Labor Relations Board on time due to an
                             untimely crash in the firm’s Microsoft
                             Outlook.


                             The dispute, called a statement of position,
                             was aimed at stalling the organizational
                             voting of several upstate New York stores.
                             The dispute stated that holding elections for
                             individual stores would be inappropriate and
                             should instead tally votes on a regional
                             basis. In order to be considered valid, this
                             paperwork needed to be submitted to the NLRB
                             by noon on February 11th but didn’t find its
                             way to the appropriate inbox until 12:08PM.


                      # ⚓ Microsoft_Outlook_Fail_Screws_Up_Latest_Starbucks
                        Union-Busting_Effort⠀⇛


                             For much of the last several years, Starbucks
                             Corporation has been engaged in a ham-fisted
                             effort to crush fledging unionification
                             efforts among store employees. But the
                             company’s latest effort to undermine such
                             efforts were thwarted by an unforeseen
                             adversary: company lawyers’ inability to
                             understand how Microsoft Outlook attachments
                             work.


          o § Defence/Aggression⠀➾


                # ⚓ ‘We_Will_Not_Lay_Down_Any_Weapons’:_Ukraine_Resists_as_Kyiv
                  Under_Attack⠀⇛


                       Ukrainian President Volodymyr Zelenskyy implored
                       people in the capital of Kyiv to brace for an all-
                       out Russian assault overnight, and as a result of
                       intense resistance from the Ukrainian military and
                       civilians alike, they were able to fend off the
                       invading army, though fighting continues throughout
                       the country on Saturday morning.


                       “The invaders wanted to block the center of our
                       state and put their puppets here… We broke their
                       plan.”


                # ⚓ Hundreds_of_Anti-War_Protesters_Have_Been_Arrested_Across
                  Russia⠀⇛


                # ⚓ Stay_hidden_or_get_drafted_How_the_breakaway_regions_of
                  eastern_Ukraine_are_forcing_local_men_into_the_military⠀⇛


                       On February 17, the breakaway governments in
                       Ukraine’s Donetsk and Luhansk regions began
                       spreading claims of a massive Ukrainian artillery
                       attack on the territories they control. The leaders
                       of the self-declared Donetsk and Luhansk “people’s
                       republics” used these claims not only to evacuate
                       women and children into Russia but also to
                       implement a universal conscription policy among men
                       between 18 and 55 for “the protection of the Donbas
                       and of all Russian people.” On February 23 and 24,
                       the self-proclaimed republics reported a successful
                       military recruitment campaign that allegedly
                       brought in many new volunteer troops. However,
                       local residents told Meduza that soldiers are
                       conducting raids to sweep the streets for potential
                       conscripts.


                # ⚓ The_150,000_Ukrainians_fleeing_Russia’s_war_—_in_pictures⠀⇛


                       The war in Ukraine — which Meduza will continue to
                       call a war, despite demands from Russia’s state
                       censor that we do otherwise — has already seen no
                       fewer than 150,000 civilians forced to leave their
                       homes. Poland, Moldova, and Hungary are all
                       accepting Ukrainian refugees. Slovakia has declared
                       a state of emergency due to the large wave of new
                       arrivals. In addition, the United States has
                       declared its readiness to help refugees, and
                       Ireland has cancelled its visa requirements for
                       Ukrainian arrivals. Here, Meduza rounds up
                       photographs capturing the scale of the displacement
                       crisis already in progress.


                # ⚓ Opinion_|_Russia’s_Invasion_of_Ukraine_Marks_a_Deep_Turning
                  Point_in_the_World_Order⠀⇛


                       David Harvey prepared this text, which he calls a
                       provisional statement on recent events in Ukraine,
                       for the 2022 meeting of the American Association of
                       Geographers. It is republished here with his
                       permission.


                # ⚓ Meduza’s_brief_guide_to_accessing_online_resources_blocked
                  by_the_Russian_authorities⠀⇛


                       Facebook has started to slow down in Russia.
                       Judging by similar measures the authorities have
                       taken against Twitter, we know this might make the
                       site significantly harder to use — photos and
                       videos will probably take especially long to load.
                       And it’s highly likely that the authorities won’t
                       stop there. In the near future, we anticipate them
                       blocking independent (and other) media outlets.
                       Here are the things you can do right now to prepare
                       for life in the new Internet reality.


                # ⚓ Anti-War_Coalition_Holds_Online_Rally_for_Peace_in
                  Ukraine⠀⇛


                       Update:


                       At least 2,000 people from every corner of the
                       globe attended an anti-war coalition’s emergency
                       online discussion and rally on Saturday afternoon,
                       during which organizers announced that they are
                       planning an international day of action for peace
                       in Ukraine and beyond to be held on Sunday, March
                       6.


                # ⚓ Opinion_|_Even_Without_Russia’s_Military_Might,_Ukraine_Can
                  Defend_Against_Invasion⠀⇛


                       As with so many around the world, including
                       thousands of brave Russians protesting against
                       their country’s brutal invasion of neighboring
                       Ukraine, I’m aware of the inadequate resources for
                       defending Ukraine’s independence and wish for
                       democracy. Biden, NATO countries, and others are
                       marshalling economic power, but it seems not to be
                       enough.


                # ⚓ Unreliable_at_best:⠀⇛


                # ⚓ Opinion_|_How_George_W._Bush_Laid_the_Groundwork_for
                  Putin’s_Invasion_of_Ukraine⠀⇛


                       George W. Bush issued a statement about the Russian
                       invasion of Ukraine. It went like this:


                # ⚓ Opinion_|_Holodomor_Belies_Putin’s_Words_and_Actions_on
                  Ukraine⠀⇛


                       Putin’s invasion of Ukrainian territory and his
                       rejection of Ukraine legitimacy as an independent
                       nation has made that country an unwilling pawn in
                       the conflict between the U.S., its European
                       partners and Russia. As expected, Putin responded
                       to the sanctions imposed by Biden with threats of
                       retaliation, which set the stage for conflicts of
                       unpredictable but probably ominous consequences.
                       Ukrainian civilians, mainly children, will carry
                       the biggest burden.


                # ⚓ Russian_Labor_Confederation:_Workers_“on_Both_Sides”_Will
                  Suffer_Most_From_War⠀⇛


                # ⚓ Opinion_|_Ukraine_and_the_Myth_of_War⠀⇛


                       Last September 21st, in commemoration of the 40th
                       anniversary of the International Day of Peace, as
                       U.S. forces withdrew from Afghanistan, our local
                       peace organization emphasized that we would be
                       relentless in saying no to the calls for war, that
                       those calls for war would come again, and soon.


                # ⚓ Opinion_|_Conflict_Between_Nuclear-Powered_Nations:
                  Chernobyl_Is_Now_a_War_Zone⠀⇛


                       The invasion of Ukraine by Russia poses several
                       nuclear threats, including the possibility of
                       deliberate or inadvertent military strikes or
                       cyber-strikes on nuclear facilities.


                # ⚓ Russian_Labor_Confederation_Demands_Peace_in_Ukraine⠀⇛


                       With Ukraine under attack, a Russian labor
                       confederation boasting an estimated two million
                       members on Friday called for a “cessation of
                       military action” and “renewal of peaceful dialogue”
                       between officials in Moscow and Kyiv, arguing that
                       workers in both countries are the victims of war.


                       “Intensification of the conflict threatens a
                       devastating shock to our nations’ economies and
                       social support systems, and a fall in workers’
                       living standards.”


                # ⚓ Unreliable_at_best_What_we_know_about_Ukrainian_and_Russian
                  casualties_on_day_three_of_the_invasion⠀⇛


                       Three days into the war against Ukraine, Russia’s
                       Defense Ministry has yet to report any losses, both
                       in terms of military personnel and technical
                       equipment. Russian state media outlets have also
                       been silent on this front. Two anonymous sources —
                       one at a major wire agency and one at a federal
                       television channel — confirmed to Meduza that their
                       newsrooms received a memo telling them to rely
                       strictly on “official Russian state sources” in
                       their reporting. These consist mostly of briefings
                       held once per day by Russian Defense Ministry
                       representative Igor Konashenkov. The journalists
                       were also told not to cite any Ukrainian state
                       sources, with an exception for announcements by the
                       Ukrainian government about its own losses to
                       Russian forces.


                # ⚓ Sean_Penn_on_Invasion_of_Ukraine:_‘If_We_Allow_It_to_Fight
                  Alone,_Our_Soul_as_America_Is_Lost’⠀⇛


                       Sean Penn, who is in Ukraine filming a documentary
                       about Russia’s invasion, released a statement on
                       Friday night after appearing at a press briefing in
                       the capital of Kyiv on Thursday, where he listened
                       to government officials talk about the crisis.


                       “Already a brutal mistake of lives taken and hearts
                       broken, and if he doesn’t relent, I believe Mr.
                       Putin will have made a most horrible mistake for
                       all of humankind,” Penn said. “President Zelensky
                       and the Ukrainian people have risen as historic
                       symbols of courage and principle. Ukraine is the
                       tip of the spear for the democratic embrace of
                       dreams. If we allow it to fight alone, our soul as
                       America is lost.”


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ Top_Climate_Publisher_Has_Played_Major_Role_in
                        Supporting_Fossil_Fuel_Industry⠀⇛


                      # ⚓ How_Ukrainians_are_fundraising_in_cryptocurrency⠀⇛


                             More than $15 million in cryptocurrency has
                             been donated to Ukrainian groups since Russia
                             attacked the country on February 24th,
                             according to research firm Elliptic.
                             Decentralized autonomous organizations (DAOs)
                             have formed to support Ukrainians. NFTs have
                             been sold to raise money for the Ukrainian
                             people and military. The country’s official
                             Twitter account has said it accepts Bitcoin,
                             Ether, and Tether.


                      # ⚓ ‘Mining’_Bitcoin_takes_more_energy_than_mining_gold⠀⇛


                      # ⚓ Illegal_Crypto_Mining_Facilities_Busted_in_Kazakhstan
                        Amid_Prevailing_Power_Crisis⠀⇛


                             Crypto mining, the process of generating
                             assets such as Bitcoin, is legally permitted
                             in Kazakhstan, but only via authorised mining
                             facilities. A total of 13 crypto mining
                             facilities have been busted in Kazakhstan
                             that were consuming huge chunks of
                             electricity to generate Bitcoin, illegally.
                             The Ministry of Energy of the Republic of
                             Kazakhstan conducted raids after having
                             identified illegal crypto mining farms in
                             cities and regions like Karaganda, Turkistan,
                             Pavlodar, Akmola, and Kostanay. Illegal
                             crypto miners are also called grey miners.


                             The development comes under the backdrop of
                             Kazakhstan trying to manage its power supply.
                             Since crypto mining is legal in the country,
                             its grids have been bearing the loads the
                             mining machines require.


                      # ⚓ Founder_of_cryptocurrency_company_BitConnect_charged
                        in_$2.4-billion_fraud⠀⇛


                             The founder of a cryptocurrency company was
                             charged by a San Diego federal grand jury
                             Friday in a wide-ranging indictment alleging
                             he defrauded global investors out of more
                             than $2.4 billion in what prosecutors said is
                             believed to be the largest swindle of its
                             kind ever criminally charged.


                             Satishkumar Kurjibhai Kumbhani, 36, a citizen
                             and resident of Surat, India, is charged with
                             numerous conspiracy counts relating to wire
                             fraud, money laundering and commodities
                             fraud, as well as one count of operating an
                             unlicensed money transmitting business. His
                             whereabouts were unclear Friday night.


                             Kumbhani, who used aliases to hide his
                             identity, is accused of running BitConnect,
                             the company he formed in 2016, as a “textbook
                             Ponzi scheme,” according to the indictment.


          o § Finance⠀➾


                # ⚓ Inflation_Talk_Belies_Deeper_Question:_Why_Was_Everything
                  So_Cheap_Before?⠀⇛


                # ⚓ Support_open_source_that_you_use_by_paying_the_maintainers
                  to_talk_to_your_team⠀⇛


                       I think I’ve come up with a novel hack for the
                       challenge of getting your company to financially
                       support the open source projects that it uses:
                       reach out to the maintainers and offer them
                       generous speaking fees for remote talks to your
                       engineering team.


                # ⚓ Explosions,_shelling_rock_Ukraine_as_allies_double_down_on
                  punishments_against_Russia⠀⇛


                       As Ukraine’s forces battled troops on the ground,
                       the U.S. along with the European Commission,
                       France, Germany, Italy, the United Kingdom and
                       Canada announced Saturday that select Russian banks
                       would be removed from the SWIFT messaging system.


                       The option had been on the table, but some allies
                       in Europe with economies more closely tied to
                       Russia’s had been reluctant to include SWIFT among
                       sanctions because of the possible impact it could
                       have.


                # ⚓ Russia-Ukraine_live_updates:_US,_other_nations_to
                  disconnect_some_Russian_banks_from_SWIFT⠀⇛


                       The U.S., along with the European Commission,
                       France, Germany, Italy, the United Kingdom and
                       Canada, are disconnecting some Russian banks from
                       the Society for Worldwide Interbank Financial
                       Telecommunication (SWIFT) banking network and are
                       “imposing restrictive measures that will prevent
                       the Russian Central Bank from deploying its
                       international reserves in ways that undermine the
                       impact of our sanctions,” the White House said.


                # ⚓ Select_Russian_banks_are_being_booted_off_the_SWIFT_bank
                  messaging_system⠀⇛


                       The U.S., Canada and European allies are moving to
                       cut off certain Russian banks from the SWIFT bank
                       messaging system as part of a dramatic new round of
                       sanctions meant to punish Russia for the ongoing
                       invasion of Ukraine.


                       The White House issued a statement saying, in part,
                       “we commit to ensuring that selected Russian banks
                       are removed from the SWIFT messaging system. This
                       will ensure that these banks are disconnected from
                       the international financial system and harm their
                       ability to operate globally.”


                       SWIFT is a key mechanism in the global financial
                       system that supports millions of secure messages
                       daily to facilitate bank transactions worldwide.


                # ⚓ US_and_Europe_will_block_some_Russian_banks_from_SWIFT⠀⇛


                       A coalition of NATO-aligned countries has committed
                       to new measures meant to sever Russia from the
                       global financial system, countries announced in a
                       joint letter today. The letter, signed by the
                       United States, UK, Canada, and European allies,
                       lays out new measures to isolate Russia’s central
                       bank, and announces a new trans-Atlantic task force
                       to freeze the foreign assets of sanctioned
                       individuals.


                       In a dramatic escalation, the order also blocks
                       select Russian banks from using SWIFT — the
                       international payment system employed by banks to
                       send money around the world.


                # ⚓ Why_SWIFT_is_the_nuclear_option_of_Russian_financial
                  sanctions⠀⇛


                       Using the global financial network as a sanctions
                       weapon could, however, have long-lasting
                       repercussions outside Russia’s borders. For one, it
                       could undermine confidence in the US dollar and
                       SWIFT itself as an apolitical network. It might
                       accelerate the creation of alternatives such as
                       trading in local currencies, using cryptocurrency,
                       and forming new bilateral free trade agreements,
                       Prakash said. China, Iran, and India, for example,
                       already trade in local currency.


                # ⚓ West_to_cut_some_Russian_banks_off_from_[SWIFT]⠀⇛


                       The assets of Russia’s central bank will also be
                       frozen, limiting Russia’s ability to access its
                       overseas reserves.


                       The intention is to “further isolate Russia from
                       the international financial system”, a joint
                       statement said.


                       Russia is heavily reliant on the [SWIFT] system for
                       its key oil and gas exports.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Truth_Social_Users_Whine_About_Censorship_After_Being
                  Banned_From_Trump’s_New_App⠀⇛


                       Conservatives who make up Truth Social‘s target
                       audience rushed to be among the first to sign up.
                       But now even those who are among Donald Trump’s
                       most loyal followers are accusing the app billed as
                       a “free speech” alternative to other platforms of
                       “rank hypocrisy” for censoring content and banning
                       accounts.


                       It’s just another problem to add to the list of
                       setbacks Trump’s latest venture faced upon its
                       launch. Aside from technical glitches which put
                       users on a waiting list–complete with an unironic
                       message that assured the user just assigned a
                       number that they were loved and “not just a number”
                       to Truth Social–the app’s questionable funding is
                       still under a microscope. Now, users are getting
                       banned just as they would on Twitter: a right-wing
                       broadcaster who has pushed conspiracy theories
                       about the coronavirus in recent months was censored
                       for posting what the platform classified as
                       ‘sensitive content.’


                # ⚓ YouTube_bans_ads_on_RT_and_other_Russian_channels⠀⇛


                       YouTube spokesperson Farshad Shadloo told Reuters
                       that YouTube will recommend Russian state-run media
                       to users less often. Some of these channels —
                       including RT — will also be restricted in Ukraine
                       due to “a government request,” potentially in
                       response to Ukraine digital minister Mykhailo
                       Fedorov’s call for YouTube to block Russian
                       propaganda on the platform. YouTube started
                       labeling videos posted by state-run networks in
                       2018.


                # ⚓ Google_blocks_RT,_other_Russian_channels_from_earning_ad
                  dollars⠀⇛


                       Alphabet Inc’s Google barred on Saturday Russia’s
                       state-owned media outlet RT and other channels from
                       receiving money for ads on their websites, apps and
                       YouTube videos, similar to a move by Facebook after
                       the invasion of Ukraine.


                       Citing “extraordinary circumstances,” Google’s
                       YouTube unit said it was “pausing a number of
                       channels’ ability to monetize on YouTube.” These
                       included several Russian channels affiliated with
                       recent sanctions, such as those by the European
                       Union.


                       Ad placement is largely controlled by YouTube.


                # ⚓ Russia_blocks_Twitter_as_Ukraine_invasion_escalates⠀⇛


                       Journalists on the ground in Russia have confirmed
                       the block. A BBC reporter described access as
                       “severely restricted,” saying “this message got
                       through, but took a while.”


                # ⚓ Twitter_pauses_ads_in_Ukraine_and_Russia_amid_growing
                  conflict⠀⇛


                       The social network also says it’s “proactively
                       reviewing tweets to detect platform manipulation”
                       and is taking “enforcement action” against them.
                       Twitter is monitoring the accounts of journalists,
                       government officials, activists, and other high-
                       profile accounts to prevent “targeted takeover or
                       manipulation” as well.


                # ⚓ Social_media_platforms_prevent_Russian-backed_media_from
                  earning_ad_revenue⠀⇛


                       Social media platforms are preventing Russian-
                       backed media from earning ad revenue as Russia
                       continues its assault on Ukraine.


                       The head of security policy at Meta, the parent
                       company of Facebook and Instagram, announced Friday
                       night that Russian state media would not be able to
                       earn money from ads on the company’s platforms.


                # ⚓ Russia_restricts_Facebook_access_claiming_platform_censors
                  Russian_media_amid_Ukraine_conflict⠀⇛


                       In a statement posted on Twitter, Nick Clegg, the
                       vice president of global affairs for Facebook
                       parent company Meta, said the company refused
                       orders by Russian authorities to stop independent
                       fact-checking and labeling of content posted to
                       Facebook by the media organizations.


                # ⚓ Facebook_bans_Russian_state_media_from_running_ads,
                  monetizing_platform⠀⇛


                       “We are now prohibiting Russian state media from
                       running ads or monetizing on our platform anywhere
                       in the world. We also continue to apply labels to
                       additional Russian state media. These changes have
                       already begun rolling out and will continue into
                       the weekend,” Gleicher said in a tweet.


                # ⚓ Russia_Will_Restrict_Access_to_Facebook,_Claiming_Social
                  Giant_Violated_‘Human_Rights’_in_Restricting_Kremlin-Backed
                  Media⠀⇛


                       UPDATED: The Russian government announced that it
                       has taken steps to “partially restrict access” to
                       Facebook in the country, asserting that the social
                       network censored official news outlets amid
                       Russia’s invasion of Ukraine.


                       Facebook was “involved in the violation of
                       fundamental human rights and freedoms, as well as
                       the rights and freedoms of Russian citizens,” by
                       restricting Kremlin-backed news sources, according
                       to an announcement released Friday (Feb. 25) by
                       Roskomnadzor, the Russian governmental agency
                       responsible for monitoring and censoring Russian
                       media.


          o § Censorship/Free Speech⠀➾


                # ⚓ 3_int’l_news_outlets_in_Turkey_face_ban_as_deadline_set_by
                  media_watchdog_expires⠀⇛


                       The move has been described by the media outlets as
                       an attempt at censorship and at expansion of the
                       Turkish government’s control over domestic media to
                       foreign outlets, which are the only source of free
                       and independent journalism for some people in
                       Turkey, where the majority of the media is
                       controlled by the government.


                       Deutsche Welle and VOA announced earlier this week
                       that they would appeal RTÜK’s decision and take
                       legal action in court.


                # ⚓ Ukrainian_cities_are_suffering_[Internet]_blackouts⠀⇛


                       IODA, a research team at the Georgia Institute of
                       Technology, an American university, is tracking
                       these disruptions in two ways: by probing networks
                       that automatically respond to the sender and by
                       watching networks on the Border Gateway Protocol, a
                       global routing system. They found that the
                       responsiveness of Triolan, one of the main service
                       providers in Kharkiv, plummeted in the early hours
                       of the invasion.


                       Finding the cause of such outages can be tricky.
                       Kyivstar, the country’s largest mobile provider,
                       reported that its networks were underperforming
                       because of a high volume of calls and texts.
                       Blackouts may also occur when shelling destroys
                       physical infrastructure.


                # ⚓ Chinese_censors_delete_academics’_post_decrying_Russian
                  invasion⠀⇛


                       A post on Chinese social media platform Weixin
                       jointly signed by five prominent academics
                       denouncing Russia’s invasion of Ukraine was almost
                       immediately taken down by China’s censors on
                       Saturday (Feb. 26).


                       Among the five scholars were Sun Jiang (孫江) of
                       Nanjing University, Wang Lixin (王立新) of Peking
                       University, Xu Guoqi (徐國琦) of the University of
                       Hong Kong, Zhong Weimin (仲偉民) of Tsinghua
                       University, and Chen Yan (陳雁) of Fudan University,
                       per CNA.


                       The authors criticized Russia for, despite being a
                       permanent member of the UN Security Council and a
                       nuclear power, ruthlessly attacking a weaker
                       “brotherly state.” “We feel the pain of the
                       Ukrainian people,” the professors proclaimed.


                # ⚓ Her_senior_recital_was_on_historically_censored_songs._Then
                  her_school_censored_her⠀⇛


                       Caitlyn Fox put on a show – just not the one she
                       proposed. Caitlyn Fox, a senior in the honors
                       program at Friends University in Wichita, Kan. – a
                       Christian university of Quaker heritage, as its
                       website explains – mounted a senior recital called
                       “The Shows They Don’t Want Us To Produce: A Study
                       Of Censorship Through The History Of Musical
                       Theatre” – for mature audiences, her playbill
                       advised. Just two days before she was set to
                       perform, the president of the university sent an
                       email saying, people who have worked at and/or
                       supported the university for a long time are
                       considering withdrawing their support if we move
                       forward with having the recital at Friends and
                       suggested moving the show off campus. A show about
                       censorship censored, more or less.


                       Caitlyn Fox joins us now from Wichita. Thanks so
                       much for being with us.


                # ⚓ Twitter_restricted_in_Russia_amid_conflict_with_Ukraine⠀⇛


                       Network data show that access to the Twitter
                       platform and backend servers are restricted on
                       leading networks including Rostelecom, MTS, Beeline
                       and MegaFon as of 9:00 a.m. Saturday morning UTC.


          o § Civil Rights/Policing⠀➾


                # ⚓ Union_Files_“Precedent-Setting”_Charges_of_Misconduct
                  Against_Amazon⠀⇛


                # ⚓ Retired_SWAT_commander_who_killed_man_after_fight_over
                  phone_in_movie_is_acquitted⠀⇛


                       But prosecutor Scott Rosenwasser countered that
                       Reeves killed Oulson because he threw popcorn in
                       his face, angering him because it violated his
                       self-image as an “alpha male.”


                # ⚓ Florida_jury_finds_former_SWAT_commander_not_guilty_of
                  second-degree_murder⠀⇛


                       A Florida jury on Friday acquitted a retired police
                       captain who shot and killed a man at a movie
                       theater in 2014.


                       The six-member jury found Curtis Reeves not guilty
                       on charges of second-degree murder for the killing
                       of Chad Oulson and aggravated battery of Oulson’s
                       wife, NBC affiliate WFLA reported.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Fearing_for_Gemini⠀⇛


                       After posting about the utility of data URLs,
                       particularly as they relate to images, a few people
                       contacted me with their concerns about how this
                       could impact Geminispace. Let’s reflect a bit.


                       People on Gemini undoubtedly have a lot of
                       affection for this circumlunar space. I feel it
                       myself. This small and simple protocol is beautiful
                       as it exists today, and trying to “advance” it
                       could mean Geminispace changes in substantial and
                       negative ways.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Audiobook_Pirate_Still_Plagues_Authors_After_Being
                        Deported_For_Selling_Honey⠀⇛


                             A man who was deported from Norway for
                             offenses including the illegal sale of honey
                             and then threatened to “destroy the entire
                             audiobook industry” in retaliation is said to
                             be plaguing the industry once again from
                             overseas. Nikita Volgin was previously
                             ordered to remove pirated content from his
                             websites but according to police, new ones
                             keep appearing with slightly changed domains.



                    ䷩ 𝚕𝚒𝚗𝚎 3784

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.27.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_27/2/2022:_Astro_Slide_From_Planet_Computers_and_TeXworks_0.6.7⠀✐


Posted in News_Roundup at 5:51 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o ⚓ Linux_Weekly_Roundup_#171⠀⇛


                 Welcome to this week’s Linux Weekly Roundup.


                 We had a wonderful week in the world of Linux releases,
                 with Ubuntu 20.04.4, LMDE 5 Beta, and Manjaro 21.2.4.


                 I am back at my workstation, so expect more Linux distro
                 reviews in the future.


          o § Audiocasts/Shows⠀➾


                # ⚓ Is_ChromeOS_A_Linux_Distro_Or_Not?_–_Invidious⠀⇛


                       Some people want to call ChromeOS a linux distro
                       but to decide if it’s a distro we first need to
                       decide on what the term linux distro means in the
                       first place.


                # ⚓ Fragmentation_is_a_GOOD_thing_for_Linux_–_Invidious⠀⇛


                # ⚓ Enterprise_Linux_Security_Episode_19_–_The_RBS_Year-End
                  Vulnerability_Report_–_Invidious⠀⇛


                       2021 is now in the past, but there’s some very
                       interesting details in the year-end vulnerability
                       report produced by RBS. These details give us a
                       look at some of the trends that will impact 2022
                       and beyond. In this episode, Joao and Jay discuss
                       the report and some of its findings.


          o § Kernel Space⠀➾


                # ⚓ lrzip_version_0.650⠀⇛


                       A number of accumulated bug reports had collected
                       since the last lrzip release and since I regularly
                       use lrzip I want to make sure it stays bug free as
                       far as I am aware, even if I’m not planning any new
                       features for it. As some of the changes are
                       potentially security fixes, I urge any user to
                       update.


          o § Applications⠀➾


                # ⚓ 14_Best_Free_and_Open_Source_Network_Analyzers_–
                  LinuxLinks⠀⇛


                       A network analyzer (also known as a packet
                       analyzer, packet sniffer, or protocol analyzer) is
                       software that intercepts and logs traffic that
                       passes over a computer network or part of a
                       network. Packet capture is the process of
                       intercepting and logging traffic. As data streams
                       flow across the network, the analyzer captures each
                       packet and, if needed, decodes the packet’s raw
                       data, showing the values of various fields in the
                       packet, and analyzes its content according to the
                       appropriate RFC or other specifications.


                       Maintaining a live network is one of a system
                       administrator’s most essential tasks, and keeping a
                       watchful eye over connected systems is essential to
                       keeping a network functioning at its best.


                       A good network analyzer helps a network developer
                       with daily Linux plumbling. They can be used for
                       network development, debugging, analysis, auditing
                       or network reconnaissance.


                       Here’s our verdict on the finest network analyzers,
                       captured in a LinuxLinks ratings chart. We only
                       feature free and open source software here.


                # ⚓ Gaphor:_An_Open_Source_&_Simple_Graphical_Modeling_Tool⠀⇛


                       Architects and designers need to use top-notch
                       modeling apps to make designs. There are tons of
                       software available for that purpose. But not all of
                       them support technical modeling languages like
                       RAAML, SysML, C4, UML, etc. That would be a great
                       problem when the architects and designers are in
                       something technically complicated. However, if you
                       face a similar situation, I would like to introduce
                       Gaphor. And this content will lead you to a
                       detailed discussion on Gaphor.


                # ⚓ TeXworks_0.6.7_Released!_How_to_install_it_in_Ubuntu_via
                  PPA_|_UbuntuHandbook⠀⇛


                       TeXworks, the free open-source application for
                       authoring TeX (LaTeX, ConTeXt, etc) documents,
                       released 0.6.7 today. Here’s how to install it in
                       Ubuntu 18.04, Ubuntu 20.04, Ubuntu 21.10, and
                       Ubuntu 22.04.


                       TeXworks 0.6.7 added some minor new features,
                       improved dark mode support, and fixed various bugs.


                # ⚓ Top_open_source_audio_editors_for_Linux⠀⇛


                       Almost everybody loves music. We can agree that
                       music is a universal language. Some people say
                       music is the food for the soul because it can evoke
                       powerful emotions from within us. If you love a
                       great tune, depending on your favorite genre, you
                       are definitely into audio editing software.


                       Audio editing software can help you edit audio into
                       music by arranging sounds, melody, harmony, and
                       rhythm elements. The article will review some of
                       the top open-source audio editing software.


                # ⚓ The_Kate_Text_Editor_–_UI_Improvements⠀⇛


                       In the last few weeks we had time to nicely improve
                       the general UI of our editor.


                       Naturally, the overall structure of the main window
                       stays the same, with a central splitter area and
                       some tool views around.


                       But if you take a look at the two screenshots below
                       that show the last release and the current master
                       branch version, you will spot some differences that
                       in my eyes improve on what we have in a nice way.


                # ⚓ recordMyDesktop_CLI_screen_recorder⠀⇛


                       While revising the EasyApps utility, I realised
                       there is one kind of app missing from EasyOS — a
                       video and audio screen recorder. There have been
                       many of these used in the pups over the years, and
                       I perused the old forum, looking to see what has
                       come and gone.


                       A couple of them, Drec (dpuprec) and EasyCast, are
                       GUI apps that use the ‘rmd’ CLI utility. I searched
                       and found that the binary utility is now named
                       ‘recordmydesktop’, and uses libtheora, libogg and
                       libvorbis to record video actions on the desktop,
                       and audio using alsa-lib, and save as an ‘ogv’
                       video file.


          o § Instructionals/Technical⠀➾


                # ⚓ How_To_Install_Gaucho_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Gaucho on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, Gaucho is an open-source, customizable
                       task launcher to run your apps, commands, or
                       scripts. Gaucho is a great alternative when you
                       need to create, modify and run tasks with a simple
                       graphical interface.


                       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 Gaucho Task Manager on Ubuntu
                       20.04 (Focal Fossa). You can follow the same
                       instructions for Ubuntu 18.04, 16.04, and any other
                       Debian-based distribution like Linux Mint.


                # ⚓ How_to_Turn_a_Picture_into_Wallpaper_on_Android_(And_Make
                  It_Fit)⠀⇛


                # ⚓ How_to_install_MyPaint_on_a_Chromebook⠀⇛


                       Today we are looking at how to install MyPaint 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.


                # ⚓ How_to_Change_File_Permissions_on_Linux_Desktops⠀⇛


                       One of the most confusing and often frustrating
                       parts of Linux for new users is the concept of file
                       system permissions. It used to be that if you
                       wanted to change file permissions on a Linux
                       system, you had to enter cryptic commands at the
                       terminal. Now, however, desktop environments like
                       GNOME and KDE Plasma make it easy to check and
                       adjust these settings.


                       In this article, we’re going to explain what each
                       of the file permission settings is and show you how
                       to adjust them on each of the four major Linux
                       desktop environments: GNOME, Plasma, Cinnamon, and
                       XFCE.


                # ⚓ How_to_Manage_Your_Linux_Clipboard_Effectively_Using
                  CopyQ⠀⇛


                       Have you ever copied a text snippet, then copied
                       another shortly after, only to realize that the
                       initial text snippet is now gone?


                       Well, it’s quite a common sight on most operating
                       systems, including Linux. And it’s got to do with
                       your system’s clipboard/pasteboard, which can hold
                       only one instance of text at a time.


                       Fortunately, you have clipboard managers, like
                       CopyQ, that allow you to store multiple snippets in
                       your clipboard and use them wherever required.


                       Let’s check out CopyQ, its installation steps on
                       Linux, and how to use it to manage your clipboard
                       history.


                # ⚓ How_to_Microsoft_Fonts_on_Manjaro_21_Linux_–_LinuxCapable⠀⇛


                       Most Linux Distributions use open-source fonts to
                       substitute Microsoft’s iconic typefaces like Arial,
                       Courier New, and Times. Red Hat created the
                       Liberation family to replace these similar-looking
                       but different sizes — all you have to do is select
                       your preferred font when editing documents so that
                       they’ll be readable without any disruptions!


                       In the following tutorial, you will learn how to
                       install Microsoft Core Fonts on Manjaro 21 Linux.
                       The tutorial will use the yay AUR helper, ideally
                       most users may be using some wrapper for Pacman,
                       for new users, it is essential to install one to
                       keep your packages up-to-date while you learn Arch/
                       Manjaro.


                # ⚓ How_to_Zoom_Client_on_Manjaro_21_Linux_–_LinuxCapable⠀⇛


                       Zoom is a communications technology platform that
                       provides videotelephony and real-time online chat
                       services through the cloud. It’s used for
                       everything from teleconferencing to distance
                       education. Still, its most widespread application
                       may be an effective way of communicating between
                       employees geographically located far away from one
                       another.


                       In the following tutorial, you will learn how to
                       install Zoom Video Conference Client on Manjaro 21
                       Linux. The tutorial will use the yay AUR helper,
                       ideally most users may be using some wrapper for
                       Pacman, for new users, it is essential to install
                       one to keep your packages up-to-date while you
                       learn Arch/Manjaro.


                # ⚓ Install_Wine_7.3_On_Ubuntu_21.10_/_20.04_&_Linux_Mint_|
                  Tips_On_UNIX⠀⇛


                       Winehq Team released its new Development version
                       7.3


                       This tutorial will be helpful for beginners to
                       install wine 7.3 on Ubuntu 20.04 LTS, Ubuntu 21.10,
                       and Linux Mint 20.3.


                # ⚓ Vectorization_How_To_|_Inkscape⠀⇛


                       This is the 8th part of Inkscape for Students the
                       Series. After we had learned about Cropping in the
                       previous part, now we will learn about
                       vectorization, also known as tracing or simply
                       redrawing. We will practice through examples of the
                       two of vectorization methods, automatic and manual.
                       Now let’s start practicing.


          o § Games⠀➾


                # ⚓ Developers_–_let_us_know_if_you_need_help_with_Steam_Deck
                  testing_|_GamingOnLinux⠀⇛


                       Valve’s new handled PC the Steam Deck is starting
                       to ship out but there’s going to be a long wait for
                       some, and others might not be able to get one at
                       all for various reasons – I’m here to help.


                       Now that any embargo is up and I can do whatever
                       Steam Deck content I like, I had a thought. I know
                       a lot about Linux, and since I have a Steam Deck
                       why not help out those who need it? So that’s
                       exactly what I’m announcing: a free Steam Deck
                       testing service for developers.


                # ⚓ Linux_Gaming_in_2022_|_Bryan_Quigley⠀⇛


                       I’d bet the Steam Deck (and other changes) will
                       have the following impacts on Linux overall by the
                       end of 2022.


                       [...]


                       I’m expecting at least 20% increase on the Steam
                       Hardware Survey (so 1% to 1.20%) not including
                       Steam Deck. Right now, the Steam Linux usage is
                       less than half what you get from other sources.


                       [...]


                       Encourage Linux consumer focused pre-installs with
                       similar AMD chips to what’s in the Steam Deck (I
                       know many have asked for more AMD preinstalls for a
                       long while)


                # ⚓ GabeN_Confident_About_the_Steam_Deck’s_Future_–_Boiling
                  Steam⠀⇛


                       So the Steam Deck has just launched, and IGN had
                       the good idea to reconnect with GabeN to collect
                       some of his thoughts about the device, as well as
                       asking him what he thinks of the Ukraine conflict.
                       Nah, that second part did not happen.


                # ⚓ Yes,_‘Elden_Ring’_Is_Perfectly_Playable_On_Linux_(Including
                  Online_Features)⠀⇛


                       Based on the amount of misinformation being dished
                       out on social media and the gaming press this
                       weekend, you deserve to hear this: Elden Ring is
                       perfectly playable on Linux, including online
                       functionality. That doesn’t just apply to Valve’s
                       Steam Deck; it applies to any modern desktop Linux
                       distribution running Steam.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ ’Desktop_Cube’_GNOME_Extension_Now_Supports_Click_&
                        Drag_Deform⠀⇛


                             On Ubuntu you do need to disable the DING
                             extension for the drag feature to work, but
                             once you have you can click, hold and then
                             pull the desktop in any direction to ‘deform’
                             it in to the rotating 3D cube switcher:


                             If you don’t fancy disabling DING you can
                             also click and drag from any empty part of
                             the top bar. You can also tap super to enter
                             the switcher and drag from any non-
                             interactive bit of the overview…


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ EPEL_Office_Hours_–_Fedora_Community_Blog⠀⇛


                             The EPEL Steering Committee is implementing
                             monthly office hours for the EPEL project.
                             These will be held on the first Wednesday of
                             each month at 1700 UTC. The first session
                             will be on 2022-03-02. The openSUSE Heroes
                             team has agreed to let us host the meeting on
                             their Jitsi Meet Instance.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Xubuntu_22.04_Wallpaper_Contest_is_Open_For_Entries_–
                        OMG!_Ubuntu!⠀⇛


                             Artists, photographers, and digital designers
                             have until March 12th to submit up to 5
                             pieces of original work for potential
                             inclusion in the Xubuntu 22.04 LTS release in
                             April.


                             The Xubuntu team plan to pick 6 winners from
                             those submitted (which means there’s more
                             chance of being picked than in regular
                             Ubuntu’s wallpaper contest which is only
                             going to select 2 winners).


                             The usual sort of rules apply: no brand names
                             or trademarks; nothing saucy, salacious, or
                             subversive; nothing political, religious, or
                             nationalistic; and, perhaps most importantly
                             of all, no artwork that isn’t entirely
                             original (or derived from something that has
                             a permissive license)!


          o § Devices/Embedded⠀➾


                # ⚓ MWC_2022_Day_0:_Live_updates_from_Barcelona_–_Android
                  Authority⠀⇛


                       Among the highlights out of the show: the new/old
                       Astro Slide from Planet Computers.


                       We had hands-on time with the prototype you see
                       above, which is now running Ubuntu with a physical
                       keyboard. There’s also an option to buy one with
                       Android 11, or dual-boot with Linux as well. Price?
                       $975. Sales start in a “few weeks.”


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Honor_teases_blockbuster_Magic4_Series_phone_launch
                        tomorrow_|_Express.co.uk⠀⇛


                      # ⚓ The_Best_Android_Games_of_February_2022_–_Inua,
                        Encodya_and_More_–_Droid_Gamers⠀⇛


                      # ⚓ Best_cheap_smartwatch_for_Android_2022_|_Android
                        Central⠀⇛


                      # ⚓ Galaxy_S22,_S22+_and_S22_Ultra:_7_Hidden_Android
                        Features_and_Settings_to_Know_–_CNET⠀⇛


                      # ⚓ Google_Chrome_is_removing_its_data_saving_mode_on
                        Android_–_lets_celebrate_|_TechRadar⠀⇛


                      # ⚓ Budget_Android_Phones_With_Upscale_Performance⠀⇛


                      # ⚓ Is_The_Truth_Social_App_On_Android?_Here’s_What_We
                        Know⠀⇛


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


                # ⚓ KeePass:_The_Open-source_Password_Manager_that_sets_the
                  standards⠀⇛


                       KeePass is considered the most popular open-source
                       password manager, and not just among end-users, but
                       also among developers who ported it to all known
                       platforms.


                       KeePass helps users to manage their passwords
                       securely and privately, without having to worry
                       about many technical details.


                       It supports several encryption standards, AES and
                       Twofish. It also encrypts the entire database.


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Robert_Kaiser:_Connecting_the_Mozilla
                              Community⠀⇛


                                   After some behind-the-scenes
                                   discussions with Michael Kohler on what
                                   I could contribute at this year’s
                                   FOSDEM, I ended up doing a presentation
                                   about my personal Suggestions for a
                                   Stronger Mozilla Community (video is
                                   available on the linked page). While
                                   figuring out the points I wanted to
                                   talk about and assembling my slides for
                                   that talk, I realized that one of the
                                   largest issues I’m seeing is that the
                                   Mozilla community nowadays feels very
                                   disconnected to me, like several
                                   islands, within each there is good
                                   stuff being done, but most people not
                                   knowing much about what’s happening
                                   elsewhere. That has been helped a lot
                                   by a lot of interesting projects being
                                   split off Mozilla into separate
                                   projects in recent years (see e.g.
                                   Coqui, WebThings, and others) – which
                                   is often taking them off the radar of
                                   many people even though I still
                                   consider them as being part of this
                                   wider community around the Mozilla
                                   Manifesto and the Open Web.


                # § FSFE⠀➾


                      # ⚓ Free_Software_Fellowship:_Snake_Island_Code_of
                        Conduct⠀⇛


                             To honor the defiance of these Ukrainian
                             victims, we created a new sticker in the
                             Ukrainian national colours and we are
                             publishing examples of fascism in the FSFE…


    * § Leftovers⠀➾


          o § Hardware⠀➾


                # ⚓ Need_To_Probe_Circuits?_Remember_About_Clothespins!_|
                  Hackaday⠀⇛


                       After browsing Thingiverse for some printable PCB
                       probe designs, [Henry York] looked around and found
                       a wooden clothespin on his desk. After some
                       collaboration between his 3D printer and his CNC,
                       Henry graced us with a nifty helper tool design
                       that many of us might want to make in a pinch – a
                       small, cheap and easy to make PCB probe, for
                       circuits where soldering and headers are out of the
                       question. Small magnets are glued to the
                       clothespin, holding it flush to a magnetizable work
                       surface (aka a toaster tray), and the probing
                       itself is done by an extruder cleaning needle end.
                       3D printer and Edge.Cuts files are shared with us –
                       thanks to Henry’s helpfulness, it should be easy to
                       repeat if ever needed!


                # ⚓ ESP32_Virtual_Machine_Lets_You_Change_Programs_On_The_Fly_|
                  Hackaday⠀⇛


                       Often, reprogramming a microcontroller involves
                       placing it in reset, flashing the code, and letting
                       it fire back up. It usually involves shutting the
                       chip down entirely. However, [bor0] has built a
                       virtual machine that runs on the ESP32, allowing
                       for dynamic program updates to happen.


                       The code is inspired by the CHIP-8, a relatively
                       ancient interpreter that had some gaming
                       applications. [bor0] had already created a VM
                       simulating the CHIP-8, and repurposed it here,
                       taking out the gaming-related drawing instructions
                       and replacing them with those that control IO pins.
                       Registers have also been changed to 16 bits for
                       added flexibility and headroom.


                # ⚓ Teaching_You_Everything_You_Might_Have_Missed_About
                  Addressable_LEDs_|_Hackaday⠀⇛


                       Often, financial motivation results in people
                       writing great educational material for hackers.
                       Such is absolutely the case with this extensive
                       documentation blog post on addressable LEDs by
                       [DeRun]. This article could very be named
                       “Addressable LEDs 101”, and it’s a must-scroll-
                       through for anyone, whether you’re a seasoned
                       hacker, or an artist with hardly any technical
                       background and a desire to put LEDs in your
                       creations.


                       This blog post is easy to read, painting a complete
                       picture of what you can expect from different
                       addressable LED types, and with apt illustrations
                       to boot. Ever wonder which one of the addressable
                       strips you should get from your retailer of choice,
                       and what are the limitations of any specific type?
                       Or, perhaps, you’d like to know – why is it that a
                       strip with a certain LED controller is suspiciously
                       cheap or expensive? You’re more than welcome to, at
                       least, scroll through and fill into any of your
                       addressable LED knowledge gaps, whether it’s
                       voltage drops, color accuracy differences, data
                       transfer protocol basics or dead LED failsafes.


                # ⚓ Retro_And_New_Tech_Combine_In_This_Hybrid_Ham_Transmitter_|
                  Hackaday⠀⇛


                       We’ve said it before and we’ll say it again: the
                       best part about holding an amateur radio license is
                       that it lets you build and use your own
                       transmitting equipment. Hams have been doing this
                       for more than a century — indeed, it was once the
                       only way to get on the air — using whatever
                       technology was available. But the mix of
                       technologies in this low-power transmitter for the
                       80-meter band is something you don’t see every day.


                       As ham [Helge Fykse (LA6NCA)] describes in the
                       video below, the project began when he came into
                       possession of a bonanza of vacuum tubes — 12A6
                       tetrodes, specifically. The new-old-stock tubes
                       were perfect for an RF power amplifier, but that
                       left the problem of what to use for an oscillator.
                       [Helge] chose to meld the old with the new and used
                       oscillator board that he designed. The board has an
                       ATmega88 microcontroller and an Si5351 oscillator,
                       along with a 3V3 regulator to let the module run on
                       12 volts. And for a nice retro touch, [Helge] put
                       the board in a 3D printed case that looks like an
                       old-fashioned quartz crystal.


                # ⚓ AllSpice_Building_A_Hardware_Development_Ecosystem_For
                  Companies_|_Hackaday⠀⇛


                       In our “hardware development gets serious” news,
                       we’ve recently learned about AllSpice, a startup
                       building hardware development collaboration
                       infrastructure for companies. Hardware developers
                       are great at building hardware tools for
                       themselves, but perhaps not always so when it comes
                       to software, and AllSpice aims to fill that gap at
                       the “hardware company” level. Nowadays, what
                       commonly happens is that software development tools
                       and integrations are repurposed for hardware needs,
                       and the results aren’t always as stellar as they
                       get in the software world. In other words, AllSpice
                       is learning from the positive outcomes of software
                       industry and building a platform that takes the
                       best parts from these tools, aiming to get to
                       similarly positive outcomes in areas where
                       currently hardware team experiences are lacking.


                       What AllSpice is building seems to be an umbrella
                       platform designed to augment, integrate and hook
                       into a slew of different already-developed
                       platforms like GitHub, GitLab, Jira (and some other
                       ones), and add much-needed features that large-
                       scale hardware developers can’t afford to maintain
                       and develop themselves. “Design review by
                       screenshot” isn’t unheard of in hardware circles,
                       and likely a thing that everyone of us with
                       hardware collaboration experience has partaken in.
                       On a company scale, there’s a myriad of hardware-
                       related problems like that to solve and polish
                       over.


                # ⚓ Apple_Extended_Keyboard_(m0115)_Repair_Teardown⠀⇛


                       I recently repaired an Apple Extended Keyboard
                       (M0115). I took some pictures. This post is an
                       excuse to show them. Repairs were successful, and
                       I’m typing this post on it.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Bionic_Implants_Can_Go_Obsolete_And_Unsupported,_Too⠀⇛


                       When a piece of hardware goes unsupported by a
                       company, it can be frustrating. Bugs may no longer
                       get fixed, or in the worst cases, perfectly good
                       hardware can stop working entirely as software
                       licences time out. Sadly, for a group reliant on
                       retinal implants from company Second Sight, the
                       company has since stopped producing and supporting
                       the devices that give them a crude form of bionic
                       sight.


                       The devices themselves consist of electrodes
                       implanted into the retina, which can send signals
                       to the nervous system which appear as spots of
                       light to the user. A camera feed is used to capture
                       images which are then translated into signals sent
                       to the retinal electrodes. The results are low-
                       resolution to say the least, and the vision
                       supplied is crude, but it gives users that are
                       blind a rudimentary sense that they never had
                       before. It’s very much a visual equivalent to the
                       cochlear implant technology.


                       [...]


                       It’s a sobering tale of what can happen when a tech
                       company goes out of business. It’s a story that
                       bears thinking about for anyone taking on a medical
                       device from a new, untested company. Video after
                       the break.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Updates_To_The_EPO_Guidelines_For_Examination [Ed:
                        Guidelines that do_not_comply_with_the_law]⠀⇛


                             The EPO have announced their upcoming
                             amendments of the Guidelines for Examination
                             which will enter into force on 1 March 2022.
                             A number of notable amendments to the
                             Guidelines are scheduled; we will follow with
                             more detailed discussions regarding the
                             changes to Description Amendments and
                             Electronic Signatures of Assignments, whereas
                             here we will look at some of the other
                             significant updates with regard to Priority,
                             the Designation of Inventor, the Claims Fee,
                             Extension of Periods under Rule 134(1),
                             Double Patenting, Selection Inventions,
                             Unity, and Oral Proceedings.


                      # § Software Patents⠀➾


                            # ⚓ Another_Blow_to_DABUS_as_Patent_Offices_Reject
                              AI_as_Inventors_|_GJE [Ed: This patent lunacy is
                              merely provocation of the system, discredited the
                              system]⠀⇛


                                   Artificial intelligence (AI) stands as
                                   a powerful tool undergoing rapid
                                   progression and adoption at the
                                   forefront of research and development.
                                   The continued growth in the importance
                                   of AI raises several questions for
                                   patent systems across the world. In
                                   particular, the issue of inventorship
                                   continues to unfold controversy, as the
                                   ‘inventor’ status is tested by patent
                                   offices worldwide.


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