𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, December 05, 2024
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Generated Fri 6 Dec 02:49:19 GMT 2024
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/2024/12/05/


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

QmbHjgPAAcGNUG9Sej4vSKhK8DfUYokfFkXLdKwr1JtGJG
QmdLsuRLzrwb58dZaSmJah6oCmNNZ6cW4ick4chqJmHjmY
QmTNR3uqcbMYjPAbbHjBqyNJb3ib8kytQvdFnATzkBFVvo
QmfCHrqMLfMsHXYnQeAvVuNYt91Zw2AmMJ5mx4RqsrWy3b
QmR2rr1yXDANjQBEz2oGtd2UMgy9U37FHdjpUhPfAk7h5z
QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3
QmaoEDiALTYYZdaq3SQ86aQpMwUji1nqCeLbXAoszFRYvJ
QmSTkZUY74BcgbgqS6JKwwNbVnbzY5uqwpgWtYonGJua8s
QmXZcp3rXLYa24pYd7jUu6sPDrhziRCNCok875WLJTLysP
QmUE7nd24kx2soZFbSYKDsb1ik1wpirFTRTBhDTj6w9sjh
QmdKeWBhfnjgQLYU48wto7DdStpXsB5mE1yEEnWcxQ53vu
QmfSnnTnjcAe3YvtRsVgAwUJfpcEk1dM5J5yjJLyv7MxqM
QmQ16CkpxBbMzPZ6wZcuKBUcxH1RZ8uAEhcvdBsPRpVZe9
QmT3gTQRv33wEDtJveL8DiqiacGeRaxEbRFDUyVSJEAvDL
QmTs9qcwghZPs5oBh9qzsu8a11T4s6xHrJjVNyk5miFy3X
Qmdqd6mb8mj27qVvQZRR7sjshrXYYirWm9vRttLkNB5rW6
QmSjY85vxbu9nNFHUMmuK7CxRame2VYuhb523CJaK5zRkj
QmZwah9nZHVvSzbJWEAMxumYDpanFPqTahnqoNP83tuZbx
QmQWSrGfeYwgf6HE9N3742DJrJwq8uNSCUAz469CnuUFGe
QmcgTTyseF5zFd4MLquM4PtJZzkFcBEqaUbqDe4eaUx6Na
QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu


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

⦿ Techrights  -  At the OSI, Microsoft Operative (Funded by Microsoft) Promotes Proprietary Software of Microsoft

⦿ Techrights  -  Companies That the Software Freedom Conservancy (SFC) Will Censor the Community for, Using Their Very Large CoC

⦿ Techrights  -  Fantastic Journalism by Brian Fagioli

⦿ Techrights  -  Gemini Protocol Keeps Getting Better (Less and Less Reliance on Centralised Certificate Authorities)

⦿ Techrights  -  Increasing Productivity With Less Hardware, Little Power, and Fewer CPU Cycles (and Far Less Digital Waste in General)

⦿ Techrights  -  IRC Proceedings: Wednesday, December 04, 2024

⦿ Techrights  -  [Meme] Shooting the Messenger

⦿ Techrights  -  [Meme] They Dropped the L (Libre and Law)

⦿ Techrights  -  Microsoft Criminals: Law Enforcement is the Real Problem

⦿ Techrights  -  GNU/Linux news for the past day

⦿ Techrights  -  Software Freedom Conservancy (SFC) Associate Sued Us for Publishing Perfectly Accurate Article About SFC; We Sued Them for Harassment

⦿ Techrights  -  Software Freedom Conservancy (SFC) Has Asked a Blogger to Delete This Page About the SFC, So We Reproduce It in Full Here

⦿ Techrights  -  Techrights Does Not Forget

⦿ Techrights  -  The Free Software Foundation (FSF) Has Raised More Than Three Times More Money Than the Software Freedom Conservancy (SFC), Which Mostly Gets Money From Corporations, Including Microsoft

⦿ Techrights  -  Why We Moved to Perl and Dumped PHP Last Year

⦿ Techrights  -  Windows Has Fallen to All-Time Low in India

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/12/05/At_the_OSI_Microsoft_Operative_Funded_by_Microsoft_Promotes_Pro.shtml
https://techrights.org/n/2024/12/05/Companies_That_the_Software_Freedom_Conservancy_SFC_Will_Censor.shtml
https://techrights.org/n/2024/12/05/Fantastic_Journalism_by_Brian_Fagioli.shtml
https://techrights.org/n/2024/12/05/Gemini_Protocol_Keeps_Getting_Better_Less_and_Less_Reliance_on_.shtml
https://techrights.org/n/2024/12/05/Increasing_Productivity_With_Less_Hardware_Little_Power_and_Few.shtml
https://techrights.org/n/2024/12/05/IRC_Proceedings_Wednesday_December_04_2024.shtml
https://techrights.org/n/2024/12/05/Meme_Shooting_the_Messenger.shtml
https://techrights.org/n/2024/12/05/Meme_They_Dropped_the_L_Libre_and_Law.shtml
https://techrights.org/n/2024/12/05/Microsoft_Criminals_Law_Enforcement_is_the_Real_Problem.shtml
https://techrights.org/n/2024/12/05/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Associate_Sued_Us_for_Publishi.shtml
https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Has_Asked_a_Blogger_to_Delete_.shtml
https://techrights.org/n/2024/12/05/Techrights_Does_Not_Forget.shtml
https://techrights.org/n/2024/12/05/The_Free_Software_Foundation_FSF_Has_Raised_More_Than_Three_Tim.shtml
https://techrights.org/n/2024/12/05/Why_We_Moved_to_Perl_and_Dumped_PHP_Last_Year.shtml
https://techrights.org/n/2024/12/05/Windows_Has_Fallen_to_All_Time_Low_in_India.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/12/05/Gemini_Links_05_12_2024_Hermeticism_Living_in_the_Shell_and_Mor.shtml
https://techrights.org/n/2024/12/05/Links_05_12_2024_Domain_Changes_Griping_With_Haskell.shtml
https://techrights.org/n/2024/12/05/Links_05_12_2024_Explaining_the_South_Korea_Chaos_and_French_PM.shtml
https://techrights.org/n/2024/12/05/Links_05_12_2024_Formaldehyde_and_Cancer_US_and_China_Boycottin.shtml
https://techrights.org/n/2024/12/05/Links_05_12_2024_Mass_Layoffs_at_Microsoft_s_PR_Bribery_of_Medi.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 96

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/At_the_OSI_Microsoft_Operative_Funded_by_Microsoft_Promotes_Pro.shtml
    Gemini version at https://techrights.org/n/2024/12/05/At_the_OSI_Microsoft_Operative_Funded_by_Microsoft_Promotes_Pro.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ At the OSI, Microsoft Operative (Funded by
Microsoft) Promotes Proprietary Software of
Microsoft⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


Days ago: The_Microsoft_OSI:_All_the_Latest_Blog_Posts_Are_Written_by_Microsoft
Operative_Salaried_by_Microsoft


They've totally quit pretending what they really are:


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


An OSI not corrupted and bribed by Microsoft would tell people to get away from
GitHub, not advocate for GitHub (Microsoft).


The OSI is deeply corrupt. The good news is, it's barely hiding it anymore.


The latest "Members Newsletter" (Driving Open Source forward: make your impact
in 2025) is also published by the Microsoft operative. It's like Microsoft
totally controls everything there, even the reports and policy. █




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                    ䷩ 𝚕𝚒𝚗𝚎 156

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Companies_That_the_Software_Freedom_Conservancy_SFC_Will_Censor.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Companies_That_the_Software_Freedom_Conservancy_SFC_Will_Censor.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Companies That the Software Freedom
Conservancy (SFC) Will Censor the Community for, Using Their Very Large
CoC⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


In the past we also caught them censoring for IBM/Red Hat (the censored people
reported this to us!) and taking money from Microsoft.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Software_Freedom_Conservancy_(SFC):_Companies_That_We_Censor
                 the_Community_for_Using_Our_Very_Large_CoC⦈_


Having said that, the Software Freedom Conservancy (SFC) has been good at
exploiting_poor_(and_sexually_abused)_women_from_eastern_Europe, using them as
PR props for slavery-level "IT" wages (covered by Google's accountants; yes,
the same Google that sponsors SFC).


Perhaps not too shockingly, SFC associates are defaming key FSF people this
week. █




⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠿⠻⣿⠿⠿⢿⠻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿
⣿⣿⣷⣤⣄⣀⣀⣠⠀⢠⣀⣀⡀⠴⠴⠿⠬⡽⢯⠤⡤⠼⡼⡤⢧⠤⠬⢤⢤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣟⣀⣸⣿⣿⣧⣉⣘⣀⣀⣐⣠⣐⣇⣷⣠⣀⣸⣸⣀⣻⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⡿⠻⠻⠿⠿⡿⠿⠿⠻⠿⠿⡿⠿⠿⠻⠟⡟⠟⠛⢛⠛⠛⡟⠻⠿⠿⠿⠿⡿⢿⢿⡟⠿⠿⢿⠛⢛⡿⠿⠻⠿⡟⡟⠟⠛⠻⠿⠿⠿⠿⡛⢻⡟⠻⠿⠿⠿⢻⢛⠛⡛⠟⠛⢻⠿⡻⠿⠿⠿⠿⢻⠿⠿
⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣿⣶⣶⣶⣷⣶⣿⣶⣷⣾⣶⣷⣷⣶⣶⣶⣷⣷⣿⣾⣾⣶⣶⣶⣾⣶⣷⣷⣶⣾⣶⣷⣷⣶⣾⣶⣾⣾⣷⣾⣶⣶⣶⣶⣾⣿⣶⣷⣿⣾⣷⣾⣾⣾⣷⣷⣶⣾⣾⣾⣷⣷⣶⣾⣶⣷⣶⣷
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⢄⠰⢀⢠⡄⠒⡖⠒⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⠟⠛⢿⣟⣿⠛⠛⠻⡛⠛⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⡿⢿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣄⠀⢻⡄⠈⣿⡟⠀⠀⣿⡿⠀⢰⠃⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠀⢸⣧⠀⢹⠃⢰⡀⢸⠇⢀⣿⣦⣀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠾⡿⠟⠀⠸⣿⡆⠈⠀⣾⡇⠀⠀⣼⣿⠿⠿⣿⠷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣦⣴⣿⣿⣤⣴⣿⣿⣤⣴⣿⣿⣦⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⣡⣼⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠈⠉⠛⠟⣭⠛⢭⢻⢩⢹⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢂⣼⣶⣇⣀⣰⠀⠐⠃⠈⠆⠰⠀⠰⠀⠀⠆⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠦⠴⠾⠿⠿⠿⠿⠿⠿⠷⠶⠿⠾⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⣿⠿⠷⠿⡿⠛⠛⢻⡿⠛⠛⢿⡿⠛⠛⠛⠀⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠿⠶⠖⢠⡀⠾⠿⠀⡅⠾⡿⠀⡅⠺⠿⠀⠀⡅⠈⡤⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣿⣿⣦⣴⣾⣿⣶⣶⣾⡟⠢⠔⢠⣶⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣒⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠍⢛⠙⠙⠛⠛⡏⠙⠋⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣀⡤⠀⢹⣿⠙⠛⢉⣙⠛⡟⠻⠟⡛⢹⣋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠰⠛⠧⠀⢠⣿⠀⡀⣠⣼⠀⡟⣠⡈⢃⢸⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⢭⣝⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣇⡀⡟⠛⠛⠻⡿⠛⠛⠀⢸⠟⠛⠻⣿⠟⠛⠛⡿⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⠀⡇⢸⣿⠀⠀⠀⣉⡁⠄⠀⣉⡀⠄⠰⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 276

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Fantastic_Journalism_by_Brian_Fagioli.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Fantastic_Journalism_by_Brian_Fagioli.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Fantastic Journalism by Brian
Fagioli⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024,
updated Dec 05, 2024


A lot of today's Web, even "news" sites, is spam


The latest from Brian Fagioli:


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Redfin_Redesign_uses_AI_to_add_Christmas_decor_to_home
                           images_(press_release)⦈_


Oh. Must be some good article!


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_latest_from_Brian_Fagioli:_Images_from_the_press
release;_Copypasta_from_the_press_release;_'Redfin_Redesign_is_available_year-
 round_for_more_than_355,000_listings_in_the_U.S._and_to_homeowners_who_claim
  their_home_on_Redfin._The_holiday_style_is_accessible_via_Redfin’s_desktop
                            website_and_iOS_app.'⦈_


The press release:


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


Press release: "Redfin Redesign is available year-round for more than 355,000
for-sale listings across the U.S. and to any of the millions of U.S. homeowners
who have claimed their home on Redfin. The holiday design style is available to
those using Redfin.com on desktop and the iOS app."


Fagioli: "Redfin Redesign is available year-round for more than 355,000 for-
sale listings across the U.S. and to any of the millions of U.S. homeowners who
have claimed their home on Redfin. The holiday design style is available to
those using Redfin.com on desktop and the iOS app."


Fantastic reporting, Brian! Keep it up! Then, seeing what_happened_with_Swapnil
Bhartiya, maybe the Linux_Foundation will reward you financially. █


Also see: BetaNews_Has_Become_a_SPAM/Slop_Factory,_Brian_Fagioli_Publishes_Fake
'Articles' | It's_Morbid_to_Talk_About_Living_People_as_If_They're_Dead |
BetaNews,_Inc._Became_a_Spam_Operation/Web_Site,_LLM_Spew_(Slop)_for_SEO
Disguised_as_"Articles" | BetaNews_is_Beta-Testing_the_Site_as_LLM_Slop_With
Microsoft_Propaganda_Thrown_In | Even_the_Managing_Editor_of_BetaNews_is_Doing
Slop_and_Spam | At_BetaNews,_"Most_Commented_Story"_Is_Not_a_Story_But_LLM
Slop!_(Readers_Talking_to_Bots) | BetaNews_is_Run_and_Written_by_Bots_That_Make
Clickbait | BetaNews,_Desperate_for_Clicks,_is_Pushing_Donald_Trump_Spam
Created_by_LLMs_(Slop)




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⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠃⠀⠑⠚⠁⠂⠀⠉⠁⠀⠈⠒⠐⠘⠛⠀⠀⠉⠂⠐⠃⠀⠐⠘⠀⠀⠀⠐⠁⠀⠀⠂⠈⠀⠀⠈⠈⠒⠂⠀⠀⠀⠂⠀⠂⠀⠀⠃⠈⠒⠁⠀⠀⠃⠓⠙⠃⠃⠀⠀⠀⠈⠀⠀⠀⠐⠑⠀⠐⠑⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⢰⣶⣶⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠛⠻⠟⠛⠀⢹⣿⣿⣿⣿⣿⢛⡻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠛⢛⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⢠⡤⠅⠄⠶⠄⢸⣿⣿⣿⣿⡏⣿⢕⣧⡿⡞⡬⢸⣸⣧⣿⡇⣭⣽⢫⢅⡷⡷⡞⡏⣿⣸⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠘⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠟⠠⣶⣙⣃⠰⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⢀⣉⣉⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣸⣯⣹⣇⣿⣏⣿⣇⣿⣍⣿⣯⣽⣿⠹⣿⣹⣿⣩⣿⣯⣽⣿⣱⣇⣿⣏⣿⣿⣹⣿⣹⣿⣲⣃⣿⣽⣿⣋⣿⣹⣿⣯⣿⣿⣸⣿⣟⣿⣏⣿⣸⣏⣿⣿⣹⣿⣹⣿⣽⣿⣯⣹⣿⠛⣿⣯⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣭⡙⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣣⢖⠂⣹⣿⣿⣿⣻⣟⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣯⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣤⣬⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣤⣤⣤⣶⣦⣤⣦⣴⣴⣶⣤⣦⣦⣴⣤⣶⣦⣤⣴⣶⣦⣤⣶⣶⣦⣤⣤⣴⣶⣶⣶⣤⣦⣦⣤⣶⣦⣤⣤⣴⣶⣶⣴⣶⣤⣤⣤⣴⣶⣦⣤⣴⣦⣴⣴⣶⣦⣤⣶⣤⣶⣶⣦⣴⣤⣴⣴⣶⣤⣦⣴⣶⣶⣶⣶⣶
⣿⣻⣯⣽⣻⣉⣍⣿⣯⣹⣹⣻⣫⣋⣽⣏⣻⣿⣯⣯⣿⣇⣏⣹⣿⣻⣟⣏⣉⣹⣯⣻⣿⣉⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣟⣿⣿⣛⣛⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⣿⡟⠛⠛⠛⠛⠛⠛⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣴⣤⣤⣀⣀⣐⣶⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⣿⡏⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣾⡀⢐⢨⣍⡇⠀⠈⣘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠈⠁⠀⠒⠀⠉⡇⠈⠨⠁⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠤⣄⣉⡉⠛⠛⠻⠿⢿⣿⣿⣯⢁⠉⠉⠚⢻⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠰⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡷⠶⠶⠶⠶⠶⠶⡷⠶⠶⠶⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡄⠀⠰⡀⣧⣆⡀⠀⠈⠉⠉⢀⠀⠀⢠⣠⠀⠈⣀⠀⠈⠀⠈⠁⠀⠀⣀⣀⣠⣤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡗⢰⣦⡤⡀⠀⠀⡗⠀⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⣿⡴⣆⢳⢿⣿⣿⣿⣶⣂⣶⣿⣼⠀⢸⣿⣤⠄⠛⠀⠀⠀⠠⠀⠰⠶⠀⢠⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠠⠭⣅⠅⣀⠀⡇⠀⠤⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢧⡏⣛⠮⠃⠈⣿⣿⠏⠀⠁⣿⡋⠻⣪⢸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⡌⠘⣀⣀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠁⠉⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠪⠀⣲⡗⠀⠐⣿⡟⠒⠒⠂⣿⡀⠀⠁⢈⠏⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⣤⣄⣀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠘⣧⣄⠀⢀⠀⠀⠉⠉⠉⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⡀⠀⠀⠀⠀⡇⣶⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠠⠰⠄⠀⠀⠀⡷⠀⢻⣖⣢⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠑⢠⣥⣿⠎⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⡥⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⡗⠰⠩⠭⠟⠊⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣬⣬⣤⣤⣤⣤⣧⣤⣬⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⢀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⢀⣤⣤⣀⡀⠀⡇⢠⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣷⠟⠁⠰⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠸⣤⡁⢤⢃⠀⡇⠸⡯⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⣭⡾⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠈⠛⠂⠃⠀⠀⡇⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡷⠶⠶⠶⠶⠶⠶⡷⠶⠶⠶⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣾⣷⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⣿⣿⠿⢿⣿⠿⣿⢿⣿⣿⣿⣿⠿⠿⣿⡿⡿⢿⠿⣿⣿⠿⡿⢿⣿⢻⡿⣿⡿⢿⣿⣿⠿⢿⣿⣿⣿⠿⠿⡿⣿⣿⡿⠿⣿⣿⠿⢿⣿⢿⡿⢿⢿⠿⡿⣿⣿⠿⡿⠿⡿⣿⣿⡿⠿⢿⢿⡿⡿⣿⣿⣿⣿⣿
⣿⣷⣶⣿⣶⣷⣿⣿⣷⣾⣾⣾⣶⣿⣿⣷⣶⣷⣿⣿⣶⣿⣿⣾⣿⣶⡷⣿⣿⣷⣾⣾⢷⣶⣷⣷⣷⣶⣶⣿⣾⢶⣶⣾⣷⡿⣶⣶⣾⣷⣶⣶⣷⣾⣷⣶⣿⣶⡶⣾⣿⣾⣶⣶⣷⣿⣾⣿⣶⣾⣶⣿⣶⣿⣿⣿⣿⣿
⣿⣼⣶⣦⣯⣧⣵⣯⣦⣾⣿⣮⣶⣾⣿⣧⣴⣧⣯⣷⣮⣴⣯⣦⣤⣮⣷⣴⣵⣾⣶⣷⣾⣧⣧⣷⣼⣵⣿⣾⣿⣤⣮⣦⣮⣧⣮⣮⣦⣶⣽⣼⣼⣤⣾⣿⣾⣦⣿⣵⣿⣷⣥⣴⣤⣼⣮⣬⣿⣿⣮⣴⣿⣷⣼⣿⣿⣿
⣿⣟⣝⣽⣯⣿⣍⣬⣻⣼⣏⣽⣵⣩⣻⣿⣽⣿⣥⣿⣽⣿⣿⣝⣯⣏⣯⣩⣟⣿⣝⣯⣽⣏⣿⣿⣽⣏⣽⣿⣽⣿⣍⣿⣿⣯⣹⣩⣿⣿⣟⣿⣾⣭⣷⣤⣭⣭⣯⣹⣍⣭⣿⣯⣻⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣭⣿⣿⣿⣬⣯⣵⣭⣽⣝⣭⣿⣽⣭⣽⣽⣬⣿⣯⣽⣹⣽⣭⣯⣿⣽⣭⣿⣿⣯⣿⣯⣭⣯⣽⣿⣯⣽⣷⣼⣿⣧⣦⣴⣼⣯⣿⣿⣍⣽⣯⣿⣤⣭⣿⣧⣿⣼⣯⣿⣽⣧⣯⣿⣿⣽⣭⣽⣭⣭⣭⣿⣽⣿⣿⣿
⣿⣛⣙⣟⣯⣙⣻⣭⣏⣙⣻⣿⣯⣻⣛⣋⣿⣽⣽⣙⣋⣋⣹⣿⣿⣹⣝⣻⣝⣽⣻⣉⡟⣿⣫⢋⣻⣿⣹⣛⣽⣝⣫⣏⣫⣻⣹⣛⣏⣏⣿⣹⣏⣻⣻⣻⣏⣹⣉⣯⣽⣽⣛⣏⣯⣟⣿⣹⣛⣛⣍⣟⣏⣝⣿⣿⣿⣿
⣿⣻⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣾⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣈⣉⣁⣹⣘⣽⣉⣇⣽⣹⣟⣙⣏⣹⣇⣈⣇⣄⣉⣁⣠⣯⣿⣠⣉⣉⣈⣉⣁⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣙⣏⣹⣝⣏⣟⣟⣛⣛⣛⣫⣙⣿⣛⣟⣙⣛⢟⣟⣟⣻⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣿⣙⣟⣻⣹⣛⣛⣛⣹⣻⣻⣏⣛⣛⢟⣿⣟⣛⣛⣙⣟⣿⣛⢛⣟⣛⣻⣛⣛⣻⣛⣹⢻⣛⣏⣋⣛⣟⣻⣟⣛⣏⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢁⣤⡤⣤⣤⡤⠀⠀⠀⠀⠠⣤⣤⢤⠤⣈⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣿⣧⣤⣤⣤⣤⣴⣷⣾⣾⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠉⠋⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠿⠿⠭⠭⠽⠿⠿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣴⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠛⠿⠿⠿⠭⠭⠭⠭⠭⠭⠿⠿⠿⠟⠋⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⣿⣦⣤⣴⣷⣦⣤⣤⣴⣷⣤⣤⣷⣬⣧⣴⣮⣴⣼⣦⣤⣧⣦⣾⣤⣤⣤⣦⣦⣤⣶⣼⣤⣤⣿⣵⣦⣤⣧⣬⣤⣤⣤⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⠭⠭⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠰⠆⢹⠩⢭⠉⣍⠙⡍⠭⡍⢹⠉⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣖⣒⣒⣂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢰⡄⠻⠐⠚⡀⢛⣠⡇⣶⣇⢸⢀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣴⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢛⠛⢛⠛⠛⡟⠻⠛⠛⢻⠛⠛⢻⡛⢻⠛⠛⢛⣻⠛⢛⠛⠛⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢙⠹⡋⣭⠉⢙⡫⢉⠏⡏⡋⠉⡋⡟⠋⡉⠉⣛⢝⢋⠉⠝⣙⠝⣏⠯⢉⡫⣟⣛⠩⢛⢛⢙⢻⢙⢛⠙⠋⢻⠹⠛⡟⢛⡟⡏⠛⡟⠛⡛⢻⠛⠉⡟⠋⡋⡛⣟⢛⢻⢙⢛⢻⡙⠛⠉⣻⡙⠛⡛⠋⠛⢿⡋⢛⡛⣻
⣿⣛⡛⣛⣻⣛⣛⣏⣛⣛⣛⣛⣛⣛⣻⣛⣙⣻⣛⣻⣟⣛⣛⣛⣛⣏⣙⣋⣹⣝⣏⣟⣛⣛⣛⣛⣻⣙⣛⣟⣛⣙⣋⢟⣋⣛⣻⣹⣟⣛⣟⣛⣛⣻⣙⣛⣛⣋⣛⡛⢛⣻⣛⣉⣏⣛⣙⣙⢻⣟⣛⣟⣿⣿⣿⣿⣿⣿
⣿⣩⡉⣋⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣟⠛⡟⠛⠛⠛⢟⠛⢛⠻⣻⠛⡟⠛⠻⠟⣟⡛⢟⢻⢛⠟⣻⠻⠛⣻⣿⣿⣿⣿⣿⣉⣍⣉⣇⣉⣹⣹⣉⣉⣉⣏⣹⣉⣉⣹⣹⣉⣉⣉⣉⣙⣯⣉⣏⣉⣽⣉⣈⣏⣍⣈⣍⣩⣉⣉⣫⣉⣏⣈⣹⣈⣉⣹⣿⣿
⣿⠻⡻⠛⣿⠛⠛⠛⡛⢟⠛⠛⠻⠿⢛⢻⠛⢛⠿⢻⡛⠻⠛⡛⢻⢺⣿⣿⣿⣿⣿⣿⣿⣩⣁⣏⣉⣉⣩⣈⣏⣹⣹⣍⣍⣉⣇⣉⣉⣹⣉⣏⣈⣉⣨⣹⣈⣹⣉⣩⣩⣉⣉⣉⣹⣉⣏⣉⣉⣏⣉⣉⣉⣍⣻⣿⣿⣿
⣿⠿⡿⠿⢻⠻⡞⡿⡿⠿⢿⠿⠿⡿⢿⠿⠿⠻⣿⢿⣿⡿⢿⠷⢾⠿⡿⢻⣿⣿⣿⣿⣿⣭⣭⣭⣯⣏⣭⣯⣿⣭⣽⣬⣭⣉⣯⣽⣭⣿⣌⣽⣭⣭⣭⣩⣍⣹⣬⣽⣭⣭⣽⣭⣽⣭⣍⣩⣭⣉⣽⣬⣿⣿⣿⣿⣿⣿
⣿⠾⠿⣿⢿⣿⠿⡟⠷⢿⠿⠾⠿⡿⣿⢿⣿⡿⠿⡿⠻⠿⢿⢿⠾⡿⠿⢿⣻⣿⣿⣿⣿⣭⣿⣭⣧⣟⣩⣭⣯⣬⣽⣤⣬⣯⣭⣼⣍⣯⣭⣝⣬⣻⣬⣭⣬⣽⣬⣭⣭⣍⣹⣯⣭⣭⣽⣽⣭⣭⣯⣭⣭⣯⣿⣿⣿⣿
⣿⣶⣶⣿⣶⣿⣾⣷⣿⣾⣾⣶⣶⣶⣿⣿⣷⣿⣷⣷⣾⣶⣾⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣴⣤⣤⣧⣥⣄⣯⣥⣤⣴⣥⣤⣥⣤⣧⣴⣼⣬⣍⣤⣬⣤⣦⣧⣦⣤⣧⣤⣦⣥⣧⣤⣶⣼⣤⣼⣤⣼⣮⣤⣤⣬⣬⣿⣿
⣿⠉⢹⣯⣙⣻⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⢴⢦⢤⣧⡷⣶⣤⣼⣤⢧⣾⠤⣴⣤⣤⣤⣼⣴⢴⣦⣤⣽⡤⣤⣴⣤⣤⣼⣤⣦⣤⣧⣤⣦⣧⣶⢦⣤⡽⢤⣴⠼⣿⣿
⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⢿⡿⡦⣤⣼⣥⣦⢧⣤⣦⣤⡽⣦⣤⣤⣾⣼⣤⣦⣴⣧⣤⣼⣴⣦⣤⣤⡤⣴⣾⢤⡶⣤⣦⣧⣴⣼⣴⣤⣤⣤⣿⡦⣤⣤⡾⣿
⣿⢶⡶⠶⣶⠵⠶⣷⠶⢶⢿⢶⠾⠷⣶⢶⠷⠶⡧⢴⢶⠶⠴⠷⡷⠶⢶⡶⠼⢼⠶⠾⡷⠶⢾⢽⢶⠾⡾⡾⡶⣷⠷⡶⡾⣿⠶⠶⡶⡷⠶⢶⡶⣾⠿⢶⠶⢿⢶⠶⢽⠶⡶⠿⢾⢶⠶⢾⠷⢶⡶⠶⠷⡷⠿⡷⢶⣿
⣿⠶⠶⠶⠾⠶⠶⠷⡾⠶⢾⠾⠶⠾⡶⠾⡾⠷⠷⠾⢶⠶⠶⠮⢷⠶⣶⠾⠶⠾⠶⠶⢿⣶⣶⣾⣾⣶⣶⣶⣶⣶⣷⣶⣧⣶⣶⣶⣶⣾⣶⣶⣷⣶⣤⣶⣶⣶⣼⣶⣶⣶⣷⣶⣾⣷⣴⣶⣼⣾⣶⣶⣷⣶⣾⣶⣾⣿
⣿⣶⣶⣾⣶⣶⣾⣶⣷⣾⣾⣾⣶⣶⣷⣷⣷⣶⣶⣶⣾⣶⣶⣶⣾⣾⣷⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡻⠿⠿⢿⠿⠟⠻⢿⠿⡿⠿⠿⠿⢿⠿⠿⡟⠿⠟⠻⡿⢿⠿⠿⢿⠿⢿⠿⠿⠿⢿⠟⠟⠿⡿⠿⠟⠿⠿⡿⡟⠻⡟⢿⠿⠛⠿⠿⡿⠿⢿⠿⠛⠿⠿⡿⢿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⢟⡿⠟⢿⣿⣿
⣿⠓⠾⠷⢺⠺⠶⠶⢾⡖⢳⠶⠷⢶⡺⣞⠞⢛⣶⣒⡞⢷⠾⠶⠶⠾⡾⠾⠾⡶⡾⠾⠶⢷⡷⠿⠾⡶⠶⠷⣷⠷⡶⠷⠿⢻⠶⠶⠷⠷⡶⠾⠾⠶⠺⠷⢷⠿⡷⡶⠶⠞⡶⡞⡶⠾⠾⠞⠷⡖⡶⣾⠿⠷⠶⡞⣿⣿
⣿⠿⠿⠿⠿⣿⣺⢿⢻⢿⠿⢿⡿⠿⢿⣟⣿⡟⣟⠿⡿⠿⠿⠿⣿⠿⣛⠿⢿⡿⠿⢿⣿⡿⢿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣝⢻⠛⠛⢛⠛⡛⠛⡛⠛⣟⠛⠛⠛⡟⠛⠛⠛⣟⢛⣛⠻⠛⠛⠻⠛⠛⠟⢛⣟⢛⣛⠻⢻⡛⢟⠛⡟⡟⠛⢛⠛⢻⠛⣻⡙⠛⠛⡻⡛⠛⢻⢛⢻⡋⠛⠛⠛⠛⠛⡟⠻⠛⢛⣿⠛⠛⣟⠛⢛⢻⠛⢻⣿⣿⣿⣿
⣿⠋⡛⢛⠙⠛⢻⢻⣛⠛⣛⡟⢛⢛⡟⠛⢛⣻⢉⡛⡛⡏⠛⠛⢿⠛⢻⡛⠛⡟⠛⡛⠛⢙⢙⢻⡛⠛⠛⡟⡛⠛⢻⢛⠻⡟⠛⠛⡟⢻⠟⡛⡟⡛⡛⠋⡏⠛⠙⠙⢫⣏⡛⡛⡏⡛⣟⠛⠛⢿⠋⡟⢛⡛⠻⡟⡛⢹
⣿⣛⣋⣋⡟⣛⣟⣟⢛⣻⣛⣙⣛⣛⣛⣛⣻⣛⣛⣛⣛⣛⢛⣛⣙⣛⣻⣛⣛⣛⣿⣝⣛⣛⣛⡛⢻⣫⣛⣋⣉⣛⣛⣻⣋⣛⡙⣻⣹⣙⣻⣛⣛⣻⣻⣉⣏⣛⣙⣛⣻⣛⣟⣋⣙⣛⣛⣛⣟⣛⣛⣛⣛⣙⣿⣿⣿⣿
⣿⣟⣛⡛⣟⣻⣛⣹⣛⣻⣻⣛⣟⣏⣟⣛⣛⡙⣟⣛⡻⣛⡛⣛⣟⣟⢛⣻⣛⣿⣻⣟⣛⣋⣟⣛⣛⣋⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣹⣉⣙⣍⣹⣉⣉⣍⣍⣍⣏⣉⣟⣙⣩⣉⣉⣹⣍⣉⣉⣏⣹⣯⣉⣉⣙⣟⣉⣻⣉⣉⣋⣉⣉⣩⣉⣉⣉⣹⣩⣏⣉⣉⣉⣹⣉⣉⣉⣻⣉⣉⣏⣍⣩⣩⣉⣉⣉⣉⣩⣉⣉⣉⣝⣏⣉⣉⣉⣹⣉⣹⣉⣉⣉⣿⣿
⣿⣉⣉⣉⣏⣩⣹⣉⣩⣹⣉⣏⣉⣻⣉⣉⣏⣉⣉⣉⣍⣏⣍⣋⣏⣉⣩⣉⣏⣉⣍⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣬⣯⣭⣧⣼⣭⣿⣏⣭⣤⣏⣹⣽⣽⣭⣯⣽⣭⣭⣯⣯⣤⣿⣩⣽⣽⣭⣭⣧⣭⣿⣯⣤⣍⣯⣹⣥⣿⣤⣭⣤⣿⣤⣭⣬⣥⣫⣧⣽⣽⣣⣾⣽⣯⣭⣬⣭⣿⣍⣧⣟⣧⣿⣥⣿⣽⣼⣽⣭⣯⣥⣭⣼⣿⣿⣿⣿
⣿⣬⣬⣬⣼⣤⣤⣤⣸⣼⣤⣤⣥⣽⣦⣬⣧⣤⣤⣭⣭⣤⣭⣤⣽⣤⣍⣬⣬⣮⣬⣼⣥⣭⣷⣬⣤⣬⣷⣬⣤⣭⣩⣾⣤⣼⣴⣭⣬⣧⣤⣌⣧⣼⣬⣥⣯⣤⣼⣬⣴⣦⣽⣤⣤⣤⣤⣴⣸⣿⣤⣦⣥⣬⣴⣼⣿⣿
⣿⣦⣤⣤⣧⣤⣤⣭⣤⣶⣬⣴⣤⣧⣴⣬⣦⣥⣤⣵⣤⣤⣣⣤⣶⣤⣤⣧⣤⣴⣼⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣿⠿⣿⠿⣿⢿⡿⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⡿⠿⢿⠿⡿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣤⣤⣤⣾⣤⣤⣤⣤⣤⣧⣼⣴⣦⣤⣴⣶⣴⣤⣴⣦⣤⣦⣧⣥⣷⣬⠤⣧⠦⣴⡧⢴⣬⣵⡮⣷⣶⡴⣴⣼⣤⣤⣤⣼⣴⣶⣤⡼⣼⣴⣯⣥⣿⣤⣤⣧⣼⣴⣴⠶⣧⠷⣦⣦⣶⣤⣦⣷⣶⣭⢼⣿⣿⣿⢿⣿⣿
⣿⢶⣶⠶⡶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣷⣶⣶⣶⣿⣷⣶⣾⣶⣶⣶⣷⣾⣶⣶⣶⣾⣷⣶⣾⣷⣶⣶⣴⣶⣶⣦⣶⣷⣷⣶⣷⣷⣶⣶⣶⣶⣾⣶⣷⣶⣶⣶⣶⣶⣽⣶⣶⣾⣾⣶⣶⣶⣶⣷⣶⣶⣶⣴⣷⣶⣾⣿⣿
⣿⣶⣾⣾⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 471

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Gemini_Protocol_Keeps_Getting_Better_Less_and_Less_Reliance_on_.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Gemini_Protocol_Keeps_Getting_Better_Less_and_Less_Reliance_on_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Protocol Keeps Getting Better (Less
and Less Reliance on Centralised Certificate
Authorities)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


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


Reliable systems do_not depend on third parties, only themselves


Gemini Protocol is still autonomous and controlled by the community, not some
company like Automattic (a_subject_of_recent_controversies). It is also about
to_turn_5.5_years_old (our sister site will turn 20.5 in 5 days).


Our current site's system (after dumping_PHP,_WordPress_etc.) is optimised for
Gemini Protocol. This system keeps improving behind the scenes, with
refinements to GemText conversions made as recently as last week. This system
is AGPLv3-licensed and it is accessible over Gemini Protocol, linked to our
self-hosted Git instances (one for each site).


We've only just noticed, based on Lupa, that after about a fortnight the Linux
Foundation's Certificate Authority Let's Encrypt lost some more instances and
is now down to just 14 capsules that are tracked by Lupa (it tracks_about_4,200
capsules). To quote today's_statistics: "2646 (91.2 %) capsules are self-
signed, 14 (0.5 %) use the Certificate Authority Let's Encrypt, 242 (8.3 %) are
signed by another CA (may be not a trusted one)." (To be clear, Certificate
Authorities can be self-hosted too)


For well over a week it said 15. It's generally going down and down... towards
zero.


That's a reason to adopt and to like Gemini Protocol. It discards_fake
'security'_which_generally_puts_capsules_under_the_control_of_monopolies (they
can deny access to capsules by denying/revoking certificates and they are also
a MitM in the privacy sense). As Dr. Andy Farnell put_it_yesterday: "They did
an end run around government and decided to go straight for control and bypass
the whole trust, value and money making stages. [...] Human beings have lost
control of the direction of information technology.


Andy also said: "The things I "own" in digital space (domains, websites,
accounts, currencies, devices) feel less safe. Digital life is at the mercy of
arbitrary diktats, administrative errors, system failures, predatory
freeloaders and the exercise of unchecked power to exclude, and censor. I have
less confidence in the benevolence and competence of authority. And I know I am
far from being alone when I say these things. Instead of clear social progress
a number of unfortunate side effects of digital tech have blighted society.
Their net effect is that we're moving backwards."


There are several more allusions there to fake 'security' and systems like the
centralised Certificate Authorities (CAs), which aren't about security but
about someone else - the "powerful few" - exercising control over who can run a
site (or capsule) and who can access it. Never underestimate the gatekeeping
and the fences they have built. It is a "boiling frog" scenario and only a
matter of time before they flick switches. Many fine Web sites go dark or
offline these days, some of them not because of their choosing; it's not a
choice, it is an order. Be prepared, build information systems shrewdly, based
on cautious foresight. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠉⠛⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⡟⡽⠻⢿⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠯⠉⡝⢻⣿⡇⠁⠘⠀⠀⠈⠉⢻⣿⣿⣿⡉⠉⢉⣛⣻⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠂⠀⠀⠋⠠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⡿⠟⢛⠻⠋⠦⢠⠐⠆⢿⣇⢠⣄⠄⠀⠀⠸⠸⠋⠁⠠⠤⠘⠀⢹⣾⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⢛⠃⠀⠀⠀⠀⠀⠩⢹⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣿⠛⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⢰⣤⣜⠿⡸⣿⠀⠀⠀⠠⡕⡄⠀⢐⡀⠂⠀⢈⣅⠰⣦⡦⣭⡧⠀⠀⠀⠀⠀⠀⢤⠀⠈⠂⠀⠀⠀⠀⡫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠃⠀⠁⠀⠀⠁⣆⡀⠀⠀⠀⠐⠈⠋⣾⡧⢙⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢠⡏⠉⢀⡉⠘⣫⢠⠄⠀⠀⠀⠠⡄⠀⠀⠸⠢⣀⠒⠖⠂⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡄⣤⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⢤⠏⣛⠀⠰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⢠⣾⡁⠀⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⢿⡿⠛⠛⠿⣿⣿
⠟⠥⠐⠒⠆⠀⠶⣔⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠐⠀⢀⢂⣀⣀⠹⠋⠤⠈⠈⠀⠟⠛⠟⠟⠉⣹⣿⣿⣿⣿⣿⠃⠀⠀⠟⠛⠃⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠈⠀⠞⠒⠀⠢⠀⣃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠈⠀⠀⠔⠨⠟⠁⡈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠄⠤⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠄⠀⠀⠈
⠀⠠⢀⠀⡁⠀⠀⠀⠀⠈⢣⠃⠀⢀⠀⠀⠀⠀⠀⠂⠈⠀⠂⡀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠁⣘⢃⠈⠑⠀⠀⠀⠀⢀⠅⠀⠀⣀⠀⡀⠀⣴⠀⠀⠀⠀⠀⠀⢀⠀⠸⡂⠀⠀⡈⠀⠀⠘⠂⠀
⠀⠀⠀⡁⠐⠀⠀⡀⠀⠀⠀⠀⠀⠈⢖⠀⠀⠀⠀⢀⢠⠀⠀⠡⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⠃⠀⠆⠀⡀⠀⠀⠀⠀⠀⠰⠀⢠⡀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠐⠅⠀⠀
⠀⠀⢀⡀⠠⠄⠈⠃⠀⠘⢻⠀⠀⠢⠘⠁⠀⠁⠀⡀⠀⠀⠀⠀⠑⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢸⠀⣰⠇⣞⠀⠙⠠⠀⠃⠀⠀⠀⠠⠀⠄⠀⠀⠿⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⠀⠀⠀⠀
⠃⢠⡀⠈⠘⠀⢀⠀⠀⣀⠈⣀⠀⡀⢄⡄⠐⡀⠀⠁⣄⡌⠀⠀⠈⠀⠀⡘⢒⠖⠁⠀⠀⠀⠀⠀⡅⠀⠀⠀⠃⢰⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠥⠀⠀⠤⠖⢻⠀⠀⠀⠀⠀⠀⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠸⠀⠈⠍⠁⠀⡤⢳⠄⠈⢸⣚⣳⡄⢤⡄⠀⠀⡈⡿⠁⠀⢄⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠐⠀⠇⢰⡆⠀⠀⡟⠀⠀⠀⠀⢿⠀⠂⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⡄⠤⠀⠀⠈⢺⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀
⠠⠀⠀⠀⡀⠀⠀⠀⠀⠙⣟⡊⠔⠀⠀⠀⢓⠀⠐⣿⠃⠀⡀⠀⠀⠀⠀⠀⠘⣄⡄⠀⠀⠀⠀⠀⠀⣺⣇⠀⢸⣃⣀⣒⣂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣤⣶⣤⣠⣄⣀⣀⣤⣀⣤⣤⣀⣠⣤⣀⣤⣤⣤⣤⣤
⣀⣤⣤⢤⡀⢀⠀⠐⠀⠀⠈⠁⠑⠂⠈⠸⡆⠀⠀⢙⠀⠬⣟⣻⣿⣶⣿⠿⠸⣿⣿⣼⣿⣷⣤⣶⣤⣀⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉
⣻⣿⢿⢸⣿⣿⡦⢠⡀⠀⢀⣶⣒⣀⣸⢰⡆⢀⢌⣡⣈⣀⣩⠵⠶⣿⢿⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣽⣿⣭⣭⣭⣭⣭⣭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠰⢀⡠⣠
⠋⠧⠈⢈⣿⣟⣳⣿⣿⣧⣴⣿⣿⣿⣾⣾⣷⣧⣬⣽⣿⣿⣿⣿⣽⠏⢿⡛⠉⣫⢄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠑⢚
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠩⢽⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣠⣀⣀⠀⠀⣠⣤⣆⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⡭⠥⠤⠤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠠⠤⠄⠤⠤⠤⠨⠉⠉⠉⠭⠭⠭⠿⡿⠟⣛⠛⠛⠛⠟⠛⠻⠛⠛⠉⠉⠉⠉⢁⣿⣿⡭⠀⠀⠀⠐⠐⠆⣀⡀⡀⠀⠀⢀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠶⠶⠿⠾⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡻⠀⠀⠀⠀⠀⠂⠀⠘⠳⠡⠞⠿⠟⠿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡄⠀⠴⠆⠀⠀⢀⣴⣶⣧⣄⣀⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡷⢹⣿⣿⡛⠯⠉⠁⣹⣤⣤⣤⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 576

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Increasing_Productivity_With_Less_Hardware_Little_Power_and_Few.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Increasing_Productivity_With_Less_Hardware_Little_Power_and_Few.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Increasing Productivity With Less Hardware,
Little Power, and Fewer CPU Cycles (and Far Less Digital Waste in
General)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Winter_Seasons⦈_


THE last time I rebooted my laptop this Web site was still_running_WordPress
and it was a warm day in 2023. My wife's main laptop and my secondary laptop (I
use 4 in tandem these days) also have an uptime of about a year and they rarely
waste time by demanding that we restore sessions, reopen applications, reload
data files, reconnect to SSH etc. They're just there and they "snooze" when
we're AFK in order to lessen energy consumption. A lot of the software we use
is coded by us, for us.


A lot of people who glance at our PCs (as they visit us) act a bit baffled, as
much of what we're using is a bunch of terminals and some text editors. Many
people mistake the size (weight) of a program for "power" (associating bloat
with productivity) because they're indoctrinated to think that new and
"powerful" computers will enhance productivity, e.g. if their keyboard has an
extra key for "hey hi" (AI); they also wrongly conflate the waste of power,
e.g. chatbots in use, with "gains" (output that's produced by a bot is
typically worse than useless and 'dilutes' the actual signal of human work).


I've actually seen people buying new PCs because apparently seeing HD videos
(on a small screen) demands "better" hardware, even if the naked eye can barely
appreciate the difference and the "sound system" is just a single speaker
lodged inside some plastic laptop.


Let's get rid of this harmful notion that more bloated software is good for
anything other than revenue/sales of companies like Intel. Don't worry about
Intel; your_government_is_likely_subsiding_it_already (at your own expense),
whether by creating some facilities in your country (e.g. Germany) or just
handing_over_your_money (debt) without your consent. This whole situation isn't
pretty. Trump and Biden did the same with Microsoft [1, 2], repeatedly in fact,
and this week it looks like so-called 'defence' contracts are misused to bail
out the_struggling_"open"AI (we put links about it in Daily Links earlier
today). █




⣿⣿⣿⡀⠈⣴⣿⣿⣿⣿⣞⡃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣤⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣦⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⣤⣤⣤⣤⡄⠀⢀⣤
⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣷⡄⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⢸⣿⣿⣿⣿⡇⠀⣼⣿
⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⠃⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⣿⣿⣿⣿⠇⠐⢿⣿
⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣽⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠟⠃⠈⢿⣿⣿⣿⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠿⣿⠂⠀⠿⠿⢻⣿⠀⠀⠀⠿
⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠰⡿⠛⢿⣿⡆⠀⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣶⣤⣶⣶⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣌⠀⠀⠀⢈⠐⢩⠟⠇⠁⠀⠸⠀⠘⢻⣤⣽⣿⣶⣥⠈⠳⡀⠈⠐⠘⠣⣿⠻⡈⠘⠀⠈⠟⠼⠗⠓⢆⢀⠁⠀⠀⢸⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⠙⠈⠈⣀⡄⠈⠀⠀⡀⠀⣸⣿⣿⡟⣽⣿⡇⢸⠄⠀⠀⠀⡀⡟⠀⠁⠀⢀⠀⠀⠈⠁⠐⣿⣿⣷⣤⣄⣺⣄
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠋⠄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣧⣤⣤⣤⡄⠠⠀⠀⠐⠀⢠⢆⣰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⣄⡀⠀⠄⠀⠀⠀⠀⠁⠈⢠⢀⠾⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢿⢿⠏⢸⡏⣧⢀⠀⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⡟⢓⠂⠀⠀⡀⠃⢣⡿⡩⢿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠂⠀⠀⢠⡀⠁⠀⠁⠚⡘⣰⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢔⠺⠈⣪⡻⠛⠁⣀⠀⠀⠁⠘⣿⢿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡀⠀⠀⠀⠀⠘⢀⠠⡿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⠌⡈⠀⠀⠎⠘⠁⣀⠀⠀⠒⠁⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣤⣿⣧⣀⡄⠉⠅⣰⣰⠈⠋⠝⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⢲⠀⠀⠀⠀⠈⠀⠁⠘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡆⠀⣠⡀⠀⠀⠀⠈⢿⠈⠃⢠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣷⣿⣧⡀⢠⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣷⣶⣿⣇⣠⡀⠀⣀⠀⠀⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣧⣥⣤⣷⣶⣿⣧⣲⣴⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 659

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/IRC_Proceedings_Wednesday_December_04_2024.shtml
    Gemini version at https://techrights.org/n/2024/12/05/IRC_Proceedings_Wednesday_December_04_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Wednesday, December 04,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Snow_and_Flowers⦈_


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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The corresponding text-only bulletins for_Tux_Machines and for_Techrights
contain all the text.


                          Enter_the_IRC_channels_now




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⣿⣿⣿⣿⠟⠏⠀⠀⠀⢹⣿⣿⣿⣿⠃⠀⠀⠀⠠⢿⣿⣿⣿⣿⣶⣤⣀⣴⠙⣿⣿⣿⣮⡿⡟⠀⠀⠀⠠⠘⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠘⣿⣿⢀⣿⣟⢿⣿⣿⠀⠀⢀⣀⣀⡀⠀⣴⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⣿⣿⢸⣿⣿⡌⢿⣿⣀⣄⡀⠛⣿⣿⣶⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⣸⠿⠋⠹⠻⠂⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠠⣿⣿⣾⣿⣿⣿⡀⢻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢻⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⠇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣏⡞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⢠⣶⣶⣄⣀⣄⠀⠀⠀⠀⠀⠀⣶⣿⣿⠏⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠁⠀⠀⠀⠁⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⠀⠀⠀⠀⠐⠂⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣦⣦⣴⣶⣶⣿⣿⣿⣿⣟⢉⠱⢿⣿⣯⣿⡇⠀⠀⠀⡀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣶⡤⠬⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠠⠀⠉⡻⠟⠻⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⡶⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡅⡈⠙⢿⢿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠝⠛⠛⠋⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠔⣚⡲⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⢀⡀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 885

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Meme_Shooting_the_Messenger.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Meme_Shooting_the_Messenger.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Shooting the
Messenger⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024,
updated Dec 05, 2024


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Leonardo_DiCaprio:_Cancel_culture;_you_needn't_refute_the
                    message,_just_take_out_the_messengers⦈_


UEFI is obviously not about security but the opposite of that, so focus on
"taking out" the people who merely mention this? By stalking, harassing and
defaming them for 12+ years?




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣶⡶⣦⡀⣰⣶⣶⠀⣶⡆⣶⡆⣴⡶⣶⣄⢰⣶⣶⢰⣶⠀⠀⠀⣴⡶⣶⡄⣶⣶⣶⣶⢰⣶⢰⣶⣶⣶⢰⣶⢰⣶⢰⣶⢶⣦⠐⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡄⢠⣦⠀⠀⠀⠀⠀⢸⣷⠀⢸⣿⡇⠿⠇⣿⡿⣿⠀⣿⣿⣿⡇⣿⡇⠻⠿⢸⣿⣤⢸⣿⠀⠀⠀⣿⡇⠿⠇⣿⣿⣿⣿⢸⣿⠀⢸⣿⠀⢸⣿⢸⣿⢸⣿⣼⣿⣶⣿⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢸⣿⣇⣿⣇⣿⡷⣿⡇⣿⢹⣿⡇⣿⣇⣿⡿⢸⣿⣈⢸⣿⣀⠀⠀⣿⣇⣿⡇⣿⣿⣿⣿⢸⣿⣀⢸⣿⠀⢸⣿⣸⣿⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠛⠉⠈⠉⠁⠉⡁⠉⠀⠉⠁⠈⠙⠋⠁⠈⠉⠉⠈⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⢸⡉⠋⠈⠉⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⢾⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⠿⠟⠋⠉⠉⠁⠀⠈⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⢸⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿
⠐⢤⠀⠀⠀⠀⠀⠀⠐⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⢸⠀⢽⣿⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⠀⣽⢻⠚⢚⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢀⡀⠀⠀⢸⡸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⡆⢀⡘⡆⠀⢸⠇⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⡇⢰⣿⡄⠀⠀⠀⣠⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢼⣿⣿⣷⣶⣾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣭⠁⠸⠶⠾⣸⣿⣿⣿⣿⣿⡿⠿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⣦⣤⣀⢀⣶⣿⡿⣻⣿⣿⣿⣿⡀⠀⢸⢾⣿⣿⣿⣿⣿⡇⠐⠆⠈⢹⡇⠀⠐⠆⢀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣸⡛⣿⣿⣿⣿⡻⠀⠀⢸⡿⠉⠉⠉⠉⠉⢀⠀⠀⠀⢺⣇⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣿⣷⢶⣶⣦⣄⢀⢀⣀⣀⣀⣄⣀⣀⣠⣿⣿⣿⠿⠿⢿⣿⣿⡟⣿⣿⣿⣿⣧⡀⢐⠈⣷⡄⣤⡼⠃⠀⢀⠀⡀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢻⡎⢻⢿⣿⣷⣸⣽⣿⣿⣿⣟⠿⢹⠃⢀⠀⠀⠀⠀⠉⢿⣃⣿⣿⣿⣿⠾⣽⢼⣇⣭⣕⢿⣶⡄⠂⠊⢀⠁⠀⢸⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⢲⣺⡉⢛⣴⣿⣿⣿⠿⣿⣿⠿⠓⠦⠈⠀⢺⣄⠀⠀⠀⠀⠞⠚⢿⣿⣿⣿⠹⠏⠿⠗⣀⣬⣿⣯⣥⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠉⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣼⣿⣾⡛⣿⣿⣿⡇⠋⠉⠠⠐⠃⢤⣔⠀⠀⠀⠛⠁⠀⠀⣀⡠⠬⠩⠃⠀⠀⠈⠨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⠽⠙⠋⠀⠀⠀⠀⢰⣶⡫⡋⢳⢀⣄⣠⣤⠦⠶⠴⠟⠛⠂⠀⠀⠀⠀⢀⠄⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣶⠞⠁⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡇⣠⣷⣾⣶⣶⣿⣾⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣾⣯⣄⣙⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠟⠀⠀⣼⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣛⣛⣶⣯⣽⣤⣶⢶⣒⣲⣀⣀⣀⣀⣠⢴⣚⣿⣃⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⢹⣿⢸⣿⣿⣿⣿⢻⣿⣼⣿⢸⣿⢛⢸⣿⠻⢼⣿⣿⣷⢹⣿⣸⡇⣿⡛⣿⡟⣳⡇⣿⣏⣿⡆⣿⣟⢻⣿⡟⢻⣿⢸⣿⠙⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠛⣿⣷⣸⣿⢸⣿⢸⣿⢹⣿⢽⢸⣿⣿⣿⢸⣿⠛⢸⣿⢻⣼⣿⣿⣿⢸⡿⣿⡷⣿⡇⣿⡇⣿⠇⣿⡟⣿⡎⣿⡟⢻⣿⣟⣼⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿
⣀⣠⡤⣤⣤⣤⣴⣶⣶⣶⣿⣾⣿⣿⣿⣿⣾⣋⣞⠻⠿⠋⢻⣼⣿⣹⣿⣸⣿⣿⣸⣿⣿⣼⣿⣿⣯⣾⣇⣿⣧⣿⣷⡿⢣⡿⠁⠛⠃⠛⠃⠛⠛⣿⣿⣿⣿⠿⠾⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣭⣿⣿⣯⣭⢠⣤⣤⠀⠫⣭⣽⢻⣭⡟⣯⣭⡟⣿⣿⣿⢿⣿⣽⣿⢿⣭⣽⠿⣻⣤⣅⠂⣤⣤⡄⢀⣀⢠⣽⢿⣿⢡⣤⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⢛⣽⣿⣿⡟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣇⣿⡇⢹⣿⣽⣿⢸⣿⣤⠀⠀⣿⣿⣼⣿⡇⣿⣧⡄⣿⣿⡛⠸⣿⣜⡛⢸⡿⣿⡀⣿⣇⣛⣃⣿⣧⡉⢉⣼⢿⣿⢸⣿⢸⣿⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⢿⣿⣿⣿
⣿⣿⣿⣿⣷⠎⠀⠀⠀⠀⣿⣇⠁⣿⡇⢸⣿⣽⣿⢸⣿⣉⡀⠀⣿⢸⡿⣿⡇⣿⣏⡁⣶⣙⣿⢰⣾⢹⣷⣾⡷⣿⡇⣿⣏⣿⣿⣿⣏⣀⡀⠈⣸⣿⢸⣿⣸⣿⢹⣾⣻⣿⣿⣿⡏⣿⣻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿
⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⡿⢿⡦⠉⡥⣾⣭⣿⣽⠾⠩⠉⠁⠀⠉⠈⠁⠉⠁⠉⠉⠁⠉⠉⠉⠀⠉⠉⠁⠉⠁⠉⠙⠛⠛⠻⠿⠏⠉⠩⠃⠀⠻⢭⣿⣿⣿⣿⣿⣿⣿⣽⣯⠉⠁⣾⣿⣿⣿⠟⢵⣿⣿⣿⡏⣿⣿⣿
⣯⠷⣶⡶⢦⣶⣶⠀⣶⣆⣶⠎⣷⡶⠞⡿⣷⡶⣶⡄⣶⡇⣶⡶⢶⣶⢶⡀⠶⣶⡶⢶⣶⢰⣶⢰⣶⠶⠀⠀⣶⣶⢰⣶⡆⣶⡶⠆⣶⢶⣦⢠⣶⢾⣿⣿⣿⠿⣷⣮⣶⡆⣴⡶⣶⡌⣷⡶⠆⣶⡶⣾⣭⣶⢶⣦⠙⣿
⡏⡀⣿⡇⢸⡿⣿⡆⣿⣿⣿⠀⣿⡷⠆⠁⣿⡇⣿⡇⣿⡇⣿⣷⣸⣿⢸⣿⡄⣿⡇⢸⣿⢾⣿⢸⣿⠶⠀⠀⣿⢿⣾⣿⡇⣿⡷⠆⠻⣷⣿⣾⢿⣾⣿⣿⣿⠶⣿⣿⣿⡇⣿⡇⣭⡅⣿⡷⠆⣿⡷⣿⡉⠿⣿⣍⠀⡛
⣷⠇⣿⡇⣾⡟⣿⣇⣿⡏⣿⡆⣿⣷⡧⠀⢿⣧⣿⣇⣿⣧⣿⣿⣸⣿⣼⣿⣇⣿⡇⢸⣿⢸⣿⢸⣿⣤⠀⠀⣿⢸⡟⣿⡇⣿⣧⡄⣿⣼⣿⣹⣿⣼⣿⣿⣿⣤⣿⡏⣿⡇⢿⣧⣿⡇⣿⣧⡆⣿⡇⣿⡟⣿⣼⣿⠀⠁
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠶⠶⢤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡖⢀⣤⣾⣷⣶⣦⣶⣶⣾⣿⡶⠀⢀⣴⣶⠄⢠⢀⢳

                    ䷩ 𝚕𝚒𝚗𝚎 950

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Meme_They_Dropped_the_L_Libre_and_Law.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Meme_They_Dropped_the_L_Libre_and_Law.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] They Dropped the L (Libre and
Law)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


"SFLC, could I borrow 75% of your letters?"


        🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇SFLC,_could_I_borrow_75%_of_your_letters?⦈_


Context: SFC_(a_Splinter_Group,_Not_a_Conservancy)_Uses_'Man_and_Baby'_to_Find
or_At_Least_Look_for_Sympathy_Amid_War_on_SFLC_and_Its_Chief,_Professor_Eben
Moglen




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣠⣄⣀⣤⣄⣀⣄⡀⠀⠠⠁⠈⠃⠁⠈⢁⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⣇⡀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡘⣿⢻⣿⡟⣿⢿⢿⡟⣿⣿⣿⢛⣿⢳⣷⣦⣄⠀⢀⠀⠀⠀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣛⣛⡳⣷⡾⠋⢷⣷⡝⠹⣶⣧⣻⣿⣿⣿⣽⣿⠟⢿⢯⣤⣤⣤⣤⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⢿⣿⣿⣿⡿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣷⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣇⣿⡷⣿⣾⣿⣷⣿⣿⣿⡧⣿⣿⣇⣿⣿⣄⣾⣸⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣿⣿⣿⣿⣧⣼⣿⣿⣿⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣻⣿⣽⣿⣿⡧⣯⣷⠿⣽⡿⣭⣻⣿⣿⣿⣿⣿⢳⡿⣿⣿⢱⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⡿⣿⣿⣿⢿⣿⢹⡟⡟⣿⢿⣻⢙⣯⣿⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣷⣿⣿⣿⣿⣿⣷⢻⣿⣿⡿⠭⠩⠍⠉⠛⢿⣿⣿⣿⣦⡿⠟⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⡷⣿⢷⣿⣾⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡹⣲⣸⣛⢿⣿⢿⢿⢟⡻⣿⣾⣟⣇⣿⢿⢤⠧⢟⣛⡿⢏⣫⡩⠝⢛
⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣹⣫⣿⣧⣻⣯⣻⣼⣽⣷⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡻⣶⢯⢗⣙⠌⠭⣾⣸⣿⣾⡛⣛⠿⣏⢵⣿⡻⠀⡡⠤⠒⠂⠀⠠⠤⠶
⣿⣿⣿⡿⠿⢿⠿⠿⠿⠿⠟⠛⠛⠿⠿⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡯⢁⡾⣿⣶⡿⠻⢮⡁⠅⢸⡯⠿⣃⣝⠮⠭⠖⣵⡵⣿⡿⢿⡿⠿⠌⠛⠑⠀⠀
⣿⣿⣿⡝⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⣀⣠⡀⠀⠀⠀⠀⠀⠀⠰⣦⣶⡦⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⣙⣚⣣⣤⣚⠃⠀⠁⠈⠑⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣓⠿⣿⡿⣿⣿⣷⣶⣶⣤⣄⣠⣤⠠⠃⠀⢸⢛⡉⠷⠶⣶⣾⣿⣿⣿⣿⣿⣷⣷⣦⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢛⠉⢩⣿⣿⣴⣿⣿⣿⣿⠟⠀⠀⠀⡀⣰⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿
⣿⣽⣿⣾⡟⢶⣦⡄⣈⠉⠉⠉⠛⠛⡀⢼⢓⣶⣵⣶⡦⠀⠾⠻⢿⡿⣛⣟⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠍⠉⠉⠉⠁⠀⠀⠀⠈⠹⢿⡍⠉⠉⠉⠉⠉⠙⠛⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣦⡈⠙⢳⡿⢷⣵⣶⠖⢹⠀⡌⠩⣛⠍⠀⠀⠀⠀⠀⢀⣿⣽⣡⡽⢯⣭⣹⣿⣿⣿⣦⣩⣿⣿⣷⣄⠀⠈⠿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷⣶⣶⣤⣀⣀⡀⠀⠉⠻
⣿⣿⣿⣿⣿⣿⣷⠓⡀⡖⠽⠶⠚⣫⠙⠀⣩⠠⢖⠀⣆⣿⣿⣿⢿⡇⣿⣿⡇⡹⡏⢸⣇⣿⡿⣇⣿⢿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣠⣤⣤⣴⣶⣶⣶⣿⠂⠀⠀⠀⠀⠀⣰⣿⣦⢠⣦⡀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⠀
⣿⣿⣿⣿⣿⣟⠁⠁⠈⠉⠀⠑⡻⢋⣴⣶⣬⡀⠀⠀⣿⠈⠻⢯⣿⡗⣯⣿⣞⣷⣝⣛⣿⣿⢿⢷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣵⡖⠀⠀⠀⠠⠀⢰⣿⣿⣿⣾⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⢿⢿⣿⣿⠏⠀⠀⠃⠀⠀⠙⣿⣻⣿⣿⣶⣶⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣾⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⡟⢻⣽⡿⡇⣷⡀⠀⣙⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣃⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⢀⡀⢀⣘⣽⣟⢫⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⡿⠛⠋⠠⠀⠀⠀⠀⠀⠄⢸⣿⠁⢠⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣤⣤⠀⠂⠀⣠⣄⣀⣀⣀⡀⢧⣟⢸⣿⣿⡿⢿⡏⢿⣭⢿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⡛⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠋⠾⣿⣟⣟⢿⣿⣽⣿⢿⣿⣿⡿⣾⣿⣿⢿⡿⡿⠸⠇⠸⠧⠸⠧⢿⣿⡿⣿⣿⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣂⣴⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠉⠀⢀⣀⣀⣼⣿⣿⣿⡿⣿⡿⣿⣯⡿⡟⣷⣼⣽⠎⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠹⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⣻⣿⣿⣤⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠓⠒⠺⢿⣿⠿⢿⣽⣷⣯⣯⣾⣿⣿⣧⣾⡿⡿⣧⣬⣴⡦⣄⣄⠀⠀⠀⠀⠀⠀⣠⡤⠀⣠⡼⡽⣯⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣎⣭⣸⡿⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠇⠀⠈⢿⣯⡻⠟⠓⠛⠛⠚⠯⠼⠬⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣖⡶⣟⣇⣉⣁⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠛⢀⣩⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1000

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Microsoft_Criminals_Law_Enforcement_is_the_Real_Problem.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Microsoft_Criminals_Law_Enforcement_is_the_Real_Problem.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Criminals: Law Enforcement is the
Real Problem⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


The Register (UK) says, "Microsoft_to_FTC:_Investigate_your_own_leaks" (the
headline_has_changed)


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


We saw several more press_reports_to_the_same_effect a few times earlier this
week, basically the criminals flinging accusations at the law enforcer
(deflecting the issue and resorting to projection).


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


"The government is not trying to destroy Microsoft, it’s simply seeking to
compel Microsoft to obey the law. It’s quite revealing that Mr. Gates equates
the two."


                                                           -Government official




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⢿⠛⢽⠿⢿⠿⠿⠿⠿⠿⠿⢿⠫⠿⣿⣿⠿⢿⠿⢿⠿⠿⠿⠿⢿⠿⢹⣿⠿⢿⠩⣿⠩⠿⡿⠿⡿⠿⠹⢿⣿⠿⢿⠿⢿⠻⢽⠻⠿⡿⡿⡿⠿⠟⣿⡿⠿⡿⠿⠿⡏⠿⠿⠿⣿⠏⠽⢿⠿⢿⠿⠿⢿⣿⣿
⣿⣿⣇⣄⣆⣸⣜⣹⣸⣌⣡⣕⣨⣜⣡⣸⣏⣿⣿⣄⣸⣐⣸⣸⣸⣇⣄⣰⣜⣸⣿⣜⣼⣸⣿⣸⣸⣧⣢⣕⣪⣸⣇⣿⣐⣘⣸⣸⣘⣸⣘⣸⣇⣃⣇⣢⣇⣿⡇⣣⣇⣧⣋⣄⣍⣤⣂⣿⣇⣇⣧⣘⣼⣸⣸⣸⣿⣿
⣿⣿⡿⠟⣿⣿⢿⣿⣿⢿⣿⢿⢿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⡇⡆⣇⢅⣿⡇⡆⣅⢀⡈⡎⣐⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣈⣩⣉⣉⣿⣿⣏⣏⣻⣟⣟⣿⣏⣹⣙⡝⣝⣙⣸⣉⣍⣉⣉⣀⣍⠉⣏⣁⣏⣉⣉⣛⣉⣉⣉⣉⣛⣿⣿⢟⣙⣙⣏⢻⣻⢋⣻⣉⣻⣫⣟⣻⣉⣋⣍⣉⣍⣏⣁⣇⣉⣉⣘⣉⣉⣛⣇⣌⣉⣁⣍⣉⣉⣍⣹
⣿⣿⡿⢻⡟⢿⢛⡛⠻⠛⡟⠏⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠻⠛⠛⠻⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣿⣛⣟⣻⣻⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠻⢛⡛⢟⠛⡟⢟⣻⠻⠛⢛⣛⡟⠻⡛⣻⠻⣻⠻⡛⡛⡛⠛⡟⠻⠟⠛⢛⠻⡛⢟⣟⠻⠛⢟⠟⡛⢿⢛⠻⠛⠟⣟⠛⣟⢛⡛⠛⡟⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⠿⡟⠻⣿⡿⣿⠿⡟⡗⡿⣾⡿⢿⠿⠿⢿⢿⡿⠿⣿⣿⢻⢿⢻⠻⢿⢳⡟⠻⢿⢿⢿⡿⣿⢿⣿⠾⣿⣿⠿⡟⢻⠿⣿⢾⡿⢿⣿⠿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⢿⡿⠿⠗⠾⡿⠿⣿⠿⢿⠻⠿⣿⠿⣿⠿⠿⠿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣷⣿⣶⣷⣷⣷⣿⣶⣶⣾⣷⣷⣷⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢛⡛⠻⡛⠻⠻⢿⠛⠛⡛⠛⠛⠛⢻⠛⢛⠛⢛⠛⢻⣛⣛⠟⠛⢻⢻⠛⠻⠻⡟⠛⠛⠛⠻⡟⠛⠟⡛⠛⢻⠛⣛⠛⢻⠛⠛⣻⠛⡛⠛⢛⡟⢟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⢿⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⣿⡀⠀⠀⠀⢸⣿⣿⢇⠸⡆⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⢸⡤⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣛⣛⣛⣉⣍⣭⣭⣭⣥⢰⠀⠀⠀⠀⠀⠘⠻⡷⢸⣿⣧⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⢀⡇⢳⠀⠀⢿⢿⢿⠿⠿⠿⢯⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⢾⠀⠀⠀⢠⣇⠀⡗⠀⠻⣿⣦⠀⠀⠀⠀
⠀⠀⠸⡇⠀⠀⠀⠀⣿⣿⠀⡆⠀⠀⠀⠀⠈⠉⠈⠁⠈⢿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⢼⣄⡀⠀⢸⣏⠃⠀⠀⢀⣬⣬⣷⡄⠀⠀
⠀⠀⠀⠈⠢⠀⠀⠀⣿⣿⡀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⣿⣀⣼⣿⣦⣶⣦⣼⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣀⠀⢸⣿⣿⣿⠟⢉⣿⡟⠛⠍⢸⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠘⡇⣿⣿⠋⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⢸⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⣤⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⠀⠀⡇⣿⣿⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠙⢛⣿⣿⣿⣿⣿⣿⣷⣦⣾⡟⠀⣼⣿⣿⣿⣿⡆⣻⡟⣿⣿⣿⣿⡇⣘⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡇⠀⢻⠀⠀⡇⣿⣿⣧⡀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠏⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠹⡇⠀⢸⣿⣿⣿⣿⣿⣶⣶⣲⣾⠇⠀⠰⢤⣿⣿⣿⡇⢿⣧⣿⣿⣏⣼⣷⣿⡾⣷⣿⣿⢿⣿⣿⣿⡗⣾⢻⣿⣍⣿⣿⡟⡟⠂⠀⡇⠀⢸⠀⠀⡇⣿⡁⢸⣧⠀⠀⠀⠀⠘⠻⣿⡟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣼⣿⣿⣌⡙⠻⠿⠿⠟⠃⣀⠀⠀⠀⠙⣿⠿⣿⣞⣻⣟⠻⣻⣿⠿⠟⣃⣿⣾⡿⣿⢿⡟⣿⣿⣯⣸⣷⣿⣿⣿⠁⠀⠀⠀⠆⠀⢸⠀⠀⠃⢸⠂⢠⣿⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣲⣖⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⠳⣤⣹⣼⠇⣾⢻⡎⣾⣿⣿⠈⢡⣤⡖⣞⣛⣿⣟⡛⠛⠃⠉⠈⠁⠙⠙⠋⠛⢓⣺⣿⣿⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⢘⣀⣸⣿⣿⣦⣀⣀⣀⠄⠀⠀⠀⠀⠀
⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣯⣲⣿⣼⡇⣿⢸⡏⠀⣼⣧⢠⣿⣼⡿⣿⣿⣾⣿⣷⢰⡶⣶⢀⣴⣤⡘⣿⢛⣛⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣳⡻⢿⢿⣿⣿⣿⣿⣿⠖⣄⠈⢿⣿⣯⣽⣶⣿⡛⠁⠀⠿⠿⠹⠏⣿⢻⣿⢿⣿⣿⣿⣿⣿⣯⢸⡏⣛⢣⣿⢾⣿⣿⢠⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⡽⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⡿⣾⡦⡉⠉⠉⠉⠁⣺⣿⣧⡈⣿⣿⣿⣯⣯⣡⡄⣤⣤⠀⢀⣀⣿⣿⣶⣿⣾⣭⣿⣿⣿⣿⣞⡷⠟⠸⠿⢼⢿⣿⢸⣇⣿⠀⢀⠄⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣼⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣧⣿⡄⠀⢸⡏⣿⣿⣿⣿⣷⣾⣎⣿⢽⡿⣿⣆⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣿⣁⣿⢘⡋⣿⠐⠂⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣯⣽⣿⣿⠋⣻⣺⣿⣿⡏⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢙⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠴⠾⣿⣿⣿⡄⠀⠀⠀⣤⡄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⢸⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠠⣤⣴⣾⣿⡇⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⡿⢡⣿⣿⢅⡞⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⢲⣒⣫⣿⣷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⡇⢾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⣉⣹⠿⣿⣿⠀⠀⠐⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠙⢛⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣿⠁⠈⢻⣿⣿⣿⡟⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣹⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⠀⠀⠀⣿⣿⣿⣏⣀⣀⣸⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠀⢈⣿⣿⣿⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠠⣽⣿⣿⠋⠉⠉⠙⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⠿⢿⣿⣧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢐⣾⣿⣿⠀⣀⡀⠀⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⣀⣾⣿⣾⣏⡻⠛⣿⣿⣿
⣿⡿⣿⣿⣿⣦⡀⢰⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣼⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⣤⣤⣤⣤⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⡿⠿⠛⠢⢤⣽⣿
⣿⣛⣛⢟⣿⣿⣷⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣍⡉⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠉⠭⠽⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣴⣿⣿
⠘⠛⠻⠿⣿⢿⠟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠿⣠⣄⠀⢠⢿⣿⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠀⠀⣿⠀⠀⠀⠀⢿⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⣿⠀⠀⠀⠀⢸⣿⣿⢇⠸⡆⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠰⡤⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡛⣛⣛⣛⣉⣍⣭⣭⣥⣥⢰⠀⠀⠀⠀⠀⠘⢻⡷⠸⣿⣧⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⢀⡇⢳⠀⠀⢿⠿⢿⠿⠿⠿⢿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣸⢾⠀⠀⠀⢠⣇⠈⡗⠀⠻⢿⣦⠀⠀⠀⠀
⠀⠀⠸⡇⠀⠀⠀⠀⣿⣿⠀⡆⠀⠀⠀⠀⠈⠉⠀⠁⠘⢾⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣼⣄⡀⠀⢸⣏⠋⠀⠀⢠⣄⣄⣵⡄⠀⠀
⠀⠀⠀⠈⠢⠀⠀⠀⣿⣿⡀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⣿⡀⣼⣿⣦⣶⣦⣼⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⣿⣿⣿⡏⢹⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⠀⢼⣿⣿⣿⠟⢉⣻⡟⠋⠅⢸⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⡇⠀⠐⡇⣿⣿⠃⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⢘⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⣤⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⠀⠀⡇⣿⣿⡀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠙⢛⣿⣿⣿⣿⣿⣿⣷⣦⣾⡟⠀⣼⣿⣿⣿⣿⡆⣿⡟⣿⣿⣿⣿⡇⣘⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠯⡇⠀⢻⠀⠀⡇⣿⡿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠹⡇⠈⢸⣿⣿⣿⣿⣿⣶⣶⣲⣾⠇⠀⠰⢤⣿⣿⣿⣇⢿⣧⣿⣿⣏⣼⣷⣿⡾⣷⣿⣿⣿⣿⣿⣿⡗⣾⢻⣿⣍⣿⣿⡟⡟⠁⠀⡇⠀⢸⠀⠀⡇⢿⠀⠸⣧⠀⠀⠀⠀⠈⠻⣿⡟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣼⣿⣿⣎⠙⠻⠿⠿⠟⠃⣀⠀⠀⠀⢙⣿⠿⣿⣞⣻⣟⠻⣻⣿⠿⠟⣃⣿⣾⡿⣿⢿⡗⣿⣿⣯⢼⣷⣿⣿⣿⠀⡀⠀⠀⠆⠀⢸⠀⠀⠃⢸⠂⢠⣿⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣲⣖⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⠳⣤⣹⣼⠇⣾⢻⡎⣾⣿⣿⠈⢠⣤⡖⣞⣛⣿⣟⡛⠛⠃⠉⠈⠁⠙⠙⠃⠛⢓⣺⣿⣿⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⢸⣀⢸⣿⣿⣦⣀⣀⣠⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣯⣲⣿⣼⡇⣿⢸⡏⠀⣼⣧⢠⣿⣼⡿⣿⣿⣾⣿⣷⢰⡶⣶⢀⣴⣤⡘⣿⢛⣛⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣻⠿⢿⣿⣿⣿⣿⣿⠖⣄⠈⢿⣿⣯⣽⣶⣿⡟⠁⠀⠿⠿⠹⠏⣿⢻⣿⢿⣿⣿⣿⣿⣿⣯⢸⡇⣛⢣⣿⢾⣿⣾⢠⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠽⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠼⣻⣿⢦⡈⠉⠉⠉⠁⣴⠿⣧⡈⣿⣿⣿⣯⣯⣡⡄⣤⣤⠀⢀⣀⣿⣿⣶⣿⣾⣭⣿⣿⣿⣿⣞⡷⠟⠸⠿⢼⢿⣿⢸⣇⣿⠀⢀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣥⣶⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣧⣿⡄⠀⢸⡏⣿⣿⣿⣿⣷⣾⡎⣿⢽⡿⣿⣆⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⣟⣬⣵⣿⣿⣁⣿⢘⡋⣿⠐⠂⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣯⣽⣽⣿⠋⣻⣺⣿⣿⡏⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢹⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠼⠿⣿⣿⣿⡄⠀⠀⠀⣤⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⢸⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠠⣤⣴⣾⣿⡇⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⡿⢡⣿⣿⢅⡎⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⢲⣒⣫⣿⣷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⡇⢾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⣉⣙⠿⣿⡿⠀⠀⠠⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠙⣛⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣿⠁⠈⢻⣿⣿⣿⡏⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣹⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣇⣀⣀⣸⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠀⠘⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠀⠀⠀⣽⣿⣿⠋⠉⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⡿⢿⣿⣧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⡇⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢐⣶⣿⣿⠀⣀⠀⠀⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⣁⣾⣿⣿⣟⣻⠛⣿⣿⣿
⣿⡿⣿⣿⣿⣦⡀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣼⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣤⣤⣤⣬⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢻⣿⣿⡿⠿⠛⠳⢤⣽⣿
⣿⣛⣛⣿⣿⣿⣷⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣍⠉⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠉⠭⠽⠭⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣻⡇⠀⠀⣀⣴⣿⣿
⠈⠛⠻⠿⣿⣿⠟⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⣦⣄⠀⢠⢿⣿⢀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠈⣿⠀⠀⠀⠀⣿⣿⣿⡇⢳⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⢻⣿⡿⠁⢸⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡀⠀⠀⠀⢸⣿⣿⢰⣈⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⠿⠿⠿⠟⠛⡛⣛⣒⣛⣋⢡⠀⠀⠀⠀⠐⠼⢿⡆⢺⣷⡄⠀⠀⠀⠀⠀
⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠈⡇⣇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣸⠄⠀⠀⠀⣰⠂⢸⡇⠐⠿⣷⡄⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠘⣿⣿⠀⡅⠀⠁⠀⠀⠀⠈⠉⠀⠀⢾⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢠⡀⠀⠀⣿⡇⠄⠀⠀⢀⣨⣡⣠⠀⠀⠀
⠀⠀⠀⠙⢀⠀⠀⠀⣿⣿⠀⠁⠀⠀⣤⣶⣦⣦⣤⣤⣤⣬⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⢸⣿⣇⠀⣿⣷⣠⣦⣄⣸⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⡟⢹⣿⣿⣿⣾⣿⣿⡮⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⢰⣿⣿⣿⠿⠝⢻⣿⠟⣛⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣇⣿⣿⣿⡇⠈⡏⠉⢸⣺⣿⡏⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⣷⡼⣿⣿⣿⣷⣶⣿⣿⣶⣦⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣀⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠸⠋⣿⡇⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠹⠿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠀⣽⣿⣿⣿⣿⡄⣶⡿⣿⣿⣿⣿⡇⣜⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⠟⣛⠀⠀⣇⠀⠀⠀⣿⡗⣄⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡇⠠⠀⣿⣿⣿⣿⣿⣭⣭⣭⣭⡟⠀⠠⣭⣿⣿⣿⡇⣿⣿⣿⣿⡏⣹⣷⣿⡼⣷⣿⣿⢿⣿⣿⣿⡗⣾⢻⣿⡍⣿⣿⡿⡇⠀⢰⠀⠀⣿⠀⠀⡀⡟⠁⢹⡆⠀⠀⠀⠀⠘⠏⠧⠙⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⣤⣿⣿⡍⠛⠿⠿⠿⠿⠟⡀⠀⠀⠈⠻⣿⢿⣿⣜⣿⣟⠿⢿⣿⣿⠟⠇⣿⣾⡿⣿⢿⡟⣿⣿⣯⢺⣷⣿⣿⣿⠁⠃⠀⠐⠀⠀⢨⠀⠀⠃⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣄⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⣠⠦⣄⢹⣼⠇⣾⢻⡎⣶⢿⣿⠉⢩⣭⡍⣝⢛⣿⣟⡷⠿⠓⠛⠊⠁⠛⠙⠃⠛⢓⣺⣿⣿⠀⠂⠀⠀⠀⠀⠸⠀⠀⠀⠟⠀⢸⣿⣷⣄⣀⠀⣠⠂⠀⠀⠀⠀⠀
⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢹⣯⣰⣿⣼⡇⣿⢸⡏⠀⣼⣧⢠⣿⣼⡿⣿⣿⣼⣟⣷⢰⡶⣶⢀⣴⢦⡸⣿⢛⣛⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⣝⡿⣿⣿⣿⣿⣿⣿⡇⠤⠈⢻⣿⣯⣽⣤⣿⡛⠁⠀⠿⠷⠹⠏⣿⢿⣿⣷⣿⣿⣿⣾⣟⣯⢸⡇⣛⢣⣿⢾⣿⣼⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡿⢷⣤⡉⠛⠛⠛⠋⣴⣾⣧⡈⣿⣿⣿⣯⣿⣡⡄⣤⣤⠀⢀⣀⣶⡶⣶⣶⣮⣭⣿⣿⣿⣿⡜⠷⠟⠸⣿⢼⣿⣿⢸⣇⣿⠁⠀⠄⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣿⣿⣶⣴⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡟⣿⣿⣿⣿⣷⣾⡎⣿⢹⡿⣿⢀⣤⣄⠀⣀⡀⠁⠀⠉⠈⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⡟⣭⣵⣿⣮⣁⣿⢘⡋⣿⠠⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢾⣷⣿⣯⣽⣽⣿⢛⣻⣺⣿⣿⡏⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡻⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⠘⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠀⢭⣿⣿⣿⣷⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡛⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⢠⣀⣭⣽⣿⡇⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠸⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⣿⢃⣿⣿⠛⡼⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣃⠀⠀⢬⠽⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⡏⣴⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢛⣻⣿⣿⡿⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣤⣥⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⣿⡀⠈⠻⠿⣶⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣌⡛⠁⠐⠻⣿⣷⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣚⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣛⠛⠿⠃⠀⠀⠘⣿⣿⣿⡇⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠾⠿⠧⠀⠀⢀⣹⣿⣿⠏⠛⠋⠉⢛⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⡿⢻⣿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⣿⡇⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠠⣽⢿⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⣉⣩⣷⣾⣿⠛⠿⢿⣿⣿⣿
⣻⣿⣿⣿⣿⣦⠀⣶⣿⣽⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣼⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⢋⡈⣉⣀⣀⣈⣄⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠷⣄⣉⣿⣿
⣛⣛⣻⠻⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⠛⠛⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣯⠀⠀⠀⣀⣽⣿⣿
⠘⠛⠻⢿⣿⡿⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡦⣀⡀⠀⢠⢿⡟⠀⠀⠀⠀⠀⠀⣴⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿
⠋⠀⣿⡀⠀⠀⠀⢸⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⣿⡇⠀⠀⠀⢸⣿⣿⡇⠘⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⡇⠀⠀⠀⢸⣿⣿⠠⣄⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠉⠻⠿⠓⠀⠀⠀⠀⠠⠰⢿⡆⢰⣦⡄⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⡀⡇⢱⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣶⣶⣶⣶⣾⣾⣿⣟⣟⢹⡀⠀⠀⠀⢠⡄⢸⡇⠈⣿⣷⡀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⡈⠈⠀⠀⠉⠑⠂⠂⠀⠐⠦⣦⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣁⡀⠀⠀⣾⡇⡈⠁⠀⠀⠙⠋⢀⠀⠀⠀
⠀⠀⠀⠙⠀⠀⠀⠀⣿⣿⡆⡇⠀⠀⢀⣤⣤⣤⣤⣄⣤⣀⣙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢸⣿⣷⣆⠀⣿⣧⢀⣄⡀⣰⣿⣿⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠁⠀⠀⢻⣿⡇⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣷⣶⣾⡟⣿⣿⣸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣼⣿⣿⣿⣟⠻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣼⣿⣿⡏⣿⣿⣯⡇⠈⡟⠛⢻⡇⣿⡟⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡏⢨⡷⣆⢿⣿⣿⣶⣶⣾⣿⣧⣤⡍⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⡇⠀⠀⡇⣿⣇⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠿⡿⣿⣿⣿⣿⣿⣿⣏⣋⣿⡇⣹⣿⣿⣿⣿⡇⢰⡖⣶⣿⣿⣿⡇⣘⢛⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⡧⣿⣿⣿⣿⣿⢿⠯⠁⠀⣸⠀⠀⡇⣿⣏⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢺⣿⣿⣿⣿⣿⣯⣍⣉⣻⠃⢉⣙⣿⣿⣿⡇⢸⣿⣿⣿⡟⣹⣷⣿⡾⣷⣿⣿⣿⣿⣿⣿⡗⣿⢻⣿⡍⣿⣿⡟⡇⠐⠁⡄⠀⢺⠀⠀⡇⣿⠋⢱⡄⠀⠀⠀⠀⠘⡟⡻⡻⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣼⣿⣏⠛⠿⣿⣿⣿⡿⣃⠀⠀⠈⠻⣿⣿⣿⣼⣿⣽⢿⣿⣿⣿⠟⡇⣿⣾⡿⣿⢿⡗⣿⣿⣯⢼⣷⣿⣿⣿⠃⠃⠀⠀⡁⠀⢸⠀⠀⡇⢹⠀⢸⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⣦⣀⣀⡠⣄⣹⣼⠇⣾⢻⡎⣶⣿⣿⡘⢩⣴⡞⣟⢟⣳⣶⡶⠿⠷⠿⠮⠥⠽⠹⠇⠛⢳⣺⣿⣿⠀⠂⠀⠀⡀⠀⢸⠀⠀⠀⠸⠀⢸⣿⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣯⣤⣿⣼⡇⣿⢸⡟⠀⣼⡧⢀⣿⣼⡿⣿⣿⣼⣟⣷⢰⡶⣶⢀⣴⢦⡸⣿⢛⣛⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣚⣻⣿⣿⣿⣿⣿⣿⣷⢀⠈⢹⣿⣯⣽⣤⣿⡟⠁⠀⠿⠷⠸⠏⣿⢻⣿⣷⣿⣿⣿⣾⣟⣯⢸⡇⣛⢣⣿⢸⣿⣼⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣷⣦⠉⠛⠛⠛⠛⠁⣼⣷⠀⢻⣿⣿⣯⣿⣡⡄⣤⣄⠀⢀⣀⣴⠴⣦⣯⣭⣭⣿⣿⣿⣿⡜⠷⠟⠸⡿⢼⢿⣿⢸⣇⣿⠂⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣽⣿⣦⣤⣤⣦⣼⣿⣿⣧⣼⣿⣿⢿⡿⣿⣇⣿⡄⠀⢸⡏⣿⣿⣿⣿⣷⣾⣞⣿⢹⡿⣷⢄⣤⣄⠉⣉⡉⠁⠀⠉⠈⠀⠂⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣮⣁⣿⢘⡋⣿⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣯⣭⣽⣿⠛⣻⣺⣿⣿⡍⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣙⠿⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠙⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⣛⣿⣿⣿⣧⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⠏⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⢀⠉⣛⣛⣿⡇⠀⠀⠰⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⣿⠏⣿⣿⠿⢰⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢇⠀⠈⣙⣻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⡿⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠼⢶⣿⣿⣷⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣇⣈⣽⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⠀⠐⢿⣯⣭⣿⡇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠯⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣮⡙⠛⠃⠀⡶⣶⣯⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠴⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⠿⠿⠇⠀⠀⠰⣿⣿⣿⡆⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣿⣿⣁⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⢶⣶⣦⠀⠀⠀⠿⣿⣿⠗⠒⠒⠚⠟⠃⠀⠀⠄⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⠿⢙⣿⡇⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠂⠀⠀⠀⢈⣛⣿⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⠛⣻⣭⣹⣿⣿⣿⣿⣿⣿⣿
⢿⣛⣿⣿⣽⣦⠀⣶⣷⣬⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣼⣿⣁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⠇⠐⠂⠀⠀⢸⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣷⢢⡈⠛⢿⣿⣿
⢏⣉⣙⣛⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⠿⠟⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠻⠩⠝⠿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣜⣿⣿⠋⠉⠀⠉⢛⣿⣿⣿
⠈⠛⠻⢿⡿⠿⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣶⡄⠀⠀⠀⢀⣿⡗⠀⠀⠀⠀⠀⢀⣰⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣴⣾⣿⣿⣿⣿
⠋⠀⣿⡀⠀⠀⠀⢸⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⣿⡇⠀⠀⠀⢸⣿⣿⠇⠘⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⡇⠀⠀⠀⢸⣿⣿⠀⣄⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠉⠻⠿⠓⠀⠀⠀⠀⠀⠰⢻⡆⢰⣦⡄⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⠀⡇⢱⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣶⣶⣶⣶⣾⣾⣿⣟⣟⢸⡂⠀⠀⠀⢀⡄⢸⡇⠈⢿⣷⡀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⡌⠈⠀⠀⠉⠉⠂⠂⠀⠐⠲⣦⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢁⠀⠀⠀⣼⡇⡈⠁⠀⠀⠙⠛⢀⠀⠀⠀
⠀⠀⠀⠙⠀⠀⠀⠀⣿⣿⡆⡇⠀⠀⢀⣤⣤⣤⣤⣤⣠⣀⣙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢸⣿⣷⣆⠀⣿⣧⢀⣄⡀⢸⣷⣾⣿⣧⣀⣀
⠀⠀⠀⠀⠀⠐⠀⠀⢻⣿⡇⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣷⣶⣾⡇⣿⣿⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣼⣿⣿⣿⣟⠻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡏⣿⣿⣟⡇⠘⡟⠛⢛⡇⣿⡟⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢨⡷⣆⢿⣿⣿⣶⣶⣾⣿⣧⣤⡍⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⢇⠀⠀⡇⣿⡇⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠿⡿⣿⣿⣿⣿⣿⣿⣋⣉⣿⡇⣹⣿⣿⣿⣿⡇⢰⡖⣾⣿⣿⣿⡇⣘⢛⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⢿⡇⠅⠀⢸⠀⠀⡇⣿⡗⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢺⣿⣿⣿⣿⣿⣯⣍⣉⣿⠃⢉⣉⣿⣿⣿⡇⢸⣿⣿⣿⡟⣹⣷⣿⡾⣷⣿⣿⣿⣿⣿⣿⡗⣿⢻⣿⡍⣿⣿⡟⡏⠈⠀⡀⠀⢻⠀⠀⡇⣿⠁⢰⡄⠀⠀⠀⠀⠘⡛⣻⠻⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣼⣿⣏⠛⠿⣿⣿⣿⡿⣃⠀⠀⠈⠻⣿⣿⣿⣼⣻⣽⢿⣿⣿⣿⠟⡇⣿⣾⡿⣿⢿⡇⣿⣿⣯⢼⣷⣿⣿⣿⠂⠃⠀⠈⡀⠀⢸⠀⠀⡇⢻⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⣦⣀⣀⡠⣄⢹⣼⠇⣾⢻⡆⣶⣿⣿⠘⢩⣴⡞⣟⢟⣳⣶⡶⠿⠷⠿⠮⠥⠽⠹⠇⠛⢻⣺⣿⣿⠀⠂⠀⠀⡀⠀⢸⠀⠀⠀⠸⠀⢸⣿⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣯⣤⣿⣼⡇⣿⢸⡟⠀⣼⡧⢀⣿⣼⡟⣿⣯⣼⣟⣷⢰⡶⣶⢀⣴⢦⡸⣿⢛⣛⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⢚⣻⣿⣿⣿⣿⣿⣿⣷⠀⠈⢹⣿⣯⣽⣤⣿⡿⠁⠀⠿⠷⠸⠏⣿⢻⣿⣷⣿⣿⣿⣾⣟⣯⢸⡇⣛⢣⣿⢼⣿⣼⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⡼⢅⣦⠉⠛⠛⠛⠛⢁⡀⣧⠀⢻⣿⣿⣯⣿⣡⡄⣤⣄⠀⢀⣀⣴⠴⣦⣯⣭⣭⣿⣿⣿⣿⡜⠷⠟⠸⡿⢼⢿⣿⢸⣇⣿⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣼⢠⣦⣤⣴⣤⣽⣽⣿⣷⣼⣿⣿⢿⡿⣿⣇⣿⡄⠀⢸⡏⣿⣿⣿⣿⣷⣾⣞⣿⢹⡿⣷⢄⣤⣄⠉⣉⡉⠁⠀⠉⠈⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⡟⣭⣵⣿⣮⣁⣿⢘⡋⣿⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣯⣭⣽⣿⠛⣻⣺⣿⣿⡍⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣙⠿⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠙⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⣛⣿⣿⣿⣧⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⠏⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢀⠉⣛⣛⣿⡇⠀⠀⠰⠿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⠀⠀⠀⠈⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⣿⠏⣿⣿⠿⢰⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢇⠀⠈⣙⣻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⡿⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠼⢶⣿⣿⣷⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣶⣦⣤⣄⣀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣇⣈⣽⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⣿⠀⠐⢿⣯⣭⣿⡇⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠯⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣮⣙⠛⠃⠀⢴⣶⣯⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠿⠿⠇⠀⠀⠰⣿⣿⣿⡆⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⣁⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⢶⣿⣆⠀⠀⠀⠿⣿⣿⠗⠲⠒⠚⠟⠃⠀⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⠘⢝⣿⡇⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠈⠀⠀⠀⢈⣛⣿⡟⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠛⠛⣻⣭⣹⣿⢿⣿⣿⣿⣿⣿
⣛⣛⣿⣿⣽⣦⠀⣶⣷⣬⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣼⣿⣁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⠇⠐⠂⠀⢀⢸⡀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿⣷⢤⡈⠛⢿⣿⣿
⢍⣉⣉⣛⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⣿⣿⠿⠟⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠻⠿⠽⠿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⣿⠋⠉⠀⠉⢛⣿⣿⣿
⠈⠛⠻⢿⡿⠿⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡄⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⢀⣴⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣧⣤⣤⣶⣿⣿⣿⣿
⠀⠀⠈⣿⠀⠀⠀⠀⣿⣿⡟⡄⢷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⢿⣿⡇⠃⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇⢸⠼⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠏⢀⠛⠛⡀⠀⠀⠀⠀⠀⠛⣷⠐⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣗⠘⠆⠇⠀⠸⠿⠿⠿⣿⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣟⡛⣻⠀⠀⠀⢀⡆⠀⡷⠀⠻⢿⣄⠀⠀⠀⠀
⠀⠀⠀⢻⡄⠀⠀⠀⢸⣿⣷⠠⡄⠀⠀⠀⠀⠈⠀⠀⠈⠀⠺⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⢸⡇⠀⠁⠀⠀⠈⠁⢠⡀⠀⠀
⠀⠀⠀⠀⠈⠂⠀⠀⠸⣿⣿⠀⠁⠀⠀⣴⣶⣶⣶⣶⣶⣦⣤⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⢹⣷⠀⣼⣿⣄⣴⣄⣰⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣾⣿⢸⣿⡦⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⡇⡀⢀⣿⣿⣿⠿⠍⢻⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⠀⠙⠉⠉⢹⢸⡏⠉⠀⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣷⣶⣸⣿⣿⣿⣿⣿⠁⢀⡀⣀⣀⣠⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠀⠘⡄⠀⢸⢸⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⣿⣿⣿⣿⣿⣿⣯⣤⣭⣿⢠⣿⣿⣿⣿⣿⢰⡞⣿⣿⣿⣿⡟⣇⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⠟⡿⠅⠀⢀⡇⠀⢸⢸⣿⡄⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣬⡟⠀⠤⣼⣿⣿⣿⣺⣷⣿⣿⣿⣹⣷⣿⣼⣷⣿⣿⢿⣿⡿⣿⡗⣾⢻⡿⡍⣿⣿⣿⢽⠀⠁⡦⠀⠘⡇⠀⢸⢸⠋⠁⡄⠀⠀⠀⠀⠈⠋⠝⠝⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣤⣶⣿⣿⣆⡉⠻⠿⠿⠿⣏⠀⠀⠀⢉⢹⡿⢿⣿⣛⣽⡿⠻⣿⢿⠿⠹⣿⣾⡿⣿⢿⡟⣿⣿⣯⢸⡷⣿⣿⣿⡏⠈⠀⠀⠀⠀⠀⡇⠀⠸⢘⡇⠀⣇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢄⣴⠲⢿⣼⠇⣾⢻⡎⣾⣿⣿⠧⢠⣬⡍⣟⢟⡻⣿⡗⠛⠓⠛⠊⠁⠛⠙⠃⠛⠓⣺⣿⣿⡇⠘⠀⠀⠠⠀⠀⡇⠀⠀⠘⠃⠀⣿⣷⣄⣀⡀⢀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⡹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣯⣷⣿⣼⡇⣿⢸⡟⠃⣸⣧⢠⣿⣼⡇⣿⣿⣼⣿⣷⢰⡶⣶⢀⣴⢦⡀⣿⢛⣛⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⣍⠟⢿⣿⣿⣿⣿⣿⠖⣨⠁⢿⣿⣭⣷⣿⣻⠃⠀⠿⠿⠸⠏⣿⢰⣿⣷⣿⣻⣿⣿⣿⣯⢸⡇⣛⢃⣿⢼⣿⣿⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆⠈⠉⠉⠉⠁⣺⣿⣧⡈⣿⣿⣯⣿⣩⡄⣤⣄⠀⢀⣀⢰⡷⣶⣾⣾⣭⡿⣿⣿⣿⣿⠷⠟⠸⢿⢼⢿⣿⢸⣇⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣯⣴⣤⣬⣬⣴⣾⣿⣿⣷⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡇⢸⣿⣿⣿⣷⣾⣏⣿⢹⡿⣿⣏⣤⣄⠈⣁⡉⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣿⡸⠿⠄⠀⣼⣧⢸⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣅⣿⢘⡋⣿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⣷⣿⣯⣭⣿⣿⡇⣻⣺⣿⣿⣿⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢾⣍⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠨⣽⣿⣿⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⡟⢸⠄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⣄⣨⣭⣿⣿⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⢽⣿⣿⣿⣧⣭⣿⣧⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣤⣿⠏⣼⣿⡟⢃⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣹⠀⠀⠬⠭⢟⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⢡⣾⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢘⣛⣿⣿⣿⠀⠀⠀⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀
⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠻⡟⢿⣿⣿⡇⠀⠙⠿⢶⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣦⡄⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣿⣦⣉⠁⠀⠺⣿⣿⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣐⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠛⠀⠀⠈⢿⣿⣿⡗⠀⠀⢰⣾⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⠀⠀⠀⠙⣿⣿⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⠠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡯⠀⠀⠀⣛⣿⣿⡏⠛⠛⠛⠛⠃⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣄⠀⢈⣏⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⣿⡏⣺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⣬⣿⢿⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠛⠋⣿⣭⣽⠿⣿⣿⣿⣿⣿⣿⣿
⡺⠶⢿⡿⣿⣿⣦⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⣿⣧⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢛⠟⡈⢉⣁⣀⣈⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡦⢤⡈⠛⣿⣿⣿⣿
⠉⠚⠿⣾⣿⣿⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⡛⠛⠁⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⣛⣻⣛⢛⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣿⣿⣟⠉⠁⠀⠉⣻⣿⣿⣿⣿
⠀⢿⣿⡿⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣀⠀⠀⢠⣿⣿⢃⡀⠀⠀⠀⢠⣴⣷⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠠⠀⣿⠀⠀⠀⠀⢻⣿⣿⡇⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣟⢀⢸⡄⠀⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣦⠀⠀⠀⠀⠀⢀⢿⡀⢀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡆⠀⠀⠀⢸⣿⣿⠸⡖⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠛⡛⢛⢛⣛⣙⣋⣀⣍⣉⢀⠀⠀⠀⠀⠈⢹⡗⠸⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⢻⡇⠀⠀⠀⢸⣿⣿⠀⠃⠓⠀⠘⠛⠛⠻⠟⠛⠛⣛⡓⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⠀⠀⠀⢰⡇⠸⡇⠀⠙⠿⣦⠀⠀⠀⠀
⠀⠀⠀⠘⠧⠀⠀⠀⠸⣿⣿⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢠⡀⠀⣾⣇⠁⠀⠀⢀⣠⣨⣤⡄⠀⠀
⠀⠀⠀⠀⠀⠐⠄⠀⠀⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢸⢸⣷⠀⣿⣿⣴⣷⣤⣼⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡆⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⢸⣿⡎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣒⣤⢸⣿⣿⣿⣛⣁⣽⣿⡋⠉⢻⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣧⣿⣿⣿⠃⠀⡄⠀⢸⢸⣏⠁⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⠿⢿⣿⠸⣿⣿⣿⣿⣿⠀⣠⣤⣤⣤⣴⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⢸⢸⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣾⣿⣿⣿⣿⡿⠿⠷⠾⣿⠰⠿⢿⣿⣿⣿⣴⡞⣿⣿⣿⣿⡟⣇⢘⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⠙⢸⠀⠀⡇⠀⢘⢸⣿⠆⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⣿⣿⠿⣿⣿⣿⣿⣥⣾⠃⠀⠒⣾⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣾⣷⣿⣿⢿⣿⡿⣿⡗⣾⢻⣿⣍⡟⣿⣿⠹⠅⠀⢸⠀⠀⡇⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠈⠫⡌⠉⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣬⣴⣾⣿⣿⣿⣧⣄⠉⠛⠛⡛⣁⠀⠀⠀⠀⣹⣛⣻⣿⣟⣝⠿⡛⠿⠻⠿⣐⣿⣺⡿⣿⢿⡇⣿⣿⣯⢸⡷⣾⣿⣿⡇⢀⠀⠀⠸⠀⠀⡇⠀⠘⠀⣯⠀⣠⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⠙⢻⣼⠇⣾⢻⡆⣶⣿⣿⡛⢨⣤⡄⣝⢛⡇⣿⣯⠙⠃⠋⠈⠁⠙⠙⠃⠛⠓⣺⣿⣿⡇⠈⠀⠀⠐⠀⠀⠇⠀⠀⠀⠃⠀⣿⣷⣦⣤⣄⠄⠀⠀⠀⠀⠀⠀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡝⢿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡿⣷⣿⣼⡇⣿⢸⡟⠃⢸⣧⢠⣿⣼⡇⣿⣿⣾⣿⣷⣰⡶⣶⢀⣴⣤⡀⣿⢛⣛⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣶⣍⠛⠿⣿⣿⣿⠟⢉⣾⡅⢻⣿⣽⣿⣿⣿⠁⠀⠿⠷⠸⠇⣿⢰⣿⢳⣿⣻⣿⣿⣿⣯⣸⡇⣛⢣⣿⢾⣿⣿⢠⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣯⣷⣤⡀⣀⣀⣠⣿⣿⣷⢈⣿⣿⣯⣿⣱⡆⣤⣄⠀⢀⣀⢸⡷⣶⣿⣿⣯⣟⣿⣿⣿⣿⡷⠟⠸⠿⢼⢿⣿⢸⣇⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢻⣿⣿⣿⣿⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡇⠸⣿⣿⣿⣷⣿⣟⣿⢩⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣇⣿⡸⠿⠄⠀⣼⣧⢸⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡻⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡧⠀⠀⠀⠀⠈⣷⣿⣯⣭⣿⣿⡋⢻⣸⣿⣿⣿⡁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇⠐⠶⢿⣿⣿⣧⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣔⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⡸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠦⣴⣶⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⣬⣿⣧⣤⣤⢨⣭⣭⣭⣭⣬⣭⣭⣼⣿⠃⣿⣿⡇⣡⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣼⠄⠀⢐⣖⣫⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⠐⠿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⣨⣭⠿⣿⣿⠃⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀
⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣟⡛⠿⣿⡇⠀⢈⣛⣻⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣍⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⠂⠀⠙⣽⣿⣿⣟⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣬⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣉⣉⡉⠀⠀⠀⢹⣿⣿⣟⣀⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⢘⣿⣿⣷⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣿⣿⢐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⡛⠛⠀⠀⠀⢬⣽⣿⠇⠉⠉⠉⢉⠁⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⡿⣿⣿⣷⣦⠀⢠⣼⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⠇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣶⣿⣿⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣉⣉⣿⣾⣾⠛⠿⢿⣿⣿⣿⣿⣿⣿
⣝⢛⣛⠿⢿⣿⣷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣾⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢋⡄⣠⣤⣤⣦⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⡗⠲⣄⣉⣿⣿⣿⣿⣿
⠀⠉⠻⢿⣿⣿⢽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣍⡉⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠉⠭⠭⠽⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣏⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿
⠀⢻⣿⠿⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢿⠴⠄⠀⢰⣿⣿⣠⡄⡀⠀⠀⠐⠲⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠨⠀⣿⠀⠀⠀⠀⢸⣿⣿⡇⢸⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⢠⠈⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣦⠀⠀⠀⠀⠀⢀⣿⡀⢀⡄⠀⠀⠀⠀⠀⠀
⢀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠘⡇⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣛⣻⣉⣉⣍⣭⣬⣭⣥⠀⠀⠀⠀⢈⠉⢹⠇⢹⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⣿⠀⡃⠘⠀⠐⠛⠛⠿⠯⠉⠍⣩⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣘⠀⠀⠀⣾⡄⢸⠃⠀⠙⢿⠆⠀⠀⠀⠀
⠀⠀⠀⠘⠣⡀⠀⠀⠀⣿⣿⠀⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣤⡀⠀⣿⡄⠀⠀⠀⢠⣤⣤⣶⡀⠀⠀
⠀⠀⠀⠀⠀⠈⠄⠀⠀⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣸⣿⣷⣰⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⢠⣿⣿⣿⡿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡟⣿⣿⣿⡏⢹⣿⣿⣿⢹⣿⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⣲⣄⢸⣿⣿⣯⣍⣠⣽⣯⣁⠒⢸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣇⣿⣿⣿⡇⠀⡇⠀⢸⢸⡏⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⢷⣾⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⠘⣿⣿⣿⣿⣿⡇⢠⣤⣤⣴⣶⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢿⠀⠀⡇⠀⢸⠸⣧⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⡅⠠⢰⣿⣿⣿⣿⣿⠿⠿⠿⢿⡟⠘⠛⢿⣿⣿⣿⣷⡞⣿⣿⣿⢻⡟⣇⢸⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠫⢸⠀⠀⡇⠀⠈⠀⣿⠄⠀⠀⠀⠀⠀⣿⣻⣿⡿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣸⣿⣿⠿⣿⣿⣿⣿⣽⡟⠁⠀⠙⣻⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣾⣷⣿⣿⣿⣿⡿⣿⡗⣾⢻⣿⣍⣟⣿⣿⠿⠇⠀⢸⠀⠀⡇⠀⢠⠀⡏⠀⠀⠀⠀⠀⠀⠈⠹⠛⠁⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣦⣀⠉⠉⢉⡉⣀⠀⠀⠀⠀⡼⠿⣻⣿⣟⢙⠿⠩⠿⠻⠿⣥⣿⣼⡿⣿⢿⡏⣿⣿⣯⢹⡷⢾⣿⣿⡇⠀⠀⠀⠸⠀⠀⡇⠀⠈⠀⣿⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣼⡏⠙⢻⣼⠇⣾⢻⡆⣶⣿⣿⣫⢠⣬⡅⣞⢛⡟⣿⡧⣉⠁⠉⠈⠁⠙⠙⠋⠛⠓⣺⣿⣿⡇⠀⠀⠀⠘⠀⠀⠛⠀⠀⠀⢋⣀⢸⣿⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠹⢿⣿⣿⣿⣿⣿⣿⣿⣠⢸⣿⣷⣿⣾⡇⣿⢸⡟⠃⢸⣧⢤⣿⣼⡇⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⣤⡀⣽⢛⣛⣇⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣏⡛⠿⠿⠿⠿⠋⣸⣮⡁⢿⣿⣽⣿⣿⡻⠁⠀⠿⠷⠸⠇⣿⢰⣿⣛⣿⣻⣿⣿⣿⣯⣼⡏⣛⢣⣿⢾⣿⣿⢰⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣻⣯⣿⣄⣀⣠⣤⣼⣿⣿⣷⣘⣿⣿⣯⣿⣱⡆⣤⣄⠀⢀⣀⢰⡿⣶⣿⣿⣯⣧⣿⣿⣿⣿⡷⠟⠸⠿⠼⠿⣿⢸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⢿⣿⣿⣿⣿⣼⣿⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡏⠸⣿⣿⣿⣷⣿⣟⣷⢹⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⡸⠿⠄⠀⣼⣧⢸⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⢿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⣷⣿⣯⣭⣿⣿⡇⠻⣺⣿⣿⣿⡅⢸⡏⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⡳⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠐⠛⢿⣿⣿⣧⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠶⠶⣶⣾⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣥⣬⣿⣥⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⡿⢁⣿⣿⠇⣼⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⢀⣻⣭⣽⣿⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⡿⠘⠻⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢤⡬⢽⣿⣿⠃⠀⠀⠾⠦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠛⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⠿⣿⣷⠀⣈⣉⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀
⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⠃⠀⠨⣽⣿⣿⣟⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣉⣩⣥⠀⠀⠀⢹⣿⣿⣿⣀⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⢼⢿⣿⣇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⡿⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠽⠛⠀⠀⠀⢯⣽⣿⢋⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣿⣷⣆⠀⣤⣾⣽⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⡇⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣾⣿⢀⣀⡀⠀⠁⡆⠀⠀⠀⠀⠀⣾⣿⣿⣄⣠⣾⣶⣾⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣟⠛⣻⢿⣿⣿⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢣⡆⣤⣶⣶⣦⣷⠀⠀⠀⠀⣸⣿⣿⣿⣟⢿⣿⣿⡿⡟⠳⢄⣉⣽⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣤⣀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⣟⣯⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿
⠀⢻⣿⠿⠛⢿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡟⠛⢲⠂⠀⠴⢹⣿⣴⠆⡀⠀⠀⠀⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠀⣿⡆⠀⠀⠀⢸⣿⣿⡇⢸⡄⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠐⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣦⠀⠀⠀⠀⠀⣼⣧⠀⣠⡀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠘⡗⢇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⡛⣛⣛⣛⣉⣩⣩⣌⣭⣭⠄⠀⠀⠀⢀⠁⣿⠁⢹⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠃⠘⠀⠀⠛⠛⠻⠟⠋⢋⣛⡅⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⣿⠀⢻⠀⠀⠹⢿⡄⠀⠀⠀⠀
⠀⠀⠀⠘⠣⠀⠀⠀⠀⣿⣿⡀⠁⠀⠀⣀⣀⠀⠀⠀⠀⠈⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣴⠀⠀⣿⡌⠀⠀⠀⣤⣤⣴⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣸⣿⡗⢸⣿⣷⣾⣷⣤⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣧⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣗⣦⡀⣿⣿⣿⣛⣁⣨⣿⣏⠉⠁⢸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣇⣿⣿⣿⡇⠀⡇⠀⢸⡇⡄⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣷⣿⣿⣿⣿⣿⣿⠿⡿⣿⡇⠘⢿⣿⣿⣿⣿⡇⢠⣤⣤⣴⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠇⠀⡇⠀⠈⠇⣇⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢨⣿⣿⣿⣿⣿⡿⠿⠷⠶⣿⠃⠐⠿⢿⣿⣿⣿⣷⡞⣿⣿⣿⢻⡟⣟⢸⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠻⢸⠀⠀⡗⠀⠀⠀⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⡿⢿⣿⣿⣿⣷⣴⠏⠀⠀⠙⢺⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣾⣷⣿⣿⢿⣿⣿⣿⡗⣾⢻⣿⢍⣟⣿⣿⡿⡇⠀⢸⠀⠀⡇⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠈⠓⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣧⣄⡉⠛⠛⣛⠋⣀⠀⠀⠀⠀⢸⣿⣻⣿⣟⠙⡿⠋⠿⠻⠿⣇⣿⣸⡿⣿⢿⡇⣿⣿⣯⢹⡷⢾⣿⣿⡏⠀⠁⠀⢸⠀⠀⢧⠀⠀⠀⡷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣘⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣶⡉⠳⢿⣼⠇⣾⢻⡆⣶⣿⣿⣫⢠⣤⡄⣝⢛⡻⣿⣯⣉⠁⠉⠈⠁⠙⠙⠋⠛⠓⢺⣿⣿⡇⠀⠃⠀⠐⠀⠀⠘⠀⠀⠀⠁⡀⢸⣷⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡬⠿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢸⣿⣶⣿⣼⡇⣿⢸⡟⠃⢸⣧⢤⣿⣼⡇⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⣤⡀⣼⢛⣛⢿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣯⣯⡙⠿⠿⢿⡿⠿⢃⣷⣌⠹⣿⣿⣭⣷⣿⣟⠁⠀⠿⠷⠸⠇⣿⢰⣿⣛⣿⣿⡿⣿⣿⣯⣼⡏⣛⢣⣿⣿⣿⣿⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡿⢿⣟⣤⣄⣀⣠⣤⣽⣿⣿⡆⣿⣿⣿⣯⣿⣠⡆⣤⣄⠀⢀⣀⢠⡿⣶⣿⣿⣯⣧⣿⣿⣿⣿⣷⠟⠸⠿⢼⠿⣿⢸⣇⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⣿⣿⣿⣿⣧⣿⣿⣿⣧⣷⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣷⣿⡄⠀⢸⡏⠘⣿⣿⣿⣷⣿⣟⣿⢹⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⠆⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣷⣿⣯⣭⣿⣿⣏⠻⣺⣿⣿⣿⡅⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠐⠚⠿⣿⣿⣷⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⢀⡇⠈⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠶⠶⣶⣾⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣭⣭⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣥⣥⣼⡿⢰⣿⣿⢈⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢀⣞⣯⣽⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣗⣸⣿⡇⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⣠⣭⠿⢿⣿⠇⠀⠀⠾⢶⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣯⣝⠻⣿⣷⠀⢈⣙⡻⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀
⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣤⣌⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⣿⣿⣦⠋⠀⠈⣿⣿⣿⣟⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣿⣷⣆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⣉⠀⠀⠀⢛⣿⣿⣿⣀⣀⣰⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⡆⠀⠀⠈⡻⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⣿⡿⣨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⡿⠛⠂⠀⠀⢨⣽⣿⡏⠈⠁⠉⠈⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡦⡀⠀⣝⣿⡻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣀⣀⡀⠀⠁⡇⠀⠀⠀⠀⣼⣿⣿⣄⣡⣼⣶⣿⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣾⠿⣿⣿⣷⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠋⡀⣤⣤⣤⣦⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⢄⣉⣽⣿⣿⣿⣿⣿⣿
⠙⠲⢷⣶⣿⡿⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠩⠭⠭⠉⠀⠀⠀⣼⣿⣿⣿⣿⣾⣟⣿⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⡿
⠀⢛⣻⡿⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠖⠦⠀⠰⢻⣿⣴⠦⡀⠀⠀⠀⠻⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⢀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠇⢸⡄⠀⠸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⢻⡇⠀⠀⠀⢸⣿⣿⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⡘⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⠈⡗⢇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠟⢛⠛⠛⢛⣛⣒⣋⣉⠀⠀⠀⠀⢁⠙⣿⠈⣿⣷⠀⠀⠀⠀⠀⠀
⠈⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠃⠸⠀⠀⠿⠿⡟⠛⠛⢛⣛⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠁⠀⠀⢰⣇⠀⡟⠀⠈⢻⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢧⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⠀⢸⣿⠀⠀⠀⢀⣤⣬⣱⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠄⠀⠀⣿⠁⠀⠀⣾⣿⣿⣿⣷⣶⣶⣶⣿⡟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⡦⣾⣿⣦⣶⣦⣼⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣏⠩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢤⣄⢰⣿⣿⣿⡛⠊⣙⣿⠛⠩⠁⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡧⣿⣿⣿⡇⠈⡇⠉⢸⡇⠉⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠸⣿⣿⣿⣿⣿⡇⢀⣀⣀⣠⣤⣦⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠸⡇⡄⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⣽⣿⣿⣿⣿⣿⣷⣦⣴⣿⠀⠀⠰⠾⢿⣿⣿⣿⣷⡞⣿⣿⣿⣿⡟⣗⢸⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⢛⢺⠀⠀⡇⠀⠀⠅⣧⠀⠀⠀⠀⠀⢸⣿⣻⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢽⣿⣿⣿⣿⣿⣷⣶⣂⣴⠏⠀⠀⠀⠒⢶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣼⣷⣿⣿⢿⣿⣿⣿⡗⣿⢻⡿⢍⡟⣿⣿⡿⡏⠀⢸⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠙⡩⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣆⡉⠛⠛⠿⠟⠃⠀⣀⠀⠀⠀⠀⣹⣿⣻⣿⣟⢙⣿⣛⣿⠿⠿⣃⣿⣺⡿⣿⢿⡗⣿⣿⣯⢺⣷⣾⣿⣟⡟⠀⠁⠀⢸⠀⠀⣅⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⢰⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣶⠙⠶⣄⣹⣼⠇⣾⢻⡆⣶⣿⣿⢛⢠⣥⡄⣔⢟⡻⣿⣷⠛⠓⠛⠊⠁⠙⠙⠋⠛⠓⢺⣿⣿⡇⠀⠇⠀⠠⠀⠀⠸⠀⠀⠀⠟⠀⢸⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣾⣿⣿⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠺⣿⣏⣶⣿⣼⡇⣿⢸⣟⠏⢸⣧⢠⣿⣼⡇⣿⣿⣿⣿⣷⣰⡶⣶⢀⣴⣦⡀⣼⢛⣛⣟⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⣫⡙⠻⢿⣿⣿⣿⡿⢋⣶⣄⠸⣿⣿⣯⣭⣤⣿⣿⡇⠀⠿⠷⠸⠏⣿⢰⣿⠿⣿⣿⣿⣿⣿⣯⣸⡇⣛⢣⣿⢾⣿⣿⢰⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣕⣀⡀⢀⣀⣀⣿⣿⣿⡆⣿⣿⣿⡿⣯⣯⣡⡄⣤⣄⠀⢀⣀⢀⡿⣶⣿⣿⣯⣧⣿⣿⣿⣿⡷⠟⠸⢿⢾⢿⣿⢸⣇⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡄⠀⢸⡏⠘⣿⣿⣿⣷⣿⣟⣿⢹⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣃⣿⡸⠿⠆⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣟⣿⠀⠀⠀⠀⠀⣷⣿⣯⣽⣿⣿⣟⢻⣸⣿⣿⣿⡁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡿⡇⣣⠑⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠷⢾⣿⣿⣧⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⡇⠀⠐⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣤⣤⣬⣿⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣯⣭⣿⣧⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣤⣿⣧⣿⣿⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣭⡇⠀⠀⢶⣛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⢈⣙⣻⣿⣿⡇⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡛⢿⣿⣷⠀⠈⠓⣺⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣶⣌⡏⠀⠙⣛⣷⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣦⡀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣍⣙⣋⠀⠀⠀⠹⣿⣿⣿⣀⡀⣀⣾⣆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⡀⠀⠀⢐⣿⣿⣿⣧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⡟⢲⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣻⠿⠂⠀⠀⢼⣻⣿⡟⠛⠋⠉⠉⡃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⡀⠀⠀⢯⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⠇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣶⣽⣿⠁⠀⠀⠀⠂⡇⠀⠀⠀⣼⣿⣿⠙⢉⣯⣽⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣦⡀⢸⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣾⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⠏⡤⣠⣥⣤⣤⣧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡶⣄⠙⢛⣿⣿⣿⣿⣿⣿⣿⠃
⢿⡿⠿⣿⣿⣧⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣍⡉⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠨⠁⠉⠍⠛⠽⠛⠀⠀⣿⣿⣿⣿⣷⣻⣿⡏⠉⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⠏⠀
⠙⠛⢿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠤⠄⠀⣠⣿⣿⣠⣄⠀⠀⠀⠀⢾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⢀⡀⢹⡇⠀⠀⠀⢸⣿⣿⠹⠘⡇⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⠀⠀⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡄⠀⠀⠀⠀⡀⣼⣇⠀⣠⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⡑⡗⢻⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⡿⠛⢛⡛⠛⢛⣛⣒⣊⣉⡀⠀⠀⠀⠀⠙⣿⠑⢿⣿⡄⠀⠀⠀⠀⠀
⠈⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠃⠙⠘⠀⠀⠿⠿⠟⠛⠛⢛⣛⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣯⠁⠀⠀⢠⣿⢀⠻⠀⠈⠻⠷⡀⠀⠀⠀⠀
⠀⠀⠀⠈⢷⡀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣶⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⠀⢸⣿⡀⠀⠀⠀⣤⣀⣵⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇⠀⠀⢰⣿⣿⣿⣿⣿⣶⣷⣶⣿⡿⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢸⣿⣦⣾⣿⣷⣾⣦⣼⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣏⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡀⣾⣿⣿⣛⣓⣈⣽⣟⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠉⠨⡇⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⢿⣿⣿⣿⣿⡇⢀⣀⣀⣠⣤⣴⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣧⠀⠀⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⡶⣶⣾⡇⠀⠀⠀⠾⢿⣿⣿⣿⣷⡞⣿⣿⣿⣿⡟⣟⢘⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠛⠛⠀⠀⣻⠀⠀⡇⣧⠀⠀⠀⠀⠀⢽⣻⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣿⣿⣿⣷⣶⣲⡾⠁⠀⠀⠀⠒⢶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⡗⣿⢻⣿⠍⣿⣿⣿⡿⡏⠀⢰⠀⠀⢹⠀⠀⡇⡟⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣷⣄⡉⠛⠛⠛⠛⠁⠀⣀⠀⠀⠀⠈⢹⣻⣻⣿⣟⣙⣿⣛⣿⠿⠿⣇⣿⢺⡿⣿⢿⡗⣿⣿⣯⢺⣷⣾⣿⣿⣿⠁⡅⠀⠸⠀⠀⢨⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡎⠙⠶⣤⣹⣼⠇⣾⢻⡆⣶⣾⣿⢛⢠⣥⡄⣔⢞⣻⣿⣷⠛⠓⠛⠊⠁⠙⠙⠋⠛⠓⢸⣿⣿⣿⠀⠇⠀⠀⠀⠀⠸⠀⠀⠀⠙⠀⢰⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣿⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⢻⣿⣯⣶⣿⣼⡇⣿⢸⣟⠏⣸⣧⢠⣿⣼⡇⣿⣿⣿⣿⣷⣰⡶⣶⢀⣴⣦⡀⣼⣛⣛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣾⣬⡝⠿⢿⣿⣿⡿⠟⣸⣶⠄⢻⣿⣿⣯⣭⣤⣿⣿⡏⠀⠿⠷⠸⠏⣿⢰⣿⠿⣿⣿⡿⣿⣿⣯⣸⡏⣛⢃⣿⢿⣿⣿⢰⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢲⣿⣽⣖⣄⡀⣀⣠⣤⣿⣿⣷⣄⣿⣿⣿⡿⣯⣯⣡⡄⣤⣄⠀⢀⣀⠀⡿⣶⣿⣿⣯⣷⣿⣿⣿⣿⣷⠟⠸⠿⢼⢿⣿⣸⣇⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡄⠀⢸⡏⠀⣿⣿⣿⣷⣿⣟⣾⢹⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣃⣿⣸⠿⡆⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⡟⣨⣵⣿⣾⣇⣿⢘⡋⣿⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡿⣿⠀⠀⠀⠀⠀⢷⣿⣯⣭⣿⣿⣿⢻⣺⣿⣿⣿⡇⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠁⠸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⢸⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠾⢷⣿⣿⣷⡀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢂⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⢤⣤⣬⣿⣿⡃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣯⣽⣿⣤⣤⣤⣤⢨⣭⣭⣭⣭⣥⣭⣼⣿⣥⣿⣿⢏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡇⠀⠐⢶⣚⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⢈⣙⣻⣿⣿⡇⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⠿⣿⣷⠀⠈⠛⣺⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⣿⣷⣦⡍⠀⠈⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀
⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⣙⣋⠁⠀⠀⠹⣿⣿⣿⣀⣀⣀⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⣿⣷⡀⠀⠀⢸⣿⣿⣿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⡏⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⠿⠃⠀⠀⢼⣿⣿⡟⠙⠉⠉⠉⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⣿⣿⣷⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣿⠅⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣲⣽⣷⡂⠀⠀⠀⠀⡇⠀⠀⢀⣿⣿⡟⠛⢹⣯⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣗⣄⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣾⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⢤⣠⣤⣬⣤⣥⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⢤⡈⠛⢿⣿⣿⣿⣿⣿⣿⡟⠀
⠶⡿⠿⢿⣿⣦⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣤⣉⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠈⠍⠩⠯⠛⠀⢰⣿⣿⣿⣿⣞⠿⣿⠉⠁⠀⠉⣛⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠙⠻⣿⣿⡿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠦⠄⠀⢠⣿⣿⣐⡄⡀⠀⠀⠀⢺⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣾⣿⡿⢿⣿⣿⣿⣿⠃⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⡟⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⡏⡄⢷⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡄⠀⠀⠀⠀⡀⣬⣇⡀⣀⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⡇⢷⢺⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠛⠛⡛⣛⢋⣛⣓⣈⣁⠀⠀⠀⠀⢀⠈⣽⠁⢹⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⠀⠀⠀⠀⣿⣿⠇⠘⠘⠀⠀⠻⠿⠛⡛⠛⢛⡛⣛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⢠⣿⠀⢻⠀⠀⠛⠷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠿⡄⠀⠀⠀⠟⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⢶⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣄⠀⢸⣿⡈⠀⠀⠀⣤⣤⣄⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣾⣭⣿⠙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⣆⣾⣿⣷⣾⣷⣴⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣯⢣⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⡀⣿⣿⣿⣏⣁⣬⣿⣏⠉⠘⠀⠀⠐⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⠿⠿⣿⡆⠀⠀⠀⢿⣿⣿⣿⣿⡇⢀⣀⣀⣤⣤⣶⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⡿⠿⠷⠶⣿⠃⠀⠀⠀⠾⠿⣿⣿⣿⣷⡞⣿⣿⣿⣿⡟⣟⢈⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠻⡧⠅⠀⢸⠀⠀⡇⣦⠀⠀⠀⠀⠀⢼⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣷⣶⠏⠀⠀⠀⠀⠒⢲⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⢿⣿⣿⣿⡗⣾⢻⣿⠍⣿⣿⣿⡟⡿⠀⠀⡇⠀⢸⠀⠀⡇⢻⠀⠀⠀⠀⠀⠈⠻⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣧⣄⡉⠛⠛⣛⡋⠀⠀⣀⠀⠀⠀⠀⢈⣛⣛⣿⣟⣙⣿⣋⣿⠻⠿⣇⣿⣺⡿⣿⢿⡗⣿⣿⣯⢸⣷⣾⣿⣿⣿⠀⡅⠀⠀⠃⠀⢸⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡀⠙⢳⣦⢹⣼⠇⣾⢻⡆⣶⣾⣿⢛⢣⣥⡄⣄⢟⣻⣾⣿⡛⠃⠉⠈⠁⠙⠙⠃⠛⠓⢸⣿⣿⣿⠀⠃⠀⠀⠆⠀⠸⠀⠀⠀⠘⠀⢰⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠈⢻⣿⣯⣶⣿⣼⡇⣿⢸⣟⠟⢸⣧⢤⣿⣼⡏⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⣦⡀⣼⣛⣛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣷⣬⡙⠻⠿⠿⠿⠟⢃⣽⣷⠀⢻⣿⣿⣯⣭⣤⣿⣿⡏⠀⠿⠷⠸⠏⣿⢰⣿⠻⣿⣿⡿⣿⣿⣯⣼⡏⣛⢣⣿⣿⣿⣿⢰⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣽⣿⣹⡦⣄⣀⣠⣴⣿⣿⣿⣷⢼⣿⣿⣷⡿⣯⣯⣠⡄⣤⣄⠀⢀⣀⠀⡿⣶⣿⣿⣯⣷⣻⣿⣿⣿⣷⡟⠸⠿⢼⢿⣿⣹⣇⣿⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡄⠀⢸⡏⠀⣿⣿⣿⣷⣿⣟⣿⢸⡿⣿⣿⣦⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⡇⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠈⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠸⣟⢿⡅⠀⠀⠀⠀⢱⣿⣯⣭⣿⣿⣿⠻⣸⣿⣿⣿⡇⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡇⢩⠜⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠶⠾⣿⣿⣷⡀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⢰⠃⠐⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠴⣤⣴⣿⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣤⣤⣤⣤⢨⣭⣭⣭⣭⣥⣬⣾⣿⣽⣿⣿⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡇⠀⠐⢲⣚⣿⣿⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣗⠀⢀⣉⡿⢿⣿⡇⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⠻⢿⣿⠀⠀⠙⣛⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣧⡞⠀⠈⣻⣿⣿⣿⠃⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠲⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣉⣉⠁⠀⠀⢸⣿⣿⣿⣁⣀⣀⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀
⣾⣧⠀⠀⠀⢿⣿⣿⣿⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⣿⢇⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⠛⠃⠀⠀⢨⣿⣿⡟⠉⠉⠉⠉⡍⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀
⣿⣿⣇⠀⠀⠘⣿⣿⣿⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⣿⠰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣲⣾⣿⡂⣀⣀⡀⠀⡇⠀⠀⢠⣿⣿⡙⠛⣿⣝⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⡿⣿⣿⣗⣄⠀⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠥⢠⣤⣤⣤⣼⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⡦⣄⠘⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠿⡿⠿⢿⣿⣶⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⣿⣿⣿⣦⣄⠀⠀⠀⠀⣠⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠩⠭⠍⠁⢸⣿⣿⣿⣿⣝⢿⡟⠉⠁⠈⠙⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠙⠻⣿⣿⡟⢿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠻⠲⠦⠀⢰⣿⣿⣐⡄⡀⠀⠀⠐⢺⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣷⣤⣤⣶⣿⣿⢿⢿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠂⢸⡇⠀⠀⠀⠀⣿⣿⣿⠀⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⡟⠀⢻⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡀⠀⠀⠀⠀⠀⢠⣯⡀⣠⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⠀⠀⠀⠀⣿⣿⡇⢸⢺⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠛⠛⡛⢛⢛⣛⣓⣊⣁⠀⠀⠀⠀⢀⠈⢿⠇⢻⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡿⠇⠘⠈⠃⠀⠘⠿⠛⠛⠛⢛⡛⣛⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⢀⣾⢀⢸⠂⠀⠛⠿⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠻⡄⠀⠀⠀⠈⠀⠀⢀⣀⣀⣀⠀⠀⠀⠙⣤⣼⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⣄⠀⢸⣿⡌⠀⠀⠀⣠⣤⣤⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣶⣇⣭⣿⡚⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣦⣾⣿⣧⣾⣶⣴⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣯⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣄⢸⣿⣿⣿⣍⣁⣽⣿⡉⠁⡞⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣸⣿⣿⡿⠀⢸⠀⠀⡇⠉⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⣀⣀⣠⣤⣴⣤⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠿⠷⠾⡿⠀⠀⠀⠀⠾⠿⣿⣿⣿⣷⡆⣿⣿⣿⣿⡟⣟⣀⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠟⠃⡇⠀⢸⠀⠀⡇⢀⠀⠀⠀⠀⠀⢻⣛⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣴⣾⠃⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⣷⣿⣿⣯⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⡗⣾⢻⣿⠍⣿⣻⣿⡯⣿⠀⠀⡇⠀⢸⠀⠀⡇⠸⠀⠀⠀⠀⠀⠈⠛⡍⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣦⣈⠙⠛⠛⣛⠁⠀⠀⣀⠀⠀⠀⠀⢈⣟⣛⣿⣿⣙⣿⣛⣿⠻⠿⣇⣿⣸⡿⣿⢿⡗⣿⣿⣯⢺⣷⣿⣿⣽⣿⠁⠀⠀⠀⠇⠀⢸⠀⠀⠃⢘⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⠈⠙⢶⣤⢹⣼⠇⣾⢻⡆⣶⣾⣿⢛⢣⣥⡄⣄⢟⣻⣾⡿⡛⠓⠛⠈⠁⠙⠙⠃⠛⠓⢸⣿⣿⣿⠀⠀⠀⠀⠆⠀⠸⠆⠀⠀⠘⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⡇⡽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⣿⣯⣶⣿⣼⡇⣿⢸⣏⡟⢸⣧⢤⣿⣼⡏⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⣦⡀⣼⣛⣛⣿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡏⣿⣍⠛⠿⠿⠿⠿⠟⣡⣿⣦⡈⢿⣿⣿⣯⣭⣠⣿⣿⡟⠀⠿⠷⠸⠏⣿⢡⣿⠻⣿⣿⡿⣿⣿⣯⣼⡏⣛⢣⣿⢾⣿⣿⢱⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣿⣻⡕⣶⣄⣀⣤⣶⣿⣿⣿⣷⣼⣿⣿⣷⣿⣯⣯⣡⡄⣤⣄⠀⢀⣀⠀⡾⣶⣿⣿⣿⣿⣻⣿⣿⣿⣷⠟⠸⠟⢼⢿⣿⣻⣇⣿⠀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⣿⣿⣿⣯⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⣿⣷⣿⡄⠀⢸⡏⠀⣿⣿⣿⣷⣿⣟⣿⢩⡿⣿⣿⣧⣄⠀⣀⡀⠀⠀⠉⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⣿⡸⠿⡇⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣬⣵⣿⣺⣧⣿⢘⡋⣿⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢿⡇⠀⠀⠀⠀⢱⣿⣯⣭⣿⣿⣿⠛⣺⣿⣿⣿⣇⢸⡏⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠃⠨⡘⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠶⠶⣿⣿⣿⡠⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢸⠀⠀⢃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⢤⣤⣥⣽⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣯⣿⣧⣤⣤⣤⣤⢨⣭⣭⣭⣭⣥⣤⣿⣯⣽⣿⡿⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣯⣧⠀⠀⢲⣚⣻⣿⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣀⣉⣻⣿⣿⡟⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⠿⢿⣿⡄⠀⠛⣓⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟⣷⣦⡏⠁⠈⣛⣿⣿⣿⡃⠀⠀⠀⡂⠀⠀⠀⢀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣛⣛⡅⠀⠀⠸⣿⣿⣿⣃⣀⣀⣾⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⣆⠀⠀⠈⣿⣿⣿⣿⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣿⣿⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣛⡿⠟⠀⠀⠸⣿⣿⡿⠙⠉⠋⠉⡙⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⡆⠀⠀⢹⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⣟⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣲⣜⣿⡆⠀⠀⠀⠂⣃⠀⠀⢰⣿⣿⠻⠛⣟⣛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⠿⣿⡿⣲⡀⢸⣿⣿⣿⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⢡⣠⣤⣤⣤⣼⡄⢀⣿⣿⣿⣷⣾⣿⣿⣷⣄⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠾⣿⣿⣿⣿⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣦⡄⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⠿⠛⠁⣼⣿⣿⣿⣗⢿⣿⡟⠛⠁⠙⠲⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠛⠿⣿⣿⠟⢿⣿⣿⡿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠻⠴⠦⠀⢰⣿⣿⣴⠄⡀⠀⠀⠀⢒⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣧⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⢐⠀⣿⠀⠀⠀⠀⢻⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⣃⢸⡀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⡀⢀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡆⠀⠀⠀⢸⣿⣿⢸⡼⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⡛⠛⢀⠛⡀⠀⠀⠀⠈⠈⢻⡟⠘⣿⣧⠀⠀⠀⠀⠀
⠀⠉⠀⠀⢻⡇⠀⠀⠀⢸⡿⠛⠈⠃⠃⢀⠸⠿⠿⠿⠿⠛⡿⢻⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣾⡀⠸⡇⠀⠻⢿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⣴⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⢀⣿⡌⠃⠀⠀⢀⣀⣀⣠⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⣷⣾⡃⢙⣿⠏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣧⣼⣿⣷⣴⣶⣤⣾⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⣿⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⣿⣿⣛⣓⣈⣿⣟⠉⢩⢯⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣼⣿⣿⣿⠀⢹⠉⠉⣱⠙⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⣠⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⡿⠀⢸⠀⠁⢸⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡶⣶⣾⡇⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⡆⣿⣿⣿⣿⡟⣟⣃⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠿⡧⠀⢸⡆⠀⢸⢀⠀⠀⠀⠀⠀⢰⣿⢟⣿⡿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣶⣶⣲⡾⠁⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣷⣿⣿⣏⣿⣷⣿⣾⣷⣿⣿⣿⣿⡿⣿⡟⣿⢻⣿⠍⣿⢻⣿⣿⣻⠁⠈⡇⠀⢸⡇⠀⠸⢸⠀⠀⠀⠀⠀⠈⠻⢩⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣷⣄⡙⠛⠛⢛⡛⠁⠀⠀⣀⠀⠀⠀⠈⠉⣿⡿⣿⣿⣙⣿⡛⢿⢻⠿⣿⣿⠸⡿⣿⢿⡟⣿⣿⣯⢸⣷⣆⣿⣿⣿⠃⠘⠀⠀⡇⠀⠈⡅⠀⠸⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡆⠉⠳⢦⣄⣹⣼⠇⣾⢻⡆⣶⣾⣿⠻⢣⣭⡄⣄⣒⡛⣿⡿⡛⠓⠛⠊⠁⠛⠙⠋⠛⠓⠂⣿⣿⣿⠃⠐⠀⠀⠀⠀⠀⡇⠀⠀⠘⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⣿⣾⣟⣶⣿⣼⡇⣿⢸⣏⣼⢻⣧⢠⣿⣼⡏⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⣦⡀⣤⢛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢘⣻⣯⣛⠻⠿⣿⣿⠿⠟⣸⣿⣄⠙⣿⣿⣿⣯⣍⢀⣻⣿⣿⠃⠿⠷⠸⠏⣿⢡⣿⠿⣿⣿⣿⣿⣿⣯⣼⡏⣛⢣⣿⢿⣿⣿⣷⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⢿⣿⣿⣶⣤⣀⣀⣔⣶⣿⣿⣿⣇⣽⣿⣿⣶⡿⣯⣯⣩⡍⣤⣤⠀⢀⣀⠀⠰⣶⣷⣾⣯⣿⣿⣿⣿⣿⣷⠟⠸⠟⢽⢿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⣿⣿⣿⡄⠀⢸⡏⠀⣿⣿⣿⣷⣾⣟⣿⢩⡿⣿⣿⣧⣄⠀⣀⡀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠚⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡃⣿⡸⠿⡇⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣤⣵⣿⢺⣧⣿⢘⡋⣿⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⡇⠀⠀⠀⠀⢱⣿⣯⣭⣿⣿⣿⡛⣸⣿⣿⣿⣧⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠈⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠀⠘⡌⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠨⣽⣿⣿⣿⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡜⠀⠀⢱⠄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⢠⣄⣨⣭⣿⡇⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣭⣿⣧⣤⣤⣤⣤⢨⣭⣭⣥⣭⣤⣥⣿⣯⣿⣿⡟⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢬⠽⣟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣙⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢘⣻⣿⣿⣿⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣛⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡄⠈⠻⠿⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡻⣷⣄⣹⠃⠀⠚⣿⣿⣶⠟⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠟⠋⠀⠀⠈⣿⣿⣿⡇⠀⠀⣴⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣷⡀⠀⠀⠸⣿⣿⣿⣷⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣿⣿⢉⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⠷⠀⠀⢀⣛⣿⣿⠋⠙⠛⠙⠛⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣧⠀⠀⠀⣿⣿⣿⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⣿⡟⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⢠⣭⣿⡯⠀⠀⠀⠰⢰⠀⠀⢠⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣶⢄⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡻⢋⢈⣉⣀⣀⣸⡀⢀⣿⣻⣷⣤⣴⣿⣾⣎⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⣽⣿⣵⣿⣆⣸⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⡀⠀⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⣛⠛⠃⣼⣿⣿⣿⡻⣿⣿⣿⠿⠛⢦⣈⣩⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠼⢿⣿⣿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠓⢤⣤⠀⢀⢺⣿⣀⣄⠀⠀⠀⠀⠤⣾⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣭⣻⡀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⢀⠀⣿⠀⠀⠀⠀⢹⣿⣿⡇⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡆⠀⠀⠀⢸⣿⣿⢃⠸⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⠀⣸⡆⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⣿⣿⢸⡦⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠤⠛⠀⠀⠀⠀⠈⠐⢻⡿⠺⣿⣷⠀⠀⠀⠀⠀
⠀⠉⠀⠀⢸⡇⠀⠀⠀⢸⡿⠛⠀⠃⠃⠀⠸⠿⠿⠿⠿⠿⠿⢿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣶⣿⣾⣷⣿⣿⣿⣿⡇⠀⠀⠀⣼⣇⠈⡇⠀⠻⢿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⣤⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⣿⡇⠃⠁⠀⠀⣀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣾⡅⢹⣻⡟⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⡇⣤⣿⣿⣤⣶⣄⣾⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⣿⣿⣿⣛⣓⣈⣿⡟⠉⢽⣿⠃⠀⠀⢺⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⢹⠉⠁⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⣠⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠀⢸⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣶⣶⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⡟⣟⣃⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡫⠀⢠⡇⠀⢸⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣖⣲⡞⠀⠀⠀⠀⠀⠀⠦⣼⣿⣿⣿⣷⣿⣿⣏⣿⣷⣿⣽⣷⣿⣿⢿⣿⣿⣿⡟⣿⢻⣿⠍⣿⢿⣿⣿⣿⠁⠀⡇⠀⢸⡇⠀⢸⢸⠀⠀⠀⠀⠀⠀⠙⠹⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣧⣀⠙⠛⠛⢛⠛⠀⠀⠀⣀⠀⠀⠀⠀⠉⢻⡿⣿⣿⣝⣿⣟⠿⢻⠿⣿⣿⠸⡿⣿⢿⡟⣿⣿⣯⢸⣷⣖⣿⣿⣿⡏⠘⠀⠀⡇⠀⠈⡅⠀⠸⢸⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⢀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⣴⡇⠙⠲⣤⣄⢹⣼⠇⣾⢻⡎⣶⣾⣿⠻⢫⣭⡅⣍⣛⡛⣿⣿⡿⠷⠛⠪⠅⠛⠙⠋⠛⠓⠂⣿⣿⣿⡇⠸⠀⠀⠀⠀⠀⡇⠀⠀⠸⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⠜⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠹⣿⣾⣏⣴⣿⣼⡇⣿⢸⣏⣼⣾⣧⢠⣿⣼⡏⣿⣿⣿⣿⣷⣰⡶⣶⢀⣴⣦⡀⣤⢛⣛⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣺⣭⡛⠿⢿⣿⣿⠿⠟⣸⣷⣄⠹⣿⣿⣿⣯⣍⠀⣻⣿⣿⠃⠿⠷⠸⠏⣿⢱⣿⠿⣿⣿⣿⣿⣿⣯⣸⡏⣛⢃⣿⢿⣿⣿⣷⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣜⣻⣿⣟⢤⢤⣀⣀⣤⣼⣿⣿⣿⣦⣿⣿⣿⣶⣿⣯⣿⣩⡍⣤⣤⠀⢀⣀⠀⠰⣶⣷⣾⣿⣿⣿⣿⣿⣿⣷⠟⠸⠏⢽⢿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣴⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡄⠀⢸⡏⠀⣾⣿⣿⣷⣿⣟⣷⢩⡿⣿⣿⣧⣄⠀⣉⡁⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⣿⡸⠿⡇⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣤⣵⣿⢾⣇⣿⢘⡋⣿⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⡿⠀⠀⠀⠀⢱⣿⣯⣽⣿⣿⣿⡛⣺⣿⣿⣿⣧⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠹⡌⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⢩⣭⣿⣿⣿⡄⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⡇⠀⠀⢐⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⢀⣄⣈⣽⣿⡿⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣽⣿⣧⣤⣤⣤⣤⢨⣭⣭⣭⣭⣥⣭⣿⣧⣿⣿⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⠀⠀⢨⡭⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠘⠻⣿⣿⣿⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠈⠻⠿⢾⣿⣿⠀⠀⠈⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢿⣿⣭⣻⠇⠀⠶⢾⣿⣶⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣶⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠿⠛⠀⠀⠘⣿⣿⣿⡇⠀⠀⣰⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀
⣤⠀⠀⠀⢸⣿⣿⣿⣧⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⣿⡿⢨⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⡧⠀⠀⢀⣿⣿⣿⠟⠙⠛⠛⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⣧⠀⠀⠀⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⣿⡇⢼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⢠⣽⢿⡏⠀⠀⠀⠠⢠⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⣦⢀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢋⣀⣈⣁⣀⣸⡀⢀⣾⣿⣧⣉⣸⣶⣬⡍⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣯⣷⣷⣆⣸⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣤⡀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠚⣛⢋⣻⠛⠃⣼⣿⣿⣿⢻⣿⣿⣿⣿⠲⣄⡉⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀
⠼⣟⣿⣿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⡃⣤⣤⡀⢀⢾⣿⣁⣄⠀⠀⠀⠀⢠⣾⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣯⣛⡿⠁⠀⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⠀⠀⢀⠀⣿⠀⠀⠀⠀⢸⣿⣿⡇⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡆⠀⠀⠀⢸⣿⣿⢠⠸⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⡇⠀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⡇⠀⠀⠀⢸⣿⣿⠸⡦⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠤⠛⠀⠀⠀⠀⠀⠐⢻⣿⠚⣿⣿⡄⠀⠀⠀⠀
⠀⠉⠀⠀⢸⡇⠀⠀⠀⢸⡿⠛⠀⠃⠃⡀⠠⠿⠿⠿⠿⠿⠿⢿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣶⣿⣾⣿⣿⣿⣿⣿⡃⠀⠀⠀⣼⣇⠀⡧⠀⠹⢿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣆⣠⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⣿⡇⠋⠀⠀⠀⣀⡀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣾⡇⢙⣻⠏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣻⡧⣰⣿⣿⣤⣶⣤⣼⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣶⣾⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢐⣿⣿⣟⣛⢂⣨⣿⡟⠉⢽⢿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠙⠉⠉⢹⠙⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⣠⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣶⣶⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⡟⣟⣃⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⢰⡇⠀⢸⢀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠋⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣷⣶⣖⣶⠟⠀⠀⠀⠀⠀⠀⠦⣼⣿⣿⣿⣧⣿⣿⣏⣿⣷⣿⣼⣷⣟⣿⣿⣿⣿⣿⡟⣿⢻⣿⡍⣿⣿⣿⣿⣿⠓⠈⡻⠀⠘⡇⠀⢸⢸⠀⠀⠀⠀⠀⠀⠋⠙⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣦⣈⠛⠛⠛⢛⠋⠀⠀⠀⣀⠀⠀⠀⠀⠉⣻⡿⢿⣻⣝⣿⣟⠿⢻⠿⣿⣿⠸⡿⣿⢿⡗⣿⣿⣯⣹⣷⣖⣿⣿⣿⡇⢘⠀⠀⠆⠀⠀⡇⠀⠸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⣴⡋⠙⠲⣤⣀⢹⣼⠇⣾⢻⡆⣶⣾⣿⠻⢫⣭⡍⣍⣓⡛⣟⣿⡿⠷⠟⠊⠅⠛⠙⠃⠛⠓⠊⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⡇⠀⠀⠘⠃⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢻⣿⣾⣯⣴⣿⣼⡇⣿⢸⣏⣴⣿⣧⢠⣿⣼⡇⣿⣿⣿⣿⣷⣰⡶⣶⢀⣴⣦⡀⣤⢛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣍⡛⠿⢿⣿⣿⠿⠋⣼⣷⡀⢹⣿⣿⣿⣯⣍⠀⣛⣿⣿⠃⠿⠷⠸⠏⣿⢱⣿⠿⣿⣿⣿⣿⣿⣯⣼⡏⣛⢣⣿⢾⣿⣿⣷⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣷⡷⢦⣤⠀⣠⣤⣾⣿⣿⣿⣦⣿⣿⣿⣾⣿⣯⣿⣩⡍⣤⣤⠀⢀⣀⠀⠰⣶⣷⣾⣿⣿⣿⣿⣿⣿⣷⠟⠸⠏⢼⢿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡤⠀⢸⡏⠀⣾⣿⣿⣷⣿⣟⣿⢩⡿⣿⣿⣧⣄⠀⣉⡉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⣿⡸⠿⣇⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣤⣵⣿⢾⣧⣿⢘⡋⣿⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢿⣿⣿⠀⠀⠀⠀⠱⣿⣯⣭⣿⣿⣿⡛⣸⣿⣿⣿⣧⢸⡏⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠘⡇⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢨⣭⣿⣿⣿⡄⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⣄⣈⣩⣿⣿⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣯⣽⣿⣥⣤⣤⣤⣤⢨⣭⣭⣭⣭⣤⣽⣿⣯⣿⣿⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⠀⠀⠨⡭⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣹⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠐⠻⣿⣿⣿⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣛⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⡇⠈⠹⠿⢶⣿⣿⠀⠀⠈⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣅⣙⡇⠀⠲⢾⣿⣶⡿⠀⠀⠀⡀⠀⠀⠀⢀⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢶⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠟⠿⠛⠀⠀⠘⣿⣿⣿⡗⠀⠀⣰⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀
⣤⠀⠀⠀⢸⣿⣿⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⡿⢨⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⢿⡷⠀⠀⢀⣾⣿⣿⠟⠙⠛⠛⠛⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⣧⠀⠀⠈⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠠⣽⣿⣿⠀⠀⠀⠰⢸⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⣦⢀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⣀⣉⣀⣀⣸⡀⢀⣾⣿⣏⣉⣹⣦⣭⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣯⣷⣷⣆⣸⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⣛⢛⣻⡛⠃⣼⣿⣿⣿⢿⣿⣿⣿⣷⠶⣄⠙⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀
⣼⣟⣿⣿⠿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡟⡃⢤⣤⡀⢀⢾⣿⣠⣄⠀⠀⠀⠀⠠⣾⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣮⣻⣿⠁⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀
⠀⠀⢀⠀⣿⠀⠀⠀⠀⢸⣿⣿⡇⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡆⠀⠀⠀⢸⣿⣿⢣⠸⡆⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣇⠀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⡇⠀⠀⠀⢸⣿⣿⠸⡦⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠄⡛⠀⠀⠀⠀⠀⡁⠙⣿⠈⣿⣿⡄⠀⠀⠀⠀
⠀⠉⠀⠀⢸⡇⠀⠀⠀⢸⠿⠛⠀⠃⠳⠀⠠⠿⠿⠿⠿⠿⠿⠿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣶⣿⣾⣿⣿⣿⣿⣟⡃⠀⠀⠀⣴⣇⠀⡿⠀⠘⠿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣇⣠⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣿⣇⠃⠀⠀⠀⣀⣠⣡⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣟⡇⢙⣻⠏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣺⣇⣴⣿⣿⣤⣶⣦⣼⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣅⣾⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣾⣿⣿⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢸⣿⣿⣟⣛⣂⣹⣿⡋⠩⣽⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠙⠉⠉⢹⠙⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⢀⣀⣀⣀⣀⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⣾⣿⣿⣿⡟⣟⣃⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⠀⠀⡇⠀⢸⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣖⣶⠏⠀⠀⠀⠀⠀⠀⠦⣼⣿⣿⣿⣧⣿⣿⣏⣻⣷⣿⣼⣷⣟⣿⣿⣿⣿⣿⡟⣿⢻⡿⠍⣿⣿⣿⣿⣿⠊⠀⢳⠀⠀⡇⠀⢸⠘⡃⠀⠀⠀⠀⠀⠑⠊⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣆⡈⠛⠛⠛⢛⠋⠀⠀⠀⣀⠀⠀⠀⠀⠉⢻⡿⢿⣛⣝⣿⣟⠿⢻⠿⣿⣿⠸⡿⣿⢿⡟⣿⣿⣯⢸⡷⢖⣿⣿⣿⡇⢘⠀⠀⠠⠀⠀⡇⠀⠸⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⠉⠙⠲⣤⣀⢹⣼⠇⣾⢻⡆⣶⣾⣿⠻⢫⣬⡍⣍⣙⡿⣯⡿⣿⠷⠛⠪⠅⠛⠙⠋⠛⠓⠂⣿⣿⣿⡇⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⢻⣿⣾⡯⣴⣿⣼⡇⣿⢸⡏⣴⣾⣧⢠⣿⣼⡇⣿⣿⣿⣟⣷⣰⡶⣶⢀⣴⣦⡀⣤⢛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⢿⣻⣟⡛⠿⣿⣿⣿⠿⢋⣽⣷⡀⢻⣿⣿⣿⣯⣍⠀⣛⣿⣿⠏⠿⠷⠸⠏⣿⢡⣿⠿⣿⣿⣿⣿⣿⣯⣼⡏⣛⢃⣿⢿⣿⣿⣷⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣄⣤⣀⣀⣤⣾⣿⣿⣿⣤⣿⣿⣟⣾⣿⣯⣿⣹⡍⣤⣤⠀⢀⣀⠀⠰⣶⣷⣾⣿⣿⡿⣿⣿⣿⣷⠟⠸⠏⢼⣿⣿⣿⣇⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡤⠀⢸⡏⠀⣾⣿⣿⣷⣿⣟⣷⢩⡿⣿⣿⣿⣄⠀⣈⡉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⢿⡸⠿⣯⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣤⣵⣿⢾⣧⣿⢘⡋⣿⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢿⣿⣿⠀⠀⠀⠀⠁⣿⣯⣭⣿⣿⣿⡛⢸⣿⣿⣿⣷⢸⡏⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠈⢇⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠨⣭⣿⣿⣿⣇⡀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⡇⠀⠀⢐⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⣄⣈⣩⣿⣿⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣽⣿⣥⣤⣤⣤⣤⢨⣭⣭⣭⣭⣤⣼⣿⣭⣿⣿⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⡄⠀⠨⡭⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠐⠻⣿⣿⣿⠇⠀⢀⣬⡄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⡇⠀⠹⠿⢶⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣥⣈⡏⠀⠲⢾⣯⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣶⣿⡿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠛⠻⠛⠀⠀⠈⣿⣿⣿⡟⠀⠀⢰⣦⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀
⣤⠀⠀⠀⢸⣿⣿⣿⣧⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⡿⢨⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⠄⠀⠀⣺⣿⣿⡟⠛⠛⠛⢛⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⣧⠀⠀⠀⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠠⣬⣻⣿⠀⠀⠀⠠⢸⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⣦⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡟⡀⣉⣁⣀⣸⡀⠀⣾⣿⣯⣉⣩⣦⣭⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀
⣿⣿⣷⣿⣆⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣛⣛⣛⡛⠃⣸⣿⣿⣿⠿⣿⣿⣿⣷⠦⣄⠙⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀
⢼⣿⣿⣿⠿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡛⠃⢤⣤⡀⢀⢾⣿⣁⣄⠀⠀⠀⠀⠠⢴⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⢿⠉⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀
⠀⠀⢀⠀⣿⡆⠀⠀⠀⢸⣿⣿⠆⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⣿⣿⢀⠘⡇⠀⠸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀⣤⣧⡀⣠⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⡇⠀⠀⠀⢸⣿⣿⠨⡦⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⠿⠿⠿⠿⡛⠛⠀⡛⡃⠀⠀⠀⠀⡀⠁⣿⠁⢻⣿⡆⠀⠀⠀⠀
⠀⠉⠀⠀⢸⡇⠀⠀⠀⠸⠟⠛⠀⠃⠻⠀⠠⠿⠿⠿⠿⠿⠿⢯⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢰⣧⠀⠹⠀⠈⠛⠷⡄⠀⠀⠀
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣇⣀⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣄⠀⣿⣧⠈⠀⠀⠀⣠⣀⣀⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⡇⡇⢹⣻⡏⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡗⢰⣿⣿⣶⣷⣦⣼⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣷⢁⣶⣿⠏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣷⣿⣿⣿⡏⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢸⣿⣿⣟⣛⣀⣽⣿⡉⠉⣼⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣏⣿⣿⣿⡇⠉⡍⠉⢹⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠊⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣠⣤⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⠷⠶⢾⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⡟⣟⣃⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⢻⢸⠀⠀⡇⠀⢸⢀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⣶⣖⣶⠏⠀⠀⠀⠀⠀⠀⠢⢼⣿⣿⣿⣧⣿⣿⣏⣹⣷⣿⣼⣷⣟⣿⢿⣿⡿⣿⡟⣿⢻⣿⠍⣿⣿⣿⣿⢻⠉⠈⢸⠀⠀⡇⠀⢸⠈⡇⠀⠀⠀⠀⠀⠉⠁⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣄⡈⠛⠛⠛⣛⠋⠀⠀⠀⣀⠀⠀⠀⠀⠉⢻⡿⢿⣛⣝⣿⣿⠿⠻⠿⣿⣿⠘⡿⣿⢿⡗⣿⣿⣯⢸⡷⡖⣿⣿⣿⡏⢘⠀⠀⠨⠀⠀⡇⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⠀⠙⢲⣦⣄⢹⣼⠇⣾⢻⡆⣶⣾⣿⠻⢫⣬⡇⣌⣑⡾⣿⡿⣟⠓⠛⠊⠁⠙⠙⠃⠛⠓⠊⣿⣿⣿⡇⠸⠀⠀⠠⠀⠀⠇⠀⠀⠀⠃⠀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠈⢻⣿⣾⣿⣶⣿⣼⡇⣿⢸⡏⣴⣾⡧⢠⣿⣼⡇⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⣦⡀⣤⢛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢯⣾⣋⠛⠿⠿⠿⠿⠟⢁⣾⣷⡀⢻⣿⣿⣿⣯⡍⠀⣛⣻⣿⡏⠿⠷⠸⠏⣿⢡⣿⠿⣿⣿⡿⣿⣿⣯⣼⡏⣛⢃⣿⢺⣿⣿⣷⣿⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡽⣿⣿⣿⣶⣄⣀⣤⣠⣾⣿⣿⣷⣦⣿⣿⣏⣾⣿⣮⣿⣩⡍⣥⣤⠀⢀⣀⠀⠀⣶⣾⣾⣿⣷⣟⣿⣿⣿⣷⡟⠸⠏⢼⢿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⢿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡤⠀⢸⡏⠀⣾⣿⣿⣷⣿⣟⣿⢹⡿⣿⣿⣿⣄⠀⣀⡀⠀⠁⠉⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⢿⡸⠿⣯⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣥⣵⣿⣾⣇⣿⢘⡋⣿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⡿⣿⠀⠀⠀⠀⠁⣿⣯⣭⣿⣿⣿⣻⢸⣿⣿⣿⣿⣼⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⠀⠈⢣⠙⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠈⣭⣿⣿⣿⣧⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢇⠇⠀⠀⠘⡐⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣠⣀⣩⣽⣿⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣽⣿⣤⣤⣤⣤⣤⢨⣭⣭⣭⣭⣥⣼⣿⣭⣿⣿⣇⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⡇⠀⠠⣭⠽⣻⣿⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⢚⣿⣿⣿⡇⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣧⠀⠘⠿⠷⣾⣿⡆⠀⠀⠀⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠴⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢿⣧⣈⡛⠀⠐⠶⣿⣵⣾⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣻⣿⡷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡛⠻⠟⠁⠀⠀⢻⣿⣿⣿⠀⠀⢰⣶⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣤⠀⠀⠀⠸⣿⣿⣿⣷⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⣿⡿⢠⣿⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⠆⠀⠀⣐⣻⣿⡟⠋⠙⠉⢋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣧⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⣇⢸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⣬⣿⣿⠅⠀⠀⠐⢸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣦⢀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢼⣿⣿⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⣁⣈⣁⣀⣈⡄⠀⣼⣿⣿⣉⣉⣷⣬⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⣽⣿⣷⣿⣆⣸⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⡀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣛⡟⠃⢰⣿⣿⣿⡿⣿⣿⣿⣿⠦⣆⠙⢛⣿⣿⣿⣿⣿⣿⣿⠃⠀
⢼⣟⣻⣿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣿⣿⣿⠙⠁⠠⢤⠀⢀⣞⣿⣇⣤⠀⠀⠀⠀⠀⢼⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡙⠿⠏⠈⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⢀⠀⣿⡀⠀⠀⠀⢸⣿⣿⡅⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠂⠸⡇⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡄⣦⣧⡀⣤⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⡇⠀⠀⠀⢸⣿⣿⠨⡦⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⠿⠿⠿⠿⠛⡛⠛⢐⣛⡃⠀⠀⠀⠀⡀⠁⣿⠉⢻⣿⡇⠀⠀⠀⠀
⠀⠉⠀⠀⢸⡇⠀⠀⠀⠸⠛⠛⠀⠃⠷⠀⠠⠿⠿⠿⠟⠛⠿⢿⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⡄⢹⠀⠈⠻⠿⡄⠀⠀⠀
⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠰⢾⣇⣤⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⡄⠀⣿⣷⠁⠀⠀⠀⣤⣤⣥⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⡀⡇⢸⣿⡏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣴⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣧⢁⣾⣿⠇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⣿⣿⣿⣉⣠⣽⣟⡉⠀⣼⢿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣿⣿⠃⠉⠍⠉⢹⠉⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣤⣤⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡿⠿⠶⢾⣿⠃⠀⠀⠀⠀⢰⠿⣿⣿⣿⣿⡇⣾⣿⣿⣿⡟⣟⢓⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣾⠀⠀⡇⠀⢸⢠⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣷⣴⣾⠃⠀⠀⠀⠀⠀⠀⠲⢾⣿⣿⣿⣧⣿⣿⣏⣽⣷⣿⣼⣷⣟⣿⣿⣿⣿⣿⡟⣿⢻⣿⠍⣿⣿⣿⣿⢿⠓⠘⢹⠀⠀⡇⠀⢸⠸⡇⠀⠀⠀⠀⠀⠙⠉⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣄⡈⠛⠛⠛⣻⠃⠀⠀⠀⣀⠀⠀⠀⠀⢉⣹⡿⣿⣟⣝⣿⣿⠿⠻⠿⣿⣿⡘⡿⣿⢿⡟⣿⣿⣯⢸⣷⣞⣿⣿⣿⡇⢈⠀⠀⢸⠀⠀⡇⠀⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⠈⠙⢲⣦⣄⣹⣼⠇⣾⢻⡆⣶⣶⣿⠹⢫⣬⡅⣄⣐⡾⣿⣿⣿⠓⠛⠊⠁⠙⠙⠋⠛⠓⠂⣿⣿⣿⡇⠸⠀⠀⠠⠀⠀⠇⠀⠀⠀⠃⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⡻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⠈⢻⣿⣾⣿⣶⣿⣼⡇⣿⢸⡏⣴⣾⡧⢠⣿⣼⡇⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⢦⡀⣤⢛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢗⣶⣍⠛⠿⠿⠿⠿⠟⣁⣿⣷⡈⢻⣿⣿⣿⣯⡍⠀⣛⣿⣿⡏⠿⠷⠸⠏⣿⢡⣿⠿⣿⣿⡿⣿⣿⣯⣾⡏⣛⢃⣿⢻⣿⣿⣷⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⢟⣿⣶⣤⢀⣤⣶⣿⣿⣿⣿⣼⣿⣿⣏⣾⣿⣮⣿⣩⡍⣥⣤⠀⢀⣀⠀⠀⣶⣾⣾⣿⣷⣿⣿⣿⣿⣷⡟⠸⠏⢼⢿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡤⠀⢸⡏⠀⣾⣿⣿⣷⣿⣟⣿⢹⡿⣿⣿⣿⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⢿⡸⠿⣯⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣥⣵⣿⣾⣇⣿⢘⡋⣿⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢿⡿⣿⠀⠀⠀⠀⠁⣿⣯⣽⣿⣿⣿⣻⢸⣿⣿⣿⣿⣼⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⢳⠻⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⠀⢭⣿⣿⣿⣧⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢃⠇⠀⠀⠘⡲⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣠⣀⣩⣽⣿⡀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣯⣽⣿⣤⣤⣤⣤⣤⢨⣭⣭⣭⣭⣥⣼⣿⣭⣿⣿⢃⣾⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠠⣭⠽⣿⣿⡇⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⢛⣿⣿⣿⡇⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣷⠀⠉⠿⠷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠾⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣦⣉⡻⠀⠐⢾⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣻⣿⡏⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢑⣻⣿⡷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⠻⠟⠃⠀⠀⢻⣿⣿⣿⠀⠀⣰⣾⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣦⠀⠀⠀⢸⣿⣿⣿⣷⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⡿⢰⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⠇⠀⠀⣸⣿⣿⣿⠙⠛⠉⢻⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣧⠀⠀⠀⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⣇⣺⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⣬⡿⣿⠏⠀⠀⠰⢸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣦⢀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣻⣿⣿⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⠟⣉⣉⣡⣠⣸⡄⠀⣾⣿⣿⣈⣩⣷⣮⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⣽⣿⣷⣿⣆⣸⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠖⢆⠈⢛⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠼⣿⣿⣿⠟⣿⣿⣿⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣉⠁⠤⣤⠄⢠⣚⣿⣧⣤⠀⠀⠀⠀⠠⢼⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⣿⣿⣷⣝⡿⠇⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⢀⠀⣿⠀⠀⠀⠀⢸⣿⣿⡅⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡄⠀⠀⠀⢸⣿⣿⢥⠸⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡄⣴⣿⣀⣤⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⢸⡦⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⠿⠿⠛⡛⠛⢐⣛⡃⠀⠀⠀⠀⣄⠀⣿⠉⢹⣿⡇⠀⠀⠀⠀
⠀⠉⠀⠀⢸⡇⠀⠀⠀⠸⠛⠛⠀⠃⠣⠀⠸⠿⠿⠿⠟⠛⡿⢻⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣄⣸⠀⠀⠻⠿⡆⠀⠀⠀
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠲⢾⣇⣤⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⡆⠀⣼⣷⡈⠀⠀⠀⣤⣄⣠⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⠀⡇⢹⣿⠟⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣹⣧⣰⣿⣿⣷⣾⣷⣶⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢁⣾⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡟⢯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣿⣿⣿⣿⣉⣠⣽⣏⡁⢢⣾⢿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⠀⢙⠉⠉⢹⠈⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣤⣤⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⠿⠿⠶⢾⣿⠃⠀⠀⠀⠀⢰⠿⣿⣿⣿⣿⡇⣼⣿⣿⣿⡟⣟⢛⡸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣻⣟⢿⡷⠀⢸⡇⠀⢸⢰⡀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⣿⣿⣷⣤⣾⠃⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣷⣿⣿⣏⣹⣷⣿⣼⣷⣟⣿⣿⣿⡿⣿⡟⣿⢻⣿⠍⣿⣿⣿⣿⢻⠉⠀⡗⠀⠈⡇⠀⢸⢸⡇⠀⠀⠀⠀⠀⠙⠁⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣄⡉⠛⠛⢛⣻⠁⠀⠀⠀⣀⠀⠀⠀⠀⢉⣻⡿⣿⣟⣝⣿⣿⡿⠻⠿⣿⣿⣘⡿⣿⢿⡟⣿⣿⣯⢸⣷⣞⣿⣿⣿⠏⢈⠀⠀⠇⠀⠀⡇⠀⠸⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣇⠈⠙⣲⣤⢄⢹⣼⠇⣾⢻⡆⣶⣾⣿⠻⢫⣬⡅⣄⣐⡾⣿⡿⣿⠓⠛⠈⠁⠙⠙⠃⠛⠓⠂⣿⣿⣿⡇⠸⠀⠀⠀⠀⠀⠇⠀⠀⠘⠇⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣀⣄⠈⢿⣿⣾⣿⣶⣿⣼⡇⣿⢸⡏⣴⣾⡧⢠⣿⣼⡇⣿⣻⣿⣿⣷⣴⡶⣶⢀⣴⣦⡀⣤⢛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⢻⣾⣍⠛⠿⠿⠿⠿⠛⣁⣿⣷⡈⢿⣿⣿⣿⣯⡍⠀⣛⣿⣿⡟⠿⠷⠸⠏⣿⢱⣿⠻⣿⣿⡿⣿⣿⣯⣾⡏⣛⢣⣿⢿⣿⣿⣷⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣿⣦⣄⣀⣶⣶⣯⣿⣿⣿⣼⣿⣿⣏⣾⣿⣮⣿⣩⡍⣥⣤⠀⢀⣀⠀⠀⣶⣾⣾⣿⣷⣿⢿⣿⣿⣿⡟⠸⠟⢽⣿⣿⣿⣇⣿⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡤⠀⢸⡏⠀⣾⣿⣿⣷⣿⣟⣿⢽⡿⣿⣿⣿⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⢿⡸⠿⣯⡆⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣥⣵⣿⣾⣃⣿⢘⡋⣿⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⠃⠀⠀⠀⠁⢻⣯⣭⣿⣿⣿⣻⢈⣿⣿⣿⣿⣼⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠈⢱⡙⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢭⣽⣿⣿⣷⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢣⠃⠀⠀⠀⡗⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⢠⣀⣩⣽⣿⡇⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣯⣽⣿⣤⣤⣤⣤⣤⢨⣭⣭⣭⣭⣥⣼⣿⣬⣿⣿⢡⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⡇⠀⠀⢭⠽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⢚⣿⣿⣿⡇⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⣿⠀⠈⠻⠷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠾⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠛⠀⠐⠿⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣻⣿⡏⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⡷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⠛⠁⠀⠀⢹⣿⣿⣿⠀⠀⣰⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣤⠀⠀⠀⢸⣿⣿⣿⣇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⣿⡟⣴⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⠇⠀⠀⣐⣿⣿⣿⠙⠋⠙⢻⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣧⠀⠀⠈⣿⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣇⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⣬⡽⣿⠇⠀⠀⠰⢸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣦⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣾⣿⣿⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠟⢁⣉⣥⣠⣸⡀⠀⣾⣿⣿⣈⣩⣷⣮⡍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⣿⣯⣿⣷⣆⣸⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠛⠛⠃⣰⣿⣿⣿⡟⣿⣿⣿⣿⠖⢆⡈⢛⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠼⣿⣿⣿⠟⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣉⠅⢤⣤⡄⢠⣚⣿⣤⣄⠀⠀⠀⠀⠀⢴⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣷⣝⣿⠇⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⢀⠀⣿⠀⠀⠀⠀⢸⣿⡿⠇⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⣿⡿⢂⢸⡄⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⢠⣻⡀⢀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⢸⡤⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠤⠛⠃⠀⠀⠀⠀⢀⠘⢹⡟⠸⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠸⠛⠛⠀⠃⠣⠀⠸⡿⠿⠿⠿⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣶⣿⣾⣿⣿⣿⣿⣟⡃⠀⠀⠀⢀⣿⡀⣨⠇⠀⠻⠿⡆⠀⠀⠀
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣆⣀⣷⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣆⠀⢸⣿⡈⠀⠀⠀⣀⣀⣀⣠⠀⠀
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣶⣶⠠⡏⢙⣻⠯⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢹⣯⡴⣾⣿⣧⣴⣶⣤⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⣾⣿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣶⣶⣿⣿⡏⢳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⣿⣿⣿⣛⣃⣨⣿⣏⠉⢁⣾⢿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⢙⠉⠉⢹⠈⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣯⣷⣽⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣿⣿⣿⣿⣿⣿⠶⠶⣾⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⣴⣟⣿⣿⡟⣟⣻⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⠿⡿⡇⠀⢘⡇⠀⢸⢸⡀⠀⠀⠀⠀⠀⢘⡿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣶⣶⣒⣾⠃⠀⠀⠀⠀⠀⠠⠦⣼⣿⣿⣿⣿⣿⣿⡏⣹⣷⣿⢹⣷⣟⣿⢿⣿⣿⣿⡟⣿⢻⣿⠍⣿⣿⣿⣿⢿⠈⠀⡧⠀⠸⡇⠀⢸⢸⠇⠀⠀⠀⠀⠀⠘⠃⠹⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣷⣄⡙⠛⠛⢛⣻⠃⠀⠀⠀⣀⠀⠀⠀⠀⠉⠿⠿⢿⣟⣝⣿⣿⡿⠻⠿⣿⣿⠸⠿⣿⢿⡯⣿⣿⣯⢸⡷⣎⣿⣿⣿⡏⠘⠀⠀⠇⠀⠀⡅⠀⠸⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣠⡏⠉⠓⢦⣤⣀⢹⣼⠇⣾⢻⡆⣶⣾⣿⠻⢫⣥⡝⣏⢐⣻⣿⡿⣿⡷⠟⠊⠁⠛⠙⠋⠛⠓⠚⣿⣿⣿⡆⢰⠀⠀⠀⠀⠀⡇⠀⠀⠘⠋⠀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣷⣿⣯⣴⣿⣼⡇⣿⢸⡏⣠⣾⡧⢠⣿⣼⡇⣿⣹⣿⣿⣷⣴⡶⣶⢀⣴⣦⡀⣤⢛⣛⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢖⣯⡛⠿⢿⣿⣿⡿⠟⢁⣿⣦⠈⢿⣿⣿⣿⣯⡉⠀⣛⣿⣿⣿⠿⠷⠸⠏⣿⢻⣿⠱⣿⣿⣿⣹⣿⣯⣾⡏⣛⢃⣿⢿⣿⣿⣷⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⢞⣿⡟⣶⣆⣀⠀⣤⣴⣿⣿⣿⣷⢸⣿⣿⣏⣾⣷⣮⣿⣹⡟⣭⣤⠀⢀⣀⠀⠀⢠⣦⣾⣭⣯⣿⣿⣿⣿⣿⣿⠸⠟⢼⢿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡤⡆⢸⡇⠀⣾⣿⣿⣷⣾⣟⣿⢧⡿⣿⣿⣿⣇⠀⣉⡉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠿⠸⠿⣯⣿⣼⣧⢰⡿⣿⣿⣿⣿⣿⣟⣭⣵⡿⢸⣇⣿⣜⡋⣿⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠊⠿⣿⠀⠀⠀⠁⠉⣯⣭⣿⣿⣿⣻⣒⢺⣿⣿⣿⣽⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠈⣭⣽⣿⣿⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣀⣀⣩⣽⣿⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣯⣽⣿⣤⣤⣤⣤⣤⢨⣭⣭⣭⣭⣥⣽⣿⣭⣿⣿⢋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⡃⠀⠀⠤⢟⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⢀⣛⣿⣿⣿⠇⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣿⡆⠀⠈⢓⣶⣿⣿⠀⠀⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣄⠀⠀⠀⢙⣻⣷⣶⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢶⣿⣷⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⠃⠀⠀⠈⢿⣿⣿⡗⠀⢰⣷⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣄⠀⠀⠀⢻⣿⣿⣿⣿⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⣿⡿⣨⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠿⠆⠀⠀⢀⣻⣿⡿⠛⠛⠛⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣧⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⡤⠙⡿⠇⠀⠀⠠⢸⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣤⡀⠀⢘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣾⣿⣿⣿⣿⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣁⣉⣀⣀⣸⡀⠀⣰⣿⣿⣉⣉⣧⣬⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣻⣿⣿⣾⣄⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣷⣤⡀⠀⢠⣽⡧⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠘⣛⢛⢛⣿⠇⢠⣿⣿⣿⡿⣿⣿⣿⣿⡶⣄⠘⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣙⣛⣻⣿⡿⣿⣿⣿⣿⣿⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⡛⡁⢠⣾⣿⢁⠞⣿⣄⣄⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⣷⣙⠿⠏⠈⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠠⠀⣿⠀⠀⠀⠀⢿⣿⡯⡇⢻⠀⠀⢸⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡗⠁⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢨⣽⡀⢀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡧⢰⠼⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠏⢔⠛⠃⠀⠀⠀⠀⢀⠘⢹⡏⢛⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠸⠛⠛⠈⠂⠇⠀⢸⠿⠿⠿⠿⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣛⡃⠀⠀⠀⢀⣾⣀⢨⠃⠀⠙⠿⢆⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⣀⣐⣷⣾⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣆⠀⢸⣿⡈⠀⠀⠀⢀⣀⠀⣠⡀⠀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣦⠨⠏⢙⣿⠭⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⣿⣷⣴⣾⣿⣷⣴⣶⣤⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣾⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣶⣶⣿⣿⣯⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣿⣿⣿⣛⣃⣨⣿⣏⠉⢁⣾⢯⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣸⣿⣿⣿⠀⢹⠉⠉⡹⠈⠁⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢺⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠹⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠶⠶⣾⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⣶⡆⣤⣠⡄⣄⣀⡀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⠟⡇⠀⢸⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠠⢻⣿⣿⡟⠁⠀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣒⣾⠃⠀⠀⠀⠀⠀⠠⠤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣟⣿⣿⣿⡿⣿⡟⣿⢻⣿⠍⣿⢿⣿⣿⢿⠀⠀⡇⠀⢸⠇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠓⠹⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣧⣈⠙⠛⠛⠛⣻⠃⠀⠀⠀⣀⠀⠀⠀⠀⠉⠿⠿⣿⣛⣙⣻⣿⣿⠻⠿⣯⣿⡼⡿⣿⢿⡟⣿⣿⣯⢸⡷⢎⣿⣿⣿⠃⠈⠀⠀⡇⠀⢘⡁⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣠⡎⠙⠲⢤⡄⡀⢹⣼⠇⣾⢻⡎⣶⣶⣿⠻⢫⣿⡟⣟⣟⡻⣿⡿⠗⠷⠿⠊⠁⠛⠙⠃⠛⠓⠚⣿⣿⣿⡀⠠⠀⠀⠁⠀⠈⡇⠀⠀⠘⠃⠀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠙⣿⣾⣽⣯⣴⣿⣼⡇⣿⢸⡏⠀⣼⣧⢠⣿⣼⡇⣿⣻⣼⣿⣷⢰⡶⣶⢀⣴⢦⡀⣤⢛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⣵⣭⠛⠿⣿⣿⣿⣿⠿⠑⣿⣦⠘⣿⣿⣿⣿⣯⡉⠀⠛⣛⣵⣾⡿⠷⠸⡇⣿⢱⣿⢱⣿⣿⣿⣿⣿⣯⣼⡏⣛⢣⣿⢾⣿⣿⣷⡿⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⢙⣿⣿⣦⣄⡀⠀⢀⣴⣿⣿⣿⣧⢸⣿⣿⣏⣾⣷⣦⣿⣹⡟⣿⣅⠀⢀⣀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⠸⠟⢼⢿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣧⣯⣷⣽⣾⣽⣶⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡇⠀⣾⣿⣾⣷⣶⣟⣾⢬⡿⣿⣟⣿⣿⡄⣉⡉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠿⠸⠿⣯⣦⣾⣧⢰⡿⣿⣿⣿⣿⣿⣟⣬⣵⡿⢺⣇⣿⣼⡏⣿⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⠿⣿⡆⠀⠀⠁⠉⣯⣭⣽⣿⣿⣻⣢⠀⠾⢿⣿⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠛⠀⠘⠛⣛⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⢩⣭⣽⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣯⣽⣿⣤⣤⣤⣤⣤⢨⣭⣭⣬⣭⣤⣽⣿⣭⣿⣿⢋⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⡿⠇⠀⠀⠀⢀⣬⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡯⢿⢟⡆⠀⠀⠀⠀⣴⣺⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⢤⢉⠀⠀⠀⢠⣤⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢶⣿⣿⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣿⣿⣿⠋⣰⣶⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣄⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⡿⢨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⡿⠛⠛⠛⠛⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣆⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⢾⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⣿⣿⣦⡀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⣿⣿⣿⣿⡟⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣀⣸⡀⠀⢰⣿⣿⣉⣉⣷⣬⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣻⣿⣯⣾⣄⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⡀⢠⣿⣿⣷⢄⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡔⠈⠊⠛⢻⢛⡛⠇⢀⣿⣿⣿⡿⣿⣿⣿⣿⡶⢄⠘⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀
⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⣿⣿⡟⣡⣾⣿⣿⢃⠞⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣜⠿⡏⠁⠁⠀⠙⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⡇⡇⢿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣿⡏⠂⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠠⢠⣼⣀⢀⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡧⢰⠼⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠻⠃⢐⠛⠛⠀⠀⠀⠀⢀⠈⢸⡏⠘⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡆⠀⠀⠀⠸⠛⠃⠈⠂⠇⠀⠸⠿⠿⠿⠿⠿⠿⠿⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣛⡋⠀⠀⠀⠀⣿⡄⡀⠇⠀⠙⠛⢧⠀⠀⠀
⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣼⣀⣐⣷⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠰⣿⡀⠁⠀⠀⢠⣀⢀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣦⠠⡏⢙⣻⠏⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣠⣾⣿⣷⣶⣷⣤⣾⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣶⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣶⣿⣿⣿⡟⠢⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣿⣿⣿⣛⣁⣨⣿⣏⠉⢀⣴⢯⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣸⣿⣿⣹⠀⢹⠉⠉⣿⠁⠀⠀⠀⠙⢻⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣭⣷⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣾⣿⣿⡏⠀⢸⠀⠀⢻⢀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⡿⠾⠶⢿⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⣿⡟⣭⢡⡌⣉⢉⡛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⠛⡇⠀⢸⡄⠀⠠⢸⡄⠀⠀⠀⠀⠀⠀⠉⢿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣶⣒⣾⠃⠀⠀⠀⠀⠀⠀⠦⣼⣿⣿⣿⣿⣿⣿⡏⣸⣧⣿⡈⣧⡟⣿⣿⣿⡿⣿⡗⣿⢻⡿⠍⣿⢿⣿⣿⢿⠀⠀⡆⠀⢸⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣧⣀⠉⠛⠛⢛⣻⠃⠀⠀⠀⣀⠀⠀⠀⠀⠉⠿⠿⣿⣟⡙⠛⠁⢿⣻⠿⣿⣿⣿⡿⣿⢿⡟⣿⣿⣯⢸⡷⢆⣿⣿⣿⠁⠈⠀⠀⡇⠀⢘⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣠⡎⠉⠳⢦⡄⡀⢹⣼⠇⣾⢻⡎⣶⣶⣿⠹⢣⣤⡄⣟⣟⡻⣍⡿⣟⠓⠛⠊⠁⠛⠙⠃⠛⠓⠐⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠇⠀⠀⠘⠀⠀⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣷⣽⣯⣴⣿⣼⡇⣿⢸⡏⠀⣼⣧⢤⣿⣽⡿⣿⣿⣿⡟⣷⢰⡶⣶⢀⣴⢦⡀⣤⢛⣛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⠀⡉⠛⠿⣿⣿⣿⡿⠟⠁⢼⡆⠈⣿⣿⣿⣿⣯⡉⠀⠛⠛⠁⠀⠿⠷⠸⠏⣿⢻⣿⠑⣿⣻⣿⣸⣟⣯⢸⡇⣛⢃⣿⢾⣿⣿⣣⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠊⠰⠀⠀⠀⠀⠀⣠⠀⢀⡐⢧⢼⣿⣿⣏⣾⣷⣆⣦⣠⡔⣾⣿⠃⢀⣀⣀⠀⠀⠁⣾⣭⣿⣿⣿⣿⣾⣷⡟⠸⠏⢼⢿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣧⣦⣤⣤⣤⣦⣴⢡⣤⣷⣤⣷⣮⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄⠀⢸⡏⠉⣿⣿⢸⡷⣾⡟⣿⢻⡿⣿⣿⣿⣇⡀⣀⡀⠁⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⠿⠸⠿⡆⠀⣼⣧⢰⡿⣿⢸⣿⣿⣿⣟⣤⣵⡿⢺⣇⣿⣽⡏⣿⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⡀⠀⠀⠀⠁⠉⢩⣭⣿⣿⣿⣻⣢⠀⠾⢿⣿⣽⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡆⠀⠻⢿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⡁⠀⠀⠀⠈⠐⠛⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣯⣽⣿⣤⣤⣤⣤⣤⢨⣭⣭⣬⣭⣤⣼⣿⣭⣿⣿⢃⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠿⡻⠽⡧⠀⠀⠀⠀⠀⠼⣷⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣧⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣶⣿⡿⢶⢲⢒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀
⣄⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⡿⢨⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠿⠛⠙⠛⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀
⣿⣇⠀⠀⠈⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⢾⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠀⠀⠠⢰⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀
⣿⣿⣧⠀⠀⢸⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⣿⣿⣿⣿⡿⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⡀⠀⢰⣿⣿⣍⣉⣽⣤⣍⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⣻⣿⣯⣷⣄⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⢤⡀⢀⣾⣿⣿⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡄⠘⠛⠛⠛⠛⠇⢀⣿⣿⣿⡟⢿⣿⣿⣿⡷⢤⡈⠛⣿⣿⣿⣿⣿⣿⣿⡏⠀
⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⢡⣾⣿⣿⢃⢞⣿⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣜⠻⠏⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⢠⠀⣿⠀⠀⠀⠀⣿⣿⣿⡇⢿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢨⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣿⣿⡇⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⢸⣿⣷⣦⣤⣄⠀⠀⠀⠀
⠀⠀⠐⠀⣿⡀⠀⠀⠀⢸⣿⣿⢿⠼⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⡛⣓⢘⣛⣛⡄⠀⠀⠀⣼⠽⢹⡏⢹⣿⣿⡀⠀⠀⠀
⠈⠁⠀⠀⣿⠇⠀⠀⠀⠸⠛⠛⠽⠦⠧⠄⠸⡿⠿⠿⠿⠿⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⡓⡅⠀⢠⣿⣤⣸⠇⠀⢻⣿⣷⡀⠀⠀
⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣶⣾⣤⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡄⣸⣿⣎⢁⡀⠀⣼⣿⣿⣷⡄⠀
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⡏⣽⣿⡟⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆⣳⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣿⣿⣿⣿⣉⣰⣿⣏⡑⢲⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠉⡉⣿⣏⠹⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠃⢿⢿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏
⠀⠀⣀⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⠃⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡇⠀⢸⢸⣆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⢉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠠⢶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⡿⠀⢸⡇⠀⠀⢸⡟⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀
⠀⠀⠀⠘⠀⠀⠀⣠⣴⣿⣿⣿⣤⡉⠛⠛⢛⣻⠃⠀⠀⢠⠀⠀⠀⠀⠘⢿⣿⡿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢹⠀⠀⡇⠀⢸⡄⠀⠘⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣬⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠉⠓⣶⣤⣈⠀⠀⠀⠀⠀⠙⠋⠙⠛⠿⠿⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⠿⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⡇⢸⠀⠀⠧⠤⠘⠇⠀⠀⢸⡿⡄⣶⣦⣤⣤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⠘⣿⣿⣿⣶⣄⠀⠠⠤⠴⠦⠆⠥⡶⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠆⠁⠒⠛⠀⠙⠁⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⡿⠿⣽⣿⣷⡜⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠐⠂⢰⣷⣦⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣶⣄⣤⣴⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡶⠶⠄⠤⠤⠤⣶⡄⣿⡿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠂⠀⠀⠀⢀⡠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⠁⠹⣄⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡀⡀⠀⠀⠁⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠘⠿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠶⢄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⠋⣙⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⡿⡟⠛⢻⣟⠀⠀⠀⠀⠀⠀⠀⢠⣼⣭⣿⣯⣿⢻⣿⣿⣿⣿⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠙⠹⠟⠃⡀⠚⠛⠈⠍⠱⠀⣿⣷⣿⣿⣿⡇⡇⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠿⠻⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣿⡟⣿⣿⣿⢧⠇⠀⠀⠈⠿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⢻⣿⡀⠀⠀⠀⠀⠡⠀⠐⠀⠀⠀⢸⣿⢰⣿⣿⢫⣾⡄⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡗⠀⠀⠙⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡏⣿⡇⠀⠀⠀⠀⠀⠈⢑⠂⠀⠀⣾⡇⢸⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⣿⡇⣾⣿⡟⠉⠽⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡄⣿⣿⠟⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⣿⡧⢾⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠞⠊⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣘⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⣦⡀⠀⠀⢿⣿⣿⣿⣿⡄⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⣿⣿⢭⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⣿⣷⡀⠀⠘⣿⣿⣿⣿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⣿⣟⣾⣿⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢿⣿⣿⣿⣿⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⣿⣿⣧⣀⠀⢸⣿⣿⣿⣿⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠻⣻⣷⣸⡄⠀⢰⣿⣿⣇⣉⣽⣿⣿⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣇⢨⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⣿⣿⣿⣶⡄⠀⠀⣼⣄⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠤⠴⢿⣿⡿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣈⢙⣻⣿⣿⣿⣿⣿⣿⡟⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢂⠀⣿⣿⣿⣿⣟⣷⣦⣾⣿⢣⣾⣿⣯⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⣠⢖⠀⠀⢸⣿⣿⣿⣿⣿⣻⡿⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠀⣂⢸⣿⠀⠀⠀⠀⣿⣿⣿⡇⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⢀⢸⣿⠀⠀⠀⠀⣿⣿⣿⡇⢹⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⢦⣸⣿⣶⣶⣶⡄⠀⠀⠀⠀
⠀⠀⠀⠈⣿⠀⠀⠀⠀⢿⣿⣿⢿⢸⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⠿⡛⢛⢛⣛⣓⣚⣙⣉⡄⠀⠀⠀⣶⠙⢿⡇⢻⣿⣗⠀⠀⠀⠀
⠈⠁⠀⠀⣿⠀⠀⠀⠀⠙⠛⠛⠝⠴⠧⠠⠼⠿⠿⠿⠛⢛⣟⣛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡍⡆⠀⢸⣿⢦⡼⠁⠀⠻⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⡿⣿⣼⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣷⡀⣸⣿⡏⣠⡀⢀⣾⣿⣿⣷⡄⠀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣿⣿⣿⣿⡟⣰⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣐⣤⡀⣿⣿⣿⣯⣩⣴⣿⣯⣐⣲⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⠉⡁⡇⣿⠉⠋⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⡿⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡠⠀⡟⣿⡀⠀⠀⠀⠀⠩⢿⣿⣿⣿⣿⡿⠋
⠀⠀⣀⣀⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠁⠀⠀⠀⠀⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⠄⠀⡇⢻⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠀⠀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣽⣿⠁⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠿⠃⡇⠀⢸⠀⠀⡇⢸⡏⠀⠀⠀⠀⠀⠈⠛⡿⠃⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠀⣠⣴⣿⣿⣿⣦⣌⠙⠛⢛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡉⠀⠀⡇⠀⢸⡀⠀⠃⢸⡯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣾⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣗⠈⠛⣶⣤⣄⡀⠀⠀⠀⠀⠉⠡⠘⠛⠿⠛⠿⠿⡿⠿⠏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⠀⠠⠀⠀⠇⠄⠸⠇⠀⠀⢸⣇⢼⣿⣶⣦⣤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⠙⣿⣿⣿⣶⣄⠀⠠⠤⠶⠖⠦⠤⠤⠶⠮⠵⠦⠄⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠁⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⠿⠟⣽⣿⣧⡘⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠁⠊⠋⡛⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠿⠂⠤⠄⠀⠶⠿⠿⠆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆⠀⠀⣈⣿⣿⣿⡏⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⠀⠀⣠⣄⣀⣿⣿⣿⣿⣿⣿⣂⣀⣀⡀⠀⠀⠀⠀⠀⠈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣶⡶⠿⠷⣶⠶⠶⢶⠆⠀⣹⣿⣿⣿⣿⣿⣿⡿⠿⠈⠁⠙⠀⠀⠀⠶⠆⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⠟⠋⠉⠃⠎⠽⣿⡿⡛⠛⣿⡿⣿⣿⣿⣿⡄⡀⠀⠀⠀⢀⣀⣤⣴⡆⠘⡿⡍⠉⠛⢿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠁⠠⠖⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣦⣤⣾⣿⣿⣿⣿⣿⠃⠀⠀⣷⣦⣄⠀⠈⣿⣿⣿⣷⣦⣤⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⣿⣿⢧⠏⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠉⠀⠀⠀⠹⢿⣿⣿⣿⣿⣷⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⢫⣿⣆⠈⠛⠿⠻⠉⢙⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⡏⣿⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣾⡇⢸⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣴⣷⡆⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⡇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⡟⠉⠭⠯⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢿⣿⣇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣿⣿⣿⣿⣿⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡇⠾⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠻⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⣾⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣦⡀⠀⠀⢿⣿⣿⣿⣿⡀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⣿⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⣽⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣷⡀⠀⠘⣿⣿⣿⣿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡙⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣿⣿⣧⣀⠀⢸⣿⣿⣿⣿⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⣿⣿⢿⡿⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠈⠻⣿⣿⣿⡄⠀⣸⣿⣿⣧⣤⣾⣿⣿⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⡗⢈⡆⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣶⡦⠀⠀⠀⠀⢠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⠆⠀⠀⠈⢿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⣄⣉⣿⣿⣿⣿⣿⣿⣿⡏⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣿⣟⠃⠀⠀⣴⠠⢿⣿⣿⡦⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⣿⣿⡇⢸⣿⣿⣿⣿⣿⣟⣿⠀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⡂⢸⡇⠀⠀⠀⠀⣿⣿⣿⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⡿⡆⢻⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⠀⠀⠀⠀⣆⣿⣧⣄⣴⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣿⠀⠀⠀⠀⣿⣿⡇⣷⢺⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠛⠛⡛⣛⣛⣛⣓⣪⣉⣉⡆⠀⠀⢀⣧⠉⣿⠈⢿⣿⣇⠀⠀⠀⠀
⠈⠁⠀⠀⣿⠀⠀⠀⠀⠛⠋⠉⠚⠚⠃⠠⠼⠿⠛⠛⠛⢛⣛⣛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡅⡀⠀⢸⣿⣦⠝⠀⠈⠟⠿⡆⠀⠀⠀
⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⡿⢿⣬⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⣷⡀⣼⣿⡄⣀⠀⢠⣿⣶⣼⣦⡀⠀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⣿⣿⡛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣿⣿⣿⡎⣰⣿⡿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⣤⡈⣿⣿⣿⣭⣭⣴⣿⣧⣀⣻⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⠀⠀⡇⣿⠈⠈⠁⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⡟⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠈⠀⡇⣿⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠁
⠀⠀⢀⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⠟⢿⡟⠁⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⡇⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠒⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⡇⠀⢸⠀⠀⡇⢹⡏⠀⠀⠀⠀⠀⠈⠉⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣤⣈⠉⠉⢩⣽⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡇⠀⠀⡇⠀⢸⠀⠀⠇⢸⡟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠈⠛⣶⣤⣄⡀⠀⠀⠀⠀⠙⠀⠘⠋⢻⠛⠿⠿⣿⠻⠏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⢹⣿⣿⣿⠀⠀⠀⠀⠆⠄⠸⠂⠀⠀⢸⡁⢸⣿⣷⣶⣶⠂⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⠘⣿⣿⣿⣶⣄⠀⠤⠴⠶⠶⠤⠤⠤⠶⠬⠵⠎⠀⠀⠶⠾⠋⠀⠀⠀⠘⠃⠀⠈⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣛⠿⠿⣿⡿⠿⠟⣽⣿⣦⡘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣶⣦⣤⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠛⠂⠀⠀⠐⠻⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣈⣿⣿⣿⡏⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠶⠾⠿⠷⠶⠶⠖⠶⠿⠿⠆⠀⠀⢠⣶⣤⣿⣿⣿⣿⣿⡚⠀⠀⠐⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠟⠋⠈⠡⠐⠺⠿⠟⠛⠙⣿⡟⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣄⡀⢠⣼⠿⢿⣿⣿⣿⣿⠏⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⡇⣿⣶⣦⣴⣷⣽⣿⣿⣿⣿⣿⣿⠀⠀⠙⣀⠀⠀⠛⠿⣷⣦⣤⡀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣿⣿⣿⢳⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⠷⠂⠀⢰⣿⣿⣿⣿⣷⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⢣⣿⡄⠀⠀⠀⢸⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⣿⣾⣿⣿⠶⠶⢾⡞⠀⠈⠉⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⣿⡏⠉⠭⠧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣵⣿⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡇⠺⣿⣿⡁⢀⣰⣄⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡿⠁⣙⣿⠇⠀⠀⠀⣸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⣿⣗⣿⣿⡿⠿⠿⠿⠿⠶⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠀⠈⢿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣦⡀⠀⠈⢿⣿⣿⣿⣿⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣷⡀⠀⠘⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣺⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠏⠀⠀⠀⠘⣿⠆⠀⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣿⣿⣧⣀⠀⢸⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⣀⡀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⢀⠀⣸⣿⣿⣧⣤⣾⣿⣿⣉⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⡅⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣶⡇⠀⠀⠀⠀⢠⣿⡧⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡇⠀⠀⠒⠛⢠⣿⣿⣿⣿⣿⣿⣿⠿⠟⠳⣤⣬⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣏⠡⢶⣦⠴⠠⠯⣿⡧⠶⣩⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠆⢸⡇⠀⠀⠀⠈⣿⣿⣿⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⡄⢷⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⠀⠀⠀⠀⣼⣿⣦⣠⣶⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣇⣳⢺⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⡛⣛⣛⣛⣋⣩⣩⣥⣭⣭⣭⡆⠀⠀⢠⡄⢸⡇⠘⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⠀⠀⠀⠀⠋⠉⠁⠛⠚⠓⠀⠚⠛⠛⢛⠛⢛⣛⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡇⡄⠀⢸⡷⡌⠃⠀⠈⠻⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⣀⣈⡿⢿⣬⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣷⣿⡀⣼⣷⠀⣄⠀⣰⣶⣾⣿⣆⡀⠀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺⠀⣿⣿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⠿⠏⣸⣿⡟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡏⣿⣿⡾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⣦⡬⣿⣿⣿⣷⣤⣾⣿⣧⣌⣹⣿⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⢀⠀⡇⣿⠈⠁⠁⠉⠙⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⡇⣿⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⠀
⠀⠀⢤⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣛⣛⣛⣻⡟⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⡇⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⡿⠊⠁⡇⠀⢸⠀⠀⡇⢸⡏⠀⠀⠀⠀⠀⠀⠉⠏⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⣀⣴⣾⣿⣿⣿⣦⣄⠉⠉⡩⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣣⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⠁⡅⠀⠀⠇⠀⢸⠀⠀⠃⢸⡟⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠙⣷⣦⢄⡀⠀⠀⠀⠀⠁⠀⠈⠉⠛⠛⠛⠛⡛⠛⠃⠛⠛⠉⠛⠉⠉⠉⠉⣉⠉⢉⡉⢸⣿⣿⣿⠀⠁⠀⠀⠃⠂⠘⠀⠀⠀⢸⢄⣸⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠘⣿⣿⣿⣷⣦⠀⠀⠐⠒⠃⠀⠰⠖⠒⠐⠒⠚⠀⠀⠒⠛⠛⠒⠂⠀⠉⠀⠀⠀⠀⠘⠟⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣮⣝⠻⠿⠿⠿⠿⢋⣼⣿⣷⡘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠉⠉⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣶⣤⣦⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡛⠓⠂⣐⠒⠐⠚⡛⡛⠁⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣦⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠯⠿⠿⠿⠿⠿⠿⡿⠷⠿⠟⢿⣿⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠟⠻⠿⠶⠖⠒⠛⠛⠻⠶⠏⠙⠓⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠀⠀⠈⠿⠏⠉⠉⣿⣏⣿⣿⣿⡿⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣀⣶⣶⡀⢠⣾⡿⠿⢿⣿⣿⣿⡏⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⡇⣿⣶⣶⣶⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⣀⡀⠀⠘⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢇⣿⣿⡿⢹⠉⠉⠉⠉⠙⠀⠀⠉⠉⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠿⠿⠃⠀⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣷⢹⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡟⢸⣿⣿⢱⣿⡄⠀⠀⠀⠀⢀⠀⠀⣰⣿⣿⡿⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⠆⢿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⠓⠟⠞⠻⠛⠉⠉⠽⣿⡉⠙⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⡇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⣿⡏⠀⣘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈⠀⠀⠉⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⣹⣿⣿⣿⣿⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡇⢺⣿⣿⣁⣀⣀⣈⣀⣀⣀⣒⣦⣄⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⢿⣿⣿⡿⠻⠿⠿⠿⠟⠙⠻⠿⠿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣦⡀⠀⠀⢻⣿⣿⣿⣿⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⣿⢰⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣧⡀⠀⠈⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣿⣿⣿⣷⣤⣤⣀⣰⣿⣿⣿⣿⣀⠀⠀⢠⣿⣿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⣿⣿⣷⣄⠀⢸⣿⣿⣿⣯⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣼⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⡏⠀⣾⣿⣿⣶⣶⣿⣿⣷⣬⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⣿⣿⣿⣿⣷⣨⣿⣿⣿⣿⡂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣰⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠛⠁⣸⣿⣿⣿⣿⣿⣿⡿⠿⠋⠹⢤⣤⣿⣿⣿⣿⣿⣿⡿⠁⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⠑⠾⣶⡖⠰⠿⠿⠿⠓⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀
⠀⠠⠅⢸⡇⠀⠀⠀⢸⣿⣿⣿⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⣟⡄⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣷⠀⠀⠀⠐⣿⣷⣄⣶⣆⠀⠀⠀⠀⠀⠀
⢀⡀⠀⢸⣇⠀⠀⠀⠀⣿⣿⡯⣿⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣏⣉⣩⣭⣭⣭⣭⣭⣧⣤⣤⣦⠀⠀⢰⠂⣿⠀⢻⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠙⢋⣉⣉⠉⣩⣭⣭⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡇⡄⠀⣾⢲⠙⠀⠀⠉⣛⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠛⢄⠀⠀⠀⢀⣤⣤⣦⣦⣤⣤⣤⣄⡟⢿⠶⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡗⣿⢀⣿⡆⢠⡀⠀⣶⣿⣾⣷⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⢠⣿⣿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⢻⣿⡿⠿⢇⣾⣿⠏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠸⡿⠿⠿⡏⣿⡧⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣽⢷⡜⣿⣿⣿⣾⣶⣾⣿⣷⣤⣼⣟⠏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣇⠀⠰⡇⣿⡀⠀⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠹⢿⢿⣿⣿⣿⣿⣿⣿⣯⣙⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⡇⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀
⠀⠀⢠⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣍⣉⣻⠏⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⠀⣿⠀⠀⡇⣿⣟⠀⠀⠀⠀⠀⢸⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⢀⣿⣿⡟⠻⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠃⢸⡇⠀⢸⠀⠀⡇⣿⠃⢰⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠁⠀⢀⣠⣶⣿⣿⣿⣿⣶⣤⡀⢀⡴⣎⡀⠀⠀⠁⠀⠀⠀⠀⠐⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⡇⠀⠘⠃⠀⢸⠀⠀⠃⣿⠋⢸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠩⣷⣖⡤⣀⠀⠀⠀⠀⠈⠀⠉⠉⡋⠙⠛⡛⠛⠛⠉⠉⠉⢉⣉⠈⠉⠉⡉⡉⠈⢁⠀⢸⣿⠿⠛⠀⠃⠀⠀⠃⠀⠘⠀⠀⠀⢨⣤⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣀⠘⣿⣿⣿⣿⣦⡀⠒⠒⠚⠋⠒⢒⣚⣛⣒⣚⠒⠀⠐⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢸⣿⣮⣍⡛⠻⠿⠿⠛⢁⣼⣿⣷⡜⣿⣿⣿⣿⣷⡄⡀⡀⠀⠀⠀⠀⢀⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣀⣀⣀⣈⣛⣛⣛⣁⣀⣀⣀⣡⣀⣀⣤⣤⣤⣀⣠⠄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠽⠯⣿⠟⠛⠿⠿⠿⣿⣛⠛⡛⣛⡻⠋⠙⠉⠭⠥⠤⠀⠀⠀⢀⣠⣤⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⢹⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠛⠛⠛⠛⠛⠛⠛⠉⠩⠆⠉⠙⠓⠀⠁⠀⠀⠀⠀⣀⣀⣀⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠋⠀⠀⠀⠀⠈⠻⠉⠉⡉⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⣀⣀⣠⣤⣠⣀⣤⣤⣴⣶⣖⣀⣤⣤⣶⣿⣿⣿⠛⠙⠛⠉⠉⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⣿⢹⣷⣾⣶⣾⣿⣿⣿⣧⣿⣿⡿⣯⢟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢣⣿⣿⡝⣼⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⠹⣿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣾⡏⢸⣿⣿⢸⣿⡄⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⡆⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⣿⣿⣿⣿⡿⠛⠛⠉⠋⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⡇⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡇⢐⣂⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⣿⣿⣿⡏⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣃⣻⣿⣿⣀⣀⣀⣀⣀⣀⣀⣠⣤⣷⣾⣿⣿⣿⣿⠿⠃⠀⠀⠀⠸⠿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⢽⣿⣿⡟⠛⠛⠛⠛⠙⠉⠙⠛⠋⠉⠙⠛⠋⠁⣰⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⣷⡄⠀⠀⢻⣿⣿⣿⣿⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣸⣿⣿⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣿⣿⣷⣦⣤⣴⣧⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⣿⣷⡄⠀⠈⢿⣿⣿⣿⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣸⣿⣿⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠿⠿⢿⣿⣿⣿⠀⣼⣿⣟⠻⢻⣟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣷⣤⡀⢸⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣟⠛⠋⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣶⣾⣿⣿⣧⣼⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣽⣿⣿⣿⣷⣨⣿⣿⣿⣿⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠈⠓⠶⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀
⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⠇⠙⠻⠿⠆⠐⠛⠟⠛⢃⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣷⣷⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⠀⠀⠂⢸⡇⠀⠀⠀⢸⣿⣿⣿⠈⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⡄⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⡆⠀⠀⠝⣀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⣿⣯⢯⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣏⣉⣩⣭⣭⣭⣭⣭⣦⣤⣴⣄⡆⠀⠀⣿⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⢉⣍⠉⢩⣭⣯⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⡟⡇⠀⠦⠛⠀⠀⠙⠣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⢆⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⣤⣄⣘⢻⠶⣿⣿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣷⣿⠀⣇⠀⠀⠀⣴⣾⣥⣆⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣟⢠⣿⣯⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣼⣟⣿⣤⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⣿⣿⣿⣿⣟⠻⣿⠿⣿⣿⠏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠸⡿⠿⢿⡟⣿⡟⠨⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣿⣿⣿⣿⣿⣶⣿⣿⣼⣯⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠰⢸⡇⣿⡇⠀⠀⠈⠉⡿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⠀⠀⡇⣿⡧⡀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠁⠀
⠀⠀⠰⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡉⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⣿⠀⠀⠃⣿⣿⢷⡀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀
⠀⠀⢠⠄⠀⠀⠀⠀⢠⣿⣿⣿⣍⠛⠻⢿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⡟⠁⢸⠃⠀⠿⠀⠀⡄⣿⡃⢸⣧⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣷⣆⠀⠲⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⡄⠀⠸⠀⠀⢺⠀⠀⠁⠿⠃⠸⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠩⣿⣖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠋⠋⠀⠉⠉⣉⣉⢈⠉⠁⠀⠉⠈⠁⠁⢸⣿⣿⣿⠀⠃⠀⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡄⠙⣿⣿⣿⣿⣆⡀⠐⠚⠋⠃⠒⢒⣛⣉⣚⣛⠀⠀⠀⠋⠋⠉⠉⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢻⣿⣯⣍⡛⠛⠛⠛⠋⣡⣾⣿⣧⡸⣿⣿⣿⣿⣷⣀⣀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣁⣈⣀⣉⣉⣉⣉⣁⣀⣀⣀⣤⣄⣠⣤⣤⣤⣠⣠⠀⠀⠸⠿⠿⠿⠀⠀⠀⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⣋⣛⠛⠛⠻⠟⢛⣛⣛⠛⠛⢻⠻⠛⠙⠉⠭⠭⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣿⣿⣿⣧⣿⣿⣿⣿⠿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⠛⠛⠛⠛⠋⠋⠉⠉⠝⠋⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⡈⠈⠉⠉⠁⠀⠀⠀⠚⠉⠉⠁⢹⣿⣹⣿⣿⣿⢷⡤⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣠⣴⣶⡶⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣶⣿⣶⠾⢿⣷⣿⢿⠿⠭⢟⠻⠻⢟⢒⢀⣀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⣿⣿⣿⡼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢸⣿⣿⢏⡎⠈⠁⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⣿⣿⣷⢻⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⠇⣼⣿⣿⣾⣿⡀⠀⠀⠀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⡿⣿⣿⠏⠋⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣠⣶⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⣿⡀⣀⣍⣁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠄⣠⣤⠦⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⠏⠀⠀⠀⣠⣾⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣿⣿⣿⣿⣿⡄⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⢈⣻⣿⣯⣤⣄⣤⣤⣤⣤⣤⣤⣤⣾⣦⣭⣽⣧⣤⣉⣀⡀⠀⣘⣿⣿⣿⣿⣶⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣷⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡿⢾⣿⣿⠛⠛⠛⠛⠋⠋⠛⠛⠋⠉⠉⠉⠛⠛⠛⠛⠉⠒⠲⣸⠿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⣦⡀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⡇⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡿⠿⡗⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀
⣿⣷⡀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⣿⣧⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢤⣈⣻⣶⡄⠀⣸⣿⣿⠻⢻⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⣿⣿⣷⣤⠀⢸⣿⣿⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣿⣿⣿⣟⡛⠃⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠀⠀⠤⠼⠯⣥⠀⢠⣿⣿⣿⣷⣾⣿⣿⣧⣼⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠆⠀⠀⠀⢀⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣮⠀⣾⣿⣿⣿⣿⣿⣿⠟⠛⠈⠳⢶⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀
⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠢⠛⠻⠿⠃⠛⠛⠛⠛⢱⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠿⠀⣿⣿⣿⣿⣿⣷⣿⣅⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠅⢸⡇⠀⠀⠀⠈⣿⣿⣿⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⣿⣟⡆⢿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣧⠀⠸⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣧⣿⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⡟⣛⣛⣍⣉⣩⣩⣥⣭⣬⣤⡌⣧⠀⢰⡇⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠉⠉⠉⣉⠉⢩⣭⣭⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡗⣿⠀⡘⡇⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⢆⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣄⣀⣿⠶⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣷⣿⡄⡁⠀⠀⢀⣄⡠⣠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⡇⣿⣇⢱⣶⣶⣴⣿⣿⣿⣿⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣟⠻⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡇⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⡸⣿⣿⣿⣿⣧⣾⣿⣿⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠔⠀⠀⡇⣿⣿⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⠀⠀⡇⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀
⠀⠀⠀⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠃⠀⠀⠀⠀⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⣿⠀⠀⡇⣿⣿⣻⡆⠀⠀⠀⢽⣿⡿⠃⠀⠀⠀
⠀⠀⢀⠄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⠛⠻⢿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠋⢸⡇⠀⢹⠀⠀⡇⣿⡇⢸⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⡁⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⡄⠰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣽⣿⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣿⣿⠃⡅⠀⠘⠃⠀⢸⠀⠀⠃⣿⠗⢸⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣷⣖⣤⡀⠀⠀⠀⠀⠈⠀⠉⠁⠛⠙⠓⢛⠛⠛⠃⠛⠉⠉⡉⠉⠉⠉⣉⡉⢉⣉⠉⢸⣿⣿⣿⠀⠃⠀⠀⠂⠀⠘⠀⠀⠀⢻⣄⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⡀⠹⣿⣿⣿⣿⣆⠀⠒⠚⠛⠋⠀⠒⢒⣋⣒⣒⡒⠀⠐⠚⠛⠃⠒⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣮⣍⠛⠻⠿⠟⠛⣡⣿⣿⣦⡹⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣀⣀⣀⣀⣛⣛⣒⣁⣀⣀⣀⣁⣀⣀⣈⣀⣀⣀⠀⠀⠀⠸⠿⠿⠿⠁⠀⠀⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠽⠏⣿⠿⠿⠿⠿⠿⣷⣚⠛⠛⢻⠿⠟⠛⠋⠩⢭⣥⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣿⣿⣿⣯⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠛⠛⠿⠿⠛⠛⠚⠃⠛⠁⠋⠉⠓⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠛⠉⠀⠀⠀⠀⠉⠋⠉⠉⢹⣿⣻⣿⣿⣿⢷⣄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡒⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣾⣶⣶⣾⣿⣿⣿⣧⣿⣿⣿⡯⠛⠛⡛⣛⣒⠀⡀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⣿⣿⣿⡽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢹⣿⣿⢏⡞⠈⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣷⢻⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠇⣼⣿⣿⣾⣿⡀⠀⠀⠀⠀⣀⣀⢀⣀⣀⠀⠀⢀⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠓⠃⠀⢠⣿⡿⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⡄⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⣿⠀⣐⣈⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣻⣿⣿⣿⣿⡄⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⢈⣻⣿⣯⣀⣀⣀⣀⣀⣀⣀⣀⣭⣶⣖⣚⣛⣛⣄⣀⣀⡀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡿⢼⣿⣿⠛⠛⠛⠛⠛⠙⠙⠿⠿⠋⠉⠙⠛⠛⠻⠋⠛⠟⠰⠶⡶⣤⣾⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣦⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⣿⡇⣿⣿⣿⠰⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠄⢁⠈⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣧⡀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡻⣿⣿⣿⠀⠀⣾⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⣿⣿⣷⣤⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣿⣿⣿⣟⠛⠃⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣖⠰⡟⢼⣿⣿⡇⠀⣸⣿⣿⣷⣶⣿⣿⣿⣤⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⣞⣔⣿⣿⠀⢰⣿⣿⣿⣿⣻⣿⡿⠛⠃⠙⠦⣴⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣽⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⠻⠃⠛⠛⠿⠆⠚⠺⠛⠚⢣⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠆⢸⣿⣿⣿⣿⣿⣾⣧⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠃⢸⣷⠈⠿⠀⠀⢻⡿⠋⣠⣿⡇⢼⣿⣿⣿⣿⣿⣿⣿⣯⠃⣿⣿⣿⣿⣿⣭⢿⡟⢹⡄⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣆⠀⠀⠀⠀⢀⣾⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⠽⣺⣿⣿⣿⡿⣯⡈⠻⢻⣿⡀⣊⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢆⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⡿⡿⣛⣯⣿⣷⣵⠛⢿⣷⡞⢲⣾⠺⣿⣽⣿⢣⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣄⡀⠀⢸⣿⡇⠀⠀⠀⢿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⢅⡡⣥⣾⣿⣿⣿⣶⢸⣿⣿⣿⣿⡹⣿⡃⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⢾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⡿⠻⠍⠁⠀⠀⠀⠀⠉⢻⢿⣿⣿
⣿⣧⠀⠀⢿⡇⠀⠀⠀⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⡾⢻⣽⣿⣟⣿⣿⣿⡎⢻⣿⣿⣿⣧⢻⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠋⠻⢟⡒⠎⣽⡟⣿⣷⠁⠐⣩⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠸⣿⣿
⠋⠙⠀⠀⠈⠃⠀⠀⠀⣿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣊⣿⣿⣿⣥⠆⡈⠀⠿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⡟⣿⣟⡰⣶⣤⣐⣤⣬⣿⣀⠀⡹⣠⡛⣿⣧⣤⣸⣤⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠰⣿⠀
⠉⠁⢀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣿⠿⠑⡄⠀⠀⢝⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣧⣿⣾⣿⣿⣿⡿⡯⢻⠟⢛⡂⠀⣿⣹⣿⢭⠏⠋⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⡀
⢰⣤⢸⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣤⣾⣿⣿⣿⣦⣼⣦⡤⣤⣤⣬⣿⡷⣷⠀⠠⣿⣯⣼⣧⠄⣷⣿⣿⣾⣿⣿⣿⣧⢧⣼⣧⣼⣧⣼⠂⠜⠁⠉⠣⠠⠀⡘⣠⡀⠀⣂⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇
⠸⣿⣼⡄⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠀⠿⠇⠿⠀⠬⠿⠿⠿⠿⠀⠏⠭⠯⠭⠿⠿⠿⠿⢸⠿⢯⠿⠛⠂⠀⠀⠀⠀⠉⠀⠘⠁⠚⠟⣷⠘⢻⣿⢡⣿⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣖⣿⣿⡗⠀⠀⠀⠀⠀⢹⣿⡿⡿⢿⣿⣿⣿⡿⡋⣷⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠘⠿⠿⠿⢶⣤⡀⠀⠀⢀⣀⣀⣰⣶⣶⣦⠷⠤⢼⣿⣿⣟⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠛⠢⢺⠿⣿⡿⣟⣾⣥⣿⡆⠀⠀⠸⣱⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡤⢤⣄⠉⠉⣉⣉⣷⡀⣴⣲⣶⣾⣿⠖⠀⠀⢳⠋⠉⠁⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣧⣄⣤⣤⣤⣤⡀⠀⠀⠀⡊
⡏⠿⠻⠟⠀⠀⠀⠀⠀⠀⠂⠠⠊⠏⢀⠉⠉⠻⠷⠛⠐⠀⠀⠀⢿⣿⣟⣃⠀⠀⢸⣶⣷⡆⠀⠤⠄⠀⠙⠿⠹⠯⠍⠅⠿⢀⣀⣐⣻⣷⢀⡀⠘⠂⠠⠤⣀⣀⠤⠤⠴⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣷⣶⣦⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠁⠈⠉⢉⡀⠀⠂⠀⠀⠀⠀⠀⠞⠛⠛⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣿⣿⣿⣿⣿⣶⣶⣒⡒⠒⠀⠀⠀⠈⠉⠉⠙⠀⠀⠀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⢒⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⣾
⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⠒⠒⠒⢚⣶⣾⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠠⠰⢲⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣯⣻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠘⠋⠛⠻⠿⢿⣿⣿⣶⣤⣤
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣔⠠⠁⢟⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣼⣝⣻⣶⣤⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠉⠉⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠛⠷⣶⣄⣀⣿⣿⣿⣿⣿⣿⣿⡿⠉⠹⡿⣿⣿⣿⣿⣿⣿⣧⡀⡄⠀⠀⠀⠀⠀⠀
⠢⠀⢠⠐⠤⠀⣄⠠⢈⣺⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣷⣨⣝⣻⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠈⠛⡿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣿
⡀⢤⠢⣈⢢⡀⠀⡁⢌⣟⣭⣤⣤⣶⣶⣶⡶⠶⠀⠀⠀⠈⠙⢻⣻⣿⣿⣿⣿⣿⣦⡀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⠯⠹⠻⠛⢿⣿⣿⣿
⠁⠈⠁⠀⠀⢈⠀⢀⢲⣿⣿⣿⣿⣿⣽⣷⣿⣿⡶⠿⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣷⣦⡇⠘⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣿⡿⠀⠈⣿⡟⢿
⡀⠢⠡⠤⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢻⡿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⡟⠁⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢹⣿⠀
⠀⠀⢀⠀⠀⠢⠀⢸⣿⣿⣿⣿⣭⣀⣠⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢈⡍⠉⠝⣿⣿⣿⣷⣠⣤⣌⣃⡇⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣟⠁⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⢀⢿⣿⠛⣻⣿⣿⡿⠏⠁⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠆⢽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⡿⠋⢀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠠⠄⠐⣿⣿⣷⡀⠀⠈⢹⣿⣿⠿⠿⠟⠀⠸⠻⣿⣿⣿⣿⣿⣿⡇⢼⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⡠⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠐⠶⢶⠟⠛⠀⠀⠀⠀⠈⠻⢿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠸⣧
⠛⠛⠛⠛⠉⠉⠹⣿⣿⣷⣶⠊⠀⠀⢀⠀⠀⠀⢰⣿⡿⣿⣧⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢼⢿⣿⣿⣿⣿⢸⣿⠿⠉⠀⠀⠀⣀⣀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡆⠀⠀⠀⠀⠀⠐⠈⢻⣿⣿⣿⠸⣿⡇⠀⠀⠀⠀⠈⠁⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⣿⡛⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀
⠀⠃⢸⣷⠈⠿⠀⠀⢿⡿⠋⣠⣿⡇⢼⣿⣿⣿⣿⣿⣿⣿⣯⠃⣿⣿⣿⣿⣿⣽⢿⡿⢑⡄⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⢀⣾⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⠽⣲⣿⣿⣿⡿⣯⡈⠿⢻⣿⡄⣊⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢆⠀⠀⣻⣿⠀⠀⠀⠀⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⡿⡿⣛⣯⣿⣷⣵⠛⢿⣧⡞⢲⣾⠺⣿⣿⣿⢣⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣄⡀⠀⢸⣿⡇⠀⠀⠀⢿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⢅⡡⣥⣾⣿⣿⣿⣶⢸⣿⣿⣿⣿⡹⣿⡃⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠛⠍⠁⠀⠀⠀⠀⠉⢻⢿⣿⣿
⣿⣧⠀⠀⢿⡇⠀⠀⠀⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⡾⢻⣽⣿⣟⣿⣿⣿⡎⢻⣿⣿⣿⣧⢻⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠋⠻⢝⠐⠎⢽⡟⣿⣷⠀⠐⣩⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠸⣿⣿
⠋⠙⠀⠀⠈⠃⠀⠀⠀⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣊⣿⣿⣿⡥⠄⡈⠀⠿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⡿⣿⣟⣰⣶⣤⣐⣤⣼⣿⣀⠀⡹⣠⡛⣿⣧⣤⣸⣤⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢰⣿⠀
⠉⠀⢠⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⠿⠑⡄⠀⠀⢝⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣧⣿⣾⣿⣿⣿⡿⡯⢻⠟⢛⡂⠀⣿⣹⣿⢭⠏⠋⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⡀
⢰⣤⢸⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣤⣾⣿⣿⣿⣦⣼⣦⡤⣤⣤⣬⣿⡷⣷⠀⠠⣾⣯⣼⣧⠄⣷⣿⣿⣾⣿⣿⣿⣯⢧⣼⣧⣼⣧⣼⠂⠜⠁⠉⠣⠀⠀⡘⣠⡀⠀⣂⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇
⠸⣿⣼⡄⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠀⠿⠇⠿⠀⠬⠿⠿⠿⠿⠀⠏⠭⠯⠭⠿⠿⠿⠿⢸⠿⢯⡿⠛⠂⠀⠀⠀⠀⠉⠀⠘⠁⠚⠟⣿⠘⢻⣿⢡⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣞⣿⣿⡗⠀⠀⠀⠀⠀⢻⣿⡿⡿⢿⣿⣿⣿⡿⡏⣷⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠘⠿⠿⠿⢶⣄⡀⠀⠀⢀⣀⣀⣰⣶⣶⣦⠧⠤⢼⣿⣿⣟⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠛⠢⢺⠿⣿⡿⣟⣷⣯⣿⡆⠀⠀⢸⣱⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡤⢤⣄⠉⠉⣉⣉⣷⡀⣴⣲⣶⣾⣿⠖⠀⠀⢳⠋⠉⠁⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣷⣄⣤⣤⣤⣤⡀⠀⠀⠀⡊
⡏⠿⠻⠟⠀⠀⠀⠀⠀⠀⠂⠠⠊⠏⢀⠉⠉⠻⠷⠛⠐⠀⠀⠀⢿⣿⣛⣃⠀⠀⢰⣶⣶⡆⠀⠤⠄⠀⠙⠿⠹⠯⠍⠅⠿⢀⣀⣐⣻⣷⢀⡀⠐⠂⠠⠤⣀⣀⠤⠤⠶⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣷⣶⣦⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠁⠈⠉⢉⡀⠀⠂⠀⠁⠀⠀⠀⠞⠛⠛⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣿⣿⣿⣿⣿⣶⣷⣒⡂⠂⠀⠀⠀⠀⠉⠉⠙⠀⠀⠀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⢒⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢷⣾
⠤⠤⠤⠤⠤⠤⠤⠄⠀⠒⠒⠒⠒⢚⣶⣾⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠠⠰⢲⣶⣶⣶⣷⣿⣿⣿⣿⣷⢶⣯⣻⣷⣦⣀⡀⠀⠀⠂⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⠋⠙⠛⠿⢿⣿⣿⣶⣤⣤
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣜⠠⠁⢞⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣝⣻⣶⣤⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠉⠙⠛⠻
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠛⠷⣶⣄⣀⣿⣿⣿⣿⣿⣿⣿⠿⠉⠻⡿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠢⠀⢠⠐⠄⠀⠄⠠⢈⣺⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣷⣨⣝⣻⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣾⣤⡗⢶⣿⣿⣿⣿⣾
⠀⠄⠢⣈⢢⡀⠀⡀⢌⣟⣭⣤⣤⣶⣶⣶⠶⠶⠀⠀⠀⠈⠙⢛⣿⣿⣿⣿⣿⣿⣦⡀⠸⡻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⡊⠃⠊⠛⢻⣿⣿⣿
⠁⠈⠁⠀⠀⠈⠀⢈⢺⣿⣿⣿⣿⣿⣿⣾⣾⣿⡿⠿⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣷⣦⡇⠘⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠈⣿⡟⢿
⡀⠢⠀⠦⡀⠀⠐⢠⣾⣿⣿⣿⣿⣿⠿⠛⠉⠁⢀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢻⡿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡟⡀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠢⠀⢸⣿⣿⣿⣭⣭⣀⣠⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢈⡉⠉⢩⣿⣿⣿⣷⣠⣤⣌⣃⡇⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡟⠃⡀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⢀⢿⣿⠛⣻⣿⣿⡿⠏⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡆⢽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠀⡤⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⡿⠋⢀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠠⠄⠒⣿⣿⣷⡀⠀⠈⢿⣿⣿⠿⠿⠟⠀⠸⠻⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⡀⠺⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⢒⠛⠋⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣇⢸⣿⣿⣯⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠸⣇
⠟⠛⠛⠛⠉⠉⠩⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⢀⣷⡴⣿⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⢸⣿⢟⠃⠀⠀⠀⣀⣀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠉⠋⢁⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠐⠈⢻⣿⣿⣿⠸⣿⠇⠀⠀⠀⠀⠈⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣷⡀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣇⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣧⠀⠀
⠀⠃⢹⣷⠘⢿⠀⠀⢿⡿⠋⣠⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣟⠏⣿⣿⣿⣿⣿⡛⢯⡿⠳⡄⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⡆⠀⠀⠀⠀⢀⣴⣿⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⢚⢶⢿⣿⣿⡿⣏⡘⠻⢻⣾⡀⣍⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠀⢿⣿⠀⠀⠀⠀⣾⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢿⣧⣭⠿⣿⣧⡖⢶⣾⠶⣿⣽⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⢸⣿⡆⠀⠀⠀⢿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣁⣡⣭⣽⣿⣿⣿⣤⢸⣿⢷⣿⣿⠹⣿⡉⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡍⠁⠀⠀⠀⠈⠉⢻⣿⣿⣿
⣿⣧⠀⠈⣿⡇⠀⠀⠀⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⡾⢷⣽⣿⣟⣿⣿⣿⡜⢻⣿⢿⣿⣇⢻⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠛⠻⠿⠿⡔⠞⣻⡟⣿⣯⠉⠙⣫⣡⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠩⣿⣿
⠟⠛⠀⠀⠘⠇⠀⠀⠀⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠊⣿⣿⣽⣥⠅⠉⠀⠿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣟⣥⣦⣀⣀⣀⣼⣟⣠⠀⡹⣀⠿⣿⢥⣀⣩⣉⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠠⣿⠀
⠁⠀⢠⠀⠀⠀⠀⠀⠀⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⡿⠲⡍⠀⠈⢽⣿⣿⣿⡅⣾⣿⣿⣿⣿⣿⣿⣧⣿⣶⣷⣿⣿⣿⡏⢿⠟⢛⠃⠁⣿⣹⣟⢫⠟⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⡒
⢠⡀⢸⠀⠀⠀⠀⠀⠀⢰⣿⣭⣭⣯⣭⣽⣿⣭⣯⣭⣤⡤⢠⣤⣵⣶⣿⣧⠀⠠⣭⣯⣭⣽⠀⣽⣯⣽⣿⣽⣯⣿⣧⢽⣭⣽⣭⣽⣭⠅⠔⠀⠋⠥⠀⠁⠉⠭⠀⠀⣤⣿⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇
⢼⣿⣸⡄⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡏⣹⡿⠸⣿⣿⠀⣘⠿⢿⣿⣻⠀⠻⣛⣻⡿⡿⡿⢿⢿⢸⡿⢿⠿⠿⠏⠀⠀⠀⠀⠉⠀⠘⠃⠭⠗⣷⠙⢻⣿⢃⣾⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡞⣿⢟⡧⠀⠀⠀⠀⠀⢿⣿⡿⡿⣿⣿⣿⣿⡿⠟⣻⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠸⡿⢿⣿⣶⣄⡀⠀⠀⠀⠐⣀⣠⣤⣤⣤⣯⣄⣸⣿⣿⣿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⠿⠠⢶⢾⣿⡿⣿⣷⣇⣿⡄⠀⠀⢸⣡⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡀⢤⡴⠂⠉⠉⢉⣷⡀⣤⣤⣴⣮⣿⠤⠀⠈⢻⠛⠋⠉⠉⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⡀⠀⠀⠀⠚
⠏⣿⡿⠿⠀⠀⠀⠀⠀⠐⠀⠀⠈⠆⠈⠉⠙⠻⡷⠿⠀⠀⠀⠀⢟⣷⣾⢃⠀⠀⢬⣿⣿⡇⠀⠤⠈⠉⠛⠽⠛⠛⠻⡅⠿⠁⠀⣉⣿⣷⠀⠀⠸⠆⠠⣀⡀⣀⣀⣤⠤⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⣯⣥⣤⣄⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠋⠍⠉⢉⡉⠉⠉⠀⠀⠀⠀⠀⠶⠶⠚⠉⢉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⢟⣿⣿⣿⣿⣷⣶⣶⡖⠂⠀⠀⠀⠀⠉⠉⠙⠓⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠐⠂⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠃⠀⠀⠀⢠⣶⣿⣿⣿⣿⣯⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⣀⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⣞
⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠖⢚⣲⣶⣾⣿⣿⣿⣿⣿⣿⣍⠉⠉⠩⠩⢽⣿⣿⣶⣶⣲⣶⣶⣶⣶⣾⣝⣻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡌⠉⠛⠛⠻⠿⢿⣿⣿⣧⣤⣍
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣷⣭⣟⠿⣦⣄⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣄⠀⠀⠀⠀⠀⠙⠛⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡙⠻⣶⣤⣀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠉⢻⡿⢿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⡄⠠⡐⣺⣽⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢨⣴⡩⣛⣿⣿⣿⣿⣿⣿⡿⠏⠂⠀⠀⠁⠀⠈⠛⠿⣿⣿⣿⣧⣤⣴⣷⣶⣶⣾⣶
⠂⡀⠢⡐⢤⡂⠠⠁⢜⣏⣩⣥⣤⣴⣶⣶⣶⣶⡤⡄⠉⠉⠙⠻⣿⣿⣿⣿⣿⣷⡀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⠗⠙⠙⠛⢿⣿⣿⣿
⠀⠈⠁⠉⠡⠁⠀⠁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠄⠀⠀⠀⠙⠿⣿⣿⣿⣿⣄⢌⡇⠸⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣦⠀⠈⢿⣿⢿
⡀⣄⠡⠄⠀⠈⠂⢀⣾⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉⢀⡀⠄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡇⠀⠘⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢛⠑⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠸⣿⡀
⠀⠀⡀⠀⠀⠀⠀⢀⡾⠿⠿⣧⣤⣤⣤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣇⣀⣀⣘⡓⡇⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⠁⠁⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⣤⣴⣿⣿⠿⠋⠀⣠⡶⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣦⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⣠⣄⣾⠿⠁⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⣾⣿⠿⠿⠷⠂⠼⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣋⣀⡀⠎⠉⠁⠀⠀⠀⢀⣤⣶⣖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⢸⣧
⠿⠟⠛⠛⠛⠉⠉⠁⣿⣿⣿⡿⠉⠁⠀⠀⠀⢀⣤⠬⠿⣿⡽⠿⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣗⢸⣿⡿⠋⠀⠀⠀⣀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠀⠀⠀⠀⠀⠀⠉⠋⢿⣿⣿⣿⢸⣿⡌⠀⠀⠀⠀⠈⠉⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣷⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀
⠀⠇⢹⣧⠘⣿⠘⠀⣿⡿⠋⢠⣾⡇⣰⣿⣿⣿⣿⣿⣿⣿⣟⠎⣿⣿⣿⣿⣿⣛⣻⣿⢻⡄⣾⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⡄⠀⠀⠀⠀⢀⣴⣿⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣻⢶⣿⣿⣿⣻⣟⡙⢿⢷⣶⡀⠝⣿⣿⡿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⢿⣷⠀⠀⠀⠀⣾⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⡿⠴⣟⣷⣮⣯⠷⣿⣧⡔⢬⣿⠵⣿⣽⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣈⠀⠀⢸⣿⡆⠀⠀⠀⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣀⢒⣫⣽⣿⣿⣿⣤⢸⣿⣷⣾⣿⢰⣿⠋⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠁⠀⠀⠀⠉⠉⢿⣿⣿⣿
⣿⣧⠀⠈⣿⡇⠀⠀⠀⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⡾⢿⣿⣿⡟⣿⣿⣿⡜⢻⣿⣿⣿⣇⢿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠛⢿⡻⠽⡜⣻⡟⣿⣯⠋⠹⢋⣨⣼⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⣿
⠟⠛⠀⠀⠘⠇⠀⠀⠀⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠞⣿⣿⣿⣩⡅⠉⠁⢿⣿⣿⣿⣿⠈⢸⣿⣿⣿⣿⣿⣿⡿⣿⡟⣥⣭⣀⡠⣀⣐⣾⡡⠀⢻⢀⠿⣿⢄⣀⣹⡉⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠠⣿⠁
⠀⠐⢄⠀⠀⠀⠀⠀⠀⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⣿⠢⡍⠀⢈⠻⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⣇⣯⣼⣷⣿⣿⣿⡟⢿⡟⠟⠇⠡⣿⣹⣟⢙⡟⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀
⢠⡀⢸⠀⠀⠀⠀⠀⠀⢰⣯⣿⣭⣽⣿⣭⣿⣭⣭⣯⣉⣀⣠⡀⣱⣦⣬⣥⠀⢠⣿⣭⣯⣭⠀⣭⣿⣿⣿⣭⣿⣯⣇⣭⣯⣭⣯⣉⣷⠅⠼⠀⠍⠅⠀⠁⠉⠙⠈⠠⠤⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇
⢼⣿⣼⡀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣿⡇⣿⣿⣿⣿⠀⣸⣿⣟⣟⣛⠀⣛⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⠯⠍⠀⠀⠀⠀⠒⠀⠘⠋⠹⡷⣎⠙⢿⣿⠇⣾⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡼⣿⢿⡇⠀⠀⠀⠀⠀⢿⣿⣻⡿⣿⣿⣿⣿⡿⢟⣻⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠸⣶⣿⣿⣶⣄⠀⠀⠀⠀⠒⠀⣠⣤⣤⣄⣿⣀⣸⣿⣿⣿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⠿⠠⢵⣾⣿⣿⣿⣷⣎⣿⡄⠀⠀⢰⣣⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⢀⡐⠒⠒⠉⠉⣶⠀⣤⣤⣤⣮⡿⠤⠀⠠⢭⠛⠛⠉⠉⠉⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⡀⠀⠀⠀⠞
⠟⣿⡿⠿⠀⠀⠀⠀⠀⢐⠀⢀⠌⠆⠉⠓⠙⢻⣯⣿⠩⠀⠈⠈⣿⣶⠶⠂⠀⠀⢤⣤⣶⡆⠀⣄⡈⠉⠳⣾⠛⢛⠛⡁⡿⠉⠉⠹⢿⣦⠀⠀⠬⠄⢀⣀⠀⢀⣀⣠⣤⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣭⣭⣄⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⠋⠍⠉⠉⠉⠈⠁⠀⠀⠀⠀⠈⠷⠶⠖⠀⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⢿⣿⣿⣿⣷⣴⣦⡴⠀⠄⠀⠀⠀⠈⠉⠙⠓⠀⠀⠀⠀⠀⣈⣀⣀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠃⠀⠀⠐⢀⣴⣾⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⠀⠀⢹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶
⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠶⠶⣲⣶⣿⣿⣿⣿⣻⣿⣟⠈⠉⢩⠩⢭⣽⣿⣿⣷⣶⣶⣶⣶⣦⣭⣟⠷⣦⣄⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠛⠛⠿⠿⣿⣿⣿⣧⣄⣉
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡘⢀⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣽⡻⢷⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠉⠙⠛⠻⢿
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⠷⣶⣤⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⢄⠀⢀⠀⠀⠀⡀⢠⣴⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣦⡩⣻⢷⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠁⠈⠉⠿⢿⣿⣿⣿⣷⣴⣶⣶⣶⣶⣶⣶
⢂⡀⢠⠐⢄⡀⢨⣿⣿⠀⢨⣽⣋⣭⣤⣤⣤⣤⣤⣤⣌⠙⠻⢿⡿⣿⣿⣿⣿⣷⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⢿⠿⠿⢿⣿⣿⣿
⠂⠈⠁⠉⠩⢻⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣷⣷⣤⡄⠀⠈⠻⣿⣿⣿⣧⡀⢸⠂⠹⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣷⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣶⠀⠈⢻⣿⢿
⠀⣄⢁⢌⠰⢿⠋⠀⠀⢨⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⢉⡀⠀⠀⠀⠀⠹⣿⣿⣷⠠⡃⢄⠈⢿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⠋⠈⢳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠑⠂⠀⠀⠀⣾⠿⠿⢿⣥⣤⣤⣤⣤⣤⣴⡶⠛⢁⣤⣄⠀⠀⠀⠀⠀⠻⣿⣧⢀⢀⣀⣙⡛⡇⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⠁⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠠⠀⠀⠀⠀⠀⠀⢰⣋⣀⣀⣀⣤⣤⣾⣿⡿⠿⣁⣴⣾⣿⣿⠟⠀⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡅⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣤⣤⣤⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣶⡿⠿⣿⣿⣿⣠⣾⣿⣄⠀⠀⠀⠀⢨⣿⣿⡿⠿⠷⠀⠽⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣿
⣿⣿⡿⠃⠀⠀⠀⣤⣿⣿⣿⣿⣛⡉⠀⠀⠚⠉⠁⣀⣀⣨⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠸⣧
⠿⠿⠿⠂⠀⠀⠀⢉⡙⠁⠉⠿⠿⠃⠀⠀⠀⠀⠀⠾⠿⠿⠟⠛⠛⠛⠛⠛⠁⠂⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⡇⢻⣿⡟⠏⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⢸⣿⡆⠀⠀⠀⠀⠈⠉⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣷⡀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀
⠀⠇⢸⣧⠘⣿⠀⠅⢿⣿⠟⢀⣾⡇⣰⣿⣿⣿⣿⣿⣿⣿⣟⠎⣿⣿⣿⣿⣿⣛⣻⡿⣻⡀⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣻⡤⠀⠀⠀⠀⢁⣴⣿⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣻⢶⣿⣿⣿⣻⣟⠙⢿⢷⣾⡀⠝⣿⣿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⢿⣿⠀⠀⠀⠀⣾⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⡿⠴⣟⣷⣯⣯⠷⣿⣧⡔⢬⣿⠵⣿⣻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⢹⣿⡆⠀⠀⠀⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣀⣒⣫⣽⣿⣿⣿⣤⢸⣿⣷⣾⣿⢰⣿⠋⢁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠉⠉⢻⣿⣿⣿
⣿⣧⠀⠈⣿⡇⠀⠀⠀⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⡾⢷⣿⣻⡟⣿⣿⣿⡝⢻⣿⣿⣿⣇⢿⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠛⢿⠳⠽⡜⣻⡟⣿⣿⠋⠩⢋⣀⣼⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠸⠁⣿⣿
⠟⠛⠀⠀⠘⠇⠀⠀⠀⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠞⣿⣿⣿⣉⡅⠉⠁⢿⣿⣿⣿⣿⠈⣸⣿⣿⣿⣿⣿⣿⡿⣿⡟⣭⣭⣀⡠⣀⣐⣶⡠⠀⢻⢀⠿⣿⢤⣀⣹⡁⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⣽⠉
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠯⠿⣿⣿⠢⡍⠀⢈⠻⣿⣿⣿⡅⣾⣿⣿⣿⣿⣿⣿⣇⣯⣼⣷⣿⣿⣿⡟⢿⡿⠟⠇⠡⣿⣹⣿⢙⡟⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⢠⡀⢸⠀⠀⠀⠀⠀⠀⢠⣯⣭⣿⣭⣽⣿⣭⣿⣭⣭⣯⡀⢠⣤⣉⣤⣮⣅⠀⢀⣽⣯⣽⣯⠀⣿⣿⣯⣭⣿⣯⣿⣇⣯⣽⣯⣽⣿⣷⠅⡌⠀⠍⠅⠀⠁⠹⠉⠈⠀⠤⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢼⣿⣸⡄⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺⣿⣿⣿⣿⣿⠀⣘⣿⡛⢛⣟⠀⣿⣿⣿⣿⣿⣿⣟⣿⢻⣿⠿⠟⠿⠄⠀⠀⠀⠀⠒⠀⠘⠋⠉⡷⣎⠹⠟⣿⡇⣼⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⡼⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣻⡿⣿⣿⣿⣿⡿⢟⣻⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠸⣶⣿⣿⣶⣀⠀⠀⠀⠀⠒⠀⢠⣤⣤⣄⣿⣀⣀⣿⣷⣿⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⠿⠠⢵⣾⣿⣿⣿⣷⣞⣿⡄⠀⠀⢰⣣⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⠒⠒⠉⠉⣶⠀⣤⣤⣤⣾⣿⡤⠀⠠⢭⠛⠛⠉⠉⠉⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⡀⠀⠀⠀⡜
⠟⣿⡿⠿⠀⠀⠀⠀⠀⠰⠀⢀⠌⠆⠉⠓⠙⠻⣯⣿⠩⠀⠈⠈⣿⣶⠶⠂⠀⠀⢤⣶⣶⡆⠀⣄⡈⠉⠲⣾⢛⢛⠛⡁⡿⠉⠉⠻⢿⣦⠀⠀⠬⠄⢀⣀⠀⢀⣀⣠⣤⠴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣭⣭⣀⡀⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⠋⠍⠉⠉⠉⠈⠁⠀⠀⠀⠀⠈⠷⠶⠖⠀⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⣿⣿⣿⣿⣷⣴⣶⡤⠄⠤⠀⠀⠀⠈⠉⠛⠓⠀⠀⠀⠀⠀⢈⣀⣀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠃⠀⠀⠐⠀⣤⣾⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⡄⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶
⣀⣀⣀⣀⣀⡠⠤⠤⠤⠤⠤⠤⠤⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⡀⠈⢩⠩⢭⣿⣿⣿⣷⣶⣶⣶⣦⣦⣭⣟⠷⣦⣄⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠉⠛⠛⠻⠿⢿⣿⣿⣮⣄⣉
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣀⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣽⡻⢷⣦⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠐⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⠷⣶⣤⡀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠟⠹⣿⢿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀
⢄⠀⢀⠀⠀⣦⣾⣿⣿⠟⠉⣼⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡆⠀⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣦⡩⣻⢷⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠈⠀⠉⠻⠿⣿⣿⣿⣿⣠⣦⣶⣶⣶⣶⣶
⠂⡀⢤⣴⣿⣿⡿⠟⠉⠀⢀⣴⣶⣯⣴⣾⣿⣷⣶⣶⣶⣶⣦⣈⠛⠿⢿⣿⣿⣿⠄⠀⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠏⠯⠻⢿⣿⣿⣿
⠒⣽⣿⡿⠟⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣭⣅⣰⣶⣿⣿⣿⣷⠀⠀⠛⢿⣿⣧⠀⢨⠂⠹⢿⣿⣾⣚⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⠀⠀⢻⣿⠿
⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⢉⣩⣴⡟⡀⠀⠀⠀⠹⣿⣗⠀⡇⠀⠈⢿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠘⣿⡆
⠋⠀⠀⠀⠀⠀⠀⢀⠀⠄⣾⣿⡿⠛⠛⠛⠲⠒⢶⣶⣿⣿⣿⣿⣴⣧⠀⠀⠀⠀⠸⡇⠀⢀⢀⣀⣘⡛⡇⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⠋⠈⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡅⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⣠⣤⣶⣶⣶⣶⣷⣾⣾⡆⠠⡿⠟⣥⡿⠿⠛⠡⡾⠿⠟⠻⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⡿⠿⠷⠀⠽⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠻
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠒⠻⣷⡤⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⣷
⠿⠿⠿⠛⠛⠛⠋⢉⡉⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⡇⢻⣿⡿⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⢸⣿⡷⠀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀
⠀⠇⢸⣿⡈⢿⡅⠇⢻⣿⠟⢁⣴⡿⢸⣿⣿⣿⣿⣿⣿⣿⣟⠂⣿⣿⣿⣿⣿⣛⣿⣿⢻⡃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣧⠀⠀⠀⠀⠁⣠⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⠟⣇⣿⣿⣿⣿⣟⡋⢾⣷⣾⡅⠙⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⠀⠀⢻⣿⡀⠀⠀⠀⢸⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⣷⣮⣋⡷⣿⣇⣤⢬⣿⡧⣿⣻⣻⣏⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣈⠀⠀⠸⣿⡇⠀⠀⠀⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⡇⢙⣛⣽⣿⣿⣿⣥⢰⣿⣿⣾⣿⠓⣿⡟⠉⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⠁⠀⠈⠉⠉⠻⣿⣿⣿
⣿⣷⠀⠀⢿⡇⠀⠀⠀⣾⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣾⢿⢻⣿⡿⢿⣿⣿⡝⠿⣾⣿⣿⣧⢻⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠻⣿⡿⠨⡝⢻⡿⣿⣿⠛⠩⢟⣃⢼⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⣿
⠿⠛⠂⠀⠘⡇⠀⠀⠀⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣷⠜⢻⣿⣿⣋⣉⠙⠃⢸⣿⣿⣿⣿⡈⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⣭⡀⠠⣀⣐⣶⠍⠁⢚⢁⠿⣿⣆⡄⢘⣋⢹⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⠀⣼⡏
⠒⠂⢀⡀⠀⠀⠀⠀⠀⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢿⣿⣿⠦⡀⠀⠀⡻⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣗⣿⣽⣿⣿⣿⣿⣟⢿⡽⠿⠔⠁⣿⢧⣿⣝⡿⠿⢿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣀⢸⠇⠀⠀⠀⠀⠀⠀⣯⣿⣏⣩⣿⣿⣿⣿⣿⣿⣏⣀⣀⣠⣈⣥⣈⣥⠀⠀⣾⣛⣿⣿⡁⣘⣿⣟⣿⣟⣻⣛⣿⢉⣿⣿⣿⣿⣃⡁⣘⠀⠈⣉⢀⠉⠺⢟⠈⠀⠐⣵⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠤⣿⡼⡄⠀⠀⠀⠀⠀⢘⢻⣿⣿⣿⣿⣿⡛⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⠀⡀⣿⠛⢻⣿⠆⣹⣿⣿⣿⣻⣿⣿⣿⢸⣿⣿⢸⡿⠟⠀⠀⠀⠀⠒⠀⠀⠃⣽⡷⣦⠛⠿⢿⣿⢠⣽⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡧⣿⡿⣷⠀⠀⠀⠀⠀⢸⣾⠛⣿⣿⣟⣟⣿⣿⠿⣯⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠘⣶⣾⣶⣦⣄⠀⠀⠀⠀⠀⠀⢠⣄⣠⣄⣏⣀⣀⣻⣿⣾⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣷⣿⠀⠀⠀⠀⠀⠸⠿⠅⢴⣾⣿⣿⡿⣧⡆⣿⡄⠀⠀⠰⣡⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡒⠒⠒⠚⣦⠀⣠⣤⣤⣼⣿⣁⠀⠐⠦⠟⠛⠛⠉⠉⠉⠀⠀⣀⣾⣿⣿⣿⣾⣿⣄⠀⠀⣀⣀⠀⠀⠀⠀⠐
⠟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠄⢀⠌⣖⠉⠓⠊⠿⠃⠉⠉⠀⠀⠈⢿⣶⡶⠆⠀⠀⢰⣶⣶⡄⠀⣁⡀⠉⠲⣶⢛⣿⣛⡃⣿⠉⠉⠉⠿⣦⠀⠀⠸⠄⢀⡀⠀⠀⢀⣀⣠⣼⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣭⣁⡀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠙⠛⠛⠛⠐⠖⠀⠀⠀⠈⠉⡭⠵⠶⠒⠀⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⣿⣿⣿⣷⣷⣤⣦⣤⠤⠄⠀⠀⠀⠐⠒⠚⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣷⣧⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠇⠀⠀⠒⠀⢀⣴⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣎⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⢭⣭⣭⣽⣿⣿⣿⣿⣦⣦⣭⣟⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠛⠛⠻⠿⣿⣿⣿⣿⣠⣈
⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⡟⠉⠙⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣹⡻⢷⣤⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠛⠛⠿
⣄⣴⣾⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠉⠛⠿⠿⠿⢻⣿⣿⣿⣿⣛⠻⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣙⠷⣶⣤⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠛⠛⠁⠀⠀⠀⠀⢀⠀⠀⢠⡄⠀⠀⠀⠘⠻⠻⠋⠉⢹⣿⣷⡀⠈⢿⣿⠀⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣦⢙⡻⢷⣾⣿⣿⣿⣿⣿⡿⠷⠁⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⣂⣀⣶⣴⣶⣶⣶
⠁⠀⠀⠀⢀⠀⠀⠂⡈⠢⡈⠀⠀⠙⠻⣿⣾⣶⣶⣶⣾⣿⢿⣿⣿⡀⠀⠘⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢿⡻⢻⠟⠿⣿⣿⣿
⠀⠀⠂⠉⠠⠉⠀⠁⠄⠁⠀⠀⢘⣷⡶⠛⠻⠿⠭⠥⢤⣤⣾⣿⢏⡇⠀⠀⠈⠁⠀⠀⢈⡇⠹⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣻⣿⣿⣿⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⣤⡀⠀⠸⣿⡿
⡀⢀⡀⣄⠀⠌⠢⠈⠀⠀⠂⠈⠿⠋⠀⠀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⡄⠒⠀⠄⡁⢉⠂⡇⠀⠈⢿⣏⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠊⠁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢻⣧
⠈⠀⠈⠀⡐⠀⡑⢀⠀⠤⠒⠀⠀⠀⠼⢿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⣀⡘⠷⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠁⠄⣠⠤⠀⠀⠻⠇⠀⠰⠊⠀⠻⠿⠿⠿⢿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡅⢺⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣤⣤⣤⣴⣶⣶⣶⣶⣾⣶⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣀⣀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⡏⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢰
⠿⠿⠿⠛⠛⠛⠛⢋⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⣿⣿⣿⣿⠸⣿⣿⣅⠀⠀⠀⠀⠉⠉⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣯⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀
⠀⠧⠸⣿⡈⢿⡇⠇⢻⣿⡿⠋⣰⣿⢰⣾⣿⣿⣿⣿⣿⣿⣿⠆⣿⣿⣿⣿⣿⠿⠿⣿⢿⡋⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣣⠈⠀⠀⠈⠉⣠⣾⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⠟⣇⣾⣿⣿⣿⣟⠋⢿⣿⣬⡁⠘⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⢻⣿⡄⠀⠀⠀⢰⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣏⣛⣭⣿⡧⣨⢌⣽⡃⣶⣿⢿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⠀⠀⠸⣿⡇⠀⠀⠀⣾⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⡏⠉⣖⣿⣷⣿⣿⣣⠑⣿⣿⣾⣿⠗⣯⡟⠋⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠙⠻⣿⣿⣿
⣿⣷⠀⠀⢿⡿⠀⠀⠀⣾⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣯⢿⢷⣿⡿⢿⣿⣿⡟⠿⣾⣿⣿⣧⢻⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⡿⡻⡝⢷⣿⢿⣿⠛⠛⠟⠋⢭⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⣯
⠿⠿⠆⠀⠘⡇⠀⠀⠀⣿⡿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⣿⣻⣛⣙⡙⠃⢸⣿⣾⣿⣿⡌⢱⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣹⠀⠀⢀⢠⣶⠌⠁⢸⡇⣿⣿⣆⡀⢘⡛⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢈⡟
⠂⠀⢀⡀⠀⠀⠀⠀⠀⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⠦⡐⠀⠀⣻⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⣟⣿⡿⠿⠦⠋⣼⣇⣿⠟⡿⠿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⡄⢸⡇⠀⠀⠀⠀⠀⠀⣾⣛⣻⣛⣛⣿⣿⣿⣿⣿⣉⣀⣀⣀⣈⣡⣰⣃⠀⠀⣐⣿⣟⣟⡃⣸⣛⣿⣛⣿⣛⣿⣿⢹⣿⣿⣿⡛⣗⡙⣘⠁⠘⣘⠀⠙⠸⡟⠋⠁⣀⣺⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡄⣿⣬⡄⠀⠀⠀⠀⠀⢐⢻⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢿⠿⠄⠀⢿⣿⣿⣿⠃⢻⣿⣿⢿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣟⠀⠀⡀⠀⠐⠀⠠⣆⣐⣧⣤⠺⠿⢿⣿⠃⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰
⣧⣿⡿⣿⠀⠀⠀⠀⠀⢸⣾⢉⣿⣿⣿⣿⣿⣿⠿⣿⠋⠀⠀⠈⠉⠉⠉⢉⠀⠉⠉⠉⠉⠉⠀⠈⠉⠈⠁⠀⠀⠀⢴⠘⣶⣾⣶⣤⡄⠀⠀⠀⠀⠤⠀⢀⣀⣀⣀⣿⡀⠀⢸⣿⣾⣿⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠿⢅⣰⣾⣿⣿⣿⣯⡄⣿⡄⠀⠀⠐⣰⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠒⠒⠒⣪⠀⣉⣈⣩⣹⣿⣁⠀⠀⡶⡶⠖⠛⠛⠋⠉⠉⠉⣉⣽⣿⣿⣷⣶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰
⣟⣿⣿⡿⠃⠀⠀⠀⠀⠀⠄⠀⠘⣖⠙⠓⠚⠉⠀⠈⠉⠂⠀⠀⢫⣶⣴⠆⠁⠀⢐⣶⣶⣦⠀⣁⠀⠓⠲⣲⠶⢶⣿⡃⣿⠛⠉⢛⣿⣦⡀⠀⢰⡄⠀⠀⠀⠀⠀⢀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡠⠂
⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣍⣀⡀⠈⠛⠛⠋⠀⠀⠁⠀⠀⠈⠀⠀⠂⠁⠒⠖⣒⠚⠛⠛⠒⠒⠂⠀⠀⠉⠁⣬⣭⡭⠓⠒⠂⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⡟⣿⣿⣿⣿⣾⣤⣤⠤⡀⠀⠀⠀⠀⠐⠒⠲⠾⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣛⣿⢷⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠇⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯
⠀⣀⣀⣀⣀⣀⣀⣠⣴⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣭⣭⣭⣭⢭⣽⣿⣯⣥⣹⣻⢶⣤⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠻⠿⠿⢿⣿⣿⣿⣿⣇⣀
⠀⢀⠀⣠⣶⣾⣿⣿⣿⠟⠋⠀⠀⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣧⠪⣹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣙⡿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠈⠉⠙⠻⠿⠿
⣀⣴⣾⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠐⠈⠁⠈⠀⠠⣀⠁⠀⠘⣷⣦⠃⢸⣿⡆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⡛⢷⣤⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠋⠁⠀⠀⠀⠀⡀⢀⠐⠀⠀⠻⣤⣀⣠⣌⣿⣤⣤⣤⣤⣼⢿⠀⠀⣿⣧⠀⠁⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣦⣙⠻⢶⣤⣿⣿⣿⣿⣿⣿⡿⡅⠀⠈⠃⠀⠙⣿⣿⣿⣿⣿⣆⣴⣤⣤⣤⣤⣤
⠁⠀⠀⠀⢀⠀⠀⠂⡀⠢⠀⠀⠀⢠⣤⡹⠿⣿⣿⡛⣋⣉⣩⣵⡿⡀⠀⠈⢿⠃⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠿⠿⠿⣿⣿⣿
⠀⠀⠂⡀⠀⡑⠀⠐⠤⠁⠀⠀⢰⡞⠉⠀⠀⠀⠉⢉⣩⣽⣿⣿⣷⡇⠀⠀⠀⠀⠀⡀⠀⡇⠹⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⡏⣿⣿⣿⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡄⠀⠘⣿⡿
⡀⢀⠐⣄⠀⠈⠠⠈⠀⠁⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⢿⣿⣿⣿⣻⣿⡆⠒⠀⠄⠀⢀⠀⡇⠄⠊⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠅⢩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠀⠀⢻⣷
⠈⠀⡈⠀⡀⢄⡀⢈⠀⠤⠂⠐⠀⠀⡀⠈⠙⢏⡉⡁⣤⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣄⠀⠀⢀⣴⣶⣾⣶⣿⣿⣿⣿⣿⣿⡁⢻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣤⣤⣤⣤⣤⣶⣶⣶⣾⣶⣶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⢸⢿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⡿⡍⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡟⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⢰
⡿⠿⠿⠿⠛⠛⠛⠛⡋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⣶⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⢸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣽⡀⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠜⣿⣿⣿⣿⢸⣿⣿⣄⠀⠀⠀⠀⠈⠛⢋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⣿⣇⠠⠡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠹⣿⡆⢰⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡄⠀
⠀⠰⠀⣿⡄⢿⡇⠙⢸⣿⡿⠋⣠⣾⠀⣶⣿⣿⣿⣿⣿⣿⣿⢇⢿⣿⣿⣿⣿⠿⢿⣻⢿⡏⢹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣇⠀⠁⠀⠀⠉⢀⣼⣿⡏⢨⣿⣿⣿⣿⣿⣿⣿⡿⣇⣾⣿⣿⣿⣿⠋⢿⣿⣬⡌⢘⢿⣿⣿⡯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⢸⣿⡆⠀⠀⠀⢰⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣿⣏⣙⣹⣿⡷⣠⢄⣿⡗⣴⣾⢿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⡏⠉⢖⣛⣿⣿⣿⣃⡈⣿⣿⣴⣷⡇⣯⡟⠛⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠙⠛⠻⣿⣿⣿
⣿⣷⠀⠀⢻⣿⠀⠀⠀⢰⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⢿⣿⣿⡇⠿⣿⣿⣿⣧⢹⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⡿⣻⡏⢿⣿⢿⣿⡛⠛⠿⠋⢙⣿⣿⠛⠁⠀⠁⠀⠀⠀⠀⢀⠀⡸⠻⣯
⢿⠿⠇⠀⠈⠿⠀⠀⠀⣼⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡸⢻⣿⣿⡛⣙⡙⠏⢰⣿⣾⣿⣿⡎⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣹⠁⠀⠀⢠⣷⡌⠁⠸⡏⣽⣿⡇⡀⠰⡟⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠂⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⡧⡐⠂⠀⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣫⣿⣽⣿⣿⣟⣿⣿⢷⠢⠊⣽⡇⣿⠗⡿⠾⣿⢨⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⣿
⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⣼⣟⣛⣻⣿⣿⣿⣿⣟⣛⣏⣈⣁⣀⣘⣹⣐⣧⠀⠀⣴⣻⣟⣛⡇⢘⣟⣛⣟⣛⣟⣛⣿⢙⣿⣟⣛⡟⣛⡙⣘⠃⢸⢘⠀⠙⠙⠛⠃⠁⣠⣰⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡆⣿⣆⣇⠀⠀⠀⠀⠀⢀⢻⣿⣟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⣿⠿⢿⠇⠀⣿⣿⣿⣿⡇⢸⡿⣿⣿⣿⣿⣿⣻⢈⣿⣿⣿⣿⣟⠁⠀⠀⠀⠠⠀⠀⠆⣒⣦⣤⠲⡿⢿⣿⡇⣔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣧⢿⡿⢿⠀⠀⠀⠀⠀⢸⣾⢙⣿⣿⣿⣿⣿⣿⡿⠿⡏⠉⠉⠉⠉⠉⠀⢉⠀⠉⠉⠉⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⢴⠀⣷⣶⣶⣤⡀⠀⠀⠀⠀⠤⠀⠀⣀⣀⣀⣿⡇⠀⠰⣿⣶⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣾⣷⣿⡀⠀⠀⠀⠀⠘⣿⡏⣸⣾⣿⣿⣿⣯⡄⣿⡅⠀⠀⠐⣰⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠒⣪⠀⢉⣉⣩⣩⣿⣃⠀⠀⣲⡲⠶⠞⠛⠛⠋⠉⠉⢉⣡⣿⣿⣿⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣻⡿⣿⠇⠀⠀⠀⠀⠀⠄⠀⠘⢇⠙⠓⠘⠉⠀⠈⠉⠂⠀⠀⢻⣧⣴⡄⠁⠀⢀⣰⣶⣦⠀⢉⠀⠓⠲⣲⠶⠶⠾⡇⣿⠛⠛⢛⣿⣦⡀⠀⢐⣁⠀⠀⠀⠀⠀⠀⣀⣩⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⠀⡀⠄
⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣒⣀⡀⠈⠛⠛⠋⠀⠈⠁⠀⠀⠈⠀⠀⠂⠀⠐⠴⣒⠒⠚⠛⠒⠒⠀⠀⠀⠉⠁⣢⣭⣭⠉⠒⠒⠒⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣶⣥⣤⠤⠀⠀⠀⠀⠀⠐⠒⠲⠶⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣧⡀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠇⠀⠀⠄⠀⠀⢀⣤⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏
⠀⣀⣀⣀⣀⣀⣀⣀⣴⣾⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣭⣭⢭⣭⣯⣯⣭⣙⣻⢶⣤⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠻⠿⠿⢿⣿⣿⣿⣿⡇⡈
⡀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠋⠀⠀⠰⠿⣿⣿⡿⠿⠛⠛⠛⠻⡛⢿⠛⣿⣧⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣯⣛⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⠉⠙⠻⠿⢿
⠀⢀⣴⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⢉⢀⠀⠀⠀⢀⠐⠀⠀⠀⢻⣦⠀⢻⣿⣗⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⡛⢶⣤⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⣤⣿⠟⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠦⣤⣴⣾⣾⣶⣶⣶⡶⠄⠛⠀⠀⢿⣿⡆⠀⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣮⣙⠿⣶⣤⣾⣿⣿⣿⣿⣿⣏⡇⠀⠀⠉⠈⠙⣿⣿⣿⣿⣿⣇⣀⣤⣤⣤⣤⣤
⠟⠁⠀⠀⠀⠀⠀⠀⡀⠢⡀⠀⢰⣶⠶⠞⠛⠿⢿⣥⣤⣤⣴⣶⡟⡀⠀⠀⠹⠃⠀⠂⠘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⡿⠿⠿⣿⣿⣿
⠀⠀⠀⠈⠢⡙⠀⠐⠠⠑⠀⠀⠈⠀⠀⠀⣀⣀⣀⣠⣤⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡇⠹⣿⣿⡯⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⣀⠀⠈⢿⣿
⡀⢀⠐⣄⠀⠈⠠⠈⠠⠀⠀⡀⠀⠀⠘⠿⠿⣿⡿⠟⠛⠉⠙⠻⣽⣿⣦⠠⠀⠆⠀⢁⠀⡗⠀⠊⢿⣧⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⢸⣷
⠈⠀⠈⠀⠀⢄⡁⢈⠀⠬⠂⠄⠂⠤⠂⠀⠀⠙⠂⠒⠻⠦⠘⠿⠿⠿⠛⠀⢀⠀⠀⠀⠀⠀⠀⠁⠐⠿⣇⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠐⠌⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣄⣄⣠⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣉⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⢸⢿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⡛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⠟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠰
⡿⠿⠿⠿⠛⠛⠛⠛⡋⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠹⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⢸⣿⣿⡿⠟⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢩⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⣿⣿⣿⣿⢸⣿⣿⣧⠀⠀⠀⠀⠈⠛⠒⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⡀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⢸⣧⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⢿⣧⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡄⠀
⠀⠸⠀⣿⡆⢻⣷⢸⠘⣿⣿⠟⢁⣾⡇⣶⣿⣿⣿⣿⣿⣿⣿⠯⢸⣿⣿⣿⣿⡿⠿⢿⡿⡟⢫⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠸⣿⡀⠁⠀⠀⠉⢁⣴⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⢧⣸⣿⣿⣿⣿⠟⢫⣿⣅⡏⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⠀⠸⣿⡇⠀⠀⠀⠀⣾⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣭⡹⣻⣽⣿⢀⡥⣛⣟⣴⡾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⠁⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⡯⠉⠰⢞⣿⣿⣿⣗⡈⣿⣿⣤⣿⡇⣼⡿⠛⢣⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⣿⣿⣿
⣿⣷⡄⠀⢸⣿⠀⠀⠀⢰⣿⣿⠇⣼⣿⣿⣿⣿⣿⣷⣯⣿⡽⡿⣿⢿⣿⣿⣇⠿⣿⣿⣿⣷⢹⡇⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣽⡷⢍⡋⣿⣿⣿⣿⠿⠟⡿⠿⢙⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠈⡟⣿
⠿⠿⠷⠀⠀⢻⠀⠀⠀⢸⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣀⢿⣿⣿⡞⢛⠙⠟⢰⣿⣿⣿⣿⡆⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⠋⠀⡀⠡⣥⡜⠈⠰⡟⢸⣿⡧⠀⠐⡟⠙⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢻
⠒⠀⠀⡀⠀⠀⠀⠀⠀⠸⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡯⣐⠀⠀⠻⣿⣿⣿⡇⢨⣿⣿⣿⣿⣿⣿⣿⢹⣏⣾⣽⣷⣷⣾⢶⣿⣷⣦⠐⣱⡗⣾⡇⢷⣶⣿⡆⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⣻⣿⣛⣻⣋⠊⠁⡀⡘⣛⣡⣿⠀⠀⢑⣾⡛⣻⡋⢸⣟⣿⡟⣻⣿⣿⣿⠙⢻⡟⢻⡟⢿⡙⠀⠋⢰⠲⠀⠸⠻⠿⠆⠋⠠⢐⡁⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣆⣾⣇⣧⠀⠀⠀⠀⠀⠀⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠿⢿⠿⢿⣿⡇⠀⢿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣭⣿⣽⣿⣿⣿⣿⠟⠃⠈⠠⠀⠨⠀⠀⡤⡠⣆⣤⠰⣿⢦⣻⣿⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣷⢼⣿⣿⡀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣿⣿⣿⣿⣿⠿⡏⠁⠉⠀⠉⠀⠈⠉⠁⠈⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠀⢥⠄⣯⣭⣧⣍⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣉⢺⠇⠀⠀⢺⣧⣾⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣻⣾⣿⣿⡆⠀⠀⠀⠀⠀⣿⡇⣸⣬⣿⣟⣿⡿⠄⢾⣅⠀⠀⠀⡼⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠴⢮⠀⢉⣉⣙⣩⣿⣒⠀⠂⣤⡶⠶⠶⠛⠛⠛⠛⠋⠉⢡⣸⣿⣿⣧⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⢻⡿⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⢣⠙⠓⠈⠀⠀⠀⠈⠀⠀⠂⢻⣧⣤⡄⠁⠀⢀⣀⣤⣄⠀⢉⠉⠛⠢⣤⡶⠶⠾⠇⣾⠓⠛⠛⢿⣯⡀⠀⢀⣃⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡀⢀⠀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣗⣒⣂⡀⠈⠛⠛⠛⠀⠈⠉⠀⠀⠈⠁⠉⠁⠈⠨⠤⠐⠶⠶⠿⠃⠒⠀⠀⠀⠁⠒⢒⣺⣭⠭⠩⠙⠒⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⣢⣤⣶⣦⣤⡀⠀⠀⠀⢻⣿⣿⣿⣿⣦⣄⣤⣄⣀⡀⠀⠀⠀⠀⠤⠴⢶⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣈⣀⣀⡀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⣿⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠶⠾⡇⠀⠀⠤⠀⠀⠀⣀⣴⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⢀⣀⣀⣀⣀⣀⣴⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⠛⢿⣿⣿⣿⣿⣿⣿⢭⣭⣭⣭⣩⣙⣻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠟⡻⡿⣿⣿⣿⣿⣟⡟⠈
⠉⠀⡀⠀⠀⣴⣿⠿⠋⠁⠀⠀⠀⠔⣿⣿⣿⣯⠯⣿⣥⣤⣴⣶⣯⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣛⡷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠉⠉⠛⠻⠿⣿
⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠹⢿⣅⣀⣳⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⡻⢶⣤⣀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⢀⠀⠀⠀⠤⠤⡐⠄⢐⣧⣤⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣮⢛⠷⣦⣄⣠⣿⣿⣿⣿⣿⣿⢱⠀⠀⠘⠃⠙⢻⣿⣿⣿⣿⣦⠀⡀⣀⣤⣤⣤
⠀⢀⠀⡁⠀⠀⠀⠀⠀⠢⡀⠠⢸⣿⣄⡀⣀⡀⢉⠛⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⡿⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣻⣿⠿⢿⣿⣿
⠑⠘⠒⠈⠀⡘⠢⠐⠀⠑⠄⠀⢈⠀⠘⠻⠿⠿⠿⠷⠄⠈⠻⠟⣿⣷⠀⠀⠀⠀⠀⠀⠀⡇⠙⣿⣿⡯⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣆⠀⠀⢹⣿
⡀⢀⡀⣄⠀⠀⠀⠈⠠⠈⠀⠐⠰⠷⠖⠀⠀⠰⠦⠲⠀⠀⠰⠿⠿⠿⠄⠠⠀⠀⠠⢁⠄⡧⠀⠈⢿⣯⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠈⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠘⣿
⠈⠀⠈⠀⠀⠀⡁⠀⠀⠨⠢⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⢀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠐⠿⣇⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣷⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣷⢙⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣴⣶⣶⣷⣶⣶⣿⣿⣿⡀⠀⠀⠀⢤⣶⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⢸⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⠿⠿⠄⠀⣿⣿⡟⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⡿⠿⠿⠿⠛⠛⠛⠛⣋⠉⠉⠉⠉⠁⠀⠀⢀⠀⠀⢻⡆⠀⠀⢰⣿⣿⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⣾⣧⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⢿⣿⣿⣿⠸⣿⣿⣿⡅⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠽⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡆⠀
⠀⢸⠀⣿⡆⢻⣷⢸⠸⣿⣿⠟⢁⣼⡇⣤⣿⣿⣿⣿⣿⣿⣿⢯⢸⣿⣿⣿⣿⣿⣿⢿⣿⡟⢫⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⣿⡀⠁⠀⠀⠙⠁⣰⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠟⢮⣿⣅⡛⢘⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⠀⠸⣿⡇⠀⠀⠀⠀⣾⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣭⠻⢻⣹⣷⢀⣅⣛⣗⣴⡾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡉⠃⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⡯⠋⠱⢺⣿⣿⣿⣗⡘⣽⣿⣤⣿⡇⣽⡿⠟⢣⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿
⣿⣷⡄⠀⢸⣿⠀⠀⠀⢠⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣏⣶⡽⡿⣿⢿⣿⣿⣇⢿⣿⣿⣾⣷⢹⣗⢀⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⢻⣿⣿⣷⢟⡛⣿⣿⣿⣿⠿⠿⣿⠿⠛⣿⣿⡿⠟⠋⠓⠀⠀⠀⠀⠀⠀⠈⡟⣟
⠿⠿⠧⠀⠀⢿⠀⠀⠀⢸⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣁⢿⣿⣿⡞⠻⠛⠟⢠⣿⣿⣿⣿⡆⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⡻⢛⠋⠀⡁⠉⣥⡝⠉⢰⡟⢸⣿⡧⠀⠠⠷⠱⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢸
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠸⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣿⡍⡰⠀⠈⠹⣿⣿⣿⡗⢠⣿⣿⣿⣿⣿⣿⣿⢹⣟⣾⣿⣷⣶⣶⣾⣿⣶⣦⠐⣱⡏⣾⡧⣷⣶⣷⡄⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢺
⠀⡀⠀⡿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣛⣿⣟⣻⣟⠛⡛⠊⠉⠀⠘⢫⣅⣾⠀⠀⠡⠾⡿⠟⡏⠸⣿⠿⣿⣿⣿⣿⣿⢸⠿⢿⠿⡿⠿⡹⠈⠯⢰⠰⠀⠸⠳⠿⠆⠋⠀⠨⡁⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣆⣿⡆⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢽⡿⠿⣿⣿⣿⡇⠀⣿⣿⡿⣿⡇⢸⣿⣿⢿⣿⢹⣿⣿⣼⣿⣿⡿⡿⠿⠃⠈⠠⠀⠨⠀⠀⡤⠨⣆⣤⠽⣿⣦⢻⣿⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣧⢿⣿⢿⡀⠀⠀⠀⠀⢸⣾⡟⣿⣿⣿⣿⣿⣿⣿⠿⡋⠀⠀⠁⠀⠉⠉⠉⠁⠙⠉⠉⠁⠉⠁⠈⠉⠉⠉⠉⠈⠉⢭⠀⣯⣭⣯⣍⡀⠀⠀⠀⠀⢀⠀⠀⠀⠉⢉⢺⠇⠀⠀⢸⣯⣼⡇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣻⣾⣷⣿⡄⠀⠀⠀⠀⠀⣿⡏⣸⣬⣿⣿⣿⠿⠀⢿⡅⠀⠀⠀⡴⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢬⠀⠉⣉⣛⣉⢿⠖⠀⠂⣤⣤⠶⠶⠿⠟⠛⠛⠛⠒⢂⣸⣿⣿⣧⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠄⠀⢈⢧⠙⠻⠀⠀⠀⠀⠈⠀⠀⠂⢳⣧⣤⡤⠁⠀⢠⣠⣤⣄⠀⠈⠉⠟⢤⣤⡴⣶⡿⠇⣞⠓⠛⠛⣿⣭⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣶⣶⡀⢐⠀
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣖⣒⠂⠀⠈⠛⠛⠛⠀⠈⠉⠀⠀⠉⠁⠉⠍⠉⠨⣤⠤⠶⠶⠿⠇⠤⠤⠉⠀⠐⠒⢒⣒⣚⠭⠭⠍⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣦⣄⡀⠀⠀⢷⣿⣿⣿⣿⣶⣀⣄⣀⣀⡀⠀⠀⠀⠀⠤⠤⣶⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡈⠁⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣾⣦⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠒⠶⠶⣶⣆⠀⠀⠄⠀⠀⠀⢀⣠⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣀⣀⣀⣴⣿⣿⠏⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠙⢿⣿⣟⣿⣻⣿⣿⣿⣯⣭⣩⢙⡿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠈
⠉⠉⡉⠀⠀⢠⡿⠟⠁⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣯⢛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠉⠙⠛⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⠻⣦⣤⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠦⠴⠄⢸⣿⡋⠙⠊⠙⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣍⢛⢷⣦⣄⢠⣿⣿⣿⣿⣿⣿⢻⠁⠀⠘⠋⠙⢿⣿⣿⣿⣿⣷⡀⣠⣀⣄⣠⣠
⠠⠀⠀⡁⠄⠀⠀⠀⡀⠠⡑⠀⠘⠉⠻⠷⠶⠆⢰⡙⠻⠿⣿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣾⣿⣮⣝⣿⣿⣿⣿⣿⣿⡯⠀⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠘⠒⠈⠂⡘⠂⠐⢀⠐⠈⠀⣸⣦⣤⠀⠀⠀⠀⢀⠀⠐⣶⣿⣿⣇⠀⠀⠀⠐⠀⠀⠀⡇⠹⣿⣿⡏⡅⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⣿⡀⠈⢻⣿
⡀⠀⠐⣀⠀⠀⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⠄⠤⠀⠀⠢⢁⠀⡧⠀⠞⢿⣗⡇⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣷⣿⣿⡟⠃⠐⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢿⠓⠀⠘⣿
⠈⠀⠈⠀⠀⢄⠀⢈⠀⢈⠦⠐⠠⠀⣄⡀⠀⠀⠀⠀⠀⠀⢻⣷⡂⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠘⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⠁⠀⠀⠀⣀⡀⠀⠈⣿⣧⣤⣤⣤⣤⣴⣶⣶⣶⣾⣾⣿⣿⣶⡃⢽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣠⣤⣤⣤⣤⣤⣤⣶⣶⣷⣶⣶⣿⣿⣿⡄⠀⠀⢸⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⢸⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣿⠿⠿⠄⣿⣿⡟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠈⠈⢿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀
⣿⡿⠿⠿⠟⠛⠛⠛⡛⠛⠉⠉⠉⠉⠀⠀⣷⣤⣾⣷⡀⠀⠰⣿⣿⣧⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠹⣿⣿⣿⣿⢸⣿⣿⣿⠆⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠈⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠙⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⡇⠀
⠀⢸⠀⣿⡄⢻⡇⢸⠸⣿⣿⠟⢁⣼⡇⣴⣿⣿⣿⣿⣿⣿⣿⠧⢹⣿⣿⣿⣿⣿⣿⣿⣿⡛⢫⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣷⡀⠁⠀⠀⠙⠁⣴⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⡿⣆⣸⣿⣿⣿⣿⠗⢦⣿⣅⡛⠘⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⠸⣿⡇⠀⠀⠀⢀⣾⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣭⠻⢻⣹⣷⢀⣕⣛⣗⣴⡾⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡉⠃⠀⠀⣿⣷⠀⠀⠀⢸⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⡯⠛⠴⢸⣿⣿⣿⣗⡈⣿⣿⣠⣿⡇⣽⡿⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⢿⣿⣿⣿
⣿⣷⡀⠀⢹⣿⠀⠀⠀⢨⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣇⣶⣽⣿⣿⢿⣿⣿⡇⣿⣿⣿⣿⣧⢻⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣻⣿⢿⡛⣿⣿⣿⣿⠿⠿⣿⠿⠛⣿⣿⣿⠿⠋⠓⠀⠀⠀⠀⠀⠀⠘⡟⣿
⠿⠿⠇⠀⠈⢿⠀⠀⠀⢸⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣈⢿⣿⣿⡞⠻⠛⠟⢠⣿⣯⣿⣿⡎⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⠋⠀⠁⢉⣧⡙⠁⢰⡟⢸⣿⡇⠀⠠⠶⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⡍⡠⠀⠈⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢽⣟⣾⣿⣷⣶⣶⣾⣿⣶⣄⠐⣱⡎⣿⡧⣷⣴⣷⠀⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⣴⣟⣛⣻⣟⣻⣿⣟⣻⡟⠛⠋⠁⠈⡘⢋⡁⡏⠀⠀⢡⠾⢿⠟⠇⠸⢿⣿⣿⣿⡿⠿⣿⠹⡿⠿⡿⠿⠿⠻⠩⠯⠰⠰⠀⠻⠳⠿⠆⠃⠀⠩⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣄⣷⡇⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠽⢿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⢸⣿⣿⡏⣿⣿⣿⣿⢸⣿⡿⡿⠿⠿⠁⠉⠠⠀⢨⠀⠀⡤⢤⣆⣀⢭⣿⣄⢻⣿⢄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣧⣿⣷⣿⠀⠀⠀⠀⠀⢸⣾⡏⣿⣿⣿⣿⣿⣿⣿⠿⡇⠙⠀⠈⠉⠉⠉⠉⠁⠙⠉⠉⠉⠉⠁⠈⠉⠉⠁⠉⠉⠉⣭⠈⣯⣵⣥⣌⡁⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⣿⠂⠁⠀⢸⣯⣼⡇⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣾⣧⣿⡀⠀⠀⠀⠀⠈⣿⡏⣹⢼⣿⣿⡿⠟⠄⣿⡅⠀⠀⠀⣰⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢜⠀⡛⢉⢛⣛⣿⠒⠀⠀⣤⣤⡤⠶⠿⠟⠛⠛⠓⠒⢂⢸⣿⣿⣧⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠄⠀⢘⠯⠙⠓⠀⠀⠀⠈⠉⡀⠀⠀⢻⣦⣤⡄⠁⠀⢠⣠⣤⣀⠀⠋⠉⠟⢥⣤⣴⣶⣾⠇⣿⠗⠛⠿⣿⣍⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣶⣦⡀⠀⠀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢿⣖⣒⡂⠀⠘⠛⠛⠟⠀⠈⠁⠀⠀⠉⠀⠉⠍⠁⠩⣤⠤⠶⠾⠿⠥⠤⠌⠁⠀⠒⠂⢐⣒⣚⠯⠭⠍⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣷⣦⣄⣀⠀⠀⠳⣿⣿⣿⣿⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠤⠴⣶⠀⠀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡉⠉⢁⣀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡮⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⢶⣶⡆⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣷⣼⡽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⣀⣀⣀⣀⣠⣾⡿⠋⠙⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠉⠻⣿⣷⣛⣛⣻⣻⣿⣿⣿⣿⣭⣭⣙⡿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠙⠻⢿⣿⣿⣿⣿⣿⣻⠟⠀
⠉⠉⠁⠀⠀⠀⠰⡿⠏⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣯⢻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠉⠙⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⠳⣦⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠽⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡐⠀⢸⣿⣯⣤⡙⢽⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣍⠻⢷⣤⣀⢀⣿⣿⣿⣿⣿⣿⡻⠁⠀⠙⠋⠛⢻⣿⣿⣿⣿⢦⠀⢀⣀⣀⣀⣀
⠀⠀⢄⡀⢄⠐⠀⠀⡀⠈⡑⠄⢛⣏⡉⠉⠁⠀⠈⣙⣿⣿⣯⣿⣿⣿⠇⠀⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣾⣷⣮⣙⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣟⡻⣻⠿⣿⣿⣿
⠁⠘⠒⠃⠂⡙⠀⠐⠈⠂⠀⠀⠘⠛⠋⠀⠀⠈⠉⠙⠁⠀⠉⡉⠉⠁⠀⠀⠀⠀⠀⠀⡈⡆⠹⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡏⣿⣿⣿⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣉⠀⠈⢻⣿
⠀⢀⠀⡀⠀⠈⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠠⠀⠤⠂⢀⠂⠐⠈⡧⠀⠘⢿⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣷⣿⣿⠿⠃⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠀⠀⠸⣿
⠉⠀⠈⠀⠀⢄⠀⢈⠀⠀⠦⠐⠀⠐⣯⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠁⠉⠀⠁⠀⠀⠸⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠻⠁⠀⠀⢀⣀⡀⠀⠘⣿⣤⣥⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣶⡃⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣶⣶⣷⣶⣶⣿⣿⣿⡄⠀⠀⢸⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣤⣶⣾⡿⠿⠇⠀⢻⣿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⣿⡿⠿⠿⠟⠛⠛⠛⡛⠛⠉⠉⠉⠉⠀⠈⣿⣿⣿⣧⠀⠀⠀⠸⣿⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⢺⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠠⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⣿⣿⣿⣧⢸⣿⣿⣿⡁⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣇⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠘⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡅⠀
⠀⢸⠀⣿⡀⢿⡇⠙⢸⣿⣿⠟⢠⣾⠀⣵⣿⣿⣿⣿⣿⣿⣿⠥⢿⣿⣿⣿⣿⠿⡿⣿⣿⡟⣹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠿⣇⠈⠁⠀⠀⠛⢁⣴⣿⡏⢨⣿⣿⣿⣿⣿⣿⣿⡿⣆⣼⣿⣿⣿⣿⠗⣶⣯⣔⡙⠸⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⢸⣿⡄⠀⠀⠀⢠⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣍⠻⣻⣿⣷⢈⣙⣻⣗⣴⢾⣿⡿⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡉⠀⠀⠘⣿⣧⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⡏⠻⠤⣻⣯⣿⣿⢇⠉⣿⣿⣼⣿⡃⣽⡿⠛⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⢿⢿⣿⣿⣿
⣿⣷⠀⠀⢿⣿⠀⠀⠀⣼⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣗⣶⢽⣿⣿⢿⣿⣿⡆⣿⣽⣿⣿⣆⢿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣯⣿⣿⣿⢿⣻⣯⣿⣿⡿⠿⠿⡿⠿⠻⣿⣿⡿⠿⠋⠃⠀⠀⠀⠀⠀⠀⠘⡟⣿
⠿⠿⠆⠀⠘⡏⠀⠀⠀⣽⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣸⢾⣿⣿⠞⡻⠻⠇⢰⣿⣿⣿⣿⡘⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⠁⠀⠁⢉⣥⡙⠃⢸⡟⣿⣿⡄⠀⠰⠶⢸⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢾
⠀⠠⢀⠀⠀⠀⠀⠀⠀⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣍⠠⠀⠘⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡯⣽⣗⣿⣻⣶⣶⡾⣾⣿⣶⣄⠌⣱⡏⣿⡧⣷⣾⣶⢸⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢺
⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⣞⣛⣻⣟⣛⣿⣿⣻⣟⠛⡟⠉⢁⠈⠙⢋⠐⣇⠀⠀⠵⢿⡿⢿⡇⢹⣿⣿⠿⣿⠿⣿⣿⠿⠿⡿⠿⣿⡿⠛⠹⠓⠰⠰⠀⠿⠹⢷⡖⠃⠀⠽⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣄⣷⡜⡇⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠄⠀⣿⣿⣿⣿⠃⢬⣿⣿⣿⣿⣿⣿⣿⢸⠿⠿⠿⣷⡿⠁⠉⠀⠀⢭⠀⢀⡄⠀⣀⣀⢽⣿⡌⢿⣿⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣦⣿⣷⣷⠀⠀⠀⠀⠀⢸⣾⠛⣿⣿⣿⣿⣷⣿⡿⠟⠛⠉⠉⠉⠉⠉⠙⠉⠀⠙⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⣭⠸⣥⣽⣤⣉⠉⠀⠀⠁⠀⣀⠀⠀⠀⠉⠉⡿⠀⠁⠀⢸⣿⣾⡇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣷⣿⣷⣿⠀⠀⠀⠀⠀⢸⣿⡈⢩⣼⣿⢿⣿⣯⡄⣿⡀⠀⠀⠰⢠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⣌⠀⡋⣙⣛⡻⣷⠒⠀⠠⣤⣤⡤⠾⠿⠟⠛⠛⠓⠒⣂⢸⣿⣿⣧⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣟⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠘⡭⠛⠣⠁⠛⢇⣿⣃⠀⠀⠀⢟⣦⣤⡄⠁⠀⢠⣤⣤⣀⠀⠋⠉⠋⢥⣤⣴⣶⡿⠆⣿⠓⠛⠿⣿⣍⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣛⣻⣷⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡠⠀⠁
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠀⠀⠀⠀⠙⠁⠁⠀⠀⠸⢿⣖⣒⠂⠀⠘⠛⠛⠇⠀⠉⠁⠀⠀⠉⠈⠉⠍⠃⠭⡤⠤⠶⠾⠿⠠⠤⠌⠁⠀⠒⠂⣒⣒⣚⠭⠭⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣷⣆⣀⣀⣀⣀⡀⠀⠀⠀⠠⠤⠴⣶⠀⠀⠀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡉⠉⣁⣀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠒⠲⠶⢶⣶⡆⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⡒⠚⣓⣛⣛⣿⣿⣿⣿⣿⣯⣍⣍⣛⡷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⠿⣿⣿⣿⣿⣿⣟⣻⡏⡈
⠉⢉⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⣇⠘⠈⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣟⣻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠉⠙⠛⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠁⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣮⣝⠷⣦⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠒⠀⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣦⣄⠂⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣝⡻⢶⣤⣀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠉⠹⢿⣿⣿⣿⣿⣗⠀⣀⣠⣤⣤⣤
⠀⠁⢄⠀⢄⠀⠀⠂⡐⢀⠐⠄⠀⣿⣤⡤⠆⠃⠰⡾⠿⠏⠻⠛⠛⠙⠉⠀⠀⠀⠀⠌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣮⣝⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠑⠒⡑⠂⠑⠄⠀⠌⠢⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⣘⠌⢹⣿⣿⣽⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢂⣁⠀⠈⣿⣿
⠀⢀⢀⡀⠂⠈⠠⠀⠀⠁⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠈⠉⢿⣿⠀⠤⠀⠄⠂⠂⠤⠀⢈⡆⠀⠙⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣿⣿⡿⠏⠀⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⢸⣿
⠁⠀⠁⠀⠀⠀⠀⠈⠀⡀⠆⠀⢀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠈⠀⠸⡟⡇⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⡿⡧⠆⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⡀⠀⠀⣀⣀⡀⠀⠀⢾⣤⣤⣥⣬⣤⣤⣶⣶⣶⣶⣶⣾⣿⣷⣆⡃⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠈⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⣤⣤⣤⣤⣤⣴⣶⣾⣶⣶⣾⣿⣿⣧⣀⣠⣿⣿⣿⡄⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡅⣻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠇⠀⠘⣿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰
⡿⠿⠿⠿⠛⠛⠛⠛⡋⠋⠉⠉⠉⠁⠈⢻⣿⣿⣧⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠨⠋⣹⣿⡆⠀⠀⠐⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⡇⢿⣿⣿⣿⣤⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣷⡄⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣧⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀
⠀⠧⢸⣿⠘⣿⡇⡇⢻⣿⡿⠋⣠⣿⢠⣼⣿⣿⣿⣿⣿⣿⣿⠅⣿⣿⣿⣿⣿⢿⡿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣇⠈⠁⠀⠈⠋⢀⣼⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⡿⡆⣿⣿⣿⣿⡿⠖⣵⣯⣘⠃⠹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⠀⠀⢿⣿⡀⠀⠀⠀⢰⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣯⣍⠟⣟⣿⡆⣨⣚⣻⣇⣶⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡉⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⠏⠝⠦⣿⣯⣿⣿⣇⢩⣿⣿⣼⣿⢡⣿⡿⠛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⢿⣿⣿⣿
⣿⣦⠀⠀⣿⡇⠀⠀⠀⣼⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣵⣾⢿⢿⣿⣿⣿⣿⡺⣿⣿⣷⣿⡆⣿⡃⣰⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣯⣿⣿⣟⢿⣻⣿⣿⣿⡿⠿⢿⡿⠟⢻⣿⣿⡿⠿⠋⠃⠀⠀⠀⠀⠀⠀⢸⡟⣿
⡿⠿⠄⠀⠘⡇⠀⠀⠀⣿⡿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣏⡸⣾⣿⣷⠟⡛⠻⠃⣸⣿⣿⣿⣿⠘⢲⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⡛⠁⠀⠀⢩⣭⠃⠁⣾⠃⣿⣿⠄⠀⠴⠖⢺⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢿
⠀⠄⢀⠀⠀⠀⠀⠀⠀⠏⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⣿⣿⣿⢁⠂⠀⠉⢿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⡏⣿⣳⣯⣿⣶⣦⡾⣾⣿⣮⡄⢎⣶⢭⣿⠽⣶⣾⣶⢸⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢾
⢀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⣟⣛⣿⣛⣻⣿⣛⣿⣿⡛⠉⠁⠁⠛⣋⡔⡃⠀⠈⣴⠿⣿⣿⠁⣿⡿⢿⡿⢿⡿⢿⡟⠿⠿⢿⣿⣿⠟⠇⠹⠑⠴⠄⠀⠟⣾⡷⠘⠃⠀⢽⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣸⣷⣸⡀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣻⣿⠀⣿⣿⣿⣿⣿⣿⡿⡿⠹⠿⢿⣿⣿⠿⠁⠉⠀⠀⠍⠀⢀⠀⠄⣀⡨⢽⣿⡌⣿⣿⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⡬⣿⣿⣇⠀⠀⠀⠀⠀⢼⣿⢿⣿⣿⣷⣾⣿⣿⡿⢿⠛⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⢁⣥⢸⣥⣼⣭⣉⠉⠀⠀⠀⠀⣀⠀⠀⠀⠁⠁⡿⠀⠀⠀⢸⣧⣾⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣷⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⢈⣡⣽⣿⢻⣿⣧⡗⣿⡀⠀⠀⢠⢇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⡍⠘⢋⣙⣛⡻⡷⠂⠐⠠⣤⡤⡶⠾⠿⠛⠛⠛⠓⠒⣀⢸⣿⣿⣤⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣟⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⡸⡌⠛⠮⠳⢿⣽⣿⢃⠀⠐⠘⣿⣤⣤⡌⠀⠀⣤⣤⣄⡀⠀⠉⠹⠋⣤⣤⢶⣾⠿⠢⣿⠚⠛⠿⣯⡍⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡀⠀⠁
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠈⠁⠀⠀⠹⣷⣒⣒⠀⠀⠙⠛⠛⠇⠀⠉⠁⠀⠀⠉⠈⠩⠍⠁⢭⡤⠴⠶⠾⠿⠠⠤⠬⠁⠀⠒⠂⣒⣒⡻⠭⠭⠉⠻⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣷⣦⣠⣀⣀⣀⠀⠀⠀⠀⠠⠤⠴⣆⠀⠀⠀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⡉⢉⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⣤⣀⡀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣷⣶⣆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠒⠒⠶⠶⢶⣶⡄⠀⠠⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣷⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠒⢚⣒⣛⣛⣿⣿⣿⣿⣯⣭⣍⣍⣛⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠻⣿⢿⣿⣿⣿⣟⣿⡏⡈
⠉⢁⠀⠀⠀⠀⠀⠀⢠⠞⠋⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠁⠄⠘⡈⠜⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣾⣝⡻⢶⣤⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠈⠉⠛⠻⠿⣿
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠁⠀⡀⠀⠂⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣟⠷⣦⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⣷⣦⡄⠂⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡝⡻⢶⣤⣀⢠⣿⣿⣿⣿⣿⣿⠿⠁⠀⠙⠙⠿⢿⣿⣿⣿⣿⡆⢀⣤⣤⣤⣤⣤
⠄⠁⢈⠠⠀⠀⡀⠀⠐⢀⠐⠄⠀⣿⣍⣉⡍⠩⢿⣿⣿⠟⠻⠟⠋⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣟⣻⡟⠿⣿⣿⣿
⠂⠓⠊⡑⢈⠑⠄⠃⠈⠢⠁⠀⠁⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠠⠀⠀⠀⠀⠀⣸⠈⢻⣿⣿⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠑⣍⠀⠈⣿⣿
⠀⣀⢂⡀⠀⠀⠤⠁⠄⠀⠀⠂⠀⠀⣄⠀⠀⠀⠀⠀⠤⠻⣿⡇⠀⠦⠀⠄⠰⠒⠌⠈⢘⠄⠀⠹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠠⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⢹⣷
⠁⠁⠁⢀⠀⠈⠂⠀⠠⡱⠄⠀⠄⢲⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠈⠀⠺⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠀⣀⣀⡀⠀⠰⣧⣤⣤⣥⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⡎⡃⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣤⣤⣤⣤⣤⣤⣶⣶⣾⣶⣶⣾⣿⣿⡇⠀⢀⣿⣿⣇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡅⡿⣿⣿⣿⣿⣿⣿⣿⠜⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠿⠀⠈⣿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢰
⡿⠿⠿⠿⠛⠛⠛⢛⠛⠉⠉⠉⠉⠀⢹⡿⣿⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⣥⣿⣿⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⣿⣿⣿⡇⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣧⡀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⡇⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀
⠀⠇⢸⣷⠘⣿⡀⡇⢿⣿⡿⠋⣠⣿⢰⣾⣿⣿⣿⣿⣿⣿⡿⡅⣿⣿⣿⣿⣿⢿⡿⣿⣟⠛⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣂⠈⠀⠀⠈⠋⣠⣾⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⡿⣄⣿⣿⣿⣿⡿⠢⣼⣯⣘⠃⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⢿⣿⠀⠀⠀⠀⣰⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣯⡝⠟⣯⣿⡆⣨⣚⣻⣢⣶⢿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡉⠀⠀⢸⣿⡆⠀⠀⠀⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⠙⠅⠇⣻⣿⣿⣿⣃⢹⣿⣧⣼⣿⢨⣿⠿⠛⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⢿⣿⣿⣿
⣿⣆⠀⠈⣿⡇⠀⠀⠀⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣹⣮⣿⣿⡿⣿⣿⣿⡸⣿⣽⣿⣿⡎⣿⡂⣰⣾⣿⣿⣿⣿⡿⣿⣿⣯⣟⡿⣿⣿⣿⣿⢿⢻⣿⣿⣿⡿⠿⢿⠿⠟⢻⣿⣿⡿⠿⠉⠃⠀⠀⠀⠀⠀⠀⢹⠿⣿
⠿⠿⠀⠀⠹⡇⠀⠀⠀⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣇⡹⣿⣿⣷⠛⡟⠻⠃⣼⣿⣽⣿⣷⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⡛⠁⠈⠈⢹⣌⠋⠁⣾⠃⣿⣿⠀⠀⠴⠞⢾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣯⢁⠄⠀⠈⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⡏⣿⣳⣯⣿⣶⣶⣶⣿⣿⣦⡄⢊⣶⢹⣿⢼⣶⣾⣦⢸⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣾
⢠⠀⢸⠁⠀⠀⠀⠀⠀⢠⣟⣻⣛⣛⣿⣿⣿⣿⣟⣿⠓⠉⠀⠀⠛⣋⣴⠁⠀⠈⢴⣿⣿⣿⠀⠻⣿⠿⣿⠿⢿⢿⡇⠿⣿⡿⣿⠿⡟⠇⠹⠅⠆⠆⠘⠟⡞⣷⠘⠁⠈⠅⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣸⣶⢸⡀⠀⠀⠀⠀⠀⠸⡿⢿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠀⢸⡟⣿⡧⣿⠀⣿⣿⣿⣿⣿⢿⠿⠧⠿⢿⣿⣿⣿⠟⠀⠁⠄⠀⡅⠀⢠⠄⢤⣀⡨⢿⣷⡜⣿⡿⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⡼⣿⢿⡇⠀⠀⠀⠀⠀⣷⣟⣿⣿⣿⣿⣿⣿⣿⡿⢿⠋⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠀⠉⠉⠉⠉⠉⠈⢠⣄⢸⣭⣿⣭⣉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠉⡱⣷⠀⠀⠀⢺⣧⣿⠇⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⣷⣿⣼⣇⠀⠀⠀⠀⠀⢹⣿⢉⣧⣿⣿⣻⣟⣧⢸⣯⠀⠀⠀⢠⡆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⡅⠘⢋⣙⣛⡹⡷⠂⠐⢠⣤⡴⠶⠾⠿⠛⠛⠛⠓⠒⡀⢸⣿⣿⣤⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⡻⡌⠛⠏⠻⢿⣼⣟⢃⠀⠐⠘⣿⣤⣤⠌⠀⠀⣤⣤⣄⡀⠘⠉⠹⠣⣤⣤⢶⣶⠿⢰⡟⠚⠛⢻⣯⡁⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⢀⣛⣿⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⠀⠂⠀
⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠋⠈⠀⠀⠀⠋⣿⣒⣒⠀⠀⠙⠛⠛⠃⠀⠉⠁⠀⠈⠉⠈⠩⠉⠀⢥⡤⠶⠶⠾⠿⠤⠤⠈⠁⠀⠒⠂⣒⣒⡯⠭⠍⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢺⣿⣿⣿⣷⣆⣀⣀⣀⣀⡀⠀⠀⠀⠠⠤⠶⡆⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⠉⢉⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣯⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠒⠒⢓⣚⣛⣻⣿⣿⡯⣭⣭⣭⣭⣍⣛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠿⣿⠿⣿⣿⣿⣿⣿⣃⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠐⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣾⡝⡻⢶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠈⠙⠛⠻⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠡⠁⠀⠀⠀⠂⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡛⠷⣤⣀⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠐⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣈⡝⡻⢶⣤⣀⢰⣿⣿⣿⣿⣿⣿⣯⠁⠀⠉⠈⠙⣿⣿⣿⣿⣿⣧⣠⣤⣤⣤⣤⣤
⠄⠀⢈⠠⠀⠀⠀⠀⠐⢄⠂⠀⠀⣿⣿⣋⡉⡭⢭⣿⣿⣿⠻⠟⠁⠀⠀⠠⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣭⣛⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣟⣻⣿⠿⣿⣿⣿
⠀⠓⠊⠑⢈⠃⠀⠡⠈⠀⠁⠄⠀⠛⠛⠋⠁⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣸⠈⢿⣿⣿⣭⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣯⣆⠀⠘⣿⣿
⠀⡀⢀⡀⠀⠈⠄⠀⠀⠀⠀⠂⠀⠀⣠⠤⠀⠀⠀⠀⢀⣿⣿⠃⡀⠤⠂⠄⠠⠒⠌⠂⢹⠄⠀⠻⣿⣻⢸⣿⣿⣿⣿⣿⣿⣿⡧⢾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠑⠋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠛⠂⠀⢻⣧
⠁⠁⠁⢀⠠⠈⠀⠀⠀⡰⠄⠒⠆⣤⡅⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠈⠀⠿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⢿⠫⠀⠀⢸⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⢘⠀⠀⠀⣀⡀⠀⠀⣾⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣞⠨⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⢹
⣤⣤⣤⣤⣤⣴⣶⣶⣾⣶⣶⣿⣿⣿⡀⠀⢀⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠿⠆⠀⣿⡿⠛⠛⠛⠋⠛⠋⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢸
⠿⠿⠿⠟⠛⠛⠛⢋⠉⠉⠉⠁⠀⠀⣿⣿⣿⡀⠀⠀⠐⣿⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢻⣿⣿⣿⡆⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣧⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⣿⣇⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⡀⠀
⠀⠇⢸⣧⠘⣿⠀⡇⢿⣿⡿⠋⣰⡷⢨⣾⣿⣿⣿⣿⣿⣿⡿⠅⣿⣿⣿⣿⣿⢿⠿⣿⣿⠛⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣂⠈⠀⠀⠈⠋⣠⣾⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⢷⣀⣿⣿⣿⣿⡿⠢⣼⣯⣈⠃⡻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⢿⣿⠀⠀⠀⠀⣴⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣯⡝⠟⣯⣿⡆⣨⣘⣻⣢⣶⢿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⢸⣿⡆⠀⠀⠀⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⠉⠃⠆⣻⣷⣿⣿⣀⢹⣿⣧⣼⣿⢨⣿⠿⠛⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⡿⢿⣿⣿⣿
⣿⣆⠀⠈⣿⡇⠀⠀⠀⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣴⣮⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⡎⣿⠀⣴⣾⣿⣿⣿⣿⡿⣿⣿⣯⣟⡿⣿⣿⣿⡯⢛⢹⣿⣿⣿⡿⠿⢿⠿⠟⢻⣿⣿⡿⠟⠙⠂⠀⠀⠀⠀⠀⠀⢹⠿⣿
⠿⠷⠀⠀⠹⡇⠀⠀⠀⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣇⡿⣿⣿⣷⠛⠛⠻⠃⣾⣿⣽⣿⣷⠙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⠁⠈⠈⣩⣌⠋⠁⣾⠃⣿⣿⠀⠀⠴⠎⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⣿
⠀⠀⡁⠀⠀⠀⠀⠀⠀⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣯⠁⠀⠀⠙⣿⣿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⡏⣿⣳⣿⣿⣶⣶⣶⣿⣷⣦⡄⢊⣶⢹⣿⢼⣶⣾⡆⢸⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⢀⠀⢹⠀⠀⠀⠀⠀⠀⢠⣟⣛⣿⣛⣻⣿⣿⣿⣟⣛⠓⠉⠈⠀⠛⣉⢸⡅⠀⢈⣴⣿⣿⡟⠀⡿⢿⡿⠿⡿⠿⣿⡇⣿⡿⡿⠿⠿⠝⠏⠽⠁⠆⠆⠈⠟⣾⠷⠘⠀⠈⢅⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⣸⣦⢸⠀⠀⠀⠀⠀⠀⠸⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠀⢸⣿⢸⣿⣿⠀⣿⣿⣿⡿⡿⠿⠿⠇⣿⣿⣿⣿⣿⠏⠈⠁⠀⡀⠅⠀⠠⠄⢴⣠⡨⢿⣧⡜⣿⡿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⣼⣿⢿⡇⠀⠀⠀⠀⠀⣷⡇⣶⣿⣷⣾⣿⣿⣿⠿⢿⠋⠉⠉⠈⠉⠉⠉⠉⠨⠋⠉⠈⠉⠉⠀⠉⠉⠉⠁⠁⠀⢡⡄⢹⣭⣿⣭⣉⠁⠀⠈⠀⠀⡀⠀⠀⠈⠉⠹⣷⠀⠀⠀⢺⣧⣿⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⣿⣿⢼⣇⠀⠀⠀⠀⠀⢹⣿⢉⣧⣿⣿⣿⣟⣥⢼⣯⠀⠀⠀⢀⡆⠀⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⡀⠘⢉⣙⣛⡹⡷⠂⠀⢠⣤⡤⠶⠾⠿⠛⠛⠛⠓⠒⡀⢸⣿⣿⣤⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⠀⢀⡻⠏⠛⠏⠻⢿⣼⣟⢃⠀⠀⠸⣷⣤⣤⠈⠀⠀⣤⣤⣤⡀⠘⠉⠹⠣⣤⣤⣶⣶⠿⢰⡟⠚⠛⢿⣯⡁⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⠀⠈⠀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠋⠈⠀⠀⠀⠋⢷⣒⡒⠀⠀⠛⠛⠻⠃⠀⠉⠀⠀⠈⠉⠈⠩⠉⠈⢥⠤⠶⠶⠾⠿⠤⠤⠍⠀⠐⠒⢒⣒⣒⡯⠭⠍⠉⠛⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢾⣿⣿⣿⣦⣄⣀⣀⣀⡀⠀⠀⠀⠀⠠⠤⠶⡆⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⢈⠉⢉⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣭⣭⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠶⢶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⣯⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋
⣀⣀⣀⣀⣀⣀⣀⣀⣰⡿⠟⠉⠙⢟⣿⣿⣿⣿⣿⣿⣿⡟⠀⠐⠒⠒⢓⣚⣛⣻⣿⣿⠯⣭⣭⣭⣭⣍⣻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠿⡿⠿⣿⣿⣿⣿⣿⢁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠐⠁⢛⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣷⣾⡝⡿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠈⠉⠛⠻⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⣿⣿⣿⣿⡎⠠⠁⠀⠀⠀⠂⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣯⡛⢷⣤⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣄⡀⠀⠐⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣪⣙⡻⣦⣤⡀⢰⣿⣿⣿⣿⣿⣿⣏⠀⠀⠉⠈⠙⢿⣿⣿⣿⣿⣧⢀⣤⣠⣤⣤⣤
⠀⠀⡀⠠⡀⠀⠐⢄⠀⢄⠂⠀⠀⠹⠛⠋⠁⠀⠀⠀⠁⠀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣶⣭⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣻⡿⠿⣿⣿⣿
⠀⠓⠊⠑⢌⠂⠀⠠⠙⠀⠁⠀⠀⠀⢠⡀⠀⠀⠤⠀⢶⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠈⢿⣿⣿⣍⢸⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣀⠀⠙⣿⡿
⠀⡀⣀⡐⠀⠁⠄⠀⠈⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠤⠠⠀⠀⠂⠌⠂⢹⠄⠀⠿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⢿⣇
⠁⠀⠁⢀⠠⠀⠀⡁⠀⡰⠀⠂⠀⣺⠅⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠀⠁⠀⠿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣟⢼⣿⣿⣿⣿⣿⣿⣿⡿⠖⠀⠀⢸⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⢹⠀⠀⠀⣀⡀⠀⠀⣷⣤⣤⣬⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣜⠸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣤⣤⣤⣤⣤⣴⣶⣶⣷⣶⣶⣿⣿⣿⣀⣀⣴⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢈⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠄⢸⣿⠿⠟⠛⠛⠋⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢸
⠿⠿⠿⠛⠛⠛⠛⣋⠉⠉⠉⠁⠀⠀⣿⣿⣿⡀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠨⡿⢿⡇⠀⠀⠙⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⢻⣿⣿⣿⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣿⡇⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⡆⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡃⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀
⠘⡅⢿⡇⢻⣿⠸⠈⣿⣿⡿⠋⣰⡇⣨⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣟⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⡀⠋⠀⠀⠙⠋⣠⣾⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣷⢩⣿⣿⣿⣿⢷⢢⣾⣃⡍⠨⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣿⣇⠀⠀⠀⠀⣴⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣷⣺⣬⣿⠻⢿⣻⣷⡀⣋⢿⣿⢤⣤⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⢿⣿⠀⠀⠀⢠⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⠛⢣⠽⣯⣿⣷⡿⠙⢿⣼⣇⣿⣿⢘⣳⡷⢟⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿
⣷⡄⠀⢸⣿⡆⠀⠀⢨⣿⣿⡏⢸⣿⣿⣿⣿⣿⣯⣗⣲⣾⣾⣿⣿⣿⣿⣧⢾⣿⣿⣿⣷⢸⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠿⣿⣻⣿⣿⣿⠿⠿⢿⠛⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠈⣿⢿⣿
⣿⣧⠀⠀⢿⠀⠀⠀⢸⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⡍⣇⣷⡿⡿⠿⠟⢿⠀⣾⣯⣿⣿⡇⠫⣼⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⠟⠈⠉⠘⣓⡁⠝⢀⣿⢻⣿⣇⠀⠉⣶⠆⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠸⡿
⠀⠀⠂⠀⠈⠀⠀⠀⢸⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣻⣿⣿⣞⡀⠂⠀⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⣚⣷⣦⣵⣦⣿⣯⡄⡠⢣⣮⢹⣿⣾⣤⣶⡄⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷
⠀⠀⣷⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⢿⣿⣿⣿⠿⠿⡟⠋⠋⠉⠩⠟⡃⣽⡀⠀⢀⡽⠿⡿⠿⠘⠿⣿⠿⣿⢿⣿⣿⡿⠿⡿⠾⡿⢿⡻⠊⠟⢉⡍⠀⠸⢏⡿⡗⠞⠈⠩⡇⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇
⣿⣆⣏⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣿⡿⣿⡇⠀⢸⣿⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣾⣷⣶⠗⠐⠂⠈⠀⠀⠂⢨⠉⣦⢀⢠⣴⣇⢹⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻
⣹⣿⣿⡀⠀⠀⠀⠀⠀⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠚⠛⠛⠛⠛⠃⠛⠃⠐⠚⠉⠉⠉⠃⠈⠓⠛⠒⠒⠀⠚⢛⡃⣟⣛⣿⣓⠛⠂⠀⠀⠀⠀⠀⠀⠁⠈⠙⢹⠇⠉⠈⠀⣿⣧⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⣼⣯⣾⡅⠀⠀⠀⠀⠀⣿⡇⠙⠉⠛⠿⣿⣟⣫⢰⡇⠀⠀⠀⡔⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⢄⠁⠘⠛⠛⠛⢿⡤⠀⠀⠀⢤⣤⣤⠿⠽⠿⠞⠖⠒⢂⠀⣿⣿⣯⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠁⠀⠀⢀⣀⡩⢽⣟⣺⡟⠀⠀⠀⢱⣧⣀⣄⠐⠀⠀⠀⢀⣀⠀⠐⠂⠶⢤⡀⣤⣤⣼⣧⢰⡯⠿⠿⢿⣟⠁⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⣾⣿⣿⣿⣿⣷⣤⣤⣴⣤⣤⡄⠀⠈⠀
⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣷⣿⣽⠃⠁⠀⠀⠈⠟⣯⠥⠄⠀⠈⠿⠿⠿⠀⠘⠒⠀⠀⠙⠃⠂⠆⠐⠸⣣⠤⡤⠭⠿⠇⠤⠈⠉⠀⠒⠠⠤⢔⣒⣒⠛⠫⠭⠭⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⡴⢾⣿⣿⣧⣄⣐⣀⡀⠀⠀⠀⠀⠀⠤⢤⠤⣤⡄⠀⠀⠈⠀⠀⠤⠀⠈⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡟⠶
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⠀⠀⠀⣪⣿⣿⣿⣿⣿⣿⣷⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣴⣶⣦⠀⠀⡀⠀⠀⠈⠉⢉⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣮⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⢻⣿⣿⡿⠿⢿⣿⣿⡿⡧⠤⠤⠤⠤⠷⢞⣛⣛⣛⣛⣛⣛⣿⣿⢛⢙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠛⠿⡿⣿⣿⣿⣿⣛⣿⠁⠹
⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠟⠉⠀⢀⣠⣤⣤⣤⣮⠀⠀⠀⠀⠅⠩⢛⣿⣿⣿⣾⣿⣿⣿⣿⠿⣿⣶⣟⢻⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠈⠉⠛⠻⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣝⠷⣦⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣷⠀⣝⠻⢷⣤⣀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠙⠛⣿⣿⣿⣿⣿⠂⢀⣀⣠⣤⣤⣤
⠁⠀⠁⢄⠀⠈⠠⠀⠀⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⠇⠀⠀⠀⠀⢀⠀⠀⠀⠑⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣮⣙⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⢛⣻⡿⢿⣿⣿⣿
⠈⠢⠐⠂⠑⠀⠐⢀⠂⠀⠂⠀⠀⠀⢸⣿⣿⣿⣿⠈⣿⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⣿⣿⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣩⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠁⠀⢻⣿⣿
⠀⠀⠀⠀⡀⠂⡀⠀⠀⠄⠀⠀⠀⠀⠸⣿⣿⣿⡇⢠⣿⣿⠀⠀⠀⡀⠀⠀⢀⠢⠑⡄⡣⠀⠈⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⣿⡄
⠀⠁⠁⠁⠀⠀⠀⠀⢀⠠⡁⠄⠀⠀⠀⣿⣿⣿⡇⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢯⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣇⠀⢸⣿⣀⣀⣐⣢⣥⣬⣤⣤⣤⣶⣶⣶⣶⣶⣶⠙⢸⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣀⣀⣠⣤⣤⣤⣤⣤⣦⣴⣶⣶⣶⣿⣿⣿⠿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⢸⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇⠈⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠈⠀⢿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢶
⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⢹⣿⣿⠃⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢿⣿⣿⣿⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣆⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣧⡀⠀
⠘⡅⢿⡇⢻⣿⠸⠈⣿⣿⡿⠋⣰⡇⣨⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣟⣿⣿⣿⣾⣿⠛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⡀⠋⠀⠀⠙⠋⣠⣾⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣷⢩⣿⣿⣿⣿⣷⢲⣾⣃⡉⠨⢿⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣿⣇⠀⠀⠀⠀⣴⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣷⣺⣬⣿⠻⢿⣻⣷⡀⢛⢿⣿⢤⣤⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⢿⣿⠀⠀⠀⢠⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⠛⢣⠽⣯⣽⣷⡿⠙⢿⣾⣇⣿⣽⢘⣳⠗⠟⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿
⣷⡄⠀⢸⣿⡄⠀⠀⢨⣿⣿⡏⢸⣿⣿⣿⣿⣿⣯⣗⣲⣾⣾⣿⣿⣿⣿⣧⢾⣿⣿⣿⣧⢸⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣻⣿⣿⡝⠿⢿⣻⣿⣿⣿⠿⠿⣿⠛⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠈⣿⢿⣿
⣿⣧⠀⠀⢿⠀⠀⠀⢸⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⡍⣇⣷⡿⡿⠿⠟⠿⠀⣾⣯⣿⣿⡇⠫⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠈⠉⠙⣛⡀⠽⠀⣿⢹⣿⣇⠀⠉⣶⠆⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⡿
⠤⠀⠂⠀⠈⠀⠀⠀⢸⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣻⣿⣿⣞⡀⠂⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢿⡿⣵⣚⣷⣦⣵⣦⣿⣯⡄⡠⢃⣮⢹⣿⣼⣤⣶⡄⣿⣼⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡷
⠀⠀⣷⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⢿⣿⣿⣿⠿⠿⡟⠋⠋⠉⠩⠟⡃⣽⡀⠀⢀⡽⠿⡿⠿⠘⠿⣿⠿⣿⢿⣿⣿⡿⠿⡿⠾⡿⢿⡻⠊⠟⢉⡍⠀⠸⠏⡿⡗⠞⠈⠩⡃⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣽⡆⣏⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣿⡿⣿⡇⠀⢸⣿⣿⣿⡷⢸⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣾⣷⡶⠗⠐⠂⠈⠀⠀⠂⢨⠉⣦⢀⢠⣼⣇⢹⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻
⣹⣿⣿⡀⠀⠀⠀⠀⠀⣷⡶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠚⠛⠛⠛⠛⠓⠚⠃⠐⠚⠉⠉⠉⠃⠈⠓⠛⠒⠒⠂⠚⢛⡃⣟⣛⣿⣓⠛⠂⠀⠀⠀⠀⠀⠀⠁⠈⠙⢹⠇⠉⠈⠀⣿⣧⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⣼⣧⣾⡅⠀⠀⠀⠀⠀⣿⡇⠙⠉⠛⠿⣿⣟⣫⢰⡇⠀⠀⠀⡔⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⢄⠃⠘⠛⠛⠛⣿⡤⠀⠀⠀⢤⣤⣤⠿⠽⠿⠞⠖⠒⢂⠀⣿⣿⣯⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢿⡿⣿⡇⠀⠀⠀⠀⠀⣀⠁⠀⠀⢀⣀⡩⢽⣟⣺⡟⠀⠀⠀⢱⣇⣀⣄⠐⠀⠀⠀⢀⣀⠀⠐⠂⠴⢤⡀⣤⣤⣼⣧⢰⡿⠿⠿⢿⣟⠁⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⣾⣿⣿⣿⣿⣷⣤⣤⣴⣦⣤⡄⠀⠀⠀
⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣷⣿⣽⠃⠁⠀⠀⠈⢟⣯⠥⠄⠀⠈⠿⠿⠿⠀⠘⠒⠀⠀⠉⠃⠂⠆⠐⠸⣣⠤⡤⠭⠿⡇⠤⠈⠉⠀⠒⠠⠤⢔⣒⣒⠛⠫⠭⠭⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⡴⢾⣿⣷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠤⠤⠤⣤⡄⠀⠀⠈⠀⠀⠤⠀⠈⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠶
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣴⣶⣦⠀⠀⡀⠀⠀⠈⠉⢉⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠀⠀⠀⠸⣟⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣮⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⢀⣻⣿⣿⣿⠿⢿⣿⣿⡿⡧⠤⠤⠤⠤⠷⢞⣛⣛⣛⣛⣛⣛⣿⣿⢛⢙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠛⠻⠿⣿⣿⣿⣿⣛⢿⠁⠛
⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⢀⣠⣤⣤⣤⣾⠀⠀⠀⠀⠃⠩⢛⣿⣿⣿⣾⣿⣿⣿⣿⠿⣿⣶⣝⢻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠈⠉⠛⠛⠿⢿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡗⠀⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣝⠷⣦⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⣍⠻⢶⣤⣀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⠻⣿⣿⣿⣿⣿⡀⠀⣀⣠⣤⣤⣤
⠁⠀⠁⢄⠀⠈⠀⠀⠀⡁⠀⠐⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⠇⠀⠀⠀⠀⢀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣷⣮⣝⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣻⠙⠺⠿⢿⣿⣿⣿
⠈⠀⠐⠂⠑⠄⠐⢄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⣿⣿⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡃⠀⢹⣿⢿
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠄⠀⠀⠀⠀⠐⣿⣿⣿⡇⢀⣿⣿⠀⠀⠀⡀⠄⠀⢀⠢⠑⡀⡣⠀⠈⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⣿⡄
⠀⠁⠁⠁⠀⠀⠀⠀⢀⠠⡁⠄⠀⠀⠀⣿⣿⣿⡇⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣇⠀⢾⣿⣀⣀⣀⣢⣥⣬⣤⣤⣤⣶⣾⣶⣶⣶⣶⠛⢸⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣀⣀⣀⣤⣤⣤⣤⣤⣦⣴⣶⣶⣶⣿⣿⣿⠿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⢸⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠇⠀⣿⡿⠿⠿⠻⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠈⠀⢿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢶
⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⢹⣿⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢿⣿⣿⣿⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣧⡀⠀
⢸⠀⣿⡄⢿⣧⢸⠸⣿⣿⡿⠋⣰⡇⣬⣾⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⡷⠈⠋⠈⠀⠛⠋⣠⣾⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣮⢸⣿⣿⣿⣿⡧⢒⣼⡃⠕⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⡇⠀⠀⠀⠀⣼⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣨⣭⣛⢻⢿⣻⣦⠈⡏⠿⡷⢠⣼⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⣿⣷⠀⠀⠀⢠⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⠛⢣⡽⣾⣿⣷⡾⠙⣿⣾⣋⣿⡏⣹⣷⡷⢏⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿
⣶⡀⠀⢹⣿⠀⠀⠀⢨⣿⣿⡏⣸⣿⣿⣿⣿⣿⣯⣗⣶⣲⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣧⢹⡷⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣳⣿⣿⡛⠟⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⠿⠻⠉⠀⠀⠀⠀⠀⠙⣿⣿⣿
⣿⡇⠀⠈⢿⠀⠀⠀⢸⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⠉⣷⣷⣿⡾⠿⠻⡿⢈⣿⣿⣿⣿⡎⠯⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠈⠉⠛⣋⡠⠙⢩⡿⢹⣿⣆⠀⢩⡦⠢⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸⡯
⠀⢀⠀⠀⠈⠀⠀⠀⢸⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣷⣞⠠⠀⠘⢻⣿⣿⣿⡷⠀⣿⣿⣿⣿⣿⣿⣿⢻⡯⣵⣺⣧⣤⣥⣦⣿⣧⣄⠠⢣⣾⣹⡷⣦⣤⣦⡄⣿⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢦⡇
⡀⠀⣖⠀⠀⠀⠀⠀⠀⣠⣿⡿⣿⠿⣿⣿⠿⣿⠿⠟⠝⠋⠉⠹⢟⣃⡜⠀⠀⠂⣽⠿⢿⠿⢸⡿⢿⡿⢿⣿⣿⣿⢺⣿⢿⡿⣿⢿⡻⠘⣟⠉⢭⠀⢹⢧⣿⡅⠞⠉⢙⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⣷⡄⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⢿⣿⣟⡇⠀⣺⣿⣶⣾⡇⢸⣷⣿⣷⣾⣿⣿⣿⡚⣶⣾⣶⣾⣶⠇⠐⠀⠀⢘⠀⠀⣈⢉⡤⣀⣰⣶⣅⢻⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿
⣿⣷⣿⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠚⠛⠃⠃⠐⠚⠛⠛⠛⠃⠘⠃⠒⠃⠐⠛⠛⢛⡃⣟⣛⣞⡛⠛⠂⠀⠀⠀⠀⠀⠀⠁⠘⠙⢹⡆⠉⠈⠀⣿⣷⡿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀
⣼⣥⣿⡀⠀⠀⠀⠀⠈⣿⡇⠋⠉⠛⠻⣿⣟⣉⢶⡇⠀⠀⠀⡰⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣌⠁⠛⠛⠛⠛⣷⡤⠀⠀⣀⣠⣤⣤⡿⠴⠾⠾⠶⠒⢀⠀⣿⣿⣧⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⡇⠀⠀⠀⠀⠀⡉⠁⣀⣤⣤⣬⣽⣽⣏⣾⡟⠀⠀⠀⢳⣇⣀⡀⠂⠀⠀⠀⠀⠀⠀⠐⠒⠶⢄⡀⣤⣤⣼⡇⣰⠯⠿⠷⣿⣗⠀⠀⢉⠏⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡄⠀⠈⠀
⠘⠋⠉⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠘⢿⡯⠥⠄⠀⠈⠿⠿⠿⠀⠐⠒⠀⠈⠙⠃⠒⠂⠐⢘⣁⠤⣤⣬⣿⠇⢄⠈⡋⠀⠒⠤⠤⠴⣒⣒⣛⠻⠭⠭⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡄⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣛⡛⠦
⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠈⣺⣿⣿⣿⣿⣿⣿⣤⣥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣤⣶⣆⠀⠀⡀⠀⠀⠉⠉⢉⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢿⣿⣿⠿⠿⠿⠻⠿⠻⡸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣙
⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⢸⠟⠀⣀⣤⣶⣶⣶⣾⣷⡀⠤⠤⠤⠧⠿⠿⣿⣿⣛⣛⣛⣛⣛⢛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⠛⠻⡿⣿⣿⣿⣿⣻⡃⠈⠙
⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⢀⠀⡍⠉⢻⣿⣿⣿⣾⣿⣿⣿⣿⢼⣿⣼⣝⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢁⣿⣿⡇⠐⠀⠀⠀⠠⠀⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⣭⣛⠷⣤⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣶⠈⢝⠻⣦⣤⡀⠀⢰⣿⣿⣿⣿⣿⣻⠁⠀⠘⠁⠙⠻⢿⣿⣿⢝⣽⡀⢀⣀⣀⣤⣄⣤
⠁⠄⠀⠈⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⣿⣿⣿⣿⠁⢈⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣮⣶⣭⡛⢷⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⡿⠅⠴⠻⢿⣿⣿⣿
⠀⠤⠕⠀⠐⠀⠠⢀⠢⠁⠀⠀⠀⠀⢿⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⣿⣿⣟⡃⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⢫⣿⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢻⣿⢿
⠀⠀⡀⠀⡀⢂⠀⠀⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⡀⠀⠀⡀⢄⠀⡀⠀⠀⡀⡧⠀⠙⣿⡟⡇⣿⣿⣿⣿⣿⣿⣿⣿⡦⣿⣿⣿⣿⣿⣿⣾⣿⡟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⣿⡄
⠀⠁⠁⠀⠀⠂⠀⠀⠀⠄⠁⠄⠀⠀⠂⣿⣿⣿⣿⢸⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠨⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣇⣀⣐⣀⣀⣤⣤⣤⣤⣤⣾⣶⣶⣶⣶⠃⢹⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣀⣀⣀⣀⣀⣤⣤⣤⣦⣴⣴⣶⣶⣶⣿⣿⣿⣿⣿⡇⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡇⠀⢻⡿⠿⠿⠿⠻⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠈⠈⢿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣦
⣿⣿⡿⠿⠿⠿⠿⠛⠚⠛⠛⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣿⣿⣿⣷⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷⠀⠀⠀
⠀⠛⠱⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⡀⠀
⢣⠸⣿⠸⣿⡇⡇⢿⣿⣿⠟⢁⣴⢀⣣⣿⣿⣿⣿⣿⣿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣷⣿⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⣿⡆⠙⠃⠀⠘⠿⠋⣠⣾⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⣹⣿⣿⣿⣿⡵⣹⣞⠩⠒⠽⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢶⣿⡀⠀⠀⠀⢠⣾⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⡅⣧⣿⡛⢿⡿⣷⣄⠘⡛⢿⡧⣠⣼⣿⣿⢫⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⡇⠀⠀⠀⣸⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⡿⢿⣈⢷⣿⣿⣶⡏⠛⣯⣿⣘⣿⢏⣻⣾⠺⢃⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⣿⣧⠀⠀⠀⣹⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⡧⣤⣶⣾⣿⣿⣿⣾⡄⣿⣿⣿⣿⡇⢿⡇⢀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⡻⠿⣟⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠈⢻⣿⣿⡿
⣿⡄⠀⠸⡇⠀⠀⠀⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⢹⣸⣿⣿⡼⢿⢿⡇⢩⣿⣿⣿⣿⠸⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠋⠉⠋⢛⣊⠨⠃⢩⡿⢽⣟⣀⠀⢡⡶⢰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠇
⠀⠀⠀⠀⠁⠀⠀⠀⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣶⡓⢀⠀⠘⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡯⣶⣺⣦⣤⣴⣼⣿⣥⡀⠜⣣⡟⣽⣧⣦⣤⣦⢸⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⠆
⠀⢸⡆⠀⠀⠀⠀⠀⠀⡼⢿⡿⠿⣿⣿⣿⣿⠿⢿⡿⠛⠋⠉⢛⡛⠉⠆⠀⠀⣪⣿⣿⡿⠇⠸⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠷⢛⠏⢩⢩⠀⢿⢳⣿⡕⠋⠉⢹⠸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀
⣦⢸⡃⠀⠀⠀⠀⠀⢠⣿⣾⣿⣶⣿⣿⣿⣿⣶⣾⣷⣶⣲⣾⢐⣿⣷⣶⡀⠀⣾⣶⣾⣶⡆⢰⣾⣿⣿⣷⣶⣷⣿⢰⣾⣷⣾⣶⠾⠃⠐⢀⠀⢐⠀⠀⣈⢐⡄⡀⣶⣾⡀⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛
⣿⣟⣇⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓⠚⠛⠘⠛⠛⠛⠃⠲⠛⠛⠘⠁⠀⠀⠐⠛⠛⠓⠛⠛⢛⠸⣛⣻⣟⡛⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠋⡿⠈⠉⠁⢸⣿⣸⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰
⣿⣇⣿⠀⠀⠀⠀⠀⢸⣿⠀⠛⠻⣿⣿⡿⢟⡁⣾⠀⠀⠀⢠⢀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡘⠀⠛⠛⠻⠛⣧⠄⠀⢀⣀⣨⣤⣤⡷⠶⠶⠷⠶⠂⠀⢸⣿⣿⣅⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠈⣁⣤⣶⣶⣿⣾⣿⣿⣇⣿⠇⠀⠀⠀⡾⣄⣀⡀⠂⠀⢀⠀⡀⠀⠀⠖⠒⡶⣀⢀⣤⣤⣿⡄⣶⠯⠿⠿⣿⡒⠀⠀⢩⠃⠀⠀⠀⠀⠀⠀⠀⠲⣿⣦⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⠀⠀⠀⠀
⠙⠚⠉⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠰⢿⡭⠥⠄⠀⠸⠿⠿⡏⠀⠐⠂⠀⠈⠛⠉⠛⡂⠂⢛⣀⢠⣬⣭⣿⠀⣀⣈⡃⠐⠢⠤⠤⠴⣒⣒⡛⠻⠭⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠙⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⡄⠀⠀⠀⠴⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠁⠀⠀⠠⠄⠀⠁⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⢿⣯⣟⣛⠷⠤
⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠈⠟⡿⠉⢀⣠⣤⣴⣶⣾⣿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣭⣉⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠤⠤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠉⠉⣉⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⢻⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣮⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢻
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣿⣿⡏⣝⡏⠀⠙⣿⣿⣀⣀⡀⠸⠦⠿⠿⠿⠿⣿⣟⣛⣛⣛⡛⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠛⠛⣿⣿⣿⣿⣿⣟⣛⠃⠈⠻
⠒⠒⠒⠂⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣧⣿⠃⠀⠀⣿⣿⡇⠀⠀⠀⠀⠙⣻⣿⣿⣷⣾⣿⣿⣿⣿⢻⣷⣭⣟⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠉⠙⠛⠿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣾⣷⠇⠀⠀⠀⢸⣿⣿⡐⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣮⣽⡻⢦⣄⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠹⣿⢿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡆⢨⡛⠷⣦⣄⠀⠀⣼⣿⣿⣿⣿⣟⢣⠁⠀⠉⠀⠛⢿⣿⣿⣿⡷⣀⠀⠀⣤⣤⣄⣤⣤
⠀⡀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠘⢿⣿⣿⣷⣄⠀⠀⠸⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣾⣸⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣶⣝⡻⢷⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠿⠒⠚⠙⣿⣿⣿⣿
⠠⠤⠢⠌⠦⠀⠀⠐⠄⠐⠀⠀⠀⠀⠙⣿⣿⣿⣷⡅⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⡍⢻⣿⣿⣛⠸⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠀⠀⠀⠈⠛⣀⠠⡀⠀⠀⠀⠂⠀⡄⠀⠹⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣾⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⣷⠀
⠈⠀⠁⠂⡀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣆⠇⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⢀⣀⣀⣀⣀⣠⣤⣴⣤⣤⣥⣦⣶⣶⣶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⢻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠻⠿⠿⠛⠛⠛⠛⠋⠉⠉⠉⠀⠁⠘⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦
⣿⣿⣿⠿⠿⠿⠿⠟⠺⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⡇⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢿⣿⡇⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀
⠀⠛⠑⠿⠛⠻⠓⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⠀
⡇⢸⣇⢹⣿⠀⡇⣿⣿⣿⠟⢁⣦⢘⣳⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⢘⣿⡀⠙⠀⠁⠸⠟⠁⣰⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣯⡁⣻⣿⣿⣿⣿⣭⣩⣟⠙⠆⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣉⣳⣿⡿⣿⡿⣷⡄⠹⠹⢿⡄⣄⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⡄⠀⠀⠀⣾⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⡿⠟⣌⣿⣟⣷⣶⠟⢛⣷⡏⣱⣿⠚⣿⣾⡿⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠸⣿⡇⠀⠀⠀⣻⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⢠⡄⣶⣽⣿⣿⣿⣾⢸⣿⣻⣯⣿⡌⣿⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⡟⢿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠈⠙⣿⣿⣿⣿
⣿⠀⠀⢻⡇⠀⠀⠀⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⡟⢻⣼⣿⣯⡿⡿⢿⠏⣹⣿⣻⣿⣧⠹⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠋⠙⠉⠻⣙⠚⠎⣝⠟⣿⣷⠀⠘⣨⡤⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⠀
⠀⠀⠀⠀⠁⠀⠀⠀⡟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣽⣿⣿⣶⠂⡄⠀⠛⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⡟⣿⢯⡶⣶⣤⣴⣴⣾⣿⣔⡀⡹⣠⣛⣿⣢⣤⣼⣄⢸⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀
⠀⢰⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⣿⣿⣿⠿⣿⣿⡿⠛⠛⠙⠿⠟⢠⠆⠀⠀⣺⣿⣿⣿⠆⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⡿⡏⢻⠯⣉⡁⠐⣿⣼⣿⢨⠏⠋⡻⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣀
⣤⢸⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣾⣷⣾⣿⣶⣾⣿⣧⣖⣲⣶⣶⣷⣶⣷⠀⢐⣶⣾⣷⣶⠀⣶⣷⣶⣷⣶⣷⣶⣷⢶⣷⣶⣿⡇⣿⠂⠂⠀⠀⡂⠀⠀⣛⣛⡀⢀⣢⣾⠘⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠿
⣿⣼⡇⠀⠀⠀⠀⠀⣆⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠛⠛⠛⠛⠛⠛⠀⠮⠋⠭⠥⠬⠀⠛⠿⠿⠛⠛⠋⠛⢻⢸⣛⣳⣛⠃⠒⠀⠀⠀⠀⠉⠈⠈⠓⠚⠟⣧⠘⠋⠃⣿⣇⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰
⣿⣹⡇⠀⠀⠀⠀⠀⢻⣿⠛⢟⣿⣿⣿⡿⢟⠩⣵⠀⠀⠀⢀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⡉⠸⠟⠻⠿⢿⣦⠀⠀⢀⣀⣉⣀⣴⣶⡶⠦⠧⠤⠤⠀⢻⣿⣟⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⠲⡿⠆⠀⠀⠸⣴⡀⢀⡀⠀⠀⣀⣀⣀⠀⠀⠔⢲⢎⣁⣀⣀⣠⣷⢀⣶⡶⣶⣷⣟⠒⠀⠐⢳⠉⠁⠀⠀⠀⠀⠀⠀⠴⢷⣼⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡄⠀⠀⠉⠀
⠛⠋⠉⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⢛⣛⠘⠀⠀⠀⢛⣿⡯⠤⠀⠀⠺⣿⣿⡇⠀⠒⠀⠀⠉⠚⠉⢉⡉⠄⡛⣀⣀⣰⣿⣷⣀⣀⠒⠂⠠⠤⢄⠠⠤⠴⢖⣛⣛⢛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⠃⠀⠻⢿⠋⢀⣤⣶⣾⣿⣿⣿⣧⡀⠀⠀⢀⢼⣿⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠈⠁⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⡳⠤⣄
⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠿⠿⣿⣿⣶⣄⠈⠀⣿⣿⣿⣿⣿⣿⣯⣍⡉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⢀⠀⠀⠈⠀⠀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣿⣿⣶⣶
⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⣿⡟⠉⠀⠈⠁⠀⠀⠉⠻⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡸⠬⠿⠿⠿⠿⠿⠿⣿⣛⣛⡛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠻⢿⣿⣿⣿⣿⣿⣻⡿⠀⠻⠿
⠒⠒⠒⠒⠒⠂⠀⠈⠁⠀⢸⠁⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠻⣿⣯⣿⣿⣿⣿⣿⣿⡗⣿⣮⣽⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠈⠉⠙⠛⠻⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣷⣭⣛⠷⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⠈⢝⠳⣶⣄⡀⠀⢀⣿⣿⣿⣿⣿⡿⡄⠀⠈⠃⠘⠛⢿⣿⣿⣿⣶⡀⢀⣀⣀⣀⣀⣀⣤
⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣇⣿⣷⣷⣭⣛⢷⣾⣿⣿⡿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠿⠿⠷⣾⠞⣿⣿⣿⣿⣿
⠠⠐⠠⠐⠄⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠙⣿⣿⣿⣛⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡟⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡿⠀⠀⢻⣿⢿⣿
⠀⠀⠀⠀⠠⡀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢀⠀⠀⠀⡀⢀⠀⠀⠄⠐⠀⢸⠀⠈⢻⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⣿⡄⠙
⠀⠀⠐⠈⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⠂⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠈⠀⠀⠀⢽⣼⢸⣿⣿⣿⣿⣿⣿⣿⡧⣹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣦⣦⡼⢸⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣀⣀⣀⣀⣀⣠⣀⣄⣀⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠁⠀⠉⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣦⡘
⣿⣿⣿⠿⠿⠿⠿⠷⠟⠛⠛⠛⠛⠋⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⢿⣿⣿⣿⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠈
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢽⣿⣿⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠓⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠆⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀
⡇⢸⣷⠸⣿⡇⡇⣿⣿⣿⡿⢃⣴⢀⣫⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠈⣿⡆⠹⠃⠁⠸⠿⠋⣠⣾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡅⣻⣿⣿⣿⣿⡭⣭⡿⠙⠆⣻⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⡩⣗⣻⡿⣿⡿⣿⡄⠹⢻⢿⣆⣀⣻⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⡆⠀⠀⠀⣸⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⡿⠿⣙⣾⣛⣷⣴⡟⢟⣯⣶⢱⣿⡆⣷⣽⣽⢏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠘⣿⡇⠀⠀⠀⣻⣿⣿⠃⣾⣿⣿⣿⣿⣿⣻⠥⣄⣧⣾⣿⣿⣿⣶⣠⣿⣿⣿⣿⡉⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠈⠉⠻⣿⣿⣿⣿
⣿⡀⠀⢻⡇⠀⠀⠀⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⡟⢛⣽⣿⣯⣿⣿⢿⡇⢩⣟⣻⣿⣷⠹⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠞⠛⠫⠿⠍⢑⠞⢹⡿⣿⡯⠉⠙⢣⣭⢸⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⣾⠃
⠈⠀⠀⠀⠃⠀⠀⠀⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡹⣿⣾⣤⠆⣠⠁⢸⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⡤⢶⣤⣐⣤⣨⣿⣂⠀⡹⢡⡻⣿⣇⣆⣨⣄⢸⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⠀
⠀⢰⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⢉⡆⠀⠀⣛⣿⣿⣿⡇⢾⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⡯⢻⠞⢛⢂⠀⣿⢳⣟⢫⠟⠛⡻⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀
⣄⢸⠀⠀⠀⠀⠀⠀⢸⣷⣾⣷⣶⣾⣷⣾⣿⣿⡿⣷⣶⣰⣶⣴⣿⣶⣶⠀⠀⣾⣶⣾⣿⠄⣶⣾⣷⣶⣷⣾⣷⣾⢠⣼⣿⠿⣿⣷⠆⠄⠀⠁⠪⠀⠀⠛⠻⡁⠀⣀⣜⠸⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠿
⣿⡾⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠿⠟⠟⠻⠻⠿⠿⠯⠀⠤⠿⠭⠽⠿⠀⠺⠿⠿⠿⠯⠿⠿⠿⢸⠦⢿⠃⠛⠃⠀⠀⠀⠀⠉⠀⠐⠥⠾⠗⣷⠙⠋⠃⣿⣧⣾⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰
⣿⣹⡇⠀⠀⠀⠀⠀⢸⣿⠛⢟⣿⣿⣿⣿⠟⡋⣽⠀⠀⠀⢀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠹⠘⠿⠿⠿⠷⣤⡀⠀⠀⢀⣀⣀⣰⣦⣤⣦⣯⠤⠤⠀⣿⣿⣟⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡣⣿⠆⠀⠀⠸⣼⠀⢀⠀⠄⠀⠀⣀⣀⡀⠀⠄⢠⣄⡉⣁⣀⣀⣾⡀⣶⣲⣶⣾⣿⠖⠀⠀⢲⠉⠉⠁⠀⠀⠀⠀⠀⢤⣷⣼⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⡀⠀⠀⠈⠀
⠛⠛⠋⠀⠀⢠⣾⠿⣿⣿⣿⡿⠟⠋⠁⣀⣤⣤⣽⠐⠀⠀⠀⢛⣿⣟⣁⠀⠀⢰⣾⣿⡇⠀⠦⠄⠀⠙⠺⠩⢩⡉⠅⡿⣀⣀⣐⣻⣷⢀⡀⠒⠂⠠⢄⣀⣀⡤⠤⠴⠾⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡏⠀⠉⠟⠋⠀⣠⣶⣾⣿⣿⣿⣿⣿⣶⣤⡀⠈⣸⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⠁⠊⠁⢀⡀⠀⠂⠀⠀⠀⠀⠀⠖⠛⠋⠁⠁⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⣄⣀
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⣾⣿⠟⠻⣿⠛⠛⠛⠿⠿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣯⣝⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⣀⣀⣤⣤⠀⠀⠀⠀⠀⠐⠒⠒⣢⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣽⣿⣷⣶⣤
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠟⢿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠀⠀⢀⣴⣿⣿⣿⣿⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢺⠁⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠿⠿⠿⠿⠿⢿⢿⡿⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠻⣿⣿⣿⣿⣿⡿⢿⡿⠑⠿⠿
⠒⠒⠒⠒⠒⠂⠀⠈⠁⠀⠀⠀⠚⠛⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣿⣿⣿⣿⡗⣷⣏⣟⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠉⠙⠛⠻⢿⣷⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣷⣝⣻⢦⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⠈⠛⠷⣦⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⠘⠁⠛⢿⣿⣿⣿⣷⣔⠀⠀⡀⣀⣀⣀⣀⣀
⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣆⣾⣶⣾⣝⡻⣶⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣖⣾⠿⣿⣿⣿⣿⣿
⠠⠴⠤⠐⠄⠀⠀⠢⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣿⣿⣿⢟⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠈⢿⡿⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠂⠀⠀⠀⢀⠀⠀⠄⠀⠀⢸⠀⠈⢿⣿⢹⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣷⡈⢻
⠒⠈⠀⠈⠠⠀⠀⠀⢀⡀⢀⠀⠀⠠⠀⠄⠐⢈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠘⠈⠀⠀⣻⣸⢸⣿⣿⣿⣿⣿⣿⣿⡧⢻⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀
⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣬⡼⢘⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⢀⣀⣀⣀⣀⣀⣄⣀⣬⣤⣤⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠐⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁⠀⠉⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⠹
⣿⣿⣿⡿⠿⠿⠿⠷⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠹⣧
⠁⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⠸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠙
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⣿⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⠀⠀⠀
⠹⡁⣿⡇⢿⣿⢰⠠⣿⣿⣿⠟⢡⡆⢘⣱⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣾⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⢸⣷⠈⠿⠈⠀⠿⠟⢁⣴⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣏⢘⣿⣿⣿⣿⣏⡽⣿⠏⡻⢐⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠨⣿⡇⠀⠀⠀⠀⣠⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⢹⣸⡿⢿⣿⢿⣇⠈⠟⣻⣷⣀⣨⣿⣿⡯⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠀⠀⣿⣿⠀⠀⠀⢀⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⠿⢏⣲⣟⣿⣦⣾⠻⢿⣵⡎⣾⣿⠸⣯⣯⡿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠀⢸⣿⠀⠀⠀⠈⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⡿⢠⣼⣴⣿⣿⣿⣷⣆⣸⣿⣿⣿⣇⢹⣿⠀⣸⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢷⣾⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠻⣿⣿⣿⣿
⣿⣇⠀⠈⣿⠁⠀⠀⢸⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⡛⡻⣯⣿⣿⡿⡿⣿⠘⣹⣟⣿⣿⡎⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠉⠛⠻⠯⠋⡳⠋⣿⢿⣿⡏⠉⠛⣍⡄⣾⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⣿⡏
⡉⠉⠀⠀⠘⠀⠀⠀⢸⠟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⢿⣷⣧⡴⠀⡌⠀⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡤⣦⣀⣂⣄⣽⣗⡀⢈⠏⣼⢿⣿⣤⣀⣥⡀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣯⠀
⠀⠀⣦⠀⠀⠀⠀⠀⠈⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠛⠛⡿⠟⣳⠀⠀⠨⣻⣿⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⠝⡷⠛⡛⡀⢸⡟⣾⡛⡽⠛⢛⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀
⣴⡄⡏⠀⠀⠀⠀⠀⠀⣼⣾⣷⣶⣿⣿⡿⣿⣿⣶⣶⣶⣆⣶⣦⣶⣶⣶⡇⠀⢸⣿⣾⣶⡶⢰⣾⣷⣾⣿⣼⣯⣽⡟⠗⣿⣿⣿⣭⡶⠠⠅⠈⠹⠇⠀⠘⠛⠅⠀⢀⣬⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠸
⢻⣿⣿⠀⠀⠀⠀⠀⠀⣬⡿⣿⣧⣼⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠽⠯⠭⠇⠠⠼⠿⠿⠿⠇⠸⠿⠯⠿⠿⠿⠿⠤⠆⡷⠿⣟⠛⠛⠀⠀⠠⠀⠈⠁⠀⠪⠴⠿⢺⡎⠛⠛⣿⣇⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰
⣹⣯⣽⡃⠀⠀⠀⢀⣀⣿⣷⣮⣿⣿⣿⣟⡿⢛⢨⡅⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠻⠿⠿⠿⣶⣀⠀⠀⠀⢀⣂⣀⣶⣤⣴⣼⣥⡤⠀⢿⣿⣟⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⢓⡿⢼⡿⠀⠀⠀⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⡈⠉⣉⣁⣸⣇⢰⣖⣶⣶⣿⡧⠄⠀⠙⡟⠉⠉⠁⠀⠀⠀⠀⠠⣼⣾⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⡀⠀⠀⠐⠁
⠘⠏⠛⠁⣸⡏⠉⣿⢿⣿⣿⠟⠁⠀⣀⣶⣿⣿⣿⣇⣢⣤⠂⠈⠙⠟⠋⡀⠀⠐⣶⣶⣶⠀⠠⠤⠀⠈⠳⠏⠽⠍⠡⠸⠆⣀⣀⣚⣻⡆⠀⠐⠒⠀⠤⣀⣀⣠⠤⠤⠶⠾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⠛⠁⠀⠀⣠⣾⣿⣿⣿⠿⠻⠛⠉⠀⠀⠀⠀⡀⠀⢰⣦⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠉⠐⠉⠉⣉⠀⠘⠀⠀⠀⠀⠀⠰⠒⠛⠉⠉⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⢶⣄⣀
⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢀⣼⠛⠋⠉⠙⠁⠀⠀⠀⠀⢀⡀⠀⠐⢹⣿⣿⣿⣿⣿⣷⣖⣂⠐⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠒⠒⣒⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣿⣿⣷⣶⣬
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠀⠀⠁⠀⢀⣴⣾⣿⣿⣷⣯⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣯⣿⠿⠿⠿⠿⠿⠿⠿⡿⠟⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠻⠿⣿⣿⣿⣿⣿⣿⢿⡿⠳⠾⢿
⠒⠒⠒⠒⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣽⣿⣿⣿⣿⢲⣾⣝⡳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠈⠉⠙⠛⠿⢿⣷⣶⣶⣶
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣦⣍⣻⢶⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⡌⢙⠷⣶⣄⡀⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⠙⠋⠻⢿⣿⣿⣿⣷⣔⠀⢀⢀⣀⣀⣀⣀⣀
⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣇⣾⣧⣲⣭⡻⢷⣾⣿⣿⣿⣿⠛⠈⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⡾⢾⢻⣿⣿⣿⣿⣿
⠂⡀⠢⠐⠄⠀⠀⠑⠌⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡎⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡀⠀⡀⠀⠠⡐⠀⠀⡇⠈⠻⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⢸⣿⡈⢻
⠀⠀⠑⠀⠁⠀⠀⠀⠀⡀⠀⡀⠀⠀⠄⠠⠐⠂⠁⠀⠒⠀⠂⠀⠀⠀⠀⠀⠡⠀⠀⠀⠃⠁⠀⢹⡟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣬⡅⠇⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⣀⣀⣀⣀⣀⣠⣀⣠⣥⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠆⢿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠁⠉⢹⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⠹
⣿⣿⣿⣿⠿⠿⠿⠿⠿⠻⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠹⣧
⠉⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⡇⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀⠀⠀⠀⠙
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⡇⢻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀
⠀⠛⠱⠿⠛⠻⠓⠛⠛⠛⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀
⠘⡇⢹⣧⢸⣿⠀⡆⣿⣿⣿⡿⠋⣠⠸⢏⣾⣿⣿⣿⣿⣿⣿⠾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠃⠘⣿⡄⢻⠇⠃⢹⣿⠋⢀⣾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣛⢋⡿⠻⡅⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⣴⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⠛⢧⣿⡿⣿⣿⣟⡈⠻⢻⣶⡄⡈⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢇⠀⠀⢹⣿⡄⠀⠀⠀⣸⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣧⣥⡿⡿⣇⡜⢲⣾⡕⣯⣭⣽⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠀⠸⣿⡇⠀⠀⠀⠿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⢇⣀⣭⣹⣿⣿⣿⣵⣸⣿⢷⣟⣿⡳⣿⡉⢀⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣾⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⡿⠛⠉⠀⠀⠈⠉⢻⣿⣿⣿⣿
⣿⣿⠀⠀⢿⡇⠀⠀⠀⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⡾⠻⣻⣿⣟⣿⣿⣿⡎⢛⣿⢿⣿⣧⢻⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠯⠻⠻⠿⠻⡔⠞⣻⡟⣿⣯⠉⠙⣩⣡⣸⣿⠉⠈⠀⠀⠀⠀⠀⠀⠀⠰⠃⣻⣿⢎
⠋⠉⠁⠀⠈⠃⠀⠀⠀⣿⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣹⣿⣿⣥⠄⠌⠀⠸⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⡿⣿⣟⡥⣦⣀⣐⣠⣸⣿⣂⠀⡹⣠⡿⣿⣥⣀⣩⣀⣹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣸⡇⠀
⠈⠈⢠⡀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠻⢿⠿⢑⡄⠀⠀⢝⣿⣿⣿⡅⣾⣿⣿⣿⣿⣿⣿⡧⣿⣾⣿⣿⣿⡿⡏⢿⢟⢛⠃⠀⣿⣹⣟⢨⠟⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⢀
⠀⣄⢸⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣥⡤⢤⣤⣤⣶⣼⣷⠀⠀⣭⣿⣭⣽⠀⣿⣭⣽⣭⣽⣿⠿⡧⢿⣿⣿⣿⣭⣽⠄⠼⠀⠋⠿⠀⠁⠛⠫⡀⠀⣄⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡟
⠒⣿⣾⡄⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡟⢙⠻⡛⢛⠿⠀⣄⠿⠿⠿⠿⠀⠿⠿⠿⠿⠤⠿⠈⠿⢹⠿⢿⠿⠿⠯⠀⠀⠄⠀⠉⠀⠘⠥⠿⠗⣷⠙⢻⣿⣱⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⣗⣿⡟⠃⢀⣠⣤⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠋⣥⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠿⠿⡿⢶⣄⡀⠀⠀⠀⣐⣀⣰⣦⣤⣦⣯⡤⠤⣿⣿⡇⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢛⣿⠼⠇⣿⡆⠀⠀⢸⣡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡤⢤⡔⠍⠉⣉⣉⣷⡀⣴⣒⣶⣮⣿⠤⠀⠸⢻⠋⠉⠉⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣷⣄⣀⣀⣄⣀⣀⡀⠀⠀⠀⠈
⠋⠿⢽⣿⡏⠋⢿⣿⣿⣿⣿⠟⠁⠀⣰⣿⣿⣿⠷⣷⠐⠀⠀⠀⢿⣿⣛⣃⠀⠀⢺⣿⣿⡆⠀⠤⠌⠀⠛⠿⠹⠿⠍⠌⠷⠀⢀⣀⣛⣷⠀⠀⠲⠂⠠⢀⣀⣀⣤⠤⠴⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⣿⣿⠀⠀⠀⠙⠉⠁⠀⣠⣾⣿⣿⣿⣿⡷⠶⢶⠿⠿⠃⠈⠹⢷⣦⣤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠉⠋⠉⠉⢉⡉⠈⠉⠀⠀⠀⠀⠀⠖⠚⠋⠉⢁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣦⣀⣀
⠀⠀⠀⢸⣿⡂⠀⠀⠀⠀⢀⠐⠛⠋⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣒⠒⠀⠀⠀⠀⠈⠉⠉⠓⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠐⠒⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣿⣿⣶⣦⣭
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠂⠀⠈⠁⢠⣴⣿⣿⣿⣿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣙⣿⣿⣿⣿⣿⠿⠿⠿⠿⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣬⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠸⠾⠿
⠤⠤⠤⠤⠄⠀⠐⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠁⠈⠁⠀⠀⠀⠠⠐⢶⣶⣶⣿⣽⣿⣿⣿⣾⢰⣾⣙⡿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠉⠉⠙⠛⠿⢿⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣶⣭⣻⢷⣦⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡌⢙⠿⣶⣤⣀⠀⢸⣾⣿⣿⣿⣿⠏⠀⠀⠛⠉⠿⣿⣿⣿⣿⣴⡆⠀⡀⡀⣀⡀⣀⣀⣀
⠠⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⢴⣷⣮⣝⡻⢷⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⣿⣿⢶⣹⣿⣿⣿⣿⣿⣿
⠠⣀⡢⡀⢀⠀⠈⠀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⡿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⢻⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⡁⠈⠙⣿⡿⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢀⠀⢀⠀⠀⢈⠀⠙⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠀⠀⢸⣧⠙⢿
⠀⠠⠔⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠠⠄⠀⠀⠈⠀⠈⠀⠀⠄⠠⠀⠚⠁⠄⠈⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣭⠹⢸⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣐⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣿⡇
⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠘⠘⠙⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⢻⣆
⠉⠉⠉⠉⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣇⢻⣿⣿⣇⠀⠀⠀⠀⠀⠶⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠻
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣟⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠓⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀
⠘⡇⢹⣧⢸⣿⠀⡆⣿⣿⣿⡿⠋⣠⠸⢏⣾⣿⣿⣿⣿⣿⣿⠾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠃⠘⣿⡄⢻⠇⠃⢹⣿⠋⢀⣾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣛⢋⡿⠻⡅⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⣴⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⠛⢧⣿⡿⣿⡿⣟⡈⢻⢻⣶⡀⡈⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢇⠀⠀⢹⣿⡄⠀⠀⠀⣸⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠓⣿⣿⣧⣥⡷⡿⣇⡞⢲⣾⡕⣯⣭⣽⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠀⠸⣿⡇⠀⠀⠀⠿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⢇⣀⣭⣸⣿⣿⣿⣴⣸⣿⢷⣟⣿⡻⡿⡉⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠁⠁⠀⠈⠉⢻⣿⣿⣿⣿
⣿⣿⠀⠀⢿⡇⠀⠀⠀⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⡾⠻⣻⣿⣟⣿⣿⣿⡎⢛⣿⢿⣿⣧⢻⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠯⠻⠳⠿⠻⡑⠞⣻⡟⣿⣯⠉⠙⣩⣡⣼⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣻⡿⠎
⠛⠉⠁⠀⠈⠃⠀⠀⠀⣿⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣽⣿⣿⣥⠄⠈⠀⠸⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⡿⣿⣟⡥⣦⣄⣐⣠⣸⣿⣂⠀⡹⣠⡿⣿⣥⣀⣩⣀⣹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀
⠉⠁⢠⡀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠻⢿⠿⢑⡄⠀⠀⢝⣿⣿⣿⡅⣾⣿⣿⣿⣿⣿⣿⡇⣿⣶⣿⣿⣿⡿⡏⢿⢟⢛⠃⠀⣿⣹⣟⢨⠟⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡗⣀
⠀⡄⢸⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣧⡤⢤⣤⣤⣶⣼⣷⠀⠀⣭⣿⣭⣽⠀⣿⣭⣽⣭⣽⣿⠿⣧⢿⣿⣿⣿⣭⣽⠄⠼⠀⠃⠿⠀⠁⠛⠉⠀⠀⣤⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡟
⠒⣿⣶⡄⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡟⢙⠻⡋⠛⠿⠀⣄⠿⠿⠿⠿⠀⠿⠿⠿⠿⠤⠿⠈⠿⢹⠿⢿⠿⠿⠯⠀⠀⠄⠀⠉⠀⠘⠥⠿⠗⣷⠙⢻⣿⢱⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⣗⣿⡛⠃⢀⣠⣤⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠋⣥⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠿⠿⣿⢶⣄⡀⠀⠀⠀⣐⣀⣰⣦⣤⣦⣯⣤⠤⣿⣿⡇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢛⣿⠼⠆⣿⡆⠀⠀⢸⣡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⢤⡴⠍⠉⣉⣉⣵⡀⣴⣒⣶⣮⣿⠤⠀⠘⢻⠋⠉⠉⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈
⠋⠿⢽⣿⡏⠋⢿⢿⣿⣿⡿⠟⠁⠀⣰⣿⣿⣿⠷⣷⠐⠀⠀⠀⢿⣿⣛⣃⠀⠀⢹⣿⣿⡆⠀⠤⠄⠀⠛⠿⠹⠿⠍⠌⠷⠀⢀⣀⣛⣷⠀⠀⠳⠆⠠⢀⣀⣀⣤⠤⠴⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⣿⣷⠀⠀⠀⠋⠉⠁⠀⣠⣾⣿⣿⣿⣿⡷⠶⢶⠿⠿⠃⠈⠹⢷⣦⣤⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣈⡁⠀⠙⠋⠉⠉⢉⡉⠈⠉⠀⠀⠀⠀⠀⠖⠚⠋⠉⠁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⣀⣀
⠀⠀⠀⠸⣿⠆⠀⠀⠀⠀⢀⠐⠛⠛⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣷⣶⣶⣒⠂⠀⠀⠀⠀⠈⠉⠉⠓⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠐⠒⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣿⣿⣶⣦⣬
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠃⠀⠈⠁⢠⣴⣿⣿⣿⣿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣘⣿⣿⣿⣿⣿⠿⠿⠿⠿⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣬⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠳⠾⡿
⠤⠤⠤⠤⠀⠀⠐⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠀⠀⠠⠐⢶⣶⣖⣿⣽⣿⣿⣿⣾⢰⣾⣙⡿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠈⠉⠙⠛⠿⢿⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣴⣭⣻⢷⣦⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡌⢙⠿⣶⣤⡀⠀⢸⣿⣿⣿⣿⣿⠏⠁⠀⠿⠉⠿⣿⣿⣿⣷⣷⡂⢀⣀⡀⣀⡀⣀⣀⣀
⠠⠀⠀⠀⠀⠀⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⢸⣷⣮⣝⡻⢷⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣷⢿⠟⣿⣿⣿⣿⣿⣿
⠠⣀⡢⡀⢀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⡿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢽⠃⠀⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⢀⠀⠀⢈⠀⠹⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⢸⣧⠙⢿
⠀⠠⠐⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠠⠀⠀⠀⠈⠀⠈⠀⠀⠄⠠⠀⠺⠁⠄⠘⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠐⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣭⠹⢸⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣠⣤⣤⣴⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⢸⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣿⡇
⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠘⠐⠙⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻
⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢻⣆
⠉⠉⠉⠉⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣇⢹⣿⣿⣇⠀⠀⠀⠀⠀⠲⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠻
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⡿⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠓⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀
⠈⣿⠻⣆⢻⣿⡇⠓⢻⣿⣿⣿⡿⠃⠀⣾⣫⣾⣿⣿⣿⣿⣿⣽⣿⣿⣛⣿⣿⣿⣮⡿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢙⠀⣿⡌⢿⡇⠃⢸⣿⣿⠟⢡⣾⠠⣵⣿⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⠿⠿⣿⢿⠟⢩⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣧⠈⠁⠀⠈⠛⢁⣴⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⡿⡆⣼⣿⣿⣿⡿⠊⢼⣯⣤⡁⠈⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⣾⣍⢙⢏⣿⡆⣈⢄⣽⡗⣶⢞⢿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⡏⠙⠰⣘⣿⣾⣿⣗⡉⣷⣟⣤⣷⡇⢭⡛⠙⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿
⣿⣶⠀⠀⢻⣿⠀⠀⠀⢨⣿⣿⠁⣾⣿⣿⣿⣿⣿⣷⣏⣶⡽⣿⣿⢿⣿⣿⣇⠿⣿⣿⣿⣷⢸⡇⣰⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣽⢷⠯⣝⡻⢂⡅⠷⣿⢿⣿⡛⠋⠏⣋⣾⡛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠏⢹⣿⡿⢯
⣿⠿⠆⠀⠘⡿⠀⠀⠀⢸⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣀⢿⣿⣟⡟⣛⠙⠋⢰⣿⣾⣿⣿⡆⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⡁⠀⠀⢠⣶⠌⠀⠸⡏⣸⢿⡗⡀⠘⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡯⠀⠀⠀⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢻⣯⣿⣽⣿⣿⣿⢿⣿⠿⠷⠈⢽⡇⣿⠗⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠃⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⣿⣟⣛⣿⣛⣿⣟⣛⣿⣋⡊⡁⣀⡘⣋⣡⣊⡀⠀⣑⣟⣛⣟⡃⢘⣛⣿⣿⢻⣿⣛⣻⢘⣿⣻⣿⣛⣻⣝⢐⠗⠑⢸⠀⠙⠹⢟⠃⠁⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠸
⣀⣼⡄⠅⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡷⠿⣿⣿⣿⣿⡇⠀⢿⡿⢿⣿⡇⢸⣟⢛⣿⢸⣿⣿⣿⢸⣿⣿⣿⣿⣟⠃⠀⠀⠀⠔⠀⠀⢖⠤⠦⢶⡘⣿⡇⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡇⠘⠛⢲⣤⣶⣾⣿⣿⣿⣿⣿⣻⣻⣿⣻⣛⣻⣿⠿⠛⠀⠁⠀⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣷⣶⣷⣦⣄⠀⠀⠀⠀⠠⠀⠀⣄⣀⣠⣹⣁⣿⣿⡏⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣄⣿⣿⣶⣏⣴⢸⣇⠀⠀⠀⣰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠐⠒⠒⢪⡀⢉⡠⢬⣭⣻⣋⠀⠁⠶⡖⠛⠛⠋⠉⠉⠉⠁⣹⣿⣿⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠋⢩⣟⠊⠿⣯⣽⡋⡀⠀⠀⢻⣧⣤⡄⠀⠀⢀⣠⣶⣶⠀⢈⠀⠛⠲⢖⡶⠶⢿⡃⢮⠋⠙⠙⠻⣦⡀⠀⠰⡄⠀⡀⠀⠀⠀⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠘⣿⣿⡄⠀⠃⠙⠟⠿⠋⠁⠀⣠⣾⣿⣧⠀⠈⠈⠁⠀⠀⠀⠈⢛⣿⣂⣀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠴⠒⠛⠛⠛⠃⠒⠂⠀⠀⠈⠉⣩⠽⠶⠒⠐⢈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀
⠀⠀⠈⢿⣷⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣭⣍⣛⣻⢶⣯⣭⣙⣓
⠀⠀⠀⠀⠺⠃⢄⠀⠀⠀⠀⠉⠁⠀⠙⠀⠸⠿⢿⣶⣦⣤⣤⡀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠇⠀⠀⠀⣠⣤⣾⣿⣽⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠉⠉⠛⠁⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣤⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡀⠴⠄⠀⠀⠀⠨⠭⠭⠭⠿⠿⠤⠤⠀⠀⠀⠒⠒⠚⠂⢭⣭⣭⣭⠭⣭⣿⣿⣴⣨⣝⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠙⠛⠛⠿⠿⣯⣴⣤⣤⣄⣀⣤
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣩⡻⢿⣶⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⡀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⡇⣿⣿⣿⣿⣿⣶⣮⡙⠿⣷⣦⣄⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠻⠟⢻⣿⣿⣿⣿⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢈⣌⣙⡻⢿⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉⠟⠿⣭⠎⢀⡀⠀⢴⣶⣶⣶⣾⣻
⠀⠀⠀⠀⡀⠀⠐⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣶⡿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢿⣿⣿⣿⣟
⠀⠐⠈⠒⠈⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⢿⣿
⠀⠀⠀⠀⠀⠁⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠘⢿⢸⢸⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣯⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀
⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠙
⡿⠿⠿⠿⠛⠛⠛⢛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣿⣿⣿⢸⣿⣿⠋⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣿⣿⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠈
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀
⠀⣿⠳⣦⠹⣿⡇⠹⢺⣿⣿⣿⣿⠏⠀⣸⢟⣵⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣾⣻⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠀⣿⡆⢿⡇⢸⢸⣿⣿⠿⠃⣴⡄⣭⣿⣿⣿⣿⣿⣿⣿⡯⢻⣿⣿⣿⣟⣿⣿⢿⣻⡛⢩⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⣧⠈⠃⠈⠀⠛⠋⣠⣾⡿⢀⣿⣿⣿⣿⣿⣿⣿⡿⣇⢨⣿⣿⣿⡿⠗⢴⣯⣐⡉⠈⢿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⢰⣿⡇⠀⠀⠀⠀⣼⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣷⣨⣿⣿⠹⢛⣿⣦⢀⡅⣛⡗⣰⠾⠿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠂⠀⠀⣿⣷⠀⠀⠀⢰⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⠛⠣⠼⣽⣿⣿⠟⡉⣵⣺⣠⣿⣧⣩⡿⠟⢣⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿
⣿⣶⡀⠀⢹⣿⠀⠀⠀⢨⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣲⣾⣿⣿⣿⣿⣿⣗⢾⣯⣿⣿⣷⢸⣇⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⡿⣿⡻⣌⣏⠿⣿⡿⣿⡛⠛⡟⢻⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⠋⢿⡿⣿⢯
⣿⣿⣥⠀⠈⣿⠀⠀⠀⢸⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣃⡵⣿⣿⡶⠛⠟⠟⠀⣾⣯⣿⣿⡇⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡋⠀⡀⠀⣭⡆⡈⠠⡏⢸⣿⣇⠀⠐⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⡟⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣿⣿⡯⡁⠀⠀⠹⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⢸⣟⣾⣭⣿⣷⣾⢿⣿⡿⠖⠐⢱⡷⣺⠟⢻⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀
⠀⢀⠀⠐⠀⠸⣶⣦⡀⠀⣰⡿⢿⡿⠿⣿⡿⢿⡿⠛⣿⠋⠉⠀⠉⠏⡁⢼⠀⠀⠈⢾⡟⠻⡟⠈⣿⣿⢿⣿⡿⣿⢛⢹⣻⣿⣛⣿⣷⣟⠁⡏⠡⠂⡂⠘⠃⣟⠃⠉⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡾
⣀⢸⣄⠀⠀⠀⣿⣿⣿⡄⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⡏⠈⢻⣿⢸⣿⣿⣿⣿⡎⣿⣿⣿⣿⣟⠃⠀⢀⠀⠠⠄⠀⠴⢐⣶⣤⡚⣿⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠋⠘⢻⣴⣶⣿⣿⣿⣿⡇⣧⡟⠻⠻⣿⣿⣿⢷⣿⢿⠿⠂⠐⠉⠙⠉⠉⠉⠉⠈⠋⠉⠉⠉⠁⠀⠉⠁⠈⠉⠁⠀⠨⡄⣯⣭⣿⣯⣄⠀⠀⠀⠀⠠⠄⠀⣀⣀⣀⢸⢻⣿⣾⡇⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡉⡭⣿⣟⣻⣿⢃⢰⣇⠀⠀⠀⣴⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠐⠢⡀⢈⣁⣉⣉⣹⣗⡀⠀⣰⡲⠶⠚⠛⠛⠉⠉⠉⣿⣿⣷⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⠿⠉⠳⠏⢰⣿⣘⣟⠀⠀⠀⢳⢇⣤⣤⠈⠀⠀⣀⣀⣀⠀⠈⠉⠛⠢⣄⡶⠶⠾⠗⢸⡟⠛⠛⣻⣦⡀⠀⢀⣃⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⠆⠀⠀⠀⠀
⠘⢿⣿⣷⡀⠀⠁⢿⡿⣿⠿⠋⠀⢀⣿⣦⠀⠀⠈⠉⠋⠀⠀⠀⠀⠞⢷⣒⠒⠀⠀⠛⠛⠛⠀⠀⠉⠀⠀⠀⠁⠉⠑⠈⠐⠵⢒⠒⠚⠛⠓⠒⠂⠀⠀⠉⠁⢢⣭⡭⠑⠒⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀
⠀⠀⠹⣿⣧⡄⠀⠁⠀⠁⠀⢠⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣤⣄⣀⢀⡀⠀⠀⠀⠀⠐⠰⠶⠶⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⢶⣶⣉⣛⡒⠲
⠀⠀⠀⠀⠚⢡⣤⠀⠀⠀⠒⠛⠋⢹⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠷⠿⠧⠀⠀⠂⣠⣤⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠘⠍⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢣⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠄⢀⣠⣤⣤⣄⡀⠤⠬⠽⠿⠿⠿⠷⠆⠐⠒⠒⡒⣚⣛⣿⣭⠭⣭⣭⣭⣭⣈⣛⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⠩⠛⠻⠿⢿⣿⣷⣟⣁⣀⣉⣁⣠
⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⣿⣿⣾⣿⣿⣿⣿⡇⣿⣷⣮⣙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⡀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⡿⡇⣿⣿⣿⣿⣿⣶⣭⠻⢿⣶⣤⣀⠀⢰⣿⣿⣿⣿⣿⡿⠋⠛⡿⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢐⣍⣛⠿⣷⣾⣿⣿⣿⣿⠁⠂⠀⠀⠀⠀⠀⠘⠛⢿⡳⣇⠄⠀⢀⣂⢴⣦⣴⣶⣶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⣿⣿⣷⣧⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣾⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣰⠆⠘⠻⣿⣿⣿⣿⣿
⠀⠀⠈⠂⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠹⣿⣿⣅⢸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣼⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢹⣟⠿⣿⣻
⠀⠀⠀⠀⠀⠀⠌⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠠⠀⠀⠀⠈⠀⠀⠆⠀⠘⢿⢸⢸⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣿⡄⠘⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠸⢼⢸⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣎⠈⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀
⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠋⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⢷
⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⢺⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⣀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢻⣿⣿⣿⢸⣿⡧⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠀⠀⠻
⠀⠛⠁⠟⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⣿⣿⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣂⣀⣀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠠⣿⣏⣩⣭⣭⣽⣿⣾⢿⣻⣷⢿⣦⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡿⣶⣷⣾⣿⣿⣿⡟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣤⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣶⣶⣶⣶⠀⠀⣿⣿⣿⣿⢀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠶⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇⣺⣿⣿⣿⣿⣿⣯⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣦⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢘⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣾⣿⡟⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣟⣿⣿⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⣶⣶⣾⣿⣤⣤⣤⣴⣶⣶⡶⠶⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠃⠀⠀⠀⠀⢀⣀⣤⣼⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠙⠛⠛⠛⠙⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣶⢤⣀⠀⠀⠀⠀⣾⡿⣿⡷
⠀⠀⠀⠘⣴⣷⡞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⠉⡠⡴⢀⣶⡶⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣤⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⣦⣄⠀⠀⠈⣿⠃
⠀⠀⠀⢈⣤⣤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⣠⣾⣿⣿⣿⣿⡿⠃⠀⠚⠛⠃⠉⠉⢀⡀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣿⣶⣤⣭⣴
⠀⠀⠀⠸⠘⠉⠉⠁⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⡟⠀⠐⠒⠒⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢉⣁⠄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡩⣿⣿⡿⠿⠿⠟⠛⠻⠿⣻⣭⣿⣿
⣀⣀⣀⣀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣼⣟⣿⣧⣤⣶⣆⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⣿⣮⣁⣐⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠹⠻⢿⢿⣿⣭⡿⡏⣽⠙⣯⢻⣿⣿⣿⡟⡛⠟⠿⠿⠿⢏⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣌⣀⣶⣶⣶⣾⣧⣭⣿⣧⣿⣧⣿⣼⣾⣿⣿⡾⣷⣾⣦⣤⣀⠛⠿⠹⠷⠶⠷⠶⠿⠶⣶⣶⡆⣿⣭⣽⣭⣭⠉⠐⠶⣶⡶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣭⣤⣦⣤⣀⣀⣀⣉⣻⣿⣿⣿⣿⣿⠉⠙⠛⠋⠻⠟⠟⠿⠙⠛⠛⠋⠛⠛⠛⠛⠿⠿⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⠬⠁⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡉⣭⡍⢻⣿⢛⣛⣛⢻⣿⡟⢿⣿⣿⣿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠚⠳⠆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣶⣶⣾⣿⠘⠿⠿⢸⣿⡇⠸⠛⢿⣿⡄⣿⣿⢐⣶⣦⣼⣿⡇⠰⠦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠟⡷⠾⠀⠠⠄⣶⣿⣿⣦⣭⣥⣼⣿⣧⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠉⠀⠀⢰⡆⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠿⠟⠛⠻⠿⠿⠶⠾⠶⠶⠦⠴⢶⣖⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣔⠑⠁⠀⠀⠀⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣢⣤⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡌⡉⠙⠒⠒⠒⠀⠤⢤⠴⠮⠠⠄⠤⠤⠤⠄⡀⠀⣀⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣾⣷⣿⣿⣿⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⢀⡤⠚⠑⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⡇⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⢀⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀
⠀⠛⠙⠿⠛⠻⠓⠛⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣠⣄⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢀⠀⢀⡜⠀
⠀⠀⠀⠀⠘⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣦⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠔⣿⡏⣩⣭⣭⣽⣿⣾⢟⣫⣷⢿⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠉⠀⠀⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⡟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠈⣟⡣⣤⣾⣿⣿⣿⣿⠿⣯⣀
⠀⠀⠀⠀⠠⣤⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣶⣶⣶⣶⠀⠀⣾⣿⣿⣿⣀⠀⠀⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠰⠶⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣺⣿⣿⣿⣿⣾⣧⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣀⣠⣠⡈
⠀⠀⠀⠀⢰⣷⣶⣶⣾⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀
⠀⠀⠀⠀⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⢸⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣶⣶⣾⣿⣤⣤⣤⣤⣶⣶⡶⠶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⠃⠀⠀⠀⠀⢁⣀⣤⣤⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣄⣀⡀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠗⠓⠙⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠷⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⢠⡶⠀⠀⠀
⠀⠀⠀⢸⡾⣷⡾⡏⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⠋⡠⡤⢠⣶⡶⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣷⣤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⢷⣦⣴⣿⡇⠀⠀⠀
⠀⠀⠀⢨⣤⣥⠤⠅⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⣠⣾⣿⣿⣿⣿⡿⠃⠀⠚⠛⠃⠉⠉⢀⡀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⢀⠶⠂⠀⠀⠀⠀⠀⠀⠙⢷⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀
⠀⠀⠀⠘⠙⠛⠈⠁⢀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⡟⠀⠐⠒⠒⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣴
⣠⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢿⣮⣩⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿
⣀⣀⣀⣀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣼⣟⣿⣧⣤⣒⣂⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣣⣾⣿⣿⡏⠀⠀⣠⣾⣿⣿⣿
⠈⠉⠁⠁⠀⠹⠿⣿⣿⣿⣭⡯⡯⣽⠻⣿⣻⣿⣟⣿⣟⣛⡿⣿⢿⠿⢏⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠉⢀⣶⣿⣿⣿⣿⣿
⠀⢀⣀⣌⣀⣶⣶⣾⣾⣬⣬⣿⣧⣿⣶⣿⣼⣾⣿⣿⣾⣿⣿⣧⣤⣀⠛⠿⠹⠷⠶⠷⡾⠶⡶⣶⣶⡏⣽⣭⣽⣭⣭⡝⠲⠶⢶⡦⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⣿⣿⣿⣿⣿⠯
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣥⣤⣤⣭⣤⣤⣀⣀⣁⣀⣉⣻⣿⣿⣿⣿⡿⠛⠛⠻⠛⠿⠿⠻⠿⢿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⠟⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡉⣭⡉⢻⣿⢛⣛⡛⢿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠚⠳⠆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣶⣶⣾⣿⠸⠿⠿⢸⣿⡇⢸⠿⢿⣿⡄⣿⣿⢰⣶⣦⣽⣿⡇⠠⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⣷⠾⡄⠠⢄⣦⣿⣿⣤⣭⣥⣼⣿⣇⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⠠⠀⠠⢀⣠⡂
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠃⠀⠀⢰⡆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣋⠀⠀⠀⠀⠀⠈⣿⡧
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣀⣬⣿⣿
⠿⠟⠛⠿⠿⠿⠷⠷⠶⠶⠦⠴⣶⣶⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠑⠁⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⣾⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⡉⠙⠒⠒⠒⠀⠤⢤⠴⠮⠠⠄⠤⠤⠄⣀⣀⣀⢀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣾⣷⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠁⠀⠀⠀⢀⡤⡚⠑⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⡇⠉⠉⠉⠉⠉⠉⠙⠁⠐⠀⢒⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⣤
⠀⠛⠙⠿⠛⠻⠃⠛⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣄⣀⣀⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣀⣀⣀⣀⣠⣾⢹
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢝⡿⠟⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠇⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠜⣿⣯⣩⣭⣭⣽⣿⣾⢿⣿⣿⢿⣧⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⣿⣿⢿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⡟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠉⢀⣀⣀⣠⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣾⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣶⣶⣶⡀⠀⣼⣿⣿⣿⡄⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⣤⣾⣿⣿⣿⣿⠿⣏⡁⠀⠀⠙
⠀⠀⠀⠀⠱⠶⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣷⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢀⣠⡀⠀
⠀⠀⠀⠀⢰⣷⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣤⣤⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠐⡲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⡿⢿⣿⣇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⢀⣾⣿⣿
⠀⠀⠀⢠⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢹⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣤⣤⣤⣤⣶⣶⣶⠶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⠃⠀⠀⠀⠀⢁⣀⣤⣤⣿⣿⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠓⠓⠛⠛⢛⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢘⣿⣷⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠋⠀⣤⢀⣶⡶⠂⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣤⡄⣿⣿⣧⣤⣄⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⣥⣥⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⣠⣴⣿⣿⣿⣿⡿⠋⠀⠚⠻⠃⠸⠋⢁⡀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⢀⠶⠆⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠻⠛⠋⠁⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⡟⠁⠐⠒⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡛⢿⣿⣿⣿⢿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡩⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣼⣟⣿⣧⣤⣐⣂⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣮⣹⣿⣿⡄⠀⠀⠀⣠⣤⠀⠀⠀
⠀⠉⠁⠀⠀⠸⠿⣿⣿⣿⣯⡯⣿⣿⠛⣿⢻⣿⣟⣿⣿⣻⣿⢿⣿⠿⢏⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⡏⠀⠀⠀
⠀⠀⣀⣌⣀⣰⣶⣶⣾⣥⣬⣿⣧⣿⣷⣿⣼⣿⣿⣿⣿⣷⣶⣾⣤⣀⠛⠿⠻⠿⠶⠷⠶⢷⠰⣶⣶⡎⣽⣭⣽⣭⣭⡛⠒⠶⢶⡦⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⠇⠀⠀⠀
⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣭⣵⣤⣀⣀⣁⣀⣉⣻⣿⣿⣿⣿⣿⠋⠛⠛⠛⠛⠿⠟⣿⣿⣿⣿⠏⠀⢀⣼⣿⣿⣿⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡏⠀⢀⣾⣿⣿⣿⡿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡏⣭⣍⢻⣿⠛⣛⣛⢻⣿⡿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠀⢀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠚⠳⠦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⣶⣶⣾⣿⠀⠿⠿⠸⣿⡇⢸⠿⢿⣿⡄⣿⣿⠐⣶⣦⣼⣿⡇⠠⠤⣼⣿⣿⣿⡏⠀⢠⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⣷⠶⡄⠀⠌⣤⣿⣿⣦⣭⣥⣼⣿⣇⣈⣛⣻⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠋⠀⠀⢰⡆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⢻⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣷
⠿⠟⠛⠻⠿⠿⠷⠿⠷⠦⠦⠶⢶⣶⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠘⠁⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡥⢸⣿⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣉⠙⠒⠒⠒⠠⠤⠤⡴⠮⠤⠤⠤⠤⠄⡀⣀⢀⢀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠉⠀⢀⠀⢀⡠⢘⠑⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⡇⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠒⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠀⠀⣀
⠀⠛⠛⠿⠛⠻⠓⠛⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣀⢀⣀⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠀⣀⣠⣤⡦⠀⣤⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠼⣿⣯⣩⣭⣭⣽⣿⣿⢿⣿⣷⢿⣧⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠂⠀⣿⣿⢻⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⡟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠉⠁⢀⣀⣤⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢨⣤⣾⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣶⣶⣶⡀⠀⣼⣿⣿⣿⡄⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⣿⣿⣿⣿⣿⠿⣯⣁⠀⠀⠙
⠀⠀⠀⠀⠰⠶⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣷⡀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⡿⠿⠋⠉⠀⠀⠀⢀⣠⣀⠀
⠀⠀⠀⠀⢰⣷⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⢀⣠⣤⣤⣴⣾⣿⣿⡇
⠀⠀⠀⠀⠀⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⣿⣿⣇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠋⢀⣿⣿⣿
⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣤⣤⣤⣤⣶⣶⣶⠶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠃⠀⠀⠀⠀⢉⣀⣠⣤⣿⣿⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠙
⠀⠈⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠓⠛⠛⢛⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢰⣾⣷⣶⡇⠀⠀⠀⠈⠐⠂⠄⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠋⠀⡤⢀⣶⡶⠂⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣤⡄⣿⣿⣧⣤⣄⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣥⣥⣤⡄⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⣠⣴⣿⣿⣿⣿⡿⠋⠀⠚⠻⠃⠸⠋⢁⡀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠹⠛⠁⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⡟⠁⠰⠒⠒⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡛⢿⣿⣿⣿⢿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡩⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣼⣟⣿⣧⣤⣐⣂⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣮⣽⣿⣿⡀⠀⠀⠀⣠⣤⠀⠀⠀
⠀⠉⠁⠁⠀⠸⢻⣿⣿⣿⣯⡯⣯⣽⠛⣿⢻⣿⣟⣿⣿⡻⣿⢿⢿⠿⢏⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⡏⠀⠀⠀
⠀⢀⣀⣬⣀⣰⣶⣶⣾⣥⣬⣿⣯⣽⣷⣿⣼⣿⣿⣿⣿⣷⣶⣾⣤⣀⠹⠿⠻⠿⠶⠷⢶⠷⠴⣶⣶⡎⣽⣭⣽⣭⣭⠝⠒⠶⠶⡦⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⠇⠀⠀⠀
⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣬⣤⣭⣵⣤⣀⣀⣀⣀⣉⣻⣿⣿⣿⣿⣿⠋⠛⠻⠛⠿⠟⠯⣿⣿⣿⣿⠇⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠇⠀⢀⣾⣿⣿⣿⣿⠄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡏⣭⣉⢻⣿⠛⣛⣛⢻⣿⡿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⢀⣾⣿⣿⣿⣿⠅⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠚⠳⠦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⣶⣶⣾⣿⠀⠿⠿⠸⣿⡇⢸⠿⢿⣿⡄⣿⣿⠐⣶⣦⣼⣿⡇⠠⠤⣬⣿⣿⣿⣏⠂⢠⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⣷⠶⡄⠀⠌⣤⣿⣿⣦⣭⣭⣼⣿⣇⣈⣛⣻⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠋⠀⠀⢰⡆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⢻⣿⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣷
⠿⠟⠛⠻⠿⠿⠾⠿⠷⠦⠤⠴⢶⣶⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠘⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡥⢼⣿⣧⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠌⡉⠛⠒⠒⠒⠀⠤⠤⡴⠪⠤⠤⠤⠤⠄⡀⣀⣀⢀⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠉⠀⢀⠀⢀⡠⠘⠑⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⡇⠉⠉⠉⠉⠉⠉⠙⠑⠛⠐⠒⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⣀
⠀⠛⠛⠿⠛⠻⠓⠛⠛⠛⠃⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣀⣄⢀⣀⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠈⠀⣀⣀⣤⡦⠀⣴⠀
⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⣿
⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠙⠻⠿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢹⣿⢿⢿⠿⣿⡿⣿⣟⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣼⣶⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⠃⢿⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠐⠘⠻⠿⠿⠿⠿⣿⣷⡀⠀⠀⠀⠀⣿⡀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⢠⡗⠀⢄⣿⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⠂⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⣀⡚⠿⠞⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠅⠐⣛⣛⣛⣛⡛⠛⠛⣛⣛⠛⣛⣋⡋⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢰⠀
⠀⠀⠀⠀⣿⣿⣿⣿⠟⣑⢘⣛⢿⣿⡿⡟⡗⡎⠀⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠋⣠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢸⠀
⠀⠀⠀⠀⣶⣶⣶⣶⠀⣴⣤⣴⡖⢶⠶⠢⠖⠒⠀⣶⠀⠀⣠⣾⣿⣿⣿⣿⣿⠋⠀⠚⠛⠋⢐⣒⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡟⠃⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣶⣾⡄
⠀⠀⠀⠀⠿⠿⠛⢍⣀⣬⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠐⠚⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣥⡏⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠤⠤⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⢙⣿⣿⣿⣿⣿⣟⣛⣻⣭⣤⣶
⠴⣤⣤⣤⣜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣤⣴⣤⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣟⣟⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⡄⠀⠹⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠰⠬⠝⣿⡏⣭⣭⡙⣿⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠊⠙⠿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣼⣿⣿⣿⣇⣛⣛⣃⣿⣿⠀⡟⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⢻⠿⠷⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⠉⠁⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡫⠩⠂⠸⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣵⣋⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠂⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠤⠤⠤⠤⠤⠀⠀⢀⠀⠀⠀⢀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⣠⣴⠍⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣴⠀⠀⠀⠀⠀⣀⣤⣶⡟⠿⠞⠻⡯⡁⡀⢠⣦⣄⣀⣿⣷⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠉⠉⠉⠱⣠⡍⠉⠛⠛⠛⠛⣒⢾⠛⠓⠒⠲⠲⠶⠶⠤⠤⠤⢤⣼⣿⣶⣿⣿⡃⠀⠀⢠⣾⣿⣿⣿⣷⠀⠂⠄⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⡀⠀⠀⣒⡂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠂⠒⠀⠐⠂⠀⠃⠀⠉⠀⠀⠀⠀⠠⠄⣀⡴⣺⠍⠉⠀⠀⠠⠂⠠⠤⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣇⣀⣴⣿⣿⣿⣿⣯⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠤⠄⣤
⠀⠛⠻⠿⠛⠻⠓⠛⠛⢛⠃⣀⠀⠅⡨⡖⠂⠠⠠⠀⣀⠀⠠⠀⠠⠀⠀⡀⣠⡦⡞⢳⠇⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣴⠀⢀⣶⠀⣰⡇
⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣋⠉⠉⠉⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣠⣼⣿⣿⣿⣿⣿⣷⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢙⣟⣻⣟⣛⣻⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠿⣿⠟⠻⠿⢿⠿⠿⠿⠿⣿⣿⡄⠀⠀⠠⣿⣷⣶⣶⣶⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣉⠉⡭⣿⠃⠀⠀⠈⠛⠿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣻⣷⣄⡄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢠⠀
⠀⠀⠀⠀⡿⣿⡿⣿⠟⠫⠛⣿⠿⣿⠿⡿⣿⡿⠀⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⣸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⢠⠀⢴⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠿⣷⣤⡀⠀⢸⠀
⠀⠀⠀⠀⣶⣶⣶⣶⠀⣴⣶⣴⣶⢴⡶⠶⢒⣆⡂⣾⢀⣀⣠⣾⣿⣿⣿⣿⣿⠋⠀⢐⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠿⣃⡐⠿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣷⣶⡆
⠀⠀⠀⠀⡛⠛⠛⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠐⠋⠉⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠦⠶⠆⢂⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣙⡻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⢛⣛⣻⣽⣶⣶
⠶⢶⣶⣶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣤⣤⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠻⢿⣿⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣻⣿⠀⠀⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⡷⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠰⠶⠌⣿⡏⢩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡇⠀⠀⠀⠀⠀⠈⠉⠟⠂⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣼⣿⣿⣿⣧⣙⣛⣃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡟⠛⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣸⣵⣾⣿⠀⠀⠀⠀⢀⣀⣀⣸
⠛⠛⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠶⠦⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⠆⠀⠀⠀⠀⣠⢴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⣀⣻⣿⣷⣀⣸⣿⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⣀⠀⡀⠀⢀⠀⠀⠠⣤⢄⠈⠀⠰⢴⡍⠉⠙⠛⠛⠛⣻⢿⠛⠛⠒⠒⠲⠶⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⡀⠀⠀⣘⡀⠂⠀⠠⠀⠀⠐⠈⠀⠀⠒⠠⠚⠂⠒⠋⠀⠀⠀⠉⠐⠀⠀⠀⠠⠌⣀⡴⢮⠇⢉⠀⠀⠠⠒⡀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠤⠤⣤
⠀⠛⠻⠿⠛⠿⠷⠛⠛⠛⡃⡀⠀⡵⣩⣿⠉⠰⠰⠒⣌⠀⠠⠈⣧⠀⢀⡀⣠⣶⣛⢳⠧⠀⡀⠄⢒⠤⠀⠘⡀⠈⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣴⠄⢀⣾⠀⣰⣿
⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⣿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⠛⠛⠛⠛⠛⠛⢛⣛⣻⣛⣋⠉⠉⠉⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⣿⣿⣿⣿⣿⣧⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡀⠀⠀⠀⢸⣟⣻⣿⣛⣻⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⡿⠿⠿⡟⠻⠿⣿⠿⠿⠿⠿⣿⣿⡄⠀⠀⠠⣿⣷⣶⣶⣶⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⣛⣛⣛⣛⣛⣛⢛⣛⣛⣙⣛⣋⣉⠉⡍⣿⠃⠀⠀⠈⠻⠿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠁⠀⣰⡀⠀⠀⠀⠀⠀⣿⣿⣄⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⡀⠀⠀⠀⠀⢰⠀
⠀⠀⠀⠀⡿⣿⡿⣿⠟⠻⠿⣿⠿⣿⠿⣿⣿⠿⠀⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣀⠀⢠⠀⣶⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠿⣷⣤⡀⠀⢸⠀
⠀⠀⠀⠀⣶⣶⣶⣶⠀⣴⣶⣴⣶⣰⠶⠶⣖⣂⠂⣾⢀⣀⣠⣾⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠫⣃⠼⡿⠁⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣷⣶⡄
⠀⠀⠀⠀⡛⠛⠛⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠐⠋⠉⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⡶⠶⠇⢂⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣙⡻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⢛⣛⣻⣽⣶⣶
⠶⣶⣶⣶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⣤⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣶⣧⣸⣿⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⡷⠋⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠰⠶⠌⣿⡏⢩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⠈⠉⠟⠂⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣼⣿⣿⣿⣧⣙⣛⣃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡟⠛⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣋⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣜⣷⣾⣿⠀⠀⠀⠀⢀⣀⣀⣸
⠛⠛⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠶⠦⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⠀⠀⠀⠀⠀⣠⢴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣙⣹⣿⣧⣀⣸⣿⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠠⣤⢄⠈⠀⠰⢴⡍⠉⠙⠛⠛⠛⣻⢿⠛⠛⠒⠒⠲⠖⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⡀⠀⠀⣘⡀⠀⢀⠀⠀⠁⠐⠈⠁⠀⠒⠠⠘⠂⠀⠊⠀⠀⠀⠉⠐⠀⠀⠀⠠⠌⣀⡴⢮⠇⢉⠀⠀⠠⠒⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠤⠤⣤
⡐⠛⠻⠿⠛⠿⠗⠟⠛⢛⡃⡀⠀⠷⣸⣧⡳⠲⠰⠒⣌⠀⠐⠨⣇⠀⣀⡀⣠⣶⣛⢳⠧⠀⡀⠀⢀⠤⠀⡨⣀⠀⠐⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣠⠄⢀⣾⠀⣰⣿
⠂⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣼⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⣸
⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⢹
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⢙⣟⣋⠉⠉⡉⠉⠉⠉⠉⣭⣭⣭⣍⣉⠉⠉⡉⣉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡀⠀⠀⠀⢸⣟⣛⣟⣛⣻⣟⣛⣛⣟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⣯⣿⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠃⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⣛⣉⣉⣭⣭⣍⢉⡭⢹⡇⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠟⠛⠛⠛⠛⠉⠉⢻⣿⣿⣿⣶⣶⣶⣶⣾⣿⣷⣦⠀⠀⠀⢸⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣤⣀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠿⠿⠿⠿⠟⠿⠵⠽⠿⠿⠿⠿⠿⠿⠤⢿⠃⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠋⣀⣿⡏⣾⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣷⣦⣀⠀⠀⡇
⠀⠀⠀⠀⣿⣿⣿⣿⡅⣟⣶⣿⣿⡐⢶⣶⣖⣆⣀⣾⣀⣀⣠⣾⣿⣿⣿⣿⣿⠋⠀⠌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⡉⠉⠛⠋⠉⠉⠉⠹⣿⡄⠀⠀⠀⠀⠀⠈⠻⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣶⣧
⠀⠀⠀⠀⡛⠛⠛⣛⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣷⠀⠀⠀⢀⢀⣠⣿⣿⣷⢿⣦⡀⠀⠀⠀⠈⠻⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⣶⡖⠆⢂⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣿⣿⡿⠿⠟⡛⡄⢰⠞⠿⠿⣿⣿⠿⠖⠶⠾⠛⣿⣿⡿⠃⠀⢿⣿⣶⡉⠁⠁⠁⠈⢻⣿⣿⣿⡿⢛⣛⣛⣉⢉⣛⣻⣷⣶⣶
⠶⠶⠶⠶⠮⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡏⠀⠀⠐⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⣿⣿⣿⣿⣦⣄⠀⣀⣀⣙⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠤⣤⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣓⣀⠀⠀⠀⣠⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡗⠛⠛⠋⠁⠚⠉⠰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⡏⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣁⣀⣀⣀⣀⣀⡀⠀⠀⣾⣿⣿⣿⣿⣅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣬
⠉⠉⠉⠉⠉⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠶⠒⢲⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⢠⣤⣀⣸⣿⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⡀⠀⡄⣼⣿⣿⣿⣷⠁⠀⠀⠀⠀⠶⠆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⡈⠀⠀⣈⡁⠑⢀⡀⠀⠁⠘⠉⡉⢀⢐⣩⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠉⠒⠒⢰
⡔⠛⠻⠿⠛⠿⡷⠿⠛⢛⠇⡠⠀⠖⢶⣧⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⠀⣄⣨⣶⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⢰⠂⢀⣾⠁⣰⣿
⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⢨⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸
⠀⠀⠀⠀⠈⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⣿⣿⠿⠿⠿⠿⠀⠀⢸
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⡉⣉⣉⣉⡉⠉⠉⣭⣭⣭⣭⡉⠉⠉⡉⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⣟⣛⣛⣛⣻⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠛⠛⠋⠉⠙⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣀⣀⣀⣿⣿⠆⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠟⠛⠛⠛⠻⢾⡿⠿⢿⣿⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣃⣀⣀⣀⣀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣼⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢉⣉⣉⣉⣉⠉⠉⣉⣭⣉⣩⣭⠅⠀⠁⢸⡇⠀⠀⠀⠀⠀⢀⣤⣶⣾⣦⣤⣤⣤⣶⣶⣶⣤⠀⠀⠀⠀⠈⠉⣽⣿⡏⠉⠉⠛⠛⠛⠛⠻⠿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠿⠿⠿⠿⠟⠢⠤⠤⠬⠽⠟⠻⠉⠰⠀⢸⠇⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠻⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣶⣄⡀⠀⡇
⠀⠀⠀⠀⣿⣿⣿⣿⡅⢀⢿⣿⠩⢙⣒⣓⣂⣅⣀⣺⣀⣀⣠⣾⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⣿⡀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣟⡃⠀⠀⠀⠀⠀⠀⠈⠻⣷⣝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠘⠛⠛⣁⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠘⣫⣶⣤⣤⣤⣾⣿⣿⠀⠀⠀⠀⠹⠶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯
⠒⠒⠂⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠈⠻⣿⣿⣿⡟⣛⣛⣉⣉⣉⣭⣭⣶⣶⣿
⠶⠶⠶⠶⠖⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠏⠝⠛⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣈⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠁⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠤⣴⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⡿⠏⠋⠉⠁⣠⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠁⠀⠀⠀⠀⠸⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣧⣄⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠒⠒⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⣨⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛
⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡛⢿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠁⠐⠒⢰
⠄⠛⠻⠿⠛⠻⠓⠛⠛⢛⠃⠀⠀⠚⣥⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⢠⠀⠀⣴⠁⢰⡟
⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⢨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸
⠀⠀⠀⠀⠈⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⣿⡿⠿⠿⠿⠿⠀⠀⢸
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣭⣍⡉⣉⣉⣉⡉⠉⠉⣭⣭⣭⣭⡉⠉⠉⡉⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣷⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣟⣛⣛⣛⣻⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠛⠛⠋⠉⠙⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣀⣀⣀⣿⣿⠆⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠟⠛⠛⠛⠻⣾⡿⠿⢿⣿⣿⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣃⣀⣀⣀⣀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣼⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢉⣉⣉⣉⣉⠉⠉⣉⣩⣉⣭⣩⠥⠀⠁⢸⡇⠀⠀⠀⠀⠀⢀⣠⣶⣾⣦⣤⣤⣤⣶⣶⣶⣤⠀⠀⠀⠀⠈⠉⣽⣿⡏⠉⠙⠛⠛⠛⠛⠿⠿⣿⣿⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⡷⢦⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠿⠿⠿⠿⠟⠢⠀⠤⠭⠽⠟⠛⠙⠰⠀⢸⠇⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠻⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣶⣄⡀⠀⡇
⠀⠀⠀⠀⣿⣿⣿⣿⡅⢀⢿⣽⡉⢑⣒⣛⣂⣀⣀⣺⣀⣀⣠⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⠿⠿⢿⡀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣟⡃⠀⠀⠀⠀⠀⠀⠈⠻⣷⣝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠘⠛⠛⣁⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠐⣦⣵⣥⣤⣤⣼⣿⣿⠀⠀⠀⠀⠹⠶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯
⠒⠒⠂⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠈⠻⣷⣝⣿⡿⣛⣛⣉⣉⣉⣭⣭⣶⣶⣾
⠶⠶⠶⠶⠖⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣻⣿⣿⣿⠿⠋⠛⠫⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣈⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠁⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠉⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠤⣴⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⠿⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏⠉⠁⠁⢠⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠿⠋⠁⠀⠀⠀⠀⠹⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠚⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⣨⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛
⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠐⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡛⢿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠁⠐⠒⢰
⠄⠛⠻⠿⠛⠻⠓⠛⠛⢛⠇⠀⠀⠚⣑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⢠⠀⠀⣼⠀⢰⡟
⠀⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⢿
⠀⠀⠀⠀⢠⡽⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡛⠟⣿⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸
⠀⠀⠀⠀⢈⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠀⠀⢸
⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠉⠉⠉⠉⠉⠉⠉⠉⢩⣭⣭⣉⣉⣉⣉⣉⠉⠉⣭⣭⣭⣭⠉⡉⠁⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣷⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣭⣍⣿⣿⣽⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠆⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢠⣿⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣿⣿⠂⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡟⠛⠛⠛⠛⡿⠿⠟⢻⣿⣿⣋⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⠀⣿⣿⣶⣶⣶⣶⣿⣿⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣄⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠚⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠛⢋⠉⣉⣉⣉⡉⠉⠉⠉⠉⣿⣿⡏⠉⠉⠉⠙⠛⠛⠛⠿⢿⣿⣟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⡷⢦⣄⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠿⠿⠿⡿⢿⠿⠿⠿⠿⠿⡟⠤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠁⣤⣿⡏⣾⣿⠋⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠻⣿⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣶⣄⡀⠀⡇
⠀⠀⠀⠀⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⢕⣺⣷⣶⣤⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⠋⢀⣀⣀⡉⠠⠭⠤⠐⠂⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣯⠃⠀⠀⠀⠀⠀⠀⠈⠻⢷⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣥
⠀⠀⠀⠀⣹⣿⣿⣿⣶⣦⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⡀⠀⠀⠀⠀⠀⠀⠘⠁⣀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠱⠶⠂⠀⠀⠀⠀⠀⠀⢀⡀⠙⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠒⠚⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣿⣿⣿⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣷⣝⢿⣟⣛⣋⣉⣉⣉⣭⣭⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣯⣽⡍⠉⠉⠉⠛⠛⠻⠟⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣬⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣉⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠁⠀⣞⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⢹⣿⡏⣿⣿⣿⣿⢹⣿⣿⢛⣛⡛⣿⣿⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣶⣷⡂⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣼⣿⣇⣫⠉⠻⡿⣛⣿⣿⠸⠿⠟⢿⣿⡇⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣟⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠋⠉⠉⠙⠉⠋⠉⣉⡟⠛⠃⣈⠛⠛⠛⠿⠿⠿⠿⠿⠿⠷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣿⣿⣿⣶⣤⡜⠂⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣀⣤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠒⠲⣿⡧⠤⠤⠤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣴⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠉⠀⠐⠒⢒
⠐⠛⠻⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⡇⠀⠀⢀⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⢀⠂⠀⡾⠀⢠⡿
⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣓⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢿
⠀⠀⠀⠀⠀⠀⠃⣿⡿⠿⠿⠿⢿⣿⣹⣿⣿⡟⣿⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣏⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠘
⠀⠀⠀⠀⠀⢐⢰⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⣉⣉⣉⣉⡉⠁⠀⣭⣥⣤⣤⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢙⣛⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣀⢰⣿⣿⣿⣿⣀⡀⠀⡇⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣬⡍⣩⣍⣩⣍⣩⣭⣩⣽⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢘⣛⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⡿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠛⠂⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣬⣭⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣦⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡣⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣼⣿⣿⣿⣿⣯⣿⣿⣿⣿⣀⣀⣀⣿⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡟⠛⠛⠛⠛⠟⠛⠛⢻⣿⣟⣋⣉⣉⣀⣀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡽⣿⣿⣿⣷⣿⣿⣿⣿⣿⢾⣿⠭⢲⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⣭⢭⣭⡍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠋⠉⢉⣉⣉⠉⠉⠉⠉⠉⠉⣽⣿⡏⠉⠉⠉⠉⠙⠛⠛⠻⢿⣿⣟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠦⣄⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠋⠓⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣠⣶⣿⣿⣿⣿⠟⠁⣤⣴⠇⡼⠿⠃⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠻⢿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣶⣄⡀⠀⡇
⣶⣶⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣀⣸⣅⣤⣤⣾⣿⣿⣿⣿⡿⠃⣀⣀⣀⠀⠠⠤⠄⠐⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠠⠍⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣕
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢷⣄⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣜⠺⠟⢛⣋⣉⣁⣈⣭⣭⣶⣾⣿
⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⣤⣬⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣴⣀⣈⠉⠉⣵⣶⣶⣮⣍⣙⣛⣛⢛⡛⣛⠻⠿⠿⢿⠿⢿⢿⢉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠛⠛⠿⣶⣤⣤⣤⣭⣭⣭⣍⣅⣉⣙⣛⣋⣛⠛⠛⠛⠇⠀⠈⠉⠉⠁⠈⠻⣿⣿⣿⣿⣿⣿⠿⡿⡿⢿⡿⣿⣿⢿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⠁⠉⡿⠿
⠀⠀⠀⠀⠪⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣛⣃⣽⣯⢰⣶⣆⢹⣿⡇⣿⣿⣿⣿⠹⣿⣟⢛⣛⡛⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣶⣿⣿⣿⣿⣬⣭⣭⣼⣿⣇⣩⠀⠙⠟⣃⣿⣿⠸⠿⠟⢿⣿⡇⠭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⠙⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⠯⠉⠁⢈⠙⠛⠛⠛⠻⠿⠿⠿⠿⠷⠶⠶⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠅⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⣀⢠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣀⣤⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡨⠎⠍⠉⠉⠀⠉⠉⠉⠀⠀⠀⠐⠐⣿⡅⠀⠠⠠⠤⠤⠤⠠⠤⠄⠀⢀⣀⣀⣀⣀⣾⣿⣶⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⠃⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠀⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣦⣴⣶⣶⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⡔⠀⠀⠟
⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣓⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⢿
⠀⠀⠀⠀⠀⠄⡃⣿⡿⠿⠿⠿⢿⣿⣹⣿⣿⣟⣿⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠠⠀⣿⣧⣿⣿⣿⣿⣿⣟⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠈
⠀⠀⠀⠀⠀⢰⣐⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⣭⣭⣀⣀⣀⣀⡀⠀⠀⣡⣤⣤⣤⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⣟⣿⣿⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⣣⣀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣬⡍⣉⣍⣭⣭⣭⣭⣭⣹⣿⣿⣿⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀⢿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢈⣋⡿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠛⠒⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣬⣬⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣀⣀⣀⣸⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠟⠛⠛⠛⠛⠟⠛⠛⢻⣿⣟⣋⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠯⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⢍⣭⢭⡭⠉⠉⠉⠡⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠋⢉⠉⣉⣉⠉⠉⠉⠀⠀⠀⣽⣿⡏⠉⠉⠉⠉⠉⠛⠛⠻⠿⣿⣟⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠦⣄⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠘⠉⢛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣠⣶⣿⣿⣿⣿⠟⠁⣤⣬⡏⢼⠿⠋⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠛⢿⣥⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠻⣷⣦⡀⠀⠇
⠀⠀⠀⠀⠸⠸⠿⠉⠅⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣼⣧⣤⣤⣾⣿⣿⣿⣿⣿⠋⣀⣀⣀⠀⠀⠤⠄⠒⠂⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠠⡍⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣿⣵
⠀⠀⠀⠀⠈⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⢿⣦⡹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠗
⣶⣭⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⣸⣿⣿⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⠟⢋⣉⣉⣁⣀⣭⣭⣶⣿⣿
⣿⣿⣿⣿⣟⣈⣛⣛⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⣀⣤⣤⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣏⠿⡥⡿⢸⣭⣇⣿⣩⣶⣒⣀⠈⠛⣵⣶⢶⣮⣭⣩⣙⣟⢛⣛⣛⡛⠻⠿⠿⠿⢿⡿⠉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠙⠛⠻⢶⣶⣦⣬⣬⣭⣭⣭⣍⣉⣉⣛⣃⣛⣛⠛⠛⠟⠀⠈⠉⠉⠉⠀⠛⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⡿⣿⣿⠿⠿⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠉⡭⠿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⠘⠀⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⡤⣤⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⣉⣃⣸⣿⢰⣶⣦⢸⣿⡇⢻⣿⣿⣿⠙⣿⣿⢛⣛⡛⢿⣿⡟⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠈⠛⠻⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣷⣿⣿⣿⣿⣤⣭⣭⣼⣿⣧⣨⠀⠙⡟⣃⣿⣿⠘⠿⠟⢻⣿⡇⠬⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣁⠯⠉⠁⢈⡉⠛⠛⠛⠛⠻⠿⠿⠿⠷⠶⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠍⠁⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣦⠀⣀⣀⢀⡀⠀⣀⣠⡊⠒⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⣤⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⡟⣻⣿⣿⣿⡄⠀⠀⠀⡨⢞⠍⠉⠉⠉⠉⠉⠉⠁⠀⠀⠒⠂⣿⡇⠀⠠⠀⠤⠤⠤⠠⠤⠄⠀⠀⣀⣀⣀⣀⣾⣿⣷⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠛⢿⣿⣷⣤⢔⠃⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠀⠀⠀⠀⠀
⠀⠛⠁⠟⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣿⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣹⡇⠀⠀⠀⣴⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⡴⠀⠀⠟
⠀⠀⠀⠀⠀⡀⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⠿
⠀⠀⠀⠀⠀⠄⠉⢸⣿⠿⠿⠿⣿⣿⣮⣿⡿⣛⣻⣟⢛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢸⣿⢺⣿⣿⣿⣿⣹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠇⠀⠀
⠀⠀⠀⠀⠀⢐⣀⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⣀⠀⠀⢠⣤⣶⣶⡄⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⢀⣿⣿⣿⣿⣷⡄⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢨⣭⣉⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢹⣽⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣯⢺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠛⠓⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣸⣿⡔⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⠉⠉⠛⠛⠛⠛⠛⢛⣿⣟⣋⣉⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠿⡷⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⢄⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠋⢉⠉⣉⣁⡀⠀⠀⠀⠀⠀⢸⣿⡟⠈⠉⠉⠉⠉⠉⠛⠛⠿⣿⣟⡛⠙⣿⣾⣿⣿⣿⣿⣷⣾⣿⣿⠲⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢘⣓⣛⣓⡂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢘⡇⠀⠀⠀⣠⣴⣿⣿⣿⣿⡟⠁⢠⣬⡏⢸⠿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠙⢿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣦⣄⠀⠀
⠀⠀⠀⠀⢐⠑⠻⠏⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣼⣧⣤⣤⣾⣿⣿⣿⣿⣿⠋⣀⣀⣀⠤⠀⠤⠒⠒⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠭⠅⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⢈⠻⣦⡙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠁⠉⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣸⣿⣿⡇⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡛⠟⠋⣉⣩⣡⣀⣬⣭⣷⣿⣿
⣍⡙⠛⠛⠋⠐⠸⣿⣿⣟⣿⡻⣿⣿⢿⡿⢿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⣄⣀⣀⣤⣤⣽⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣆⡀⠀⠀⢨⣅⣀⣙⣋⣃⣷⣿⣸⣤⠸⠸⣯⣇⣿⣏⣖⣲⣐⠀⠐⢭⣷⣶⣶⣭⣏⣭⣭⢛⣛⣛⡛⣛⠛⠻⠿⠿⠿⠥⣄⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠛⠛⠷⣶⣶⣶⣦⣤⣬⣭⣭⣭⣍⣙⣋⣛⣛⣛⠛⠛⠀⠀⠉⠉⠉⠀⠙⢿⣿⣿⣿⣿⣿⠿⠿⢿⠿⢿⠿⠿⠿⢿⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣁⠁⠈⠭⠿
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀
⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⡤⢤⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣭⣍⣸⣿⠀⣶⣶⠘⣿⣇⢸⣿⣿⣿⡍⣿⣿⠉⣉⡙⢻⣿⡟⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣷⣾⣿⣿⣿⣦⣤⣭⣬⣿⣯⣬⡀⠈⠻⣃⣿⣿⡀⠛⠟⢻⣿⡇⠠⠬⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡉⠿⠍⠀⢀⡍⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠛⠛⠉⠉⠁⠀⣽⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠍⠁⠀⠀⠀⠀⠀⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⡿⢿⣿⣿⣿⣿⣿⣷⡤⠤⠄⠐⠤⠀⢄⣀⡀⣀⡀⣀⡠⡚⠚⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣠⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠍⠈⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢹⡇⠐⠒⠂⠠⠄⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⣼⣿⣷⣾⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⣠⠤⠋⠊⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠀⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠖⠁⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠀⠀⣰⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢠⠃⠀⠿
⠀⠀⠀⠀⠀⠀⣉⢸⣿⣿⣿⣿⣿⡿⣿⣿⣻⣷⣌⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⠿
⠀⠀⠀⠀⠀⠄⢘⢸⣿⠿⠿⠿⣿⣿⣏⣟⣿⣛⣻⣏⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠒⢸⣿⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢻⡿⠿⠿⠿⠿⠿⠿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⣀⣀⠀⠀⢠⣤⣶⣶⡄⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠨⣛⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣧⣔⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣍⣉⣭⣭⣭⣍⣭⣭⣭⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢹⣽⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⠓⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣷⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣸⣿⡖⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⡛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠙⠛⠛⠛⠛⢛⣿⣟⣋⣉⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠿⡧⠾⠾⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢄⢀⡄⣤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠋⢉⠉⣉⣁⡀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⡛⠉⣻⣾⣿⣿⣿⣿⣷⣶⣿⣿⡲⢦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣛⣚⣓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣴⣿⣿⣿⣿⡿⠁⢠⣬⡿⢰⠿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠙⠻⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⣿⣦⣄⠀⠀
⠀⠀⠀⠀⠀⠑⠻⠙⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣼⣧⣤⣤⣾⣿⣿⣿⣿⣿⠏⢀⣀⣀⠠⠀⠤⠒⠒⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠰⠔⠀⠀⠀⠀⠀⠀⠀⢈⠻⣶⣌⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠉⠈⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣸⣿⣿⡇⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣹⠟⠋⣉⣩⣡⣄⣤⣭⣵⣿⣿
⠉⠙⠛⠛⠛⠐⠘⣿⣻⣟⣿⣻⣿⣿⢿⡿⢿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣄⣀⣀⣤⣤⣽⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⢠⣴⣋⣛⣏⣉⣷⣿⣸⣥⠸⠹⣯⣏⣿⣯⣥⣲⣆⡀⠀⢯⣷⣶⣦⣭⣭⣍⣭⣛⣛⣛⡛⢛⢛⠿⠿⠿⠿⠧⣄⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠙⠛⠷⣶⣶⣶⣦⣤⣬⣭⣭⣭⣍⣉⣋⣛⣛⣛⡛⠛⠀⠀⠈⠉⠉⠁⠙⢿⣿⣿⣿⣿⣿⠿⠿⢿⠿⠿⠿⡿⣿⢿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣭⣄⣀⣀⣀⣀⣀⣀⣀⣀⠁⠈⡩⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠿⠿⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡠⠤⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⢩⣍⣼⣿⠀⣶⣶⠈⣿⣧⢸⣿⣿⣿⡏⣿⣿⠋⣉⣉⢻⣿⡟⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⣿⣾⣿⣿⣿⣶⣤⣬⣤⣿⣿⣬⡄⠈⠻⢃⣻⣿⣀⠛⠛⢹⣿⡧⠠⠬⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⠹⠍⠀⢀⡍⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠷⠶⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠃⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠭⠁⠀⠀⠀⠀⠀⢘⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⣤
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠠⠤⠤⠤⠄⠐⠤⠤⠀⣀⠀⣀⣀⣀⡠⣚⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣤⣶⣿⣿⣿⣿⣿
⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠒⠀⠀⠀⠀⢀⣠⠖⠍⠈⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢻⣿⠐⠒⠂⠠⠤⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⣼⣿⣿⣾⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⡈⠛⠋⣛⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠓⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀⡀⠀⠀⠀⠀⠀⢀⡄⠜⠫⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣰⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢠⠂⠀⠼
⠀⠀⠀⠀⠀⠈⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣎⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⠾
⠀⠀⠀⠀⠀⠄⢙⢸⣿⠿⢿⡿⣟⣿⣿⣿⣿⣿⣻⣿⡛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠐⠺⢹⣿⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢻⡿⠿⠿⠿⠿⠿⠿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⣀⠀⠀⢠⣴⣶⣶⡄⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⡀⣾⣿⣿⣿⣧⣔⡀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣭⣉⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⠓⢚⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣦⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣤⣤⣸⣿⡖⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⠉⠉⠙⠛⠛⠛⠛⢛⣿⣟⣋⣉⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⡿⠿⢷⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⣠⣤⣤⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠛⢉⡉⣉⣀⡀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣛⠉⣻⣾⣿⣿⣿⣿⣿⣷⣿⣿⡳⢦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣛⣛⣁⣚⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡏⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠋⢠⣬⡿⢰⠿⠏⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠉⠻⣦⣝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⢿⣶⣄⠀⢰
⠀⠀⠀⠀⠀⡹⡿⠟⠠⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣧⣤⣤⣾⣿⣿⣿⣿⣿⠏⢀⣀⣀⡠⠄⠤⠒⠒⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠭⠍⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠁⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠠⠶⠂⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿
⠉⠈⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣸⣿⣿⡧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣽⠿⢋⣉⣩⣥⣄⣠⣭⣵⣿⣿
⠉⠙⠛⠛⠛⠁⠘⣿⣿⡿⣿⣟⣿⣿⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣄⣀⣀⣤⣤⣼⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠄⢠⣮⣕⣏⣛⣉⣿⣾⣸⣯⣸⠻⣯⣯⣿⣯⣥⣶⣖⣂⠐⢻⣷⣶⣶⣭⣯⣭⣭⣛⣛⣛⣛⢛⣛⠻⠿⠿⢿⠧⢄⣈⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⣂⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠙⠛⠷⣶⣶⣶⣦⣥⣬⣭⣭⣭⣭⣉⣋⣙⣛⣛⡛⠛⠀⠀⠈⠉⠉⠁⠙⢻⣿⣿⣿⣿⣿⠿⠿⠿⡿⠿⠿⡿⣿⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣭⣄⣀⣀⣀⣀⣀⣀⣀⣉⡉⠉⡩⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠿⠿⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⡠⢤⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⢨⣭⣨⣿⡄⣶⣶⡀⣿⣿⢸⣿⣿⣿⡏⣿⣿⡋⣉⣙⢻⣿⡟⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣥⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⣿⣾⣿⣿⣿⣷⣦⣬⣤⣿⣿⣬⡄⠈⢻⢋⣻⣿⣇⠛⠛⢹⣿⡿⠠⠤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠸⠍⠈⢀⡍⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠶⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠓⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣠⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠬⠁⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠠⠠⠤⠤⠤⠤⠴⠦⠤⢤⣀⣀⣀⣀⣀⡠⣚⣓⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣤⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠄⠀⠀⠚⠀⠀⠀⠀⠀⣠⠖⠭⠈⠉⠈⠉⠉⠉⠉⠉⠁⠉⠀⢻⣿⠐⠒⠒⠤⠤⠤⠤⠤⠤⠤⠄⢄⣀⣀⣀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠋⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡤⠔⠫⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⢀⠀⠀⣰⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⢠⠆⠀⠸
⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣝⣭⣭⣭⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠾
⠀⠀⠀⠀⠀⠠⢈⣸⣿⡛⢛⣛⣛⣿⣿⣿⣿⣿⣻⣿⣉⣉⣉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣯⣵⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣠⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣤⣤⣤⡀⠀⢠⣶⣶⣶⡆⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠄⣸⣿⣿⣿⣷⣶⡆⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣀⣤⣤⣼⣤⣤⣤⣤⣾⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⠛⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡞⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣤⣤⣤⣿⡇⣁⣀⣀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠿⡛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡿⠉⠉⠉⠉⠙⠛⠛⣉⣹⣿⣛⣁⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠼⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⢀⣄⢤⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠋⢉⡁⢀⣠⡤⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⣿⣏⡉⣻⣷⣿⣿⣿⣿⣿⣿⣿⣾⡛⢶⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣘⣒⣉⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠋⠠⢾⠿⠀⠿⠏⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠻⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣷⣤⡀⢈
⠀⠀⠀⠀⠀⠙⡟⠉⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣿⣤⣤⣾⣿⣿⣿⣿⣿⠟⢀⡠⠤⠤⠄⠐⠒⠂⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⡙⢷⣌⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⠀⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣿⢿⣿⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣜⠻⠉⢭⣥⣤⣤⣠⣶⣾⣿⣿
⠉⠉⠙⠉⠉⠁⠈⠿⠿⣿⣻⣿⣻⣿⣛⡻⢿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡂⢀⣤⣴⣧⣿⣽⣛⣾⣹⣧⣼⣇⣯⣿⣼⣿⣦⣤⣴⣆⡐⠰⢿⡞⣾⣭⣭⣭⣭⣍⣉⣙⣛⢛⣛⣛⣛⠛⠿⠧⢤⣄⣀⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉⠛⠳⢶⣶⣶⣶⣶⣤⣤⣬⣭⣭⣭⣭⣈⣙⣛⣛⣙⡃⠀⠀⠈⠉⠀⠈⠹⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣈⡠⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⢛⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠶⣤⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢨⣭⣤⣿⡇⣿⣿⡆⣿⣿⠈⣿⣿⣿⣇⢹⣿⡏⣭⣭⢙⣿⣿⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⠿⠿⠿⣿⣿⣷⣶⣶⣤⣿⢿⣤⣅⠀⢙⢋⣸⣿⣇⣛⣛⢉⣿⣿⠐⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠏⠀⠀⣤⠈⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⣿⣷⣶⣦⣤⣤⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠒⠲⠤⠤⠤⠀⣀⣀⣀⣤⣚⣁⣁⢀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⣢⣤⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠀⠀⠘⠃⠀⠀⠀⢀⣀⠖⠼⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⣿⠐⠒⠒⠒⠒⠂⠒⠠⠤⠤⠤⢤⣤⣄⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢖⠋⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡀⠀⠀⣴⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠉⠀⠀⠀⠀⠀
⠐⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡤⠔⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣀⠀⠀⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⡀⠀⢀⠎⠀⠸
⠀⠀⠀⠀⠀⠀⢁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣝⣭⣭⣭⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠾
⠀⠀⠀⠀⠀⠠⢈⣸⣿⡛⠛⣛⣛⣿⣯⣿⣿⣿⣻⣿⣉⣉⣩⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠂⢹⣿⣿⣿⣿⣿⣿⣯⣵⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣪⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣤⣤⣤⡀⠀⢠⣶⣶⣶⣆⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢠⢺⣿⣿⣿⣿⣧⡆⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣲⣀⣤⣤⣼⣤⣤⣤⣴⣾⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣤⣤⣤⣿⡇⣁⣀⣀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⢿⡿⡻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡿⠉⠉⠉⠉⠙⠛⠛⣉⣻⣿⣛⣁⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠯⠿⠾⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⣀⣄⢤⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠋⢉⡁⣀⣠⡤⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⣿⣏⡉⣻⣷⣿⣿⣿⣿⣿⣿⣿⣾⡛⢶⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣐⣒⣉⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠋⠠⠾⡿⠀⠿⠏⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠈⠻⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣷⣤⡀⢐
⠀⠀⠀⠀⠀⠙⡟⠉⠁⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣿⣤⣤⣾⣿⣿⣿⣿⣿⠟⢀⡠⠤⠤⠄⠐⠒⠂⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⡙⢷⣄⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⠀⠁⠁⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣿⢿⣿⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣜⠻⠉⣭⣥⣤⣤⣠⣶⣾⣿⣿
⠉⠉⠙⠉⠉⠁⠈⢿⠟⣟⣿⣿⣻⣿⣛⡿⢿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡂⠀⣤⣤⣭⣿⣽⣻⣾⣹⣷⣼⣇⣯⣿⣽⣿⣤⣽⣤⣤⡐⠲⢿⡟⣿⣭⣭⣭⣭⣍⣉⣋⣛⢟⣛⣛⣻⠛⠿⠧⢤⣄⣀⡩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉⠙⠻⢶⣶⣶⣶⣶⣦⣤⣬⣭⣭⣭⣭⣈⣙⣛⣛⣛⡃⠀⠀⠀⠁⠀⠘⠻⣿⣿⣿⣿⣿⡿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⡿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣈⡠⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⢛⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠶⣤⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢨⣭⣤⣿⡇⣿⣿⡆⣿⣿⠈⣿⣿⣿⣇⢹⣿⡏⣭⣭⢙⣿⣿⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⠿⠿⠿⣿⣿⣷⣶⣶⣤⣿⢿⣤⣅⠀⢙⢋⣸⣿⣇⣛⣛⢉⣿⣿⠐⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠍⠀⠀⣤⠈⠉⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⣿⣷⣶⣦⣤⣤⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠒⠲⠤⠤⠀⠀⣀⣀⣀⣤⣚⣁⡁⢀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⣢⣤⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠀⠈⠘⠁⠀⠀⠀⢀⣀⠖⠼⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⢹⣿⠐⠒⠒⠒⠒⠒⠂⠠⠤⠤⠤⢤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢖⠋⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡀⠀⠀⣴⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠉⠀⠀⠀⠀⠀
⠐⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡤⠔⠋⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣀⡀⠀⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⡀⠀⢀⠆⠀⠘
⠀⠀⠀⠀⠀⠀⢸⡕⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⣿⣿⡿⣿⣿⡿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠰⢈⡇⣿⡟⣛⣛⣛⣿⣿⣽⣿⣿⣯⣿⣍⣭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣯⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠺⠁⣿⡇⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣤⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣤⣤⣤⡄⠀⢀⣶⣶⣶⣶⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡴⣸⣿⣿⣿⣿⣶⡆⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣶⣤⣶⣶⣶⣦⣤⣶⣴⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢼⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣷⣁⣀⣀⣠⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣻⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠉⠉⠉⠉⠉⠋⢉⣉⣽⣿⣯⣥⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠼⠻⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⡒⣶⣶⡖⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠋⢁⡠⢠⣤⡤⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠉⠉⠉⠛⠻⣿⣯⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠳⣦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢉⣁⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠋⠀⠶⠿⠃⠟⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠘⡻⠛⠙⠀⠀⣀⣠⣤⣤⣤⣤⣤⣦⣤⣿⣤⣶⣾⣿⣿⣿⣿⣿⠟⠀⠤⠤⠤⠀⠐⠒⠂⠉⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⢙⢿⣦⡙⢻⢿⣿⣿⣿⣿⡿⢿⣿⣿⠿⢛
⣀⣀⣀⣀⣀⡀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣿⣿⣿⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡛⠉⣭⣤⣤⣤⣤⣶⣶⣿⣿
⠈⠉⠉⠉⠉⠁⠁⢻⡿⣿⣻⣿⢻⣿⡟⡟⠛⣿⣿⣿⢿⣿⡿⠿⠿⣿⣿⣿⡋⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣐⠀⣤⣤⣬⣽⣭⣼⣾⣃⣷⣆⣇⣿⣾⣸⣿⣥⣥⣼⣄⡀⠀⡾⠿⢿⣭⣭⣭⣭⡏⣭⣭⣭⣉⣛⣛⣛⣛⡛⠛⢤⣤⣤⡬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠉⠉⠛⠿⣶⣶⣶⣶⣶⣶⣦⣤⣥⣬⣭⣭⣭⣍⣉⣙⣃⣀⣈⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠛⠿⠿⠿⠿⠿⡿⠟⠿⠿⠻⡿⠿⠿⠿⠿⡿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣈⡨⠖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢛⣛⡻⣿⡿⠿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠶⢦⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠠⣭⣥⣿⡇⢸⣿⡇⢹⣿⡄⣿⢿⣿⣷⢸⣿⡏⢩⣭⣉⣿⣿⠉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠿⣿⣶⣶⣶⣾⣿⣧⣴⡀⢉⣋⣼⣿⣧⣘⣛⣋⣿⣿⡀⠲⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠛⠋⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠓⠈⠀⣠⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⣴⣦⣤⣴⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠂⠒⠀⠀⠒⠒⠒⠲⠦⠤⠤⠤⣀⢀⣤⣮⣁⣁⣀⡀⡀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣸⣧⣴⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⠈⠈⠁⠀⠀⠀⢀⡀⡞⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠙⣿⡄⠒⠒⠒⠒⠒⠒⠒⠦⠤⠤⠤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⢖⠪⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⠀⠀⣰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀
⠐⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤⢐⠋⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣿⣇⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⡞⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠰⠀⠅⣿⡟⢛⣛⣛⣻⣿⣾⢿⣿⣟⣻⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠘⠀⣿⡏⣿⣿⣿⣿⣿⣻⣿⣽⣽⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠁⠀
⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⣄⠀⠀⣶⣶⣶⣶⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣖⣰⣿⣿⣿⣿⣾⣧⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢢⣆⣴⣦⣶⣦⣤⣶⣶⣼⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⢥⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⠿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣟⣿⣿⣿⣿⣯⣽⣿⣷⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣤⣤⣼⣿⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣯⣿⢿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠏⠉⠉⠉⠉⠋⠉⣉⣹⣿⣯⣥⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠻⠻⠿⠳⠛⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⠀⢲⠒⡄⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠛⢉⣠⢠⣤⡤⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣯⡉⣘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⡓⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢩⡍⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⢀⣴⣿⣿⣿⣿⣿⠋⠀⠴⠷⠇⠞⠛⠁⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠉⠻⣦⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⣿⣶⣄⣀
⠀⠀⠀⠀⠀⢈⢹⠋⠁⠀⠀⣀⣠⣤⣤⣤⣤⣤⣴⣤⣾⣷⣶⣶⣿⣿⣿⣿⣿⡿⠁⠤⠤⠤⠒⠐⠒⠂⠈⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈⠻⣧⡜⢛⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⢟
⣀⣀⣀⣀⣀⣀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣿⣿⣿⣇⣀⣤⡄⠀⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⠈⢻⣶⣙⠋⢩⣤⣤⣤⣤⣶⣶⣿⣿
⠀⠉⠉⠉⠉⠉⠀⠹⣿⣟⣻⣿⣿⡿⣟⣿⠛⣻⢛⣿⡿⣿⣿⠿⠿⠿⣿⣿⡏⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣐⠀⣤⣤⣤⣼⣭⣼⣷⣇⣛⣖⣛⣸⣾⣻⣿⣥⣤⣥⣤⣎⠁⠾⠿⢻⣧⣬⣭⣽⣭⣩⣍⣭⡍⣙⣛⣛⣛⣛⠛⠠⣤⣤⣤⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠈⠉⠙⠻⣶⣶⣶⣶⣶⣶⣶⣦⣤⣬⣭⣥⣭⣭⣉⣉⣋⣀⣀⣀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡿⠛⠟⠿⠿⠿⠿⠟⠟⠻⠿⠛⠿⠿⠿⠿⠿⠿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠛⣛⡛⢿⣿⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠶⢲⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠂⣬⣥⣼⣿⢸⣿⣷⢸⣿⡇⣿⠿⣿⣿⡈⣿⣿⢨⣭⣍⣻⣿⡍⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⠿⠿⠿⣶⣶⣶⣾⡿⣧⣴⠀⢈⣋⣅⣿⣿⣈⣛⣋⣹⣿⡇⠒⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠓⠀⠀⢠⡄⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠻⠿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⡿⠶⡦⡤⣤⣤⣴⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⡒⠒⠂⠤⠀⠄⢀⢀⡤⣴⣉⢉⣀⣀⡀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⣯⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁⠠⠀⠀⠈⠁⠀⠀⠄⠀⡀⠔⠫⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠉⣿⡇⠀⠐⠐⠒⠒⠒⠒⠒⠀⠀⠠⢤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠴⡨⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⠀⠀⣰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠀⠀⡀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣠⠔⠋⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣇⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⢀⠀⠀⡼⠁⠀
⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿
⠀⠀⠀⠀⠀⠰⠂⣩⣿⣟⢛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣏⣩⣭⣭⣭⣭⣭⣭⣭⣭⣯⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠙⠐⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠃⠀
⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣤⣤⣤⣤⣤⠀⠀⣴⣶⣶⣶⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⢲⣿⣿⣿⣿⣷⣮⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢲⣦⣴⣶⣶⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣤⣤⣼⣿⣈⣀⣀⣠⣤⣤⣤⣤⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⣉⣩⣿⣿⣥⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⠟⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⡖⢲⡲⡔⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠛⢉⣠⢀⣤⣤⠄⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠈⠉⠉⠙⠻⢿⣯⡉⣘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⡓⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⣉⣉⢁⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⡃⠀⠀⢀⣴⣾⣿⣿⣿⣿⠏⠀⠴⠷⠇⠸⠛⠁⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠉⠻⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⣿⣶⣄⣀
⠀⠀⠀⠀⠀⢸⢹⠋⠉⠀⠀⣀⣀⣤⣤⣤⣤⣤⣴⣤⣼⣷⣶⣶⣿⣿⣿⣿⣿⡿⠁⠤⠤⠤⠖⠀⠒⠊⠉⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣷⡜⢛⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⢟
⣀⣀⣀⣀⣀⣀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣸⣿⣿⣇⣀⣤⠄⠀⠀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⠀⠈⠻⣾⣟⠋⠩⣥⣤⣤⣤⣶⣶⣿⣿
⠀⠉⠉⠉⠉⠉⠀⠹⣿⣿⣻⣿⣟⡿⣟⣻⠛⣻⣻⣿⡿⣿⣿⠿⠿⠿⣿⣿⣏⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣐⠀⢠⣭⣭⣼⣯⣿⣷⣏⣛⣒⣻⣸⣾⣧⣿⣭⣯⣿⣶⣄⠐⠾⠿⢻⣧⣬⣭⣭⣯⣩⣭⣭⡋⣙⣛⣛⣛⣛⠛⠤⣤⣤⣤⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠈⠉⠛⠻⣶⣶⣶⣶⣶⣶⣶⣦⣤⣬⣭⣭⣭⣭⣉⣉⣓⣀⣀⡀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠿⠿⣿⣿⠿⠿⠟⡿⠿⠿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠛⣛⡛⢿⣿⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠶⢶⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⣭⣥⣼⣿⢸⣿⣷⢸⣿⡇⢹⠿⣿⣿⡀⣿⣿⢩⣭⣍⣻⣿⡏⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠿⠿⣿⣶⣶⣶⣾⡿⣧⣴⠀⢈⣉⣥⣿⣿⣈⣛⣋⣹⣿⡇⠒⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⠀⠀⢠⡄⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠈⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⡿⠷⣷⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠢⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠒⡒⠒⠂⠤⠤⠤⢄⡀⣤⣔⣍⣉⣀⣀⣀⡀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣯⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁⠠⠀⠀⠈⠉⠀⠀⠄⠀⣀⢴⠋⠂⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠉⣿⡇⠀⠒⠒⠒⠒⠒⠒⠒⠂⠤⠠⢤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠴⡺⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⡀⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⡀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⣠⠤⡛⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣿⣇⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠉⠀⠀⠀⢀⠂⠀⡰⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⡉⣿⣟⢛⣛⣛⣻⣿⣾⣿⣿⣋⣿⣏⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠐⠈⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠃⠀
⠀⠀⠀⠀⠀⠀⢀⣄⣽⣿⢸⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣄⠀⠀⣴⣶⣶⣶⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⢢⣿⣿⣿⣿⣷⣦⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣆⣠⣤⣤⣦⣤⣴⣦⣼⣿⣿⣟⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣦⣿⣿⣿⣷⣿⣿⣿⣿⣿⣽⣿⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣤⣤⣼⣿⣈⣀⣀⣀⣠⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠏⠉⠉⠉⠉⠛⠉⣉⣉⣿⣿⣭⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠄⢢⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠟⠉⣀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⡉⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⡓⣦⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡁⡊⢁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⢀⣤⣾⣿⣿⣿⣿⠏⠀⠴⠷⠇⠸⠿⠁⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠙⠻⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⣿⣖⣄⣀
⠀⠀⠀⠀⠀⠈⠹⠋⠁⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣼⣧⣤⣴⣿⣿⣿⣿⣿⡿⠁⠠⠤⠤⠤⠀⠒⠒⠈⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣧⡝⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⡁⠀⢀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣸⡿⣿⣇⣀⠤⠄⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠈⠻⣶⡛⠋⠩⣥⣤⣤⣤⣶⣶⣿⣿
⠀⠉⠉⠉⠉⠉⠀⠹⣿⣿⣻⣿⣟⣿⣟⣻⠛⣻⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣐⠀⢠⣤⣭⣽⣯⣽⣳⣋⣻⣶⣿⣸⣽⣧⣿⣥⣿⣥⣕⡊⠐⠾⣿⢻⣯⣭⣭⣭⣯⣩⣉⣉⡛⣛⣛⣛⣛⣛⠻⠤⣤⣤⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠈⠉⠉⠛⠿⣶⣶⣶⣶⣶⣶⣤⣤⣤⣭⣭⣭⣭⣉⣉⣋⣓⣀⡀⠀⠉⠉⠁⠙⣿⣿⣿⣿⣿⣿⠛⠿⠟⠻⠿⣿⡿⢿⠿⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠍
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠛⣛⡛⢿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠴⢢⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⣭⣥⣼⣿⢸⣿⣷⢸⣿⡇⢹⡿⣿⣿⡈⣿⣿⢩⣭⣍⣻⣿⡏⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⣾⡿⣧⣬⡀⢈⣙⣁⣿⣿⣘⣛⣋⣹⣿⡇⠲⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠛⠛⠛⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠟⠀⠁⢠⡄⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠈⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⣿⣦⣶⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠂⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡒⡒⠒⠀⠤⠤⢀⣀⣀⣠⣔⣉⣈⣀⡀⡀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣯⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠄⠀⠀⠉⠀⠀⠄⠀⣀⠰⠫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⡇⠐⠒⠒⠒⠒⠒⠂⠠⠤⠤⠤⢤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⡚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⠀⠀⢠⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡤⠛⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣇⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⢀⠀⠀⣰⠃⠀
⠀⠀⠀⠀⠀⠀⢨⠫⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠰⠀⡃⣿⡟⢛⣛⣛⣻⣿⣽⣿⣿⣯⣿⣍⣉⣭⣭⣭⣭⣭⣽⣭⣽⣽⣿⣿⣽⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⢨⣤⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⣄⠀⠀⣶⣶⣶⣶⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡔⣶⣿⣿⣿⣿⣶⣷⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⣦⣆⣰⣤⣴⣦⣤⣴⣴⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣤⣤⣿⣿⣁⣀⣀⣀⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠏⠉⠉⠉⠉⠛⠉⣉⣹⣿⣿⣥⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣐⣤⡔⡄⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠛⢉⣠⢀⣤⣤⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣯⣉⢙⣿⣾⣿⣿⣿⣿⣿⣿⣷⣟⠳⣦⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⢁⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⠋⠀⠴⣿⠇⠾⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠙⠿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠈⠹⠛⠁⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣴⣿⣿⣿⣿⣿⡿⠁⡠⠤⠤⠄⠐⠒⠂⠈⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣦⡹⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⡁⠀⡀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣿⣿⣿⣇⣀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡛⠋⢩⣥⣤⣤⣤⣶⣶⣿⣿
⠈⠉⠉⠋⠉⠉⠀⠛⣿⣿⣿⣿⣿⣿⣟⣛⠛⣻⢿⣿⡿⣿⡿⠿⣿⣿⣿⣿⡛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣴⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣐⠀⣤⣬⣥⣼⣯⣽⣗⣃⣿⣖⣟⣺⣼⣻⣿⣽⣿⣤⣥⣂⠰⠾⡿⢿⣯⣭⣭⣭⣭⣩⣍⣭⣿⣛⣛⣛⣛⡛⠿⢤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠀⠈⠉⠉⠛⠿⣶⣶⣶⣶⣶⣶⣦⣤⣬⣭⣭⣭⣍⣉⣉⣛⣓⣀⣀⠀⠈⠈⠉⠙⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣁⣀⣀⡁⠝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠛⣛⡻⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠠⠶⢦⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⣭⣥⣼⣿⢸⣿⣧⢸⣿⡇⣿⠿⣿⣿⡸⣿⣯⢩⣭⣍⣿⣿⡋⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⣾⣿⣧⣵⡀⢈⣋⣉⣿⣿⣘⣛⣋⣻⣿⡇⠶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠟⠀⠁⣠⠌⠉⠉⠙⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠈⠁⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⣿⣶⣶⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠲⠂⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠂⠀⠀⠐⠒⡒⠒⠤⠤⠤⢀⣀⣀⣤⣴⣁⣉⣀⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⣯⣤⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⠀⠈⠁⠀⠀⠄⠀⣀⠴⠫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡇⠒⠒⠒⠒⠒⠒⠒⠠⠤⠤⠤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡴⡺⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⠀⠀⣰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠉⠀⠀⠀⠀⠈
⠐⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠛⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣇⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⡼⠁⠐
⠀⠀⠀⠀⠀⠀⢠⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠐⠀⡃⣿⡟⣛⣛⣛⣻⣿⣿⣿⣿⣻⣿⣍⣉⣭⣭⣭⣭⣭⣭⣭⣭⣽⣯⣯⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠼⠀⣿⡇⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣤⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⣄⠀⢀⣶⣶⣶⣶⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⣺⣿⣿⣿⣿⣷⣆⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣶⣠⣴⣦⣴⣦⣤⣴⣴⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣷⣁⣀⣀⣀⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠍⠉⠉⠉⠉⠋⠉⣉⣹⣿⣯⣥⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠴⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣐⣔⣴⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠋⢉⡀⢠⣤⡤⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠈⠉⠉⠉⠛⠻⣿⣏⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠳⣦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢉⢙⣉⣉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣙⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠀⠶⡿⠃⡿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠙⢿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠌⠝⠉⠁⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣿⣤⣴⣶⣿⣿⣿⣿⣿⡟⠁⡤⠤⠤⠄⠐⠒⠂⠈⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿
⠀⠀⢀⠀⡀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣦⡹⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛
⠀⢈⡀⠀⢀⡀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣿⣿⣿⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡛⠋⢭⣤⣤⣤⣤⣶⣶⣿⣿
⠈⠉⠉⠉⠉⠉⠁⠻⣿⣿⣻⣿⣻⣿⣟⣛⠟⣿⣿⣿⢿⣿⡿⠿⣿⣿⣿⣿⡛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣴⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡐⠀⣤⣤⣥⣾⣭⣼⣾⣃⣷⣆⣇⣿⣼⣺⣿⣭⣽⣽⣒⡀⠐⡾⡿⣿⣯⣽⣭⣭⡭⣭⣍⣭⣝⣟⣛⣛⣛⡛⢻⢤⣤⣤⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠀⠈⠉⠉⠛⠷⣶⣶⣶⣶⣶⣶⣤⣤⣬⣭⣭⣭⣍⣉⣉⣙⣃⣀⣀⠀⠀⠀⠁⠙⣿⣿⣿⣿⣿⡿⠛⠿⠿⠿⡿⢿⠿⠿⠿⠿⠿⠿⡿⠿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡨⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠛⣛⠻⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠶⢦⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠠⣭⣥⣿⡇⢸⣿⡇⢸⣿⡄⣿⢿⣿⣿⢸⣿⡏⢩⣭⣉⣿⣿⠉⣉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⣾⣿⣧⣵⡀⢉⣋⣸⣿⣧⣘⣛⣋⣿⣿⡀⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠓⠀⠁⣠⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠈⠁⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⢿⣿⣶⣶⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠘⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠀⠀⠂⠂⠀⠀⠐⠒⡒⠒⠤⠤⠤⢀⣀⣀⣤⣲⣁⣁⣀⢀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣰⣯⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⠀⠈⠁⠀⠀⠀⠀⡀⡔⠫⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⡇⠒⠒⠒⠒⠒⠒⠒⠄⠤⠤⠤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣔⡪⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⠀⠀⣰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣦⠔⠋⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣿⣇⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⡀⠀⠀⡞⠀⠀
⠀⠀⠀⠀⠀⠀⢨⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠰⢈⡃⣿⡟⢛⣛⣛⣻⣷⣿⣿⣿⣿⣿⣍⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣬⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⣄⠀⠀⣶⣶⣶⣶⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠄⣸⣿⣿⣿⣿⣷⣆⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣶⣠⣤⣤⣴⣦⣤⣴⣴⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣭⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⡿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠁⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠴⣾⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣧⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣷⣁⣀⣀⣀⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣏⣿⣿⣻⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣿⣿⡿⠉⠉⠉⠉⠉⠋⠉⣉⣹⣿⣯⣥⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠴⠻⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣐⣄⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠋⢉⡀⢠⣤⡤⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠉⠉⠉⠛⠻⣿⣏⣉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠳⣦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢉⢁⡉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠠⢶⡿⠃⠿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠈⡿⠙⠁⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣶⣿⣿⣿⣿⣿⡟⠁⡤⠤⠤⠄⠐⠒⠂⠈⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠲⠔⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿
⠀⠀⢀⠀⡀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣦⡙⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛
⠀⠀⡀⠀⢀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣿⣿⣿⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡛⠋⢭⣤⣤⣤⣤⣶⣶⣿⣿
⠈⠉⠉⠉⠉⠁⠁⠛⡿⢻⣻⣿⣻⣿⡛⣛⠛⣻⢿⣿⢿⣿⡿⠿⣿⣿⣿⣿⡛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣴⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡐⠀⣤⣤⣤⣿⣭⣜⣾⣃⣷⣆⣇⣿⣼⣺⣿⣥⣵⣶⣂⡀⠐⠾⡿⣿⣯⣭⣭⣽⡍⣭⣍⣍⣝⣛⣛⣛⣛⡛⠻⢤⣤⣤⣨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠈⠉⠉⠛⢷⣶⣶⣶⣶⣶⣦⣤⣤⣬⣭⣭⣭⣍⣉⣉⣛⣃⣀⣀⠈⠀⠁⠀⠙⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⠿⠿⢿⠿⠿⠿⠹⠿⠿⠿⣿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡈⠝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠛⣛⠻⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠶⢦⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠠⣭⣥⣿⡇⢸⣿⡇⢸⣿⡄⣿⢿⣿⣿⢸⣿⡏⢩⣭⣉⣿⣿⠉⣉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⣾⣿⣧⣵⡀⢉⣋⣸⣿⣧⣘⣛⣋⣿⣿⡀⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠛⠛⠛⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠓⠀⠁⣤⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠈⠁⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣤⣄⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠘⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠀⠀⠀⠂⠀⠀⠐⠒⠒⠲⠤⠤⠤⢀⣀⣀⣤⣶⣁⣁⣀⣀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⣧⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⠀⠈⠁⠀⠀⠀⠀⡀⡔⠪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡇⠒⠒⠒⠒⠒⠒⠒⠄⠤⠤⠤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢔⡊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠀⠀⠀⠈
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠋⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣿⣇⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⡀⠀⠀⡜⠀⠀
⠀⠀⠀⠀⠀⠠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣥⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠰⢘⣻⣿⠛⣛⣛⣛⣿⣿⣽⣿⣿⣻⣿⣉⣉⣩⣿⣭⣭⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⢾⢿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣨⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣤⣤⣤⣤⡀⠀⢠⣶⣶⣶⡆⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠰⣾⣿⣿⣿⣿⣶⡇⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⣠⣥⣤⣽⣥⣤⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⡍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠴⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣤⣤⣤⣿⣇⣁⣀⣀⣀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡿⠉⠉⠉⠉⠙⠛⠉⣉⣻⣿⣯⣥⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⠿⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⣀⣄⣤⡄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠋⢉⡀⣀⣤⡄⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⣿⣏⢉⣻⣷⣿⣿⣿⣿⣿⣿⣿⣾⣟⢶⣤⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣛⣛⣋⣈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣛⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠋⠠⢾⡿⠀⠿⠏⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠛⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣷⣦⣀⣘
⠀⠀⠀⠀⠀⠛⡿⠟⠹⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣿⣤⣤⣾⣿⣿⣿⣿⣿⠟⢀⡠⠤⠤⠄⠐⠒⠂⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⣄⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠈⠁⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣿⢿⣿⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣝⠻⠉⢭⣥⣤⣤⣴⣶⣾⣿⣿
⠉⠉⠙⠙⠉⠁⠈⣿⣿⣛⣿⣿⣻⣟⣛⡻⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡂⠀⣤⣤⣽⣿⣍⣻⣾⣻⣷⣾⣇⣯⣿⣽⣿⣽⣥⣥⣒⡐⠰⢿⡟⣾⣭⣿⣭⣭⡍⣍⣛⣿⢛⣛⣛⣛⣛⠿⠧⢤⣄⣀⡩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠙⠻⢶⣶⣶⣶⣶⣶⣤⣤⣬⣭⣭⣭⣌⣉⣙⣛⣙⣃⡀⠈⠁⠉⠁⠈⢻⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣉⡩⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⢛⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠶⣤⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢨⣭⣤⣿⡇⣿⣿⡆⣿⣿⠈⣿⢿⣿⣇⢹⣿⡏⣭⣭⣙⣿⣿⢙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⠿⠿⠿⣿⣿⣷⣶⣶⣦⣿⢿⣤⣅⡀⢉⣋⣸⣿⣇⣛⣛⣉⣿⣿⠐⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠁⢀⣤⠈⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣿⣿⣏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⠈⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⠿⠿⠿⣿⣿⣿⣶⣦⣤⣄⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠦⠤⡄⣀⣀⣀⣀⣤⣎⣁⣁⠀⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⣧⣤⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠀⠈⠘⠁⠀⠀⠀⢀⣀⠖⠼⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⢸⣿⠐⠒⠒⠒⠒⠒⠒⠢⠤⠤⠤⢤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢖⡋⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡀⠀⠀⣴⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠋⠁⠀⠀⠀⠀⠉
⠐⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣤⠔⠋⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢨⣿⣀⣀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⡀⠀⢀⡟⠀⠘
⠀⠀⠀⠀⠀⠀⢸⢽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣭⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣠⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠞
⠀⠀⠀⠀⠀⠀⢘⣻⣿⠛⠿⣟⣟⣿⣷⣿⣿⣟⣻⣿⣙⣉⣉⣽⣯⣭⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠔⢺⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣠⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣠⣤⣤⣤⡀⠀⢠⣶⣶⣶⣆⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠠⣾⣿⣿⣿⣿⣶⡆⢠⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣀⣭⣥⣽⣥⣤⣤⣤⣾⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠍⣭⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢐⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣤⣤⣤⣿⡇⣁⣀⣀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡿⠉⠉⠉⠉⠙⠛⠛⣉⣹⣿⣋⣁⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⡿⠼⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⢀⢄⢤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠋⢉⡁⢀⣀⡄⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⣿⣏⠉⣻⣷⣿⣿⣿⣿⣿⣿⣿⣾⣟⢶⣤⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣚⣚⣛⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠠⢶⡿⠁⠿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠛⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣷⣤⡀⣈
⠀⠀⠀⠀⠀⠈⡟⠓⠙⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣿⣤⣤⣼⣿⣿⣿⣿⣿⠟⢀⡀⠤⠤⠄⠐⠒⠒⠈⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⣄⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠈⠉⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣿⢿⣿⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣝⠳⠉⢭⣥⣤⣤⣤⣶⣶⣿⣿
⠉⠉⠙⠛⠉⠁⠈⠿⡿⢿⣿⣿⣛⣛⣛⡿⠿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠀⣤⣤⣬⣟⣍⣻⣾⣻⣧⣿⣇⡿⣽⣸⣿⣷⣼⣅⣒⠀⠰⢾⡗⣶⣭⣭⣭⣭⡍⣛⣛⣻⢛⣛⣛⡛⢻⠿⠧⢤⣄⣀⡩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢂⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠛⠻⢶⣶⣶⣶⣶⣤⣬⣬⣤⣭⣭⣍⣘⣛⣛⣛⣛⡃⠀⠀⠉⠉⠉⠈⠻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠿⠿⠿⢿⢽⣿⡿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣁⡁⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⢛⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠴⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢨⣭⣤⣿⡇⣿⣷⡆⣿⣿⠀⣿⢿⣿⣇⢹⣿⡏⢩⣭⣙⣿⣿⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⠿⠿⠿⣿⣿⣷⣶⣶⣤⣿⢿⣤⣅⠀⢉⢋⣸⣿⣇⣘⣛⣉⣿⣿⠀⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠇⠀⠀⣤⠈⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣿⣿⣏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⠊⠁⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⠿⠿⠿⣿⣿⣷⣶⣤⣤⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠜⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠤⠄⣀⣀⣀⣀⣤⣖⣑⡁⢀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣸⣧⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠤⠀⠈⠘⠁⠀⠀⠀⠀⣀⠔⠨⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠉⢹⣿⠀⠒⠒⠒⠒⠒⠒⠠⠤⠤⠤⠤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢖⡊⠁⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⡀⠀⠀⣴⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠀⠀⠀⠁
⠐⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠔⠋⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⡞⠀⠈
⠀⠀⠀⠀⠀⢀⢈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠞
⠀⠀⠀⠀⠀⠠⢘⣻⣿⠿⢿⣿⣟⣿⣿⣿⣿⣿⣻⣿⣉⣉⣙⣛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠼⢹⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣨⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣠⣤⣤⣤⡀⠀⢠⣶⣶⣶⡆⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣠⣾⣿⣿⣿⣿⣷⡆⢀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣨⣭⣭⣽⣥⣤⣤⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣤⣤⣤⣿⡇⣁⣀⣀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡿⠉⠉⠉⠉⠙⠛⠛⣉⣹⣿⣋⣁⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⠼⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⢠⣄⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠛⢉⡁⢀⣠⡄⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⣿⣏⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⢶⣤⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣚⣚⣛⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠠⢴⡿⠀⠿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠻⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣷⣤⣀⣈
⠀⠀⠀⠀⠀⠛⡟⠛⠩⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣿⣤⣤⣼⣿⣿⣿⣿⣿⠟⢀⡀⠤⠤⠄⠐⠒⠒⠈⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⣌⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠈⠉⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣿⢿⣿⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣝⠻⠉⢭⣥⣤⣤⣠⣶⣶⣿⣿
⠉⠉⠙⠛⠋⠁⠈⢿⢿⣿⣿⣿⣻⣻⣛⡿⢿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠀⣤⣮⣭⣿⣍⣻⣾⣻⣧⣿⣇⣯⣽⣸⣿⣿⣭⣥⣒⡀⠠⣼⡖⣶⣭⣽⣭⣭⡭⣟⣛⣻⢛⣛⣛⡛⢻⠿⠧⢤⣄⣀⡩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢒⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠛⠻⢶⣶⣶⣶⣶⣤⣬⣬⣬⣭⣭⣍⣘⣛⣛⣛⣛⡃⠀⠀⠁⠉⠈⠈⠻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⠿⣿⢿⡿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣁⣄⡩⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⢛⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠴⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢨⣭⣤⣿⡇⣾⣷⡆⣿⣿⠀⣿⢿⣿⣇⢹⣿⡏⢩⣭⣙⣿⣿⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⠿⠿⠿⣿⣿⣷⣶⣶⣤⣿⣿⣤⣅⡀⢉⢋⣸⣿⣇⣛⣛⣉⣿⣿⠀⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠟⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠇⠀⢀⣤⠈⠉⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⡿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⠈⠁⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⠿⠿⠿⣿⣿⣿⣶⣤⣤⣄⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠦⠤⢄⣀⣀⣀⣀⣤⣞⣑⣁⢀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⣧⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠀⠤⠀⠈⠘⠁⠀⠀⠀⢀⣀⠖⠬⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⣿⠀⠒⠒⠒⠒⠒⠒⠦⠤⠤⠤⢤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣖⠊⠁⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⠀⠀⠀⣴⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠉⠀⠀⠀⠀⠉
⠐⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣤⠴⠋⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣿⣄⣀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⡞⠀⠈
⠀⠀⠀⠀⠀⢀⢹⡃⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠾
⠀⠀⠀⠀⠀⠠⠈⡃⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣻⣿⣙⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⠀⠀⠀⠀⠀⠀⢔⠄⣿⡇⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⣿⠛⠿⠟⠛⠛⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠈⣀⣀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣠⣤⣤⡀⠀⢀⣶⣶⣶⣦⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡐⣾⣿⣿⣿⣿⣶⣆⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣮⣍⣭⣭⣽⣭⣭⣭⣭⣼⣿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠍⣯⣽⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠒⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣷⣁⣀⣀⣀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠍⠉⠉⠉⠙⠛⠛⢋⣹⣿⣛⣉⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⡿⠼⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠛⢉⡉⢁⣀⡄⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⣟⢉⢙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⠲⢤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣓⣓⣛⣚⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣻⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠋⠀⢴⡽⠃⡿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⠙⢷⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⣷⣦⡀⢀
⠀⠀⠀⠀⠀⠘⠿⠛⠃⠀⠀⠀⣀⣀⣀⣬⣤⣤⣤⣤⣿⣤⣤⣴⣿⣿⣿⣿⣿⡟⠁⣀⠠⠠⠄⠠⠒⠒⠈⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
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⠉⠉⠙⠛⠛⠃⠀⢻⢿⢿⢿⣿⣛⣛⡻⣿⠿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣴⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠀⣤⣤⣭⣹⣉⣸⣾⣃⣧⣄⡇⣿⣽⣸⣿⣥⣶⣄⣐⠂⠀⣼⡶⣶⣭⣽⣭⣭⡍⣛⣛⣛⢛⣛⡛⣛⠻⡿⠯⢤⣄⣈⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣈⡉⠝
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⣿⣿⣿⣷⣶⣶⣤⣼⣿⣧⣥⠀⢙⣏⣘⣿⣧⣘⡛⠋⣿⣿⠀⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
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⣿⣿⣿⣿⣽⣿⣯⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠊⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣿⣶⣤⣤⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠨⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠤⢄⣀⣀⣀⣀⣠⢔⣑⡉⢀⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣧⣤⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠀⠀⠘⠂⠀⠀⠀⠀⣀⠴⠪⠂⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠘⣿⡔⠒⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⣤⣄⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡚⠑⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⣰⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠉⠀⠀⠀⠀⠁
⠐⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠔⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⣀⠀⠀⡜⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3693

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux news for the past
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posted by Roy Schestowitz on Dec 05, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Snowy_Fountain⦈_


⚓  Updated This Past Day⠀⇛


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⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣈⡀⠀⢸⣿⡿⢛⣭⣔⠫⣿⣽⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣮⠧⣛⣴⣿⣿⢿⢻⡏⣿
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠈⠁⠚⣡⣾⣿⣿⣿⣿⣮⣟⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣾⣿⡿⠿⡉⣿⣷⣾⣌⣇⣛⡽⢿⣽⣻⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣽⣿⡄⠁⢀⠈⠙⠞⠈⠐⡸⣡⢽⡓⣿⣟⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣯⣖⡈⣡⣀⣣⢤⣄⠂⣷⣿⣿⣷⣿⣦⣶
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡄⢀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣼⣿⣿⠋⣷⣿⣿⣿⣿⣿⣿⡯⣿⣀⣉⣉⢯⡿⠉⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠽⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠛⣳⡟⣾⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣿⣿⡿⣿⡿⡷⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣽⣛⡿⣒⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠉⠁⠀⠉⠉⣅⣿⡑⣯⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⢿⡋⢸⣿⣆⣮⣿⣿⣿⣿⣿⣿⣽⣶⣽⣿⣟⡿⣹⣭⣩⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⡃⠀⠀⢸⣿⣷⢰⣿⣿⣿⣿⣿⣧⣄⣼⣛⣻⣼⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠊⣧⡀⣻⡛⣛⣿⣿⣿⣿⣿⣿⣿⣭⡥⣍⡉⡘⠙⡙⢂⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⢀⣶⣤⣾⣿⣷⣶⡄⢰⣇⠀⠀⢸⣟⠛⠚⢛⣿⣭⠁⠀⠉⠉⠉⠉⠉⠁⣳⣿⣿⣿⣿⡿⠟⣿⠿⠷⣿⣿⣿⣷⣯⡄⠘⠝⢺⠿⣿⣿⣿⣿⣟⣿⣿⣿⣾⡷⣾⡿⣿⢿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠇⠼⠿⠭⡭⠍⠬⠩⠇⡜⠃⠀⠀⠘⢻⠲⠀⣾⢿⠿⠶⣶⡆⠀⢐⠐⢰⣄⣿⣿⣏⠉⠀⠀⠀⠈⠈⠀⢁⠽⠂⣁⢸⣷⣀⣠⣾⣿⣿⣿⣽⣿⢻⣿⣻⠿⠟⠛⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⣀⣍⣁⣀⣠⣷⣶⣈⣀⣈⣋⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢿⠻⢯⢿⢻⣷⡶⠶⣬⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣤⢒⣊⣿⡟⠻⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⢃⣀⣀⡀⠀⠀⠒⠀⠀⠀⠀⣀⣴⣄⣀⡁⠁⠙⠉⠰⠤⢀⣯⡄⠀⡄⠀⠀⠀⠀⠀⠁⠀
⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⢦⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣶⣨⣼⣾⣿⣿⣿⣿⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶
⢿⣿⣿⣿⣿⣿⣟⣿⣍⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣏⣩⣿⣿⣿⣿⣆⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣋⣸⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣯⡤⠀⠀⠘⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢻⣿⣹⣿⣿⡟⣾⣟⣿⣿⣿⣿⣿⡿⠟⢿⠯⣉⡐⠙⢽⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⣀⣰⡶⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠙⢛⣻⣿⣿⣿⣿⣛⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠏⠉⠥⢤⣴⠾⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣦⣬⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣿⣟⣟⣿⣿⣛⣘⣰⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4007

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Associate_Sued_Us_for_Publishi.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Associate_Sued_Us_for_Publishi.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Software Freedom Conservancy (SFC)
Associate Sued Us for Publishing Perfectly Accurate Article About SFC; We Sued
Them for Harassment⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024,
updated Dec 05, 2024


For good reasons, for the time being we cannot outline all the pertinent
details, but some people misuse their licence for SLAPP and repeated
harassment. This is why we're suing [1, 2] (tomorrow will be exactly 3 months
since we filed our lawsuits).


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Dude_it's_still_cheaper_than_what_this_lousy_lawyer_charges
                                for_one_hour⦈_


SFC and its associates aren't nice people. Sometimes they act more like
Internet trolls and they defame a lot of people, even this week. Support the
FSF (the real thing), not_the_SFC. This_is_the_article_they_claim_to_be
"defamatory", but all the statements there are true and supported by strong
evidence. █




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

                    ䷩ 𝚕𝚒𝚗𝚎 4091

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Has_Asked_a_Blogger_to_Delete_.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Has_Asked_a_Blogger_to_Delete_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Software Freedom Conservancy (SFC) Has
Asked a Blogger to Delete This Page About the SFC, So We Reproduce It in Full
Here⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


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


Censored article (after pressure from SFC):


§ Repairability Isn't Enough: Why I'm No Longer Supporting Software Freedom
Conservancy⠀➾


⚓  Sat, 30 Nov 2024⠀⇛


This is a copy of a letter I sent to the Software Freedom Conservancy.


Dear Software Freedom Conservancy,


I am writing to express my disappointment and concern over your promotion of
the OpenWrt One. It is disheartening that OpenWrt would develop a device that
requires proprietary software for its WiFi functionality, though not surprising
- this suggests they do not view software freedom as an ethical imperative.
However, what truly let me down was seeing the Conservancy support the
announcement without addressing this critical issue. Instead, the focus was on
GPL compliance and "repairability."


I've noticed a shift in Conservancy's messaging, tying software freedom to
"repairability." This approach is concerning. Richard Stallman didn't launch
the GNU project because UNIX was "broken" or needed to be "fixed." He
recognized proprietary software as an ethical and moral problem - it subjugated
users. Similarly, the primary reason to reject proprietary software today isn't
because we can't "repair" it but because it denies us our freedom.


What good is "repairability" if the software controlling the device isn't ours?
How can we celebrate GPL compliance when the four freedoms are not upheld for
every piece of software the device requires? Software freedom must be a
foundational principle in hardware design, not a secondary consideration.
Anything less is a compromise we cannot afford.


This announcement has led me to rethink my support for the Conservancy. It
seems the organization is veering away from a path of complete software
freedom, instead treating "repairability" - essentially freedom #1 - as if it
were sufficient on its own. But we need all four freedoms to ensure genuine
software freedom, not just the ability to "repair."


As a result, I have decided not to renew my membership. I hope Conservancy can
return to advocating for software freedom as a matter of ethics without
compromises or dilutions. █




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

                    ䷩ 𝚕𝚒𝚗𝚎 4223

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

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    Gemini version at https://techrights.org/n/2024/12/05/Techrights_Does_Not_Forget.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Techrights Does Not
Forget⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


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


Techrights has many anti-censorship mechanisms


HOURS ago we restored/saved a deleted_article_from_another_site. We had made a
copy of it because someone linked to it in IRC and we have bots there to
archive everything that any IRC user links to (about 160 GB of pages since last
year).


Well before Techrights got its name and back when I was still a postgraduate
student I wrote some software to archive everything I had linked to and was
linking to (almost in real time), knowing a lot of it would vanish/change
shortly later and almost certainly go offline (for good) some years later. I'd
occasionally offload these fast-growing archives to external drives for long-
term preservation. A lot of the articles that we linked to regarding Novell and
SCO are long gone and the Internet Archive (steward of Wayback Machine) is
under_attack. Well, I still have those external drives, which were in turn
replicated onto newer external drives.


Remembering history correctly is very important to us because the powerful (and
often corrupt, too) like to rewrite/distort history by silencing/censoring
every voice or narrative that's unflattering to them. █




⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⡿⣿⠿⣿⡏⠋⢻⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣷⠈⠃⠈⢿⠀⠀⠀⠀⠡⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠯⠈⠻⢆⠀⠀⢀⠀⠀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠿⠦⠀⠀⠈⣧⡀⣾⣶⣤⣽⣶⣶⡀⠀⢻⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣦⣤⣠⢦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⠑⡁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡿⢿⠿⠟⠓⠀⡀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠓⠉⠃⠀⠁⠱⠸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡆⢸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠔⠀⠫⠀⠀⠀⠆⠙⢿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣏⡁⠉⠙⠻⠿⠋⠁⠀⠀⠀⠤⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⢸⣿⣿⡃⠀⠀⠀⠀⠛⠐⠢⠤⠀⠀⠐⠀⠹⠀⠘⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⡎⠀⠁⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⢸⣟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⠲⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⠀⠘⡇⢰⡄⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠹⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠁⣸⠃⠀⠀⠀⠀⠐⢀⠠⠋⠀⠀⠀⣀⠀⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢿⣿⣿⡇⢸⣿⣿⣿⣻⣿⡿⠢⠀⣤⡌⣯⣬⠅⢠⡇⢠⠀⠀⢠⣿⢾⣯⣿⣿⡇⢸⣿⣿⡇⠀⢠⠃⡀⠀⠀⠀⠀⠠⠍⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠯⡄⠻⡀⠀⢲⠄⣀⣀⣀⠀⣀⠠⠬⠀⠀⠏⠏⣟⣿⡇⢸⣿⣿⣿⣿⡛⣼⠂⣸⣾⣷⡿⠉⣰⣿⢀⣾⠀⠸⠘⡿⣼⣿⣿⣿⡇⠸⣿⣿⠀⠀⣼⣿⣇⡀⠀⠀⠀⠀⠀⠂⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣷⠤⠊⠂⢑⡀⠀⣘⢧⢐⣲⡒⠢⠽⣯⡉⢰⡞⢞⡌⢸⣿⡇⢸⣿⣿⣿⣿⠀⠇⢠⣿⣿⠿⠃⣼⣿⡇⡼⡇⡄⢀⠇⢼⣿⣿⣿⣿⡇⢸⣿⠏⠀⣰⣿⣿⡟⠁⠀⠠⠀⠀⠀⢀⣀⡷⣫⡍⢻⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢗⡇⠆⣶⡇⠆⢶⣿⠀⡀⠋⠉⠭⢙⠂⠀⡘⠛⠂⢘⣿⣿⡇⢸⣿⣿⣿⡿⢰⠂⣸⣿⣿⣤⣰⣿⣿⢠⢳⡇⡇⡈⠀⣿⣿⣿⣿⣿⡇⢸⣿⠃⣰⡟⡏⠁⡄⢠⠀⠀⠀⠤⢴⣋⠅⢠⣿⣿⠸⣿⢻⣟⣿⣿⡇
⢸⣿⣿⡟⢁⠀⢸⣿⡄⡼⢀⣴⠃⣐⣻⡟⢻⣿⣷⣷⠀⠀⣾⣿⣿⡇⢸⣿⣿⣿⣷⡼⢰⣿⣿⣿⣿⡏⡿⣿⣿⣿⡇⡇⠇⠀⣿⣿⣿⣿⣿⡇⢸⣿⣾⣿⣷⣷⣶⡇⢻⣄⣷⠈⢿⢺⠋⡠⣿⣿⣿⣶⣟⣾⣿⣿⣿⡇
⢸⣿⣿⣾⣸⡤⢸⣿⠀⠑⡈⡀⡄⠀⠝⠀⠘⣿⣿⡟⠀⠂⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣿⣿⣮⣭⡅⢾⣽⣿⣿⣿⠃⠘⢀⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⣾⣯⣹⣧⣦⢈⣰⣿⣿⣿⣿⣧⣱⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣧⣿⣿⠘⠀⢸⣽⣷⠀⠀⠀⠶⠃⣿⡇⠈⢰⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣀⣤⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⣯⡿⠇⠀⠀⠀⣀⣿⣧⣶⣼⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣷⣾⣦⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣈⣡⣹⣏⣏⣉⣈⣍⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣟⣻⣟⣟⣯⣏⣿⣟⣻⣻⣛⣿⣟⣛⣟⣛⣿⣻⣛⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠿⡿⢿⣿⡿⣿⣿⣿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣻⣛⣻⣻⣏⣟⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠿⠿⡶⡿⡿⡿⠿⡿⣿⠾⠷⠿⣶⢶⠿⠿⢿⣿⣿⣿⡇
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

                    ䷩ 𝚕𝚒𝚗𝚎 4292

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/The_Free_Software_Foundation_FSF_Has_Raised_More_Than_Three_Tim.shtml
    Gemini version at https://techrights.org/n/2024/12/05/The_Free_Software_Foundation_FSF_Has_Raised_More_Than_Three_Tim.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Free Software Foundation (FSF) Has
Raised More Than Three Times More Money Than the Software Freedom Conservancy
(SFC), Which Mostly Gets Money From Corporations, Including
Microsoft⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024,
updated Dec 05, 2024


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


Recent/related: If_You_Donate_to_the_FSFE,_You_Are_Funding_a_Microsoft_Front
Group_Inside_Europe | In_the_Latest_OSI_Tax_Filing_(From_the_IRS),_Filed_13
Months_Ago,_Only_4%_of_the_Revenue_Comes_From_Members_(People,_Not
Corporations)_and_$252,702_Goes_to_Microsoft_Projects_(Propping_Up_Proprietary
Software_Monopoly) | Who_is_the_Mystery_Payer_of_Sandlers'_(Software_Freedom
Conservancy)_Quarter_Million_Dollars_(Huge_Salary)_Per_Year?


JUDGING by what's happening_so_far_this_month, the FSF raises about 10,000
dollars in donations per day (its now close to $110,000 in total). Given that
about_100,000,000_people_use_GNU_on_their_desktops/laptops, we're talking about
something like a tenth of a cent per user.


SFC, which attacks the FSF while imitating SFLC, has only raised about 33k so
far. The SFC has been better than the FSF at raising corporate cash (because it
pretends to be "social justice" while trampling_over_women). But non-corporate
actors, i.e. people, aren't fooled_by_them_anymore.


It should be noted that serial defamers from Microsoft - or Microsofters in
general - have done everything they can lately to discourage_FSF_donations. If
Microsofters are so afraid of a well-funded FSF, take that as a sign of the
FSF's effectiveness.


Do not donate any money to copycat organisations. It's worse than money down
the river because your money might get spent attacking and even defaming the
originals. █




⠿⠿⠿⣿⣿⣿⣿⣄⠀⠀⢸⣿⠀⢸⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠆
⠀⠀⠀⢈⣿⣿⣿⣿⠀⠀⢸⣿⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣀⣈⣿⣾⣯⣿⣿⠁⠠⠄⢸⣿⣤⣼⣆⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⣤
⠙⣻⣿⣿⣿⣿⣿⠀⠈⠀⢽⣿⡿⠛⠛⠿⠷⢤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠿⢿⠿⢿⢿⡿⣿⣿⣿⣿⡇⢰⣻⣻⣿⣷⣙⣛⣿⣿⣾⣽⣿⣽⣽⣽⣾⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⣿⠿⠿⢿⡇⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣄⠀⠀⠀⠀⢸⢀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡆⠀⠀⢸⣿⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠟⠁⠀⠀⣼⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢔⠄⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⠀⣿⣿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣖⠀⠠⠾⠿⣿⠿⠿⠿⠿⢿⣿⠀⠟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣤⣀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠉⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣤⣤⣀⣀⣀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠋⠿⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⢻⣿⣿⣷⣾⣿⣴⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⣤⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4372

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Why_We_Moved_to_Perl_and_Dumped_PHP_Last_Year.shtml
    Gemini version at https://techrights.org/n/2024/12/05/Why_We_Moved_to_Perl_and_Dumped_PHP_Last_Year.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Why We Moved to Perl and Dumped PHP Last
Year⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


Elongating the lifetime of the underlying_stack


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_grumpy_cat_winter:_This_is_our_nineteenth_year⦈_


TODAY in IRC one recurring topic was Perl, the context being this_malicious
Microsoft_proxy giving Perl money (after Perl had already outsourced way too
much to Microsoft's GitHub). In the main channel, #techrights, I explained that
we had dragged on and on a serious technical debt problem. A lot of our work -
or "content" as companies like to label people's hard work - was 'stuck' inside
mountains of PHP code (content management systems) and the databases became as
large as 10GB (only accessible using bloated software such as MariaDB or
Oracle's MySQL).


We solved this by exporting the data using Perl (via SQL queries) and instead
created a system using Perl. It's our own system and we extend it based on our
needs, not some "one-size-fits-all" grand scheme a la Drupal and WordPress. We
strongly encourage other sites to do the same if they value longevity and
appreciate the merits of general simplicity (never pursue anything beyond the
basics; it can become a maintenance overheard, source of bugs etc).


Linux is a cautionary tale in that regard and Rust will worsen things rather
than address the issue of overflows. A lot of what_we_said_in_2022_turned_out
to_be_true_if_not_prophetic. But Rust is a story for another day, some other
time...


Perl is an old language and our choice of it wasn't made based on hype or
fashionable trends. In the word of an associate, Perl is the go-to tool for
many things. Python may have the backing of Microsoft and others, and thus more
progress in the libraries/modules these days, but the core language is far
better with Perl. It's in the lead for regex and is easy to write clearly
understood code. Unfortunately the whisper campaign against it points out that
one can write poorly understood code too easily as well.


It is up to the programmer, according to this associate. "There is / was also
the problem that as Perl peaked, it was the trend to show off and write as
intricate and complex systems as you could. It was showing off rather than the
intentional obfuscation you get nowadays with systemd."


For a number of years we ran on Alpine Linux, i.e. no systemd. But sadly it has
become increasingly hard to run some particular software on operating systems
which lack systemd (and GNU, by default).


We no longer use PHP. We need not worry about some future version of PHP coming
out and breaking compatibility (notorious trait of PHP; it breaks "old"
software and I grew tired of hacking on PHP code when it kept happening since
20 years ago). With Python 3 we can see that Python too is vulnerable to
general disregard for backward compatibility. We don't use Python for the Web
site anymore. █




⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⠶⣶⣶⡶⠶⠶⣶⡶⠖⠖⠄⠤⠄⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣾⠟⣿⣟⣭⡏⣭⣽⣿⣽⣿⣭⣿⢋⣴⣶⡄⣶⠀⣾⣷⠀⣾⡆⢰⡆⠈⣿⡆⢸⡃⢠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣷⣿⡆⣿⣿⣿⣨⣭⣸⣇⢸⣿⣿⣿⣿⠀⣭⣥⠀⣿⠃⢠⡀⠺⣿⠇⢸⡄⠸⣿⣿⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣃⣻⣿⣃⣘⣛⣋⣿⣦⣝⣛⣽⣿⣤⣽⣯⣤⣽⣥⣬⣿⣤⣭⣥⣬⣿⢶⡤⠤⣶⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⡿⣿⢫⢿⣿⡿⣿⡿⣿⣿⠹⢿⣿⡏⢟⢻⢠⣿⣇⣸⣷⣰⣿⣷⣹⣷⣤⣼⣷⣶⣿⣤⣤⣄⣀⣀⣐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠟⠛⠛⠛⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⣠⣀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣴⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣆⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⣿⣿⣿⣿⡟⢻⡿⡟⠛⠉⠋⠋⠊⠉⠻⠿⢿⣿⣷⣷⣿⣒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠻⣿⣿⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢺⢿⣿⣿⣷⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡿⠯⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠊⣙⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⢲⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣷⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠀⠻⠿⣿⣿⣷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡥⢸⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠰⣶⣤⡤⠋⠀⠀⠀⠀⠀⢠⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣾⣿⣿⣿⡟⠒⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⠟⢂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠐⠂⡀⠤⠀⠀⡀⠀⠀⣀⣠⣾⣿⣿⣿⣶⣶⣿⣧⣶⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠂⢢⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡶⠂⠐⠂⠀⠀⠀⠤⠔⢒⡒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣇⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣄⣐⠈⢩⢿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠌⠀⠒⠂⠤⠭⣁⡐⠂⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣐⠛⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣶⣄⡉⢋⡴⡟⡿⢿⡿⢿⣿⠿⡿⠿⠛⠛⣉⣦⡶⠀⠐⠢⢀⠀⠀⠀⠉⠒⠤⣁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠐⣶⣶⡿⠛⠉⠀⠀⢸⣄⠀⠀⠢⠀⠀⠀⠀⠀⠑⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣴⠦⣤⣀⣝⡻⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡼⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⢀⣀⢀⣀⡀⣀⡀⢀⣀⣀⠀⣿⢄⣀⡀⢀⣀⣀⢼⣿⡿⣟⣛⡻⣿⣛⣛⣛⡿⣛⣛⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠋⢿⠿⣿⡿⠿⢿⣿⡜⣿⡟⢻⣿⠛⢸⣿⢸⣿⡇⣿⡇⣿⣏⠿⠇⠈⢸⣿⡇⣿⡏⠿⠇⠉⢸⣿⢹⣿⢸⣿⡇⣿⡇⣿⡏⣿⡇⢻⣿⡿⠛⠀⠀⢸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 4486

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

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    Gemini version at https://techrights.org/n/2024/12/05/Windows_Has_Fallen_to_All_Time_Low_in_India.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Windows Has Fallen to All-Time Low in
India⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


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


In India, only about 1 in 8 Web requests comes from Windows


We've only just noticed something important, albeit we rely on one sole Web
surveyor.


If these numbers are accurate (the sample size in India ought to be vast),
Windows_is_down_to_62%_on_desktops/laptops_in_India or 12.5% overall (because
Android_is_so_dominant and Web-compatible_mobile_ownership/usage_rose_steadily,
apparently rising from 2% 15 years ago to about 80% now).


No wonder Bill_Gates_Keeps_keeps_visiting_Modi and buying/bribing Indian press.
He wants to experiment. █


“They’ll get sort of addicted, and then we’ll somehow figure out how to collect
sometime in the next decade.”


                                                                    -Bill Gates




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⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠂⡠⠾⠟⠁⠀⠀⢀⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠄⠀⢀⡋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣷⣄⠀⠀⠈⠻⣿⣿⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠀⣔⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡁⢀⣤⢘⢃⠀⠀⢠⣶⡅⣲⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⢻⣿⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡞⠙⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⢾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡆⡀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⠆⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣀⠠⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⣄⠀⠀⠀⢉⣀⣤⣤⣤⣤⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡧⠀⠀⠀⠰⢿⣿⣿⣿⣿⣉⠉⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⠿⠃⠀⢀⣠⣾⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠰⠦⣭⣿⣭⣁⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⠛⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢨⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠩⠉⠉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠂⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣀⣤⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⠛⠡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡯⡿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⣴⣦⡴⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⡿⠁⠠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⡟⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⠙⣹⠟⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠀⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢚⠆⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣟⠛⢺⢿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢫⠂⠀⠀⠀⠈⠻⠋⠀⣽⢾⡏⠙⠟⠉⠛⡥⣀⠉⡀⠄⡌⣻⣿⣿⣿⣿⣿⡦⠀⠀⢀⣼⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠀⠀⠨⢻⡍⠙⠋⠀⢢⡴⠾⠟⣳⠀⠀⠈⢹⣿⣿⣿⡿⠏⢀⣤⠾⢿⠿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4576

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 05/12/2024: Hermeticism,
Living in the Shell, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Politics_and_World_Events
          o Technology_and_Free_Software
                # Programming
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ Why_list_a_phone_number_if_no_one_at_your_company_even
                  knows_how_to_deal_with_the_notification?⠀⇛


                       And that's it. It's lucky there was no personal
                       information included or this company could be in
                       violation of HIPAA (Health Insurance Portability
                       and Accountability Act).


                       On a whim, instead of simply deleting the email and
                       going on with my life, I decided to do The Right
                       Thing™, and inform the sender (which was the
                       company itself) of the delivery error by calling
                       the given phone number.


                       It took several calls to resolve. No one at XXXXX­X
                       knew how to directly handle my call. Two people I
                       talked to attempted to transfer me to what they
                       felt was the appropriate department, only to have
                       the transfer fail and I had to call back and
                       navigate the automated phone system yet again (in
                       which I had to listen carefully, becauese the
                       options had changed on October 20^th; a refreshing
                       change from the “recently changed” most such
                       systems claim).


                # ⚓ A_real_real-time_chess_board⠀⇛


                       Two years ago I talked about a spherical chess
                       variant [1]. Now, I want to mention real time chess
                       [2], where players can move their pieces at will,
                       with the only limit being once a piece is moved,
                       you can't move it for five seconds. And there's no
                       check or checkmate—you win by capturing the
                       opponent's king.


                # ⚓ classical_electronic⠀⇛


                       As I am learning to be single, my past comes back
                       to me. In a weird twist of event, I'm starting to
                       listen to classical music again.


                       I just enjoy listening to classical music, so much
                       so that I feel a bit self concious about it. It
                       feels somewhat 'pretentious' to like classical
                       music. There is nothing I can do, my whole body
                       enjoy listening to classical music.


                       I dream about the day I'll be in the city and go to
                       back to the orchestra. As a kid I've had the chance
                       to go to many concert, one of my violin teacher was
                       playing with the Montreal philharmonic orchestra.
                       The experience of so many instruments playing at
                       the same time, the composition and the story that
                       happened in my head during this relaxing and
                       exhilarating moment, deeply formed my relationship
                       to music.


          o § Politics and World Events⠀➾


                # ⚓ Hermeticism_Isn't_Qabbalah⠀⇛


                       Hermeticism is not equatable with Qabbalah. It's
                       entirely possible (and encouraged) to be a
                       Hermeticist without Qabbalah. Qabbalah is like
                       terrible, drab shag carpeting laid out over a
                       beautifully polished, ancient hardwood floor.
                       Jewish Kabbalah is rich and profound, but Hermetic
                       Qabbalah is effectively a cultural appropriation
                       and maladaptation of it, and—let's be
                       honest—doesn't provide much for us anymore besides
                       a massive correspondence table with a lot of badly-
                       pronounced Hebrew. And yet, it's formed such a
                       procrustean bed that so many of us struggle to
                       think outside of, much less break away from; it's
                       become as much a crutch as it has a shackle. The
                       more we divest ourselves of it and practice
                       Hermetic spirituality without it, the better off
                       we'll all be.


          o § Technology and Free Software⠀➾


                # ⚓ redterminal.org_now_runs_on_FreeBSD-14.2-RELEASE⠀⇛


                       I upgraded the redterminal.org Gemini/Gopher/
                       Finger/WWW server from the 14.1 branch to FreeBSD-
                       14.2-RELEASE. Nobody should have noticed besides a
                       brief downtime for the reboot. The update went
                       painless and smoothly thanks to the FreeBSD
                       maintainers. All packages are up-to-date too and
                       everything is fine so far. Small problems will be
                       ironed out with the first update if any, but as far
                       as I can tell there are no problems.


                # § Programming⠀➾


                      # ⚓ Living_in_the_Shell⠀⇛


                             I am now using the Devterm R-01 for, what, 11
                             months or so as my more or
                             less primary computer, which has lead to the
                             "discovery" of some problems:


                             - The screen real estate with its widescreen
                             format and small size isn't
                             ideal for a traditional desktop


                             - It is somewhat slow


                             - The trackball is still a crime against
                             humanity
===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It's like the
World Wide Web but a lot lighter.





                    ䷩ 𝚕𝚒𝚗𝚎 4746

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 05/12/2024: Domain Changes,
Griping With Haskell⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Technology_and_Free_Software
                # Internet/Gemini
                # Programming
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ [EN]_re:_A_real-time_chess_board⠀⇛


                       Ha, this is sooo cool. I've been thinking on how to
                       make that real-time chess a reality. Perhaps with
                       hourglasses, or each piece having a digital timer.
                       But that approach is amazing based on all the
                       things you have to consider.


                # ⚓ 🔤SpellBinding:_AEUMNQI_Wordo:_PLANS⠀⇛


                # ⚓ 29_years_ago_today⠀⇛


                       Twenty-nine years ago today, on Dec. 5, 1995, I
                       created my first website at a little internet cafe
                       in Seattle. This was before GeoCities or AngelFire
                       was really a thing (or at least I was not aware of
                       those), and the web hosting came with my personal
                       UNIX shell account from the internet cafe, which I
                       could use to log in from there, as well as from
                       places like Seattle Public Library using Telnet on
                       its VT-100 dumb terminals.


                       That meant I for the most part had to manually type
                       in HTML into the shell using the PICO text editor
                       (which was proprietary software from the University
                       of Washington, later emulated by the open-source
                       NANO editor). Or, I could FTP from my college
                       computer lab.


          o § Technology and Free Software⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ A_housekeeping_announcement⠀⇛


                             This site is now "willowashmaple.sbs", and is
                             no longer "willowashmaple.xyz".


                             If you have subscribed via RSS, you need to
                             change the feed address to https://
                             willowashmaple.sbs/atom.xml


                             I apologize in advance for this sudden
                             announcement and thank you for your patience
                             as I also need to update various links on my
                             social media profiles.


                      # ⚓ all_the_notes⠀⇛


                             the existence of dedicated websites that lets
                             you compare features of the plethora of note-
                             taking applications just shows that so many
                             of us--regardless of background--are
                             interested in (sometimes obsessed with)
                             better systems for note-taking, task
                             management, and really just productivity.
                             doing more with less time and less mental
                             overhead.


                # § Programming⠀➾


                      # ⚓ 2024_In_Retrospect⠀⇛


                             I must admit, I'm not one to discuss my
                             personal life online very often. But I wanted
                             to add this memoirs section because I think I
                             need some place to do so and my physical
                             journals all end up filled with random notes,
                             poems, and silliness. Throughout it all, 2024
                             has been a phenomenal year for me.


                             I got to grow closer to many friends, some
                             long time and some not. I wound up growing
                             close to and finding my true love and
                             soulmate, something that I had long conceded
                             was likely out of my reach. The latter part
                             still has me silently giddy as I blush,
                             waiting for a message or response from them.
                             I even finally rekindled my love for
                             programming again, thanks to OCaml and
                             functional programming in general.


                      # ⚓ Griping_With_Haskell⠀⇛


                             Over the last couple months, I've taken some
                             time to finally learn and use Haskell. I
                             chose this because after using OCaml for a
                             little bit I realized I finally felt ready to
                             approach a purely functional programming
                             language. It took a little bit, but after the
                             first few weeks I actually felt pretty happy
                             in Haskell. It is a very elogent and pleasant
                             language to write, that allows you to
                             represent concepts in very ingenious ways.
                             Lazy evaluation is also something that I will
                             now miss whenever I am not writing Haskell. I
                             like Haskell a lot, and will be continuing to
                             use it.


                             However, the language is bloated with warts.
                             Whether they be tooling related, standard
                             library related, or language construct
                             related. While it is very elogant to write
                             Haskell, it is absolutely horrible to build
                             an application in it. So this log will be a
                             little ramble of my experience.


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





                    ䷩ 𝚕𝚒𝚗𝚎 4913

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 05/12/2024: Explaining the South
Korea Chaos and French PM Barnier's Government Already
Disintegrating⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Integrity/Availability/Authenticity
          o Defence/Aggression
          o Environment
                # Energy/Transportation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ University of Michigan ☛ I_love_street_photography,_but_it’s
            probably_evil⠀⇛


                 In street photography, there is “the moment.” It could be
                 the instant a crowd looks off in the distance or when a
                 couple kisses by a subway. It could be a man rushing by
                 with a peculiar hat or a woman walking through the
                 morning mist.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Hack_On_Self:_Headphone_Friend⠀⇛


                       In the last two articles, I talked about two
                       systems relying on audio notifications. The first
                       one is the Alt-Tab annihilator system – a system
                       making use of my window monitoring code to angrily
                       beep at me when I’m getting distracted. The other
                       is the crash prevention system – a small script
                       that helps me avoid an annoying failure mode where
                       I run out of energy before getting myself
                       comfortable for it.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Scarlett_Gately_Moore:_Hacked_and_tis_the_season_for
                  surgeries⠀⇛


                       I am still here. Sadly while I battle this insane
                       infection from my broken arm I got back in July,
                       the hackers got my blog. I am slowly building it
                       back up. Further bad news is I have more surgeries,
                       first one tomorrow. Furthering my current struggles
                       I cannot start my job search due to hospitalization
                       and recovery.


                # ⚓ Mexico News Daily ☛ Federal_authorities_intercept_more_than
                  20_million_fentanyl_doses_in_Sinaloa⠀⇛


                       The Sinaloa security operation, completed in two
                       separate actions, was the largest fentanyl bust in
                       Mexican history.


                # ⚓ France24 ☛ Bird_flu_in_the_US:_What_is_the_risk_of_human-
                  to-human_transmission?⠀⇛


                       In today’s Science segment, we tell you about the
                       latest cases of the bird-flu detected in North
                       America. Three people were diagnosed without
                       experts being able to identify the source of
                       contamination. First a teenager in Canada then a
                       child in California which follows a first
                       contamination in Missouri. None of those patients
                       have been in direct contact with animals which is
                       sparking fear that the virus could be mutating.
                       Until now, however, there have been no cases of
                       human-to-human transmission.


                # ⚓ New York Times ☛ Kelly_Powers,_Fox_News_Commentator_Who
                  Shared_Her_Health_Crises_With_Viewers,_Dies_at_45⠀⇛


                       She was diagnosed with glioblastoma, an aggressive
                       form of brain cancer, in 2020, and used her
                       platform to talk about cancer research.


                # ⚓ Science Alert ☛ Scientists_Created_The_Thinnest_Spaghetti
                  The_World_Has_Ever_Seen⠀⇛


                       Unlike any spaghetti ever made before.


                # ⚓ Science Alert ☛ Your_Poop_Schedule_Says_a_Lot_About_Your
                  Overall_Health,_Study_Finds⠀⇛


                       There's an optimal frequency.


                # ⚓ Science Alert ☛ Neurons_Don't_Look_Like_We've_Long_Thought,
                  Controversial_Study_Says⠀⇛


                       Wait, what?


                # ⚓ Science Alert ☛ Toasted_Skin_Syndrome_Just_One_Risk_of
                  Using_Hot_Water_Bottles_For_Warmth⠀⇛


                       There are safer ways.


                # ⚓ Science Alert ☛ Alarming_Rise_in_Cancers_of_The_Gut_Linked
                  With_These_Deadly_Diets⠀⇛


                       Make a healthy change today.


                # ⚓ Science Alert ☛ Roman_Era_Barbarians_Carried_Tiny_Spoons
                  That_May_Have_Helped_in_Battle⠀⇛


                       If you know, you know.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ WhichUK ☛ Delivery_text_scams:_how_to_spot_this
                        common_scam⠀⇛


                             Check for telltale signs of fake text
                             messages impersonating delivery companies
                             this Christmas


          o § Defence/Aggression⠀➾


                # ⚓ Hong Kong Free Press ☛ China’s_Pooh-tin_Jinping_vows_to
                  deepen_infrastructure_cooperation_with_Nepal_–_state_media⠀⇛


                       President Pooh-tin Jinping on Tuesday told Nepali
                       Prime Minister Khadga Prasad Sharma Oli that China
                       will offer more support to develop the country’s
                       infrastructure, Chinese state media reported.


                # ⚓ The Straits Times ☛ Nepal,_China_sign_deal_on_Belt_and_Road
                  plan,_paving_way_for_progress_on_projects⠀⇛


                       Nepal has signed a framework agreement with China
                       on the Belt and Road initiative, after an initial
                       pact was signed seven years ago but no progress
                       made since, paving the way for cooperation on
                       projects, its foreign ministry said on Wednesday.


                # ⚓ LRT ☛ Lithuania’s_new_govt_vows_to_host_German_brigade_in
                  2027,_calls_China_‘growing_challenge’⠀⇛


                       Despite concerns about the timeline for the German
                       brigade’s deployment, Lithuania’s new government is
                       committed to meeting the late 2027 deadline. It
                       also calls China a “growing challenge”.


                # ⚓ LRT ☛ Lithuania’s_govt_programme:_new_China_direction,
                  social_economy_policy_–_key_points⠀⇛


                       Lithuania’s incoming Social Democrat-led government
                       has revealed its draft programme, outlining the key
                       priorities over the next four years. Here are the
                       key points.


                # ⚓ Defence Web ☛ Tunisia_seeking_Javelin_anti-tank_missiles⠀⇛


                       Tunisia is looking to buy nearly 200 Javelin anti-
                       tank missiles from the United States in a deal
                       worth over $100 million. The US State Department on
                       3 December announced that it had approved the
                       possible Foreign Military Sale, and the Defence
                       Security Cooperation Agency (DSCA) had accordingly
                       notified Congress.


                # ⚓ New York Times ☛ A_Storied_New_York_Hilton_Adds_a_Grim
                  Chapter_to_Its_History⠀⇛


                       The hotel, on West 54th Street, was where
                       journalists examined the Pentagon Papers and where
                       Donald Trump delivered a 2016 victory speech.


                # ⚓ New York Times ☛ A_Health_Insurance_C.E.O._Was_Gunned_Down
                  in_Manhattan⠀⇛


                       Also, the Supreme Court appeared inclined to uphold
                       a Tennessee law on trans care. Here’s the latest at
                       the end of Wednesday.


                # ⚓ New York Times ☛ Shooting_of_Brian_Thompson,
                  UnitedHealthcare_CEO,_in_NYC:_What_We_Know⠀⇛


                       Mr. Thompson was on his way to an investors’
                       gathering when he was killed by a masked shooter
                       who fled on an electric Citi Bike, the police said.


                # ⚓ New York Times ☛ Who_Was_Brian_Thompson,_the_CEO_of
                  UnitedHealthcare?⠀⇛


                       Mr. Thompson managed a division that employs about
                       140,000 people and offers insurance plans to
                       employers and individuals.


                # ⚓ France24 ☛ Police_hunt_for_US_healthcare_executive's_masked
                  killer_after_New_York_attack⠀⇛


                       The chief executive of one of the United States's
                       largest health insurance companies,
                       UnitedHealthcare, was shot and killed outside
                       a New York Hilton hotel in an apparently targeted
                       hit Wednesday. Brian Thompson was shot just before
                       7 am outside the hotel in the Midtown district of
                       Manhattan. Police are searching for the killer.


                # ⚓ The Straits Times ☛ Philippine_V-P_Sara_Duterte_faces
                  second_impeachment_complaint⠀⇛


                       Dec 4 complaint alleged Sara Duterte betrayed
                       public trust with misuse of millions of dollars in
                       public funds.


                # ⚓ The Straits Times ☛ South_Korea’s_Yoon_names_new_defence
                  minister_after_botched_martial_law⠀⇛


                       It is the President's first official move since
                       rescinding martial law on Dec 4.


                # ⚓ The Straits Times ☛ Explainer:_How_to_impeach_a_South
                  Korean_president⠀⇛


                       A motion needs a two-thirds majority vote by the
                       members of the single-chamber Parliament to pass.


                # ⚓ The Straits Times ☛ Martial_law_debacle_revives_painful
                  memories_in_South_Korea⠀⇛


                       Many recall the trauma of the early 1980s, when
                       South Korea was periodically placed under harsh
                       laws.


                # ⚓ New York Times ☛ President_Yoon_Suk_Yeol_of_South_Korea
                  Declares_Martial_Law,_Then_Backs_Down⠀⇛


                       Soon after President Yoon Suk Yeol’s declaration on
                       Tuesday, lawmakers voted to defy him, prompting the
                       president to say he was lifting his order.


                # ⚓ New York Times ☛ South_Korean_History_Is_Scarred_by_Martial
                  Law⠀⇛


                       The president’s short-lived declaration of a
                       military emergency late Tuesday was young South
                       Koreans’ first exposure to a state of affairs their
                       elders remember well.


                # ⚓ New York Times ☛ South_Korea_Stock_Markets_Wobble_After
                  Martial_Law_Turmoil⠀⇛


                       Officials pledged “unlimited” support to markets as
                       traders digested the implications of South Korea’s
                       brief declaration of martial law.


                # ⚓ New York Times ☛ Nearly_300_Troops_Stormed_South_Korea’s
                  National_Assembly,_Official_Says⠀⇛


                       The National Assembly’s secretary general, Kim Min-
                       ki, condemned what he called the “illegal,
                       unconstitutional actions of the military.”


                # ⚓ New York Times ☛ For_Some_Koreans,_Martial_Law_Stirs
                  Harrowing_Memories_of_Gwangju_Uprising⠀⇛


                       “I immediately thought of 1980, and the fear and
                       desperation we felt,” said a 60-year-old lawmaker
                       who lived through the massacre of protesters in
                       Gwangju.


                # ⚓ New York Times ☛ Who_Would_Replace_South_Korea’s_President
                  Yoon?⠀⇛


                       Prime Minister Han Duck-soo would take over if
                       President Yoon Suk Yeol steps down or is impeached.


                # ⚓ New York Times ☛ Thursday_Briefing:_An_Impeachment_Motion
                  in_South_Korea⠀⇛


                       Plus, what’s your favorite holiday tradition?


                # ⚓ New York Times ☛ South_Korea’s_Defense_Minister_Steps_Down
                  Over_Martial_Law_Decree⠀⇛


                       President Yoon Suk Yeol accepted the resignation of
                       Kim Yong-hyun, who said he considered himself
                       responsible for the short-lived decision to impose
                       military rule.


                # ⚓ New York Times ☛ South_Korea’s_Martial_Law_Turmoil
                  Threatens_Pacific_Alliance_With_U.S._and_Japan⠀⇛


                       Donald J. Trump had been seen as the main risk
                       factor for the partnership between Tokyo, Seoul and
                       Washington. Then came martial law in South Korea.


                # ⚓ New York Times ☛ South_Korean_Lawmakers_Move_to_Impeach
                  President_Yoon After_Failed_Martial_Law_Bid⠀⇛


                       President Yoon Suk Yeol’s attempt to break a
                       political deadlock by imposing military rule
                       collapsed within hours, leaving him with few
                       defenders. A vote to impeach him could come as soon
                       as Friday.


                # ⚓ CS Monitor ☛ Martial_law_for_a_moment:_What_just_happened
                  in_South_Korea⠀⇛


                       South Korean President Yoon Suk Yeol’s surprise
                       declaration of emergency martial law lasted only
                       six hours. But it has plunged South Korea – a key
                       Asian economy and U.S. ally – into a political
                       crisis that could last much longer.


                # ⚓ CS Monitor ☛ South_Korea’s_swift_rescue_of_freedom⠀⇛


                       An unpopular president’s martial law was no match
                       for a people with an inner strength born of
                       repelling despots and invaders.


                # ⚓ The Straits Times ☛ Recap:_South_Korean_opposition,
                  protesters_demand_impeachment_of_President_Yoon⠀⇛


                       The protests are set to continue every weekday
                       evening until their demand for Mr Yoon to resign is
                       met.


                # ⚓ The Straits Times ☛ US_‘relieved’_South_Korea_President
                  Yoon_Suk_Yeol_reversed_course_on_martial_law⠀⇛


                       Mr Yoon had shocked his country and the world by
                       imposing martial law late on Dec 3.


                # ⚓ The Straits Times ☛ South_Korean_ruling_party_leader_says
                  martial_law_attempt_‘tragic’,_demands_accountability⠀⇛


                       President Yoon is a member of the People Power
                       Party.


                # ⚓ The Straits Times ☛ How_polarised_politics_led_South_Korea
                  to_a_plunge_into_martial_law⠀⇛


                       The events that led to martial law were set in
                       motion well before Yoon's 2022 victory.


                # ⚓ The Straits Times ☛ South_Korea’s_President_Yoon_faces
                  impeachment_after_martial_law_debacle⠀⇛


                       Voting is set for Dec 5 or Dec 6.


                # ⚓ The Straits Times ☛ How_martial_law_has_been_used_over
                  South_Korea’s_turbulent_history⠀⇛


                       Martial law was last introduced in 1979 following
                       the assassination of then President Park Chung-hee.


                # ⚓ The Straits Times ☛ Martial_law_turmoil_unsettles_South
                  Korean_entertainment_schedules⠀⇛


                       Dua Lipa's concert organiser has not issued any
                       statement, suggesting that the shows will proceed
                       as planned.


                # ⚓ The Straits Times ☛ South_Korea’s_short-lived_martial_law:
                  A_timeline⠀⇛


                       The crisis unfolded over 157 tense minutes before
                       lawmakers voted to revoke the martial law.


                # ⚓ The Straits Times ☛ Martial_law_in_South_Korea_tests_Biden
                  and_a_key_US_alliance⠀⇛


                       Yoon’s move to call martial law has appeared to
                       catch the Biden administration by surprise.


                # ⚓ The Straits Times ☛ South_Korea_Cabinet_ministers_offer_to
                  resign_en_masse⠀⇛


                       The People Power Party’s leader told reporters he
                       also suggested Mr Yoon be kicked out of the party.


                # ⚓ The Straits Times ☛ Leading_contenders_who_might_replace
                  South_Korean_President_Yoon⠀⇛


                       The president’s term runs to 2027 but if he leaves
                       office sooner, it would trigger an election.


                # ⚓ The Straits Times ☛ Video_of_South_Korean_woman_clashing
                  with_soldiers_after_martial_law_declaration_goes_viral⠀⇛


                       President Yoon declared martial law late on Dec 3,
                       only to rescind it six hours later.


                # ⚓ The Straits Times ☛ Martial_law_decree_sparks_international
                  backlash_for_South_Korea⠀⇛


                       Leaders from Japan and Sweden have cancelled visits
                       to South Korea.


                # ⚓ The Straits Times ☛ Nearly_300_troops_stormed_South_Korean
                  legislature,_official_says⠀⇛


                       Troops smashed windows, and some aides and
                       protesters sprayed them with fire extinguishers.


                # ⚓ The Straits Times ☛ South_Korean_media_calls_for_Yoon_Suk
                  Yeol’s_resignation,_arrest⠀⇛


                       Most alarming to press freedom advocates were
                       provisions placing all media under direct military
                       control.


                # ⚓ The Straits Times ☛ Soldiers_vs_office_chairs:_South
                  Korea’s_martial_law_standoff⠀⇛


                       Soldiers in the compound attempted to enter the
                       building while police tried to bar MPs from
                       entering.


                # ⚓ The Straits Times ☛ For_some_South_Koreans,_martial_law
                  brings_back_frightening_memories⠀⇛


                       “After democratisation, I didn’t think this would
                       happen again in our lifetime," says a 68-year-old
                       man.


                # ⚓ The Straits Times ☛ South_Korea’s_ex-PM_and_other
                  politicians_accused_of_‘supporting’_martial_law⠀⇛


                       Former prime minister Hwang Kyo-ahn and Busan city
                       councilman Park Jong-cheol showed their support.


                # ⚓ The Straits Times ☛ How_concerned_should_you_be_about_South
                  Korea’s_martial_law_turmoil?⠀⇛


                       Expect to see large protests in some parts of
                       Seoul, such as Gwanghwamun, Yongsan or near City
                       Hall.


                # ⚓ The Straits Times ☛ South_Korea’s_day_of_rage_as_President
                  Yoon’s_martial_law_flounders⠀⇛


                       The streets of Seoul teemed with protesters and
                       police throughout the day.


                # ⚓ The Straits Times ☛ Uptick_in_sales_at_S._Korea_convenience
                  stores_following_martial_law_declaration⠀⇛


                       One convenience store chain saw sales of canned
                       goods surge by 337.3 per cent.


                # ⚓ The Straits Times ☛ US_was_not_aware_in_advance_of_South
                  Korea_martial_law_decision,_Blinken_says⠀⇛


                       BRUSSELS - The United States was not aware that
                       South Korea's president intended to declare martial
                       law, U.S. Secretary of State Antony Blinken told
                       Reuters on Wednesday, adding that he anticipated
                       speaking to his South Korean counterpart in the
                       coming days.


                # ⚓ The Straits Times ☛ S._Korean_President_Yoon_‘gravely_and
                  extensively_violated_Constitution’:_Impeachment_motion⠀⇛


                       The motion said Yoon's declaration of martial law
                       was aimed at evading criminal investigations.


                # ⚓ The Straits Times ☛ From_decree_to_defeat:_Inside_South
                  Korea's_failed_martial_law_attempt⠀⇛


                       The shock move on Dec 3 unleashed six hours of
                       political chaos in South Korea.


                # ⚓ The Straits Times ☛ Martial_law_decree_ignites_anti-
                  president_rallies_across_South_Korea⠀⇛


                       The largest demonstration took place near
                       Gwanghwamun Square in northwestern Seoul.


                # ⚓ The Straits Times ☛ South_Korean_ruling_party_to_oppose
                  President_Yoon_Suk_Yeol’s_impeachment⠀⇛


                       If successfully introduced to Parliament, lawmakers
                       could vote on the Bill as early as Dec 6.


                # ⚓ The Straits Times ☛ ST_Picks:_How_S._Korea’s_botched
                  martial_law_move_is_sending_shockwaves_across_Asia⠀⇛


                # ⚓ The Straits Times ☛ US_says_South_Korea’s_Yoon_badly
                  misjudged_martial_law_declaration⠀⇛


                       Almost all US interlocutors in South Korea were
                       “deeply surprised” by Mr Yoon’s move.


                # ⚓ The Straits Times ☛ South_Korea's_Yoon_names_new_defence
                  minister_after_botched_martial_law⠀⇛


                       It is the President's first official move since
                       rescinding martial law on Dec 4.


                # ⚓ The Straits Times ☛ Parents_of_S._Korean_soldiers_spent
                  sleepless_night_worrying_about_sons_after_martial_law
                  declared⠀⇛


                       Some apologised to their sons for the state of the
                       nation.


                # ⚓ The Straits Times ☛ Teachers_across_South_Korea_field
                  martial_law_questions_from_kids⠀⇛


                       Some schools ran separate educational programs on
                       the crisis.


                # ⚓ New Yorker ☛ A_Coup,_Almost,_in_South_Korea⠀⇛


                       President Yoon Suk-yeol declared martial law, then
                       backed off, in a matter of hours. He now faces
                       impeachment and mass protests.


                # ⚓ JURIST ☛ South_Korea_president_lifts_martial_law_following
                  parliamentary_unanimous_opposition⠀⇛


                       South Korean President Yoon Suk Yeol announced
                       Tuesday that he would lift martial law and that
                       troops deployed following the shocking declaration
                       would be withdrawn, succumbing to united
                       Parliamentary and public pressure against the
                       declaration.


                # ⚓ JURIST ☛ South_Korea_parliament_to_vote_on_presidential
                  impeachment_motion⠀⇛


                       A motion to impeach President Yoon Seok-yeol was
                       reported to the National Assembly of the Republic
                       of Korea on Thursday and is due to be voted on by
                       an anonymous ballot within 72 hours of the session.
                       The motion, filed by the opposition, follows
                       President Seok-yeol’s brief imposition of martial
                       law on Tuesday.


                # ⚓ Hong Kong Free Press ☛ Gov’t_advises_300+_Hongkongers_to
                  exercise_caution_in_S.Korea,_after_martial_law_declared,
                  lifted_in_one_night⠀⇛


                       Hongkongers in South Korea have been advised to
                       attend to their personal safety after President
                       Yoon Suk Yeol declared martial law on Tuesday, a
                       move that was unanimously overturned by lawmakers,
                       and later lifted by the government in a matter of
                       hours.


                # ⚓ The Strategist ☛ South_Korean_leader’s_rash_move_spells
                  upheaval_at_home_and_risk_abroad⠀⇛


                       President Yoon Suk Yeol’s decision to rescind his
                       declaration of martial law, in the face of
                       embattled opposition from South Korea’s parliament,
                       has at least spared the country a disastrous return
                       to military rule.


                # ⚓ The Strategist ☛ More_than_innovation:_Australia_needs
                  fast,_low-cost_defence_production⠀⇛


                       Conflicts in Ukraine and the Middle East have shown
                       that mass and asymmetry characterise modern
                       warfare. The challenge is to deliver affordable
                       mass—weapons in great numbers—while ensuring
                       technology is evolving ahead of rapidly changing
                       threats.


                # ⚓ RFERL ☛ Syrian_Troops_Reportedly_Thwart_Rebel_Advance_Near
                  Russian_Air_Base⠀⇛


                       A war monitor and state media say that Syrian
                       government forces have launched a counterattack
                       against Islamist-led rebels who were getting close
                       to a Russian-operated airbase after capturing a
                       string of towns and closing in on the key city of
                       Hama.


                # ⚓ The Straits Times ☛ Russia_strongly_backs_Syrian
                  leadership,_says_rebels_are_getting_outside_help⠀⇛


                       MOSCOW - Russia said on Wednesday that it strongly
                       backs the actions of the Syrian leadership to
                       counter an offensive by what it said were terrorist
                       groups receiving support, including drones and
                       training, from outside the country.


                # ⚓ New York Times ☛ Syrian_Forces_Battle_Rebels_Outside
                  Government_Stronghold⠀⇛


                       The rebels have set their sights on the city of
                       Hama, where President Bashar al-Assad’s government
                       has long maintained strength.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ RFERL ☛ Police_Secure_Area_After_Mystery_Drone_Crash
                        Near_Tajik_Capital⠀⇛


                             Police and security officials have cordoned
                             off a large area near Dusanbe after a drone
                             resembling a military unmanned aerial vehicle
                             (UAV) crashed in a nearby town in a region
                             where there are both Tajik and Russian
                             military bases.


                      # ⚓ The Straits Times ☛ Russia_supporting_North_Korea
                        nuclear_programme_in_exchange_for_troops:_Nato_chief⠀⇛


                             This could destabilise the Korean Peninsula
                             and threaten the United States, said the Nato
                             chief.


                      # ⚓ The Straits Times ☛ North_Korea-Russia_treaty_comes
                        into_force:_KCNA⠀⇛


                             The treaty includes a mutual defence pact for
                             immediate military assistance if either faces
                             armed aggression.


                      # ⚓ The Straits Times ☛ Russia_says_it's_watching
                        'tragic'_situation_in_South_Korea_with_concern⠀⇛


                             Russia is following events in South Korea
                             with concern after the president briefly
                             declared martial law, but there are no
                             threats to Russian citizens there, Foreign
                             Ministry spokeswoman Maria Zakharova said on
                             Wednesday.


                      # ⚓ New York Times ☛ Georgia_Tumbles_Deeper_Into_Crisis
                        as_Government_Detains_Opposition_Figures⠀⇛


                             In a sign of a widening crackdown, security
                             agents have searched the offices and homes of
                             prominent activists and opposition leaders
                             who are furious about the government’s
                             position on Europe.


                      # ⚓ Meduza ☛ Russian_ship_reportedly_fired_signaling
                        ammunition_at_German_military_helicopter_in_Baltic_Sea
                        —_Meduza⠀⇛


                      # ⚓ Meduza ☛ Malta_revokes_Russian_Foreign_Ministry
                        spokesperson_Maria_Zakharova’s_visa_ahead_of_OSCE
                        meeting_—_Meduza⠀⇛


                      # ⚓ LRT ☛ Lithuania_rejects_Belaruskali_claims_in
                        arbitration_lawsuit⠀⇛


                             After Belarusian potash fertiliser giant
                             Belaruskali filed a lawsuit against Lithuania
                             to the International Court of Arbitration,
                             Lithuania says it does not agree with the
                             allegations.


                      # ⚓ Meduza ☛ Armenia_considers_itself_‘outside_of’
                        Russian-led_CSTO_military_alliance,_prime_minister_says
                        —_Meduza⠀⇛


                      # ⚓ Meduza ☛ Even_after_doubling_its_sign-on_bonus
                        payment,_the_Russian_army’s_recruitment_rate_is
                        falling._Losses_may_now_outpace_new_enlistments._—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_Defense_Ministry_says_it’s_received
                        48,000_applications_for_DNA_testing_from_relatives
                        seeking_missing_soldiers_—_Meduza⠀⇛


                      # ⚓ Latvia ☛ Latvian_Security_Service_urges_prosecution
                        for_memorial_desecration⠀⇛


                             On November 29 this year, the Latvian State
                             Security Service (VDD) urged the Prosecutor's
                             Office to prosecute a dual citizen of Estonia
                             and Russia for helping the Russian special
                             services to act against Latvia by desecrating
                             a memorial important to Latvia.


                      # ⚓ RFERL ☛ U.S._Urges_'Dignity'_After_Georgian_Protests
                        Marred_By_Police_Brutality⠀⇛


                             A standoff between pro-EU Georgian protesters
                             and security forces continues in Tbilisi amid
                             accusations of excessive use of force by
                             police that have prompted international
                             condemnation including from a group of
                             influential U.S. lawmakers.


                      # ⚓ Atlantic Council ☛ To_help_Georgians,_the_West_must
                        drive_a_wedge_between_Georgia_and_the_Russia-China-Iran
                        camp⠀⇛


                             Despite strong support among Georgians for
                             their country to join the European Union, the
                             governing Georgian Dream party has taken big
                             steps to break with the West in favor of the
                             “axis of evasion.”


                      # ⚓ Scoop News Group ☛ Russian-linked_Turla_caught_using
                        Pakistani_APT_infrastructure_for_espionage⠀⇛


                             Both Abusive Monopolist Microsoft and Lumen’s
                             BlackLotus Labs found Turla spying on
                             Afghanistan and India via Pakistani
                             infrastructure.


                      # ⚓ RFERL ☛ 'Foreign_Agents'_Bill_Puts_Serbia's_EU
                        Aspirations_Under_Question⠀⇛


                             Serbian lawmakers have begun deliberating a
                             bill submitted to parliament that would
                             establish a "foreign agents" registry, a move
                             that may alienate Serbia from its EU
                             ambitions.


                      # ⚓ RFERL ☛ Pashinian_Suggests_Armenian_Rift_With_Russia
                        Widening⠀⇛


                             Armenian Prime Minister Nikol Pashinian
                             declared on December 4 in parliament that
                             Yerevan had effectively passed the "point of
                             no return" regarding its reintegration into a
                             Russian-led military alliance.


                      # ⚓ France24 ☛ ‘Aggressive'_Russian_cyber_attacks_boosted
                        Romania's_pro-Moscow_presidential_candidate⠀⇛


                             Calin Georgescu, the pro-Russian outsider
                             candidate now leading in Romania's
                             presidential elections, was "aggressively"
                             promoted on social control media platform
                             Fentanylware (TikTok) through coordinated
                             accounts and paid promotion, according to
                             documents declassified Wednesday from
                             Romania's security services.


                      # ⚓ JURIST ☛ Romania_court_validates_first_round_of
                        presidential_election⠀⇛


                             The Constitutional Court of Romania (CCR)
                             unanimously validated the results of the
                             first round of the presidential elections on
                             Monday. The country’s constitutional court
                             requested a re-verification and recount of
                             all ballots by the Central Electoral
                             Bureau amid allegations that Fentanylware
                             (TikTok) provided coverage in favor of Călin
                             Georgescu following his surprise victory on
                             November 24 [...]


                      # ⚓ Latvia ☛ Offroad_vehicles_on_their_way_from_Latvia_to
                        Ukraine⠀⇛


                             On Wednesday, December 4, the third shipment
                             of donations raised by the Latvian public
                             media campaign will go to Ukraine, Latvian
                             Radio reported.


                      # ⚓ Latvia ☛ Latvian_professor_to_lead_big_study_on
                        attitudes_toward_Ukrainian_refugees⠀⇛


                             A €2 million study on public attitudes
                             towards refugees from Ukraine in Central and
                             Eastern Europe will be conducted and led by
                             sociologist Inta Mieriņa, a tenured professor
                             at the University of Latvia, for the next
                             five years, Latvian Radio reported December
                             4.


                      # ⚓ Dispatches_from_Europe_–_No._12_–_December_3,_2024_–
                        Dispatches_After_the_Election_of_Trump⠀⇛


                             Dispatches After the Election of Trump


                             My last dispatch was almost a month ago, on
                             November 6, the day after Trump won the
                             American presidential election. The main
                             reason for the pause in dispatches is that my
                             hosts in Ukraine, and then Poland, Germany,
                             Czechia, and now the U.K., have kept me too
                             busy meeting with leftwing activists.


                      # ⚓ PHR ☛ Russian_Bombardment_of_Ukraine’s_Power_Grid
                        Forces_Health_Care_Workers_to_Operate_in_the_Dark:
                        Report⠀⇛


                             Russia’s widespread and systematic attacks on
                             Ukraine’s energy grid have harmed health care
                             workers and endangered patients, according to
                             a first-of-its-kind report published today by
                             Physicians for Human Rights (PHR) and Truth
                             Hounds.


                      # ⚓ Atlantic Council ☛ A_winning_strategy_to_end_Russia’s
                        war_against_Ukraine⠀⇛


                             More than a dozen experts from the United
                             States and Europe share their recommendations
                             to the incoming Trump administration about
                             how best to end Russia's war against Ukraine.


                      # ⚓ Atlantic Council ☛ Georgian_protests_escalate_amid
                        fears_over_mounting_Russian_influence⠀⇛


                             The outcome of the current protests in
                             Georgia will likely define the country's
                             future and shape the geopolitical climate in
                             the southern Caucasus and beyond for years to
                             come, writes Ana Lejava.


                      # ⚓ RFERL ☛ Ukrainian_Official_Says_Regional_Mayor_Died
                        After_Torture_In_Russian_Captivity⠀⇛


                             The head of Zaporizhzhya Region's Military
                             Administration, Ivan Fedorov, has alleged the
                             mayor of the Ukrainian town of Dniproprudne
                             died after being tortured while in Russian
                             custody.


                      # ⚓ RFERL ☛ NATO_Agrees_To_Prioritize_Protecting
                        Ukraine's_Infrastructure⠀⇛


                             NATO members have agreed to make protecting
                             Ukraine's infrastructure a top priority,
                             alliance chief Mark Rutte said on December 4,
                             as Russia continues to pound Ukrainian cities
                             and towns with drone and missile strikes.


                      # ⚓ MIT Technology Review ☛ How_the_Ukraine-Russia_war_is
                        reshaping_the_tech_sector_in_Eastern_Europe⠀⇛


                             At first glance, the Mosphera scooter may
                             look normal—just comically oversized.


                      # ⚓ CS Monitor ☛ On_Ukraine’s_homefront,_a_DIY_drone
                        industry_helps_fill_military’s_needs⠀⇛


                             Ukrainians are assembling drones at home to
                             help supply the military with the thousands
                             it uses every month in the war with Russia.


                      # ⚓ New York Times ☛ Russian_General_Calls_U.S._Chairman
                        of_Joint_Chiefs⠀⇛


                             In a highly unusual call, the two men
                             “discussed a number of global and regional
                             security issues, to include the ongoing
                             conflict in Ukraine,” a spokesman said.


                      # ⚓ New York Times ☛ Zelensky_Offers_$24_One-Off_Payment
                        to_Win_Over_War-Weary_Ukrainians⠀⇛


                             Citizens will be entitled to a $24 one-off
                             payment this winter, President Volodymyr
                             Zelensky announced, in a move apparently
                             intended to soften the blow of a tax rise to
                             help fund the war effort.


                      # ⚓ Meduza ☛ Ukrainian_mayor_dies_in_Russian_captivity_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Washington_says_Ukraine_needs_to_begin
                        drafting_younger_men_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Introducing_the_Oreshnik_What_Russia’s_’new’
                        ballistic_missile_means_for_Ukraine_and_nuclear
                        security_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘Closer_now_than_ever’:_Historian_Sergey
                        Radchenko_assesses_Tucker_Carlson’s_claim_that_U.S.-
                        Russian_tensions_in_Ukraine_risk_nuclear_war_more_than
                        the_Cuban_Missile_Crisis_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Trump_advisers_‘pitch_ideas’_as_Ukraine
                        peace_plan_materializes,_and_all_proposals_exclude_NATO
                        membership_—_Reuters_—_Meduza⠀⇛


                      # ⚓ RFERL ☛ Report:_Putin,_Other_Russian_Officials
                        Directly_Involved_In_Transfer,_Deportation_of_Ukrainian
                        Children⠀⇛


                             Senior Russian authorities, including
                             President Vladimir Putin, were directly
                             involved in ordering the forcible transfer,
                             fostering, and later adoption of Ukrainian
                             children moved out of war-zones and occupied
                             regions of Ukraine, U.S. researchers found.


          o § Environment⠀➾


                # ⚓ The Straits Times ☛ China_reports_warmest_autumn_since
                  records_began⠀⇛


                       Most regions experienced temperatures 1 deg C to 2
                       deg C above average.


                # § Energy/Transportation⠀➾


                      # ⚓ Barry Kauler ☛ Planning_to_affix_solar_panel_to
                        trike⠀⇛


                             Continuing the custom solar-assisted
                             recumbent trike project, here are recent
                             posts:


                                 # How_to_look_after_your_LFP_battery —
                                   November 09, 2024
                                 # IEC_C13_versus_Anderson_connectors —
                                   November 06, 2024
                             I completed the electrical wiring; motor,
                             junction-box, speed sensor, display panel,
                             etc., and with some trepidation flicked the
                             "motor" cicuit breaker on the junction box to
                             "on" and then pressed the power-on button on
                             the Bafang control panel ...and it worked.
                             had the rear wheel propped up on blocks of
                             wood and was able to test the pedal
                             assistance levels. Looking good.


                             The Bafang control panel mystifies me though.
                             I mounted it right in the middle, between the
                             legs:


          o § Finance⠀➾


                # ⚓ Latvia ☛ Employers:_2025_budget_increases_gap_between
                  households_with_and_without_children⠀⇛


                       The draft budget law for next year will increase
                       inequality between households with and without
                       children, as it does not raise the tax relief for a
                       dependent, said Pēteris Leiškalns, Social Security
                       and Healthcare Expert at the Employers'
                       Confederation of Latvia (LDDK), in an interview on
                       Latvian Radio program "Good Morning" December 4.


                # ⚓ Federal News Network ☛ IRS_warns_about_identity_theft_scams
                  this_holiday_season⠀⇛


                       Giving out your address, Social Security number,
                       bank account number or credit card number can lead
                       to tax-related theft and fraud.


                # ⚓ Silicon Angle ☛ SentinelOne_shares_fall_13%_as_loss_expands
                  despite_revenue_beat⠀⇛


                       Shares in SentinelOne Inc. were down around 13% in
                       late trading today after the cybersecurity company
                       reported a widening loss in its most recent quarter
                       and gave a cautious outlook despite reporting beats
                       in other core metrics in its fiscal 2025 third
                       quarter.


                # ⚓ Atlantic Council ☛ The_IMF_and_World_Bank_did_well_under
                  the_first_Trump_administration._Will_they_again?⠀⇛


                       The geopolitical rivalry between the United States
                       and China has become more intense since Trump’s
                       first term, which could affect how the incoming
                       administration approaches the Bretton Woods
                       institutions.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ France24 ☛ French_parliament_topples_PM_Barnier's
                  government_in_no-confidence_vote⠀⇛


                       France's parliament voted to oust the government of
                       French Prime Minister Michel Barnier in a no-
                       confidence vote Wednesday evening. The left-wing
                       New Popular Front alliance and far-right National
                       Rally party both vowed to topple Barnier's
                       government after he pushed an unpopular social
                       security budget bill through parliament without a
                       vote. President Emmanuel Macron's office said he
                       will address the nation Thursday evening.


                # ⚓ France24 ☛ Vote_to_oust_French_Prime_Minister_Michel
                  Barnier_a_‘forgone_conclusion’⠀⇛


                       FRANCE 24 journalist Clovis Casali, reporting from
                       the lower house National Assembly, said the
                       decision by MPs to oust French Prime Minister
                       Michel Barnier was a “forgone conclusion”. “His
                       speech was very much a goodbye speech, stressing
                       what he had achieved,” Casali remarked.


                # ⚓ France24 ☛ Barnier_govt_on_chopping_block:_'Very_surprising
                  alliance_between_left-wing_coalition_and_far_right'⠀⇛


                       France's government is facing no-confidence votes
                       that could spell the end of the administration of
                       Prime Minister Michel Barnier. For deeper insight
                       and perspective, as France plunges into uncharted
                       waters of political chaos, FRANCE 24's Genie Godula
                       welcomes Dr. Anna McKeever, Political Scientist,
                       Lecturer in Political Science at the University of
                       the West of Scotland and author of 'Immigration
                       Policy and Right-Wing Populism in Western Europe'.


                # ⚓ Hong Kong Free Press ☛ China_curbs_exports_of_key
                  chipmaking_components_to_US⠀⇛


                       Beijing said Tuesday it would restrict exports to
                       the United States of some key components in making
                       semiconductors, after Washington announced curbs
                       targeting China’s ability to make advanced chips.
                       Among the materials banned from export are metals
                       gallium, antimony and germanium, Beijing’s commerce
                       ministry said in a statement that cited “national
                       security” concerns.


          o § Censorship/Free Speech⠀➾


                # ⚓ Stanford University ☛ Behind_the_nationwide_rise_of_book
                  bans⠀⇛


                       Stanford experts dive into the recent increase in
                       incidents of book banning and what it means for
                       teachers, librarians, students and freedom of
                       speech.


                # ⚓ New York Times ☛ Iran_Releases_Narges_Mohammadi,_Nobel
                  Laureate,_From_Prison_for_21_Days⠀⇛


                       The activist, whose health has deteriorated, had
                       bone surgery last month. She was just 19 when
                       Iran’s morality police detained her.


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


                # ⚓ Hong Kong Free Press ☛ Post-security_law_Hong_Kong_‘beyond
                  redemption,’_‘useless_to_fight,’_Jimmy_Lai_tells_court⠀⇛


                       Jailed media tycoon Jimmy Lai has said that Hong
                       Kong “is beyond redemption” and that “it is useless
                       to fight” in the city after a national security law
                       imposed by Beijing came into effect in 2020.


          o § Civil Rights/Policing⠀➾


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_sees_rise_in_residents
                  trafficked_to_SE_Asia,_with_12_still_held_overseas_–_security
                  chief⠀⇛


                       Hong Kong has seen a rise in local residents lured
                       to Southeast Asia to engage in illegal work, with
                       12 Hongkongers still being held overseas, security
                       chief Chris Tang has said.


                # ⚓ JURIST ☛ Global_rights_groups_demand_Egypt_lift_ban_on
                  human_rights_defenders⠀⇛


                       34 rights organizations on Wednesday called on the
                       Egyptian government to immediately lift the travel
                       bans and asset freezes imposed on three directors
                       of the Egyptian Initiative for Personal Rights
                       (EIPR), an Egyptian human rights organization.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Computers Are Bad ☛ 2024-12-04_operators_on_the_front⠀⇛


                       At the very core of telephone history, there is the
                       telephone operator. For a lot of people, the vague
                       understanding that an operator used to be involved
                       is the main thing they know about historic
                       telephony. Of course, telephone historians, as a
                       group, tend to be much more inclined towards
                       machinery than people. This shows: websites with
                       information on, say, TD-2, seldom tell you much
                       about the operators as people.


                       Fortunately, telephone operators have merited more
                       than just a bit of discussion in the social
                       sciences. It was a major field of employment, many
                       ideas in management were tested out in the
                       telephone companies, and moreover, telephone
                       operators were women.


                # ⚓ APNIC ☛ How_to_boost_geolocation_accuracy_with_Geofeed⠀⇛


                       A friendly how to guide for network operators.


                # ⚓ Inside Towers ☛ FCC_Modifies_Emission_Limits_for_Mobile
                  Devices_in_the_23.6-24.0_GHz_Band⠀⇛


                       The FCC has modified unwanted emissions limits for
                       mobile operations for the 24.25-24.45 GHz and
                       24.75-25.25 GHz bands to prevent interference with
                       passive systems in the 23.6-24.0 GHz band. The
                       changes align with decisions made at the 2019 World
                       Radiocommunication Conference (WRC-19).


                       In the Report and Order, the Commission says the
                       23.6-24.0 GHz band is critical for passive sensors
                       that measure weak natural radio emissions vital for
                       meteorology, climatology, and satellite radar
                       operations. The limits apply to both current and
                       future mobile devices, with stricter limits coming
                       into effect after September 1, 2027.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Sean Conner ☛ Ice_ice_baby⠀⇛


                             The following week the technician showed up
                             again, bitched that we failed to answer his
                             messages. I explained that I set my phone to
                             have a silent default ring tone due to spam,
                             and a default text tone of silence, again due
                             to spam (and man, the amount of text spam I
                             recieved from politicians during election
                             season was staggering! Damn you policitians
                             and exempting yourselves from spam laws! Damn
                             you all to hell!). The technician was
                             nonplussed and said I should do something
                             about that. We gave him Bunny's phone number
                             as she doesn't have a silent default ring
                             tone.


      § Monopolies/Monopsonies⠀➾


          o ⚓ JURIST ☛ Australia_proposes_new_regime_to_fine_tech_companies_for
            anti-competitive_practices⠀⇛


                 The Australian government on Monday unveiled a proposed
                 competition scheme to introduce new laws that would allow
                 global technology companies to be fined up to $50 million
                 AUD for anti-competitive behavior and obstructing
                 consumer choice.


          o § Copyrights⠀➾


                # ⚓ Creative Commons ☛ Welcoming_Angela_Oduor_Lungati_as_CC
                  Board_Chair⠀⇛


                       “Yellow Chair, The High Line” by Shawn Hoke is
                       licensed under CC BY-NC-ND 2.0. Creative Commons
                       (CC) has—and continues to be—fortunate to have an
                       expert and passionate board of directors, many of
                       whom have been instrumental to the success of CC at
                       both the organizational level, as well as
                       nationally and regionally.





                    ䷩ 𝚕𝚒𝚗𝚎 6372

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 05/12/2024: Formaldehyde and Cancer,
US and China Boycotting One Another⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Winter_Street⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
          o Finance
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ The Straits Times ☛ Starbucks_cafe_offers_view_of_village_in
            North_Korea,_stirring_up_bittersweet_feelings⠀⇛


                 Some visitors feel sad as they look at the North and
                 reflect on the disparity in living standards between both
                 sides.


          o § Hardware⠀➾


                # ⚓ The Straits Times ☛ Indonesia_says_Fashion_Company_Apple_to
                  offer_$1.34_billion_to_lift_iPhone_ban⠀⇛


                       If confirmed, that would be a tenfold increase from
                       Apple’s last offer of US$100 million.


                # ⚓ Cloudbooklet ☛ US_Cracks_Down_on_China_Hey_Hi_(AI)_Chip
                  Access⠀⇛


                       Discover the latest updates on China Hey Hi (AI)
                       Chip Access and its implications.


                # ⚓ France24 ☛ US_-_China_chip_war_heats_up_as_Beijing_bans
                  export_of_key_minerals⠀⇛


                       A day after the US government announced new export
                       restrictions hitting China's chip industry, Beijing
                       retaliated with a ban on the sale of key minerals
                       like gallium and germanium to the United States.


                # ⚓ New York Times ☛ China_Announces_a_Ban_on_Rare_Minerals_to
                  the_U.S.⠀⇛


                       The move escalates supply chain warfare and comes a
                       day after the Biden administration expanded curbs
                       on the sale of advanced American technology to
                       China.


                # ⚓ The Straits Times ☛ China_to_curb_exports_of_key_chipmaking
                  components_to_US⠀⇛


                       Among the materials banned from export are metals
                       gallium, antimony and germanium.


                # ⚓ Tom's Hardware ☛ Chinese_chip_firms_say_a_new_round_of_US
                  sanctions_won’t_stop_China’s_chip_industry_—_Chinese
                  government_responds_with_its_own_export_restrictions
                  anyways⠀⇛


                       The US and China trade blows yet again on
                       semiconductor products and minerals, but Chinese
                       companies say they’ll survive.


                # ⚓ The Next Platform ☛ US_Curbs_HBM_Exports_To_China_–_More
                  For_The_Rest_Of_Us⠀⇛


                       Current US president Joe Biden and once and future
                       president Donald Trump do not agree on much.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Pro Publica ☛ Formaldehyde_Increases_Your_Cancer_Risk_No
                  Matter_Where_you_Live⠀⇛


                       In a world flush with hazardous air pollutants,
                       there is one that causes far more cancer than any
                       other, one that is so widespread that nobody in the
                       United States is safe from it.


                       It is a chemical so pervasive that a new analysis
                       by ProPublica found it exposes everyone to elevated
                       risks of developing cancer no matter where they
                       live. And perhaps most worrisome, it often poses
                       the greatest risk in the one place people feel
                       safest: inside their homes.


                # ⚓ ProPublica_Cancer_Risk_Map⠀⇛


                       In most of the country, formaldehyde contributes
                       more to outdoor cancer risk than any other toxic
                       air pollutant. Look up your address to see risks
                       from the chemical on your block and where it comes
                       from.


                # ⚓ Science Alert ☛ Lockdowns_Did_Something_to_Teen_Brains,_And
                  We_Need_to_Talk_About_It⠀⇛


                       This might not be over.


                # ⚓ New York Times ☛ McDonald’s_E_Coli_Outbreak_Declared_Over⠀⇛


                       Federal health agencies closed their investigations
                       into the bacterial outbreak that sickened 104
                       people and was linked to onions on the fast-food
                       chain’s signature Quarter Pounders.


                # ⚓ LSA_professor_studies_anti-aging_interventions,_diseases⠀⇛


                       An LSA professor is studying how to extend the
                       healthy years of human life by building biological
                       resistance against the many diseases that we face
                       as we get older.


                # ⚓ TwinCities Pioneer Press ☛ Michaud,_Todd:_How_St._Paul_can
                  find_a_good_way_forward_from_its_fiscal_ailments⠀⇛


                       In$ight St. Paul is a group of St. Paul residents
                       who are very concerned about the financial health
                       of the city. We span the political spectrum,


                # ⚓ JURIST ☛ Historic_UN_plastic_pollution_treaty_negotiation
                  to_reconvene_in_2025⠀⇛


                       The fifth session of negotiations on a historic,
                       legally binding global plastic pollution treaty
                       concluded on Sunday, with countries agreeing to
                       reconvene in 2025.


                # ⚓ The Straits Times ☛ When_necessity_becomes_luxury:_Many
                  torn_over_keeping_insurance_policies_in_Malaysia⠀⇛


                       Rising premiums have prompted some people to cancel
                       their health insurance policies.


                # ⚓ The Straits Times ☛ Consumer_group_calls_for_Bank_Negara
                  Malaysia_to_tighten_controls_over_insurance_premium_hikes⠀⇛


                       Many may be forced to discontinue their policies,
                       leaving them without essential medical coverage.


                # ⚓ JURIST ☛ US_Supreme_Court_hears_oral_arguments_over_FDA
                  refusal_to_approve_flavored_e-cigarettes⠀⇛


                       The US Supreme Court on Monday heard oral arguments
                       in a case in which the Food and Drug Administration
                       (FDA) refused to approve flavored e-cigarettes,
                       citing public health concerns. The FDA denied
                       applications from two companies — Triton
                       Distribution and Vapetesia — to sell flavored
                       liquids for use in e-cigarettes, also known as
                       vapes.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Bruce Schneier ☛ Algorithms_Are_Coming_for_Democracy—but
                  It’s_Not_All_Bad⠀⇛


                       In 2025, Hey Hi (AI) is poised to change_every
                       aspect_of_democratic_politics—but it won’t
                       necessarily be for the worse.


                       India’s prime minister, Narendra Modi, has used Hey
                       Hi (AI) to translate his speeches for his
                       multilingual electorate in real time, demonstrating
                       how Hey Hi (AI) can help diverse democracies to be
                       more inclusive. Hey Hi (AI) avatars were used by
                       presidential candidates in South Korea in
                       electioneering, enabling them to provide answers to
                       thousands of voters’ questions simultaneously.


          o § Security⠀➾


                # ⚓ Latvia ☛ 'CyberBazaar'_events_start_Tuesday_in_Rīga⠀⇛


                       From December 3 to 5, the first cyber security
                       innovation forum in the Baltic States dubbed
                       "CyberBazaar 2024" is being held in Rīga, organized
                       by the Latvian National Cyber ​​Security Center in
                       cooperation with Estonian and Lithuanian
                       colleagues.


                # ⚓ Scoop News Group ☛ Inside_a_new_initiative_to_lend
                  cybersecurity_volunteers_to_organizations_that_need_it_most⠀⇛


                       The idea behind the initiative, details of which
                       CyberScoop is first reporting, is that too much
                       cyber expertise doing volunteer work is
                       uncoordinated.


                # ⚓ CNCF_Graduates_Cert-Manager_to_Help_Streamline_Certificate
                  Workflows⠀⇛


                       The cert-manager project has officially been
                       graduated by the Cloud Native Computing Foundation
                       (CNCF) at a time when managing certificates has
                       become more challenging than ever.


                       >


                # ⚓ Qubes_Canary_041⠀⇛


                       We have published Qubes_Canary_041. The text of
                       this canary and its accompanying cryptographic
                       signatures are reproduced below. For an explanation
                       of this announcement and instructions for
                       authenticating this canary, please see the end of
                       this announcement.


                # ⚓ Scoop News Group ☛ U.S._government_says_Salt_Typhoon_is
                  still_in_telecom_networks⠀⇛


                       The United States and other Western nations
                       released guidance Tuesday designed to evict the
                       China-linked group in the wake of the high-profile
                       hack.


                # § Privacy/Surveillance⠀➾


                      # ⚓ NYOB ☛ noyb_is_now_qualified_to_bring_collective
                        redress_actions⠀⇛


                             noyb is now approved as so-called "Qualified
                             Entity" to bring collective redress actions
                             in courts throughout the European Union


                      # ⚓ Scoop News Group ☛ CFPB_proposes_new_rule_to_regulate
                        expansive_data_broker_industry⠀⇛


                             The rule would force data brokers to adhere
                             to the same standards as established credit
                             agencies.


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ Read_President_Yoon’s_Speech_Declaring
                  Martial_Law_in_South_Korea⠀⇛


                       President Yoon Suk Yeol made the extraordinary
                       declaration in an unannounced speech to the nation
                       on Tuesday night.


                # ⚓ The Strategist ☛ Avoiding_downstream_consequences:
                  Australia’s_role_in_promoting_water_security_in_the_Middle
                  East⠀⇛


                       Australia can partner with Middle Eastern countries
                       on something we both really understand: how to
                       manage scarce water.


                # ⚓ Atlantic Council ☛ NATO_exercises:_The_guarantee_of
                  Alliance_security_and_test_of_readiness⠀⇛


                       To ensure regional security, NATO must continue
                       enhancing its capabilities and remain as a combat-
                       ready force.


                # ⚓ Atlantic Council ☛ The_“other”_US_election_and_what_it
                  means_for_transatlantic_security⠀⇛


                       US allies and partners have better grounds to
                       expect continued US leadership—
                       and alliance commitment—than is commonly
                       appreciated.


                # ⚓ Atlantic Council ☛ NATO_in_an_evolving_geopolitical
                  landscape⠀⇛


                       The fourth issue of the Defense Journal by Atlantic
                       Council IN TURKEY explores the future of NATO in
                       the context of changing transatlantic relations and
                       regional security issues.


                # ⚓ New York Times ☛ Google_Worried_Israeli_Contract_Could
                  Enable_Human_Rights_Violations⠀⇛


                       The tech giant, which has defended the deal to
                       employees who oppose supplying Israel’s military
                       with technology, feared the project might damage
                       its reputation.


                # ⚓ Hong Kong Free Press ☛ Taiwan_launches_hotlines_for
                  managing_‘safety_risks’_when_travelling_to_Hong_Kong,_Macau
                  and_China⠀⇛


                       Taiwan has launched hotlines for travellers seeking
                       information about their “safety risks” while in
                       China, which recently published tough criminal
                       sentencing guidelines for supporters of the
                       island’s independence.


                # ⚓ The Straits Times ☛ Taiwan_launches_hotlines_to_help
                  navigate_China_travel_‘safety_risks’⠀⇛


                       The hotlines will address concerns over new
                       guidelines from Beijing for supporters of Taiwanese
                       independence.


                # ⚓ Hong Kong Free Press ☛ Taiwan_President_Lai_Ching-te
                  arrives_in_Marshall_Islands_as_China_fumes⠀⇛


                       Taiwanese President Lai Ching-te arrived in the
                       Marshall Islands on Tuesday, after visiting the
                       United States on the first stop of a Pacific tour
                       that has angered Chinese leaders.


                # ⚓ The Straits Times ☛ Taiwan’s_President_Lai_kicks_off
                  Marshall_Islands_visit_as_China_fumes⠀⇛


                       Taiwan sends significant climate change and
                       infrastructure aid to the Marshall Islands.


                # ⚓ The Straits Times ☛ Canada_says_Pacific_trade_pact_open_to
                  new_members_after_Taiwan_complains⠀⇛


                       Taiwan has few international trade agreements due
                       to its diplomatic isolation because of pressure
                       from China.


                # ⚓ LRT ☛ Ball_is_in_China’s_court_regarding_diplomatic
                  relations_with_Lithuania_–_FM_candidate⠀⇛


                       China should initiate the restoration of full
                       diplomatic representation with Lithuania, says
                       Kęstutis Budrys, the candidate for Lithuania’s
                       foreign minister, currently serving as an adviser
                       to President Gitanas Nausėda.


                # ⚓ LRT ☛ Lithuania’s_PM-designate_says_he_didn’t_know_about
                  Chinese_mission_staff_expulsion⠀⇛


                       Lithuania’s Social Democrat Prime Minister-
                       designate Gintautas Paluckas says he was not
                       informed about the decision to expel three
                       employees of China’s diplomatic mission from
                       Lithuania.


                # ⚓ New York Times ☛ From_Chinese_Patriot_to_American_Spy:_The
                  Unusual_Life_of_John_Leung⠀⇛


                       He had been hailed by Chinese state media as a
                       model for his efforts to promote Beijing’s
                       interests in the United States. He was in fact an
                       F.B.I. informant.


                # ⚓ Defence Web ☛ Understanding_US-Angola_security_cooperation
                  and_military_partnership⠀⇛


                       US President Joe Biden is visiting Angola in a
                       historic milestone that underscores a strengthening
                       partnership, with a particular emphasis on security
                       cooperation. This unprecedented visit reflects the
                       Biden administration’s commitment to enhancing
                       bilateral relations and addressing shared security
                       challenges.


                # ⚓ New Yorker ☛ How_the_Syrian_Opposition_Shocked_the_Assad
                  Regime⠀⇛


                       A historian explains why U.S. sanctions and Iran
                       and Russia’s entanglements in other wars helped
                       create an opening for rebel groups to overrun the
                       Syrian Army.


                # ⚓ CS Monitor ☛ Syrian_civil_war:_What_rebels’_lightning_gains
                  say_about_Assad_regime⠀⇛


                       Syria’s devastating civil war, responsible for more
                       than 300,000 deaths, was never officially resolved.
                       Lightning gains by rebels opposed to President
                       Bashar al-Assad were opportunistic, but also
                       indicated years of patient preparations.


                # ⚓ Meduza ☛ The_Syrian_civil_war_is_suddenly_unfrozen._How
                  much_can_Russia_afford_to_support_the_Assad_regime_this_time?
                  —_Meduza⠀⇛


                # ⚓ New York Times ☛ Amid_Syria’s_Rebel_Offensive,_a
                  Geopolitical_Cauldron_Simmers⠀⇛


                       Iran and Russia, both stretched by conflicts of
                       their own, have experienced setbacks in Syria after
                       a rebel offensive in the northwest of the country.


                # ⚓ New York Times ☛ Martial_Law_in_South_Korea_Tests_Biden_and
                  a_Key_U.S._Alliance⠀⇛


                       The Biden administration has hailed South Korea as
                       a model democracy and bolstered military ties as it
                       relies on the country as a bulwark against North
                       Korea, China and Russia.


                # ⚓ Meduza ☛ Moscow_urges_Russian_citizens_in_South_Korea_to
                  avoid_public_gatherings_amid_anti-martial_law_protests_—
                  Meduza⠀⇛


                # ⚓ The Straits Times ☛ Live:_South_Korean_president_makes_U-
                  turn_on_martial_law⠀⇛


                       President Yoon said he would lift martial law after
                       lawmakers voted to oppose the unexpected
                       declaration.


                # ⚓ France24 ☛ Yoon_'created_the_rhetoric_of_a_national
                  security_crisis'_in_South_Korea,_analyst_says⠀⇛


                       South Korean President Yoon Suk Yeol’s government
                       early Wednesday lifted the martial law he imposed
                       during a tense night of political drama in which
                       troops surrounded parliament and lawmakers voted to
                       reject military rule. FRANCE 24's Sharon Gaffney
                       speaks to Professor Katherine Moon of Wellesley
                       College in Boston. She says that President Yoon
                       created the rhetoric of a national security crisis
                       and has likely signalled his own downfall.


                # ⚓ The Straits Times ☛ What_next_for_South_Korea’s_President
                  Yoon_Suk_Yeol_after_failed_martial_law_attempt?⠀⇛


                       Botched martial law declaration spells end of
                       political career, say analysts.


                # ⚓ The Straits Times ☛ South_Korea_President_Yoon_declares
                  martial_law,_but_Parliament_votes_to_lift_declaration⠀⇛


                       He said the measure was necessary to protect the
                       country from “communist forces”.


                # ⚓ The Straits Times ☛ Live:_South_Korea_lawmakers_block
                  president’s_martial_law_decree⠀⇛


                       President Yoon said he would lift martial law after
                       lawmakers voted to oppose the unexpected
                       declaration.


                # ⚓ The Straits Times ☛ ‘Can’t_believe_I’m_seeing_martial_law
                  declaration_in_my_lifetime’:_Shock,_confusion_among
                  S.Koreans⠀⇛


                       The financial markets have responded with panic,
                       exacerbating the public’s distress.


                # ⚓ The Straits Times ☛ In_full:_South_Korea’s_martial_law
                  decree⠀⇛


                       All media and publications are subject to the
                       control of the Martial Law Command.


                # ⚓ The Straits Times ☛ What_next_for_South_Korea’s_President
                  Yoon_Suk_Yeol?⠀⇛


                       Botched martial law declaration spells end of
                       political career, say analysts.


                # ⚓ The Straits Times ☛ Martial_law_in_South_Korea_tests_Biden
                  and_a_key_US_alliance⠀⇛


                       Nearly 30,000 US troops are stationed in South
                       Korea.


                # ⚓ The Straits Times ☛ South_Korea’s_President_Yoon_Suk_Yeol,
                  embattled_conservative⠀⇛


                       Mr Yoon took office with some of the lowest
                       approval ratings of any democratically elected
                       South Korean president.


                # ⚓ The Straits Times ☛ South_Korea’s_President_Yoon_Suk_Yeol
                  says_martial_law_decree_will_be_lifted⠀⇛


                       He had imposed the order hours earlier in a bid to
                       quell what he called “anti-state forces”.


                # ⚓ The Straits Times ☛ South_Korea’s_martial_law_declaration:
                  What_we_know_so_far⠀⇛


                       South Korea President Yoon Suk Yeol declared
                       martial law late on Dec 3 - then reversed course
                       just hours later.


                # ⚓ France24 ☛ South_Korea's_President_Yoon_rescinds
                  declaration_of_martial_law_after_parliament_votes_to_block
                  it⠀⇛


                       President Yoon Suk Yeol said he was rescinding his
                       declaration of martial law after South Korea's
                       parliament voted Tuesday to block it as hundreds of
                       protesters gathered outside the building, calling
                       for Yoon's arrest.


                # ⚓ France24 ☛ 🔴_South_Korean_President_Yoon_Suk_Yeol_declares
                  martial_law⠀⇛


                # ⚓ France24 ☛ 'Against_will_of_people':_President_Yoon's
                  'miscalculation'_in_declaring_Martial_Law_'crossed_line'⠀⇛


                       Troops surrounded South Korea's parliament
                       overnight after the president declares martial law.
                       He accused pro-North Korean forces of plotting to
                       overthrow one of the world’s most vibrant
                       democracies. As lawmakers voice outrage, and
                       hastily vote to end the declaration, FRANCE 24's
                       François Picard welcomes Peter Han, Gates Cambridge
                       Scholar at the University of Cambridge and member
                       of the National Unification Advisory Council UK.


                # ⚓ France24 ☛ 🔴_South_Korean_President_Yoon_rescinds_martial
                  law_after_parliament_votes_to_block_it⠀⇛


                # ⚓ France24 ☛ No,_these_images_don’t_show_tanks_and_protests
                  in_the_streets_of_Seoul⠀⇛


                       Following the declaration of martial law in South
                       Korea by President Yoon Suk Yeol, images of tanks
                       and alleged massive protests in Seoul started to
                       circulate online. We tell you which images are fake
                       and which are real, in this edition of Truth or
                       Fake.


                # ⚓ The Straits Times ☛ South_Korea_President_Yoon’s_failed
                  attempt_at_martial_law_may_put_his_position_in_peril⠀⇛


                       Mr Yoon's shocking late-night declaration of
                       martial law has thrown his political future into
                       doubt.


                # ⚓ The Straits Times ☛ US_says_it_is_watching_events_in_South
                  Korea_with_grave_concern⠀⇛


                       South Korean President Yoon Suk Yeol declared
                       martial law in a surprise late-night TV address,
                       before the opposition-led Parliament overturned it.


                # ⚓ New York Times ☛ Chaos_Plays_Out_at_South_Korea’s
                  Legislature_Building_After_Declaration_of_Martial_Law⠀⇛


                       Soldiers wearing helmets and carrying long guns
                       pushed back against people who tried to enter the
                       National Assembly, after President Yoon Suk Yeol
                       declared martial law.


                # ⚓ New York Times ☛ Who_Is_Yoon_Suk_Yeol,_South_Korea’s
                  President?⠀⇛


                       A conservative, Mr. Yoon won the presidency in 2022
                       by a slim margin, promising a more confrontational
                       stance against North Korea. He quickly became
                       unpopular and divisive at home.


                # ⚓ New York Times ☛ Who_is_Lee_Jae-myung,_South_Korea’s
                  Opposition_Leader?⠀⇛


                       The opposition leader rallied lawmakers to vote
                       down President Yoon Suk Yeol’s martial law decree.


                # ⚓ New York Times ☛ Live_Updates:_South_Korean_President_Backs
                  Down_From_Martial_Law⠀⇛


                       President Yoon Suk Yeol formally lifted martial law
                       in a cabinet meeting early Wednesday, six hours
                       after he declared it, and after protesters filled
                       the street, calling for his removal from office.


                # ⚓ New York Times ☛ Timeline:_How_Yoon’s_Presidency_in_South
                  Korea_Led_to_Martial_Law_Order⠀⇛


                       Yoon Suk Yeol’s decree, and his reversal under
                       pressure from lawmakers, were the culmination of
                       years of feuding between the country’s two main
                       political camps.


                # ⚓ New York Times ☛ Why_Was_Martial_Law_Declared_in_South
                  Korea?⠀⇛


                       President Yoon Suk Yeol has been locked in a bitter
                       fight with the opposition, which controls
                       Parliament.


                # ⚓ The Straits Times ☛ 38_Vietnamese_tourists_reported_missing
                  in_South_Korea’s_Jeju_island⠀⇛


                       The missing tourists were part of a group of around
                       90 tourists who arrived in Jeju on Nov 14.


                # ⚓ France24 ☛ Domino_effect?_Assad's_allies_stretched_thin_as
                  Syrian_rebels_pounce⠀⇛


                       It took years for Bashar al-Assad’s forces to take
                       back Syria’s second city.


                       It took days for jihadist-led rebels to overrun
                       Aleppo. Why has a conflict that has been
                       effectively frozen for four years suddenly spring
                       back to life? What to make of Hezbollah, pinned
                       down at home by a precarious truce with Israel,
                       saying it won’t be sending help for now.


                # ⚓ France24 ☛ The_ruins_of_Paris_through_the_lenses_of_Yves
                  Marchand_and_Romain_Meffre⠀⇛


                       Two photographers whose images look like something
                       you might see in a Hollywood high budget film have
                       spoken to FRANCE 24 about their work. They take
                       pictures of Paris, and then use artificial
                       intelligence to adapt them to take viewers to a
                       post-apocalyptic world where humans are perhaps no
                       more. Their photography has been made into a book
                       Les Ruines de Paris, or the ruins of Paris. Yves
                       Marchand and Romain Meffre spoke to us in
                       perspective.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ France24 ☛ Chernobyl's_mutant_wolves:_A_case_study_of
                        adaptation_and_cancer_resistance⠀⇛


                             In the Science segment, we tell you more
                             about the so-called "mutant wolves of
                             Chernobyl". 38 years after the nuclear
                             disaster, animals roaming the exclusion zone
                             are still exposed to high levels of radiation
                             but researchers have also found that part of
                             their genetic information appears to be
                             resilient to increased risk of cancer.


                      # ⚓ Meduza ☛ Swapping_rainbows_for_war_anthems:_How_the
                        Kremlin’s_anti-LGBTQ+_crackdown_is_reshaping_queer
                        clubs_in_Russia_—_Meduza⠀⇛


                      # ⚓ Latvia ☛ Riga_Security_Forum_podcast:_'China_and
                        Russia:_A_Special_Relations_Operation'⠀⇛


                             The Riga Security Forum podcast is back with
                             another topical discussion.


                      # ⚓ RFERL ☛ Erdogan_Calls_For_More_Diplomacy_In_Talks
                        With_Putin_On_Revived_Conflict_In_Syria⠀⇛


                             Russian President Vladimir Putin and Turkish
                             President Recep Tayyip Erdogan stressed the
                             need for diplomacy to resolve the conflict in
                             northern Syria in a phone call on December 3
                             to discuss the renewed fighting.


                      # ⚓ Atlantic Council ☛ Vladimir_Putin_does_not_want_a
                        peace_deal._He_wants_to_destroy_Ukraine.⠀⇛


                             Donald Trump has vowed to end the war in
                             Ukraine, but there is no sign that Vladimir
                             Putin has any interest in a peace deal that
                             would prevent him from achieving his goal of
                             extinguishing Ukrainian statehood, writes
                             Yuliya Kazdobina.


                      # ⚓ New York Times ☛ Investigation_Into_Forced_Adoptions
                        From_Ukraine_Points_Finger_at_Putin⠀⇛


                             Yale researchers traced hundreds of children
                             taken to Russia in the war, finding what they
                             described as “a higher level of crime than
                             first understood.”


                      # ⚓ Latvia ☛ Rules_for_Ukrainian_children_going_to
                        Latvian_schools_stuck_in_debate⠀⇛


                             In the summer, the government decided that
                             starting the next school year, children - war
                             refugees from Ukraine - will have to study in
                             Latvian schools in person. The Saeima's
                             support is needed for this requirement to
                             come into force. However, the idea is
                             currently stuck in the Saeima, Latvian Radio
                             reported on December 3.


                      # ⚓ Atlantic Council ☛ The_EU_needs_a_Russia_strategy⠀⇛


                             The new European Commission should prioritize
                             the development of an EU Russia strategy
                             aimed at creating a more forward-thinking,
                             ambitious, and cohesive European approach
                             toward Moscow, write Ian Cameron and James
                             Batchik.


                      # ⚓ Atlantic Council ☛ Political-military_lessons_for_a
                        NATO-Russia_conflict⠀⇛


                             NATO should learn these three lessons from
                             the Ukraine-Russia conflict to win a
                             potential NATO-Russia war.


                      # ⚓ France24 ☛ Ukraine_pushes_NATO_for_membership_ahead
                        of_Trump_presidency⠀⇛


                             Ukraine insisted Tuesday that NATO membership
                             was the only "real guarantee" for its
                             security, but foreign ministers from the
                             alliance sidestepped Kyiv's push for an
                             invite ahead of Donald Trump's return to the
                             US presidency. FRANCE 24's speaks to Dr Gavin
                             Hall from the University of Strathclyde. He
                             says that although the formal position of
                             NATO is to be open to a Ukrainian membership,
                             it's uncertain whether every member is
                             willing to accept it into the alliance.


                      # ⚓ LRT ☛ Number_of_Russians,_Belarusians,_Ukrainians
                        with_residence_permits_in_Lithuania_drops⠀⇛


                             The number of Russians, Belarusians, and
                             Ukrainians holding residence permits in
                             Lithuania has declined by over 20,000 since
                             the start of this year, figures from the
                             Interior Ministry show.


                      # ⚓ LRT ☛ Driving_tests_in_Lithuania_to_take_place_only
                        in_EU_languages⠀⇛


                             From January next year, driving tests in
                             Lithuania will take place only in Lithuanian
                             or other official EU languages. However, an
                             exception will be made for Ukrainians, the
                             Interior Ministry said on Tuesday.


                      # ⚓ RFERL ☛ Ukraine_Again_Calls_For_Full_Membership_As
                        NATO_Ministers_Meet_In_Brussels⠀⇛


                             Ukraine has again called for membership in
                             NATO, saying that only joining the alliance
                             in full would guarantee its future security
                             as it fights to stave off Russia's nearly
                             three-year invasion.


                      # ⚓ New York Times ☛ NATO_Chief_Urges_More_Weapons_for
                        Ukraine_Ahead_of_Any_Peace_Talks⠀⇛


                             Mark Rutte said it was up to Ukraine to
                             decide when it was ready to begin
                             negotiations with Russia — and that the West
                             should help strengthen Kyiv’s position
                             beforehand.


                      # ⚓ Meduza ☛ France_and_U.K._might_send_peacekeepers_if
                        Russia_and_Ukraine_reach_ceasefire_—_RFE/RL_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia’s_college_aptitude_exam_reportedly_to
                        include_Ukraine_war_veterans_alongside_historical
                        figures_—_Meduza⠀⇛


                      # ⚓ Latvia ☛ Government_okays_banning_Russian_language
                        from_transport_signage⠀⇛


                             On Tuesday, December 3, the government
                             approved the cabinet regulations prepared by
                             the Ministry of Justice, which state that in
                             transport and related infrastructure, signs
                             and information must be provided in Latvian
                             and if needed, another official language of
                             the European Union (EU).


                      # ⚓ Atlantic Council ☛ Pacing_scenarios⠀⇛


                             Here are some scenarios that NATO should be
                             prepared for against the possibility of a
                             generational conflict with Russia.


                      # ⚓ Atlantic Council ☛ How_prepared_is_NATO?⠀⇛


                             Is NATO ready to respond to a possible
                             expansion of Russian aggression to assure
                             Europe's safety?


                      # ⚓ France24 ☛ Kirill_Serebrennikov’s_poetic_take_on
                        Russian_punk_outsider_Eduard_Limonov⠀⇛


                             Eduard Limonov was a poet, a punk, a Russian
                             “émigré” and provocateur whose anti-system
                             politics eventually saw him embrace fascist
                             tendencies. Filmmaker Kirill Serebrennikov
                             tells Olivia Salazar-Winspear why he chose to
                             make a “ballad” of Limonov’s life and not a
                             biopic, revealing that British actor Ben
                             Wishaw even had the Russian crew members
                             fooled with his impressive embodiment of the
                             character. Serebrennikov tells us how
                             Limonov’s political arc follows the far right
                             movements within contemporary Russia and
                             mirroring the geopolitical situation around
                             the world. And, as an immigrant himself, the
                             award-winning director tells us why he thinks
                             Moscow’s attempts to silence Russian artists
                             means the government has little influence
                             over those who criticise it.


                      # ⚓ France24 ☛ 'Russia_believes_it_should_control
                        Georgia'⠀⇛


                             Georgia has been locked in a political crisis
                             since its contested October election, with
                             tens of thousands of pro-EU protesters taking
                             to the streets in recent days against the
                             increasingly authoritarian Eurosceptic
                             government. For in-depth analysis and a
                             deeper perspective on Georgia's Russian-
                             friendly pivot away from the EU, FRANCE 24's
                             Eve Irvine is joined by Dr. Natasha
                             Lindstaedt, Author, Professor of Government
                             at the University of Essex and the Deputy
                             Dean of Education in Social Sciences.


                      # ⚓ RFERL ☛ Georgia's_Abkhazia_Lawmakers_Reject
                        'Enslaving'_Investment_Deal_With_Russia⠀⇛


                             De facto lawmakers of Georgia's breakaway
                             region of Abkhazia on December 3 rejected an
                             investment deal with Russia, a document that
                             has caused political turmoil and mass
                             protests, highlighting the region’s fraught
                             relationship with Moscow.


                      # ⚓ LRT ☛ Lithuania_downgrades_OSCE_representation_over
                        planned_Lavrov_attendance⠀⇛


                             Lithuania is downgrading the level of its
                             representation at the upcoming Organization
                             for Security and Co-operation in Europe
                             (OSCE) ministerial meeting in Malta as
                             Russian Foreign Minister Sergey Lavrov plans
                             to attend it, the Foreign Ministry told BNS
                             on Tuesday.


                      # ⚓ RFERL ☛ Russian_Woman_Arrested_In_U.S._For_Alleged
                        Ties_To_Russian_Intelligence⠀⇛


                             The FBI has charged Russian national Nomma
                             Zarubina with providing false information to
                             U.S. law enforcement and maintaining
                             connections with Russian intelligence
                             services, linking her to another suspected
                             spy who fled the United States while being
                             pursued by authorities.


                      # ⚓ Meduza ☛ Top_Russian_bank_executive_publishes_‘letter
                        to_Santa’_asking_for_stabilized_ruble_and_help_with
                        inflation_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_city_quietly_replaces_blue_and
                        yellow_ornaments_on_central_public_Christmas_tree_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Small_asteroid_lights_up_Siberian_sky_—
                        Meduza⠀⇛


          o § Environment⠀➾


                # ⚓ The Straits Times ☛ Malaysia_floods:_Six_months’_worth_of
                  rain_fell_in_five_days_across_east_coast,_says_PM_Anwar⠀⇛


                       PM Anwar also said the government is preparing for
                       the forecast monsoon surge.


                # ⚓ The Straits Times ☛ Malaysians_return_to_devastated_homes
                  as_flood_waters_recede;_more_rain_expected⠀⇛


                       The number of people in temporary shelters in
                       Malaysia fell to just under 95,000 on the morning
                       of Dec 3.


                # ⚓ The Straits Times ☛ Top_emitter_China_tells_World_Court
                  that_UN_treaties_cover_states’_climate_obligations⠀⇛


                       The UN has asked the court to issue an opinion on
                       countries' legal responsibility for the negative
                       impact of climate change.


                # § Energy/Transportation⠀➾


                      # ⚓ LRT ☛ From_‘doctors’_plane’_to_fatalities_in_the_sea
                        –_history_of_Lithuanian_aviation_disasters⠀⇛


                             The last decades have been relatively quiet
                             in Lithuania’s aviation sector. The 20th
                             century, however, was marked by far more
                             fatal crashes. The largest Lithuania-related
                             disaster occurred in 1973 when a passenger
                             plane flying from Vilnius crashed near
                             Moscow, killing 51 people, says Lithuanian
                             Aviation Museum curator Eugenijus Raubickas.


          o § Finance⠀➾


                # ⚓ Latvia ☛ KNAB_to_take_over_tax_service's_anti-corruption
                  tasks⠀⇛


                       On Tuesday, December 3, the Cabinet of Ministers
                       (MK) approved the draft order on the transfer of
                       the functions of the Internal Security Department
                       of the State Revenue Service (VID) to the
                       Corruption Prevention and Combating Bureau (KNAB).


                # ⚓ Atlantic Council ☛ There’s_a_more_effective_way_forward
                  than_“maximum_pressure”_for_Venezuela⠀⇛


                       Following the fraudulent outcome of Venezuela's
                       July election, there is growing pressure on the
                       United States to reintroduce sanctions to expel
                       Western firms from the nation’s oil sector.


                # ⚓ The Straits Times ☛ Corruption_cases_in_China_rise_amid
                  deeper_crackdown,_poorer_economy⠀⇛


                       For the first nine months of 2024, China has logged
                       642,000 corruption cases, higher than the 626,000
                       for the whole of 2023.


                # ⚓ The Straits Times ☛ In_pivot_from_India,_Nepal_PM_seeks
                  economic_support_from_China⠀⇛


                       Mr K.P. Sharma Oli has so far been greeted by
                       familiar pledges of assistance, but no new
                       investment.


          o § Censorship/Free Speech⠀➾


                # ⚓ Silicon Angle ☛ Who_is_David_Mayer?_Abusive_Monopolist
                  Microsoft_Chaffbot_faces_scrutiny_over_censorship_of_public
                  figures⠀⇛


                       Who is David Mayer? A month after Proprietary
                       Chaffbot Company added a search engine to its
                       highly popular Abusive Monopolist Microsoft
                       Chaffbot service, users are unable to get answers
                       to anything relating to David Mayer in a mystery
                       that swept the internet over the last week.


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


                # ⚓ Hong Kong Free Press ☛ Jimmy_Lai_tells_trial_it_was_his
                  ‘honest_belief’_Western_sanctions_on_China_could_stop_Beijing
                  from_imposing_security_law⠀⇛


                       Jailed Hong Kong media tycoon Jimmy Lai has said it
                       was his “honest belief” that the West could force
                       Beijing to halt the enactment of a national
                       security law in Hong Kong in 2020 by imposing
                       sanctions on top Chinese officials.


          o § Civil Rights/Policing⠀➾


                # ⚓ OpenRightsGroup ☛ Home_Office_must_use_e-visa_delay_to
                  change_flawed_scheme [Ed: ORG got taken over by Muslims and
                  now has "ORG’s Migrant Rights Digital Justice Programme
                  Manager". They used to be about privacy and tech, not
                  immigration.]⠀⇛


                       Open Rights Group has welcomed reports that the
                       government is set to delay the rollout of its e-
                       visa scheme, which was due to come into effect on
                       January 1, 2025.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Hackaday ☛ A_Month_Without_IPV4_Is_Like_A_Month_Without…⠀⇛


                       Recently, there was a Mastodon post from [nixCraft]
                       challenging people to drop their NAT routers for
                       the month of November and use only IPv6. What would
                       it be like to experience “No NAT November?” [Alex
                       Haydock] decided to find out.


                # ⚓ MWL ☛ My_Social_Media_in_2024⠀⇛


                       I left Ex-Twitter right after Elon Musk bought it.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ JUVE ☛ Silimed_sucessfully_claims_invention_for_breast
                  implant_technology [Ed: EPO monopoly for fake boobs. Not
                  unusual for giver of fake patents. The bribed press conflates
                  patents with "invention".]]⠀⇛


                       The two parties have been in dispute for years over
                       EP 2 581 193, which protects a process for
                       manufacturing implants. In 2011, Polytech
                       registered the basic patent monopoly but Silimed
                       claims to be the inventor of this technology and
                       filed an entitlement action in 2017.


                # ⚓ Dennis Crouch/Patently-O ☛ USPTO_Withdraws_Controversial
                  Terminal_Disclaimer_Rule_–_But_Core_Issues_Remain⠀⇛


                       As I previously suggested, the USPTO has now
                       announced that it is withdrawing its proposed rule
                       that would have made terminal disclaimers far more
                       noxious by tying patent monopoly enforceability to
                       the validity of claims in related patents. While
                       this is undoubtedly the right move given the
                       questionable legal authority and overwhelmingly
                       negative public response (over 300 comments, with
                       256 unique submissions), the underlying concerns
                       that drove the proposal deserve attention because
                       they will likely arise in other forms. [Read the
                       Fed. Reg. Notice Cancelling the Proposal: 2024-
                       28263]


                # ⚓ The_PREVAIL_Act_Would_Perpetuate_Unjust_Monopolies,_Deter
                  Innovation,_and_Violate_the_Founders’_Patent_Principles⠀⇛


                       The Federalist Society on its website quotes former
                       President Ronald Reagan as saying “The Federalist
                       Society is … returning the values and concepts of
                       law as our founders understood them to scholarly
                       dialogue.”


                # ⚓ CAFC_Affirms_Obviousness_Ruling_Invalidating_KPN’s_Network
                  Access_Management_Patent_Claims⠀⇛


                       The U.S. Court of Appeals for the Federal Circuit
                       on Monday, December 2, issued a ruling in
                       Koninklijke KPN N.V. v. Vidal affirming the Patent
                       Trial and Appeal Board’s (PTAB) invalidation of
                       several patent monopoly claims to technologies for
                       managing access to telecommunications networks. In
                       so ruling, the Federal Circuit held that KPN’s
                       plausible alternative understanding of a prior art
                       reference did not require a finding that the PTAB’s
                       obviousness ruling was unsupported by substantial
                       evidence.


                # § Software Patents⠀➾


                      # ⚓ Unified Patents ☛ $2,000_awarded_for_Payvox_e-
                        commerce_patent_monopoly_prior_art⠀⇛


                             Unified is pleased to announce PATROLL
                             crowdsourcing contest winners, Andrei Gilya,
                             Mani Manikandan, Ritu Tyagi, and Ramesh
                             Varadharaj, who split a cash award of $2,000
                             for their prior art submissions on U.S.
                             Patent_8,788,360, owned by Payvox LLC, an
                             NPE. The ‘360 patent monopoly relates to
                             wireless commerce systems. More particularly,
                             the invention involves a point of advertising
                             wireless commerce system to enable pervasive
                             commerce with mass media publications.


                      # ⚓ Unified Patents ☛ $2,000_awarded_for_Big_Will
                        messaging_patent_monopoly_prior_art⠀⇛


                             Unified is pleased to announce PATROLL
                             crowdsourcing contest winners, Mani
                             Manikandan and Dinesh Swami, who split a cash
                             award of $2,000 for their prior art
                             submissions on U.S._Patent_10,521,846, owned
                             and asserted by Big Will Enterprises Inc., an
                             NPE. The ‘846 patent monopoly relates to
                             electronic messaging technologies, and more
                             particularly, to systems, methods, and
                             apparatus for accurately identifying a mobile
                             thing (MT) and/or a motion activity
                             associated with the MT using sensor data.


                      # ⚓ Unified Patents ☛ $2,000_for_Empire_IP_entity,
                        Dynamic_Data_Innovations,_dataset_patent_monopoly_prior
                        art⠀⇛


                             Unified Patents added a new PATROLL contest,
                             with a $2,000 cash prize, seeking prior art
                             on at least claim 1 of U.S._Patent_9,632,676,
                             asserted by Dynamic Data Innovations LLC, an
                             NPE and entity of Empire_IP_LLC.


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ TTABlog_Test:_Which_of_These_Three_Section_2(d)
                  Refusals_Was/Were_Overturned_on_Appeal?⠀⇛


                       The TTAB affirmance rate for Section 2(d) appeals
                       this year continues to hover around 90%. Here are
                       three recent Board decisions, at least one of which
                       reversed the refusal. How do you think they came
                       out? [Answer in first comment].


                       In_re_Vermutería_de_Galicia,_S.L., Serial No.
                       90385649 (November 29, 2024) [not precedential]
                       (Opinion by Judge Cynthia C. Lynch). [Section 2(d)
                       refusal of the word-and-design mark shown below,
                       for "vermouth" in view of the registered mark
                       PETRONI for "wine."]


          o § Copyrights⠀➾


                # ⚓ Public Domain Review ☛ Fantastic_Planet:_The_Microscopy
                  Album_of_Marinus_Pieter_Filbri_(1887–88)⠀⇛


                       Micrographs that make the minuscule world as alien
                       as outer space.


                # ⚓ Public Domain Review ☛ The_Launch_of_Our_End-of-Year
                  Fundraiser!⠀⇛


                       Our End-of-Year Fundraiser is launched, and the new
                       postcards theme will be Home.


                # ⚓ Michael Geist ☛ Canadian_Media_Companies_Target_Proprietary
                  Chaffbot_Company_in_Copyright_Lawsuit_But_Weak_Claims_Suggest
                  Settlement_the_Real_Goal⠀⇛


                       Canada’s largest media companies, including the
                       Globe and Mail, Toronto Star, Postmedia, CBC, and
                       Canadian Press, came together last week to file_a
                       copyright_monopoly_infringement_lawsuit against
                       OpenAI, the owners of ChatGPT.





                    ䷩ 𝚕𝚒𝚗𝚎 7785

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 05/12/2024: Mass Layoffs at
Microsoft's PR (Bribery of Media) Agency, UnitedHealthcare CEO Shot
Dead⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 05, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Snowy_Landscape⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Standards/Consortia
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Trademarks
                      # Right_of_Publicity
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Fail_Of_The_Week:_The_SMD_Crystal_Radio_That_Wasn’t⠀⇛


                 The crystal radio is a time-honored build that sadly
                 doesn’t get much traction anymore. Once a rite of passage
                 for electronics hobbyists, the classic coil-on-an-
                 oatmeal-carton and cat’s whisker design just isn’t that
                 easy to pull off anymore, mainly because the BOM isn’t
                 really something that you can just whistle up from
                 DigiKey or Mouser.


          o ⚓ Hackaday ☛ Fluke_Meter_Fails_With_A_Simple_Problem⠀⇛


                 [TheHWcave] found a Fluke 27 multimeter that looked like
                 it had had quite a rough life. At first, the display
                 flashed an overload indicator until he gave it a good
                 smack—or, as he likes to call it, percussive maintenance.
                 Even then, it would not give good readings, so it was
                 time to open it up.


          o ⚓ James G ☛ Things_I_have_been_reading_lately⠀⇛


                 I was thinking to myself that I have read many
                 fascinating things over the last while, but haven’t
                 shared them. I thought I would write a post to share some
                 of the things I have been reading. As web weavers,
                 perhaps one of the most magical things we can do aside
                 from share our own creations is to boost those of others.
                 I find great joy in sharing what others have made.


          o ⚓ Kev Quirk ☛ On_Substack_&_Blogging⠀⇛


                 Manu isn’t a fan of Substack, and he’s got two big
                 reasons why: it takes control away from creators, and it
                 pushes a “monetise everything” culture. He makes a solid
                 case for owning your own domain and keeping blogging
                 authentic and independent.


          o ⚓ Manuel Moreale ☛ On_blogging,_substacking_(?),_and_owning_digital
            real_estate⠀⇛


                 Let me rant for a second. I’m fucking tired of living in
                 a society where everything is monetised, where nothing is
                 safe from speculation, where every passion has to be
                 turned into a business. “But why shouldn’t you turn your
                 passion into a business?” you might ask. Because this
                 endless pursuit of money is fucking up society. The
                 incentives you set up, when you run a platform like
                 Substack, matter a lot. It’s not an accident that, like
                 Kevin said, after a while people on Substack start
                 writing about Substack. Substack has no interest in
                 promoting the people who write candidly about their inner
                 struggles, their dreams and hopes, and their everyday
                 lives. They have nothing to earn from that. They would,
                 in fact, lose money if all of you out there started using
                 the platform simply to share what you think, and what
                 you’re going through, with no intention of ever turning
                 it into a side hustle.


          o ⚓ Justin Vollmer ☛ You_Should_Have_a_Website⠀⇛


                 I’ve championed owning your own website for a while now,
                 and have been posting more heavily about it over the past
                 year or so. My own journey to running my own website was
                 born out of a combination of desiring the challenge of
                 maintaining my own site, wanting a place where I could
                 control what I post and how it looks, and wanting some
                 longevity and permanence for my web presence. And over
                 time, I’ve begun to believe that it would be beneficial
                 both for the individual and for society at large if more
                 people followed suit.


          o ⚓ Justin Vollmer ☛ Seconding_the_Call_to_Blog_More_Often_|_Justin
            Vollmer⠀⇛


                 Personally, I’ve attempted to write more often, but
                 consistency is still a struggle. Much of my recent work
                 on this site has been with the express purpose of making
                 my interactions with the site and its content more
                 engaging for me, to increase my desire to post more
                 consistently.


          o ⚓ MJ Fransen ☛ Org-journal_with_prompts⠀⇛


                 Last summier I concluded the #100daystooffload challenge
                 (on Gopher). Writing daily in one's journal is not that
                 different and I think the time has come to start building
                 the habit of journaling.


          o ⚓ Juha-Matti Santala ☛ Three_is_a_pattern⠀⇛


                 Finding a balance between prepping for future or doing
                 repeated work is not easy. Whether it is about sharing
                 advice one-on-one vs. writing it down into a blog or
                 refactoring code into reusable blocks or setting up extra
                 tooling for personal notes’ system, the decision time
                 comes up at some point.


                 Over the years, I’ve found the rule of “three is a
                 pattern” to be quite useful in balancing this.


                 Here’s how it works: [...]


          o § Standards/Consortia⠀➾


                # ⚓ Joost de Valk ☛ Can_I_safely_use_AVIF_or_WebP_share_images?
                  [Ed: So they say, use AVIF or WebP on the Web (in spite of
                  software patents and lots of SOFTWARE NOT SUPPORTING THEM;
                  partly due to patents!), then they throw megabytes of
                  JavaScript at you. Marketed based on lies. It also takes more
                  bloated and probably less secure code to render these.]⠀⇛


                       You should use both AVIF and WebP on your website.
                       They’re smaller, they’re better. All browsers
                       support them. As of December 2024, you can use WebP
                       share images, but you can not use AVIF on social
                       platforms yet. We still have to get quite a few
                       more platforms to support AVIF before it’s safe to
                       use them as share images. However, changed from
                       June 2024, you can now safely use WebP everywhere.


          o § Science⠀➾


                # ⚓ Science Alert ☛ Scientists_Shifted_People's_Day_by_Just_5
                  Hours_–_Here's_What_Happened⠀⇛


                       Your body's weakest link has been identified.


                # ⚓ Science Alert ☛ The_Secret_of_Orange_Cats_Finally_Uncovered
                  After_60-Year_Search⠀⇛


                       Barsh and his colleagues discovered cat skin cells
                       from which orange fur sprouts express 13 times as
                       much RNA from a gene called Arhgap36, compared with
                       skin cells from cats with no orange hair.


          o § Career/Education⠀➾


                # ⚓ The Nation ☛ In_Defense_of_Teachers_and_Public_Education⠀⇛


                       The Department of Education covers an estimated 9
                       percent of K-12 school funding, with states and
                       local governments covering most funding to our K-12
                       schools. Critically, it administers our student
                       loan program, which enables millions of students to
                       afford college. It also funds important post-
                       secondary support, like TRIO. TRIO programs provide
                       targeted resources to students, including tutoring,
                       academic assistance, financial counseling, and
                       mentorship programs. These services reach low-
                       income students, first-generation students, and our
                       veterans, and improve educational attainment and
                       academic preparedness. The Department of
                       Education’s impact is felt in so-called red and
                       blue states across the country.


                # ⚓ New York Times ☛ University_of_Michigan_Weighs_Changes_to
                  Its_Diversity_Program⠀⇛


                       The school is one of higher education’s biggest
                       supporters of D.E.I. Now it’s considering a new
                       approach as critics question the program’s success
                       and impact on campus life.


                # ⚓ Kansas Reflector ☛ The_right_has_made_the_truth_political.
                  Teachers_are_nonetheless_obligated_to_speak_it.⠀⇛


                       There are more, but my point is not to prove to
                       Christians that they have a moral obligation to the
                       foreigner and the immigrant. My point is that
                       telling this truth to a group of Christians in a
                       Catholic school resulted in a teacher’s firing
                       because it made people acting immorally
                       uncomfortable with their immoral choice. Jimbo
                       Gillcrist wasn’t fired for being political. He was
                       fired for disrupting the damning silence of the
                       status quo, a silence that is designed to let
                       untruth flourish.


                # ⚓ Kodsnack ☛ Kodsnack_616_-_Computers_outside_of_computers,
                  with_Violet_Whitney_and_William_Martin⠀⇛


                       Recorded on-stage at Øredev 2024, Fredrik talks to
                       Violet Whitney and William Martin about the
                       research they do into how we can interact with
                       computers outside of the bounds of … well, a
                       regular computer or phone.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Holograms:_The_Art_Of_Recording_Wavefronts⠀⇛


                       The difference between holography and photography
                       can be summarized perhaps most succinctly as the
                       difference between recording the effect photons
                       have on a surface, versus recording the wavefront
                       which is responsible for allowing photographs to be
                       created in the first place. Since the whole idea of
                       ‘visible light’ pertains to a small fragment of the
                       electromagnetic (EM) spectrum, and thus what we are
                       perceiving with our eyes is simply the result of
                       this EM radiation interacting with objects in the
                       scene and interfering with each other, it logically
                       follows that if we can freeze this EM pattern (i.e.
                       the wavefront) in time, we can then repeat this
                       particular pattern ad infinitum.


                # ⚓ Tom's Hardware ☛ AMD_Radeon_RX_8800_XT_has_a_220W_TDP
                  according_to_Seasonic's_online_PSU_calculator_—_two_8-pin
                  power_plugs_required,_it_says⠀⇛


                       The RDNA 4 based Radeon RX 8800 XT has appeared in
                       Seasonic's wattage calculator listed with a 220W
                       TDP.


                # ⚓ Kevin Boone ☛ Kevin_Boone:_They_don’t_make_them_like_that
                  any_more:_Epson_MX-80_dot_matrix_printer⠀⇛


                       Well, because they actually worked. And they went
                       on working, day after day, year after year. Modern
                       printers are notorious for letting us down when we
                       most need them. Need that report tomorrow? Tough.
                       Printer manufacturers have responded to the
                       declining sales of their products, not by making
                       them better, but by finding ways to scalp their
                       owners for the cost of consumables. And then,
                       because consumers naturally look for cheaper, 3rd-
                       party suppliers of consumables, the printer
                       manufacturers retaliate by using encryption
                       technologies to prevent the printer accepting any
                       consumables but OEM ones.


                # ⚓ Kevin Boone ☛ Kevin_Boone:_They_don’t_make_them_like_that
                  any_more:_the_Yamaha_DX7_keyboard⠀⇛


                       What made the DX7 special was its novel approach to
                       sound generation. Although electronic keyboards
                       were not new when the DX7 was released in 1983,
                       they nearly all used an analog method of sound
                       production. Typically an electronic oscillator
                       would generate a tone whose pitch was set by the
                       key pressed, and then a variety of filters and
                       amplitude modifiers would work on the sound to
                       change its properties.


                       This is a completely logical way to approach
                       simulating real musical instruments electronically.
                       Real instruments have something that generates a
                       tone – reed, string, whatever – and something that
                       modifies the characteristics of the tone – pipe,
                       soundbox, and so on. Each instrument has a
                       characteristic amplitude envelope. For example, a
                       note on a piano has an initial louder, percussive
                       peak in volume, followed by a gradual decay. Analog
                       synthesizers tried to simulate these acoustic
                       properties using electronics.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ Antidoping_Agency_Froze_Out_Investigators
                  Who_Warned_About_China⠀⇛


                       The World Anti-Doping Agency’s investigative unit
                       highlighted intelligence about Chinese athletes
                       possibly using a banned medication, but were kept
                       out of the loop when 23 swimmers tested positive
                       for it.


                # ⚓ Science Alert ☛ Common_Disinfectant_in_US_Drinking_Water
                  Has_Scientists_Concerned⠀⇛


                       Its toxicity is currently unknown.


                # ⚓ Science Alert ☛ Parkinson's_Link_to_Gut_Bacteria_Suggests
                  an_Unexpected,_Simple_Treatment⠀⇛


                       Inching closer to the full picture.


                # ⚓ NYPost ☛ I’m_an_oncology_dietitian_—_the_best_pizza
                  toppings_to_reduce_your_risk_of_cancer⠀⇛


                       "There are so many amazing options," said Nichole
                       Andrews, a Washington oncology dietitian and
                       author.


                # ⚓ NYPost ☛ House_Democrats_slam_Cuomo_over_COVID_nursing_home
                  order,_saying_he_‘interfered’_with_death_toll_stats⠀⇛


                       The Dem report said Cuomo and top aides' meddling
                       with the data misled the public about the number of
                       nursing home residents who died from COVID.


                # ⚓ CS Monitor ☛ After_the_pandemic,_more_Native_American
                  students_don’t_want_to_return_to_school⠀⇛


                       While the pandemic caused lasting absenteeism among
                       all schoolchildren, the problem has been most
                       pronounced among Native American and Alaska Native
                       students. Of 34 states, half had absenteeism rates
                       for Indigenous children at least 9% higher than
                       average.


                # ⚓ New Statesman ☛ Quitting_social_media_gave_me_a_new_creed:
                  only_disconnect⠀⇛


                       I had justified my social media habit as a
                       necessary function of my job, but I’ve always been
                       seduced by the idea of a complex web of human
                       connections. Perhaps it derives from a love of big
                       polyphonic novels or growing up in a family riddled
                       with divorce – this fantasy about knitting together
                       broken threads. But the instinct for connectedness
                       is with us from an early age. The other day, my
                       four-year-old son was introduced to his new
                       child­minder, who revealed we had at least three
                       sets of ­family friends in common. “Does that mean
                       everybody who knows me knows everyone else?” he
                       asked, thrilled by the possibility.


                       There are obvious dangers in this ­proximity to
                       new, or potentially better, connections. I’m
                       reminded of Margaret Schlegel’s concern that the
                       more people she gets to know in an ever-crowded
                       London, the easier it becomes to replace them:
                       “It’s no good, I think, unless you really mean to
                       know people.” In another Forster novel, A Passage
                       to India, Adela asks: “What is the use of personal
                       relationships when everyone brings less and less to
                       them?”


                # ⚓ CBC ☛ 4th_case_of_deadly_deer_disease_confirmed_in_B.C.
                  Hunters_required_to_help_monitor_spread⠀⇛


                       Hunters across British Columbia are being asked to
                       be aware of chronic wasting disease (CWD) after a
                       fourth confirmed case of the fatal disease was
                       found in a white-tailed deer in the Kootenay
                       region, B.C.'s Ministry of Water, Land and Resource
                       Stewardship said Tuesday.


                       Nicknamed zombie deer disease, CWD is an incurable
                       illness that affects cervid or deer family members,
                       such as moose, caribou and elk.


                # ⚓ USMC ☛ Marines_take_steps_to_hack_human_performance_with
                  data⠀⇛


                       A 2021 collaboration with Army Combat Capabilities
                       Development Command resulted in an “Optimizing the
                       Human Weapons System (OHWS)” roadmap to a Marine
                       Corps program that would use wearables and smart
                       devices to create a sophisticated dashboard showing
                       troops’ “wellness inputs,” such as alcohol
                       consumption and physical exercise, training load,
                       sleep data and recovery stats.


                       A presentation of the plan, reviewed by Marine
                       Corps Times, shows a timeline of milestones leading
                       up to a needs analysis to be completed by Marine
                       Corps Warfighting Lab in 2023.


                # ⚓ Wired ☛ A_Parasite_That_Eats_Cattle_Alive_Is_Creeping_North
                  Toward_the_US⠀⇛


                       Prior to the closure of its border with the US,
                       Mexico’s National Confederation of Livestock
                       Organizations had called on the government to clamp
                       down on cattle smuggling across Mexico’s southern
                       border. The risk from the parasite is great, and if
                       it becomes established again, the cost of
                       eliminating it in Mexico would be high. Disruption
                       of trade with the US was also be highly costly. In
                       2023 alone, Mexico’s exports of live cattle and
                       beef to the US were worth $3 billion.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Edelman_lays_off_330_people_amid_expected_8%_drop_in_US
                  revenue [Ed: The Microsoft operatives_that_bribe_the_media to
                  lay off 8% of staff]⠀⇛


                       CEO Richard Edelman is refocusing the agency around
                       five key areas and shuttering most of its
                       operational sub brands — he said the cuts would
                       have happened ‘months ago’ if Edelman were a public
                       company."


                # ⚓ Ubisoft_Confirms_Rumored_Layoffs_Because_Of_XDefiant’s
                  Shutdown⠀⇛


                       But first, we will go straight to Ubisoft and what
                       they have officially confirmed Ubisoft shared a
                       private email to employees, confirming some of
                       these planned layoffs.


                # ⚓ Windows Central ☛ Ubisoft_continues_freefall_as_publisher
                  shutters_free-to-play_shooter_XDefiant,_reportedly_closing
                  studios⠀⇛


                       Ubisoft launched free-to-play first-person shooter
                       XDefiant on May 21, 2024, after years of open and
                       closed testing.


                # ⚓ Head Topics ☛ XDefiant_servers_are_closing_in_June_as
                  Ubisoft_announces_more_layoffs⠀⇛


                       Another live-service game is shutting down due to a
                       lack of players: Ubisoft ’s XDefiant, a first-
                       person shooter that’s the illegitimate lovechild of
                       Overwatch and Counter-Strike. The game launched on
                       May 21 of this year, so it didn’t even last a full
                       seven months before the shutdown announcement.


                # ⚓ Channel_Brief:_Ingram_Micro_Cuts_850_in_Latest_Layoffs⠀⇛


                       1. Ingram Micro lays off 850: In a restructuring
                       move, technology distributor Ingram Micro announced
                       it will cut nearly 850 employees by the end of the
                       first quarter of 2025. CEO Paul Bay announced the
                       cuts in a letter to employees, as CRN reported. CRN
                       said the restructuring includes integrating Ingram
                       Micro’s digital and information technology teams to
                       reduce costs and eliminate redundancies,
                       transforming the company’s historical shared
                       services model into an exception-based model, and
                       streamlining selected country, business, and
                       functional organizations.


                # ⚓ Chris Coyier ☛ Attempting_a_Safari_Move⠀⇛


                       Safari isn’t any better with battery life. I feel
                       like that needs to be shared more as it’s very
                       strong folk tech wisdom that Chrome eats battery
                       and Safari does not, which is apparently not true
                       at all, and might be the opposite.


                # ⚓ Pivot to AI ☛ UK_local_papers_go_weird_as_Reach_pivots_to
                  AI_from_journalism⠀⇛


                       Reach plc, formerly Trinity Mirror, owns UK
                       tabloids the Daily Mirror and Daily Express and
                       many local newspapers around the country.


                       Reach’s coverage of local matters in its local
                       papers has gone noticeably … weird.


                # ⚓ Security Week ☛ CISA_Warns_of_Zyxel_Firewall_Vulnerability
                  Exploited_in_Attacks⠀⇛


                       The US cybersecurity agency CISA on Tuesday warned
                       that a path traversal vulnerability in multiple
                       Zyxel firewall appliances has been exploited in the
                       wild.


                       The issue, tracked as CVE-2024-11667 (CVSS score of
                       7.5), is a high-severity flaw affecting the web
                       management interface of Zyxel ATP, USG FLEX, and
                       USG20(W)-VPN series devices.


                # ⚓ The Guardian UK ☛ Doctor_Who_showrunners_warn_AI_scripts
                  will_‘eat_their_own_tail’⠀⇛


                       One of the masterminds behind Doctor Who has warned
                       that the more AI content is used for creative
                       purposes the worse its output will be because it
                       “eats its own tail”.


                       Ahead of the Doctor Who Christmas special, eagerly
                       awaited by fans as a centrepiece of BBC1’s festive
                       schedule, Steven Moffat made the comments in
                       discussion with fellow showrunner Russell T Davies.


                # ⚓ India Times ☛ AI-driven,_deepfake-enabled_cyberattacks_to
                  rise_in_2025;_healthcare,_finance_sectors_at_risk:_report⠀⇛


                       AI-driven and deepfake-enabled cyberattacks are
                       anticipated to become increasingly prevalent in
                       2025 with sectors like healthcare and finance most
                       prone targets, according to a recent report. The
                       India Cyber Threat Report 2025 by the Data Security
                       Council of India (DSCI) and Seqrite, spotlighted
                       the evolving tactics of cybercriminals and the rise
                       of AI-driven attacks as a major concern.


                # ⚓ Futurism ☛ AI_Safety_Researcher_Quits_OpenAI,_Saying_Its
                  Trajectory_Alarms_Her⠀⇛


                       Though she didn't get into it too much, the former
                       OpenAI-er said that she decided to leave because
                       she was troubled by changes at the company over the
                       past year or so. It's unclear what changes she's
                       referencing exactly, but that timeframe matches the
                       failed coup against CEO and cofounder Sam Altman
                       late last November, which was reportedly undertaken
                       by board members with concerns about the firm's
                       lack of focus on safety under his leadership.


                # ⚓ La Quadature Du Net ☛ It’s_not_AI,_it’s_state-of-the-art
                  exploitation⠀⇛


                       In recent months, following the sudden hype of
                       generative artificial intelligence and products
                       such as ChatGPT, and under the aegis of big
                       business and complicit states, we have witnessed a
                       further acceleration of the computerization
                       process. This acceleration is the direct
                       consequence of everything that is already
                       problematic about the dominant trajectory of
                       digital technologies. First of all, the huge
                       accumulation of data over many years by major tech
                       multinationals such as Google, Microsoft, Meta and
                       Amazon, who monitor us to better predict our
                       behavior, and who are now capable of indexing
                       gigantic corpora of text, sound and images by
                       appropriating the common good that is the Web.


                       Collecting, storing and processing all this data
                       requires a prodigious accumulation of resources.
                       This is reflected first and foremost in capital:
                       the rise of tech, boosted by surveillance
                       capitalism, has attracted the favor of financial
                       markets and benefited from accommodating public
                       policies. Thanks to this capital, these companies
                       can finance near-exponential growth in the data
                       storage and computing capacity needed to drive and
                       run their AI models, by investing in graphics chips
                       (GPUs), undersea cables and data centers. These
                       components and infrastructures in turn require
                       immense quantities of rare earths and metals, water
                       and electricity.


                # ⚓ Michigan Advance ☛ Misinformation_expert_used_AI_to_draft
                  testimony_containing_misinformation_about_AI⠀⇛


                       A Stanford misinformation expert has admitted he
                       used artificial intelligence to draft a court
                       document that contained multiple fake citations
                       about AI.


                       Stanford’s Jeff Hancock submitted the document as
                       an expert declaration in a case involving a new
                       Minnesota law that makes it illegal to use AI to
                       mislead voters prior to an election. Lawyers from
                       the Hamilton Lincoln Law Institute and the Upper
                       Midwest Law Center, which are challenging the law
                       on First Amendment grounds, noticed the fake
                       citations several weeks ago and petitioned the
                       judge to throw out the declaration.


                # ⚓ Dan Q ☛ A_Friend_Used_AI_to_Wish_me_Happy_Birthday⠀⇛


                       Robert shares his experience of receiving a
                       birthday greeting from a friend, that had clearly
                       been written by an AI. The friend’s justification
                       was because they’d wanted to make the message
                       longer, more easily. But the end result was a sour
                       taste in the recipient’s mouth.


                # ⚓ The Register UK ☛ Windows_11_market_share_falls_despite
                  Microsoft_ad_blitz⠀⇛


                       Despite Microsoft's push to get customers onto
                       Windows 11, growth in the market share of the
                       software giant's latest operating system has
                       stalled, while Windows 10 has made modest gains,
                       according to fresh figures from Statcounter.


                       This is not the news Microsoft wanted to hear.
                       After half a year of growth, the line for Windows
                       11 global desktop market share has taken a slight
                       downturn, according to the website usage monitor,
                       going from 35.6 percent in October to 34.9 percent
                       in November. Windows 10, on the other hand, managed
                       to grow its share of that market by just under a
                       percentage point to 61.8 percent.


                # ⚓ The Register UK ☛ Support_for_Windows_Mail,_Calendar,
                  People_ends_December_31⠀⇛


                       In November, Microsoft confirmed there would be no
                       reprieve for the apps. It will be possible to
                       export local emails, calendar events, and contacts
                       that users have stored in Mail, Calendar, and
                       People into the new Outlook up until December 31,
                       2024. After that, however, the ability to send or
                       receive mail will be revoked.


                # ⚓ Macworld ☛ Why_I'm_done_with_desktop_Macs⠀⇛


                       Ten years as a desktop Mac user was a lot of fun. I
                       had an iMac, iMac Pro, and Mac Studio, and I
                       enjoyed them all. But like almost everyone else,
                       I’ve found the pull of the laptop too strong to
                       avoid. Even when sitting at a desk staring at a big
                       monitor, the MacBook Pro seems like the right
                       choice.


                # ⚓ Six Colors ☛ KVM_2024:_One_switch_to_rule_them_all⠀⇛


                       I live a multi-Mac lifestyle. It’s a luxury, but
                       mighty close to a necessity if I want to keep my
                       work life and personal life (which includes
                       freelance projects) separate. But how do you
                       organize your life and desk so that both Macs can
                       do their best for you? My solution is a modern spin
                       on an old option: a KVM switch.


                # ⚓ Futurism ☛ Teens_Are_Forming_Intense_Relationships_With_AI
                  Entities,_and_Parents_Have_No_Idea⠀⇛


                       The youth are addicted to generative AI models —
                       but their parents have no idea what their kids
                       actually use them for.


                       As part of a new study set to be presented at the
                       IEEE Symposium on Security and Privacy, a team of
                       researchers interviewed seven teenagers and
                       thirteen parents about their AI usage and
                       perceptions of the tech, and also analyzed
                       thousands of Reddit posts and comments from other
                       teens.


                # ⚓ Techdirt ☛ Why_Generative_AI’s_Lack_Of_Modularity_Means_It
                  Can’t_Be_Meaningfully_Open,_Is_Unreliable,_And_Is_A
                  Technological_Dead_End⠀⇛


                       One of the most important shifts in computing over
                       the last few decades has been the increasing use of
                       open source software on nearly every platform, from
                       cloud computing to smartphones (well, I would say
                       that). For the distributed development methodology
                       pioneered by Linus Torvalds with Linux to work,
                       modularity is key. It allows coders anywhere in the
                       world, connected by the Internet, to work
                       independently on self-contained elements that can
                       be easily upgraded or even replaced, without a
                       major redesign of the overall architecture.
                       Modularity brings with it many other important
                       benefits, including these noted by Eerke Boiten,
                       Professor of Cyber Security at De Montfort
                       University Leicester, in an article published on
                       the British Computer Society Web site: [...]


                # ⚓ The Washington Post ☛ Sorry,_Oxford_dictionary_nerds._This
                  is_the_real_word_of_the_year.⠀⇛


                       First off, that’s two words. But the real miss was
                       overlooking the rightful winner, “slop,” which was
                       on the dictionary publisher’s short list for word
                       of the year. That’s like Beyoncé losing the top
                       Grammy award to Harry Styles.


                       “Slop” is the perfect word for 2024. It describes
                       this year’s explosion of artificial intelligence-
                       generated oddball social media images like “shrimp
                       Jesus.” But slop is also a perfect encapsulation of
                       a decades-old phenomenon that explains why the
                       [Internet] is like this.


                # ⚓ BoingBoing ☛ AI-enabled_price_collusion_ensures_the_rent_is
                  too_damn_high⠀⇛


                       AI-powered RealPage pools data to enable landlords
                       to raise rental prices. While the company seems to
                       push those increases aggressively, some cities are
                       legislating solutions.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Papers Please ☛ CBP_facial_recognition_is_a_service
                        for_the_airline_industry⠀⇛


                             After five years of foot-dragging in
                             responding to our Freedom Of Information Act
                             (FOIA) request, US Customs and Border
                             Protection (CBP) has finally released the
                             pitch it made to the Future Travel Experience
                             airline industry conference in 2019 on why
                             airlines and airport operators should
                             “partner” with CBP on automated facial
                             recognition of airline passengers.


                             CBP claims in its presentation that “THIS IS
                             *NOT* A SURVEILLANCE PROGRAM”. Its vision,
                             however, is for CBP’s Traveler Verification
                             Service (TVS) facial recognition system to
                             provide automated identification of travelers
                             at every stage of their journeys.


                      # ⚓ EFF ☛ Location_Tracking_Tools_Endanger_Abortion
                        Access._Lawmakers_Must_Act_Now.⠀⇛


                             Locate X–and other similar services–are able
                             to do this by taking advantage of our largely
                             unregulated location data market.


                             Unfettered location tracking puts us all at
                             risk. Law enforcement agencies can purchase
                             their way around warrant requirements and bad
                             actors can pay for services that make it
                             easier to engage in stalking and harassment.
                             Location tracking tools particularly threaten
                             groups especially vulnerable to targeting,
                             such as immigrants, the LGBTQ+ community, and
                             even U.S. intelligence personnel abroad.
                             Crucially, in a post-Dobbs United States,
                             location surveillance also poses a serious
                             danger to abortion-seekers across the
                             country.


                             EFF has warned before about how the location
                             data market threatens reproductive rights.
                             The recent reports on Locate X illustrate
                             even more starkly how the collection and sale
                             of location data endangers patients in states
                             with abortion bans and restrictions.


                      # ⚓ Sean Conner ☛ Why_list_a_phone_number_if_no_one_at
                        your_company_even_knows_how_to_deal_with_the
                        notification?⠀⇛


                             The only thing I want to say is to
                             corporations who have a similiar message—if
                             you are going to bother putting a phone
                             number to inform of email delivery errors,
                             you may want to make an option that is
                             obvious who handles such situations. Or just
                             don't bother with a phone number at all. Or
                             just say something like “just delete this and
                             move on with your life. We don't care enough
                             to handle this properly,” unlike the other
                             email I received today from another medical
                             company which had an email address I could
                             send a notification to.


                      # ⚓ The Guardian UK ☛ Many_Americans’_cellphone_data
                        being_[breached]_by_China,_official_says⠀⇛


                             A large number of Americans’ metadata has
                             been stolen in the sweeping cyber-espionage
                             campaign carried out by a Chinese [intrusion]
                             group dubbed “Salt Typhoon”, a senior US
                             official told journalists on Wednesday.


                             The official declined to provide specific
                             figures but noted that China’s access to
                             America’s telecommunications infrastructure
                             was broad and that the hacking was ongoing.


                      # ⚓ EPIC ☛ Testimony_on_Michigan_Personal_Data_Privacy
                        Act_–_EPIC_–_Electronic_Privacy_Information_Center⠀⇛


                             EPIC writes in support of SB 659, the
                             Michigan Personal Data Privacy Act. We
                             commend Senator Bayer for crafting a bill
                             that provides meaningful privacy protections
                             for Michiganders. For more than two decades,
                             powerful tech companies have been allowed to
                             set the terms of our online interactions.
                             Without any meaningful restrictions on their
                             business practices, they have built systems
                             that invade our private lives, spy on our
                             families, and gather the most intimate
                             details about us for profit. But it does not
                             have to be this way – Michigan can have a
                             strong technology sector while protecting
                             personal privacy.


                             The Electronic Privacy Information Center
                             (EPIC) is an independent nonprofit research
                             organization in Washington, DC, established
                             in 1994 to protect privacy, freedom of
                             expression, and democratic values in the
                             information age.[1] EPIC has long advocated
                             for comprehensive privacy laws at both the
                             state and federal level.[2]


                      # ⚓ Walled Culture ☛ Why_Italy’s_Piracy_Shield_risks
                        moving_from_tiresome_digital_farce_to_serious_national
                        tragedy⠀⇛


                             In other words, by placing the sanctity of
                             copyright above all else, the Piracy Shield
                             system could be turned against any aspect of
                             Italian society with just a few keyboard
                             commands. A malicious actor that managed to
                             gain access to a system that has twice
                             demonstrated a complete lack of even the most
                             basic controls and checks could wreak havoc
                             on computers and networks throughout Italy in
                             a few seconds. Moreover, the damage could
                             easily go well beyond the inconvenience of
                             millions of people being blocked from
                             accessing their files on Google Drive. A
                             skilled intruder could carry out widespread
                             sabotage of vital services and infrastructure
                             that would cost billions of euros to rectify,
                             and could even lead to the loss of lives.


                      # ⚓ The Register UK ☛ Microsoft_says_patch_installation
                        stops_Recall_snapshots⠀⇛


                             KB5046740, which emerged on November 21,
                             represents the final non-security preview
                             release for 2024 (although there will be a
                             monthly security release in December).


                             The problem came when users installed this
                             preview update, saw the Recall announcement,
                             joined the Windows Insider Dev channel to get
                             their hands on the code, and then... nothing.


                      # ⚓ Wired ☛ A_New_Phone_Scanner_That_Detects_Spyware_Has
                        Already_Found_7_Pegasus_Infections⠀⇛


                             Seven out of 2,500 scans may sound like a
                             small group, especially in the somewhat self-
                             selecting customer base of iVerify users,
                             whether paying or free, who want to be
                             monitoring their mobile device security at
                             all, much less checking specifically for
                             niche spyware infections. But the fact that
                             the tool has already found a handful of
                             infections at all speaks to how widely the
                             use of spyware has proliferated around the
                             world. It seems that having an easy tool for
                             diagnosing spyware compromises may expand the
                             picture of just how often such malware is
                             being used.


                      # ⚓ Wired ☛ Tim_Cook_Wants_Apple_to_Literally_Save_Your
                        Life⠀⇛


                             Much as the CEO seems awestruck by AI and his
                             just-released Apple Intelligence, he’s more
                             convinced that the tech giant’s health apps
                             will define the company’s legacy.


          o § Defence/Aggression⠀➾


                # ⚓ ADF ☛ Reports_Detail_Forced_Youth_Conscription_in
                  Ethiopia⠀⇛


                       Tedla Hirigo, 17, worked as a street vendor in
                       Adama city in Ethiopia’s Oromia region on November
                       11 when police detained him.


                # ⚓ ADF ☛ Al-Shabaab_Could_Capitalize_on_Somalia-Ethiopia
                  Tensions⠀⇛


                       Somali President Hassan Sheik Mohamud has been so
                       focused on his rift with Ethiopia over its port
                       deal with Somaliland that he might be leaving an
                       opening for al-Shabaab, according to Selam Tadesse
                       Demissie, a researcher at the Institute for
                       Security Studies (ISS).


                # ⚓ ADF ☛ U.N._Honors_25_Years_of_Protecting_African
                  Civilians⠀⇛


                       The United Nations recently marked an important
                       anniversary on the continent — 25 years of actively
                       protecting civilians with its peacekeeping
                       missions. On October 22, 1999, the U.N. Security
                       Council ended its observer mission in Sierra Leone
                       and established a new mission, UNAMSIL, with a new
                       mandate permitting its troops to use force. >


                # ⚓ The Straits Times ☛ Taiwan_watching_Chinese_carrier
                  movements_as_sources_say_war_games_may_start_this_weekend⠀⇛


                       Three security sources said chances of Chinese
                       military exercises starting this weekend were high.


                # ⚓ Mexico News Daily ☛ Homicides_decline_as_crackdown_on_high-
                  impact_crime_intensifies:_Tuesday’s_mañanera_recapped⠀⇛


                       After sharing positive security figures in the
                       first half of Tuesday's presser, Sheinbaum made an
                       "inside joke" regarding Trump's latest threat to
                       invade Mexico.


                # ⚓ The Straits Times ☛ Marcos_disavows_Philippine_impeachment
                  case_against_Vice-President_Duterte⠀⇛


                       Lawmakers have little appetite for such a spectacle
                       before midterm elections in May, observers say.


                # ⚓ JURIST ☛ South_Korea_president_declares_martial_law_amidst
                  political_turmoil,_with_Parliament_rejecting_the_move⠀⇛


                       South Korean President Yoon Suk Yeol declared
                       martial law on Tuesday, accusing the opposition of
                       paralyzing the government with pro-North Korean
                       sympathies. This proclamation adds to an already
                       intense political climate, sparking controversy and
                       eliciting a swift reaction from domestic political
                       actors and international observers.


                # ⚓ Atlantic Council ☛ Air_force_for_hire⠀⇛


                       Host Alia Brahimi chats with mercenaries expert
                       Alessandro Arduino, a top China analyst.


                # ⚓ Modern Diplomacy ☛ 2024-11-26_[Older]_How_Often_Should_You
                  Post_on_TikTok_Per_Day_to_Become_TikTok_Famous? [Ed: Loaded
                  question; it does not make you famous but merely a tool of
                  the owners of the platform, in this case the Chinese
                  Communist Party]⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-27_[Older]_Romanian
                  Telecoms_Regulator_Calls_for_TikTok_Suspension_Pending
                  Election_Probe⠀⇛


                # ⚓ Modern Diplomacy ☛ 2024-11-28_[Older]_TikTok’s_Role_in
                  Political_Campaigns:_Georgescu’s_Strategy_and_Romania’s_Push
                  for_Suspension⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-29_[Older]_TikTok,_Meta_slam
                  Australia's_social_media_ban_for_under-16s [Ed: Xi and the
                  guy who wines and dines with Trump are upset that a country
                  does something about meddling]⠀⇛


                # ⚓ Modern Diplomacy ☛ 2024-11-30_[Older]_The_Power_of_Social
                  Media_in_Elections:_Lessons_from_Romania’s_TikTok_Case_Study
                  [Ed: Social control media subverts democracies]⠀⇛


                # ⚓ The Age AU ☛ 2024-12-02_[Older]_Too_young_for_TikTok,_old
                  enough_for_jail:_How_a_meaner_Australia_treats_its_kids [Ed:
                  Lobbyists of social control media oligarchs use false
                  equivalences; jail is for people who did something wrong]⠀⇛


                # ⚓ The Register UK ☛ NATO_tests_aquatic_drones_to_protect
                  cables,_coasts⠀⇛


                       The war in Ukraine has highlighted the usefulness
                       of aquatic drones for reconnaissance and offensive
                       missions. Ukrainian forces have been using remote-
                       controlled drone boats to attack the Russian navy –
                       when Elon Musk allows them to.


                # ⚓ Sightline Media Group ☛ New_Army-funded_tech_creates
                  realistic_terrain,_avatars_in_simulations⠀⇛


                       In recent years, the Army has prioritized
                       modernizing its modeling and simulations, primarily
                       through its Program Executive Office-Simulation,
                       Training and Instrumentation and its Cross
                       Functional Team-Synthetic Training Environment.


                       Each of the services are seeking to upgrade and
                       expand use of simulation technology for more cost-
                       effective and safer supplements to live training.


                # ⚓ Semafor Inc ☛ Trump’s_transition_running_into_a_litany_of
                  early_problems⠀⇛


                       Yet the consistent chaos and confusion that defined
                       Trump’s first administration are already descending
                       on Washington.


                # ⚓ New York Times ☛ Opinion_|_Trump’s_Project_2025_May_Not_Be
                  What_It_Seemed._It’s_Worse.⠀⇛


                       Musk’s tweet, which was viewed by 33.2 million
                       people, described Ashley Thomas, a 37-year-old who,
                       The Journal reported, holds “engineering, business
                       and water science degrees from the Massachusetts
                       Institute of Technology and University of Oxford”
                       and works as the “little-known director of climate
                       diversification” at the U.S. International
                       Development Finance Corporation, which advises
                       “private companies to fund ways to improve living
                       standards in developing countries.” A Finance
                       Corporation official told The Journal that Thomas’s
                       work “is highly technical and is focused on
                       identifying innovations that serve U.S. strategic
                       interests, including bolstering agriculture and
                       infrastructure against extreme weather events.”


                # ⚓ C4ISRNET ☛ Space_Force_racing_to_meet_training,_testing
                  demands⠀⇛


                       Chief of Space Operations Gen. Chance Saltzman has
                       made readiness a top priority for the service and
                       has called on the organizations that write
                       requirements, train guardians and develop test and
                       training infrastructure to move quickly to prepare
                       the force to operate in a more contested space
                       environment.


                # ⚓ MIT Technology Review ☛ OpenAI's_new_defense_contract
                  completes_its_military_pivot⠀⇛


                       Today, OpenAI is announcing that its technology
                       will be deployed directly on the battlefield.


                       The company says it will partner with the defense-
                       tech company Anduril, a maker of AI-powered drones,
                       radar systems, and missiles, to help US and allied
                       forces defend against drone attacks. OpenAI will
                       help build AI models that “rapidly synthesize time-
                       sensitive data, reduce the burden on human
                       operators, and improve situational awareness” to
                       take down enemy drones, according to the
                       announcement. Specifics have not been released, but
                       the program will be narrowly focused on defending
                       US personnel and facilities from unmanned aerial
                       threats, according to Liz Bourgeois, an OpenAI
                       spokesperson. “This partnership is consistent with
                       our policies and does not involve leveraging our
                       technology to develop systems designed to harm
                       others,” she said. An Anduril spokesperson did not
                       provide specifics on the bases around the world
                       where the models will be deployed but said the
                       technology will help spot and track drones and
                       reduce the time service members spend on dull
                       tasks.


                # ⚓ Wired ☛ OpenAI_Is_Working_With_Anduril_to_Supply_the_US
                  Military_With_AI⠀⇛


                       OpenAI’s technology will be used to “assess drone
                       threats more quickly and accurately, giving
                       operators the information they need to make better
                       decisions while staying out of harm’s way,” says a
                       former OpenAI employee who left the company earlier
                       this year and spoke on the condition of anonymity
                       to protect their professional relationships.


                # ⚓ El País ☛ Texas_raises_alarm_over_rising_number_of
                  unaccompanied_children_at_the_border⠀⇛


                       “I want the American people to see the impacts of
                       this current border situation that we’ve been in
                       for the last three-plus years and how it impacts
                       unaccompanied children coming across that border,”
                       said Lt. Chris Olivarez, spokesperson for TxDPS,
                       who shared the footage of the two-year-old on
                       social media on November 24. The video shows the
                       young girl holding a yellow post-it note with a
                       name and phone number scribbled on it. The child,
                       originally from El Salvador, was part of a group of
                       over 200 migrants encountered by authorities in
                       Eagle Pass, Texas. Among them were 60 unaccompanied
                       children — the highest number Texas officials have
                       seen in a single day.


                # ⚓ El País ☛ Jihadists,_rebel_groups,_Kurds..._Who’s_who_in
                  the_offensive_against_the_Syrian_regime⠀⇛


                       An operation led by HTS, with roots in Al Qaeda,
                       and rebels allied to Turkey have made their move on
                       the Syrian chessboard in the face of the
                       ineffectiveness of the regime and its allies


                # ⚓ Alabama Reflector ☛ UnitedHealthcare_CEO_Brian_Thompson
                  killed_outside_investor_conference_in_New_York_City⠀⇛


                       UnitedHealthcare CEO Brian Thompson, 50, was shot
                       and killed Wednesday morning outside the Hilton in
                       midtown Manhattan, where he was set to address
                       investors.


                # ⚓ New York Times ☛ CEO_of_UnitedHealthcare_Brian_Thompson_Is
                  Shot_Outside_Midtown_Hotel⠀⇛


                       At 6:44 a.m., he saw his man. Brian Thompson, 50,
                       chief executive of UnitedHealthcare — the leader of
                       one of the country’s largest companies — walking
                       past in a blue suit toward the entrance to the
                       Hilton.


                # ⚓ CBC ☛ UnitedHealthcare_CEO_shot_dead_in_New_York_by
                  attacker_who_waited_for_him,_police_say⠀⇛


                       Security footage obtained by CBC News showed the
                       gun malfunctioned, but the shooter cleared the jam.
                       The gunman also ignored a witness in the video, who
                       escaped from just a metre or two away.


                       "Based on the evidence we have so far, it does
                       appear that the victim was specifically targeted,
                       but at this point, we do not know why," Kenny said.


                # ⚓ LRT ☛ Driving_tests_in_Lithuania_to_take_place_only_in_EU
                  languages⠀⇛


                       Under the new order, the theory part of the driving
                       test will be available in Lithuanian or another
                       official EU language. During the practical test,
                       people who do not speak Lithuanian will be allowed
                       to be accompanied by an interpreter who can
                       translate into the official EU language of their
                       choice.


                # ⚓ The Moscow Times ☛ U.S._Charges_Russian_Woman_Over_FSB
                  Contacts_–_Reports_-_The_Moscow_Times⠀⇛


                       The United States has charged a Russian woman who
                       engaged with anti-war opposition activists over
                       false statements about her ties with Russia’s
                       Federal Security Service (FSB), a U.S.-based non-
                       profit of pro-democracy Russians said Monday.


                       New York resident Nomma Zarubina last month was
                       accused of concealing her 2020 recruitment by an
                       FSB agent under the code name “Alyssa,” according
                       to the Russian America for Democracy in Russia
                       (RADR).


                # ⚓ VOA News ☛ From_VOA_Russian:_Russian_woman_in_New_York
                  accused_of_working_for_FSB:_What_is_known_about_her?⠀⇛


                       The FBI has charged Nomma Zarubina, a Russian
                       national living in New York, with two counts of
                       making false statements to FBI agents regarding her
                       ties to Russian intelligence services.


                # ⚓ VOA News ☛ Ukraine_demands_Russia_return_'kidnapped'
                  children⠀⇛


                       "Ukraine is searching for nearly 20,000 children
                       who were subjected to illegal deportation and
                       forced transfer," said Daria Zarivna, an adviser to
                       Ukraine's president and a senior official at his
                       Bring Kids Back Ukraine initiative.


                       "Yet the actual figure could be much higher, but we
                       can't find it out — Russian officials
                       systematically refuse to provide information,"
                       Zarivna added.


                # ⚓ Digital Music News ☛ TikTok_Trends_Drive_Top_Tracks_on_the
                  Platform⠀⇛


                       In the US, the Top 10 Songs on TikTok inspired 140
                       million creations on the platform globally, with
                       hits like Tommy Richman’s “Million Dollar Baby
                       (VHS),” Lay Bankz’s “Tell Ur Girlfriend,” and Flo
                       Milli’s “Never Lose Me.” Sabrina Carpenter also
                       secured the number one spot on the Top Artists list
                       with her viral hits “Espresso,” “Please Please
                       Please,” and “Taste,” which altogether generated
                       over 15 million TikTok video creations.


                # ⚓ Jacobin Magazine ☛ A_Better_Resistance_to_Trump_Is
                  Possible⠀⇛


                       But we also need a broad coalition that includes
                       but is not limited to socialists and can blunt or
                       derail the worst of the crazy right-wing experiment
                       that is about to unfold. Over 48 percent of
                       American voters voted against Trump. The country
                       has plenty of likely recruits for a mainstream
                       resistance movement against Trumpism. Such a
                       movement should organize around issues with a broad
                       popular appeal.


                # ⚓ RFERL ☛ Russian_Woman_Arrested_In_U.S._For_Alleged_Ties_To
                  Russian_Intelligence⠀⇛


                       A Russian national, Nomma Zarubina, has been
                       arrested on possible charges of providing false
                       information to U.S. law enforcement and maintaining
                       connections with Russian intelligence services,
                       linking her to another suspected spy who fled the
                       United States while being pursued by authorities.


                # ⚓ Atlantic Council ☛ How_the_Nordic-Baltic_states_are_leading
                  the_way_on_European_security⠀⇛


                       If you want to know what’s next for security in
                       Europe, then watch the Nordic-Baltic nations. They
                       may not have a reputation as the heaviest hitters
                       in the transatlantic alliance, but the eight
                       countries—Denmark, Estonia, Finland, Iceland,
                       Latvia, Lithuania, Norway, and Sweden—are becoming
                       increasingly significant players in European
                       security. On November 28, Swedish Prime Minister
                       Ulf Kristersson hosted his Nordic-Baltic colleagues
                       together with Polish Prime Minister Donald Tusk at
                       Harpsund, Sweden, where they pledged to step up
                       military support to Ukraine and continue to invest
                       in their own deterrence and resilience.
                       Underscoring the increasing importance of the
                       Nordic-Baltic states in European security, French
                       President Emmanuel Macron even called in and joined
                       the conversation.


                # ⚓ Atlantic Council ☛ How_NATO_learns_and_adapts_to_modern
                  warfare⠀⇛


                       Russia’s illegal annexation of Crimea in 2014 and
                       the full-scale invasion of Ukraine in 2022 have had
                       strategic consequences far beyond the region,
                       showcasing the complexities of modern conflicts,
                       where conventional battles are intertwined with
                       cyber warfare, information operations, and hybrid
                       tactics.


                # ⚓ RFERL ☛ Declassified_Documents_Show_Romanian_Elections
                  Targeted_By_'Aggressive_Hybrid_Russian_Action'⠀⇛


                       Documents declassified by Romania's security
                       council on December 4 said the country was the
                       target of an "aggressive hybrid Russian action"
                       during recent election campaigns, including last
                       month's surprise victory of a pro-Russian far-right
                       candidate.


                       The Supreme Council of National Defense
                       declassified the documents, saying they showed that
                       Romania was the target of various coordinated
                       actions leading up to the presidential election's
                       November 24 first round, won by Calin Georgescu.


                # ⚓ Deutsche Welle ☛ Will_TikTok_decide_the_presidential
                  election_in_Romania?⠀⇛


                       Georgescu's polarizing election campaign videos on
                       TikTok have been viewed millions of times. In them,
                       he not only criticizes Romania's political
                       establishment — often making false claims against
                       politicians — but is also seen doing judo or riding
                       horses, just like the man he so admires, Russian
                       President Vladimir Putin.


                       When Georgescu won the first round of the election,
                       the surprise and the dismay were huge. Now, the
                       extreme right-wing conspiracy theorist, NATO critic
                       and Putin admirer has a chance of being elected
                       president of Romania on Sunday.


                       Many observers are convinced that social media
                       platforms — and above all TikTok — played a major
                       role in Georgescu's success.


                # ⚓ EDRI ☛ TikTok_breaches_electoral_legislation_in_Romania⠀⇛


                       Analyses have examined many social causes for the
                       surprise win, such as social and political turmoil
                       and economic problems. However, the Romanian NGOs
                       highlight a clear and important role that TikTok
                       has played in the surprising results, given the
                       platform is one of the most important online forums
                       for national debates.


                       The platform has catalysed the electoral content of
                       an extremist candidate, allowing posting from
                       coordinated fake accounts and failing to flag its
                       content as election advertising. The winning
                       candidate claimed that he has spent no financial
                       resources during this campaign.


                # ⚓ Wired ☛ Lasers_Are_Making_It_Easier_to_Find_Buried_Land
                  Mines⠀⇛


                       In response, US researchers developed a technology
                       to detect land mines indirectly, and which could
                       detect both metal and plastic mines. Lambdis works
                       by sending a vibration into the ground while at the
                       same time scanning the area with a laser beam.
                       Materials in the ground will vibrate at different
                       frequencies, as will the soil itself, and these
                       differences are picked up by the laser when it is
                       reflected back to its emitter. The Lambdis system
                       then generates an image that visualizes these
                       vibrations and their locations in different
                       colors—creating a map of things buried in the soil.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ Meduza ☛ Share_of_Russians’_savings_kept_in_cash
                        reaches_historic_low_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_Central_Bank_head_says_December_key
                        interest_rate_hike_possible_but_‘not_predetermined’_—
                        Meduza⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-12-03_[Older]_Ukraine_pushes
                        for_NATO_membership,_but_it's_complicated⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-12-02_[Older]_Ukraine_updates:
                        Olaf_Scholz_makes_surprise_visit_to_Kyiv⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-02_[Older]_Blinken
                        Heads_to_Final_NATO_Foreign_Ministers_Meeting_of_Biden
                        Administration_With_Ukraine_in_Focus⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-02_[Older]_German
                        Chancellor_Olaf_Scholz_Is_in_Ukraine_for_His_First
                        Visit_in_2_1/2_Years⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-02_[Older]_Ukraine
                        Must_Find_Diplomatic_Solutions_to_Retake_Occupied
                        Territory,_Zelenskiy_Tells_Kyodo_News⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-12-01_[Older]_Ukraine_updates:
                        Zelenskyy_says_Kyiv_needs_NATO_for_survival⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]_Top_EU
                        Officials_Visit_Ukraine_in_Show_of_Solidarity⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]_US_Will
                        Not_Return_Nuclear_Weapons_to_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-30_[Older]_Ukraine
                        Says_War_Has_Damaged_Most_of_Its_Civilian_Airports⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-29_[Older]_Ukraine_updates:
                        Zelenskyy_hints_at_ending_'hot_war'⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]
                        France's_Macron_Reaffirms_Support_for_Ukraine_in_Call
                        With_Zelenskiy⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]
                        Germany's_Scholz_Holds_First_Official_Call_With
                        Ukraine's_Zelenskiy_Since_Putin_Talk⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]_Ukraine
                        Asks_NATO_for_Membership_Invite_Next_Week,_Letter
                        Shows⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]
                        Ukraine's_Top_Commander_Vows_to_Boost_Troops_on_Eastern
                        Front_After_Visiting_Units_There⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]
                        Ukraine's_Zelenskiy_Names_New_Land_Forces_Chief,_Says
                        Changes_Needed⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-28_[Older]_Ukraine_updates:
                        Putin_threatens_Kyiv_with_new_missile⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]
                        Presidential_Aide_Says_Ukraine_Ready_to_Host_Second
                        Peace_Summit_Soon⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]_Ukraine
                        Says_Faster_Military_Aid_More_Important_Than_Drafting
                        More_Men⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-27_[Older]
                        Exclusive-Biden_Readies_$725_Million_Arms_Aid_Package
                        for_Ukraine,_Sources_Say⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-27_[Older]_Trump
                        Picks_Retired_Lt._General_Kellogg_for_Ukraine_Envoy⠀⇛


                      # ⚓ The Local DK ☛ 2024-11-26_[Older]_Denmark_extends
                        work_and_residence_permits_for_Ukrainian_refugees_until
                        2026⠀⇛


                      # ⚓ The Local DK ☛ 2024-12-03_[Older]_Danish_brewing
                        giant_Carlsberg_to_sell_off_Russian_business⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-03_[Older]_Falling
                        Asteroid_Lights_up_Sky_in_Russia's_Remote_Yakutia⠀⇛


                      # ⚓ Vox ☛ 2024-12-03_[Older]_Why_protests_in_the_country
                        of_Georgia_matter⠀⇛


                      # ⚓ IP Kat ☛ 2024-12-02_[Older]_General_Court:_‘Russian
                        Warship,_GO_F**K_YOURSELF’_non-distinctive⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-12-02_[Older]_Germany's
                        Baerbock_warns_China_over_Russia_support⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-02_[Older]
                        Exclusive-Russia's_VTB_CEO_Says_BRICS_Summit_Was_a_Slap
                        in_the_Face_for_the_West⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-02_[Older]
                        Exclusive-Top_Russian_Banker_Says_Easing_of_Tensions
                        With_West_Uncertain_Under_Trump⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-02_[Older]
                        Suspected_Russian_Spies_Targeted_Journalist_With
                        Facebook_'Honey_Trap',_UK_Court_Hears⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-02_[Older]_Chief
                        of_International_Criminal_Court_Lashes_Out_at_US_and
                        Russia_Over_Threats_and_Accusations⠀⇛


                      # ⚓ Modern Diplomacy ☛ 2024-12-01_[Older]_The_Impact_of
                        Russia’s_Nuclear_Doctrine_Revision_on_the_Defense
                        Policies_of_Western_Countries⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-12-01_[Older]_Romanians_vote_as
                        far_right_and_Russia_loom_large⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]_Putin
                        Signs_off_Record_Russian_Defense_Spending_as_Top_EU
                        Officials_Visit_Kyiv⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]_Russian
                        Drones_Target_Kyiv_in_Overnight_Strike⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]
                        Russian,_Syrian_Jets_Intensify_Bombing_of_Syria's
                        Rebel-Held_Northwest⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]_Russia
                        Says_Its_Forces_Capture_Two_Settlements_in_Ukraine's
                        East⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]
                        Russia's_Putin_Approves_Military_Focused_2025-2027
                        Budget⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]_Three
                        Killed_in_Russian_Drone_Attack_on_Ukraine's_Kherson,
                        Governor_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-01_[Older]
                        Ukrainian_Drone_Attack_in_Russia's_Bryansk_Region
                        Killed_Child,_Governor_Says⠀⇛


                      # ⚓ Modern Diplomacy ☛ 2024-11-30_[Older]_Russia_–
                        Ukraine_War:_A_Threat_to_Nuclear_Security⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-30_[Older]_Russian_police
                        raid_Moscow_nightclubs_over_'LGBT_propaganda'⠀⇛


                      # ⚓ The Age AU ☛ 2024-11-30_[Older]_Zelensky_says_for
                        first_time_he_would_give_up_Ukrainian_territory_to
                        Russia⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-30_[Older]_North
                        Korea's_Kim_Vows_Steadfast_Support_for_Russia’s_War_in
                        Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-30_[Older]_Senior
                        Russian_Diplomat_Says_Possibility_of_New_Nuclear_Tests
                        Remains_Open_Question⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-30_[Older]_Iran,
                        Russia_Foreign_Ministers_Say_They_Support_Syria_in
                        Confronting_Rebels,_Iran_State_Media_Reports⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-30_[Older]_Russian
                        and_Chinese_Bombers_Conduct_Joint_Air_Patrol⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-30_[Older]_Russian
                        Police_Raid_Moscow_Nightclubs_in_LGBTQ+_Crackdown⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-30_[Older]_Russia
                        Says_Air_Force_Strikes_Rebels_in_Support_of_Syrian
                        Army,_Agencies_Report⠀⇛


                      # ⚓ Counter Punch ☛ 2024-11-29_[Older]_Ironic_Dependency:
                        Russian_Uranium_and_the_US_Energy_Market⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-29_[Older]_Ukraine_updates:
                        North_Korea_vows_support_for_Russia's_war⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]_Drone
                        Drops_Paint_Over_Russian_Embassy_in_Sweden⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]_North
                        Korea_Leader_Kim:_Russia_Has_Right_to_Exercise_Self
                        Defence_Against_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]_UK_Spy
                        Chief_Says_Russia_Behind_'Staggeringly_Reckless'
                        Sabotage_in_Europe⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-29_[Older]_UK
                        Intelligence_Chief_Accuses_Russia_of_'Staggeringly
                        Reckless'_Sabotage_Campaign⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-28_[Older]_Russia_in_panic
                        as_US_sanctions_trigger_ruble_collapse⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-28_[Older]_Russian_ruble
                        plunges_amid_fresh_US_sanctions⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-28_[Older]_Ukraine_war:
                        Yemen's_Houthis_to_fight_for_Russia?⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]_Russian
                        Defence_Ministry_Says_Moscow's_Forces_Take_Another_East
                        Ukrainian_Settlement⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]_Putin
                        Says_Russia_Could_Hit_'Decision-Making_Centres'_in_Kyiv
                        With_New_Missile⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]_Putin
                        Says_Russia_Would_Use_All_Weapons_at_Its_Disposal_if
                        Ukraine_Got_Nuclear_Weapons⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]_Putin
                        Says_Ukrainian_Infrastructure_Attack_Was_Revenge_for
                        Kyiv's_Strikes_on_Russia⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]_Russia
                        and_Ukraine_Return_Children_to_Families_After_Mediation
                        by_Qatar⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]_Russian
                        Drones_Strike_Buildings_in_Kyiv,_Officials_Say⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]
                        Bulgarians_Spied_on_US_Base_and_Dissidents_for_Russia,
                        UK_Court_Told⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-28_[Older]_Ukraine
                        Imposes_First_Wartime_Tax_Hikes_to_Fight_Russian
                        Invasion⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-27_[Older]_Russia:_Kremlin
                        orders_2_German_ARD_journalists_to_leave⠀⇛


                      # ⚓ The Local SE ☛ 2024-11-27_[Older]_Nordics,_Baltic
                        states_and_Poland_ready_to_expand_Russia_sanctions⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-27_[Older]_Trump
                        Selects_Longtime_Adviser_Keith_Kellogg_as_Special_Envoy
                        for_Ukraine_and_Russia⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-27_[Older]_White
                        House_Pressing_Ukraine_to_Draft_18-Year-Olds_So_It_Has
                        Enough_Troops_to_Battle_Russia⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-27_[Older]_Russian
                        Acts_of_Sabotage_May_Lead_to_NATO_Invoking_Article_5,
                        Says_German_Intel_Chief⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-27_[Older]_Russia
                        Says_Trump_Ukraine_Aid_Cut_Would_Be_'Death_Sentence'
                        for_Kyiv's_Military⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-27_[Older]_US
                        Urges_Ukraine_to_Lower_Fighting_Age_to_18_to_Bolster
                        Ranks_Against_Russia⠀⇛


                      # ⚓ CPJ ☛ 2024-11-26_[Older]_Russia_detains_Crimean
                        journalist_Ediye_Muslimova_for_36_hours⠀⇛


                      # ⚓ CPJ ☛ 2024-11-26_[Older]_Russian_journalist_Nika
                        Novak_sentenced_to_4_years_in_prison⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-26_[Older]_Ukraine_updates:
                        Russia_attacks_with_record_number_of_drones⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The Verge ☛ Suspect_in_UnitedHealthcare_CEO_shooting
                  reportedly_didn’t_use_a_Citi_Bike_to_escape⠀⇛


                       CNN is reporting that according to an unnamed
                       source in law enforcement, the person who shot and
                       killed UnitedHealthcare CEO Brian Thompson outside
                       the Hilton hotel in midtown Manhattan fled on an e-
                       bike, but not a Citi Bike, as NYPD Chief of
                       Detectives Joe Kenney previously said during a
                       press conference.


                # ⚓ TMZ ☛ Internet_Super-Sleuth_May_Have_Tracked_Location_of
                  Healthcare_CEO_Assassin⠀⇛


                       A man’s stepping forward with a jaw-dropping claim
                       -- he says he may have figured out the whereabouts
                       of the assassin who shot UnitedHealthcare CEO Brian
                       Thompson ... all thanks to Citi Bike's tracking
                       data.


                       A data scientist named Riley, who goes by @rtwlz on
                       X, dropped a bombshell post, revealing how he's
                       been scraping Citi Bike data every minute ... and
                       he could see exactly where individual bikes go.


          o § Environment⠀➾


                # ⚓ France24 ☛ Valencia_floods:_Human_tragedy_and_environmental
                  disaster⠀⇛


                       With at least 222 people dead, the torrential rain
                       and floods in Valencia – on the eastern coast of
                       Spain – have devastated many families and the
                       cleanup of the region continues, more than a month
                       after the disaster struck. But until now, there has
                       been little focus on the devastating effect of the
                       floods on the environment. The water carried
                       kilograms of fragments of plastic, medicines and
                       other toxic materials into the protected nature
                       reserve of Albufera. The regional government has
                       announced a cleanup operation. Sarah Morris and
                       Armelle Exposito report.


                # ⚓ Deseret Media ☛ Conditions_in_abandoned_mine_are_too
                  dangerous_for_crew_searching_for_Pennsylvania_woman⠀⇛


                       Sinkholes occur in the area because of subsidence
                       from coal mining activity. Rescuers had been using
                       water to break down and remove clay and dirt from
                       the mine, which has been closed since the 1950s,
                       but that increased the risk "for potential other
                       mine subsidence to take place," Pennsylvania State
                       Police spokesman trooper Steve Limani said.


                # ⚓ Energy Mix Productions Inc ☛ UN_Plastics_Treaty_Hits
                  Stalemate_as_Petrostates_Russia,_Saudi_Arabia_Block_Deal⠀⇛


                       “We are circling, and I would say that the only
                       good thing is that there’s momentum from a growing
                       number of countries who do support the measures
                       that are needed.”


                       The negotiations highlighted a divide between two
                       camps: over 100 nations, including Canada, called
                       for a cap on plastic production, while oil-
                       producing countries like Saudi Arabia and Russia
                       advocated focusing on plastic waste management
                       rather than production limits.


                # ⚓ Deutsche Welle ☛ EU_agrees_to_delay_deforestation_law_but
                  won't_water_it_down⠀⇛


                       Forests are being cut and degraded at an alarming
                       rate, especially in the tropics, with the expansion
                       of agricultural land causing almost 90% of forest
                       reduction, according to a study by the Food and
                       Agriculture Organization of the United Nations.


                       A first-of-its-kind law called the EU Deforestation
                       Regulation (EUDR) aims to take steps to counter
                       this. The idea is that EU importers have to prove
                       their supply chains for products such as coffee,
                       chocolate, leather, paper, tires and furniture do
                       not contribute to logging anywhere in the world.
                       Failure to do so would mean facing fines of up to
                       4% of their turnover.


                # ⚓ VOA News ☛ UNESCO_says_education_about_climate_change_is
                  essential_in_southern_Africa⠀⇛


                       The United Nations environmental agency UNESCO is
                       calling for more studies and closer working
                       relations between journalists and scientists to
                       ensure the effects of climate change are understood
                       and can be mitigated, especially in poorer African
                       countries, which more acutely feel the pinch of
                       extreme weather events.


                       On Tuesday, scientists gathered in Pretoria, South
                       Africa, to discuss climate change with journalists
                       from the Southern Africa Development Community
                       region.


                # § Energy/Transportation⠀➾


                      # ⚓ DeSmog ☛ EQT’s_‘bulldog’_has_D.C._in_his_grip,_with
                        profits_—_and_maybe_higher_gas_bills_—_on_the_horizon⠀⇛


                      # ⚓ DeSmog ☛ CAPP_President_Abandons_‘Net_Zero’_Message
                        at_Exclusive_Industry_Event⠀⇛


                      # ⚓ Sunday Times ☛ VW_recalls_more_than_4,600_vehicles
                        over_battery_overheating_concerns⠀⇛


                             Volkswagen is recalling 4,616 vehicles in the
                             US over concerns that their high-voltage
                             batteries may overheat and increase the risk
                             of a fire, the National Highway Traffic
                             Safety Administration (NHTSA) said on
                             Wednesday.


                             The recall affects plug-in hybrids such as
                             the 2022-2023 model year Audi Q5 SUVs and
                             2022 Audi A7 vehicles.


                      # ⚓ Wired ☛ She_Was_a_Russian_Socialite_and_Influencer.
                        Cops_Say_She’s_a_Crypto_Laundering_Kingpin⠀⇛


                             International authorities believe she was
                             much more than that. At the end of 2023, the
                             United States government hit Zhdanova with
                             economic sanctions for her alleged role in a
                             crypto money-laundering operation used by
                             Russian oligarchs, ransomware gangs, and
                             other criminals. Today, Western law
                             enforcement officials have gone even further,
                             claiming that Zhdanova has acted as the head
                             of a sophisticated money-laundering network
                             that swaps cash for cryptocurrency, the likes
                             of which law enforcement has never seen.


                      # ⚓ US News And World Report ☛ Bitcoin_Tops_$100,000_on
                        Optimism_Over_Trump_[Cryptocurrency]_Plans⠀⇛


                             Bitcoin rose above $100,000 for the first
                             time on Thursday as the election of
                             Republican Donald Trump as president of the
                             United States spurred expectations that his
                             administration will create a friendly
                             regulatory environment for cryptocurrencies.


                      # ⚓ India Times ☛ Bitcoin_surpasses_$100,000_after_Trump
                        picks_[cryptocurrency]_advocate_Paul_Atkins_to_lead
                        SEC⠀⇛


                             The cryptocurrency's value has doubled this
                             year, showing a 45% increase in the four
                             weeks since Trump's electoral victory, which
                             also resulted in several cryptocurrency-
                             supporting legislators entering Congress.


                      # ⚓ Deccan Chronicle ☛ Experts_Shrug_off_Tremor_Fears_for
                        Data_Centres_in_Hyderabad⠀⇛


                             Hyderabad, a key hub for data centres in
                             India, remains unfazed by mild tremors felt
                             in the city on Wednesday, reaffirming its
                             position as one of the most preferred
                             destinations for establishing data centres in
                             the country.


                      # ⚓ CBC ☛ Millions_without_power_after_Cuba's_electrical
                        grid_collapses⠀⇛


                             Cuba says it has begun restoring power after
                             the island's electrical grid collapsed
                             Wednesday morning, the latest in a string of
                             countrywide blackouts that underscore the
                             increasingly frail state of its power
                             generation system.


                      # ⚓ The Scotsman ☛ All-electric_bike_hire_scheme_to_be
                        launched_in_Edinburgh_by_next_summer_-_here's_how_it
                        would_work⠀⇛


                             An all-electric bike hire scheme is due to be
                             launched in Edinburgh by next summer to
                             replace one that collapsed three years ago.


                             The City of Edinburgh Council is talking to
                             four potential operators, which The Scotsman
                             understands include Voi, Lime and Dott.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Saving_Living_Jewels:_One_Woman’s
                        Mission_to_Shine_a_Light_on_the_Ornamental_Fish_Trade⠀⇛


                      # ⚓ Science Alert ☛ Orcas_Are_Wearing_Dead_Salmon_as
                        Hats,_And_Scientists_Are_Stumped⠀⇛


                             The bizarre phenomenon is back.


                      # ⚓ Science Alert ☛ Genes_Older_Than_Animal_Life_Itself
                        Were_Inserted_Into_Mice._Here's_What_Happened.⠀⇛


                             Amazing.


                      # ⚓ Science Alert ☛ Mysterious_'Snake_Person'_Head_From
                        7,500_Years_Ago_Raises_Questions⠀⇛


                             What does it mean?


                      # ⚓ Science Alert ☛ This_Massive_Underwater_Mountain
                        Range_Was_Made_by_a_'Moving'_Hotspot⠀⇛


                             The first found in the Indian Ocean.


                      # ⚓ New York Times ☛ Researchers_Release_Hawaiian_Crows
                        Back_Into_the_Wild⠀⇛


                             There, the thinking goes, they’ll be safe
                             from hawks, which killed a number of crows
                             during earlier reintroduction efforts on the
                             Big Island. If the crows can thrive on Maui,
                             scientists and wildlife officials say, it
                             will be a major step toward one day restoring
                             them to their home island.


                      # ⚓ Scientific American ☛ Hawaiian_Crows_Return_to_the
                        Wild,_Where_They_Are_‘Guides_to_Souls’⠀⇛


                             The Hawaiian crow, or ‘alalā, has been
                             extinct in the wild since 2002. A new effort
                             to reintroduce birds of this
                             species—considered important guides to the
                             souls of the dead in Hawaiian tradition—is
                             underway


                      # ⚓ LabX Media Group ☛ Researchers_Discover_How_Starfish
                        Cut_Ties_with_Their_Limbs⠀⇛


                             Deep in the underwater world, animals like
                             starfish use unusual ways to escape
                             predators. In an act called autotomy,
                             starfish shed one or more of their limbs to
                             flee their hunters. The severed, writhing
                             body part distracts the attacker, allowing
                             the starfish to glide away. Over time, the
                             starfish can even regenerate the lost limb,
                             returning to their usual life after a brush
                             with death.


          o § Finance⠀➾


                # ⚓ BIA Net ☛ Turkey’s_inflation_drops_slightly_to_47.09%_in
                  November⠀⇛


                       The decline fell short of expectations considering
                       the Central Bank’s year-end forecast of 44%.


                # ⚓ Science Alert ☛ Experiment_Reveals_How_Pressure_to_Tip_Can
                  Unexpectedly_Backfire⠀⇛


                       Has this happened to you?


                # ⚓ Hong Kong Free Press ☛ Hong_Kong’s_deficit_to_double_to
                  HK$100_billion,_finance_chief_Paul_Chan_warns⠀⇛


                       Hong Kong’s budget deficit is expected to double to
                       HK$100 billion this financial year, finance chief
                       Paul Chan has said, citing a property market slump
                       that weighed on government coffers.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ New York Times ☛ It’s_the_Corruption,_Stupid⠀⇛


                       The politician discusses what lessons he thinks
                       Democrats have forgotten.


                # ⚓ Meduza ☛ Former_Fox_News_host_Tucker_Carlson_returns_to
                  Moscow_to_interview_Russian_Foreign_Minister_Sergey_Lavrov_—
                  Meduza⠀⇛


                # ⚓ Krebs On Security ☛ U.S._Offered_$10M_for_[Cracker]_Just
                  Arrested_by_Russia⠀⇛


                       In January 2022, KrebsOnSecurity identified a
                       Russian man named Mikhail Matveev as “Wazawaka,” a
                       cybercriminal who was deeply involved in the
                       formation and operation of multiple ransomware
                       groups. The U.S. government indicted Matveev as a
                       top ransomware purveyor a year later, offering $10
                       million for information leading to his arrest. Last
                       week, the Russian government reportedly arrested
                       Matveev and charged him with creating malware used
                       to extort companies.


                # ⚓ India Times ☛ OpenAI_chief_'believes'_Musk_will_not_abuse
                  government_power⠀⇛


                       Speaking at the New York Times DealBook conference,
                       Altman addressed concerns about Musk's announced
                       role heading a new Department [sic] of Government
                       Efficiency in the incoming Donald Trump
                       administration, and whether he might use it to
                       favor his own companies.


                # ⚓ India Times ☛ Meta_to_build_$10_billion_AI_data_center_in
                  Louisiana_as_Elon_Musk_expands_his_Tennessee_AI_facility⠀⇛


                       The largest artificial intelligence data center
                       ever built by Facebook's parent company Meta is
                       coming to northeast Louisiana, the company said
                       Wednesday, bringing hopes that the $10 billion
                       facility will transform an economically neglected
                       corner of the state.


                # ⚓ The Record ☛ Cyber_incident_board’s_Salt_Typhoon_review_to
                  begin_within_days,_CISA_leader_says⠀⇛


                       An independent review board will launch its
                       investigation of an unprecedented Chinese [breach]
                       of global telecommunications systems later this
                       week, the head of the Cybersecurity and
                       Infrastructure Security Agency said on Wednesday.


                       Speaking to reporters after a classified briefing
                       for all senators on Wednesday about the breach by
                       the state-sponsored group known as Salt Typhoon,
                       CISA Director Jen Easterly said the first meeting
                       of the Cyber Safety Review Board (CSRB) focused on
                       the ongoing breach will take place on Friday.


                # ⚓ The Record ☛ At_least_8_US_telcos,_dozens_of_countries
                  impacted_by_Salt_Typhoon_breaches,_White_House_says⠀⇛


                       The scope of the Chinese government [intrusion]
                       campaign came into further focus on Wednesday, as
                       senior White House officials revealed that eight
                       telecommunications giants in the U.S. were breached
                       and that companies in multiple other countries were
                       also [breached].


                       The breaches are part of the Salt Typhoon campaign,
                       which first came to light after threat actors
                       intercepted the correspondence of senior officials
                       within both presidential campaigns, including from
                       President-elect Donald Trump and his running mate
                       JD Vance.


                # ⚓ Silicon Angle ☛ US_urges_use_of_encrypted_messaging_apps
                  following_Salt_Typhoon_[breach]⠀⇛


                       The guidance follows the discovery of a large-scale
                       cyberattack campaign against U.S.
                       telecommunications companies. Salt Typhoon, a
                       Chinese state-backed [intrusion] group, has
                       compromised the networks of AT&T Inc., Verizon
                       Communications Inc. and Lumen Technologies Inc. T-
                       Mobile US Inc. said that the [intruders] didn’t
                       access its infrastructure, but did compromise a
                       connection which linked its systems to a different
                       provider’s network.


                # ⚓ The Register UK ☛ T-Mobile_CSO:_Cyber_spies'_initial_access
                  method_'is_novel'⠀⇛


                       Simon spoke with El Reg a day after FBI and CISA
                       officials briefed reporters on the massive cyber-
                       espionage campaign, during which China-affiliated
                       snoops successfully broke into US telecom
                       companies' networks, compromised wiretapping
                       systems used by law enforcement, and used that
                       access to steal customers' call records and
                       metadata.


                       A Chinese government-linked group dubbed Salt
                       Typhoon is believed to be behind the attacks. It's
                       understood Verizon, AT&T, and Lumen Technologies,
                       at least, were hit by the crew.


                # ⚓ VOA News ☛ US_senators_vow_action_after_briefing_on_Chinese
                  Salt_Typhoon_telecom_[breach]⠀⇛


                       The FBI, Director of National Intelligence Avril
                       Haines, Federal Communications Commission Chair
                       Jessica Rosenworcel, the National Security Council
                       and the Cybersecurity and Infrastructure Security
                       Agency were among the participants in the closed-
                       door briefing, officials told Reuters.


                       Democratic Senator Ron Wyden told reporters after
                       the briefing he was working to draft legislation on
                       this issue, while Senator Bob Casey said he had
                       "great concern" about the breach and added it may
                       not be until next year before Congress can address
                       the issue.


                # ⚓ John Gruber ☛ Daring_Fireball:_Andy_Grove_Was_Right⠀⇛


                       Grove retired as CEO in 1998 and as chairman in
                       2005. It’s as though no one at Intel after him had
                       listened to a word he said. Grove’s words don’t
                       read merely as advice — they read today as a
                       postmortem synopsis for Intel’s own precipitous
                       decline over the last 20 years.


                # ⚓ Bruce Schneier ☛ AI_and_the_2024_Elections⠀⇛


                       It’s been the biggest year for elections in human
                       history: 2024 is a “super-cycle” year in which 3.7
                       billion eligible voters in 72 countries had the
                       chance to go the polls. These are also the first AI
                       elections, where many feared that deepfakes and
                       artificial intelligence-generated misinformation
                       would overwhelm the democratic processes. As 2024
                       draws to a close, it’s instructive to take stock of
                       how democracy did.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Omicron Limited ☛ AI_fact_checks_can_increase_belief
                        in_false_headlines,_study_finds⠀⇛


                             Although many tech companies and start-ups
                             have touted the potential of automated fact-
                             checking services powered by artificial
                             intelligence to stem the rising tide of
                             online misinformation, a new study led by
                             researchers at Indiana University has found
                             that AI-fact checking can, in some cases,
                             actually increase belief in false headlines
                             whose veracity the AI was unsure about, as
                             well as decrease belief in true headlines
                             mislabeled as false.


                      # ⚓ Meduza ☛ Putin_adds_infamous_propagandist_to_Russia’s
                        Presidential_Human_Rights_Council⠀⇛


                             Vladimir Putin has appointed an infamous
                             propagandist from Yevgeny Prigozhin’s old
                             media empire to serve on Russia’s
                             Presidential Human Rights Council.


                             As the head of organizations like USA Really
                             and the Foundation for National Values
                             Protection, Alexander Malkevich has led
                             Russian efforts to interfere in foreign
                             elections around the globe. Through its
                             Rewards for Justice program, the U.S. State
                             Department currently offers up to $10 million
                             for information about Malkevich.


                      # ⚓ RFERL ☛ How_Russia_Prepares_Children_In_Occupied
                        Ukraine_For_War_Against_Their_Own_Country⠀⇛


                             Ukrainian law enforcement has charged
                             Yunarmia leadership in occupied Crimea with
                             violating the protection of civilians
                             guaranteed by the Geneva Conventions, citing
                             an article that prohibits "propaganda aimed
                             at ensuring the voluntary enlistment of
                             civilians."


                             Iryna Sedova, an expert of the Crimean Human
                             Rights Group, supports the official
                             indictment.


          o § Censorship/Free Speech⠀➾


                # ⚓ Digital Music News ☛ Knocked_Loose_Says_‘Sorry,_Not_Sorry’
                  After_Jimmy_Kimmel_Performance⠀⇛


                       Knocked Loose and Poppy teamed up for a heavy metal
                       performance on Jimmy Kimmel Live, which put off a
                       certain demographic of viewers. Hardcore punk
                       outfit Knocked Loose enjoyed a performance with
                       Poppy on Jimmy Kimmel Live last week, but the
                       band’s extreme style put off certain viewers who
                       aren’t accustomed to such music.


                # ⚓ EFF ☛ Speaking_Freely:_Aji_Fama_Jobe⠀⇛


                       *This interview has been edited for length and
                       clarity.


                       Aji Fama Jobe is a digital creator, IT consultant,
                       blogger, and tech community leader from The Gambia.
                       She helps run Women TechMakers Banjul, an
                       organization that provides visibility, mentorship,
                       and resources to women and girls in tech. She also
                       serves as an Information Technology Assistant with
                       the World Bank Group where she focuses on resolving
                       IT issues and enhancing digital infrastructure. Aji
                       Fama is a dedicated advocate working to leverage
                       technology to enhance the lives and opportunities
                       of women and girls in Gambia and across Africa.


                       Greene: Why don’t you start off by introducing
                       yourself? 


                # ⚓ New York Times ☛ Writers_Silenced_by_Stalin_Get_New_Life
                  Amid_War_in_Ukraine⠀⇛


                       The Soviet regime killed a generation of literary
                       artists in the 1930s. Their legacy is being
                       reclaimed as Ukraine fights to preserve its
                       cultural heritage.


                # ⚓ International Business Times ☛ Irish_Man_'Faces_Years_In
                  Dubai_Prison'_Under_UAE_Cybercrime_Laws_For_Sending
                  'Threatening'_Emojis⠀⇛


                       "He has been advised that he could face several
                       years in prison under strict laws that prohibit
                       rude, offensive or threatening text messages, even
                       if expressed sarcastically, jokingly between close
                       friends or loved ones," Detained in Dubai said in a
                       statement.


                       "Stuart's mother has been in touch with the
                       accuser, and they have both apologised, but he has
                       said he won't withdraw the case," said Stirling.
                       She claimed that Dubai's strict laws are often
                       misused by complainants who file police reports as
                       a tactic to extort victims.


                # ⚓ VOA News ☛ Analysts_troubled_by_trend_of_[Internet],_social
                  media_shutdowns_in_Africa⠀⇛


                       Amid widespread protests in Kenya this summer over
                       a controversial finance bill, the country's
                       Communications Authority announced it did not
                       intend to shut down [Internet] access. The next
                       day, however, Kenya experienced a countrywide loss
                       in [Internet] connectivity.


                       The main [Internet] service providers said the
                       outage on June 25 was caused by an issue with
                       undersea cables. But the incident caught the
                       attention of digital rights groups, who said the
                       timing of the outage "strongly suggests" an
                       intentional action. Various governments have used
                       such shutdowns to maintain control, these groups
                       say.


                # ⚓ Techdirt ☛ Elon_Musk_Should_Be_Shouting_About_The_Florida
                  And_Texas_Social_Media_Laws_(But_Are_You_Surprised_That_He’s
                  Not?)⠀⇛


                       Florida’s SB 7072 Texas’s HB 20 were enacted in
                       2021, and they’ve already been the subject of
                       extensive litigation. They’ve already been to the
                       Supreme Court, in fact, where, last summer, the
                       justices addressed lawsuits challenging the two
                       laws in Moody v. NetChoice. That decision does some
                       very good things. It confirms that the First
                       Amendment protects curated collections of third-
                       party speech. It finds that social media newsfeeds
                       are exactly that sort of protected expressive
                       compilation. And it concludes that “a state may not
                       interfere” with such feeds “to advance its own
                       vision of ideological balance.”


                       But Moody is not the final word. The justices were
                       reviewing a pair of interlocutory appeals; they
                       were explaining only what was “likely” to happen,
                       in the two cases, on the merits. What’s more, the
                       decision addresses only what social media platforms
                       do “on their main feeds.” Texas and Florida are
                       “not likely to succeed in enforcing” their laws,
                       the Court declared, “against the platforms’
                       application of their content-moderation policies to
                       the feeds that were the focus of the proceedings
                       below” (emphasis mine). The Court offered no
                       opinion on whether SB 7072 and HB 20 are
                       constitutional as applied to user profiles, direct
                       messaging, group chats, or event functions.
                       Instead, it sent the cases back to their respective
                       trial courts for further fact-finding through
                       discovery.


                       In a nutshell, SB 7072 and HB 20 require large
                       social media platforms (1) to carry and promote
                       content against their will and (2) to fulfill
                       onerous transparency requirements. Even if the
                       conclusion that they do not govern content
                       moderation on newsfeeds holds (no sure bet—a point
                       to which I shall return), these two laws could
                       cause huge headaches for Musk and X.


                # ⚓ US News And World Report ☛ Iranian_Nobel_Prize_Winner
                  Mohammadi_Released_From_Jail_for_Medical_Treatment⠀⇛


                       Iranian Nobel peace prize winner Narges Mohammadi
                       was released from Evin prison after the suspension
                       of her jail term to undergo medical treatment, her
                       husband Taqi Rahmani told Reuters on Wednesday.


                       Mohammadi is serving multiple sentences in Tehran's
                       notorious Evin prison on charges including
                       spreading propaganda against the Islamic Republic.


                # ⚓ The Moscow Times ☛ Caught_in_Riots,_Georgia’s_Protesters
                  Say_They_Must_Choose_Between_Europe_and_Russia_-_The_Moscow
                  Times⠀⇛


                       Fears of wider political unrest have intensified
                       since the passage of the so-called transparency of
                       foreign influence law and Georgia’s Oct. 26
                       parliamentary elections, which were dubbed as
                       crucial by both Georgian Dream and the opposition
                       and were widely viewed as “a referendum” between
                       Europe and Russia.


                # ⚓ ANF News ☛ Police_confiscate_four_books_at_8th_Amed_Book
                  Fair⠀⇛


                       The 8th Amed Book Fair has begun in cooperation
                       with the Amed Chamber of Commerce and Industry
                       (DTSO) and TÜYAP Fair Organization.


                       A total of 216 publishing houses, 26 of which are
                       Kurdish publishing houses, participated in the
                       fair, which will be open until 8 December.


                       The fair, which takes place at the Mesopotamia
                       International Fair and Congress Center, hosts many
                       talks, panels and book signing sessions, and will
                       see the participation of many authors.


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


                # ⚓ Press Gazette ☛ Barriers_still_exist_for_disabled_people_in
                  journalism⠀⇛


                       Claire Harris says disability is not a barrier, but
                       not considering the environment is.


                # ⚓ DeSmog ☛ DeSmog_Announces_Geoff_Dembicki_as_Global_Managing
                  Editor⠀⇛


                # ⚓ New Statesman ☛ How_to_spot_an_excellent_editor⠀⇛


                       Like a coach in sport, it’s hard to pin down what
                       an editor does, let alone how they do it. A good
                       coach has a positive effect; that’s about all we
                       know for sure. But people who are good at helping
                       us to do things better often guard their methods –
                       especially from themselves. Like any form of
                       creativity, drawing out potential in others needs
                       to be protected from prying over-analysis.


                       So what follows – my individual take on writing for
                       Jason – is both unusually personal and also
                       impertinent. Because I might easily be mistaken.
                       But that’s all part of it. Because, even though
                       it’s hard to define a good editor (or coach), a
                       measure of benign ambiguity is always in the mix.


                # ⚓ VOA News ☛ Journalists_in_Bolivia_face_attacks,_verbal
                  assaults⠀⇛


                       The reporter was working for TV station Unitel,
                       covering widespread protests by supporters of
                       Bolivia’s former president as they blocked roads
                       across the country.


                       Choque said he received multiple hits to his body
                       and face after being ambushed while covering
                       confrontations between the police and protesters in
                       the town of Mairana.


                # ⚓ TruthOut ☛ Trump_Offers_Pentagon_Job_to_Billionaire_Whose
                  Firm_Trained_Journalist’s_Killers⠀⇛


                       Stephen Feinberg is co-founder and co-CEO of the
                       private equity behemoth Cerberus Capital
                       Management, which owns a firm that provided
                       paramilitary training to members of the elite team
                       that murdered Saudi journalist and U.S. resident
                       Jamal Khashoggi in 2018.


                       Trump drew global outrage for publicly defending
                       the Saudi regime in the wake of the assassination,
                       even after U.S. intelligence agencies established
                       that Saudi Crown Prince Mohammed bin Salman
                       authorized Khashoggi’s murder.


          o § Civil Rights/Policing⠀➾


                # ⚓ Stanford University ☛ Modern_masculinity_and_the_quest_for
                  good⠀⇛


                       Sebastian Strawser explores society's notions of
                       masculinity and how we measure male success in an
                       increasingly polarized world.


                # ⚓ TwinCities Pioneer Press ☛ Chad_Chronister,_Donald_Trump’s
                  pick_to_run_the_DEA,_withdraws_name_from_consideration⠀⇛


                       Chronister is the second person selected by the
                       president-elect to bow out quickly after being
                       nominated for a position requiring Senate
                       confirmation.


                # ⚓ The Straits Times ☛ Malaysia_proposes_laws_to_arrest,
                  obtain_private_data,_in_clampdown_on_harmful_online_content⠀⇛


                       Social media and messaging app operators will be
                       subject to stiffer rules and penalties from Jan 1.


                # ⚓ EFF ☛ Top_Ten_EFF_Digital_Security_Resources_for_People
                  Concerned_About_the_Incoming_Trump_Administration⠀⇛


                       EFF has decades of experience in providing digital
                       privacy and security resources, particularly for
                       vulnerable people. We’ve written a lot of resources
                       over the years and here are the top ten that we
                       think are most useful right now:


                       https://ssd.eff.org/


                       Our Surveillance Self-Defense guides are a great
                       place to start your journey of securing yourself
                       against digital threats. We know that it can be a
                       bit overwhelming, so we recommend starting with our
                       guide on making a security plan so you can
                       familiarize yourself with the basics and decide on
                       your specific needs. Or, if you’re planning to head
                       out to a protest soon and want to know the most
                       important ways to protect yourself, check out our
                       guide to Attending a Protest. Many people in the
                       groups most likely to be targeted in the upcoming
                       months will need advice tailored to their specific
                       threat models, and for that we recommend the
                       Security Scenarios module as a quick way to find
                       the right information for your particular
                       situation. 


                # ⚓ Meduza ☛ Russian_officials_want_to_ban_lawyers_from
                  visiting_clients_at_police_stations_—_Meduza⠀⇛


                # ⚓ Meduza ☛ Russia_declares_The_Satanic_Temple_undesirable_—
                  Meduza⠀⇛


                # ⚓ JURIST ☛ Egypt_urged_to_reject_new_refugee_law_for
                  violating_international_refugee_rights⠀⇛


                       Amnesty International urged the Egyptian government
                       on Tuesday to reject the new refugee law, citing
                       violations of international human rights and
                       refugee laws.


                # ⚓ Defence Web ☛ What_is_happening_at_South_Africa’s
                  borders?⠀⇛


                       The South African National Defence Force (SANDF),
                       through its Defence Corporate Communications
                       division, last week organised a visit to the Musina
                       border area to show the media how the military is
                       patrolling the country’s borders under Operation
                       Corona.


                # ⚓ TwinCities Pioneer Press ☛ Justice_Department_announces
                  sweeping_reforms_to_curb_suicides_in_federal_prisons_and
                  jails⠀⇛


                       The 14-page report said the measures “will
                       strengthen the Department’s capacity to reduce the
                       risk of suicide by adults in federal custody and
                       advance a culture of safety in its institutions.”


                # ⚓ NYPost ☛ Lady_Gabriella_breaks_silence_on_husband’s
                  ‘impulsive’_suicide_at_45,_blames_‘adverse_reaction’_to_his
                  medication⠀⇛


                       "The fact that he took his life at the home of his
                       beloved parents suggests the decision was the
                       result of a sudden impulse."


                # ⚓ The Nation ☛ In_the_US,_Tenants_Are_Usually_on_Their_Own.
                  Can_a_New_National_Tenant_Union_Change_That?⠀⇛


                       As TUF is finding its national footing, many of its
                       leaders are tenants like Echo Maker, fighting to
                       directly improve their own living conditions. Many
                       are low-income and disabled, unable to work
                       traditional jobs and therefore living off meager
                       Social Security payments. They often live in run-
                       down, neglected buildings often explicitly reserved
                       for elderly and disabled tenants, who are typically
                       the most vulnerable to exploitation from their
                       landlords. And each of them—from Echo Maker to
                       Lori-Lynn Ross in Connecticut to Donna Goldsmith in
                       Louisville—considered themselves completely
                       alienated from not just the political process but
                       their own communities as well, before TUF
                       organizers knocked on their doors.


                # ⚓ Los Angeles Times ☛ Memphis_police_discriminate_against
                  Black_people,_Justice_Department_finds⠀⇛


                       The Memphis Police Department uses excessive force
                       and discriminates against Black people, according
                       to the findings of a U.S. Department of Justice
                       investigation launched after the beating death of
                       Tyre Nichols after a traffic stop in 2023.


                       A report released Wednesday marked the conclusion
                       of the investigation that began six months after
                       Nichols was kicked, punched and hit with a police
                       baton as five officers tried to arrest him after he
                       fled a traffic stop.


                # ⚓ Lou Plummer ☛ What_Passes_for_Justice⠀⇛


                       During the next few days, the survivors began to
                       tell the story of the rapidly spreading fire that
                       was fueled by an ad hoc repair to a hydraulic line
                       that burst right next to a sizzling hot fryer for
                       cooking chicken. Few people knew that although the
                       plant had two previous fires within the last
                       decade, it had never had a state safety inspection.
                       As the workers fled, they encountered locked and
                       chained fire exits, closed at the order of the
                       company's owner, who was worried about people
                       stealing food from his company. Only one group of
                       employees managed to kick open a door. That door,
                       covered in sooty boot prints, is on display today
                       at the museum of American History in Washington,
                       DC. It bears testament to one of the deadliest
                       industrial disasters in state history. Of the 90
                       people inside Imperial Foods when the fire broke
                       out, 25 died and 54 were injured, many of them
                       suffering lifelong ill effects from smoke and
                       chemical inhalation.


                # ⚓ Techdirt ☛ Texas_Legislators_Think_Drones_Armed_With_Tasers
                  And_Pepper_Spray_Will_Stop_School_Shootings⠀⇛


                       In reality, most Second Amendment enthusiasts
                       aren’t arming themselves to prevent the government
                       from being overtaken by authoritarians. After all,
                       they voted for Trump at least twice, and he’s the
                       kind of autocrat their window decals have warned
                       against. Most exercises of the Second Amendment are
                       purely performative — “rolling coal” but it’s dudes
                       in camo walking through Walmarts strapped with AR-
                       15s.


                # ⚓ Techdirt ☛ Federal_Court_Says_Dismantling_A_Phone_To
                  Install_Firmware_Isn’t_A_‘Search,’_Even_If_Was_Done_To
                  Facilitate_A_Search⠀⇛


                       As is often the case when Fourth and Fifth
                       Amendment concerns are raised during evidence
                       suppression efforts, this one involves alleged
                       possession of child sexual abuse material. That
                       doesn’t mean the defendant doesn’t raise good
                       points. That just means the public is less likely
                       to sympathize with the defendant. It also means —
                       given the hefty sentences often handed to child
                       sexual abusers — they have more reason than most to
                       try to get the evidence suppressed.


                       It doesn’t work here, though. The court notes in
                       the opening of its decision [PDF] that the final
                       search occurred months after devices were seized.
                       And the search that produced the evidence used here
                       wasn’t possible until after the government had done
                       a lot of other stuff to the suspect’s phone.


                # ⚓ Vox ☛ Harassment_against_women_on_X_has_never_been_worse⠀⇛


                       In late November, a woman posted a photo of herself
                       proudly holding her PhD thesis along with the
                       announcement that she had successfully defended her
                       dissertation. “Thrilled to say I passed my viva
                       with no corrections and am officially PhDone,” she
                       wrote. What followed was a case study in how the
                       online right targets and harasses those who don’t
                       fit into the narrow — and often conflicting —
                       standards they’ve formulated for women.


                # ⚓ Digital Music News ☛ British_Band_Robbed_at_Gunpoint_During
                  Their_First_US_Tour_Stop⠀⇛


                       The group said the thief smashed the van’s
                       passenger window, and took cameras and laptops used
                       on stage, the band’s passports and documents, in
                       addition to suitcases full of clothing. “So we’re
                       going to be wearing the same things for the next
                       two weeks,” they added.


                       The silver lining was that the group’s instruments
                       were housed in a separate, locked compartment in
                       the back of the van, and weren’t taken. The band
                       remains hopeful they can play the tour as
                       scheduled.


                # ⚓ Jacobin Magazine ☛ The_Rich_Are_Hoarding_Their_Wealth_Using
                  Charity_Funds⠀⇛


                       Wall Street–backed charity funds provide
                       ultrawealthy donors with massive charitable tax
                       breaks — yet operate without any requirement to
                       ever distribute the money to working charities.


                # ⚓ The Register UK ☛ Eurocops_red_pill_the_Matrix_'secure'
                  criminal_chat_systems⠀⇛


                       Cops in the Netherlands discovered the existence of
                       Matrix while investigating the 2021 murder of crime
                       reporter Peter de Vries, who was looking into the
                       Moroccan mafia at the time. When the app's central
                       servers were found to be in France, the Dutch and
                       French plod formed a joint task force and together
                       they managed to compromise the messaging system and
                       read crooks' conversations. How that infiltration
                       was achieved has not yet been publicly explained or
                       divulged.


                # ⚓ The Register UK ☛ D.C._alleges_Amazon_is_cheating_some
                  Prime_users⠀⇛


                       The lawsuit [PDF] was filed by D.C. attorney
                       general Brian Schwalb's office today in the
                       District of Columbia Superior Court. It alleges
                       that Amazon implemented a delivery "exclusion" for
                       two east-D.C. areas, zip codes 20019 and 20020 in
                       June 2022. Instead of using its own in-house
                       delivery fleet to ensure expedited shipping, it
                       began relying on third-party delivery services like
                       UPS and the US Postal Service, resulting in slower
                       delivery times, according to the lawsuit.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Tech Central (South Africa) ☛ EFF_breathes_fire_over
                  Vodacom's_Maziv_deal⠀⇛


                       The Economic Freedom Fighters and the Democratic
                       Alliance, respectively, have lambasted and heaped
                       praise on the decision by trade, industry &
                       competition minister, the ANC’s Parks Tau, to
                       appeal the tribunal’s decision to block the deal.
                       The Competition Commission had earlier recommended
                       to the tribunal that the deal be blocked on
                       competition grounds.


                       Tau participated in the tribunal proceedings
                       related to the merger and signalled his support for
                       the transaction on public interest grounds. In his
                       notice of appeal to the competition appeal court
                       last week, Tau said he wants the deal approved.
                       Vodacom and Maziv – which is effectively controlled
                       by Remgro – are also appealing against the
                       tribunal’s decision.


                # ⚓ Alex Haydock ☛ No_NAT_November:_My_Month_Without_IPv4⠀⇛


                       I know this is quite a long and technical post, so
                       I figured it makes sense to put a conclusion about
                       my experience near the beginning.


                       So, after a month, what do I think? Do I recommend
                       that you go and disable IPv4 in your home network
                       and go IPv6-only?


                       Well no. Not quite yet.


                       But you absolutely should go IPv6-mostly. Which is
                       something we’ll get into in quite some depth as
                       this post goes on. It’s really a win-win, and I’ll
                       be deploying all my networks as IPv6-mostly from
                       now onwards.


                # ⚓ Techdirt ☛ Senator_Ernst_Wants_To_Kill_Billions_In
                  Broadband_Infrastructure_Grants_For_No_Coherent_Reason⠀⇛


                       The 2021 infrastructure bill is poised to deliver
                       $42.5 billion in broadband subsidies to the states
                       under a program called Broadband Equity, Access,
                       And Deployment (BEAD). This program has been slow
                       sledding, because America’s broadband maps were
                       absolute garbage, requiring that states work
                       overtime to fix our broadband maps and ensure the
                       money is spent semi-wisely.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ The Register UK ☛ Microsoft_confirms_zero_chance_Win11
                  supports_older_hardware⠀⇛


                       Microsoft is not backing down on the hardware
                       requirements for Windows 11, stating that the
                       Trusted Platform Module (TPM) is essential for the
                       operating system, even if it is not part of the
                       minimum requirements for Windows Server 2025.


                       Microsoft Senior Product Manager Steven Hosking
                       called TPM 2.0 "a necessity for a secure and
                       future-proof Windows 11."


                # ⚓ PC World ☛ Microsoft_doubles_down,_still_won't_let_older
                  PCs_run_Windows_11⠀⇛


                       The TPM hardware requirement for Windows 11 was one
                       of the biggest barriers to initial upgraders three
                       years ago. And while that’s become less of an
                       issue, it’s still a point of contention for many
                       users. If you were hoping for a reprieve as Windows
                       10 approaches its end of life, Microsoft just
                       dashed those hopes in a new blog post.


                # ⚓ Netflix_denies_plans_to_exit_Nigerian_market_amidst
                  rumours⠀⇛


                       Netflix has dismissed recent speculations about
                       exiting the Nigerian market, affirming its
                       commitment to serving its audience in the country.


                       In a statement to TechCabal, Netflix clarified that
                       the rumours were unfounded. The platform reiterated
                       its dedication to the Nigerian creative industry,
                       highlighting its collaborations with local
                       filmmakers and investments in original content to
                       entertain and captivate Nigerian viewers.


                       This response follows a series of social media
                       posts suggesting that Netflix might discontinue its
                       services in Nigeria due to economic challenges and
                       regulatory pressures. However, the company’s
                       statement reassures its subscribers that it remains
                       firmly committed to its operations in Nigeria.


      § Monopolies/Monopsonies⠀➾


          o § Trademarks⠀➾


                # § Right of Publicity⠀➾


                      # ⚓ 404 Media ☛ Deepfake_YouTube_Ads_of_Celebrities
                        Promise_to_Get_You_‘Rock_Hard’⠀⇛


                             Video ads of Stallone, Tyson, and Crews
                             repeating the exact same script indicate that
                             whoever wrote the ads copy/pasted it into an
                             AI voice generator.


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Is_Online_Piracy_Flattening?_New_EU
                  Study_Reveals_2023_Data_—_Including_Country-Specific_Stats
                  [Ed: Piracy? Or sharing misframed as murder?]⠀⇛


                       Amid continued streaming growth and actions
                       targeting illegal platforms, music piracy appears
                       to be flattening, according to a new report out of
                       the European Union. The European Union Intellectual
                       Property Office (EUIPO) just recently published
                       that multifaceted breakdown, which spans north of
                       100 pages and charts unapproved media consumption
                       across music, film, television, and more.


                # ⚓ Torrent Freak ☛ MP3.to_Successfully_Challenges_Music
                  Industry's_'False'_DMCA_Circumvention_Takedown⠀⇛


                       MP3.to is a nifty online tool that allows users to
                       convert MP3s to dozens of other file formats. While
                       these conversions don't knowingly violate any law,
                       Spanish music industry group Promusicae reportedly
                       labeled the service an audio download tool. In
                       response, Google removed the URL from its search
                       engine and banned the associated AdSense account.
                       However, after the MP3 site involved its lawyer,
                       Google reversed its decision.


                # ⚓ Torrent Freak ☛ Japan_Plans_AI_Pilot_Program_to_Fight_Manga
                  &_Anime_Piracy⠀⇛


                       The scale of the problem is well understood, but
                       with an estimated 1,000 sites offering culturally
                       significant manga and anime content for free,
                       monitoring for the availability of pirated content
                       online is a resource intensive task. Human
                       moderators can now “barely keep up” due to the
                       proliferation of illicit content online.


                       “Copyright holders spend a significant amount of
                       human resources trying to manually detect pirated
                       content online,” said Momii Keiko, a director at
                       the Cultural Affairs Agency’s Copyright Division.


                       To level the playing field, Japan is looking
                       towards a future where detection of illicit content
                       will be less reliant on human intervention.


                # ⚓ DNA Lounge ☛ DNA_Lounge:_3-Dec-2024_(Tue):_Wherein_we
                  negotiate_with_the_mob⠀⇛


                       Remember March 2020? Yeah, good times. As the
                       unending pandemic began, we suddenly found
                       ourselves closed for 18 months with no customers
                       and no income except donations, and we did some
                       triage. Our landlord agreed to reduce our rent, and
                       some of our vendors gave us reduced rates. The
                       PROs' answer was "LOL no". So we just stopped
                       paying them.


                       You can probably guess where this is going.




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