𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, August 22, 2022
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Generated Tue 23 Aug 02:41:52 BST 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/2022/08/22/


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

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QmT23V7rp3Ae5ZxqXsMyaTefUq1s6QBb2oAixwDFJtaTCP
QmU5ELpXwLE1ZfJ8H6mSshDjG3x19rMkZWZ8Qx6PKkBWRB
QmUReWtcWQ5HsqPCLHEspV2D51CR7gkA9PiDKC7b763DgE
QmUZHkoHzitUm38ZMdJ3aeGJsFbcEbrpbxRqLxgvnLFKPL
QmRYZ5KjYGZuv3b7JvqAbV4rfX2ZVkMWBfC4aXFKwZjrct
QmcPmtYjQ627Bey3DX46YG4WiSgmpF8GB5yDWsvH4ohkxP
QmQeorfyCyeAdMaNzuRmrXYgrqiqrzPKP9SHtd6mCKWrFe
QmUiMdJ65F7h2Cxy54N5XhhxXLLQwtpgk8b6bvC942r2xY
QmNb2ydzs2uqBuBowYxV8oB66PL2Ed3KkRKEaU3DCDTSZ9
QmQe9CSmi7hJdXsrLQALzxjVKn6GwdcmeGuS1KbgZg6DfD
QmY8oB1Qg87HBxwHopNxS6LMozLiwmSxad31Ttse73Fh2q
QmXt1BammAJUuBrf4QPcungjNg2ePnbbrjoTfCoibP7XTL
QmdDSQKaZJPnyDHFjeXTz7ZrVGb39ksdMdmtNhpx75EgdH
QmZ7mLY8uo6YvRrfUTtX3hPHDhQgDNyt4AB4fPvzYWrcC4
QmTZezLwd5vekievmKZscKgr1hkxvuHoSSsWhkA4iTy7Tu
QmNWKKu3gEEUM8UjAb868zLoy5CP9rUmyUWSSFH78F7ZGy
Qmc1hpdpKJMrmE55WT3tg3aQBqe3inuQhnbsjTc8RVVKFq
QmZNGE6NoRBC2J66AEvKbXxsP9j48e5nLCkLncW2SuYUD5
Qmd1qRcbFUvYnekMd31x6KbniK82hv6mEweUfvuLLLU3Dn
QmPGPjyuWmmi4WH1Pm1qxX7pzZhtRC3umeb4DmdE7NfXdU


╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ By August 2022 Windows Estimated to Have Secured Majority Market Share in Just a Couple Dozen Medium- or Large-Sized Nations (Android Dominates About 50) | Techrights

⦿ Going Public With New Site Code | Techrights

⦿ [Meme] EPO Has Failed to Comply With Straightforward ILOAT Ruling for Almost Two Months Already | Techrights

⦿ IRC Proceedings: Sunday, August 21, 2022 | Techrights

⦿ Russia’s Invasion of Ukraine Turns 6 Months; Windows Share in Russia Down Every Month Since Then (From Over 55% to 47%) | Techrights

⦿ The Web is a Corporate Monoculture, Whereas Gemini is Still a Diverse Community | Techrights

⦿ Spamnil is Still Clickfrauding and the Linux Foundation Supports the Clickfraud | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/08/22/august-2022-share/#comments
		http://techrights.org/2022/08/22/code-going-public/#comments
		http://techrights.org/2022/08/22/iloat-rulings-disregarded/#comments
		http://techrights.org/2022/08/22/irc-log-210822/#comments
		http://techrights.org/2022/08/22/windows-loses-majority/#comments
		http://techrights.org/2022/08/22/www-corporate-monoculture/#comments
		http://techrights.org/2022/08/22/youtube-clickfraud/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/08/22/mozilla-firefox-104/#comments
		http://techrights.org/2022/08/22/rc2-of-linux-6-0-released/#comments
		http://techrights.org/2022/08/22/risc-v-products-with-linux/#comments
		http://techrights.org/2022/08/22/starbook-mk-vi/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 68

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/22/august-2022-share/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/22/august-2022-share/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ By_August_2022_Windows_Estimated_to_Have_Secured_Majority_Market_Share_in
Just_a_Couple_Dozen_Medium-_or_Large-Sized_Nations_(Android_Dominates_About
50)⠀✐


Posted in Microsoft, Windows at 8:50 am by Dr. Roy Schestowitz


                    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇August_2022_share⦈_
  The blue (Windows) is going or fading away each month this year. Orange is
   Android. Russia will turn orange some time soon (maybe next year) because
Android_grows_in_Russia_since_the_invasion_of_Ukraine (from 21% to 33% in less
                              than six months)..


                   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇August_Android_share⦈_
             See the underlying_data as OpenDocument Format (ODF)


Summary: Data from the Web (about 3 million Web sites) helps reveal the decline
of Windows, especially in regions where mobile devices have become ubiquitous


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

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/22/code-going-public/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/22/code-going-public/

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Gemini_version_available_♊︎


✐ Going_Public_With_New_Site_Code⠀✐


Posted in Site_News at 8:09 am by Dr. Roy Schestowitz


Video_download_link | md5sum 61c40e9bbcb4e65c8dd5d49579988b7a
Last Night We Published New CMS Code
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/going-public-with-cms-code.webm


Summary: Content management systems that support several protocols (not just
the World Wide Web or HTML) are something more people ought to look into; in
our case, we’ve made our own and the code is tentatively public


AT the start of July we said we’d adopt and gradually move to static pages,
essentially by developing our own CMS for our specific needs. Writing one’s own
CMS isn’t a massive coding job if things are kept simple (narrow set of
features) and the investment pays off if the code will be used for decades
(deployed across several sites). This CMS isn’t a Web CMS; it’s not limited to
the Web, it supports several protocols.


“…investment pays off if the code will be used for decades (deployed across
several sites).”What was recently deployed in Tux Machines (it went live a week
ago) will later be deployed here, albeit gradually.


At the moment there’s not much to see as we have only this_small_prototype_of
commit_history (akin to a proof of concept that will improve over time) and
full_code_listing along with the_licence. Suffice to say, the code is not yet
“production” quality, but at least it is developed in the open now (updated
every hour). The system is very “custom-made” (tailored to our unique needs and
workflow), but if it gets generalised, it’ll likely need a project name. █



                    ䷩ 𝚕𝚒𝚗𝚎 242

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/22/iloat-rulings-disregarded/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/22/iloat-rulings-disregarded/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_EPO_Has_Failed_to_Comply_With_Straightforward_ILOAT_Ruling_for_Almost
Two_Months_Already⠀✐


Posted in Europe, Patents at 9:17 am by Dr. Roy Schestowitz


All it had to do was remove a filter (that should take a couple of minutes)


            🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Lost ILO Case; Still not complying⦈
EPO_censorship_ruled_illegal, but the censors who dictate illegal_policies just
 ignore the Rule of Law, egged on by patent maximalists (the patent litigation
                                    cartel)


Summary: EPO criminals Benoît_Battistelli and António_Campinos continue
disregarding judges from the courts in Geneva and elsewhere; they
metaphorically laugh at the law


⠀⠀⠀⠘⠃⠀⠈⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁⢀⣼⣿⡿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⠃⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣠⣤⣤⣤⣤⣤⣶⣶⣤⡀⠀⠀⠀⣲⣾⣿⣿⣧⠀⠀⣰⣤⣿⣿⣿⣿⣿⣾⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢌⠹⢿⠟⠻⠀⠀⠈⠛⠉⠛⠛⠉⠉⢿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣷⡆⣠⡀⣀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠹⣿⣧⣰⣷⣀⢀⣴⣀⣀⠀⠀⠀⠀⠁⠀⠀⣰⡆⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣃⡻⡇⢻⡗⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⡀⠀⠀⠀⠇⠀⠉⠃⠀⠀⢀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢠⣿⣿⣿⣿⣿⣿⡟⠛⠿⠟⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣸⡿⠋⢉⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⠅⠀⠀⣀⡀⣀⣨⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠦⠀⣤⣾⣿⣆⠀⠀⢸
⠀⠿⢿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣭⣀⡀⠀⠀⣿⣧⣾⠿⠛⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⠀⡀⠀⠉⠻⣿⣿⣇⢠⢧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⡄⢻⣿⣿⣿⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⢸⣿⣿⣿⢿⡏⣷⡄⢸⣿⣿⣿⣧⣬⣇⣀⣠⣄⣤⣼⣿⣿⣿⣶⣶⣿⣶⣿⣾⣿⣿⣿⠸⣾⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡟⠀⠀⠻
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⣿⣿⣿⡿⠞⢷⡿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⠀⠀⠀⠀⣰⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢘
⠀⢀⣰⣦⣀⣠⣦⣠⡀⠀⢸⣿⠷⠶⢾⠇⠀⠀⢀⣤⣤⣤⡀⣿⡋⠀⠀⠀⠸⣧⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⣿⠏⣴⣿⣿⡏⢀⣹⣿⣿⣿⣿⣿⡄⠀⠀⠊
⢴⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣄⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢻⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⠏⣰⢿⣿⣿⣧⠛⠻⠿⣿⡏⠉⠻⠇⠀⠀⠀
⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⡃⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣴⣿⡇⠀⠉⠀⣹⣿⣿⠇⠠⠾⠿⠇⠀⢰⣧⣀⡀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⡟⢠⣿⠿⣿⡟⢋⣄⣴⣾⣿⣿⣿⣦⣀⢀⣤⡀⠀⢠⣬⠀⠙⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣧⣤⠀⠀⠈⢿⣿⣿⣿⣿⣶⣦⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠁⠈⢣⣤⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⡞⠛⢴⣦⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣿⣿⣿⠟⠁⠀⠀⢸⡟⠿⡟⠻⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⢤⠙⣿⡿⠋⠀⣾⣟⣿⣿⣿⣿⣿⣿⣿⣍⣯⣹⣿⣯⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⣿⣦⡁⠐⠗⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣱⣿⡷⡠⣺⣾⣶⡀⠀⠀⠀⢹⣿⣿⣿⠿⠿⢇⣬⣭⢿⣿⣿⣿⢿⣆⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⢟⣿⣿⣿⣿⡇⠀⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠋⠁⠉⠙⠙⠿⣿⣿⠀⢸⣿⣧⡀⠀⠀⠀⠉⠈⠙⠛⠛⠉⠁⠀⠞⠛⠉⠨⢊⣤⣿⣿⣷⠀⠀⠀⠀⠙⢿⣿⣤⣤⣸⣿⣿⣿⣿⣿⣿⣄⣿⣶
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠿⠿⠿⠟⠛⠛⠛⠛⠋⠁⠀⣠⠀⣶⡄⠀⠈⣿⡄⠀⢿⣿⣿⣶⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠵⠋⢐⣿⣿⡿⠋⠀⠀⠀⠀⠀⠰⠇⠘⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣏⣠⡿⠀⢀⣀⢹⣀⠀⠈⣿⣛⣿⣿⣯⡤⣀⣀⠀⠀⣀⣀⠈⠀⣀⣾⡿⢛⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⠋⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⢧⡿⣿⡟⠁⠀⢸⣿⢸⣿⠀⢰⣿⢹⣿⢹⣿⣾⣿⢹⣷⢀⣿⢿⡧⢼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠷⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⢸⣿⢸⣼⣿⢸⣿⠸⠿⣿⡿⢪⣄⢸⣿⣸⣧⢌⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⠿⠷⠆⠻⠧⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⠶⣞⣿⠾⠿⠌⠭⠹⠿⠾⡏⠼⠿⡹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣴⠆⠾
⠘⣿⣿⣿⣿⡿⠿⢿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣛⣺⣷⣺⣓⣾⣓⣊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣍⡙⠀⣦
⠀⠾⣿⣿⣿⣿⠿⢷⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⡿⠟⡟⠛⠟⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⢀⡿
⠀⠀⠀⠛⠃⠀⠘⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠀⢠⣾⣿⠇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⠛⠃⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣤⣤⣤⣤⣴⣶⣤⡀⠀⠀⠀⣦⣾⣿⣷⡆⠀⠀⣴⣤⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣼⣿⣧⡄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⡉⠿⠿⠛⠿⠀⠀⠘⠟⠈⠻⠋⠉⠙⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠠⣿⣿⣿⣿⣿⣿⣿⡆⣤⡀⣠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢳⣿⣄⣰⣦⡀⣀⣄⣀⡀⠀⠀⠀⠈⠀⠀⠀⣴⡄⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣟⣁⣻⡃⣻⠇⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⡠⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣠⡀⠀⠀⠀⠂⠀⠙⠃⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣾⡿⠋⢉⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⠏⠀⠀⣀⡀⣀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠦⠀⣤⣿⣿⣆⠀⠀⠀
⠘⠿⠿⠿⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣤⣅⣀⠀⠀⢠⣿⣷⣾⠿⠛⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⡀⠀⠉⠻⣿⣿⡆⣰⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣤⡀⢿⣿⣿⣿⠀⠐⠀
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⣿⣿⣿⣿⢿⢫⣦⠀⢸⣿⣿⣿⣧⣬⣇⣀⣀⡄⣠⣼⣿⣿⣿⣶⣶⣿⣶⣿⣾⣿⣿⣷⢠⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠏⠀⠀⢀
⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⡿⢻⣾⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠀⢠⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⣰⣄⣀⣠⣧⣀⡀⢀⣻⡿⠿⠿⣿⠀⠀⠀⢀⣤⣤⣤⢸⣿⠁⠀⠀⠀⣿⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣿⡿⢠⣶⣿⣿⡋⠈⣽⣿⣿⣿⣿⣿⡀⠀⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⣿⣧⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⢿⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⡿⠁⣿⣿⣿⣿⣇⠛⠻⢿⣿⡏⠉⢿⠇⠀⠀⠀
⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣴⣿⡀⠀⠃⠀⣽⣿⣿⠂⠀⠾⠿⠇⠀⣸⣷⣄⠀⠀
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣾⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⠇⢀⣿⠿⣿⡛⢃⣠⣶⣿⣿⣿⣿⣄⣀⢀⣄⠀⠀⣠⣍⠀⠲⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣷⡆⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡟⠀⠈⣫⣠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣳⣶⡿⠋⣴⣆⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡁⠀⠀⠀⢱⠙⣿⡿⢿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⡠⣍⢿⣿⠟⠋⢠⣾⣛⣿⣿⣿⣿⣿⣿⣿⣹⣟⣽⣿⣟⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⠟⠁⢹⣿⣿⣿⣿⣿⠿⣿⣿⣷⣶⣄⡀⢸⣷⣌⠁⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣽⣿⢇⢔⡵⣷⣆⠁⠀⠀⠀⢻⣿⣿⣿⠿⢿⢇⣭⣭⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠁⠀⠉⠉⠉⠻⣿⡇⠀⣿⣿⣆⠀⠀⠀⠈⠁⠈⠙⠛⠋⠉⠉⠀⠞⠛⠕⠕⣋⣼⣿⣿⡆⠀⠀⠀⠈⠹⣿⣟⣤⣄⢸⣿⣿⣿⣿⣿⣿⣸⣿⣶
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠿⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⡤⠀⣷⠀⠀⢸⣇⠀⠸⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠶⠁⢴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣴⣇⣰⡿⠀⢀⣘⢏⣀⠀⠹⣿⣛⣿⣿⣄⡀⣀⣀⠀⠀⣀⣀⠁⠀⣰⣿⡿⢋⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⣧⠿⣿⡏⠁⠀⢸⣿⢸⣿⠀⢸⣿⢹⣿⢹⣿⣾⣿⢹⣷⢀⣿⢿⡧⢼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢾⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⢸⣿⢀⢸⣿⢸⣿⢸⡿⣿⡿⢢⣄⢸⣿⣸⣧⢉⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡠⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⢶⣙⡿⠾⠿⠈⠀⠹⠷⠾⣏⠼⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠠⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣒⣾⣲⣒⣲⣚⣒⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣛⠯⢠⣤
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⠿⢿⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⢸⡿
⠀⠀⠀⠛⠃⠀⠘⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⢠⣾⣿⠇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⠛⠃⠀⠀⠀⣀⣀⣀⣀⣀⣠⣠⣤⣴⣤⣤⣤⣤⣴⣶⣤⡀⠀⠀⠀⣦⣾⣿⣷⡆⠀⠀⣴⣤⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣼⣿⣧⡄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⡉⠿⠿⠟⠿⠀⠀⠘⠟⠈⠻⠏⠉⠙⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠠⣿⣿⣿⣿⣿⣿⣿⡆⣤⡀⣠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢣⣿⣄⣰⣦⡀⣀⣄⣀⡀⠀⠀⠀⠈⠀⠀⠀⣴⡄⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣟⣉⣻⡃⣻⠇⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⡠⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣠⡀⠀⠀⠀⠂⠀⠙⠃⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⠁⠈⠉⠁⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣾⡿⠋⢉⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⠏⠀⠀⣀⡀⣀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠆⠀⣤⣿⣿⣄⠀⠀⠀
⠘⠿⠿⠿⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣤⣅⣀⠀⠀⢠⣿⣷⣾⠿⠛⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⡀⠀⠉⠻⣿⣿⡆⣰⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⡀⢿⣿⣿⣿⠀⠐⠀
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⣾⣿⣿⣿⢿⢋⣦⠀⢸⣿⣿⣿⣧⣬⣇⣀⣀⣄⣠⣼⣿⣿⣿⣶⣶⣿⣶⣿⣶⣿⣿⣷⢠⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠏⠀⠀⢀
⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡿⢻⣾⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠀⢠⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⣰⣄⣀⣠⣇⣀⡀⠀⣾⠿⠿⠷⠿⠀⠀⠀⢀⣤⣤⣤⢸⣿⠁⠀⠀⠀⢿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣿⡿⢠⣶⣿⣿⡋⢈⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⣿⣧⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⣿⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⡿⠁⣿⣿⣿⣿⣇⠛⠻⣿⣿⡏⠉⢿⠇⠀⠀⠀
⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣴⣿⡀⠀⠃⠀⣽⣿⣿⠀⠠⠾⠿⠇⠀⣸⣷⣄⠀⠀
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣾⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠘⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⠇⢀⣿⠿⣿⡛⢃⣠⣶⣾⣿⣿⣿⣄⣀⢀⣄⠀⠀⣠⣍⠀⠲⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣷⡆⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡏⠀⠈⣩⣠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣳⣶⡿⠋⣴⣆⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡁⠀⠀⠀⢱⠻⣿⡿⢻⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⡠⣍⢿⣿⠟⠋⢠⣾⣛⣿⣿⣿⣿⣿⣿⣿⣹⣟⣽⣿⣟⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⠟⠁⢹⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣄⡀⠸⣷⣌⠁⠘⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣽⣿⢇⢔⡵⣷⣄⠁⠀⠀⠀⢻⣿⣿⣿⠿⢿⢇⣭⣭⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠁⠀⠁⠉⠉⠻⣿⡇⠀⣿⣿⣄⠀⠀⠀⠀⠁⠈⠙⠛⠋⠉⠉⠀⠞⢋⠕⠕⣋⣼⣿⣿⡆⠀⠀⠀⠈⠹⣿⣟⣤⣤⢸⣿⣿⣿⣿⣿⣿⣸⣿⣤
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠿⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⡤⠀⣷⠀⠀⢸⣇⠀⠸⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠶⠁⢴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣰⣇⣰⡿⠀⢀⣘⢏⣀⠀⠹⣿⣛⡿⣿⣊⡁⣀⣀⠀⠀⣀⣀⠁⠀⣰⣿⡿⢋⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⠸⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⣧⠿⣿⡏⠁⠀⢸⣿⢸⣿⠀⢸⣿⢹⣿⢹⣿⣾⣿⢹⣷⢀⣿⢿⡧⢼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢾⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⢸⣿⣀⢸⣿⢸⣿⢸⡿⣿⡿⢢⣄⢸⣿⣸⣧⢉⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡠⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⢶⣙⡿⠾⠟⠈⠀⠹⠷⠾⣏⠼⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠠⣿
⠘⣿⣿⣿⣿⡿⠿⠿⣿⣿⡏⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣒⣾⣲⣒⣲⣚⡒⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣛⠃⢠⣤
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⠿⢿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⢸⣿
⠀⠀⠀⠛⠃⠀⠸⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⣰⣿⣿⠇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⠛⠂⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⢠⣤⣾⣿⣶⡆⠀⠀⣤⣤⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⣿⣿⣧⠄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢈⠻⠟⢿⠿⠷⠀⠀⠙⠟⠙⠿⠏⠉⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣶⡀⣀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⣤⣿⣄⣰⣆⠀⣠⣆⠀⡀⠀⠀⠀⠈⠀⠀⠀⣴⡀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣿⣟⣙⢿⠃⣿⠇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⡠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⡗⢀⣠⡀⠀⠐⠂⠀⠛⠁⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠉⠈⠉⠁⠀⢁⣤⣿⣿⣿⣷⠀⠀⠀⠀⠂⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⠟⠛⠻⠻⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⡿⠛⠉⠉⠉⠉⠛⠛⣿⣿⣿⣿⣿⡏⢀⠀⣀⠀⣀⣉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠄⢀⣠⣿⣷⡄⠀⠀⡀
⠸⠿⢿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣈⣀⡀⠀⠀⢸⣿⣧⣾⠿⠓⠀⠀⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⠈⠙⢿⣿⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣄⠈⣿⣿⣿⣇⠀⠀⠀
⠀⠀⢀⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⣿⣾⣿⣿⡟⣱⡄⠀⣾⣿⣿⣿⣤⣜⣆⡀⣀⡄⣠⣸⣿⣿⣷⣶⣶⣿⣶⣶⣶⣿⣿⡇⣰⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀⠀
⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⣧⣿⡿⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡀⠀⠀⠀⣰⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⣠⣄⣀⣠⣄⣀⠀⠀⢿⠷⠶⠶⡶⠀⠀⠀⢀⣤⣤⣌⢸⡟⠉⠀⠀⢸⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣿⡇⣠⣼⣿⣿⠋⢈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣆⣀⢀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣻⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⣾⣿⣶⣿⣿⣿⣿⡔⠛⠿⣿⣿⡏⠉⢿⠀⠀⠀⠀
⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⠀⠀⠀⠀⠀⠀⠀⢠⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣴⣿⠀⠘⠋⢀⣿⣿⣿⠀⠠⠾⠿⠇⠀⣼⣦⡀⠀⠀
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢰⣾⣷⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠁⠀⣿⣿⣿⠛⢃⣠⣴⣿⣿⣿⣷⣀⡀⢀⣀⠀⠀⣠⡍⠀⢤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⡏⠀⠈⣫⣀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⣶⠿⠇⣤⣄⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⡎⠻⣿⠿⢿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣄⠻⣿⣿⠿⠋⢠⣾⣛⣿⣿⣿⣿⣿⣿⣷⣛⣛⣿⣿⡟⠏⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠻⠋⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣄⠄⣷⣆⠉⠱⢰⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⢀⢬⢾⣦⠈⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⢏⣍⣻⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠿⣿⣿⣿⣿⡇⢠⣶⣶⣶⣶⣿⣿⣿⣿⡿⠉⠁⠀⠈⠉⠉⠻⡏⠀⢸⣿⣧⡀⠀⠀⠀⠉⠁⠈⠛⠛⠛⠉⠉⠠⠼⡋⠩⠕⣡⣿⣿⣷⠀⠀⠀⠀⠈⢻⣿⣟⣤⣀⢺⣿⣿⣿⣿⣿⣿⣸⣷⣄
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⢸⠿⢿⡿⠿⠟⠛⠛⠉⠀⠀⠀⣤⢸⣷⠀⠀⣾⡀⠀⢿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢄⡪⠖⠠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⢴⡏⢸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣇⣾⡟⠀⢀⣳⢁⣀⠈⢿⣿⣛⡿⣧⣄⡀⣀⣀⠀⠀⣀⣐⠉⠀⣴⣻⡿⢉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⢹⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⢧⠟⣿⡏⠁⠀⢸⣿⢸⣿⠀⢸⣿⣹⣿⢹⣿⣾⣿⢹⣷⢀⣿⢿⡧⣼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣾⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⢹⣿⠀⢸⣿⢹⣿⢸⣿⣿⡿⢠⣀⢸⣿⣸⣧⢋⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⡾⢙⡿⠾⠟⢐⡀⢹⠷⠾⡟⠾⠟⠻⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢸⣷
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⡶⢴⡶⢴⡶⢴⡷⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣔⠛⠅⢠⣌
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣽⠿⡿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⡿
⠀⠀⠀⠛⠃⠀⢸⣿⣧⣤⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠀⣴⣿⡿⠂⠀⠀⠀⠉⠋⠀⠀⠈⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠛⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⣠⣾⣷⣶⡀⠀⠀⣦⣰⣿⣿⣿⣿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠚⢿⠿⡿⠿⠧⠀⠀⠹⡟⠹⡿⠟⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣴⣤⣤⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠳⣰⣷⣀⣰⣆⠀⢀⡄⠀⡀⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠀
⢹⣿⣿⣿⣿⣿⣿⠟⢸⡷⢰⣿⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⢀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣄⠀⠰⠀⠈⠟⠀⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣧⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠙⠋⠉⠙⠉⢸⡇⠀⣽⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⣨
⣽⣿⣿⣿⣿⣿⣿⠿⠿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢠⣿⡿⠛⠉⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⠏⠁⠀⠉⠁⠉⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⣸⣿⣿⡿⠆⢀⣠⣿⣶⡀⠀⠀⡼
⢿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣉⡀⠀⠀⠀⣸⣿⣦⣾⡿⠟⠀⠀⠀⠀⠙⣿⣿⣿⠃⠀⠀⠀⠉⠛⣟⣿⣇⢠⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄⠸⣿⣿⣿⡇⠀⢰⡟
⠀⠀⣩⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣿⣶⣿⣿⠏⣧⡀⠀⣿⣿⣿⣷⣄⣸⡔⠀⣀⡀⣀⣸⣿⣿⣶⣤⣼⣶⣴⣶⣾⣿⣿⡈⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠇⠀⠈⢽
⠀⡞⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⣇⠀⠀⠀⠀⣴⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣘
⠀⠀⢠⣄⡀⣠⣆⣀⠀⢀⣶⣤⣤⣤⡆⠀⠀⠀⢀⣠⣤⣍⢸⡟⠋⠉⠈⢿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣿⡇⣰⣼⣿⣿⠉⣩⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⡄⠀⠈⠁⠀⠀⠀⠿⣿⣿⣿⣿⣿⣄⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⣾⣿⣷⣿⣿⣿⣿⡘⠛⠿⢿⣿⡏⠻⣿⠀⠀⠀⠀
⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣿⣤⣿⡋⠙⠏⢉⣿⣿⣷⠀⢠⣾⣿⠀⢀⣾⣤⠀⠀⠀
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣴⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⠻⢃⣠⣴⣾⣿⣿⣧⡀⠀⢀⡀⠀⠀⣩⡛⠩⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡇⠀⠘⣿⣿⣿⣿⣿⣿⣤⣄⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⠃⠀⠀⢿⣀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⢿⡿⣤⣴⠿⠇⣤⡈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⡀⠀⣦⠛⢿⣿⠿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⡀⣿⣿⣿⡿⠋⣠⣿⢻⣿⣿⣿⣿⣿⣿⣆⢻⡛⣶⣶⡿⠇⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢸⣶⡈⠙⠠⠾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⡇⡠⣢⣧⡌⢻⠋⠀⠀⠙⣿⣿⣿⣿⣿⣿⢋⣛⠳⣿⣿⣿⣿⣧⠀⠀
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠿⣿⣿⣿⣿⡇⢠⣦⣶⣶⣾⣿⣿⣿⡿⠉⠛⠁⠀⡉⠈⠁⢹⡇⠀⣿⣿⣄⠀⠀⠀⠉⠉⠉⠙⠿⠿⠟⠛⠋⡠⠞⡫⠪⢚⣹⣿⣿⡦⠀⠀⠀⠀⠙⢿⣿⣇⣀⡀⣾⣿⣷⣿⣿⣿⣯⢹⣧⣀
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠇⠛⠿⣿⠿⠿⠛⠛⠉⠀⠀⠀⠀⢰⣿⣷⠀⢸⣇⠀⢸⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣤⠖⢠⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⣼⠋⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣴⣿⣿⡟⠀⢸⣞⢀⣀⠹⣿⣿⣛⣿⣟⠊⡀⣀⣀⠀⠀⣀⣐⠁⠠⣔⣿⡟⢋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠟⣿⡏⠁⠀⢸⣿⣸⣿⠀⢹⣿⣹⣿⢹⣿⣾⣿⢹⣷⢀⣿⢿⡏⣼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⢻⣿⠀⢸⣿⢾⣿⢸⣿⣿⡟⢠⣄⢸⣿⣹⣷⢋⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⠶⠘⠿⠾⠟⠈⠀⠹⠷⠾⠏⠼⠿⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣶⣾
⠘⣿⣿⣿⣿⡿⠿⢿⣿⣿⡏⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⡷⠮⡴⠤⡤⠬⡴⠭⡽⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡴⢿⠀⣌⣉
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣷⣟⣿⣿⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⣿⣿
⠀⠀⠈⠟⠂⠀⢹⣿⣧⣠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢀⣼⣿⡿⠀⠁⠀⠈⠙⠃⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠃⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣤⣤⣄⣀⣀⣤⣀⠀⠀⠀⠀⠀⣤⣾⣷⣶⡀⠀⢀⣄⣰⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣾⣿⣯⣕⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠺⣿⢿⡿⠿⠇⠀⠈⠻⡟⠻⣿⠟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣠⣄⣀⣀⣀⡀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠑⢆⣰⣧⣄⣰⡄⠀⢀⡀⠀⡀⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡧⣴⡆⢰⣦⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⢐⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣇⠀⢀⣄⠀⢰⠀⠘⠻⠀⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣶⣮⣧⣼⣇⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠋⠉⠋⠉⣽⡁⠀⣻⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢰⣿⡿⠛⠙⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣽⣿⣿⡿⠀⢀⣠⣾⣦⡀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣁⠀⠀⠀⠀⣿⣿⣤⣶⡿⠇⠀⠀⠀⠀⢹⣿⣿⣿⠁⠈⠁⠀⠐⠻⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⡇⠀⠀⢸
⠉⠉⣻⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣶⣿⣿⢻⣄⠀⢸⣿⣿⣿⣇⣀⣣⠀⠀⣀⢀⣀⣿⣿⣿⣦⣤⣼⣦⣴⣤⣿⣿⣷⢸⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇⠀⠀⢈
⢠⡏⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢲⣿⣿⣿⣏⣾⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣀⠀⠀⠀⠀⢰⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⢀⠨
⢨⠀⢀⣀⡀⢀⣄⣀⠀⢠⣤⣀⣀⣀⡀⠀⠀⠀⢀⣀⣩⡏⢸⣿⠟⠛⠻⣯⠉⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣿⡏⣰⣿⣿⣿⢉⣽⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈
⢾⣷⣿⣿⣿⣿⣿⣿⣧⣾⣯⡉⠉⠙⠁⠀⢀⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⠀⣼⣿⣷⣿⣿⣿⣿⠘⠻⢿⣿⣿⠛⢻⡇⠀⠀⠀⠀
⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠈⠀⠀⣌⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣥⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣤⣿⡏⠙⠟⢉⣿⣿⡧⠀⣰⣿⣿⠀⢀⣷⡄⠀⠀⠀
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⠻⢃⣠⣶⣾⣿⣿⣅⠀⠀⢀⠀⠀⠉⣙⠛⠐⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢱⣧⠀⢻⣿⣿⣿⣿⣿⣯⣅⣀⣀⣀⣤⣤⣤⣤⣴⣶⣿⣿⣿⡿⠀⠀⠀⣿⢁⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡷⣤⣼⡿⢇⣤⡈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣀⣤⣼⣿⡀⠰⡜⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⠇⠀⣀⡠⡿⣿⣿⡟⠃⣨⡿⢿⣿⣿⣿⣿⣿⣷⡞⡿⠟⣶⣾⠿⠃⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢷⣆⠈⠛⢼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⠀⣐⣽⣧⠉⣿⠋⠀⠀⠻⣿⣿⣿⣿⣿⣿⢙⡛⢻⣿⣿⣿⣿⣆⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣠⣦⣶⣶⣾⣿⣿⣿⠏⠙⠛⠁⢀⡁⠈⠉⣻⠁⠸⣿⣧⡀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠟⠛⠋⡰⠟⡫⡪⢊⣺⣿⣷⡇⠀⠀⠀⠀⠛⣿⣿⢇⣀⠁⣿⣿⣿⣿⣿⣿⣏⣿⣆⣀
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⡿⠿⣿⠿⠿⠛⠛⠁⠀⠀⠀⠀⢸⣿⣷⠀⣼⡀⠀⢿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡤⠂⣴⣿⣿⡟⠋⠀⠀⠀⠀⠀⢀⣼⠉⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣰⣿⣿⡏⠀⢻⣃⢀⣈⢿⣿⣿⣛⡿⣗⠂⠀⣀⣀⠀⠀⣀⣊⠁⢠⣶⣾⠟⢉⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠙⣿⡏⠁⠀⢸⣿⢸⣿⠈⢻⣿⢹⣿⢹⣿⣾⣿⢹⣷⢠⣿⢿⣧⣼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⢿⣿⠀⢸⣿⢼⣿⢸⣿⣿⡟⢠⣄⢸⣿⣹⣟⢉⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⠶⠘⠿⠾⠟⠈⠉⠹⠷⠾⠏⠾⠿⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣾⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠊⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⢭⣤⣥⣤⣅⡴⣝⠶⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠾⢿⠀⣉⡉
⠀⠾⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣳⣶⣿⣶⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿
⠀⠀⠈⠛⠂⠀⢹⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⢠⣾⣿⠗⠈⠀⠀⠘⠙⠃⠀⠀⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⡿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠂⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀⣀⣄⣀⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⣠⣾⣷⣶⡀⠀⢀⣄⣰⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣿⣧⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣭⡃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠐⢶⠻⢿⡿⠿⠇⠀⠈⠻⠯⠻⣿⠛⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠳⠁⣰⣦⣀⣴⡆⠀⢠⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣆⣶⡄⣴⡄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⣢⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣽⣿⣿⣿⣿⣿⣾⣿⣿⡿⠇⣠⣤⠀⠀⢰⠀⠈⠿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣯⣤⣽⣅⣽⢁⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠛⠋⠉⠉⠉⠈⣡⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⣿⠿⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⠷⠀⢀⣠⣶⣦⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⣿⣧⣠⣶⠷⠂⠀⠀⠀⠈⣿⣿⣿⡿⠁⠀⠀⠀⠒⢿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡄⢸⣿⣿⣿⡇⠀⠀⠸
⠛⠻⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣶⣿⡟⣡⡀⠀⣼⣿⣿⣿⣆⣐⠆⠀⢀⡀⢀⣸⣿⣿⣷⣤⣤⣷⣤⣤⣴⣿⣿⡇⢱⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡇⠀⠀⠀
⢠⡟⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⢺⣿⣿⣿⣳⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠈
⢘⠀⢀⣀⠀⢀⣆⡀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⢀⣈⣽⡃⢸⣿⡿⠿⢿⣇⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣆⠀⢀⣾⡿⢠⣿⣿⡟⣥⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣾⣷⣿⣿⣿⣿⣿⣿⡆⠙⣙⠛⠛⠛⠀⠀⢀⠀⢿⣿⣿⣿⣿⣿⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⡄⣾⣿⣷⣿⣿⣿⣿⠙⠻⢿⣿⣿⠙⢻⡇⠀⠀⠀⠀
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⢀⣌⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣿⣿⣧⣿⡃⠙⠏⢙⣿⣿⡷⠀⣾⣿⡿⠀⢀⣷⡀⠀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⠻⣃⣠⣶⣿⣿⣿⣅⠀⠀⣀⠀⠀⠀⣙⠛⠁⢦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣯⣁⣀⣀⣀⣀⣤⣤⣤⣤⣾⣿⣿⣿⡏⠀⠀⠀⢻⣁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⣤⣼⠿⢃⣤⠘⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⣰⣿⡆⠀⢠⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⠀⠈⣄⢤⣿⣿⣿⡟⠃⣬⡿⢿⣿⣿⣿⣿⣿⣷⡞⡿⢻⣶⣾⢿⠃⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠸⣷⡄⠙⠱⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢀⢼⣿⣄⢹⣿⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⢙⡛⣹⣿⣿⣿⣿⡄⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣠⣦⣶⣶⣾⣿⣿⣿⡿⠉⠛⠁⠉⠉⠋⠙⡏⠀⢿⣿⣇⠀⠀⠈⠙⠛⠛⠛⠿⠿⠿⠟⠛⢉⠼⢟⢕⠵⣃⣿⣿⣿⠃⠀⠀⠀⠀⠛⣿⣿⢃⣈⠁⣿⣿⣿⣿⣿⣿⡏⣿⣆⣀
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⡿⠿⣿⡿⠿⠛⠛⠋⠀⠀⠀⠀⢸⣷⡆⠀⣧⠀⠸⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⡴⢀⡼⣿⣿⠟⠉⠀⠀⠀⠀⠀⢠⣼⠉⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣰⣿⣿⡃⠘⢏⣂⢀⣘⢿⣿⣿⣛⡿⡖⠂⠀⣀⣀⠀⠀⣀⣊⠀⣤⣶⣿⠛⢁⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠿⢿⣿⣿⣷⣿⣿⣿⡏⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠙⣿⡏⠁⠀⢸⣿⢸⣿⠸⣿⣿⢹⣿⢸⣿⣾⣿⢹⣷⢤⣿⣿⣯⣿⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⣼⣿⠀⢸⣿⣾⣿⢸⣿⣿⡇⢀⣄⢸⣿⣺⣏⢉⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠿⠿⠶⠘⠿⠾⠟⠈⠁⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢰⣶⣿
⠘⣿⣿⣿⣿⡿⠿⢿⣿⣿⡏⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣬⣥⣬⣠⡬⣡⡮⣿⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣠⠾⡇⢀⣉⠉
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣷⣶⣳⣾⣶⣾⣳⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡆⢸⣿⡿
⠀⠀⠘⠛⠀⠀⢻⣿⣧⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢃⣼⣿⡿⠀⠁⠀⠈⠉⠃⠀⠀⠁⠈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠓⠀⠀⠀⠀⠀⣀⣀⣀⢠⣀⣀⣀⣤⣄⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦⠀⠀⢠⣤⣼⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣥⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠲⡄⠻⠿⠿⠿⠄⠀⠈⠻⠏⠻⠿⠋⠛⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣦⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⠆⢀⣼⣧⣀⣶⣆⠀⣠⡀⢀⠀⠀⠀⠀⠉⠀⠀⢀⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⣿⠠⣿⠆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢐⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⡀⠀⠀⠀⠰⠀⠘⠟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⠿⠛⠛⠋⠙⠛⠻⢿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠇⠀⢠⣰⣿⣦⠀⠀⠀⢦
⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⣿⣿⣠⣶⠿⠟⠀⠀⠀⠈⢻⣿⣿⣿⠁⠀⢀⠈⠑⠻⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⡄⢻⣿⣿⣿⡇⠀⠀⠙
⠉⢉⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⣿⣶⣿⢛⣄⠀⢸⣿⣿⣿⣧⣀⣻⡀⠀⣀⠀⢐⣿⣿⣿⣦⣤⣾⣦⣤⣤⣿⣿⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣨⣿⣿⣿⠃⠀⠀⠀
⢰⠏⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡇⣾⣿⣿⣏⣾⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣁⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠈⠀⣠⣀⣀⣠⣆⣀⠀⣴⣶⣦⣤⣴⠀⠀⠀⠀⣠⣤⣭⡀⣿⡿⠟⠻⣿⡐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⠀⢠⣾⡿⢻⣿⣿⡟⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣷⣿⣿⣿⣿⣿⣿⣦⣿⣭⠁⠀⠉⠀⠀⡀⠐⣿⣿⣿⣿⣿⣷⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣤⣿⡿⠃⣾⣿⣿⣯⠙⠻⢿⣿⡿⠈⠻⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⣿⣿⣿⣿⠀⠘⠁⢸⣿⣿⡷⠀⣾⣿⠿⠀⠀⣷⡄⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣠⣤⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣛⣦⣴⣾⣿⣿⣿⣄⡀⠀⣀⠀⠀⠀⣈⠁⠀⢢⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣀⡀⠻⣿⣿⣿⣿⣿⣯⣅⣀⣀⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⡿⠁⣾⠀⠀⢹⣍⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢧⣤⣼⠿⢀⣤⠀⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠾⠛⡿⠟⠹⣿⣿⣿⣷⣤⣾⣿⣿⣿⠷⠀⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⢩⡀⢠⣿⣿⣿⠟⠁⣼⡟⣿⣿⣿⣿⣿⣿⣷⡜⣟⢻⣶⣾⠿⠁⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⡧⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣧⣤⡄⢿⣦⠈⠋⢌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⡠⣷⣧⡈⢾⡿⠁⠀⠀⢻⣿⣿⣿⣿⣿⡿⢉⡛⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⣰⣶⣶⣶⣶⣶⣾⣿⣿⣿⠋⠀⠛⠛⠛⢻⠁⠸⣿⣷⡀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠟⠛⠋⡠⠟⡫⡪⢎⣸⣯⣿⡞⠃⠀⠀⠀⠀⠛⣿⣿⢁⣀⢰⣿⣿⣿⣿⣿⣿⡍⣿⣆⣠
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠿⢿⣿⣿⡿⠿⠿⠟⠋⠁⠀⠀⠀⣶⡀⢸⡄⠀⢻⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣬⠒⢤⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢠⣾⠉⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣟⡃⢸⢕⣀⢀⣻⢿⣿⣟⣛⡗⠂⠀⠀⣀⣀⠀⠀⣐⣁⢠⣴⣿⣟⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⠏⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠁⠀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⣷⣾⡟⢹⣷⢀⣿⢿⣿⢼⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⣼⣿⠀⢹⣿⢸⣿⢸⣿⣿⡇⢠⣄⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠽⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣾⣿⣏
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡶⠬⡤⣬⣤⠥⡴⠭⡿⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣞⠻⠀⣠⣈⡉
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣟⣷⣟⣷⣟⣷⣟⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⡿
⠀⠀⠈⠛⠀⠀⢻⣿⣧⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢃⣼⣿⡿⠀⠁⠀⠈⠉⠃⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠓⠀⠀⠀⠀⠀⣀⣀⣀⢠⣀⣀⣀⣤⣄⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦⠀⠀⢠⣤⣼⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣅⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠲⡄⠻⠿⠿⠿⠄⠀⠈⠿⠏⠻⠿⠋⠛⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣦⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡋⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠑⠆⢀⣼⣧⣀⣶⣆⠀⣠⡀⢀⡀⠀⠀⠀⠉⠀⠀⢀⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠚⣿⠀⣿⠆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢀⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⡀⠀⠀⠀⠰⠀⠘⠟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⠿⠛⠛⠋⠛⠛⠻⢿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠇⠀⢠⣰⣿⣦⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⣿⣿⣠⣶⠿⠟⠀⠀⠀⠈⢻⣿⣿⡿⠁⠀⢀⠈⠐⠺⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⡄⢻⣿⣿⣿⡇⠀⠀⠙
⠉⠉⣿⣿⡿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⣿⣶⣿⢛⣄⠀⢸⣿⣿⣿⣧⣀⣻⡀⠀⣀⠀⢐⣿⣿⣷⣦⣤⣾⣦⣤⣤⣿⣿⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣨⣿⣿⣿⠃⠀⠀⠀
⢰⠏⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡇⣾⣿⣿⣏⣾⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣁⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⣠⣀⢀⣠⣆⣀⠀⣴⣶⣶⣤⣴⠀⠀⠀⠀⣠⣤⣭⡀⣿⡿⠟⠻⣿⡘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⠀⢠⣾⡿⢻⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣷⣿⣿⣿⣿⣿⣿⣆⣝⣭⠁⠀⠉⠀⠀⡀⠐⣿⣿⣿⣿⣿⣷⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣤⣿⡿⠃⣾⣿⣿⣷⠉⠙⢿⣿⡟⠈⠻⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⢠⣹⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⣿⣿⣿⣿⠀⠘⠀⢸⣿⣿⡷⠀⣾⡿⠿⠀⠀⣷⡄⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣠⣤⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣛⣧⣴⣾⣿⣿⣿⣆⡀⠀⣀⠀⠀⠀⣈⠁⠀⢢⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣁⡀⠻⣿⣿⣿⣿⣿⣯⣅⣀⣀⣀⣤⣤⣤⣤⣴⣾⣿⣿⣿⡿⠁⣾⠀⠀⢹⣉⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢧⣤⣼⠿⢠⣤⠀⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠾⠛⡻⠟⠹⣿⣿⣿⣷⣤⣾⣿⣿⣿⠇⠀⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⢩⡀⢤⣿⣿⣿⠟⠁⣼⡟⣿⣿⣿⣿⣿⣿⣷⡜⣟⢻⣶⣾⠿⠃⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⡧⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣧⣤⡄⢿⣦⠈⠉⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡠⣷⣧⡈⢿⡿⠁⠀⠀⢻⣿⣿⣿⣿⣿⡿⢉⡛⣽⣿⣿⣿⣿⡄⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣰⣶⣶⣶⣶⣶⣾⣿⣿⣿⠋⠀⠛⠛⠛⢻⠁⠸⣿⣷⡀⠀⠀⠉⠛⠛⠛⠿⠿⠿⠛⠛⠋⡠⠟⡫⠪⢎⣸⣯⣿⡞⠃⠀⠀⠀⠀⠛⣿⣿⢁⣀⠰⣿⣿⣿⣿⣿⣿⡌⣿⣆⣠
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠇⠿⢿⣿⣿⡿⠿⠿⠿⠋⠁⠀⠀⠀⣶⡀⢸⡄⠀⢻⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣬⠂⢠⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢠⣾⠉⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣟⡃⢸⢕⣀⢀⣻⢿⣿⣿⣛⡗⠂⠀⠀⣀⣀⠀⠀⣐⣁⢠⣴⣾⣟⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⠏⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠙⣿⡏⠁⠈⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⣷⣾⡟⢹⣷⢀⣿⢿⣿⢼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⣼⣿⠀⢹⣿⢸⣿⢸⣿⣿⡇⢠⣄⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠽⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣾⣿⣍
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⠬⡤⢤⣤⢥⡴⠭⡵⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣞⠻⠀⣠⣈⡉
⠀⠸⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣟⣷⣟⣷⣟⣷⣟⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠛⠂⠀⢹⣿⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣣⣿⣿⠇⠀⠀⠀⠈⠈⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣟⠛⠃⠀⠀⠀⣀⣀⣀⣀⣀⣢⣤⣄⣤⣦⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⡄⠀⣴⣿⣷⣶⠀⠀⢠⣤⣼⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡤⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⠳⠀⠙⠻⡿⠻⠧⠀⠀⠻⠏⠙⠟⠉⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⣶⡄⣤⡄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠀⢀⣸⣿⣀⣾⣆⡀⣠⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣤⣿⣅⣿⣃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡠⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣇⣤⣀⠀⠀⠘⠀⠘⠛⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀⠉⠁⠈⠉⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⡟⠙⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⣼⡿⠟⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⡟⢀⠀⠀⠀⣀⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠗⠀⢠⣴⣿⣷⡀⠀⠀⣼
⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⢰⣿⣷⣴⠿⠟⣃⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⣠⠀⠉⠻⣿⣿⡄⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⡄⢸⣿⣿⣿⡇⠀⠠⣿
⠀⣠⣼⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀⢠⣿⣿⡟⣱⣄⠀⣸⣿⣿⣿⣦⣤⣻⣂⣀⣄⣀⣨⣿⣿⣿⣶⣶⣿⣷⣶⣶⣿⣿⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠃⠀⠀⣋
⢰⠏⠈⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠿⠇⣿⣿⣿⣧⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣀⣀⣀⡀⠀⠀⣸⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢴
⢈⠀⣠⣀⣀⣰⣧⣀⢀⡿⡿⠿⠿⠿⠀⠀⠀⠀⣠⣤⣤⣄⣿⡋⠀⠹⣧⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣰⣿⡇⣼⣿⣿⡟⢁⣩⣿⣿⣿⣿⣿⡏⠀⠀⢠⢿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣙⣿⣟⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠹⣿⣿⣷⣿⠿⣿⣿⣿⣿⣷⠈⠛⠻⢿⣿⠁⠙⠇⠀⠀⣈⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⡀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⣿⠀⠘⠁⣨⣿⣿⡷⠀⠰⠿⠟⠀⠀⣿⡄⠀⠋⠓
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⣶⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠇⢠⠀⠀⢹⣿⣿⣟⣤⣴⣾⣿⣿⣿⣦⣀⢀⣀⡀⠀⢀⣤⠉⠐⠢⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⡟⠀⣿⠀⠀⢘⡭⣭⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣶⣾⠟⢠⣦⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⡜⠛⢿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣨⡄⢠⣿⣿⣿⠛⠁⣾⣟⣿⣿⣿⣿⣿⣿⣿⣎⣛⣹⣿⣎⠛⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠙⠻⠟⠁⠸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⡄⢿⣦⡀⠉⠐⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⢀⢔⢽⣶⡈⢾⡿⠁⠀⠀⢹⣿⣿⣿⣿⣿⡟⣩⣝⢾⣿⣿⣿⣷⣄⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⣤⣶⣶⣶⣾⣿⣿⣿⣿⠋⠛⠋⠉⠉⠛⢻⠀⠸⣿⣷⡀⠀⠀⠈⠉⠉⠙⠻⠿⠟⠋⠉⢁⠜⢛⠕⠕⣋⣼⣽⣿⠟⠁⠀⠀⠀⠀⠙⣿⣿⣠⣄⢸⣿⣿⣿⣿⣿⣿⡆⣿⣆⣠
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠿⠿⣿⠿⠿⠛⠛⠋⠀⠀⠀⠀⢰⣶⣦⣸⡄⠀⢻⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⠴⠃⢼⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢰⣮⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣿⣛⡋⢻⢃⣀⢀⣻⢿⣿⣟⣛⡟⣁⠀⡀⣀⣀⠀⠀⣈⣀⢰⣿⣿⣋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⡏⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡏⠁⠀⢸⣿⢸⣿⢸⣿⣿⣹⣿⢸⣷⣾⡏⢹⣷⢀⣿⢿⡿⢺⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⣸⣿⠀⢻⣿⢹⣿⢸⡿⣿⡇⢠⣀⢸⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡽⠿⠶⠘⠿⠾⠟⢀⡀⠹⠿⠾⣟⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡴⠠⠿⣿⣯
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠯⡶⠤⠶⠦⡶⠥⡾⠭⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣝⡋⠀⣦⣤⣀
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⠷⢿⠿⠭⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⡏⠀⣿⣿⠇
⠀⠀⠀⠛⠃⠀⠸⣿⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣳⣿⣿⠏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠛⠁⠀⠀⠀⣀⣀⣤⣤⣤⣠⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⡄⠀⣴⣿⣿⣶⡄⠀⠠⣤⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⠄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⡓⠀⠙⠛⠿⠛⠇⠀⠀⠹⠏⠙⠛⠋⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⣤⡀⣤⡄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠀⢀⣰⣿⣀⣾⣧⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣥⣻⣁⣿⣃⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⡠⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣇⣤⣴⡆⠀⠸⠀⠀⠛⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⢸⡇⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⣼⣿⠟⠉⠉⠉⠉⠉⠛⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣾⣿⣿⠿⠀⢠⣴⣿⣷⡀⠀⠀⣿
⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⡀⠀⠀⢰⣿⣿⣤⠿⠟⣃⠀⠀⠀⠀⠻⣿⣿⡟⠀⠀⣠⡄⠈⠙⣿⣿⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣄⠸⣿⣿⣿⡇⠀⠀⡛
⠀⣀⣼⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⢠⣿⣿⡟⣹⣄⠀⢸⣿⣿⣿⣧⣤⣿⣂⣀⣤⣀⣤⣿⣿⣿⣶⣶⣿⣷⣶⣶⣿⣿⣧⢸⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠁
⢰⠏⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇⣿⣿⣿⣧⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣀⣀⣀⡀⠀⠀⣸⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⣂
⢈⠀⣤⣤⣀⣴⣧⣀⢀⡿⡿⠿⠿⠿⠃⠀⠀⠀⢀⣤⣤⣄⣿⡅⠀⠸⣧⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⡇⣼⣿⣿⣿⠉⢉⣿⣿⣿⣿⣿⣿⠀⠀⣬⣎
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⠀⢿⣿⣿⣿⣿⣿⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠙⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⠈⠛⠻⢿⣿⠁⠙⠟⠀⠀⠀⣢
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡁⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢻⣿⣿⣿⡅⠈⠋⣠⣿⣿⡷⠀⠀⠺⠟⠀⠀⢸⡆⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣶⣾⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⠛⠛⠿⢿⣿⣿⣿⣿⠇⢠⠀⠀⢸⣿⣿⣟⣣⣴⣾⣿⣿⣿⣦⣀⢀⣀⡀⠀⠀⣤⠀⠈⠰⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⡆⢻⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⡏⠀⣾⡇⠀⠈⡍⣭⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣶⣾⠟⢁⣦⡀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣧⢸⡏⠙⢿⣿⢿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⠂⠀⣸⡅⢠⣾⣿⣿⠛⠁⣾⣟⣿⣿⣿⣿⣿⣿⣿⡆⣛⣹⣿⣯⠛⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠉⠻⠟⠁⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡄⢿⣦⡀⠁⠐⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⢀⢔⢾⣷⡀⢻⣿⠁⠀⠀⠹⣿⣿⣿⠿⠿⠏⣨⣍⢾⣿⣿⣿⣯⣄⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⣤⣶⣶⣶⣿⣿⣿⣿⠟⠈⠛⠉⠉⠁⠉⢻⠀⠸⣿⣧⡀⠀⠀⠀⠉⠉⠁⠛⠻⠛⠉⠉⢀⠜⠋⠕⠕⣡⣼⣿⣿⠟⠉⠀⠀⠀⠀⠉⢿⣿⣠⣤⣘⣿⣿⣿⣿⣿⣿⡆⢻⣧⣠
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠇⠟⠻⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⢰⣿⣦⣸⡄⠀⢻⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠞⠁⢼⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢰⣷⠀⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣴⣿⣛⡋⢻⢑⣀⢀⣻⢿⣿⣟⣛⡆⣀⠀⠀⣀⣀⠀⠀⣈⣀⢰⡿⣿⣋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⡇⢻⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡏⠁⠀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⣦⣾⡏⢹⣷⢀⣿⢿⡿⢺⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢷⣾⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⣸⣿⠀⢻⣿⢸⣿⢸⠿⣿⡇⢀⣀⢸⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡽⠿⠶⠘⠿⠾⠟⢀⡀⠹⠿⠾⣟⠿⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡶⠐⠿⢿⣦
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠯⡶⠤⡶⠦⡶⠤⡾⠼⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣍⡑⠀⣦⣤⣀
⠀⠸⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⢷⣿⠿⠭⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠐⣿⣿⡇
⠀⠀⠀⠻⠃⠀⠸⣿⣷⣤⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣟⠛⠁⠀⠀⠀⣀⣀⣤⣤⣤⣐⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⡄⠀⣰⣿⣿⣶⡄⠀⠀⣤⣼⣿⣿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⡤⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠳⡀⠙⠻⡿⠛⠇⠀⠀⠹⠟⠘⠛⠋⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣶⡄⣀⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠅⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠀⢀⣰⣿⣄⣼⣧⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣟⣁⢿⡃⣿⠇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡡⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣀⣰⣦⠀⠘⠀⠀⠛⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠈⠁⠈⠉⠀⣾⡁⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠿⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⣸⣿⠟⠋⠉⠉⠉⠉⠛⠻⣿⣿⣿⣿⡟⠁⠀⠀⠀⣀⣈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣸⣿⣿⣿⠄⢀⣴⣿⣷⣄⠀⣼⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⢠⣿⣿⣤⡾⠟⢃⡀⠀⠀⠀⠻⣿⣿⡟⠀⠀⢠⡄⠉⠙⣿⣿⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣥⣄⠘⣿⣿⣿⣿⠀⣿⣿
⠀⢀⣼⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⢀⣿⣿⡟⣹⣄⠀⢸⣿⣿⣿⣧⣤⣻⣆⣀⣤⣀⣀⣿⣿⣿⣶⣶⣿⣷⣶⣶⣿⣿⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠋⣿⣿
⢠⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⣾⣿⣿⣧⣿⡿⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣀⣀⣀⡀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣽
⢈⠀⣤⣤⣀⣴⣧⣀⠀⡰⣷⡶⢶⣾⠆⠀⠀⠀⢀⣤⣤⣄⣹⡏⠉⠹⣧⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣾⡟⣰⣿⣿⣿⠛⠙⣿⣿⣿⣿⣿⣿⠀⠘⠁⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⡄⣀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡀⠛⠿⠿⣿⠃⠙⡟⠀⠀⢈⣽
⢈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡅⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣿⣿⡏⠈⠋⢀⣽⣿⡷⠀⠀⠐⠿⠁⠀⣷⢀⣀⠀⠉
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣤⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠇⢰⡄⠀⠘⣿⣿⣿⣣⣤⣾⣿⣿⣿⣦⣄⠀⣀⡀⠀⠀⣠⡀⠙⢳⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⡆⢹⢿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⡟⠀⣼⡇⠀⠈⣋⣡⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣶⣶⠟⠃⣤⡀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣇⣀⣾⣷⠘⡆⠙⢿⢿⢿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⣨⡑⢀⣼⣿⣿⠟⠃⣴⣿⣻⣿⣿⣿⣿⣿⣿⡆⣛⣛⣿⣿⠛⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠻⠿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⢿⣦⡀⠀⠄⠶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⢀⢔⢽⣷⡀⢻⣿⡏⠀⠀⠙⣿⣿⣿⡿⣿⡿⣨⣝⣻⣿⣿⣿⣿⣦⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⣠⣴⣶⣶⣿⣿⣿⣿⡿⠙⠛⠉⠋⠉⠉⢹⠀⠸⣿⣧⡀⠀⠀⠀⠉⠁⠈⠛⠿⠟⠛⠉⠁⠐⢋⠕⠕⣋⣼⣽⣿⡞⠉⠀⠀⠀⠀⠉⢿⣿⣣⣄⡀⣿⣿⣿⣿⣿⢿⣇⢹⣧⣀
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠿⠿⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⢠⣿⣦⣸⡄⠀⢻⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⠴⠃⢼⣿⣻⠟⠉⠀⠀⠀⠀⠀⠀⢠⣾⠀⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣿⣟⡋⢻⢓⣀⢀⣻⢿⣿⣿⣛⡀⠀⠀⠀⣀⣀⠀⠀⣈⣀⢰⣿⣿⣋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⡇⢹⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡏⠁⠀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⣦⣾⡏⢹⣷⢀⣿⢿⡷⢺⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣧⣾⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⣸⣿⠀⢻⣿⢸⣿⢸⠿⣿⡇⢠⣄⢸⣿⣻⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡽⠿⠶⠘⠿⠾⠟⢀⡀⠹⠿⠾⢟⠿⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣾⠐⠿⢿⣯
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠯⡶⠤⠶⠤⡶⠤⡾⠭⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣍⡑⠀⣦⣤⣀
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⢷⢿⠿⠭⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠐⣿⣿⡕
⠀⠀⠀⠻⠇⠀⠸⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⠟⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⡀⠀⢠⣾⣷⣶⡄⠀⠀⣤⣠⣿⣿⣿⣿⣧⣾⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣂⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠻⡀⠘⠻⣿⠿⠧⠀⠀⠙⡿⠙⠻⠟⠙⠙⣿⡧⠀⠀⠀⠀⠀⠀⣿
⣤⣄⣠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠄⠀⣀⣿⣆⣠⣦⠀⢀⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⢤⡀⠀⢠⣿
⣿⣿⣿⣿⣿⣿⣿⠧⣾⡆⣾⡆⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢐⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⣇⣠⡀⠀⠀⠀⠂⠀⠘⠁⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣽⣤⣿⣠⣿⠁⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠸⡏⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠀⠁⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄⠀⣤⣾⣿⣄⢀⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣀⣴⡶⠀⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⢀⠀⠒⠺⣿⣿⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⣁⠘⣿⣿⣿⣿⣸⣿⣿
⠛⠛⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣼⣶⣾⢻⣄⠀⢸⣿⣿⣿⣆⣀⣿⠀⠀⣀⠀⢀⣿⣿⣷⣦⣤⣿⣦⣤⣤⣿⣿⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⢿⣿⣿
⠀⡶⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⣿⡇⣾⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢁⣀⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢸⣿⣿
⠐⠀⣤⣄⡀⣠⣇⢀⠀⢠⣤⣤⣀⣠⡄⠀⠀⠀⠀⣀⣬⣅⣿⣿⠿⠿⣯⠁⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⠀⣰⣿⡏⣸⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⠀⢸⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣆⠘⣉⠋⠉⠙⠁⠀⠀⠀⠀⠿⣿⣿⣿⣷⡀⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⢻⣿⣿⣾⣿⠿⣷⣿⣿⣿⡀⠰⢾⡿⣿⡏⠙⢿⠀⠐⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⢠⣈⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⣿⣏⠀⠙⠀⣹⣿⣧⠀⠀⠰⠿⠇⠀⣴⣤⡀⠀⠙
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⣀⢄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⡆⠀⠀⣿⣿⣿⢛⣤⣴⣾⣿⣿⣧⣀⠀⢀⡀⠀⠀⣈⡛⠀⢠⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡃⡀⠻⣿⣿⣿⣿⣿⣯⣁⣀⣀⣀⣀⣤⣤⣤⣤⣾⣿⣿⣿⡿⠁⢠⣿⠀⠀⢛⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣤⣤⠿⠇⣤⡀⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣴⣿⣿⣿⣿⠀⡍⠻⢿⣿⢿⣿⣿⣿⣿⣿⣋⣝⣿⣿⣿⣿⣿⣿⣿⡇⠀⢩⡛⡀⣠⣾⣿⡿⠟⢠⣿⢿⣿⣿⣿⣟⣿⣿⣦⢻⠛⣶⣶⠻⠇⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠻⡿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣿⣄⠀⠀⠈⢩⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠅⡠⣹⣧⡈⢿⣾⡟⠁⠀⠘⣿⣿⣿⣿⣿⣿⢉⣛⢻⣿⣿⣿⣿⣤⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⢀⣤⣴⣦⣶⣶⣿⣿⣿⣿⡟⠋⠋⠋⠛⢹⠁⠸⣿⣦⠀⠀⠀⠈⠛⠋⠙⠿⠿⠿⠟⠛⠋⡀⠝⡫⡪⢊⣸⣿⣿⡾⠛⠃⠀⠀⠀⠙⢿⣿⣇⣀⡀⣿⣿⣷⣿⣿⣿⣇⢹⣧⠀
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠇⠘⠻⣿⣿⣿⡿⠿⠿⠟⠋⠀⠀⠀⣴⣦⢸⡀⠀⢿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣼⠂⢰⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣾⠉⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣿⡟⢻⢃⣀⢈⣿⢿⣿⣟⣋⡀⠀⠀⠀⣀⣀⠀⠀⣘⣁⢠⡶⣾⣟⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠛⣿⡏⠁⠈⢸⣿⢸⣿⢸⣿⣿⢹⣿⢠⣄⣾⡏⢹⣷⢀⣿⢿⣿⢼⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣷⣼⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⢸⣿⠈⢿⣿⢺⣿⢸⣿⣿⡇⢠⣄⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡹⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⢿⣿⣭
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣗⣴⣅⣤⣅⣤⣅⣴⣝⠶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣟⠻⠀⣦⣄⡈
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣷⣶⣷⣶⣗⣶⣓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⣿⣿⠤
⠀⠀⠀⠿⠇⠀⠸⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⠟⠀⠀⠀⠈⠙⠃⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠛⠃⠀⠀⠀⠀⣀⣀⣀⣀⣠⣄⣀⣠⣤⣤⣀⣀⣠⣤⣀⠀⠀⠀⠀⡀⠀⢠⣾⣷⣶⡄⠀⠀⣤⣠⣿⣿⣿⣿⣯⣾⡄⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⡂⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠻⡀⠘⠿⣿⠟⠧⠀⠀⠹⡿⠙⠿⠛⠙⠙⣿⣧⠀⠀⠀⠀⠀⢸⣿
⣤⣀⣤⣀⣄⣀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠑⠅⠀⣀⣿⣆⣰⣦⠀⢀⣄⠀⢀⠀⠀⠀⠈⠁⠀⠀⣠⡀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⢧⣷⣄⣾⡄⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢒⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣀⠀⠀⠀⠀⠆⠀⠛⠁⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣽⣤⣿⣥⣿⠁⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠸⡏⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠀⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⣸⣿⠿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡄⢀⣤⣾⣿⣄⢀⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣀⣴⡶⠄⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⢀⠀⠒⠺⣿⣿⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⣀⠘⣿⣿⣿⣿⣽⣿⣿
⠛⠛⣿⣿⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣼⣶⣾⢻⣄⠀⢸⣿⣿⣿⣆⣀⡧⠀⠀⣀⠀⣨⣿⣿⣷⣤⣤⣿⣦⣤⣤⣿⣿⣷⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡟⢹⣿⣿
⠀⡶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⣸⣿⣿⡇⣾⣿⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠃⢀⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿
⠐⠁⣤⣀⠀⣠⣆⠀⠀⢠⣤⣄⣀⣠⡄⠀⠀⠀⠀⣀⣭⣁⣿⣿⣿⣿⣯⠉⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⠀⣰⣿⡟⣹⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⠀⢸⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⡆⠘⣙⠛⠉⠛⠁⠀⠀⠀⠀⠿⣿⣿⣿⣯⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣾⣿⠟⠁⣿⣿⣿⡀⠲⢿⣿⣿⡏⠙⢿⠀⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⢀⣄⣹⣿⣿⣇⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⣿⡇⠀⠈⠀⣹⣿⣷⠀⠀⠰⣿⠇⢀⣴⣦⡀⠀⡭
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⣀⢐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡄⠀⠀⣿⣿⣿⢛⣤⣴⣾⣿⣿⣧⣀⠀⢀⡀⠀⠀⣙⡛⠒⠠⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢻⣿⣿⣿⣿⣿⣏⣉⣀⣀⣀⣀⣠⣤⣤⣤⣾⣿⣿⣿⡿⠁⢠⣿⠀⠀⢻⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣤⣤⠿⠇⣤⡀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣿⣿⣿⡿⠀⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⡻⡀⣠⣾⣿⡿⠟⢠⣿⢿⣿⣿⣿⣟⣿⣿⣦⢻⡛⣶⣶⡻⠏⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠻⣿⠟⠉⣿⣿⣿⣿⣿⣿⢿⣿⣿⣤⣄⣷⣄⠈⠉⠉⢻⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⡠⣪⣧⡈⢿⣿⡟⠁⠀⠘⣿⣿⣿⣿⣿⣿⢉⣛⢻⣿⣿⣿⣿⣠⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⢠⣤⣤⣤⣶⣶⣿⣿⣿⣿⡟⠉⠁⠉⠋⢹⠁⢸⣿⣧⠀⠀⠀⠙⠛⠛⠻⠿⣿⠿⠟⠛⠋⡠⠟⡫⣪⠞⣹⣿⣿⡼⠟⠃⠀⠀⠀⠙⢿⣿⢇⣀⡀⣿⣿⣷⣿⣿⣿⣧⢹⣷⡀
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⢸⠿⣿⣿⣿⣿⠿⠿⠟⠋⠀⠀⠀⢰⣤⢸⡀⠀⢿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣨⠆⣰⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣾⠉⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣎⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣾⡿⢿⢃⣀⢈⣿⢿⣿⣟⣓⡀⠀⠀⠀⣀⣀⠀⠀⣐⣃⢀⡴⣾⣟⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠛⣿⡏⠁⠈⢸⣿⢸⣿⢸⣿⣿⢹⣿⢰⣠⣾⡟⢹⣷⢀⣿⢿⣿⢽⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⢸⣿⠈⢻⣿⣹⣿⢸⣿⣿⡇⢠⣄⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡻⠿⠶⠘⠿⠾⠟⠈⠁⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⣾⣿⣝
⠘⣿⣿⣿⣿⠿⠿⢿⡿⣿⡏⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣤⣁⣤⣁⣠⣁⣴⣳⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣚⠫⠀⣤⣀⠉
⠀⠸⣿⣿⣿⣿⠿⢷⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣷⣶⣶⣶⣷⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⣿⣿⣏
⠀⠀⠀⠻⠇⠀⠸⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⠗⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠂⠀⠀⠀⢀⣀⣀⣀⣀⣠⣄⣀⣠⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⡀⠀⢠⣾⣷⣶⡄⠀⠀⣤⣠⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⡂⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠻⠀⠘⠿⢿⠟⠧⠀⠀⠸⠿⠉⠻⠛⠉⠙⣿⡷⠀⠀⠀⠀⠀⢸⣿
⣶⣦⣶⣤⣤⣤⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠑⠄⠀⣀⣾⣆⣰⣦⠀⢀⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡄⠀⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠳⣿⠦⣿⠆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⣀⠀⠀⠀⠀⠆⠀⠚⠁⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡏⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠁⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⣼⣿⠿⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠄⢀⣤⣾⣿⣦⣸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣠⣴⠦⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠐⠒⢿⣿⣿⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⣄⠈⣿⣿⣿⣿⣿⣿⣿
⠉⠙⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣼⣶⣾⢳⡄⠀⣼⣿⣿⣿⣀⣐⠇⠀⢀⡀⠀⣸⣿⣿⣧⣤⣤⣷⣤⣤⣴⣿⣿⣧⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⡿⣿⣿⣿
⠀⡶⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⣸⣿⣿⡇⣾⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡃⢀⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢹⣿⣿
⠀⠁⣤⣀⠀⣠⣆⠀⠀⣠⣤⣤⣤⣤⡄⠀⠀⠀⠀⣀⣬⣁⣿⣿⣿⣿⣯⠁⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⠀⣴⣿⠟⣹⣿⣿⠛⠉⢻⣿⣿⣿⣿⣿⠀⢸⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣆⡉⣉⠉⠉⠉⠁⠀⠀⠀⠀⠻⢿⣿⣿⣯⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣾⣿⠟⠰⣿⣿⣿⡀⠛⠿⣿⣿⡇⠉⢿⠀⠘⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡂⠀⠀⠀⠀⠀⠀⠀⢀⣄⣹⣿⣿⣇⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⣿⡇⠀⠉⠀⣹⣿⣧⠀⠀⠰⡿⠃⠀⣴⣦⢀⠀⠘
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣤⣤⣔⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣆⠀⠀⣿⣿⣿⢛⣠⣴⣾⣿⣿⣧⣀⡀⢀⡀⠀⠀⣈⡉⠀⠰⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣍⣁⣀⣀⣀⣀⣠⣤⣤⣴⣾⣿⣿⣿⡿⠀⢠⣿⠀⠀⢻⡛⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣤⣤⠿⠇⣤⡀⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⡀⠀⡌⠻⣿⣿⣿⣿⣿⣿⣿⣟⣉⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢉⡻⡀⣠⣾⣿⡿⠛⢠⣿⣿⣿⣿⣿⣟⣿⣿⣦⢛⡛⣶⣶⠻⠏⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠻⡿⠏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣷⣄⠈⠀⠉⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡇⠠⣢⣧⡈⢿⣾⡟⠁⠀⠘⣿⣿⣿⣿⣿⣿⢉⣙⢫⣿⣿⣿⣿⣲⠀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⢀⣤⣴⣶⣶⣶⣿⣿⣿⡟⠋⠀⠁⠀⠉⢹⠁⠸⣿⣆⠀⠀⠀⠙⠛⠋⠙⠿⡿⠿⠟⠛⠋⡐⠛⡫⡨⠞⣹⣿⣿⡼⠟⠃⠀⠀⠀⠘⢿⣿⣇⣀⡀⣿⣿⣿⣿⣿⢿⣧⢸⣷⡀
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠸⠻⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⣰⣦⢸⡀⠀⢿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣨⠆⣠⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣶⠍⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣏⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣿⡿⢿⢃⣀⢈⣿⢿⣿⣟⣁⡀⠀⠀⠀⣀⣀⠀⠀⣐⣃⢀⡴⣾⣟⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⡧⠛⣿⡏⠁⠈⢸⣿⢸⣿⢸⣿⣿⢹⣿⢠⣀⣾⡟⢹⣷⢀⣿⢿⣯⢽⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣴⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⢸⣿⠈⢻⣿⢸⣿⢸⣿⣿⡇⢠⣄⢸⣿⣸⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡻⠿⠶⠘⠿⠾⠟⠈⠁⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠾⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⣾⣾⣍
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣖⣤⣁⣤⣁⣈⣁⣴⣓⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣚⠫⠀⣤⣀⠉
⠀⠚⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣷⣦⣶⣶⣶⣶⣗⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⠀⢿⣿⠍
⠀⠀⠀⠻⠇⠀⠸⣿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣿⣿⠅⠀⠀⠀⠁⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣟⣟⠉⠁⠀⠀⢀⣀⣀⣤⣤⣠⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⡄⠀⢠⣾⣿⣷⡆⠀⠀⣤⣤⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀
⣀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠙⡀⠈⠛⠛⠛⠃⠀⠀⠈⠛⠈⠙⠋⠉⠉⢿⡷⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣄⣤⡀⣤⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠆⢀⣀⣿⣆⣰⣷⡀⢀⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣭⣻⣉⣿⠇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⢿⣿⠟⡇⣤⣤⣦⠀⠀⠁⠀⠙⠁⠀⠀⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⣶⣰⣿⣿⣿⠀⠀⠀⢀⡀⠀⣶⡆⣿
⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠇⠀⠀⠀⢀⣿⡿⠟⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⡉⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠀⢀⣤⣿⣿⡆⠿⡇⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢸⣿⣇⣤⠴⠏⠂⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⡀⠉⠙⢻⣿⣿⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⡇⠀⢡⣿
⠀⠀⣰⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⢀⣼⣷⡿⢹⡄⠀⣿⣿⣿⣷⣠⣘⣀⣀⣀⠀⣀⣾⣿⣿⣶⣤⣾⣷⣴⣶⣶⣿⣿⣧⢁⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡧⣾⣹⣿
⠀⡞⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠇⣾⣿⣿⡇⣾⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣀⣀⣀⠀⠀⢀⣿⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⣀⣤⣄⣀⣰⣇⣀⠀⢸⣿⡷⠶⣿⠀⠀⠀⠀⠀⣠⣤⣄⣿⡿⠛⠻⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠀⣾⣿⢀⣿⣿⣿⢧⣴⣿⣿⣿⣿⣿⣿⠈⠉⠘⡿
⣼⣿⣿⣿⣿⣿⣿⣿⣦⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⢹⣿⣿⣿⣿⠻⣿⡿⣿⣿⣆⠉⠉⠛⣿⡇⠈⠛⠀⠁⠐⠧
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣸⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠈⣿⣿⣿⣇⠀⠉⢀⣼⣿⣿⠇⠀⠘⠿⠁⠀⠀⠀⣀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣴⣶⣶⣖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⣦⠀⠀⢻⣿⡿⣫⣤⣾⣿⣿⣿⣷⣤⡀⢠⣄⠀⠀⣠⡄⠀⠈⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⡿⢻⢿⣿⣿⣿⣿⣤⣀⣀⣠⣠⣤⣤⣤⣤⣶⣿⣿⣿⣿⡟⠀⣠⣿⠀⠀⢸⡋⣱⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣰⣶⡛⠃⣴⡄⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⠀⡜⠻⢿⣿⣿⣿⣿⣿⣿⣋⣉⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⡛⠀⣠⣾⣿⡟⠋⢰⣿⣻⣿⣿⣿⣿⣿⣿⣷⢘⣋⣿⣿⡝⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠙⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⢷⣄⠀⠀⠈⢼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⡇⡠⡢⡧⡄⢹⣾⡏⠀⠀⠈⣿⣿⣿⣿⠿⢿⢃⣭⡁⣿⣿⣿⣿⢤⡄⠀
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡇⣠⣤⣶⣶⣾⣿⣿⣿⠏⠉⠉⠉⠀⠀⠀⢸⠁⠸⣿⣧⠀⠀⠀⠙⠛⠈⠻⠿⠿⠟⠛⠛⠁⠴⠛⡫⡪⢎⣸⣿⣿⡾⠛⠁⠀⠀⠀⠈⢹⣿⣏⣤⡄⢺⣿⣿⣿⣿⡿⣷⡈⣿⣄
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠇⠛⠻⡿⠿⠟⠛⠋⠁⠀⠀⠀⠀⢰⣿⣧⢸⡀⠀⢿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣤⠆⢠⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿⣿⣿⣟⢿⣷⣿⣧⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣾⣿⡓⢸⢃⣀⢈⣻⢿⣿⣟⣁⡀⠀⠀⠀⣀⣀⠀⠀⣘⣁⢠⡶⣾⣟⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠻⠿⢿⣿⣻⣿⣿⣿⣿⣿⠈⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠛⣿⡏⠁⠈⢸⣿⢸⣿⢸⣿⣿⢹⣿⢠⣤⣾⡟⢹⣷⢀⣿⢿⣿⢼⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⢿⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⢸⣿⠈⢻⣿⢸⣿⢸⡿⣿⡇⢠⣄⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡹⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⢾⣷⣍
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣗⣴⢄⣤⣅⣤⢥⡴⢽⠴⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣜⠻⠀⣠⣄⡉
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣟⣶⣟⣶⣗⣶⣗⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢿⣿⡇
⠀⠀⠀⠻⠃⠀⠸⣿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣿⣿⠅⠀⠀⠀⠁⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣟⣛⠋⠁⠀⠀⢀⣀⣠⣤⣤⣠⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⡄⠀⢠⣾⣿⣷⡆⠀⠀⣤⣤⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀
⣀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠹⡀⠈⠛⠟⠋⠃⠀⠀⠈⠛⠈⠙⠋⠉⠈⢿⡷⠀⠀⠀⠀⠀⡄⢰
⣿⣿⣿⣿⣿⣿⣿⣄⣤⡀⣤⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠆⢀⣀⣿⣆⣰⣧⡀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣭⣻⣉⣿⠇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠿⣿⠟⡇⣤⣤⣦⠀⠀⠁⠀⠈⠀⢀⠀⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣶⣰⣿⣿⣿⠀⠀⠀⢀⡀⠀⣰⡆⣿
⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠅⠀⠀⠀⠀⣾⡿⠟⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⡉⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠀⢀⣤⣿⣿⡆⢿⡅⣿
⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢸⣿⣇⣤⠤⠎⠂⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⡀⠉⠙⢻⣿⣿⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⡇⠈⢡⣿
⠀⠀⣰⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⢀⣼⣷⡿⢱⡄⠀⣿⣿⣿⣷⣠⣘⣀⣀⣀⠀⣀⣾⣿⣿⣶⣤⣾⣷⣴⣶⣾⣿⣿⣧⢁⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣼⢸⣿
⠀⡞⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠃⣾⣿⣿⡇⣾⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣀⣀⣀⠀⠀⢀⣿⡟⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿
⠀⣀⣤⣄⣀⣰⣆⣀⠀⢸⣿⣿⢶⣿⠀⠀⠀⠀⠀⣠⣤⣄⣿⡿⠛⠻⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠀⣾⣿⢀⣿⣿⣿⢣⣴⣿⣿⣿⣿⣿⣿⠈⠛⠸⠿
⣼⣿⣿⣿⣿⢿⣿⣿⣦⣼⣶⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢹⣿⣿⣿⣿⠻⣿⡿⣿⣿⣆⠈⠉⠛⣿⡇⠈⠛⠀⠁⠸⣫
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣸⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠈⣿⣿⣿⣇⠀⠉⢀⣼⣿⣿⠇⠀⠘⠿⠁⠀⠀⠀⡀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣴⣶⣶⣖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⣦⠀⠀⢻⣿⡿⣋⣤⣾⣿⣿⣿⣷⣤⡀⢠⣄⠀⠀⣠⡄⠀⠘⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⡿⢻⢿⣿⣿⣿⣿⣤⣀⣀⣠⣠⣤⣤⣤⣤⣶⣿⣿⣿⣿⡟⠀⣠⣿⠀⠀⠸⡋⣱⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣰⣶⡛⠃⣴⣄⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣿⠀⡌⠻⢿⠿⣿⣿⣿⣿⣿⣋⣩⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⡛⠀⣠⣾⣿⡟⠋⢰⣿⣻⣿⣿⣿⣿⣿⣿⣷⢙⣋⣿⣿⡝⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠟⠃⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣦⢷⣄⠀⠀⠉⢽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⡇⡠⣢⣧⡄⢻⣾⡏⠀⠀⠈⢿⣿⣿⣿⠿⢿⢃⣭⡁⣿⣿⣿⣿⢤⡀⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⣠⣤⣶⣶⣾⣿⣿⣿⠏⠉⠉⠁⠀⠀⠀⢸⠁⠸⣿⣧⠀⠀⠀⠋⠛⠙⠛⠿⠿⠟⠛⠋⠁⠴⠛⡫⡪⢊⣸⣿⣿⡾⠛⠁⠀⠀⠀⠈⢹⣿⣏⣤⡄⢻⣿⣿⣿⣿⡿⣷⡈⣿⣄
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣴⣿⣿⣿⠇⠛⠻⡿⠿⠟⠛⠋⠁⠀⠀⠀⠀⢰⣿⣧⢸⡀⠀⢿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣤⠂⢠⣿⣿⡿⠋⠁⠀⠀⠀⠠⠀⠀⣾⡇⢸⣿⣿⣿⣿⣿⣟⢿⣷⣿⣧⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣾⣿⡛⢰⢃⣀⢀⣻⢿⣿⣟⣁⡀⠀⠀⠀⣀⣀⠀⠀⣘⣁⢠⡶⣾⣟⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠻⠿⢿⣿⣻⣿⣿⣿⣿⣿⠈⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠛⣿⡏⠁⠈⢸⣿⢸⣿⢸⣿⣿⢹⣿⢰⣄⣾⡟⢹⣷⢀⣿⢿⣿⢼⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⢿⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⢸⣿⠈⢻⣿⢺⣿⢸⡿⣿⡇⢠⣄⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡹⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢾⣷⣍
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣗⣴⢄⣤⣅⣤⢥⡴⢽⠴⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣞⠻⠄⣠⣄⡉
⠀⠚⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣟⣶⣟⣶⣷⣶⣟⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠀⢿⣿⠁
⠀⠀⠀⠘⠋⠀⠈⢿⣿⣦⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡭⠉⠀⠀⠀⣠⣤⣤⣤⣤⣤⣴⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⣰⠀⢰⣿⣿⣿⡇⠀⠀⢲⣶⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠂⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢌⠣⠀⠉⢉⠉⠁⠀⠀⠀⠉⠀⠈⠁⠀⠀⠹⠿⠀⠀⠀⠀⠀⠀⣸
⣿⣷⣿⣿⣿⣾⣷⡀⣀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⢀⣤⣿⣧⣴⣿⣄⣠⣶⣄⣄⠀⠀⠀⠀⠀⡀⠀⢰⡆⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣟⣙⢿⠚⣿⠇⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣇⠔⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠸⡿⠿⣿⠿⢿⡿⠿⠿⠋⠛⣤⡄⣸⣶⠀⠁⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣿⣿⣿⡿⠀⠀⢀⣀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡿⠛⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣈⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣸⣿⣿⣉⠁⠀⣶⣿⣿⣇⠠⠐⢿
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣀⠀⠀⢸⣿⣇⡄⠿⢛⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⡄⠀⠉⠻⣿⣿⣇⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⣹⣿⣿⡇⠀⠀⢸
⠀⢀⣽⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⣰⣾⣿⣿⢩⣦⠀⣾⣿⣿⣿⣤⣌⣀⣀⣠⣀⣠⣼⣿⣿⣷⣶⣶⣿⣶⣶⣾⣿⣿⣿⢸⣶⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠀⢸
⡀⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠂⣿⣿⣿⣿⣿⡿⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣀⣀⣀⡀⠀⠀⣿⡿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⠇⠘⠀⢸
⢛⣄⣶⣤⣄⣴⣆⣀⠀⢰⣿⣶⣶⣾⠀⠀⠀⠀⠀⣴⣶⣦⣿⠋⠉⠉⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡄⣸⣿⣇⣾⣿⣿⡳⣿⣿⣿⢿⣿⢿⣿⡇⠀⠀⠘
⣼⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⠻⣿⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⣿⣿⣿⣿⡟⢿⡿⠿⣿⣧⡀⠀⢀⣾⡏⠀⢻⡇⠀⠀⠀
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⠀⠀⣀⣴⣿⡿⠃⠀⠈⠛⠁⠀⠀⠫⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣶⣶⣨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⠿⠟⠻⠿⠿⣿⣿⣿⣿⣿⡇⠀⣶⠀⠀⢸⣿⣿⣭⣷⣾⣿⣿⣿⣿⣦⣄⣠⣤⠀⠀⢰⣦⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣻⣿⣿⣿⠄⠙⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⡿⠀⢠⣿⠀⠀⠈⣉⣠⣿⠟⢿⣿⣿⣿⣿⣿⣿⣛⣛⢸⣿⣏⣉⣸⣦⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠀⠀⡍⠙⠿⠻⢿⣿⣿⣿⣿⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣩⠂⣠⣿⣿⠟⠉⢰⣿⣽⣿⣿⣿⣿⡼⣿⣿⢠⣭⣸⣿⡏⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⠁⠀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡶⢻⣆⠀⠀⠀⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣱⣿⡇⡠⡱⣷⣆⠸⣿⡏⠀⠀⠀⢻⣿⣿⣿⠻⠿⢣⣴⣄⣻⣿⣿⣿⠲⣦⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⢠⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠁⢸⠃⠈⣿⣷⡀⠀⠀⠉⠉⠀⠙⠛⠛⠛⠉⠉⠀⠰⢉⠅⠪⢊⣬⣿⣿⡷⠉⠁⠀⠀⠀⠀⠘⢿⢯⣴⣤⣸⣿⣿⣿⣿⣟⣿⣄⣿⣧
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠈⠙⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⣿⣷⢸⡄⠀⢻⣿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠵⠋⠠⣻⣿⡿⠋⠀⠀⠀⠀⠐⠀⠀⣾⡇⢘⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣴⣟⡋⠸⢏⣀⢀⣹⢿⣿⣟⣁⡀⠀⠀⠀⣀⣀⠀⠀⣈⣁⢠⣾⣿⣏⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⠁⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠋⣿⡏⠁⠀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⣦⣾⡏⢹⣷⢀⣿⢿⣿⢾⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⣸⣿⠀⢸⣿⢸⣿⢸⠿⣿⡇⢀⣀⢸⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠽⠿⠶⠘⠿⠾⡟⠀⡀⠹⠿⠾⢏⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠆⠼⢿⣷
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⠯⡷⠦⡴⠦⠶⠤⠾⠯⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣬⡙⠀⣴⣤⡀
⠀⠚⣿⣿⣿⣿⠾⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣷⣯⡷⢿⠿⠯⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢻⣿⡃
⠀⠀⠀⠘⠋⠀⠀⢿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⣤⣤⣦⣴⣧⢠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⠌⠀⠀⠀⣠⣤⣴⣶⣶⣦⣶⣶⣶⣾⣿⣿⣶⣶⣾⣿⣶⣄⠀⠀⠀⢰⠀⢰⣿⣿⣿⡇⠀⠀⠰⣶⡿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠂⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢌⡡⠀⠉⢉⡉⠁⣀⠀⠀⠉⠀⠈⠁⠀⠀⠹⠿⠀⠀⠀⠀⠀⠀⣼
⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠂⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⢀⣤⣿⣷⣴⣿⣦⣤⣾⣤⣤⠀⠀⠀⠀⠀⡀⠀⢸⡃⠀⠀⣿
⣿⣿⣿⣿⣿⣿⡿⠲⣿⢤⣿⡄⣿⡆⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⣇⠔⠁⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⠿⡿⠿⠿⠿⠟⢿⠛⠙⣤⣤⣿⡆⠀⠃⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣿⣴⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣿⣿⣿⡇⠀⠀⢀⣄⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⠃⠀⢀⠀⢀⣀⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣅⠀⠀⣶⣿⣿⡇⠀⠀⢿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⣄⠀⠀⢸⣿⣇⣤⠟⢋⠁⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⡄⠀⠈⠙⣿⣿⣇⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⡇⠀⠀⣿
⠉⢙⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣰⣿⣿⣿⢡⣧⠀⣾⣿⣿⣿⣦⣬⣤⣤⣤⣄⣠⣼⣿⣿⣿⣶⣾⣿⣶⣿⣾⣿⣿⣿⠸⣾⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿
⠀⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠄⣿⣿⣿⣿⣾⡿⢂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣠⣤⣄⣀⠀⠀⣸⣿⢿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿
⢀⣄⣶⣤⣤⣼⣧⣠⡀⢠⣦⣤⣤⣴⠀⠀⠀⠀⠀⣴⣾⣶⣿⠛⠛⠉⢿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡆⣰⣿⡇⣼⣿⣿⡿⣿⣿⡿⢻⣿⢿⣿⡇⠀⠀⠹
⣾⣿⣿⣿⣿⣿⣿⣿⣷⡈⢉⡉⠉⠉⠀⠀⠀⠀⠀⠛⠛⢿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⠻⢿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣿⣿⣿⣿⠟⢿⡿⠿⣿⣷⡄⠀⢀⣿⡇⠀⠻⡇⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡇⠀⠀⠀⠀⠀⠀⢀⢠⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⢿⣿⣿⣿⠀⠀⣀⣴⣿⡿⠃⠀⠈⠛⠁⠀⠀⠃⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣤⣤⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⡏⠀⢸⠀⠀⢸⣿⣿⣬⣷⣾⣿⣿⣿⣿⣷⣦⣰⣦⠀⠀⢰⣷⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢛⣿⣿⣤⣄⠙⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⡿⠁⢠⣿⠂⠀⠈⣏⣡⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣛⢹⣿⣏⣁⣸⣷⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠿⣿⣿⣿⠿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠿⠀⡆⠙⠿⠟⠿⡿⡿⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⢨⠣⣠⣿⣿⡟⠉⢰⣿⣿⣿⣿⣿⣿⡼⢿⣿⢠⣤⣼⣿⡇⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⢻⣦⡀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣱⣿⡗⡠⡳⣿⣦⡘⣿⡟⠀⠀⠀⢹⣿⣿⣿⠛⠿⢣⣶⣦⣸⣿⣿⣿⠓⣦⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠁⢘⠇⠀⣿⣷⡀⠀⠀⠉⠉⠀⠙⠻⠟⠛⠉⠉⠀⠰⢉⠥⠪⢊⣤⣿⣿⣿⠉⠁⠀⠀⠀⠀⠘⡿⢯⣶⣦⣸⣿⣿⣿⣿⣿⣿⣆⢿⣷
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠈⠛⠿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⣼⣦⢠⡇⠀⠹⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠵⠋⠠⣻⣟⡿⠋⠁⠀⠀⠀⠐⠀⠀⣾⡇⢈⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣠⣟⡃⠘⢏⣀⢀⣹⢿⣿⣟⣈⡀⠀⠀⠀⣀⣀⠀⠀⣈⣁⢠⣾⣿⣟⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⡁⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠛⣿⡏⠁⠀⢸⣿⢸⣿⠸⣿⣿⢹⣿⢸⣲⣾⡏⢹⣷⢀⣿⢿⣿⢾⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⣼⣿⠀⢸⣿⢸⣿⢸⠿⣿⡇⢠⣄⢸⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠽⠿⠶⠘⡿⠾⡟⠀⣀⠹⠷⠾⢏⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡆⠸⣿⣧
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠯⡶⠦⡴⠦⠴⠤⠾⠯⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣬⡛⠇⢰⣤⡀
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣯⡷⢿⠻⠯⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠸⣿⡟
⠀⠀⠀⠈⠋⠀⠀⢻⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡽⠍⠀⠀⠀⣠⣤⣶⣶⣶⣦⣶⣶⣶⣾⣿⣿⣶⣶⣾⣿⣶⣤⠀⠀⠀⢰⡀⢰⣿⣿⣿⡇⠀⠀⠲⣶⡿⣿⣿⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⣿⣶⡆⠀⠀⠀⠀⠘⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠂⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢌⡡⠀⠈⢉⡋⠁⣀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⣿
⣀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⢀⣤⣿⣷⣴⣿⣦⣤⣾⣤⣤⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣿⣿⢤⣶⢀⣶⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⣇⠔⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⠿⡿⠿⠿⠿⠛⠿⠋⠉⣶⣦⠀⠀⠀⠁⠀⠀⠀⠀⢠⣿
⣿⣿⣿⣿⣿⣿⣧⣤⣽⣬⣿⣡⣟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⢀⣄⠀⠀⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⡿⠉⠀⠀⠀⠀⣀⣀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣀⠀⠀⣴⣿⣿⠀⠀⢀⣿
⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣄⠀⠀⢸⣿⣇⡴⠝⢋⠁⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⡄⠀⠈⠙⣿⣿⣧⢀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡀⢸⣿⣿⠀⠀⢸⣿
⠛⠿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣰⣿⣿⣿⢡⣧⠀⣿⣿⣿⣿⣦⣬⣤⣤⣤⣄⣠⣾⣿⣿⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⠘⣾⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⢸⣿
⠀⠞⠛⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡆⣿⣿⣯⣽⣾⠿⢂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣠⣤⣄⣀⠀⠀⣠⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿
⠀⣄⣶⣤⣤⣼⣧⣠⠀⢀⣄⣀⣀⣠⡀⠀⠀⠀⠀⣤⣾⣾⣿⠛⠛⠛⢿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡆⣰⣿⡟⣼⣿⣿⡟⣿⣿⡿⢻⣿⢿⣿⠀⠀⠀⠛
⣰⣿⣿⣿⣿⣿⣿⣿⣷⠈⢙⡋⠉⠙⠀⠀⠀⠀⠀⠛⠻⢿⣿⣆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⠻⢿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⠟⢻⡿⠻⣿⣷⡄⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡇⠀⠀⠀⠀⠀⠀⢀⢀⣦⣼⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢹⣿⣿⣿⡀⠀⣀⣴⣿⣿⠋⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⠀⣤⣄⣨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⡟⠀⢸⠀⠀⢸⣿⣿⣭⣷⣿⣿⣿⣿⣿⣷⣦⣠⣦⡀⠀⢰⣷⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣻⣿⣿⣷⣆⠙⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠁⢠⣿⡇⠀⠈⣏⣡⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⡏⣉⣸⣷⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠿⣿⣿⣿⠿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠁⠀⣇⠙⢿⠟⠿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⢨⠣⣠⡿⣿⡟⠋⠐⣿⣯⣿⣿⣿⣿⡮⢿⣿⢡⣬⣼⣿⡇⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⠁⠀⣿⣿⣿⣿⣿⠟⠿⣿⣿⣶⡦⢻⣆⡀⠀⠀⠶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⡇⡠⡢⣿⣦⡘⣿⡟⠀⠀⠀⠹⣿⣿⣿⠛⠿⢋⣴⣦⣸⣿⣿⣿⠓⣦⡀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⢠⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠁⢸⠇⠀⣿⣷⡀⠀⠀⠉⠉⠀⠙⠛⠟⠛⠋⠉⠀⡴⠛⠩⠪⢊⣡⣯⣿⣷⠉⠁⠀⠀⠀⠀⠈⣿⢿⣴⣶⣸⣿⣿⣿⣿⣿⣿⣆⢿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠇⠈⠛⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠀⣼⣶⢠⡇⠀⠹⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠥⠊⠠⣿⣿⡿⠛⠁⠀⠀⠀⠐⠂⠀⢼⡟⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣠⣟⡋⠸⢏⣀⢀⣸⢿⣿⣟⣃⡀⠀⠀⠀⣀⣀⠀⠀⣈⣁⢠⣾⣿⣟⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠹⢿⣿⣿⣿⣿⣿⣿⡇⣸
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠛⣿⡏⠁⠀⢸⣿⢸⣿⠸⣿⣿⢹⣿⢹⣶⣾⡟⢹⣷⢀⣿⢿⣿⢼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⣸⣿⠀⢸⣿⢸⣿⢸⡿⣿⡇⢠⣄⢸⣿⣸⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠽⠿⠶⠘⡿⠾⠟⠀⡀⠹⠿⠾⢏⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢰⣿⣮
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠯⡶⠤⠤⠤⠤⠤⠼⠭⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣜⡛⠇⢠⣄⡈
⠀⠸⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣟⣷⣟⣷⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠸⣿⣿
⠀⠀⠀⠈⠛⠀⠀⢻⣿⣦⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡽⡍⠁⠀⠀⢀⣤⣤⣴⣦⣤⣥⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⡆⠠⣿⣿⣿⣷⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢾⣷⣦⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠖⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢈⠓⡀⠉⢙⡋⠉⣀⠀⠀⠙⠁⠈⠋⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⣿
⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⠀⣤⣾⣿⣤⣿⣧⣠⣼⣦⣤⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠐⣿
⣿⣿⣿⣿⣿⣿⣿⡆⣶⠀⣴⡄⢰⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⠴⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠁⠸⣿⠿⣿⡿⠿⡿⠿⠿⠟⠙⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣧⣤⣬⣄⣼⣁⣼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⡀⠀⠀⢀⣀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣾⡿⠛⠋⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣈⣉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡋⠁⠀⣸⣿⣿⡄⠀⠀⣿
⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣄⠀⠀⢠⣿⣧⣤⡾⠛⡃⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⡀⠈⠉⠻⣿⣿⣷⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⡀⢸⣿⣿⡇⠀⠀⣿
⠛⢻⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⣾⣿⣿⢋⣦⡀⢸⣿⣿⣿⣦⣬⣣⣠⣀⣄⣀⣼⣿⣿⣿⣶⣶⣿⣷⣶⣶⣿⣿⣿⡄⣾⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⠇⠀⠀⣿
⠀⡾⠛⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡇⣼⣿⣟⣹⣼⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣀⣀⣀⡀⠀⠀⣠⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣿
⠀⣅⣶⣤⣄⣼⣧⣤⡀⠀⣠⣠⣀⣠⡄⠀⠀⠀⠀⣠⣶⣷⣿⣿⣿⣿⣿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⡟⣼⣿⣿⣷⣾⣿⣿⢻⣿⣿⣿⠀⠀⠀⠿
⣴⣿⣿⣿⣿⣿⣿⣿⣷⢀⣩⡁⠀⠈⠀⠀⠀⠀⠐⠛⠻⣿⣿⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠙⣿⣿⣿⣿⠿⣷⡿⢿⣿⣷⡉⠁⠁⣾⡿⠈⠉⠀⠀⠀⠀
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡇⠀⠀⠀⠀⠀⠀⢀⠀⣤⣼⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⢻⣿⣿⣿⠀⠀⢀⣠⣿⣿⠟⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣤⣤⠘⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡄⠀⠸⣿⣿⣿⣶⣶⣿⣿⣿⣿⣦⣤⣠⣤⡀⠀⢠⣶⠀⠀⢢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢿⣿⠀⠛⢻⣿⣿⣿⣿⣿⣿⡟⠉⣸⡟⠛⢿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⠃⢀⣾⡇⠀⠈⣟⢡⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⣛⢳⣿⡟⣋⢰⣶⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⣻⣦⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡀⣿⠻⣿⣿⣿⣿⣿⣿⣿⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⣝⢧⣀⣾⣿⡿⠛⠁⣿⣿⣿⣿⣿⣿⣿⢿⣿⢃⣭⣽⣿⡏⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⢀⣠⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⢿⣦⡈⠨⠽⢽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡧⢀⣪⣾⣄⠹⣿⣿⠀⠀⠀⢹⣿⣿⣿⡿⠿⢟⣴⣮⣼⣿⣿⣿⠿⣦⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣤⣶⣿⣿⣿⣿⣿⡿⠃⠀⠁⠀⠀⠀⠈⢡⠃⠈⣿⣧⡀⠀⠀⠉⠋⠉⠻⠿⠿⠟⠛⠛⠁⣰⠛⡫⢜⠗⣁⣿⣿⣷⠛⠃⠀⠀⠀⠀⠉⢿⣿⣴⣦⣬⣿⣿⣿⣿⣿⣿⣇⢻⣷
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠛⠻⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⣸⣿⣦⢸⡄⠀⢻⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⣪⠖⢠⣾⣿⣿⠟⠁⠀⠀⠀⠠⠄⠀⣼⡿⠀⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⡾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣰⣿⣿⡟⢸⢇⣀⢀⣻⢿⣿⣿⣃⡇⣀⠀⠀⣀⣀⠀⠀⣐⣁⢀⣴⣾⣿⠋⢁⣀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠿⠟⣿⣿⣿⣿⣿⣿⣿⡇⣻
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠛⣿⡏⠃⠀⢸⣿⢸⣿⢸⣿⣿⣹⣿⢹⣦⣾⡟⢹⣷⢀⣿⣿⣿⢼⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⢸⣿⠈⢻⣿⢸⣿⢸⡿⣿⡇⢠⣄⢸⣿⣺⣏⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡹⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⠟⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢰⣶⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣗⣴⣅⣤⣥⣤⣍⣴⣟⡵⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣔⠿⡇⢠⣉⠉
⠀⠾⣿⣿⣿⣿⠿⢶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⣶⣗⣶⣷⣶⣟⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠆⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠯⠁⠀⠀⢀⣠⣤⣤⣤⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⡄⠠⣾⣿⣿⣷⠀⠀⢰⣶⣻⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢈⠳⡀⠉⢛⡏⠉⠀⠀⠀⠙⠃⠈⠋⠀⠀⠹⡿⠁⠀⠀⠀⠀⠀⢰
⣤⣄⣠⣄⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠑⠀⣠⣾⣿⣤⣿⣆⣀⣼⣄⣤⡀⠀⠀⠀⠀⢀⠀⢰⡀⠀⠀⣿
⢿⣿⣿⣿⣿⣿⣿⠇⢼⡆⢰⡆⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠂⠸⣿⣿⣿⣿⣿⣿⠿⠿⠟⠫⣧⣦⡀⠀⠀⠈⠀⠈⠁⠀⠀⢻
⣸⣿⣼⣿⣿⣿⣷⣶⣦⣦⣴⣇⣴⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡄⠀⠀⠀⣀⠀⠀⠀⢿
⣿⡿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠙⠛⠛⠛⠻⢿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠃⠀⢰⣾⣿⡇⠀⠀⣼
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⢠⣿⣇⣀⡶⠞⡂⠀⠀⠀⠀⢹⣿⣿⡟⠀⠉⢀⠀⠙⠻⣿⣿⣷⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣦⠀⢸⣿⣿⡇⠀⠀⣸
⠈⢉⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⣾⣿⣿⢋⣦⡀⢸⣿⣿⣿⣧⣬⣣⣀⣀⣄⣀⣸⣿⣿⣷⣦⣴⣾⣦⣶⣶⣿⣿⣿⡄⣽⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⡇⠀⠀⢸
⣀⡞⠛⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⣸⣿⣿⣻⣼⣿⢇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢀⣀⣀⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⣿⣅⣶⣤⣀⣼⣧⣠⠀⠀⢤⡤⢤⢠⡄⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡆⣰⣿⢇⣼⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⠈⢿⣿⣿⣿⣿⣿⣿⣷⣴⣶⡄⠀⠀⠀⠀⠀⠀⠐⠻⠿⣿⣿⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣻⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⣿⣿⣿⣿⠿⢿⡿⢿⣿⣯⠙⠉⠁⣼⣿⠉⠻⡇⠀⠀⠀
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢿⣿⣿⣿⠀⠈⠀⣠⣿⣿⠗⠀⠚⠿⠃⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠠⢴⣶⣶⢚⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⢰⠀⠀⢸⣿⣿⣿⣶⣶⣿⣿⣿⣿⣦⣄⢀⣤⡀⠀⢠⣦⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢸⣿⠻⣿⣿⣿⣿⣿⣥⣄⣀⣀⣀⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⠃⢀⣾⡇⠀⠈⡟⢩⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢳⣶⡞⠛⢰⣦⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠇⡝⠿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⡄⡏⠻⣿⢿⣿⣿⣿⣿⣿⣟⣉⣽⣿⣿⣿⣿⣿⣿⣿⡯⠀⠈⣛⢇⢀⣾⣿⡿⠛⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⢊⣩⣹⣿⡏⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⣹⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣷⢿⣆⠉⠨⠉⢽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡇⢀⣪⣯⡌⢻⣿⡟⠁⠀⠀⢻⣿⣿⣿⠿⠿⢇⣬⣍⣾⣿⣿⣿⢧⣦⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⡇⣠⣤⣶⣾⣿⣿⣿⡿⠁⠉⠁⠀⠀⠀⠈⢰⠃⠸⣿⣧⠀⠀⠈⠙⠛⠛⠿⢿⡿⠿⠿⠟⠉⣠⠿⢛⢕⠕⣳⣟⣿⣦⠿⠃⠀⠀⠀⠀⠹⣿⣿⣤⣤⣸⣿⣿⣿⣿⣿⣿⣆⣿⣆
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠛⠻⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⢸⣷⡄⢸⡀⠀⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣢⠖⣀⣾⣿⣿⠟⠃⠀⠀⠀⢠⡄⠀⣴⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣴⣿⣿⡇⢸⢃⣀⢈⣿⢿⣿⣟⣛⡦⠀⠀⠀⣀⣀⠀⠀⣐⣋⢀⡴⣾⣟⠛⢁⣀⣀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡇⢻
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠛⣿⡏⠁⠈⢸⣿⢸⣿⢸⣻⣿⢹⣿⢱⣤⣾⡟⢹⣷⢀⣿⢿⣿⣽⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠀⢸⣿⢸⣿⠘⢿⣿⢽⣿⢸⣿⣿⡇⢠⣄⢸⣿⣼⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⡻⠿⠶⠘⠿⠾⠟⠈⠁⣹⠷⠾⠿⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣰⣮⣝
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣬⣁⣀⣀⣈⣂⣰⣒⣶⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡰⠾⡇⢈⡉⠛
⠀⠸⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣮⡶⣾⣶⣬⣶⣾⡶⣮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⠄⢸⣿⣶
⠀⠀⠀⠙⠛⠀⠀⢿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣏⠉⠀⠀⠀⣀⣤⣤⣤⣤⣤⣴⣤⣤⣶⣶⣤⣤⣤⣤⣤⣄⠀⠀⠀⢀⡄⢀⣾⣿⣿⣦⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡼⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠐⠧⠀⠛⢻⡿⠋⠀⠀⠀⠛⠃⠙⠟⠉⠉⠹⣿⠂⠀⠀⠀⠀⠀⢠
⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠳⠁⣀⣼⣷⣠⣿⣄⣀⣴⣀⣀⡀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⣼
⢸⣿⢿⣿⣿⣿⣿⠟⠸⡇⠰⡷⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡨⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠆⢸⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣧⣄⣠⡄⠀⠈⠀⠈⠀⠀⠀⢹
⣼⣿⣾⣿⣿⣿⣿⣷⣶⣶⣴⣧⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣆⠀⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⠀⢸
⣿⣟⣿⣟⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠟⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠙⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⠿⠃⠀⢰⣾⣿⡇⠀⠀⢸
⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⢀⣿⣟⣀⡴⠶⠂⠀⠀⠀⠀⢹⣿⣿⡿⠁⠀⢀⠀⠒⠲⣿⣿⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⠀⢸⣿⣿⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⣾⣿⣿⢫⣦⠀⢸⣿⣿⣿⣦⣄⣃⣀⣀⣀⣀⣠⣿⣿⣷⣦⣤⣾⣦⣴⣤⣿⣿⣿⡀⣹⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⣼⣿⣿⣯⣾⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⣷⠀⣀⣀⣀⣼⣆⣄⠀⠠⠶⠰⠦⠤⠆⠀⠀⠀⠀⣠⣤⣶⣿⡿⠿⠿⣿⡈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡄⢰⣿⠇⣽⣿⣿⣁⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⠁⢻⣿⣿⣿⣿⣿⣿⣷⣾⣶⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠙⣿⣿⣿⣿⣿⣾⣿⣿⣿⣟⠛⠛⠃⣼⣿⠙⠻⡇⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⠈⠹⠃⣨⣿⣿⠆⠀⠘⠿⠇⠀⠀⠁⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣶⣶⣷⣴⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⠀⠀⢸⣿⣿⣛⣤⣶⣿⣿⣿⣷⣤⣄⢀⣄⠀⠀⢠⣄⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⡟⠿⣿⣿⣿⣿⣿⣥⣀⣀⣀⣀⣀⣤⣤⣤⣤⣾⣿⣿⣿⣿⠃⠀⣾⡆⠀⠈⡟⢉⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⣶⡞⠛⢠⣤⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣇⠸⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠻⡇⢀⣴⣿⣿⠟⢡⣾⣟⣿⣿⣿⣿⣿⣿⣿⢈⣛⣹⣿⡞⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠈⠛⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣌⠉⠢⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⢀⢎⣏⡈⢿⣿⡿⠁⠀⠈⢿⣿⣿⣿⢿⣿⢇⣭⣍⣾⣿⣿⣿⣷⣄⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣤⣤⣶⣶⣿⣿⣿⣿⠏⠉⠉⠁⠀⠀⠉⢹⠁⢹⣿⣆⠀⠀⠈⠛⠿⠛⢿⣿⣿⡿⠿⠟⠋⣡⡿⢟⢕⠕⢳⣿⣷⣼⠿⠇⠀⠀⠀⠈⠹⣿⣿⣠⣄⢸⣿⣿⣿⣿⣿⣿⡈⣿⣄
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠿⠿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⢠⣦⡀⣠⠀⠘⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⣢⠅⢡⣾⣿⣿⠿⠃⠀⠀⠀⣤⡀⠀⣴⡏⠘⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣾⣿⡇⣿⢆⣀⢘⣿⢿⣿⣟⣃⡀⠀⠀⠀⣀⣀⠀⠀⣴⣊⢉⡤⣾⣿⠟⢁⣀⣀⠀⠀⠀⠀⠀⠀⠛⠃⠸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁⢿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠛⣿⡏⠁⠘⢸⣿⢸⣿⢸⣿⣿⢹⣿⢰⣤⣾⡟⢹⣷⢀⣿⢿⣿⢹⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠃⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⢸⣿⠸⣿⣿⢼⣿⢸⣿⣿⡇⢠⣄⢸⣿⣼⣏⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠺⠿⠶⠘⠿⠾⠟⠈⠁⠹⠷⠾⠿⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣭⡿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣦⣀⣂⣐⣂⣐⣂⣤⡲⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢠⣾⡇⢙⠛⠛
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⢯⣽⠯⣭⣯⣭⢯⣭⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⠁⣸⣿⢦
⠀⠀⠀⠙⠛⠀⠀⢻⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⡋⠉⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣀⠀⠀⠀⢀⡄⢀⣾⣿⣿⣦⠀⠀⢰⣤⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠹⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡼⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠐⢧⠀⠛⠻⡿⠛⠀⠀⠀⠻⠃⠙⠟⠉⠁⢹⣿⠃⠀⠀⠀⠀⠀⠀
⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠍⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠢⠁⣀⣼⣷⣠⣷⣄⣀⣴⣀⣀⡂⠀⠀⠀⠁⠀⠀⢠⣆⠀⠀⢸
⢸⣿⢿⣿⣿⣿⣿⠟⠸⡗⠠⡷⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡨⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣇⡄⢀⣤⠀⠈⠀⠘⠁⠀⠀⢸
⣼⣿⣾⣿⣿⣿⣿⣷⣶⣶⣴⣧⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠉⠀⠀⠀⢠⡄⠀⠀⣿⣷⣸⣿⡇⠀⠀⣀⠀⠀⠀⢸
⣿⣟⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⣿⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⢸⣿⣿⠿⠟⠀⢠⣾⣿⡇⠀⠀⢸
⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢠⣿⣗⣀⣴⠦⠒⠀⠀⠀⠀⢹⣿⣿⣿⠉⠂⠀⠀⠒⠶⣶⣾⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⣄⠀⢻⣿⣿⡇⠀⠀⣾
⠀⠀⠀⢿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⣾⣿⡿⢹⣄⠀⣼⣿⣿⣿⣦⣄⣃⣀⣀⡀⡀⣰⣿⣿⣷⣤⣤⣿⣦⣤⣤⣿⣿⣿⠐⢣⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⣿⣿⣿⣇⣿⡿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡿⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿
⠀⠀⣀⣀⣀⣼⣄⣀⠀⠀⠶⠲⠦⠴⠄⠀⠀⠀⠀⣠⣤⣼⡿⠿⠿⠿⣧⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡄⢰⣿⢇⣽⣿⣿⣉⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿
⣴⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⣿⣿⣷⣿⣿⣾⣿⣿⣿⣟⠻⠛⠃⣽⣿⠛⢿⠇⠀⠀⠀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⠋⠹⠋⣨⣿⣿⠆⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠠⣶⣶⣶⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⠀⠀⠸⣿⣿⣛⣤⣴⣿⣿⣿⣷⣤⣀⢀⣀⠀⠀⢠⣄⠀⠀⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣤⠈⢿⣿⣿⣿⣿⣿⣉⣀⣀⣀⣀⣀⣠⣠⣤⣤⣿⣿⣿⣿⣿⠃⠀⣾⡇⠀⠈⡟⢋⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣶⡾⠟⢠⣄⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⡟⠀⢰⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢿⡇⢀⣴⣿⣿⠟⢡⣾⣟⣿⣿⣿⣿⣻⣿⣿⠘⣛⣻⣿⡞⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠟⠁⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⣼⣷⡄⠋⢍⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⢀⣪⣇⠙⣿⣿⡟⠁⠀⠈⢿⣿⣿⣿⣿⣿⣇⣩⣋⢿⣿⣿⣿⣧⡄⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣠⣤⣤⣶⣶⣾⣿⣿⣿⡿⠁⠀⠀⠀⠉⡿⠀⢻⣿⡄⠀⠀⠉⠛⠿⠛⢿⣿⣿⡿⠿⠿⠋⣡⡿⢟⢔⠕⢻⣿⣷⣜⠿⠇⠀⠀⠀⠈⠻⣿⣿⣠⣀⢸⣿⣿⣿⣿⡿⣿⡈⣿⣄
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠿⢿⣿⣿⡿⠿⠿⠟⠋⠀⠀⠀⢠⣶⡀⣇⠀⠸⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡡⣐⡅⢡⣾⣿⣿⠿⠃⠀⠀⠀⣤⡀⠀⣴⡏⢹⣿⣿⣿⣿⣿⣿⢻⣿⣿⣷⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣼⣿⡷⡿⢀⣀⢹⣿⢿⣿⣟⣓⡤⠀⠀⠀⣀⣀⠀⠀⣴⣊⢉⣤⣽⣿⠟⢁⣀⣀⠀⠀⠀⠈⠁⠀⠙⠃⠰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠈⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠛⣿⡏⠁⠑⢸⣿⢸⣿⢸⣿⣿⢹⣿⢠⣤⣾⡟⢹⣷⢀⣿⢿⣟⣻⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣦⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠂⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⠀⠀⢸⣿⢸⣿⢸⣿⣿⢸⣿⢸⣿⣿⡇⢠⣄⢸⣿⣸⣏⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠾⠿⠶⠘⠿⠾⠟⠘⠁⠹⠷⠾⢿⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣝⡿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⢤⣐⠀⣐⠀⡐⢀⣠⠤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⣾⡃⠙⠛⠿
⠀⠼⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣽⣭⣭⣭⣹⣭⣽⢭⣽⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣬⠁⣸⣷⣤
⠀⠀⠀⠈⠛⠀⠀⢻⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠯⠉⠀⠀⠀⢠⣤⣤⣴⣦⣤⣵⣶⣤⣴⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⢠⠀⠠⣿⣿⣿⣧⠀⠀⢰⣦⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣷⣦⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡷⠂⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⡙⢆⠀⠙⢻⡟⠉⠀⠀⠀⠙⠁⠈⠉⠉⠀⠹⡿⠁⠀⠀⠀⠀⠀⠀
⣀⡀⢀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠆⠀⣤⣾⣿⣤⣿⣆⣀⣴⣄⣤⠀⠀⠀⠀⠀⢀⠀⢀⡶⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⢠⡄⢠⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠗⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠸⣿⢿⣿⣿⣿⣿⠿⢿⠟⠛⣵⣶⣶⠀⠀⠉⠀⠀⠀⠀⠀⠀
⣹⣿⣿⣿⣿⣿⣯⣤⣈⣁⣸⠃⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣿⣿⣿⡆⠀⠀⢀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠙⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠃⠀⣴⣾⣿⣷⠀⠀⠀
⣿⣾⣿⣾⣿⣿⡇⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⣸⣿⣃⣠⠤⠒⠂⠀⠀⠀⠈⢿⣿⣿⡏⠉⠁⡀⠉⠙⠻⣿⣿⡇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣄⠀⢻⣿⣿⣿⡅⠀⠀
⠉⠛⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣿⣿⡏⣷⡄⠀⣿⣿⣿⣷⣤⣌⣀⣀⣀⣀⣀⣼⣿⣿⣷⣦⣶⣷⣶⣶⣶⣿⣿⣷⢁⡇⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⡟⠃⠀⠀
⠀⠀⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣿⣿⣿⣸⣿⠗⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣀⣀⣀⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⢀⣤⣤⣤⣾⣤⣄⠀⠀⣀⣀⡀⢀⠀⠀⠀⠀⢀⣤⣾⣿⡛⠉⠉⢻⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣠⣿⡟⣽⣿⣿⣁⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈
⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⠀⠈⠀⠀⠀⠀⠸⠿⢿⣿⣧⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⠛⠁⣿⡧⠈⢿⡇⠀⠀⠀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣿⣿⠀⠙⢁⣰⣿⡿⠆⠀⠚⠿⠃⠀⠸⡷⠀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣤⣤⣄⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⢸⣿⣿⣍⣴⣶⣿⣿⣿⣷⣦⣄⣠⣄⠀⠀⣠⣤⠐⠀⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢛⣿⣿⣷⣄⠘⢿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⣿⡟⠀⢀⣾⡇⠀⠀⣟⣭⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣶⡟⠋⣴⣦⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⢿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⡃⠀⣾⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢘⢿⣇⣠⣾⣿⡿⠛⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣹⣿⡏⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⠁⢸⣿⣿⣿⣿⡿⠿⢿⣿⣷⣶⢿⣶⡀⠉⠈⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⣰⣹⣇⠙⣿⣿⡟⠀⠀⠈⢿⣿⣿⣿⠿⠿⢇⣬⣅⣿⣿⣿⣿⢷⣄⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣤⣤⣶⣶⣶⣿⣿⣿⣿⠏⠀⠀⠈⠉⢩⡇⠀⣿⣿⡄⠀⠀⠈⠛⠛⠛⠿⣿⣿⠿⠿⠟⢉⡼⠟⡫⡪⠚⣾⣻⣧⡜⠛⠃⠀⠀⠀⠈⠹⣿⣟⣤⣤⣸⣿⣿⣿⣿⡿⣿⡈⣿⣤
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠿⢿⣿⡿⠿⠟⠟⠛⠉⠀⠀⠀⢰⣷⣼⡄⠀⢹⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢔⡩⢄⣰⣿⣿⡿⠛⠀⠀⠀⠠⣤⡀⠀⣾⡇⢸⣿⣿⣿⣿⣿⣯⣻⣿⣿⣧⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣠⣽⣿⣿⡝⢀⣀⢻⣿⢿⡿⣟⣓⡀⠀⠀⠀⣀⣀⠀⠀⣒⣉⣡⣴⣾⣛⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠙⠀⠺⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠈⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡏⠁⢡⢸⣿⢸⣿⢸⣿⣿⢹⣿⢰⣰⣾⡏⢹⣷⢀⣿⢿⣯⢹⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣦⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠉⠃⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠸⢸⣿⢸⣿⢸⣿⣿⢸⣿⢸⡿⣿⡇⢠⣄⢸⣿⣿⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠾⠿⠶⠘⠿⠾⠟⠈⠀⡹⠷⠾⢿⠾⠟⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⣮⡿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣦⣄⣀⣐⣀⣐⣀⣔⣲⣔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠴⢿⠁⣉⠙⠛
⠀⠺⣿⣿⣿⣿⠿⢷⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣽⣭⣵⣯⣽⣥⡽⢧⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⣿⣿⣶
⠀⠀⠀⠈⠙⠀⠀⢻⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠯⠀⠀⠀⢀⣤⣤⣴⣶⣶⣤⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⣤⠀⠠⣿⣿⣿⣇⠀⠀⢺⣶⡿⣿⣿⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣷⣦⠀⠀⠀⠀⠘⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⡙⡄⠀⠉⢹⡏⠉⣀⠀⠀⠙⠁⠀⠋⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠂⢀⣤⣿⣿⣶⣿⣦⣠⣶⣤⣤⠀⠀⠀⠀⠀⡀⠀⢰⡷⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⡄⣀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠊⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠸⡿⠿⣿⡿⠿⠿⠟⢿⠟⢻⣶⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⡟⣿⣿⣿⣿⡟⣁⠻⠁⢻⠃⠸⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢛⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠛⠉⠋⠙⠛⠛⠿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⢙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡿⠛⠂⠀⣾⣿⣿⣷⠀⠀⠀
⣿⣽⣿⣿⣿⣿⡟⠉⠙⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⣿⣿⣠⡴⠖⣒⠀⠀⠀⠀⠈⣿⣿⣿⠁⠉⢈⠀⠈⠙⢿⣿⣿⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⢻⣿⣿⣿⣇⠀⠀
⠿⢿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⣿⣿⢋⣷⡀⢸⣿⣿⣿⣧⣤⣕⣄⣄⣤⣀⣀⣿⣿⣿⣶⣶⣾⣷⣶⣶⣾⣿⣿⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⡿⠃⠀⠀
⠀⠈⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⣾⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⣀⣠⣀⣀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⢀⣦⣤⣴⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡉⠉⠉⣿⣄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿⣿⣿⣿⡆⣰⣿⡟⣽⣿⣟⣠⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠈
⣴⣿⣿⣿⣿⣿⣿⣿⣆⡈⠉⠁⠀⠘⠀⠀⠀⠀⠿⠟⢿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢙⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⠟⢳⡿⢿⣿⣿⠛⠛⢀⣿⡧⠉⢻⡇⠀⠀⠀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣿⣿⣿⣿⠀⠀⢀⣴⣿⡿⠂⠀⠚⠛⠃⠀⠸⣷⠀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⢀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢼⡀⠀⢸⣿⣿⣭⣶⣾⣿⣿⣿⣿⣦⣄⣠⣤⠀⠀⣴⣶⠈⠀⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡀⠹⢿⣿⣿⣿⣿⣧⣄⣀⣠⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⠏⠀⢀⣿⡇⠀⠈⣏⣩⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣼⣿⣛⣉⣴⣦⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠸⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣇⠛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣘⢿⣇⣠⣾⣿⡿⠋⢰⣿⣿⣿⣿⣿⣿⡽⣿⣿⣨⣭⣼⣿⡎⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠋⠀⣻⣿⣿⣿⣿⡟⠿⢿⣿⣿⣷⢿⣶⡀⠉⠹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢀⢔⣾⣄⠹⣿⣿⡟⠀⠀⠈⢿⣿⣿⣿⠿⠿⢣⣶⣅⣿⣿⣿⣿⢷⣆⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣶⣴⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢰⠃⠘⣿⣷⡀⠀⠀⠉⠛⠛⠛⠿⢿⠿⠿⠟⠋⢡⠾⢛⢕⠵⢋⣿⣿⣧⠍⠛⠃⠀⠀⠀⠀⠹⣿⣯⣴⣤⣿⣿⣿⣿⣿⣿⣿⡈⣿⣦
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠛⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⣾⣷⣼⡀⠀⢿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⣂⡵⢀⣾⣿⣿⡿⠋⠀⠀⠀⠰⣦⡀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣯⣻⣿⣿⣷⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⢠⣾⣿⣿⣿⠃⢀⣈⢻⣿⢿⡿⣟⣃⡀⠀⠀⠀⣀⣀⠀⠀⣋⣀⣠⣶⣿⣛⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠺⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⡀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠿⠏⠉⣿⡏⠁⠣⢸⣿⢸⣿⢸⣿⣿⢹⣿⢰⣿⣾⡏⢹⣷⢀⣿⢿⡯⢹⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠉⠃⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠸⢼⣿⢸⣿⢸⣿⣿⢸⣿⢸⡿⣿⣧⢠⣄⢺⣿⣻⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠾⠿⠶⠘⠿⠾⠟⠀⢀⠹⠷⠾⠿⠾⠏⠹⠿⠘⠿⠾⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣴⣮⡟
⠘⣿⣿⣿⣿⡿⡿⢿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣤⣄⣀⣁⣀⣑⣠⣖⣲⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡶⢿⠀⣉⡉⠛
⠀⠾⣿⣿⣿⣿⠿⢶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣧⡷⣦⡶⣧⡷⣶⣷⣦⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡦⠀⣿⣿⣶
⠀⠀⠀⠈⠋⠀⠀⢻⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣯⣠⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣾⣶⣦⡀⠀⠀⠀⠄⠀⠰⣿⣿⣿⣇⠀⠀⠺⣿⡿⣿⣿⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡷⣦⠀⠀⠀⠀⠘⢿⣿⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢈⡑⡄⠀⠉⢹⡏⠁⣀⠀⠀⢉⠀⠀⠃⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢛⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⢀⣴⣿⣿⣶⣿⣦⣤⣾⣦⣴⠀⠀⠀⠀⠀⡄⠀⢰⡷⠀⠀⠀
⣶⣦⣶⣤⣦⣤⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣧⠔⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠃⡀⠘⠿⠿⡿⠿⠿⠿⠟⠻⠋⢹⣷⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠀⠿⠀⢿⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀
⣿⣷⣿⣿⣿⣿⣿⣿⣾⣶⣿⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣾⣿⠟⠋⠙⠙⠛⠛⠻⢿⣿⣿⣿⣿⣟⠉⠉⠉⠉⢉⢉⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⠛⠀⠀⣾⣿⣿⣿⡄⠀⠀
⣿⣻⣿⣿⣿⣿⡟⠛⠛⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⠀⠀⢰⣿⣇⣄⠤⠒⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠉⠛⣿⣿⣿⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣆⠀⢹⣿⣿⣿⡏⠀⠀
⣿⣿⣿⣿⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢹⣦⠀⣼⣿⣿⣿⣦⣤⣤⣤⣤⣄⣀⣼⣿⣿⣿⣶⣶⣶⣶⣿⣶⣿⣿⣿⡆⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⡟⠇⠀⠀
⠀⠙⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣴⣿⣿⣇⣿⡿⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢀⣠⣤⣤⣀⠀⠀⣰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⡇⢰⣷⣤⣴⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡏⠉⠙⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣆⣴⣿⡟⣽⣿⣷⣴⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠈
⠀⠘⣿⣿⣿⣿⣿⣿⠆⠈⠑⠓⠂⠒⠀⠀⠀⠀⠿⠟⢿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⣿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⠛⠳⠿⢿⣿⣿⠉⠉⢀⣿⡗⠈⢻⡃⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⡆⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⣀⣼⣿⡿⠂⠀⠛⠛⠃⠀⠀⠁⠀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⡀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⠀⠀⢸⡀⠀⢸⣿⣿⣧⣶⣾⣿⣿⣿⣿⣶⣤⣤⣤⠀⠀⣴⣆⠀⠀⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢸⣿⠻⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⠃⠀⢀⣿⡇⠀⢀⣏⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢾⣿⢋⣁⣾⣦⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣜⢿⣧⣠⣿⣿⡿⠋⢰⣿⣿⣿⣿⣿⣿⡽⣿⣿⣬⣥⣼⣿⡏⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠉⣠⣿⣿⣿⣿⣿⡿⠛⠻⢿⢿⡿⣿⣦⡀⠹⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⡇⢀⣪⣾⣄⠹⣿⣿⡟⠀⠀⠈⢿⣿⣿⣿⠻⠿⣣⣶⣤⣿⣿⣿⣿⢳⣆⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣴⣶⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⢀⠀⢰⠁⢸⣿⣧⠀⠀⠀⠉⠛⠋⠛⠿⠿⠿⠻⠛⠉⣠⠿⣛⢔⠝⣑⣿⣿⣧⠈⠙⠃⠀⠀⠀⠀⠹⡿⢧⣶⣤⣿⣿⣿⣿⣿⣿⣿⡌⣿⣦
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠏⠛⠻⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣿⣷⣾⡀⠀⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⣪⠖⢠⣾⡿⣿⠛⠉⠀⠀⠀⠰⣶⠄⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣠⣴⣿⣿⣟⣿⠃⢀⣈⢿⣿⢿⡿⣟⣀⡀⠀⠀⠀⣀⣀⠀⠐⣋⣀⣴⣶⣟⣋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠻⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠀⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⣇⡄⣿⡇⠀⣾⡏⣿⡇⢸⣏⠿⠇⠉⣿⡏⠁⠄⢸⣿⢸⣿⢸⣿⣿⢹⣿⢰⣿⣾⡏⢹⣷⢀⣿⣿⡯⢹⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠉⠁⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠻⢼⣿⢸⣿⢸⣿⣿⢸⣿⢸⠟⣿⡧⢠⣄⢺⣿⣻⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠾⠿⠶⠘⠿⠾⠟⠀⠀⠹⠿⠾⠿⠿⠏⠹⠿⠘⠿⠾⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣶⣮⡟
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣤⣁⣠⣁⣠⣁⣠⣒⡲⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⠾⢏⠀⣍⡉⠛
⠀⠺⣿⣿⣿⣿⠿⢷⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣮⡷⣦⣶⣦⣷⣦⣷⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⣶
⠀⠀⠀⠈⠉⠀⠀⢻⣿⣷⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣗⡀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⣰⠀⠀⠐⣿⣿⣿⣧⠀⠀⠘⣿⡿⢿⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠿⣿⣶⠀⠀⠀⠀⠈⠻⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⡱⠄⠀⠀⣨⣅⠀⣀⠀⠀⠈⠀⠀⡀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠉⠀⢠⣶⣿⣿⣶⣿⣶⣴⣿⣶⣶⡄⠀⠀⠀⠀⡤⠀⠸⡿⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⠆⣴⡀⣤⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⡷⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠿⠻⠿⠟⠻⠿⠛⠻⠋⠉⣷⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣶
⣿⣏⣿⣿⣿⣿⣧⣤⣭⣄⣽⢁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡆⠀⠀⢠⣤⡄⠀⢠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⠋⡀⠀⠀⣀⣀⣈⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡉⠀⠀⣾⣿⣿⣿⡆⢐⣿
⣿⣾⣿⣿⣿⣿⡇⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⣾⣿⣤⡔⠒⠀⠀⡄⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⢠⡉⠻⣿⣿⣇⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣷⢼⣿
⠛⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣿⡏⣼⣆⢠⣿⣿⣿⣷⣶⣤⣤⣥⣶⣀⣤⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣼⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠁⣺⣿
⠀⠉⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣦⣿⣿⣷⡿⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⢀⣤⣤⣤⣄⠀⢀⣿⡟⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿
⠀⣼⣷⣤⣴⣿⣦⣆⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⣰⣾⣿⣿⣇⠀⠹⣷⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⣿⣿⣧⣾⣿⢱⣿⣿⣿⣶⣿⣿⡿⣷⣿⣿⣿⡇⢸⣿⣿
⣾⣿⣿⣿⡿⣿⣿⣿⣆⣀⢀⡉⠀⠉⠀⠀⠀⠀⠛⠛⠻⣿⣿⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣉⢿⣿⡋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⡿⢻⣿⠟⠿⣿⣿⠁⠀⣰⣿⡯⠀⠹⣧⣸⣿⣿
⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⡀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⠀⠀⢹⣿⣿⣇⠀⢉⣠⣼⣿⡟⠃⠀⠛⠛⠁⠀⠀⢿⣿⡿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠠⠀⣄⣀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡄⠀⢸⣿⣿⣾⣶⣿⣿⣿⣿⣿⣷⣦⣴⣶⠀⡀⣴⣷⠀⠈⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⡿⢿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢠⣿⡇⠀⢀⣯⣴⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣟⢼⣿⢏⣅⣾⣷⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡙⠻⣿⣿⣿⣿⣿⣿⣿⣯⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣘⢿⣧⣴⣿⣿⡟⠉⢸⣿⣿⣿⣿⣿⣿⡼⢿⡿⣤⣤⣾⣿⡇⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢉⣠⣿⣿⣿⢿⣿⠏⠋⠻⢿⢿⡿⣷⣆⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡇⡠⡣⣷⣄⠹⣿⣿⡟⠀⠀⠀⢻⣿⣿⣿⠛⠛⣱⣶⣦⣿⣿⣿⣿⢻⣦⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⢀⡀⡜⠀⢹⣿⣆⠀⠀⠀⠉⠉⠙⠻⠿⠿⠛⠛⠛⢁⡼⢟⡫⡪⢊⣹⣿⣿⡦⠁⠉⠁⠀⠀⠀⠀⢘⡿⢧⣶⣶⣽⣿⣿⣿⣿⣿⣿⡄⣿⣧
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠏⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠘⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢔⣥⠂⢴⣿⣿⡿⠛⠁⠀⠀⠀⠲⢶⠄⠀⣿⡇⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⢠⣾⣟⣛⡏⠂⢀⣘⢿⣿⢿⣿⣇⣀⡀⠀⢀⡀⣀⣀⠀⠚⣁⣠⣶⡿⣟⣋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠿⢿⢻⣿⣿⣿⣿⣿⣿⣿⠀⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⣇⡄⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠙⣿⡏⠣⠀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⣿⣾⡏⢹⣷⢀⣿⣿⡏⢸⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠁⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠻⢸⣿⢸⣿⢸⣿⣿⢺⣿⠸⠃⣿⡷⢠⣄⢻⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⠹⠿⠾⠿⠽⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⣷⣽⡛
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣣⣤⣀⣬⣀⣬⣡⣼⣓⢶⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣰⠾⡇⢀⣉⠙⠛
⠀⠺⣿⣿⣿⣿⠿⢷⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⣶⣶⣶⣼⣷⣶⣲⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡆⢸⣿⣿⣶
⠀⠀⠀⠈⠉⠀⠀⢹⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣠⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣗⡀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢰⠀⠀⠐⣿⣿⣿⣇⠀⠀⠘⣿⡿⢿⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠿⠷⣶⠀⠀⠀⠀⠈⠻⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⡱⠄⠀⠀⢨⡅⠀⣀⠀⠀⢈⠀⠀⠁⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠀⢀⣶⣿⣿⣶⣿⣷⣴⣿⣦⣶⡄⠀⠀⠀⠀⡄⠀⠸⡟⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⠆⣴⡀⣤⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡷⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠿⠻⠿⠟⠻⠿⠛⠛⠋⠉⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⣏⣿⣿⣿⣿⣧⣤⣭⣄⣽⢁⣜⠁⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄⠀⠀⢠⣤⡀⠀⢀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⠋⡀⠀⠀⣀⣀⣈⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡉⠁⠀⣾⣿⣿⣿⡆⢈⣿
⣿⣾⣿⣿⣿⣿⡇⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⣾⣿⣤⡄⠒⠀⠀⡄⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⢠⡉⠻⣿⣿⣇⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⡷⣸⣿
⠛⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣿⡏⣼⡆⢠⣿⣿⣿⣷⣶⣤⣤⣥⣦⣀⣤⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⢸⣼⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣾⣿
⠀⠉⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣦⣿⣿⣵⡿⠏⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⢀⣤⣤⣤⣄⠀⢀⣿⡟⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⣼⣷⣤⣴⣿⣤⣄⠀⢀⣀⣀⠀⢀⠀⠀⠀⠀⣰⣾⣿⣿⣇⠀⠹⣷⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⣿⣿⣧⣾⣿⢱⣿⣿⣿⣶⣿⣿⡿⣷⣿⣿⣿⡇⢸⣿⣿
⣾⣿⣿⣿⡟⢿⣿⣿⣆⡀⠀⡈⠀⠈⠀⠀⠀⠀⠛⠛⠻⣿⣿⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢉⢿⣿⡋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⡿⠻⣿⠟⠿⣿⣿⡀⠀⣰⣿⡟⠀⠹⣧⣸⣿⣿
⢹⣿⣿⣿⣷⣿⣿⣿⣿⣯⣽⡇⠀⠀⠀⠀⠀⠀⡀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢹⣿⣿⡇⠀⢉⣠⣼⣿⡟⠃⠀⠙⠛⠁⠀⠀⠻⣿⠿⢿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣄⣠⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠟⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡄⠀⢘⣿⣿⣶⣶⣿⣿⣿⣿⣿⣷⣦⣴⣶⠀⠀⣴⣷⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣸⡟⢻⣿⣿⣿⣿⣧⣦⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢀⣿⡇⠀⢀⣧⣰⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣟⢼⣿⢏⣅⣾⣷⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡈⠻⠿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣘⢿⣧⣴⣿⣿⡟⠉⢸⣿⣿⣿⣿⣿⣿⡼⢿⡿⣤⣦⣾⣿⡇⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢉⣠⣿⣿⣿⠿⣿⠏⠋⠹⡿⢿⡿⣷⣆⠀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⠇⡠⡣⣯⣄⠹⣿⣿⡏⠀⠀⠀⢻⣿⣿⣿⠛⠛⣱⣶⣦⣿⣿⣿⣿⢻⣦⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⢀⡀⡜⠀⢹⣷⣄⠀⠀⠀⠉⠉⠙⠿⠿⠿⠛⠛⠋⢁⡼⢟⡫⡪⢊⣹⣿⣿⡦⠈⠉⠁⠀⠀⠀⠀⢘⡿⢧⣶⣶⣽⣿⣿⣿⣿⣟⣿⡄⣿⣦
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠘⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⣥⠂⢴⣿⣿⡿⠛⠁⠀⠀⠀⠲⢶⠄⠀⣿⡇⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⢠⣾⣟⣛⡏⠃⢀⣘⢿⣿⢿⣛⣁⣀⡀⠀⠀⠀⣀⣀⠀⠊⣁⣠⣶⡿⣟⣋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠿⢿⢻⣿⣿⣿⣿⣿⣿⣿⠀⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⡄⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠙⣿⡏⠣⠀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⣿⣾⡟⢹⣷⢀⣿⣿⡏⢸⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠁⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⠻⢸⣿⢸⣿⢸⣿⣿⢼⣿⠸⠃⣿⡗⢠⣄⢻⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⠹⠿⠾⠯⠽⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⣶⣽⠛
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣣⣤⣀⣬⣀⣬⣁⣼⣓⢶⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣰⠾⡇⢀⣉⠙⠛
⠀⠺⣿⣿⣿⣿⠿⢷⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⣶⣶⣶⣬⣷⣶⡲⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡆⠸⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣄⠀⠀⢀⡀⣴⣾⣿⣿⣿⣠⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⡀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢰⡀⠀⠀⢿⣿⣿⡿⠀⠀⠘⢿⡟⠻⡿⠟⠛⢿⣿⡄⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠠⡙⠆⠀⠀⢠⣧⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡧⢠⡄⢠⣄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢍⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠀⢀⣶⣿⣿⣿⣿⣿⣶⣿⣷⣶⠁⠀⠀⡀⠀⠰⠀⠀⠛⠀⠀⠀
⣹⣿⣿⣿⣿⣿⣿⣥⣘⣇⣸⡏⣸⠛⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠗⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⠻⠛⠛⠛⠋⠙⠋⠀⣴⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⢠⣿⣿⣿⡿⠀⢀⣠⣶⣄⠀⠀⠨
⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠉⠀⠉⠉⠉⠉⠛⢿⣿⣿⣿⡟⠁⠀⠀⢀⣀⣀⣀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⣿⣯⣄⡀⠀⢸⣿⣿⣿⡇⠀⣰
⠛⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠄⠀⠀⣿⣿⣤⠄⠀⠀⠀⡄⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⢰⡌⢹⣿⣿⣇⢠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⠇⠀⣿
⠀⣴⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡄⣼⣿⡇⣾⡆⢰⣿⣿⣿⣶⣶⣦⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣼⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣿
⠸⠉⡉⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⣿⣿⣼⡟⢃⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⢀⣤⣤⣤⣤⡀⢀⣿⡟⢻⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿
⣰⣾⣿⣶⣾⣿⣶⣦⡀⠈⠹⠛⠒⠚⠀⠀⠀⠀⣴⣿⣿⣷⣦⠀⠸⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠛⠿⣿⣿⣧⣼⣿⣧⣿⣿⣿⣿⣿⣿⠟⣿⣿⢿⣿⡇⢰⣿⣿
⢿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠋⠻⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡌⠿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢽⣿⣿⣿⠟⢿⡿⠛⣿⣿⣄⢀⣼⣿⣿⠀⠹⣧⣸⣿⣿
⢸⣿⣿⣿⣷⣿⣿⣿⣷⣯⣬⡇⠀⠀⠀⠀⠀⠀⡀⣰⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⠀⠀⢸⣿⣿⢿⠀⢀⣤⣾⣿⣿⡉⠀⠉⠉⠁⠀⠀⠛⠻⠿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢺⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⠇⠀⠀⢸⡆⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣀⣸⣿⠀⠀⢨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣿⣿⣿⣿⣿⣿⣿⣏⢉⣩⣿⣿⣷⣶⠹⢿⣿⣿⣿⣷⣦⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡟⠀⠀⢀⣼⡇⠀⢀⣷⣴⣿⠟⣻⣿⣿⣿⣿⣿⢿⣿⣯⠸⣿⢧⣤⣸⣿⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⢿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⠈⠛⠛⠻⠿⢿⢿⢿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⡜⢿⣷⣴⣿⣿⠟⠁⠸⣿⣿⣿⣿⣿⣿⡞⠿⠿⣶⣶⣾⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢉⣀⣸⣿⣿⣿⡟⠛⠻⠿⠿⢿⠟⣷⡄⠀⠒⠐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⢇⢔⣵⣷⣄⠙⣿⣿⡿⠀⠀⠀⠹⢿⣿⣿⠉⠛⣱⣿⣶⣿⣿⣿⣿⠻⣧⠀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣀⡇⠀⢿⣷⣄⠀⠀⠀⠉⠁⠙⠻⠿⠟⠛⠋⠉⢠⠞⢛⠕⠑⢋⣼⣿⣿⡦⠀⠈⠁⠀⠀⠀⠀⣈⡿⢳⣿⣷⣾⣿⣿⣿⣿⣟⣿⡆⣿⣷
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠈⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⢀⣾⣿⣧⠀⠘⣿⣿⣷⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣪⡵⠃⢼⣿⣿⡿⠋⠀⠀⠀⠀⠺⠿⠆⠀⢿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⢤⣾⣛⣛⡏⠀⢀⣈⣿⣿⢿⣄⣀⣀⡀⠀⠀⠀⣀⣀⠀⠉⣀⣴⣾⡿⣟⣉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⢻⣿⣿⣿⣿⣿⣿⣿⠀⢹
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⡄⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡏⠣⡀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⡏⣾⡏⢹⣷⣀⣿⣿⡇⢸⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠀⢻⢸⣿⢸⣿⢸⣽⣿⢹⣿⠘⠀⣿⡷⢠⣔⣻⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠀⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠄⠹⠿⠾⠏⠼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⣷⣿⠛
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠦⡤⠤⡤⠬⣤⡬⡽⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡰⠿⠀⢠⣉⠉⠛
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣿⣳⣞⣷⣾⣳⣾⡳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠸⢿⣿⠢
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠁⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⢀⣀⢰⣾⣿⣿⣿⣤⣶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠨⣄⠀⠀⠻⢿⣿⠿⠀⠀⠀⠻⠟⠛⠿⠟⠛⢻⣿⡆⠀⠀⠀⠀⠀⠀
⣠⣄⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠰⣌⠂⠀⠀⢠⣦⠀⢠⡄⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡷⢰⡆⢠⣦⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⡂⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⠈⠀⠀⣾⣿⣿⣿⣿⣿⣶⣿⣿⣾⡇⠀⣀⡀⠀⠰⠀⠀⠛⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣤⣌⣇⣨⡏⣨⡋⠀⠀⠀⠀⠀⠀⠀⢰⡀⢸⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠙⠋⠛⠛⠉⠛⠉⢉⠋⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣿⣿⣿⡏⠀⢀⣠⣶⣆⠀⠀⣸
⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠁⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⡟⠁⠀⠀⠀⣠⣄⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣦⣄⠀⢸⣿⣿⣿⡇⠀⣾
⠙⠛⣻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⢆⠀⢀⣿⣿⣶⡄⠁⠀⠀⠆⠀⠀⠈⣿⣿⣿⣀⠀⠀⠀⣰⣄⣹⣿⣿⣇⢠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⣨⣿⣿⣿⠇⢀⣿
⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⣼⣿⣇⣿⣇⢸⣿⣿⣿⣿⣷⣶⣶⣶⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣼⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿
⠀⢁⡁⠀⠀⣠⠀⠀⠀⢀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⣙⠃⠿⠿⣾⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⢀⣴⣶⣶⣦⡄⠀⣼⣿⢹⣿⣿⣋⣹⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⣼⣾⣿⣶⣾⣿⣶⣷⣀⣈⢙⠛⠉⠙⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠸⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠛⠻⣿⣿⣷⣼⣿⣧⣿⣿⣿⣿⡿⠿⠟⣻⣿⠿⣿⡇⢸⣿⣿
⢿⣿⣿⣿⡏⢻⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡌⢿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢹⣿⣿⣿⠏⠿⡟⠙⣿⣿⣧⠀⣼⣿⣿⠀⠸⣷⣼⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡇⠀⠀⠀⢀⣀⠀⣄⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⠀⠀⢸⣿⣿⡻⠀⣀⣴⣾⣿⣿⣉⠀⠈⠉⠀⠀⠀⢙⠛⠛⠛
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢻⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⠇⠀⠀⢸⡇⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⣤⣸⣿⠀⡀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⡇⠻⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣾⡇⠀⢀⣶⣼⣿⠟⣹⣿⣿⣿⣿⣿⢿⣿⣿⡼⠿⢇⣤⡼⣿⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠛⠿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⡈⠻⠿⢿⣿⢟⡿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡠⡌⠻⣿⣴⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿⡟⢻⠿⣳⣿⣾⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀⣀⣀⣠⣼⣿⣿⣿⠏⠉⠙⠛⠿⢿⠛⣿⡄⠀⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣿⡿⢃⢔⢟⣷⣆⠘⠿⣿⡿⠀⠀⠀⠘⢿⣿⣿⠉⠉⢱⣿⣷⣾⣿⣿⣿⠙⣷⡀
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢠⣀⡇⠀⢻⣿⣄⠀⠀⠀⠈⠉⠉⠛⠟⠛⠋⠉⠁⠠⠞⡩⠖⠕⣡⣼⣿⣿⡇⠀⠈⠁⠀⡀⠀⠀⢨⡟⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⢿⣷
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠈⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠘⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠨⠞⠁⢾⣿⣻⠟⠉⠀⠀⠀⠀⠹⠿⠇⠀⢻⠇⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠞⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⡴⣟⣋⣙⡏⠀⢀⣘⢿⣿⢿⣮⣀⣀⡀⢀⣀⠀⣀⣀⠀⠁⣀⣴⣿⡿⣋⣁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⡆⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡏⢃⡀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢸⡏⣾⡏⢹⣷⣤⣿⣿⡇⢸⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠈⢻⢸⣿⢸⣿⢸⣽⣿⢺⣿⠘⠀⣿⣗⢢⣔⣹⣿⣸⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠈⠸⠿⠸⠿⠶⠘⡿⠾⢟⠀⠀⠻⠿⠾⠏⠼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⢸⣷⣿⡛
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠯⡷⠦⠤⠤⠤⠤⠴⠯⠽⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣚⠻⠀⢠⣉⠉⠛
⠀⠺⣿⣿⣿⣿⠿⢷⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣾⣿⣿⠿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⢺⢿⣿⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣤⠀⠀⢀⣀⣰⣿⣿⣿⣿⣦⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢹⣿⣦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣕⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠸⣄⠀⠀⠻⠿⢿⠿⠀⠀⠀⠻⠟⠛⠿⠛⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⢌⠃⠀⠀⢠⣷⡀⣠⡄⠀⢀⡀⠀⡀⠀⠀⠀⠉⠀⠀⠀⣠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⢠⣦⢠⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣅⡢⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⢿⣇⣀⠀⠀⠀⠸⠀⠀⠙⠀⠀⠀
⣸⣿⣻⣿⣿⣿⣿⣥⣌⣅⣨⡏⣠⡟⠀⠀⠀⠀⠀⠀⠀⢰⡄⢸⠋⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠙⠉⠙⠋⠉⠛⠉⠈⠁⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡷⠆⠀⢀⣠⣾⣦⡀⠀⢀
⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠀⢀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠏⠀⠀⠀⠠⢤⣤⣤⣾⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣄⠀⢸⣿⣿⣿⡇⠀⢸
⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣂⠀⢠⣿⣷⣶⠀⠁⠀⠀⠆⠀⠀⠈⣿⣿⣿⣀⠀⣀⣀⣴⣄⣹⣿⣿⣧⢰⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⠇⠀⣿
⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣸⣿⢣⣿⡇⢸⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⣿
⣄⢁⣄⠀⠀⣴⠀⠀⠀⢀⣀⣀⠀⢀⠀⠀⠀⠀⠀⣀⣙⡃⣿⠿⣾⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⢀⣶⣶⣶⣶⡄⢀⣼⣿⢻⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿
⢹⣿⣿⣿⣿⣿⣿⣷⣀⠀⠛⡟⠉⠙⠀⠀⠀⠀⣾⣿⣿⣿⣷⡀⠸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠻⣿⣿⣿⣾⣿⢧⣼⣿⣿⣿⡿⠿⠿⣻⣿⠻⣿⡇⢠⣿⣿
⢸⣿⣿⣿⡏⣻⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣘⣻⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⠉⠹⠏⢙⣿⣿⣧⠀⣴⣿⣿⠀⠈⣷⢼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣃⠀⠀⠀⢀⣀⠀⣤⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⠀⠀⠸⣿⣿⡛⡀⣀⣤⣾⣿⣿⣍⡀⠀⠀⠀⠀⠀⣙⠛⠛⠙
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢻⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠉⠉⠛⠋⠉⠙⠛⣛⣿⣿⣿⣿⣿⠃⠀⠀⢸⡇⠀⠀⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣴⣿⠂⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠹⢿⣿⣿⣿⣿⣶⣶⣶⣶⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣾⡇⠀⣠⣶⣾⣿⠏⣽⣿⣿⣿⣿⣿⣻⣿⣷⡜⠿⢗⣶⣜⢿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠛⠻⡿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠻⢛⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡰⡌⠻⣿⣶⣿⣿⠟⠀⠀⢿⣿⣿⣿⣿⣿⡿⢛⡻⢱⣿⣿⣿⣟⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣠⣤⣤⣾⣿⣿⡿⠿⠉⠁⠉⠛⡻⠛⣿⡆⠈⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢣⣿⡿⡢⣪⢾⣷⣆⠘⠿⣿⡿⠀⠀⠀⠘⢻⣿⣿⢉⡉⢱⣿⣿⣾⣿⣿⣿⡉⣿⡄
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣤⣤⡇⠀⢿⣿⣄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠁⠰⠋⡩⠊⢟⣡⣼⣿⣿⡇⠀⠀⠁⢀⣀⠀⠀⢠⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣇⠀⠸⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠵⠞⢁⣾⣿⣿⠟⠁⠀⠀⠀⠀⠙⠿⠧⠀⢹⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣰⠿⣛⣉⣙⡆⠀⢀⣘⢿⣿⢿⣧⣀⣀⡀⢀⡄⠀⣀⣀⠈⠁⣀⣶⢿⠿⣋⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⡿⣿⣿⣿⣿⣿⣿⣿⡀⢸
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⡄⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡏⢣⡀⢸⣿⢸⣿⢸⣿⣿⣹⣿⢸⠇⣾⡟⢹⣷⢤⣿⢿⡇⢸⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠈⢻⢸⣿⢸⣿⢸⢼⣿⢸⣿⠈⠀⣿⣗⢢⣤⣹⣿⣸⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠈⢸⠿⡸⠿⠶⠘⡿⠾⠟⠀⠀⠻⠿⠾⠏⠼⠏⠹⠿⠘⠿⠾⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢼⣷⣿⡛
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠯⣷⠦⠰⠦⣴⠦⠴⠯⠝⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡚⠻⠀⣠⣈⠉⠙
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⢿⠯⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡷⠀⠻⡿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⡛⠋⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣾⣶⣦⠀⠀⢀⣄⣰⣿⣿⣿⣿⣧⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠸⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡤⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠺⣄⠀⠀⠙⠿⠿⠿⠀⠀⠀⠹⠏⠙⠛⠛⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠑⢌⠀⠀⠀⣰⣷⣀⣠⣄⠀⢀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠀⠀⠀
⣾⣷⣶⣶⣶⣶⣶⡄⢀⡀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⠄⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⣀⠀⠀⠀⠰⠀⠀⠙⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⠃⠻⡇⠸⡗⠸⡿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠟⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⠟⠿⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⠷⠀⢀⣤⣾⣧⡀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⠀⠤⣤⣤⣶⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣤⡀⢸⣿⣿⣿⡇⠀⢠
⢿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⡄⠀⣼⣿⣷⣆⠀⠀⠀⠰⠀⠀⠀⢸⣿⣿⣇⣄⣀⣀⣠⣷⣀⣽⣿⣿⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣀⣿⣿⣿⠇⠀⢸
⠀⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢸⣿⣰⣿⠀⢿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡗⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿
⣄⢀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡟⣿⠿⣿⠁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡇⢠⣶⣶⣶⣶⡄⢀⣾⡿⢹⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾
⢹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠶⡶⠆⠲⠆⠀⠀⢀⣾⣿⣿⣿⣿⣆⢹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠻⣿⣿⣷⣾⣿⣧⣿⣿⣿⣿⣿⠿⠿⣻⣿⠛⢿⡇⠀⣸⣿
⢺⣿⣿⣿⡏⢻⣿⣿⣿⣦⠤⡆⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣔⣛⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠹⠋⢉⣿⣿⣷⠄⢠⣿⣿⠀⠀⣿⣴⣾⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣃⠀⠀⠀⠀⠀⠀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⠀⠀⠸⣿⣿⣛⣀⣠⣴⣿⣿⣿⣯⣄⠀⣀⡀⠀⠀⣈⡛⠛⠾
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣟⠛⠋⠉⠉⠉⠉⠉⠉⠙⣛⣻⣿⣿⣿⣿⡿⠀⠀⠀⢸⡇⠀⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣤⣤⠿⠇⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣿⠻⣿⣿⣿⣿⣿⣶⣶⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣾⡇⠀⣠⣶⣾⡿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡮⠿⠟⣶⣦⠿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠻⠿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡘⠛⣿⣿⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⢐⠎⠻⣿⣶⣿⣿⠟⠀⠀⢻⣿⣿⣿⣿⣿⡿⣙⡛⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣤⣴⣶⣿⣿⡿⠻⠿⠏⠁⠈⠙⡟⢹⣷⠀⠈⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠛⣹⣿⠟⡠⡲⣺⣷⡄⠙⠿⣿⡿⠀⠀⠀⠈⢻⣿⣿⣁⣀⢰⣿⣿⣿⣿⣿⣿⡅⣿⡄
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡷⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⣤⣼⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁⠀⠜⢉⢔⠉⢋⣤⣿⣾⣿⠂⠀⠀⠁⣀⣀⡀⠀⣰⣿⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⢻⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡆⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠵⠋⢐⣿⣿⡿⠋⠀⠀⠀⠀⠀⠛⠿⠇⠀⠹⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠞⣋⣉⣹⡀⠀⢀⣹⣿⣿⢿⣆⣀⣀⡀⣀⡀⠀⣀⣀⠈⠀⣠⣾⠿⠟⣁⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⢣⡀⢸⣿⢹⣿⢸⣿⣿⢹⣿⢸⠁⣾⡟⢹⣷⢤⣿⢿⡇⢸⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠘⣷⢸⣿⢸⣿⢸⢾⣿⢸⣿⠀⠀⣿⣗⢠⣬⢹⣿⣸⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣿⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠘⣸⠿⡸⠿⠶⠘⠿⠾⠟⠀⡐⠻⠿⠾⠏⠼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⣾⣿⣟⠛
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠯⡾⠦⠲⠦⡶⠦⢾⠮⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣤⡛⠯⠀⣄⣉⠉⠛
⠀⠸⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⢽⣿⣽⠷⡿⠿⠽⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠿⠯⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠋⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣤⣄⡀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣶⣦⠀⠀⢀⣄⣰⣿⣿⣿⣿⣧⣶⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠘⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡤⠂⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠺⣄⠀⠀⠘⠿⠿⠟⠀⠀⠀⠙⠏⠙⠛⠛⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠻⠇⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠲⢌⠀⠀⠀⢠⣶⡀⢠⣄⠀⢀⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⠀⠀⠀
⣴⣶⣴⣦⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢐⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⣀⠀⠀⠀⠠⠂⠀⠹⠁⠀⠀
⢿⣿⣿⣿⣿⣿⣿⠇⠸⡇⢸⡷⢰⣿⠀⠀⠀⠀⠀⠀⠀⢰⡆⠟⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠀⠀⠉⠋⠙⠋⠉⠉⠉⠀⠁⢀⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣧⣾⡆⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠷⠀⠀⣠⣾⣷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⡟⠀⠠⠀⠠⠤⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⡀⠸⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡀⠀⣼⣿⣶⡆⠀⠀⠀⠴⠀⠀⠀⢹⣿⣿⣅⡀⡀⣀⣀⣦⣈⣿⣿⣿⡆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⠀
⠀⠈⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢠⣿⣰⣿⠀⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣿⣾⠿⣿⠁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⡇⢀⣶⣶⣶⣶⡄⢀⣾⡟⢀⣼⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤
⢀⣴⣿⣷⣿⣿⣿⣷⣀⠀⢶⣦⣤⢴⡆⠀⠀⠀⣼⣿⣿⣿⣿⣆⢹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠻⣿⣿⣿⣾⣿⣧⣿⣿⣿⣿⣿⠿⠿⢋⣿⡟⢿⣯⠀⠀⠉
⠲⣿⣿⣿⡋⢻⣿⣿⣿⣤⡄⣤⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠛⣿⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⠁⢹⠏⠉⣿⣿⣿⡄⢠⣾⣿⡇⠀⣿⡆⠋⠀
⣀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣻⠀⠀⠀⠀⠀⠀⣄⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡀⠀⠸⣿⣿⡟⠀⣀⣤⣾⣿⣿⣯⣀⡀⢀⡀⠀⠀⢈⡃⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋⠉⠛⠛⠛⠛⠛⢛⣻⣿⣿⣿⣿⣿⠁⠀⠀⢸⡇⠀⠀⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⡇⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣾⡇⠀⢀⣼⣶⣿⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⠿⣳⣦⢿⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠻⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠯⣻⣿⣿⣿⣛⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⢤⠜⢿⣿⣶⣿⣿⡟⠁⠀⠻⣿⣿⣿⣿⣿⣿⢙⣛⢿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⣠⣤⣶⣿⣿⡿⠿⠋⠉⠙⠛⡟⢻⣷⠀⠙⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣱⣿⡿⡠⣪⢺⣷⡄⠹⠿⣿⣿⠀⠀⠀⠀⠛⣿⣿⢇⣈⡁⣿⣿⣿⣿⣿⣿⡏⢿⡆
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢠⣼⠀⠀⣿⣧⡀⠀⠀⠀⠁⠈⠙⠛⠛⠋⠉⠉⠀⠜⢉⠭⠪⢚⣠⣿⣿⣿⠆⠀⠀⠋⣀⣄⡀⠀⢠⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣸⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⢹⣿⣿⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠵⠛⠰⣿⣿⡿⠛⠁⠀⠀⠀⠀⠻⠿⠇⠀⠘⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠴⣛⣉⣹⡁⠀⢀⣹⣿⣿⢿⡄⣀⣀⡀⢀⡀⠀⣀⣀⠈⠁⣠⣾⣿⠿⣉⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡏⢃⡀⢸⣿⢻⣿⢸⣿⣿⢹⣿⢸⠁⣼⡿⢹⣷⢤⣿⢿⡇⢸⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠘⢷⢸⣿⢸⣿⢸⢼⣿⢸⣿⠀⠀⣿⣗⢠⣗⢺⣿⣸⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠙⠸⠿⡺⠿⠶⢘⠿⠾⠟⠀⠐⠻⠿⠾⠏⠼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣾⣾⣟⠟
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⢭⠶⠤⠤⠤⠤⠤⠶⢭⠷⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠾⢏⠀⣌⡉⠙⠓
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣷⣛⣶⣷⣶⡻⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⣗⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣤⡀⠀⠀⣀⡀⣾⣿⣿⣿⣧⣾⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠸⡀⠀⠀⠘⠿⢿⡿⠇⠀⠀⠙⠿⠛⠛⠟⠛⠙⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠻⠇⠀⠀⠀⠀⠈⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠲⣌⠂⠀⠀⠀⣴⡄⠀⣤⠀⠀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡀⠀⠀
⢰⣶⣶⣶⣶⣦⣤⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢁⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠈⠀⠀⢰⣿⣿⣿⣿⣿⣷⣾⣿⣿⡷⠀⠀⣀⠀⠀⠆⠀⠘⠃⠀⠀
⢸⣿⣿⣿⣿⣿⣿⠟⠸⡿⠠⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡆⡟⠉⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⠙⠛⠋⠛⠛⠉⣉⠀⢈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣴⣧⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⢿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⣿⣿⡇⠀⣀⣴⣶⡄⠀⠀
⣸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠉⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⡿⠁⠀⠀⠀⣀⣀⣀⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣷⣦⡀⠀⣿⣿⣿⣿⠀⠀
⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡀⠀⢸⣿⣦⠄⠈⠀⠀⢠⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⢀⣦⡈⣻⣿⣿⡇⢰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡿⠀⠀
⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⣿⢠⣿⡀⣿⣿⣿⣷⣿⣶⣶⣶⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣾⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣿⢼⠿⣿⠋⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⠀⣴⣶⣶⣶⣄⠀⣼⣿⠁⣸⣿⣿⡛⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⣤⣾⣶⣾⣿⣷⣷⣀⠀⠲⣶⣤⠀⡦⠀⠀⠀⣴⣿⣿⣿⣾⣦⢻⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠻⣿⣿⣿⣴⣿⣷⣾⣿⣿⣿⣿⣿⠿⠟⣻⡿⢿⣿⠀⠀⠉
⠾⣿⣿⣿⡏⢻⣿⣿⣿⣧⡄⢠⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡨⠿⢿⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⡿⠻⡿⠛⢿⣿⣿⣇⠀⣴⣿⣇⠀⢻⡆⠀⠀
⣀⢿⣿⣿⣿⣿⣿⣿⣷⣾⣄⣘⠀⠀⠀⠀⠀⠀⢄⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⡀⠀⠀⣿⣿⡿⠇⢀⣠⣴⣿⣿⣿⣅⡀⠁⠉⠁⠀⠈⠙⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠟⢻⣿⣿⣿⣿⣿⠃⠀⠀⢀⣧⠀⠀⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⣤⣸⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣿⣿⠿⢻⣿⣿⣿⣿⣉⣥⣿⣿⣏⡿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⠀⠀⣸⣦⣿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠿⢧⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠁⠙⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠛⠙⠿⠿⢿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡠⡜⢿⣿⣦⣾⣿⡿⠋⠀⠸⣿⣿⣿⣿⣿⣿⡟⣛⢿⣶⣿⣾⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣀⣀⣀⣹⣿⣿⣿⠟⠛⠛⠟⡿⢻⣦⠀⠘⠇⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢫⣿⣿⢀⢔⢼⣷⡄⠙⣿⣿⣿⠇⠀⠀⠀⠙⣿⣿⡟⣈⡉⣾⣿⣿⣿⣿⣿⣿⢹⣧
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢰⠁⠈⣿⣦⠀⠀⠀⠉⠈⠈⠛⠿⠿⠛⠛⠋⠁⡠⠟⡫⠔⠕⣁⣾⣽⣿⡆⠀⠈⠛⢀⣀⡀⠀⢀⣾⡟⢿⣿⣿⣾⣿⣿⡿⣿⣯⣿⡼⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⡀⣿⡄⠀⢻⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣮⠞⠠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠸⢿⣿⠀⠘⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠠⣞⣀⣹⡁⠀⢀⣹⢿⣿⢦⠀⣀⣀⡀⠀⠀⠀⣀⣀⠐⠉⣀⣴⣿⡿⣛⣁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠻⠇⠉⣿⡟⢃⠀⢸⣿⢹⣿⢸⢻⣿⢹⣿⢸⠃⣼⡯⢹⣷⣀⣿⣿⡇⢸⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠘⢷⢸⣿⢸⣿⢸⣹⣿⢸⣿⠀⠀⣿⡧⢠⣕⢺⣿⣸⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⡉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠸⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠠⠽⠿⠾⠏⠼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣴⣮⣟⠻
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣤⣤⢤⣅⣤⣅⣴⣕⢶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠴⢏⠀⣈⠙⠛⠓
⠀⠘⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣷⣶⡶⣦⡶⣶⣖⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡦⠀⣽⣿⢖⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣠⣶⣤⣄⠀⠀⢀⡀⢠⣶⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣂⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠰⣇⠀⠀⠀⠿⢿⣿⠿⠀⠀⠈⢿⡞⠻⠿⠻⠛⢻⣿⡄⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠢⣌⠆⠀⠀⠀⢠⣤⠀⢠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⡧⢰⣆⢠⣄⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠩⡁⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠈⠀⠀⠀⣶⣿⣿⣿⣿⣷⣶⣿⣷⣶⠆⠀⢀⠀⠀⠰⠀⠀⠟⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣥⣜⣏⣸⡏⣸⡟⠀⠀⠀⠀⠀⠀⠀⢠⡿⠊⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠀⠛⠛⠛⠛⠛⠛⠋⢙⠉⠈⢱⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⣿⣿⣿⠀⢀⢀⣴⣄⠀⠀
⢠⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠋⠁⠉⠈⠉⠉⠙⢻⣿⣿⣿⣿⠏⢀⣀⠀⣀⣀⣀⣨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣿⣿⣯⣀⠀⢸⣿⣿⣿⡇⠀
⠀⠛⠛⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⣿⣥⡄⠐⠀⠀⢠⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⣤⠉⢻⣿⣿⡇⢀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⠇⠀
⠀⠀⠀⣿⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⢸⢃⣷⡀⣼⣿⣿⣶⣶⣤⣤⣤⣴⣄⣤⣼⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⣿⣼⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⠀⢀⣤⣤⣤⣤⠀⠀⣼⡿⠀⣸⣿⣿⣛⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⣀⣴⣶⣶⣿⣷⣶⣆⠀⠹⢿⡟⠓⠹⠃⠀⠀⠀⣴⣿⣿⣷⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠿⣿⣿⣿⣧⣼⣿⣧⣾⣿⣿⣿⣿⣿⣿⠟⣿⢿⣿⡀⠀⠀
⠀⢿⣿⣿⣿⠻⣿⣿⣿⣿⣾⢺⡇⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣻⣿⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⡟⢿⡟⠻⣿⣿⣿⡀⠀⣰⣷⠀⢹⣧⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣅⡀⡃⠀⠀⠀⠀⠀⠀⡀⢤⣴⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⠀⠀⢽⣿⣿⠿⠀⢀⣠⣾⣿⣿⣿⡁⠀⠉⠉⠀⠈⠛⠇⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠰⣿⠀⢁⡸⠏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡄⠀⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⢀⣀⣾⡧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢻⠀⠀⠀⢰⣶⣼⣿⣉⣽⣿⣿⣮⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣶⣴⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⠁⠀⢀⣧⣰⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⣥⣄⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⢻⠛⢿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⢿⣿⣧⣴⡿⣿⡟⠁⠀⢿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣶⣶⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⡿⠛⠙⠛⢿⠿⣦⠀⠰⠄⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠇⡠⣥⡧⣄⠙⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⣿⠏⣉⠉⣾⣿⣾⣿⣿⣿⡏⣷
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⡎⠀⣿⣦⠀⠀⠀⠉⠉⠙⠻⢿⠿⠿⠿⠟⠋⢀⡾⢟⡣⡪⠎⣸⣿⣿⣦⠀⠘⠻⠃⣀⣀⠀⠀⢠⣿⠛⣿⣿⣷⣿⣿⣿⣿⣿⣽⣷⢼
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠈⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⡀⠘⡆⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢐⡥⠆⣰⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣿⠂⠀⢹⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣴⣇⣘⡝⠀⢀⣹⢿⣿⢦⠀⣀⣀⡀⠀⠀⠀⣀⣀⠠⠚⣈⣠⢶⣾⣟⣋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡁
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠃⠀⢸⣿⢻⣿⢸⣿⣿⢹⣿⢰⡆⣾⡟⢹⣷⢀⣿⣿⡏⢸⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠸⢧⢸⣿⢸⣿⢸⣸⣿⢺⣿⠸⠀⣿⣧⢠⣴⢹⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣻⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠸⠸⠿⠸⠿⠾⠙⠿⠾⠟⢀⠀⢸⠷⠾⡟⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣬⣿⢿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣤⣐⢀⣀⣀⣀⢠⡒⢠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⣼⡋⠘⠛⠻⠷
⠀⠚⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣯⡿⣭⡷⣭⣿⣬⡭⣭⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣬⡁⢘⣷⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣠⣶⣤⣄⠀⠀⢀⡀⢠⣶⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣂⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠰⣇⠀⠀⠀⠿⣿⣿⠿⠀⠀⠈⢻⡞⠻⠿⠛⠛⢿⣿⡄⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠢⣈⠆⠀⠀⠀⢠⣦⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⡧⢰⣆⢠⣄⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠯⡁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠈⠀⠀⠀⣶⣿⣿⣿⣿⣿⣶⣿⣷⣶⠆⠀⢀⠀⠀⢰⠀⠀⠿⠀⠀
⠀⣸⣿⣿⣿⣿⣿⣿⣥⣜⣏⣸⡏⣸⡟⠀⠀⠀⠀⠀⠀⠀⢠⡿⠊⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋⢉⠉⠀⢲⣷⣾⣷⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⣿⣿⣿⠀⢀⢀⣴⣄⠀⠀
⠀⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠋⠁⠉⠈⠉⠉⠙⢻⣿⣿⣿⣿⠋⠀⡀⠀⣀⣀⣀⣨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣿⣿⣯⣀⠀⢸⣿⣿⣿⡇⠀
⠀⠛⠛⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⣿⣥⡄⠐⠀⠀⢠⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⣤⠉⢻⣿⣿⡇⢀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⠇⠀
⠀⠀⠀⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⢸⢃⣷⡀⣼⣿⣿⣶⣶⣤⣤⣤⣶⣄⣠⣼⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⣿⣼⠟⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⠀⢠⣤⣤⣤⣤⠀⠀⣼⡿⠀⣸⣿⣿⣛⣻⣿⣿⣿⣿⣿⠇⠀⠀
⠀⣀⣴⣶⣶⣾⣷⣶⣆⡀⠺⢿⠟⠚⠹⠃⠀⠀⠀⣴⣿⣿⣷⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠿⣿⣿⣿⣧⣼⣿⣧⣾⣿⣿⣿⣿⣿⣿⠟⡿⢿⣿⠀⠀⠀
⠀⢿⣿⣿⣿⠻⣿⣿⣿⣿⣾⢺⡇⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢉⢻⣿⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⡟⢿⡟⠻⣿⣿⣿⡀⠀⣰⣷⡀⢹⣧⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣅⡀⡃⠀⠀⠀⠀⠀⠀⡀⢤⣤⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⠀⠀⢹⣿⣿⡿⠀⢀⣠⣼⣿⣿⣿⡁⠀⠉⠉⠀⠈⠛⠇⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠰⣿⠀⢁⡸⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡄⠀⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⢀⣀⣾⡧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢻⠀⠀⠀⢰⣶⣾⣿⣉⣽⣿⣿⣮⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⠁⠀⢀⣧⣴⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⣬⣄⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⠿⠛⢿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⢿⣿⣧⣴⡿⣿⡟⠁⠀⢿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣶⣶⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⡿⠛⠛⠟⢻⠿⣦⠀⠰⠀⢠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠇⡠⣥⣧⣄⠙⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⣿⠏⣉⠉⣾⣿⣾⣿⣿⣿⡏⣷
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⠠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀⡎⠀⣿⣤⠀⠀⠀⠉⠉⠙⠻⠿⠿⠿⠿⠟⠋⢀⠾⢟⡣⡪⠎⣸⣿⣿⣦⠀⠈⠻⠃⣀⣀⠀⠀⢠⣿⠛⣿⣿⣷⣿⣿⣿⣿⣿⣽⣷⢼
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠈⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠘⡇⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢐⡥⠆⣰⣿⣿⣟⠟⠁⠀⠀⠀⠸⣿⣿⠂⠀⢹⡿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣴⣃⣘⡝⠀⢀⣻⢿⣿⢦⠀⣀⣀⡀⠀⠀⠀⣀⣀⠠⠚⣈⣠⢶⣾⣟⣋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡁
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠃⠀⢸⣿⢹⣿⢸⣾⣿⢹⣿⢰⡆⣾⡟⢹⣷⢀⣿⣿⡏⢸⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠸⢧⢸⣿⢸⣿⢸⣸⣿⢸⣿⠸⠀⣿⣧⢠⣶⢹⣿⣹⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣻⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠸⠸⠿⠸⠿⠾⠙⠿⠾⠟⢀⠀⢹⠷⠾⡟⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣬⣿⢿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣤⣐⢀⣂⣀⣂⢠⡒⢠⣔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⣼⠋⠘⠛⠻⠷
⠀⠸⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣯⡿⣭⡷⣭⡿⣬⡭⣭⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣬⡁⢘⣷⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⣴⣦⣤⡀⠀⠀⣀⠀⣴⣾⣿⣿⣇⣴⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣂⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠠⣏⠀⠀⠀⠸⢿⣿⡿⠇⠀⠀⠙⣿⠝⠿⠟⠛⠻⣿⣇⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠙⠋⠈⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠰⣌⠃⠀⠀⠀⠀⣠⡄⠀⣤⠀⠀⡀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⣶⡀⣴⡄⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⠫⡁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡀⠁⠀⠀⢰⣾⣿⣿⣿⣿⣷⣾⣿⣶⣖⠀⠀⠀⠀⠀⡆⠀⠘⠃⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣯⣤⣹⣅⣻⢃⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠊⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠄⠀⠀⠘⠛⠛⠛⠛⠛⠛⠉⠉⠀⣱⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡄⠀⣀⣴⣦⡀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠋⠁⠉⠀⠉⠉⠙⠻⣿⣿⣿⣿⠋⢀⡀⠀⢀⣀⣀⣈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣥⡀⠀⢿⣿⣿⣿⠀
⠀⠘⠻⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢸⣿⣥⡄⠐⠀⠀⢠⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⣤⠉⢻⣿⣿⣧⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⢸⣿⣿⡿⠀
⠀⠀⠀⣿⠟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢠⢇⣷⡀⣼⣿⣿⣶⣶⣤⣤⣤⣶⣀⣠⣼⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀
⣶⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢸⣼⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡇⠀⣤⣤⣤⣤⡀⠀⢀⣾⡿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀
⠛⢁⣠⣶⣶⣾⣷⣶⣦⣀⠘⠿⠿⠛⠛⠟⠀⠀⠀⢀⣾⣿⣿⣾⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠿⢿⣿⣿⣿⣠⣿⣿⢁⣿⣿⣿⣿⣿⠿⠿⢻⡿⢿⣧⠀⠀
⠀⠸⣿⣿⣿⡿⢿⣿⣿⣿⣿⡗⣿⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢉⣻⣿⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢹⣿⣿⣿⠟⠁⠏⠙⢿⣿⣿⣧⠀⠀⣾⣇⠈⢿⡀⠀
⢀⡀⣿⣿⣿⣿⣿⣿⣿⣷⣌⡀⢘⠀⠀⠀⠀⠀⠀⢀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢀⠀⠀⠸⣿⣿⡿⠀⠀⣀⣴⣿⣿⣿⣏⡀⠈⠉⠉⠀⠈⠁⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⣾⡇⠈⣄⠽⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⡇⠀⠀⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⣀⣠⣿⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠸⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⣹⣿⣿⣿⣿⣧⣤⣄⣀⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⢁⠀⠀⢀⣾⡇⠀⢀⣹⣤⣾⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⠿⣥⣔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⡟⠻⣿⣿⣿⢿⣿⣟⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⢾⣿⣷⣤⣾⢻⣿⠟⠀⠘⣿⣿⣿⣿⣿⣿⣿⠻⠿⣷⣶⣾⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣠⣼⣿⣿⡿⣿⡿⠛⠛⠉⢽⣦⠀⠡⡄⢴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⡇⠠⣪⣿⣄⠉⠿⣿⣿⣿⠇⠀⠀⠀⠘⢿⣿⣿⢉⡉⢱⣿⣷⣿⣿⣿⣿⠙
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⡎⠀⣿⣧⠀⠀⠈⠙⠛⠙⠻⣿⡿⡿⠿⠿⠛⠀⡴⠿⡫⣤⠕⢑⣟⣿⣧⠀⠉⠹⠟⣄⣀⡀⠀⠀⣼⡟⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠀⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢄⣪⠆⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⡇⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣴⣿⣻⡝⠀⢀⣻⢿⣿⢇⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⠕⣉⣁⣴⣾⣟⣛⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠃⠀⢸⣿⢸⣿⢸⣿⣿⢹⣿⢰⡆⣾⡟⢹⣷⢀⣿⣿⡏⢸⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠘⣧⢸⣿⢸⣿⢸⣹⣿⢸⣿⠸⠀⣿⣇⢀⣴⢻⣿⣻⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠈⠸⠿⠸⠿⠶⠙⠿⠾⠟⠀⠀⢹⠷⠾⡟⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣛⠿
⠘⣿⣿⣿⣿⠿⠿⢿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡴⣄⡀⢀⡂⢀⠂⢀⡐⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣴⡟⠐⠛⠿⠷
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣭⣯⣭⡭⣍⣩⣭⣭⣭⡭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣬⡉⠀⣶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣠⣦⣤⡀⠀⠀⣀⠀⣴⣾⣿⣿⣿⣠⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣃⠄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠠⣏⠀⠀⠀⠘⠿⣿⡿⠇⠀⠀⠘⢿⠙⠿⠟⠛⠛⢿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠛⠻⠂⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠰⣌⠃⠀⠀⠀⠀⣠⣄⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⣠⡀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠁⠀⠀⢠⣶⣿⣿⣿⣿⣷⣶⣿⣷⢶⠀⠀⠀⠀⠀⡄⠀⠸⠇⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣟⣁⢻⠃⢻⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀⣿⠊⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠄⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠉⠁⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡄⠀⢀⣠⣶⣀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠋⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⠏⠁⡀⠀⠀⢀⣀⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣀⠀⢸⣿⣿⣿⡇
⠀⠸⠿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢰⣿⣃⡀⠐⠀⠀⢀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⣬⠙⢻⣿⣿⣧⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠈⣿⣿⡿⠃
⠀⠀⢠⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢀⢇⣷⡀⣸⣿⣿⣷⣶⣤⣤⣬⣤⣀⣀⣸⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀
⠃⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⣼⠻⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⡇⠀⣠⣤⣤⣤⡄⠀⢀⣾⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢠⣤⣿⣶⣾⣿⣶⣶⡀⠀⠾⢷⡶⠶⡶⠀⠀⠀⠀⣴⣿⣿⣶⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⣿⣿⣿⣠⣿⣿⠁⣾⣿⣿⣿⣿⡿⠿⠛⣿⢿⣿⠀⠀
⠀⠸⣿⣿⣿⡿⢿⣿⣿⣿⣦⡤⢴⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢙⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⡟⠃⠊⠛⢻⣿⣿⣿⡀⠀⣴⣧⠀⢹⣆⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⡁⢈⡃⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⡀⠀⠀⣿⣿⡿⠁⠀⢀⣤⣾⣿⣿⣟⡀⠀⠉⠉⠀⠈⠛⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⠀⠀⠀⢰⡆⢈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⢿⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣧⠀⠀⣿⣿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣀⣀⣾⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣿⣯⣤⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⡏⠀⠀⣨⣥⣾⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⣭⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠛⣿⣿⣿⣿⣿⣿⣷⣿⣏⠹⠿⠟⢿⣿⣿⣿⣿⡿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⢸⣿⣿⣤⣼⢿⣿⠟⠁⠈⢿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣉⣁⣴⣿⣿⡿⣿⣿⠟⠋⠈⣹⣦⠀⠀⡀⢉⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⡇⢀⢎⣮⣄⠉⢿⣿⣿⣿⡏⠀⠀⠀⠘⢿⣿⣿⢏⡉⠩⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⢰⣾⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⡎⠀⣿⣧⠀⠀⠀⠙⠛⠛⠿⣿⣿⣿⡿⠿⠟⠁⡤⠿⣋⢔⠕⢓⣟⣿⣧⠀⠉⠹⢿⣇⣀⠀⠀⠀⣨⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣽⣧
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠇⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⣪⠄⣡⣾⣿⣿⠿⠋⠀⠀⠀⠈⣿⣿⡇⠀⠀⢿⡿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣠⣿⡱⠀⢀⣻⢿⣿⠆⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⠵⣈⣁⣤⣾⣟⣛⠉⢀⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠸⣷⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠃⠀⢸⣿⢹⣿⢸⣻⣿⢹⣿⢠⡄⣾⡟⢹⣷⢀⣿⣿⡟⢹⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠨⣦⢸⣿⢸⣿⢸⢻⣿⢸⣿⢸⠁⣿⣇⢀⣴⢻⣿⣻⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠨⠸⠿⠸⠿⠶⢘⠿⠾⠟⠀⠀⣹⠷⠾⡟⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡤⣄⡀⠀⠀⠀⠀⠀⠠⠄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⡞⠀⠻⠿⠷
⠀⠸⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣭⣯⣍⣭⣍⣭⣍⣩⣍⡥⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣬⡑⠀⣦⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⢀⡀⢠⣶⣶⣿⣿⣠⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠉⠉⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣂⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠠⣿⠀⠀⠀⠀⠿⣿⣿⠿⠀⠀⠈⢿⡞⠿⠿⠟⠛⢿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠟⠛⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠢⣌⠣⠀⠀⠀⠀⢠⣤⠀⢠⡀⠀⢠⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀
⠀⠀⣴⣦⣴⣦⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠩⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠃⠀⠀⢠⣶⣿⣿⣿⣿⣷⣶⣿⣷⣶⠀⠀⠀⠀⠀⢰⠀⠀⠋⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⢾⡇⢺⡇⢰⣷⠀⠀⠀⠀⠀⠀⠀⣿⠊⠁⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠄⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠙⠋⢈⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣶⣷⣾⣧⣾⡅⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⢀⢠⣶⣄⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⠏⢁⠀⠀⠀⣀⡀⣉⣿⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣄⠀⢸⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⣿⣀⡠⠐⠀⠀⢀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⣬⠙⢿⣿⣿⣧⠀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⠃
⠀⠀⠹⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⢇⣷⠀⣾⣿⣿⣦⣤⣄⣠⣭⣤⣀⣀⣼⣿⣿⣷⣶⣶⣶⣶⣿⣷⣾⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀
⠦⠀⠀⠉⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⠟⢁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡿⠂⣠⣤⣤⣤⣄⠀⢠⣿⡟⢀⠸⣿⣿⣿⠿⣿⣿⣿⣿⣿⠇⠀
⠀⠀⢠⣿⣶⣶⣿⣶⣷⡄⠀⣤⣤⣤⣄⣤⡄⠀⠀⠀⣠⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠿⢿⣿⣿⣿⣤⣾⣿⣠⣾⣷⣿⣿⣿⣷⣿⠟⢿⣿⣿⡀⠀
⠀⠐⣿⣿⣿⡿⢿⣿⣿⣿⣄⣀⢈⡁⠀⠈⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⢿⠛⢻⣿⣿⣿⡁⠀⣰⣷⠀⢻⣇⠀
⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣬⡃⠈⠇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡀⠀⠀⣿⣿⣿⠇⠀⢀⣠⣾⣿⣿⣿⡁⠀⠉⠙⠁⠀⠛⠃
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⣀⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣷⠀⠀⢽⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣀⣀⣾⡧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⠀⠀⢈⣥⣼⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⡿⣭⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠐⢿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⡞⢻⣿⣿⣿⣿⣿⣿⣿⢟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⣀⢸⣿⣿⣄⣴⣿⣿⡿⠁⠀⢿⣿⣿⣿⣿⣿⣿⠛⡿⣿⣾⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢙⣃⣀⣼⣿⣿⣿⡿⠛⠛⠉⣿⣦⠉⢠⡙⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⡇⢀⢌⣮⡄⠉⢿⣿⣿⣿⡏⠀⠀⠀⠈⢿⣿⣿⠏⣉⠉⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⡜⠀⣿⣇⠀⠀⠉⠛⠿⠻⢿⣿⣿⣿⣿⠿⠿⠁⣠⡿⢟⢕⠕⢣⣿⣿⣧⠈⠉⠹⣿⣷⣤⡀⠀⠀⢠⣿⠛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠇⠀⠀⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⢸⡇⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⡡⣺⡅⢁⣶⣿⣿⠿⠛⠀⠀⠀⠈⣿⣿⡷⠀⠀⢹⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣠⣿⡳⠀⢀⣻⢿⣿⢮⡀⣀⣀⡀⠀⠀⠀⣀⣀⢀⠵⣈⣁⣠⣽⣾⣿⠋⢀⣀⣀⠀⠀⠀⠈⠉⠁⠐⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠃⠀⢸⣿⢸⣿⢸⢻⣿⢹⣿⢠⡖⣾⡟⢹⣷⢀⣿⣿⡟⢻⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⠠⣆⢸⣿⢸⣿⢸⢽⣿⢸⣿⢸⠃⣿⡧⢀⣤⢺⣿⣿⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⠸⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⢹⠷⠾⡟⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡻⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣤⣀⡀⠀⠀⠀⠀⠀⠠⠄⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡾⠀⠿⠿⢧
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣟⣿⣍⣩⣙⣺⣉⣊⣉⣪⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣍⡓⠀⣶⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣆⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠉⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡓⢂⠀⠀⢀⣴⣶⣶⣿⣷⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣿⡇⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⢻⣶⠻⡿⠟⠟⢿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⢿⡆⠀⠀⠀⠀⠙⠿⠗⠁⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠢⡈⠧⠀⠀⠀⠀⢀⣨⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠈⠇⠀⠀⠀⣰⣾⣿⣷⣿⣿⣦⣾⣷⣤⡄⠀⠀⠀⠀⢠⠄⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷⢰⣦⢠⣦⢠⣦⠀⠀⠀⠀⠀⠀⠀⡧⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⡄⠀⠀⠀⠻⠛⠻⠿⠛⠟⠛⠙⠋⠉⢠⣦⣤⣷⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⣬⣧⣬⣏⣨⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⣿⣿⣿⠃⠀⠀⣠⡄⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠛⠙⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⣙⣿⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣾⣿⣿⡉⠀⠀⣿⣿⣧⠀
⠀⠀⣿⣿⣿⣿⣿⣿⡏⠉⠀⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⣿⢀⡠⠄⠀⠀⡀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⠀⣘⠛⣿⣿⣿⡇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣶⡀⣿⣿⣿⠀
⠀⠀⠹⣿⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢁⣦⠀⣿⣿⣿⣤⣤⣀⣀⣉⣀⠀⣀⣿⣿⣿⣶⣦⣤⣶⣶⣿⣶⣾⣿⣿⣿⢸⣯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠿⣿⣿⣿⣿⣿⣿⣧⣼⣿⡟⠀
⣦⡄⠀⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣼⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠇⢀⣤⣄⣀⣀⠀⠀⣸⣿⠁⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⡇⠀
⠟⠁⠀⣾⣶⣴⣿⣷⣶⣄⠀⢀⣀⣀⣀⢀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠁⠀⢿⣿⣿⣿⣿⡄⢠⣿⡇⣼⣿⣾⣿⣿⡄⢸⡿⢻⣿⣿⡄⠀
⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⡆⠁⠉⠋⠉⠉⠁⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⡇⠀⠀⣾⡏⢻⡇⠀
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⢉⣠⣾⣿⣿⡇⠀⠀⠙⠃⠀⠃⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠀⠀⠀⠀⠀⣀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣷⠀⠀⢹⣿⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣀⣰⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣻⣿⣿⣿⣿⣏⡉⠁⠀⠀⠀⢀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⢰⣿⠀⠀⠈⣉⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢏⣥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣷⡙⢿⡿⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⡀⢠⣿⣿⣄⣠⡿⣿⣿⠏⠀⠻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣶⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢹⣿⠁⣀⣿⣿⣿⣿⠏⠉⠙⣷⡌⠀⠀⠉⠩⣯⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⣔⣾⡈⠉⣿⣿⣿⣾⣿⠃⠀⠀⠀⠹⣿⣿⡿⢉⠛⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⡜⠈⣿⡀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠋⣀⢿⢟⡡⡢⠫⣿⣿⣆⣼⠿⠿⣿⣿⣷⡄⠀⠀⠀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠇⠀⠀⠉⠻⠿⠟⠛⠛⠋⠁⠀⠀⠀⢰⡀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠘⡁⢔⡉⢈⣴⣾⣿⣿⠟⠀⠀⠀⢿⣿⣿⡿⠀⣾⠘⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣼⡧⠀⢈⣿⢿⣿⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⡪⣐⣋⢀⣽⣿⣿⠋⢀⣀⣀⠀⠀⠀⠉⠉⠀⠰⠇⠀⢸⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡟⠃⠀⢸⣿⢸⣿⢸⢸⣿⢹⣿⢀⡀⣾⡏⢹⣷⢀⣿⢿⡿⢻⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⢠⡄⢸⣿⢸⣿⢸⢻⣿⢸⣿⢸⠃⣿⡇⢀⣤⢺⣿⣿⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠀⢹⢼⡿⠸⠿⠶⠘⠿⠾⠟⠀⠀⠹⠿⠾⡯⠼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣀⣉⠀⠀⠀⠀⠀⠀⠀⢀⣉⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⢿⣿⣦
⠀⠸⣿⣿⣿⣿⠿⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢓⣛⠒⣒⠒⢖⠒⢔⡒⢂⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣤⡛⠁⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⣤⣶⣶⣾⡆⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠙⠛⣿⣇⡀⠀⠀⠀⠀⠀⠀⢨⣿⡷⢀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣿⡇⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⢻⣶⠿⣿⠿⠛⠿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠿⠷⠆⠀⠀⠀⠀⠙⠿⠿⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⡈⡧⠀⠀⠀⠀⠀⣉⡀⠀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀
⠀⠀⢠⣦⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠈⡇⠀⠀⠀⢠⣾⣿⣷⣾⣿⣦⣴⣷⣤⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀
⠀⠀⢺⣿⣿⣿⣿⣿⣿⡿⠰⣷⠠⣿⠀⣶⡀⠀⠀⠀⠀⠀⠀⡧⠊⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠈⠀⣼⠀⠀⠀⠹⠿⠿⠿⠟⠿⠟⠛⠛⠉⠃⣴⣴⣷⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣴⣿⣤⣏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⣿⣿⠀⠀⠀⣠⡄⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⢛⣿⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⣸⣿⣿⡛⠀⠀⣿⣿⣧⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⣇⡀⠠⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠁⠀⡑⠻⣿⣿⣿⡇⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣶⡀⢹⣿⣿⠀
⠀⠀⠘⣿⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢁⣆⠀⣿⣿⣯⣀⣄⣀⣀⣁⣀⠀⢀⣿⣿⣿⣶⣤⣤⣤⣴⣿⣶⣾⣿⣿⣷⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⡿⠀
⣷⣤⡔⠛⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣾⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⡷⢀⣀⣀⣀⡀⠀⠀⢠⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠙⠻⢫⣿⣷⣤⣾⣷⣶⣆⠀⢠⣤⣄⣄⣀⡄⠀⠀⠀⠀⣰⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢾⣿⣿⣿⣿⡄⠀⣾⣿⣠⣿⣾⣿⣯⡀⢸⣿⠿⣿⣿⡄⠀
⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⡆⠀⠈⢉⠉⠈⠁⠀⠀⠀⠘⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠹⣿⣿⣷⣾⣿⢿⣿⠿⣿⣿⣿⡇⠀⠁⣴⡏⢻⡇⠀
⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣋⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⢉⣠⣾⣿⣿⡇⠀⠀⠙⠓⠀⠃⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⣀⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣾⠀⠀⢹⣿⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣶⣴⣶⡄⣀⣰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣋⡉⠁⠀⠈⠉⢉⣀⣀⣉⣥⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⠀⠀⠈⢋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠂⡀⢀⣿⣿⣧⣠⡾⣿⣿⠟⠁⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠙⣟⣁⣠⣿⣿⣿⡿⠛⠛⠈⣧⡀⠀⠈⠉⢙⣩⣽⣿⣶⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⡔⣼⡈⢻⣿⣿⣿⣷⣿⡏⠀⠀⠀⠸⣿⣿⣿⢙⠛⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡔⠘⣿⡀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠋⣰⣿⠟⡡⡪⢎⡷⣿⣆⣿⣿⣿⣿⣿⣿⣆⠀⢀⡄⣹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠏⠀⠀⠙⠻⠿⠛⠛⠉⠉⠀⠀⠀⠀⢸⠀⠀⢿⣿⣄⡀⠀⠀⠀⠀⠘⠛⠙⠉⠁⠀⠀⠰⢁⢔⡊⢊⣴⣾⣿⣿⠟⠁⠀⠈⣿⣿⣿⡟⠀⣾⠇⣿⡇⣸⣿⣿⣿⣿⣿⣿⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣼⡇⠀⢘⣿⣿⣧⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⡪⣐⣋⢀⣺⣯⣿⠟⢀⣀⣀⠀⠀⠀⠉⠛⠀⠠⠏⠀⢨⣽⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡟⠃⠀⢸⣿⣼⣿⢰⢸⣿⢹⣿⢀⡀⣾⡏⢹⣿⢀⣿⣿⡿⢻⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⢠⡄⢸⣿⢸⣿⢸⢸⣿⢸⣿⢸⠃⣿⡇⢀⣀⢼⣿⣿⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠈⠻⣸⠿⠸⠿⠶⠘⠿⠾⠟⠈⠀⠹⠷⠾⣏⠼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡁⣀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣾⣷⣍
⠀⠚⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠯⡲⠦⠰⠦⣴⠶⠔⠦⠔⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⡚⠡⠀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⣠⣴⣦⣴⣇⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣇⡀⠀⠀⠀⠀⠀⠀⢨⣿⠧⡀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⣿⡇⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠻⣷⡿⣿⡿⠿⠿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠀⠀⠀⠀⠀⠀⣾⣿⠗⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢄⡙⣧⠀⠀⠀⠀⠀⣉⡁⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀
⠀⠀⢠⣿⣷⣿⣶⣶⣶⣶⡀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠓⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⣿⠀⠀⠀⢠⣶⣿⣷⣶⣿⣦⣤⣷⣤⣤⠀⠀⠀⠀⠀⡄⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠁⢿⠂⣿⠇⢿⡇⠀⠀⠀⠀⠀⠸⡥⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⣿⠀⠀⠀⠸⠿⠿⠿⠟⠿⠿⠟⠻⠋⢹⣶⡆⠀⠀⠀⠁⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣀⠀⠀⠀⣀⣄⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠉⠉⠙⢻⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠁⠀⣿⣿⣿⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⡇⠀⠀⠄⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇⠐⠀⠀⠀⡚⠿⣾⣿⣿⡇⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣤⡀⢹⣿⣿⠀
⡄⠀⠀⣸⣿⡟⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢩⣄⢀⣿⣿⣏⣀⣀⠀⣐⣁⡀⠀⢀⣿⣿⣿⣴⣤⣤⣠⣴⣷⣦⣿⣿⣿⣧⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⠀
⣿⣶⣜⠋⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⣾⠿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⣿⣷⠀⣀⣀⣀⡀⠀⠀⠀⣾⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠻⠟⣯⣾⣧⣤⣼⣧⣴⣄⠀⣲⣶⣦⣤⣠⡦⠀⠀⠀⠀⣠⣶⣾⣧⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠉⠁⢾⣿⣿⣿⣿⡄⢀⣼⣿⢧⣾⣿⣿⣏⠉⠉⣿⠿⣿⣿⡇⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⣀⡀⣉⠀⠀⠀⠀⠀⠀⠐⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⣿⣿⣷⣾⣿⠿⣿⠿⣿⣿⣿⡇⠈⠋⣰⡏⠹⣧⠀
⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣧⡙⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣻⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠉⢀⣼⣿⣿⡇⠀⠀⠙⠛⠀⠿⠇
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡀⠀⠀⠀⢠⣄⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣄⠀⢸⣿⣿⣇⣠⣴⣾⣿⣿⣿⣿⣿⣶⣴⣶⡄⣀⢰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡉⠉⠉⠁⠉⠉⠉⣉⣉⣉⣭⣼⣿⣿⣿⣿⣿⠁⠀⠀⢠⣾⣿⣿⡄⠈⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣏⠹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠂⠀⢸⣿⣿⣿⣧⣴⣿⣿⠏⠀⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⣷⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢙⣟⣁⣴⣿⣿⡿⠿⠿⠟⠉⣦⠉⠀⠈⠙⢹⣏⣿⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡔⡔⠈⠻⡝⣿⣿⣷⣿⣿⠀⠀⠀⠸⣿⣿⣿⢛⠛⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣏⠀⠀⣶⣾⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠔⢹⣇⠀⠈⠀⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣰⣿⡿⡣⣪⢞⡾⣿⣄⣶⢻⣿⣿⣿⣿⡆⠀⢠⡶⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠏⠀⠀⠙⠛⠟⠛⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⣿⣷⣄⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠁⠀⠰⢁⠥⡊⢊⣥⣾⣿⣿⡟⠁⠀⠘⣿⣿⣿⠟⠀⣿⠇⢿⡇⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣼⡆⠀⢸⣿⣿⣇⠄⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⣂⣵⣊⢁⣺⣯⣻⠟⢁⣀⣀⠀⠀⠈⠉⠉⠀⢠⣿⠀⠀⣍⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡟⠃⠀⢸⣿⢹⣿⢰⢸⣿⢹⣿⢀⠀⣾⡏⢹⣿⢀⣿⣿⡿⢿⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⢀⡀⢸⣿⢸⣿⢸⢸⣿⢸⣿⢸⠁⣿⡗⢀⣀⢼⣿⣾⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠈⢷⡸⠿⠸⠿⠶⢘⠿⠾⠟⠈⠀⠹⠷⠾⣏⡼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⠁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣾⣶⣍
⠀⠚⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠭⠴⠤⠠⠤⠤⠤⠠⠤⠌⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠞⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⣠⣤⣦⣴⣇⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⣷⢇⡀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠺⣶⠻⣿⣿⠿⠿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠀⠀⠀⠀⠀⠀⣾⣿⠗⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢄⠙⣯⠀⠀⠀⠀⠈⢉⡉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄⣠⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⢸⡟⠓⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠙⣿⠀⠀⠀⢀⣴⣿⣷⣶⣿⣦⣠⣷⣤⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣟⣁⢻⡇⢻⠇⢺⠗⠀⠀⠀⠀⠀⢸⡥⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⣿⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠟⠻⠋⣷⣴⡄⠀⠀⠀⠁⠀⠀⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⢀⣄⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠛⠿⠛⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠙⢻⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⣶⣿⣿⡦
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⠐⠀⠀⢐⠒⢶⣾⣿⣿⡆⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠀⢸⣿⣿⡇
⣆⠀⠀⣼⣿⡟⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢱⡄⢰⣿⣷⣏⣀⣀⢀⢐⣁⠀⠀⢠⣿⣿⣿⣴⣠⣀⣤⣼⣷⣤⣿⣿⣿⣧⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⣸⣿⣿⠇
⠛⠃⠘⠛⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣿⠟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣀⣀⣀⡀⠀⠀⠀⣰⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⣠⣾⣧⣤⣴⣧⣤⣄⠀⠲⠶⣶⡶⠄⡶⠀⠀⠀⠀⢀⣴⣾⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢸⣿⣿⣿⣿⡄⢀⣴⣿⠏⣰⣿⣿⡟⠉⠉⣿⠿⣿⣿⡇⠀
⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⣶⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⣿⣿⣷⣾⣿⠟⠤⠿⣿⣿⣿⡆⠈⠛⣰⡏⠙⣿⡀
⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣯⡉⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣜⣻⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢀⣀⠀⠀⣿⣿⣿⣿⠃⠀⠈⢀⣼⣿⣿⡇⠀⠀⠙⠛⠀⢻⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡄⠀⠀⠀⢴⣶⣀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⡇⠀⢸⣿⣿⣇⣠⣤⣶⣿⣿⣿⣿⣿⣦⣤⣶⡄⣀⢰⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠙⠉⠉⠉⠉⠉⠉⠉⣉⣉⣭⣼⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⡏⠀⠘⡟⢉⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣍
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⣿⣶⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠒⠀⢈⣿⣿⣆⢀⣴⣿⣿⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠙⣿⣋⣤⣿⣿⡿⠿⠿⠟⠉⣄⠈⠀⠈⠙⢻⣟⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⡔⡴⠘⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⢛⠛⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣏⠀⠀⣴⣾⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠄⢹⣧⠀⠀⠀⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣰⣿⡿⡡⣪⢟⣮⣷⡄⠸⣿⣿⣿⣿⣿⡆⢠⣶⡶⢘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⠟⠀⠀⠉⠻⠟⠛⠉⠉⠀⠀⠀⠀⠀⢸⠀⠈⣿⣧⡀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠁⠀⠰⢃⠥⡊⢊⣥⣾⣿⣿⡟⠀⠀⠘⣿⣿⠟⠱⢿⣿⠀⢸⡇⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣸⡄⠀⢹⣿⣿⣇⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⣂⣱⣎⢁⡺⣟⣻⠟⢁⣀⣀⠀⠀⠈⠀⠀⠀⢠⣿⠀⠀⣀⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡟⠃⠀⢸⣿⣻⣿⢠⢸⣿⢹⣿⢀⠀⣾⡏⢹⣿⢀⣿⢿⡿⢻⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⢠⠀⢸⣿⢹⣿⢸⢸⣿⢸⣿⢸⠀⣿⡗⢀⣀⢸⣿⣿⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠘⢷⡸⠿⠸⠿⠶⠘⠿⠾⠟⠈⠀⠹⠷⠾⣏⡼⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣍⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣴⣦⡉
⠀⠸⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⣽⠶⠤⠠⠤⠤⠤⠠⠭⠑⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠴⠁⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣧⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠛⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⣸⣟⡖⠀⠀⠀⣠⣶⣶⣿⣿⣷⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣐⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠘⣷⡛⠿⡿⠿⠿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢄⡙⣿⠀⠀⠀⠀⠀⢉⡁⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀
⠀⠀⢀⣾⣶⣶⣶⣶⣶⣶⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⣿⠀⠀⠀⢀⣴⣾⣿⣶⣿⣷⣤⣾⣦⣤⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠃⢿⠇⢾⡇⢸⡷⠀⠀⠀⠀⠀⢸⡔⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⣿⠀⠀⠀⠘⠿⠛⠿⠟⠻⠿⠛⠛⠋⢉⣴⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣶⣾⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⡀⠀⠀⢀⣤⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⠋⠛⠙⠛⠛⠻⢿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⠙⢻⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠃⠀⣼⣿⣿⠀
⡄⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣿⠀⠀⠤⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠀⠂⠁⠀⢀⠚⢿⣿⣿⣿⡄⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⢸⣿⣿⠀
⣇⠀⠀⣽⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣰⡀⢸⣿⣿⣄⣤⣀⣀⣈⡀⠀⠀⢸⣿⣿⣷⣦⣤⣄⣤⣾⣷⣴⣿⣿⣿⣇⢸⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣘⣿⣿⠀
⠿⠃⠐⠛⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣀⣀⣀⣀⠀⠀⠀⣾⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⢠⣾⣶⣤⣼⣷⣴⣆⠀⢰⣶⣦⣤⡄⣴⠀⠀⠀⠀⢀⣴⣿⣧⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢉⣵⣾⣿⣿⣿⣿⡆⠀⣼⣿⠃⣾⣿⣿⣏⠀⢩⣿⠟⢿⣿⣿⠀
⠀⠀⠻⣿⣿⣿⡿⣿⣿⣿⣷⣀⡀⢨⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢾⣿⣿⣿⠿⣿⣿⣿⣾⣿⠿⣿⠿⣿⣿⣿⡇⠈⠉⢰⣆⠈⠟⠀
⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣯⡁⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣝⣻⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⣿⣿⡟⠀⢻⣿⣿⣿⠇⠀⠈⢀⣼⣿⣿⡇⠀⠀⠈⠛⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡄⠀⠀⠀⢰⣶⣄⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠁⠀⠸⣿⣿⣧⣴⣶⣾⣿⣿⣿⣿⣿⣶⣤⣶⡆⣀⣠⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣿⣇⣉⠉⠀⠀⠉⠉⢉⣉⣉⣩⣴⣾⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⣟⣹⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠒⠀⣸⣿⣿⣷⣤⣾⣿⡟⠁⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡏⣀⣻⣿⣿⣿⣿⠋⠹⣄⠁⠀⠉⠉⣙⢛⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠁⢀⢔⡖⠙⠛⣿⣿⣿⣿⣿⣧⠀⢀⣀⠈⢿⣿⣿⢛⡛⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣯⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⠂⢹⣆⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣸⣿⠟⢤⡢⢫⣯⣧⡀⠘⢿⣿⣿⣿⣿⣠⣿⣿⠟⢈⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⡟⠀⠀⠀⠹⠿⠟⠛⠛⠋⠉⠁⠀⠀⡆⠀⠸⣿⣦⡀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠁⠀⠀⠜⢀⢔⠙⢊⣴⣾⣿⣿⠟⠀⠀⠈⠉⠁⠙⠻⠿⣿⠀⠸⠟⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣱⡀⠀⢻⣿⣿⣀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⡊⣶⣋⢐⡻⣟⣻⠏⢁⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣠⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡟⠁⠀⢸⣿⣹⣿⢀⢸⣿⢹⣿⠀⠀⣾⡟⢹⣷⢀⣿⢿⡿⢻⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⣤⠀⢸⣿⢹⣿⢸⢸⣿⢸⣿⠘⠀⣿⡗⢀⣠⢸⣿⣾⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠙⣆⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⠸⠷⠾⣏⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡉⢐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣶⣦⡛
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠿⠥⠦⠄⠤⠄⠤⠄⠤⢌⠰⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠮⠀⠀⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⢠⣴⣶⣶⣷⢀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⠛⢻⣿⣀⠀⠀⠀⠀⠀⠀⣼⣟⠂⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣘⣿⣿⠀⠀⠀⠀⣿⣿⣿⡧⠀⠀⠘⣷⡿⠿⡿⠟⠿⢾⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠺⠷⡶⠀⠀⠀⠀⠈⠻⢿⡆⠀⠀⠀⠀⢰⣿⡿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢄⡙⣿⠀⠀⠀⠀⠀⢈⣁⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀
⠀⠀⠀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠙⣿⠀⠀⠀⢀⣶⣾⣿⣶⣿⣷⣤⣾⣶⣴⠀⠀⠀⠀⠀⢠⠀⠀⠀
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠇⣿⡆⣾⡆⢰⣆⠀⠀⠀⠀⠀⢱⠞⠁⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢀⣿⠀⠀⠀⠘⠿⠛⠿⠿⠛⠟⠛⠛⠋⠉⣴⣶⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣾⣦⣾⣥⣾⡁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⣿⣿⣿⡇⠀⠀⢀⣤⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⢉⣻⣧⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⣟⡛⠃⠀⢼⣿⣿⠀
⡀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢰⣿⠀⡀⠄⠂⠀⠀⠀⠀⠀⢿⣿⣿⡗⠀⠀⠁⠀⢈⠛⢿⣿⣿⣿⡀⠀⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡀⢸⣿⣿⠀
⡇⠀⠈⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣴⡀⣾⣿⣿⣤⣤⣀⣀⣈⣀⠀⠀⣸⣿⣿⣷⣦⣤⣤⣴⣾⣶⣶⣿⣿⣿⡇⢸⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣷⣀⣿⣿⠀
⣿⣆⠀⠛⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠿⠃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣤⣶⣄⣀⣀⠀⠀⢀⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠿⠃⢰⣾⣷⣤⣾⣷⣶⣆⠀⢀⣤⣤⣤⣀⣠⡀⠀⠀⠀⢀⣴⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡆⠀⣼⣿⢁⣾⣿⣿⣧⠀⢸⣿⢟⣿⣿⣿⠀
⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⣷⠀⠈⢉⠉⠁⠉⠀⠀⠀⠀⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⣿⣿⡟⠛⣿⣿⣿⣾⣿⣿⣿⡿⢿⣿⣿⡇⠀⠁⣸⣇⠈⣿⠀
⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣉⣻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⣿⣿⠁⠀⢻⣿⣿⣿⠏⠀⠉⢀⣼⣿⣿⡇⠀⠀⠈⠛⠀⠙⠠
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⢀⣤⣀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣿⣿⡄⠀⠸⣿⣿⣷⣼⣾⣿⣿⣿⣿⣿⣿⣷⣴⣶⡆⣀⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣇⣉⠀⠀⠀⠉⢉⣁⣀⣀⣤⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣇⠀⣀⣿⣿⡿⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡙⢿⢿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠓⠀⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⣿⡏⢀⣹⣿⣿⣿⣿⠉⢹⣀⠀⠈⠉⣙⣽⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⢀⢮⡆⠙⠻⣿⣿⣿⣿⣿⣷⠀⣠⣀⡈⢿⣿⣿⢋⡛⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣧⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⠊⢿⣄⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣸⣿⢟⢔⡵⣻⣿⣧⡀⠘⢿⡿⣿⣿⣯⣾⣿⡿⠇⢀⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⡿⠀⠀⠐⠟⠿⠟⠛⠛⠛⠉⠁⠀⠀⡇⠀⢸⣿⣦⣀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠀⠀⠀⠞⡨⢔⠑⢉⣴⣿⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⢿⣧⠀⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣧⡀⠀⢻⣿⢿⣤⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⢐⡨⣶⣋⢐⣿⣽⣿⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡠⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡟⠁⠀⢸⣿⣺⣿⢠⢸⣿⢹⣿⠀⠀⣾⡟⢹⣷⢀⣿⢿⡿⢻⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⡇⣄⠀⢸⣿⢹⣿⢸⢼⣿⢸⣿⠈⠀⣿⡟⢀⣤⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠛⣆⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⣏⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠉⢐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣶⣮⡛
⠀⠸⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠯⡵⠦⠄⠤⠄⠤⠄⠤⠌⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⡠⠎⠀⠀⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⢠⣶⣶⣶⣿⢀⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠋⢻⣿⣀⠀⠀⠀⠀⠀⠀⣾⣟⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⢿⣿⣿⡷⠀⠀⠈⢿⡞⠿⡿⠟⠻⢿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠀⠀⠀⠀⠈⠻⢿⡆⠀⠀⠀⠀⣸⣿⠟⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢄⡙⣿⠀⠀⠀⠀⠀⢀⣁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠹⣿⠀⠀⠀⢀⣶⣾⣿⣶⣿⣷⣤⣾⣷⣶⠀⠀⠀⠀⠀⢠⠀⠀⠀
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡆⣴⡄⣴⡄⢠⡄⠀⠀⠀⠀⠀⢷⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⠁⠀⠀⠈⠟⠛⠻⠟⠛⠛⠛⠛⠋⠈⢰⣶⣾⡆⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣤⣽⣅⣽⣃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⠀⠀⣿⣿⣿⡇⠀⠀⢀⣤⡄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠉⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⠏⠉⠉⠉⠀⠉⠉⠉⣻⣇⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⣰⣿⣟⠛⠁⠀⢸⣿⣿⡇
⡄⠀⢰⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⣸⣿⠀⡀⠔⠂⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⢈⠛⢿⣿⣿⣿⠀⢀⢾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡀⢸⣿⣿⡇
⡇⠀⠀⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣦⠀⣿⣿⣯⣤⣤⣀⣀⣉⡀⠀⢀⣿⣿⣿⣷⣦⣤⣤⣴⣿⣶⣾⣿⣿⣿⡆⣾⣼⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⡇
⣷⣤⣴⠛⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣤⣀⣀⠀⠀⠀⣿⡟⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠿⣿⣿⣾⣷⣤⣼⣷⣴⣆⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣴⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣸⣿⠁⣾⣿⣿⣇⠀⢸⣿⠛⢿⣿⣿⠀
⠀⠀⠈⢿⣿⣿⡿⣿⣿⣿⣷⠈⠉⠙⠋⠉⠙⠁⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠀⠈⣿⣿⣿⣶⣿⡿⣿⡿⢿⣿⣿⡇⠈⠁⣼⣆⠈⣿⣄
⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣙⣻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⣇⠀⠀⢹⣿⣿⣿⣿⠀⠈⣀⣼⣿⣿⡇⠀⠀⠈⠋⠀⠻⠿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡆⠀⠀⠀⠀⣠⣄⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⣀⣰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡁⠀⠀⠀⠉⢉⣁⣀⣠⣤⣶⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣧⣴⣾⣿⠿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠯⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷⡙⣿⠿⢿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠒⢸⡿⢿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⣿⣋⣀⣽⣿⣿⣿⡿⠋⢳⡀⠀⠈⠋⢛⣙⣻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⢀⢢⣆⠙⠈⢿⣿⣿⣿⣿⡇⢀⣤⣄⡈⢻⣿⣿⣹⣟⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣏⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⡠⠈⣿⡄⠀⠀⠸⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣾⡿⢋⢔⠵⣹⣿⣧⡀⠈⠉⠉⠹⣿⣷⣿⣿⡿⠃⣨⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⠟⠀⠀⠀⠻⠿⠟⠛⠋⠉⠁⠀⠀⠀⡇⠀⢸⣿⣦⡀⠀⠀⠀⠀⠉⠛⠋⠉⠁⠀⠀⠠⠊⡨⢒⠑⣡⣴⣿⣿⣿⠇⠀⠀⠀⠀⠈⠉⠛⠿⣧⠀⠻⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣧⡀⠈⢿⣿⢷⣄⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⢐⡩⣶⣉⢐⣿⣏⣻⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣠⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠁⠀⢸⣿⢼⣿⠀⢸⣿⢹⣿⠀⠀⣾⣏⢹⣷⢀⣿⢿⡿⢻⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⡄⠀⢸⣿⢽⣿⢸⢸⣿⢸⣿⠀⠀⣿⡟⢀⣤⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠻⣆⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⣏⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣯
⠘⣿⣿⣿⣿⠿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⠉⢐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣶⣮⡛
⠀⠸⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡟⠯⠴⠦⠀⠤⠄⠤⠀⠤⠅⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡠⠎⠀⠀⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠁⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⢀⣴⣶⣶⣾⡄⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⠻⣿⣆⠀⠀⠀⠀⠀⢀⣿⣯⡡⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠼⣿⣿⠇⠀⠀⠀⠺⣿⣿⡿⠀⠀⠈⢿⡿⠻⠿⠟⠛⠻⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⡄⠀⠀⠀⠀⠙⠿⡗⠀⠀⠀⠀⣼⣿⠟⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢦⣈⣿⡄⠀⠀⠀⠀⠀⣠⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀
⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠨⣿⡇⠀⠀⠀⣴⣾⣿⣷⣾⣿⣦⣾⣷⣴⡆⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⢸⣧⢰⣷⢠⣶⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⡇⠀⠀⠀⠻⠛⠛⠟⠛⠛⠛⠙⠋⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣶⣦⣧⣼⣇⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣼⣿⣧⡄⠀⠀⠀⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠈⣉⣻⡇⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣉⠁⠀⢸⣿⣿⡇
⡇⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⣼⣧⢀⠀⠒⠀⠀⡀⠀⠀⠈⣿⣿⣿⠇⠀⠁⠀⠀⣉⠛⢿⣿⣿⣿⠀⢀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠈⣿⣿⡇
⣿⠀⠀⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⣧⠀⣿⣿⣧⣤⣤⣀⣀⣅⣀⠀⣀⣿⣿⣿⣶⣧⣤⣴⣶⣿⣶⣾⣿⣿⣿⡆⢾⣼⣁⣤⣶⣾⣿⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⣿⣦⢐⠋⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⣸⣿⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠃
⠟⠀⢨⣾⣷⣶⣾⣷⣶⣦⡀⢀⣤⣤⣤⣄⣠⡄⠀⠀⠀⠀⣠⣿⣄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⡿⢿⣿⣿⣧⠀⣰⣿⡟⣰⣿⣿⣷⡄⢰⣿⠋⠻⢿⣿⡀
⠀⠀⠘⢿⣿⣿⡿⣿⣿⣿⣷⠀⠈⠈⡉⠁⠈⠁⠀⠀⠀⠐⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⣿⠃⠀⢿⣿⣿⣧⣿⡟⢿⡿⠻⣿⣿⣿⠀⠀⢰⣷⠀⢹⡇
⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣉⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⣿⠀⠀⠸⣿⣿⣿⣿⣀⣀⣠⣴⣿⣿⣿⠀⠀⠈⠉⠁⠈⠛
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⣠⣤⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⡇⠀⣠⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣠⣄⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠉⢉⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡙⣿⠟⢿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠺⡿⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠈⣻⣋⣠⣾⣿⣿⠿⢿⠿⢷⡀⠀⢀⠉⢯⣹⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠠⣣⣃⠉⠀⢿⣿⣿⣿⣿⣁⣴⣶⣤⡄⠙⣿⣿⣯⣏⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣯⠀⠀⢰⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⡐⠈⣷⣀⠈⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣾⡿⣋⣔⠽⣽⢿⣧⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠃⣤⡝⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⡟⠀⠀⠀⠙⠿⠛⠉⠉⠉⠀⠀⠀⢰⠀⠀⢹⣿⣦⡀⠀⠀⠀⠀⠈⠙⠋⠉⠁⠀⠀⠠⠃⡡⣊⠙⣡⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠻⣿⠀⠛⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣇⡀⠈⢿⣿⢷⣢⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⢐⡵⣞⣁⣐⣿⣍⣻⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⣠⣽⣿⣿⣎⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠃⠀⢸⣿⢸⣿⢀⢸⣿⢹⣿⠀⠀⣾⣏⢹⣷⢀⣿⢿⡿⢻⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⣇⡄⠀⢸⣿⣿⣿⢸⢸⣿⢸⣿⠀⠀⣿⡏⢀⣤⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⢻⣂⠸⠿⠹⠿⠶⠘⠿⠾⠟⠀⠀⡹⠷⠾⣏⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⢒⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣷⣮⡙
⠀⠘⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠯⠴⠤⠀⠤⠤⠤⠠⠤⡅⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠠⠎⠀⢀⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠁⠀⠀⠀⠀⠀⡀⡀⠀⢀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣄⣤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⠻⣿⣆⠀⠀⠀⠀⠀⢀⣿⣏⡡⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠼⣿⣿⠇⠀⠀⠀⠺⣿⣿⡿⠀⠀⠈⢿⡞⠻⠿⠟⠛⠻⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡿⢶⠄⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⣼⣿⠏⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢤⣈⣿⡅⠀⠀⠀⠀⠀⣠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀
⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠨⣿⡇⠀⠀⠀⣴⣾⣿⣷⣾⣿⣦⣾⣷⣶⡆⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⢸⡧⢰⣷⢠⣶⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⡇⠀⠀⠀⠻⠛⠻⠟⠛⠛⠛⠙⠋⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣦⣧⣴⣇⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣼⣿⣧⡄⠀⠀⠀⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠈⣉⣻⡇⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣉⠁⠀⢸⣿⣿⡇
⡇⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⣼⣧⣀⠀⠒⠀⠀⡀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⠈⣉⠛⢿⣿⣿⣿⠀⢀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠈⣿⣿⡇
⣿⠀⠀⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⣧⠀⣿⣿⣧⣤⣤⣀⣠⣥⣀⠀⣀⣿⣿⣿⣶⣧⣤⣴⣶⣿⣶⣾⣿⣿⣿⡆⢾⣼⣁⣤⣶⣾⣿⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⡇
⣿⣦⢐⠋⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⣰⣿⠋⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠃
⠟⠀⢨⣾⣷⣶⣾⣿⣶⣦⡀⢀⣠⣤⣤⣀⣠⡄⠀⠀⠀⠀⣠⣿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⡿⢿⣿⣿⣧⠀⣰⣿⡟⣰⣿⣿⣷⡄⢸⣿⠋⢿⣿⣿⠀
⠀⠀⠘⢿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠉⡉⠀⠈⠁⠀⠀⠀⠐⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⣿⠃⠀⢿⣿⣿⣧⣿⡟⢿⡿⠿⣿⣿⣿⠀⠀⢰⣷⠀⢻⡇
⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣮⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣍⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⣿⠀⠀⢸⣿⣿⣿⣿⣀⣀⣠⣴⣿⣿⣿⠀⠀⠈⠉⠀⠈⠛
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣿⣿⣿⡆⠀⣀⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣠⣀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠉⢉⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡙⢿⠿⢿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠺⡿⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠈⣻⣋⣠⣾⣿⣿⠿⢿⠿⢷⡀⠀⠀⠙⢋⣉⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠠⣳⣃⠙⠀⢿⣿⡿⣿⣿⣁⣴⣶⣤⡄⠙⣿⣿⣯⣏⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣯⠀⠀⢰⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⡐⠈⣿⡄⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⠿⠋⢀⣾⡿⢋⣔⠜⣽⢿⣧⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠃⣤⡝⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⡿⠀⠀⠀⠛⠿⠛⠋⠉⠉⠀⠀⠀⢰⠀⠀⢹⣿⣤⡀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠀⠀⠠⠃⡡⣊⠑⣡⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠻⣿⠀⠛⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣇⡀⠈⢿⣿⢷⣀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⢐⡵⣞⣁⢐⣿⣍⣻⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⣠⢹⣿⣿⣎⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠃⠀⢸⣿⣼⣿⠀⢸⣿⢹⣿⠀⠀⣾⣏⢹⣷⢀⣿⢿⡿⢻⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⣇⡄⠀⢸⣿⣿⣿⢸⢸⣿⢸⣿⠀⠀⣿⡏⢀⣤⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⢻⣆⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⡹⠷⠾⣏⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⢒⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣷⣮⡛
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⠯⠴⠤⠀⠤⠠⠤⠀⠤⡁⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⡠⠎⠀⠀⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⢼⣿⠛⠃⠀⠀⠀⢀⣀⣀⣀⣀⣄⣀⣀⣀⣤⣤⣄⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⣴⣶⣶⣾⡇⣠⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣧⡀⠀⠀⠀⠀⢀⣿⣯⡡⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠬⣿⣿⡗⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠙⣿⠝⠿⠿⠛⠻⢿⡧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⣼⣿⠏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠢⣀⣿⣇⠀⠀⠀⠀⠀⢀⡄⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄⣤⠀⣀⡀⢀⡀⠀⠀⠀⠀⡿⢅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠀⣿⣿⠀⠀⠀⢠⣶⣿⣿⣾⣿⣷⣴⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣟⣀⢻⠁⣻⠇⣺⠇⠀⠀⠀⠀⠻⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠛⠁⣻⣶⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⣠⣶
⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠟⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠉⠉⠁⠉⠉⠉⠻⣿⣿⣿⣿⡿⠋⠀⡀⠀⠀⢀⣀⣉⣹⣷⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⡁⠀⠀⣿⣿⣿
⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⣼⣯⣀⠀⠂⠀⠀⡀⠀⠀⠈⣿⣿⣿⠇⠁⠀⠀⠀⣈⠙⢻⣿⣿⣿⡄⠀⢸⣿⣿⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⣽⣿⣿
⣿⣆⠀⢠⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣷⠀⣿⣿⣯⣤⣤⣤⣤⣤⣤⣀⣀⣿⣿⣿⣿⣧⣶⣶⣶⣿⣷⣾⣿⣿⣿⡇⢸⣿⡏⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿
⠟⠛⠀⠋⡋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⢠⣾⡿⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⣾⣿⣶⣶⣿⣶⣶⡄⠀⠲⠷⠶⠶⠒⠶⠀⠀⠀⠀⢀⣿⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⢿⣿⣿⣿⡀⢰⣿⡿⢁⣿⣿⣿⣦⣰⣿⠏⡸⢿⣿⣇
⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣧⣦⠄⣤⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⡇⠀⢸⣿⣿⣿⣿⡟⠱⠜⠛⢿⣿⣿⠀⠀⠀⣿⡄⠉⢟
⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣉⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣸⣿⣿⡇⠀⠈⣿⣿⣿⣿⣀⣀⣀⣠⣿⣿⣿⡀⠀⠀⠉⠁⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣷⠀⣀⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣀⣄⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣄⣀⠀⠀⣀⡀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣿⣿⣿⡿⢻⣿⣿⣿⣿⣷⡙⢿⠿⢿⣿⣿⣿⣿⣿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠲⣿⡻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣟⣁⣠⣿⣿⣿⣿⠿⢷⡄⠀⠀⠙⣫⣹⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⢀⢪⣇⠘⠀⠙⠿⣿⣿⣿⣇⣤⣶⣦⣄⠙⣿⣿⣟⣽⡙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣯⡄⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠃⡰⠈⣿⣄⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣾⡿⢋⢔⠵⣹⢾⣷⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠋⣠⡜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠃⠀⠀⠈⠻⠿⠛⠛⠉⠉⠉⠀⢰⠁⠀⢹⣿⣦⡀⠀⠀⠀⠀⠉⠋⠋⠉⠁⠀⠀⠠⠋⡠⣒⠑⣩⣴⣾⣿⣿⠟⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣇⡀⠈⢿⣿⢷⣀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⢐⡍⣞⣉⢐⣿⣯⣹⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⢠⣸⣿⣿⣧⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠁⠀⢸⣿⣽⣿⠀⢸⣿⢹⣿⠀⠀⣾⣟⢹⣷⢀⣿⢿⡿⢻⣯⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⣆⠀⣿⣇⡄⠀⢸⣿⣿⣿⢸⢸⣿⢸⣿⠈⠀⣿⡟⢀⣤⢸⣿⣺⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⢻⣆⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⣏⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⢒⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣦⡝
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⠯⠴⠤⠀⠤⠠⠤⠠⠬⡁⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡠⠔⠁⠀⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢼⣿⠛⠃⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣤⣀⡀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⣠⣦⣄⡀⠀⠀⠀⠀⢠⣶⣶⣶⣿⢠⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣄⠀⠀⠀⠀⢀⣿⣯⣡⠂⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠰⢿⣿⣿⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠘⢿⡞⠻⠿⠛⠛⢿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⣼⣿⠏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠢⢄⣿⣿⠀⠀⠀⠀⠀⢀⣄⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⣠⡀⢀⡀⢀⡀⠀⠀⠀⠀⡿⢅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⣿⣿⠀⠀⠀⢀⣶⣾⣿⣷⣿⣷⣶⣿⣷⢶⠀⠀⠀⠀⠀⢰⠀⠀
⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣟⣁⠻⠃⣻⠇⢸⠟⠀⠀⠀⠀⠻⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋⠉⠁⢸⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣤⡀⠀⠀⢠⣶
⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠈⠀⠉⠉⠉⠛⢿⣿⣿⣿⡿⠋⡀⡀⠀⠀⢀⣀⣉⣹⣿⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣉⠀⠀⢼⣿⣿
⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣸⣯⣀⠄⠂⠀⠁⣀⠀⠀⠀⣿⣿⣿⡇⠈⠉⠀⠀⢩⡙⠻⣿⣿⣿⡆⠀⣸⣿⣿⣦⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿
⣿⣆⠀⢠⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣷⠀⣿⣿⣯⣤⣦⣤⣤⣤⣤⢀⣀⣿⣿⣿⣿⣧⣶⣶⣶⣾⣷⣾⣿⣿⣿⣧⢸⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿
⣿⡟⠁⠈⢛⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⢠⣿⡟⢹⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿
⣿⠇⠀⣶⣿⣶⣶⣿⣶⣶⣄⠀⠲⠾⠿⠶⠖⠶⠀⠀⠀⠀⠀⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠿⣿⣿⣿⡄⢀⣿⣿⢰⣿⣿⣿⣧⡤⣿⠏⢸⠿⣿⣿
⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣧⣦⡄⣴⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⠁⠀⠸⣿⣿⣿⣿⡿⠻⣿⠛⢿⣿⣿⡇⠀⠀⣾⡇⠈⢻
⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣥⡈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣉⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣥⣀⣠⣤⣾⣿⣿⡇⠀⠀⠉⠁⠀⠈
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⣾⣿⣿⡎⠂⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠰⣿⣿⣿⣧⣀⣤⣾⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣆⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢸⣿⠛⠁⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣤⣀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠺⣿⣿⡄⠀⠀⠀⢀⣶⣷⡿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠂⠐⠻⡟⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⠁⠀⣀⣀⣼⣿⣿⢷⡌⠀⠀⠝⣋⣩⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⢀⢌⣖⡈⠀⠈⠛⢻⣿⣿⣄⣤⣶⣦⣄⠉⢿⣿⣿⣽⣉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⣅⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⡿⡿⠈⣷⣄⠀⠀⠛⢻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣼⣿⢟⢔⡵⢻⣾⣷⡄⠀⠀⠀⠈⠿⣿⣿⣿⣿⠏⣠⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⠟⠀⠀⠀⠹⠿⠿⠟⠛⠛⠉⠉⠀⡇⠀⢸⣿⣧⣀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠀⠀⠀⠞⡨⢔⠑⢋⣴⣾⣿⣿⠟⠀⠀⠀⠀⠀⠈⠙⠛⢿⡇⠙⠃⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣇⡀⠀⢿⣿⢿⣄⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⢐⡈⣶⣋⢐⡿⣿⣻⠏⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢠⣼⣿⣿⣷⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡏⠃⠀⢸⣿⣾⣿⢠⢸⣿⢹⣿⠀⠀⣾⣟⢹⣷⢀⣿⢿⡿⢿⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⡄⠀⢸⣿⣿⣿⢸⣸⣿⢸⣿⠀⠀⣿⡟⢀⣤⢸⣿⣾⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠻⣆⠸⠿⠸⠿⠶⠘⠿⠾⠟⠀⠀⠹⠷⠾⣏⠾⠏⠹⠿⠘⠿⠾⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⣦⣝
⠀⠸⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡯⡠⠤⡀⠤⡀⠄⡠⡤⡁⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠴⠁⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⢸⣿⠛⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣀⣤⣤⣄⡀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣶⣤⡄⠀⠀⢀⠀⢰⣶⣶⣶⣿⠀⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠉⢻⣿⣄⠀⠀⠀⠀⠀⣿⣯⣡⠂⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠸⢽⣿⣿⠀⠀⠀⠀⠻⢿⣿⠟⠀⠀⠈⢿⡏⠛⠿⠛⠛⢻⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⣼⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⢄⣹⣿⡀⠀⠀⠀⠀⠀⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀
⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⡄⣀⠀⢀⡀⢀⡀⠀⠀⠀⠀⡿⢇⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⢹⣿⡇⠀⠀⠀⣴⣾⣿⣿⣿⣿⣦⣾⣷⣶⠂⠀⠀⠀⠀⢠⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃⠻⠇⢸⡇⢸⡷⠀⠀⠀⠀⢸⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⡇⠀⠀⠀⠛⠛⠻⠛⠛⠛⠛⠙⡉⠀⢰⣿⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣿⣿⡇⠀⠀⢀⣴
⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠿⠛⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠉⠉⠀⠈⠉⠉⠙⢿⣿⣿⣿⣿⠏⠁⡀⠀⠀⢀⣀⣈⣹⣿⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣅⠀⠀⢸⣿⣿
⣿⡀⠀⠸⣿⣿⣿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣸⣿⣀⡄⠂⠀⠀⢀⠀⠀⠀⢿⣿⣿⡗⠀⠀⠀⠀⢨⡉⠻⣿⣿⣿⡇⠀⣸⣿⣿⣇⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿
⣿⣧⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⣶⡀⣿⣿⣷⣶⣶⣤⣤⣥⣤⣀⣀⣼⣿⣿⣷⣧⣶⣶⣶⣾⣿⣶⣿⣿⣿⣿⠸⣷⡏⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⢿⣿⣧⡘⢙⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⢠⣿⡟⢰⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿
⠐⣿⣿⣷⣿⣷⣶⣿⣷⣶⣆⠀⠀⠶⣶⡶⠶⢶⠀⠀⠀⠀⠀⣹⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠿⢿⣿⣿⡇⢀⣾⣿⢠⣿⣿⣿⣷⣆⢿⡟⠀⠻⢿⣿
⠀⠀⠀⠘⢿⣿⣿⠿⣿⣿⣿⣿⠄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣿⣿⡇⠀⠀⣿⣿⣿⣾⣿⠻⣿⠟⢿⣿⣿⡇⠀⠀⣸⣷⠀⢹
⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣉⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣇⠀⠀⢻⣿⣿⣿⣧⣤⣬⣤⣾⣿⣿⡇⠀⠀⠉⠉⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⡀⠀⠀⠀⢴⣿⣿⡾⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣤⣤⣾⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣶⣿⣇⣠⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⠟⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⠟⠀⠀⠀⠀⠘⢿⣿⣿⡝⢿⡿⣿⣿⣿⣿⣿⣿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠻⡿⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⢿⡆⠁⢀⠹⣛⣹⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠜⡜⡈⠀⠈⠛⠿⣿⣿⣦⣴⣶⣶⣤⠈⢹⣿⣿⣽⣍⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣧⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⠂⢿⣆⠀⠀⠙⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣸⣿⢟⡡⡪⢫⡾⣿⣄⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⢠⣄⠙⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⠟⠀⠀⠈⠟⠿⠟⠛⠋⠉⠉⠉⠀⡇⠀⢸⣿⣧⣄⠀⠀⠀⠀⠈⠛⠛⠉⠉⠀⠀⠀⠞⢁⢔⡋⢊⣤⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠛⢻⣇⠘⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣧⡀⠀⢿⣿⣿⣔⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⡊⣷⣋⢐⡺⣿⣻⠟⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢠⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⣿⡇⠀⣾⡏⣿⡇⢸⣏⠹⠇⠉⣿⡟⠃⠀⢸⣿⣻⣿⢀⢸⣿⢹⣿⢀⠀⣾⡟⢹⣿⢀⣿⣿⡿⢿⣿⠹⠇⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⣿⡇⠀⣿⡇⣿⡇⢈⡛⢿⡆⠀⣿⡇⣀⠀⢸⣿⢻⣿⢸⣸⣿⢸⣿⠘⠀⣿⡗⢀⣠⢸⣿⣿⣇⢈⣙⢿⣦⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⠷⠆⠻⠷⠿⠃⠸⠷⠾⠏⠀⠿⠇⠻⣆⠸⠿⠸⠿⠶⢘⠿⠾⠟⠀⠀⠹⠷⠾⣟⠾⠏⠹⠿⠘⠿⠼⠟⠸⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣦⣝
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣶⡠⠤⡀⠤⡀⡤⣀⡤⣁⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠠⠊⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠀⠀⠀⠀⣀⣀⣀⣀⣠⣀⣀⣀⣤⣤⣤⣀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⣴⣤⣄⠀⠀⠀⡀⢠⣶⣾⣿⣿⣇⣤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠙⠛⠻⣿⣧⡀⠀⠀⠀⠀⣿⣿⣷⠂⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠠⢿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⠄⠀⠈⢻⣿⠻⣿⡿⠛⠿⣿⡇⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡇⠀⠀⠀⠀⠙⠿⣿⠀⠀⠀⣸⣿⡟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⢦⣸⣿⡇⠀⠀⠀⠀⠀⣹⡀⢀⣤⠀⠀⡄⠀⠀⠀⠀⠀⠙⠁⠀⠀
⠀⠀⠀⠀⣠⣄⣠⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡀⢸⣿⡇⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⣾⣿⣶⡦⠀⢀⡀⠀⠀⠄⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣶⡆⢰⡆⢰⣦⠀⠀⠀⠀⢹⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⢸⣿⡇⠀⠀⠀⠙⠛⠻⠟⠛⠟⢛⠉⠛⠉⢙⣶⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣬⣧⣼⣇⣾⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⢸⣿⣿⣿⠀⠀⡀⡀
⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣟⣁⣀⠀⢀⣀⣀⣈⣹⣿⡆⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣠⣿⣿⣯⡀⠀⢸⣿⣿
⣿⡇⠀⠠⣿⠿⠿⠙⠿⢿⡇⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⣰⠄⠀⣸⣿⣤⡴⠒⠀⠀⢀⠀⠀⠀⢿⣿⣿⡿⠈⠋⠀⠀⢈⡉⠻⣿⣿⣿⣇⠀⠀⣿⣿⡟⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿
⢻⣧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣾⡄⣿⣿⣿⣶⣦⣤⣤⣭⣤⣄⣀⣼⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣿⣿⣿⣿⠀⣿⣯⠉⣀⣶⣿⣿⣿⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿
⣾⣿⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣿⡟⢁⣿⣿⣿⠿⣿⣿⡿⣿⣿⣿
⢿⣿⠿⠀⢠⣶⣶⣾⣷⣶⣦⠀⠀⣀⣤⣤⣄⣀⡄⠀⠀⠀⠀⢹⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿⣇⣾⣿⣿⣿⣿⡿⠟⠁⣻⢿⣿
⠀⠀⠀⠀⠻⣿⣿⠟⣿⣿⣿⣿⡄⣀⠉⡉⠉⠈⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⡿⠀⣿⣿⣿⣧⣿⡿⢿⡿⠿⣿⣿⣿⠀⠀⢰⣷⠀⢻
⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡉⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣙⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⣸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣅⣀⣁⣴⣿⣿⣟⠀⠀⠉⠉⠀⠀
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⡄⠀⠀⠀⠀⣴⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⠀⣨⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣉⣀⣀⣈⣉⣉⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠂⠺⢼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢈⣿⣋⣤⣾⣿⣿⡿⠿⣿⣎⠿⢤⣭⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⡰⣷⠊⠋⠈⠿⢿⢿⣿⣿⣀⣴⣶⣤⡘⢻⣿⣿⢿⡛⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠿⠁⢀⠊⢿⣧⡀⠉⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣰⣿⡿⣣⢪⢞⣿⣿⣄⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⢁⣄⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡿⠀⠀⠈⠛⠛⠛⠋⠋⠉⠀⠀⠀⡇⠀⢸⣿⣷⣄⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⡼⢋⡭⠊⠚⣡⣼⣷⣿⣿⠂⠀⠀⠀⠀⠈⠙⠛⠿⡇⠸⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢵⠞⠁⣾⣟⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⢠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⢿⣿⣿⣷⡀⢀⡀⠀⣤⡄⠀⠀⢀⠘⠉⠁⣴⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣶⣿⠃⠀⠀⠃⢀⣤⣽⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⡦⠀⠀⠘⢿⣿⣿⣿⣿⡿⠋⠀⠀⠠⠄⠛⠺⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉
⠘⣿⣿⣿⣿⡿⢿⢿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⡓⠠⠄⠀⠈⠉⠉⠀⠀⠀⠠⠌⠀⠾⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣍
⠀⠾⣿⣿⣿⣿⠿⢷⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣞⣢⣄⡀⣈⣀⣀⡀⣀⡒⡲⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣴⠋⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠀⠀⠀⠀⣀⣀⣀⣀⣠⣀⣀⣀⣤⣤⣤⣀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⣴⣤⣀⠀⠀⠀⠀⢠⣶⣾⣿⣿⡇⣤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠙⠛⠻⣿⣧⡀⠀⠀⠀⠀⣿⣿⣷⠂⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⠄⠀⠈⠻⣿⠻⢿⠿⠛⠻⣿⡇⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡆⠀⠀⠀⠀⠙⠿⣿⠂⠀⠀⣸⣿⡟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⢤⣸⣿⡇⠀⠀⠀⠀⠀⣩⡀⠀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠙⠁⠀⠀
⠀⠀⠀⠀⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⢸⣿⡇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⣾⣿⣶⡆⠀⣀⡀⠀⠀⡄⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣶⡆⢴⡦⢰⣦⠀⠀⠀⠀⢹⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⢸⣿⡇⠀⠀⠀⠹⠟⠻⠟⠛⠛⠛⢋⠛⠉⢹⣾⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣬⣧⣼⣇⣼⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢸⣿⣿⣿⠀⠀⡀⣠
⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠉⠉⠉⠉⠉⠻⢿⣿⣿⣿⣿⣟⣁⣀⠀⢀⣀⣀⢈⣹⣿⡆⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣿⣿⣯⡉⠀⢰⣿⣿
⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⠀⠀⣸⣿⣠⡤⠒⠉⠁⢀⠀⠀⠀⢿⣿⣿⡿⠀⠉⠁⠀⢩⡙⠻⣿⣿⣿⣧⠀⠀⣿⣿⠇⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿
⢻⣧⠀⠀⠋⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣶⡀⣿⣿⣿⣧⣤⣄⣤⣭⣤⣀⣀⣾⣿⣿⣿⣿⣴⣶⣶⣾⣿⣶⣿⣿⣿⣿⠀⣿⣿⢁⣰⣾⣿⣿⡇⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿
⣸⣿⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⣾⡿⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠘⠋⠁⠀⣠⣶⣤⣾⣷⣶⣆⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢻⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣇⠀⣰⣿⣇⣼⣿⣿⣿⣶⣿⡿⠀⣿⣿⣿
⠀⠀⠀⠀⠙⣿⣿⠟⣿⣿⣿⣿⡉⡉⠉⡛⠉⠉⠁⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⡏⠈⣿⣿⣿⣧⣿⡿⢿⡿⠿⣿⣿⣿⠀⠀⢰⣷⠈⢿
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡁⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣛⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⣿⡇⠀⢸⣿⣿⣿⣿⣅⣈⣁⣴⣿⣿⣟⠀⠀⠉⠋⠀⠈
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⡆⠀⠀⠀⠀⣴⣤⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⣿⣿⣿⣇⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⢉⣉⣉⣉⣛⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠀⠲⢼⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⠙⣿⣋⣤⣿⣿⣿⡿⣿⣿⣌⠩⣫⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⡰⣳⠌⠃⠈⠿⢿⢿⣿⣿⣁⣠⣶⣤⠘⢿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣯⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠟⠀⢀⠊⣿⣆⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣿⡿⢃⢐⢞⣿⣿⣄⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⢀⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡿⠀⠀⠘⠿⠿⠛⠛⠋⠉⠀⠀⠀⡆⠀⢸⣿⣧⡀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠀⡼⠛⡩⠞⠕⣡⣼⣷⣿⣿⠆⠀⠀⠀⠀⠈⠙⠻⠿⡇⠸⠟⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⢭⠞⠁⢴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⢀⣀⣼⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠘⣿⣿⣿⣧⡀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠉⠀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣤⣿⠃⠀⠠⠃⠀⣀⣩⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠹⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠄⠛⠺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠲⠠⠀⠈⠉⠉⠉⠀⠀⠀⠀⠄⠠⢶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣝
⠀⠾⣿⣿⣿⣿⠿⢷⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣤⢠⣄⠀⢀⠀⢀⠀⢀⠒⡠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣤⠏⠀⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢼⣿⡛⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⣴⣤⣀⠀⠀⠀⠀⢀⣶⣶⣿⣿⡇⣠⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠙⠋⠻⣿⣇⡀⠀⠀⠀⠀⣿⣿⡷⠂⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠠⢽⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⠄⠀⠈⢻⣿⠻⢿⠟⠛⠻⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⡆⠀⠀⠀⠀⠙⠿⣿⠂⠀⠀⣼⣿⡏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⠦⣸⣿⡇⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠁⠀⠀
⠀⠀⠀⠀⣤⣤⣤⣄⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡀⢸⣿⡇⠀⠀⠀⣰⣾⣿⣿⣾⣿⣦⣾⣿⣶⣦⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⣶⡆⢶⡆⢰⣦⠀⠀⠀⠀⠷⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⢸⣿⡇⠀⠀⠀⠹⠟⠻⠿⠛⠛⠛⠛⠛⠁⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣼⣧⣼⣃⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣠⠀⠀⡀⣤
⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣟⣁⣀⠀⠀⣀⣀⢈⣹⣿⡄⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡁⠀⢸⣿⣿
⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⡤⠀⠀⣸⣿⣤⡤⠒⠀⠀⣀⠀⠀⠀⣿⣿⣿⡟⠈⠋⠀⠀⢩⡙⠻⣿⣿⣿⣇⠀⠀⣿⣿⠃⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣆⠈⣿⣿
⢹⡇⠀⠈⢻⣿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣶⠀⣿⣿⣿⣦⣤⣄⣤⣥⣤⣀⣀⣿⣿⣿⣷⣷⣴⣶⣶⣾⣷⣶⣿⣿⣿⣿⠠⣿⣯⣡⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿
⣾⣷⡄⠀⠀⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⣼⣿⢟⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⡟⠋⠁⠀⣰⣶⣤⣾⣷⣶⣆⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢿⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠀⣼⣿⡟⣾⣿⣿⣿⣶⣿⠿⠀⢿⣿⣿
⠀⠀⠀⠀⠙⣿⣿⠻⣿⣿⣿⣿⣉⡉⠉⡋⠉⠙⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⠀⠈⣿⣿⣿⣶⣿⠟⢻⡿⠻⣿⣿⣿⠀⠀⢰⣷⠈⢻
⠀⠀⣀⣰⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣛⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣀⣀⣀⣴⣿⣿⣟⠀⠀⠙⠋⠀⠈
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡆⠀⠀⠀⠀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢸⣿⣿⣿⡀⣀⣸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣆⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠈⠉⠉⢉⣉⣙⣛⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠀⠰⣿⡟⢻⣿⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢹⣿⣋⣤⣿⣿⣿⡿⠿⢿⡎⠽⢈⡿⣿⣿⣿⣿⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡰⣵⠈⠃⠉⠻⠿⢿⣿⣯⣀⣴⣶⣤⠘⢿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣏⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠟⠁⢀⠈⣿⡆⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣰⣿⡿⢣⢜⢞⣿⣿⣄⠀⠀⠀⠉⠹⣿⣿⣿⣿⡟⢠⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡿⠀⠀⠘⠿⠿⠟⠛⠋⠉⠀⠀⠀⡇⠀⢹⣿⣆⡀⠀⠀⠀⠉⠛⠻⠛⠛⠛⠋⠉⠀⡼⠛⡩⠞⠝⣡⣼⣷⣿⣿⠂⠀⠀⠀⠀⠈⠙⠻⢿⡇⠻⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⣭⠞⠁⢼⣟⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⢀⣀⣿⣿⣿⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠘⣿⣿⣿⣦⡀⢀⠀⠀⣀⠀⠀⠀⠀⠘⠉⠀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⣴⡿⠀⠀⠠⠃⢀⣀⣨⣯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠹⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠻⠺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛
⠘⣿⣿⣿⣿⡿⠿⢿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠦⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠄⠠⢶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣙
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠏⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⣿⣟⠛⠁⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⢀⣴⣤⡀⠀⠀⠀⠀⢠⣶⣶⣷⣿⡇⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠙⠻⣿⣇⡀⠀⠀⠀⢸⣿⣽⡖⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠰⢽⣿⣿⡇⠀⠀⠀⠺⣿⣿⠿⠀⠀⠈⢻⡏⠻⢿⠿⠛⠻⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡆⠀⠀⠀⠀⠙⠿⡟⠀⠀⢀⣿⣿⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⢄⣹⣿⡇⠀⠀⠀⠀⠀⣠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⢿⣿⡇⠀⠀⠀⣴⣾⣿⣷⣿⣿⣦⣾⣷⣶⡆⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⢠⣄⢀⣤⠀⣤⠀⠀⠀⠀⠈⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⡇⠀⠀⠀⠻⠛⠻⠿⠛⠛⠛⠙⠋⢸⣿⣶⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣏⣘⢿⢈⣿⢈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⣴
⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠋⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⠋⢀⡀⠀⢀⣀⡀⢉⣹⣿⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⡀⠀⢸⣿⣿
⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⠿⠿⠿⠀⠀⠀⠀⠀⢀⡤⠀⠀⣿⣇⣀⠔⠂⠈⠀⡀⠀⠀⠘⣿⣿⣿⡇⠈⠁⠀⠀⢉⠛⢻⣿⣿⣿⡆⠀⢸⣿⠟⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣆⠈⣿⣿
⠀⠀⠀⣿⣿⡿⠋⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣆⢸⣿⣿⣧⣤⣄⣀⣠⣤⣄⣀⣀⣿⣿⣿⣷⣧⣤⣶⣶⣿⣷⣶⣿⣿⣿⣷⢰⣷⣇⣤⣤⣶⣿⣿⡇⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿
⣠⣄⠀⠈⠛⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⢀⣼⣿⢯⣿⣿⡿⠿⣿⣛⣿⣿⣿⣿
⢿⣿⡗⢀⣿⣶⣶⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⣿⣿⣿⣿⣿⣿⡄⠀⣾⣿⠃⣾⣿⣿⣿⣿⣿⠿⠀⠿⣿⣿
⠀⠀⠀⠈⢻⣿⡿⢻⣿⣿⠿⠷⠶⡿⣿⡶⠶⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⠏⠈⣿⣿⣿⣼⡿⠋⠿⠟⢿⣿⣿⣏⠀⠀⣴⡇⠈⢻
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣦⣤⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣙⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣼⣿⣿⠀⠀⢿⣿⣿⣿⣧⣀⣀⣀⣾⣿⣿⡟⠀⠀⠙⠃⠀⠀
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣆⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠀⠀⠈⠉⠉⠉⢉⣙⣛⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀⠦⣾⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⣿⣿⡏⢀⣹⣿⣿⣿⣿⣧⡘⡅⢸⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡰⡵⠙⠏⠙⢿⡿⣿⣿⣿⣠⣴⣦⣄⠘⠻⣿⣿⢙⠛⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡋⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣷⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣴⣿⡿⣠⣪⢞⣿⣧⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⢀⣄⠛⢿⣿⣷⣼⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠇⠀⠀⠘⠿⠿⠿⠟⠛⠛⠛⠉⢸⠁⠀⣿⣷⣄⠀⠀⠉⠉⠙⠻⠿⠿⠛⠛⠋⠁⢀⡾⠋⡩⠪⠟⣡⣼⣷⣿⣿⠀⠀⠀⠀⠀⠈⠛⠻⢿⡇⢿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣭⠞⠠⢼⣟⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢀⣠⣿⣿⣿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢀⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠺⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣤⣄⣄⣠⡷⠀⠀⠠⠁⢀⣀⣼⣭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠐⠯⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠤⠀⠀⠉⠉⠁⠁⠀⠀⠀⠀⡀⠐⣞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡛
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠋⠐⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⣿⣟⠛⠁⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⢀⣴⣤⡀⠀⠀⠀⠀⢀⣶⣶⣶⣾⡆⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠙⠙⠻⣿⣇⠀⠀⠀⠀⢸⣿⣿⡖⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠰⢽⣿⣿⡇⠀⠀⠀⠺⣿⣿⡿⠀⠀⠈⢻⡞⠻⢿⠿⠛⠻⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡆⠀⠀⠀⠀⠙⠿⡟⠀⠀⢀⣿⣿⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⢄⣹⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⢿⣿⡇⠀⠀⠀⣴⣾⣿⣷⣾⣿⣦⣾⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⢠⣄⢀⣤⠀⣤⡀⠀⠀⠀⠈⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⡇⠀⠀⠀⠻⠛⠻⠟⠛⠛⠛⠙⠋⢸⣿⣶⡄⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣏⣘⢿⢈⣿⢈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡄⠀⠀⠀⣴
⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠋⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⠋⠀⡀⠀⢀⣀⡀⢉⣹⣿⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⡀⠀⢸⣿⣿
⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠟⠻⠿⠿⠿⠀⠀⠀⠀⠀⢀⡤⠀⠀⣿⣇⣠⠔⠂⠀⠀⡀⠀⠀⠘⣿⣿⣿⡇⠈⠁⠀⠀⢉⠛⢻⣿⣿⣿⡆⠀⣸⣿⠟⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣆⠈⣿⣿
⠈⠀⠀⢿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣆⢸⣿⣿⣧⣤⣤⣀⣠⣤⣄⢀⣠⣿⣿⣿⣷⣧⣤⣶⣶⣿⣷⣾⣿⣿⣿⣷⢰⣷⣇⣤⣤⣶⣿⣿⡇⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿
⣠⣄⠀⠈⠛⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⢀⣼⣿⢯⣿⣿⡿⠿⣿⣿⡿⣿⣿⣿
⢿⣿⡗⢀⣿⣶⣶⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⣿⣿⣿⣿⣿⣿⡄⠀⣾⣿⠃⣾⣿⣿⣿⣿⣿⠿⠀⠿⣿⣿
⠀⠀⠀⠀⠻⣿⡿⢻⣿⣿⠿⠷⠶⠶⣿⣷⠶⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⠏⠈⣿⣿⣿⣾⡿⠛⠻⠟⢿⣿⣿⣏⠀⠀⣴⡇⠈⢻
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣦⣤⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣊⣙⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣼⣿⣿⠀⠀⣿⣿⣿⣿⣧⣀⣀⣀⣾⣿⣿⡏⠀⠀⠙⠋⠀⠀
⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣆⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠀⠀⠈⠉⠉⠉⢉⣙⣛⣻⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⣿⣿⣿⣿⠟⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀⠦⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⣻⣿⡏⢀⣹⣿⣿⣿⣿⣧⡘⢅⣸⣿⣟⣻⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡐⡵⠘⠏⠘⢿⡿⣿⣿⣿⣠⣴⣦⣄⠘⢻⣿⣿⢙⠛⢳⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡏⠁⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣷⡀⠙⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣴⣿⡿⣠⣪⢞⣿⣷⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⢀⣄⠛⢿⣿⣷⣾⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡏⠀⠀⠘⠿⠿⠿⠟⠛⠛⠛⠋⢸⠁⠀⣿⣷⣄⠀⠀⠉⠉⠙⠻⠿⠿⠛⠛⠋⠁⢀⡾⠛⡩⠪⠟⣡⣼⣷⣿⣿⠀⠀⠀⠀⠀⠈⠛⠻⣿⡇⢿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣭⠞⠠⢾⣿⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢀⡀⣿⣿⣿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⢹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣤⣤⣤⣠⡿⠀⠀⠠⠁⢀⣀⣽⣭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠐⠿⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠤⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀⠐⣞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡙
⠀⠚⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠊⠐⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⢰⣿⡿⠛⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⢀⣴⣶⣶⣾⡅⣠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠛⠙⠻⣿⣆⠀⠀⠀⠀⣼⣿⣿⡅⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠠⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠈⢿⡟⠻⣿⠿⠛⠿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⡆⠀⠀⠀⠀⠹⣿⡿⠀⠀⢠⣿⡿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠢⣀⣿⣿⡆⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠀⣿⣿⡇⠀⠀⠀⣰⣾⣿⣷⣾⣿⣤⣾⣷⣴⡄⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠞⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⣾⣿⡇⠀⠀⠀⠻⠟⠻⠿⠛⠟⠛⢛⠟⠀⢲⣾⣷⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⣴⣆⣠⣆⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣸⣿⣿⣧⠀⠀⠀⣤
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⡟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠈⢉⣻⣧⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣿⣿⣏⡁⠀⢸⣿⣿
⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⡄⠀⢠⣿⣀⡠⠔⠒⠀⠀⠀⠀⠀⢹⣿⣿⣿⠇⠘⠈⠁⠈⠙⠻⢿⣿⣿⣿⡀⠀⢸⣿⡟⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣆⠈⣿⣿
⠀⠀⠀⣿⣿⡿⠛⠉⠉⠉⠛⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⡜⣰⡄⢸⣿⣿⣧⣤⣀⣀⣈⣀⡀⠀⣸⣿⣿⣿⣶⣤⣤⣤⣤⣿⣶⣾⣿⣿⣿⡇⢰⣿⣇⣠⣴⣾⣿⣿⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿
⠀⢀⡀⠛⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⢰⣿⠏⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿
⠀⣾⣿⣾⣷⣤⣴⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⣿⣿⣿⣿⣿⣿⡄⢀⣾⣿⢰⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿
⠀⠀⠁⠹⣿⣿⡟⢿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⠉⣿⣿⣷⣼⣿⠿⣿⡿⢿⣿⣿⡏⠀⠀⣴⡇⠈⢿
⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣶⣶⣷⠀⠀⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣙⢻⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣼⣿⣿⠀⠀⣿⣿⣿⣿⣇⡀⢈⣀⣾⣿⣿⡟⠀⠘⠛⠋⠀⠈
⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⡄⡀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠉⠉⠙⠛⠛⠉⠙⠛⢛⣻⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⠿⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠆⠀⠄⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠉⣿⣿⣋⣀⣿⣿⣿⣿⡿⣌⠛⠉⠻⣿⡿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡰⡤⠹⠁⠹⣿⡿⣿⣿⡟⢀⣠⣤⡀⠘⢿⣿⣿⠛⠻⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠿⣿⣿⣿⣿⣿⡉⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⠟⡀⢻⣧⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣴⣿⡿⣀⢮⢞⣷⣦⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⢀⡘⠿⣿⣿⣷⣼⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⠃⠀⠀⠹⠿⠿⠿⠛⠛⠛⠉⠀⢸⠀⠈⣿⣷⡀⠀⠈⠉⠉⠻⠿⡿⠿⠿⠿⠛⠉⢀⡼⠟⡫⢂⠕⣁⣽⣽⣿⣷⠀⠀⠀⠀⠀⠉⠛⠻⢿⡀⢾⡿⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢔⣨⠖⢠⣼⣿⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⣼⣿⣿⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⢻⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⢀⣴⣶⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣲⢶⣀⣸⡄⠀⠀⡀⠀⠀⢀⣾⣭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⡀⠰⡮⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⡀⠀⠉⠛⠉⠉⠁⠀⠀⢀⠀⠠⡔⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻
⠀⠺⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣤⡄⢀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠐⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⢠⣿⠿⠟⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡀⠀⣀⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⢀⣤⣴⣴⣼⣄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠛⠻⣿⣇⠀⠀⠀⠀⣼⣿⣯⡄⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠤⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⢷⡾⢻⣿⠿⠿⢿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣶⡆⠀⠀⠀⠀⠹⣿⡷⠀⠀⢠⣿⡿⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠢⡈⣿⣿⡆⠀⠀⠀⠀⠉⣉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠯⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠈⣿⣿⡇⠀⠀⠀⣠⣶⣿⣶⣾⣿⣤⣴⣷⣤⡄⠀⠀⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⣾⣿⡇⠀⠀⠀⠻⠿⠿⠿⠿⠿⣿⠛⠟⠉⢣⣴⣾⣷⠀⠀⠀⠀
⠀⠀⠀⣤⣠⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣧⣿⣧⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠉⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠛⣻⣇⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⢀⣿⣿⣛⠉⠀⢸⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⡏⠀⠀⠀⠀⠀⢠⡄⠀⢰⣿⠀⣀⠤⠐⠂⠀⠀⠀⠈⢻⣿⣿⣿⠇⠀⠈⠀⠀⠚⠿⣷⣿⣿⣿⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⡄⠘⣿⣿
⠀⠀⠀⣿⣿⡿⠋⠉⠉⠉⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡞⣰⡄⣸⣿⣿⣅⣀⣀⣀⣈⣀⠀⠀⢸⣿⣿⣿⣶⣤⣤⣤⣤⣿⣤⣼⣿⣿⣿⡇⢰⣾⣏⣠⣴⣶⣿⡇⠀⠀⠀⠀⠀⣠⣾⡿⣽⣿⣿⣿⣿⣿⣿⣠⣿⣿
⠀⠀⠀⠛⠋⠀⠀⡀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⣷⡿⠇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⢰⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠀⢰⣦⣤⣴⣿⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⡄⠀⣼⣿⢠⣾⣿⣿⣷⣾⣿⣿⠙⣿⣿⣿
⠀⠀⠀⠘⢿⣿⠟⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⡿⠉⠙⣿⣿⣷⣀⣿⡿⣿⡿⢿⣿⣿⡟⠉⠀⣴⡏⠹⣿
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⠛⢿⣵⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡀⠙⣁⣼⣿⣿⡟⠀⠚⠻⠃⠀⠙
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠀⣀⣴⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡄⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⢛⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠀⠄⢿⡏⢻⣿⣿⣿⣿⣷⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙⣿⣿⢋⣨⣿⣿⣿⣿⣷⡈⠃⠈⢿⣟⣿⡿⣿⣇⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡰⡤⠹⠀⠘⣿⣿⣿⣿⡏⢀⣠⣄⡀⠸⢿⣿⣿⠻⠿⢿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⡏⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⠟⠁⡀⢿⣄⠐⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣹⣿⡿⢀⢜⢼⣷⣆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⢀⡘⠿⣿⣿⣶⣼⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⠇⠀⠀⠙⠿⠿⠿⠛⠛⠋⠁⠀⢰⠀⠸⣿⣆⠀⠀⠉⠉⠛⠻⠿⡿⢿⠿⠿⠟⠋⢀⡴⠛⣫⢕⠕⢉⣸⣯⣿⣷⠀⠀⠀⠀⠀⠙⠻⢿⣿⡀⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠤⣪⠶⢀⣾⣿⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⣿⣿⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠈⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠉⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣉⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⠀⢠⡄⠀⠀⡠⠀⠀⠀⣺⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠠⣞⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿
⠘⣿⣿⣿⣿⡿⢿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢦⠀⠀⠈⠉⠛⠉⠉⠉⠀⠀⢀⠀⣠⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠺
⠀⠺⣿⣿⣿⣿⠷⢷⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⢠⣿⠿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⢀⣤⣤⣤⣼⡀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠛⠻⣿⣇⠀⠀⠀⠀⣼⣿⣯⡄⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠤⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⠀⠀⠐⢷⣾⢿⣿⣿⠿⢷⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣶⡆⠀⠀⠀⠀⠹⣿⡷⠀⠀⢠⣿⡿⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢦⡈⣿⣿⡆⠀⠀⠀⠈⠉⣉⠁⠀⠀⠀⠈⠃⠀⠈⠀⠀⠀⠻⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠯⡁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⣠⣴⣿⣦⣾⣷⣄⣴⣷⣄⣤⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠞⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣿⣿⡇⠀⠀⠀⢻⠿⢿⣿⠿⢿⡿⠻⠿⠉⢻⣤⣠⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⣠
⠀⠠⢠⣶⣦⣴⣶⣶⣷⣶⡆⢒⡔⣦⣠⣖⣀⠀⠠⠶⠶⣶⠀⠀⠀⠀⣿⠿⠛⠉⠙⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠉⠉⠙⠛⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⢀⣿⣿⣟⠋⠀⢰⣶⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⡀⠀⢸⣿⠀⢠⠤⠀⠂⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠉⠀⠐⠲⠿⣶⣿⣿⣿⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣿⣿⣿⣿⣷⡄⠘⣿⣿
⠀⠀⠘⠻⣿⡿⠛⠋⠉⠉⢹⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⡏⣰⡀⣾⣿⣿⣁⣀⢀⡀⣈⣀⠀⠀⢸⣿⣿⣷⣴⣀⣀⣤⣤⣧⣤⣽⣿⣿⣿⡆⣰⣾⡏⠁⣠⣤⣶⣷⠀⠀⠀⠀⠀⣀⣼⡿⣽⣿⣿⣿⣿⣿⣿⣠⣿⣿
⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣷⡿⠃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⡏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣤⣤⣴⣷⣤⣦⠀⠈⠉⠙⠛⠋⠃⠀⠀⠀⠀⠀⢻⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣷⡀⠀⣸⣿⢀⣶⣿⣿⣷⣶⣿⣿⢨⣿⣿⣇
⠀⠀⠀⠿⣿⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠉⠙⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⣼⡟⢿⣿
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⠻⢿⣥⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡃⠘⣃⣼⣿⣿⡟⠀⠚⠿⠇⠀⠻
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⠀⠀⠀⣀⣤⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣤⡀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠛⠛⠛⠛⠛⠛⠻⠛⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⡿⠿⠋⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⠀⠀⢿⡏⢻⣿⣿⣿⣿⣧⠀⠀⠀⠻⢿⣾⣿⣿⣿⣿⣼⣿⣿⣿⣯⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠛⣿⡿⢋⣸⣿⣿⣿⣿⣷⡈⠩⠙⢿⠟⢿⣿⣿⣏⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡰⣄⠻⠀⠸⣿⣿⣿⣿⡏⢀⣠⣄⡀⠻⢿⣿⣿⠻⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡋⠁⠀⣤⣾⣿⣿⣿⣿⣿⣿⠟⠀⡀⣿⡄⠐⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣽⣿⡿⢀⢜⢼⣷⣆⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠀⡘⢿⣿⣷⣦⣸⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡇⠀⠀⠻⢿⠿⠿⠛⠛⠋⠁⠀⡜⠀⢸⣿⣆⠀⠀⠋⠋⠛⠿⣿⣿⣿⡿⠿⠟⠋⠀⡼⠟⣋⢕⠵⢉⣾⣿⣿⣧⠀⠀⠀⠀⠀⠙⠿⢿⣿⡀⣿⣷⠀⢹⣿⣿⣿⣿⣿⣿⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠤⣪⡴⣀⣾⡿⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠁⢀⣾⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣮⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⣠⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⣠⡀⠀⠀⡰⠀⠀⠀⣾⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢤⠀⠀⠈⠋⠙⠋⠙⠉⠀⠀⠀⠀⢠⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠺⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠠⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢾⡿⠟⠃⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠛⠻⣿⣄⠀⠀⠀⠀⣿⣭⡁⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠤⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡧⠀⠀⠀⢦⡜⢿⣿⠿⠟⢠⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣴⡀⠀⠀⠀⠀⠙⢿⡇⠀⠀⣼⡿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⢄⠈⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡀⠨⣿⣿⡇⠀⠀⠀⣠⣴⣿⣶⣶⣷⣄⣴⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠿⠿⠿⠿⠿⠿⠟⠛⠟⠐⣷⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⣠
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣦⠀⠀⠀⠀⠀⢸⡿⠛⠉⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠉⠻⣿⡄⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠁⠀⢰⣶⣿
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣷⣿⣿⣿⣿⣄⡀⡤⠀⠀⣾⡇⠀⠠⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠐⠒⢷⣶⣿⣿⣇⠀⠀⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡄⠈⣿⣿
⠀⠀⣷⠀⠀⠂⠀⠀⠀⠀⢀⡟⣿⣯⣷⣯⠉⠛⠛⠛⠛⣻⢃⣦⢀⣿⣿⣇⣀⣀⠀⢀⢁⠀⠀⠀⣿⣿⣿⣧⣆⣀⣠⣤⣼⣧⣤⣿⣿⣿⣿⠀⣶⣼⠉⠋⢀⣠⣤⣶⣦⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣾⠛⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢻⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣼⣿⠙⣿⣿⡿⡿⣿⠿⣿⣿⣽⣿
⣷⠀⢀⢀⣤⣤⣶⣦⣴⡄⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠉⠉⣿⣿⣿⣿⣿⣧⠀⠀⣼⣿⠇⣴⣿⣿⣿⣿⣿⡗⠸⣿⣿⡄
⠁⠀⢸⣿⡿⠛⠙⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡟⢹⣿⣿⣆⢰⣿⠋⠀⠿⢿⣿⣿⡏⠀⠀⣼⠟⢻⣷
⠀⠀⣘⣿⣷⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣀⠙⠻⣯⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣿⣿⡇⠈⣿⣿⣿⣿⣇⠀⠀⣀⣼⣿⣿⠇⠀⠈⠛⠃⠀⠋
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣤⡀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣟⡈⠙⠋⠉⠉⠙⠛⠛⠛⠛⠛⠛⣛⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣧⣶⣿⣿⡿⠋⠀⣤⡟⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⡞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠰⡆⠀⠂⠀⠀⠀⠀⠀⠙⣿⣟⠻⠿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠄⠀⠀⢸⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠻⢧⣾⣿⣿⣿⣷⣸⣿⣿⣨⣭⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣆⠀⠀⠈⠛⠛⠿⣿⣟⣁⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢆⡄⠾⠇⢻⣿⣿⣿⣿⡟⠀⣠⣀⠀⠻⢿⣿⣟⠻⠿⢣⣿⣽⣿⣿⣿
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⡟⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣇⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢁⣾⣿⠇⡠⡢⢻⣲⣄⠀⠀⠉⠁⠈⢿⣷⣾⣿⣿⠇⠀⠘⢿⣯⣶⣄⢸⣿⣿⣿⣿⡟
⣿⣿⣾⣶⣶⣿⣿⣿⣶⣧⣴⣿⣿⣿⠟⠀⠀⠀⠈⠿⠿⠿⠟⠛⠛⠋⢉⠇⠀⢻⣷⡀⠀⠀⠈⠉⠙⠿⠿⡿⠿⠿⠛⠋⠀⢠⠊⢛⠥⠨⠊⣁⣿⣽⣿⡆⠀⠀⠀⠀⠈⠙⠛⢿⣿⠀⣾⡇⠀⢻⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣘⢿⡿⠦⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠠⠀⠵⠂⠠⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⣿⡟⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢰⣿⠙⣿⢸⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢺⣿⣇⣼⣿⡟⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣇⣿⡗⣾⡟⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⠿⢸⣿⢀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡯⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⠀⢸⣿⠈⠒⠂⠿⣧⡿⠇⠹⣧⣼⠟⢹⡿⢹⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠀⠉⠈⠛⠻⠿
⠘⣿⣿⣿⣿⡿⠿⠿⠿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠖
⠀⠘⣿⣿⣿⣿⠶⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⣿⡟⠛⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⣤⣴⣤⣤⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠉⢻⣿⣄⠀⠀⠀⢸⣿⣍⠐⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠬⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡧⠀⠀⠀⢶⡘⠻⣿⠟⠛⢶⣿⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣴⡀⠀⠀⠀⠀⠹⠿⠇⠀⢀⣾⡟⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⠄⢘⣿⣿⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣤⣾⣿⣦⣾⣷⣄⣴⣦⣀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠛⠛⠟⢹⣦⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⣠
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣆⠀⠀⠀⠀⠀⣼⡟⠛⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠁⠀⠉⠉⢻⣿⡀⠀⠀⢸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣍⠀⠀⢸⣾⣿
⢈⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣾⡄⠈⠛⠛⠛⠀⢀⡄⠀⢀⣿⡃⠀⠠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠇⠀⠀⠀⠀⠐⠒⢷⣾⣿⣿⡇⠀⠀⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡄⠈⣿⣿
⠸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣦⣤⣴⣶⣿⢰⡆⢸⣿⣿⣅⣀⣀⣀⣀⡁⠀⠀⠀⣿⣿⣿⣶⣆⣤⣠⣤⣾⣦⣤⣿⣿⣿⣿⠀⣶⣿⠉⠉⣀⣤⣶⣶⡄⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿
⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣇⠈⠉⠙⠋⠋⢻⡿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⠟⣿⣿⡿⠿⣿⠿⢿⣿⣽⣿
⣿⣿⣄⣠⣤⣤⣾⣦⣴⡄⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠉⠙⣿⣿⣿⣿⣿⣧⠀⢀⣾⣿⠏⣴⣿⣿⣿⣿⣿⡟⠸⣿⣿⡄
⠉⠉⢹⣿⡛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⣿⣿⠋⢹⣿⣿⣆⣸⡿⠋⠀⠻⢿⣿⣿⡏⠀⠀⣴⠉⢻⣷
⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠙⠻⣥⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⣼⣿⣿⠀⠈⣿⣿⣿⣿⣇⠀⢀⣠⣾⣿⣿⠃⠀⠊⠛⠁⠀⠁
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣯⡈⠙⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⣷⣾⣿⣿⠿⠉⠀⣤⡽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡾⠂⠀⠀⠀⠀⠀⢶⣾⡜⢿⣿⡿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⠀⠀⣿⡟⢿⣿⣿⣿⣿⣇⠀⠀⠀⠻⣧⣿⣿⣿⣿⣷⣸⣿⣿⣨⣭⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⡆⠀⠀⠘⠛⠻⠿⢿⣟⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⣣⠌⠻⠃⠸⣿⣿⣿⣿⡋⢀⣤⣄⠀⠻⢿⣿⡟⠻⠿⢣⣾⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣦⠀⠀⠀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢡⣿⣿⢇⢔⡵⣻⣶⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠘⠿⣧⣶⣄⣻⣿⣿⣿⣿⡟
⣿⣿⣾⣶⣾⣿⣿⣿⣶⣧⣴⣿⣿⣿⠟⠀⠀⠀⠘⠿⠿⠿⠟⠛⠛⠉⢡⠁⠀⣿⣷⡀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠟⠛⠉⠀⡰⠉⣋⠕⠵⢊⣈⣯⣿⣿⠄⠀⠀⠀⠀⠀⠙⠛⠿⣇⠀⣿⡇⠀⢻⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣸⢿⡿⠦⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠤⠊⠴⠀⠰⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⢸⣿⡟⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢰⣿⠛⣿⣙⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢹⣿⣇⣼⣿⡟⣿⡟⢻⡆⣿⡇⠀⢿⣠⡿⢸⣿⠀⣿⣇⣿⡷⣾⡟⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⠿⣼⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡏⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⠀⢸⣿⠈⠹⡂⠿⣧⡿⠇⠹⣧⣼⠟⢽⡿⢹⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠀⠀⠈⠙⠛⠿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠃
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣄⠀⠀⠀⠀⠰⣻⣛⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⢀⣤⣴⣤⣤⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⢻⣿⣄⠀⠀⠀⢸⣯⣧⠆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠈⢷⡜⠻⡿⠟⠛⢶⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢴⡄⠀⠀⠀⠀⠹⠿⠇⠀⢠⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⠄⣸⣿⣿⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣤⣾⣿⣶⣾⣷⣤⣴⣦⣄⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠻⠟⠿⠿⠛⠿⠛⠛⠛⢹⣧⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⡀⠀⠀⠀⣠
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣆⠀⠀⠀⠀⠀⣾⠟⠋⠁⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⣹⣿⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⢸⣾⣿
⢈⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣼⡄⠈⠛⠛⠛⠀⢠⠄⠀⢠⣿⠀⠀⠠⠐⠂⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⠀⠒⠒⢷⣾⣿⣿⡇⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠈⣿⣿
⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠆⠀⠀⠀⠀⡜⣰⡆⢸⣿⣿⣀⣤⣄⣀⣀⢀⠀⠀⣀⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣷⠀⣷⣯⠉⢉⣤⣶⣶⣦⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣿⠛⠶⠶⠦⠤⠀⢷⡟⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣷⣾⣿⣿⣿⣿⣀⠀⠀⠀⢀⣾⡟⠙⣿⣿⡿⠿⣿⡻⢿⣿⣿⡿
⢸⣿⣄⣠⣤⣤⣾⣤⣴⡀⣠⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢹⣿⣿⣿⣿⣿⣇⠀⢀⣾⣿⢃⣾⣿⣿⣿⣿⣿⠟⠘⣿⣿⡇
⠀⠉⠈⣿⣿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿⡟⠀⢹⣿⣿⣆⣸⡟⠁⠘⠻⣿⣿⣿⡏⠀⠀⣾⡀⠹⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣄⠘⠛⣧⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⣿⣿⡇⠀⢸⣿⣿⣿⣿⣅⠀⣀⣠⣾⣿⣿⠃⠀⠉⠛⠁⠀⠉
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠴⠀⠘⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣾⣿⣿⣇⠀⣀⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⣤⣤⣦⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣯⡈⠉⠉⠉⠉⠉⠛⠛⠉⠉⠛⢋⣉⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⣴⡍⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠾⠀⠀⠀⠀⠀⠀⢰⣾⣌⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠀⠀⠀⣿⠁⢻⣿⣿⣿⣿⡇⠀⠀⠀⠛⣧⣿⣿⣿⣿⣷⣼⣿⣿⣨⣭⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣆⠈⠁⠈⠛⠛⠻⣿⣏⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⡱⠈⠂⠀⠸⣿⠿⣿⣿⡁⣠⣤⣄⠀⠛⢻⣿⡟⠻⠿⢣⣾⣿⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡇⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⡿⡧⢸⣦⠀⠀⠀⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣿⡿⢃⢔⡔⣭⣶⡄⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⠇⢀⠘⠿⣷⣶⣄⣸⣿⣿⣿⣿⡟
⣿⣿⣾⣶⣾⣿⣿⣿⣶⣧⣴⣿⣿⣿⠇⠀⠀⠀⠘⠻⠿⠛⠛⠉⠉⠁⢸⠀⠀⣿⣦⡀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠟⠛⠉⠀⡐⠉⡫⠔⠕⢃⣜⣧⣿⣿⠆⠀⠀⠀⠀⠀⠙⠛⠿⣇⠀⣿⠇⠀⢻⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣹⢿⡿⠦⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠔⠪⠖⠀⠴⢷⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢸⣿⡏⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢠⣿⠛⣿⢙⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢹⣿⣇⣼⣿⡟⣿⡟⢻⡆⣿⡇⠀⢿⣠⡿⢸⣿⠀⣿⣇⣿⡿⣾⡟⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⠿⣸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠟⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⠀⢸⣿⠐⠓⠆⠿⣧⡿⠇⠹⣧⣼⠟⢼⡿⢹⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠀⠀⠈⠙⠛⠻
⠘⣿⣿⣿⣿⡿⠿⠿⠿⢟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃
⠀⠘⣿⣿⣿⣿⠶⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⣄⠀⠀⠀⠀⠰⣻⣛⠃⠀⠀⠀⢀⣀⣀⣤⣀⣀⣠⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⢀⣤⣴⣤⣤⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠉⠻⣿⣆⠀⠀⠀⢸⣿⣧⠆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠺⣿⣿⣿⠀⠀⠀⠀⢾⣿⣿⡧⠀⠀⠈⢷⡞⠿⣿⠟⠛⢶⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢴⡄⠀⠀⠀⠀⠹⠿⠇⠀⢰⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⠠⣸⣿⣿⠀⠀⠀⠀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣠⣶⣿⣶⣾⣷⣤⣴⣦⡄⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠻⠟⠿⠿⠟⠟⠛⠛⠛⠐⣷⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣇⠀⠀⠀⠀⣠
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣧⠀⠀⠀⠀⠀⣾⠟⠋⠁⠀⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠈⣹⣿⡄⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣍⠀⠀⢸⣾⣿
⢨⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣼⣇⠈⠛⠛⠛⠀⢠⠄⠀⢀⣿⣀⠀⠠⠒⠂⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠈⠀⠈⠛⠻⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠈⣿⣿
⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠀⠀⠀⠀⠀⡜⣰⡆⢸⣿⣿⣦⣤⣄⣀⣀⣀⠀⠀⣀⣿⣿⣿⣷⣦⣤⣦⣦⣴⣶⣦⣿⣿⣿⣿⠀⣷⣯⠉⠉⣡⣶⣶⣦⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⡤⠀⢳⡟⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣷⣾⣿⣿⣿⣿⣀⠀⠀⠀⢠⣿⠏⠀⣿⣿⡿⠿⣿⡻⣿⣿⣿⣿
⣿⣿⣄⣠⣤⣤⣾⣤⣤⡀⡀⢀⣄⢀⣠⠀⠀⠀⠀⠀⠀⢸⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢻⣿⣿⣿⣿⣿⣧⠀⢀⣾⡟⢠⣾⣿⣿⣿⣿⣿⡿⠀⣿⣿⣧
⠉⠉⢻⣿⠿⡏⢹⣿⣿⣿⣿⢾⣿⣾⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿⡟⠈⢻⣿⣿⣆⣸⡿⠃⣾⠿⣿⣿⣿⣏⠀⠀⣴⡇⠙⣿
⠀⠀⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⠛⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⣿⣿⡇⠀⢸⣿⣿⣿⣿⣅⣀⣀⣤⣾⣿⣿⠏⠀⠉⠛⠃⠀⠈
⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠸⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣾⣿⣿⣧⠀⣀⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣷⣦⣤⣶⡄⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣂⣉⠉⠀⠉⠉⠉⠉⠉⠉⠉⣋⣉⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⣴⡎⢿⣿⣿⣿⣿⢿⣿⣿⢷⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⣾⣌⠻⣿⡿⣿⣿⣷⣶⣶⣶⣶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠀⠀⠀⣿⠁⢻⣿⣿⣿⣿⡇⠀⠀⠀⠙⢣⣾⣿⣿⣿⣿⡜⣿⣿⣬⣭⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⡿⣄⠀⠀⠈⠛⠛⣻⢿⣿⣠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡠⡱⠈⠃⠀⠸⠿⠿⣿⣿⣀⣤⣶⣄⡀⠘⢻⣿⣿⠛⠿⢣⣶⣯⣿⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡇⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⠏⡀⠹⣧⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⡿⢃⢔⡔⣭⣶⡄⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⠏⢀⡈⠿⣿⣶⣦⣸⣿⣿⣿⣿⡟
⣿⣿⣾⣶⣶⣿⣿⣿⣶⣧⣴⣿⣿⣿⠏⠀⠀⠀⠘⠻⠟⠛⠋⠉⠁⠀⢰⠀⠀⣿⣷⡀⠀⠀⠀⠀⠉⠻⠻⠿⠟⠛⠛⠉⠀⠐⠉⡩⠔⠕⢃⣜⣯⣿⣿⠆⠀⠀⠀⠀⠀⠙⠛⠿⣿⠀⣿⡇⠀⢹⣿⣿⣿⣿⣿⣯⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣸⢿⡿⠶⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠄⠪⠶⠀⠼⢷⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⢸⣿⣏⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⡿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢠⣿⠛⣿⢹⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣷⢹⣿⣧⣼⣿⡟⣿⡟⢻⡆⣿⡇⠀⢿⣠⡿⢸⣿⠀⣿⣇⣿⡟⣾⡟⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⠿⣸⣿⢰⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⠀⢸⣿⠈⣿⠃⠿⣧⡿⠇⠹⣧⣼⠟⢼⡿⢹⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠀⠀⠈⠙⠛⠻
⠘⣿⣿⣿⣿⡿⠿⠿⠿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠲⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⢔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃
⠀⠘⣿⣿⣿⣿⠷⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣦⣄⡀⠀⠀⠀⠠⣾⣿⠛⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣧⠀⠀⠀⢰⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠼⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⢦⡼⠿⣿⣿⠿⢷⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢦⣆⠀⠀⠀⠀⠈⣿⣷⠄⢀⣾⡿⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠢⣸⣿⣿⡇⠀⠀⠀⠀⠉⢉⠁⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠛⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⢠⣤⣿⣷⣴⣿⣄⣠⣶⣄⡄⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡖⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠰⣿⣿⡇⠀⠀⠀⠸⠿⠿⡿⠿⠿⠿⠟⠿⠋⠀⣤⣤⣤⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⣿⣿⣿⠀⠀⠀⢀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⡀⠀⠀⠀⠀⢰⡿⠟⠋⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠀⠀⠉⠉⣻⣇⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⣸⣿⣿⣉⠀⠀⣷⣿
⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣰⣧⠈⠻⠛⠿⠃⠀⡄⠀⠀⣸⣿⠀⠀⠤⠒⠒⠀⠀⠀⠀⢹⣿⣿⣿⠅⠐⠈⠀⠀⠒⠻⢷⣿⣿⣿⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⣿⣿⣿⣶⡀⢹⣿
⠉⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⢸⢡⣆⠀⣿⣿⣿⣀⣀⣈⣀⣀⢀⠀⠀⢨⣿⣿⣿⣤⣀⣤⣴⣤⣤⣤⣴⣿⣿⣿⡆⣶⣿⠙⠻⠟⣠⣤⣶⣶⡄⠀⠀⠀⠀⣀⣾⡏⣿⣿⣿⣿⣿⣿⣇⢸⣿
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠀⠀⠀⠀⠀⢢⡿⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣦⣀⣀⣿⣿⣿⣿⠁⠀⠀⠀⣼⡟⠉⢸⣿⣿⠿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⢀⣄⣀⣴⣤⣤⡄⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⠉⠁⢹⣿⣿⣿⣿⣷⠀⠀⢀⣿⠇⣴⣶⣿⣿⣿⣿⣿⠇⢹⣿⣧
⠀⠀⠐⢻⠿⢟⢻⣿⣿⢟⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⠻⣿⣿⣦⠀⣸⣿⣷⣿⢿⣿⣿⣿⠁⠀⢠⣾⠻⣿
⠀⠀⣀⣸⣷⣿⣿⣿⣿⣾⣷⣰⣷⢸⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠽⠿⣯⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣿⣿⡿⠀⣿⣿⣿⣷⣿⣃⣨⣥⣴⣿⣿⡿⠃⠐⠛⠛⠀⠈
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣾⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣇⠈⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⢛⣉⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⠿⠟⠀⢠⣬⢿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢰⣯⢻⣿⣿⣿⣿⣷⣦⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠀⠀⠀⠠⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢿⣼⣿⣿⣿⣿⣇⣿⣿⡇⣙⡋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⣀⣠⣴⣿⡿⣇⠁⠈⠈⠻⠿⢿⡿⣿⢟⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⢀⢆⡄⠄⠛⠈⣿⣿⣿⣿⣿⠁⣠⣤⡀⠸⠿⣿⣿⡹⠿⠿⣩⣍⣱⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣟⠁⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⡿⢁⠘⣧⡀⠀⠁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣹⣿⡇⡠⣪⢾⣲⣄⠀⠀⠀⠘⠘⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣥⣤⠀⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣶⣧⣼⣿⣿⣿⡿⠀⠀⠀⠉⠙⠻⠿⠛⠛⠋⠁⢠⠃⠀⢿⣷⡀⠀⠀⠈⠉⠉⠻⡿⣿⡿⠿⠿⠟⠋⠀⠘⠛⡩⠪⠞⣁⣿⣽⣿⡆⠀⠀⠀⠀⠈⠙⠻⢿⣿⡇⢸⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣘⢿⡿⠷⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠈⠔⠩⠆⠠⠾⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠁⠀⢀⡹⣿⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⢿⠏⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢡⣿⠛⣿⣸⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢸⣿⣇⣼⣿⡟⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣇⣿⡇⣾⡟⣿⣿⣧⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⠿⣺⣿⢠⡄⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠇⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⠀⢸⣿⠸⢷⡆⢿⣧⡿⠇⠹⣧⣼⢟⢻⣿⢻⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠀⠈⠉⠙⠛⠿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡄⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⣤⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠺
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣄⡀⠀⠀⠀⠀⣾⣿⠛⠋⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⠀⣀⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣧⡀⠀⠀⢠⣿⣯⣣⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠨⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠲⣴⠿⣿⣿⠿⠷⣾⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢦⣦⠀⠀⠀⠀⠈⢿⣿⠄⠀⣾⡿⠟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠢⣈⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠹⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠈⣿⣿⣗⠀⠀⠀⢀⣤⣾⣷⣴⣶⣄⣠⣶⣄⣀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⣿⣿⣿⠀⠀⠀⠸⡿⠿⣿⠿⠿⠿⠿⠿⠋⠀⣤⣤⣤⡀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⡄⠀⠀⠀⠀⢀⣿⠿⠛⠉⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠉⢻⣷⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⣠⣿⣿⣋⠀⠀⢴⣾
⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣷⠀⠻⠿⠿⠇⠀⣀⠀⠀⢸⣿⠀⠀⠠⠤⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠊⠀⠀⠒⠲⢷⣾⣿⣿⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣷⡄⢸⣿
⠉⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡇⠀⠀⠀⠀⢰⢁⣆⠀⣿⣿⣿⢁⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣠⣬⣤⣤⣤⣤⣿⣿⣿⡇⢰⣼⠙⠿⠿⣧⣴⣶⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢨⣾⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣤⡀⢀⣿⣿⣿⣿⠁⠀⠀⠀⢠⣿⠋⠉⣿⣿⡿⣿⣿⢿⣿⣿⣿
⡄⠀⠀⢀⣀⣀⣴⣄⣤⡄⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣷⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠉⠉⢱⣿⣿⣿⣿⣷⠀⠀⠀⣼⡿⢀⣴⣿⣿⣿⣿⣿⡇⢸⣿⣦
⠃⠀⠐⠺⡿⠟⠻⣿⣿⠿⠹⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⠛⣿⣿⣧⠀⢰⣿⣷⣾⣿⣿⣿⣿⡋⠀⠀⣼⣿⣿
⠀⠀⣀⣰⣶⣿⣿⣿⣿⣦⣄⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠸⠿⢟⣅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣾⣿⣿⠀⣿⣿⣿⣷⣿⡟⠈⣯⣤⣿⣿⡿⠇⠀⠒⠛⠁⠘
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡈⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⣛⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⡿⠿⠁⢀⣬⣹⣿⣿⣿⣿⣿⣿⣿⠿⣰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣷⣦⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠿⣣⣿⣿⣿⣿⣏⢹⣿⣷⢘⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣤⣼⣧⠈⠉⠀⠛⡿⣿⢿⣿⣿⡋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠄⡄⠀⠙⠀⢻⣿⣿⣿⣿⠃⣀⣤⡀⠈⠿⣿⣿⡟⢿⡿⢉⣭⣁⣿⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡟⠃⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⠟⣧⡀⠀⠀⠨⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢩⣿⡿⠀⢈⢞⣶⣄⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣧⣤⡀⣿⣿⣧⣯⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠂⠀⠀⠙⠻⠿⠿⠿⠟⠻⠋⢋⠃⠀⢹⣷⡀⠀⠀⠀⠉⠋⠻⢿⢿⣿⣿⡿⠿⠛⠁⠐⠛⡫⢔⠕⢁⣿⣽⣿⡦⠀⠀⠀⠀⠈⠙⠻⢿⣿⡇⢰⣿⠀⠀⣿⣿⣷⣿⣿⣿⡟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣘⢿⡿⠷⠄⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠤⢪⠄⠀⢾⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠉⠀⢀⡸⣿⡻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⢿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢱⣿⠙⣿⢸⣻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢼⣿⣇⣼⣿⣿⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣟⣿⡇⣾⡟⣿⣿⣧⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⠿⢸⣿⠀⡀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⠹⣿⠘⢿⣴⡿⠀⢸⣿⠠⢑⢦⢿⣧⡿⠇⠹⣧⣼⠟⢺⣿⢿⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠀⠉⠉⠙⠻⠿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣄⡀⠀⠀⠀⠀⣼⣿⠛⠋⠀⠀⠀⠀⠀⣀⣀⣀⢀⢀⣀⠀⣀⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⡀⠀⠀⢀⣿⣯⣯⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠠⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠰⣄⠿⣿⣿⡿⠿⣼⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣶⣦⠀⠀⠀⠀⠈⢿⣿⠄⠀⣼⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠢⡈⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠘⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⠈⣿⣿⣿⠀⠀⠀⠀⣤⣼⣷⣤⣶⣦⣀⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠸⣿⠿⣿⡿⣿⠿⠿⠿⠏⠉⣤⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣄⡅⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡄⠀⠀⠀⠀⠀⣿⠿⠛⠋⠋⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠉⠙⠻⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣋⠀⠀⢰⣾
⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣾⡀⠛⠿⠿⠇⠀⣀⠀⠀⢰⣿⠀⠀⢠⠤⠀⠀⠀⠀⠀⠉⣿⣿⣿⡏⠀⠀⠀⠀⠐⠲⢶⣶⣿⣿⡄⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠘⣿
⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡷⠀⠀⠀⠀⢰⢁⣆⠀⣾⣿⣿⣅⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣀⣀⣤⣠⣤⣄⣽⣿⣿⣇⢰⣼⠙⠿⢿⣷⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⢀⣿
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⢸⣾⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣤⡀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⠻⣿⣿⣿⣿⣿⢿⣿⣿⢿
⣤⣤⠀⢀⣀⣀⣴⣄⣠⡄⢠⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠙⠋⢸⣿⣿⣿⣿⣷⠀⠀⠀⣸⣿⠃⣠⣽⣿⣷⣾⣿⡗⢸⣿⣿
⠛⠛⠁⠘⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⠛⣿⣿⣧⠀⢰⣿⣿⣰⣿⣿⣿⣿⡟⠉⠀⣸⣿⣿
⠀⠀⣀⣰⣶⣿⣿⣿⣿⣦⣍⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠘⠿⢿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢠⣿⣿⡇⠀⣿⣿⣿⣷⣿⡟⠀⢩⣠⣽⣿⣿⠇⠀⠐⠿⠃⠘
⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠉⠛⠛⠛⠛⠛⠿⠿⠟⠛⠛⠛⣛⣻⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⣤⡽⣿⣿⣿⣿⣿⣿⣿⡿⢰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⠉⢻⣿⣿⣿⣿⡇⠀⠀⠀⠿⣇⣿⣿⣿⣿⣯⣹⣿⣿⢘⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠉⠉⠉⠻⡿⠿⣿⣿⣿⠏⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡐⡄⠀⠉⠀⢸⢿⣿⣿⣿⠃⣀⣤⡀⠀⠿⣿⣿⡟⢿⣿⢏⣝⣋⣾⣿
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⣿⠁⠀⠀⢠⣤⣶⣶⣶⣶⣶⣿⣿⣿⠿⣧⠀⠀⠀⠵⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢫⣿⣿⢀⢜⢼⣦⣄⠀⠀⠀⠀⠘⢿⣿⣾⣿⣿⣿⠆⠀⠸⣿⣇⣤⡀⢼⣿⣿⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣴⣿⣿⣿⡿⠂⠀⠀⠙⢻⣿⣿⡿⠿⠿⠿⠟⠇⠀⢻⣷⡄⠀⠀⠈⠉⠋⠻⢿⣿⣿⣿⡿⠿⠟⠁⠠⠾⢋⢕⠵⠋⢾⣻⣿⣄⠀⠀⠀⠀⠈⠙⠻⢿⣿⡇⢰⣿⡆⠀⢻⣿⣷⣾⣿⣿⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣘⠿⡿⠶⠄⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠡⢂⠅⠀⢴⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⠀⠉⠀⢀⡘⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢱⣿⠛⣿⣸⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢸⣿⣇⣼⣿⣷⣿⡟⢻⡆⣿⡇⠀⢿⣠⡿⢸⣿⠀⣿⣟⣿⡇⣾⡟⣿⣿⣷⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⢿⣼⣿⢐⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡏⣿⡷⠟⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⠹⣿⠘⣿⣴⡿⠀⢸⣿⠘⠹⣤⠿⣧⡿⠇⠹⣧⣼⠏⢾⣿⢽⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠈⠉⠉⠙⠻⠿
⠘⣿⣿⣿⣿⡿⠿⠿⠿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠊⠀⠈⠀⠂⠀⠀⠀⠀⢀⠠⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣦⣄⡀⠀⠀⠀⢀⡾⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⠀⠀⠀⢠⣿⣿⣤⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠠⣤⠿⣿⣿⢿⠿⣼⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠘⢿⣷⡆⢀⣾⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠤⣸⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠘⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⣤⣼⣷⣤⣶⣄⣀⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⡦⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⣿⣿⣿⠀⠀⠀⠘⣿⠿⣿⣿⣿⡿⠿⠿⠟⠉⢀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡄⠀⠀⠀⠀⠀⣿⡿⠿⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠙⠛⢻⣧⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⠀⠀⢠⣾
⣶⣿⡀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣰⠀⠻⠿⠿⠟⠀⡀⠀⠀⢸⣿⠀⠀⣀⡤⠄⠀⠀⠀⠀⠙⣿⣿⣿⡯⠀⠐⠀⠀⠲⠶⣦⣶⣿⣿⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡄⠘⣿
⠏⢻⣿⣷⣿⠿⠛⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⢸⢡⡄⠀⣿⣿⣶⡂⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⣀⣐⣄⣀⣠⣀⣿⣿⣿⡇⢰⣽⠙⠿⠿⢇⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡀⣿
⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⢇⣾⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣠⡀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⠟⣿⣿⣿⣿⣿⡿⣿⣿⣿
⠀⠀⢀⣴⣄⢀⣴⣄⣠⡀⢠⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⣇⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠉⠛⠋⣿⣿⣿⣿⣷⠀⠀⠀⣰⣿⡟⢠⣼⣿⣷⣾⣿⣿⠈⣿⣿
⠀⠀⠻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡿⣿⣿⣧⠀⢰⣿⡟⠀⢿⣿⣿⣿⡟⠉⠁⣠⡿⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⡉⠙⢿⣿⣯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣼⣿⣿⠀⣿⣿⣿⣷⣿⣇⠀⡀⣀⣼⣿⣿⡿⠀⠀⠛⠗⠀
⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⣤⠀⠀⠀⠀⠀⠀⢠⠌⠙⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣄⢀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣥⠌⠛⠛⠛⠛⢛⠻⠿⠟⠛⠛⠛⣫⣽⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⣠⡝⣿⣿⣿⣿⣿⣿⣿⣿⢧⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⢇⡀⠀⠀⠀⣿⠟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠻⣇⣬⣿⣿⣿⣿⡙⣿⣿⠚⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣠⣾⣎⠈⠁⠉⠻⣿⣿⣿⣿⣿⡟⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⠀⡀⡐⠄⠘⠀⢸⣿⣿⣿⣿⠃⣀⣤⡀⠀⠿⢿⣿⣿⢿⣿⡇⣙⡛⣸⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⠋⠀⠀⣀⣤⣶⣶⣶⣶⣿⣿⣿⣿⢻⣆⠀⠀⠄⢩⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣿⣿⠀⢔⣜⢥⡀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣿⣿⡇⠀⠘⣿⣟⣤⡀⢸⣿⣿⣽⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣴⣿⣿⣿⠿⠀⠀⠀⠙⢿⣿⣿⡿⠿⠿⠟⢋⠃⠀⣿⣧⡀⠀⠀⠘⠛⠻⠻⣿⣿⣿⣿⣿⣿⠟⠉⠠⠾⢟⠥⡡⠊⣾⣻⣿⡄⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⢠⣿⡆⠀⢸⣿⣷⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣸⠿⡷⠦⠀⠀⠀⠀⠀⣀⠉⠉⠉⢀⡀⠀⠀⠁⠔⡥⠈⢴⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠉⠁⢀⡈⣿⡿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⢿⠏⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢣⣿⠛⣿⢽⣻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⣸⣿⣏⣼⣿⣷⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣿⣿⡇⣾⡟⣿⣿⣷⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⢿⣿⣿⢀⡀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡏⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⠹⣿⢘⢿⣴⡿⠈⢹⣿⠈⠃⣠⢿⣧⡿⠇⠹⣧⣼⢏⢼⣿⣽⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠉⠉⠉⠙⠿⢿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣦⣄⡀⠀⠀⠀⢀⡾⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⡀⠀⠀⢠⣿⣯⣤⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠢⣤⠿⣿⣿⠿⠿⣼⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠘⢿⣷⡦⢀⣾⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢤⣸⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠘⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠁⠀⢸⠟⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⣤⣼⣷⣤⣶⣄⣀⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⡦⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⣿⣿⣿⠀⠀⠀⠘⣿⠿⣿⣿⣿⡿⠿⠿⠟⠉⢀⣀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡄⠀⠀⠀⠀⢀⣿⡿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠙⠛⢻⣧⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⠀⠀⢰⣾
⣶⣿⡀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣰⠀⠻⠿⠿⠟⠀⡀⠀⠀⢸⣿⠀⠀⣀⡤⠄⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⠀⠀⠲⠶⣦⣶⣾⣿⡀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡄⠘⣿
⠏⢻⣿⣷⣿⠿⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⢸⢠⡄⠀⣿⣿⣶⡃⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⣀⣀⣄⣀⣠⣀⣽⣿⣿⡇⢰⣽⠙⠿⡿⢇⣤⣶⣶⣆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡀⣿
⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⢇⣾⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣠⡀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⠟⣿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠀⢀⣴⣄⢀⣴⣄⣠⡀⢠⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⣇⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠉⠛⠋⣿⣿⣿⣿⣷⠀⠀⠀⣰⣿⡟⢠⣼⣿⣿⣾⣿⣷⠈⣿⣿
⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡿⣿⣿⣧⠀⢰⣿⡟⠀⢿⣿⣿⣿⡟⠉⠁⣠⡿⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⡉⠙⢿⣿⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣼⣿⣿⠀⣿⣿⣿⣷⣿⣇⠀⠀⣀⣼⣿⣿⡿⠀⠀⠛⠓⠀
⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⣤⠀⠀⠀⠀⠀⠀⢠⠌⠙⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣄⢀⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣥⡌⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⣋⣽⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⣠⡝⣿⣿⣿⣿⣿⣿⣿⣿⢧⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⢇⡀⠀⠀⠀⣿⠟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠻⣇⣈⣿⣿⣿⣿⡹⣿⣿⠊⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣠⣾⣎⠈⠉⠙⠻⣿⣿⣿⣿⣿⡟⠫⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⠀⠀⡀⡀⠀⠙⠀⢸⣿⣿⣿⣿⠃⣀⣤⡀⠀⠿⢿⣿⣟⢿⣿⡇⣙⡛⣸⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⠋⠀⠀⢀⣤⣶⣶⣶⣶⣿⣿⣿⡿⢻⣆⠀⠀⠀⢩⣟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⠀⢔⡼⢥⡀⠀⠀⠀⠀⠙⢿⣿⣷⣿⣿⣿⡇⠀⠘⣿⣟⣤⡀⢸⣿⣿⣼⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⢿⠀⠀⠀⠛⢿⣿⣿⡿⠿⠿⠛⢋⠃⠀⣿⣧⡀⠀⠀⠘⠛⠛⠻⣿⣿⣿⣿⣿⣿⠟⠉⢠⠺⢟⠅⡡⠋⣾⣻⣿⡄⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⢠⣿⡆⠀⢸⣿⣷⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣸⠿⡷⠦⠀⠀⠀⠀⠀⣀⠉⠉⠉⢀⡀⠀⠀⠀⠔⡥⠈⢴⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠉⠁⢀⡈⣿⡿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠏⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢣⣿⠛⣿⢹⣿⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⣸⣿⣏⣼⣿⣷⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣿⣿⡇⣾⡟⣿⣿⣷⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⢿⣿⣿⢠⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡏⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⠹⣿⢘⢿⣴⡿⠈⢹⣿⠘⢇⣢⠿⣧⡿⠇⠹⣧⣼⢏⢼⣿⣽⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡇⠈⠉⠉⠙⠿⢿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣤⣀⠀⠀⠀⠀⢠⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣷⠀⠀⠀⣼⣿⡗⡀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⣺⣿⣿⣿⡷⠀⠀⠀⠀⣾⣿⣿⡀⠀⠀⢠⣤⠿⣿⣿⣿⡷⣼⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⠀⠀⠀⠀⠘⢿⣷⡄⢰⣿⣿⠋⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢄⢹⣿⣿⣿⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠹⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠉⠁⢿⢟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⣠⣼⣧⣤⣶⣄⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⢠⣿⡿⠿⠻⠟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⢿⡇⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⣿⡛⠁⠀⢠⣼
⣶⣶⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣴⠀⠺⣿⣿⡇⢀⠀⠀⠀⣾⡏⠀⠀⢀⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡗⠀⠀⠀⠀⠴⢴⣤⣶⣿⣷⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡄⠘⣿
⡟⢻⣿⣶⣿⠟⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⡞⢠⠀⢠⣿⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⣀⣀⢀⣀⣄⣈⣿⣿⣿⡄⣤⡟⠻⠿⠿⠁⣠⣶⣶⣶⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⣣⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣇⣤⡀⢀⢠⣿⣿⣿⣿⠀⠀⠀⠀⣠⣴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⠀⢀⣤⣀⣀⠀⣴⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⢻⡅⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡟⠋⠋⠉⣾⣿⣿⣿⣿⠀⠀⠀⢰⣿⠇⣠⣽⣿⣷⣾⣿⣷⠈⣿⣧
⠀⠀⢿⣿⣿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢀⣿⣿⢠⣿⣿⣿⣿⡿⠋⠁⢠⡿⣿
⠀⠀⣀⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡋⠉⠻⣿⣟⡋⢛⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⣿⠋⣛⣉⣿⣿⣿⡷⠀⠀⠿⠇⠙
⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⣤⡄⠀⠀⠀⠀⠀⠠⠙⢟⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⡇⢹⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣴⣾⣿⣆⣀⣸⡿⣿⣿⣿⣧⢦⠙⠛⠛⠛⠛⢻⠿⢿⣛⣛⡛⠛⣩⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⡿⠏⠀⣠⡙⣿⣿⣿⣿⣿⣿⣿⣿⢧⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡉⢻⠿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣃⣀⠀⠀⠀⢸⡟⠻⣿⣿⣿⣿⣿⠀⠀⠀⢿⣇⣩⣿⣿⣿⣿⣹⣿⣷⠘⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢀⣿⣿⣿⡿⠋⢹⣿⣿⣿⣷⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡟⢋⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⠁⡀⠀⠀⠸⠃⢸⣿⣿⣿⣿⠟⢀⣀⡀⠀⣿⣿⣿⣿⢿⣿⡇⣙⡛⢸⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⠃⠀⠀⣀⣽⣿⣷⣶⣿⣿⣿⡿⠉⢳⡀⠀⠀⠈⡽⣫⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⡇⢀⢔⣼⣁⠁⠀⠀⠀⠈⠹⣿⣿⣶⣿⣿⣿⡆⠀⢸⣿⣿⣀⡀⢸⣿⣿⣼⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣶⣧⣴⣿⣿⣿⣿⠀⠀⠀⠛⢿⣿⣿⠿⠿⠟⠉⢠⠂⠘⣷⣄⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠉⡀⢿⠟⠑⡠⠋⣾⢿⣷⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⢠⣶⡄⠈⢹⣿⣷⣼⣿⣿⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠿⡦⠀⠀⠀⠀⠀⠀⣉⠉⠉⠉⢀⡀⠀⠀⠀⢔⠁⠈⢴⠶⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠈⠙⠁⢀⡈⣿⡿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⢿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢠⣿⠛⣿⢹⣻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢸⣿⣇⣼⣿⣯⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣿⣿⡇⣾⡟⣿⣿⣧⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⢿⣺⣿⢀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⠹⣿⢘⢿⣴⡿⠘⢿⣿⢘⠁⣀⠿⣧⡿⠇⠹⣷⣼⢏⢼⣿⣽⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡏⠙⠛⠛⠻⢿⣿
⠘⣿⣿⣿⣿⠿⠿⠿⠿⢟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡀⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣤⡀⠀⠀⠀⠀⢠⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⢿⣿⣷⠀⠀⠀⣼⣟⠒⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⣻⣿⣿⣿⡷⠀⠀⠀⠀⣾⣿⣶⠀⠀⠀⢠⣠⢿⣿⣿⣿⣧⣼⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⠀⠀⠀⠀⠘⣿⣦⡄⣰⣿⡿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠠⡈⣻⣿⣿⣧⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠙⠀⠈⠁⠀⠀⠹⠿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠈⠉⠀⣿⠟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⣀⣼⣦⣠⣶⣀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠃⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⡟⠋⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⢸⣿⡿⠟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠻⣿⡄⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⢀⣿⣿⡟⠁⠀⢠⣼
⣴⣶⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠺⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠃⠀⠂⠀⠠⠤⣤⣤⣶⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣿⣿⣿⣦⡀⢸⣿
⡿⢿⣷⣴⣿⠿⠟⠀⠀⠀⠀⠀⠀⣿⣾⣿⣧⠀⠀⠀⠀⡎⣀⠀⢰⣿⣧⡖⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⢀⣀⣀⣀⣹⣿⣿⣿⠀⣄⡟⠻⡿⠟⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿
⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⢰⢱⣿⡆⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣇⣄⢀⣀⣿⣿⣿⣿⠁⠀⠀⠀⠀⣠⣼⡿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⢀⣄⠀⢀⣄⠀⡀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⡀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⠛⠛⢋⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⡇⢀⣽⣿⣯⣭⣿⡮⢙⣿⡌
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⣼⣿⢡⣿⣿⣿⣿⡿⠛⠁⢰⣿⣿
⠀⠀⣈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⠋⠙⢿⣿⣟⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⣿⠈⣿⣿⣿⣦⣴⣿⡿⣿⣏⣿⣿⣿⡧⠀⠠⢿⠟⠻
⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⢀⣤⠀⠀⠀⠀⠀⠀⣠⣻⣯⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠀⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢀⣴⣿⣿⣿⣿⣿⡝⣿⣿⣿⣇⡌⠛⠛⠛⠛⠛⠿⠿⢿⢛⢛⠛⢋⣩⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⠿⠋⠉⣉⡻⣿⣿⣿⣿⣿⣿⣾⣿⣆⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⢿⣿⣿⣷⣦⣤⣤⣄⣉⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⣿⠟⢻⣿⣿⣿⣿⡇⠀⠀⠀⢿⡇⣙⣿⣿⣿⣟⢹⣿⣷⠘⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣿⣿⣿⣿⠛⠙⣿⣿⣿⣧⠀⠈⠁⠉⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠉⠁⠀⢀⠀⠘⠀⢸⣿⣿⣿⡿⠇⢀⣀⠀⠀⣿⣿⣿⣟⣿⣿⡇⣛⠛⣰⣿
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⣿⠗⠀⠈⠉⣻⣿⣧⣶⣾⣿⣿⣿⠟⣦⡀⠀⠀⠈⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⡇⢀⢌⣼⣀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣿⣿⣿⡆⠀⢸⣿⣇⣀⡀⢸⣿⣷⣸⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠀⠀⠐⠿⣿⣿⣿⣿⡿⠿⠛⢡⠂⢸⣧⡀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡠⣿⠟⠁⡠⠫⡿⢿⣆⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⢠⣶⡄⠉⢿⣿⣷⣼⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠎⠀⠀⣿⢿⡄⠀⠀⠀⠀⠀⠈⣉⠙⠋⠉⢀⡀⠀⠘⠁⢔⠁⠊⠤⠶⠿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⠈⠛⠁⢀⡈⣿⡿⣿⣿⣿⣿⣼
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢠⣿⠛⣿⢹⣻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢸⣿⣇⣼⣿⣯⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣟⣿⡇⣾⡟⣿⣿⣧⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⣿⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡏⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⠹⣿⢘⢿⣤⡿⠸⢾⣿⠨⠀⣀⠿⣧⡿⠇⠹⣷⣼⢏⢸⣿⣹⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡏⠛⠻⠿⠿⣿⣿
⠘⣿⣿⣿⣿⠿⠿⠿⡿⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⢿⣿⣇⣀⡀⠀⠀⠀⠀⣰⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⠀⠀⢀⣿⣿⠂⠀⠀⠀⢀⣴⣶⣶⣿⣷⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣷⣶⠀⠀⠀⢄⢠⣾⣿⣿⣿⡧⣼⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠹⣿⣦⡀⣴⣿⡿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⠉⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠈⠃⠀⠉⠉⠁⠀⢻⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠀⠀⠀⠀⠀⠉⠋⠀⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣀⣰⣆⣀⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡰⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣼⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠿⣿⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⢈⣿⣿⡟⠁⠀⢠⣴
⣤⣦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⣿⣿⡇⠀⠀⠀⢀⣿⠁⠀⠀⣀⡀⠀⠀⠀⠈⠻⣿⣿⣿⣟⠁⠀⠀⠀⠠⢤⣤⣤⣶⣿⡇⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣾⣿⣿⣷⣤⠀⢸⣿
⡿⣿⣦⣴⣿⠿⠏⠀⠀⠀⠀⠀⠀⣷⣶⣿⣆⠀⠀⠀⢀⠞⡀⠀⢸⣿⣤⠂⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⡀⢀⣀⣈⣻⣿⣿⣧⠀⣼⡟⢿⣿⠟⢀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿
⠁⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠃⠀⠀⠀⢸⣰⣿⡄⣿⣿⣿⣶⣿⣿⣶⣶⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⣄⢀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡟⠛⠟⢻⣿⣿⣿⣿⡆⠀⠀⠀⢀⣿⡏⢀⣻⣿⣯⣽⣿⡎⠹⣟⠉
⠇⢰⣿⣿⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⢿⣿⣿⡄⠀⠀⣼⣿⣡⣿⣿⣿⣿⡿⠛⠃⢸⣿⣿
⠀⠀⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣶⡟⠉⠻⢿⣿⢟⠛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⠸⣿⣿⣿⣠⣴⣿⡿⣿⣟⣿⣿⣿⡇⠀⠀⣾⡿⠻
⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⣀⠀⠀⠀⠒⠂⠀⣈⣻⣏⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡯⠀⠀⠀⣸⣿⣿⣧⠀⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢻⣿⣿⣿⣠⠘⠛⠛⠻⠿⠻⠿⠿⠿⢿⣟⠛⢋⣥⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⡿⠿⠋⠉⣉⡛⣿⣿⣿⣿⣿⣷⣾⣿⣆⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣏⠜⠟⢿⣿⣿⣶⣤⣄⣀⣈⣁⣈⣡⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠛⢿⣿⣿⣿⣿⡇⠀⠀⠀⢿⡇⣙⣿⣿⣿⣟⠻⣿⣧⠸⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⢰⣿⣿⣿⣿⠏⠹⣿⣿⣿⣆⠀⠈⠀⠹⣿⣿⣿⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢟⡍⠉⠁⠀⠀⠀⠙⠀⢸⣿⣿⣿⡿⠃⢀⣀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠻⠟⣰⣶
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⣿⠇⠀⠈⠙⣿⣿⣧⣤⣤⣿⣿⣿⣿⣆⠀⠀⠀⠙⢏⣽⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⠁⢀⢌⣜⡈⠀⠀⠀⠀⠉⢿⣿⣷⣶⣿⣿⣷⡄⠀⢹⣿⣇⣈⠉⢸⣿⣧⣸⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣶⣧⣴⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢿⠋⢹⣆⡀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡰⣿⠟⠀⡠⢋⣿⣿⡄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢠⣶⡌⠉⣿⣿⣧⣼⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠇⠀⠘⣿⢷⡀⠀⠀⠀⠀⠀⠈⣉⠛⠋⠉⢁⡀⠀⠀⠀⠔⠀⠊⠠⠾⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⠘⠛⠁⢀⡸⣿⣿⣿⣿⣿⣷⣽
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢠⣿⠛⣿⣹⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⣸⣿⣇⣼⣿⣟⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣟⣿⡇⣾⡟⣿⣿⣇⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⠀⣿⢿⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡏⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡏⣿⡇⠀⣿⡇⢿⣷⡆⢿⣷⡆⠀⢸⡇⠹⣿⠘⢿⣤⡿⢸⢼⣿⠀⠀⠀⠿⣧⡿⠇⠹⣧⣼⢏⢸⣿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠻⠿⠿⢿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⠿⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣅⡀⠉⠁⠀⠀⠀⣰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⠀⠀⢀⣷⠷⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣶⣤⠀⠀⠀⣀⢀⣶⣿⣿⣿⣇⣰⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠉⠉⠹⣿⣄⡀⣼⣿⡿⠊⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢈⠙⣿⣿⣿⡇⠀⠀⠀⠈⠿⠿⠟⠀⠀⠀⠘⠇⠈⠛⠋⠉⠉⢿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠿⠀⠀⠀⠀⠀⠙⠛⢰⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠑⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣄⢀⣤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣾⣿⡗⠕⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠁⠈⠀⢀⣴⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠿⢿⣇⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠷⠀⠀⢀⣰
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣿⣿⡇⠀⠀⠀⢸⡏⠁⠀⠀⣀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⢄⣀⣤⣠⣾⣿⠀⠀⢠⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⣄⠀⢸⣿
⣿⣿⣄⣰⣿⣿⠇⠀⠀⠀⠀⠀⠀⣶⣶⣿⡄⠀⠉⠉⠁⠏⡀⠀⣾⣷⡤⠀⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡁⠀⠀⠀⠀⠀⣀⠙⣿⣿⣿⡇⢀⣸⡿⢿⣿⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠘⣿
⠃⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠇⠀⠀⠀⢸⣰⣷⠀⣿⣿⣷⣶⣿⣶⣶⣶⣤⣄⣠⣤⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣇⡄⢀⡀⢰⣾⣿⣿⡇⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣴⣿
⠀⠈⢈⠀⠀⢀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠘⣯⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⡿⠉⢿⣿⣏⣿⣯⡍⠛⠟⠉
⠀⣾⣿⣷⣶⣿⣷⣾⣦⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⢀⣾⣿⠃⣾⣿⣿⣿⡿⠛⠃⢰⣿⣿
⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⠟⠛⢿⣿⡿⠛⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣀⣼⡟⠃⠀⠙⣿⣿⣿⡇⠀⠀⣾⣿⠿
⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢙⡂⠀⠀⠀⠀⠀⠀⣘⣿⣋⣿⣿⣿⣿⣿⣏⣾⣿⣿⣷⣦⣄⣈⣽⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣾⣿⣿⡍⣿⣿⡿⣿⣿⣧⣤⣶⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣾⣿⣿⣿⣯⢿⣿⣿⣇⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠛⣋⣭⣿⣾⣿⣿⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⣇⣽⣿⣷⣿⡟⠛⠛⠿⣿⣿⣿⣿⣿⣷⣴⣷⡀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡙⡺⠿⣿⣿⣷⣦⣄⣀⣀⣉⣀⣈⣩⣥⣵⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⣿⡆⠻⣿⣿⣿⡻⢻⣿⣯⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢠⣿⣿⣿⣿⠟⢻⣿⣿⣷⡀⠀⠀⠘⢻⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠑⠓⠀⠀⡀⠀⢿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠈⣷⣿⣿⡿⣿⣿⡆⠿⡿⢠⣦
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⣿⡆⠀⠹⠻⣿⣿⣏⣀⣨⣿⣿⣿⣿⡀⠀⠀⠈⠻⢯⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⠀⢀⢌⡖⠐⠀⠈⠀⠘⠿⢿⣿⣿⣥⣶⣿⣶⡄⠉⢱⣿⡇⠉⠛⢱⣷⣦⢸⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣶⣧⣴⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⡄⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⣴⣿⠛⠀⡰⣫⣿⣧⡀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⢁⣤⠈⠛⣷⣿⣆⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠏⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠁⠇⠀⠸⣿⢇⠀⠀⠀⠀⠀⠈⠙⣙⠛⠛⠉⢉⡀⠀⠎⠈⠔⠡⠊⢠⠼⠶⢿⡻⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⠸⠿⠃⢀⡘⣿⣿⣿⣿⣿⣷⣹
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢠⣿⠟⣿⣸⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣧⢸⣿⣇⣼⣿⣟⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣟⣿⡇⣾⡟⣿⣿⣏⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⠀⣿⢿⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⣿⣿⡏⣿⡷⠟⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣾⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⣿⡇⠀⣿⡇⢿⣷⡆⢿⣷⡆⠀⢸⡇⠹⣿⠈⢿⣴⡿⣸⢸⣿⠀⠀⠀⠿⣧⡿⠇⠹⣧⣼⢏⢸⣿⢹⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡿⢿⣿⣾⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⠿⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠐⠡⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠛⠁⠀⠀⠁⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⡀⢀⣿⣿⣿⣿⣷⣦⠀⠀⢀⣷⠷⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⢀⢀⣴⣾⣿⣿⣇⣰⡄⠀⠀
⣀⠀⠀⠀⠀⠀⠉⠉⠉⢠⣄⢀⠀⠈⠉⠉⢹⣿⣄⡀⣼⣿⡿⠊⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢈⠙⣿⣿⣿⣯⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠈⠓⠈⠛⠟⠉⠁⢿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠾⠀⠀⠀⠀⠀⠙⠛⢸⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠑⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣄⢀⣠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣿⡗⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠋⠉⠛⠋⠉⠉⠁⠉⠁⠀⢰⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠻⠿⣿⣇⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⠷⠀⠀⢀⣠
⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣾⣿⣧⠀⠀⠀⢸⡟⠁⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣿⣿⠛⠁⢀⠀⠀⢀⣀⣀⣠⣼⣿⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣄⠀⢸⣿
⣿⣿⣄⣰⣶⣿⠇⠀⠀⠀⠀⠀⠀⣶⣤⣿⣄⠀⠉⠉⠁⠇⡀⠀⣾⣧⠤⠂⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⡈⠙⣿⣿⣿⡆⢀⣸⡿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⣿
⠃⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠟⠀⠀⠀⢸⣰⣷⠀⣿⣿⣿⣶⣿⣶⣶⣦⣤⣀⣠⣼⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⡇⣀⣀⡀⢠⣶⣿⣿⡇⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣦⣿
⠀⠈⢀⠀⠀⢀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠘⣯⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⠉⢻⣿⣟⣛⣯⡍⠛⡟⠉
⠀⣶⣿⣶⣴⣾⣷⣾⣦⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⠇⣸⣿⣿⣿⣿⠟⠃⢠⣷⣿
⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣱⣾⠟⠻⢿⣿⡿⠛⢿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣀⣼⡿⠋⠀⠙⣿⣿⣿⣧⠀⠀⣸⡿⢿
⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢃⠀⠀⠀⢀⠀⠀⡙⢿⣋⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣤⣈⣉⣿⣶⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣼⣿⣿⡏⣿⣿⡿⣿⣿⣧⣤⣴⣶⣿⣿⣿⡁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣯⣿⣿⣿⡇⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢋⣭⣿⣾⣿⣿⣿⡿⠁⠀⠀⠀⢰⣿⣿⣿⡇⣸⣿⣷⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣶⣴⣷⡀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡘⡾⠿⣿⣿⣶⣦⣀⣀⣀⠉⠀⣈⣉⣭⣵⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⣾⡆⠿⣿⣿⣿⠿⠿⣿⣯⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢠⣿⣿⣿⣿⠟⢻⣿⣿⣷⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠓⠓⠂⠀⠀⠀⢺⡟⢙⣿⣿⣿⣿⣿⠀⠀⠀⠉⣷⣶⣿⣿⣿⣿⡆⠿⡿⢠⣦
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⣿⡆⠀⠸⢿⣿⣿⣏⣀⣨⣿⣿⣿⣷⡀⠀⢠⠈⠿⢻⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⣱⣿⠀⢀⢌⡖⠐⠀⠈⠁⠘⠿⣿⣿⣿⣁⣴⣾⣦⡀⠙⢻⣿⡿⠙⠛⢡⣶⣦⢸⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣶⣧⣴⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⡀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⣼⡿⠛⠀⡰⣫⣿⣧⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠁⣤⡈⠛⢷⣿⣆⣘⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠏⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠀⠇⠀⠸⣿⢆⠀⠀⠀⠀⠀⠈⠛⣛⠛⠛⠉⢉⡀⠀⠎⠀⠔⠡⠋⢠⠽⠶⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠸⠿⠃⢀⡸⣿⣿⣿⣿⣿⣷⣹
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢠⣿⠟⣿⣸⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣇⣼⣿⣟⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣟⣿⡇⣾⡟⣿⣿⣏⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⡧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⠀⣿⣿⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡏⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣾⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡏⣿⡇⠀⣿⡇⢿⣷⡆⢿⣷⡆⠀⢸⡇⠹⣿⠈⢿⣴⡿⣸⢸⣿⠀⠀⠀⠿⣧⡿⠇⠹⣧⣼⠏⢸⣿⢹⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡿⢿⣿⣟⣿⣿⣿
⠘⣿⣿⣿⣿⠿⠿⠿⠿⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠡⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⠀⠘⣿⣿⣿⣿⠶⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⢀⣀⠛⠁⠀⠀⠁⣰⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣷⣦⠀⠀⢀⣷⡷⠂⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⣴⣷⣦⠀⠀⠀⣄⣀⣴⣿⣿⣿⣷⣠⣆⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠈⠹⣿⣦⡀⣼⣿⡿⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢈⠙⣿⣿⣿⣿⠀⠀⠀⠀⠿⠿⠿⠁⠀⠀⠈⠻⠈⠙⠟⠉⠉⢻⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠟⠀⠀⠀⠘⠛⢻⡿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠑⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣄⣀⣠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠔⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⠀⣻⣿⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣶⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠛⠉⠛⠋⠉⠋⠉⠉⠁⠀⢰⣶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⠿⣿⡇⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⡷⠀⠀⢀⣠
⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣾⣿⣧⠀⠀⠀⢸⡏⠀⠀⢀⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⠠⠀⠀⢤⣤⣀⣠⣾⣿⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣄⠀⠘⣿
⣿⣿⣄⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⣴⣤⣾⣆⠀⠉⠉⢉⠇⡀⠀⣿⣧⠤⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⢙⣿⣿⣿⡆⢀⣸⡿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⣿
⠃⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡟⠀⠀⠀⢸⣰⣷⠀⣿⣿⣿⣾⣿⣶⣶⣶⣦⣀⣤⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣇⣄⣀⡀⣠⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣦⣿
⠀⠈⢈⠀⠀⢀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠘⣯⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿⠿⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣴⣿⠛⢻⣿⣏⣛⣯⣍⠛⠏⠉
⣿⣷⣿⣶⣶⣿⣷⣾⣦⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⣰⣿⠇⢸⣿⣿⣿⣿⠿⠃⢠⣿⣿
⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⠛⠻⣿⣿⠿⠛⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣀⣰⣿⠿⠀⠙⣻⣿⣿⣇⠀⠀⣼⣿⠿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⠀⠀⠀⢀⠀⠀⣙⣿⣫⣿⣿⣿⣿⡟⣴⣿⣿⣿⣷⣤⣀⣭⣿⣾⣿⣿⣿⣿⣷⡞⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣼⣿⣿⠀⣿⣿⡿⣿⣿⣿⣴⣾⣶⣿⣿⣿⡁⠀⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⣠⣶⣿⣿⣿⣟⣿⣿⣿⣅⡜⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⠛⠛⣋⣭⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢰⣿⣿⣿⡇⣸⣿⣷⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣴⣷⡄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡫⠿⠿⣿⣿⣷⣦⣄⣀⣈⠉⢉⣉⣩⣬⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣾⡆⠿⣿⣿⣿⡿⠿⣿⣯⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⠟⢻⣿⣿⣷⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠓⠒⠂⠀⠀⠀⢸⡏⢹⣿⣿⣿⣿⣿⠀⠀⠀⠈⣷⣶⣿⣿⣿⣿⡆⠿⠿⢠⣶
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⣿⡇⠀⠺⢿⣿⣿⣏⣠⣼⣿⣿⣿⣷⡀⠀⢠⡘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣹⣿⠀⢠⢢⠂⠐⠀⠈⠁⠈⠿⣿⣿⣿⣃⣴⣶⣦⡀⠛⢻⣿⣿⠙⠛⢱⣿⣦⢾⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣷⣧⣴⣿⣿⣿⣿⠁⠀⢰⣾⣿⣿⣿⣿⣿⣿⡿⡻⠈⣿⡄⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢼⡿⢋⢔⡵⣳⣿⣧⡀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⠃⣀⡈⠛⢿⣿⣦⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠈⠙⠛⠋⠉⠈⠀⠠⠁⠀⠸⣿⢄⠀⠀⠀⠀⠀⠙⠛⣿⠛⠛⠉⢁⡀⠀⠁⠨⠒⠕⠉⢤⠿⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⠸⠿⠇⢀⡸⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡘⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣇⣼⣿⣟⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣟⣿⡇⣾⡟⣿⣿⣯⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⠻⣿⣿⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⣿⣿⡏⣿⡷⠟⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡟⣿⡇⠀⣿⡇⢿⣷⡆⢿⣷⡆⠀⢸⡇⠹⣿⠈⢿⣴⡿⣸⢸⣿⠀⠀⠀⠿⣧⡿⠇⠹⣧⣼⢟⢸⣿⢹⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡿⢿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠘⠤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠘⣿⣿⣿⣿⠶⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢡⡿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣷⣶⣄⣿⣿⣿⣿⣶⠀⠀⢸⣿⣳⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣐⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣷⣶⡀⠀⠀⣀⢀⣶⣿⣿⣿⣿⣴⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⢹⡙⠻⠿⠛⠙⣿⣧⣠⣾⣿⠏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢄⠙⣿⣿⣿⣿⠀⠀⠀⠀⠛⠿⠿⠃⠀⠀⠈⠛⠉⠙⠋⠉⠉⠹⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠁⠀⠀⠀⠀⠈⠛⢿⣟⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣦⣀⣠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠊⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⡿⠿⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠻⣿⡆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡷⠀⠀⢀⣠
⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⣾⣿⣇⡀⠀⠀⣿⡇⠀⢀⡤⠄⠀⠀⠀⠀⠉⣿⣿⣿⣟⠀⠀⠄⠀⠀⠤⣦⣤⣴⣿⣧⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⡀⠸⣿
⣿⢿⣄⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⣴⣦⣾⣦⠀⠀⠈⢹⢡⡀⢰⣿⣷⡂⣀⡀⠂⠀⠀⠀⠀⠀⢹⣿⣿⣧⡀⣀⡀⣀⣀⣠⣀⣹⣿⣿⣿⡀⢠⣸⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⣿
⠁⢼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠀⠀⠀⣇⣾⠇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠈⣀⠀⠀⣠⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢹⣇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⠿⢿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⢠⣿⡟⢻⣿⣯⣿⣯⣄⠉⡏⣈
⠀⢶⣿⣷⣶⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⢰⣿⣿⣿⣿⠛⠃⢠⣿⣿
⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⢛⣴⣿⣏⠉⠛⢿⣿⣋⢉⣿⣿⣿⣎⡛⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣄⣤⣾⣿⣯⡜⣿⣿⣿⣷⠀⠀⣼⣿⠿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣀⠀⠀⠀⠀⠀⣙⢯⣾⣿⣿⣿⡿⠰⣾⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⢿⡏⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠈⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⠄⠀⠀⠀⠀⠙⠈⠉⢟⠻⣿⣷⣦⣉⠛⠛⢛⢛⣛⣛⣛⣛⣛⣿⠉⣩⣴⣾⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⢠⣿⣿⡇⠀⢻⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣶⣿⡆⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡟⠀⠀⢀⠀⠀⠀⠀⠀⠘⠂⠘⠻⢿⣿⣿⣦⣤⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣴⣿⣿⡿⠟⠃⠀⢸⣧⠻⣿⣿⣿⣿⠿⣿⣯⡹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⡆⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡼⠈⠉⠁⠠⠀⠀⢿⡏⢹⣿⣿⣿⣿⡷⠀⠀⠀⠈⢹⣾⣿⣿⣿⣿⡏⠿⠿⢡⣶
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣷⠟⠋⠸⢿⣿⣿⣇⣀⣤⣶⣾⣿⣧⡀⠐⠶⠘⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠛⢡⣾⡇⠀⠔⣽⢁⠁⠀⠘⠀⠀⢻⣿⣿⣿⣃⣤⣶⣦⡄⠘⢻⣿⣿⠉⠙⢱⣿⣷⢸⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣶⣧⣴⣿⣿⣿⣿⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⠟⠙⣷⡄⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠐⡽⠟⠡⡢⢊⡾⣿⣦⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⠋⣀⡀⠛⢿⣿⣷⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠈⠙⠛⠋⠉⠉⠀⡸⠀⠀⠿⣿⢄⠀⠀⠀⠀⠈⠙⠚⣛⠋⠉⠀⢀⡀⠈⠀⠐⠁⠊⠠⢶⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⠆⠿⠟⢀⡸⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣸⣿⢀⣿⡿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣇⣼⣿⣏⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣿⣿⡇⣾⡟⣿⣿⣷⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⢿⣿⣷⢺⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠟⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⠹⣿⠈⢿⣴⡿⣸⢸⣿⠀⢀⠀⠿⣧⡿⠇⠹⣧⣼⢏⣸⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡿⠿⠿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⠿⢟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠁⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠘⣿⣿⣿⣿⠶⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⢡⡾⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⣤⣿⣿⣿⣿⣶⠀⠀⢸⣿⣳⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣐⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣷⣶⡀⠀⠀⣀⠀⣴⣿⣿⣿⣷⣴⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢹⡙⠿⠿⠛⠙⣿⣧⣠⣾⣿⠏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢄⠙⣿⣿⣿⣿⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠈⠳⠉⠙⠋⠉⠁⢹⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠁⠀⠀⠀⠀⠘⠛⢿⢟⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠑⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣦⣀⣠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡥⠊⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⡿⠿⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⣿⡆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡷⠀⠀⢠⣠
⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢰⣾⣿⣇⡀⠀⠀⣿⡇⠀⢀⡤⠤⠄⠀⠀⠀⠙⣿⣿⣿⣯⠀⠀⠀⠀⠀⠤⣦⣤⣶⣿⣧⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⡀⠸⣿
⣿⢿⣄⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⣴⣦⣾⣦⠀⠈⠈⢹⢡⡀⢰⣿⣷⡂⣀⡀⠂⠀⠀⠀⠀⠀⢹⣿⣿⣧⡀⣀⡀⢀⣀⣠⣀⣹⣿⣿⣿⡀⢠⣸⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⣿
⠁⢼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⠿⠀⠀⠀⣇⣾⠇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠈⣀⠀⠀⣀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⢹⣇⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⠿⢿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⢠⣿⡟⢻⣿⣯⣿⣯⣄⠙⡏⣈
⠀⢶⣿⣷⣶⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⢰⣿⣿⣿⣿⠛⠃⢠⣿⣿
⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⢛⣴⣿⣟⠉⠛⢿⣿⣋⢉⣿⣿⣿⣮⡛⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣄⣠⣾⣿⣯⡞⣿⣿⣿⣧⠀⠀⣼⣿⠿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⡀⠀⠀⠀⠀⢀⣙⣯⣾⣿⣿⣿⡿⠰⣾⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⢿⡏⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠈⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠙⠉⠉⠿⠻⣿⣷⣬⣉⠙⠙⢛⢛⣛⣛⣛⣛⣛⣿⠉⣩⣴⣾⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⢠⣿⣿⡇⠀⢻⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣶⣿⡆⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⠻⠿⣿⣿⣦⣤⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣴⣿⣿⡿⠟⠃⠀⢸⣧⠻⣿⣿⣿⣿⠿⣿⣿⡹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⡆⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠏⡼⠈⠉⠁⠠⠀⠀⢿⡟⢹⣿⣿⣿⣿⡷⠀⠀⠀⠈⢹⣾⣿⣿⣿⣿⡇⠻⠿⢡⣶
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⣷⠟⠃⠸⢿⣿⣿⣇⣠⣤⣶⣾⣿⣧⠀⠐⠶⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⢡⣾⡇⠀⠔⣹⢁⠁⠀⠘⠀⠀⠻⣿⣿⣿⣇⣴⣶⣦⣄⠘⢻⣿⣿⠉⠙⢡⣿⣷⢺⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣴⣿⣿⣿⣿⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⠟⠹⣷⡄⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡐⡽⠟⠡⡢⢊⡾⣿⣦⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⠋⣀⡀⠛⢿⣿⣷⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠈⠙⠛⠋⠉⠉⠀⠸⠀⠀⠿⣷⠄⠀⠀⠀⠀⠈⠙⠚⣛⠉⠉⠀⢀⡀⠘⠀⠐⠁⠊⠠⢶⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⠆⠿⠟⢀⡸⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣯⣿⣿⡿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣸⣿⢀⣿⣿⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣇⣼⣿⣏⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⣿⣷⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⢿⣿⢧⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣼⡿⡰⢸⣿⠀⣀⢀⠿⣧⡿⠇⠹⣧⣼⢏⣸⣿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡿⠿⠿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⠿⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠁⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀
⠀⠀⠀⠀⠁⢤⠀⠀⠀⠀⠀⡀⢸⣿⣯⣀⡈⠉⠀⠀⢱⢿⠿⠟⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⠿⣦⣤⠗⠀⠀⢿⣿⣿⣿⣶⠀⠀⣼⣿⡧⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣷⣶⡄⠀⠀⣠⣀⣾⣿⣿⣿⣿⣰⣶⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⠀⠀⠀⠀⠙⣿⣧⣴⣿⡿⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢄⢹⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⠿⠃⠀⠀⠈⠙⠋⠉⠋⠉⠉⠹⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠇⠀⠀⠀⠀⠘⠛⢿⠏⠉⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣦⣀⣰⣄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠔⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⢠⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠰⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⡿⠟⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠛⠻⣿⡄⠀⠀⢀⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⡿⠂⠀⢠⣤
⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢰⣿⣿⣧⠀⠀⠀⣿⠀⠀⣠⠤⠄⠀⠀⠀⠀⠙⣿⣿⣿⣟⠀⠄⠄⠀⠒⠶⢶⣤⣾⣿⣇⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠈⣿
⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣼⣷⡀⠀⠈⡟⣠⠀⢸⣿⣿⣅⣀⣀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⣀⣀⣀⣠⣤⣤⣽⣿⣿⣿⠀⣠⣽⠻⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⢻
⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠁⠀⠀⣷⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣠⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢻⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠿⠿⣿⣶⣶⣶⣶⣦⠀⠀⠀⠀⢠⣾⡟⠛⣿⣿⣿⣿⣭⠙⡋⣀
⣿⣷⣿⣷⣶⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠛⠛⢿⣿⣿⡄⠀⠀⢀⣾⡿⢀⣾⣿⣿⣿⠟⠋⠀⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠛⢡⣾⣿⣏⠉⠛⠿⢿⣋⣉⣿⣿⣿⣯⡙⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣄⣤⣾⣿⢇⡈⣿⣿⣿⣿⠀⠀⢼⣿⠟
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣀⡀⠀⣈⣡⣿⣛⣿⣿⡇⠀⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⠿⣏⣻⣿⣿⣿⣿⡧⠀⠀⠀⠀⣰⣾⣷⣾⣿⣿⡟⠻⣿⣿⣷⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠉⠀⠙⢯⠐⣿⣷⣦⣀⡈⠉⣭⣭⣽⣟⣿⣯⣯⣿⠍⣠⣶⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⣿⢇⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣧⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣶⣤⣄⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣡⣾⣿⡟⠁⢰⣿⠻⢿⣿⣿⣿⠿⣿⣿⡅⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡍⠈⠉⠀⠀⠀⠀⢰⣿⢫⣿⣷⣿⣿⣿⠛⠀⠀⠈⢻⣾⣿⣿⣿⣿⡧⠻⠿⢣⣶
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣿⠉⠛⠏⠀⣀⡀⠀⠀⢀⣠⣴⣾⣧⡀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢡⣿⡇⢀⢌⣬⣀⠀⠀⠘⣿⠀⢿⣿⣿⣿⣿⠀⠀⣀⣀⠀⠻⣿⣿⠈⠙⢡⣿⣷⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣶⣧⣴⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣧⡄⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠰⡿⢋⢔⡱⢫⡿⣿⣦⠀⠀⠋⠀⠈⢿⣿⣿⣯⣴⣾⣿⡟⠀⣀⠛⢻⣿⣿⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠉⠉⠉⠈⠀⠈⡏⠀⠈⡿⣷⠀⠀⠀⠀⠀⠈⠙⠛⣛⠛⠉⠀⢀⡀⢀⠠⠊⠑⠉⠴⢶⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⠇⠐⠿⢀⡸⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⢿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣹⣿⢠⣿⣿⣿⢘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢺⣿⣇⣼⣿⣯⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣿⣿⡇⣾⡟⣿⣿⣿⡽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⣿⣿⣟⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣼⡿⡸⢸⣿⢀⣀⣀⠿⣧⡿⠇⠹⣧⣼⢟⣸⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡿⠿⠿⢿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠃⠆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣀⡈⠉⠁⠀⢸⣿⠿⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡄⠀⣾⣿⣥⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣷⣶⡄⠀⠀⢀⡀⣾⣿⣿⣿⣿⣴⣷⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠈⣿⣷⣴⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢄⢹⣿⣿⣿⣿⠀⠀⠀⠀⠙⠛⠻⠃⠀⠀⠀⠙⠃⠉⠛⠉⠀⠹⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠇⠀⠀⠀⠀⠈⠛⢿⠏⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣶⣀⣰⣄⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠔⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠆⠀⠀⠀⠀⠰⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠨⣿⣿⣿⣿⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⠿⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⠙⠻⣿⡄⠀⠀⢠⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⡿⠂⠀⢠⣤
⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢰⣿⣿⣧⠀⠀⢠⣿⠀⢀⣤⠴⠄⠀⠀⠀⠀⠹⣿⣿⣿⡏⠀⠔⠀⠀⠒⠲⢶⣶⣾⣿⣇⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣄⠀⣿
⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣼⣷⡀⠀⠀⡏⣤⠀⢸⣿⣿⣅⣀⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣧⢀⣀⣀⣀⣠⣤⣤⣽⣿⣿⣿⠀⣴⣿⠻⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⢸
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠁⠀⠰⣷⠿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣹⣿⣠⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢻⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠻⠿⣿⣶⣶⣶⣶⣦⠀⠀⠀⠀⢠⣾⡟⠛⣿⣿⣽⣿⣭⠛⠋⣁
⠀⠤⣶⣶⣶⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠛⠛⢿⣿⣿⡄⠀⠀⢀⣾⡿⢀⣾⣿⣿⣿⠟⠛⠀⣿⣿
⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠋⢰⣾⣿⣏⠉⠛⠿⠟⣉⣉⣿⣿⣿⣿⣈⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣤⣾⡿⠀⠈⣻⣿⣿⣿⠀⠀⣾⣿⠿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⣀⠀⣈⣱⣿⢭⣿⣿⠀⠀⢿⣿⣿⣿⣷⣤⣶⣾⣿⣿⣿⣿⣿⡿⢿⣇⣹⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⡟⠻⢿⣿⣤⣾⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠈⠉⠏⠸⣿⣷⣦⣄⡀⠨⣭⣭⣭⣯⣽⣭⣿⣿⠆⣠⣶⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⢀⣶⣤⣤⣿⡿⢃⣶⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣿⡇⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠙⠻⣿⣿⣦⣤⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⢀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤⣾⣿⡿⠃⢰⣾⠿⣿⣿⣿⣿⠿⣿⣿⡅⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡏⠀⠀⢄⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢻⣿⣿⣿⣿⣿⣧⠻⠿⢣⣾
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣯⠉⠹⠏⠀⣀⣀⠀⣀⣠⣴⣶⣿⣧⡀⠙⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⣿⡇⢀⢎⢎⣀⠁⠀⠀⣸⡇⢹⣿⣿⣿⣿⡄⠀⠀⣀⠀⢻⣿⣿⠈⠉⢡⣿⣿⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣷⡄⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠿⡋⢐⠕⢡⡿⣿⣧⠀⠀⠹⡇⠀⣿⣿⣿⡿⠇⣠⣾⡟⠁⣀⠟⢻⣿⣿⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⡇⠀⠈⡿⣧⠄⠀⠀⠀⠀⠈⠛⠛⣛⡋⠋⠁⢀⡀⢀⠄⠊⠈⠡⠴⢶⠿⠿⠟⠀⠀⠀⠀⠀⠈⠛⠋⠀⠈⠻⢿⠇⠀⠻⢂⡰⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠏⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣱⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣷⢹⣿⣇⣼⣿⡯⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣿⣿⡇⣾⡟⣿⣿⣿⡽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⣿⣿⣇⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣿⡿⣹⢸⣿⢀⣄⠀⠿⣧⡿⠇⠹⣧⣼⢟⣾⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠻⠿⠿⢿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠙⠿⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠸⣿⣿⣀⡈⠉⠁⠀⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⡄⠀⣿⣿⣅⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣶⡄⠀⠀⢀⣀⣾⣿⣿⣿⣿⣠⣶⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠉⠉⣿⣷⣴⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢄⢹⣿⣿⣿⣿⠀⠀⠀⠀⠙⠛⠿⠃⠀⠀⠀⠙⠋⠉⠛⠉⠁⠹⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠇⠀⠀⠀⠀⠈⠛⣿⠏⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⢀⣀⣶⣀⣰⣄⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠖⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⢸⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠆⠀⠀⠀⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⠿⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⠛⠻⣿⡀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡿⠂⠀⢠⣤
⣀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⣾⣿⣇⠀⠀⢰⣿⠀⢀⡤⠤⠄⠀⠀⠀⠀⠹⣿⣿⣿⡏⠀⠀⠀⠀⠒⠶⢶⣶⣿⣿⣇⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣄⠀⣿
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣼⣷⡀⠈⠈⡇⣤⠀⣸⣿⣯⣄⣀⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣧⢀⣀⣀⣀⣤⣤⣤⣽⣿⣿⣿⠀⣦⣿⠻⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⢸
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠃⠀⠸⣾⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣹⣿⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⢻⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠿⣿⣶⣶⣶⣶⣦⠀⠀⠀⠀⢀⣶⡾⠛⣿⣿⣽⣿⣯⡽⠛⢁
⠀⢤⣴⣶⣶⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠛⠛⢿⣿⣿⡄⠀⠀⢀⣼⡿⠀⣾⣿⣿⣿⠟⠛⠀⣿⣿
⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⠟⠉⣰⣿⣿⣍⠉⠛⠿⠟⣉⣉⣿⣿⣿⣷⣈⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣤⣾⡿⠁⠀⢻⣿⣿⣿⠀⠀⣼⣿⠿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣀⠀⡈⣵⣿⢿⣿⣿⠀⠉⢿⣿⣿⣿⣷⣴⣶⣾⣿⣿⣿⣿⣿⡿⠿⡇⣸⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⡟⠻⢿⣿⣤⣴⣾⣿⣿⣿⣏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠁⠈⠙⡅⠹⣿⣷⣤⣄⠀⠠⣮⣭⣭⣭⣿⣽⣿⣷⠆⣠⣶⣾⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⣿⠇⣦⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣿⡇⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣦⣤⣀⣀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⢈⣵⣾⣿⣿⠟⢡⣾⠿⣿⣿⣿⣿⠿⣿⣿⡅⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡇⠀⢀⢄⠠⠂⠀⠀⢿⣿⣶⣶⣿⣿⣿⡿⠋⠀⠘⢿⣾⣿⣿⣿⣿⣧⠻⡿⢣⣶
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡇⠋⠿⡟⠀⣀⡀⣀⣠⣤⣶⣿⣿⣦⠀⠻⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⣿⡇⠠⢊⢎⣀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠈⢿⣿⣿⠉⠛⢡⣿⣷⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣶⣧⣼⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣦⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠿⡋⢘⠔⢡⡷⣿⣦⠀⠀⠻⣿⡿⣿⣿⣿⣿⣷⠀⣰⡾⠀⢈⡿⢻⣿⣷⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⡇⠀⠘⡿⣧⠀⠀⠀⠀⠀⠙⠋⠻⣿⡛⠉⠉⢀⡀⢀⠄⠊⠈⠡⠴⢶⠿⠿⠟⠀⠀⠀⠉⠀⠸⠿⠿⠏⠁⠸⢿⠇⠀⠺⢇⡨⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣱⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣷⢹⣿⣇⣼⣿⡯⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠀⣿⣿⣿⡇⣾⡟⣿⣿⣿⡝⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⣿⣿⡷⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣿⡿⠸⢸⣿⢀⣀⡀⠿⣧⡿⠇⠹⣧⣼⢟⣾⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠿⠿⠿⢿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⠿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠙⢻⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠓⠀⠻⠇⠀⠸⣿⣿⣀⡈⠉⠁⠀⢾⣿⠟⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡄⠀⣾⣿⣇⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡀⠀⠀⠀⣰⣿⣶⡄⠀⠀⣤⡀⣴⣿⣿⣿⣿⣴⣷⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠁⠉⢿⣷⣴⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢄⢹⣿⣿⣿⣿⡇⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⠙⠋⠉⠛⠉⠁⠘⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠇⠀⠀⠀⠀⠈⠛⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⣿⣿⣿⣿⡃⠀⠀⠀⢀⣀⣶⣀⣠⣄⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠚⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠁⢸⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⠟⠋⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠙⣿⡀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⡿⠂⠀⠀⣤
⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⣾⣿⣧⠀⠀⢸⣿⠀⡀⠴⠒⠒⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠂⠀⠀⠒⠒⠷⣶⣿⣿⣇⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⠀⢻
⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣴⣷⡄⠀⢉⠇⣦⠀⣾⣿⣿⣤⣤⣤⣀⣀⣀⠀⠀⠀⣿⣿⣿⣧⣀⣀⣤⣤⣤⣴⣤⣿⣿⣿⣿⠀⣶⣿⠻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡆⢸
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡿⠃⠀⠘⣾⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣹⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣼
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⢻⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠻⢿⣿⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣽⣿⣿⡟⢻⣁
⠀⠀⢴⣶⣶⣿⣿⣿⣧⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠛⠛⢿⣿⣿⡄⠀⠀⠀⢠⣿⡟⢸⣿⣿⣿⠟⠛⠀⣾⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋⢀⣸⣿⣿⣤⠈⠙⠻⢋⣥⣤⣿⣿⣿⣷⣌⠹⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⣤⣴⣿⣿⢁⣾⣿⣿⣿⠀⠀⣼⣿⠟
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠈⣸⣿⢿⣿⣇⠀⠀⠻⠿⢿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠆⣹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⠈⠛⠈⠘⢿⡀⢠⣄⠀⠶⡷⢶⣾⣿⣿⣶⡷⡿⠖⣠⣶⣾⣾⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⣿⢃⣦⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣧⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠈⠃⢸⣿⣷⣦⣤⣀⣀⣀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⡟⢿⠁⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⣀⣵⣾⣿⣿⡿⢁⣾⡿⣿⣿⣿⣿⡿⣿⣿⡅⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⡿⠃⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡆⠀⢈⢀⢀⠂⠀⠘⢿⣿⣦⣴⣿⣿⣿⡟⠋⠀⠈⢿⣿⣿⣿⣿⣿⣷⠻⣿⢧⣶
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡿⠁⠀⠈⠀⠀⠀⣀⣤⣴⣾⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⣰⣿⠇⠠⣊⣎⣀⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⢿⣿⣿⠏⠛⠋⣾⣿⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⡿⠃⢹⣦⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠟⡫⣚⠔⢡⡷⣿⣦⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⡆⠀⣠⠀⢀⣿⢻⣾⣿⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⡇⠀⠘⡿⣇⠀⠀⠀⠀⠀⠉⠉⠛⣛⠋⠉⠉⢀⡀⢁⠄⠈⠈⠡⠴⢶⠿⠿⠟⠀⠀⠀⠀⠀⣶⣿⠿⠿⠿⠃⢾⠿⠄⠸⢏⡀⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⢿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣱⣿⢠⣿⣿⣿⢘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣷⢹⣿⣇⣼⣿⡧⣿⡟⢻⡆⣿⡇⠀⢿⣽⡿⢿⣿⠁⣿⣿⣿⡇⣾⡟⣿⣿⣿⡝⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⣿⣿⣿⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣽⡿⢸⢸⣿⢠⣀⡀⠿⣧⡿⠇⠹⣧⣼⢟⣾⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠿⠿⢿⣿⣿⣿
⠘⣿⣿⣿⣿⠿⠿⠿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠐⠻⢿⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⠗⠀⠘⣿⣿⣀⡈⠉⠁⠀⢸⣿⡟⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡆⠀⣾⣿⣗⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠼⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⣷⡆⠀⠀⢠⣀⣴⣿⣿⣿⣿⣦⣿⡀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠁⠈⢿⣿⣶⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⢄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⠿⠃⠀⠀⠀⠘⠃⠉⠋⠉⠀⠈⢿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠿⠀⠀⠀⠀⠈⠛⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣶⣄⣠⣦⡀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠚⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⢠⣿⣿⣿⣿⡇⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⠛⠉⠉⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠀⠉⠉⠙⣿⡀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠃⠀⠀⣤
⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣾⣿⣧⠀⠀⢰⣿⣀⡤⠶⠒⠒⠂⠀⠀⠀⠙⣿⣿⣿⡇⠀⠐⠀⠀⠒⠚⠷⣾⣿⣿⣇⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⢹
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣴⣿⡄⠀⢈⠇⣤⠀⣼⣿⣿⣦⣤⣤⣤⣤⣀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣴⣶⣤⣾⣿⣿⣿⠀⣶⣿⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡆⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠃⠀⠘⣿⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣤⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣼
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤⣴⣤⡄⠀⠀⠀⠀⠀⢹⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠻⣿⣶⣿⣿⣶⣦⠀⠀⠀⠀⠀⢀⣾⡿⢿⣿⣽⣿⣿⡟⢻⣂
⠀⠀⢰⣶⣶⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠛⠛⢿⣿⣿⣆⠀⠀⠀⢀⣾⣿⢱⣿⣿⣿⠟⠛⠀⣿⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⡿⠋⢀⣼⣿⣿⣤⡀⠙⠛⢋⣥⣤⣿⣿⣿⣷⣤⠙⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣤⣤⣿⣿⣇⣼⣿⣿⣿⠀⠀⢼⣿⠟
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⢽⣿⣧⠀⠀⠛⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⢿⠿⠿⠛⠆⣹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡀⠀⠀⢻⣿⣟⠛⠿⢟⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡷⠋⠈⠙⠀⠙⢿⡄⢠⣄⠀⠻⡷⠶⣶⣷⣾⡾⡿⡿⠟⣠⣶⣾⣶⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⣿⢏⣴⣶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⠛⠁⠀⠀⠀⣠⠀⠈⠁⢸⣿⣷⣦⣤⣀⣀⣀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠁⢀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣀⣴⣾⣿⣿⡿⢁⣾⡿⣿⣿⣿⣿⡟⣿⣿⡏⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⢸⡟⠅⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⡆⠀⢀⢁⠠⠀⠀⠀⢿⣿⣶⣴⣿⣿⣿⠟⠋⠀⠀⢿⣿⣿⣿⣿⣿⣷⠹⢿⢇⣶
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⠂⠀⠈⠀⢀⣀⣀⣠⣤⣴⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⢠⣿⠇⠠⣊⣎⣀⠁⠀⠀⠀⠻⠿⢿⣿⣿⣿⡀⠀⠀⠀⠀⢿⣿⣿⠏⠉⠉⣾⣿⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠄⠀⠀⢶⣿⣿⣿⣿⣿⣿⡿⠋⢸⣧⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠟⡫⢚⠔⢡⡷⣿⣦⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣦⠀⢀⡀⢀⣿⠛⣾⣿⣦⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⡇⠀⠘⡿⣧⠀⠀⠀⠀⠀⠙⠉⠙⣛⠋⠉⠉⢀⡀⢀⠔⠈⠈⠡⠴⢿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠠⠿⠿⠿⠟⢴⠿⠇⠸⢿⡀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣱⣿⢠⣿⣿⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣷⢹⣿⣇⣼⣿⡧⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢿⣿⠇⣿⣿⣿⡇⣾⡟⣿⣿⣿⡟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⣿⣿⣇⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠇⢸⣿⠀⣿⢿⣿⡗⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣼⡿⢸⢸⣿⢠⣠⠄⠿⣧⡿⠇⠹⣧⣼⢟⣼⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠿⠿⢿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠻⠿⡈⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠿⠀⠈⣿⣿⣄⣈⠉⠁⠀⢸⣿⡛⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣠⣀⣀⣤⣤⣤⣤⣄⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⣾⣿⣷⠖⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠵⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣷⡆⠀⠀⣠⣄⣼⣿⣿⣿⣿⣧⣿⡄⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠁⠈⢻⣿⣶⣿⡟⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢄⣘⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠈⠃⠈⠛⠉⠀⠈⢿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠿⠀⠀⠀⠀⠈⠛⣿⠯⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣶⣄⣠⣦⣀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠚⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠈⠉⠁⠈⠁⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⠛⠉⠉⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠀⠀⠉⠉⣻⡄⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠃⠀⠀⣤
⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣾⣿⣧⠀⠀⢠⣿⣂⡀⠜⠒⠒⠂⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠐⠒⠻⣿⣿⣿⣧⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠹
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⡆⠀⢀⢇⣶⠀⢸⣿⣿⣶⣤⣤⣤⣤⣀⡀⠀⠀⣿⣿⣿⣿⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⠀⣴⣿⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠇⠀⠈⣿⠛⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣤⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠⣤⣶⣦⡄⠀⠀⠀⠀⠀⢹⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⡟⢻⣇
⣷⠆⢴⣶⣷⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣩⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⠛⢿⣿⣿⣆⠀⠀⠀⢀⣼⣿⢱⣿⣿⣿⡟⠛⠀⣼⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⣿⡿⣿⣿⣿⡿⠋⢀⣼⣿⣿⣦⡀⠙⠛⢏⣣⣤⣾⣿⣿⣿⣄⠙⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⣤⣤⣾⣿⣯⣼⣿⣿⣿⡄⠠⣼⣿⠟
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⠀⠀⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠇⢸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⡀⠀⠀⢻⣿⣟⠛⠿⢟⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣧⠇⠈⠙⠉⠘⢿⡆⢠⣄⡀⠻⠿⠾⢾⣷⣾⡶⠿⠿⠟⣠⣶⣾⣷⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿⢫⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⢩⣿⠋⠀⠀⠀⣾⣧⠀⠈⠓⢺⣿⣿⣦⣤⣄⣀⣀⣀⣤⣤⣤⣾⣿⣿⣿⣿⣿⡿⠿⠇⢀⡀⠀⠀⠀⠀⣴⣿⠀⠀⣠⣧⣾⣿⣿⡿⢃⣾⡿⣿⣿⣿⣿⡿⣿⣿⡇⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠟⠁⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡆⠀⢀⢀⠠⠀⠀⠀⢻⣿⣷⣶⣿⣿⣿⠟⠛⠁⠀⢿⣿⣿⣿⣿⣿⣿⠻⠿⢇⣾
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣟⠉⠀⠈⠀⣀⣀⣀⣀⣀⣠⣿⣿⣧⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢱⣿⡇⡠⣊⣏⣄⠁⠀⠀⠀⠙⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⠏⠉⠉⣾⣿⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⢸⣧⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠐⠟⡫⣪⠔⢡⣟⣿⣧⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣦⠀⠀⡀⢠⣿⠛⣾⣿⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠁⠀⠀⠈⠉⠛⠛⠛⠉⠉⡇⠀⠘⡿⣆⠀⠀⠀⠀⠈⠙⠃⠙⣟⠛⠋⠁⢀⡀⡀⠔⠨⠈⠡⠴⢿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠼⡿⠿⠿⢧⠾⠇⠸⣿⡀⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣹⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣷⢻⣿⣇⣼⣿⡯⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢿⣿⡇⣿⣿⣿⣧⣾⡟⣿⣿⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⣿⣿⢯⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⢸⣿⠇⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣼⡿⣹⢸⣿⢠⡤⠄⠿⣧⡿⠇⠹⣧⣼⢟⣼⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠛⠿⠿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠘⠙⠿⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⢉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛
⠀⠘⣿⣿⣿⣿⠾⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠀⠀⣿⣿⣅⣀⠉⠁⠀⢸⣿⣛⠋⠀⠀⠀⠀⣀⣀⣠⣄⣀⣂⣠⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣇⠀⣾⣿⣷⠆⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠤⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣆⠀⠀⢠⣤⢴⣿⣿⣿⣿⣧⣾⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠻⣿⣶⣿⣟⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠢⣈⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠈⠋⠈⠉⠉⠀⠀⢻⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠀⠀⠀⠀⠀⠙⢿⠏⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⣾⣆⣠⣶⣀⢀⣤⡀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⠟⠉⠀⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠟⠉⠉⠉⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠀⠀⠈⠉⣻⡇⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠋⠀⠀⢠
⣄⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢾⣿⣷⠀⠀⢀⣿⣆⡀⠸⠒⠒⠂⠀⠀⠀⠈⣿⣿⣿⣷⠁⠐⠀⠀⠈⠚⠺⢿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣄⠀⠈
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣦⠀⢀⡇⣶⡀⢸⣿⣷⣶⣴⣦⣤⣤⣄⡀⠀⢀⣸⣿⣿⣿⣄⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⡄⢰⣼⠙⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠈⣿⡛⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡴
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣠⣴⣶⣶⣄⠀⠀⠀⠀⠀⢸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣽⣿⠉⢻⣦
⠰⠇⠀⢾⣷⣾⣿⣿⣿⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠙⠻⣿⣿⣇⠀⠀⠀⢀⣾⣿⠁⣿⣿⣿⠟⠋⠀⣸⣿
⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⢿⡿⣿⣿⣿⡿⠋⠀⣼⣿⣿⣧⣄⠈⠛⠋⣡⣤⣾⣿⣿⣿⣆⡈⢿⣿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣤⣤⣾⣿⡃⣰⣿⣿⣿⡆⠀⠼⠿⠟
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣧⠀⠀⠀⠀⠀⠀⣀⣸⣿⠟⢿⣷⠀⠀⠙⠻⠿⠿⣿⣶⣿⣿⣿⣿⣿⠿⠿⠿⠋⠀⢸⣿⣿⣿⣷⡷⠀⠀⠀⠀⠀⣀⠀⠀⢹⣿⣿⠛⠻⢛⣿⣿⣿⣿⣿⣿⣧⣀⠀⢀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣾⣿⣿⣿⡀⠈⢻⣇⢠⣦⡀⠻⠿⠿⢾⣷⢾⠿⠿⠿⠟⢁⣴⣶⣧⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠸⢿⠏⣴⣶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⢠⣴⡈⠉⠙⠻⣿⣷⡀⠀⠉⠸⣿⣿⣶⣤⣤⣀⣠⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⠿⠇⢀⡀⠀⠀⠀⠀⣴⣿⠀⠀⣠⣦⣾⣿⣿⡿⠃⣴⡿⣿⣿⣿⣿⡟⣿⣿⡇⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡾⠋⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡆⠀⢀⢀⠠⡀⠀⠀⢻⣿⣷⣶⣿⣿⣿⡟⠙⠁⠀⢻⣿⣿⣿⣿⣿⣿⠛⡿⢧⣾
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣀⣀⣀⣀⣠⣿⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢡⣿⠇⡠⣂⣮⣄⠀⠀⠀⠀⠙⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣿⠏⠉⠉⣿⣿⣾⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⡇⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⠋⢸⣧⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠟⡫⣪⠔⢡⣟⣿⣧⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⡄⠀⠀⢠⣿⠛⣾⣿⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠁⠀⠀⠈⠉⠛⠛⠛⠋⠉⡇⠀⠈⡿⣇⠀⠀⠀⠀⠀⠀⠀⠙⣛⠛⠉⠀⢀⡀⡀⠔⠨⠈⠠⠶⢿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⢧⠶⢇⠸⣿⡀⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣹⣿⢠⣿⣿⣿⢘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢹⣿⣇⣼⣿⡷⣿⡟⢻⡆⣿⡇⠀⢿⣠⡿⢸⣿⠧⣿⣿⣿⣿⣾⡟⣿⣿⣿⣏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⣿⣿⢇⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⢸⣿⠃⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣼⡿⢨⢸⣿⢠⣤⠀⠿⣧⡿⠇⠹⣧⣼⢟⣼⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠛⠻⠿⢿⣿⣿
⠘⣿⣿⣿⣿⠿⠿⠿⡿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⡀⠀⠈⠛⠿⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙
⠀⠘⣿⣿⣿⣿⠾⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠃⠀⠸⣿⣿⣄⣈⠁⠀⠀⣿⣟⡉⠁⠀⠀⠀⣀⣠⣤⣤⣤⣄⣠⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡄⢸⣿⣷⠤⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⠄⠀⠠⣤⣀⣾⣿⣿⣿⡿⣴⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⡀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠐⢄⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠙⠃⠉⠉⠁⠀⠸⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠈⢻⡿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣠⣷⣀⣴⣆⡀⣠⣄⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡿⠉⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠉⠉⠙⠛⢿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠉⢙⣧⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⠛⠀⠀⢰
⣧⣠⣶⡆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠸⣿⣿⠀⠀⠀⣾⣇⣀⠘⠒⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠈⠀⠈⠙⠛⠿⣿⣿⣿⡀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀
⣿⡿⠟⢁⣾⡿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣷⣾⣷⡄⠀⡏⣼⡆⢠⣿⣿⣶⣶⣶⣶⣦⣤⣀⠀⠀⣸⣿⣿⣿⣦⣠⣤⣤⣤⣶⣶⣶⣿⣿⣿⡇⢰⣾⡟⠻⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀
⠉⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠀⠀⢻⡏⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣿⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣤⡀⣀⠀⢠⣶⣶⣶⣦⡀⠀⠀⠀⠀⠘⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⢻⣿⣭⣭⣤⠉⢹⣦
⠀⠐⠀⠺⣿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣭⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠉⠛⣿⣿⣷⡀⠀⠀⠀⣼⣿⠁⣿⣿⣿⡟⠉⠀⢸⣿
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠿⣿⢿⣿⣿⠋⠀⢠⣿⣿⣷⣆⠈⠙⠛⣁⣤⣶⣿⣿⣿⣧⡀⠹⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣴⣾⡿⠃⣀⣽⣿⣿⡇⠀⠀⠻⠿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣀⣀⣀⣀⣀⣀⣿⠛⠻⣿⡀⠀⠈⠛⠻⠿⠿⠷⣿⣿⣿⣿⣿⠿⠿⠟⠛⠘⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⠛⠛⠿⢻⣧⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⡆⠈⠙⣧⠀⣤⣄⠘⠿⠿⠿⠿⠾⠿⠿⠿⠿⢃⣴⣷⣾⣾⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢸⡆⠀⠀⢿⠟⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⢠⣼⣿⣿⣿⣿⣿⣿⡄⠀⠉⠘⣿⣿⣷⣤⣤⣤⣠⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⠻⠇⢀⣀⠀⠀⠀⠀⣠⣿⡇⠀⢀⣦⣶⣿⣿⣿⠿⣡⣿⢿⣿⣿⣿⡿⢻⣿⣯⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⡿⠋⣿⣿⣿⡄⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡔⠀⠀⣀⡠⡁⠀⠀⠹⣿⣷⣶⣿⣿⣿⡿⠉⠉⠀⠸⣿⣿⣿⣿⣿⣿⡎⠿⠟⣴
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⠙⠛⠈⠙⣿⣏⣀⣀⣾⣿⣿⢷⡀⠘⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣿⡇⠀⢊⢾⣤⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⡇⠉⠉⣼⣿⣷⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠋⠘⣷⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘⡫⢺⠔⠡⣟⣻⣷⡀⠀⠀⠀⠀⠀⠘⠻⣿⣧⣴⣄⠀⠀⢀⣿⡟⣷⣿⣦⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠉⠙⠛⠋⠉⠉⡏⠀⠀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣛⠛⠉⠁⢀⡀⠀⠔⠨⠄⠁⠖⢿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⢿⠆⢶⠘⣿⡁⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⡿⠏⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣸⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣇⣼⣿⡷⣿⡟⢻⡆⣿⡇⠀⢿⣠⡿⢸⣿⡿⣿⣇⣿⣿⣾⡟⣿⣿⣿⣯⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⠿⣿⣏⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⢸⣸⣿⢠⣄⠀⠿⣧⡿⠇⠹⣧⣼⢟⣼⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠛⠻⠿⢿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠛⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉
⠀⠘⣿⣿⣿⣿⠾⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠃⠀⠸⣿⣿⣄⣀⠉⠀⠀⣿⣿⡉⠁⠀⠀⠀⣀⣤⣤⣤⣤⣠⣀⣤⣀⣤⣴⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⢸⣿⣷⠗⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠠⢼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⣤⣄⣾⣿⣿⣿⣿⣴⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⡀⠀⠀⠀⠈⢿⣿⣿⣟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠐⢄⣽⣿⣿⣿⣿⡀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠉⠁⠈⠉⠁⠀⠘⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠈⢹⡟⡂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⢿⣿⣿⣿⣿⡃⠀⠀⠀⢀⣀⣶⣀⣴⣆⡀⣠⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⠀⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡅⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⣙⣿⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠁⠀⢠
⣷⣤⣶⡆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⢿⣿⠀⠀⠀⣾⣧⠀⠙⠚⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠐⠀⠈⠉⠛⠻⣿⣿⣿⡄⠀⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀
⣿⣿⠿⢁⣾⡿⠿⠇⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⡄⠀⡏⣼⡆⢠⣿⣿⣿⣶⣶⣶⣶⣤⣄⣀⢀⣠⣿⣿⣿⣷⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⡇⢰⣾⡟⠻⠟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀
⠉⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⢹⡏⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣦⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆
⣄⠀⠀⠀⠀⠀⣠⣀⢀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠈⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⢿⣿⣽⣭⣥⡈⠩⣷
⠟⠀⠀⠺⠿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣩⣾⡿⠿⢿⣿⣿⣿⡿⢿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠉⠛⢿⣿⣷⡀⠀⠀⠀⣰⣿⠃⣾⣿⣿⡿⠋⠀⢈⣿
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠿⣿⠻⣿⣿⠋⠀⢤⣿⣿⣿⣦⡀⠉⠙⣡⣤⣶⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣠⣤⣶⣿⠇⣀⣿⣿⣿⡇⠀⠀⠸⠿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣄⣀⣀⣿⠕⠼⣿⡄⠀⠀⠛⠛⠛⠿⠿⢿⣿⣿⣿⢿⠿⠿⠛⠋⠈⢀⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⡛⠛⠿⢻⣷⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿⡆⠀⠙⣷⠀⣴⣄⠘⠻⠟⠿⠿⠿⠿⠿⠿⠟⢃⣴⣿⣿⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠿⢥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣄⠀⠉⠘⢿⣿⣷⣶⣤⣤⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⠟⠇⠀⣀⠀⠀⠀⠀⢠⣿⡇⠀⢀⣤⣴⣿⣿⣿⡿⢡⣿⢿⣿⣿⣿⡿⢻⣿⣿⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⡄⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡼⠀⠀⢄⡐⡔⠀⠀⠸⣿⣿⣶⣿⣿⣿⣿⠏⠉⠀⠸⣿⣿⣿⣿⣿⣿⡎⢿⠿⣰
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⡏⠉⠛⠋⠙⢻⣟⣀⣠⣾⣿⣿⢿⡄⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣿⡇⠀⢪⢞⣄⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⡏⠀⠀⠀⠀⠹⣿⣿⡇⠉⠛⢹⣿⣷⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⡇⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠃⠈⣿⡄⠀⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠚⡫⢊⠕⠡⣟⣻⣷⡀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣄⠀⠀⠀⣽⡟⣷⣿⣷⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠈⠙⠛⠋⠉⠁⠹⠀⠀⡿⣷⠀⠀⠀⠀⠀⠀⠉⠀⣙⠉⠉⠁⢀⡀⠀⠔⠨⠄⠁⠖⢿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠇⢤⠜⣿⡃⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⡿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡸⣿⢠⣿⣿⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⣻⣧⢹⣿⣇⣼⣿⡷⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠿⣿⣇⣿⣿⣾⡟⣿⣿⣿⣧⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⠿⣿⣇⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⣸⣸⣿⢰⣤⠄⠿⣧⡿⠇⠹⣧⣼⢟⣼⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠛⠻⠿⢿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⢟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠙⠻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠃⠀⠸⣿⣿⣄⣀⠉⠀⠀⣿⣿⡉⠁⠀⠀⠀⣀⣤⣤⣤⣤⣠⣀⣤⣀⣤⣶⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⣸⣿⣷⠖⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠠⢼⣿⣿⣿⣿⣿⡀⠀⠀⠀⣸⣿⣿⡄⠀⠀⣤⡄⣾⣿⣿⣿⣿⣴⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⡀⠀⠀⠀⠈⢻⣿⣿⣟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠒⢄⣿⣿⣿⣿⣿⠁⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠙⠋⠉⠉⠉⠀⠸⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⠀⠀⠀⠀⠈⢹⡟⡂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣀⣶⣀⣤⣆⡀⣠⣆⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⡀⠈⣙⣷⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃⠀⢀
⣷⣤⣶⡆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⣿⣿⠀⠀⠀⣼⣧⠀⠘⠚⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⡄⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣄⠀⠀
⣿⣿⠟⠁⣾⡿⠿⠏⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⡄⠀⡏⣼⡆⢀⣿⣿⣿⣶⣶⣶⣶⣤⣄⣀⢀⣰⣿⣿⣿⣦⣠⣤⣤⣶⣶⣶⣶⣿⣿⣿⡇⢰⣾⡟⠻⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀
⠉⠁⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⢻⡏⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣠⣄⢀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠘⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣫⠟⠛⣷
⠇⠀⠀⠸⣿⣿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣭⣮⡿⠿⢿⣿⣿⣿⡿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠉⠛⢿⣿⣷⡀⠀⠀⠀⢀⣿⡿⢸⣿⣿⡿⠋⠀⠀⣿
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠿⣻⢻⣿⣿⠋⠀⢤⣿⣿⣿⣆⡀⠉⠛⣡⣤⣶⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣤⣴⣾⣿⢣⣼⣿⣿⡇⠀⠀⠸⠿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⣀⣀⣿⠘⡙⣿⡄⠀⠀⠛⠛⠛⠿⠿⢿⣿⣿⢿⢿⠿⠿⠛⠛⠈⢀⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⠛⠛⠟⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⣿⣿⣿⣿⡆⠀⠙⣷⠀⣴⣄⠘⠻⠟⠿⠿⠿⠿⠿⠿⠟⢃⣴⣿⣿⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠿⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣄⠀⠉⠈⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⠟⠇⠀⣀⠀⠀⠀⠀⢠⣿⡇⠀⢀⣴⣶⣿⣿⣿⡿⢡⣿⢿⣿⣿⣿⣿⢿⣿⣯⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⣿⣿⣿⡄⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡔⠀⠀⢄⡐⡌⠀⠀⠸⣿⣿⣶⣿⣿⣿⣿⠋⠉⠀⠸⣿⣿⣿⣿⣿⣿⡎⠿⠿⣰
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⠈⠛⠋⠙⢻⣟⣀⣠⣾⣿⣿⢷⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣿⡇⡀⢊⢞⣤⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡏⠀⠀⠀⠀⠻⣿⣿⡇⠉⠛⢱⣿⣶⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠋⠈⣿⡄⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘⡫⢊⠕⠡⣟⣻⣷⡀⠀⠀⠀⠀⠀⠘⠻⣿⣧⣀⣀⠀⠀⠀⣽⡟⢷⣿⣦⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠈⠙⠛⠋⠉⠁⠹⠀⠀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠁⣛⠋⠉⠀⢀⡀⠀⠔⠨⠄⠁⠶⢿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠇⢠⡸⣿⡃⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⡿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡸⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⣻⣧⢹⣿⣇⣼⣿⡷⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠶⣿⣏⣿⣿⣾⡟⣿⣿⣿⣧⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⠿⣿⣇⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⣸⣸⣿⢰⣤⠀⠿⣧⡿⠇⠹⣧⣼⢟⣼⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠛⠻⠿⢿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠙⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠇⠀⠸⣿⣿⣄⡈⠉⠀⢼⣿⣟⠋⠀⠀⠀⠀⣀⣀⣠⣄⣀⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡄⣾⣿⣧⠄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠶⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡀⠀⠀⣦⣄⣾⣿⣿⣿⣿⣴⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠢⣈⣿⣿⣿⣿⣿⡀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠈⠙⠋⠉⠛⠁⠀⠸⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⠇⠀⠀⠀⠀⠈⢿⠏⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣶⣀⣰⣆⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠈⠉⠉⠁⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠛⠉⠁⠈⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢈⣹⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⢠
⣷⣀⣴⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠰⣿⡷⠀⠀⢀⣿⣇⡀⠐⠒⠂⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠁⠉⠉⠛⢾⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⡀⠀⠀
⣿⣿⡿⢃⣴⡿⠿⠟⠀⠀⠀⠀⠀⠀⢸⣶⣾⣷⡄⢈⣇⣶⡀⢸⣿⣿⣶⣶⣶⣶⣤⣤⣀⡀⢀⣸⣿⣿⣿⣆⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⡆⢼⣾⠙⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠀
⠛⠁⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⣿⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣤⣤⣴⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⣴⣶⣶⣤⠀⠀⠀⠀⠀⢸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠛⠻⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠻⢿⣛⠛⢻⣶
⢼⡿⠆⠰⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣼⡿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠛⠻⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⠋⣿⣿⡿⠟⠀⠀⣿
⠀⠀⣀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠿⡟⡟⢿⣿⣿⠋⠀⣤⣿⣿⣷⣆⠀⠙⢛⣡⣶⣾⣿⣿⣿⣧⡄⢹⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⣤⣤⣾⣿⣿⣼⣿⣿⡄⠀⠀⠠⠿
⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⣀⣿⠀⢹⣿⡀⠀⠈⠛⠛⢻⠿⠿⣿⣿⢿⠿⢿⠿⠿⠛⠃⠀⢸⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⠛⠻⠟⢛⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⡄⠀⠻⣇⠀⣤⣀⠙⠿⠿⠿⠿⠿⠿⠿⠻⠛⣡⣾⣷⣷⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠿⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠉⠘⣿⣿⣷⣦⣤⣤⣠⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⠛⠇⢀⣀⠀⠀⠀⠀⣠⣿⡇⠀⢀⣬⣴⣿⣿⣿⠟⣠⣿⣿⣿⣿⣿⡿⣿⣿⡏⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⡀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡆⠀⢀⢀⡠⡀⠀⠀⠻⣿⣷⣶⣿⣿⣿⣿⠏⠉⠀⢻⣿⣿⣿⣿⣿⣿⠘⠿⠏⣶
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⠙⠛⠃⠀⢻⣟⣀⣀⣼⣿⣿⣧⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣾⠇⡠⣢⡪⣄⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠿⣿⣿⡏⠙⠋⣾⣿⣶⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣶⣧⣼⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠋⢸⣧⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠚⡩⣪⠔⢱⣟⣿⣷⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧⣀⣀⠀⠀⢀⣿⠿⣿⣿⣦⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠉⠙⠛⠛⠛⠉⠻⠀⠀⡿⣧⠀⠀⠀⠀⠀⠈⠁⠈⣛⠋⠉⠀⢀⡀⡠⠔⠥⠈⠠⠾⢿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⠇⢠⡸⣿⡀⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠏⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡸⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢹⣿⣇⣼⣿⡷⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠦⣿⣇⣿⣿⣾⡟⣿⣿⣿⣏⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⢿⣿⣏⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⣸⣺⣿⢠⣤⠄⠿⣧⡿⠇⠹⣧⣼⢟⣼⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠛⠛⠿⠿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠛⠻⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⠇⠀⠸⣿⣿⣄⡈⠉⠀⢼⣿⣟⠋⠀⠀⠀⠀⣀⣀⣠⣄⣀⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡄⣾⣿⣧⠄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠶⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡀⠀⠀⣤⣄⣾⣿⣿⣿⣿⣤⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⠀⠀⠈⢿⣿⣿⡟⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠢⣈⣿⣿⣿⣿⣿⡀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠙⠋⠉⠛⠉⠀⠘⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⠇⠀⠀⠀⠀⠈⢿⠏⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⣶⣀⣰⣆⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠈⠉⠉⠈⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⠛⠉⠁⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⢈⣹⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠂⠀⢠
⣧⣀⣴⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠰⣿⡷⠀⠀⢀⣿⣇⡀⠐⠒⠂⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠁⠈⠉⠛⢿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⡀⠀⠀
⣿⣿⠿⢃⣴⡿⠿⠟⠀⠀⠀⠀⠀⠀⢸⣶⣾⣷⡄⢈⣇⣶⡀⢸⣿⣿⣶⣶⣶⣶⣤⣤⣀⠀⢀⣸⣿⣿⣿⣆⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⡆⢼⣾⠙⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠀
⠛⠁⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⣿⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣤⣤⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⣴⣶⣶⣤⠀⠀⠀⠀⠀⢸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠛⠻⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠻⢟⣛⠛⢻⣷
⢼⡿⠆⠰⣿⣷⣿⣿⣿⣷⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣼⡿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠛⠻⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⠛⣿⣿⡿⠛⠀⠀⣿
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠿⡿⡿⣻⣿⣿⠋⠀⣤⣿⣿⣷⣆⠀⠙⢛⣡⣴⣾⣿⣿⣿⣧⡄⢹⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⣤⣴⣾⣿⣿⣼⣿⣿⡄⠀⠀⠠⠿
⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣀⣀⣿⠊⢻⣿⠀⠀⠈⠛⠻⢿⠿⠿⣿⣿⣿⠿⢿⠿⠿⠛⠃⠀⢸⣿⣿⣿⣷⣶⠂⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⠛⠻⠟⢛⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⡄⠀⠻⣇⠀⣤⣀⠙⠿⠿⠿⠿⠿⠿⠿⠻⠛⣡⣾⣷⣷⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⢸⡄⠀⠀⢿⠿⣴⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠉⠘⣿⣿⣷⣦⣤⣤⣠⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⠛⠇⠀⣀⠀⠀⠀⠀⣠⣿⡇⠀⢀⣾⣾⣿⣿⣿⠿⣠⣿⣿⣿⣿⣿⡿⣿⣿⣏⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠉⣿⣿⣿⡀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡆⠀⢀⢀⡠⡐⠀⠀⠹⣿⣷⣶⣿⣿⣿⣿⠏⠉⠀⢻⣿⣿⣿⣿⣿⣿⠘⠿⠏⣶
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⣿⡿⠘⠛⠁⠀⣻⣟⣀⣀⣼⣿⣿⣧⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣾⡇⡠⣢⡪⣄⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠿⣿⣿⡏⠙⠋⣾⣿⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣴⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠋⢸⣧⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠚⡩⣪⠔⢱⣟⣿⣷⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧⣀⣀⠀⠀⢀⣿⠿⣿⣿⣦⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠉⠙⠛⠛⠛⠉⠻⠀⠀⡿⣧⠀⠀⠀⠀⠀⠈⠁⠀⣛⠋⠉⠀⢀⡀⡠⠔⠥⠈⠠⠶⢿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠇⢠⡸⣿⡀⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣯⣿⣿⢿⠏⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣸⣿⢠⣿⣿⣿⢘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢹⣿⣇⣼⣿⡷⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠦⣿⣏⣿⣿⣾⡟⣿⣿⣿⣯⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⢿⣿⣏⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⣸⣺⣿⢠⣤⠄⠿⣧⡿⠇⠹⣧⣼⢟⣼⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠛⠛⠿⠿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠛⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠇⠀⠘⣿⣿⣄⣀⠉⠀⢾⣿⣏⠉⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣠⣴⣶⣶⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆⣿⣿⡧⠄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠲⢤⣿⣿⣿⣿⣿⡀⠀⠀⠀⣼⣿⣿⡄⠀⠀⣦⣤⣾⣿⣿⣿⣿⣦⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⠀⠀⠈⢿⣿⣿⡟⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠢⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠛⠛⠂⠀⠀⠀⠘⠃⠈⠉⠁⠀⠘⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⠀⠀⠀⠀⠈⢿⠟⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣷⣄⣰⣤⡀⣠⣆⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⠋⠉⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⣀⣹⡇⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠂⠀⢰
⣷⣠⣴⡆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⣿⡷⠀⠀⢀⣿⣇⠀⠘⠛⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠈⠀⠈⠉⠙⢺⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣄⠀⠀
⣿⣿⠿⢧⣴⡿⠿⠟⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⡄⢸⣇⣶⡀⢸⣿⣿⣷⣶⣶⣶⣶⣦⣄⡀⣀⣸⣿⣿⣿⣦⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⡆⢺⣿⠙⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀
⠉⠁⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⣿⡉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⡀⠀⢠⣄⢀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⢸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣼⣿⣟⡛⣻⣿⠛⠻⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣥⣾⡿⠿⢿⣿⣿⣿⠿⢿⣿⣿⣏⠛⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠛⣿⣿⣷⠀⠀⠀⠀⢀⣼⣿⢉⣿⣿⡿⠛⠀⠀⣿
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠘⠻⠿⡟⣿⣿⣿⠃⠀⢴⣿⣿⣷⣦⠀⠉⣉⣰⣶⣾⣿⣿⣿⡷⠄⢻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣤⣤⣤⣾⣿⢡⣼⣿⣿⠅⠀⠀⠴⠯
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣄⣄⠷⠽⣿⣷⡀⠀⠀⠙⠛⣛⠿⠿⡿⡿⡿⣿⣿⡟⠛⠛⠁⠀⢠⣿⣿⣿⣷⣿⠂⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⠙⠛⠟⣛⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢿⠿⢿⣿⣯⣼⡂⠈⢻⣇⠀⣤⣄⠘⠻⠻⠿⠿⠿⠿⠿⠻⠛⣡⣾⣿⣗⣿⣿⣿⡿⠻⠃⠀⠀⠀⠀⠀⣸⡆⠀⠀⣿⠿⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢨⣿⠀⢠⣿⣿⣿⣿⡄⠀⠙⠘⣿⣿⣷⣶⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠛⠇⠀⡀⠀⠀⠀⠀⣠⣿⡇⠀⢠⣾⣶⣿⣿⣿⠿⣰⣿⣿⣿⣿⣿⣿⢿⣿⣏⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠘⠋⢰⣿⡿⠉⣿⣿⣿⡀⠠⢠⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡆⠀⢀⢂⡐⡜⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⠏⠁⠀⠹⣿⣿⣿⣿⣿⣿⠘⠿⢟⣾
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢘⣟⣀⣠⣼⣿⣿⢷⡀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣿⠇⡠⣣⣲⣤⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⡟⠀⠀⠀⠀⠻⣿⣿⡏⠙⠋⣼⣿⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠸⣷⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢘⡡⡪⠞⠱⣟⣿⣷⡀⠀⠀⠀⠀⠀⠘⠻⣿⣷⣤⣄⠀⠀⢀⣿⠟⣷⣿⣧⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠉⠙⠛⠛⠉⠉⠻⠀⠀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⠁⠀⢀⡀⠠⠒⠥⠀⠠⠾⢿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠇⢠⡸⣿⡀⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠏⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⣘⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢹⣿⣧⣼⣿⡗⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠆⣿⣏⣿⣿⣾⡟⣿⣿⣿⣯⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⢿⣿⣷⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡏⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠈⢿⣴⡿⣹⣺⣿⢰⡦⠀⠿⣧⡿⠇⠹⣧⣼⢟⣾⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡏⠛⠛⠻⠯⢿⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣀⠀⠀⠙⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉
⠀⠚⣿⣿⣿⣿⠿⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠘⣿⣿⣤⣄⠁⠀⢾⣿⣏⡉⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣤⣤⣤⣴⣶⣶⣦⣤⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆⣿⣿⡧⠄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠒⢤⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⡆⠀⠀⣤⣤⣾⣿⣿⣿⣿⣶⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⢻⣿⣿⡏⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠢⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠉⠃⠈⠉⠁⠀⠘⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⠀⠈⢻⠛⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣿⣤⣴⣦⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⠁⢀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⠋⠁⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡀⢀⣀⣀⣹⡇⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠀⠀⠠
⣷⣤⣴⡆⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⣿⡷⠀⠀⢠⣿⡧⠄⠚⠉⠉⠉⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠀⠀
⣿⣿⠿⢷⣾⡿⠿⠟⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⡄⢰⣧⣷⡄⢸⣿⣿⣷⣶⣷⣶⣶⣦⣤⣀⣀⣼⣿⣿⣿⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡆⢺⣿⠉⠻⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀
⠉⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠃⠀⣿⡉⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦
⠀⢀⡀⢀⡄⠀⢠⣄⢀⡀⠀⣴⣶⣶⣦⡀⠀⠀⠀⠀⢸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣿⣿⡟⠻⣿
⠀⠙⠓⠸⣿⣿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣴⣾⡿⠛⢿⣿⣿⡿⠿⢿⣿⣿⣯⡙⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠙⣿⣿⣧⠀⠀⠀⠀⢀⣾⡿⠉⣿⣿⡿⠟⠁⢀⣽
⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠘⠻⠟⡟⣿⣿⡿⠁⠀⠶⣿⣿⣿⣦⡀⢉⣉⣴⣶⣿⣿⣿⣿⡷⠄⠹⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣧⣠⣤⣶⣾⡿⢡⣴⣿⣿⠇⠀⠀⠴⠿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣄⡄⠿⠻⠻⣿⡀⠀⠈⠉⢛⣛⣛⡻⡿⢿⡿⣿⣟⣛⡛⠛⠁⠀⢠⣿⣿⣿⣷⣿⠂⠀⠀⠀⠀⢠⠀⠀⠸⣿⣿⠉⠛⠛⣻⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠛⢿⣿⣦⣴⡒⠀⢹⣇⢀⣶⣄⠘⠻⠛⠻⠿⠿⠿⠛⠛⠛⣡⣾⣿⣷⣿⣿⣿⡟⠻⠃⠀⠀⠀⠀⠀⣸⡆⠀⠀⢿⠿⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠂⠀⢠⣤⢀⣼⣿⣿⣿⣷⡄⠀⠉⠙⣿⣿⣿⣶⣦⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⡟⠛⠓⠀⣀⠀⠀⠀⠀⣴⣿⡇⠀⣠⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⡿⢿⣿⣯⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠋⣼⣿⠟⠉⣿⣿⣿⡀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡇⠀⢀⢂⠐⠜⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⠏⠁⠀⢹⣿⣿⣿⣿⣿⣿⠘⢿⠟⣶
⣿⣿⣿⣿⢿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⣘⣏⣀⣤⣿⣿⣿⢷⡀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢰⣿⠇⠰⡡⣳⣤⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡟⠀⠀⠀⠀⠻⣿⣿⡏⠉⠋⣼⣿⣷⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⢸⣧⠀⠀⠈⠛⠿⠿⣿⣿⠿⣿⣿⣿⢿⠿⠉⠀⠀⢚⢕⡨⠊⠰⣟⣿⣷⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⣄⠀⠀⢀⣿⠟⣿⣿⣧⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠙⠋⠉⠉⠁⠻⠀⠀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣋⠁⠀⠀⢀⡀⠠⡂⠴⠀⠰⠾⢿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠇⢠⠸⣿⡀⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠏⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡘⣿⢠⣿⣿⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣯⢸⣿⣧⣼⣿⡟⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠄⣿⣇⣿⣿⣾⡟⣿⣿⣿⣯⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⢿⣿⣧⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡟⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡏⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠈⢿⣴⡿⣸⣺⣿⢰⡆⠀⠿⣧⡿⠇⠹⣧⣼⢟⣾⡿⢸⡇⣿⡇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡏⠙⠛⠻⠿⢿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠉⠛⠋⠈⠁⠀⠀⠀⠀⠀⠀⡠⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠘⣿⣿⣤⣄⡀⠀⢾⣿⡍⠁⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣴⣤⣤⣶⣶⣶⣦⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣿⣿⡷⠂⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠲⣬⣿⣿⣿⣿⣿⡀⠀⠀⠀⣸⣿⣿⡄⠀⠀⣤⣄⣾⣿⣿⣿⡿⣴⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⠀⢻⣿⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠢⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠈⠃⠀⠉⠁⠀⠘⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠇⠀⠀⠀⠀⠈⣿⢃⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣿⣤⣤⣦⣀⣠⣦⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⠀⢀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠋⠀⢀⡀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣀⣀⣀⣠⣹⡇⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠀⠀⠰
⣷⣤⣶⡆⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠸⣿⡇⠀⠀⢰⣿⡥⠄⠚⠉⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣤⠀⠀
⣿⣿⠿⣷⣾⡿⠿⠟⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⡆⢸⣡⣷⠀⢸⣿⣿⣿⣾⣿⣶⣶⣦⣄⣀⣀⣸⣿⣿⣿⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡄⢿⡿⠙⠻⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⠉⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠈⣿⠉⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣧⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⢠⣀⠀⣠⣄⣀⡀⠀⣶⣶⣶⣦⡀⠀⠀⠀⠀⢹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠛⠿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣝⣿⣿⡿⠛⢿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣶⣾⡟⠛⢿⣿⣿⡿⠿⢿⣿⣿⣯⠛⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⠉⠛⣿⣿⣧⠀⠀⠀⠀⢀⣾⡿⠉⣿⣿⡿⠋⠀⢀⠘
⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠻⠟⣏⣿⣿⡟⠁⠀⢾⣿⣿⣿⣆⣀⣉⣁⣴⣶⣿⣿⣿⣿⡷⠄⢹⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣤⣤⣶⣿⡿⣣⣴⣿⣿⠀⠀⠰⠾⠇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣦⣶⣦⣀⡄⠗⠉⢻⣷⠀⠀⠈⠉⣛⣛⣛⣻⡿⢿⡿⣿⣿⣛⡛⠋⠀⡀⣰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣯⠉⠛⠛⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠉⣽⣿⣿⣷⡀⠀⢻⡇⢀⣦⣄⠙⠛⠛⠛⠿⠿⠟⠛⠛⢋⣤⣿⣿⣷⣿⣿⣿⡟⠻⠁⠀⠀⠀⠀⠀⣼⡄⠀⠘⢿⠿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢠⡄⣠⣿⣿⣿⣿⣷⡄⠀⠉⠉⣿⣿⣿⣶⣶⣦⣤⣤⣦⣶⣶⣿⣿⣿⣿⣿⣿⡟⠙⠃⠀⡀⠀⠀⠀⠀⣴⣿⡀⠀⣠⣿⣾⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⡿⣿⣿⡏⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠁⣿⣿⠟⠘⣿⣿⣷⡀⠰⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⡇⠀⢠⣠⠐⡁⠀⠀⠻⣿⣷⣶⣿⣿⣿⣿⠋⠁⠀⢻⣿⣿⣿⣿⣿⣿⠙⡿⢧⣾
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣙⣭⣠⣴⣿⣿⡿⢷⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢰⣿⢃⢔⡵⣣⣦⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⠏⠉⠋⣾⣿⣾⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣴⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⢸⣧⠀⠀⠈⠛⠛⠿⢿⠿⠿⣿⣿⣿⠿⠟⠁⠀⠀⣋⢔⠵⠊⣸⣟⣿⣧⠀⠀⠀⠀⠀⠀⠘⠻⡿⣷⣤⣄⠀⠀⢠⣿⠛⣿⣿⣦⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⡇⠀⠈⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⢀⡀⠔⡪⠶⠀⠴⠿⢿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠇⢠⠸⣿⡀⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡸⣿⢠⣿⣿⣿⣘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣧⣼⣿⡟⣿⡟⢻⡆⣿⡇⠀⢿⣠⡿⢸⣿⠄⣿⣇⣿⣿⣾⡟⣿⣿⣿⣏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⢿⣿⣯⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡏⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣴⡿⣹⣾⣿⠰⠦⠀⠿⣧⡿⠇⠹⣧⣼⢟⢾⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡏⠉⠛⠛⠿⢿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠸⣿⣿⣤⣀⠀⠐⣿⣿⠍⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣾⣿⣿⠟⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠐⠲⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣷⠀⠀⠠⣦⣀⣿⣿⣿⣿⡿⣼⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠈⣿⣿⡿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠢⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠙⠁⠀⠉⠀⠀⠘⠿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠸⣿⣢⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⡀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣰⣷⣤⣴⣤⣀⣰⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⡟⠉⠀⣀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣿⠁⠀⡀⡀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣀⣀⣀⣠⣽⡄⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⢰
⣧⣴⣾⡆⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⣿⠇⠀⠀⣸⣿⣤⠔⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣇⠀⠀⡞⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⠀⠀
⣿⡿⢿⣷⣾⡿⠿⠟⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⡄⢸⣼⣷⠀⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣾⣿⣿⣿⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⣷⡇⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠘
⠁⠀⠸⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠸⣧⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣧⣴⣦⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶
⡀⠀⠀⣤⣀⠀⣠⣀⣀⠀⢠⣶⣶⣶⣄⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠋⠻⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣭⣿⣿⠛⠉⢹
⠟⠀⠘⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠡⣶⣿⠛⠛⢿⣿⣿⡿⠟⢿⣿⣷⣍⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣆⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⠛⠃⢀⡀⠀
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⠿⢻⣟⢿⣿⡏⠀⠐⢾⣿⣿⣿⣦⣀⣉⣡⣶⣾⣿⣿⣿⣿⡶⠀⢻⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣶⣾⣿⣿⣾⣿⣿⠀⠀⠺⠿⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠤⣤⣤⡤⣄⣀⣤⡇⠀⢹⣧⠀⠀⠈⠉⣙⣛⣛⣻⡿⣿⣟⣟⣛⣛⠛⠉⠀⠀⣼⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⡄⠀⠀⢿⣿⡅⠉⠛⢟⣻⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⢀⣾⣿⣿⣿⣷⠀⠀⢻⡄⣰⣦⣄⠙⠛⠛⠛⠟⠛⠛⠛⠛⢉⣴⣿⣿⣿⣿⣿⣿⠋⠛⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡿⢳⣶⣶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⡧⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢹⣿⣿⣿⣶⣶⣦⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⠋⠛⠂⢠⡀⠀⠀⠀⢠⣾⣿⠀⠀⣼⣷⣿⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⡟⣿⣿⡄⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⡇⢿⣿⣿⣿⠟⢹⣿⣿⣧⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⠀⠀⡄⡄⠢⠁⠀⠈⠿⣿⣷⣾⣿⣿⣿⣿⠋⠀⠀⢿⣿⣿⣿⣿⣿⣷⠹⡿⢳⣿
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⠃⠉⠁⠀⠈⣻⣥⣠⣼⣿⣿⡿⣦⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⣼⡿⡀⢪⢞⣢⣄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢿⣿⣿⢈⡉⠁⣿⣿⣾⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡏⠀⣿⡇⠀⠀⠈⠛⠛⠿⠿⠿⢿⣿⣿⡿⠿⠛⠁⠀⠀⡩⣪⠖⢁⣿⣽⣿⣆⠀⠀⠀⠀⠀⠀⠙⠿⢿⣧⣤⣄⠀⠀⣸⣿⢻⣿⣿⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠈⠉⠉⠉⠀⠸⡄⠀⢸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⢀⡠⢒⡱⠆⢀⠾⠿⢿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠇⢠⠻⣟⣰⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠏⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡡⣿⢰⣿⣿⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣧⣼⣿⡏⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠖⣿⣇⣿⣿⣾⡟⣿⣿⣿⡝⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⡿⣿⣧⣸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⣸⣿⣿⡿⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡏⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣼⡿⣹⣾⣿⢰⠀⠀⠿⣧⡿⠇⠹⣷⣼⢿⢾⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡏⠉⠛⠻⠻⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢹⣿⣷⣤⣀⠀⠀⣿⣿⠍⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣾⣿⣿⠖⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠐⠢⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣷⠀⠀⠠⣤⣠⣿⣿⣿⣿⡷⣼⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⠀⠀⠀⠀⠈⣿⣿⣿⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠢⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠙⠁⠈⠉⠀⠀⠸⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠸⡟⣂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣰⣧⣄⣴⣄⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⢿⡟⠉⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⠿⠿⢿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣿⠁⠀⡀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣀⣀⣀⣀⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠰
⣧⣴⣾⡆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠸⣿⠂⠀⠀⣸⣿⣤⠔⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⡇⠀⢰⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣄⠀⠀
⣿⡿⢿⣷⣾⡿⠿⠟⠀⠀⠀⠀⠀⠀⢾⣷⣿⣷⠀⣏⣼⡧⠀⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀⣀⣾⣿⣿⣿⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⣿⡇⠙⠻⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀
⠀⠀⠸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⢸⣇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣦⣴⣦⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣷
⣀⣠⣠⣤⡀⠀⣠⡀⢀⠀⢠⣶⣶⣦⡄⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⠛⠻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣯⣿⣿⠛⠉⢹
⠻⠿⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣶⣿⠛⠛⢿⣿⣿⡿⠟⢿⣿⣷⣍⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⢟⣿⣿⠛⠃⠀⡀⠀
⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠟⢻⢹⢿⣿⡏⠀⠐⢾⣿⣿⣷⣤⣀⣉⣡⣶⣾⣿⣿⣿⣿⡦⠀⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣀⣤⣤⣶⣾⣿⣿⣾⣿⣿⠀⠀⠰⠿⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢀⠀⣀⣠⣼⡀⠂⢿⣧⠀⠀⠈⠉⣙⣛⣛⢻⡿⣿⣟⣛⣛⣛⠛⠁⠀⠁⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⡈⠙⠛⠛⣻⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣦⣴⡆⢀⣾⣿⣿⣿⣧⠀⠉⢿⡄⣠⣦⡀⠙⠛⠛⠛⠿⠛⠛⠛⠛⢉⣴⣿⣿⣾⣿⣿⣿⠛⠟⠀⠀⠀⠀⠀⢀⣧⠀⠀⢹⠟⢱⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣿⣶⣶⣦⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⠛⠻⠀⢀⠀⠀⠀⠀⢠⣾⣏⠀⢀⣼⣴⣿⣿⣿⡿⢧⣼⣿⣿⣿⣿⣿⠿⣿⣿⡕⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⡿⠏⢻⣿⣿⡆⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣼⠀⠀⡄⡌⠂⠀⠀⠘⢿⣿⣶⣾⣿⣿⣿⣿⠋⠀⠈⢿⣿⣿⣿⣿⣿⡇⠻⠿⢳⣾
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣿⡇⠘⠋⠀⠈⣙⣁⣀⣸⣿⣿⢿⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣾⠟⡠⣪⢾⣤⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⠈⠉⢡⣿⣿⣼⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣶⣧⣴⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡆⠀⠀⠈⠛⠛⠻⠿⠿⢿⣿⣿⡿⠿⠋⠁⠀⢘⡡⡪⠖⢁⣿⣽⣿⣄⠀⠀⠀⠀⠀⠀⠙⢿⢿⣧⣤⣄⠀⠀⣸⡿⢻⣿⣿⣬⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠏⠀⠀⠀⠈⠉⠛⠛⠋⠉⠹⡀⠀⢿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀⡠⢒⡱⠆⢀⠾⠿⢿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠆⠀⠿⢗⡨⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡁⣿⢰⣿⣿⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣧⣾⣿⡏⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⠷⣿⣇⣿⣟⣾⡟⣿⣿⣿⡙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⣟⣿⣇⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⣻⣿⣿⡟⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣶⡿⣸⣾⣿⠐⠀⠀⠿⣧⡿⠇⠹⣷⣼⡿⢾⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡏⠛⠛⠿⠿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢻⣿⣧⣄⡈⠀⠰⣿⣯⠉⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣵⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣾⣿⣿⠖⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠐⢤⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣧⠀⠀⢠⣄⢠⣿⣿⣿⣿⣷⣼⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⠄⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠙⠉⠉⠉⠁⠀⢹⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠀⠀⠀⠀⠀⠹⡟⣢⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣰⣦⣀⣴⣄⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠉⠉⠈⠉⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣟⠁⢀⡀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣀⣀⣈⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠠
⣦⣤⣶⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⣿⠀⠀⠀⣼⣿⡤⠐⠋⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⡧⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡆⠀⢰⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⠀⠀
⣿⡿⣿⣦⣾⡿⠿⠗⠀⠀⠀⠀⠀⠀⢼⣶⣿⣧⠀⣇⣾⡆⠀⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣀⣀⣿⣿⣿⣷⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣧⢰⣾⠏⠙⠿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠠
⠁⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠀⢹⡇⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣤
⠀⢀⣀⣤⡀⠀⣠⡀⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠛⠛⢻⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣽⣿⣿⠟⠛⢿
⠀⠿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⢡⣶⣿⠛⠻⣿⣿⣿⡿⠿⢿⣿⣿⡍⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⡀⠀⠀⠀⠀⠀⣰⣿⢟⣿⣿⠿⠏⠀⡀⠘
⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⠟⢻⢹⣿⣿⠏⠀⠰⣾⣿⣿⣷⣄⣀⣉⣡⣴⣶⣿⣿⣿⣿⠦⠈⢿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⣀⣤⣤⣾⣿⣿⣼⣿⣿⠀⠀⣼⡿⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢧⡀⠀⠀⠀⢀⢀⣠⣨⠘⠈⢻⣆⠀⠀⠉⠙⣛⣛⣛⢻⠿⢿⢿⣿⣟⡛⠛⠋⠀⠀⣼⣿⣿⣿⣾⠆⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⡈⠛⠿⠟⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣤⣠⣄⢠⣾⣿⣿⣿⣇⠀⠘⣿⡀⣰⣦⡀⠛⠟⠛⠻⠿⠿⠿⠟⠟⢋⣴⣿⣾⣼⣿⣿⣿⠛⠏⠀⠀⠀⠀⠀⢠⡇⠀⠀⢿⡿⣽⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⠈⢻⣿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⠛⠻⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⢀⣼⣤⣿⣿⣿⡿⢣⣼⣿⣿⣿⣿⣿⢿⣿⣯⠑⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⡄⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡖⠀⠀⢄⡑⠄⠀⠀⠸⣿⣿⣶⣾⣿⣿⣿⣿⠋⠀⠘⣿⣿⣿⣿⣿⣿⡇⠻⠿⢠⣶
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡿⠀⠘⠛⠀⠈⣛⣁⣀⣸⣿⣿⢿⣄⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣾⠇⠠⣪⢞⢤⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡏⠀⠀⠀⠸⣿⣿⣿⠙⠛⢡⣿⣷⣼⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⣿⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠃⠈⣿⡀⠀⠀⠙⠛⠿⠿⣿⠿⢿⣿⣿⣿⠿⠋⠀⠀⠘⡩⡪⠔⠑⣟⣻⣷⡄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⣀⡀⠀⠀⣸⡿⢳⣿⣧⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠏⠀⠀⠀⠈⠙⠛⠛⠛⠛⠻⠀⠀⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠉⠀⠀⢀⡠⢐⡤⠆⢀⡾⠿⢿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠀⠀⣿⢇⡸⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣯⣿⣿⡿⠇⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⢰⣿⡿⣿⢘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣇⣾⣿⡏⣿⡟⢻⡆⣿⡇⠀⢿⣠⡿⢸⣿⠶⣿⣇⣿⣧⣾⡟⣿⣿⣿⡻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣿⣿⢸⣿⡿⣿⢇⢼⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢾⣿⣿⡟⣿⡇⣿⡷⠿⠃⣿⡇⠀⠸⣿⠃⢸⣿⠀⣿⢿⣿⡟⣿⡇⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠈⢿⣿⡿⣸⣽⣿⢠⠀⠀⠿⣧⡿⠇⠹⣷⣼⢿⢺⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣧⠿⡟⠛⠻⠿⢿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁
⠀⠘⣿⣿⣿⣿⠷⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠟⠀⠘⣿⣿⣅⣀⠉⠉⣾⣿⣛⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣄⣄⣀⣠⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣿⣿⣧⠆⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢤⡀⣾⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣶⡄⠀⠀⣄⡀⣠⣶⣿⣿⣿⣆⣴⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠉⠉⢻⣿⣿⡟⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢄⠱⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⠿⠇⠀⠀⠈⠙⠿⠉⠛⠋⠉⠘⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠀⠀⠀⠀⠈⣿⡏⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣄⣀⣄⠀⠀⣀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠊⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⡗⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠋⠉⠋⠉⠉⠉⠉⠉⠀⠀⣶⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠁⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠀⠀⠀⠉⢻⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠆⠀⠀⣀
⣄⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢾⡆⠀⠀⢀⣿⣃⡠⠝⠛⠒⠂⠀⠀⠀⠀⢹⣿⣿⣿⡇⠐⠂⠀⠀⠑⠚⢿⣿⣿⣧⠀⠀⡄⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣄⠀⠀⠉
⣿⡿⣿⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⣶⣴⣿⣄⢸⢡⣶⠀⢸⣿⣿⣶⣶⣶⣶⣤⣤⣀⠀⠀⣸⣿⣿⣿⣦⣠⣤⣤⣴⣶⣶⣶⣿⣿⣿⡀⣦⡇⠙⢿⣿⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⡀
⠉⠀⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠇⠸⣿⠋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣀⣄⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⢈⡅⠀⠀⣀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⣿⣷⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡻⢿⣿⣿⡿⢿⣧
⠀⠐⣿⣿⣷⣾⣿⣿⣷⣤⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠛⢿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣾⡿⢻⣿⣿⠿⠋⠀⠀⢿
⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⢿⠿⡟⣿⢿⡿⠋⠀⣤⣿⣿⣷⣄⠀⠙⠛⢉⣤⣶⣿⣿⣿⣧⡀⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⣀⣀⣤⣤⣿⡿⣁⣼⣿⡇⠀⠀⣼⡆⠘
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⠀⠀⣀⡇⠫⠻⣷⠀⠀⠈⠛⠻⠿⠿⠶⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⢠⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠛⠿⣿⠿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣄⠘⣹⣿⣿⣿⣷⠀⠈⢻⣇⠀⣤⡀⠘⠿⠿⠷⣿⣾⠿⠿⠿⠿⢃⣴⣶⣤⣾⣿⣿⡟⢻⠇⠀⠀⠀⠀⠀⢸⡀⠀⠘⣿⠟⣦⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⣴⣿⣿⣿⣿⣿⣧⠀⠀⠉⠚⣿⣿⣶⣤⣤⣄⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢀⣇⣴⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣇⠀⠀⣀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⠆⠀⢀⠑⢄⠂⠀⠀⢿⣿⣧⣤⣿⣿⣿⣿⡿⠋⠁⢹⣿⣿⣿⣿⣿⣿⡜⣿⣿⣠⣤
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣷⠜⠿⠏⠉⠙⣋⣀⣀⣿⣿⣿⣆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣿⠀⡠⣣⢏⡀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⡏⠛⠛⢱⣶⣆⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⡇⠀⠀⣾⣶⣾⣿⣿⣿⣿⡟⠁⢿⣇⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠟⡡⣪⠞⢵⣗⣿⣆⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡀⣀⠀⠀⠀⣿⡿⣷⣶⣆⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠃⠀⠀⠉⠉⠛⠿⠛⠛⠹⠇⠀⠸⣿⡄⣀⠀⠀⠀⠀⠈⠁⠘⠛⣋⠋⠀⠀⢀⡀⠐⡩⠈⢠⡶⠿⢿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⠿⢷⠀⢸⣿⢃⣻⣿⣿⣿⣿⣿⣯⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⣟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⣷⣿⣿⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣯⢸⣿⣧⣽⣿⡇⣿⡟⢻⡆⣿⡇⠀⣿⣤⡿⢸⣿⣷⣿⣇⣿⡇⣾⡟⣿⣿⣟⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⣧⣿⢷⢼⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢻⣿⣿⡟⣿⡇⣿⡷⠿⠃⣿⡇⠀⢸⣿⠃⢸⣿⠁⣿⢿⣿⡧⣿⡏⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⣹⣿⠈⢿⣿⡿⣸⣸⣿⠀⠀⠀⠿⣧⡿⠇⠹⣧⣼⡿⢺⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣯⠿⡿⠿⢿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠘⠻⠿⠏⠛⠁⠀⠀⠀⠀⠀⠀⢀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠛⠁
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠘⣿⣿⣅⣀⠉⠉⣾⣿⣛⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣄⣄⣀⣠⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣿⣿⣧⠆⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢴⡀⣼⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣶⡄⠀⠀⣄⡀⣠⣾⣿⣿⣿⣇⣴⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠉⠉⢹⣿⣿⡟⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢄⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⠿⠇⠀⠀⠉⠙⠟⠉⠛⠋⠉⠉⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠀⠀⠀⠀⠈⣿⡏⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣄⣀⣄⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠊⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣾⣿⡗⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠋⠉⠋⠉⠉⠉⠈⠉⠀⠀⣴⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠁⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠀⠀⠀⠉⢻⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠆⠀⠀⣀
⣄⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢿⡆⠀⠀⢀⣿⣃⡠⠝⠚⠒⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠂⠀⠀⠙⠛⢿⣿⣿⣧⠀⠀⡄⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣄⠀⠀⠁
⣿⡿⣿⣤⣾⡿⡿⠇⠀⠀⠀⠀⠀⠀⣶⣴⣿⡄⢸⢡⣶⠀⢸⣿⣿⣶⣶⣶⣶⣤⣤⣀⠀⠀⣸⣿⣿⣿⣦⣠⣤⣤⣴⣶⣶⣶⣿⣿⣿⡀⣦⡇⠘⢿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⡀
⠉⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠇⠸⣿⠛⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡇⢀⣄⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⢈⣅⠀⠀⣀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⣿⣿⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡻⢿⣿⣿⠿⢿⣧
⠀⠐⣿⣿⣷⣾⣿⣿⣷⣤⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠛⢿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣾⡿⢻⣿⣿⠿⠏⠀⠀⢿
⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⠿⡟⣿⣿⡿⠋⠀⣤⣿⣿⣷⣄⠀⠙⠛⣉⣤⣶⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⣀⣀⣠⣤⣿⣿⣁⣼⣿⡇⠀⠀⣸⣆⠘
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⣀⡇⠋⠺⣷⠀⠀⠈⠛⠻⠿⠿⠷⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⢨⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠛⠿⣿⠿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣌⠘⣻⣿⣿⣿⣷⠀⠈⢻⣇⠀⣤⡀⠘⠿⠿⠷⣿⣾⠿⠿⠿⠿⢃⣴⣶⣦⣾⣿⣿⡟⢻⠇⠀⠀⠀⠀⠀⢸⡀⠀⠘⣿⠟⣦⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡟⣴⣿⣿⣿⣿⣿⣧⠀⠀⠉⠘⣿⣿⣶⣤⣤⣄⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⡿⠿⡇⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢀⣅⣴⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣇⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⠆⠀⢀⠑⢄⠂⠀⠀⢿⣿⣧⣤⣿⣿⣿⣿⡿⠋⠁⢹⣿⣿⣿⣿⣿⣿⡜⣿⣿⣠⣤
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⣷⠘⠿⠏⠉⠙⣋⣀⣀⣿⣿⣿⣆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣿⠀⡠⣣⢏⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⡏⠛⠟⢱⣶⣄⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣼⣿⣿⣿⡇⠀⠀⣾⣾⣾⣿⣿⣿⣿⡟⠁⢿⣇⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠟⡡⣪⠞⢵⣟⣿⡆⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣀⣀⠀⠀⠀⣿⡿⣷⣶⣆⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠃⠀⠀⠈⠉⠛⠻⠛⠛⠹⠇⠀⠸⢿⡄⣀⠀⠀⠀⠀⠈⠁⠐⠛⣛⠋⠀⠀⢀⡀⠐⡭⠈⢠⡶⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠿⢷⠀⢸⣿⢆⣻⣿⣿⣿⣿⣿⣯⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⣟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⣷⣿⣿⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣼⡟⢻⣯⢸⣿⣧⣽⣿⡏⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⣷⣿⣇⣿⡇⣾⡟⣿⣿⣟⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠁⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢸⣿⣿⣿⣷⣼⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢻⣿⣿⡟⣿⡇⣿⡷⠿⠃⣿⡇⠀⢸⣿⠇⢸⣿⠁⣿⢿⣿⡧⣿⡏⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⣹⣿⠈⢿⣿⡿⣸⢽⣿⠀⠀⠀⠿⣧⡿⠇⠹⣧⣼⡿⢺⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠈⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣯⠿⡿⠿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠘⠛⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠁
⠀⠘⣿⣿⣿⣿⠶⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠟⠀⠸⣿⣿⣀⡈⠉⢱⣿⣿⣛⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣠⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣾⣿⣷⡥⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠠⢇⠠⣿⣿⣿⣿⣿⡀⠀⠀⠀⣰⣷⣶⡀⠀⠀⣀⢀⣴⣾⣿⣿⣿⣠⣶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠉⠉⢿⣿⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⠄⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⠿⠿⠅⠀⠀⠉⠙⠏⠋⠛⠋⠉⠹⣿⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⢸⣟⢁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣤⡀⢀⣄⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⠗⠂⠀⠀⠀⠀⠰⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠋⠉⠛⠉⠉⠉⠉⠁⠀⢀⣶⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠁⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠁⠈⠉⠉⢻⡀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠆⠀⢀⣀
⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣷⠀⠀⠀⢸⣿⣀⠀⠓⠒⠒⠀⠀⠀⠀⠀⢿⣿⣿⣿⠅⠀⠀⠀⠀⠒⠻⢶⣿⣿⡇⠀⢀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣥⡀⠀⠈⠉
⣿⢿⣧⣴⣿⠿⡿⠂⠀⠀⠀⠀⠀⢠⣦⣶⣷⡀⣇⣼⡆⠀⣿⣿⣷⣶⣶⣶⣶⣤⣤⣀⠀⠀⢸⣿⣿⣿⣄⣠⣤⣤⣴⣶⣶⣾⣿⣿⣷⠀⣼⠀⠻⣿⣿⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⡀
⠁⠀⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡿⠃⢿⡏⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀
⠀⠀⣠⡄⠀⢀⡀⠀⠀⠀⣠⣤⣤⡄⠀⠀⠀⠀⢸⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠿⠿⠿⣿⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⢿⣿⣿⡿⢿⣤
⠀⠰⣿⣿⣿⣾⣿⣿⣷⣤⣿⣿⣿⣿⣄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣭⣽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣾⡟⣿⣿⣿⡿⠋⠀⠀⢿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠻⠿⢻⢛⣿⣿⡿⠉⠀⣤⣿⣿⣷⡀⠈⠛⠛⣉⣤⣾⣿⣿⣿⣆⡈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⣀⣀⣠⣤⣿⡿⣁⣿⣿⡃⠀⠀⣴⡄⠘
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⣈⠨⠉⢻⣇⠀⠀⠑⠛⠿⠿⠿⢷⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⢸⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⡃⠻⠿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢉⣿⣿⣿⣿⣇⠀⠟⢿⡄⢀⣄⡀⠻⢿⠿⢶⣷⣾⡿⠿⠿⠿⢀⣶⣦⣦⣿⣿⣿⠏⠿⠁⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿⢗⣤⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠘⠁⠾⣿⣷⣶⣤⣤⣄⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⠿⠿⠄⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⢨⣡⣼⣿⣿⣿⡿⣩⣿⣿⣿⣿⣿⣿⢿⣿⣟⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢾⣿⣿⣿⡟⢻⣿⣿⡀⠀⢀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡠⠀⠀⡈⡳⡀⠂⠀⠀⣿⣿⣦⣴⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⠸⣿⡿⣠⣤
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡿⠀⠀⠀⠉⢙⣉⣀⣼⣿⣿⣷⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣴⡏⢀⢜⡼⣁⠈⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⢿⣿⣿⡏⠛⠟⣰⣶⣄⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣴⣿⣿⣿⡇⠀⠠⣶⣷⣿⣿⣿⣿⣿⠋⠸⣿⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠸⢋⢔⡵⠫⣾⣺⣷⡀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⡀⡀⠀⠀⢀⣿⠿⣷⣶⣄⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠀⠀⠀⠉⠙⠛⠛⠋⠉⠻⠀⠀⠿⢆⠀⣀⠀⠀⠀⠀⠈⠀⠘⠛⣉⠁⠀⠀⢀⡠⢊⠅⠁⢴⡾⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⠿⠇⠀⢸⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⠏⡛⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⣷⣿⡟⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⢸⣿⣧⣼⣿⡇⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⣿⣿⣇⣿⡇⣾⣟⣿⣿⡟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣍⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢻⣿⡇⣿⣷⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢿⣿⣿⡟⣿⡇⣿⡷⠿⠃⣿⡇⠀⢸⣿⠇⢸⣿⠉⣿⢿⣿⣷⣿⡏⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣷⡿⣸⢸⣿⠀⠀⠀⠿⣧⡿⠇⡹⣷⣼⠟⢸⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣿⠿⡿⠿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⢿⡿⢟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠛⠻⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠋⠁
⠀⠘⣿⣿⣿⣿⠾⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠀⠈⣿⣿⣄⡈⠉⢱⣿⣿⣉⠁⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀⣄⣄⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣾⣿⣷⡤⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠠⢥⠠⣿⣿⣿⣿⣿⡀⠀⠀⠀⣰⣷⣶⡀⠀⠀⣄⡀⣴⣾⣿⣿⣿⣠⣶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⢿⣿⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⠄⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⠿⠿⠃⠀⠀⠉⠙⠏⠙⠛⠋⠉⠸⣿⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⢸⡿⢂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣶⣀⣀⣄⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⠗⠂⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣾⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠀⠀⠀⠉⢻⡄⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠆⠀⢀⣀
⣀⣴⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣿⠀⠀⠀⣸⣿⣀⠀⠚⠛⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠒⠛⢾⣿⣿⡇⠀⢠⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⣀⠀⠀⠉
⣿⢿⣿⣤⣿⠿⠿⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⣠⣇⣾⡆⠀⣿⣿⣿⣶⣶⣶⣶⢦⣤⣄⠀⠀⢸⣿⣿⣿⣦⣠⣤⣤⣴⣶⣶⣾⣿⣿⣷⠀⣾⠀⠙⢿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠁⢿⡉⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀
⠀⠀⣠⣄⠀⢀⣀⠀⠀⠀⣠⣦⣤⣄⠀⠀⠀⠀⢸⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠿⢻⣿⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢿⣿⣿⠿⢿⣵
⡷⠰⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣥⣼⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣼⡿⣿⣿⡿⠿⠋⠀⠀⢿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⠿⢻⠹⣿⣿⡟⠁⠀⣤⣿⣿⣷⣄⠈⠛⠋⣁⣤⣾⣿⣿⣿⣄⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡀⣀⣠⣤⣾⣿⣇⣾⣿⡅⠀⠀⢴⡆⠘
⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣈⠀⠁⢻⣧⠀⠀⠐⠛⠻⠿⠿⠷⣿⣿⣿⡿⠿⠿⠿⠟⠉⠀⢸⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⡁⠛⠿⢿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠉⢉⣽⣿⣿⣿⣇⠀⠘⢿⡄⢀⣄⡀⠻⠿⠿⠿⣿⢾⠿⠿⠿⠟⣀⣴⣦⣦⣿⣿⣿⠏⠿⠁⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿⢯⣤⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠈⠁⠺⣿⣿⣶⣤⣤⣄⣀⣀⣀⣤⣤⣾⣿⣿⣿⣿⣿⠟⠻⠂⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⢠⣀⣼⣿⣿⣿⡿⣩⣿⣿⣿⣿⣿⡿⢿⣿⣏⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⣿⣿⠏⢻⣿⣿⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡄⠀⠀⡌⠳⡀⠂⠀⠀⢿⣿⣦⣴⣿⣿⣿⣿⡿⠋⠀⢻⣿⣿⣿⣿⣿⣷⠸⣿⡿⣠⣤
⣿⣿⣿⣿⢿⡛⣿⣿⣿⠟⣿⣿⣿⣿⡿⠀⠀⠀⠈⠉⣁⣀⣸⣿⣿⢷⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣼⡇⢀⢎⢼⣀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⢿⣿⣿⡏⠛⠛⣰⣶⣤⣿⣿
⣿⣿⣾⣶⣶⣿⣿⣿⣷⣧⣴⣿⣿⣿⡇⠀⢠⣶⣿⣿⣿⣿⣿⣿⠃⢸⣷⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⡫⢨⠕⠣⣟⣻⣧⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⡀⠀⠀⢀⣿⠿⣷⣷⣄⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⠿⠿⠀⠀⠀⠈⠉⠛⠛⠋⠉⠇⠀⠸⠿⢄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠋⣉⠁⠀⠀⢀⡄⣪⠄⠁⢶⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⠿⠇⠀⢸⡿⢀⣿⣿⣿⣿⣿⣿⣯⣿
⣿⣿⣿⣿⣿⣯⣿⣿⠿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⣶⣿⡟⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⣸⣿⣧⣼⣿⡇⣿⡟⢻⡆⣿⡇⠀⢿⣤⡿⢸⣿⣿⣿⣇⣿⡇⣾⣟⣿⣿⡟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢻⣿⡇⣿⣷⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢿⣿⣿⡟⣿⡇⣿⡷⠿⠃⣿⡇⠀⢸⣿⠃⢸⣿⠁⣿⢿⣿⣷⣿⣏⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⣿⡇⠀⣿⡇⢿⣷⡆⣿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣷⡿⣸⢸⣿⠀⠀⠀⠿⣧⡿⠇⡹⣷⣼⠟⢸⡿⢸⡇⣿⠇⢿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣿⠿⡿⠿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⡿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠘⠿⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠀
⠀⠘⣿⣿⣿⣿⠷⢶⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠟⠀⠘⣿⣿⣄⣀⠉⠹⣿⣿⣉⠁⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⣄⣄⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣾⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢅⠠⣿⣿⣿⣿⣿⡀⠀⠀⠀⣰⣷⣶⡀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣀⣶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⢿⣿⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⠄⢳⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠿⠿⠁⠀⠀⠉⠙⠟⠙⠛⠋⠁⠹⣿⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠇⠀⠀⠀⠀⢸⡿⣂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣶⣀⢀⣄⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⠗⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠈⠁⠀⢀⣶⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⠀⠀⠀⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⠋⠉⠉⠈⠁⠀⠈⠉⢻⡄⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡷⠆⠀⢀⣀
⣀⣴⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡿⠀⠀⠀⣸⣿⣀⠀⠚⠚⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠐⠛⢾⣿⣿⡇⠀⢠⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⣀⠀⠀⠉
⣿⢿⣧⣤⣿⠿⠿⠂⠀⠀⠀⠀⠀⢠⣶⣾⣷⣰⢣⣾⡆⠀⣿⣿⣿⣷⣶⣶⣶⢶⣤⣄⠀⠀⢸⣿⣿⣿⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣷⠠⣼⠀⠻⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀
⠁⠀⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⣿⡉⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀
⣀⣄⣠⣄⠀⠀⣄⠀⠀⠀⣠⣦⣤⣄⠀⠀⠀⠀⢸⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠿⠻⣿⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡻⢿⣿⣿⠿⠻⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⡆⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣥⣼⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⡿⠿⠋⠀⠀⢻
⠈⠁⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⠟⢻⠛⣿⣿⡟⠁⠀⣤⣿⣿⣷⣄⠈⠙⠋⣁⣤⣾⣿⣿⣿⣆⡈⢿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣀⣀⣠⣤⣾⣿⣇⣾⣿⡃⠀⠀⢰⡄⠈
⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢀⣸⠄⠉⢹⣇⠀⠀⠀⠛⠻⠿⠷⢾⣿⣿⣿⣿⡿⠿⠿⠟⠁⠀⢸⣿⣿⣿⣴⡆⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⡃⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⣽⣿⣿⣿⡆⠀⠘⣿⡀⢀⣄⡀⠻⠿⠿⢿⣿⢾⡷⠿⠿⠟⢀⣴⣦⣦⣿⣿⣿⠋⠿⠁⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿⢏⣦⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠈⠁⢺⣿⣷⣶⣤⣤⣄⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⡿⠻⠂⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⣠⣠⣼⣿⣿⣿⡿⣩⣿⣿⣿⣿⣿⡿⢿⣿⣟⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⣿⣿⣿⠟⢹⣿⣷⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡄⠀⠀⢈⠣⠰⠆⠀⠀⢿⣿⣦⣴⣿⣿⣿⣿⡿⠋⠀⢻⣿⣿⣿⣿⣿⣷⠸⣿⡟⣠⣤
⣿⣿⣿⣿⢿⡻⣿⣿⣿⠟⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠁⠀⣈⣿⡿⢦⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣼⡇⢠⢊⣮⣄⠐⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡿⠀⠀⠀⠈⢿⣿⣿⡏⠛⠛⣰⣶⣦⣿⣿
⣿⣿⣾⣶⣾⣿⣿⣿⣷⣧⣴⣿⣿⣿⡇⠀⠠⣾⣿⣿⣿⣿⣿⡿⠁⢸⣇⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⡫⢈⠔⢱⣟⣿⣦⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣧⠀⡀⠀⠀⢈⣿⡿⣷⣶⣄⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠟⠀⠀⠀⠉⠉⠛⠿⠛⠛⡇⠀⠸⠿⢄⠀⣀⠀⠀⠀⠀⠀⠀⠛⠙⣉⠁⠀⠀⢀⡄⣪⠄⠡⢶⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⠿⠇⠀⢼⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⢿⠇⡟⣿⡟⡇⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⣿⡀⣿⣷⣿⡛⣿⠘⢻⣿⠛⠀⠀⣾⡏⣿⡆⣸⡟⢻⣧⣸⣿⣧⣼⣿⡇⣿⡟⢻⡆⣿⡇⠀⣿⣤⡿⢸⣿⣿⣿⣇⣿⡇⣾⣟⣿⣿⡟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡻⣿⣭⣿⣿⣧⠀⣿⡇⣿⡇⠀⣿⡇⠀⠀⢸⡟⣷⣿⢿⣿⡅⣿⢧⢸⣿⠀⠀⠀⣿⡇⣉⡁⣿⡇⢸⣿⢾⣿⣿⡟⣿⡇⣿⡷⠿⠃⣿⡇⠀⢸⣿⠇⢸⣿⠉⣿⢿⣿⣷⣿⣏⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⣿⡇⠀⣿⡇⢿⣷⡆⢿⣷⡆⠀⢸⡇⢹⣿⠘⢿⣷⡿⣸⢸⣿⠀⠀⠀⠿⣧⡿⠇⡹⣷⣼⠟⢸⡿⢸⡇⣿⠇⣿⡇⠀⠀⣿⣷⡆⠀⣿⠀⠸⣿⠀⣿⠈⣿⡇⠻⣿⠿⡿⢿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡿⠿⠿⠿⣟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⡀⠀⠈⠙⠛⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠀
⠀⠘⣿⣿⣿⣿⠶⢴⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2777

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/22/irc-log-210822/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/22/irc-log-210822/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Sunday,_August_21,_2022⠀✐


Posted in IRC_Logs at 2:33 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-210822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-210822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-210822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-210822.gmi
Over HTTP:


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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


CID                                              Description     Object type


                                                 IRC log for
 QmTnQHZowegFjEVtCCEysdkUoXkufAe36vhUo2jY18M8xr #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 Qmc4zYzpodMZqBcb3heDDwojFJNJSx5gv5mTH4BApRnFfN (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmVgaGn4o282fN4EceUgspnXADYADNVuBzSDE1EZbSt9c2 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmPvvkUe3ktJcZsj93LWPWqHk7H3cyqimoYgni1Hys7QUn social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmaMaFFL8T6XZhNZHL51gP2taaTpKmEwx9ifCMVfb97uJr #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmTqdTFMVhaFaNGxntVinJhXTY9NeJsD5ZS3ynCbmMrUv5 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmb4b2gf11rBCqCqPuekjV9ZSAE3AA4YAz7Na5NgCGhKo9 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmZjTDQER28GhhXsAypd2o6SKnjGWq8NgSAd9bUGDnPKdF (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmPGPjyuWmmi4WH1Pm1qxX7pzZhtRC3umeb4DmdE7NfXdU



                    ䷩ 𝚕𝚒𝚗𝚎 2904

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/22/windows-loses-majority/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/22/windows-loses-majority/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Russia’s_Invasion_of_Ukraine_Turns_6_Months;_Windows_Share_in_Russia_Down
Every_Month_Since_Then_(From_Over_55%_to_47%)⠀✐


Posted in GNU/Linux, Microsoft, Windows at 10:27 am by Dr. Roy Schestowitz


Earlier this year: Putin’s_Russia_Loves_It_When_Its_Enemies_Use_Microsoft
Windows | This_Month,_for_the_First_Time,_Microsoft_Windows_Share_is_Less_Than
50%_in_Russia | Microsoft_Windows_Market_Share_in_Russia_in_2022:_Down_From_55%
to_50%_in_5_Months


                    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Windows in Russia⦈
                       The numbers as of this afternoon


Summary: The corporate/mainstream media is not talking about it, but Windows
loses market share very rapidly and in Russia it lost about 15% (relative) of
its share in about 6 months


THIS post is not about politics. It’s purely about technology. Whenever we
write about Ukraine and Russia we try to focus on technology. That’s not to say
other aspects don’t matter; it’s just that Techrights is a technology site.


“The demise of Windows is undeniable; with it, Microsoft too will suffer an
epic demise.”There has been a lot of media coverage lately — or the past 3
months in particular — about Russia’s plan to move to GNU/Linux [1, 2].
Hardware/OEM/PC market may gradually be changing. There’s domestic stuff for
GNU/Linux. It even comes_preloaded_with_it on_desktops_and_phones. Might that
help explain the_demise_of_Windows?


Remember that Microsoft_is_laying_off_about_1_in_10_workers. The media has
helped confuse the public about this, owing to Microsoft’s operatives inside
newsrooms. The demise of Windows is undeniable; with it, Microsoft too will
suffer an epic demise.


As an associate put it, “for the last six months, [Windows] has been declining
at a rate of about 1.3% per month, but picking up speed. OS X is approximately
stable, iOS is growing ever so slightly and Android growing a bit faster. Plain
GNU/Linux is more or less stable.”


“Plain GNU/Linux” is a vague and generic thing; my browser (LibreWolf) reports
or exposes itself as Firefox on Windows and many surveys, grappling with a
broad range of distros and combinations, just classify Linux as “unknown” or
“other”. They also treat ChromeOS as a separate thing even though it’s built on
Gentoo. █


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


                       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Russia's_OS⦈_


⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣾⣷⢸⢩⣭⢻⠩⠝⡏⣭⠯⠍⡇⣽⣿⣯⣭⢻⠩⢭⣿⣇⡛⢿⢹⢏⡫⢭⡅⣽⠫⠍⡏⣭⢩⡍⣿⣿⢀⢿⢣⣿⠭⢽⡏⣭⡿⢫⡏⠭⢫⢨⣿⣧⡛⢿⣯⣭⢻⠭⠝⡏⣭⠫⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣍⣩⣼⢨⣩⣾⣌⣩⣧⣿⣌⣡⣧⣉⣿⣿⣿⡜⢠⠌⣿⣯⣉⣽⠇⣼⣍⣡⣧⣹⣌⣩⣧⣿⣼⣧⣿⣿⣼⣦⣿⣧⣈⣽⣧⣿⣷⣮⣯⣉⣽⣌⣿⣯⣉⣽⣿⣿⣼⣈⣥⣧⣿⣬⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⣉⣹⣿⣾⢿⠿⠿⠿⠿⡏⡿⠿⣿⠿⠿⣿⣿⢉⣀⡾⠿⣿⠿⠏⣾⠿⢿⠿⢿⠿⢿⠿⢿⣿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣤⠸⡿⠿⢸⠬⠙⠮⠙⡇⡏⠭⢸⢸⡇⣿⣿⢠⣤⠠⠥⡅⠾⠇⡇⠭⢼⢸⡟⠩⢼⡿⢿⣿⠺⠇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣷⣷⣶⣾⣶⣾⣶⣾⣷⣷⣾⣾⣾⣷⣿⣿⣾⣿⣷⣶⣿⣶⣶⣿⣶⣾⣾⣿⣶⣿⣷⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠤⡟⠛⡟⣛⣿⣿⣿⣿⠋⢿⢻⣿⢛⣛⣿⣥⢼⢣⡌⣧⠌⣯⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣿⣇⣂⣏⣋⣿⣷⣾⣏⣶⣎⣘⣹⠀⠘⣿⣁⣹⣎⣡⣏⣈⣏⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡋⠩⢉⠉⣿⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣧⢩⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣈⣀⡈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⡈⠉⠍⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣂⡉⠉⠉⠉⠙⠛⠛⠛⠛⠻⢛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⠋⠏⢉⠉⣿⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣒⣒⣒⣒⣂⣀⣀⣀⣀⣈⠉⠉⠛⠛⠛⠛⠸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⢡⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⣤⡀⠀⠀⠀⢠⣿⠿⠿⠟⠿⠿⠿⠟⠻⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⠛⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⡿⠀⠀⠀⢸⣿⠂⢈⡇⠛⠀⡀⡇⠘⡀⠛⡀⠓⣸⠀⠀⡇⡆⢸⠀⢃⠀⢰⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⠍⠉⢉⠉⢻⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠀⠀⠀⠀⠀⢀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣿
⣿⣷⣷⣿⣷⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⠿⠿⠻⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠾⠉⠉⠉⣉⣉⣉⣀⣀⣀⣀⣘⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⢡⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⢁⣀⣠⣤⣵⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⡿⣘⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉⢙⣃⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣷⢡⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⠍⠉⢉⠉⢻⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿
⣿⣿⣿⣿⣷⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⠍⠏⢉⠉⢻⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠋⠉⠁⢂⣿⣿
⣿⣿⣿⣿⣷⡟⠌⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠡⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⡛⠛⠛⠛⠉⠉⠉⠉⠉⠉⢁⣐⣀⣀⣠⣤⣤⣶⣶⣶⣾⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣁⣠⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⡏⠬⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⡟⠌⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠘⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠃⣿⣿
⣿⣿⡏⢉⠉⢃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿
⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡃⠈⣴⣿⣿⣿⣿⣿⣿⣿⣿⢃⠂⢡⣿⣿⣿⣿⣿⣿⣿⣿⡟⡐⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⢃⠂⢡⣿⣿⣿⣿⣿⣿⣿⣿⡟⡐⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⢃⠂⣡⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢇⡐⣰⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠀⢉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢿⢿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⢿⣿⣿⢿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣢⣼⣄⣄⣀⣀⡐⣀⢂⣀⣁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣜⣟⣼⣃⣌⣀⡀⣀⣀⢂⣀⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣠⣇⣀⢃⡂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣿⡄⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠁⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⡇⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⢰⢸⣇⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣴⣿⣷⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠘⢸⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡟⢿⣿⣿⡆⠀⣀⡀⠀⣾⣿⣿⣿⣿⣿⡀⠀⣿⠈
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⠃⣼⣿⣿⣿⣿⣿⣿⡇⡆⣿⠀
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠈⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠉⠉⠛⠛⠿⢿⣿⣇⠀⢿⡆
⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⣹⣿⣿⠿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠸⣿⣿⠿⠛⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡛⢷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠋⠀⠀⢷⣦⠙⢿⣿⣿⣿⣯⡵⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠈⠙⢛⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠓⠂⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣼⣦⣴⣶⣿⣿⡤⠼⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⢣⠀⢀⣄⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⡀⣰⣶⣦⣤⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⠟⠉⠛⠛⣛⣧⠿⠟⠛⠉⠁⠛⠿⠟⠋⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣪⠉⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣀⣠⣬⣤⣤⣶⣶⣶⣿⠿⠿⠶⠒⠛⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣟⣫⣭⣿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⢹⣿⣯⣭⣭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢝⡛⠛⠛⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠁⢀⣠⣩⣥⡀⠀⠀⠀⠀⠀⢈⡇⢿⡿⣅⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴
⠀⠀⠀⠐⠐⠀⠀⠘⣛⣁⣀⣀⣀⣸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⠾⠇⠐⠛⣿⣉⢥⣄⣠⣠⣤⣤⣯⣴⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠄⠈⠉⠉⠉⠁⠀⠁⠀⣹⣿⣿
⠀⠀⠀⠀⠒⠲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣿⣿⣿⠿⠖⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⣸⣇⣀⣈⣀⣲⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣩⣁⡈⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠟⠛⠛⠛⠉
⠀⢀⠀⠀⠀⢀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⠸⡸⢨⣹⣀⠂⠀⡇⢿⢌⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⢩⢝⣻⣟⡻⣿⢟⣿⣿⢩⢝⢻⡟⡟⣛⡯⡟⣛⢿⣿⡟⡻⢿⢟⡻⡋⣻⢟⣻⣿⡏⣿⣿⣿⢟⣻⡟⣿⢻⢻⢟⣿⡏⣛⡟⡻⣿⣿⢻⡻⣿⢿⡿⡛⣿⣿⢟⡻⡿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣒⣪⣕⣂⣿⣸⣿⣿⣰⣿⣜⣃⣷⣛⣇⣇⣿⣸⣿⣜⡋⣸⣐⣒⣇⣻⣒⣹⣿⣇⣛⣻⣿⣸⣇⣇⣛⣸⣣⣝⣿⣧⣛⣜⣛⣾⣿⣸⣧⣛⣸⣇⣿⣸⣿⣜⣃⣇⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⡻⢹⢟⡻⡿⣻⡏⡿⣿⢹⡿⣛⢿⢿⡻⣿⣿⣟⢿⡿⣗⢾⢟⠏⣿⣿⢟⠿⡻⣿⢟⢿⡏⡻⣿⢽⢹⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣜⣛⣸⣐⣒⣗⣊⣇⣮⣻⣘⣇⣛⣸⢘⣃⣿⣿⣐⣂⣇⣿⣸⣘⣃⣿⣿⣸⣇⣇⣧⣛⣣⣇⣛⣼⣸⣸⣔⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⠿⢿⠿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⠿⢿⣿⡿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⣿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠓⠠⠀⠀⠀⠀⠀⠀⠠⠤⣀⣘⣛⣷⣶⣾⣿⣿⣛⠁⠀⠀⠀⣀⣠⣤⠶⠞⠛⠙⠛⠛⣇⠀⠐⠂⠀⣠⣾⣧⣶⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⢀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⠿⠿⠿⢿⣿⣷⣦⣤⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠊⣳⣄⣀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠺⠟⠋⠀⠀⠀⠉⠙⠛⠲⠶⠦⠤⠤⣄⣀⣈⣻⣿⣿⣿⣅⡐⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠠⠤⠀⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠂⣰⣤⣄⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠓⠁⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣧⣿⣄⠀⠈⠀⠀⠒⢺⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡀⠀⠉⠙⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⣀⡈⠉⠉⠢⡀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣾⣿⣿⡿⠷⠶⡀⠀⢠⣝⣩⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⢤⣤⣶⡦⠀⠀⠀⠰⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠛⠉⠨⠧⠛⠃⠀⠀⠀⢾⣿⣿⣿⣿⣿⣦⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠆⠀⠀⠀⠀⠀⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠉⠉⠉⠑⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠚⠉⠋⠋⠉⠉⠙⠛⠉⠉⠙⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⡀⠐⠂⠀⠀⠀⠠⠚⠆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢰⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡠⠁⠀⠑⠂⠀⠀⢴⣶⣶⣶⣶⣤⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠃⠀⠀⠀⠀⠉⠉⢉⠉⠙⡿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠤⠄⠀⠄⠀⠀⠠⠚⠁⠁⠀⠀⠀⠀⠐⠠⣺⠟⠛⠙⠛⠿⠟⠤⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠲⠤⠀⠀⠀⠀⠀⠀⠀⠨⠦⣐⠇⠀⠀⠀⡀⠆⠀⠀⠀⠀⢒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠈⠙⠛⠛⠛⡋⠉⠉⠉⠉⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⣴⠇⠀⠀⠀⠀⠀⢸⡟⠃⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⡸⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⢀⠀⠀⢷⣴⢸⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢾⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢐⠄⡀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠀⠀⢀⠀⣀⣸⣿⡅⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⢺⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠑⠽⣦⡤⠀⠀⠀⠿⣦⡀⠀⠀⠉⠙⠓⢹⣞⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠠⣤⣭⣦⠀⠀⠀⠀⠀⠻⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣶⡀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⢹⣾⣿⣿⡿⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣿⣿⣷⣤⣤⣤⣬⣥⣿⣿⣿⣦⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡻⢟⠟⢿⠛⣿⣟⢟⠟⢿⠛⡿⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣼⣿⣥⣴⣿⣮⣼⣿⣷⣿⣷⣿⣷⣭⣿⣿⣤⣼⣿⣿⣷⣽⣿⣿⣴⣴⣼⣿⣧⣤⣧⣼⣿⣧⣴⣤⣶⣽⣿⣤⣴⣦⣼⣿⣤⣷⣯⣮⣿⣿⣿⣤⣤⣯⣤⣤⣾⣤⣿⣿⣦⣾⣯⣿⣿⣼⣿⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣋⣉⣿⣿⣩⣻⣿⣿⣋⣿⡏⣉⣭⣽⣿⣏⣭⣽⣿⣫⣭⣿⣯⢉⣹⣿⣯⣯⣫⣿⣯⣹⣿⣫⣉⣿⣉⣉⣿⣿⣍⣏⣽⣛⣉⣉⣿⣏⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⡿⣿⡿⡿⡿⡿⣿⣿⢿⢿⠿⢿⡿⠿⣿⣿⣿⠿⣿⣿⡿⠿⠿⢿⣿⠿⠿⣿⣿⢿⣿⡿⢿⢿⣿⣿⠿⡿⢿⢿⠿⣿⣿⡿⢿⢿⢿⣿⠿⣿⠿⢿⣿⣿⠿⢿⣿⡿⣿⠿⢿⡿⣿⡿⠿⣿⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣾⣿⣾⣷⣿⣷⣷⣿⣿⣾⣷⣶⣾⣷⣶⣿⣿⣿⣶⣿⣿⣶⣶⣾⣿⣾⣾⣶⣿⣷⢷⣿⣾⣿⣾⣿⣿⣶⣶⣾⣷⣶⣷⣿⣷⣾⣶⣿⣿⣾⣿⣶⣶⣿⣾⣶⣷⣿⣷⣿⣾⣶⣿⣶⣶⣶⣿⣷⣶⣿⣿⣿⣿
⣿⣿⣿⣥⣦⣿⣷⣿⣤⣼⣤⣿⣥⣭⣿⣿⣤⣤⣾⣿⣿⣿⣤⣴⣿⣿⣶⣴⣿⣤⣤⣬⣿⣿⣥⣼⣷⣶⣿⣶⣵⣿⣧⣼⣤⣴⣿⣿⣧⣤⣴⣿⣤⣴⣿⣿⣽⣿⣴⣥⣵⣿⣭⣤⣼⣭⣤⣿⣿⣮⣿⣿⣤⣿⣿⣿⣿⣿
⣿⣿⣿⣨⣋⣻⣏⣉⣟⣟⣝⣽⣉⣹⣟⣯⣭⣩⣫⣻⣟⣿⣿⣘⣻⣿⣻⣇⣿⣩⣍⣟⣿⣍⣇⣪⣑⣽⣭⣍⣿⣿⣍⣘⣝⣯⣿⣭⣍⣟⣈⣟⣯⣭⣛⣝⣟⣝⣍⣟⣫⣟⣭⣏⣽⣿⣟⣍⣉⣩⣩⣩⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣛⣻⣻⣏⣛⣿⣿⣋⣟⣙⣟⣹⣿⣿⣟⣛⣛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣴⣯⣴⣥⣶⣽⣽⣽⣾⣧⣥⣽⣿⣯⣤⣤⣮⣿⣴⣯⣿⣽⣽⣯⣴⣥⣯⣿⣧⣴⣿⣼⣽⣵⣵⣽⣧⣴⣤⣽⣵⣾⣮⣧⣿⣯⣷⣶⣵⣷⣧⣾⣿⣧⣤⣮⣿⣽⣥⣿⣽⣮⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣩⣭⣿⣽⣿⣭⣿⣽⣯⣽⣭⣿⣿⣼⣯⣽⣭⣽⣽⣧⣭⣿⣿⣯⣬⣽⣿⣯⣼⣭⣿⣽⣯⣽⣭⣽⣽⣿⣏⣯⣬⣽⣿⣿⣯⣽⣿⣿⣯⣭⣽⣍⣽⣍⣽⣯⣯⣽⣯⣭⣽⣿⣯⣯⣽⣾⣽⣿⣯⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣛⣛⣻⣟⣛⣿⣛⣋⣿⡻⣏⣙⣟⣛⣻⣛⣋⣙⣿⣿⣛⣛⣿⣹⣏⣟⡛⣛⣟⣿⣿⣛⣻⣹⣻⣛⣏⣿⣻⣛⣟⣿⣿⣛⣛⣛⣟⣛⢛⣟⣟⣻⣻⣟⣿⣛⣻⣻⣟⣟⣙⣻⣹⣯⣟⣻⣛⣻⣿⣿⣿⣿
⣿⣿⣿⢟⢿⣻⣟⡻⠟⣟⢟⣿⢟⣟⠻⠻⡻⡟⠿⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3114

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/22/www-corporate-monoculture/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/22/www-corporate-monoculture/

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Gemini_version_available_♊︎


✐ The_Web_is_a_Corporate_Monoculture,_Whereas_Gemini_is_Still_a_Diverse
Community⠀✐


Posted in Protocol at 11:29 am by Dr. Roy Schestowitz


                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gemini_languages⦈_
 In Gemini, languages aren’t always specified upfront in pages, but it’s still
possible to learn what (or who) makes up Geminispace; that little brown portion
                is broken down further at the bottom pie chart


Summary: The Internet is still universal and fairly diverse, but the Web is not


During the past weekend we_took_note of multi-lingual or ‘polyglot’ aspects of
NewsWaffle, which is language-agnostic and mostly site-agnostic. It just
converts millions of news pages, irrespective of their languages, into very
decent quality GemText pages with images. The Web would be better off named
GAFAMWeb as about three quarters of all Web users just use Chrom* (essentially
the same Web browser) and half_the_Net is monopolistic corporations clogging up
the switches. There are thankfully alternatives, whose adoption is consistently
growing (Lupa will soon list 2,700 Gemini capsules).


“So the Web isn’t “open” anymore. It’s not accessible either. We need to
advance and promote alternatives to it.”According to these_latest_charts, based
upon a survey of Geminispace, Europe is fast to adopt Gemini Protocol.
Curiously enough, it turns out that the home of Opera and Vivaldi, Norway, is
like a ‘last stronghold’ of Mozilla Firefox, where it’s still estimated to have
the most share and incidentally, Mozilla_recently_added_a_lady_from_Scandinavia
Online_to_its_Board_of_Directors; it’s Kristin_Skogen_Lund_from_Norway, a
country that adopts_GNU/Linux_too. Before Opera was sold to China (whereupon it
lost a lot of share and basically became another Chrom* clone) Opera used to
fight for Web standards and diversity of rendering engines. It even got the
European authorities involved in these battles.


Did Opera win? No. It surrendered. Sold, sold out, coopted.


To understand just how much of a monoculture the Web has become consider the
following: (yes, Norway stands out)


                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Dominant_browser_by_nation⦈_
                          Dominant browser by nation


Most of the other browsers are pretty much clones of Chrome/ium. So the Web
isn’t “open” anymore. It’s not accessible either. We need to advance and
promote alternatives to it. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣸⣆⡕⣟⣈⣸⢂⣅⣿⣿⣈⠐⣇⣿⣠⣇⣽⣸⣂⣺⣆⣕⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢯⢻⣿⢸⣿⣤⣤⣤⣿⣧⣧⣴⣅⣭⣧⣿⣮⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣻⣮⣿⣿⣿⢸⣿⣿⣿⣿⣿⣏⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠸⠃⠁⠈⠋⠁⠙⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⠁⠹⣿⠟⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣅⣼⣿⣿⣿⣿⢸⣿⠛⠛⠛⣿⡟⣟⢿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣯⣻⣿⢸⣿⠿⠿⠿⣿⡿⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⡿⠏⠀⢠⣤⣿⡇⢠⣤⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⡻⣮⣾⣿⣿⢸⣿⣶⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠛⠀⠀⣤⣿⣿⠏⢿⡿⠟⣿⣾⣿⣆⠀⣀⠀⠀⠘⠙⠛⠁⠀⠀⠀⠀⠀⣴⣄⠀⣼⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢸⣿⣤⣤⣤⣿⣧⣶⣽⣥⣮⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣴⣿⣦⣀⠀⣴⣴⣿⠉⠉⠀⠈⠃⠀⠈⠁⠁⠹⣴⡿⣆⠀⠀⠀⠀⠀⠀⠀⣸⣾⣶⠋⠻⡾⠃⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡛⣹⣿⢸⣿⣉⣉⣉⣿⣏⣩⣉⣩⣹⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⡿⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠹⣇⠀⠀⠀⠀⠀⣤⠏⠉⠋⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢯⣣⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠋⠉⣉⣭⣭⣽⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡯⢿⣿⣮⣾⣿⣿⣿⣿⢸⣿⣿⣿⡿⠟⠁⣠⡾⠛⠿⠿⣿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⢸⣿⣿⣿⣟⡻⣹⣿⢸⣿⣿⠋⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣼⣿⡟⣽⣫⣿⣿⣿⢸⣿⣿⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⢾⣷⣮⣾⣿⣿⣿⣿⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⡿⣻⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⣟⣪⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣮⣾⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⠧⣻⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⣛⣸⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢟⢷⣽⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣙⣷⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⡿⢿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣺⣽⣿⣿⣿⡻⣔⣷⣿⣿⣿⣟⢯⣲⣼⣿⣿⣿⢿⣎⣧⣿⣿⠿⡟⣧⣻⣿⣿⣿⢿⣿⣮⣵⣿⣿⣿⣿⣗⣭⣿⣿⣿⡿⣯⣺⣾⣿⣿⣿⣿⣗⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣾⣿⣿⣿⣿⣯⣥⣿⣿⣿⣿⣯⣩⣼⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣯⣡⣾⣿⣿⣿⣿⣍⣴⣿⣿⣿⣿⣯⣩⣼⣿⣿⣿⣿⣍⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣅⣁⣿⣟⣯⣭⣉⣻⣻⣿⣻⣿⣻⣝⣉⣿⣟⣿⣿⣟⣬⣭⣿⣿⣻⣻⣯⣭⣷⣿⣟⣿⣟⣭⣍⣭⣽⣹⣿⣹⣿⣿⣧⣭⣿⣿⣿⣏⣯⣿⣭⣿⣿⣿⣽⣻⣿⣯⣍⣻⣿⣿⣽⣥⣯⣯⣿⣤⣤⣼⣿⣿⣽⣧⣴⣧⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⠿⠿⣿⡿⣿⢿⢿⣿⣿⠿⢿⠿⠿⣿⢛⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣵⣿⣤⣼⣿⣧⣥⣼⣧⣿⣯⣤⣴⣡⣦⣿⣾⣼⣡⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⠁⣿⠈⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠰⣾⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣐⣸⣆⣦⣨⣿⣿⣿⣿⣿⣷⣤⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣷⣥⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⢿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣷⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣧⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡻⠿⠿⡿⠿⡿⠿⣿⢿⠻⠿⢿⠿⠿⡿⣻⢿⠿⠿⢿⣿⠻⠿⡿⠻⠿⣿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿
⣿⣥⣼⣵⣴⣧⣦⠼⠿⠶⣤⣤⣷⣥⣮⣯⣼⣿⣤⣴⣼⣧⣧⣬⣾⣤⣽⣦⣷⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣯⣴⣷⣴⣷⣬⣤⣥⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢛⣿⣿⣿⠿⠿⠿⣿⡟⡛⢛⣻⣿⣻⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠋⠀⠀⠄⠀⠀⠰⢦⣤⡀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣲⣾⣿⣿⡟⣩⡭⠿⠛⠊⠁⠀⠹⠿⠿⣏⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⠀⠙⠇⠀⠀⠠⠔⠛⠿⠿⠿⠋⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣴⣶⣴⣶⡶⣀⣦⣶⣶⡂⠃⠒⠃⠒⠂⠒⠂⠓⠓⠚⠒⠚⠓⠚⠐⠒⠢⠄⠒⠒⠛⠐⠃⠀⠀⠐⠃⠂⠀⠓⠐⠘⠛⠃⠀⢤⣤⠂⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣦⣤⣴⡖⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣦⣒⣒⣒⣶⣶⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⡀⢠⡄⠀⠀⠙⠛⠋⠉⢹⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣵⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⡷⠤⠬⣽⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡋⠩⣄⢙⡀⡀⠀⠀⠀⠔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⢀⣤⡀⠀⣠⠖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡗⠒⢲⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠉⠿⣿⣿⣷⣶⣄⣤⡄⠀⠀⠐⠀⢀⣼⣿⣿⣧⣼⣿⡃⢰⠋⠠⠼⠽⢭⣝⣭⣿⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠯⠽⠬⠭⠭⠿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠋⠱⣿⣿⣿⣿⣿⣷⣦⣤⡤⠄⠢⠠⣐⣍⡿⣿⠾⡼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⣬⣄⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣥⣽⣵⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡀⣴⣿⣿⢍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3257

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/22/youtube-clickfraud/#comments
    Gemini version at gemini://gemini.techrights.org/2022/08/22/youtube-clickfraud/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Spamnil_is_Still_Clickfrauding_and_the_Linux_Foundation_Supports_the
Clickfraud⠀✐


Posted in Deception, GNU/Linux at 8:54 am by Dr. Roy Schestowitz


This has gone on for several months and it’s very,_very_obvious_what's
happening_there


                    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Spamnil clickfraud⦈
 Current screenshot. Highlighted in red is the blatant clickfraud (90%-99% of
                             the views are fake).


Summary: Linux used to be associated with ethics and honesty, but nowadays with
the Linux_Foundation it gets associated with scams, fraudulent diploma mills,
and even pyramid schemes; how much more can the brand be devalued or “diluted”?
Charlatans and frauds who try to "fake_it_till_they_make_it" (and don’t even
use Linux!) are a disservice


⠀⠀⠀⠀⢀⢀⠀⢀⢀⠀⠀⡀⡀⢀⠀⢀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⠐⠙⠃⠑⠑⠀⠃⠀⠓⠁⠃⠁⠙⠁⠐⠉⠐⠀⠚⠛⠑⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣸⣛⣇⣻⣚⣴⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣾⣾⣟⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⡹⡍⣿⠟⣻⡿⠽⣿⢻⣿⡍⡏⢻⣟⣿⡹⢹⡟⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⢛⣿⡛⡟⢩⠍⢿⠛⣿⢛⣿⠫⠟⣿⢛⣿⢻⡟⢻⠟⣻⡏⡝⢻⢿⡍⡍⣿⢛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⠗⠾⠨⠟⠁⠿⠉⠹⠉⠿⠉⠟⠿⠹⠸⠿⠱⠾⠍⠛⠉⠿⠴⠇⣻⣉⣿⣻⣿⣿⣿⣿⣿⣿⡿⠛⠛⠃⠃⠉⠛⠉⠛⠛⠘⠛⠉⠛⠙⠛⠘⠈⠛⠉⠛⠈⠛⠃⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⡀⣀⣀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠈⡏⠁⡟⠃⡇⡟⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⡇⠀⠀⠇⠀⠖⠒⠰⠰⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⣀⠙⢿⣿⣷⠦⡀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣴⣶⣤⣄⠀⠀⠀⢹⣿⣿⣆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠻⢿⡿⣿⡀⡩⣔⠒⢿⣆⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⣿⣿⡿⠆⠀⠀⠀⣿⣿⣿⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢰⣦⢼⣷⣾⡇⣷⣿⣿⣿⣿⡆⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢢⢠⡀⠀⡅⠀⠀⠀⠀⣹⣿⣿⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣾⡜⠃⠀⠀⡉⣇⠿⣿⣿⡟⣿⣿⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⣿⣜⠃⠀⠀⠀⢠⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⢀⠀⢈⣤⠈⠓⠻⢻⣻⣿⡏⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠸⣏⣭⠀⠀⠀⠀⠘⠿⣿⡿⠁⠀⡇⠀⠠⡲⣀⢰⡆⢰⠄⢶⠄⣠⢆⢰⠄⠆⣆⣆⢀⠆⠘⡋⠉⠀⠀⠈⢳⣾⠏⠀⠀⠀⠀⠈⠻⠁⠀
⣿⣿⣿⣿⡇⠀⢰⡆⣶⢲⠀⢰⡆⣆⡖⣴⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⡿⠇⠀⠀⠀⠀⡀⠈⠀⠀⠀⡇⠀⢠⢤⠀⣤⠀⡤⡄⣄⡤⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠉⠈⠀⠈⠁⠈⠁⠉⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠻⠦⠤⠀⠀⡄⠀⠀⢀⠀⠀⡇⠀⠘⠙⠘⠛⠋⠳⠂⠋⠓⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⠤⠀⠀⠀⡀⠄⠀⡄⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣇⡹⣋⣝⣿⣫⢰⡿⢹⡍⡹⡇⣿⢍⣹⣹⣸⢍⣇⣯⣏⢽⡯⣹⣯⢙⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⣀⣏⣉⣿⣆⡯⡍⢟⡩⡿⢩⡏⢹⢏⣸⣿⣸⢫⡇⣙⢘⢟⣸⢉⢿⣹⢏⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣿⣴⣯⣧⣾⣷⡼⣧⣜⣧⣟⣼⣜⣽⣵⣴⣷⣜⣷⣾⣆⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦⣿⣿⣷⣼⣧⣇⣼⣫⣼⣦⣧⣴⣗⣼⣧⣟⣾⣧⣼⣣⣧⣫⣝⣤⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⡇⠀⢀⣀⣀⢀⣀⡀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠠⠤⢀⡀⠀⠀⠀⠀⠨⡇⠀⢀⣀⡀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠿⠀⠸⠛⠃⠇⠿⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⡇⠀⠀⠇⠀⠆⠀⠆⠖⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠀⠀⠀⠀⢀⡈⢿⣶⣄⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠡⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡃⢰⠿⠿⣿⡿⣷⢸⣿⣿⣧⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⢙⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⣷⣶⣴⣆⠀⢠⣸⣿⣿⣿⣇⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣃⠀⠻⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠛⢡⣬⡅⠈⢩⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠻⠯⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠟⠀⠀⠈⠑⠂⠀⢾⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⡌⢠⣴⣶⠃⠀⠀⠀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠟⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⡄⠀⠐⢌⠀⠁⢶⣿⠃⠀⠀⠀⠀⠂⠀⠀⠀⡇⠀⠸⣼⡇⡿⡀⣿⠀⢿⡘⢸⣇⠃⡎⣷⠳⡇⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠛⠒⠂⠀⢆⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠀⠀⢀⠀⢀⢀⠂⠀
⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⢿⠿⣿⣿⣿⣿⢿⣿⡿⢿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⣿⠿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣠⣪⣘⣗⣠⣛⣗⣰⣸⣀⣗⣼⣗⣩⣺⣰⣿⣗⣹⣠⣸⣥⣼⣲⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣗⣔⣇⣠⣿⣇⣇⣴⣰⣇⣸⣟⣼⣂⣾⣀⣿⣚⣷⣨⣪⣜⣿⣐⣿⣘⣥⣺⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⢻⠿⡿⠟⢿⡿⠿⣿⡛⡻⢿⣿⠻⣿⠿⢿⣿⡛⡛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⠻⡿⢿⣟⣻⠿⢿⠿⣿⢿⡿⣿⡟⣿⠿⡟⣿⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣷⣷⣾⣿⣾⣿⣶⣷⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠈⠈⠁⠉⠉⠉⠈⠉⠀⠉⠈⠉⠉⠉⠈⠈⠁⠉⠉⠉⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⡇⠀⠠⡤⠄⠤⠄⠄⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠒⠒⠒⠠⢄⡀⠀⠀⠀⠀⡇⠀⠠⡤⠄⠤⠤⠄⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⡢⠶⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠃⠀⠋⠁⠃⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣶⣶⣶⣶⡄⠀⢹⣦⡀⠀⠀⡇⠀⠀⠃⠀⠋⠁⠃⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣶⣿⣷⡟⠉⣉⣢⡀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣴⠀⣿⡿⢿⣿⣿⠇⠀⢸⣿⣷⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠿⠟⢻⠿⠻⡟⣻⣷⣿⣿⣿⣷⡀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣶⣿⣷⣿⡇⣤⣄⡃⠘⣿⣿⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⢠⣶⣾⡿⢛⠟⠛⣿⣿⣿⣿⣿⣧⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣯⣾⣿⠁⠘⠃⠁⣰⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⠿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣿⣿⣿⣿⣿⣿⣿⡃⠈⢠⣿⣿⣿⣿⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣠⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⡇⠀⢀⢀⡀⡀⢀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡟⢹⣯⡉⠀⠀⠎⠻⣿⣿⠏⠀⠀⡇⠀⢀⣀⢀⢀⡀⡀⣀⢀⠀⣀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⣿⣿⣿⣿⡇⠀⠠⠿⠇⠼⠘⠿⠰⠨⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢷⢸⡿⠿⣶⠀⠀⠀⠘⠁⠀⠀⠀⡇⠀⠐⠿⠠⠸⠇⠡⠿⠠⠇⠸⠠⠿⠇⠾⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠟⠛⠛⠛⠁⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠁⠣⠀⠺⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠐⠀⠰⠠⠅⠀
⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⡟⡿⡿⢿⠟⡿⠿⡿⢿⡟⣻⠿⡟⢿⡿⢿⢿⢿⠿⣿⢛⣿⠿⢿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢻⠿⢿⢿⠿⠿⡿⣿⡿⠿⣿⢛⡟⡿⡿⣿⠟⣿⣛⡿⡿⠿⣿⡿⢻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣼⣧⣽⣥⣦⣦⣷⣾⣯⣼⣥⣿⣾⣴⣾⣥⣼⣤⣿⣥⣯⣄⣵⣨⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣼⣵⣼⣿⣧⣦⣧⣿⣼⣦⣿⣮⣧⣮⣦⣽⣥⣿⣾⣿⣮⣶⣾⣯⣼⣤⣼⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣽⢙⡟⠋⣟⢻⣿⠛⣿⣭⣟⠟⡟⢻⡋⢟⠛⣻⡏⡏⢛⠏⢛⡟⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⢛⡟⣻⡏⡏⠟⡏⢛⣿⠹⠋⣯⠍⣍⡟⣿⢫⠟⡛⣻⠟⢻⣯⣽⡛⠟⡟⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠈⡏⠁⡭⠭⢨⣭⢭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠏⠉⡉⡑⠶⣤⣀⠀⠀⠀⠀⡇⠀⠐⢲⠒⢐⣒⡂⡂⣒⣒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠛⠛⠛⠛⠲⣤⣀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣤⣾⣿⣿⣿⣦⢸⣿⣷⡀⠀⠀⡇⠀⠀⠈⠀⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢃⣤⣴⣤⣀⠀⠀⢹⣷⡄⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣯⣩⣏⣉⣻⣿⣿⣿⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠸⢿⡿⠿⠿⡁⠀⢸⣿⣿⡄⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢻⣿⣿⣯⠍⢟⢹⣿⣿⣿⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣶⣶⣄⠂⢀⣼⣿⣿⣷⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⡹⠿⠿⠏⣩⣿⣿⣿⣿⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡶⢿⣟⠀⣸⣿⣿⣿⡟⠀
⣿⣿⣿⣿⡇⠀⢰⡔⠂⠆⠀⢂⡆⠠⠠⠐⢰⠰⢰⢲⠐⠂⠀⠀⢻⠿⠟⠋⠀⠙⢿⣦⡀⠸⢿⣿⣿⣿⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡷⠶⠟⠀⣤⢻⣿⣿⣿⠃⠀
⣿⣿⣿⣿⡇⠀⣀⣈⠀⠁⠀⡀⢁⠀⠁⠈⠈⠈⢈⠈⠀⠁⠀⠀⢀⠁⠀⡀⡀⠀⠈⢻⣇⣔⠾⣿⣿⡿⠁⠀⠀⡇⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠽⢿⣿⡿⠿⢻⣶⣤⣾⠿⠋⠉⡹⠃⠀⠀
⣿⣿⣿⣿⡇⠀⢸⢸⡇⣿⠀⣇⢸⡏⣿⣸⣹⠀⢸⢸⡇⣿⢸⡇⣿⢨⡇⡗⣿⡱⣏⣆⣻⣿⠇⣈⠉⢀⠀⠀⠀⡇⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠁⠈⠑⠠⠀⣈⣛⣋⠁⡀⢀⠈⣀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠙⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠂⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 3389

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_22/08/2022:_Mozilla_Firefox_104_and_public-inbox_1.9.0⠀✐


Posted in News_Roundup at 3:23 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Screenshots/Screencasts
          o Arch_Family
          o Fedora_Family_/_IBM
          o Debian_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Security
                # Fear,_Uncertainty,
                  Doubt/Fear-mongering/Dramatisation
          o Environment
                # Wildlife/Nature
    * Gemini*_and_Gopher
          o Technical
                # Programming
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ GamingOnLinux ☛ Star_Labs_reveal_the_StarBook_Mk_VI_with
                  Ryzen_7_or_Intel_12th_Gen_|_GamingOnLinux⠀⇛


                       Star Labs, hardware vendor with some really lovely
                       looking laptops with first-class Linux support have
                       announced the StarBook Mk VI with Ryzen 7 or Intel
                       12th Gen.


                       [...]


                       For models currently in production (sold out), they
                       give you a 5% discount if you pre-order. Pricing
                       usually £1,062.00 with a current discount to
                       £1,008.90.


                       Meanwhile, they’re also working on the bigger
                       StarFighter laptop which will be a 15.6″ beast that
                       has a 4K IPS matte display and 45W Intel / AMD
                       processors. It will be their biggest and most
                       expensive unit yet, with Star Labs mostly
                       targetting low-mid ring previously.


                # ⚓ MakeTech Easier ☛ How_to_Cast_Your_Android_Screen_onto_Your
                  Linux_Desktop⠀⇛


                       It may not be every day, but there will be times
                       when you need to mirror your Android screen to your
                       Linux desktop. You might want to give a
                       presentation from your phone, check the app you are
                       developing without touching your Android device,
                       view photos and other media on a bigger screen,
                       etc. No matter what the reason is, it is actually
                       really easy to cast your Android screen to Linux.


          o § Server⠀➾


                # ⚓ Kubernetes Blog ☛ Kubernetes_Spotlight_on_SIG_Storage⠀⇛


                       Since the very beginning of Kubernetes, the topic
                       of persistent data and how to address the
                       requirement of stateful applications has been an
                       important topic. Support for stateless deployments
                       was natural, present from the start, and garnered
                       attention, becoming very well-known. Work on better
                       support for stateful applications was also present
                       from early on, with each release increasing the
                       scope of what could be run on Kubernetes.


                       Message queues, databases, clustered filesystems:
                       these are some examples of the solutions that have
                       different storage requirements and that are, today,
                       increasingly deployed in Kubernetes. Dealing with
                       ephemeral and persistent storage, local or remote,
                       file or block, from many different vendors, while
                       considering how to provide the needed resiliency
                       and data consistency that users expect, all of this
                       is under SIG Storage’s umbrella.


                       In this SIG Storage spotlight, Frederico Muñoz
                       (Cloud & Architecture Lead at SAS) talked with Xing
                       Yang, Tech Lead at VMware and co-chair of SIG
                       Storage, on how the SIG is organized, what are the
                       current challenges and how anyone can get involved
                       and contribute.


          o § Audiocasts/Shows⠀➾


                # ⚓ Jupiter Broadcasting ☛ 5_Problems_With_NixOS_|_LINUX
                  Unplugged_472⠀⇛


                       The five most common problems when trying out an
                       immutable Linux distro like NixOS. Plus, why one
                       Linux dev says just target WINE.


          o § Kernel Space⠀➾


                # ⚓ Make Use Of ☛ Linux_Kernel_Development_Zooms_Along_With_6.0
                  Release_Candidate_2⠀⇛


                       Just a week after announcing the first Linux 6.0
                       release candidate, Linus Torvalds is back with the
                       second release candidate for the Linux kernel.


                       What’s Changed in the Linux 6.0 Release Candidate
                       2?


                       Torvalds once again downplayed the significance of
                       the release.


                       “Nothing particularly interesting here, rc2 tends
                       to be fairly calm with people taking a breather and
                       not yet having found a lot of bugs,” he wrote in a
                       message to the Linux Kernel Mailing List


                       Still, the release candidate does come with the
                       usual round of bug fixes. Torvalds noted updates
                       that smoothed out problems running tests on Google
                       cloud virtual machines.


          o § Graphics Stack⠀➾


                # ⚓ Mike_Blumenkrantz:_Sp33d⠀⇛


                       I was planning to write this Friday, but then it
                       was Friday, so I didn’t.


                       You know how it is.


                       I’ve been doing a lot of work on CPU optimizations
                       in zink lately. I had planned to do some benchmarks
                       of this, but now it’s Monday and someone has
                       already done it for me, so I won’t.


                       Sometimes it’s like that too.


                       But the overly-technical, word-heavy, bullet-point-
                       laden blog post still needs to be written, and now
                       it’s Monday, so here I am.


                       Speed: How does it work?


                       [...]


                       Descriptor set allocation was another bottleneck.
                       In order to avoid blowing out heaps on heap-based
                       hardware, I’ve capped descriptor pools to only
                       contain 100 sets at a time. This means that even if
                       a set isn’t fully utilized, it’s not consuming a
                       huge amount of resources. It also means that
                       allocation is faster when cmdbufs (and their
                       associated descriptor pools) get reset.


                       Remember when I said that there were N descriptor
                       pools for N cmdbufs? Obviously this was a lie. What
                       I meant to say was there are N * O descriptor pools
                       for N cmdbufs, where O is the number of times the
                       descriptor pool has overflowed because it had to
                       allocate more than 100 sets. In this scenario, the
                       overflowed (full) descriptor pool is appended to an
                       array which then gets freed upon cmdbuf reset.
                       Since the pools are relatively small, this
                       recycling operation is pretty fast.


                # ⚓ Alyssa Rosenzweig ☛ Alyssa_Rosenzweig:_Clip_control_on_the
                  Apple_GPU⠀⇛


                       After a year in development, the open source
                       “Asahi” driver for the Apple GPU is running real
                       games. There’s more to do, but Neverball is already
                       playable (and a lot of fun!).


                       Neverball uses legacy “fixed function” OpenGL.
                       Rather than supply programmable shaders like OpenGL
                       2, old OpenGL 1 applications configure a fixed set
                       of graphics effects like fog and alpha testing.
                       Modern GPUs don’t implement these features in
                       hardware. Instead, the driver synthesizes shaders
                       implementing the desired graphics. This translation
                       is complicated, but we get it for “free” as an open
                       source driver in Mesa. If we implement the modern
                       shader pipeline, Mesa will handle fixed function
                       OpenGL for us transparently. That’s a win for open
                       source drivers, and a win for GPU acceleration on
                       Asahi Linux.


          o § Applications⠀➾


                # ⚓ The Anarcat ☛ Alternatives_MPD_clients_to_GMPC_–_anarcat⠀⇛


                       GMPC (GNOME Music Player Client) is a audio player
                       based on MPD (Music Player Daemon) that I’ve been
                       using as my main audio player for years now.


                       Unfortunately, it’s marked as “unmaintained” in the
                       official list of MPD clients, along with basically
                       every client available in Debian. In fact, if you
                       look closely, all but one of the 5 unmaintained
                       clients are in Debian (ario, cantata, gmpc, and
                       sonata), which is kind of sad. And none of the
                       active ones are packaged.


                       [...]


                       For now, I guess that ymuse is the most promising
                       client, even though it’s still lacking some
                       features and performance is suffering compared to
                       gmpc. I’ll keep updating this page as I find more
                       information about the projects. I do not intend to
                       package anything yet, and will wait a while to see
                       if a clear winner emerges.


          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_WineHQ_on_Linux_Mint_21_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       WineHQ on Linux Mint 21. For those of you who
                       didn’t know, WineHQ can be used to run Windows
                       software and games on Linux natively without dual
                       booting windows with Linux or without using an
                       emulator. Wine is not only supported on Linux but
                       also on BSD, Solaris, and macOS.


                       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 WineHQ on Linux Mint 21 (Vanessa).


                # ⚓ Static_network_config_with_Debian_Cloud_images_–_Simon
                  Josefsson’s_blog⠀⇛


                       I self-host some services on virtual machines
                       (VMs), and I’m currently using Debian 11.x as the
                       host machine relying on the libvirt infrastructure
                       to manage QEMU/KVM machines. While everything has
                       worked fine for years (including on Debian 10.x),
                       there has always been one issue causing a one-
                       minute delay every time I install a new VM: the
                       default images run a DHCP client that never
                       succeeds in my environment. I never found out a way
                       to disable DHCP in the image, and none of the
                       documented ways through cloud-init that I have
                       tried worked. A couple of days ago, after reading
                       the AlmaLinux wiki I found a solution that works
                       with Debian.


                # ⚓ Make Use Of ☛ How_to_Install_the_build-essential_Package_on
                  Ubuntu⠀⇛


                       Every OS has in-built dependencies to function
                       smoothly. In short, these supporting programs are
                       often required to compile software and ensure all
                       dependent software is available when needed.


                       Ubuntu’s build-essential meta-package includes
                       several such packages, which ensure your Linux
                       experience is as seamless as you would like it to
                       be. These packages are a part of Debian and contain
                       all the components you need to create a Debian
                       package.


                # ⚓ H2S Media ☛ 4_Ways_to_Install_Microsoft_Teams_on_Linux_Mint
                  21_LTS_Vanessa [Ed: Microsoft malware... better not]⠀⇛


                # ⚓ H2S Media ☛ How_to_Install_SSH_Server_on_Ubuntu_20.04_LTS_–
                  Linux_Shout⠀⇛


                       There was a time when computers on the net were
                       accessible via the Telnet protocol. Since this
                       protocol did not offer encryption, recording
                       passwords became a trivial matter.


                       To secure remote access, Tatu Ylönen wrote a suite
                       of programs in the mid-1990s – consisting of
                       server, client, and utilities – which he called ssh
                       (secure shell).


                       Later he founded the company ssh.com and offered
                       version 2 of the SSH suite only commercially. As a
                       result, developers of the OpenBSD operating system
                       forked the public source code of version 1. They
                       further developed the program under the name
                       “OpenSSH”. This OpenSSH suite became an integral
                       part of virtually all Linux distributions.


                # ⚓ TechRepublic ☛ How_to_install_Ansible_on_Ubuntu_Server
                  22.04_|_TechRepublic⠀⇛


                       Ansible makes it much easier for busy admins to
                       manage a large collection of servers. Instead of
                       having to remote into each server to handle a task,
                       you can take care of much of it from a single point
                       of entry. One reason why I prefer Ansible over
                       similar tools is that Ansible doesn’t require you
                       to install clients on remote nodes. Instead,
                       Ansible uses SSH to execute all tasks, and YAML
                       files hold the definitions of the tasks to be run.


                # ⚓ HowTo Geek ☛ How_to_Install_Arch_Linux_From_a_GUI⠀⇛


                       Although Arch Linux is great, its installation is a
                       show-stopper for many people. But now there’s a
                       straightforward GUI-based installer for Arch. And
                       you already know how to use it.


                # ⚓ UNIX Cop ☛ How_to_install_the_latest_version_of_ImageMagick
                  on_Ubuntu_22.04⠀⇛


                       The ImageMagick tool is a library with which you
                       can create, edit, compose, or convert digital
                       images. It supports many available formats and is
                       presented for Linux without a lot of fuss.


                       ImageMagick can resize, flip, mirror, rotate,
                       distort, shear and transform images, adjust image
                       colors, apply various special effects, or draw
                       text, lines, polygons, ellipses, and Bézier curves.


                       One of the best things about this tool is that it
                       is open source and free, and it has excellent
                       support for Linux.


                # ⚓ Video ☛ Build_an_Awesome_Nextcloud_Server_(Updated_for
                  Ubuntu_22.04!)_–_Invidious⠀⇛


                       New: The LearnLinuxTV Nextcloud guide is now
                       updated for Ubuntu 22.04 with this video! It’s time
                       to install Nextcloud! Nextcloud is the best
                       platform for building your very own self-hosted
                       collaboration platform, complete with features such
                       as online document editing, file synchronization,
                       calendar, contacts, and countless plugins. In this
                       video, you’ll be walked through the entire process,
                       and by the end you’ll have your very own Nextcloud
                       server that’s completely set up and ready for
                       action by the end.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ OMG Ubuntu ☛ Ubuntu_22.10_May_Disable_GNOME’s_New
                        ‘Device_Security’_Panel⠀⇛


                             A bug report filed by Ubuntu developers this
                             weekend describes the new device security
                             feature as “confusing and unhelpful” in its
                             current guise.


                             “A default Ubuntu install only gets us
                             “Security Level 1”. The highest level is
                             “Security Level 3”. There isn’t anything an
                             Ubuntu user can do to get to a higher
                             security level from the Device Security
                             screen,” the bug report reads.


                             “If a user attempts to get their system to a
                             higher security level, I think they could
                             break their system since this isn’t something
                             we currently support. We can work towards
                             better integrating this screen for Ubuntu in
                             future releases”.


    * § Distributions and Operating Systems⠀➾


          o § Screenshots/Screencasts⠀➾


                # ⚓ Video ☛ SparkyLinux_“LXQt”_6.4_|_powered_by_debian_–
                  Invidious⠀⇛


                       In this video, I am going to show an overview of
                       SparkyLinux “LXQt” 6.4 and some of the applications
                       pre-installed.


          o § Arch Family⠀➾


                # ⚓ Make Use Of ☛ Manjaro_vs._EndeavourOS:_Comparing_the_Two
                  Major_Arch-Based_Distros⠀⇛


                       Arch Linux is not a distro for the typical user;
                       it’s common knowledge that Arch is one of the most
                       challenging distros to install, especially if you
                       don’t follow the proper procedures. Its rigid
                       installation and tedious setup procedures haven’t
                       deterred developers from creating alternate
                       versions based on Arch Linux, though.


                       If you are an Arch aficionado and want to make the
                       most out of your Linux installation, then you
                       should consider EndeavourOS and Manjaro: two of the
                       best Arch-based distros. Here’s a detailed
                       comparison between Manjaro and EndeavourOS.


                       [...]


                       EndeavourOS and Manjaro are spin-offs of Arch Linux
                       and both of them are geared towards making the
                       lives of newbies easier. There are plenty of
                       differences, right from installing the OSes to
                       managing the packages on your desktop environments.


          o § Fedora Family / IBM⠀➾


                # ⚓ My_podman_journey_so_far_|_IT-Hure⠀⇛


                       This blog post was rotting in my queue since
                       November of 2021, but the info is still helpfull
                       for someone, so I post it now.


                       I had a long time ago a look at docker when just
                       version 1 was released, but I never really used it
                       that much for my own production setups. I used it
                       for playing around. I hated that is runs as root
                       and even Docker itself had problem making it
                       secure.


                       I really liked it when podman was released, I’m a
                       fan of Dan Walsh from SELinux times and I really
                       liked the idea of splitting it up and running it as
                       non root (I know docker can do it now as well). But
                       I did not have the time to play with it. But
                       because my RSS Feeder (ttrss) does not support
                       normal installation anymore I was forced to try it
                       again. I started with bitwarden_rs and now ttrss.


          o § Debian Family⠀➾


                # ⚓ Linux Magazine ☛ A_New_Release_of_Lightweight_Linux
                  Distribution_SparkyLinux_is_Now_Available⠀⇛


                       SparkyLinux 6.4 is here. Based on Debian Bullseye,
                       this lightweight distribution ships with plenty of
                       updates for packages like Firefox, Thunderbird,
                       VLC, LibreOffice, LXQt, Xfce, Openbox, and KDE
                       Plasma and makes it possible to install a number of
                       those applications from Debian unstable (to enjoy
                       more recent releases). The latest release is
                       updated from both the Debian and Sparky stable
                       repositories (as of August 11, 2022).


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Star_Wars-themed_device_monitors_indoor
                  environmental_conditions_|_Arduino_Blog⠀⇛


                       We don’t need to tell you that Star Wars is a
                       wildly popular franchise. If you include all of the
                       movies, video games, novels, theme park
                       attractions, and so on, it is the fifth-highest-
                       grossing media franchise of all time (somehow just
                       behind Winnie the Pooh). Because of its popularity,
                       Star Wars themes find their way into every facet of
                       life. But fan Kutluhan Aktar took that in a
                       surprising direction when he built this Bluetooth®-
                       enabled, Star Wars-style weather and gas station.


                       We don’t mean a gas station for pumping fuel, but
                       rather a system that monitors indoor environmental
                       gasses, like methane and carbon monoxide, along
                       with climate information like temperature and
                       humidity. Aktar chose to design the device with a
                       Star Wars look and feel, which includes a
                       Millennium Falcon PCB and a 3D-printed Yoda bust,
                       but that theme has little to do with the
                       functionality. In addition to gathering
                       environmental data, this device can illuminate a
                       pair of light bulbs, control RGB LED lighting in
                       the room, and spin a pair of fans. Those outputs
                       are configurable as indicators that correspond to
                       the environmental data. A small E Ink display shows
                       relevant data, which is also accessible via a
                       smartphone.


                # ⚓ Purism ☛ Where_Is_My_Librem_5?⠀⇛


                       While our recent news has been all about Librem 5
                       USA, we also have been steadily shipping through
                       Librem 5s from previous production runs and it has
                       been gratifying to share in the excitement of
                       customers who have gotten the Librem 5 they have
                       been waiting so patiently for. While the remainder
                       of you have been waiting for your own Librem 5, we
                       have also been busy continually improving the
                       software on the Librem 5 so that the Librem 5 you
                       receive today is significantly better and more
                       capable than one we shipped a year or even six
                       months ago.


                       Now that the Librem 5 USA has hit shipping parity,
                       our mass-produced Librem 5 customers are all likely
                       wondering the same thing: “Where is my Librem 5?”
                       As we mentioned in a previous post, the supply
                       chain challenges over the past few years have
                       caused to to rethink how we approach “Just In Time”
                       manufacturing, and as a result we have made massive
                       investments in components, accessories, and other
                       supplies so that we can not only catch up on
                       backorders, but maintain sufficient stock so that
                       once a product reaches shipping parity, we have
                       ample inventory to absorb any future supply chain
                       issues. It is very much in our interest for all of
                       our products to be in stock with short lead times,
                       and all backorders to be fulfilled. As I mentioned
                       in my A Vision on Focus post, one of our goals is
                       to hit, and maintain, stability for all our
                       products with future products being developed
                       internally and announced when they are ready to
                       ship, instead of relying out pre-orders and
                       crowdfunding.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Android Headlines ☛ What_Are_The_Benefits_Of_Android_Apps
                  In_Cryptocurrency_Trading?⠀⇛


                # ⚓ Android Central ☛ Blackview’s_new_Android_tablet_lets_you
                  connect_to_the_web_without_a_Wi-Fi_or_SIM_card_|_Android
                  Central⠀⇛


                # ⚓ Digital Trends ☛ The_best_thing_about_Android_13_isn’t
                  features_or_settings_|_Digital_Trends⠀⇛


                # ⚓ Extreme Tech ☛ Android_13_Source_Code_Hints_at_64-bit_Only
                  Apps_Starting_in_2023_–_ExtremeTech⠀⇛


                # ⚓ XDA ☛ This_app_lets_you_adjust_the_flashlight_brightness_on
                  Android_13_devices⠀⇛


                # ⚓ Google_Pixel_4a_echo_during_calls_with_earphones_after
                  Android_13⠀⇛


                # ⚓ XDA ☛ Android_13_Custom_ROM_List:_Unofficially_update_your
                  Android_device!⠀⇛


                # ⚓ Android Police ☛ Mobile_Photography_Week_2022:_Android
                  Police’s_celebration_of_smartphone_cameras⠀⇛


                # ⚓ 9to5Google ☛ Discord_for_Android_having_Bluetooth_headset
                  issues_–_9to5Google⠀⇛


                # ⚓ Why_Is_Instagram_Camera_Quality_So_Bad_on_Android⠀⇛


                # ⚓ Why_is_Android_popular_in_India?⠀⇛


                # ⚓ Reddit_not_opening_links_in_external_apps_on_Android⠀⇛


                # ⚓ Notebook Check ☛ EZpad_M10S:_Jumper_introduces_budget
                  Android_tablet_at_an_affordable_price_with_6_GB_of_RAM_–
                  NotebookCheck.net_News⠀⇛


                # ⚓ SlashGear ☛ How_To_Make_AirPlay_Work_On_Android_Devices⠀⇛


                # ⚓ How_to_use_Google_Maps_to_share_location_on_Android⠀⇛


                # ⚓ MakeTech Easier ☛ AGM_Glory_G1S_Android_11_Phone_Review⠀⇛


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


          o ⚓ InfoWorld ☛ 8_open_source_projects_taking_collaboration_to_the
            next_level_|_InfoWorld⠀⇛


                 Open source projects are all about creativity and
                 collaboration, and the process really shines when the
                 project itself supports teamwork. Working together to
                 create software for working together might seem very
                 meta, but the results are quite tangible.


                 Here are eight open source projects that can help boost
                 your team’s collaboration, whether you are working in a
                 distributed team, from your home office, or onsite in one
                 of the newer hybrid workplaces.


                 [...]


                 The team at NextCloud gathered up some of the best open
                 source projects for supporting group collaboration with
                 email, chat, and calendaring.


          o ⚓ LWN ☛ public-inbox_1.9.0_released_[LWN.net]⠀⇛


                 Upgrading:

                   lei users need to "lei daemon-kill" after installation
                 to load
                   new code.  Normal daemons (read-only, and public-inbox-
                 watch)
                   will also need restarts, of course, but there's no
                   backwards-incompatible data format changes so rolling
                 back to
                   older versions is harmless.

                 Major bugfixes:

                   * lei no longer freezes from inotify/EVFILT_VNODE
                 handling,
                     user interrupts (Ctrl-C), nor excessive errors/
                 warnings

                   * IMAP server fairness improved to avoid excessive blob
                 prefetch

                 New features:

                   * POP3 server support added, use either public-inbox-
                 pop3d or
                     the new public-inbox-netd superserver

                   * public-inbox-netd superserver supporting any
                 combination of HTTP,
                     IMAP, POP3, and NNTP services; simplifying management
                 and allowing
                     more sharing of memory used for various data
                 structures.

                   * public-inbox-httpd and -netd support per-listener
                 .psgi files

                   * SIGHUP reloads TLS certs and keys in addition to
                 config and .psgi files

                   * "lei reindex" command for lei users to update
                 personal index
                     in ~/.local/share/lei/store for search improvements
                 below:

                 Search improvements:

                   These will require --reindex with public-inbox-index
                 and/or
                   public-inbox-extindex for public inboxes.

                   * patchid: prefix search support added to WWW and lei
                 for
                     "git patch-id --stable" support

                   * text inside base-85 binary patches are no longer
                 indexed
                     to avoid false positives

                   * for lei users, "lei reindex" now exists and is
                 required
                     to take advantage of aforementioned indexing changes

                 Performance improvements:

                   * IMAP server startup is faster with many mailboxes
                 when using
                     "public-inbox-extindex --all"

                   * NNTP group listings are also faster with many inboxes
                 when
                     using "public-inbox-extindex --all"

                   * various small opcode and memory usage reductions

                 Please report bugs via plain-text mail to: meta@public-
                 inbox.org

                 See archives at https://public-inbox.org/meta/ for all
                 history.
                 See https://public-inbox.org/TODO for what the future
                 holds.
          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ 9to5Linux ☛ Mozilla_Firefox_104_Is_Now_Available_for
                        Download,_This_Is_What’s_New⠀⇛


                             Firefox 104 entered public beta testing at
                             the end of July, during which it offered a
                             long-anticipated feature, namely the ability
                             to swipe left and right on web pages using a
                             two-finger horizontal swipe gesture without
                             holding down the Alt key.


                             Unfortunately, just like Firefox 103, Firefox
                             104 is missing this long-anticipated feature
                             in the final release, which now appears to
                             have been postponed for the next release,
                             Firefox 105. Of course, you can still
                             navigate back and forward with a touchpad
                             using a two-finger horizontal swipe gesture
                             while holding down the Alt key.


          o § Programming/Development⠀➾


                # ⚓ Ubuntu Pit ☛ 20_Best_C++_Projects_For_Beginners_in_2022⠀⇛


                       When it comes to programming, the best way to test
                       one’s skills is to implement their knowledge into
                       projects. While this is true for every programming
                       language out there, our focus today is on C++
                       specifically, and there are plenty of C++ projects/
                       ideas for beginners to talk about.


                       Projects can also challenge you to broaden your
                       horizons and also help you get ready to work on
                       real-time development jobs for your career. So,
                       hopefully, you’ll get some C++ project ideas today
                       to expand your portfolio as a beginner.


                # § Perl / Raku⠀➾


                      # ⚓ Remote_notification⠀⇛


                             This will send a notification message with
                             the title “compile finished”, and a body of
                             “success” or “failure” depending on whether
                             the command completed successfully, and
                             allows you to minimize (or otherwise hide)
                             the terminal window while you do something
                             else, which can be a very useful thing to do.


                             It works great when you’re running something
                             on your own machine, but what if you’re
                             running it remotely?


                      # ⚓ Rakulang ☛ Rakudo_Weekly_News:_2022.34_R(aku&ust)⠀⇛


                             Steve Roe blogged about the union of Raku and
                             Rust in: Option-Some-None, which also touches
                             on a lengthy debate on the essence of nothing
                             (/r/rakulang comments).


    * § Leftovers⠀➾


          o § Security⠀➾


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


                       Security updates have been issued by Debian (jetty9
                       and kicad), Fedora (community-mysql and
                       trafficserver), Gentoo (chromium, gettext, tomcat,
                       and vim), Mageia (apache-mod_wsgi, libitrpc,
                       libxml2, teeworlds, wavpack, and webkit2), Red Hat
                       (podman), Slackware (vim), SUSE (java-1_8_0-
                       openjdk, nodejs10, open-iscsi, rsync, and trivy),
                       and Ubuntu (exim4).


                # ⚓ Red Hat Official ☛ Getting_started_with_Red_Hat_Insights
                  malware_detection [Ed: Red Hat pushing proprietary IBM
                  garbage by pushing FUD about "malware" on Linux. There used
                  to be this not-so-joke about anti-virus companies producing
                  and spreading viruses just to sell their products.]⠀⇛


                       The beta of Red Hat Insights malware detection
                       service is now available. The malware detection
                       service is a monitoring and assessment tool that
                       scans Red Hat Enterprise Linux (RHEL) systems for
                       the presence of malware, utilizing over 175
                       signatures of known Linux malware provided in
                       partnership with the IBM X-Force Threat
                       Intelligence team


                # ⚓ CISA ☛ CISA_Adds_One_Known_Exploited_Vulnerabilities_to
                  Catalog_|_CISA⠀⇛


                       CISA has added a new vulnerability to its Known
                       Exploited Vulnerabilities Catalog, based on
                       evidence of active exploitation. These types of
                       vulnerabilities are a frequent attack vector for
                       malicious cyber actors and pose significant risk to
                       the federal enterprise. Note: to view the newly
                       added vulnerabilities in the catalog, click on the
                       arrow in the “Date Added to Catalog” column, which
                       will sort by descending dates.   


                # ⚓ Venture Beat ☛ Don’t_leave_open_source_open_to
                  vulnerabilities [Ed: 'Linux' Foundation goes out of its way
                  to help its sponsored/owners (like Microsoft) badmouth "Open
                  Source" and legitimise the FUD by distracting from
                  proprietary back doors]⠀⇛


                       “Recently, the open-source ecosystem has been under
                       siege,” said David Wheeler, director of open-source
                       supply chain security at the Linux Foundation.


                # ⚓ LinuxSecurity ☛ Black_Hat_USA_2022_&_DEF_CON_30:
                  Highlights,_Key_Findings_&_Notable…⠀⇛


                       This year, Black Hat and DEF CON events marked a
                       return to a time before the pandemic. However, in
                       many ways, it represents the effort that has been
                       made despite these substantial challenges to
                       innovate and grow within security. It has made us
                       more willing to trust our abilities and also not to
                       forget the details, especially when it comes to the
                       software we use every day.


                # ⚓ Microsoft_Defender_for_Endpoint_Boosts_Security_on_Mac_and
                  Linux [Ed: More like putting a back door, not enhancing
                  security. Microsoft works for NSA and makes things
                  intentionally vulnerable. When Microsoft calls something
                  security and keeps it entirely proprietary ask them what
                  they're trying to hide. There's not even an audit.]⠀⇛


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


                      # ⚓ CISA ☛ CISA_Updates_Advisory_on_Threat_Actors
                        Exploiting_Multiple_CVEs_Against_Zimbra_Collaboration
                        Suite_|_CISA⠀⇛


                             CISA and the Multi-State Information Sharing
                             & Analysis Center (MS-ISAC) have updated
                             joint Cybersecurity Advisory AA22-228A:
                             Threat Actors Exploiting Multiple CVEs
                             Against Zimbra Collaboration Suite,
                             originally released August 16, 2022. The
                             advisory has been updated to include
                             additional detection signatures.


          o § Environment⠀➾


                # § Wildlife/Nature⠀➾


                      # ⚓ Daniel Pocock ☛ Horsing_around_at_Festi-Cheval,
                        Houtard_/_Pontarlier⠀⇛


                             I was driving through the Jura on the weekend
                             and I saw an interesting sign about Festi-
                             Cheval on the road between Pontarlier and
                             Houtard. Cheval is French for horse.


    * § Gemini* and Gopher⠀➾


          o § Technical⠀➾


                # § Programming⠀➾


                      # ⚓ The_Camplog_update⠀⇛


                             Alright, this post will explain the various
                             updates and changes added to The Camplog[1].
                             For those of you that have a keen eye, you
                             might have seen that the source code was
                             released yesterday. You can just grab it from
                             The Camplog index page, served off right
                             Gemini.


                      # ⚓ alist-let_—_or_maybe,_plist?⠀⇛


                             Firstly, I am a Common Lisper and know very
                             little Scheme.


                             First question: what is the purpose of alist-
                             let? As I understand it (confusedly scanning
                             the code and comments), you can bind symbols
                             specified as keys to their corresponding
                             values. If you don’t know ahead-of-time what
                             the symbol names are, you cannot use them in
                             the body of the let, unless you somehow
                             define local macros that contain those
                             symbol-names… Otherwise, it’s just let with a
                             weirder syntax…


                             In Common Lisp we have another basic kind of
                             a list, a PLIST, which takes a little more
                             space but is a pretty generic datastructure.
                             An alist ‘((a . 1)(b . 2)(c . 3)) may be
                             converted to a plist `((a 1)(b 2)(c 3))…


                      # ⚓ [RFC]_alist-let⠀⇛


                             If you’re a Lisper, even if you’re not a
                             Schemer, please don’t skip this post! 🄸🄼🄰🄶🄴
                             🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈


                             Almost two years ago I wrote a macro to make
                             it easier to work with values of an alist
                             (“association list” i.e. list of key/value
                             pairs; Scheme’s “default” dictionary-like
                             structure). It was called let-aref at first
                             and it could be used to introduce a single
                             variable with the value associated with a key
                             of an alist — sort of like let but for alists
                             and for a single variable. Soon I realized I
                             could use it for several variables if I
                             changed it only slightly, which became alist-
                             let.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 4488

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_22/08/2022:_Kdenlive_22.08_and_RC2_of_Linux_6.0_Released⠀✐


Posted in News_Roundup at 2:50 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Reviews
          o Devices/Embedded
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
    * Leftovers
          o Security
          o Defence/Aggression
          o Environment
                # Energy
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ 9to5Linux ☛ Star_Labs_Unveils_StarBook_Mk_VI_Linux_Laptop
                  with_12th_Gen_Intel_or_AMD_Ryzen_7_CPUs⠀⇛


                       While Star Labs is still working hard on the
                       StarFighter Linux notebook, which looks to be the
                       first Linux-powered laptop from Star Labs to
                       feature a 4K display, the company also worked on
                       the next-generation StarBook laptop.


                       StarBook Mk VI features 12th Gen Intel CPUs, namely
                       the Intel Core i3-1220P with 10 cores and up to
                       4.40GHz clock speed and Intel Core i7-1260P with 12
                       cores and up to 4.70GHz clock speed, but you can
                       also order it with an AMD Ryzen 7 5800U processor
                       with 8 cores and up to 4.40GHz clock speed.


                # ⚓ Purism_Librem_14_review:_The_king_of_privacy-oriented
                  laptops!⠀⇛


                       Since I switched to Linux, I have become more aware
                       of the importance of privacy and data protection in
                       the dangerous world of the Internet. Today,
                       companies are voracious to user’s data, and hackers
                       will not hesitate to provoke you if they gain
                       access to your device and data. I will be frank
                       with you, there is no one hundred percent
                       protection as long as you use the Internet, but you
                       can raise the level of security by using a device
                       that respects your privacy and works to protect it.
                       In this article, we will review the Librem 14
                       laptop from Purism.


                # ⚓ Linux Made Simple ☛ Linux_Weekly_Roundup_#196⠀⇛


                       I hope that you are doing well?


                       We had another full week in the world of Linux
                       releases with Deepin 23 Preview, KaOS 2022.08, and
                       Neptune Linux 7.5.


                       LibreOffice 7.4, Krita 5.1.0 and KDE Apps 22.08 has
                       also been released.


                # ⚓ 6_Best_Programmable_and_Mechanical_Keyboards_For_Linux_2022
                  (Update)⠀⇛


                       Linux is the second most popular OS after Windows.
                       There is a very large community that prefers it and
                       uses it as their primary operating system. This is
                       why we have put together a list of the 6 best Linux
                       mechanical and programmable keyboards that are both
                       great for gaming, developers and programmers. We
                       have written this with compatibility in mind so
                       there are wired and wireless choices available.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ THE_GAMING_ON_LINUX_GUIDE:_How_to_play_anything:
                  Steam,_Epic,_Ubisoft,_Origin,_Battle.net,_GoG…_–_Invidious⠀⇛


                # ⚓ Video ☛ KaOS_2022.08_Run_Through⠀⇛


                       In this video, we are looking at KaOS 2022.08.


                # ⚓ Video ☛ Flameshot_Not_Working_On_Wlroots_&_Sway:_Here’s_The
                  Fix_–_Invidious⠀⇛


                       Flameshot is my screenshot tool of choice and
                       trying out Wayland I want keep going with flameshot
                       but it’s not as simple as just running it and it
                       works there’s a bit more tweaking to be done


          o § Kernel Space⠀➾


                # ⚓ LKML:_Linus_Torvalds:_Linux_6.0-rc2⠀⇛


                       It's Sunday afternoon (ok,early evening, just
                       randomly doing this a
                       bit later than usual), and there's a new rc out.

                       Nothing particularly interesting here, rc2 tends to
                       be fairly calm
                       with people taking a breather and not yet having
                       found a lot of bugs.

                       The most noticeable fix in here is likely the
                       virtio reverts that
                       fixed the problem people had with running tests on
                       the google cloud
                       VMs, which was the "pending issue" that we had
                       noticed just as the
                       merge window was closing. And it's noticeable - and
                       notable - mainly
                       because that problem then kept people from running
                       some of the
                       automated tests and thus finding other issues.

                       But obviously there's a lot of other things in here
                       too, as per the
                       appended shortlog. The diffs are somewhat dominated
                       by the amd gpu
                       fixes - they missed the "drm fixes" pull during the
                       merge window, so
                       there were a bunch of fixes pending on that side.
                       But there's some
                       network driver fixes, some filesystem fixes (btrfs
                       and a late ntfs3
                       half-fixes-half-updates pull), and the usual set of
                       architecture fixes
                       and other core code (mainly networking).

                       And some tooling fixes - a mix of selftests and
                       perf.

                       Go forth and test,

                                     Linus
                # ⚓ LWN ☛ Kernel_prepatch_6.0-rc2⠀⇛


                       The second 6.0 kernel prepatch is out for testing.
                       “The most noticeable fix in here is likely the
                       virtio reverts that fixed the problem people had
                       with running tests on the google cloud VMs, which
                       was the ‘pending issue’ that we had noticed just as
                       the merge window was closing”.


                # ⚓ 9to5Linux ☛ Linux_Kernel_5.18_Reaches_End_of_Life,_Users
                  Urged_to_Upgrade_to_Linux_Kernel_5.19⠀⇛


                       Released at the end of May 2022, Linux kernel 5.18
                       is yet another short-lived kernel series. It
                       introduced new features like support for “user
                       events” in the tracing system, support for AMD’s
                       “host system management port” function, support for
                       64-bit integrity checksums on NVMe devices, support
                       for Intel’s “hardware feedback interface” feature,
                       as well as indirect branch tracking support for the
                       x86 architecture.


                       Renowned kernel developer Greg Kroah-Hartman
                       announced today the release of Linux kernel
                       5.18.19, which appears to be a very small patch
                       that only includes 6 changes. What’s most important
                       is that Linux kernel 5.18.19 is also the last
                       maintenance release to the Linux 5.17 kernel
                       series, which now reached end of life and will no
                       longer receive security and bugfix updates.


                # ⚓ LWN ☛ A_collection_of_stable_kernels⠀⇛


                       I’m announcing the release of the 5.19.3 kernel.


                       All users of the 5.19 kernel series must upgrade.


                       The updated 5.19.y git tree can be found at:
                       git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.19.y
                       and can be browsed at the normal kernel.org git web
                       browser:


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


                       thanks,


                       greg k-h


                # ⚓ LWN ☛ Linux_5.18.19⠀⇛


                # ⚓ LWN ☛ Linux_5.15.62⠀⇛


                # ⚓ LWN ☛ Linux_5.10.137⠀⇛


          o § Applications⠀➾


                # ⚓ Linux Shell Tips ☛ Command-Line_Tools_to_Take_Website
                  Screenshots_in_Linux⠀⇛


                       Taking website screenshots is an essential part of
                       a Linux user’s routines. We take website
                       screenshots for a number of reasons with the most
                       common one being the need to document a project’s
                       configuration or installation procedure.


                       Various GUI apps like Flameshot assist Linux users
                       in taking these website screenshots directly
                       gazetted into active projects’ documentation or
                       archived for future reference.


                       However, we do not always have to use third-party
                       GUI apps to take website screenshots as this
                       article will demonstrate. We will look at various
                       viable command-line tools that can capture website
                       screenshots from the comfort of the Linux terminal
                       environment.


                       [...]


                       With these workable solutions, you should be able
                       to effectively capture a website’s screenshot from
                       the comfort of a Linux command-lin environment.


          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_KDE_Plasma_on_Fedora_36_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       KDE Plasma on Fedora 36. For those of you who
                       didn’t know, KDE is a well-known desktop
                       environment for Unix-like systems designed for a
                       lightweight, fast, smooth environment with superior
                       performance. By default, Fedora 36 comes with the
                       GNOME desktop environment preinstalled. If you have
                       installed the Gnome edition and now want to change
                       your Dekstop to KDE then that is not a problem at
                       all. You can do that easily.


                       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 KDE Plasma Desktop Environment
                       on a Fedora 36.


                # ⚓ iustin_–_Note_to_self:_Don’t_forget_Qemu’s_discard_option⠀⇛


                       This is just a short note to myself, and to anyone
                       who might run VMs via home-grown scripts (or
                       systemd units). I expect modern VM managers to do
                       this automatically, but for myself, I have just a
                       few hacked together scripts.


                       By default, QEMU (at least as of version 7.0) does
                       not honour/pass discard requests from block devices
                       to the underlying storage. This is a sane default
                       (like lvm’s default setting), but with long-lived
                       VMs it can lead to lots of wasted disk space. I
                       keep my VMs on SSDs, which is limited space for me,
                       so savings here are important.


                # ⚓ Linux Made Simple ☛ How_to_install_Kdenlive_22.08_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Kdenlive
                       22.08 or newer 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.


                # ⚓ Linux Capable ☛ How_to_Install_Microsoft_Teams_on_Linux
                  Mint_21_LTS [Ed: A piece of spyware that gives Microsoft
                  remote control]⠀⇛


                # ⚓ ID Root ☛ How_To_Install_Skype_on_Linux_Mint_21⠀⇛


                # ⚓ Linux Capable ☛ How_to_Install_Skype_on_Linux_Mint_21_LTS
                  [Ed: But it is spyware, it is controlled by Microsoft, and it
                  is in NSA PRISM]⠀⇛


                # ⚓ Linux Capable ☛ How_to_Install_PowerShell_on_Linux_Mint_21
                  LTS [Ed: This helps Microsoft cement a monopoly; better
                  convert existing scripts to something like Bash]⠀⇛


                # ⚓ Linux Capable ☛ How_to_Install_GIMP_on_Linux_Mint_21_LTS⠀⇛


                       As a Photoshop alternative, GIMP has been getting
                       better each year. The program can be used for
                       graphic design, photo editing, image conversion,
                       and even making digital paintings with various
                       features and functions. Despite being a free and
                       open-source program, GIMP provides users with high-
                       quality results. For example, when it comes to
                       image editing, GIMP offers a wide variety of tools
                       such as cropping, resizing, color correction, and
                       noise reduction. It also supports layers, which is
                       essential for complex graphics editing. In
                       addition, GIMP can be used to create digital
                       paintings from scratch or convert existing photos
                       into images. Whether you’re a beginner or a
                       professional, GIMP is worth checking out.


                       In the following tutorial, you will learn to
                       install GIMP on Linux Mint 21 release series using
                       the apt package manager or the flatpak package
                       manager, along with some tips for maintaining or
                       removing GIMP in the future.


                # ⚓ Linux Capable ☛ How_to_Upgrade_Fedora_36_to_Fedora_37_with
                  GNOME_43⠀⇛


                       Fedora is one of the most popular Linux
                       distributions, and Fedora 37 is set to be another
                       great release. For Workstation users, GNOME 43 and
                       Linux Kernel 5.19 are featured. Fedora 37 is
                       looking to be officially released around October
                       25th, 2022. Still, like always, this can be
                       extended an extra week or two like the previous few
                       releases for those wanting to upgrade now and
                       willing to deal with the dramas of a pre-released
                       Fedora. Do note that Fedora 35 will reach the end-
                       of-life status on roughly September 11th, 2022, so
                       make preparations.


                       The tutorial below will teach you how to
                       successfully upgrade Fedora 36 to the pre-released
                       Fedora 37 Beta/Pre-Release Development branch that
                       features the incoming GNOME 43 and Linux Kernel
                       5.19 but may feature Linux Kernel 6.0 on release.


                # ⚓ Linux Capable ☛ How_to_Upgrade_to_Linux_Mint_21_Vanessa⠀⇛


                       The Vanessa release of Linux Mint 21.0 has Cinnamon
                       5.4 and the 5.15 LTS Linux Kernel. This is the
                       first major release in the Linux Mint 21 series,
                       which most would know is based on Ubuntu 22.04 LTS
                       Jammy Jellyfish. The primary focus of this release
                       is to provide stability and improve the overall
                       experience for users. In addition, several new
                       features have been added, including support for
                       HiDPI displays, a redesigned system tray, and
                       improved performance when using multiple monitors.
                       As always, many bug fixes and security updates are
                       also included. Overall, the Vanessa release
                       provides a solid foundation for the future
                       development of the Linux Mint operating system.


                       In the following tutorial, you will learn how to
                       upgrade to Linux Mint 21 codenamed Vanessa using
                       the terminal method with tips on dealing with any
                       problematic issues during the upgrade.


                # ⚓ Linux Capable ☛ How_to_Install_TeamViewer_on_Linux_Mint_21
                  LTS⠀⇛


                       Founded in 2005, TeamViewer is a German company
                       that provides remote connectivity solutions. The
                       company offers a range of products that allow users
                       to securely access and control devices remotely,
                       regardless of location. In addition to its desktop
                       software, TeamViewer also provides mobile apps and
                       a web-based platform. The company’s products are
                       used by businesses of all sizes, from small
                       startups to large enterprises.TeamViewer is the
                       perfect solution for businesses that need to
                       provide remote support or collaborate remotely. The
                       software is easy to use and provides a secure
                       connection between devices. With TeamViewer,
                       companies can provide remote support to customers,
                       employees, and partners without needing expensive
                       VPNs (virtual private networks). The software is
                       also helpful for collaborating on projects or
                       sharing files between computers.TeamViewer is a
                       versatile tool that can be used for various
                       purposes. Whether you need to provide remote
                       support or collaborate with others, TeamViewer has
                       the perfect solution for you.


                       The following tutorial will teach you how to
                       install TeamViewer on Linux Mint 21 release series.
                       The tutorial will import the official repository
                       and gpg key and update and remove the remote
                       desktop software using the command line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Discord_on_Linux_Mint_21
                  LTS⠀⇛


                       In the world of online gaming, Discord has been the
                       reigning champion for the past few years. It has
                       cemented its place as the go-to platform for gaming
                       communities by partnering with major gaming
                       companies and e-sports organizations. However,
                       TeamSpeak self-hosted is making a comeback. The
                       future will determine if Discord can keep its
                       dominance, given these days’ privacy
                       concerns.Discord has benefited from the popularity
                       ofFortnite and other battle royale games. It has
                       also been embraced by the e-sports community.
                       However, TeamSpeak self-hosted is starting to gain
                       traction again. The main reason for this is privacy
                       concerns. With TeamSpeak, users can host their own
                       servers and have more control over their data. This
                       is becoming increasingly important to gamers, who
                       are becoming more aware of the potential risks of
                       using platforms like Discord. Only time will tell
                       if Discord will be able to keep its place at the
                       top of the gaming world.


                       The following tutorial will teach you how to
                       install the Discord client on Linux Mint 21 release
                       series using two different methods with the command
                       line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Redis_on_AlmaLinux_9⠀⇛


                       Redis is an open-source database frequently used as
                       a cache or message broker. Unlike other databases,
                       Redis stores data in memory, making it
                       significantly faster. In addition, Redis supports a
                       wide range of data structures, including strings,
                       hashes, lists, sets, sorted sets, bitmaps, and
                       streams. This makes Redis an incredibly versatile
                       tool that can be used for various purposes. For
                       example, Redis can be used as a message queue or
                       for tracking user sessions. It can also be used for
                       leaderboards or for storing real-time data. In
                       addition to its speed and flexibility, Redis is
                       highly scalable and can be easily deployed in both
                       physical and cloud environments. As a result, it is
                       no wonder that Redis has become one of the most
                       popular databases among developers.


                       In the following tutorial, you will learn how to
                       install Redis on AlmaLinux 9 workstation or server
                       using the terminal command line with two methods:
                       appstream or Remi Redis pm, along with basic setup
                       instructions to get you started using the command
                       line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_MariaDB_10.6_on_Ubuntu_22.04
                  LTS⠀⇛


                       MariaDB is one of the most popular open-source
                       databases next to its originator MySQL. The
                       original creators of MySQL developed MariaDB in
                       response to fears that MySQL would suddenly become
                       a paid service due to Oracle acquiring it in 2010.
                       With its history of doing similar tactics, the
                       developers behind MariaDB have promised to keep it
                       open source and free from such fears as what has
                       happened to MySQL. Many Linux distributions include
                       MariaDB as their default database management system
                       due to this assurance from the developers.


                       MariaDB 10.6 brings several significant
                       improvements, including improved performance,
                       scalability, and new features such as a crash-safe
                       replication mechanism and improved SQL
                       compatibility. In terms of performance, MariaDB
                       10.6 includes several optimizations that can help
                       to speed up database operations. For example, the
                       new version contains several changes that can help
                       to reduce disk IO and improve caching strategies.
                       In addition, MariaDB 10.6 introduces a new storage
                       engine called MyRocks, which is designed for modern
                       hardware architectures and can provide significant
                       performance improvements. In terms of scalability,
                       MariaDB 10.6 includes several changes that make it
                       easier to run large databases on multiple servers.
                       For example, the new version introduces sharding
                       support, which allows databases to be divided into
                       numerous pieces that can be spread across multiple
                       servers. In addition, MariaDB 10.6 includes several
                       changes that improve the ability to replicate
                       databases across multiple servers. Finally,
                       regarding SQL compatibility, MariaDB 10.6
                       introduces several features that make it easier to
                       port applications from other database systems. For
                       example, the new version includes support for
                       Oracle’s PL/SQL language and introduces a
                       compatibility mode that can make running MySQL
                       applications on MariaDB servers easier. As a
                       result, MariaDB 10.6 is a significant release that
                       includes many improvements that users of all types
                       will welcome.


                # ⚓ Linux Capable ☛ How_to_Install_Snap_&_Snap-Store_on_Rocky
                  Linux_9⠀⇛


                       As any Linux user knows, there are a variety of
                       package managers available, each with its
                       advantages and disadvantages. While some package
                       managers are more popular, they all have benefits
                       and drawbacks. One relatively new package manager
                       is Snap. Snap can be installed and, for the most
                       part, work with most packages on Rocky Linux-based
                       systems that are currently actively supported.
                       There are a few conflicts with specific packages.
                       The issue with Snaps VS DNF package manager is that
                       Snaps are self-contained, which results in an
                       increased .snap due to having all its dependencies
                       included along with various degrees of slight
                       performance degradation when compared to running
                       the same package from DNF. However, the benefits of
                       Snap’s self-containment may outweigh these
                       performance concerns for some users. In addition,
                       Snap is designed to be more secure than other
                       package managers, making it an attractive option
                       for users who prioritize security. Snap is a
                       promising new package manager with unique
                       advantages that may make it the right choice for
                       some Linux users.


                       In the following tutorial, you will learn how to
                       install Snapd on Rocky Linux 9 with the terminal
                       and GUI methods with basic tips on how to launch or
                       install/remove packages with Snapcraft.


                # ⚓ Linux Capable ☛ How_to_Install_Yandex_Browser_on_Linux_Mint
                  21_LTS⠀⇛


                       Yandex browser is the most popular internet browser
                       for all major platforms. It’s based on Chromium,
                       making it fast to load with Standards compliance
                       ensuring no compatibility issues arise due to its
                       ability to be customized through translation
                       services if needed! Yandex also has an outstanding
                       built-in ad blocker that removes annoying ads,
                       improves loading speed, and protects your privacy
                       by blocking tracking requests. Yandex Browser also
                       offers you a variety of customization options so
                       that you can make the browser work precisely how
                       you want it to. You can choose from various themes,
                       set up custom wallpapers, and even change the
                       toolbar buttons to suit your needs. Overall, Yandex
                       Browser is an incredibly stable and fast browser
                       that offers an excellent experience for all users.


                       In the following tutorial, you will learn how to
                       install Yandex Browser on Linux Mint 21 LTS desktop
                       using the command line terminal with tips about
                       maintaining and removing the browser versions.


                # ⚓ UNIX Cop ☛ How_to_install_Python_PIP_on_Ubuntu_22.04_–_The
                  Python_package_manager⠀⇛


                       In this short, but productive post, you will learn
                       how to install PIP on Ubuntu 22.04 | Linux Mint 21
                       which is a package gesture for Python.


                # ⚓ DebugPoint ☛ How_to_Fix:_Can’t_Fetch_Summary_from_Disabled
                  Remote_Flathub⠀⇛


                       Here’s how you can fix the annoying error “Can’t
                       fetch summary from disabled remote ‘flathub’”.


                       For some unknown reasons, Fedora Linux, Ubuntu and
                       other distros give this following error, despite
                       you have installed and setup Flatpak with Flathub
                       with correct steps.


                       Here’s a sample error which I encountered a while
                       back in Fedora during installation of an app via
                       Flathub.


                # ⚓ Linux Capable ☛ How_to_Install_FFmpeg_on_Linux_Mint_21
                  LTS⠀⇛


                       FFmpeg is a free, open-source multimedia framework
                       that can decode and encode just about any file
                       type. With its ability to transcode almost all
                       media files created on different platforms, it’s no
                       wonder why this program has become so popular among
                       those looking for versatility in their video
                       editing software!


                       In the following tutorial, you will learn how to
                       install FFmpeg on Linux Mint 21 release series
                       using the command line terminal and the FFmpeg PPA
                       by Rob Savory to get the latest up-to-date version
                       for your desktop.


                # ⚓ Linux Capable ☛ How_to_Install_SMPlayer_on_Linux_Mint_21
                  LTS⠀⇛


                       SMPlayer is free, open-source software that can be
                       used on any operating system. It has been localized
                       in more than 30 languages, making it easy to enjoy
                       your favorite videos no matter what language(s) are
                       spoken around them! A front end called SMplayer
                       offers graphics tools from Mpv (a forks version),
                       along with its interface widgets provided by qt.
                       This player also falls under the terms given out
                       through GPL v2 or later versions which ensures
                       freedom while providing access via financial means
                       if desired so long as copyright restrictions aren’t
                       violated during use. The best media players are
                       also portable, so you can carry them around on a
                       USB drive and use them without leaving traces
                       behind. SMPlayer is worth trying for this reason
                       alone!


                       The following tutorial will teach you how to
                       install SMPlayer Linux Mint 21 LTS release series
                       using a LaunchPAD APT PPA with the command line
                       terminal.


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ Kdenlive_22.08_released⠀⇛


                             Rendering now supports an experimental
                             Parallel Processing feature for faster render
                             speeds. This version adds support for
                             importing AVIF, HEIF, HEIC and JPEG XL image
                             formats, LOTTIE and RAWR animations, as well
                             as VTT (Web Video Text Tracks) and SBV
                             (YouTube) subtitle files. New features
                             include an improved audio recording
                             experience, global subtitle styling,
                             exporting of guides as chapters for YouTube/
                             PeerTube/Vimeo, and integration with
                             Glaxnimate vector graphics animation program.
                             Colorscopes (Waveform, Vectorscope, and RGB
                             parade) are finally working on Windows.


                             The team would like to thank the code
                             contributions from Eric Jiang, Nathan Hinton,
                             Gary Wang, Marius Pa, Daniel Novomeský,
                             Martin Owens, Brendan Davidson and Ivan
                             Sudakov; and extend our gratitude to all the
                             community members for reporting issues,
                             creating tutorials and offering support.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Ubuntu Handbook ☛ Celluloid_(Gnome_MPV)_Now_GTK4_+
                        LibAwaita_Video_Player_for_Linux_|_UbuntuHandbook⠀⇛


                             By releasing v0.24, Celluloid (formerly Gnome
                             MPV) is now a LibAwaita app. Meaning it works
                             good on any screen sizes, including mobile or
                             tablet devices.


                             Celluloid is a graphical front-end for MPV,
                             defaults in Linux Mint. As MPV is a command
                             line video player, Celluloid adds graphical
                             controls and options to make the player easy
                             to use.


                             Now, the app has ported to GTK4 plus
                             LibAwaita. Which makes it look modern and
                             stylish, and works good on small screen
                             sizes.


                             [...]


                             If you’re going to make a switch, then
                             Celluloid is really a good choice, especially
                             for Gnome desktop Linux, such as Ubuntu,
                             Fedora Workstation.


                      # ⚓ OMG Ubuntu ☛ Nautilus_43_Beta_Arrives_in_Ubuntu_22.10
                        Daily_Builds⠀⇛


                             Well, it’s not that big of a deal. However, I
                             was eager to see ‘what the plan was’ for
                             GTK4/libadwaita apps within the context of
                             Ubuntu’s Yaru theme. Ubuntu 22.04, for those
                             who’ve forgotten, intentionally held back on
                             shipping a number of GTK4/libadwaita ports
                             that were part of GNOME 42


                             Well, I’m pleased to see (and say) that the
                             new-look GTK4/libadwaita version of the
                             Nautilus file manager sits proud within
                             Ubuntu’s Yaru-themed desktop. Any custom Yaru
                             accent colour choice is applied to libadwaita
                             apps too — there had been some worry in the
                             community that libadwaita apps wouldn’t be
                             theme-able in this regard.


                      # ⚓ OpenSource.com ☛ My_first_impression_of_GNOME_Console
                        on_Linux⠀⇛


                             New on the GNOME desktop is their terminal
                             emulator application simply named Console. It
                             seems aimed at providing a no-nonsense,
                             stable command-line environment for Linux
                             users.


                             The GNOME Console isn’t as feature-rich as a
                             lot of other terminals, including the
                             previous GNOME terminal, but I like it and
                             have been using it regularly for the past few
                             months. I enjoy the simplicity of it. I waste
                             time in other terminal emulators configuring
                             fonts, colors, and profiles.


                             Console does have some options and nice
                             integration with the GNOME desktop. I’ll
                             start with the small menu accessed by
                             clicking the hamburger menu at the top-right.
                             It allows for configuring the color theme and
                             font zooming.


                      # ⚓ Phaedrus_Leeds:_GUADEC_2022_Happenings⠀⇛


                             Last month I was fortunate enough to be able
                             to attend GUADEC 2022 in Guadalajara, Mexico,
                             and overall it was a worthwhile experience
                             where I learned a lot. Also it was the 25th
                             anniversary of the GNOME project (give or
                             take a month) and where better to celebrate
                             than in the country where it all began?


                             My main contribution this year was to give a
                             talk, “Integrating Progressive Web Apps in
                             GNOME”, the recording of which you can find
                             here. The attendance of it and engagement
                             with it was pretty good so hopefully folks
                             found it useful. Now with GNOME 43 around the
                             corner, the revamped web app support should
                             be coming to a distribution near you soon so
                             you can see for yourself in case you haven’t
                             been adventurous enough to try it out in
                             GNOME OS Nightly!


                             A few days later into the conference and kind
                             of at the last minute (just the day before) I
                             organized a Flatpak/Portals BoF that took
                             place on Saturday. It was hybrid both online
                             and in-person and pretty well-attended in
                             both mediums. As with past such meetings,
                             there’s always much more to discuss than
                             there’s time for, and perhaps that means we
                             should do more of them. But in any case there
                             were some productive discussions on camera
                             portals and some triaging of open issues and
                             pull requests of Flatpak, which is imminently
                             due for a 1.14.0 release.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Makulu_Max,_What_is_it_??⠀⇛


                 Today we are going to take a look at the new upcoming
                 Makulu-Max Distro. Watch the video below for more
                 information…


          o § Reviews⠀➾


                # ⚓ Distro Watch ☛ Peropesis_1.6.2⠀⇛


                       There is a certain charm to Peropesis. It is
                       exactly what the project’s website says it is: a
                       somewhat incomplete, lightweight, cleanly organized
                       Linux distribution. It can be used for a few things
                       – education, rescuing installed systems, and
                       checking e-mail. But that’s about it, that is all
                       it seems to be intended to do, and that’s what it
                       does. There is no hype, no package manager, or
                       extension modules. It’s just… a super minimal Linux
                       system which works pretty well and very quickly.


                       This makes Peropesis quite limited, there aren’t
                       many situations where I’d use it instead of the
                       live media of a desktop distribution to do similar
                       tasks. However, there is something nice about its
                       simplicity. It’s not often I get to run a
                       distribution that does what it says it will and
                       nothing else. This may not be a practical
                       distribution for almost any situation, but I kind
                       of like it nonetheless.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Wireless_M-Bus_&_LTE_Cat_1_sensor_board_also
                  supports_Zigbee_3.0,_Z-Wave,_Bluetooth_LE_5.0,_LoRa…_–_CNX
                  Software⠀⇛


                       Geniatech SCB32IM is a sensor board based on
                       Silicon Labs EFR32FG14 Arm Cortex-M4
                       microcontroller with a sub-GHz radio enabling
                       wireless M-Bus (Wireless Meter Bus) designed for
                       remote reading of smart meters, and also equipped
                       with a Quectel EC200S “IoT/M2M-optimized” LTE Cat 1
                       module.


                       The sensor module does not actually come with any
                       sensor on board, but provides a terminal block to
                       connect any sensor you may need for your product.
                       It’s also possible to extend wireless connectivity
                       options with Zigbee 3.0, Z-Wave, Bluetooth LE 5.0,
                       LoRa, and more through the GT-IoT interface with
                       UART, SPI, and one GPIO.


                # ⚓ Linux Gizmos ☛ Mini-PC_features_Intel_i9-12900H/HK
                  processor,_triple_4K_displays_and_dual_LAN_ports⠀⇛


                       The Morefine S600-Apex Engineer is a Mini PC built
                       around the latest Intel’s i9-12900H/HK processor.
                       The product comes in an aluminum-magnesium case
                       offering features such as up to 64GB 3200 MHz of
                       RAM, triple 4K displays, flexible storage expansion
                       and a Wi-Fi 6/Bluetooth 5.2.


                       [...]


                       The operating systems supported include Windows 10
                       Pro and Ubuntu 20.04+.


                       [...]


                       According to AndroidPC.com, Morefine S600 might be
                       released on Indiegogo as other products from
                       Morefine (i.e. Morefine S500). The company didn’t
                       provide a specific date, although this post will be
                       updated if there is additional info shared. Refer
                       to the Morefine S600 product page for additional
                       information.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Top_11_Apps_To_Hide_Messages_on_Your_Android_Phone_in
                  2022⠀⇛


                # ⚓ Express ☛ Nokia_C21_Plus_review:_£109_Android_phone_is_full
                  of_surprises_|_Express.co.uk⠀⇛


                # ⚓ Android Authority ☛ Xiaomi_is_the_best_and_the_worst_thing
                  to_happen_to_Android⠀⇛


                # ⚓ HowTo Geek ☛ How_to_Turn_Off_AMBER_Alerts_on_Android⠀⇛


                # ⚓ How_to_Manage_Saved_Passwords_With_Google_Like_A_Pro?⠀⇛


                # ⚓ The Sun ☛ Four_Android_features_almost_NO_ONE_knows_about_–
                  including_App_Pausing_and_Guest_Mode_|_The_US_Sun⠀⇛


                # ⚓ GSM Arena ☛ Week_33_in_review:_Android_13_released,_iPhone
                  14_series_reportedly_coming_on_September_7_–_GSMArena.com
                  news⠀⇛


                # ⚓ Pixel_7_buyers_in_for_a_treat_if_Android_13_is_as_good_as
                  on_Pixel_6⠀⇛


                # ⚓ Android Headlines ☛ What_Are_The_Benefits_Of_Android_Apps
                  In_Cryptocurrency_Trading?⠀⇛


                # ⚓ Dignited ☛ Here_are_7_Alternative_App_Marketplace_platforms
                  for_your_Android_TV⠀⇛


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


          o ⚓ Medevel ☛ Logodust_is_a_Free-to-use_Open-source_Logo_Collection⠀⇛


                 Making a new project and want a quick logo placeholder or
                 even a free logo to use without a fuzz, then head to
                 Logodust, it collects all open-source logos that are
                 released to be used for personal and commercial use.


                 It is an ideal solution for designers and developers who
                 wanna lunch their MVP or mockup faster without getting
                 stuck in creating a brand-new logo or entrapped by ideas.


                 Logodust team adds new free logos frequently, which
                 anyone can download them for free in a high quality SVG
                 format.


          o § Programming/Development⠀➾


                # ⚓ Fabio_Alessandro_Locati:_Parse_multi-CSV_files_in_Go⠀⇛


                       As it happens every year, I had to pull a lot of
                       information from various financial intermediaries
                       and convert them into the way the local tax system
                       wanted them. For this reason, I created a Go
                       program that does this modularly. Whenever I have a
                       new financial intermediary, I create a new module
                       that can read whatever format they create and
                       returns a structured object in the form that the
                       application expects. This year I added a new
                       financial intermediary with a very “interesting”
                       CSV format.


                       To be able to condense multiple different kinds of
                       data in the same file, they created a CSV file that
                       has as the first column the name of the content (I
                       think of it as the database table name). In the
                       second column, we will find either Header or Data
                       to distinguish if the row represents the headers
                       for that “table” or rows of data, and then from the
                       third column, it looks like a normal CSV file.


                # ⚓ Using_console.log()_in_JavaScript_–_Pi_My_Life_Up⠀⇛


                       The console.log() function is an incredibly useful
                       part of JavaScript that you can use to debug your
                       code.


                       This function allows you to write messages to the
                       console from your JavaScript. It allows you to
                       easily debug your code on the fly as you can print
                       out any required values when a problem occurs.


                # ⚓ Geeks For Geeks ☛ Flutter_vs_Kotlin_–_For_Android
                  Development⠀⇛


                       Believe it or not but the future is going to be in
                       the hands of compact devices such as mobile phones,
                       tablets, etc. In the last few years, the pandemic
                       has changed the whole business metrics. That’s the
                       fact, companies are now trying to find a way to
                       reduce their production cost and speed up their
                       sales figures. and they’re focusing more on
                       developing sustainable mobile applications to
                       maintain their true existence. There’s no surprise
                       that it is one of the most important trends in the
                       world of the software development industry.


                # ⚓ Bozhidar Batsov ☛ Learning_OCaml_–_(think)⠀⇛


                       For as long as I’ve been into programming I’ve been
                       learning some new programming languages on the
                       side. The more “exotic” and “niche” they were – the
                       better.1 While my professional career was mostly
                       focused on C, C++, Java and Ruby, over the years
                       I’ve been playing to a different extent with
                       languages like Prolog, Common Lisp, Scheme/Racket,
                       Clojure, Smalltalk, Erlang, Elixir, Scala, Haskell,
                       just to name a few. It’s funny that every couple of
                       years I revisit Erlang and Haskell, but I always
                       fail to truly master them. Anyways, for some reason
                       (laziness?) I haven’t been seriously learning
                       anything new since my last (failed) stint with
                       Haskell 3-4 years ago and I’ve decided it’s time to
                       change this. After compiling a short list of
                       appealing candidates2 I’ve opted for OCaml – one of
                       the most famous members of the ML family of
                       programming languages.


    * § Leftovers⠀➾


          o ⚓ Ruben Schade ☛ Rubenerd:_It_sure_felt_like_a_long_weekend!⠀⇛


                 I still can’t believe we did this for two years; even
                 just a weekend of it left me feeling irritable and tired.
                 My dad used to say the most exhausting thing you can do
                 is nothing, and I’ve really come to understand this of
                 late.


          o § Security⠀➾


                # ⚓ 12_Vulnerable_Sites_&_Web_Applications_For_Pen_Testing
                  2022⠀⇛


                       We put together a list that includes vulnerable XSS
                       and SQL sites too. When we say this word we
                       actually mean ethical hacking and using such sites
                       and apps for testing gives a safe environment to
                       practice the craft legally while staying on the
                       right side of the law. Like this, you can hack
                       freely without the fear of being arrested.


                # ⚓ Geeks For Geeks ☛ How_Hackers_Use_Social_Engineering_to_Get
                  Passwords_on_Facebook?⠀⇛


                       Social engineering is a powerful method for hackers
                       to exploit computer systems without the use of
                       malware or computer hacking tools.


                # ⚓ Open Source Security (Audio Show) ☛ Episode_337_–_Security
                  patches_are_getting_worse_–_Dustin_Childs_from_ZDI_tells_us
                  why_–_Open_Source_Security⠀⇛


                       Josh and Kurt talk to Dustin Childs about the
                       recent ZDI Black Hat talk where they discovered the
                       current trend of security patches not actually
                       fixing the security problem. We talk about what
                       this problem means. Why is it happening, and what
                       ZDI is doing to try nudge the industry in the right
                       direction.


                # ⚓ Daniel Stenberg ☛ Increased_CVE_activity_in_curl?_|
                  daniel.haxx.se⠀⇛


                       In 2022 we have already had 14 CVEs reported so
                       far, and we will announce the 15th when we release
                       curl 7.85.0 at the end of August. Going into
                       September 2022, there have been a total of 18
                       reported CVEs in the last 12 months.


                       During the whole of 2021 we had 13 CVEs reported –
                       and already that was a large amount and the most
                       CVEs in a single year since 2016.


                       There has clearly been an increased CVE issue rate
                       in curl as of late.


          o § Defence/Aggression⠀➾


                # ⚓ [Old]_It_is_happening_here:_Massachusetts_has_a_growing
                  neo-Nazi_movement⠀⇛


                       It was a rare look inside the strategic planning of
                       an upstart neo-Nazi movement.


                       In a video posted last summer on social media,
                       Chris Hood, 23, the founder of the Nationalist
                       Social Club – 131, a New England white nationalist
                       collective, gave instructions to a 22-year-old
                       UMass Lowell student named Liam MacNeil.


                       “If you’re in college you should be getting
                       together with all the other guys on campus that
                       think like you, circling all the frat parties and
                       bullying the chicks that race mix and start
                       dominating the party and take over the campus,”
                       Hood said. “Same policy as out here [the street]
                       but just do it on campus.”


                       “We can do that,” MacNeil responded. “Everyone
                       knows where I am now, but they’re going to have to
                       physically remove me. You know, they’re going to
                       have to kick me out.”


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ Positech Games ☛ The_unavailable_gadget_we_badly_need
                        to_invent⠀⇛


                             Solar power has a problem. Its a problem that
                             we are working around, but it also represents
                             an opportunity, because if someone can seize
                             the opportunity, its seriously going to help
                             everyone. It will help energy security, it
                             will help the cost of living, it will help
                             equality, it will help fight climate change.
                             An opportunity existing precisely because
                             solar power has a problem:


                             Solar panels are things we all know about.
                             You can get big ones, and small ones, even
                             tiny ones that power something as small as a
                             pocket calculator (remember those?) or that
                             unroll and plug into your phone to charge on
                             a sunny day. We all know about solar panels.
                             What most of us are not aware of, is
                             inverters, and how our home wiring works. The
                             big thing I need to get across in this post
                             is that right now there is a LOT of
                             complexity and crap that goes in between
                             those solar panels you see on someone’s roof,
                             or in a field, and the wall socket you plug
                             your TV into.


          o § Finance⠀➾


                # ⚓ Michael West Media ☛ Qantas_takeover_of_Alliance_Airlines
                  stuttering_on_the_runway,_what’s_the_scam?⠀⇛


                       Qantas is trying to take over Alliance Airlines, a
                       competitor in the lucrative FIFO market – the
                       flying in and out of mine workers in remote
                       locations. The ACCC is not so sure it’s a good
                       idea, so what’s the scam?


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Michael West Media ☛ People_of_Cook,_you_can_make_Josh_the
                  comeback_kid_–_Michael_West⠀⇛


                       Fresh from the mortifying news that he was sharing
                       the second highest post in government with his
                       leader, former treasurer Josh Frydenberg is being
                       spoken of as a Liberal saviour. Apparently Peter
                       Dutton has not inspired the nation in his role as
                       opposition leader.


                       As outrage swirls around Scott Morrison for running
                       a secret parallel ministry, there are some wistful
                       musings about the prospect of Josh getting back
                       into parliament, even by replacing ScoMo. The
                       former PM has become an unwelcome presence on his
                       own side, and few would be sorry to see his back.
                       Perhaps only Labor really wants him to hang around.


                       Enter the Liberal elder statesman. John Howard has
                       lunches with Josh Frydenberg. They talk politics,
                       Honest John helpfully informed Radio National’s
                       Patricia Karvelas on Wednesday. She then asked him
                       about the prospects of Josh taking Scott Morrison’s
                       seat of Cook.


                # ⚓ Michael West Media ☛ Is_this_an_affront_to_the
                  constitution,_or_a_lucky_break_for_a_bunch_of_precious
                  people?_–_Michael_West⠀⇛


                       As Australians reeled from the news that Gough
                       Whitlam had been replaced as prime minister by
                       Malcolm Fraser at the whim of an unelected official
                       acting in the name of a foreign-born monarch,
                       comedian Garry McDonald inserted himself into the
                       action.


                       In character as gormless TV reporter Norman
                       Gunston, the comedian mingled with the assembled
                       politicians, journalists, lawyers and academics on
                       the steps of Parliament House. Then he turned to
                       the impassioned crowd that had gathered on the
                       forecourt. He shouted: ”Is this an affront to the
                       constitution of this country?”


                # ⚓ Michael West Media ☛ ‘Lucky_Laundry’_review:_how_Australia
                  got_caught_in_a_toxic_spin_cycle_–_Michael_West⠀⇛


                       The property market is a favourite for money
                       launderers, forcing ordinary Australians to compete
                       with organised crime for their dream home, says
                       investigative author Nathan Lynch. He blames the
                       power of lobbyists as a cancer on our democracy.
                       Lynch’s new book is a wake-up call, writes
                       Stephanie Tran.


                       Australia has been captured by a phenomenon called
                       the property industrial complex. It poisons our
                       politics and institutions, but worse, it forces
                       aspiring home-owners on restricted incomes to
                       compete with the bottomless pockets of criminal
                       networks.


                       This is the convincing hypothesis of a new book by
                       crime investigator Nathan Lynch. The Lucky Laundry,
                       subtitled How the Aussie Economy Got Hooked on the
                       World’s Dirtiest Cash, delves deep into how
                       political inertia has enabled “dark money” to
                       pollute our financial system. The book is a wake-up
                       call.


          o § Censorship/Free Speech⠀➾


                # ⚓ The Atlantic ☛
                  Xi_Jinping’s_Radical_Secrecy⠀⇛


                       Xi Jinping has never given a press conference. He
                       is the head of China’s ruling Communist Party—a
                       colossal, sprawling political machine with 96.7
                       million members—yet he does not have a press
                       secretary. His office does not preannounce his
                       domestic travel or visitor log. He does not tweet.


                       What are billed by the official media as important
                       speeches are typically not released until months
                       after Xi has delivered them in closed forums. Even
                       then, the published versions can be pallid
                       reworkings of the documents that have been
                       circulated internally and, very occasionally,
                       leaked.


                       The secretiveness of Beijing’s ruling party might
                       once have been dismissed as a mere eccentricity,
                       fodder for an industry of intelligence analysts and
                       academic Pekingologists to sort through for clues
                       about top-level machinations. But with Xi now often
                       described, without hyperbole, as the “world’s most
                       powerful man,” and on the verge of winning a norm-
                       breaking third term later this year at the party
                       congress, Beijing’s radical opacity has real-world
                       consequences.


                # ⚓ Netblocks ☛ YouTube_disrupted_in_Pakistan_as_former_PM_Khan
                  streams_speech_–_NetBlocks⠀⇛


                       NetBlocks metrics confirm the disruption of YouTube
                       on multiple internet providers in Pakistan on
                       Sunday 21 August 2022. The disruption comes as
                       former Prime Minister Imran Khan makes a live
                       broadcast to the public, despite a ban issued by
                       the Pakistan Electronic Media Regulatory Authority
                       (PEMRA).


                # ⚓ Reason ☛ How_‘Slaughterhouse-Five’_Became_a_Repeated_Target
                  of_Book_Burners⠀⇛


                       Like Billy Pilgrim, the unstuck-in-time protagonist
                       of Kurt Vonnegut’s Slaughterhouse-Five, or, The
                       Children’s Crusade, it can sometimes feel like
                       we’re all witnessing the same censorship fights
                       again and again.


                       Since it was published in 1969, Slaughterhouse-Five
                       has been a repeated target for book
                       burners—sometimes quite literally. In 1973, 32
                       copies of the book were thrown into the furnace at
                       a high school in Drake, North Dakota, on orders
                       from the local school board after parents
                       complained about the book’s sex and profanity.
                       Sensibilities about those things have come a long
                       way in the past few decades, but Vonnegut’s novel
                       is still a target. In 2011, a school board in
                       Missouri barred the book from the curriculum and
                       ordered it confined to a special section of the
                       school’s library.


                # ⚓ Reason ☛ How_Stalin_Toyed_With_Mikhail_Bulgakov⠀⇛


                       The devil went down to Moscow not long after the
                       Bolshevik takeover, along with a valet, a vampire,
                       an assassin, and a gunslinging man-sized cat called
                       Behemoth. That’s the setup for Mikhail Bulgakov’s
                       The Master and Margarita, a scathingly satiric tale
                       of Soviet censors, informers, and intellectual
                       courtiers that doubles as an unorthodox retelling
                       of the Book of Matthew. Finished in 1940, the novel
                       was not formally published until the late 1960s,
                       and then only in heavily censored form. The full
                       novel finally appeared in 1973, but even then
                       Russian readers were more likely to encounter a
                       samizdat edition than the hard-to-find official
                       printing.


                # ⚓ Reason ☛ South_Carolina_Targets_Free_Speech_To_Limit
                  Abortion_Access⠀⇛


                       One challenge prohibitionists face is that not
                       everybody supports their prohibitions. Many people
                       under their nominal authority want access to what’s
                       forbidden, no matter what the law says.


                       Aware that the procedure remains available
                       elsewhere, South Carolina lawmakers seeking a near-
                       complete ban on abortion propose to forbid speech
                       about terminating pregnancies to prevent residents
                       of the Palmetto State from learning of such
                       services. The recently rebooted Foundation for
                       Individual Rights and Expression (FIRE) is
                       reminding `them that speech that politicians don’t
                       like is not only the best speech but is also
                       protected by the First Amendment.


                # ⚓ The Atlantic ☛ End_Times_in_Aspen:_How_to_Kill_a_Newspaper
                  –_The_Atlantic⠀⇛


                       How a Soviet-born developer and a West Virginia
                       billionaire destroyed a 141-year-old Colorado
                       newspaper


                # ⚓ RFA ☛ Pro-China_pundit’s_admission_to_owning_a_house_in
                  California_sparks_backlash_—_Radio_Free_Asia⠀⇛


                       Sima Nan is roasted on social media after admitting
                       to having bought the property in 2010.


                # ⚓ Jacobin Magazine ☛ Salman_Rushdie’s_Stabbing_Should_Remind
                  Us_That_Free_Speech_Is_a_Nonnegotiable_Progressive_Value⠀⇛


                       It looks like Salman Rushdie is going to lose an
                       eye. He also has stab wounds on his neck and chest.
                       He’s finally off the ventilator that was used to
                       keep him alive in the immediate aftermath of the
                       attack, but his son has called the injuries “life-
                       changing.”


                       The novelist was getting ready to deliver a lecture
                       in New York last Friday when a man rushed the stage
                       to stab him. It seems to be a belated attempt to
                       carry out the clerical death sentence against
                       Rushdie issued decades ago by the Ayatollah
                       Ruhollah Khomeini. The fatwa was issued because
                       Rushdie wrote a “blasphemous” novel, The Satanic
                       Verses.


                       To say all of that a bit more succinctly, a writer
                       just spent days on the brink of death because a
                       religious leader found his novel offensive. It’s a
                       brutal reminder of the importance of free speech.


                # ⚓ Reason ☛ The_Satanic_Panic_Is_Back,_and_It’s_Bipartisan⠀⇛


                       A new poll looking at Americans’ belief in
                       conspiracy theories finds high levels of support
                       for loony-tunes ideas about sex, Satan, and U.S.
                       institutions. In addition, more than half of those
                       surveyed believed child sex-trafficking myths.


                       The situation echoes fears prevalent during the
                       1980s and ’90s, a mass hysteria that has in
                       retrospect been dubbed the Satanic Panic. This
                       vintage worry about ritual murders, sexual abuse
                       inspired by devil worship, and Satanists in child
                       care centers, the entertainment industry, and
                       elsewhere was unfounded—but still ruined lives.
                       (You can read much more about the Satanic Panic in
                       Reason Books Editor Jesse Walker’s The United
                       States of Paranoia: A Conspiracy Theory.)


                # ⚓ Vice ☛ Free_Speech_Bastion_Substack_Fires_Editor_for
                  Editing_a_Blog_Critical_of_Substack⠀⇛


                       In late July, the journalist Sam Thielman, who’d
                       been working on contract as an editor for Substack,
                       the newsletter company, was fired. As he would
                       explain in a newsletter published earlier this week
                       that described the firing as an act of retaliation,
                       and as Substack would quickly acknowledge—”We
                       fucked up” is the way founder Hamish McKenzie put
                       it—he not only hadn’t done anything wrong, he
                       hadn’t really done anything at all.


                       The episode ended well enough for Thielman, with
                       him being paid for the work he would have done if
                       he hadn’t been fired and Substack apologizing, but
                       raised—hardly for the first time—a number of
                       questions the company hasn’t been able to
                       convincingly answer. Most of them have to do with
                       what Substack, which at times seems to operate as a
                       mission-driven journalistic outlet and at others as
                       a neutral tech platform, actually is.


                # ⚓ Reason ☛ The_Failed_Campaign_To_Ban_‘To_Kill_a
                  Mockingbird’⠀⇛


                       People have been trying to ban Harper Lee’s To Kill
                       a Mockingbird since the 1960s. And since the 1960s,
                       they have largely failed.


                # ⚓ New York Times ☛ The_Stabbing_of_Salman_Rushdie_Renews_Free
                  Speech_Debates_–_The_New_York_Times⠀⇛


                       Two years ago Salman Rushdie joined prominent
                       cultural figures signing an open letter decrying an
                       increasingly “intolerant climate” and warning that
                       the “free exchange of information and ideas, the
                       lifeblood of a liberal society, is daily becoming
                       more constricted.” It was a declaration of
                       principles Mr. Rushdie had embodied since 1989,
                       when a fatwa by Ayatollah Ruhollah Khomeini, the
                       Supreme Leader of Iran, calling for his murder,
                       made him a reluctant symbol of free speech.


                       The letter, published by Harper’s Magazine in June
                       2020 after racial justice protests swept the United
                       States, drew a backlash, with some denouncing it as
                       a reactionary display of thin-skinnedness and
                       privilege — signed, as one critic put it, by “rich
                       fools.”


                       The reaction dismayed Mr. Rushdie, but didn’t
                       surprise him. “Put it like this: the kinds of
                       people who stood up for me in the bad years might
                       not do so now,” he told The Guardian in 2021. “The
                       idea that being offended is a valid critique has
                       gained a lot of traction.”


                # ⚓ DaemonFC (Ryan Farmer) ☛ Cook_County_Judge’s_Office_gets
                  thrown_off_GULAG_Tube_(YouTube)_and_has_to_file_an_appeal.⠀⇛


                       Amusing that it happens to one of America’s
                       kangaroo courts.


                       GULAG (Google) doesn’t even feel compelled to tell
                       them why they have been banned, and the court begs
                       GULAG to allow them back on instead of ordering
                       them to.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ I’m_Starting_a_Journal⠀⇛


                       So I’ve decided to give blogging a try, or rather
                       journaling. I’m not normally one for writing about
                       myself and I’ve never been great at keeping diaries
                       so I have no idea how this might go. I do have a
                       lot of thoughts in my head though – it’s just
                       getting them down fast enough that’s the problem!


                # ⚓ Naming_my_schemes⠀⇛


                       So I’m over-prepping for my date on Saturday.


                       I’ve been plotting out what measures I must make to
                       hide my slobbish tendencies. my actions reminded me
                       of Stradlater from Catcher In The Rye, hiding the
                       fact he’s a total slob and only Holden knowing the
                       wiser. So I decided to name my agenda for the next
                       day and a half “Operation Stradlater”.


                # ⚓ Intergalactic_Singles_Night_Devlog⠀⇛


                       I’ve been thinking a lot about games recently. I’ve
                       decided to take a break from college for an
                       indeterminate amount of time, and I have started
                       thinking about what I want to put into the world.
                       It’s been far too long since I’ve completed a
                       project that I’m proud of, so with that in mind as
                       I traveled back to my parents house to visit, I
                       resolved to participate in the Godot Wild Jam.


                       I have three larger prototypes I’ve been working on
                       in the back of my mind, but I found it hard to work
                       on them. I’m not sure if it was leftover fatigue
                       from finish school, covid, or anxiety about the
                       future, but nevertheless I was feeling burnt out.
                       The game jam was a great opportunity to put all of
                       that aside and work on a small standalone project,
                       both to further develop my skills with godot, and
                       to prove to myself that I can finish a project.


                # ⚓ Operation_Friendly_Skies⠀⇛


                       So I love crows, well really all corvids, but
                       especially crows. Something about their
                       intelligence just amazes me, they know to fly
                       towards the sound of a gunshot because it means a
                       dead animal may be on the other side. One time I
                       watched a crow drag an unopened bag of chips into
                       the road so a car could drive over it and pop it
                       open. He placed it exactly where the driver side
                       wheels were and waited until someone hit it. He
                       then flew into the road and dragged back the bag
                       where he enjoyed his feast.


                # ⚓ The_Tragedy_of_Hamlet,_Prince_of_Denmark⠀⇛


          o § Technical⠀➾


                # ⚓ Update⠀⇛


                       I completed my order of the Steam Deck last week. I
                       preordered it over


                       a year ago. Now of course I had a moment of
                       cognitive dissonance over


                       it. Do I really need a new gaming console? I
                       already have my Switch


                       Lite. And of course the price… But hey, why not? I
                       mean I have a few


                       games in my Steam library and I’m not playing those
                       as I do not want


                       to turn on my desktop computer to play a couple of
                       minutes. That is so


                       easy with the switch, I can play when my wife is
                       taking a bath, etc. A


                       click of a button and it sleeps and I can always
                       continue at the exact


                       same location. So the Deck is underway from the
                       Netherlands to me.


                # § Internet/Gemini⠀➾


                      # ⚓ Why_is_the_cosmos_the_theme_of_Gemini?⠀⇛


                             It’s interesting that the Gemini protocol is
                             in the most cases identified with the cosmos.
                             It’s probably the first time, when raw
                             technical specification in the common belief
                             is fitting some theme. There are of course
                             lots of clues. So the origin of the Gemini is
                             the Circumlunar Space, which mentions its
                             [backstory] as one of the space opera novels.
                             The second important place is Gemini protocol
                             [faq] which is describing the protocol name
                             origin. But there is no obligation to follow
                             this route.


                             So there aren’t many things in the
                             Gophersphere which are connected with a
                             gopher rodent. Gophersphere isn’t
                             conceptually related with a burrow. But the
                             Geminispace, with it’s space prefix, for me
                             is very cosmos oriented name.


                # § Programming⠀➾


                      # ⚓ TextExpander_snippets⠀⇛


                             I use TextExpander to turn easily-typed text
                             into time-consuming-to-generate text.


                             All the shell-script ones are written in zsh
                             since that’s the default shell on my system
                             of choice, but they probably run identically
                             in bash, and maybe even sh.


                             Fair warning: A bunch of these snippets use
                             common UNIX programs. One of the problems
                             with stringing together common UNIX programs
                             like date(1), tr(1), and sed(1) is that
                             they’re often implemented slightly
                             differently depending on what UNIX(alike)
                             you’re on.


                      # ⚓ There_is_another_GNU_scheme⠀⇛


                             Most people with an interest in Free Software
                             or scheme/functional
                             programming have probably heard of GNU Guile:
                             GNU’s main embedded
                             extension language. They may also have heard
                             of MIT/GNU Scheme, whose
                             main claim to fame is being the scheme
                             interpreter often used in
                             conjunction with the inimitable SICP wizard
                             book.


                             There is, however, another GNU scheme: [GNU
                             scm]


                             “GNU scm” has, as you can imagine, some
                             discoverability issues, but
                             maybe that’s for the best, or even intended,
                             making sure that no-one
                             accidentally finds it without looking for it.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 6335

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_22/08/2022:_Many_Software_Comparisons_and_New_RISC-V_Products_With
Linux⠀✐


Posted in News_Roundup at 9:46 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o WINE_or_Emulation
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
    * Free,_Libre,_and_Open_Source_Software
          o Productivity_Software/LibreOffice/Calligra
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Proprietary
          o AstroTurf/Lobbying/Politics
                # Misinformation/Disinformation
          o Internet_Policy/Net_Neutrality
    * Gemini*_and_Gopher
          o Personal
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ New_XPS_13_2-in-1,_XPS_13_Plus_Developer’s_Edition_and_Pro
                  Webcam_announced_from_Dell_–_Irish_Tech_News⠀⇛


                       The first OEM PC to be certified for Ubuntu 22.04,
                       Dell’s flagship XPS 13 Plus Developer’s Edition is
                       available pre-installed with Ubuntu 22.04 LTS. The
                       Ubuntu certification program ensures that all of
                       the components in a certified computer work as
                       expected, so the user can be sure of the best
                       experience out of the box.


                       Certified devices also include specific software or
                       drivers that differ from the default distribution
                       where required. These are defined in a meta-package
                       that automatically installs the optimal
                       configuration of packages, drivers and kernel to
                       deliver the best experience on that device. For a
                       full breakdown of the new features of Ubuntu 22.04
                       LTS, read the release notes and official
                       announcement.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ I_was_WRONG!_This_is_the_BEST_Package_Manager._–
                  Invidious⠀⇛


                       This standalone package manager is absolutely
                       stunning and I can’t believe I’m just now
                       discovering it’s true power.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to
                  Apple_Reminders_–_LinuxLinks⠀⇛


                       Apple, Microsoft, Alphabet (Google’s parent),
                       Amazon and Facebook dominate the tech landscape.
                       Their dominance is so broad they account for more
                       than 20% of the S&P 500.


                       There are many things to admire about Apple’s
                       hardware and software. Apple make great looking
                       (albeit expensive) hardware. Over the years key
                       successes include the iPhone, iPad, iPod, and the
                       MacBook Air. The company designs its own hardware
                       and software. This gives them the power to make an
                       operating system and suite of apps that are tailor-
                       made and optimized for their hardware. Apple also
                       operates the Apple Music and Apple TV media
                       distribution platforms.


                       Mac OS X is Apple’s proprietary operating system
                       for its line of Macintosh computers. Its interface,
                       known as Aqua, is highly polished and built on top
                       of a BSD derivative (Darwin). There’s a whole raft
                       of proprietary applications that are developed by
                       Apple for their operating software. This software
                       is not available for Linux and there’s no prospect
                       of that position changing.


                       Apple RemindersReminders is a task management
                       program that allows users to create lists and set
                       notifications.


                       This proprietary program runs on iOS, macOS and
                       watchOS operating systems, but it’s not available
                       for Linux. We recommend the best free and open
                       source alternatives to Reminders.


                       [...]


                       If you prefer a CLI tool, Taskwarrior ticks all the
                       boxes.


                # ⚓ Its FOSS ☛ Kooha_Screen_Recorder_Gets_Enhanced
                  Functionalities_With_Version_2.1_Release⠀⇛


                       Kooha is a fairly new screen recorder for Linux. It
                       has been in development since 2021.


                       As a modern offering, it is a good pick for users
                       who need a screen recorder for the Wayland desktop
                       session. We’ve covered it earlier.


                       [...]


                       One of the key highlights for Kooha screen recorder
                       is the ability to add a delay for recording.


                       While it already had options for five or ten-second
                       delay, with Kooha 2.1, you get a three-second
                       option.


                       It may not sound much of a big deal, but you get
                       more flexibility with options. And, the ability to
                       start a recording after a delay is one of my
                       favorite features about it.


                # ⚓ LinuxConfig ☛ Best_Video_Player_for_Linux⠀⇛


                       Any desktop Linux system should come with a default
                       video player, which is usually capable of handling
                       all of the most popular video formats and codecs.
                       However, you may find that some systems do not
                       include the proprietary software necessary to play
                       back certain file types. Or, maybe you are just not
                       satisfied with the pre installed video player that
                       came with your Linux distro.


                       We have gone through the trouble of testing out
                       various video players for Linux, weighed their pros
                       and cons, and decided on what we think is the best
                       video player (spoiler: it’s VLC). Read on to learn
                       about the best video player, some other honorable
                       mentions, and what you can expect to gain from
                       installing one of these video players on your own
                       Linux system.


                       [...]


                       In this tutorial, we learned about our choice for
                       the best video player on a Linux system: VLC.


                # ⚓ Linux Shell Tips ☛ Gum_–_A_Tool_for_Glamorous_Shell_Scripts
                  in_Linux⠀⇛


                       If you are a Linux operating system enthusiast or
                       on a path to defining yourself as one, then
                       crossing paths with shell scripting is completely
                       inevitable. By definition, a shell script is a
                       program designed to be executed on a Unix/Linux
                       shell environment.


                       We can associate command-line interpreter (shell)
                       with script operations like printing text, program
                       execution, and file manipulation. Examples of
                       popular Unix/Linux shell environments include GNU
                       Bourne-Again Shell, Bourne Shell, Korn Shell, and C
                       Shell.


                       [...]


                       This article guide makes it comfortably easy to
                       begin and evolve in the creation of glamorous shell
                       scripts.


                # ⚓ LinuxConfig ☛ Best_PDF_Reader_for_Linux⠀⇛


                       The Adobe PDF file format is commonly used for
                       instructions, manuals, boarding passes, and lots of
                       other types of documentation. You are bound to run
                       into a PDF document eventually. Is your Linux
                       system able to open and read them?


                       In this tutorial, we have compiled some of our
                       favorite PDF readers for Linux. You will learn
                       about our top picks and what makes them solid
                       choices for installation.


                       [...]


                       Each of them have their pros and cons, and the best
                       one for you will depend on your situation, whether
                       you want a beefy program, lightweight viewer, or
                       want to stick with one of the default viewers.


                # ⚓ LinuxConfig ☛ Best_firewall_for_Linux⠀⇛


                       A firewall is a line of defense on your network,
                       primarily used to filter incoming traffic, but also
                       used for outbound rules and other network related
                       security. All major Linux distros come with a
                       software firewall built into them, since it is part
                       of the Linux kernel itself. Any user can configure
                       their system firewall to get started with securing
                       network traffic, but there are many alternatives to
                       the default which will extend or simplify the
                       functionality.


                       In this tutorial, we have compiled a list of our
                       top picks for the best firewalls available on
                       Linux. The one you pick will largely depend on your
                       goals for securing your network. Of course,
                       corporations or large networks will need a very
                       different firewall solution than a typical end
                       user. You will see a few choices below to help
                       steer you in the right direction to pick a firewall
                       that best suits your needs.


                       [...]


                       The best solution largely depends on your own
                       preference and what kind of security your network
                       or individual computer needs.


                # ⚓ Linuxiac ☛ 3_Best_NGINX_Alternatives_for_Your_Linux_Web
                  Server⠀⇛


                       This article will present you with the three best
                       free and reliable NGINX alternatives for your
                       production Linux web servers.


                       NGINX is the current internet king. It has managed
                       to dethrone Apache as the most used web server in
                       the world during the last year and reclaim its
                       rightful place.


                       According to Netcraft’s most recent data, as of
                       June 2022, NGINX serves roughly one-third (30.71%)
                       of all global Internet traffic. And there’s a
                       reason behind that.


                       NGINX is a high-performance asynchronous web server
                       that uses event-driven architecture to handle
                       massive amounts of connections. It operates on a
                       multi-process basis, with one master process
                       spawning numerous worker processes to handle all
                       network events.


                       [...]


                       As you may have noticed, the term “fast” appears
                       many times in this article. This is because NGINX,
                       Lighttpd, OpenLightSpeed, and Caddy are the fastest
                       web servers.


                # ⚓ Linux Hint ☛ TrueNAS_vs._Unraid:_Which_One_is_Better?⠀⇛


                       Both TrueNAS and Unraid are capable and mature NAS
                       operating systems, but there are major differences
                       between them that determine who they can be
                       recommended. Generally, TrueNAS is a great solution
                       for those who are deeply familiar with RAID
                       technology and know how to take advantage of it to
                       achieve the best performance possible. Unraid, on
                       the other hand, is fantastic for home users who
                       want to use all kinds of random hard drives to
                       create a single central data storage repository.


          o § Instructionals/Technical⠀➾


                # ⚓ LinuxTechi ☛ 14_grep_command_examples_in_Linux⠀⇛


                       Are you looking for hands on guide on Linux grep
                       command ? In this guide, we will cover 14 grep
                       command examples in linux.


                       Grep is a command line tool in Linux/Unix systems
                       that is used to search text or string from a file.
                       Grep stands for global regular expression print.
                       When we run a grep command with specified string,
                       if its is matched, then it will display the line of
                       the file containing that string without modifying
                       the contents of the existing file.


                # ⚓ LinuxTechi ☛ How_to_Set_Static_IP_Address_on_RHEL_9⠀⇛


                       In this post, we will cover how to set static ip
                       address on rhel 9 system.


                       It is strongly recommended to set static ip address
                       on your linux system specially on servers. The main
                       benefit of static IP address is that it will be
                       persistent across the reboots.


                # ⚓ Video ☛ Install_ProtonUp-QT_and_TRANSFORM_your_games_and
                  the_Steam_Deck_experience._–_Invidious⠀⇛


                       Here’s why you NEED ProtonUp-QT on your Steam Deck
                       and how to use it.


                # ⚓ Linux Capable ☛ How_to_Install_OpenRGB_on_Linux_Mint_21
                  LTS⠀⇛


                       While LEDs are now ubiquitous, with most devices
                       coming with some form of backlighting, there is
                       still a lack of standardization in the industry.
                       This can make it challenging to find software that
                       works with all of your devices. OpenRGB seeks to
                       solve this problem by providing a free, open-source
                       solution that can be used with any RGB-enabled
                       device. The software offers many features,
                       including support for RGB amber lighting, game
                       integrations, music visualization, and more.
                       Additionally, the software comes with a plugin
                       interface that allows you to extend its
                       functionality even further. Whether you’re looking
                       to add some flair to your gaming setup or want
                       greater control over your lighting, OpenRGB is
                       worth checking out.


                       In the following tutorial, you will learn how to
                       install OpenRGB on Linux Mint 21 release series by
                       importing a third-party LaunchPAD PPA with the
                       command line terminal and maintaining and removing
                       the package if required.


                # ⚓ SUSE’s Corporate Blog ☛ Deploy_Rancher_on_an_EKS_cluster,
                  the_easy_way_|_SUSE_Communities⠀⇛


                       In case you are looking to deploy Rancher Manager
                       on an EKS cluster then look no further. We have
                       released SUSE Rancher Setup in AWS Marketplace.
                       SUSE Rancher Setup is a tool designed to make
                       deployment of Rancher Manager easy, fast and
                       headache free.


                       Various ways to deploy Rancher on EKS are already
                       documented and other tools exist to aid in
                       deployment. SUSE Rancher Setup was created to
                       simplify the setup and provide an opinionated
                       guided process that results in a production ready
                       configuration that can be turned into a supported
                       setup very easily.


                # ⚓ ID Root ☛ How_To_Install_FFmpeg_on_Rocky_Linux_9_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       FFmpeg on Rocky Linux 9. For those of you who
                       didn’t know, FFmpeg is a free and open-source
                       command line tool for transcoding multimedia files.
                       The core of this tool consists of the command line
                       FFmpeg which processes the audio and video files.
                       It supports a variety of audio/video codecs,
                       including H.264, H.265, VP8, VP9, AAC, OPUS, and
                       others, as well as MP4, FLV, MKV, TS, WEBM, and MP3
                       file formats and HTTP/HTTPS, TCP, UDP, RTMP, RTSP,
                       and HLS streaming protocols.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the FFmpeg multimedia framework on
                       Rocky Linux. 9.


                # ⚓ H2S Media ☛ Install_Yandex_Browser_on_Ubuntu_20.04_LTS
                  Linux_–_Linux_Shout⠀⇛


                       Learn the steps to install Yandex Browser on Ubuntu
                       20.04 LTS Focal Fossa using the command terminal to
                       start surfing the internet.


                       “Yandex Browser” is a free fast and visually
                       appealing alternative to Firefox, Chrome, Opera,
                       and Microsoft Edge. Users who want to switch to
                       Yandex can easily import data such as bookmarks and
                       the settings from other popular browsers in just a
                       few steps.


                       Well, this Russian Search engine company’s browser
                       is based on Chromium and Opera elements, therefore
                       we can use all addons that are compatible with
                       Google Chrome and Opera.


                       For security, the browser offers Kaspersky’s
                       integrated virus protection; tracking protection,
                       phishing protection, blocking third-party cookies,
                       and preventing unsolicited access to webcams,
                       microphones, or USB devices.


                # ⚓ LinuxConfig ☛ List_of_Browsers_available_on_Linux⠀⇛


                       Users of Linux systems have many choices when it
                       comes to web browsers, as there is a wide range
                       that can be installed. You may already have a
                       favorite browser or you may be still deciding which
                       browser is right for you. In this tutorial, we have
                       compiled a list of browsers that are available on
                       Linux, and will show you how to install them on all
                       major Linux distros.


                # ⚓ H2S Media ☛ How_to_install_CyberPanel_on_Ubuntu_20.04_LTS
                  Server⠀⇛


                       Learn the steps and commands to install open source
                       CyberPanel on Ubuntu 20.04 LTS Server for having
                       your web control panel to host & manage websites
                       and other web applications.


                       CyberPanel is a stable open source control panel
                       that is available to easily install on any VPS or
                       dedicated server running on Linux server operating
                       system. It helps the users to easily manage their
                       command line server using the web interface and
                       allows hosting websites because of the inbuilt web
                       server and other required components such as PHP.


                       Instead of Apache, CyberPanel offers a well-
                       optimized lightweight webserver Litespeed. It is
                       compatible with Apache host configuration files and
                       also can handle large amounts of requests using a
                       well-developed caching system called LSCACHE but
                       usually requires an additional license.


                       Cyberpanel is available in two editions one uses
                       LiteSpeed web server open source edition known as
                       OpenLitespeed whereas the other one is with
                       Litespeed web server enterprise, which is free for
                       a domain with one worker (process) and limited to
                       2GB RAM only. For more domains, supporting more RAM
                       and workers require the purchase of a CyberPanel
                       Enterprise license.


                       Hence, if you don’t want to invest additional money
                       on a web server control panel platform then an open
                       source version of Litespeed cache is best to opt
                       for while installing CyberPanel on Ubuntu 20.04
                       Linux.


                # ⚓ Its FOSS ☛ How_to_List_USB_Devices_Connected_to_Your_Linux
                  System⠀⇛


                       Mostly, people are interested in knowing what USB
                       devices are connected to the system. This may help
                       troubleshoot the USB devices.


                # ⚓ Red Hat Official ☛ How_to_run_Kubernetes_workloads_in
                  systemd_with_Podman_|_Enable_Sysadmin⠀⇛


                       Kubernetes YAML gives Podman a unified solution to
                       declare container workloads across environments and
                       simplify complexity for developers and sysadmins.


                # ⚓ ID Root ☛ How_To_Install_qBittorrent_on_Linux_Mint_21_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       qBittorrent on Linux Mint 21. For those of you who
                       didn’t know, qBittorrent is a free, open-source,
                       cross-platform P2P BitTorrent client developed
                       inC++ and Qt libraries. qBittorrent is very popular
                       amongst torrent users as the main alternative to
                       uTorrent. If you’re looking for a feature-rich and
                       lightweight BitTorrent client, qBittorrent should
                       be your go-to.


                       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 a qBittorrent BitTorrent client on
                       Linux Mint 21 (Vanessa).


                # ⚓ OSTechNix ☛ How_To_Find_Filesystem_Types_In_Linux_–
                  OSTechNix⠀⇛


                       GNU/Linux supports numerous filesystems, such as
                       Btrfs, ext4, ext3, ext2, exFAT, sysfs, securityfs,
                       FAT16, FAT32, NTFS, and many. The most commonly
                       used filesystems are Ext4 and Btrfs. Have you ever
                       wondered which filesystem you are currently using
                       in your Linux system? No? No problem! This guide
                       lists all possible ways to find the mounted
                       filesystem type in Linux and Unix-like operating
                       systems.


                # ⚓ Truncate_long_strings_in_columns_and_use_custom_header
                  names⠀⇛


                # ⚓ AddictiveTips ☛ How_to_install_Neptune_Linux_on_your
                  computer⠀⇛


                       Neptune is a Linux distribution for desktops based
                       on Debian Stable. It uses the KDE Plasma 5 desktop
                       environment and aims to deliver an elegant,
                       functional multimedia operating system for users.
                       Here’s how to install Neptune Linux on your
                       computer.


                       [...]


                       After booting up Neptune Linux from the USB, you’ll
                       see a live desktop.


          o § WINE or Emulation⠀➾


                # ⚓ DebugPoint ☛ 3_NES_Emulators_to_Play_Old_NES_Games_on_Linux
                  in_2022⠀⇛


                       A quick look at 3 NES Emulators to play old NES
                       games in Linux. Also, we provide an Installation
                       guide and features.


                       If you want to play the old retro games such as
                       Super Mario, Pokemon, etc in the latest Ubuntu,
                       Linux Mint versions, there are plenty of emulators
                       available. Here are three emulators that you can
                       try if you want to play old retro games.


                       [...]


                       Enjoy and play old NES games using these emulators.


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ Real-time_Analytics_News_for_Week_Ending_August_20⠀⇛


                       Red Hat announced a new iteration of Red Hat
                       OpenShift Platform Plus, with new features and
                       capabilities that go beyond the base Kubernetes
                       platform to encompass storage, management, and
                       more. Red Hat OpenShift Platform Plus is engineered
                       to provide a more consistent foundation for
                       organizations to drive transformational IT
                       standardization. The newest offering includes the
                       necessary tools to build, protect, and manage
                       applications throughout the software lifecycle and
                       across Kubernetes clusters more simply. These
                       underlying technology updates include:


                       Red Hat OpenShift 4.11
                       Red Hat Advanced Cluster Management for Kubernetes
                       2.6
                       Red Hat OpenShift Data Foundation 4.11


                # ⚓ Enterprisers Project ☛
                  Digital_transformation:_4_key_building_blocks⠀⇛


                       Digital transformation isn’t just about building
                       great websites and mobile applications. It isn’t
                       simply about providing a better user experience.
                       While these are certainly critical enablers for
                       success, truly reimagining how a business operates
                       to thrive in a digital world requires much more –
                       and skipping or failing to prioritize the “more” is
                       where many organizations fall short of meeting
                       their digital transformation goals.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ LinuxConfig ☛ Ubuntu_22.04_Review⠀⇛


                       Ubuntu 22.04 is out and ready for download. If you
                       have come across this article, you may be wary of
                       installing Ubuntu 22.04 just yet. Indeed, this is
                       the latest version of Ubuntu, and it has a lot of
                       shiny features, but it introduces some problems,
                       too.


                       In this guide, we will be reviewing the new Ubuntu
                       22.04 release. We will look at its pros and cons,
                       so you can make a decision on if it would be the
                       right system for you. We will also compare Ubuntu
                       22.04 against some of its competitors, since there
                       are many other Linux distros to choose from. Read
                       on to learn about the positives and negatives of
                       Ubuntu 22.04.


                       [...]


                       While Ubuntu 22.04 offers some positive aesthetic
                       changes, it could use some improvement under the
                       hood.


                # ⚓ Canonical_enables_Ubuntu_on_Allwinner’s_Nezha_RISC-V_boards
                  |_Canonical⠀⇛


                       After our previous announcement on the availability
                       of Ubuntu running on RISC-V processors and
                       hardware, we are proud to announce the Ubuntu
                       release for additional RISC-V hardware –
                       Allwinner’s Nezha board.


                       [...]


                       D1 is Allwinner’s first SoC based on the RISC-V ISA
                       designed for multimedia decoding platforms. Running
                       on Linux, RTOS and other systems, D1 integrates
                       Alibaba T-Head’s 64-bit core and supports RVV and
                       1GHz frequency. At the same time, it supports up to
                       4K H.265/H.264 decoding, a built-in HiFi4 DSP, and
                       an external connection of up to 2GB DDR3, which can
                       be used in many fields such as smart cars, HMI,
                       Smart home and education.


                       Nezha is an AIoT development board based on
                       Allwinner’s D1 chip. It is the world’s first mass-
                       produced development board that supports the 64-bit
                       RISC-V instruction set and a Linux system.


                # ⚓ LinuxConfig ☛ Linux_Mint_System_Requirements⠀⇛


                       Linux Mint is a user friendly distribution based on
                       Ubuntu Linux. If you are thinking about installing
                       Linux Mint, you should check first that your
                       computer can run the operating system well enough.
                       Mint’s default Cinnamon desktop is not a resource
                       hog, so most users will find that they can run
                       Linux Mint perfectly fine.


                       In this tutorial, we have compiled a list of the
                       Linux Mint minimum and recommended system
                       requirements. Check below to see if your PC has the
                       specs needed. These same recommendations can also
                       be followed when configuring Linux Mint to run
                       inside of a virtual machine.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Femto_is_a_tiny_12x12mm_Raspberry_Pi_RP2040
                  module_–_CNX_Software⠀⇛


                       Mirek Folejewski has designed the ridiculously tiny
                       Femto module based on the Raspberry Pi RP2040
                       microcontroller with a size of just 12x12mm, and
                       still including an SPI flash, a crystal, and a few
                       passive components.


                       We’ve previously covered some really tiny RP2040
                       boards with the Pimoroni Tiny 2040 and Adafruit QT
                       Py RP2040 boards, as well as the RP2040 Stamp
                       module, but the 12x12mm Femto module is about a
                       quarter of the size of 25x25mm RP2040 Stamp.


                       [...]


                       The board is comprised of two parts: the module
                       itself (aka mainboard) with the Raspberry Pi RP2040
                       microcontroller and the frame (aka solder frame)
                       exposing the I/Os in a somewhat usable way.


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


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ Document Foundation ☛ Community_Member_Monday:_Mauricio
                  Baeza_–_The_Document_Foundation_Blog⠀⇛


                       Today we’re talking to Mauricio Baeza (aka “El
                       Mau”) from the Mexican LibreOffice community…


                       [...]


                       The future, for me, is only tomorrow, so just keep
                       doing what I do every day. I think LibreOffice
                       should be consolidated as a truly community
                       project, not to depend on the whims of some
                       companies.


          o § Programming/Development⠀➾


                # ⚓ Qt ☛ Qt_Quick_and_Widgets,_Qt_6.4_Edition⠀⇛


                       QQuickWidget is a QWidget subclass, originally
                       introduced in Qt 5.3. It is the bridge between
                       traditional widgets and the world of QML and Qt
                       Quick. In this post we are going to take a look at
                       its evolution and the latest improvements in the
                       upcoming Qt 6.4 release, because there are some
                       quite significant changes happening under the hood.


                       The contents of a widget-based window and a window
                       showing a Qt Quick scene are rendered in a quite
                       different way: the latter relies on 3D graphics
                       APIs (*), such as OpenGL, Vulkan, Metal, or Direct
                       3D, whereas a widget-based user interface is
                       rendered using QPainter and then blitted to the
                       native window by windowing system specific means,
                       for example, either BitBlt or
                       UpdateLayeredWindowIndirect in the case of Windows.
                       A QQuickWindow, or its convenience subclass
                       QQuickView, are not directly usable in the QWidget
                       hierarchy of a top-level widget window. (after all,
                       QQuickWindow itself is a true QWindow, nothing to
                       do with the world of QWidgets)


                # ⚓ The_Benefits_And_Drawbacks_of_Vue.JS⠀⇛


                       Vue.js, sometimes known as the ‘progressive’
                       framework, is most recognized for its design
                       philosophy, which emphasizes gradual software
                       development adoption. Despite its moniker, Vue.js
                       does not precisely have an abundance of features.
                       In fact, Vue.js provides just the minimal
                       requirements of a JavaScript framework.


                       Being simple is often a beneficial thing in a world
                       where complexity and technical progress are
                       unfathomably vast. This is why a framework called
                       Vue.js has been created.


                # § Perl / Raku⠀➾


                      # ⚓ Suspicious_introspection_|_Playing_Perl_6␛b6xA_Raku⠀⇛


                             One of my routines is acting suspicious. I’m
                             almost certain it wilfully misinterprets
                             arguments just so it can throw an exception.
                             There is a way to spy on it.


                      # ⚓ Linux Handbook ☛ How_to_Run_Perl_Scripts_in_Linux
                        Command_Line⠀⇛


                             Call them ancient but Perl scripts are still
                             a great way of scripting automation tasks for
                             various sysadmin tasks.


    * § Leftovers⠀➾


          o § Proprietary⠀➾


                # ⚓ The Register UK ☛ Software_dev_cracks_Hyundai_encryption
                  with_Google_search_•_The_Register⠀⇛


                       A developer says it was possible to run their own
                       software on the car infotainment hardware after
                       discovering the vehicle’s manufacturer had secured
                       its system using keys that were not only publicly
                       known but had been lifted from programming
                       examples.


                       An unidentified developer posting under the name
                       “greenluigi1″ wanted to modify the in-vehicle
                       infotainment (IVI) system in his 2021 Hyundai Ioniq
                       SEL.


                       To do so, he would have to figure out how to
                       connect to the device and bypass its security.


                       After trying to figure out how to customize
                       firmware updates for the IVI’s D-Audio2 system,
                       made by the car company’s mobility platform
                       subsidiary Hyundai Mobis, and have them accepted by
                       the IVI, the unidentified car hacker found an
                       unexpected way – through Google.


          o § AstroTurf/Lobbying/Politics⠀➾


                # § Misinformation/Disinformation⠀➾


                      # ⚓ News:_Wolaita_zone_prosecutor_indicts_prominent
                        scholar_Asefa_Wodajo_with_‘spreading_hate_speech,
                        disinformation’⠀⇛


                             The public prosecutor of Sodo city, the
                             capital of Wolaita zone in Southern Nations,
                             Nationalities and People’s (SNNP) regional
                             states, has charged former Assistant
                             Professor of Dilla University, Asefa Wodajo,
                             who is also a Central Committee member of the
                             opposition party, Wolaita National Movement
                             (WNM) , with trespassing proclamation 1185/
                             2012, under “Hate Speech and Disinformation
                             Prevention and Suppression Proclamation.” The
                             prosecutor indicted the defendant for
                             allegedly violating articles 4, 5 and 7(4) of
                             the proclamation.


                             Article 4, “Prohibition of Hate Speech” which
                             states: “Any person disseminating hate speech
                             by means of broadcasting, print or social
                             media using text, image,audio or video is
                             prohibited,” and article 5, “Prohibition of
                             Disseminating Disinformation” which states:
                             “Disseminating of any disinformation on
                             public meeting by means of broadcasting,
                             print or social media using text, image,
                             audio or video is a prohibited act.”


                             Article 7/4 of the proclamation details that
                             “if the offense of hate speech or
                             disinformation offense has been committed
                             through a social media account having more
                             than 5,000 followers or through a broadcast
                             service or print media, the person
                             responsible for the act shall be punished
                             with simple imprisonment not exceeding three
                             years or a fine not exceeding 100,000 birr.”


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Forbes ☛ Whose_Side_Is_The_CPUC_On?_Not_Low-Income
                  Californians.⠀⇛


                       In a Proposed Decision scheduled for August 25, the
                       California Public Utilities Commission (CPUC)
                       proposes to limit the legal, eligible funds a low-
                       income household can access for wireless broadband
                       while increasing the amount that can be applied to
                       wireline broadband. In other words, if a low-income
                       household exercises the federal right to the
                       monthly $30 Affordable Connectivity Program (ACP)
                       discount, the CPUC will withhold $16.23 in
                       presently appropriated state funds. Essentially the
                       CPUC proposes to punish low-income California
                       citizens for accessing federally guaranteed
                       benefits by capping broadband support to $22.48
                       ($9.25 in federal LifeLine support and $16.23 from
                       California LifeLine). In practical terms, low-
                       income Californians could enjoy unlimited mobile
                       data plans with the ACP, but the CPUC wants to
                       limit them to just 6 gigabits (GB) per month.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ ACENSTV_Wordo:_DOTES⠀⇛


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 7365

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.22.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_22/08/2022:_Celluloid_0.24_and_New_StarBook_Mk_VI⠀✐


Posted in News_Roundup at 5:00 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
          o Standards/Consortia
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
    * Gemini*_and_Gopher
          o Technical
    * § GNU/Linux⠀➾


          o ⚓ 9to5Linux ☛ 9to5Linux_Weekly_Roundup:_August_21st,_2022⠀⇛


                 This week we saw the release of a lot of goodies for
                 everyone, starting with the LibreOffice 7.4 office suite
                 and KDE Gear 22.08 software suite, and continuing with
                 Ubuntu’s availability on the VisionFive RISC-
                 V development board, a new Manjaro Linux release for ARM
                 devices, and a new Proton release for Linux gamers.


                 On top of that, Mozilla Thunderbird 91 users were finally
                 able to upgrade to Thunderbird 102, GNOME fans were able
                 to test drive the beta release of the upcoming GNOME 43
                 desktop environment, and those in the market of a new
                 Linux laptop were able to pre-order the brand-new
                 StarBook MK VI from Star Labs.


          o § Desktop/Laptop⠀➾


                # ⚓ Linux Gizmos ☛ StarBook_Mk_VI_integrates_Ryzen_7_5800U_and
                  ships_with_Linux⠀⇛


                       Star Labs has recently launched the StarBook Mk VI
                       which can accommodate the Ryzen 7 58000U and
                       supports several Linux distributions. Additionally,
                       the Starbook can integrate Intel 12th gen
                       processors (i.e. i3-1220P, i7-1260P).


                       The StarBook Mk VI can be configured to integrate
                       one of the three following processors…


          o § Instructionals/Technical⠀➾


                # ⚓ Red Hat ☛ How_to_program_a_multitenant_SaaS_platform_in
                  Kubernetes_|_Red_Hat_Developer⠀⇛


                       In a previous article, I described how to create a
                       SaaS platform in a Kubernetes cluster. This article
                       takes a detailed look inside the demonstration
                       project that accompanied that earlier article. The
                       demonstration project is the code base shared by
                       all tenants using the SaaS platform. This article
                       describes the structure of the demonstration
                       application. You’ll also see how to get the code up
                       and running for multiple containerized tenants in a
                       Kubernetes cluster, and how to expose the service
                       to clients.


                       A key aspect of SaaS architecture is a generic code
                       base used by all tenants running in the Kubernetes
                       cluster. The application logic used by each tenant
                       is encapsulated in a Linux container image that’s
                       declared within the definition of the tenant’s
                       Kubernetes deployment. We’ll see multiple examples
                       of this generic approach and its benefits in this
                       article.


                       The Linux container for each tenant is configured
                       by setting a standard set of environment variables
                       to values specific to that tenant. As shown in the
                       previous article, adding a new tenant to the SaaS
                       platform involves nothing more than setting up a
                       database and creating a Kubernetes Secret,
                       deployment, service, and route resources, all of
                       which are assigned to a Kubernetes namespace
                       created especially for the tenant. The result is
                       that a single code base can support any number of
                       tenants.


                # ⚓ LinuxConfig ☛ Linux_commands:_Top_20_most_important
                  commands_you_need_to_know⠀⇛


                       There are thousands of commands that you can learn
                       to use on a Linux system, but most users will find
                       themselves executing the same few commands over and
                       over. For users looking for a way to get started,
                       we have compiled 20 of the most important Linux
                       commands you need to know. These commands are some
                       of the most useful, common, and essential tools
                       that you will need in order to administer your
                       Linux system or perform everyday tasks.


                       Every Linux distro has inherent access to a
                       terminal, though the interface may look different
                       depending on your desktop environment or
                       configuration. Join us in this tutorial to learn
                       about the 20 most important Linux commands. By the
                       end, you will know enough to begin navigating your
                       Linux terminal.


                # ⚓ LinuxConfig ☛ How_to_kill_process_based_on_the_port_number
                  in_Linux⠀⇛


                       At any given moment your Linux system is running
                       multiple processes simultaneously. Some of these
                       processes have access to your network if they are
                       being used to upload or download data. These
                       processes typically bind themselves to a particular
                       port number, and this can allow us to kill the
                       process based on a port number.


                       The kill command is one way that system
                       administrators can stop a process from running.
                       However, the kill command only accepts a process ID
                       as an argument. The pkill and killall commands are
                       two more options, but these accept process names as
                       arguments.


                       In order to kill a process based on its port
                       number, we will need to use the fuser command, or
                       use other command line tools in conjunction with
                       the usual kill command. In this tutorial, we will
                       show you multiple ways to kill a process based on
                       its port number in Linux.


                # ⚓ LinuxConfig ☛ How_to_print_environment_variables_on_Linux⠀⇛


                       The environment variables on a Linux system contain
                       changing values that are referenced mainly by
                       scripts and system programs. Environment variables
                       differ from shell variables, because they can be
                       accessed by any user or process across the entire
                       system. In this tutorial, you will learn how to
                       print environment variables on Linux.


                # ⚓ Linux Capable ☛ How_to_Install_Brightness_Controller_on
                  Linux_Mint_21_LTS⠀⇛


                       At one point, Desktop Dimmer was a popular
                       application to control screen brightness. However,
                       the Desktop Dimmer application is now outdated and
                       no longer works in Linux Mint 21. The best possible
                       alternative to the Desktop Dimmer application is
                       Brightness Controller, a graphical user interface
                       (GUI) based application that works like Desktop
                       Dimmer to help us control screen brightness. While
                       Brightness Controller may not be an exact
                       replacement for Desktop Dimmer, it does offer
                       similar functionality. It is currently the best
                       option for those looking for a screen brightness
                       controller.


                       The following tutorial will teach you how to
                       install Brightness Controller on Linux Mint 21
                       release series using a LaunchPAD APT PPA with the
                       command line terminal.


                # ⚓ Linux Shell Tips ☛ Important_cURL_Commands_for_Linux
                  Developers⠀⇛


                       Curl has made data transfer between two machines
                       connected on the same network much easier. As curl
                       command adheres to a specific URL syntax to
                       successfully transfer data over a network.


                       By default, no user interaction is needed during
                       the execution of the curl command. Out of the
                       numerous protocols it supports, the prominent ones
                       are HTTP, HTTPS, SFTP, SCP, SMTP, SMTPS, FTP, FTPS,
                       and FILE.


                       This article will walk us through some essential
                       curl-related commands that can be useful to
                       developers seeking a breakthrough under a Linux
                       operating system environment.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Its FOSS ☛ Celluloid_Video_Player_Gets_GTK_4_UI
                        Refresh⠀⇛


                             Celluloid is a front-end for mpv (an open-
                             source media player for the command-line).


                             If you want to avoid bothering with the
                             technical details, Celluloid is one of the
                             best video players for Linux. Many Linux
                             distributions offer Celluloid pre-installed
                             as the default video player, among other
                             essential packages.


                             With Celluloid v0.24 release, it finally uses
                             libadwaita along with other refinements.


    * § Distributions and Operating Systems⠀➾


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ uni Toronto ☛ The_Ubuntu_22.04_server_installer_wants_you
                  to_scrub_reused_disks_first⠀⇛


                       In theory the Ubuntu 22.04 server installer will
                       cope with reused disks that already have partitions
                       on them, perhaps partly because some vendors ship
                       server systems with pre-partitioned drives. In my
                       experience, this can often work fine in practice.
                       But every so often, things go wrong, and the
                       installer will give you an opaque message that it
                       crashed after you did network setup (sometimes,
                       after you picked the Ubuntu mirror to use), before
                       getting to disk selection and partitioning. These
                       crashes seem especially common if you have disks
                       with previous software RAIDs on them, either
                       complete or merely one disk out of several.


          o § Open Hardware/Modding⠀➾


                # ⚓ NBC ☛ Steve_Jobs’_Apple-1_computer_prototype_auctioned_for
                  nearly_$700K⠀⇛


                       The prototype was used by Apple co-founder Steve
                       Jobs in 1976 to demonstrate the Apple-1 to Paul
                       Terrell, owner of The Byte Shop in Mountain View,
                       California, one of the first personal computer
                       stores in the world, Boston-based RR Auction said
                       in a statement.


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


          o ⚓ OpenSource.com ☛ Mentoring_as_a_power_multiplier_in_open_source⠀⇛


                 Many developers struggle with work-life balance. They are
                 overloaded with regular tasks and frequently called upon
                 to solve urgent customer issues. Yet many developers,
                 like me, have ideas they want to promote if only they had
                 time to do so. Sometimes these pet ideas do not make it
                 through the product management feature-selection process.
                 Other times, a developer does not have time to complete
                 the solution end-to-end on their own, yet they know if it
                 could somehow be implemented, the project would benefit.


                 This is where mentoring comes in. Mentorship has many
                 benefits: It helps the mentee’s personal development, and
                 it can improve the mentor’s self-confidence and
                 leadership skills. I discussed these benefits in an
                 interview about skillful mentoring in the Red Hat
                 Research Quarterly that includes many tips for a
                 rewarding mentor relationship.


                 However, in the scenario I just described, mentorship has
                 another very practical benefit: It helps with enrolling
                 developers in the projects the mentor-developer wants to
                 promote. In this article, I will explain how you can use
                 mentoring as a power multiplier in the open source
                 software (OSS) world and create a multi-win situation by
                 mentoring people who further contribute to the open
                 source community.


                 This article is based on my experience mentoring students
                 as part of the collaboration between my organization and
                 Reichman University, but it can apply to any mentorship
                 situation.


          o § Programming/Development⠀➾


                # ⚓ Dhole Moments ☛ Cryptographic_Agility_and_Superior
                  Alternatives⠀⇛


                       Cryptographic agility is a vaguely defined
                       property, but is commonly understood to mean, “Able
                       to quickly swap between cryptographic primitives in
                       response to new attacks.”


                # ⚓ The_Myth_of_Mass_Collaboration⠀⇛


                       (1) After playing this for 3 years, I’ve learned
                       that you have to learn about your team mates
                       styles, and this can only happen if you
                       consistently play with the same folks. So playing
                       with random people makes that impossible. (2) If
                       you do stumble upon a stranger who is a great
                       player, they probably… don’t think the same about
                       you. The large supply of players on the internet
                       means that it’s better to move on and try new team
                       players, than to keep playing with someone with
                       worse skills than you. This means that everyone who
                       plays Apex with strangers is just constantly on the
                       outlook of great team mates, and those great
                       players don’t want to commit to anyone who is worse
                       than them. You’re left with 3 options: either you
                       keep on playing with mediocre players, and rarely
                       win; or you climb up to the top 100 players, become
                       a pro and develop friendships with the pros; or you
                       play only with friends who want to commit to
                       teamwork with you.


                # ⚓ Composability_and_generic_routes_in_Ema_0.8⠀⇛


                       tldr: Announcing a rewrite of Ema (a static site
                       generator in Haskell with hot reload destined to
                       develop an unique kind of apps) with support for
                       generic route encoders and composability.


          o § Standards/Consortia⠀➾


                # ⚓ What_is_RSS?⠀⇛


                       Some sites have a feed, but don’t tell you about
                       it. The good news is that the feed can often be
                       guessed. If the website was “example.com”, these
                       are the most likely places to find its feed: [...]


    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Knight_Rider_Keeps_On_Truckin’⠀⇛


                 [AJ] and [Joe], collectively the [Knight Rider
                 Historians] are bringing back one of the most iconic
                 vehicles of the 1980’s. Everyone remembers KITT driving
                 into the F.L.A.G. truck. Even the Mythbusters re-enacted
                 the stunt back in 2007. [KRH] managed to track down the
                 original tractor and trailer from the show. They’re
                 restoring both, part of that process means uncovering the
                 Hollywood hacks used to make the car-driving-into-trailer
                 stunt work.


          o ⚓ Hackaday ☛ Drastic_Plastic:_Enclosure_Rebuild_Uses_Donor
            Material⠀⇛


                 Although 3D printers are great, people tend to use them
                 as a universal hammer wherein almost everything becomes a
                 nail that’s just begging to be struck. So as hacker
                 appetites become finicky with the same old fare, it’s
                 refreshing to see an enclosure restoration done in such
                 an old-school fashion. To wit: [Doidão Santos]’ classic
                 repair of the crumbling side fairings on a vintage
                 amplifier.


          o § Science⠀➾


                # ⚓ Hackaday ☛ An_ASCII_Terminal_Like_It’s_1974⠀⇛


                       It’s quite probable that any of you who have built
                       a keyboard will have done so using a matrix of keys
                       connected to a microcontroller, or if you are old-
                       school, a microprocessor. A CPU can scan the
                       keyboard matrix with ease, and pass whatever is
                       typed either to whatever software it is running, or
                       to a host computer. There was a time however when
                       available CPUs were not considered powerful enough
                       to do all this and also perform a useful task, so a
                       keyboard would have its own decoder chip that would
                       output ASCII over a parallel interface. It’s an era
                       [John Calhoun] harks back to with Adam74, a little
                       ASCII terminal which takes its input from that 7-
                       bit parallel port.


                # ⚓ Reason ☛ Incompetent_People_Are_Often_Too_Incompetent_To
                  Realize_Just_How_Incompetent_They_Are,_Says_New_Study⠀⇛


                       Now, a new study in Science Advances adds to these
                       findings and reports that “knowledge overconfidence
                       is associated with anti-consensus views on
                       controversial scientific issues.” In the study, the
                       researchers first asked 3,200 participants through
                       online surveys how much they think they know
                       (subjective knowledge) using a 7-point scale about
                       each of seven scientific topics ranging from “vague
                       understanding” to “thorough understanding.” To
                       prime participants, the researchers provide a
                       complex explanation of how a crossbow is
                       constructed and works (level 7 knowledge) compared
                       to the case where a person can identify a crossbow
                       and know that it shoots arrows (level 1 knowledge).
                       Then each participant was randomly assigned to
                       answer a question about their degree of acceptance
                       of one of the seven different issues that enjoy
                       substantial scientific consensus.


          o § Education⠀➾


                # ⚓ Counter Punch ☛ Should_We_Let_Scam-Artists_‘Educate’_Our
                  Young_People?⠀⇛


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Why_Didn’t_We_Think_Of_Making_A_Remote_Trigger
                  Button?⠀⇛


                       One of the many functions a digital oscilloscope
                       offers over its analog ancestors is a trigger
                       button. Alongside the usual electronic means of
                       triggering the instrument, you can reach over and
                       press a button to “freeze-frame” the action and
                       preserve the trace. Sometimes doing it repeatedly
                       it can become a chore to reach for the ‘scope.
                       That’s where [Kevin Santo Cappuccio]’s remote
                       trigger button comes in.


                # ⚓ Hackaday ☛ Clover_Computer:_A_Modern_Z8000_CP/M_Machine⠀⇛


                       Seeing some old Zilog 16-bit chips on eBay
                       recently, [Scott Baker] was curious enough to snap
                       them up and build himself a Z8000 computer. It
                       started as a two-board solution, then he added a
                       display module. Instead of layering the boards
                       vertically à la a PC/104 stack, [Scott] decided to
                       build them flat. His first backplane was
                       triangular, but he opted for a square to
                       accommodate one more expansion board in the future.
                       The assembled contraption resembles a clover, hence
                       the name Clover Computer.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ A_Dad_Took_Photos_of_His_Naked_Toddler_for
                  the_Doctor._Google_Flagged_Him.⠀⇛


                       Google has an automated tool to detect abusive
                       images of children. But the system can get it
                       wrong, and the consequences are serious.


                # ⚓ The Verge ☛ Google_AI_flagged_parents’_accounts_for
                  potential_abuse_over_nude_photos_of_their_sick_kids⠀⇛


                       A concerned father says that after using his
                       Android smartphone to take photos of an infection
                       on his toddler’s groin, Google flagged the images
                       as child sexual abuse material (CSAM), according to
                       a report from The New York Times. The company
                       closed his accounts and filed a report with the
                       National Center for Missing and Exploited Children
                       (NCMEC) and spurred a police investigation,
                       highlighting the complications of trying to tell
                       the difference between potential abuse and an
                       innocent photo once it becomes part of a user’s
                       digital library, whether on their personal device
                       or in cloud storage.


                # ⚓ Counter Punch ☛ Gender-Based_Violence_in_the_Pandemic⠀⇛


                       The global cost of violence against women had been
                       estimated at $1.5 trillion, a figure that is bound
                       to increase as the pandemic progresses. According
                       to the American Journal of Emergency Medicine, the
                       number of domestic violence cases rose by 25-33
                       percent globally in 2020 compared to 2019. The
                       United Nations group UN Women reports that
                       incidents of domestic violence increased 300
                       percent in Hubei, China; 25 percent in Argentina;
                       30 percent in Cyprus; and 50 percent in Brazil.


          o § Proprietary⠀➾


                # ⚓ HowTo Geek ☛ Microsoft_Edge_Is_Now_More_Bloated_Than_Google
                  Chrome⠀⇛


                       People love to rag on Google Chrome for being a
                       bloated browser that eats up your computer’s
                       resources. Well, Microsoft Edge has become even
                       worse.


                # ⚓ The Telegraph UK ☛ Tony_Blair_was_warned_about_Post_Office
                  IT_deal⠀⇛


                       Courts have heard allegations that Post Office
                       bosses knew Horizon was flawed but still proceeded
                       with prosecutions. Lord Arbuthnot of Edrom called
                       for those responsible “to be held fully to
                       account,” saying: “The fact that Horizon could not
                       be relied upon was known to some people –
                       including, we now learn, the then prime minister –
                       from a very early stage.


                       “This makes it all the more dreadful that so many
                       people in authority ignored the protestations of
                       the sub-postmasters and humiliated, prosecuted,
                       bankrupted and imprisoned them.”


                # ⚓ New Scientist ☛ More_than_one_in_eight_Reddit_users_publish
                  toxic_posts⠀⇛


                       The resulting data set was used to train a neural
                       network to categorise the toxicity of the remaining
                       posts.


                       The algorithm found 2 per cent of posts and 6 per
                       cent of comments were highly toxic. A further 7 per
                       cent of posts and 11.5 per cent of comments were
                       slightly toxic, with the remainder of posts and
                       comments classed as not toxic. Highly toxic posts
                       included direct insults and swear words, slightly
                       toxic posts included milder insults (such as
                       “hideous”), while not toxic posts contained
                       neither.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ India Times ☛ CEO_of_Israeli_Pegasus_spyware_firm_to
                        step_down⠀⇛


                             Pegasus spyware is used to infiltrate mobile
                             phones and extract data or activate cameras
                             or microphones.


                      # ⚓ Vice ☛ Peter_Thiel’s_Palantir_Teams_Up_With_Better_to
                        Create_‘Bloomberg’_for_Home_Loans⠀⇛


                             The mortgage lending company that faced
                             criticism late last year for summarily laying
                             off 900 people over Zoom is “teaming up” with
                             Palantir Technologies, the big-data software
                             company co-founded by Peter Thiel, the
                             companies announced Wednesday.


                      # ⚓ The Telegraph UK ☛ Meta_risks_a_‘grotesque_betrayal’
                        of_children_by_introducing_encrypted_messaging,_says
                        Priti_Patel⠀⇛


                             In her first comments since Meta’s
                             announcement, Ms Patel says that the
                             Government wants to work with the tech giant
                             to protect children, citing proposals by UK
                             spy chiefs that would allow technology giants
                             to scan online messages and pick up child
                             abuse material without sacrificing privacy
                             rights.b2


          o § Defence/Aggression⠀➾


                # ⚓ Axios ☛ Twitter_suspends_Florida_GOP_candidate_who_called
                  for_violence_against_federal_agents⠀⇛


                       Driving the news: The candidate, Luis Miguel,
                       tweeted on Thursday, “Under my plan, all Floridians
                       will have permission to shoot FBI, IRS, ATF and all
                       other feds on sight! Let freedom ring!”


                # ⚓ RAIR Foundation ☛ Open_Borders_Sweden:_15-year-old_Migrant
                  Shot_Two_People_inside_Malmö_Shopping_Center,_One_Dead_
                  (Video)⠀⇛


                       The clans control large zones of Swedish cities and
                       towns, effectively lawless areas that police
                       increasingly fear approaching. The crime families,
                       which have thousands of foot soldiers, have been
                       allowed to operate with virtual impunity for years.
                       Swedish judges and prosecutors have been unable or
                       unwilling to stop them, apparently out of fear of
                       retribution. Furthermore, police are terrorized by
                       them and often pressured by the state to remain
                       silent.


                # ⚓ BBC ☛ Kashmir_Hindus_on_edge_after_resurgence_of_targeted
                  killings⠀⇛


                       Rajni Bala was shot in the head by anti-India
                       militants, police said.


                       It’s widely believed that she was targeted because
                       she was a Hindu, a minority in the country’s only
                       Muslim majority region. There has been a wave of
                       Hindu killings in the past year – the latest just
                       last week. Sunil Kumar Bhat was shot dead in an
                       apple orchard in the Shopian area of south Kashmir.


                       Rajni’s family say they had tried to move out of
                       Kashmir before the attack on her.


                # ⚓ Gannett ☛ Albuquerque_Muslims_thought_a_killer_was
                  targeting_them._The_truth_was_more_devastating.⠀⇛


                       But the reality of what happened was much more
                       complicated and harder to comprehend. Police
                       arrested Muhammed Syed, a Muslim and known
                       community member, this month. Syed, 51, was charged
                       in two killings, and authorities say they are
                       gathering evidence to charge him in the two others.
                       Syed’s motive is still unclear, and Syed, a married
                       father of six, has denied involvement in the
                       killings.


                # ⚓ India Times ☛ Two_Imams_arrested_in_Assam’s_Goalpara_for
                  links_with_al_Qaeda⠀⇛


                       Police said during house searches of the two Imams,
                       lots of incriminating material related to AQIS,
                       Jihadi literature, posters, books among other
                       documents were seized along with mobile phones, SIM
                       cards and ID cards.


                # ⚓ Morning Star News ☛ Terrorists_Kill,_Kidnap_Christians_in
                  Northern_Nigeria⠀⇛


                       The attack followed Islamic militants’ kidnapping
                       of 21 Christian women on June 21 in nearby Kasan
                       Kogi village. The Rev. Ezekiel Garba, pastor of
                       Chapel of Good News Church in Kasan Kogi village,
                       told Christian Solidarity International’s Nigeria
                       Report that his wife was among those held captive.


                # ⚓ Counter Punch ☛ Afghanistan_Beyond_the_Narratives_of
                  Insiders⠀⇛


                # ⚓ Counter Punch ☛ Trump_and_the_Fifth⠀⇛


                       One of the reasons that anti-Trump supporters are
                       so hopping mad over Trump’s taking of the Fifth is
                       what lawyers call a “perjury trap.” The idea is to
                       get a person to talk and talk and talk, in the hope
                       of then finding places where he didn’t tell the
                       truth, and then charge him with perjury. In fact,
                       oftentimes the person isn’t even charged with the
                       substantive offense for which he was being
                       investigated. He’s only charged with lying about
                       certain aspects of the situation while he was
                       talking or testifying. 


                # ⚓ Counter Punch ☛ The_Assassination_of_Alexander_Dugin’s
                  Daughter⠀⇛


                       The latest, including: – The assassination of
                       Alexander Dugin’s daughter – Who is Dugin? Why do
                       his ideas matter in understanding Russia? –
                       Theories behind the attack – Wagner base attacked
                       by Ukraine after social media blunder – Wagner
                       recruiting in Russian prisons for Ukraine service


                # ⚓ Counter Punch ☛ The_Nuclear_Threat_is_Now_at_the_Center_of
                  the_Ukraine_Crisis⠀⇛


                       The fate of survivors would be bleak. Strath, who
                       was head of the cabinet office central war plans
                       secretariat, said that they would suffer from
                       “disease, starvation, and the unimaginable
                       psychological effects of nuclear bombardment.”


                # ⚓ Counter Punch ☛ Liz_Cheney:_Goodbye_and_Good_Riddance⠀⇛


                       This was a bit much given how she had done little
                       by way of condemning Trump for any earlier misdeeds
                       even as the GOP was being transformed.  As a matter
                       of fact, her voting record for Trump’s proposals
                       comes in at an astonishing, distinctly non-
                       dissenting 93%.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ American Oversight ☛ ICE_Admits_To_Practice_Of_Deleting
                  Senior_Officials’_Text_Messages_During_Trump_Administration⠀⇛


                       Immigrations and Customs Enforcement (ICE) has said
                       that it instructed Trump administration personnel
                       to wipe their agency-issued cell phones when
                       leaving their posts — a practice that persisted
                       even after the agency received public records
                       requests for senior ICE officials’ text messages
                       regarding an ongoing federal criminal
                       investigation.


                       The agency made these admissions in new filings in
                       the lawsuit brought by American Oversight and the
                       American Civil Liberties Union (ACLU) of
                       Massachusetts for the release of records concerning
                       the criminal prosecution of a Massachusetts state
                       court judge who allegedly allowed a defendant to
                       avoid ICE detention in 2018.


          o § Environment⠀➾


                # ⚓ CNN ☛ Why_the_Middle_East_may_be_too_hot_to_live_in_by_the
                  end_of_the_century⠀⇛


                       The Persian Gulf is one of the few places in the
                       world ever to record a wet bulb temperature that
                       exceeds the threshold of human survivability, 35C.
                       Since 2005, there have been nine separate occasions
                       of this on record.


                       A wet bulb temperature of 35C means the body can no
                       longer cool itself to a temperature that can
                       maintain normal functions.


                # ⚓ BBC ☛ Hosepipe_bans:_What_are_water_companies_doing_to
                  tackle_leaks?⠀⇛


                       Daily demand for water in England and Wales was 14
                       billion litres (three billion gallons), in 2018.


                       But each day, another three billion litres was lost
                       through leakage, according to a National Audit
                       Office (NAO) report.


                # ⚓ Which_UK_water_companies_have_the_most_leakages?_How
                  suppliers_compare_as_bosses_take_home_millions⠀⇛


                       Despite hosepipe bans being triggered across the
                       country, analysis of data from industry regulator
                       Ofwat found the amount lost from leaks last year
                       was enough to water 4.5 billion gardens for 15
                       minutes apiece, based on one hose pipe using 1,000
                       litres per hour on average.


                # ⚓ RTL ☛ Dutch_anglers_save_fish_as_Rhine_drought_bites⠀⇛


                       Each fish will be moved nearby to the River IJssel,
                       a Dutch branch of the drought-hit River Rhine that
                       until recently had fed the lake with fresh water.


                # ⚓ Counter Punch ☛ Nowhere_to_Go:_Heat_Waves,_Climate_Change
                  and_Prisons⠀⇛


                       Prisons concentrate hundreds or thousands of people
                       in buildings that were designed without planning
                       for extreme heat and heat waves. Prison building
                       materials and designs can increase exposure to heat
                       for people inside.


                # ⚓ Common Dreams ☛ Opinion_|_America_Really_Wanted_Iraq’s
                  Basra_for_Oil_That’s_Now_Making_It_Uninhabitable⠀⇛


                       Poet Robert Frost asked if the world would end by
                       fire or ice. It turns out that it is both, the fire
                       of global heating and the melting of Earth’s
                       surface ice and resultant biblical floods. Nowhere
                       is this more clear than in Iraq.


                # § Energy⠀➾


                      # ⚓ CNN ☛ Bugatti_hopes_its_last_gas-only_car_will_also
                        be_the_world’s_fastest_convertible⠀⇛


                             The Mistral will also be the last model to
                             have Bugatti’s famous W16 16-cylinder engine.
                             Mate Rimac, CEO of Bugatti-Rimac, the company
                             that now owns the Bugatti brand, said future
                             Bugatti models will be hybrids. It is unclear
                             what sort of gas engine those future models
                             will have, but it will not be the same W16
                             that, with various developments and
                             improvements, has powered every modern
                             Bugatti car since 2005.


                      # ⚓ Car Scoops ☛ DeLorean_Alpha5_EV_Makes_Its_Public
                        Debut_At_Pebble_Beach⠀⇛


                             The grand tourer is based on a yet-unknown EV
                             architecture, with all-wheel-drive
                             capability, and powerful electric motors
                             allowing a 0-96 km/h (0-60 mph) acceleration
                             in 2.99 seconds and a projected top speed of
                             250 km/h (155 mph). According to DeLorean,
                             the estimated range is 300 miles (483 km)
                             thanks to a 100 kWh battery. The Alpha5 will
                             also come fitted with a multi-mode adaptive
                             suspension.


                      # ⚓ [Old] Long_travel_in_an_electric_car⠀⇛


                             Travelling inside Germany with an electric
                             car was basically perfect. The most efficient
                             way would involve driving fast and hard with
                             top speed of even 180 km/h (where possible
                             due to speed limits and traffic). BMW i4 is
                             very efficient at high speeds with
                             consumption maxing out at 28 kWh/100km when
                             you actually drive at this speed all the
                             time. In real situation in this trip we saw
                             consumption of 20.8-22.2 kWh/100km in the
                             first legs of the trip. The more traffic
                             there is, the more speed limits and
                             roadworks, the lower is the average speed and
                             also the lower the consumption. With this
                             kind of consumption we could comfortably
                             drive 2 hours as fast as we could and then
                             pick any fast charger along the route and in
                             26 minutes at a charger (50 kWh charged
                             total) we’d be ready to drive for another 2
                             hours. This lines up very well with
                             recommended rest stops for biological reasons
                             (bathroom, water or coffee, a bit of movement
                             to get blood circulating) and very close to
                             what I had to do anyway with a gasoline car.
                             With a gasoline car I had to refuel first,
                             then park, then go to bathroom and so on.
                             With an electric car I can do all of that
                             while the car is charging and in the end the
                             total time for a stop is very similar. Also
                             not that there was a crazy heat wave going on
                             and temperature outside was at about 34C
                             minimum the whole day and hitting 40C at one
                             point of the trip, so a lot of power was used
                             for cooling. The car has a heat pump
                             standard, but it still was working hard to
                             keep us cool in the sun.


                      # ⚓ Smithsonian Magazine ☛ This_17-Year-Old_Designed_a
                        Motor_That_Could_Potentially_Transform_the_Electric_Car
                        Industry⠀⇛


                             The highschooler had heard of a type of
                             electric motor—the synchronous reluctance
                             motor—that doesn’t use these rare-earth
                             materials. This kind of motor is currently
                             used for pumps and fans, but it isn’t
                             powerful enough by itself to be used in an
                             electric vehicle. So, Sansone started
                             brainstorming ways he could improve its
                             performance.


                             Over the course of a year, Sansone created a
                             prototype of a novel synchronous reluctance
                             motor that had greater rotational force—or
                             torque—and efficiency than existing ones. The
                             prototype was made from 3-D printed plastic,
                             copper wires and a steel rotor and tested
                             using a variety of meters to measure power
                             and a laser tachometer to determine the
                             motor’s rotational speed. His work earned him
                             first prize, and $75,000 in winnings, at this
                             year’s Regeneron International Science and
                             Engineering Fair (ISEF), the largest
                             international high school STEM competition.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Washington Post ☛ What_does_‘splooting’_mean?_And
                        why_are_squirrels_doing_it?⠀⇛


                             “That really spread-eagling position is not a
                             worry — they’re just cooling themselves,” she
                             said. “However lethargic and immobile they
                             look, they’re fine.”


          o § Finance⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_The_Climate_Movement’s_Fight_to
                  Undo_the_Worst_Provisions_in_the_IRA_Begins⠀⇛


                       Climate activists and grassroots organizers are
                       wrestling with the contradictions embedded in the
                       Inflation Reduction Act (IRA), signed into law by
                       President Biden on August 16. The IRA is
                       undoubtedly the U.S. federal government’s largest-
                       ever investment in clean energy and climate action,
                       but it also commits to major investments in
                       sustaining dirty fossil fuels, relies on profit-
                       driven markets to deliver climate benefits, and
                       banks on industry-backed solutions like ​”carbon
                       capture” to magically produce technological feats
                       that so far have failed.


                # ⚓ Common Dreams ☛ Sanders_Joins_Striking_Starbucks_Workers_on
                  the_Picket_Line_in_Boston⠀⇛


                       “What you are doing is what people all over this
                       country are beginning to do,” the Vermont
                       Independent said through a megaphone.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Counter Punch ☛ Elections_and_the_Threat_of_Uncritical
                  Political_Discourse⠀⇛


                       This requires a critical analysis. Let’s look at a
                       few elements.


                # ⚓ Common Dreams ☛ Omar_to_Democrats:_‘Let’s_Give_Working
                  Folks_a_Reason_to_Turn_Out_to_Vote_for_Us’⠀⇛


                       “We cannot assume that the politics of transaction
                       will turn out the votes when Americans are longing
                       for the politics of transformation.”


                # ⚓ Counter Punch ☛ Irrelevance_and_clashes_at_the_Summit_of
                  the_Americas⠀⇛


                       Heads of state who stayed home


                # ⚓ Common Dreams ☛ ‘Frightening_Escalation’:_Palestinian
                  Rights_Group_Says_Director_Detained_by_Israeli_Agency⠀⇛


                       Defense for Children International-Palestine (DCI-
                       P) said in a series of tweets that director general
                       Khaled Quzmar was in the custody of the agency,
                       known as Shin Bet or Shabak, “as Israeli
                       authorities again escalate attacks” against it and
                       other civil society groups.


          o § Censorship/Free Speech⠀➾


                # ⚓ Morning Star News ☛ Terrorists_Kill_More_than_20_Christians
                  in_Taraba_State,_Nigeria⠀⇛


                       Suspected members of the Islamic State West Africa
                       Province (ISWAP) shot their way onto the site of
                       St. Agnes Catholic Church in Dinya village, in
                       Taraba state’s Gassol County, at about 10 p.m. and
                       abducted the catechist, Gideon Tsehemba, said the
                       Rev. Lawrence Awua, the parish priest.


                # ⚓ Reason ☛ “Saudi_Doctoral_Student_Gets_34_Years_in_Prison
                  For_Tweets”⠀⇛


                       Activists and lawyers consider the sentence against
                       Salma al-Shehab, a mother of two and a researcher
                       at Leeds University in Britain, shocking even by
                       Saudi standards of justice….


                # ⚓ The Telegraph UK ☛ Report_microaggressions_through_QR_codes
                  on_campus,_Lamda_students_told⠀⇛


                       Policing these incidents by means of easily
                       accessible QR codes has been branded “totalitarian
                       surveillance” by critics who have raised concerns
                       about a potential “culture of denunciation”.


                       Students who feel they have suffered or seen a
                       microaggression have been able to scan QR codes
                       that give instant access to “Lamda’s Micro-
                       Aggression Reporting Form”.


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


                # ⚓ NPR ☛ Fox_CEO_Lachlan_Murdoch_threatened_an_Aussie_news
                  site._It’s_fighting_back⠀⇛


                       Murdoch’s complaints arose from a June 29th piece
                       driven by revelations about the activities of
                       former President Donald Trump and his allies ahead
                       of the insurrection at the U.S. Congress last year.


                       Crikey’s political editor said Fox was among
                       Trump’s top allies, and concluded a column by
                       calling Murdoch and his father Rupert “unindicted
                       co-conspirators” in the siege because of the
                       incendiary rhetoric Fox often aired.


                # ⚓ VOA News ☛ Nigeria_to_Revoke_Licenses_of_52_Media_Outlets⠀⇛


                       But, he said, “We caution against such large-scale
                       clampdown of broadcast stations in disregard to
                       security issues and the attendant consequence. We
                       cannot afford the unpleasant outcome of such media
                       blackout at this time.


                # ⚓ La Prensa Latina ☛ Roger_Waters_leads_pro-Assange_protest
                  in_Washington⠀⇛


                       “I’m flabbergasted that this extraordinary travesty
                       is taking place under our noses, but Julian is
                       still in Belmarsh Prison and he’s still en route to
                       being extradited to the United States so that the
                       government of the United States can kill him in
                       private,” the 78-year-old music icon said outside
                       the Department of Justice.


                       He appealed to the US attorney general by name to
                       drop the charges against the publisher.


                # ⚓ CPJ ☛ Taliban_intelligence_agents_detain_American_filmmaker
                  Ivor_Shearer,_Afghan_producer_Faizullah_Faizbakhsh_in_Kabul⠀⇛


                       The security officers then called Taliban
                       intelligence; around 50 armed intelligence
                       operatives arrived, who blindfolded Shearer and
                       Faizbakhsh and transferred them to an unknown
                       location, the journalists familiar with the case
                       said.


                       CPJ was not able to verify the reason for the
                       detention of Shearer and Faizbakhsh or where they
                       were being held.


                # ⚓ CPJ ☛ Taliban_members_beat,_threaten,_Afghan_journalist
                  Saboor_Raufi⠀⇛


                       On Monday, August 15, two armed Taliban members
                       beat Raufi, an anchor and reporter with
                       Afghanistan’s independent Ariana News TV station,
                       while he was recording the aftermath of an
                       explosion in front of Ariana’s headquarters in the
                       Bayat Media Center in the capital of Kabul,
                       according to media reports and the journalist, who
                       spoke to CPJ by phone.


                       The men confiscated the mobile phone Raufi was
                       using to film the incident and one of the men
                       slapped him in the face, causing his mouth to
                       bleed. Raufi told CPJ that he had identified
                       himself as a journalist and shown his press ID card
                       when one of the men beat him for several minutes
                       with a rifle, on his head, shoulder, back, and
                       legs.


                # ⚓ RFERL ☛ Russian_Police_Search_Homes_Of_Journalists
                  Contributing_To_RFE/RL_Programs⠀⇛


                       According to Tatar-Inform, the searches were linked
                       to the journalists’ articles covering Russia’s
                       ongoing aggression against Ukraine.


                       President Vladimir Putin in March signed a law that
                       calls for lengthy prison terms for distributing
                       “deliberately false information” about Russian
                       military operations as the Kremlin seeks to control
                       the narrative about its war in Ukraine.


                # ⚓ Independent AU ☛ Despite_resistance,_WikiLeaks_continues
                  its_fight_for_the_truth⠀⇛


                       WikiLeaks exposed the killers and their keepers
                       from the 12 July 2007 Baghdad airstrikes in which
                       air-to-ground attacks deploying U.S. AH-64 Apache
                       helicopters killed innocent civilians and
                       journalists. Three years after this horrific
                       incident, the world was aware of its inherent right
                       to know when WikiLeaks released 39 minutes of
                       “classified” footage of the slaughter of 18
                       innocents.


                # ⚓ ABAJournal ☛ WikiLeaks_founder’s_lawyers_allege_CIA
                  authorized_spying_on_their_visits⠀⇛


                       The plaintiffs, all of whom are American citizens,
                       said in their complaint they visited Assange while
                       he was living under political asylum at the
                       Ecuadorian embassy in London. They were required to
                       surrender their phones and other devices. They
                       allege that without their knowledge or consent,
                       employees of Undercover Global copied information
                       stored on their devices.


                       They allege further that the security company then
                       provided that information to the CIA with Pompeo’s
                       approval. Pompeo later would work as the U.S.
                       secretary of state in the Trump administration from
                       2018 to 2021.


                # ⚓ Scheerpost ☛ Katie_Halper_Interviews_Bob_Scheer⠀⇛


                       Katie Halper interviews Bob Scheer about the future
                       of journalism, countries lying about foreign
                       policy, and more.


          o § Civil Rights/Policing⠀➾


                # ⚓ Bridge Michigan ☛ It’s_time_for_Michigan_schools_to_double-
                  down_on_accessibility⠀⇛


                       Using technology in schools enriches the classroom
                       experience, but for many students with
                       disabilities, materials may still be out of reach
                       even when they’re connected online. Some states are
                       taking proactive steps to ensure that digital tools
                       used in K-12 schools are compliant with World Wide
                       Web Consortium’s Web Content Accessibility
                       Guidelines (WCAG), which means students with
                       blindness and low vision, deafness and hearing
                       loss, limited movement and other disabilities can
                       still engage with the same online materials as
                       their peers. As part of a growing trend, Illinois,
                       Maryland, and New Jersey have all recently passed
                       legislation that requires digital tools used in
                       schools to be compliant with WCAG 2.1. Screen
                       readers, text-to-speech technology, and sufficient
                       contrast ratios on web pages are just some of the
                       accessibility measures that are needed for digital
                       providers to comply with this regulation. Michigan
                       can be a leader in accessibility and should
                       consider legislation similar to what has been
                       passed in other states.


                # ⚓ India Today ☛ Boys_and_girls_sitting_together_in_schools
                  dangerous,_says_Kerala_Muslim_outfit_leader⠀⇛


                       Kerala Indian Union Muslim League (IUML) general
                       secretary in-charge PMA Salam sparked controversy
                       by claiming that it is ”dangerous” to allow boys
                       and girls to sit together in school classrooms.
                       This comes amid state government efforts to
                       introduce a gender-neutral education system in the
                       state.


                       “It is dangerous. What is the need for girls and
                       boys to sit together in classrooms? Why are you
                       forcing them or creating such opportunities? It
                       will only cause problems. Students will deviate
                       from studies,” Salam said, while criticising the
                       Kerala government’s gender-neutral policies.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ IT Wire ☛ .au_direct_priority_registration_period_closes
                  soon⠀⇛


                       When .au direct was launched on 24 March 2022, the
                       holders of names in the com.au, net.au and other
                       Australian namespaces were given the opportunity to
                       register the .au direct equivalent.


                       Holders in each namespace were given equal
                       priority, so the holders of example.com.au,
                       example.net.au and example.id.au had an equal claim
                       to example.au. If more than one of them wanted it,
                       then they each had to pay the registration fee to
                       stop it going to one of the others, but the name is
                       not made available until there is only one
                       claimant.


                       Priority applications must be made by 20 September
                       2022, after which it’s ‘first in, best dressed’.


    * § Gemini* and Gopher⠀➾


          o § Technical⠀➾


                # ⚓ Horus_Calendar_HiDPI_Support_–_No_More_Bluriness!⠀⇛


                       I have spent the day today working on DPI support.
                       This includes the DPI setting of the Operating
                       System which is used to scale all user-interfaces,
                       as well as HiDPI displays that would naturally have
                       this setting set above 100%.


                       If you look at some of the previous images of Horus
                       in my Gemlog, you might notice some bluriness. This
                       was due to the face that I had not turned on HiDPI
                       Awareness in the Windows application, which meant
                       that Horus’ whole interface, including fonts, were
                       being drawn at a low resolution and then scaled up
                       based on the system’s DPI.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.


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