𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, April 16, 2025
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Generated Thu 17 Apr 02:49:25 BST 2025
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/2025/04/16/


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

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


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

⦿ Techrights  -  Confirming IBM Shutdowns and Layoffs Today

⦿ Techrights  -  Google Promotes Fake Articles (LLM Slop) Instead of Originals, Relaying Microsoft's Linux FUD Emanating From Microsoft LLMs

⦿ Techrights  -  IBM Closes Offices and Labs in the United States to Open New Ones in India

⦿ Techrights  -  In Some Countries the Largest OEMs Already Dump Microsoft Windows

⦿ Techrights  -  IRC Proceedings: Tuesday, April 15, 2025

⦿ Techrights  -  It Used to be IBM, Now It's Microsoft (Why You Need to Fire Microsofters or CIOs Working for Microsoft)

⦿ Techrights  -  Linux.com as Spamfarm of the Linux Foundation, Partner of the Gates Foundation

⦿ Techrights  -  LLM Slop Says Slop is "coming for white-collar jobs. Microsoft’s layoffs are just the start"

⦿ Techrights  -  Microsoft Down From 100% to 10% in Myanmar/Burma

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Reporting Facts About Violence Against Women Deserves Awards, Not Frivolous Lawsuits and Threats

⦿ Techrights  -  Slopwatch: The Typical Slopfarms and the 'Brian Fagioli Dilemma'

⦿ Techrights  -  StatCounter Shows the Market Share of Vista 11 is Decreasing in Ukraine This Year

⦿ Techrights  -  The "Gold" Rule: Taking Money for Reputation Laundering and Openwashing Under the "Linux" Banner

⦿ Techrights  -  Trump Authority (CA) With a Trump NSA is All About Security, But Whose?

⦿ Techrights  -  When Fedora Said It Was Looking to Integrate "AI" It Meant Promoting Microsoft's Proprietary Spyware and GPL-Violating Slop

⦿ Techrights  -  You Should Probably Self-Host Your E-mail and Never Use a Web Browser for Mail

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2025/04/16/Confirming_IBM_Shutdowns_and_Layoffs_Today.shtml
https://techrights.org/n/2025/04/16/Google_Promotes_Fake_Articles_LLM_Slop_Instead_of_Originals_Rel.shtml
https://techrights.org/n/2025/04/16/IBM_Closes_Offices_and_Labs_in_the_United_States_to_Open_New_On.shtml
https://techrights.org/n/2025/04/16/In_Some_Countries_the_Largest_OEMs_Already_Dump_Microsoft_Windo.shtml
https://techrights.org/n/2025/04/16/IRC_Proceedings_Tuesday_April_15_2025.shtml
https://techrights.org/n/2025/04/16/It_Used_to_be_IBM_Now_It_s_Microsoft_Why_You_Need_to_Fire_Micro.shtml
https://techrights.org/n/2025/04/16/Linux_com_as_Spamfarm_of_the_Linux_Foundation_Partner_of_the_Ga.shtml
https://techrights.org/n/2025/04/16/LLM_Slop_Says_Slop_is_coming_for_white_collar_jobs_Microsoft_s_.shtml
https://techrights.org/n/2025/04/16/Microsoft_Down_From_100_to_10_in_Myanmar_Burma.shtml
https://techrights.org/n/2025/04/16/Over_at_Tux_Machines.shtml
https://techrights.org/n/2025/04/16/Reporting_Facts_About_Violence_Against_Women_Deserves_Awards_No.shtml
https://techrights.org/n/2025/04/16/Slopwatch_The_Typical_Slopfarms_and_the_Brian_Fagioli_Dilemma.shtml
https://techrights.org/n/2025/04/16/StatCounter_Shows_the_Market_Share_of_Vista_11_is_Decreasing_in.shtml
https://techrights.org/n/2025/04/16/The_Gold_Rule_Taking_Money_for_Reputation_Laundering_and_Openwa.shtml
https://techrights.org/n/2025/04/16/Trump_Authority_CA_With_a_Trump_NSA_is_All_About_Security_But_W.shtml
https://techrights.org/n/2025/04/16/When_Fedora_Said_It_Was_Looking_to_Integrate_AI_It_Meant_Promot.shtml
https://techrights.org/n/2025/04/16/You_Should_Probably_Self_Host_Your_E_mail_and_Never_Use_a_Web_B.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2025/04/16/Gemini_Links_16_04_2025_IndieWeb_Carnival_Tinylog_RFC_Focus_the.shtml
https://techrights.org/n/2025/04/16/Gemini_Links_16_04_2025_The_2010s_Are_Calling_and_Why_Tools_Wil.shtml
https://techrights.org/n/2025/04/16/Links_16_04_2025_Cliff_Lynch_RIP_More_Attacks_on_Science_NASA.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 97

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/Confirming_IBM_Shutdowns_and_Layoffs_Today.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/Confirming_IBM_Shutdowns_and_Layoffs_Today.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Confirming IBM Shutdowns and Layoffs
Today⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


It's not over yet.


This_morning we wrote about credible (based on prior rumours) claims of
impending communication to staff at IBM and 10 minutes ago somebody_wrote:
"Yes. It was officially announced today for the Dallas office. Move to Austin
by the 31st of December or you will no longer have a job. Great job cutting
employees without having to offer severance, and ending people's careers here
under the guise of "collaboration.""


There's_a_lot_more_here:


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


Belated resistance. There's also this_new_message from Australia (where_there
were_rumours): "They RAed people in Ballarat and then send an email for
expressions of interest asking if people want to move there to grow the team
wtffff" (11 hours ago).


The "bloodbath" at IBM is clearly not over yet. █


    * Gemini_Links_16/04/2025:_The_2010s_Are_Calling_and_Why_"Tools_Will_Not
      Liberate_Us"
    * Trump_Authority_(CA)_With_a_Trump_NSA_is_All_About_Security,_But_Whose?


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⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣀⣽⣬⣹⣈⣉⣹⣿⣇⣀⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⣿⠿⢿⠿⠿⠿⣿⢿⡿⢿⠿⣿⢟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣁⣿⣛⣇⣒⡇⣃⣛⣛⣐⣺⣈⣿⡸⣐⣇⣜⣀⣹⣘⣇⣧⣓⣘⣂⣻⣐⣃⣻⣘⣘⣇⣿⣘⣘⡅⣣⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣛⣛⣛⣛⣛⡓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠿⢿⡿⠿⣿⣿⣿⠿⣿⣿⡿⡿⣿⣿⣿⡿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⠿⣿⢿⢿⡿⣿⣿⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡉⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣭⣧⣿⣭⣥⣥⣼⣶⣤⣼⣤⣤⣶⣤⣤⣬⣥⣯⣯⣽⣧⣵⣭⣥⣤⣽⣴⣤⣼⣾⣯⣤⣯⣤⣧⣧⣭⣼⣮⣯⣬⣵⣥⣥⣭⣭⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣶⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣽⣤⣭⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡿⡿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣮⣼⣶⣴⣶⣿⣤⣤⣴⣶⣶⣤⣧⣴⣾⣠⣧⣌⣤⣤⣬⣷⣶⣷⣴⣤⣼⣯⣆⣠⣤⣬⣧⣤⣼⣤⣼⣿⣤⣴⣶⣿⣦⣤⣴⣥⣼⣤⣤⣤⣤⣤⣤⣴⣶⣴⣼⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣉⣿⣉⣅⣩⣩⣽⣯⣉⣩⣱⣍⡙⣏⣯⣉⣸⣉⡩⡩⣉⣭⣅⣉⣁⣇⣦⣚⣱⣹⣏⣝⣉⣈⣵⣍⠩⡏⣩⣋⣈⣹⣿⣏⣩⣌⣉⣝⣏⣁⣉⢍⣉⣩⡉⣽⣩⣯⣋⣈⡈⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠛⣛⢛⢟⢛⡛⡏⠛⠛⢛⠛⡛⠙⠛⠻⣏⢻⡛⡟⡟⣟⢛⠛⡛⠛⡟⠟⠛⠛⡟⢛⡛⠙⡟⣛⠛⠛⠛⢹⠛⡛⣉⠙⢻⣛⢿⠛⡛⣛⣛⠛⢛⡻⡟⠉⢛⡛⠛⢻⡛⣻⣟⡛⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⢿⢿⠿⠿⡿⡿⠿⠿⠿⠿⠿⠿⢿⠿⢿⡿⠟⠿⠿⢿⠟⠿⠿⡿⠿⠿⢿⠿⠿⡿⠿⢿⡿⠿⢿⠿⡿⠿⡿⡿⠿⢿⢿⠿⠿⠿⠿⡿⡾⠿⠿⠟⡿⢿⡿⡿⠿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡷⣷⣷⣿⢿⣾⣷⣶⢾⣶⣷⣶⣿⣷⣾⣵⣷⣷⣾⢾⣿⣶⣶⣶⣷⣶⣿⣿⣶⣿⣾⡾⡾⣶⣾⣿⣿⣾⣾⣿⢾⣿⣯⠼⣾⣶⣶⣶⣾⣾⣿⣾⣷⣿⣷⣿⣾⣾⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣦⣤⣶⣧⣤⣤⣦⣦⣖⣼⣤⣤⣠⣤⣶⣾⣦⣧⣾⣤⣴⣾⣿⣾⣮⣮⣮⣜⣧⣥⣾⣦⣤⣤⣬⣾⣜⣧⣴⣤⣼⣬⣴⣤⣭⣦⣶⣶⣧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣡⣆⣹⣊⣈⣈⣀⣎⣁⣇⣑⣇⣀⣀⣄⣏⣸⣈⣈⣀⣏⣀⣧⣒⣁⣿⣂⣑⣉⣘⣧⣬⣁⣇⣀⣀⣅⣲⣠⣸⣖⣂⣁⣁⣐⣁⣲⣘⣊⣲⣙⣧⣬⣁⣗⣀⣁⣅⣲⣩⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢽⡝⠉⡏⠫⠩⡫⢩⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠯⠟⠟⠻⠻⠛⠙⠛⢻⠙⡿⠛⢻⢿⠋⠛⠛⠟⢿⠟⠻⠟⠛⡟⠛⠻⠿⠛⢻⣿⠟⠟⢻⠟⠟⠿⠿⠛⠛⡛⣟⣛⡿⢯⢻⠛⠛⠛⠟⢿⠛⠛⠛⠿⡋⠛⠛⡿⠙⠛⢹⣛⡛⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠟⠿⢿⠿⠿⠿⠿⡷⡾⠿⠻⠿⡟⠿⠿⠿⡿⠿⢷⢾⠿⠿⠶⠻⠷⢾⠿⡿⢿⠿⠿⠿⢿⠻⠿⠿⢾⡿⡿⠾⢿⡟⠿⡟⠿⠿⠿⡿⠿⢿⠿⢿⢿⠿⠿⠿⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣶⣶⣾⣵⣶⣶⣵⣶⣿⣶⢶⣶⣷⣶⣶⣼⣿⣾⣾⣾⣶⣶⡤⡶⣶⠾⠿⣿⣷⣷⣾⡦⣿⣾⣶⣾⣾⣶⣷⡶⣵⣷⢶⣷⣶⣶⣾⣷⣶⣾⣶⣷⣾⣶⢷⣶⣷⣶⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣤⣤⣶⣤⣴⣴⣧⣤⣤⣤⣌⣧⣶⣥⣿⣤⣄⣄⣤⣤⣦⣤⣤⣿⣥⣦⣤⣾⣤⣯⣶⣤⣤⣤⣹⣤⣶⣇⣠⣤⣤⣧⣤⣤⣇⣤⣤⣴⣴⣾⣤⣼⣤⣤⣧⣤⣤⣴⣥⣤⣲⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣍⣩⡍⢉⣿⣽⣥⣭⣽⣉⣭⣏⣍⣏⣉⣡⣋⣹⣉⣹⣍⣉⣉⣈⣇⣉⣮⡏⣉⡉⣽⢍⣁⣹⣉⣉⣉⣉⣭⡉⣽⣉⣉⣉⣉⣉⡽⢩⣍⣉⣫⣩⣹⣉⢍⢉⣉⣭⣙⣭⣁⣀⣉⣙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢛⡻⢻⠟⡟⠛⠛⢛⣻⠛⠛⢛⠛⣻⡛⢫⠫⠛⡟⢛⠛⡋⢻⠛⡛⢟⢛⠛⠛⠛⠛⢛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡻⡟⣟⠛⡟⣟⡛⡛⠛⠛⠋⡟⠛⠛⠛⠛⡛⠛⣿⢻⢛⠙⢛⢻⠛⢛⡛⣛⢛⠛⡿⢛⣛⠙⠛⢻⠛⡛⡋⢻⢻⡻⣻⡟⠛⢙⡛⡟⠛⢛⡏⠛⡛⡛⡛⠛⠛⠛⢻⠛⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⠿⠿⡿⣿⢿⢿⡿⡿⠿⢿⠿⠿⡿⠿⠿⡿⡿⠿⢿⡿⡿⠿⡿⣿⡿⡿⢿⢿⢿⢿⠿⡿⡿⠿⡿⡿⡿⢿⠿⠿⢿⢿⡿⢿⠿⡿⣿⣿⡿⠿⢿⡿⡷⠾⢿⢿⢿⢷⠾⠿⠿⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣽⣧⣤⣭⣥⣤⣬⣧⣤⣤⣼⣤⣧⣷⣭⣭⣧⣿⣶⣤⣧⣦⣼⣯⣯⣥⣵⣾⣽⣽⣥⣬⣮⣦⣼⣯⣬⣯⣥⣼⣯⣥⣼⣥⣤⣥⣤⣾⣭⣤⣼⣴⣯⣮⣮⣥⣼⣾⣵⣴⣴⣭⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣊⣰⣍⣸⣂⣈⣸⣐⣪⣊⣡⣐⣆⣁⣐⣑⣲⣻⣀⣀⣀⣇⣖⣘⣆⣷⣂⣉⣒⣊⢸⣰⣂⡁⣁⣷⣒⣽⣊⣂⣀⣅⣑⣸⣁⣐⣰⣗⣃⣂⣀⣆⣁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣒⡏⣝⣝⣏⣍⣟⣋⣚⣙⣍⣉⣞⣉⣛⣛⣽⣊⣉⣉⣉⣛⡏⢹⣉⣉⣋⣍⣿⣋⣽⠁⣉⣃⣛⡉⢹⣈⣩⣍⣙⣉⣉⡘⣏⣉⢉⡪⣹⣁⣈⣉⣙⣐⢭⣇⣙⣇⣛⣋⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠟⠛⠛⠛⠻⠟⢻⠛⢛⡿⠛⠛⠟⠛⠛⠹⡏⠟⠋⡝⡟⠛⠛⠙⢻⡿⡻⢟⣟⡛⠟⠟⠛⢻⠙⠛⠻⡛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠉⢭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢸⣿⣿⣯⣉⣏⣫⣩⣉⣉⣁⣏⣩⣩⣭⣿⣏⡏⣿⣉⣝⣅⣍⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠭⡏⢹⠭⠯⡩⣏⠽⠉⣟⠍⠉⠫⡋⢿⢉⡭⠋⡯⠯⠏⡫⠋⡏⠯⠫⢹⢹⣝⡉⢝⠍⡋⡏⢝⢹⠉⠉⠉⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣯⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠛⢯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢸⣿⣗⣎⣝⣋⡙⣹⣉⣁⣉⣁⣉⣈⣙⣉⣁⣛⣛⣛⣙⣈⣉⣉⢉⣈⡉⢹⣁⣉⣉⣏⣹⣋⣙⣟⣳⣊⣊⣛⣫⣈⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠥⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣫⡏⢍⣉⣩⣏⣉⣉⣯⣉⣩⣉⣨⣹⣁⣍⣽⣍⣄⣹⣝⣭⣍⣉⠉⣏⣍⣯⣻⣹⣥⣯⣩⣽⣍⣍⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠭⠍⠭⠋⠽⢉⣝⣉⣉⣉⣭⣉⠉⠉⡋⠩⡫⡩⠉⢙⠏⠉⠉⠩⠍⠹⠉⢭⠻⣫⠝⢩⣋⢙⢫⢝⠉⠉⠹⢙⠹⡭⠩⣛⠉⢝⢙⡋⢫⠉⠉⢙⡫⣭⣋⠭⡩⠭⠭⢝⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡛⣟⡛⣛⠻⡿⢟⣻⣛⠻⣻⡻⡟⠻⠻⢟⢛⠟⠛⠛⢛⡻⢟⠟⠛⠛⣛⡻⡛⠛⣻⠻⢿⣓⠛⠿⠛⠻⠟⢟⣛⣻⣛⠟⢛⠻⠟⣛⠛⠛⠛⠛⠿⢟⢛⣛⠻⣛⣛⣛⣛⡻⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠶⡾⣶⠶⠾⢷⠶⠶⣷⠶⢶⠾⢶⡾⠾⢷⡶⠷⢶⡶⠷⢾⡷⠷⠶⡾⢾⠾⣶⡶⣾⣾⣿⣶⣶⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣾⣷⣾⣶⣶⣶⣶⣿⣷⣷⣷⣾⣾⣶⣷⣶⣷⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣥⣥⣷⣬⣼⣴⣤⣤⣶⣯⣭⣬⣵⣤⣼⣴⣦⣤⣵⣦⣴⣴⣦⣦⣭⣦⣶⣦⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣤⣥⣼⣤⣤⣬⣤⣤⣼⣤⣤⣯⣭⣯⣼⣨⣥⣮⣮⣬⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣷⣶⣾⣷⣿⣶⢶⣾⣾⣾⣶⣶⣿⣾⣶⣶⣿⡷⣾⣾⣶⣷⣷⣶⣶⢷⣷⣾⣷⣶⣷⣾⣾⠷⣿⣼⣶⣶⣷⣿⣿⣶⣿⣾⣾⣿⣾⣷⣶⣶⣶⣷⣿⣿⣾⣿⣿⣿⣿⣿⣯⣷⣶⣯⣿⣿⣿
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⣿⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 236

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/Google_Promotes_Fake_Articles_LLM_Slop_Instead_of_Originals_Rel.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/Google_Promotes_Fake_Articles_LLM_Slop_Instead_of_Originals_Rel.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Google Promotes Fake Articles (LLM Slop)
Instead of Originals, Relaying Microsoft's Linux FUD Emanating From Microsoft
LLMs⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


Microsoft "open" "hey hi" interjecting its_bias into the Web (and into Google
News)


There is strong, still-growing, overwhelming consensus that LLMs are bad and
they (or their output) need to be avoided. Cementing this consensus is
critical.


This_morning_in_Slopwatch we mentioned Google News promoting LLM slop, taking
particular note (evidence also) of the sister slopfarm of gbhackers.com. It has
just spewed out this FUD from a known slopfarm. Can nobody in the "Google
empire" figure out this site is a slopfarm? After laying off many people who
worked Google News one wonders if Google lets "hey hi" manage this whole
operation (i.e. automation but no_intelligence).


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


Fake 'article'. Same as this one (piggybacking the original [1]) which was
spewed out a short while ago:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tails_6.14.2_Released_with_Critical_Fixes_for_Linux_Kernel
                               Vulnerabilities⦈_


The image is slop, the text is slop, everything is slop. Shame on Google for
participating in the slopfest. As Baldur Bjarnason put it this week [2,3]: "We
have monopolies or oligopolies who control much of the software market and, of
particular concern to the web sector, they control how people discover
websites."


They even promote slopfarms and shoddy LLM spew (named "Gemini", nothing_to_do
with_Gemini_Protocol). That's in their own financial interest. █


______


§ (Debian-based) Tails Site and More (Baldur Bjarnason)⠀➾


   1. ⚓ New_Release:_Tails_6.14.2⠀⇛


           This release is an emergency release to fix security
           vulnerabilities in the Linux kernel and the implementation of
           the Perl programming language.


           For more details, read our changelog.


   2. ⚓ We're_in_for_a_rough_ride_as_an_industry⠀⇛


           There’s the not so small issue of the tech industry being quite
           invested in turning the US into an authoritarian dictatorship
           and seemingly succeeding. But even if you assume that the US
           will come out of this in four years’ time as a recovering
           democracy (an extremely unsafe assumption, I think), the web is
           likely to suffer as an industry either way.


           We have monopolies or oligopolies who control much of the
           software market and, of particular concern to the web sector,
           they control how people discover websites.


   3. ⚓ An_aside_on_proposed_anti-trust_remedies_against_Google⠀⇛


           The Democrats love to build or reinforce the mechanisms of
           authoritarianism, which they mistakenly think they can apply
           for good and moral purposes, but then become major building
           blocks for an authoritarian state.


           If the dominance of Chrome is a problem, then that won’t be
           solved by shifting it over to an equally large competitor. That
           solution only makes sense if your goal is to maintain the
           current oligopoly dynamic and that the biggest threat from
           Google isn’t their threat to the free market – none of these
           people seem to care about the actual economy – but Google’s
           size making them harder to control. They want to make Google
           more controllable, which is already problematic for a
           democracy, but a controllable Google is an outright gift to the
           rising fascists.


    * In_Some_Countries_the_Largest_OEMs_Already_Dump_Microsoft_Windows
    * StatCounter_Shows_the_Market_Share_of_Vista_11_is_Decreasing_in_Ukraine
      This_Year


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⡭⠭⠍⠭⠩⠭⡍⣿⠉⠭⠭⠩⠭⠭⠩⡍⠭⠭⠍⣿⠉⠩⠩⢹⡏⠭⠭⠍⠭⠉⡏⠭⠭⠭⠭⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠚⠒⠒⠚⠛⠓⠒⠒⠒⠓⠚⠒⠛⠚⠛⠚⠛⠛⠓⠚⠚⠒⠛⠚⠒⠓⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡛⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⣶⣤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⠿⠀⠀⠀⢉⣘⡋⠀⠀⠵⠞⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣵⣿⣿⣷⣿⣭⣼⣴⣧⣿⣿⣿⣯⣭⣼⣼⣵⣧⣭⣮⣿⣿⣿⣮⣥⣽⣭⣼⣮⣵⣽⣿⣿⣯⣿⣽⣯⣮⣭⣷⣽⣵⣯⣿⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣯⣿⣿⣯⣽⣽⣯⣯⣽⣭⣭⣽⣽⣿⣯⣯⣯⣯⣽⣿⣭⣭⣽⣿⣭⣽⣽⣭⣭⣿⣿⣽⣽⣽⣿⣭⣿⣯⣿⣽⣭⣽⣽⣽⣯⣽⣽⣯⣭⣽⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡻⠿⠯⡟⡿⢿⡟⠛⣿⡛⡿⠛⣿⣛⢻⡟⡛⡿⠿⠛⠿⢿⠿⢿⠿⡿⠿⡿⠟⣿⠿⠿⡯⠟⠟⠿⣿⢟⡛⡿⠯⡟⠯⡿⠿⡿⠿⡟⣿⢛⡯⡿⢿⠿⢿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣥⣤⣧⣧⣼⣧⣥⣯⣧⣧⣤⣯⣥⣼⣧⣦⣧⣤⣤⣤⣼⣬⣼⣤⣧⣤⣦⣥⣿⣤⣤⣧⣧⣧⣧⣿⣬⣭⣧⣧⣧⣥⣧⣭⣦⣥⣧⣿⣴⣧⣧⣼⣤⣬⣤⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢛⢻⢛⡏⣿⢺⢛⢻⢻⢻⠛⣿⠉⢩⠟⠛⢛⡟⡛⠟⠛⢹⣏⠻⡙⢻⠋⠙⡛⠟⠛⡟⡛⡛⠋⣛⠓⡏⡗⡋⡗⠟⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣾⣷⣶⣾⣾⣾⣶⣾⣶⣾⣶⣶⣷⣾⣾⣷⣷⣷⣶⣾⣿⣶⣿⣶⣶⣶⣷⣶⣶⣷⣷⣶⣶⣶⣶⣷⣷⣷⣷⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⢛⢛⣛⣛⣛⣛⣛⢻⠛⢛⣛⡛⣛⣛⣛⣛⢛⣛⣛⢻⠛⡛⡛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠥⠿⠯⠭⠬⠿⠿⠽⠽⠬⠭⠿⠥⠿⠿⠿⠽⠿⠿⠭⠽⠿⠿⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 409

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM Closes Offices and Labs in the United
States to Open New Ones in India⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


It's not layoffs per_se; they're substituting/swapping veteran employees for
lesser-paid ones


IBM had a "bloodbath" some weeks ago. Many thousands got fired. In a few hours
we'll likely hear more.


"New IBM Software Lab in Lucknow," an anonymous_poster_said_4_hours_ago. "A
brand new site being opened in India. Following a zero-sum rule, likely means a
location(s) somewhere else will be closing. . ."


The cited Microsoft LinkedIn post (yes, this is how IBM communicates) is shown
below:


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


That was a day ago.


Another thread was started 3 hours ago to speak_of_"Multiple_Office_Closures
8AM_4/16". To quote: "Announcement coming tomorrow for multiple offices to
close and relocate to Austin, TX by end of year. Plan has been in place for
several months but will be communicated tomorrow AM. Good luck!"


That's later today.


We mentioned this 2_days_ago and last_month (that site). █


    * Over_at_Tux_Machines...
    * It_Used_to_be_IBM,_Now_It's_Microsoft_(Why_You_Need_to_Fire_Microsofters
      or_CIOs_Working_for_Microsoft)


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⣿⣿⠿⠛⢿⡿⠿⠿⡿⠿⣿⠿⠿⠿⠿⡿⠿⠟⠿⡿⢿⠿⡿⡿⡿⠿⠿⢿⡿⠿⠿⠿⠟⠻⠿⠿⣿⠟⠿⡿⠻⠿⣿⢿⠿⢿⡿⡿⠿⢿⠿⠟⠿⡿⠟⠿⡿⠿⢿⠟⠿⠿⡟⡻⠟⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣾⣾⣾⣿⣶⣶⣷⣷⣿⣾⣶⣷⣿⣾⣾⣷⣾⣾⣾⣷⣶⣿⣧⣶⣶⣿⣷⣶⣮⣴⣶⣾⣶⣷⣾⣶⣾⣷⣷⣶⣷⣶⣷⣾⣶⣿⣾⣷⣷⣷⣼⣿⣶⣾⣿⣦⣽⣿⣷⣾⣿⣶⣶⣿⣶⣶⣶⣷⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣒⣇⣍⣁⣽⣊⢁⣅⣵⣙⣻⣐⣍⣉⣄⣪⣉⣁⣇⣈⣏⣌⣻⣊⣺⣮⣉⣁⣻⣊⣡⣇⣸⣎⠈⣈⣮⣨⣈⣽⣘⣿⣼⣍⣪⣂⣛⣑⣸⣧⣁⣉⣱⣃⡗⢉⣈⣆⣻⣇⣉⣈⣺⣯⣉⣑⣯⣁⣸⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣩⢙⠟⢟⡛⣟⡛⡛⢻⣯⣟⠛⣻⡛⣻⡟⠟⠟⢻⡛⢛⡟⣟⢻⢛⡛⡟⠛⢛⡏⢛⡛⣛⠛⢛⠻⡉⢙⢟⠛⡟⡛⡻⠙⠉⠋⠻⠙⢫⠛⠙⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣶⣾⣷⣷⣿⣿⣾⣿⣾⣿⣿⣾⣾⣾⣾⣷⣷⣷⣾⣾⣶⣷⣿⣾⣾⣾⣷⣶⣶⣷⣾⣶⣶⣷⣷⣷⣷⣶⣿⣷⣾⣾⣶⣿⣶⣷⣷⣷⣶⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣟⣈⢸⢊⠘⣹⠱⠉⣯⠉⡉⣫⠉⡏⢩⠿⠏⡩⠈⢩⡯⣉⡉⢙⢝⠈⠉⡏⢩⡏⠁⣯⠃⠱⡇⠃⣏⢉⣶⠉⠩⠈⢿⢝⠈⠍⢸⡍⡩⣟⠉⡏⣹⢿⡅⡉⢾⠉⠹⡹⡋⠅⠍⣽⢍⢋⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 510

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/In_Some_Countries_the_Largest_OEMs_Already_Dump_Microsoft_Windo.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/In_Some_Countries_the_Largest_OEMs_Already_Dump_Microsoft_Windo.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ In Some Countries the Largest OEMs Already
Dump Microsoft Windows⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇being_penguin⦈_


Last month there were media reports about Huawei dropping Windows and this week
we see_reports_about_GNU/Linux_laptops_from_Huawei (cheaper than Windows), as
expected. There's probably more on that to come (in English, not Mandarin).
Judging by statCounter, in Asia Android is now 3+ times bigger than Windows
(among Web users).


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


Windows at 18.9%, Android 60.2%. Microsoft_has_a_ton_of_layoffs_in_China_this
year and Microsoft_Copilot_is_measured_at_a_negligible_0.1%_there because
Chinese users aren't dumb enough to broadcast things to Microsoft.


Expect an eventful year for Windows. The Linux_Foundation won't talk about
Vista 10 becoming "dead"; it won't promote GNU/Linux. But we can. █


    * The_"Gold"_Rule:_Taking_Money_for_Reputation_Laundering_and_Openwashing
      Under_the_"Linux"_Banner
    * Google_Promotes_Fake_Articles_(LLM_Slop)_Instead_of_Originals,_Relaying
      Microsoft's_Linux_FUD_Emanating_From_Microsoft_LLMs


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

                    ䷩ 𝚕𝚒𝚗𝚎 639

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Tuesday, April 15,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Vintage_Easter_card_of_a_cute_little_girl_with_chicks,_large
Easter_egg_and_spring_flowers_background,_in_frame⦈_


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now


    * Gemini_Links_16/04/2025:_IndieWeb_Carnival,_Tinylog_RFC,_"Focus,_the_Web
      and_Gemini"
    * Over_at_Tux_Machines...


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⢀⡀⠀⠀⠀⢤⣄⣀⣄⢄⡀⠀⢀⣄⣤⣤⣄⡄⣠⢤⢤⣤⣤⣤⡤⣠⢤⣤⣤⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⢠⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢖⣶⠕⡀⢀⣶⡿⢾⣯⡮⢏⢗⢇⣟⢏⡏⡟⠾⣾⢾⣃⣟⡝⣿⡽⣫⣻⡽⣋⣼⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⡄⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠤⠨⢿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡉⠇⠼⣼⠈⠤⠓⠒⠎⠒⡸⠀⡔⡸⠱⣿⣭⣭⣷⣶⣲⣷⣷⣷⣶⣷⣿⣿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠨⠾⣿⣄⠀⢿⣿⠿⠿⠟⠿⠿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠐⠀⡀⠬⠀⣀⠀⢀⠀⡆⠄⡁⡷⠁⠁⠀⠀⠀⠈⠈⢨⣄⣳⢬⣿⣿⣿⣿⣿⣿⢻⣿⣏⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣲⣶⣿⣿⣿⣿⣿⣿⣌⠛⠿⠀⠀⠀⠀⠀⠀⠀⠠⠠⠡⠄⢀⠀⠀⠂⠀⠂⠀⠀⠀⣀⢶⣀⣀⠀⠀⠙⢊⡭⠝⣿⣿⣿⣻⡻⣿⣿⣿⣿⡿⣿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠸⠇⠟⠄⠀⠁⠀⠀⠽⢉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⢀⠀⠀⠀⠀⢰⣿⣶⣯⠍⠀⠄⠀⢐⠉⠀⡘⠞⣼⣿⣿⣷⣿⠣⠶⣷⣷⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠴⠖⠂⠀⠀⡀⠈⠘⠋⠉⣉⠻⣿⠉⡿⢿⣿⣿⣌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢐⡂⣡⡇⠰⣆⡰⣶⣙⣾⡉⠀⠀⠀⠀⠙⠻⣿⢬⠴⣿⣿⣽⣿⣿⣏⢽⣿⣿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠤⡑⠀⠑⡄⠀⠀⠀⠈⣁⠀⠘⣻⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣥⡀⠉⠀⢸⡿⣿⡿⢷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⠋⠋⠫⠉⠿⠈⠉⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡈⠉⠤⠐⠛⠤⠀⠐⠬⣽⡗⠴⣿⠿⢁⣀⠀⠀⢀⣤⡶⢶⠄⠀⠀⠀⠀⠰⡏⣿⠿⠛⠛⠈⠁⣶⣿⣿⣿⠃⠈⡿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠄⢠⠄⠙⠁⠀⠈⠀⣰⣿⡷⠀⠘⣿⣷⣿⣶⡀⠀⠀⠀⠀⠑⠒⠀⠀⢠⡀⠀⠘⡟⡟⣿⠁⠀⡰⢞⣭⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠀⠀⠊⠀⠀⠀⡅⠀⣾⣿⣿⣷⣤⣀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠰⠃⠀⠘⠂⠀⠈⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠆⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⣦⠀⠀⠀⠀⠘⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠈⠁⠀⠀⠀⢻⣿⣿⣿⡿⠃⠉⠉⠁⠀⠀⠀⠀⣠⣾⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⠛⢰⠀⠀⣠⠄⠀⠀⠀⢀⠤⣴⡢⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⣭⡁⠄⠀⠀⠀⠀⠀⢠⣾⣛⠶⠁⠘⣿⣿⣻⢿⣿⣟⠛⠉⣠⣼⣿⣶⡀⠀⠀⠠⣾⣿⣤⣿⠗⠀⣠⣶⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡾⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢤⣄⣀⣈⣉⢓⢀⠈⠀⠀⠈⠁⠃⢃⡘⢧⠐⢻⣿⠭⠻⢿⣥⣿⣿⣿⣿⠛⠃⠀⠀⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣾⣿⢿⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠀⠁⠁⠀⢫⡀⢁⡇⠉⢉⡄⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣦⣼⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⠘⢐⣿⣿⣿⡿⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠄⠀⢀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠿⠟⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣤⢤⢀⡀⣄⣔⣀⠀⡀⠉⠛⠿⠒⢖⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⣆⠀⠈⠶⢮⣟⡀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣄⡄⠀⠀⢀⣤⣤⣤⣤⣦⣤⣤⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣦⣨⣀⡀⠀⠀⠐⣛⣠⣀⣀⣼⣽⣧⣤⣭⣆⡀⣀⣀⣤⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠠⠁⠤⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠯⠝⠭⠀⠀⠴⠬⠗⠹⠿⠿⠿⠿⠶⠿⠿⠶⠶⠾⠿⠿⠶⠟⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 869

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ It Used to be IBM, Now It's Microsoft (Why
You Need to Fire Microsofters or CIOs Working for
Microsoft)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


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


"Start by firing the CIO." (Or "Start med at fyre CIO'en" as Version2 put is in
Danish)


It's a new article.


There's an automated_translation. The original says: "Det er svært at
overbevise folk når deres løn afhænger af at de ikke forstår og der er rigtig
mange jakkesæt i den danske IT branchen, som har haft hovedet så langt oppe i
røven på Microsoft hele deres professionelle karriere, at de ikke engang har
det nødvendige ordforråd til at deltage i debatten."


In English (poor translation): "It's hard to convince people when their salary
depends on them not understanding, and there are a lot of suits in the Danish
IT industry who have had their heads so far up Microsoft's asses their entire
professional career that they don't even have the necessary vocabulary to
participate in the debate."


Further down it says: "PS: Jeg er også træt af, at journalister ikke spørger de
samme nej-sigere hvor mange Microsoft aktier de personligt ejer."


In English: "PS: I'm also tired of journalists not asking the same naysayers
how many Microsoft shares they personally own."


This sounds like a recurring theme. A lot of companies work for Microsoft and
compel staff to do the same, even if the salaries are not paid by Microsoft.
There's this "cult mentality" driving the decision-making.


The above article mentions the "old" IBM before discussing what Microsoft
nowadays does to organisations, led by Microsofters who are disloyal to the
company/organisation paying the salary (they instead work for Microsoft and
Microsoft's interests).


We're currently suing someone who did this inside Linux [1, 2]. He's still
trying to shoehorn TPM into everything (to no avail) and advocating Microsoft's
back-doored encryption [1, 2].


It's all about taking control away from computer users.


Microsofters are a "disease" (to paraphrase Linus Torvalds on an unrelated
matter). Microsofters always serve Microsoft.


"A large and growing number of institutions lease their desktops and laptops
instead of buying and maintaining them," an associate explains. "That allows
the administration to fire staff and replace them with always-politically-loyal
consultants depending on the contracts. A side effect is total loss of control
over the software, both applications and the operating system and related
infrastructure."


"That loss of control is exploited by the Microsofters to push Vista 11 and TPM
2 onto the masses. Where do the four freedoms fit in if an institution has
neither their own staff nor their own hardware? [And] maybe that is related to
the freedom to not have to run a program" (c.f. systemd).


Nowadays systemd is pushing both restricted boot and TPM. systemd is also run
by Microsoft staff, so there are overlaps.


systemd became a "Trojan horse" of Microsofters.


Typically the only effective solution is to identity and remove Microsofters
from one's project/organisation (before they can bring more Microsofters in).
They work for interests which are external and hostile. █


    * IBM_Closes_Offices_and_Labs_in_the_United_States_to_Open_New_Ones_in
      India
    * Slopwatch:_The_Typical_Slopfarms_and_the_'Brian_Fagioli_Dilemma'


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                    ䷩ 𝚕𝚒𝚗𝚎 1013

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

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    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/Linux_com_as_Spamfarm_of_the_Linux_Foundation_Partner_of_the_Ga.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux.com as Spamfarm of the Linux
Foundation, Partner of the Gates Foundation⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025,
updated Apr 16, 2025


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Openwashing_Jim_Zemlin_on_taking_a_‘portfolio_approach’_to
                          Linux_Foundation_projects⦈_


THE Linux_Foundation fired all the staff (including editors) of Linux.com. They
didn't "cost" much*. But they promoted GNU/Linux and that's a "no-no"; managers
of the Linux Foundation don't use GNU/Linux and don't care for it; the "Linux
Foundation" is about exploiting the brand, e.g. selling "Linux" as a badge of
openwashing. It's_also_about_enabling_enemies_of_Linux_exercise_control_over
it. Remember that board seats are literally up for sale (it's openly advertised
as such) and Microsoft_bought_more_board_seats_than_any_company_is_allowed_to,
based_on_the_Linux_Foundation's_own_rules. This abject violation of rules has
gone on for several years already. Who enforces the rules? The corporations
enforce_a_CoC, but nothing else. It hardly surprised us when the Gates
Foundation also "bought some shares". It's all about control. It's relatively
cheap (to someone like Gates). If_you_contribute_to_Linux_and_have_a_Russian
passport,_then_go_away; if you attack Linux and say_you're_on_a_"Jihad"_against
it, welcome!


We didn't forget all the good writers who had been sacked without prior
warning. It_happened_more_than_6_years_ago. What has Linux.com become since?
This:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux.com:_Project_Tazama,_A_Project_Hosted_by_LF_Charities
                                With_Support⦈_


They no longer publish articles. 2 days ago they published this:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇30%_Sitewide_Savings_(Includes_THRIVE_Annual_Subscription)_+
                  Bonus_Savings_on_IT_Professional_Programs⦈_


It links to a_Clownflared_site (because nothing_says_"Linux"_like_outsourcing
to_proprietary_spyware) that sells many "Cloud" bundles. It's basically a sea
of buzzwords, e.g.:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Exclusions:_The_following_content_is_not_available_through
THRIVE-ONE:_Certifications,_instructor-led_courses;_and_FINOPS_courses,_bundles
                                 and_certs.⦈_


Linux is never mentioned.


                   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Learn._Grow._Thrive.⦈_


The other day there was a_ridiculous_puff_piece_by/for_Jim_Zemlin, the proud
"boss"_of_"Linus"_(or_"Linux") (and he proudly insists that his wife, Sheela
Microsoft, controls him). To quote directly**:


     “At the Linux Foundation, we have specialists who work in vertical
     industry efforts, but they’re not lawyers or copyright experts or
     patent experts. They’re also not experts in running large-scale
     events, or in developer training,” Zemlin said.


Right. They're marketing people like Jim Zemlin. They run the show. Some_of
them_get_their_salaries_from_Microsoft. █


_____


* Running Linux.com with about a_dozen casual contributors would only cost
about 0.1% of the total budget of the "Linux Foundation" (two_years_ago_it
spent_185_million_dollars_in_one_year). But everyone got the boot and
replacements (sometimes former Microsoft) too got_discarded. It's almost as if
the goal was to just kill the site, period. If that was the goal, then it
succeeded.


** There's a lot of nonsense in this piece. “Computing is entering a world
dominated by two platforms: Linux and Windows,” Zemlin is quoted as saying.


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


Right. Tell that to Apple, Google etc.


Ryan responded to this assertion by stating: "More like exiting the world
dominated by Windows. It's a remaining value product that is hardly even tended
to. Farmed out to India and on life support, working less and less each time
they send out updates, that shuffle around what's broken. Assuming you don't
get hit with one where the computer won't even start that time. Even in the
Windows XP era, Windows at least wasn't anywhere near as temperamental as it is
now. When you're in the C-Suite, you apparently see things like in-house
testers as expendable, so the product can push updates that don't even barely
work. Almost everyone I know that uses Windows has had to become proficient at
spending all their time backing up files, planning that it could go out at any
minute. Then hours restoring from the backup image every so often. Truly modern
computing doesn't work like this, where the OS is so rotten and horrible that
you have to plan on it failing outright at least once a year. We left that era
a while ago, in Free Software and otherwise (Chrome OS and Mac OS). People want
one thing from Windows and that's for the version their particular workload
depends on to stay running. I know an optometrist that still has Windows XP on
an air-gapped computer. He says the vendor refuses to fix the software so it
works on a supported release of Windows, because they can hold it over his head
as a reason to buy a new $40,000 machine. Meanwhile, supported versions of
Windows have definitely changed enough so that they can't run that program.
Why? Microsoft paid to throw a lot of trash on top of a system that was
basically working in the past 20 years. Why would you pay thousands of people
to deface something that basically worked and may need a few updates here and
there? I figure if they just kept developing something that was basically
Windows XP, people would still go along with it. You know, does process
scheduling and memory management have to be better than XP? Yes, does sound and
graphics APIs? Sure. But like over 90% of what they've done since XP is just
trash. And it's causing the platform to age badly and in ways they can't even
hide anymore. I would literally rather deal with a mid 90s system with one of
the OEM releases of Windows 95 than what they've created now. We've moved out
of the Windows world. You go to Walmart even, they have more Chromebooks and
even a Macbook. Over 50% of the laptops there are not running Windows. So if
they're being almost forced out of the market even at the "cheapo bargain
basement shit" level, what does that say? When not even Walmart customers will
tolerate it, increasingly. Walmart has never been beholden to Microsoft.
They'll sell whatever they can make good margins on and that people want. If
the market for consumer products wasn't shifting to Chrome OS and Mac OS, then
it would still be a bunch of poorly designed clunky PC laptops with bad
firmware, Windows, and two dozen pieces of bloatware to try to recoup some of
the licensing fees. I just don't see Microsoft ever recovering in the consumer
market. They're treading water and trying not to go under on the low end of the
market now. It's sort of like how empires die, you know, like the British, or
the US one. First you control or influence 80% of the world. Then there are
some setbacks. But people still fear or respect you. For a time. Then next
thing you know, you have an island and you're still finding new ways to lose.
When you have a brexit and then you have a close call with Scotland, you know.
And then they want another go at it. If you look at Microsoft in the last 15
years, it was clear even in the [Steve] Ballmer era that they knew they had to
be something else, they just couldn't figure out what."


Notice how Zemlin and the "Linux" Foundation never promote GNU/Linux for the
desktop (or laptop) and never say something like, replace Windows with GNU/
Linux, Vista 10 support is soon over, so move to GNU/Linux. It's just so easy
to feel like the "Linux" Foundation is controlled by Microsoft. Because it is
partly true.


    * When_Fedora_Said_It_Was_Looking_to_Integrate_"AI"_It_Meant_Promoting
      Microsoft's_Proprietary_Spyware_and_GPL-Violating_Slop
    * Reporting_Facts_About_Violence_Against_Women_Deserves_Awards,_Not
      Frivolous_Lawsuits_and_Threats


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠄⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠐⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⡿⡿⠿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠩⣢⠿⡑⢤⣸⠺⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⣿⣦⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡛⠦⣱⡟⠅⢀⣢⠾⠉⢑⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢭⣿⣩⢿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⡘⣦⡋⠍⢠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⡀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠈⠒⠒⠒⠒⢺⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢫⢽⣛⣿⡆⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⣀⠔
⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣮⣳⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡄⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠑⢄⠀⠀⠀⡄⠀⠀⠴⠆⠀⠀⢸⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⣾⠭⠆⣬⢽⡆⣷⠃⣿⠙⡇⠀⠀⠀⣏⠲⡆⢸⠛⢰⡋⣧⢹⣸⢳⡾⠀⠀⠀⠀⡇⠀⡟⢹⡆⣷⠃⣿⠘⣇⡟⢰⡯⠷⠀⠀⠀⠀⠈⠛⠀⠈⢢⣀⣜⣀⠀⠀⠀⠀⠀⠀⢸⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠀⠁⠉⠀⠀⠈⠉⠁⠈⠀⠈⠉⠁⠀⠉⠈⠁⠈⠁⠀⠀⠁⠀⠁⠈⠁⠉⠀⠉⠀⠈⠁⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢸⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠘⠊⠉⠉⠉⠑⠀⡀⠀⠐⠀⠀⠀⠄⠀⠂
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⢈⣝⢷⡀⠀⠀⠀⠐⠀⠀⠀⠈⠀⡠⠂⠐⡀⠈⢂⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⢉⠉⠍⢵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠡
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠀⠀⠀⠀⡀⡀⠀⡀⢀⠀⠀⠠⠀⡀⠀⡀⡀⠀⢀⠀⡀⠀⡀⡀⣀⠀⣀⢀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⢀⢀⢀⠀⠀⠀⡀⡀⡀⠀⢀⠀⢀⢀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠁⠁⠀⠚⠀⠘⠁⠊⠙⠁⠘⠃⠐⠃⠃⠉⠛⠀⠶⠈⠀⠃⠘⠀⠒⠛⠂⠚⠉⠘⠂⠘⠘⠈⠈⠃⠈⠁⠃⠀⠈⠀⠛⠀⠚⠘⠘⠐⠁⠓⠀⠓⠀⠒⠃⠐⠂⠘⠓⠘
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠄⢠⡄⠠⠄⠀⣤⡄⠠⠄⠀⡆⠀⢦⠀⠄⢠⡄⢠⡄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡿⢿⠟⣿⣿⡿⢿⢿⡿⣿⣿⠿⣿⣿⡟⢿⣿⣿⢻⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⡿⠿⣿⣿⠿⡿⣻⡿⣿⣿⣻⣿⡿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡶⣿⣿⣶⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⡿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⣿⡿⠿⢿⣿⡿⠿⡿⠿⠿⠿⡿⡿⠿⠿⡿⠿⠿⠿⢿⠿⠿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⢿⣿⠿⢿⢿⠿⠿⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠷⠾⠶⣿⣷⣶⣿⣿⣿⣶⣷⣶⣶⣶⣷⣶⣷⣶⣷⣷⣶⣶⣾⣷⣷⣷⣶⣾⣶⣷⣶⣶⣶⣶⣶⣾⣿⣶⣷⣾⣶⣶⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⠉⣯⡍⣉⠙⠿⣿⡉⢽⢙⣛⠛⢻⠛⠛⡏⣟⡋⠛⠻⣿⡉⢽⠛⢻⠿⡋⡟⡛⣟⡛⡟⢻⣿⢹⢹⢛⢻⢛⡋⡟⡟⣟⡋⡟⠛⠛⢻⣯⣭⡍⣛⢹⠩⢹⢹⢻⢻⢉⣹⣿⠋⢻⢛⢻⢛⢻⣿⢻⠛⡏⣿⣿⣿⣿
⣿⣿⣯⣵⣧⣴⣯⣶⣵⣿⣬⣼⣼⣬⣮⣽⣶⣶⣧⣧⣤⣦⣽⣿⣬⣼⣬⣼⣦⣧⣧⣧⣗⣡⣯⣼⣿⣼⣼⣼⣼⣮⣤⣧⣥⣧⣥⣧⣥⣬⣾⣿⣿⣧⣿⣼⣼⣮⣼⣧⣿⣤⣼⣯⣿⣮⣼⣼⣼⣼⣤⣴⣥⣧⣿⣿⣿⣿
⣿⣿⣗⡒⣿⡏⣯⡝⡉⠝⣭⡏⡅⡏⡍⡇⡅⡏⡍⣏⡍⡇⣿⣟⣛⣻⣿⢐⣸⢩⢹⢩⢹⣿⢹⠩⣿⣗⡒⠏⣹⡹⢹⢸⣭⡟⣭⣏⠩⣿⢫⣹⢩⢹⣿⢰⡆⣾⣿⣒⡏⡝⣍⡇⡌⠍⣏⢽⡉⠇⡏⡍⣏⡍⢏⣹⢸⣿
⣿⣿⣷⣶⣷⣶⣷⣾⣶⣾⣶⣷⣷⣧⣶⣷⣶⣷⣶⣿⣷⣷⣿⣿⣿⣿⣿⣶⣾⣶⣾⣾⣾⣶⣶⣶⣿⣷⣶⣶⣾⣷⣿⣾⣿⣿⣤⣷⣶⣿⣷⣾⣾⣾⣿⣾⣷⣿⣿⣿⣷⣷⣶⣷⣷⣶⣷⣾⣶⣶⣷⣶⣿⣷⣶⣾⣾⣿
⣿⣿⡇⣢⢩⡭⠌⠱⢽⢩⡇⠚⣯⣬⡞⢕⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⡿⠿⠿⡾⠯⠼⠿⠷⠿⢿⠿⠿⣷⡿⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠷⠷⠶⡶⠶⠶⢶⠶⠶⠶⡾⠶⠶⢿⠶⠶⠷⡿⠶⠶⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⣿⣿⣿⡻⣿⣿⢋⣿⣿⡏⢽⣿⣿⠛⣿⣿⡛⢹⣿⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⣭⣭⣯⣭⣭⣽⣭⣭⣭⣯⣭⣭⣽⣭⣭⣭⣯⣭⣭⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⢼⢀⠆⣢⠸⢇⠆⡇⡸⠠⢼⡧⢸⠰⣡⣈⢿⡧⢐⢰⡆⡆⠼⡈⡈⡇⡇⢎⠠⢼⡧⢘⢁⢡⢃⡇⢠⢸⡰⢸⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⡿⠿⠿⢿⠿⠿⠿⠿⠿⡿⠿⢿⠿⢿⠿⠿⢿⡿⠿⠿⠿⠿⠿⢿⡿⠿⢿⡿⠿⠿⠿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡓⠲⠓⢳⣶⣶⣿⣶⣶⣷⣶⣷⣷⣶⣾⣾⣾⣷⣶⣾⣶⣷⣶⣶⣾⣶⣾⣶⣶⣶⣷⣶⣾⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣧⣥⣤⣥⣧⣤⣦⣧⣤⣦⣤⣤⣼⣴⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡀⠠⡄⣤⣤⡤⠄⢄⢄⠤⡠⡀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠤⠤⠤⠄⠀⠠⠤⠠⠤⠆⠀⠀
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣇⡀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⠤⠆⠖⠰⠶⠲⠆⠀⠀⠀
⣀⣉⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠠⠀⠐⠿⠂⠀⠈⠛⠛⠛⠉⠀⠀⠾⠂⠀⠀⠀⠄⠘⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⢡⡄⠀⢠⡄⠀⢐⠀⠀⡄⠀⢠⡌⠀⠠⠀⠀⠀⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⣀⢀⣀⢀⢀⠀⣀⠀⢀⢀⢀⢀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣟⣿⣿⣹⣿⣿⣛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠘⠘⠘⠀⠃⠈⠂⠃⠀⠃⠂⠑⠘⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠰⠆⠿⢇⣉⠉⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⣀⢠⣤⠿⠿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣟⡛⠛⢛⣿⣿⣿⣦⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠣⠤⠈⠉⠉⠈⠀⠀⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿
⣿⣿⡿⠗⡿⢾⠵⡇⡞⢾⠸⡇⡎⠕⢼⡯⢽⢋⠕⡷⡿⢾⣵⣷⣿⣯⢷⡗⢾⣵⢈⡷⢶⢾⡧⢝⣵⠙⠊⢰⡱⢽⣟⣬⣹⠶⣯⡆⡱⢱⢫⢿⡿⠎⡱⢽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⡟⠿⢻⣟⠻⣻⣻⢻⣿⡿⠿⣾⣾⣻⡻⡚⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣷⣾⣾⣾⣾⣿⣿⣧⣾⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⣛⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣉⡙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡟⠛⢻⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣀⡙⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⢿⢿⡿⡿⣿⣿⣿⣿⢿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡉⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠉⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⡟⠛⠻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⡀⠀⠀⠀⢹⣿⠿⡿⢿⡿⢿⠿⣿⠿⣿⢿⣿⣿⣿⠿⢿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⡿⠀⠀⠀⠸⡇⠄⡆⠐⠀⠐⠀⢂⠒⡇⠆⡀⠀⠀⢰⢰⠐⠂⠀⡇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣠⣾⣦⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣼⣿⣿⣿⣿⣶⣦⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⢿⣿⣿⣿⢿⠟⠛⢉⣙⢸⣿⢸⣿⣿
⢸⣿⡟⠛⠻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠙⠿⡿⠋⠿⠛⠛⣩⡙⣿⣿⡿⠛⠙⠻⢿⠿⡏⡙⢋⣁⠹⠟⣠⣶⣤⣶⠈⠛⢿⠋⣴⣾⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣤⣤⡙⣡⣈⣉⣙⡃⠁⣡⡄⠛⠻⠒⠂⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣤⣼⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣷⣼⣿⣦⣩⣉⠋⣩⣉⠹⢿⠟⠿⣿⠿⢛⠻⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣌⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣶⣤⣶⣿⣷⣤⣌⢋⢙⠛⢸⣿⢸⣿⣿
⢸⣿⡟⠛⠻⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠏⠙⠿⠋⣉⣙⣉⣉⣥⣡⣥⣥⣭⣭⣉⣉⣡⣤⣤⣦⣦⣤⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠤⠚⣉⣉⣙⠛⡙⠛⣛⣋⣉⣩⣤⣤⣤⣤⣤⣤⣥⣴⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⠸⠿⠿⠿⠛⠛⠛⢛⣛⣛⠛⣉⢉⠉⠙⠉⠉⠉⠁⠀⠀⠚⠛⠛⠛⠛⡋⠻⠟⠻⠿⠻⠛⠟⠻⠿⠛⠛⠛⠛⠋⠈⢉⣙⢋⣭⣤⣴⣤⣤⣩⣉⣉⣉⣉⡛⠛⢛⠛⠁⢲⣶⣄⠛⠛⠛⠻⠛⢸⣿⢸⣿⣿
⢸⣿⣿⠛⠻⠐⠒⠒⠛⠛⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠓⠓⠛⠙⠛⠛⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠉⠁⠀⠀⠁⠈⠙⠛⠛⠉⠁⠉⠁⠀⠉⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠀⢸⣿⢸⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⠿⡿⠿⣿⣿⣿⣿⣿⠿⡿⣿⡿⣿⠿⣿⡿⢿⠿⠿⣿⣿⢿⡿⠿⠿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣶⣾⣶⣶⣾⣷⣿⣶⣶⣶⣶⣶⣿⣷⣷⣶⣶⣿⣷⣷⣿⣶⣷⣿⣷⣷⣾⣶⣾⣶⣶⣾⣷⣾⣶⣶⣶⣾⣿⣶⣾⣷⣶⣶⣶⣾⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⢸⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1345

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/LLM_Slop_Says_Slop_is_coming_for_white_collar_jobs_Microsoft_s_.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/LLM_Slop_Says_Slop_is_coming_for_white_collar_jobs_Microsoft_s_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ LLM Slop Says Slop is "coming for white-
collar jobs. Microsoft’s layoffs are just the
start"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025,
updated Apr 16, 2025


Plagiarists trying to seem "clever" or "productive" (they're neither)


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


LLMs 'writing' about LLMs (littering_the_Web) is like a joke that writes
itself. Here's a new one from moments ago:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇AI_is_coming_for_white-collar_jobs._Microsoft’s_layoffs_are
                               just_the_start⦈_


Look what the Web has become. "In 2024," to_quote_Wikipedia, "the dead Internet
theory was sometimes used to refer to the observable increase in content
generated via large language models (LLMs) such as ChatGPT appearing in popular
Internet spaces without mention of the full theory."


This domain, which is shown above without name or link, is a slopfarm (also
'farmed' by Google News) with slop images and no original stuff. We see
nonsense like this every day but rarely link to it or mention it.


For some context, Microsoft has had at_least_six_waves_of_mass_layoffs_this
year. It's hard to mask the effect by hiring cheaper workers, taking over
companies etc. because the headcount_still_decreases.


Chaff like the above distracts from the facts. It saturates the Web.


These LLMs are a lot like kids who in my age (and era) plagiarised by copying
works online, then editing the words a bit to obscure the source. Not much has
changed since then except the hype and the brute force. █


    * Microsoft_Down_From_100%_to_10%_in_Myanmar/Burma
    * The_"Gold"_Rule:_Taking_Money_for_Reputation_Laundering_and_Openwashing
      Under_the_"Linux"_Banner


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

                    ䷩ 𝚕𝚒𝚗𝚎 1980

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/Microsoft_Down_From_100_to_10_in_Myanmar_Burma.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/Microsoft_Down_From_100_to_10_in_Myanmar_Burma.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Down From 100% to 10% in Myanmar/
Burma⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


We have tremendous_sympathy for victims of the recent earthquake. These are
poor people with vulnerable housing. To them, buying some "hey hi PC" with
Vista 11 isn't a priority. Some of them do not have toilets and clean_water_can
be_scarce.


Earlier_this_year and last year [1, 2] we wrote about Microsoft's problems in
Myanmar/Burma. Microsoft used to be measured at a "solid" 99% or 100% in there
until 2011 and now it's_down_to_almost_10% (mobile_usage_grew):


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


The relative share of Windows fell by more than 50% since Vista 11 was
released. Considering the_Vista_version_breakdown, only about 4% of Web
requests in Myanmar/Burma come from Vista 11, soon to be the only "supported"
version of Windows. █


    * Reporting_Facts_About_Violence_Against_Women_Deserves_Awards,_Not
      Frivolous_Lawsuits_and_Threats
    * LLM_Slop_Says_Slop_is_"coming_for_white-collar_jobs._Microsoft’s_layoffs
      are_just_the_start"


⣿⣛⠿⠿⢿⠿⠿⠻⢿⢿⡟⣿⠿⠿⠿⠿⢿⡿⣿⠿⠿⡿⠿⢿⢛⠻⡿⡿⠿⣿⡿⢿⡿⡿⠿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿
⣿⠯⡯⡷⠽⠧⢬⡤⡯⢺⢯⠦⡧⣯⣽⣧⣿⣿⣾⣤⣼⣾⣽⣽⣵⣼⣧⣿⣮⣿⣾⣧⣧⣿⣼⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣷⣾⣷⣶⣿⣶⣷⣾⣾⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣥⣼⣭⣭⣭⣭⣩⣭⣭⣭⣍⣉⣛⣛⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡔⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢖⠒⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⠿⠛⠉⠀⠀⠉⠋⠛⣰⣿⣿⣷⣌⡎⢿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⡘⢋⣴⣾⣿⣿
⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣿⡤⢦⠹⠏⣭⣡⣦⠹⣿⣿⡿⢿⡿⣿⡏⠘⡏⠁⡆⠙⠻⣿⠿⠀⢻⡿⡛⢿⣿⡿⢫⣴⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⡇⠀⠀⠠⣿⢡⠆⠀⠀⢈⣿⠀⢲⠰⠆⠂⠆⠰⠡⠰⠠⠄⡀⠇⠀⡀⠀⠰⠁⠀⡇⣄⠃⠀⣿⠀⣷⣤⠀⣼⣷⣶⣷⣦⢹⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣤⡀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣿⣷⣷⣾⣿⣾⣷⣾⣷⣾⣷⣶⣿⣿⣷⣠⣰⡌⢃⣿⣦⣼⣿⣀⣿⣿⣷⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠛⠃⠠⠄⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣏⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⠙⢃⡆⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣍⣥⣄⣿⣇⣼⡇⠃⡆⠈⣿⠛⣿⡿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣆⣩⡌⣉⠻⣿⣿⣿⣿⡟⣨⠹⠛⡉⢋⡍⢡⣾⣿⣿⣿⣿⣿⣿⣧⢰⣧⡄⠟⠀⠟⣴⣤⠙⣡⣴⣦⣥⣴⣇⠻⠿⣿⣿⡿⢿⣷⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⡛⢋⣭⣡⣿⣷⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠋⠟⢿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣰⣦⠹⢮⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣿⠿⠿⠿⠿⠿⠛⣛⠻⠿⣿⠿⠿⣿⢿⠿⠿⠟⠿⠛⠋⠤⠌⠻⠿⠿⠟⠛⠟⠿⠛⠛⠛⠛⠛⠋⠩⣥⠴⡾⢶⠀⣠⣦⣌⡃⠬⠐⠀⠥⡤⠍⠉⢛⡛⠛⢺⣿⣿
⣿⣟⣛⣛⣛⣛⣛⣛⣙⣉⣛⣋⣉⣉⣋⣉⣉⣀⣁⣀⣀⣉⣁⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣉⣀⣀⣂⣐⣀⣀⣀⣀⣉⣁⣉⣛⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣈⣀⣀⣀⣈⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣹⣍⣍⣉⣉⣉⣿⣍⣍⣉⣿⣉⣉⣉⣉⣉⣿⣉⣉⣉⣿⣉⣝⣉⣹⣯⣽⣉⣉⣍⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2040

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/Over_at_Tux_Machines.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/Over_at_Tux_Machines.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Over at Tux
Machines...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Fedora_Linux_42_Is_Out_Now,_Powered_by_Linux_Kernel_6.14_and_GNOME_48
      Desktop⠀⇛


           The Fedora Project released today Fedora Linux 42 as the latest
           stable version of this powerful, Red Hat-sponsored distribution
           for the masses, featuring some of the latest and greatest GNU/
           Linux technologies.


   2. ⚓ Manjaro_25.0_“Zetar”_Released_with_Xfce_4.20,_GNOME_48,_and_KDE_Plasma
      6.3⠀⇛


           Today, the Manjaro Linux team announced the release and general
           availability of Manjaro 25.0 (codename Zetar) as the latest
           stable release for this Arch Linux-based distribution featuring
           Xfce, GNOME, and KDE Plasma flavors.


   3. ⚓ Audiocasts/Shows:_LINUX_Unplugged_and_Destination_Linux⠀⇛


           2 new episodes


      ⚓  New⠀⇛


   4. ⚓ Armbian_Announces_New_Cloud-Optimized_Images_for_ARM64_and_x86⠀⇛


           The Armbian project informs 9to5Linux today about the launch of
           new cloud-optimized images of Armbian Linux for x86 and AArch64
           (ARM64) hardware architectures with some exciting features.


   5. ⚓ Fedora-Based_Ultramarine_41_Linux_Distribution_Is_Now_Available_for
      Download⠀⇛


           The makers of the Fedora-based Ultramarine Linux distribution
           released today the ISO images of the Ultramarine 41 release,
           which is built on top of Fedora Linux 41 and was already
           available for existing users.


   6. ⚓ VirtualBox_7.1.8_Released_with_Initial_Support_for_Linux_Kernel_6.14⠀⇛


           Oracle released VirtualBox 7.1.8 today as the fourth
           maintenance update to the latest VirtualBox 7.1 series of this
           powerful, free, cross-platform, and open-source virtualization
           software for GNU/Linux, macOS, and Windows.


   7. ⚓ Fedora_Asahi_Remix_42_Released_for_Apple_Silicon_Macs_with_KDE_Plasma
      6.3⠀⇛


           The Fedora Asahi SIG and Asahi Linux projects announced the
           general availability of Fedora Asahi Remix 42 as the latest
           version of this distribution developed for Apple Silicon Macs.


   8. ⚓ today's_leftovers⠀⇛


           GNU/Linux mostly


   9. ⚓ Programming_Leftovers⠀⇛


           Development-related picks


  10. ⚓ Education_and_Free_Software_Leftovers⠀⇛


           Education focus


  11. ⚓ Web_Browsers:_Retro_Boy,_Servo_vs_Ladybird,_and_More⠀⇛


           Web stuff


  12. ⚓ Open_Hardware:_ESP32,_Pimoroni,_and_More⠀⇛


           hardware leftovers


  13. ⚓ Red_Hat_Leftovers⠀⇛


           many Red Hat buzzwords in Red Hat's site


  14. ⚓ GNOME_Foundation_Update_and_New_Concept_to_Selectively_Pin_Clipboard
      for_GNOME⠀⇛


           2 GNOME articles


  15. ⚓ Security_and_Windows_TCO_Leftovers⠀⇛


           Security picks


  16. ⚓ BleachBit_4.9.2,_Istio_1.24.5_and_1.25.2_Released⠀⇛


           some releases


  17. ⚓ today's_howtos⠀⇛


           last batch for today\


  18. ⚓ Nitrux_Project_Introduces_NX_AppHub,_a_New_System_to_Provide_Apps_for
      Nitrux⠀⇛


           Uri Herrera from the Nitrux Project unveiled today NX AppHub, a
           new system for managing and building applications for the
           Debian-based, systemd-free, and immutable Nitrux Linux
           distribution.


  19. ⚓ today's_howtos⠀⇛


           Instructionals/Technical posts


  20. ⚓ Open_Hardware/Modding:_Video_Walkie_Talkie,_Armbian,_PINE64,_and_More⠀⇛


           Hardware leftovers


  21. ⚓ OCCT,_the_PC_Stress_Testing_Utility,_has_just_arrived_on_Linux⠀⇛


           Here at OC3D, we use OCCT on an almost constant basis


  22. ⚓ Games:_Prices_Hikes,_GNOMES,_V_Rising_1.1,_and_More⠀⇛


           10 stories from GamingOnLinux


  23. ⚓ Android_Leftovers⠀⇛


           Why did Samsung pause One UI 7 release? These could be the
           possible reasons


  24. ⚓ These_5_Linux_distributions_are_the_worst_for_beginners⠀⇛


           Linux is an excellent operating system with many distributions,
           each catering to different audiences


  25. ⚓ Free_and_Open_Source_Software,_howtos_and_Installations⠀⇛


           This is free and open source software


  26. ⚓ Live_Raizo_–_live_Debian-based_Linux_distribution⠀⇛


           Live Raizo is a live distribution based on Debian to experiment
           with system administration on simulated networks and real
           devices


  27. ⚓ Journey_to_GNOME_Circle:_Community,_App_Ideas,_and_Getting_Started⠀⇛


           Hello, chat! I’m Revisto, and I want to share my journey to
           GNOME Circle and how I became a GNOME Foundation member


  28. ⚓ This_SteamOS_clone_is_the_best_Linux_distro_for_gamers⠀⇛


           Until Valve releases an official version of SteamOS


  29. ⚓ 5_things_to_do_with_the_Linux_terminal_on_your_Android_phone_-
      including_my_favorite⠀⇛


           Google launched a Linux terminal app for Android that gives you
           full command-line access


  30. ⚓ Ubuntu_Vs._Debian:_A_Look_At_Beginner_Friendly_Linux_Distribution⠀⇛


           you will compare their unique offerings


  31. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


      =========================================================================
      The corresponding text-only bulletin for Tuesday contains all the text.
      Top-read articles (excluding bot/crawler visits):


                          Span from 2025-04-09 to 2025-04-15
      1339 /n/2025/04/10/Proxmox_Virtual_Environment_8_4_Released.shtml


      668  /n/2025/04/09/
           Linux_Mint_Debian_Edition_Is_Getting_Support_for_OEM_Installati.shtml


      665  /n/2025/04/10/Sparky_7_7.shtml


      647  /n/2025/04/12/
           Pinta_3_0_Open_Source_Paint_Program_Released_with_GTK4_Port_New.shtml


      616  /n/2025/04/09/Asahi_Linux_hits_an_M4_support_roadblock.shtml


      601  /n/2025/04/09/today_s_howtos.shtml


      586  /n/2025/04/12/today_s_leftovers.shtml


      586  /index.shtml


      551  /n/2025/04/11/today_s_howtos.shtml


      532  /n/2025/04/10/
           Stable_kernels_Linux_6_14_2_Linux_6_13_11_Linux_6_12_23_Linux_6.shtml


      532  /n/2025/04/11/today.shtml


      521  /n/2025/04/12/today_s_howtos.shtml


      520  /n/2025/04/10/Git_is_More_Popular_than_Linux_Torvalds.shtml


      516  /n/2025/04/11/today_s_howtos.1.shtml


      512  /n/2025/04/12/Programming_Leftovers.shtml


      506  /n/2025/04/11/Security_Leftovers.shtml


    * IRC_Proceedings:_Tuesday,_April_15,_2025
    * IBM_Closes_Offices_and_Labs_in_the_United_States_to_Open_New_Ones_in
      India


⣿⣿⡏⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠏⠉⠛⠋⠁⠀⠀⠀⠉⠀⠀⠈⢹⣿⠟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⡏⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⣿⠟⠁⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡃⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⢀⣾⣿⣷⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣄⣠⣶⣿⣿⣿⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣀⣤⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄⣠⣶⣿⣿⣷⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠶⢶⣤⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣧⡠⣤⣤⣤⣤⣴⣄⠈⣿⣿⣿⣽⣿⣿⣿⣧⠀⠃⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⠟⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⠸⣿⣿⣿⣀⣿⡆⠠⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⡄⠀⠰⠀⠀⠺
⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⠀⢹⡟⢱⣿⣿⣿⣶⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⠀⠃⠁⢉⠙⢿⣿⡏⠉⣿⡿⡏⢻⣿⣿⣿⣿⣿⠙⣿⠀⣠⡄⠠⡇⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⡇⠘⣿⡀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⠃⣄⢹⠀⠀⠀⠸⠀⢼⣿⢿⠀⠹⠁⢰⠀⠈⠙⠿⠟⠉⠂⡁⠀⢸⠇⠀⠁⠀⠀
⢴⣦⣄⣄⣬⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡀⠘⣿⣿⣟⣿⣿⣿⡀⢻⠇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⠻⣿⣿⡿⠀⢹⢸⠀⠀⠀⠀⠀⢈⡅⠈⠂⠀⣴⠈⡄⠀⠀⠀⢸⠀⠸⠁⢠⡏⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣿⣿⡿⣿⡟⠛⠛⠓⠋⢻⠀⢿⣿⠛⠛⠋⠈⠃⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⢿⠀⠈⠛⠀⠀⠘⣿⠀⠀⠀⡄⠀⠘⠃⠀⠀⠀⢸⠀⡇⠀⠀⠀⠸⠀⡀⠀⡟⠀⠀⠀⠀⠀⠀
⣺⠿⠿⠿⡿⠛⠋⠀⠸⣿⣧⠀⠀⣀⣤⣼⡄⢸⣿⣿⣦⣴⣦⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⡀⠀⠀⠀⠀⠀⠀⢀⠀⡏⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠂⠀⡇⠀⠀⠀⠀⠈⠀⠘⢰⡆⠀⠀⠀⠀⠀
⣿⣇⠀⢀⣴⣿⣿⣶⣄⠻⣿⣿⣿⣿⣿⣿⣇⠘⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀
⣿⡏⠀⢸⣿⣿⣿⣿⣿⣦⡈⠛⣋⣯⣿⣿⠿⠀⣿⣇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⢸⠀⢀⠀⠀⢸⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀
⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⡈⠉⢲⡀⠀⣄⠀⢷⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠙⠄⠀⠇⠀⠀⡌⠀⠀⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⢀⡤⠂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⡾⠀⠀⣿⡆⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡄⠀⠀⣠⡴⠋⠀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣤⣿⠆⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⠿⢿⠛⠁⠰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⠠⠀⡀⠊⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⢀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⠈⡀⠀⡶⠀⠀⠀⠀⠀⡇⠆⡇⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀
⠋⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠁⠘⠀⠀⠀⠀⠀⠀⡇⢸⠁⠀⢠⠌⠀⠀⠀⠀⠞⠀⠀⠀⠀
⣰⠋⣉⠻⣿⣿⣿⣿⣿⣿⡏⠛⠿⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏⠁⠀⠀⠀⠀⠀⠀⢉⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠁⠀⢿⣿⣿⣿⠟⢿⣿⡀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⢠⠀⠀⠀⠀⠀⠘⢀⠂⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠙⠇⠈⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡄⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2373

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/Reporting_Facts_About_Violence_Against_Women_Deserves_Awards_No.shtml
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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Reporting Facts About Violence Against
Women Deserves Awards, Not Frivolous Lawsuits and
Threats⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025,
updated Apr 16, 2025


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


What is Microsoft's stance on women's_safety? Or about staff's safety [1, 2, 3]
for that matter? Will British_judges entertain aggressive_Americans from
Microsoft because they 'tricked' some poor law firm [1, 2] into becoming a
facilitator (by omitting key, critical facts)?


Yesterday we wrote about Mohamed_Al_Fayed's_lesson_to_the_press (Harrods should
be out of business, but it's not). If the media won't speak out for women (out
of fear, greed etc.), then more women will become victims and suffer immensely.
There's no excuse for keeping quiet. Silence_is_a_form_of_complicity.


Oligarchs do not champion women's rights; many are abhorrent_womanisers,
chasing_skirts:


      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Bill Gates pictured with Mila Antonova in 2010⦈


The corporations try_to_hijack the "women's_rights"_narrative. They call it
"Social Responsibility" or CR ("Corporate Responsibility") - it's a form of
reputation_laundering and they hire firms to give the false impression
oligarchs are in fact the guardians of those whom they attack. Apparently Bill
Gates is a SPOKESPERSON of the poor! "DEI" is not the same, but it is sometimes
related to it and overlapping it a little. Don't be easily fooled by PR.
There's a vast industry associated with whitening the reputation of rich
people; some of that industry wears the "hat" of "lawyer", issuing_threats_to
take_down_unflattering_information. It doesn't seem to matter if the
information is correct. To them, what matters is that their client wants that
information hidden from sight.


Speaking of "their client", they don't seem to mind the full context,
chronology etc. All they care about is that they get paid. That's why my wife
and I sued MJG [1, 2] (it took him more over 6 months to put in his Defence,
and it was a really poor, sloppy defence; it looks like it was just some E-mail
that he hastily wrote back with minimal formality and even outright lies*).


Regarding MJG's_'friend'_or_litigation_ally, it is even worse. As I explained
it last year when he first showed up (via the exact same lawyer!), "here are
examples from yesterday's news (and yesterday alone) to show what we're dealing
with. The article in the_SF_media says: "A tech executive is suing a journalist
for $25 million for reporting, accurately, that he had been arrested on
suspicion of domestic violence.""


Imagine that was just a few days apart from the same being done to me. He
pretended to be in SF (at the time, due to Microsoft) while his real residence
was his dad's home (or girlfriends' places). He lied to them about being
"worth" hundreds of millions of dollars. That's contradicted by what he told
the cops; he had almost nothing in the bank.


This is what the article said:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tech_exec_sues_journalist_for_$25M_for_publishing_his_sealed
                                arrest_report⦈_


To be clear, what we published was not sealed. Even if some time in the future
it becomes sealed, it was not at the time of publishing. So we did nothing
wrong. It was perfectly legal and also in the public interest (he worked at
Microsoft at the time, doing bad_things).


The SLAPP was baseless. It was meant to help MJG, who was suffering and fuming
after repeated setbacks.


This was classic SLAPP. It is just an excuse for covering up true information.


"That was yesterday," I told my lawyer at the time, "sounds similar to what
Graveley does. Also see [Trump's_attacks_on_the_media]_in_the_news; that's just
truly ridiculous an attack on the media!"


It seems ironic that this timing was chosen by the Microsofters, who acted like
Donald Trump:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Trump_sues_US_television_network_for_$10_billion_over_Harris
                                  interview⦈_


That does not make sense. Nor do the Microsoft_SLAPPs. █


____


* For instance, we never took down anything following these_invalid_threats.
That document was signed with a "statement of truth". Does MJG realise what
signing it actually means?


    * Linux.com_as_Spamfarm_of_the_Linux_Foundation,_Partner_of_the_Gates
      Foundation
    * Microsoft_Down_From_100%_to_10%_in_Myanmar/Burma


⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀
⠀⠀⣰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀
⠀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠘⠚⠐⠙⠃⠀⠀⠛⠃⠋⠛⠛⠛⠀⠀⠘⠷⠃⠛⠛⠻⠛⠛⠀⠀⠸⠧⠀⠛⠛⠛⠛⠃⠀⠀⠣⠋⠘⠛⠛⠛⠛⠛⠟⠀⠀⠘⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⣴⢄⢤⡆⣂⣖⣦⢤⣤⣰⣦⡤⢖⣰⢖⢤⣤⢤⣤⣤⣰⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⠀⠶⠦⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠀⠀⠀⠀⢀⢀⣀⣀⣀⢀⣀⣀⡀⣀⡀⢀⢀⣀⣀⡀⡀⣠⠀⣀⣀⣠⡀⣀⣄⡀⣀⢀⣀⡄⣄⡀⡀⣀⢀⡀⣀⣀⣄⣀⣀⢀⣀⣀⣄⢀⡀⣀⣀⡀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣐⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠐⠛⠛⠛⠗⠛⠛⠚⠂⠛⠃⠛⠛⠛⠻⠎⠛⠛⠐⠓⠛⠛⠚⠛⠛⠈⠾⠘⠊⠃⠛⠛⠋⠚⠋⠃⠛⠛⠛⠚⠑⠛⠛⠊⠘⠘⠋⠘⠻⠊⠑⠻⠛⠋⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⢸⠿⠾⠾⠶⠷⠧⠸⠷⠵⠇⣾⠦⠿⠿⡶⠸⠩⠆⠾⠾⠷⠷⠱⢾⠅⠽⠶⠅⠸⠾⠦⠾⠮⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⡀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⣿⣿⣟⣀⡏⠃⠁⠉⠘⡇⠀⠀⠀
⠀⠀⠀⠀⠈⠉⣈⠘⢉⣉⠈⠉⠉⣉⡉⠂⠉⢈⠉⠈⠁⠉⠉⢉⠙⠉⠈⣙⢈⠁⠉⠋⡉⠈⠁⠉⠘⠁⠉⠉⠉⠈⠉⠈⠉⠙⠃⠉⠉⠉⠉⠃⠉⠉⠋⠈⠉⠁⠁⠁⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠈⠉⠋⠉⠋⠉⠉⠈⠉⠋⠘⠉⠛⠓⠘⠋⠋⠉⠚⠈⠉⠋⠉⠉⠃⠛⠋⠋⠉⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠰⠶⠶⠶⠶⠴⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⢠⠀⣄⣀⡀⡄⡤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⡀⢠⡀⠀⠀
⠀⠀⠀⠀⠈⠑⠀⠉⠉⠉⠁⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⠀⠀⠀⠀⠸⠱⠐⠿⠶⠶⠄⠘⠾⠷⠲⠰⠶⠴⠰⠿⠰⠐⠶⢶⠰⠷⠖⡶⠐⠖⠰⠆⠷⠶⠰⠿⠿⠖⠆⠇⠶⠂⠆⠲⠶⠂⠶⠶⠲⠰⠄⠷⠆⠂⠾⠶⠇⠾⠾⠆⠆⡆⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⡿⢿⣿⡆⠀⠀
⠀⠀⠀⠀⢠⣴⠂⠤⣤⠠⣠⣤⣤⢴⢤⢤⠄⣤⡶⢠⢤⠄⣤⣴⣦⣄⠤⢤⢤⠀⢤⡤⡤⣤⢤⠀⢤⣤⣤⠀⢤⣴⢤⡄⣶⡦⡤⢀⢤⣤⢀⢤⣤⣦⢤⣤⣴⠠⣤⠤⡤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⢈⣍⢠⣁⣉⣠⠁⠈⠉⠀⠉⠉⠀⠁⠁⠉⠈⠀⠁⠈⠉⠀⠁⠉⠈⠀⠈⠈⠈⠁⠈⠀⠈⠈⠀⠁⠈⠉⠈⠀⠁⠈⠉⠀⠉⠉⠀⠉⠁⠉⠀⠉⠈⠀⠉⠈⠁⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠘⠫⠛⠃⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀
⠀⠀⠀⠀⢰⣤⣤⣤⣴⣴⢦⣤⣦⣤⣴⢰⣢⡄⣤⣤⡆⣤⣤⣄⣤⣤⣤⣤⣤⣴⣤⣤⡄⣤⣦⣤⣤⣤⡄⣤⣦⣦⣤⣤⣤⣤⣴⢤⣦⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⣤⣬⢤⢤⣤⣄⣴⡤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⢠⣤⣤⡤⣤⡄⣤⣤⡤⣤⣤⣴⢤⣤⣤⣴⢤⣤⡤⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠚⠛⠛⠛⠛⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⡆⠖⠶⠖⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀
⠀⠀⠀⠀⢀⢀⣀⣀⣀⢀⡀⣀⡀⢀⡀⡀⡀⡀⣀⣀⡀⣀⣀⢀⡄⣀⢀⣄⣀⣀⢀⡀⣀⣄⢀⣀⣀⢠⣀⡀⣀⡀⡀⢀⣀⡀⡀⡀⢀⣀⢀⣠⠀⡀⣀⠀⡀⡀⣀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀
⠀⠀⠀⠀⠘⠛⠛⠛⠗⠛⠛⠚⠂⠛⠃⠋⠋⠛⠛⠃⠘⠛⠃⠛⠃⠋⠛⠛⠚⠑⠛⠛⠊⠛⠘⠛⠚⠛⠛⠚⠛⠻⠞⠘⠚⠛⠛⠛⠘⠀⠛⠛⠛⠛⠛⠘⠚⠚⠛⠃⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠰⢶⠱⡶⠶⠜⠶⠼⠶⠶⠴⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⢀⣀⣀⣀⣀⠀⡀⡀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀
⠀⠀⠀⠀⠈⠉⣉⠘⢉⠉⠈⠈⡉⠉⡉⠊⡁⠉⢉⠉⠉⣉⠉⡈⠈⠙⠉⠉⠋⠀⠈⢉⠁⢉⠉⠈⠉⠉⠈⠉⠉⠁⠉⠑⠈⠉⠁⠉⠉⠁⠉⠉⠈⠉⠉⠉⠉⠈⠉⠋⠉⠋⠈⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠘⠃⠛⠛⠛⠛⠋⠉⠓⠘⠛⠛⠛⠛⠛⠙⠛⠛⠋⠙⠃⠛⠁⠛⠛⠛⠛⠚⠛⠛⠛⠛⠋⠊⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠰⠶⠶⠶⠶⠴⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣿⣧⣴⣥⣿⣿⣿⣼⣦⣴⣧⣬⣷⣧⣧⣷⣷⣴⣴⣶⣿⣷⣤⣤⣶⣵⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣦⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠟⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⣤⡆⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡑⠁⠀⣄⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⣉⡀⢸⣦⣐⠀⠘⠛⠀⣛⣛⣋⣉⡁⢈⣉⣉⣉⣉⣉⣉⣉⣉⣩⡅⢨⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠀⠛⠑⠘⠛⠛⠒⠀⠀⠀⠀⠈⠙⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡙⠉⡛⢛⢻⢻⠛⣿⡋⣻⠛⣟⡽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⣤⡄⠀⠀⣀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠷⠷⠷⠷⠶⠿⠾⠶⠿⠶⠿⠶⠷⠷⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⡋⠀⠀⠈⢰⠷⠁⠈⢰⣤⣄⠀⠁⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣤⣄⠀⠀⠈⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⡇⠀⠀⢀⣀⡀⠀⠀⠐⠁⠰⢀⣿⡟⠭⠀⠀⠀⠀⠐⠸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⡇⠀⠀⣿⣿⣷⣦⡄⠆⣨⣴⣾⠟⢁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣰⣦⢠⣀⣀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡆⢀⣤⣄⡀⢸⣿⣿⣿⣿⣿⣿
⡏⠉⢉⣿⣿⣿⣿⣼⣿⣿⣿⣆⡄⡌⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣾⣥⣧⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢸⡸⠟⠸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⡇⠀⢘⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢹⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢂⠸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠈⣿⣿⠟⠛⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⡌⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠿⠿⠿⠃⢀⡄⠀⠀⠀⠀⠀⠀⠀⠒⠘⠀⠛⠀⠈⠂⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⠀⢨⣽⣴⣾⣿⠤⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡉⠁⠂⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣞⠁⠀⠀⠀⠀⠀⠉⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣶⠴⣸⣿⣿⣿⡧⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⡛⠿⢷⣄⡀⠈⢸⣿⣿⣿⣿⣿⣿
⡿⠿⠾⠿⠿⠿⠿⠋⠉⠉⠉⠉⠉⠉⠁⠈⠉⠁⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡾⣿⣿⣿⣿⢟⣿⡄⠀⠈⠛⢦⣸⣿⣿⣿⣿⣿⣿
⣧⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⣶⣶⣶⣶⣶⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢿⡿⡻⣶⣿⣿⣄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣫⣚⣟⣻⣻⣾⣰⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠤⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠼⠀⠇⠼⠇⠠⠀⠞⠸⠢⠸⠵⠠⠸⠃⠰⠧⠸⠀⠇⠏⠸⠀⠗⠄⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣭⣿⣿⣭⣯⣯⣯⣯⣿⣿⣯⣽⣭⣯⣭⣿⣿⣿⣭⣽⣽⣽⣯⣽⣿⣿⣿⣽⣿⣽⣿⣭⣿⣿⣿⣯⣿⣭⣿⣿⣽⣿⣯⣿⣿⣿⣯⣽⣿⣯⣿⣿⣿⣿⣭⣿⣭⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⢩⢻⣟⣿⢘⢻⢿⣛⢛⢿⡻⣟⡟⢿⢻⠻⣟⠻⣿⢺⣛⠟⡟⡛⡛⡛⡿⢻⠙⡟⢿⢹⡏⡞⡟⢛⣿⡡⣯⢹⡉⡏⠹⡹⣿⠹⡛⡟⣻⢛⣻⢻⠋⡛⡇⣻⠻⡏⡛⡛⢛⢻⠛⣿⢙⢻⢚⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣾⣶⡾⣾⣾⡶⣶⣷⣶⣶⣶⣷⣿⣾⣶⣶⣾⣾⣼⣶⣷⣷⣷⣷⣷⣾⣾⣶⣿⣾⣾⣷⣷⣷⣾⣿⣽⣷⣶⣾⣷⣷⣷⣿⣾⣶⣷⣿⣘⣾⣾⣶⣷⣷⣿⣾⣶⣷⣷⣾⣾⣒⣽⣾⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠕⡋⢮⠁⠇⡿⢍⠷⢿⠱⠉⢽⢰⠱⡭⢳⢸⡏⣎⢮⠹⢹⠽⡉⣇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣷⣶⣶⣶⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⣿⣿⣥⣽⣭⢽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿⠏⠀⠀⠠⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⠀⠀⠀⠀⣠⡄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣠⣴⣾⠿⠃⠀⠀⢠⣾⠋⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠈⠻⣿⡿⠛⠛⠿⠄⠀⠀⠔⠿⠟⠋⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢰⣦⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⢛⡿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣦⣞⣴⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣿⣝⣟⢻⣻⢛⣛⣻⣛⡻⣿⢛⡟⡟⡟⠻⢛⣿⡏⣿⢹⡹⣿⡏⣻⠛⡏⡿⠻⣻⢛⢻⢛⡟⣟⡻⡛⡛⣿⣛⡻⠟⢻⢙⣻⢻⠻⣛⢟⣛⠹⣻⣟⣹⢛⢿⢛⣿⣿⢽⡛⡟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣯⣽⣮⣿⣼⣭⣭⣫⣽⣿⣭⣷⣥⣷⣽⣭⣾⣷⣭⣾⣭⣾⣷⣽⣭⣧⣷⣽⣧⣾⣼⣭⣧⣷⣵⣧⣧⣿⣭⣧⣮⣽⣬⣧⣧⣿⣭⣮⣽⣼⣼⣯⣽⣮⣾⣼⣿⣮⣽⣥⣵⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⣿⡏⡏⡏⡏⡿⡿⡿⡿⣿⣿⡿⢿⢿⣿⢿⣿⣿⠹⠏⣿⣿⣿⡿⣿⢹⢿⣿⡏⡿⡿⡟⡿⡿⡿⣿⣿⡏⡿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣯⣧⣧⣧⣧⣧⣯⣧⣧⣿⣮⣷⣯⣾⣽⣿⣿⣿⣼⣧⣧⣽⣿⣧⣿⣼⣷⣿⣧⣧⣧⣧⣷⣯⣧⣿⣴⣧⣧⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⣠⠀⢀⣴⠀⢀⣤⣶⣶⣶⣦⡀⠀⠀⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣰⣧⢰⡾⠃⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⣿⠿⢿⣿⣿⣿⣿⣿⡏⠀⠐⠓⠃⠈⠀⠀⠀⢿⣿⣿⣿⣟⣽⣿⣷⠀⠀⠀⠀⠛⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠛⠉⣹⡇⠀⠀⠀⠀⡟⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣌⣁⠠⠚⠛⡿⢿⣿⣿⣿⣷⠀⠀⠀⠀⢻⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⡇⠀⠀⠀⠀⠀⣼⡿⠃⢠⠂⠀⠗⠀⠈⢿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⢿⣿⣿⣿⡟⠿⠿⠄⢿⠀⠀⠀⠀⠀⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣛⠉⣤⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠸⢿⡟⠣⠏⠉⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣦⣤⣀⣤⣤⣾⣿⠟⠀⠀⠀⠀⠀⣠⣴⣶⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠈⠛⣿⣟⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⣿⣿⣿⣿⣿⣛⣋⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣀⣀⣀⣀⣠⣈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢀⣠⣦⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢹⣿⣿⣿⣿⣿⣿⣿⣶⣄⠲⣤⣀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⢄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠑⢄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠙⢍⠉⠀⠉⠉⠁⠉⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⢠⣀⢠⠤⣠⢠⢠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣦⣀⣀⣀⣀⣀⣀⣀⣈⣈⣈⣁⣉⣈⣉⣈⣈⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⡿⣿⣿⣿⡿⢿⢿⢿⡿⡿⡿⢿⣿⢿⢿⣿⣿⢿⢿⣿⣿⣿⢿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣻⣿⣟⣟⣿⣟⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣿⣿⣻⣿⣻⣿⣿⣻⣿⣟⣟⣻⣿⣿⣿⣿⣏⣝⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉⠋⠉⢀⠄⣿⣳⣷⣺⣟⣿⣿⣿⣟⣾⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡾⣿⢿⣾⡿⢿⢾⣾⢳⡿⢿⡿⣶⣾⣿⣷⢿⣾⣾⡾⣿⣾⡿⣷⣿⢿⣷⣶⡿⣷⡷⢺⣷⣾⢷⠿⣿⣿⡷⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣟⣿⣻⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⢿⡿⡿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢽⣻⠉⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2628

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/Slopwatch_The_Typical_Slopfarms_and_the_Brian_Fagioli_Dilemma.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/Slopwatch_The_Typical_Slopfarms_and_the_Brian_Fagioli_Dilemma.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Slopwatch: The Typical Slopfarms and the
'Brian Fagioli Dilemma'⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025,
updated Apr 16, 2025


Last week we saw some articles about IPFire 2.29 Core Update 193 [1, 2] and
grouped them. Days later the slopfarm called linuxsecurity.com published this:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇IPFire_2.29_Core_Update_193:_Key_Improvements_in_Security
                                and_Defense_⦈_


It's LLM slop, as usual.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LLM_slop:_The_latest_IPFire_2.29_Core_Update_193_release_is
   a_significant_milestone_for_Linux_security_admins_looking_to_boost_their
  network_defenses._This_powerful,_open-source_firewall_distribution_has_now
 integrated_post-quantum_cryptography,_enhancing_its_resilience_against_future
                         quantum_computing_threats.⦈_


So was the other fake 'article' (from the same day):


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Rising_Cyber_Crime_in_2025:_Addressing_Internet_Blackmail
                                   Issues⦈_


As almost 100% of their output is LLM slop this did not surprise us:


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


Sometimes they add some stock image (like project logo), but that does not
change the fact we're dealing with LLM slop. We noticed a number of other sites
(as lately as yesterday) that claim to cover "Linux" and instead use LLM slop
regarding "Linux". We won't name them yet, we're just keeping them under
observation for now (maybe they only experiment a little and will refrain_from
repetition).


There's a real risk that not only will such sites realise LLMs don't pay off;
when_they_revert_back_to_real_writing_nobody_will_believe_them_anymore. That is
what happened to Brian_Fagioli. He misused LLM slop to the point where even if
he actually writes something, the default assumption is that it's fake. His
editor had to intervene a number of times; he even deleted some Fagioli
articles that were clearly slop.


Looking at Google News right now, a few hours it promoted this LLM slop:


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


It's a fake 'article' (even the image is slop!) and, as usual, it is Linux-
hostile, probably generated by a Microsoft LLM.


To the Web and to society (exposed to the Web) LLMs are a net negative. After
Microsoft_filled_E-mail_with_SPAM_it_does_the_same_to_the_Net_at_large. It just
doesn't care. █


    * It_Used_to_be_IBM,_Now_It's_Microsoft_(Why_You_Need_to_Fire_Microsofters
      or_CIOs_Working_for_Microsoft)
    * When_Fedora_Said_It_Was_Looking_to_Integrate_"AI"_It_Meant_Promoting
      Microsoft's_Proprietary_Spyware_and_GPL-Violating_Slop


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

                    ䷩ 𝚕𝚒𝚗𝚎 2856

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/StatCounter_Shows_the_Market_Share_of_Vista_11_is_Decreasing_in.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/StatCounter_Shows_the_Market_Share_of_Vista_11_is_Decreasing_in.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ StatCounter Shows the Market Share of Vista
11 is Decreasing in Ukraine This Year⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025,
updated Apr 16, 2025


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


Microsoft abandoning Vista 10 users would be a victory_for_Vladimir_Putin


StatCounter (or statCounter) has this_data_suggesting_that_for_the_past_half_a
year_or_so_Vista_11's_"market_share"_decreased_in_Ukraine. The decrease is
quite consistent. Maybe their priorities aren't "buy an hey hi PC". Microsoft
no longer providing security patches for Vista 10 would devastate Ukraine. It
would make it even more vulnerable (to hostile actors) unless users delete
Vista 10 and install GNU/Linux (or BSD) instead.


This month it is estimated that 70% of Windows users in Ukraine use Vista 10
(almost_half_of_all_Web-connected_devices). That's a lot.


Historically, Microsoft failed to see what was wrong with Putin's iron grip in
Russia. Microsoft's co-founder and habitual_pervert_Bill_Gates was seen and
photographed around Dmitry Medvedev. █


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


    * Google_Promotes_Fake_Articles_(LLM_Slop)_Instead_of_Originals,_Relaying
      Microsoft's_Linux_FUD_Emanating_From_Microsoft_LLMs
    * Links_16/04/2025:_Cliff_Lynch_RIP,_More_Attacks_on_Science_(NASA)


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⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⣾⣿⠋⠉⠈⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠁⠉⠉⡉⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠦⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⣿⣿⡆⢀⠄⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣈⣋⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠓⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡧⠀⠀⣿⣿⡀⠀⠀⠀⠀⠛⢛⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠠⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⢹⡟⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠈⠃⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣻⠀⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠟⠛⠟⠁⠘⡇⠀⣀⣤⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣐⣀⢂⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣚⣋⣓⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢠⠀⢈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⣿⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⡄⠀⢸⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⠻⠀⠸⠿⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡿⠁⢀⣠⣖⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣍⡀⢠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣭⠙⡟⣿⣙⠽⣛⠟⢻⠏⡏⢟⠟⡋⢟⣏⢩⣻⢛⡿⢟⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣷⣿⣾⣶⣿⣶⣾⣗⣕⣾⣶⣷⣷⣷⣷⣿⣶⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⢉⣉⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⢉⣉⣁⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢻⣻⠛⣛⡟⢿⣿⡿⠛⢻⢻⢿⢛⢻⢿⡟⠛⠟⢛⢻⠟⢛⠛⡟⣿⠿⢿⣿⣿⣿⣿⣿⡟⠛⠛⢉⣉⣁⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣷⣶⣿⣿⣷⣿⣾⣶⣶⣾⣷⣶⣶⣾⣷⣿⣶⣾⣾⣷⣶⣶⣷⣿⣿⣶⣶⣬⣭⣙⣛⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠶⣨⢿⠿⡿⢿⠿⠿⢼⠿⠿⣿⡗⢰⡿⡰⠿⡿⠿⡿⢿⣿⢇⢸⢏⢰⢧⡿⠿⢿⢿⠿⢿⠿⢿⠿⢿⠃⠎⢿⡿⠹⠿⢿⣿⡏⠲⡼⠿⢿⠿⠿⡿⠿⠿⠿⡿⠿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣰⣆⣻⣘⣐⣓⣙⣂⣅⣨⣘⣐⣿⣇⣛⣣⣗⣈⣐⣒⣂⣹⣟⣸⣠⣇⣺⣸⣘⣻⣰⣇⣛⣜⣊⣇⣋⣜⣸⣁⣿⣇⣺⣘⣠⣟⣙⣃⣇⣊⡸⢘⣣⢃⣋⣌⣼⣄⣓⣓⣙⣂⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⣿⠆⡓⡟⣛⠛⡻⢛⢻⢛⢻⠃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣬⣭⣾⣤⣭⣼⣥⣤⣭⣭⣼⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣴⣽⣹⣙⣻⣹⣍⣿⣻⣿⣹⣹⣿⣿⣿⣟⣗⣻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣛⢟⣿⣪⣺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿
⣿⣿⣿⣿⣧⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣀⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣼⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣹⠿⠵⠿⠐⣻⠿⡿⣿⣿⡟⠶⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⡋⠨⣭⣭⣭⣉⢓⠻⠿⢿⠑⠁⠛⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡏⠀⠈⢱⣿⣶⣀⠒⡀⠈⠿⠀⠀⠀⠀⢹⣿⣿⡋⢉⠉⣩⠉⡽⠍⠉⠛⠿⣿⠟⠿⠸⣿⣷⢖⣾⣿⠎⠀⢉⠈⠐⠗⠈⠀⠀⠰⠲⠬⣭⡉⡭⠝⠚⡻⢛⣿⡿⠿⣿⠡⡞⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠉⣫⠀⠀⠀⠀⢠⠀⠀⠘⠤⠭⣻⡿⠗⠀⠀⠃⠊⠀⠀⠀⠐⠠⣾⠀⠀⢸⡏⠻⠉⣽⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠩⠸⠤⠷⠤⠏⠀⠀⠀⠀⠉⢰⡄⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠉⠄⠀⠀⠀⠂⠩⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⣨⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠀⠀⡄⠀⠧⠠⣰⣤⣒⠀⠀⠀⠀⠲⠀⠀⢀⣼⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣇⣠⢎⣾⣿⡇⠁⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⡄⣀⣤⣥⣝⠙⠀⠀⠀⠀⠐⠀⠀⣸⣿⣷⣿⡏⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣠⣤⣤⡲⣶⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣂⡐⠀⠠⢈⠉⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢳⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡏⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣶⣦⡴⡮⠂⠂⣽⣿⣿⣿⣿⣏⣁⣠⣾⣖⣶⣖⣛⣿⣿⣿⣿⣿⣿⠋⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣀⠈⠉⣙⠀⠤⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠀⠋⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⢹⠿⠿⠿⠿⡏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡉⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⡆⢰⠀⣤⢠⣤⣤⢠⢀⣤⢠⡄⣄⠀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣇⣿⢸⣼⢻⠀⢸⠀⣼⡾⡏⣿⣷⡇⠀⣿⣙⠁⣼⡇⢰⢠⡆⣤⣠⡄⢠⡀⠀⣠⣄⡀⠀⣀⣀⡀⣤⢠⡄⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
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⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠁⠛⠺⠁⠇⡟⢿⢰⡷⢿⢠⡇⢸⠀⠀⣿⡼⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⣘⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢺⣿⣿
⣿⣿⣿⣧⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡟⠻⠿⠿⠿⣿⣶⣶⣶⣿⣥⣤⣶⣀⣀⣠⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
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⣿⣿⣿⣿⣀⠀⠈⡉⢩⣼⢧⢘⢛⢐⠒⣒⡒⣰⡇⠠⠤⠀⠄⡤⠀⢀⠀⢀⡀⠈⡛⡘⣿⢿⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⡐⠁⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2993

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The "Gold" Rule: Taking Money for
Reputation Laundering and Openwashing Under the "Linux"
Banner⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025,
updated Apr 16, 2025


Seller of expensive toilet paper, Jim Zemlin (lying for a fee)


Old:


    * Three_Years_After_Openwashing_Its_Patents_Panasonic_Gives_These_Patents
      to_Patent_Trolls
    * No,_Panasonic_Did_Not_Open-Source_Anything_(Another_Example_of
      Openwashing_for_PR)
 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Jim_Zemlin_makes_$_by_openwashing_corporations_and_letting
                       them_buy_control_over_projects⦈_


The Linux_Foundation is rogue and hours_ago_we_reminded_readers_that_seats_on
the_Board_of_Directors_are_literally_for_sale. The Foundation openly admits so!
It also sells Microsoft more seats than it is allowed. Rule-breaking for
Microsoft? Not a problem when_you_work_with_Bill_Gates...


Welcome to the_"Big_Club", Jim Zemlin. We await your Gates photo_op.


Yesterday we saw a new press release from the Linux Foundation [1], saying that
"Panasonic Automotive Systems Joins the Linux Foundation as a Gold Member", so
we've just checked the Board of Directors page. Not only does it show that
another Microsoft employee was added to the Board but there's a new "Panasonic
- Gold Director":


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


Gold! Gold! Always_believe_in_bribes. █


_____


§ Linux Foundation Press Release/s⠀➾


   1. ⚓ Panasonic_Automotive_Systems_Joins_the_Linux_Foundation_as_a_Gold
      Member [Ed: Buying_a_board_seat?]⠀⇛


           The Linux Foundation, the nonprofit organization enabling mass
           innovation through open source, welcomes Panasonic Automotive
           Systems Co., Ltd (PAS) as a Gold Member of the foundation. PAS
           was established in April of 2022 as an operating company
           responsible for the automotive systems business of the
           Panasonic Group's operating company system, and is helping to
           create comfortable, safe, and secure automobiles.


    * LLM_Slop_Says_Slop_is_"coming_for_white-collar_jobs._Microsoft’s_layoffs
      are_just_the_start"
    * In_Some_Countries_the_Largest_OEMs_Already_Dump_Microsoft_Windows


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣭⢩⠻⣽⡟⣭⢻⣭⢹⢩⣹⢩⣽⣹⡙⢻⢍⢹⣩⠇⣭⢹⢹⣭⢹⢩⣽⣿⢫⡝⣭⢹⢩⡏⣭⡟⣭⢻⣭⢯⣹⢩⡏⡏⡍⡏⣭⢋⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣞⣵⣿⣿⣶⣿⣶⣾⣶⣾⣾⣿⣷⣷⣾⣶⣾⣶⣷⣿⣾⣾⣿⣾⣖⣼⣿⣷⣾⣶⣾⣾⣇⣶⣿⣶⣿⣿⣶⣾⣷⣷⣷⣶⣷⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⡟⣟⡟⣟⣿⡇⡟⠟⣿⡏⡟⡟⣟⡟⣟⣿⡏⡏⣻⠻⠛⠟⣛⣻⢻⡇⣛⠟⣿⢛⡿⣿⢟⣿⣻⢻⢻⢻⢹⢛⡟⣟⡇⣿⢟⡟⣻⢻⠻⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣷⣷⣿⣷⣷⣿⣷⣷⣿⣿⣷⣷⣷⣿⣗⣓⣿⣷⣷⣿⣾⣿⣷⣿⣿⣾⣷⣿⣶⣿⣞⣰⣿⣿⣿⣾⣾⣾⣾⣾⣾⣷⣷⣷⣿⣿⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⠩⠭⠭⠍⠭⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢸⡇⠧⠸⠸⠆⠧⠇⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⢻⡏⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣷⣾⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠛⠑⠊⠊⠐⠈⠂⠀⠛⠛⠛⠐⠀⠛⠛⠓⠀⣿⣿⣿⣿⣿⣯⣤⣤⣤⣬⣮⣤⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⣥⣭⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣤⣬⣥⣧⣧⣮⣴⣤⣿⣭⣮⣽⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣽⣥⣬⣤⣤⣶⣧⣬⣤⣤⣤⣼⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⡀⠸⡤⠤⠀⠀⠘⠠⣤⠤⢤⡼⠶⢦⢸⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣴⣤⡄⠀⠀⠀⠀⠀⣿⣿⠤⢤⠭⠠⠷⠀⠀⣤⣤⡀⠘⠤⠴⢧⡔⠼⢸⣿⡇⠀⠀⠀⣼⣗⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⠿⠇⠀⠀⠀⠀⣿⣿⠶⠶⠶⠞⠀⠀⠀⠙⣿⣁⠀⠰⠶⠞⠒⢶⣾⣿⡇⠀⠀⠀⢺⠹⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡆⠀⣿⣘⣛⡿⣙⡂⠃⢰⣤⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠒⠂⠐⢲⠂⠀⠘⡋⢻⢿⠃⠀⠒⠒⠚⠛⢻⣿⡇⠀⠀⠀⠀⡿⢻⡃⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⡇⢰⣿⣿⣿⣷⠽⡗⠀⠸⣿⠀⠀⣾⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡦⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⠂⠀⠀⠐⢾⠏⠀⠀⠒⠓⠒⠐⢸⣿⡇⠀⠀⠀⠀⠐⢷⣥⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⡇⢸⣿⠈⢿⣷⠊⠁⣤⠀⣿⠀⠀⣼⣿⡿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣭⣿⠏⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠒⠒⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⣿⠀⠉⠀⠀⢸⣿⣷
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢸⣿⡇⠀⠀⠀⠀⠀⣀⣤⣷⠆⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⢸⣿⡇⠀⠀⠀⠀⢸⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐⠃⣠⣾⡿⠁⠀⣿⣿⠀⠀⠀⠀⠛⠀⠘⠘⠉⠁⠐⠃⠘⠀⠀⠀⢸⣿⡇⠀⠀⠋⠂⠀⠀⠀⠁⠀⠐⠒⠊⠈⠂⠀⢸⣿⡇⠀⠀⠀⠀⠃⠘⠈⠂⠈⠒⠊⠋⠂⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣀⣀⣐⣐⣒⣀⣂⣂⣀⣠⣾⣿⣋⣐⣀⣀⣻⣿⣀⣀⣀⣘⣂⣀⣀⣐⣀⣁⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣀⣀⣀⣀⣈⣀⣀⣀⣂⣀⣀⣀⣀⣀⣸⣿⣇⣀⣀⣐⣂⣀⣐⣂⣀⣀⣒⣀⣀⡀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⡟⠛⢻⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⣉⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⠀⢀⠘⣿⣿⣿⠁⡄⢸⣿⡟⢻⣿⡿⠟⠛⠛⢻⣿⠛⠟⠛⢻⡿⠟⠛⠛⠻⣿⣿⠟⠛⠛⠛⣿⣿⠟⠛⠛⠛⢿⣿⠛⠀⠛⠻⠋⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⠀⢸⡄⠹⣿⠃⣰⡇⢸⣿⡇⢸⣿⠁⢰⣿⣿⣿⣿⠀⣴⣿⣿⠁⢰⣿⣿⡆⠘⣿⡀⠛⠿⣿⣿⡇⢠⣿⣿⣧⠀⣿⣿⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⠀⢸⣷⡀⠋⢠⣿⡇⢸⣿⡇⢸⣿⡀⢸⣿⣿⣿⣿⠀⣿⣿⣿⡀⢸⣿⣿⠇⢠⣿⣿⣷⣦⠀⢹⡇⠘⣿⣿⡿⠀⣿⣿⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣤⣼⣿⣧⣤⣿⣿⣧⣼⣿⣧⣼⣿⣷⣤⣀⣀⣼⣿⣤⣿⣿⣿⣷⣤⣈⣁⣤⣾⣿⣄⣉⣁⣤⣾⣿⣦⣄⣁⣤⣾⣿⣿⣤⣿⣿⣷⣄⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣻⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣟⣛⣿⣿⣿⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣟⣿⣿⣿⣻⡟⠛⠛⠛⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡛⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⢿⠻⡉⠁⠀⠑⢶⠫⣺⣿⠟⠁⠊⠿⢿⣿⣿⣿⣿⣿⣟⣿⣷⣿⣷⣔⣛⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⢸⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡏
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠖⠀⠰⠖⠄⠰⠒⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠰⠦⠔⠴⠀⠠⠔⠦⠀⠰⠀⠀⠀⢸⣿⡇⠐⠤⠄⠂⠀⠂⠆⠀⠤⠆⠖⠹⣿⣦⠆⢸⣿⡇⠀⠀⠰⠆⠢⠀⠀⠀⠲⠂⠂⠰⠤⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠢⠠⠠⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⢸⣿⡇⠠⠀⠀⠠⠀⠀⠠⠄⠠⠄⠀⠀⠌⢿⣷⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣶⣿⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⣀⣀⠈⠙⣿⣿⣿⣿⣿⣿⣇⠈⢿⣷⡽⠀⣠⣄⣤⣠⣤⡀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣫⣟⣉⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠻⠟⠓⠄⢸⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣾⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⢯⡫⢿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣴⡀⢾⣷⣄⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠤⠰⠦⠠⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣷⣭⣏⣰⣒⡱⠜⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠿⠷⠋⢾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⢿⣿⣿⠆⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠶⠶⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣯⠻⠃⠌⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⡿⣿⣻⣉⠀⠀⢤⣤⠾⠀⢈⣙⣛⡿⣿⣿⣿⠃⠀⠀⠀⠀⠁⢸⡖⠱⣿⠻⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢠⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⡎⠁⡆⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣶⣄⡆⢁⣤⣾⣿⣿⣿⡟⠈⣿⣿⠀⠀⠀⠀⠀⠀⢸⠁⠀⠏⠀⠀⠙⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠙⠉⠉⢃⠎⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠘⡝⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠛⠀⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢰⣶⠖⠁⠀⠀⠀⠀⠀⢸⣿⡗
⣿⣿⣿⣿⣿⠚⠀⠀⠘⠛⠛⠛⠋⠛⠛⠙⠛⠛⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⢠⣤⠠⡀⡤⠀⣠⣤⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⡄⠀⡄⢤⠀⢄⢤⡀⢠⠀⠄⠀⢸⣿⡟⠛⠿⢷⡀⠀⢠⣤⠀⣄⡀⠄⠄⢠⠀⠀⢸⣿⡇⠀⠀⠀⣄⠀⡀⠀⠀⣤⢠⠀⣄⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⢄⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧

                    ䷩ 𝚕𝚒𝚗𝚎 3147

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/Trump_Authority_CA_With_a_Trump_NSA_is_All_About_Security_But_W.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/Trump_Authority_CA_With_a_Trump_NSA_is_All_About_Security_But_W.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Trump Authority (CA) With a Trump NSA is
All About Security, But Whose?⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025,
updated Apr 16, 2025


"CA/Browser Forum – a central body of web browser makers, security certificate
issuers, and friends – has voted to cut the maximum lifespan of new SSL/TLS
certs to just 47 days by March 15, 2029," said_The_Register_earlier_this_week.


Turning nasty yet? Not just yet? Do_you_fancy_Microsoft_giving_GOP-NSA_back
doors_(full_access)_into_everything,_including_all_Windows-running_PCs
everywhere_in_the_world? Nope, Apple is not_the_answer!


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


A "turnkey tyranny", as the NSA_whistleblower_Thomas_Drake_loved_to_call_it, is
what we have (and have long had) being constructed under our noses while GAFAM
literally_claps_for_Trump, which it_also_funded. Drake was ruined financially
and ended up working in an Apple store as a salesperson. Sort of ironic, right?


What about keys?


Keys you say?


Yes, certificates too.


Better to say it with pictures/animations:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Awesome,_so_now_I_don't_need_to_revoke_existing_certs,_I_can
         just_wait_for_them_to_expire_and_refuse_to_issue_newer_ones⦈_


You can see where this may be going, right?


Or, if you're an irrational optimist, just trust the self-professed "free
speech absolutist" (MElon) and his executive butler, Cheeto, who cracks down on
freedom of expression in the press, in universities etc. (while also censoring
government sites, removing pages deemed too "woke" for mentioning women or
indigenous people).


Stop outsourcing trust unless you truly can trust those in charge. █


    * Confirming_IBM_Shutdowns_and_Layoffs_Today
    * next


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⣀⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣷⣤⣴⢸⠀
⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣤⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠒⢿⡿⢷⡘⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠸⠁⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣠⣤⣶⣶⣶⣶⣦⣤⣤⣤⣦⣤⣴⣶⣆⢰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠶⠶⠶⠖⠉⠻⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡠⣼⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣤⣤⣤⣤⣧⣤⣤⣤⣤⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⠉⣉⠉⠉⠉⠍⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⢤⡙⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧⠀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡄⠀⠀⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠉⠉⡏⠁⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣨⣶⣈⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣶⣴⣿⣷⠀⠘⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣀⣠⡇⣶⣶⠶⣚⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠨⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠉⠉⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠄⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡀⠀⠛⢷⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣿⣿⣿⡟⠀⠀⠀⠀⠐⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⢠⣗⠀⠀⠰⣬⣭⣭⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠅⠀⠀⣀⡄⢰⠀⡸⠀⠀⠀⠀⠀⠀⠀⠼⠀⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⣴⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠒⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠛⣀⣠⡌⠿⠿⠤⣴⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣷⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⡿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣤⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠸⣿⣿⢟⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣶⠄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣧⠀⠀⠀⠀⣾⡆⠀⠀⠀⢲⡖⠀⠀⠀⢰⢷⠂⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀
⠀⠀⠛⠂⠀⠀⠀⠊⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠐⠲⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠺⢿⠿⡿⢿⣧⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⢿⣾⠿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀⢉⡰⠀⠉⠉⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠁⠀⢀⣴⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⢀⣚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡄⠀⠀⢠⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣷⠄
⠀⠀⠘⡿⡏⠀⠀⠀⢹⠿⠅⠀⠀⠈⠿⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢄⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡁⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡰⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣷⣿⠀⣿⠀⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣟⣧⣿⣿⣼⡓⠋⠛⠘⠘⣃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢶⣠⡴⢾⡏⣧⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢻⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣀⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⢿⣸⣟⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⣽⣿⡏⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⢉⡉⠁⠉⢉⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣽⣥⣯⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⢈⣃⡐⠁⢰⠟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣴⡤⠀⠀⠀⢠⣧⠀⠀⠀⠀⣶⠆⠀⠀⠀⢾⡖⠀⠀⠀⢰⢷⠀⠀⠀⠐⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀
⠀⠐⠛⠂⠀⠀⠀⠋⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣶⡆⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠀⠀⠄⠀⠐⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⢚⢿⠟⠻⢿⣧⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⢿⡿⠿⣇⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠈⣉⡴⠀⠉⠉⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠁⠀⣠⣾⡏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣤⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢠⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠄⠀⠀⢠⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣼⡤⠀⠀⠀⢴⣧⠄
⠀⠀⠈⡿⡏⠀⠀⠀⢹⠿⠅⠀⠀⠈⠿⠿⠀⠀⠀⠨⠿⠏⠀⠀⠀⠹⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠀⠀⠀⠐⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣤⢤⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣬⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣿⣿⠀⣿⠁⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣧⣿⣿⣜⠓⠋⠛⠘⣘⣳⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢤⣰⡾⢿⡏⣥⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣁⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⢿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢬⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡍⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⢉⡉⠁⠉⢩⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣽⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⠄⠀⢈⣃⠐⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⡀⠀⠀⠀⣤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣧⠀⠀⠀⠠⣶⠄⠀⠀⠀⢾⡆⠀⠀⠀⢰⣷⠂⠀⠀⠐⣾⡂⠀⠀⠀⠺⡖⠀⠀⠀⢰⠷⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀
⠀⠀⠉⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡆⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠀⠛⢻⡛⠛⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⣻⠿⠿⣧⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣩⡔⠀⠁⢠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡁⠀⢀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣴⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣾⡦⠀⠀⠀⢶⣷⠂
⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠇⠀⠀⠀⠿⠻⠀⠀⠀⠈⠟⠇⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣅⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣬⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⡀⢠⣤⣄⢠⣤⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣷⣿⠀⣿⠁⢸⡇⣿⣿⢸⡇⣿⣿⣏⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⣧⣿⣿⡜⠓⠋⣛⣘⣘⣗⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⢻⡿⢻⡿⣿⣿⢿⡿⢻⣿⣿⣿⣷⢶⣸⡿⢿⡏⣥⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢻⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣁⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⢿⣸⣟⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣯⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡍⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣭⣥⣯⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⣀⠀⠨⡧⠜⠡⡸⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣴⡄⠀⠀⠀⢤⡦⠀⠀⠀⠠⣦⠄⠀⠀⠀⣼⡤⠀⠀⠀⢴⣧⠀⠀⠀⠠⣶⡆⠀⠀⠀⣾⡖⠀⠀⠀⢰⣷⠂⠀⠀⠐⡾⡂⠀⠀⠀⠺⠖⠀⠀⠀⠰⠷⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⠄⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠈⠟⣿⡉⣙⣿⡆⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢛⣿⠟⠛⣥⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⡎⠀⠀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢠⠀⠀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⡀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣠⣀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣴⣀⠀⠀⠀⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣧⠄⠀⠀⠠⣾⡤⠀⠀⠀⢴⣷⠄⠀⠀⠰⣾⡖⠀⠀⠀⢲⣷⠂
⠀⠀⠈⠿⠏⠀⠀⠀⠸⠿⠇⠀⠀⠀⠿⠻⠀⠀⠀⠈⠛⠇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢈⣭⣅⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⡀⢠⣤⣄⣠⣤⡺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣷⣿⠀⣿⠁⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣧⣿⣿⡘⢓⣋⣛⣘⣸⣷⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢻⡿⣿⣿⢿⡿⢻⣿⣿⡿⣿⢿⣹⡿⢿⡏⣥⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢻⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣀⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⢿⣸⣟⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣼⣿⣽⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⣽⣿⡍⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡍⠉⠉⠈⡁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣭⣥⣯⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠂⠀⠨⡧⠌⠠⡘⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣼⡄⠀⠀⠀⢴⣦⠀⠀⠀⠰⣷⠆⠀⠀⠀⣾⡖⠀⠀⠀⢲⣷⠀⠀⠀⠐⣷⠂⠀⠀⠀⡾⠖⠀⠀⠀⠰⠗⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡷⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⣀⣀
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠈⠈⢩⣝⣏⣉⣻⣷⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣹⡿⠛⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠁⠀⢠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⡄⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣄⡀⠀⠀⣀⣴⣀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⠄⠀⠀⢠⣷⡤⠀⠀⠀⢴⣷⠀⠀⠀⠰⣾⡆⠀⠀⠀⢶⣷⠂
⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠅⠀⠀⠀⠟⠻⠀⠀⠀⠸⠛⠇⢀⠀⣠⡘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢈⣭⣅⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⡀⢠⣤⣄⣠⣤⡺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣿⣿⠀⣿⠃⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣟⣧⣿⣿⣼⣗⣋⣛⣼⣾⡗⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢿⣹⡿⢿⡏⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣀⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣾⣿⣽⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⣽⣯⡍⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡍⠉⠉⠈⡁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣯⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⢨⡥⠌⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⡀⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣾⡆⠀⠀⠀⢲⣷⠀⠀⠀⠐⣷⠂⠀⠀⠀⡾⡖⠀⠀⠀⠰⠗⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡆⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠈⣭⣻⣉⣍⣿⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣋⣻⡟⠻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡎⠁⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣠⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣄⠀⠀⠀⣀⣤⣀⠀⠀⣀⣠⣆⡀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⠀⠀⠀⢤⣶⡤⠀⠀⠀⢴⣦⠄⠀⠀⠠⣾⡆⠀⠀⠀⢶⣷⠂
⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠅⠀⠀⠀⠟⠿⠀⠀⠀⠸⠛⠇⠀⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠁⠁⠀⠀⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣤⣤⣤⣤⣴⣶⣶⣶⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⡀⢠⣤⣄⣠⣤⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⣿⣾⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣟⣧⣿⣿⣼⣗⣋⣿⣼⣾⡗⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢻⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢿⣹⡿⢿⡏⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣀⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⢿⣸⣟⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡍⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣽⣥⣯⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⢄⠀⢨⡇⠌⠀⡸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣄⡀⠀⠀⠀⣴⡄⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣧⠄⠀⠀⠠⣾⡄⠀⠀⠀⢴⡶⠀⠀⠀⢰⣷⠂⠀⠀⠀⡾⡆⠀⠀⠀⠺⠖⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⢻⢿⣏⣭⣻⣷⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣙⣿⠟⣿⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠏⠉⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢠⡀⠀⢀⣴⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣤⡀⠁⣰⣦⣠⣄⡀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⠀⠀⠀⢤⣶⡄⠀⠀⠠⣼⡦⠀⠀⠀⢤⣷⠄⠀⠀⠀⣾⡶⠀
⠀⠀⠹⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠯⠀⠀⠀⠸⠻⠇⠀⢹⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠘⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⣿⣾⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⣿⣼⣗⣯⣿⣼⣿⡃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⡿⣿⢿⣹⡿⢿⡏⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⣿⡀⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⢿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣼⣿⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⣽⣽⡍⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣽⣥⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠄⠀⢸⡅⠎⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣆⡀⠀⠀⠀⣴⡄⠀⠀⠀⢤⣦⠀⠀⠀⠠⣴⠄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣧⠀⠀⠀⠠⣾⡄⠀⠀⠀⢶⡖⠀⠀⠀⢰⣷⠀⠀⠀⠐⣾⡆⠀⠀⠀⠺⠖⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⢺⣿⣿⣩⣝⣿⡆⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⣿⡿⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣶⣶⡾⠉⢁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣄⠀⠀⣠⣾⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣴⣤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣷⠄⠀⠀⠀⣾⡶⠀
⠀⠀⠹⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠯⠀⠀⠀⠸⠻⠇⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠁⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⣿⣼⣷⣯⣿⣼⡟⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⡿⣿⢿⣹⡿⢿⡇⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⣿⣅⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⣿⣸⣟⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡍⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⢩⡉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣽⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢆⠀⠀⢸⡅⠊⠐⢸⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⡀⠀⠀⢀⣰⡀⠀⠀⠀⢠⣦⠀⠀⠀⠠⣤⡄⠀⠀⠀⢴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⢰⣷⠀⠀⠀⠀⣾⡆⠀⠀⠀⢺⡖⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀
⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠄⠀⠐⠒⠀⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⡿⣿⣯⣽⣿⡆⠀⠐⠒⠊⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣛⣻⡿⢿⣧⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣬⣶⣶⣾⠟⠁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⠀⠀⣠⣾⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠉⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⢀⣴⣤⠀⠀⠀⢤⣦⡄⠀⠀⠠⣴⣤⠀⠀⠀⢤⣷⠄⠀⠀⠠⣼⡦⠀
⠀⠀⢹⠿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠅⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠉⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡿⣿⢿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣧⣿⣿⣼⣷⣯⣿⣼⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢹⣿⣿⡿⣿⢿⣹⡿⢿⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣀⣿⢻⣼⡟⠚⣷⡿⢸⣿⡇⣿⢿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣾⣿⣿⣭⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣽⡍⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⣉⠉⠁⠉⢩⡉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢼⣿⣿⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢆⡀⠀⢘⡃⠈⡐⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⡀⠀⠀⠀⣰⣄⠀⠀⠀⢠⣦⠀⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⠠⣦⠄⠀⠀⠀⣼⡄⠀⠀⠀⢰⣧⠀⠀⠀⠐⣷⠂⠀⠀⠀⣾⡖⠀⠀⠀⢲⠗⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀
⠀⠐⠙⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣦⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢺⡛⣿⠻⢿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⣻⡿⢿⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣯⣶⣶⣿⠛⢩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡀⠀⢀⣴⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢘⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⠀⠀⢚⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣤⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣦⣤⠀⠂⠀⠀⠀⠀⠀⢠⣦⡄⠀⠀⠠⣴⣤⠀⠀⠀⢤⣶⡄⠀⠀⠠⣴⣦⠄⠀⠀⠠⣶⡄⠀⠀⠀⢴⡦⠀
⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠯⠀⠀⠀⠸⠟⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠂⠀⠀⠀⠋⠑⠀⠀⠀⠘⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣤⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣇⣿⢿⣿⣷⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⣧⣿⣿⣼⣿⣯⡟⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⢻⡿⢻⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢿⣹⡦⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⣿⣀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣯⡉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣽⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⢄⠀⢨⡇⠜⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⡀⠀⠀⠀⣰⣄⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⠠⣧⠄⠀⠀⠀⣼⡄⠀⠀⠀⢰⡶⠀⠀⠀⢰⣷⠂⠀⠀⠐⡾⡆⠀⠀⠀⠺⠖⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀
⠀⠐⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠂⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢸⠿⢿⡿⡻⣿⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡾⠿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣹⣡⣭⣽⡾⢋⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⢀⣾⡿⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⠀⠀⢯⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣤⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⣄⡀⠊⠁⠀⠀⠀⠀⣤⣦⡄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣷⠄⠀⠀⠠⣼⡦⠀⠀⠀⢤⣷⠄⠀⠀⠀⣾⡶⠀
⠀⠀⠨⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠯⠀⠀⠀⠸⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣤⢄⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣟⣧⣿⣿⣼⣿⡯⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢿⣹⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣁⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣟⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡍⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣽⣥⣯⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⢄⠀⢨⡅⠌⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⡀⠀⠀⢀⣴⡀⠀⠀⠀⣤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡆⠀⠀⠀⢰⣷⠀⠀⠀⠐⣶⠂⠀⠀⠀⡾⡆⠀⠀⠀⠲⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢰⣿⣿⣿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣵⣼⣷⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣙⣗⣐⣛⣿⠿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠋⠙⠉⣰⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⢿⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⣀⠀⠐⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣦⠄⠀⠒⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⢠⣴⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣾⡖⠀
⠀⠀⢹⠿⠅⠀⠀⠀⠽⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠚⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣤⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣴⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣟⣧⣿⣿⣼⣿⠏⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢹⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢻⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢿⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣬⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣁⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣷⣾⣿⣿⣿⣿⡍⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⢹⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣾⣿⣽⣥⣯⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⠀⠀⢜⠅⠊⢈⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣆⡀⠀⠀⢀⣴⡀⠀⠀⠀⣤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡆⠀⠀⠀⢰⣷⠀⠀⠀⠐⣶⠂⠀⠀⠀⡾⡆⠀⠀⠀⠲⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢰⣿⣿⡿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣼⣷⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣙⣗⣐⣛⣿⠿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠋⠙⠉⣰⣿⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⢿⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⣀⠀⠐⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠀⠀⠀⠀⢠⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣦⠄⠀⠂⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⢠⣴⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣾⡖⠀
⠀⠀⢹⠿⠍⠀⠀⠈⠽⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠚⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣤⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣴⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣿⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣟⣧⣿⣿⣼⣿⠏⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢹⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢿⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣬⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⣿⣄⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣷⣾⣿⣿⣿⣿⡍⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⢹⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣾⣿⣯⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⠀⠀⢜⠅⠊⢈⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⡀⠀⠀⢀⣴⡀⠀⠀⠀⣤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡆⠀⠀⠀⢰⣷⠀⠀⠀⠐⣶⠂⠀⠀⠀⡾⡆⠀⠀⠀⠲⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢰⣿⣿⡿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣼⣷⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣙⣗⣐⣛⣿⠿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠋⠙⠉⣰⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠘⢿⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⣀⠀⠐⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣦⠄⠀⠒⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⢠⣴⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣾⡖⠀
⠀⠀⢹⠿⠏⠀⠀⠀⠽⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠚⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣤⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣴⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡏⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣷⣟⣧⣿⣿⣼⣟⠏⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢹⣛⣧⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢿⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣬⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⣿⣁⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⡍⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⢹⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣾⣿⣽⣥⣯⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⠀⠀⢜⠅⠊⢈⠚⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣆⡀⠀⠀⢀⣴⡀⠀⠀⠀⣤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡆⠀⠀⠀⢰⣷⠀⠀⠀⠐⣶⠂⠀⠀⠀⡾⡆⠀⠀⠀⠲⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢰⣿⣿⡿⠿⣿⡀⠀⠐⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣼⣷⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣙⣗⣐⣛⣿⠿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠋⠙⠉⣰⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⢿⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣃⣀⠀⠐⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣦⠄⠀⠂⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⢠⣴⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣾⡖⠀
⠀⠀⠹⠿⠅⠀⠀⠀⠽⠿⠁⠀⠀⠨⠟⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠚⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣤⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣴⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡏⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣿⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣟⣧⣿⣿⣼⣿⠏⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢹⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⡿⣿⢿⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣬⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣄⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣼⣽⣯⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⡍⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⢹⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣾⣿⣿⣥⣯⣭⣿⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⠀⠀⢜⠅⠊⢈⠚⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣆⡀⠀⠀⢀⣴⡀⠀⠀⠀⢤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡆⠀⠀⠀⢲⣷⠀⠀⠀⠐⣶⠂⠀⠀⠀⡾⡆⠀⠀⠀⠲⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢰⣿⣿⡿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣼⣷⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣙⣗⣐⣛⣿⡿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠋⠉⠉⣴⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⢿⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⣀⠀⠐⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣦⠄⠀⠒⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⢠⣴⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣾⡖⠀
⠀⠀⢹⠿⠍⠀⠀⠈⠽⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠚⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣤⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⡀⢠⣤⣄⢠⣴⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡏⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣷⣟⣧⣿⣿⣼⣿⠏⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢹⣛⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⡿⣿⢿⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢤⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣬⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣅⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣯⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⡍⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⢹⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣾⣿⣯⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⠀⠀⢜⠅⠊⠈⠚⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⡀⠀⠀⢀⣴⡀⠀⠀⠀⢤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡆⠀⠀⠀⢰⣷⠀⠀⠀⠐⣶⠂⠀⠀⠀⡾⡆⠀⠀⠀⠲⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢰⣿⣿⡿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣼⣷⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣙⣗⣐⣛⣿⠿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠘⠋⠙⠉⣰⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⢿⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⣀⠀⠐⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣦⠄⠀⠒⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⢠⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣾⡖⠀
⠀⠀⢹⠿⠍⠀⠀⠈⠽⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠚⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣤⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣴⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣾⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣟⣧⣿⣿⣼⣿⠏⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢹⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⡿⣿⢿⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣬⢿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⡅⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣟⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣼⣿⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⡍⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⢹⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣾⣿⣯⣧⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⠀⠀⢜⠅⠊⠈⠚⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠦⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⢠⣦⠀⠀⠀⠀⣶⠄⠀⠀⠀⢴⡆⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠾⠿⠿⠟⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⢀⣴⣶⣿⣷⡄⠐⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⡟⠛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢤⡶⠿⢿⣿⣿⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠰⠠⠼⣿⢯⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡟⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣿⣤⣀⠈⠀⠀⠀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣦⡄⠀⠀⠠⣴⣤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣼⡤⠀
⠀⠀⢙⡿⡏⠀⠀⠀⢹⢿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⣿⠟⠛⠒⠒⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢈⣥⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡶⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣟⣧⣿⣿⣼⣿⡏⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢯⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣬⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⣿⣁⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⢿⣸⣟⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣾⣿⣿⣭⣿⣿⣿⣷⣾⣿⣿⣿⣿⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⣉⠉⠁⠉⢩⡉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣽⣥⣯⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⢘⡃⠘⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣄⡀⠀⠀⠀⣠⣀⠀⠀⠀⢠⣦⠀⠀⠀⠠⣴⡄⠀⠀⠀⢤⡦⠀⠀⠀⠠⣦⠄⠀⠀⠠⣼⡄⠀⠀⠀⢴⡦⠀⠀⠀⠠⣶⠀⠀⠀⠀⣾⡆⠀⠀⠀⢲⡖⠀⠀⠀⢐⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠀⠠⠄⠀⠀⠐⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⢀⣴⣶⣿⣷⡄⠐⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⡟⠛⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢤⡶⠿⢿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠰⠠⠼⣿⢯⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣿⣦⣀⠈⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠠⣴⣤⠀⠀⠀⢤⣦⡄⠀⠀⠠⣴⡦⠀⠀⠀⢤⣷⠄⠀⠀⠀⣼⡦⠀
⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠯⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢿⠟⠛⠒⠒⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠓⠀⠀⠀⠘⠉⠂⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢈⣧⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡏⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⣿⣼⣿⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢯⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣆⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⢿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢬⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣽⣿⣿⣿⣷⣾⣿⣿⣿⡏⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣿⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⢄⠀⢨⡁⠌⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣆⡀⠀⠀⠀⣰⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⠄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣧⠄⠀⠀⠀⣶⡄⠀⠀⠀⢶⡖⠀⠀⠀⢰⣷⠂⠀⠀⠐⡾⡂⠀⠀⠀⠺⠖⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀
⠀⠘⠙⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⢠⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⣟⣋⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡐⠶⠾⠛⢻⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠸⠵⠶⠿⢿⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣖⣀⠈⠀⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣷⠄⠀⠀⠀⣾⡶⠀
⠀⠀⠨⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠯⠀⠀⠀⠸⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⢿⣿⠿⠧⠐⠂⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⠁⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢘⣧⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⡀⢠⣤⣄⣠⣤⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣿⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣧⣿⣿⣼⣿⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢻⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢥⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣁⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⢿⣸⣟⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣼⣿⣿⣽⣿⣿⣿⣿⣾⣿⣿⣿⠋⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⢩⡉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣿⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⠀⢨⡅⠊⠐⠘⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣦⠄⠀⠀⠀⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀
⠀⠈⠛⠅⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠑⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⢀⣴⣾⣿⣿⣦⠀⠐⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢻⣋⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⠶⢾⡛⢛⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠟⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠺⠵⠶⠿⢯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢙⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣴⣾⣥⣀⠐⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣄⠀⠀⠀⣀⣦⡀⠀⠀⢀⣰⣄⠀⠀⠀⢠⣦⡄⠀⠀⠠⣴⣦⠀
⠀⠀⠘⣿⡟⠀⠀⠀⢻⢿⡋⠀⠀⠈⡿⢿⠁⠀⠀⢹⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠯⠭⠄⠀⠀⠀⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠣⠀⠀⠀⠘⠛⠂⠀⠀⠀⠚⠛⠀⠀⠀⠐⠉⠂⠀⠀⠀⠋⠙⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣧⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡴⣶⢶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⣿⣼⣿⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢯⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⣅⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⢿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⢉⠉⠁⠉⢩⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣯⣥⣯⣯⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⢘⡃⡐⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠀⠀⠀⠀⢠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣰⡄⠀⠀⠀⢤⣦⠀⠀⠀⠠⣤⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⡦⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀
⠀⠈⠛⠅⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠑⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⢀⣴⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⢻⣋⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⠻⢿⣟⢛⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠻⢷⠚⠿⢯⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣥⣴⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣄⠀⠀⠀⣀⣦⡀⠀⠀⢀⣰⣄⠀⠀⠀⢀⣦⡀⠀⠀⠀⣴⣦⠀
⠀⠀⠐⣿⡖⠀⠀⠀⢺⣿⡃⠀⠀⠈⣿⣿⠁⠀⠀⢙⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠯⠭⠄⠀⠀⠀⠀⠀⠀⠸⠻⠅⠀⠀⠀⠟⠫⠀⠀⠀⠘⠛⠂⠀⠀⠀⠛⠓⠀⠀⠀⠐⠛⠂⠀⠀⠀⠊⠙⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣧⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡴⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡇⣿⢿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣧⣿⣿⣼⣿⠋⠛⠘⠘⠃⠛⠳⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⠙⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣿⢯⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣤⢿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⣿⣇⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⢿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣾⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡍⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⢉⠉⠁⠉⢩⡍⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⢸⣿⣿⣧⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⡀⠀⢘⣃⡐⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⡀⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣦⠄⠀⠀⠀⣴⡤⠀⠀⠀⢤⡦⠀⠀⠀⠠⣶⠀⠀⠀⠀⣼⡆⠀⠀⠀⢲⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠑⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢰⣿⣿⣿⣿⣿⡀⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣿⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣦⣼⣿⣏⣀⣀⣀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠙⠛⠉⠋⣬⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⢀⣴⡀⠀⠀⠀⣤⣦⠀⠀⠀⢠⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣼⡤⠀
⠀⠀⢹⢿⡇⠀⠀⠈⡿⢿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠐⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢸⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢰⣿⣿⢸⡇⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⣿⣼⠓⠋⠛⠘⠘⠃⠛⠳⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢹⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⣿⣧⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢤⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣼⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⣿⡅⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⢿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⣉⠉⠁⠉⣩⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣿⣿⣽⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠄⡀⠀⣙⡁⠊⠀⡺⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣰⣀⠀⠀⠀⢠⣦⠀⠀⠀⠠⣴⡄⠀⠀⠀⢤⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⢠⣷⠀⠀⠀⠀⣾⡆⠀⠀⠀⠺⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠀⠀⠀⠐⠛⠀⠀⠀⠀⠊⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢀⣿⣿⣿⡿⡿⡇⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡾⢷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣷⣾⣿⣿⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠋⠉⠉⣼⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⣶⣿⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣄⠀⠀⠀⢀⣦⡀⠀⠀⠀⣴⣤⠀⠀⠀⢤⣶⡄⠀⠀⠠⣴⣦⠄⠀⠀⠠⣶⡄⠀
⠀⠀⢹⢿⠁⠀⠀⠈⡿⠿⠀⠀⠀⠹⠿⠏⠀⠀⠀⠽⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠘⠛⠂⠀⠀⠀⠋⠙⠀⠀⠀⠘⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣤⢤⣤⣄⣤⡄⣤⡄⣤⡄⠀⢘⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣴⡶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢸⣿⣿⢸⡇⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣧⣿⣿⡜⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⢹⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⡿⣧⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣼⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⣿⠀⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⢿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣷⣾⣿⣿⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⣭⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣿⣿⣽⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡠⠀⠀⣛⠠⠃⠄⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⠀⠀⠀⢀⣤⡀⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⠄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣦⠀⠀⠀⠀⣶⠄⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀
⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠛⠛⠂⣿⣿⢿⡿⢿⢿⠀⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⣈⠉⠀⢁⣴⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣿⣿⡿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣦⡀⠀⠀⢀⣰⣄⠀⠀⠀⢠⣦⡄⠀⠀⠠⣴⣤⠀⠀⠀⢤⣦⠄⠀
⠀⠀⢻⢿⠃⠀⠀⠈⡿⣟⠀⠀⠀⢹⠿⡏⠀⠀⠈⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠓⠀⠀⠀⠘⠙⠂⠀⠀⠀⠋⠑⠀⠀⠀⠈⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢘⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡶⣶⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢹⣿⣿⢸⡇⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⣿⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⠋⣹⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⣿⠃⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢤⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣼⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣿⣿⡿⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⣨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣿⣾⣿⡇⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⡉⠉⠁⠉⣍⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⠉⣿⣿⣿⣧⣯⣭⣿⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⣛⢠⠃⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⡦⠀⠀⠀⠠⣦⠄⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀
⠈⠟⠏⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠓⠀⠀⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⣿⣿⣿⣿⣿⡇⠀⠠⠤⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣼⣿⣿⣯⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⣘⡿⠿⠟⠛⠟⠋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⢸⡦⠀⣠⣴⡟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣄⠀⠀⠀⣀⣦⡄⠀
⠀⠐⣾⣷⠂⠀⠀⢐⣿⡟⠀⠀⠀⢻⢿⡃⠀⠀⠈⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠏⠀⠀⠀⠸⠻⠀⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣯⣄⣠⣤⡀⣀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡏⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢹⣿⣿⢸⡇⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⡟⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠃⠙⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⠛⠛⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⡅⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢤⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣾⡇⣿⣿⡇⠀⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡯⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⣍⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⢹⣿⣿⣿⣧⣿⣿⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⠀⠀⠀⣟⠠⠂⢄⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⡦⠀⠀⠀⠠⣦⠄⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀
⠀⠟⠏⠀⠀⠀⠸⠻⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠓⠀⠀⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⣿⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⢀⢸⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⢘⡻⠿⠛⠻⠛⠋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⢰⡦⠀⣠⣴⡟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣦⡄⠀
⠀⠐⣾⣷⠂⠀⠀⠐⣿⡟⠀⠀⠀⢻⢿⡃⠀⠀⠈⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠏⠀⠀⠀⠸⠻⠀⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣯⣄⣠⣤⡀⣀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣤⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢹⣿⣿⢸⡇⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⣇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⡟⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠙⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⠛⠛⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣿⡅⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡤⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡯⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⢈⡉⠉⠁⠉⣝⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⢹⣿⣿⣿⣧⣯⣽⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⣟⠠⠂⢄⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣀⡀⠀⠀⢀⣠⡀⠀⠀⠀⢠⣦⠀⠀⠀⠠⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣴⠄⠀⠀⠀⢴⡤⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀
⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⢀⣛⡀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠒⠶⠶⠶⠶⠶⠶⠶⠂⢰⣿⣿⣿⣟⣛⡏⠀⠐⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣴⣀⠀⠀⠀⣠⣆⡀⠀⠀⢀⣴⣄⠀⠀⠀⣤⣦⡄⠀⠀⠠⣴⡤⠀⠀
⠀⢺⣿⡇⠀⠀⠈⣿⢿⠃⠀⠀⠘⡿⡏⠀⠀⠀⢹⠿⠁⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣽⣅⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⢠⣶⡶⣶⢶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⡏⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢠⣿⣿⢸⡏⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⣅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⢻⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢡⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡼⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣬⣍⣁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⣈⠉⠉⠁⣩⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⣽⣿⣿⣿⣧⣯⣽⣯⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⣙⣁⠊⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠀⠀⠀⣀⣆⠀⠀⠀⠀⠀⠂⠀⠀⠀⢤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢴⡦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡆⠀⠀⠀⢲⣖⠀⠀⠀⠐⣷⠂⠀⠀⠀⡾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠀⠰⣤⣄⡈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠄⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⣾⣿⣿⣿⠿⢿⠃⠀⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠿⠛⠃⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣮⣄⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⣤⣦⡄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣷⠄⠀⠀
⠈⡿⢿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠅⠀⠀⠈⠿⠯⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣬⣟⣡⣤⡀⠀⣄⣤⢠⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⣴⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⣻⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡤⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡼⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⣾⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⢁⡈⠉⠉⠁⣍⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⣽⣿⣿⣿⣷⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⡀⠀⠀⣫⠐⠁⠢⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⢠⣀⠀⠀⠀⣠⣆⠀⠀⠀⢀⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⠄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣦⠀⠀⠀⠀⣶⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠁⣄⣀⠀⠘⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⢲⣾⣿⣿⣿⣿⡷⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⢻⣿⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣬⣄⠀⠀⠀⠀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣦⡀⠀⠀⢀⣰⣤⠀⠀⠀⢤⣦⡄⠀⠀⠠⣴⣤⠀⠀⠀⢤⣦⠄⠀⠀
⠀⣻⢿⠁⠀⠀⠈⡿⣏⠀⠀⠀⢹⠿⡏⠀⠀⠈⠿⠿⠁⠀⠀⠨⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠂⠀⠀⠀⠋⠓⠀⠀⠀⠘⠙⠂⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣤⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣤⣟⣫⣥⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⣰⣶⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⠛⣻⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡧⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡼⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣼⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⡈⠉⠉⠁⣍⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⣽⣿⣿⣿⣧⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⣛⢠⠃⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠂⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣰⣀⠀⠀⠀⢀⣆⠀⠀⠀⠀⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⠄⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀
⠝⠋⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠳⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠂⠀⠀⠀⠋⠁⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠄⠀⠉⠀⠀⠀⠀⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⢤⣿⣿⣿⣿⣷⡀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣝⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣗⢼⠟⠛⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣄⠀⠀⠀⣀⣦⡀⠀⠀⢀⣰⣄⠀⠀⠀⢀⣦⡄⠀⠀
⠀⢺⣷⠂⠀⠀⠐⣾⣟⠀⠀⠀⢹⣿⡇⠀⠀⠈⣿⢿⠁⠀⠀⠙⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠟⠏⠀⠀⠀⠸⠛⠅⠀⠀⠀⠟⠓⠀⠀⠀⠘⠛⠂⠀⠀⠀⠛⠓⠀⠀⠀⠘⠉⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣬⣟⣻⣭⡁⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⣠⣴⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⡀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⣅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⠛⢻⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢣⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡼⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣥⡈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⡈⠉⠉⠁⣍⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠈⠉⣽⣿⣿⣿⣷⣿⣯⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣀⠀⠀⣛⢠⠂⢄⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⠀⠀⠀⠠⣴⡄⠀⠀⠀⢤⡤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠟⠏⠀⠀⠀⠹⠻⠀⠀⠀⠀⠀⠈⢂⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠑⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠦⠀⠈⠀⠀⠀⠀⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⣴⣿⣿⣿⣿⣦⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⡭⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡢⣼⠟⠋⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠋⠙⠉⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣆⠀⠀⠀
⠐⣾⣷⠂⠀⠀⢒⣿⡟⠀⠀⠀⢻⢿⠃⠀⠀⠘⡿⡟⠀⠀⠀⢹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠨⠟⠇⠀⠀⠀⠹⠻⠀⠀⠀⠀⠛⠇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣼⣟⣻⣯⡁⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⣠⣴⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⡏⣧⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⠛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢠⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣾⡇⢻⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⢁⡈⠉⠉⢁⡍⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠈⢩⣽⣿⣿⣿⣷⣿⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⠀⠀⢘⣟⡠⢃⠢⡗⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠈⡀⠀⠀⢀⣤⡀⠀⠀⠀⣰⡄⠀⠀⠀⢤⣦⠀⠀⠀⠠⣤⡄⠀⠀⠀⢴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣴⠄⠀⠀⠀⢼⡄⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠉⢄⣀⠀⠉⠂⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠿⠷⠆⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠗⠒⠒⠀⠒⠒⢲⣾⣿⣿⣿⣷⡄⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣝⡉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣗⢶⠟⠉⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣬⣅⠀⠀⠀⠀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣴⣀⠀⠀⠀⣠⣦⡀⠀⠀⢠⣴⣤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣼⡤⠀⠀⠀
⢹⣿⡇⠀⠀⠈⣿⢿⠁⠀⠀⠈⡿⡏⠀⠀⠀⢹⠿⠅⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⣄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣿⣟⣫⣭⡀⢠⣄⣤⢄⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣶⣶⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣼⣿⡟⣷⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⢛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢨⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⢻⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⣁⠈⠉⠉⣡⠉⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠈⣽⣽⣿⣿⣿⣷⣯⣽⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠤⡀⠀⣙⡁⠊⠀⡺⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠴⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣦⠀⠀⠀⠠⣴⡄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⢠⣷⠀⠀⠀⠀⣾⡆⠀⠀⠀⠺⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠈⢄⣀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠴⠶⠾⠿⠿⠟⠂⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⣲⣿⣿⣿⣿⣷⡄⠘⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡾⢿⣖⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣯⣗⢺⠋⠉⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⣔⠀⠀⠀⠀⠀⠀⢀⣰⣄⠀⠀⠀⢀⣦⡀⠀⠀⠀⣴⣦⠀⠀⠀⢤⣶⡤⠀⠀⠠⣴⣦⠄⠀⠀⠠⣶⡄⠀⠀⠀
⢹⢿⠁⠀⠀⠈⡿⢿⠀⠀⠀⠹⠿⠏⠀⠀⠀⠽⠿⠁⠀⠀⠈⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠘⠛⠂⠀⠀⠀⠋⠙⠀⠀⠀⠘⠉⠃⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢀⣿⣟⣫⣥⡀⢠⣄⣤⢄⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣴⣶⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣼⣿⡟⣷⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠈⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⢛⣻⣽⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢨⡿⣿⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢻⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⣁⠈⠉⠉⣥⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⣯⣽⣿⣿⣿⣥⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡠⠀⠀⣛⠀⠃⠄⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣆⠀⠀⠀⢀⣤⡀⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣴⠄⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀
⠯⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⢀⠓⠄⠀⠘⠛⠀⠀⠀⠀⠛⠂⠀⠀⠀⠊⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠦⠀⠈⠁⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⣾⣿⣿⣿⣿⣦⠀⠲⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⡢⣿⠛⠉⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠀⠚⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣔⡨⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣦⡀⠀⠀⢀⣰⣄⠀⠀⠀⢀⣦⡀⠀⠀⠀
⢺⣷⠂⠀⠀⠐⣾⣗⠀⠀⠀⢻⣿⡏⠀⠀⠈⣿⣿⠁⠀⠀⢘⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠟⠯⠀⠀⠀⠸⠻⠅⠀⠀⠀⠟⠻⠀⠀⠀⠘⠛⠃⠀⠀⠀⠛⠓⠀⠀⠀⠐⠛⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⣄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢘⣿⣟⣻⣭⡀⢠⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣴⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣼⣿⡏⣧⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⢛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢨⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣾⡇⢿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡗⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⣅⠉⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠈⣯⣿⣿⣿⣿⣧⣯⣽⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢀⠀⠀⣻⢀⠂⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣆⠀⠀⠀⠀⣤⡄⠀⠀⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠯⠀⠀⠀⠸⠿⠁⠀⠀⠀⠅⠀⠠⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠊⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⠶⠄⠈⠛⠁⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⢤⣾⣿⣿⣿⣿⡆⠀⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣽⣋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣛⠤⡿⠋⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣐⡨⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣄⠀⠀⠀⣀⣤⡀⠀⠀⠀
⢶⣷⠆⠀⠀⠐⣾⡖⠀⠀⠀⢲⣿⡖⠀⠀⠀⣾⣷⠂⠀⠀⢘⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠿⠯⠀⠀⠀⠹⠿⠅⠀⠀⠀⠿⠯⠀⠀⠀⠸⠛⠅⠀⠀⠀⠟⠋⠀⠀⠀⠘⠛⠂⠀⠀⠀
⠈⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⢘⣿⣟⣻⣯⡀⢠⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⣤⣤⡶⣦⢶⣴⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⡏⣷⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢸⣿⣿⢸⣷⣿⣿⣿⣿⣿⡀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⣅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠃⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠁⠛⠉⠙⢛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⣿⣿⣿⢿⡿⣻⣧⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢸⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⣁⠉⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠈⣿⣽⣿⣿⣿⣷⣯⣽⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠂⠀⠀⠿⠀⠆⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠈⠿⠏⠀⠀⠀⠉⠀⠀⠀⠀⠈⠟⠅⠀⠀⠀⠝⠋⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠂⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣼⠁⠘⣷⡦⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠀⠀⢰⣿⣿⣿⣿⣷⡄⠀⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣋⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣛⡠⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⢶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠛⡛⠛⠛⠋⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀
⣿⡤⠀⠀⠀⢶⣷⠆⠀⠀⠐⣾⡶⠀⠀⠀⢲⣿⡖⠀⠀⠐⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢹⢿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠟⠃⠀⠀⠀⠘
⠉⠁⠀⠀⠀⠉⠈⠀⠀⠀⠀⠁⠉⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠸⢿⣿⣟⣫⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⣤⣤⡤⣤⢤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣼⣿⡏⣷⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠘⢚⡷⣍⣿⢸⡇⢠⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⣇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠉⠛⠉⢹⣛⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢫⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢻⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢹⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢉⠁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⣾⣿⣽⣿⣿⣿⣷⣿⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡀⠀⠀⠻⠇⡰⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣰⡄⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠈⠿⠇⠀⠀⠀⠙⠋⠀⠀⠀⠸⠛⠁⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣄⠀⢰⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⢤⣾⣿⣿⣿⣿⡷⠀⠤⠴⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠓⠒⠂⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣧⣬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣓⡺⣟⠁⠀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠙⠫⡛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀
⣿⡖⠀⠀⠐⣾⣷⠂⠀⠀⠐⣿⡖⠀⠀⠀⢲⣷⠂⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠽⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠈⠟⠇⠀⠀⠀⠸⠻⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘
⠈⠁⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⣿⢿⣿⣟⣡⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣤⣤⡤⣤⢤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣼⣿⡏⣷⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠟⢙⡷⣍⣿⢸⡇⢸⣿⣿⢸⣷⣿⣿⣿⣿⣿⡀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⣅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠃⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠉⠛⠁⢹⣛⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⣿⣿⣿⢿⡿⣫⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢻⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⣉⠁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⣾⣿⣽⣿⣿⣿⣧⣿⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⡀⠀⠀⠻⠂⠔⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣆⡀⠀⠀⠀⣴⡀⠀⠀⠀⣠⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⣼⣿⢿⡿⡿⣿⠁⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢷⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠻⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣿⣯⣭⣙⠇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠓⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠈⠋⢠⡉⠉⠉⠀⡘⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣦⡀⠀⠀⠀⣰⣄⠀⠀⠀⢤
⣿⡖⠀⠀⠀⢺⣿⠃⠀⠀⠘⡿⣟⠀⠀⠀⢹⣿⡏⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⠻⠁⠀⠀⠀⠟⠏⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠂⠀⠀⠀⠋⠓⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⣿⣿⣯⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣴⣶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣷⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣼⣿⡏⣧⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠋⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⢘⣛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⣿⣿⣿⢿⡿⢫⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢰⢫⡿⣿⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⢿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⢉⠁⠈⠉⢩⡁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⣼⣿⣽⣿⣿⣿⣥⣯⣽⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡄⡀⠀⢸⡃⠔⠠⡸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⠀⠀⠀⠠⣴⡄⠀⠀⠀⢴⡤⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠟⠏⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⣾⣿⢿⢿⠿⡟⠀⠠⠤⠴⠾⠿⠟⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣀⣘⢿⣯⣭⣙⠧⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠀⠀⠻⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠙⠋⣆⠉⠉⠉⢀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣤⣤⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣄⠀⠀⠀⢠
⣿⡖⠀⠀⠀⢲⣷⠂⠀⠀⠐⣿⣟⠀⠀⠀⢸⣿⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠁⠀⠀⠈⠟⠏⠀⠀⠀⠸⠛⠀⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣤⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⣿⢟⣥⣄⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣼⣿⡏⣧⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠋⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⢘⣛⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢰⢻⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⢿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠈⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢩⡃⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⢼⣯⣽⣿⣿⣿⣧⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡄⠀⠀⢸⡇⠐⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣆⠀⠀⠀⠀⣰⡀⠀⠀⠀⢤⡤⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠀⠀⠀⠈⠛⠃⠀⠀⠀⠙⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠐⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⠠⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⣸⣿⡿⣿⠿⢿⠀⠤⠤⠤⠴⠶⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡾⠿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣫⠄⣛⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⢡⡈⠉⠉⠁⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠂⠠⠞⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣤⣶⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣄⠀⠀⠀⢀
⣿⡖⠀⠀⠀⢲⣷⠂⠀⠛⠛⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠸⠻⠁⠀⠀⠀⠟⠃⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⣼⡟⢁⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣤⣤⡶⣶⢶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣼⣿⡏⣧⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠎⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣷⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⣅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠃⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠁⠛⠁⢘⣛⣻⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢻⣧⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢫⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣷⡎⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢉⡃⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⢸⣿⣽⣿⣿⣿⣧⣯⣯⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠸⠇⠰⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⠀⠀⠀⠠⣴⡄⠀⠀⠀⢤⡤⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠟⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⣼⣿⡿⡿⡿⢿⠀⠤⠤⠤⠴⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡿⠿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣘⡻⣿⣭⡭⡛⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣧⡈⠉⠉⢁⡜⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠰⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠠⣶⣷⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣦⡀⠀⠀⠀⣰⣄⠀⠀⠀⢠
⣿⡖⠀⠀⠀⢲⣿⠂⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠁⠀⠀⠀⠟⠏⠀⠀⠀⠸⠛⠀⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⣄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⣼⠏⢀⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣼⣿⡏⣧⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠠⣿⣿⢸⣷⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡧⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠛⠃⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⢘⣛⣻⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⣻⣧⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢰⢫⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡎⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢩⡁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⢨⣯⣽⣿⣿⣿⣧⣯⣯⣿⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⢸⡃⠐⠠⡸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣰⡀⠀⠀⠀⢠⣦⠀⠀⠀⠠⣤⠄⠀⠀⠀⢴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⢼⡄⠀⠀⠀⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠓⠀⠀⠀⠐⠉⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠷⠶⠖⠒⠒⠂⢸⣿⡟⢿⠿⠿⠀⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⢿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡛⠿⣯⣭⣍⠃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢱⣄⠉⠉⠉⣰⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢶⣿⣷⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣴⣄⠀⠀⠀⣤⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤
⣿⡇⠀⠀⠈⣻⢿⠁⠀⠀⠈⡿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣠⣿⣿⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡟⠀⢀⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣶⣶⣶⡶⣶⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡏⣷⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⣛⣿⣷⣿⣿⣿⣿⣿⣧⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠛⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⢸⣛⣻⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⡶⢰⡾⢿⡿⣿⣿⢿⡿⢻⣧⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢫⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣷⡏⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⣉⠁⠈⠉⣩⠁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⣼⣯⣽⣿⣿⣿⣥⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠤⠀⠀⣙⣃⠈⡐⡼⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣰⡀⠀⠀⠀⢠⣦⠀⠀⠀⠠⣤⠄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⢼⡄⠀⠀⠀⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠓⠀⠀⠀⠐⠉⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠂⣼⣿⡿⣿⢿⠿⠐⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣾⠿⢷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡻⢿⣋⠭⢉⢆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶
⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣧⡀⠉⠉⢉⣼⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠂⠐⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣶⣿⣷⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣴⣀⠀⠀⠀⣠⣆⡀⠀⠀⢀⣴⣄⠀⠀⠀⣤⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤
⣿⡇⠀⠀⠈⣻⢿⠁⠀⠀⠈⡿⡏⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣼⡏⠀⢀⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣶⣶⣶⡶⣶⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣤⣼⣿⡏⣧⣿⣿⡇⣿⠎⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣳⣿⣿⣿⣿⣿⣧⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠛⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⢸⣛⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⡾⢹⡿⢹⡿⣿⣿⢿⡿⢻⣧⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢻⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣭⣬⣭⣭⣽⣿⣿⣿⣷⡏⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⣉⠁⠈⠉⣩⠁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⣼⣿⣽⣿⣿⣿⣥⣯⣯⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠤⠀⠀⣙⣃⠈⡐⡼⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣆⠀⠀⠀⠀⣤⡀⠀⠀⠀⣴⡤⠀⠀⠀⢤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠀⠀⠀⠈⠛⠁⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠂⠀⠀⠀⠊⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⢀⣿⣿⢿⣿⠿⠄⠤⠤⠤⠤⠤⠴⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣶⣷⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣛⣒⠫⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⢻⡀⠘⠛⠒⢣⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡦⠀⢴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢠⣶⣿⣷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀
⣿⡖⠀⠀⠐⢾⣷⠂⠀⠀⠐⣾⡖⠀⠀⠀⢲⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠟⠇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣼⡇⠀⢀⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣤⣴⡶⣶⢶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠃⠛⠃⣛⣿⣿⣧⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠛⠃⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠁⠛⠁⢸⣛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢱⡤⢠⡤⣤⣺⢿⡿⢻⣧⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢫⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣬⣽⣭⣭⣿⣿⣿⣿⣏⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⣉⠃⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⣼⣯⣽⣿⣿⣿⣷⣯⣯⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡤⠀⠀⠻⠇⠐⠠⣸⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⠀⠀⠀⠀⣴⡄⠀⠀⠀⢤⡦⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠟⠋⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠓⠀⠀⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⣀⣀⣀⠀⡠⠠⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⢠⣿⣿⢿⣿⠿⠀⠤⠤⠤⠤⠤⠴⠾⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣶⠷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⡻⢿⣿⣛⣒⠋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡀⠘⠛⠛⣣⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢰⣶⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣄⠀⠀⠀⣀⣦⡀⠀⠀⠀⣰⣄⠀⠀⠀⢠
⣿⡖⠀⠀⠀⢲⣿⡂⠀⠀⠐⣿⣿⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠀⠟⠯⠀⠀⠀⠸⠛⠇⠀⠀⠀⠟⠓⠀⠀⠀⠘⠛⠂⠀⠀⠀⠚⠓⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣼⡇⠀⢀⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢰⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠃⠛⠃⠛⢁⣻⣧⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠛⠃⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⣛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢠⡤⣤⠀⢴⡾⢻⣿⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢫⡿⣿⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⡇⣿⢰⣸⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣌⣩⣿⣯⣭⣿⣿⣷⣿⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢩⡁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⢸⣿⣽⣿⣿⣿⣧⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⡀⠀⢘⡇⡰⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⡤⠴⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣆⠀⠀⠀⢀⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⢠⣧⠀⠀⠀⠀⣶⡄⠀⠀⠀⢺⡖⠀⠀⠀⢲⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠴⠶⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⣼⣿⣟⢿⠿⠇⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠋⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣷⡿⠷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣍⠿⠿⢟⡉⠈⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠙⠋⠉⠉⠉⠉⢹⣄⠀⠈⠉⢩⡌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠐⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⢠⣴⣄⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡦⠀⠀⠀⢰
⠿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣿⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⡀⢠⣤⣾⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣼⣿⡟⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢀⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠛⠃⠛⠁⢛⣧⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⢸⣛⣿⣽⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡤⣤⠀⢤⡤⢸⣯⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢫⡿⣿⣿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⡇⣿⠀⢸⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⠉⠉⠉⢀⣾⣷⣾⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⣉⠁⠈⠉⢩⠁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⣼⣯⣽⣿⣿⣿⣥⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣶⣦⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢖⠀⠀⢘⡅⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⢠⣷⠄⠀⠀⠀⣼⡆⠀⠀⠀⢰⣷⠀⠀⠀⠐⣷⠂⠀⠀⠀⡾⡖⠀⠀⠀⢲⢗⠀⠀⠀⠐⠿⠂⠀⠀⠀⠾⠆⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣴⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⢠⣿⣿⠟⣻⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⡟⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⠛⠻⣯⣍⣈⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠷⠶⠾⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣄⡀⠈⠉⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⢘⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⣄⡀⠀⠀⢀⣠⣄⡀⠀⠀⢀⣴⣀⠀⠀⠀⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠄⠀⠀⠠⣾⡤⠀⠀⠀⢶⣷⠀⠀⠀⠰⣾⡖⠀⠀⠀⢲⣷⠂⠀⠀⠐⣾⡖⠀⠀⠀⢺
⠻⠇⠀⠀⠀⠿⠻⠀⠀⠀⠈⠛⠇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣤⡄⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣯⡄⠀⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠀⣤⣀⣠⣼⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢀⣿⣿⢸⡿⣿⢿⣿⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠃⠛⠁⠛⡇⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⢸⣛⣻⣽⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡦⣤⠀⢤⡤⢸⣧⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢫⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⡇⣿⠀⢸⡇⣿⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⡍⠉⠉⠀⢸⣿⣾⠉⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⣉⠁⢉⠉⢉⠉⠉⠈⠁⠈⠁⠉⠉⣬⣯⣽⣿⣿⣽⣥⣯⣭⣭⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣀⣀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣒⠀⠀⠬⠄⠁⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠾⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⠀⠀⠀⢲⢷⠀⠀⠀⠐⠿⡂⠀⠀⠀⠺⠏⠀⠀⠀⠸⠿⠁⠀⠀⠈⠟⠇⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⢰⣿⣿⣿⣿⡄⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣩⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⣿⣿⡉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⢶⠉⠉⠻⣦⣀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⢀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣋⠀⣠⣿⣿⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀
⣴⣦⠄⠀⠀⠠⣾⡤⠀⠀⠀⢴⣷⠄⠀⠀⠠⣾⡶⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡗⠀⠀⠀⢻⢿⠁⠀⠀⠘⡿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀
⠋⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣀⢠⣤⣠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣽⡄⠀⢀⣤⣄⣠⣦⡀⢠⣄⣤⢈⣤⣄⣤⢠⡄⣤⠤⣤⣤⣤⣤⣟⣻⣿⡛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣾⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢸⣿⣿⢸⡏⣿⢿⣿⣿⣿⠀⣿⠃⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⠃⠛⠁⠛⠃⡛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⢛⣻⣽⣛⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢻⡿⣧⠀⢤⡤⢠⣼⡅⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡦⣴⢤⡤⣄⢤⡤⢤⡄⣤⢠⢨⡿⣿⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⠀⢸⡇⢸⣿⡇⠀⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣽⣭⠉⠀⠈⠁⣼⣯⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⡁⠉⠉⠈⣍⠉⠈⠁⠈⠁⠉⠉⠈⣭⣽⣿⣿⣭⣥⣭⣭⣭⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡆⠀⢀⣚⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡶⠀⠀⠀⢰⣷⠂⠀⠀⠐⡾⡖⠀⠀⠀⢲⢷⠀⠀⠀⠐⠿⠂⠀⠀⠀⠻⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠅⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⢰⣾⣿⣿⣿⡄⣀⣀⣀⣀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠤⠤⠤⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡀⢸⣿⣿⢙⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠉⠉⠛⣤⣀⠰⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⣀⣻⣿⡆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⣤⣦⡄⠀⠀⠠⣼⣤⠀⠀⠀⢤⣶⡤⠀⠀⠠⣴⣧⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣗⠀⠀⠀⢲⣿⡂⠀⠀⠀⣿⣟⠀⠀⠀⢸⠿⡃⠀⠀⠀⡿⢿⠀⠀⠀⠸⠿⠇⠀⠀⠀
⠘⠙⠀⠀⠀⠀⠋⠙⠀⠀⠀⠘⠉⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣀⡀⢠⣤⣠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣼⡅⠀⢀⣤⣄⣠⣦⡀⢠⣄⣤⢈⣤⣄⣤⢠⡄⣤⠠⣤⣤⣤⣤⣝⣻⣿⡛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢠⣿⣿⢸⡏⣿⢿⣿⣿⣿⠀⣿⠃⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃⠛⠁⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⢛⣻⣽⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⢻⡿⢻⡿⣿⠀⢤⡤⢠⣤⡇⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣆⡦⣤⢤⡤⣄⢤⡤⢤⡄⣤⢠⢨⡿⣿⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⠀⢸⡇⢸⣿⡇⠀⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣭⡏⠀⠈⠁⢨⣿⠁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⣁⠉⡉⠈⣉⠉⠈⠁⠈⠁⠉⠉⠈⣯⣽⣿⣿⣿⣥⣭⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡎⠀⠀⠒⠒⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⠀⠀⠀⠀⣴⡄⠀⠀⠀⢤⡤⠀⠀⠀⢠⣦⠀⠀⠀⠠⣴⠄⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠀⠀⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⡴⢶⣶⣶⣶⠶⡶⠶⠾⠿⠿⠿⠷⠷⠾⠿⠿⠿⠀⠀⢘⣿⣿⣿⣿⣦⠤⠤⠤⠤⠤⠤⠤⠾⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣥⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⢿⣿⣿⡿⠯⢙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⢻⡀⠀⠉⠶⠦⡜⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣴⣿⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣠⣄⠀⠀⠀⢀⣦⡀⠀⠀⠀⣠⣄⠀⠀⠀⢠⣴⡄⠀⠀⠀
⢺⣿⠃⠀⠀⠐⣿⣟⠀⠀⠀⢺⣿⡏⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠯⠀⠀⠀⠸⠿⠇⠀⠀⠀⠟⠻⠀⠀⠀⠘⠛⠃⠀⠀⠀⠛⠛⠀⠀⠀⠐⠛⠃⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣼⡇⠀⢀⣤⣄⣠⣤⡀⢠⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣼⣿⡏⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢘⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠛⠁⠛⠃⢛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠛⠃⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⢛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⡯⢤⡤⢠⣤⡌⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢨⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⡇⢸⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⡇⠈⠁⠈⢩⡇⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⣁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⠈⣿⣽⣿⣿⣿⣥⣯⣭⣯⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⣻⢀⠆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀
⠏⠀⠀⠀⠸⠿⠁⠀⠀⠈⠟⠇⠀⠀⠀⠙⠻⠀⠀⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠦⠀⠀⢸⣿⣿⣿⣿⡤⠤⠤⠤⠤⠤⠤⠤⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠓⠒⠐⠂⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣩⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⡍⠙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠀⠉⠉⠶⠤⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⠀⢀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⠀⣤⣿⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀
⣾⣷⠂⠀⠀⠐⣾⡖⠀⠀⠀⢲⣿⠂⠀⠀⠐⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠸⠻⠁⠀⠀⠀⠟⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀
⠉⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣽⡇⠀⢀⣤⣄⣠⣤⡀⢠⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⣤⣤⡶⣶⢶⣴⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢸⣿⣿⢸⣷⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⠁⠛⠃⢛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠛⠃⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠁⠛⠁⠘⣛⣿⣽⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⡿⢤⡤⢠⣤⡌⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢩⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⡇⢸⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⡇⠈⠁⠈⢩⡇⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⡅⠉⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⢨⣿⣽⣿⣿⣿⣥⣯⣯⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⠄⠀⠀⠿⠀⠆⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠷⠾⠷⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⠀⠀⠀⢰⢷⠀⠀⠀⠐⡿⠆⠀⠀⠀⠺⠏⠀⠀⠀⠸⠿⠁⠀⠀⠀⠿⠇⠀⠀⠀⠹⠋⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⣿⣿⡟⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣾⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠛⢣⣀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣄⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⣠⣿⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀
⣼⣦⠄⠀⠀⠠⣾⡦⠀⠀⠀⢶⣷⠆⠀⠀⠰⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⢻⢿⠁⠀⠀⠈⡿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠀⠀⠀⠀
⠛⠛⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⢠⣤⣠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣼⡅⠀⢀⣤⣄⣠⣤⡀⢠⣄⣤⢹⣤⣄⣤⢠⡄⣤⠤⣤⣴⣦⣤⣟⣻⣿⡛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢨⣿⣿⢸⡏⣿⢿⣿⣿⣿⠀⣿⠁⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣿⠛⠁⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⢛⣻⣽⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢻⡿⣿⣿⢤⡤⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣴⢠⡤⣄⢤⡤⢤⡄⣤⢠⢨⡿⣿⢿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⡟⢸⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣭⣿⣷⠈⠁⠈⢉⡇⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⢁⠈⠉⠉⠁⠉⠉⠉⣍⠉⠈⠁⠈⠁⠉⠉⠈⣯⣽⣿⣿⣭⣥⣯⣭⣯⣼⣷⣿⣷⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠀⠛⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠾⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀
⠗⠀⠀⠀⢸⠿⠀⠀⠀⠈⠿⠇⠀⠀⠀⠹⠿⠀⠀⠀⠈⠛⠁⠀⠀⠀⠟⠇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠾⠿⠿⠶⠿⠷⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣏⣹⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣾⣿⣿⣿⣟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠀⠉⠙⠣⣄⠀⠿⠿⠿⠿⠿⠿⠟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⣠⣽⣿⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀
⣴⣧⠄⠀⠀⠰⣾⡶⠀⠀⠀⢶⣷⠆⠀⠀⠐⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡏⠀⠀⠀⢹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠀⠟⠏⠀⠀⠀⠸⠛⠁⠀⠀⠀
⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⣤⣠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣬⡇⠀⢀⣤⣄⣠⣤⡀⢠⣄⣤⢙⣤⣄⣤⢠⡄⣤⠶⣤⣶⣦⣤⣟⣻⣿⡛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⠀⣿⣿⢸⡏⣿⢿⣿⣿⣿⠀⣿⠁⢸⡇⣿⣿⢸⡇⣿⣿⣏⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣟⣿⡛⠁⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⢛⣻⣽⣛⣧⣟⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢻⡿⣿⣿⢧⡤⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢤⣄⡤⣴⢠⡤⣄⢤⡤⢤⡄⣤⢠⢨⡿⣿⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⢸⡇⢸⣿⣏⠀⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣼⣿⣽⣭⣿⣿⠈⠁⠈⠉⣥⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⢁⠈⠉⠉⠁⠉⠉⠈⣉⠉⠈⠁⠈⠁⠉⠉⠈⣭⣽⣾⣿⣭⣥⣯⣭⣯⣼⣷⣿⣷⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⠛⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢠⣦⠀⠀⠀⠀⣴⡄⠀⠀⠀⢤⡦⠀⠀⠀⢠⣦⠄⠀⠀⠀⣴⡄⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠀⠀⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡤⠤⠤⢤⠤⠤⠴⠶⠶⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⢸⣿⣿⣿⣿⡤⠤⠤⠠⠄⠤⠤⠾⠿⠿⠿⠟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣩⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣾⣿⣿⣿⡿⠏⢉⣀⣀⣀⣀⣄⣀⣠⣤⣠⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠻⠿⠿⠛⠛⠛⠛⢿⠀⠀⠉⠰⠦⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡆⠀⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⢠⣴⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣦⠀⠀⠀⢠⣶⡄⠀⠀⠀
⢿⣿⠃⠀⠀⠐⣿⣿⠀⠀⠀⢺⣿⡏⠀⠀⠀⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠸⠿⠇⠀⠀⠀⠟⠛⠀⠀⠀⠘⠛⠃⠀⠀⠀⠛⠛⠀⠀⠀⠐⠛⠃⠀⠀⠀
⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⣿⠃⢀⣤⣄⣠⣤⡀⢠⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣤⣶⣶⡶⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠎⠀⢘⡷⣍⣿⢸⡇⠘⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⢛⣿⣽⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡤⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢸⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣾⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⡟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣽⣿⣿⡏⠁⠈⠉⠁⡆⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⠉⣁⠉⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠈⣿⣽⣿⣿⣿⣧⣿⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣀⠀⠀⣿⢀⠆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣄⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀
⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠇⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⠶⠄⠀⠀⢰⣿⣿⣿⣷⡤⠤⠤⠤⠤⠤⠤⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠒⠀⠀⠀⠀⠀⠀⠂⠒⠂⠐⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣉⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣿⣿⣿⣿⣏⠙⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤
⡷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣇⠈⠉⠛⢶⡄⠸⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⢀⣬⣿⣧⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀
⣾⣷⠂⠀⠀⢰⣿⡖⠀⠀⠐⣾⣷⠂⠀⠀⠐⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠈⠟⠇⠀⠀⠀⠸⠻⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠈⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⣿⠃⢀⣤⣄⣠⣤⡀⢠⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣄⣤⣤⡤⣤⢤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣼⣿⡏⣧⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠎⠀⢘⡷⣍⣿⢸⡇⢸⣿⣿⢸⣧⣿⣿⣿⣿⣿⠀⣿⡆⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⠃⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠉⠛⠁⠘⣛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡤⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢻⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⢀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⡏⠁⠈⠉⢁⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢉⡁⠉⠉⠉⠉⠉⠈⠁⠈⠁⠉⠉⢨⣿⣽⣿⣿⣿⣧⣯⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠘⠗⠠⠂⢠⡷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣴⡄⠀⠀⠀⢴⣦⠀⠀⠀⢠⣶⠄⠀⠀⠀⣼⡄⠀⠀⠀⢰⣷⠀⠀⠀⠠⣶⠆⠀⠀⠀⣾⡆⠀⠀⠀⢰⢷⠀⠀⠀⠐⡷⠂⠀⠀⠀⠾⠆⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣠⣴⣶⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠒⠒⠒⠚⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⢨⣿⣿⡿⣿⠗⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣸⣿⣿⣶⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣟⠻⠿⠿⡟⠓⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠙⠉⠉⠉⠉⠉⠉⢹⣀⠀⠀⠘⢓⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠰⣿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⢰⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⣤⡀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣴⣀⠀⠀⠀⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠄⠀⠀⢠⣾⡤⠀⠀⠀⢴⣷⠄⠀⠀⠰⣾⡶⠀⠀⠀⢶⣷⠂⠀⠀⠐⣾⡖⠀⠀⠀⢲
⠿⠇⠀⠀⠀⠿⠿⠀⠀⠀⠈⠿⠏⠀⠀⠀⠸⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⣿⠁⢀⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠀⣤⡄⢠⣴⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢀⣿⣿⢸⡿⣿⣿⣿⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⠁⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⢸⣛⣻⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢧⡤⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢸⢫⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣽⣿⣿⡏⠁⠈⠉⢱⠀⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢩⠁⢉⠉⢉⡉⠉⠈⠁⠈⠁⠉⠉⣼⣿⣽⣿⣿⣿⣥⣿⣭⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠨⠅⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⢶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⣾⡆⠀⠀⠀⢺⢗⠀⠀⠀⢰⠿⠀⠀⠀⠀⠿⠇⠀⠀⠀⠸⠿⠀⠀⠀⠈⠿⠁⠀⠀⠀⠟⠇⠀⠀⠀⠘⠻⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣴⣾⣿⣿⣄⣀⣀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⠟⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠉⠉⠙⠋⣉⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠀⢀⣻⣄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀
⣷⡄⠀⠀⠀⣴⣧⠄⠀⠀⠠⣾⡦⠀⠀⠀⢶⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠂⠀⠀⠘⣿⡟⠀⠀⠀⢻⢿⠁⠀⠀⠘⡿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹
⠛⠃⠀⠀⠀⠋⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀⣀⢠⣤⣠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⣼⠃⢀⣤⣄⣠⣤⡀⠀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠤⣤⣤⣤⣼⣟⣻⣿⡛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢘⡷⣍⣿⢸⡇⢀⣿⣿⢸⡟⣿⢿⣿⣿⣿⠀⣿⠃⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣷⣛⣿⡛⠁⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⢘⣛⣻⣽⣛⣧⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢻⡿⣿⣿⢷⡤⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢰⢫⡿⣿⢿⣿⣿⡍⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⢸⣿⡇⠀⣿⢻⣸⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣽⣭⣿⣿⡏⠁⠈⠉⢱⡇⠉⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢉⠁⡉⠉⢨⠉⠉⠈⠁⠈⠁⠉⠉⢨⣯⣽⣿⣿⣭⣥⣯⣭⣭⣼⣷⣿⣷⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢵⠀⠀⠒⠃⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⣼⡦⠀⠀⠀⢰⣷⠂⠀⠀⠀⣾⡆⠀⠀⠀⢲⣷⠀⠀⠀⠐⢿⠂⠀⠀⠀⠾⡆⠀⠀⠀⠸⠷⠀⠀⠀⠈⠿⠀⠀⠀⠀⠟⠇⠀⠀⠀⠘⠋⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⢀⣤⣤⣤⣴⣶⣶⣤⣦⣴⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠛⠓⠋⠋⠑⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⣼⣿⣿⠿⡟⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣦⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡙⠛⠛⠿⡋⠁⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣧⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠂⠀⢄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣄⠀⠀⠀⣠⣦⡄⠀⠀⠀⣴⣦⡀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷⡆⠀⠀⠀⣾⣷⠀⠀⠀⢰⣿⡆⠀⠀⠀⣾⣷⠀⠀⠀⠰⣿⡆⠀⠀⠀⢿⣿⠀⠀⠀⠸
⠟⠏⠀⠀⠀⠸⠟⠇⠀⠀⠀⠛⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⢸⢏⣤⣄⣠⣤⡀⢀⣄⣤⢀⣤⣄⣤⢠⡄⣤⠀⣤⡄⢠⣤⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠈⢘⡷⣍⣿⢸⡇⢨⣿⣿⢸⡇⣿⢿⣿⣿⣿⠀⣿⠇⢸⡇⣿⣿⢸⡇⣿⣿⣏⡅⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡗⠛⠃⠛⠛⠘⠓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠀⠘⣛⣻⣽⣛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡧⢠⣤⡄⠀⣤⢤⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⡤⠄⢠⡤⢴⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢫⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣸⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣽⣿⣿⣿⡅⠈⠉⠁⣰⡍⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⠉⠁⠈⠉⢉⡁⠉⠉⢈⡉⠉⠈⠁⠈⠁⠉⠉⢨⣯⣽⣿⣿⣿⣥⣯⣭⣯⣼⣷⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠰⠇⠈⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⠀⠀⠀⠀⣴⡀⠀⠀⠀⣤⣄⠀⠀⠀⢠⣦⠀⠀⠀⠀⣴⡄⠀⠀⠀⢴⡆⠀⠀⠀⢠⣧⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠙⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⢤⣤⡤⡤⠤⠤⣶⣶⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⣿⣿⣿⣿⣦⠀⠀⠄⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⡳⣿⣿⣿⣿⠿⠩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⣷⠀⠀⠈⠙⠦⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⢀⣤⣤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⣠⣆⡀⠀⠀⢀⣴⣀⠀⠀⠀⣠⣦⡀⠀⠀⢠⣴⣄⠀⠀⠀⣤⣦⠄⠀⠀⢠
⣿⣿⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿⠃⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠹⠻⠀⠀⠀⠈⠟⠇⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀
⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⢠⣤⢠⡄⣤⢠⣤⣤⡄⣠⣄⢀⣤⣄⣤⡄⣤⡄⣤⡄⠀⣿⣧⣄⣠⣤⡀⢀⣄⣤⢀⣤⡄⣤⢠⡄⣤⠀⣤⠀⢠⣤⣴⣶⣶⡿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣼⣿⡟⣷⣿⣿⡇⣿⠆⣻⣯⢸⡇⣿⣿⣿⣿⡇⣿⠆⠀⢙⡷⣍⣿⢸⡇⢸⣿⣿⢸⡇⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⣿⣿⢸⡇⣿⣿⣯⡅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠛⠃⠛⠛⠘⡓⠋⠛⠘⠘⠃⠛⠻⠇⠘⠓⠋⠙⠚⠁⠘⠃⠛⠘⠛⠋⠘⠛⠛⠋⠀⠛⠁⠘⣛⣿⣽⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢻⡿⢿⡿⣿⣿⢿⡿⢠⣤⡄⠀⣤⢦⣠⡤⢤⡄⣤⢠⣤⡄⣤⣠⢤⣤⠄⢠⡤⢤⣄⡤⣤⢠⡤⣄⢤⡤⢤⡄⣤⢠⢻⡿⣿⣿⣿⣿⡏⣿⠿⣿⢿⡽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡗⢸⣇⣿⣿⣼⡇⢸⣿⡇⠀⣿⢻⣼⡗⠚⣷⡿⢸⣿⡇⣿⣿⣸⣿⠂⢸⣟⢂⣿⣇⣿⢨⡿⣦⢸⡇⢸⡇⣿⣿⢸⡗⣿⠀⣿⣯⡅⣿⠂⣿⢻⡅⣿⡇⣽⢷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠈⠉⠁⢀⣏⠈⠉⠉⠁⠉⠁⠈⠉⠁⠉⠈⠉⢉⠁⠈⠉⢉⡅⠉⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⢸⣿⣽⣿⣿⣿⣧⣯⣽⣿⣼⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠈⡗⠠⠂⢠⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣠⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢠⣤⠀⠀⠀⠀⣤⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠿⠁⠀⠀⠀⠛⠇⠀⠀⠀⠘⠛⠀⠀⠀⠈⠛⠃⠀⠀⠀⠙⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⢾⣿⣿⣿⣧⠤⠤⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣩⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡳⣿⣿⣿⣿⣿⠍⣃⣀⣀⣀⣀⣀⣠⣀⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢳⠀⠈⠉⠉⠶⠄⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣋⠀⣠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢿⣿⣴⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣄⠀⠀⠀⣀⣦⡀⠀⠀⠀⣰⣄⠀⠀⠀⢠⣦⡀⠀⠀⠀⣴
⣿⠆⠀⠀⠸⣿⣷⠀⠀⠀⢻⣿⡇⠀⠀⠈⣿⣿⠂⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠅⠀⠀⠀⠿⠯⠀⠀⠀⠘⠛⠁⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠂⠀⠀⠀⠛
⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠀⠀⠀⣿⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣦⠀⠀⠀⢠⣶⠀⠀⠀⠀⣼⡆⠀⠀⠀⢰⣷⠀⠀⠀⠰⣾⠄⠀⠀⠀⢾⡆⠀⠀⠀⠰⢷⠀⠀⠀⠀⠿⠀⠀⠀⠀⠺⠇⠀⠀⠀⠸⠷⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣦⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠀⠀⠀⠂⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣹⣿⣿⠿⡿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠛⠛⠟⠿⠛⠃⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣧⡀⠀⠀⠈⡀⠈⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀
⣄⠀⠀⠀⣤⣦⡄⠀⠀⠀⣴⣦⡀⠀⠀⢠⣶⣄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣷⡆⠀⠀⠀⣾⣷⠀⠀⠀⢰⣿⡆⠀⠀⠀⣾⣷⠀⠀⠀⠰⣿⡆⠀⠀⠀⢾⣷⠀⠀⠀⠸⣿
⠏⠀⠀⠀⠘⠿⠇⠀⠀⠀⠻⠻⠀⠀⠀⠈⠛⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢸⡇⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠸⠇⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⠿⠀⠀⠀⠈⠿⠇⠀⠀⠀⠹⠏⠀⠀⠀⠸⠻⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣶⣤⣶⣤⣤⣤⣤⠄⠀⠀⠀⠰⣿⣿⣿⣷⡤⠤⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠖⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣋⣽⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⣿⣿⣟⡛⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣤⣤
⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡆⠉⠉⠉⠣⡤⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠐⠋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⢂⣐⠙⠇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰
⣷⠄⠀⠀⠰⣾⡶⠀⠀⠀⢶⣷⠆⠀⠀⠐⣾⣷⠀⠀⠀⢲⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠟⠏⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛
⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⢀⣀⡀⣘⣿⠿⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢘⣃⢀⣀⣀⡀⢀⣀⣀⣀⡀⣒⣲⣶⣖⣒⣒⣒⡒⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣼⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⡌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣝⣛⣛⣻⡛⠀⠚⠋⠓⢛⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⢃⣛⣛⣓⣓⣻⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⢿⣿⣿⢹⣿⡏⣷⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣎⣿⣷⠾⣾⣾⣹⣷⡶⢶⣶⣿⢛⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⢸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⡷⣭⣷⢸⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣷⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠮⠀⠄⠀⣬⠁⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠂⠀⠋⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⢶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣷⠄⠀⠀⠀⣾⡆⠀⠀⠀⢰⣷⠀⠀⠀⠐⣿⡆⠀⠀⠀⢾⠗⠀⠀⠀⠸⠿⠀⠀⠀⠀⠿⠇⠀⠀⠀⠻⠇⠀⠀⠀⠸⠿⠀⠀⠀⠀⠛⠃⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣶⣿⣶⣄⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠙⠉⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣾⣿⣿⠿⡟⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣴⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠙⠛⠛⠿⣏⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣦⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠔⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⢀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⣦⡄⠀⠀⢠⣼⣤⠀⠀⠀⣤⣶⡄⠀⠀⠀⣴⣦⡄⠀⠀⢠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢻⣿⣝⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢲⣿⡆⠀⠀⠀⣾⣷⠀⠀⠀⢰⣿⡆⠀⠀⠀⢿⣿⠀⠀⠀⠸⣿⡇⠀⠀⠀⢿
⠿⠁⠀⠀⠀⠟⠛⠀⠀⠀⠘⠛⠃⠀⠀⠀⠛⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣀⠀⣀⠀⣀⣀⠀⣀⡀⣀⣾⣿⣇⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣛⢁⣀⣀⡀⢀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⡀⣘⣛⣛⢻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⣿⢘⣻⣿⡇⣿⣿⠁⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠘⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣛⣛⣻⣿⠀⠚⠋⠓⠋⡙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⢃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣷⣷⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣎⣿⣷⠶⣿⣿⣹⣷⡶⢾⣶⣿⢛⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣷⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⡇⠀⠈⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⢁⠀⠀⠀⣾⠁⡀⠀⣨⠁⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠿⠀⠁⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣴⠄⠀⠀⠀⣴⡤⠀⠀⠀⢠⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠓⠒⠒⠒⠂⠀⠀⠀⣽⣿⣿⠿⡷⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⣿⣿⣿⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠙⠻⠿⢿⣿⠟⠒⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⢹⣷⡀⠀⠀⠀⠛⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡌⠁⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠈⣘⢻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣦⡀⠀⠀⢀⣴⣄⠀⠀⠀⣠⣦⡄⠀⠀⠠⣴⣤⠀⠀⠀⢤⣧⡄⠀⠀⠠⣼
⣿⠃⠀⠀⠘⡿⡟⠀⠀⠀⢹⠿⡏⠀⠀⠈⠿⠿⠁⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠛⠓⠀⠀⠀⠘⠙⠂⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣀⣀⣤⣄⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣘⢟⣀⣀⡀⢀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⡀⣐⣒⣚⢻⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣿⠀⣿⢘⣻⣿⡇⣿⣿⠛⢹⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⢰⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣛⣛⣿⣿⡇⠚⠋⠓⠋⢙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⢃⣛⣛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣿⠁⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣎⣿⣷⠾⣿⣿⣹⣷⡶⢿⣶⣿⢿⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⡇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⣿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⠀⠈⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⢈⡁⠀⠀⠀⣮⠁⠀⠀⢈⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⣂⠀⠀⣛⠠⠃⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣦⠀⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⢠⣦⠄⠀⠀⠀⣼⡄⠀⠀⠀⢴⣦⠀⠀⠀⠰⣷⠆⠀⠀⠀⣾⡆⠀⠀⠀⢲⣷⠀⠀⠀⠐⢷⠂⠀⠀⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⢀⣀⣀⣠⣤⣤⣠⣤⣤⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠖⠲⠖⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠂⠀⠀⠀⣼⣿⣿⡟⡿⠋⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣴⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣌⠙⠛⠛⠿⢟⠋⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣤⡀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢙⠂⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⢾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⡀⠀⠀⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢈⣻⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡤⠀⠀⠀⢤⣷⠄⠀⠀⠠⣾⡦⠀⠀⠀⢲⣷⠆⠀⠀⠐⣾
⠿⠁⠀⠀⠨⠿⠏⠀⠀⠀⠹⠿⠅⠀⠀⠀⠟⠻⠀⠀⠀⠸⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀
⣶⣶⣶⣶⣶⣶⣦⣤⣄⠀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣀⣤⣶⣆⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢻⣁⣀⡀⢀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⡀⣚⣟⣛⢛⣿⣿⣟⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⠀⣿⢘⣻⣿⡇⣿⣿⠙⢹⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠸⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣛⣛⣿⣿⡆⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⢃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣿⡇⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣎⣿⣷⠾⣿⣿⣹⣷⡶⢷⣶⣿⢛⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⡆⠈⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢨⡅⠀⠀⠀⣮⠁⡀⠀⣈⠁⠀⠀⠀⠀⠁⠀⠠⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⡯⠐⠁⢢⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⡖⠀⠀⠀⢲⣷⠂⠀⠀⠐⡾⡆⠀⠀⠀⠺⢗⠀⠀⠀⠸⠿⠀⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠀⠀⠀⠈⠻⠁⠀⠀⠀⠟⠇⠀⠀⠀⠙⠋⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣄⣄⣠⣀⣤⣀⣀⣀⡀⢀⡀⠀⠀⠀⠰⣿⣿⣿⣧⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠤⠄⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢸⣿⣿⣏⣹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣦⡀⠈⠉⠉⠡⠤⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣦⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠤⠀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄
⣤⠀⠀⠀⣤⣦⡄⠀⠀⠠⣴⣦⠄⠀⠀⢤⣷⡤⠀⠀⠀⢴⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⡻⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⣾⣗⠀⠀⠀⢲⣿⡃⠀⠀⠀⣿⣟⠀⠀⠀⢹⠿⡃⠀⠀⠈⠿⠟⠀⠀⠀⠸⠿
⠃⠀⠀⠀⠘⠙⠂⠀⠀⠀⠋⠙⠀⠀⠀⠈⠉⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣷⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀
⣿⣿⣿⣿⣿⣿⣶⣶⣦⡀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣰⣿⣿⣇⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢘⣁⣀⡀⢀⣀⣀⣀⡀⣀⣀⢤⣄⣀⣀⣀⡘⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⣿⢘⣻⣿⡇⣿⣿⠙⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠘⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣛⣛⣿⣿⡆⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣷⣿⡏⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣾⣾⣹⣶⡶⢷⣶⣿⢛⣿⣿⢹⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⡄⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣷⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣷⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠁⢸⡎⢁⠀⢠⡄⠀⠀⠀⠀⠀⠁⠀⢱⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢵⡢⢀⠐⠂⡂⠈⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⡆⠀⠀⠀⢲⣷⠀⠀⠀⠐⣾⡆⠀⠀⠀⡺⡖⠀⠀⠀⢰⢷⠀⠀⠀⠐⠾⡆⠀⠀⠀⠻⠟⠀⠀⠀⠸⠿⠁⠀⠀⠈⠟⠇⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢠⠀⢸⣿⣿⣏⣹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠈⠉⠉⠩⠤⢶⣶⣶⣶⣶⣶⣶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠍⠁⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⣠⣦⡀⠀⠀⢠⣴⣤⠀⠀⠀⢤⣶⡄⠀⠀⠠⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⢿⣿⠀⠀⠀⠀⠀⠠⠆⠀⠀⠐⣾⡶⠀⠀⠀⢲⣷⠂⠀⠀⠐⣾⡗⠀⠀⠀⢲⣿⠂⠀⠀⠀⡿⡟⠀⠀⠀⢹⠿
⠇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠓⠀⠀⠀⠘⠋⠃⠀⠀⠀⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣴⣾⣿⣇⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢘⣃⣀⡀⢀⣀⣀⣀⡀⣀⣀⢀⣀⣀⣀⣀⡘⣛⣛⣛⢛⣿⢿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⣿⢘⣻⣿⡇⣿⣿⠙⢹⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠘⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣺⣽⣛⣛⣻⣿⣶⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣿⡟⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣾⣿⣹⣶⡶⢷⣶⣿⢛⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⢸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣆⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣷⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⡌⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡌⣁⠀⠁⢸⡎⢀⠈⢀⡀⠀⠀⠀⠀⠀⠁⠀⢱⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣣⠂⡀⠰⠆⠃⠄⡮⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣤⠀⠀⠀⢠⣦⡄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡖⠀⠀⠀⢰⣷⠀⠀⠀⠐⣾⡆⠀⠀⠀⣺⡖⠀⠀⠀⢲⢷⠀⠀⠀⠐⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣦⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠂⠀⢀⣀⠀⣾⣿⣿⢛⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣶⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠉⠋⠛⠛⢫⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣷⣤⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⠋⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⣀⣄⣀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⢻⣿⡆⠀⠀⠀⠀⢲⡤⠀⠀⠠⣴⣦⠄⠀⠀⠤⣶⡤⠀⠀⠀⢴⣧⠄⠀⠀⠠⣾⡤⠀⠀⠀⢶⣷⠀⠀⠀⠰⣾
⠯⠀⠀⠀⠹⠿⠇⠀⠀⠀⠽⠻⠁⠀⠀⠈⠟⠏⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡹⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠋⠙⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣀⣤⣶⣶⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣐⣀⡀⢀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⡀⣚⣿⣟⢛⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⣿⠀⣿⢘⣻⣿⡇⣿⣿⠩⢹⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠰⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣺⣝⣛⣛⣿⣿⣶⡟⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣿⡿⢷⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠾⣿⣿⣹⣷⡶⢶⣶⣿⢻⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣇⣼⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⡏⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣡⠀⠁⢰⡎⠁⠀⡀⡈⠀⠀⠀⠀⠀⠁⠀⢱⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⢨⡧⠜⠠⣸⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⣤⠀⠀⠀⢠⣦⡄⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡆⠀⠀⠀⢰⣷⠀⠀⠀⠐⣾⡆⠀⠀⠀⣺⡖⠀⠀⠀⢲⢷⠀⠀⠀⠐⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣦⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀
⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠂⠀⢀⣀⠀⣾⣿⣿⠛⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣶⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠉⠛⠛⠛⣫⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶
⠛⠛⠛⠛⠛⠛⠋⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣷⣤⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⠋⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⣀⣄⡀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⢻⣿⡆⠀⠀⠀⠀⢲⡤⠀⠀⠠⣴⣦⠄⠀⠀⠤⣶⡤⠀⠀⠀⢴⣧⠄⠀⠀⠠⣾⡤⠀⠀⠀⢶⣷⠀⠀⠀⠰⣾
⠯⠀⠀⠀⠹⠿⠏⠀⠀⠀⠽⠻⠁⠀⠀⠈⠟⠏⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡹⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠋⠙⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣀⣤⣶⣶⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣐⣀⡀⢀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⡀⣚⣿⣛⢛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣿⠀⣿⢘⣻⣿⡇⣿⣿⠩⢹⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠰⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣛⣛⣻⣿⣶⡞⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣿⡿⢷⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣿⣿⣹⣷⡶⢷⣶⣿⢛⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣇⣼⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⡇⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢨⣁⠀⠀⢰⡎⠁⠀⠀⡈⠀⠀⠀⠀⠀⠁⠀⢱⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⢨⡧⠜⠠⣸⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⡖⠀⠀⠀⢲⣷⠂⠀⠀⠐⡾⡖⠀⠀⠀⢺⢗⠀⠀⠀⠐⠿⠂⠀⠀⠀⠿⠇⠀⠀⠀⠹⠿⠀⠀⠀⠈⠿⠁⠀⠀⠀⠟⠏⠀⠀⠀⠙⠋⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣄⣠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠠⡄⠀⣿⣿⣿⣨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠉⠦⠶⠶⠶⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⣨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢸⣿⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀
⣤⠀⠀⠀⣤⣧⡄⠀⠀⠠⣴⣦⠄⠀⠀⢤⣾⡤⠀⠀⠀⢴⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠻⣿⡄⠀⠀⠀⢰⣷⠂⠀⠀⠐⣾⣗⠂⠀⠀⢲⣿⡂⠀⠀⠀⣾⣟⠀⠀⠀⢸⠿⡃⠀⠀⠈⡿⠿⠀⠀⠀⠸⠿
⠃⠀⠀⠀⠘⠙⠂⠀⠀⠀⠋⠙⠀⠀⠀⠘⠉⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀
⣿⣿⣿⣿⣿⣿⣶⣶⣦⣀⣀⠀⣀⠀⣀⣀⠀⣀⡀⣰⣿⣿⣿⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣀⣀⡀⢀⣀⣀⣀⡀⣀⣀⢤⣀⣀⣀⣀⡘⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⣿⢘⣻⣿⡇⣿⣿⠹⢻⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠘⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡅⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣝⣛⣛⣛⣿⣶⣞⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣿⡟⢿⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣶⣾⣹⣶⡶⢶⣶⣿⢛⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⢸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣄⣼⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣧⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⡏⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠀⠀⢸⡎⢀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡀⢀⠐⠒⡂⠈⠜⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠀⠀⠀⠈⠿⠅⠀⠀⠀⠟⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠙⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡤⠤⠀⠀⠀⠀⠀⢈⣽⣿⡿⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣸⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⣿⠓⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷⣀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⡷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠻⣿⣇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣆
⡶⠀⠀⠐⢾⣷⠆⠀⠀⠐⣾⡖⠀⠀⠀⢲⣿⡂⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠹⣿⠀⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠸⠻⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛
⠁⠀⠀⠀⠉⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⣠⣀⣀⢀⣀⡀⣿⣿⣿⣟⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣀⣀⡀⢀⣀⣀⣐⡒⣒⣲⢶⣖⣒⣒⣒⡚⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⣿⢘⣻⣿⡇⣿⣿⠉⢹⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⡌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣝⣛⣛⣻⣿⣶⣞⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣻⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⢿⣿⣿⢹⣿⡏⣷⣿⡟⢿⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣾⣿⣹⣷⡶⢶⣶⣿⢛⣿⣿⢹⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⢸⣟⣹⡇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣇⣸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⢇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣷⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⡅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢌⡁⠀⠀⠸⠌⠀⠈⢠⠄⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠑⠀⠉⡁⠀⡐⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠾⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⠿⠂⠀⠀⠀⡿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠇⠀⠀⠀⠽⠏⠀⠀⠀⠸⠻⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢛⣿⣿⣆⣤⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⠶⠶⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠈⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣀⣿⣿⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣿⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣶⡆⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠂⢨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⣿⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣠⣀
⡄⠀⠀⠠⣼⣦⠄⠀⠀⢰⣿⡦⠀⠀⠀⢾⣷⠆⠀⠀⠰⣾⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⢿⡆⠀⠀⠀⠀⣿⣟⠀⠀⠀⢸⣿⡇⠀⠀⠀⡿⢿⠁⠀⠀⠸⠿⡏⠀⠀⠀⠽⠿⠀⠀⠀⠈⠿⠇⠀⠀⠀⠝⠻
⠀⠀⠀⠀⠋⠙⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣤⣤⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀⣀⣀⢀⣀⣀⠀⣀⡀⣿⣿⣿⣟⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣀⣀⡀⢀⣀⣀⣀⡀⣀⣠⣤⣄⣀⣀⣀⡛⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⣿⢘⣻⣿⡇⣿⣿⠹⢹⣿⡇⣿⢻⣮⡀⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⡌⣿⡅⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣛⣛⣻⣿⣶⣞⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⢛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣿⡿⢿⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢸⣏⣿⣶⠶⣶⣾⣹⣶⡶⢶⣶⣿⢛⣿⣿⢹⣿⣿⣶⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣄⣼⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣧⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣧⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⣈⠁⠀⠁⢾⠈⡀⠈⣤⠀⠀⠀⠀⠀⠀⠁⠀⣷⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⠠⠀⠓⠂⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡦⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⠀⠀⠀⢀⣤⡄⠀⠀⠀⣴⣤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣴⡄⠀⠀⠀⢴⡦⠀⠀⠀⢠⣧⠀⠀⠀⠀⣶⡄⠀⠀⠀⢼⡆⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠴⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠟⠛⠛⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⣼⣿⡿⡒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣏⣤⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣄⣀⣀⣀⠈⠙⠛⠛⠛⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠙⢿⣿⣧⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠁⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠛⣧⠀⠀⠀⠀⠀⣀⣦⡀⠀⠀⢀⣴⣤⠀⠀⠀⣤⣦⡄⠀⠀⠠⣴⣤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣼⡦⠀⠀⠀⢤⣷
⡏⠀⠀⠀⢹⢿⠁⠀⠀⠈⡿⠿⠀⠀⠀⠹⠿⠇⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣀⣤⣤⣤⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣁⣀⡀⢤⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⡀⣒⣿⣛⢛⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⣿⠀⣿⢘⣻⣿⡇⣿⣿⠙⢻⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡯⢼⣿⡇⣿⣿⢰⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣿⣛⣿⣿⣶⣿⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⢛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣿⡿⢿⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣷⠶⣿⣿⣹⣷⡶⢾⣶⣿⢿⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣇⣼⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣧⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⣿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⡏⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⣌⠁⠀⠁⢴⡍⠁⠈⢀⡀⠀⠀⠀⠀⠉⠁⠀⢵⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢖⡀⠀⢘⡇⠈⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣼⡦⠀⠀⠀⢰⣷⠀⠀⠀⠐⣾⡆⠀⠀⠀⢺⡖⠀⠀⠀⢰⢷⠂⠀⠀⠐⠾⡂⠀⠀⠀⠺⠇⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⢀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀
⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⢀⠀⠀⣾⣿⣏⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠉⠉⠉⠉⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠙⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⣠⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣦⡀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣍⠀⠀⡤⠀⠀⠀⢤⣧⠄⠀⠀⠠⣾⡤⠀⠀⠀⢶⣷⠆⠀⠀⠐⣾⡶⠀⠀⠀⢲⣷⠆⠀⠀⠐⣾⡖⠀⠀⠀⢲⣷
⠇⠀⠀⠀⠻⠻⠀⠀⠀⠀⠟⠋⠀⠀⠀⠸⠛⠇⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀
⣶⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣰⣶⣶⣶⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣃⣀⣿⣷⣀⣀⣀⡀⣀⣀⢀⣀⣀⣀⣀⡐⣛⣿⣛⢛⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⣿⢘⣻⣿⡇⣿⣿⠙⢹⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠐⢸⡯⢼⣿⡇⣿⣿⠸⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣺⣽⣛⣛⣻⣿⣶⣾⡋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣷⣿⡿⢿⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣿⣿⣹⣷⡶⢷⣶⣿⢛⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣇⣼⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⡏⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⡬⠁⠀⠁⢸⡌⢁⠈⢀⡀⠀⠀⠀⠀⠀⠁⠀⢵⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⢄⠀⠨⠅⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢠⣦⠀⠀⠀⠠⣤⠄⠀⠀⠀⢴⡤⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠟⠇⠀⠀⠀⠙⠻⠀⠀⠀⠀⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⡀⠤⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⢙⣿⡦⠠⠤⠴⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠾⠿⠿⠁⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⣶⣶⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢠⡀⠀⠀⣠⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣴⣤⠀⠀⠀⢤⣦
⡖⠀⠀⠀⣺⣷⠂⠀⠀⠘⣿⡟⠀⠀⠀⢻⢿⡃⠀⠀⠈⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠀⠟⠏⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠘⠉
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣄⣀⢀⣀⡀⣛⣻⣿⣿⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣈⣘⣻⣿⣓⣒⣒⡒⣒⣲⣾⣞⣛⣛⣛⡛⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⣿⢘⣻⣿⡇⣿⣿⠈⢹⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣼⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢸⡇⢸⣿⡇⣿⢼⣿⣿⣿⡌⣿⡅⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣝⣛⣛⣛⣿⣶⣾⡋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣻⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣽⢹⣿⣿⡟⣿⣿⢹⡿⢿⣿⣿⢹⣿⡏⣷⣿⡟⢿⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣶⣾⣹⣶⡶⢶⣶⣿⢛⣿⣿⢹⣿⣿⣶⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⢸⡟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣄⣸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⠀⢰⡊⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢄⠂⣈⣁⠀⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⡀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⠀⣰⣀⠀⠀⠀⢠⣄⠀⠀⠀⢀⣤⠀⠀⠀⠀⣴⡄⠀⠀⠀⢤⡦⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠟⠋⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠠⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠻⣷⡤⠤⠤⠴⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠼⣾⠿⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⣶⣤⣤⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⢀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⣄⠀⠀⠀⣀⣤⣀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢠⣶
⡖⠀⠀⠀⢲⣿⡆⠀⠀⠀⣿⣿⠂⠀⠀⢘⡿⡟⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⠻⠯⠀⠀⠀⠸⠿⠅⠀⠀⠀⠟⠻⠀⠀⠀⠸⠛⠇⠀⠀⠀⠛⠛⠀⠀⠀⠐⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣤⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣄⣀⢄⣀⡀⣛⣻⣿⣿⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣛⣘⣻⢿⣛⣒⣒⡒⣒⣲⣶⣖⣒⣒⣚⡛⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⣿⢘⣻⣿⡇⣿⣿⠹⢹⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣼⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢸⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡅⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣝⣛⣛⣛⣿⣶⣾⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⢀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣽⢹⣿⣿⡟⣿⣿⢹⡿⢿⣿⣿⢹⣿⡏⣷⣿⡟⢿⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣶⣾⣹⣶⡶⢶⣶⣿⢛⣿⣿⢹⣿⡷⣶⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⢸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⣄⣸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣾⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣧⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⡀⠀⢐⠎⡠⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠂⢈⣁⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢲⣷⠀⠀⠀⠐⣿⡂⠀⠀⠀⡾⠗⠀⠀⠀⢰⠿⠀⠀⠀⠈⠿⠇⠀⠀⠀⠻⠏⠀⠀⠀⠸⠻⠁⠀⠀⠈⠟⠇⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢰⣄⣀⣀⣀⣀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⠶⠶⠶⠶⠦⠤⠠⠄⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⠀⠀⠀⠈⠉⠉⠱⠶⠾⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠
⣤⠀⠀⠀⢤⣶⡤⠀⠀⠀⣴⣧⠄⠀⠀⠠⣼⡦⠀⠀⠀⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣷⠂⠀⠀⢐⣿⡖⠀⠀⠀⢺⣷⠂⠀⠀⠐⡿⡗⠀⠀⠀⢻⢿⠁⠀⠀⠘⡿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿
⠛⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣀⠀⣀⠀⣀⣀⠀⣀⡀⣰⣿⣿⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣘⢿⣟⣘⣿⣿⣗⣀⣀⡀⣀⣠⣤⣄⣀⣀⣀⡀⣛⣛⣛⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⣿⢘⣻⣿⡇⣿⣿⠁⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠙⢸⡧⢼⣿⡇⣿⣿⠘⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣺⣽⣛⣛⣻⣿⣦⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⢿⣿⣿⢹⣿⡏⣿⣿⡏⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣎⣿⣷⠶⣾⣿⣹⣷⡶⢶⣶⣿⢛⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⡄⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣷⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⡇⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠰⡯⢁⠄⢁⣌⠀⠀⠀⠀⠀⠁⠀⢰⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡕⢀⠐⠒⡂⢄⢜⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢲⣷⠀⠀⠀⢰⣷⠂⠀⠀⠀⡾⡖⠀⠀⠀⢲⢷⠀⠀⠀⠐⠿⠃⠀⠀⠀⠿⠏⠀⠀⠀⠸⠿⠁⠀⠀⠈⠟⠅⠀⠀⠀⠙⠏⠀⠀⠀⠸⠛⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⠀⠀⠀⠀⠘⠈⠑⡶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⣤⠀⠀⠀⢤⣶⡤⠀⠀⠠⣴⣧⠄⠀⠀⢠⣼⡤⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⠀⠀⠐⣾⣷⠂⠀⠀⢲⣿⡖⠀⠀⠐⣾⣷⠂⠀⠀⢐⣿⡖⠀⠀⠀⣺⣿⠀⠀⠀⠘⡿⡏⠀⠀⠀⠻⢿⠁⠀⠀⠈⠿
⠓⠀⠀⠀⠘⠛⠃⠀⠀⠀⠚⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀
⣿⣿⣿⣿⣿⣷⣶⣶⣦⡀⠀⠀⣀⠀⣀⣀⠀⣀⡀⣰⣾⡆⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢈⣻⢿⣟⣘⣿⢿⣇⣀⣀⡀⣀⣀⣤⣄⣀⣀⣀⡀⣛⣛⣛⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠙⢸⡯⢼⣿⡇⣿⣿⠐⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣛⣛⣻⣿⡀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⣃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⢿⣿⣿⢹⣿⡏⣷⣿⠁⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣏⣿⣶⠶⣿⣿⣹⣷⡶⢶⣶⣿⢻⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⣿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣯⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⡏⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⢈⡁⠀⠀⢰⡏⢁⠀⢀⡌⠀⠀⠀⠀⠀⠁⠀⢱⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⠅⢀⠐⠖⡂⠄⢜⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣆⠀⠀⠀⠀⣤⡀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠿⠁⠀⠀⠀⠟⠏⠀⠀⠀⠹⠻⠀⠀⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠳⢤⣀⣀⡀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠
⣷⠆⠀⠀⠰⣾⣷⠀⠀⠀⢲⣿⡖⠀⠀⠀⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡟⠀⠀⠀⠹⠿⠃⠀⠀⠈⡿⠯⠀⠀⠀⠹⠿⠇⠀⠀⠀⠟⠿⠀⠀⠀⠸⠛⠇⠀⠀⠀⠟⠛⠀⠀⠀⠘⠛⠃⠀⠀⠀⠛
⠉⠀⠀⠀⠀⠁⠉⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣤⣀⣀⣀⣀⡀⣐⣟⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢙⣛⢿⣛⣃⣻⢿⣛⣓⣒⡒⣒⣲⢶⣖⣒⣒⣒⡒⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⣽⣛⣛⣻⡟⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⢃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢹⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣿⣷⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣎⣿⣶⠾⣿⣿⣹⣷⡶⢶⣶⣿⢛⣿⣿⢹⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣷⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣧⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⣡⡀⠀⠀⡾⢁⠌⡀⣬⠁⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠀⠀⠉⠠⢂⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣆⠀⠀⠀⠀⣴⡀⠀⠀⠀⢤⡤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⠄⠀⠀⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠁⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠦⣤⣀⡀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣤⣀⠀⠀⢀⣠⣄⠀⠀⠀⣀⣤⣀⠀⠀⠀⣠⣆⠀⠀⠀⢠⣶⡄⠀⠀⠀⣴
⣷⠂⠀⠀⠐⣾⣿⠀⠀⠀⢸⣿⡏⠀⠀⠀⣻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠯⠀⠀⠀⠙⠻⠅⠀⠀⠀⠟⠻⠀⠀⠀⠸⠛⠇⠀⠀⠀⠟⠻⠀⠀⠀⠐⠛⠃⠀⠀⠀⠚⠛⠀⠀⠀⠐⠋⠃⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⡄⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣄⣀⣄⣀⡀⣘⣃⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢛⣛⢛⣛⣃⣻⣿⣛⣓⣒⡲⣒⣲⣶⣞⣛⣛⣛⡛⣛⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢸⡇⢸⣿⡇⣿⢼⣿⣿⣿⡌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣺⣽⣛⣛⣛⡛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⡘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⢃⣛⣛⣓⣓⣻⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣽⢹⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣷⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣿⣶⠶⣾⣶⣹⣷⡶⢶⣶⣿⢛⣿⣿⢹⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣧⣭⣷⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣧⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⣚⣁⠈⠀⢬⠁⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢑⢀⣉⡀⡪⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠿⠃⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠇⠀⠀⠀⠝⠋⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠋⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⢀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠤⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢤⣀⣀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠
⣷⠄⠀⠀⠠⣾⣷⠀⠀⠀⢶⣿⡶⠀⠀⠀⢶⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠀⠀⠀⠸⣿⡃⠀⠀⠈⡿⣿⠀⠀⠀⢹⠿⡏⠀⠀⠈⠿⢿⠀⠀⠀⠨⠿⠏⠀⠀⠀⠽⠿⠀⠀⠀⠨⠛⠇⠀⠀⠀⠙
⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣀⣃⣻⣿⣛⣂⣀⡀⣀⣠⣶⣆⣀⣐⣒⡒⣛⣛⣛⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠈⢸⡯⢼⣿⡇⣿⣿⠈⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣬⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣺⣽⣻⣛⡛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⢃⣛⣛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢹⣿⡏⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣎⣿⣷⠶⣿⣿⣹⣷⡶⢷⣶⣿⢛⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣷⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⠁⠀⠀⠈⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⣡⠀⠀⠀⢭⠁⡄⠀⣬⠁⠀⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠢⠀⠛⠉⢔⣔⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠐⡾⡆⠀⠀⠀⠺⢗⠀⠀⠀⢰⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠈⠿⠅⠀⠀⠀⠟⠏⠀⠀⠀⠙⠛⠀⠀⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠄⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠦⢄⣀⡀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀
⣷⡤⠀⠀⠠⣴⣧⠄⠀⠀⠠⣾⡤⠀⠀⠀⢴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠀⠀⠐⣿⡖⠀⠀⠀⣺⣷⠂⠀⠀⠐⡿⡟⠀⠀⠀⢻⢿⠁⠀⠀⠈⡿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹
⠉⠃⠀⠀⠀⠋⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⣀⠀⣀⣀⢀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣀⣃⣻⣿⣿⣇⣀⡀⣀⣠⣤⣄⣀⣀⣀⡀⣘⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣼⣿⢸⡇⣿⠈⢸⡯⢼⣿⡇⣿⣿⠘⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣮⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣽⣛⡓⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⢃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⢿⣿⣿⢹⣿⡇⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣿⣷⠾⣿⣿⣹⣷⡶⢷⣶⣿⢻⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡉⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣷⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⢿⣟⣹⣿⣷⠸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡗⠀⠀⠀⠈⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⡕⠀⠀⠀⢬⠅⡠⢀⣨⡅⠀⠀⠀⠉⠁⠀⠀⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⠢⢀⡒⡂⢠⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⡿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠝⠋⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠆⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤
⣶⣾⣷⣷⣿⣾⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠤⠄⣀⣀⠀⠀⠘⠿⠿⠟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣄⠀⠀⠀⣀
⣾⡶⠀⠀⠀⢶⣷⠆⠀⠀⠐⣾⣷⠂⠀⠀⢲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡟⠀⠀⠀⢹⠿⠁⠀⠀⠈⡿⠯⠀⠀⠀⠹⠿⠅⠀⠀⠀⠿⠯⠀⠀⠀⠸⠛⠅⠀⠀⠀⠟⠛⠀⠀⠀⠘
⠉⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⠁⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⢀⣀⣐⣸⣿⣛⣓⣒⡲⣒⣲⣶⣖⣒⣒⣒⡒⣚⣛⣛⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡯⢼⣿⡇⣿⣿⠈⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣬⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣚⠙⠋⠓⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣷⢰⣆⡆⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣿⣷⠾⣿⣿⣹⣷⡾⢿⣶⣿⢿⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡋⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣷⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⣿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠈⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠈⠉⠀⠈⢁⡌⠀⠀⠨⠅⡨⢀⢨⡅⠀⠀⠀⠉⠁⠀⠀⢹⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡔⠀⠈⠉⠅⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⢀⣰⣀⠀⠀⠀⣠⣆⠀⠀⠀⢀⣦⡀⠀⠀⠀⣴⡤⠀⠀⠀⢤⡦⠀⠀⠀⠠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀
⠅⠀⠀⠀⠟⠏⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⡠⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠴⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠀⠠⣄⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣤⣀⠀⠀⢀⣠⣄⡀⠀⠀⣀⣤⡀⠀⠀⠀⣰⣤⠀⠀⠀⢠
⣾⡖⠀⠀⠀⢺⣿⡃⠀⠀⠐⣿⣿⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⠀⠀⠀⠹⠻⠅⠀⠀⠀⠟⠿⠀⠀⠀⠸⠛⠇⠀⠀⠀⠟⠛⠀⠀⠀⠘⠛⠃⠀⠀⠀⠚⠛⠀⠀⠀⠘
⠁⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣘⢓⣀⢀⣀⣚⣘⣿⣛⣛⣒⡶⣒⣲⣶⣖⣒⣒⣛⡛⣛⣛⣛⢛⣿⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡯⢼⣿⡇⣿⣿⠀⢸⡇⢸⣿⡇⣿⢼⣿⣿⣿⣎⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⠚⠙⠋⠓⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⣛⣛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣶⢰⣆⡆⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣶⢶⢰⣶⡆⣶⠆⢰⣆⣿⣷⠶⣿⣿⣹⣷⡾⢿⣶⣿⢻⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡃⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⣿⣿⣿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠈⠉⠀⠈⢁⣌⡁⠀⢘⡇⡨⢀⢨⡅⠀⠀⠀⠉⠁⠀⠁⢹⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⡂⣬⣥⢐⠵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣀⠀⠀⠀⢠⣆⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠹⠿⠀⠀⠀⠸⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠀⠀⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠂⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠓⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠂⠀⠀⠠⢄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣠⣆⡀⠀⠀⢀
⣾⣶⠀⠀⠀⢲⣿⡖⠀⠀⠐⣾⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠁⠀⠀⢹⠿⡏⠀⠀⠈⠿⠿⠁⠀⠀⠨⠟⠇⠀⠀⠀⠽⠻⠀⠀⠀⠈⠛⠇⠀⠀⠀⠘⠛⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⡀⣀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣘⢛⣒⢄⣐⣛⣘⣿⣛⣛⣒⡲⣒⣲⣶⣖⣒⣒⣒⡒⣚⣛⣛⢛⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡯⢼⣿⡇⣿⣿⠈⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣎⣿⡇⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠚⠙⢋⣛⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⣛⣛⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⠀⢰⣶⢰⣾⡏⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣶⢶⢰⣶⡆⣶⠆⢰⣆⣾⣷⠾⣿⣿⣹⣷⡾⢿⣶⣿⢿⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣏⠀⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣷⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⣿⣿⢿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠌⠀⠀⠀⢈⣿⣿⡇⠀⠀⠀⠈⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠈⠉⠀⠈⢡⣈⡀⠀⠈⠅⠨⠀⢨⡅⠀⠀⠀⠁⠁⠀⠀⢹⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠠⠈⠋⠁⡢⡪⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⠀⠀⠀⢺⢷⠀⠀⠀⠐⠿⡆⠀⠀⠀⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠇⠀⠀⠀⠽⠏⠀⠀⠀⠸⠻⠁⠀⠀⠀⠛⠃⠀⠀⠀⠙⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠷⠄⠀⠀⠀⡀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀
⣼⣦⠄⠀⠀⢤⣿⡤⠀⠀⠀⢴⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠂⠀⠀⢘⣿⡗⠀⠀⠀⣻⢿⠁⠀⠀⠘⡿⡏⠀⠀⠀⢹⢿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠈
⠋⠛⠀⠀⠀⠘⠉⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⠀⢀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣸⢟⣳⢦⣔⣛⣚⣿⣿⣿⣀⡀⣀⣠⣤⣄⣀⣀⣀⡀⣀⣛⣛⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡯⢼⣿⡇⣿⣿⠘⢹⡏⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠚⠙⣻⣿⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⣛⣛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡿⣿⣿⢹⡶⠀⢰⣶⢰⣿⡏⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣾⣷⠾⣿⣿⣹⣷⡾⢿⣾⣿⢿⣿⣿⢻⣿⣿⣿⢯⣿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣏⠀⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⣿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣾⣿⣿⡇⠀⠁⠀⠈⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠈⠉⠀⠈⢡⡈⠁⠀⠨⡥⢈⠄⣈⣥⠀⠀⠀⠉⠁⠀⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡗⡄⡐⢒⠀⣀⢺⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀
⡦⠀⠀⠀⢰⣷⠂⠀⠀⠐⣾⡖⠀⠀⠀⢲⣷⠀⠀⠀⢐⣿⠂⠀⠀⠀⡾⡖⠀⠀⠀⠺⢷⠀⠀⠀⠘⠿⠃⠀⠀⠀⠿⠏⠀⠀⠀⠹⠻⠀⠀⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⣠⣆⡀⠀⠀⢀⣴⣤⠀⠀⠀⣤⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⠆⠀⠀⠰⣾⡶⠀⠀⠀⢲⣷⠂⠀⠀⠐⣾⣗⠀⠀⠀⢲⣿⡂⠀⠀⠐⣿⡟⠀⠀⠀⢹⢿⠃⠀⠀⠈
⠟⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⣀⠀⢀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣸⢿⣿⢿⣟⣛⡟⣿⣿⣷⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣻⣛⢿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠁⢸⡯⢼⣿⡇⣿⣿⠘⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣮⣿⡇⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠙⠚⢙⣻⣟⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⢛⣛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡿⣿⣿⢱⡶⠀⢰⣶⢸⣿⡏⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡦⣴⢶⢰⣶⡆⣶⠆⢰⣆⣾⣷⠾⣿⣿⣹⣷⡾⢷⣶⣿⢿⣿⣿⢻⣿⣿⣾⢯⣿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣏⠀⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⣿⣿⣿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠉⠀⠀⠀⣽⣾⣿⣿⡇⠁⠀⠀⠈⠀⠀⠉⠁⠁⠀⠁⠀⠀⠀⠈⠉⠀⠈⠠⢌⠁⠀⠈⣧⠈⡀⠈⣥⠀⠀⠀⠉⠁⠀⠀⠁⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⢄⠀⠶⢚⠀⣱⠝⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠐⠿⡂⠀⠀⠀⡿⠟⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠫⠀⠀⠀⠸⠛⠁⠀⠀⠀⠟⠃⠀⠀⠀⠘⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠷⠶⠶⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠄⠀⠀⠀⣀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣠⣀⠀⠀⠀
⢤⣷⡄⠀⠀⠠⣾⣷⠀⠀⠀⠰⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡇⠀⠀⠈⣿⢿⠁⠀⠀⢹⠿⡏⠀⠀⠀⠿⢿⠁⠀⠀⠨⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠈⠟⠇⠀⠀⠀
⠘⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⠀⢀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣘⢟⣻⢿⣟⣛⡇⢻⣛⣛⣃⡀⣀⣰⣶⣆⣀⣐⣒⡒⣒⣚⣛⢛⣿⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠁⢸⡷⢼⣿⡇⣿⣿⠈⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠙⠚⢙⣻⣛⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⢛⣛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢱⡶⠀⢰⣶⢸⣿⡏⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣶⢶⢰⣶⡆⣶⠆⢰⣆⣶⣷⠾⣿⣿⣹⣷⡾⢿⣶⣿⢿⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣏⠀⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣧⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⣿⣿⣿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠉⠀⠀⢀⣽⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠈⠉⠀⠈⠀⣌⢁⠀⠈⢥⠉⡄⠈⣥⠀⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠛⠉⢐⢕⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⢀⣠⣀⠀⠀⠀⣠⣦⠀⠀⠀⢠⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠄⠀⠀⠠⣶⠄⠀⠀⠀⢴⡤⠀⠀⠀⢰⣦⠀⠀⠀⠐⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠾⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶
⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠄⠛⠛⠋⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⣀⣤⣀⠀⠀⠀⣠⣆⡀⠀⠀⢠⣶⡄⠀⠀⠀⣴⣦⠄⠀⠀⢠⣴⡤⠀⠀⠀⢴⣦⠄⠀⠀
⠘⣿⣿⠀⠀⠀⢹⡿⡏⠀⠀⠈⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⠀⠀⠘⠛⠃⠀⠀⠀⠛⠛⠀⠀⠀⠐⠛⠃⠀⠀⠀⠚⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡖⢀⣀⠀⣀⡀⣆⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣈⢛⣛⢿⣛⣛⣻⢉⣛⣛⣛⡻⣛⣻⣿⣟⣛⣛⣛⡛⣛⣛⣛⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢸⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠚⠙⣛⣟⡛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⢛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡶⠀⢰⣶⢰⣿⡏⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠾⣿⣿⣹⣷⡶⢿⣶⣿⢻⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣏⠀⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⡷⣭⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢨⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠈⠀⠀⠀⠀⠉⠀⠈⠀⠈⣥⠀⠈⢀⣉⡐⠀⢡⡆⠀⠀⠀⠁⠀⠀⠀⢨⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⡄⢂⣀⡢⠤⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣰⡄⠀⠀⠀⢤⣦⠀⠀⠀⠠⣴⠄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣶⠄⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀
⠟⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀⠀⠐⠉⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶
⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠗⠒⠒⠒⠒⠄⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣦⡀⠀⠀⢀⣰⣄⠀⠀⠀⣠⣦⡄⠀⠀⠠⣴⣤⠀⠀⠀⢤⣦⠄⠀⠀
⠀⣻⣿⠃⠀⠀⠘⡿⣟⠀⠀⠀⢹⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠁⠀⠀⠀⠟⠃⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠓⠀⠀⠀⠘⠛⠂⠀⠀⠀⠋⠓⠀⠀⠀⠘⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣶⣶⣶⣤⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⢀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣀⢛⣛⢿⣛⣛⣿⣇⣛⣛⣛⡻⣛⣻⣿⣟⣛⣛⣛⡛⣛⣛⣛⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠀⢸⡧⢼⣿⡇⣿⣿⠀⢸⡇⢸⣿⡇⣿⢼⣿⣿⣿⣎⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠚⠙⢋⣛⡟⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⢛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡷⠀⢰⣶⢰⣾⡏⣷⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠾⣿⣿⣹⣷⡶⢿⣶⣿⢿⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣏⠀⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣭⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⡿⣿⢿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠈⠀⠀⠀⠀⠈⠀⠈⠀⠈⡡⣀⠈⠀⣋⢠⠊⢁⡶⠁⠀⠉⠁⠀⠀⠀⠈⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡁⢀⣉⡐⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⣀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢲⣷⠂⠀⠀⠐⡿⡆⠀⠀⠀⠺⢗⠀⠀⠀⠸⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠀⠀⠀⠨⠛⠁⠀⠀⠀⠟⠇⠀⠀⠀⠘⠛⠀⠀⠀⠈⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣀⣠⣤⣤⣄⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⡀⠀⠀
⠀⢤⣷⡤⠀⠀⠠⣼⣧⠄⠀⠀⠠⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠲⣿⡖⠀⠀⠀⣻⣿⠀⠀⠀⢘⡿⡏⠀⠀⠀⢻⢿⠁⠀⠀⠈⠿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀
⠀⠘⠉⠃⠀⠀⠀⠋⠙⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⠀⣀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣘⢟⣿⢿⣟⣛⣿⣇⣻⣿⣻⡦⣀⣠⣤⣄⣀⣀⣀⡀⣀⣀⣚⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠙⢸⡯⢼⣿⡇⣿⣿⠘⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣮⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠙⠚⠙⠋⢓⡛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⢚⣓⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⠃⢰⣶⢰⣆⡎⣷⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣶⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠾⣿⣿⣹⣷⡾⢷⣶⣿⢿⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⠀⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⣿⣿⣿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⠀⠁⠀⢀⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠉⠀⠈⠀⠀⡁⠀⠈⠁⢭⠄⡠⠀⣠⠁⠀⠉⠁⠀⠀⠁⠈⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⠢⠀⣓⡃⢀⡔⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀
⢲⣷⠂⠀⠀⠐⡿⡖⠀⠀⠀⠺⢷⠀⠀⠀⠸⠿⠃⠀⠀⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠈⠟⠅⠀⠀⠀⠟⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣧⣠⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣀⠀⠀
⠀⢤⣿⡤⠀⠀⠠⢴⣧⠄⠀⠀⠰⣾⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠂⠀⠀⠐⣿⡗⠀⠀⠀⣻⢿⠃⠀⠀⠘⡿⡟⠀⠀⠀⢹⢿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀
⠀⠘⠉⠃⠀⠀⠀⠉⠙⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣘⢛⣿⢿⣟⣛⣿⣿⣛⣿⣿⡧⣀⣠⣤⣄⣀⣀⣀⡀⣀⣐⣚⢛⣿⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠙⢸⡯⢼⣿⡇⣿⣿⠈⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣮⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠛⠚⠙⠋⠛⡛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⠛⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡿⣿⣿⢹⡿⡟⢰⣶⢰⣆⡆⣷⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣶⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠾⣿⣿⣹⣷⡾⢿⣶⣿⢿⣿⣿⢻⣿⣿⣿⢯⣿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⠁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣃⣿⣿⣿⢿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠀⠀⣰⡇⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠉⠀⠈⠀⠈⠉⠀⠈⠀⠀⡅⣀⠈⠁⢩⠅⡠⢁⣠⡍⠀⠉⠁⠀⠀⠁⠈⢹⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢵⣀⠄⣙⡃⢀⣐⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣾⣿⣿⣷⣄⣴⡀⠀⠀⠀⢀⣆⠀⠀⠀⢠⣤⡄⠀⠀⠀⣴⡤⠀⠀⠀⢤⣦⠀⠀⠀⠠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠈⠿⠇⠀⠀⠀⠝⠫⠀⠀⠀⠘⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠘⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣠⢤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠶⠶⠏⠀⠀⠀⠀⠤⠤⠤⠤⠤⠴⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⢛⣶⠶⠖⠚⠛⠘⠛⠛⠁⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⣀⠀⠀⠀⢀⣤⣀⠀⠀⢀⣠⣄⡀⠀⠀⣀⣤⣀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣴⣀⠀⠀⠀⣤⣦⠀⠀
⠀⠐⣾⣗⠂⠀⠀⢺⣿⡗⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠅⠀⠀⠈⠻⠿⠀⠀⠀⠸⠿⠇⠀⠀⠀⠟⠻⠀⠀⠀⠸⠛⠇⠀⠀⠀⠚⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣈⢛⣛⢿⣛⣛⣻⣿⣙⣛⣛⡿⣒⣲⣶⣖⣒⣒⣒⡛⣛⣛⣛⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠈⢸⡧⢼⣿⡇⣿⣿⠀⢸⡇⢸⣿⡇⣿⢼⣿⣿⣿⣎⣿⡇⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠚⠙⠋⠓⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⠚⣛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣷⣶⢰⣆⡆⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠾⣿⣿⣹⣷⡾⢿⣶⣿⢻⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡃⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣁⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⠀⠈⠀⠀⠡⣀⠈⠀⢈⣇⡠⢁⢠⡏⠀⠁⠁⠀⠀⠀⠀⢹⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⡂⣈⣅⢐⠵⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣐⢿⣿⣿⣿⣷⡀⠀⠀⢀⣤⡀⠀⠀⠀⣴⡄⠀⠀⠀⢤⣤⠀⠀⠀⢠⣦⠄⠀⠀⠠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀
⠈⠿⠏⠀⠀⠀⠹⠻⠁⠀⠀⠈⠛⠇⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠈⠉⢻⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⢤⠴⣶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠰⠶⠦⠤⠀⠀⠀⠀⠨⠤⠤⠤⠤⠤⠶⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢻⣴⠶⠒⠚⠋⠛⠋⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣠⣀⠀⠀⠀⣀⣆⡀⠀⠀⢀⣰⣀⠀⠀⠀⣀⣦⡀⠀
⠀⠐⣾⣷⠂⠀⠀⠐⣿⡖⠀⠀⠀⢺⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠹⠻⠁⠀⠀⠈⠟⠇⠀⠀⠀⠸⠛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠘⠙⠀⠀
⠀⠀⠁⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡀⣈⢛⣛⢟⣛⣛⣻⣿⣋⣛⣛⡻⣒⣲⣶⣖⣒⣒⣒⡒⣒⣒⣚⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠉⢸⡧⢼⣿⡇⣿⣿⠀⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠚⠙⠋⠓⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⠚⢛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣶⢰⣆⡆⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠾⣿⣿⣹⣷⡾⢿⣶⣿⢿⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣁⣿⡿⣿⢿⣟⣹⣿⣷⠸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⣠⠈⠀⠈⢗⠀⠁⢀⣭⠀⠈⠁⠀⠀⠀⠀⠁⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢧⡀⢤⣩⡄⢈⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠙⠾⣿⣿⣿⡇⠀⠀⠀⢠⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀
⠀⢲⣷⠀⠀⠀⠐⡿⡂⠀⠀⠀⡾⠟⠀⠀⠀⠹⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠯⠀⠀⠈⣿⣿⣇⠀⠀⠀⠟⠃⠀⠀⠀⠘⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣦⣤⠴⠖⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⡀⠀
⠀⠀⢤⣷⡤⠀⠀⠠⣼⣦⠄⠀⠀⢤⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣗⠀⠀⠀⠲⣿⡆⠀⠀⠀⣿⣿⠀⠀⠀⢸⡿⡏⠀⠀⠀⡿⢿⠁⠀⠀⠈⠿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠇⠀
⠀⠀⠘⠉⠃⠀⠀⠀⠋⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢀⣀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡈⣻⢟⣻⢿⣟⣛⣿⣿⣇⣻⣻⡿⣂⣠⣤⣄⣀⣀⣀⡀⣀⣀⣀⢛⣻⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⣻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠙⢸⡧⢼⣿⡇⣿⣿⠈⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣺⠙⠋⠛⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⠚⢛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣿⢰⣆⡆⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣶⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠶⣿⣿⣹⣷⡶⢷⣶⣿⢿⣿⣿⢻⣿⣿⣾⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣁⣿⣿⣿⢿⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⣒⠈⠀⠈⢥⠈⡅⠀⣭⠀⠈⠁⠀⠀⠀⠀⠁⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠢⢀⣓⡋⢀⡵⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡈⠳⢿⣿⣿⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣠⡀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀
⠀⢲⣷⠀⠀⠀⠐⡿⡂⠀⠀⠀⡾⠗⠀⠀⠀⠸⠿⠁⠀⠀⠈⠿⠏⠀⠀⠀⠹⠯⠀⠀⢹⣿⣿⡇⠀⠀⠀⠟⠇⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⠴⠒⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⡀⠀
⠀⠀⢤⣷⡤⠀⠀⠠⣼⣧⠄⠀⠀⠠⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣗⠀⠀⠀⠲⣿⡆⠀⠀⠀⣿⣿⠀⠀⠀⢸⡿⡏⠀⠀⠀⡻⢿⠁⠀⠀⠈⠿⡏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠇⠀
⠀⠀⠘⠉⠃⠀⠀⠀⠋⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢀⣀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡘⣿⢿⣿⢿⣟⣛⣿⣿⣇⣻⣻⡿⣂⣠⣤⣄⣀⣀⣀⡀⣀⣀⣀⢚⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠙⢸⡧⢼⣿⡇⣿⣿⠈⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣌⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣞⠙⠋⠓⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⠚⢛⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣷⢰⣆⡆⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣶⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠶⣿⣿⣹⣷⡶⢷⣶⣿⢻⣿⣿⢻⣿⣿⣶⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡉⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣿⢼⣿⡇⣿⡁⢸⡿⣿⣿⣁⣿⡿⣿⣻⣟⣹⣿⣷⠸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⣒⠈⠀⠈⢥⠈⡅⠀⣭⠄⠀⠁⠀⠀⠀⠀⠁⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠢⠀⣓⡋⢄⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣍⠻⠿⣿⣿⣧⣀⠀⠀⠀⣀⣄⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀
⠀⠐⠿⡂⠀⠀⠀⠿⠏⠀⠀⠀⠹⠿⠁⠀⠀⠈⠟⠏⠀⠀⠀⠙⠋⠀⠀⠀⠘⠛⠀⠀⣹⡿⠿⢇⠀⠀⠀⠘⠛⠀⠀⠀⠐⠛⠀⠀⠀⠀⠋⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⡤⡤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠒⠂⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠
⣶⣶⣶⣶⣶⡶⡶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣶⠶⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣠⣄⡀
⠀⠀⠰⣾⡶⠀⠀⠀⢶⣿⡖⠀⠀⠐⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡃⠀⠀⠈⠿⣟⠀⠀⠀⢹⠿⡇⠀⠀⠈⠿⠿⠀⠀⠀⠹⠿⠇⠀⠀⠀⠿⠿⠀⠀⠀⠸⠛⠇⠀⠀⠀⠛⠛⠀
⠀⠀⠀⠉⠉⠀⠀⠀⠈⠈⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣄⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⠀⣀⡀⣀⣀⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⡈⣛⢛⣛⢟⣛⣛⣻⣿⣛⣙⣛⡛⣛⣲⣶⣖⣒⣒⣒⡒⣒⣒⣒⢚⣻⢿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢘⣻⣿⡇⣿⣿⠀⢸⣿⡇⣿⢻⣮⡁⣿⠀⢸⣿⣿⣿⣾⣿⢸⡇⣿⠈⢸⡯⢼⣿⡇⣿⣿⠈⢹⡇⢸⣿⡇⣿⢼⣿⣿⣿⣎⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡚⠙⠋⠓⠛⠛⠀⠚⠋⠓⠋⠙⠚⠁⠛⠀⠘⠛⠙⠃⠛⠙⠛⠃⠛⠀⠘⠃⠘⠛⠃⠛⠛⠀⠘⠃⠘⠛⠃⠛⠚⠃⣓⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⢻⣿⣿⡟⣿⣿⢹⡿⣿⣿⣷⢰⣆⡆⣶⣶⠀⢰⣶⣴⡶⢶⡶⢶⣶⡆⣶⣦⢰⡶⠀⢶⡶⣴⣶⡄⢰⣦⡶⡆⣴⢶⢰⣶⡆⣶⠆⢰⣆⣶⣶⠖⣾⣿⣹⣷⡶⢿⣶⣿⢻⣿⣿⢻⣿⣿⣿⢯⡿⣿⣿⣿⣿
⣿⣿⣏⣾⢿⣸⣟⣹⣇⣿⣿⢸⣟⡁⣿⢿⣸⣿⡇⣿⣿⠀⢸⣿⣿⣟⣹⡟⢸⣿⡇⣽⣷⢸⣏⠀⢸⡇⣿⣿⠇⢸⣧⣝⣷⣽⣷⢼⣿⡇⣿⡁⢸⡿⣿⣿⣁⣿⡿⣿⢻⣟⣹⣿⣷⡸⣿⣿⢸⢻⣿⣿⣡⣝⣷⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡈⠀⠈⠠⠌⠡⠀⢩⡄⠀⠁⠀⠀⠁⠀⠀⢸⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡖⠠⠈⠉⠅⡀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5489

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    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/When_Fedora_Said_It_Was_Looking_to_Integrate_AI_It_Meant_Promot.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ When Fedora Said It Was Looking to
Integrate "AI" It Meant Promoting Microsoft's Proprietary Spyware and GPL-
Violating Slop⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


Fedora_has_a_new_release. There's also a belated revelation. When they say "AI"
they mean Microsoft.


Some months ago IBM staff said that Fedora was "hiring" for "AI". Yesterday
IBM's staff (Christian F.K. Schaller) wrote: "So an effort we been plugging
away at recently is starting to bring AI tooling to Open Source desktop
applications. Our first effort in this regard is Granite.code. Granite.code is
a extension for Visual Studio Code that sets up a local AI engine on your
system to help with various tasks including code generation and chat inside
Visual Studio Code. So what is special about this effort is that it relies on
downloading and running a copy of the open source AI Granite LLM model to your
system instead on relying on it being run in a cloud instance somewhere. That
means you can use Granite.code without having to share your data and work with
someone else. Granite.code is still very early stage and it requires a NVIDIA
or AMD GPU with over 8GB of video ram to use under Linux. (It also runs under
Windows and MacOS X). It is still in a pre-release stage, we are waiting for
the Granite 3.3 model update to enable some major features for us before we
make the first formal release, but for those willing to help us test you can
search for Granite in the Visual Studio Code extension marketplace and install
it."


Here it is:


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


It says "Granite.code running on Linux".


No, it's running on Microsoft's proprietary spyware. And_we_know_where_that
leads.


It is not even intelligence; that's a misnomer and misleading characterisation.


When it comes to Freedom (libre), Fedora being controlled by IBM has been a
disaster and the new_leader will not_improve_matters. Consider the following
three examples:


    * IBM_and_Fedora:_Stop_Being_Poor!_Buy_a_New_PC!
    * GNOME_(IBM/Red_Hat_Staff)_Promoting_Microsoft's_'Security'_Scam_With_the
      'Secure'_Boot_Sham
    * IBM_Does_Not_Care_for_the_Blind_(Wayland_Harms_Accessibility)
There's lots more. █


    * Slopwatch:_The_Typical_Slopfarms_and_the_'Brian_Fagioli_Dilemma'
    * Linux.com_as_Spamfarm_of_the_Linux_Foundation,_Partner_of_the_Gates
      Foundation


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣶⣶⣶⣷⣶⣶⣷⣾⣶⣶⣦⣷⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5600

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/16/You_Should_Probably_Self_Host_Your_E_mail_and_Never_Use_a_Web_B.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/16/You_Should_Probably_Self_Host_Your_E_mail_and_Never_Use_a_Web_B.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ You Should Probably Self-Host Your E-mail
and Never Use a Web Browser for Mail⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025,
updated Apr 16, 2025


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


"Microsoft warns of Outlook Classic bug that can crank CPU use up to 50% when
typing," this new_report_says. Here we go again. Microsoft still cannot handle
E-mail right. It's 2025! If it couldn't get it right in about 40 years, then
folks should just stop waiting. Go elsewhere. Microsoft became notorious for
losing people's E-mail, either at the server level (e.g. Microsoft Exchange) or
the client level. Or both. Even buying Hotmail didn't solve anything; it made
things worse after moving away from BSD.


Enjoy the anxiety over lost mail (both incoming and outgoing).


One might suggest that the solution is to use a real IMAPS/SMTPS setup or self-
host. I can speak about this based on personal experience. I have about 20 E-
mail accounts at my domain (surname.com) and my wife has 2. She has used these
exclusively since 2012, i.e. for 13 years. I've used mine for over 20 years.


What does that mean and why does that matter? Well, having done so for several
decades, and prior to that experimented a little with webmail (late 90s for the
most part; the only other choice was the university account or an Internet
Service Provider (ISP) account*), I can tell the difference and we shall
revisit the subject in the future in relation to client privilege in legal
(lawyers') communications. There's a lot more to be said, then done.


Without bothering to look up other people's lists (or "research" by LLMs),
here's my personal summary of the key differences:


                webmail              self-hosted webmail  self-hosted and POP3/
                                                          IMAPS/SMTPS


                Very limited (may    It's up to you (or   Always up to you and
Storage         change at any time)  server capacity)     your drive's (or
                                                          drives') capacity


Privacy         Literally none       Usually at risk from E2EE easily feasible
                                     browser flaws


                Trust untrustworthy
Backup          companies that do    Back up the server   Back up the computer
                lost mail and cannot                      (every night perhaps)
                recover it


Access          Must have access to  Must have access to  Usable offline, many
                browser and Net      browser and Net      clients exist


                                                          Use offline during
                Beg some company to  As a customer,       server issues; POP3/
Uptime/downtime stop lying about ETA demand honest ETA    IMAPS/SMTPS simpler
                                                          and thus more robust
                                                          (thinner stack)


                Outsourced to dodgy  More customised for
                vendor, so expect    oneself (can also    Versatile options in
SPAM management false positives      create multiple      many mail clients and
                (they don't care     accounts to entrap   peripheral software
                about you)           unwanted mail)


That last point (concerning "multiple accounts") was illuminated to me by
university staff when I worked at MCC. He said that he had created multiple
accounts to know where one got the address; he said it would make isolation of
SPAM a lot easier. He was right. About 22 years later I still do this.


If you're still using webmail, you may be making life a lot harder for yourself
(than it ought to be). The "old way" of doing things is in many cases vastly
superior, but it's harder for the "free" (not really) services to "monetise".
Does anyone still believe Gmail is "free"? It wasn't too long ago that
Microsoft, Google and others put an end to 'API' (not really, open protocol)
access to one's mail, falsely citing "security" reasons when in fact webmail is
vastly worse at security because "modern" browsers are ridiculously large and
complex. Some are outdated, not fully patched, no longer maintained etc. █


____


* I know people who still use their Internet Service Provider (ISP) account. I
stopped that in the late 90s. It's not only vendor lock-in, which makes
negotiation with ISPs (e.g. over prices/fares/conditions) harder.


Like a university E-mail account, it's only temporary (cannot be kept for
eternity no matter how much one wishes so; this impacts both staff and
students). This could be added to the table above, but it needs more space to
explain.


E-mail addresses are tied to domains and domains change owners or "business
models" (and speaking of business, do not use your work E-mail with anybody,
except for work where it's mandated; it is important not just for privacy
reasons but also access/retention; employees love locking staff out of their
accounts, sometimes without announcing it). If it's not yours, then it exists
to serve somebody else. This means that when losing touch with some friends and
those friends later (much later) wish to get in touch it'll result in messages
bouncing, or worse, messages just falling onto a 'blackhole', leaving the
senders to assume you simply ignore them or moved on to some unknown newer
address.


Many workplaces try to dodge IRC and use spyware like Slack (or Webmail instead
of "real" mail) because it makes it easier to force people - immediately and
without prior warning - not to have access to past communications (in case
there's a legal dispute for example). To paraphrase common wisdom, he who
controls the domain controls the communication. So get your own domain and take
charge.


    * Links_16/04/2025:_Cliff_Lynch_RIP,_More_Attacks_on_Science_(NASA)
    * Gemini_Links_16/04/2025:_The_2010s_Are_Calling_and_Why_"Tools_Will_Not
      Liberate_Us"


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⠀⠈⣧⡼⣆⡏⠐⣦⢠⡖⢢⠀⣴⢺⡇⣴⢲⡴⡆⣰⡀⡴⣴⠢⠀⠀⠈⢳⡞⠀⣿⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢑⠙⣿⣾⡋⠀⠀⡇⠀
⠀⠀⠹⠃⠻⠃⠀⠿⠸⠇⠸⠀⠻⠼⠇⠳⠼⠃⠹⠋⠿⠁⠨⠽⠀⠀⠰⠋⠹⠄⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⡿⠋⠉⠻⠆⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠤⠤⠤⠠⠠⠃⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠺⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⡍⣭⣿⠿⢿⠿⢿⢸⢿⣿⡋⢾⡿⠿⡯⡇⡿⠿⣿⠿⠃⣿⡿⠿⡿⣿⠿⠿⢿⡿⠿⡿⠿⢿⠿⢿⠿⢿⠱⡾⣿⡿⢸⢸⢿⡿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⡿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣏⠶⢸⠮⣹⢠⡹⣿⣅⣿⡱⠆⡇⡆⡠⠖⣂⠻⠃⣿⡷⠌⣃⠿⢀⡸⠿⡸⠿⡄⠶⣲⠮⣹⠮⣹⢸⣇⠿⠃⢸⢸⡌⣼⣟⣻⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡛⠿⠷⢶⣶⡾⠟⠋⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠻⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣵⢹⡝⣿⡏⡏⣽⣿⢩⡏⣭⡿⣝⢹⢹⢸⣿⢨⡍⣯⣯⢫⠋⣿⣿⢹⣹⢽⣿⢹⡅⡯⡏⡏⣽⢩⣽⢯⡋⡏⣯⢹⣹⣹⢫⡅⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣷⣷⣷⣿⣿⣾⣷⣿⣷⣷⣾⣾⣾⣿⣾⣷⣷⣷⣷⣿⣿⣿⣶⣾⣾⣿⣾⣶⣷⣷⣶⣿⣾⣿⣾⣶⣗⣓⣼⣾⣾⣶⣷⣷⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⡶⡶⣶⢶⢶⡶⡶⣶⢶⢶⡶⡶⡶⢶⢶⠶⡶⡶⢶⢶⠶⡶⡶⢶⢶⠶⡶⡶⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⡻⡟⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠿⢇⡇⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡺⡿⣿⢿⢿⡿⡿⣿⢿⢿⡿⡿⣶⢿⢿⠿⡿⡿⢿⢿⠿⡿⡿⢿⢿⢿⡿⡿⣻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

                    ䷩ 𝚕𝚒𝚗𝚎 5766

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 16/04/2025: IndieWeb Carnival,
Tinylog RFC, "Focus, the Web and Gemini"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇browser_OS⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Tarrifs_[sic]_and_luxuries⠀⇛


                       I’ve been exposed to a lot of liberal discourse
                       about tarrifs [sic] lately. Without getting into a
                       whole digression about nations and borders, I want
                       to articulate more specific points of disagreement
                       with some of the (often implicit) arguments I’ve
                       seen: [...]


                       Many folks seem unable to conceive of a life where
                       they consume less while not living under conditions
                       of miserable austerity. This ideological blind spot
                       is going to wind up thrusting us all into miserable
                       austerity.


                       I would much rather spend half as much time engaged
                       in compulsory labor than drive a fancier fucking
                       car, or spend a couple years on sabbatical — so
                       that I could meander around the globe — than take
                       more frequent jet trips to some resort (where poor
                       people wait on me). Wouldn’t you? If not, I hope
                       you can at least see that nearly everyone benefits
                       if we’re given these options.


                # ⚓ don't_panic_until_it's_time_to_panic⠀⇛


                       the project i'd been working for was paused, but i
                       was able to bounce back onto another job.
                       thankfully. don't know when the project will be un-
                       paused, but hopefully it'll be soon.


                       the world feels dreary, but i've got a date
                       tomorrow, i've got friends to hang out with, my
                       grandmother gave me some mangos and i'll start work
                       next week. sometimes, you just have to take it one
                       day at a time.


                # ⚓ LQ’s_account_of_the_end⠀⇛


          o § Science⠀➾


                # ⚓ News_and_Links_Digest⠀⇛


          o § Technology and Free Software⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ IndieWeb_Carnival_April_2025:_(book)_renewal⠀⇛


                             The post at the link talks about spring as a
                             time of renewal. As a librarian, though, the
                             word "renewal" immediately makes me think
                             about book renewals. The thing where you
                             haven't finished reading a book yet (or maybe
                             haven't even started), but said book is about
                             to be overdue, so you re-borrow it for
                             another term.


                             I love when students renew books. It tells me
                             that they haven't given up on reading this
                             book. Maybe they haven't finished; maybe they
                             haven't even started, but they're still
                             sufficiently interested to give themselves
                             that additional three-week chance. I dig
                             that. Read on, you crazy diamonds!


                             I have the opposite problem (if it is a
                             problem): As the person responsible for
                             acquisitions around here and also a
                             professional reviewer, I read 2-3 books per
                             week on average.


                      # ⚓ Tinylog_RFC_update_-_call_for_contribution⠀⇛


                             Edit: I did a mistake and instead of creating
                             a merge request, I actually already pushed
                             the new commit… I’ve linked the diff anyway
                             and depending on the discussion I may revert
                             some of it… But it does mean that there is no
                             merge request to say to comment, instead,
                             I’ve created an issue on codeberg for
                             discussion.


                      # ⚓ Focus,_the_Web_and_Gemini⠀⇛


                             Imagine the following: You're trying to find
                             a specific information. And of course you
                             start searching for it on the internet. It is
                             convenient, quick, and can be done whenever,
                             wherever you are. Nobody wants to spend their
                             time looking through dozens of books, just to
                             find out the local library doesn't have what
                             you need today.


                             § The Experience


                             You open Google, enter your search query, and
                             boom, there you have it: Your information.
                             Well, almost...


                             Between your search query and the information
                             you are looking for is a long way: Bad or
                             incomplete information, subjective opinions
                             without any base, an ad for a mysterious
                             health trick that doctors hate, even more ads
                             for things you've already acquired and last
                             but not least a funny cat meme that tricks
                             you into a doom scrolling session.


                             And while you are trying to find out if there
                             is any useful information in between all this
                             junk on the website you are currently looking
                             at, you are interrupted again by some sketchy
                             pop-ups.


                             I guess you know what I am talking about: The
                             pain of filtering out all of these things you
                             didn't ask for in the first place.


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


    * Links_15/04/2025:_Touchable_Volumetric_Display_and_Resistance_to_American
      Spying_Firms
    * IRC_Proceedings:_Tuesday,_April_15,_2025



                    ䷩ 𝚕𝚒𝚗𝚎 5952

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 16/04/2025: The 2010s Are
Calling and Why "Tools Will Not Liberate Us"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ 🔤SpellBinding:_ABCEGKM_Wordo:_DEPTH⠀⇛


                # ⚓ First_Fermentation_of_2025⠀⇛


                       I started some sauerkraut about 2 days ago. By this
                       point last year, I had made 3 batches of
                       sauerkraut, but I also got bit by mosquitos in
                       March last year... soooooo... It was also 70F+ the
                       first week of January last year, so things were
                       quite weird last year.


                       The sauerkraut is fermenting! Maybe not as quickly
                       as I'd like, as it still does get decently cold at
                       night, so the average temperature during the day is
                       probably about 40-45F instead of 55F+, but the
                       fermentation is certainly going.


                       I'm excited for sauerkraut after dealing with
                       nearly a dozen polar vortexes this year, each
                       bringing the temperature down to around -30F to -
                       40F and bringing a lot of wind...


                # ⚓ The_2010s_Are_Calling⠀⇛


                       I've been getting back to some old hobbies and
                       making the conscious effort to avoid subreddits.
                       Reddit is honestly not bad the nicher you get - the
                       front page stuff is all low-effort replies and
                       riffing, but the specialist stuff can actually be
                       pretty good.


                       But I deleted my account when they partnered with
                       Google to allow API access for AI training on
                       posts, and have tried not to look back. Lately,
                       I've been getting back into some old musical
                       interests on guitar. But instead of going to
                       particular subreddits, I've been trying instead to
                       use forums.


                       They're not wholly dead, somehow - if you were a
                       guitar player on the internet in the 2000s, you
                       were probably aware of Ultimate Guitar (for tabs)
                       and Harmony Central (for forums). Harmony Central
                       kept getting bought and sold and eventually was I
                       think sold to Musician's Friend and given some sort
                       of terrible UI makeover. That combined with new,
                       aggressive moderation (the site was not, uhhhh,
                       particularly couth) drove a lot of people away. For
                       me personally, instead of finding another place to
                       post, I just focused on Facebook. Which, yeah, in
                       retrospect, maybe not the greatest decision.
                       Looking at it dispassionately, I think Facebook's
                       best strength is as a community resource for the
                       place you currently live in. I was using it as a
                       way to keep up with old friends in the city I'd
                       moved away from. But it felt increasingly strange,
                       like I was this ghost haunting their posts with
                       little reactions. Like. Love. Care. And so on.


                # ⚓ el_gran_tarot_esoterico_pt1?⠀⇛


                       i've been looking into el gran tarot esoterico. not
                       sure how much of what i've found is eudes picard
                       and how much is maritxu guler's synthesizing of the
                       19th century occultists overall.


          o § Politics and World Events⠀➾


                # ⚓ 16_April_2025⠀⇛


                       Man, the current news cycle is making my brain
                       hurt... every other day you either hear about some
                       astoundingly stupid idea Trump comes up with, new
                       ways of our politicians to invade our privacy our
                       the simple fact that the climate is breaking down
                       around us and simply nobody seems to care. At least
                       nobody that could drive CHANGES is caring.
                       Yesterday evening was one of those moments:


                       While with junior at my parents, the TV running in
                       the background i could follow the weather forecast:
                       While the weatherman told the audience that it is
                       now FINALLY raining after a much, much too long dry
                       period the main host of the show told the audience
                       simply "Well... whatever, i was really enjoying the
                       warm weather and hope the rain won't stay too
                       long". I had to really constrain myself to refrain
                       from the urge of slamming my head into the next
                       wall.


          o § Technology and Free Software⠀➾


                # ⚓ Tools_will_not_liberate_us⠀⇛


                       In our work as practitioners of libre and
                       experimental methods for design, a question arises
                       often. It pertains to our loyalty towards the
                       values we ascribe to libre, open, shared or
                       community software. This doesn't mean we question
                       our loyalty to specific pieces of software or
                       specific tools, but rather the steadfastness and
                       consistency with which we practice design in a
                       "libre" approach. The community formed around *PPP*
                       seems to find in libre software the embodiment of
                       the means of some form of liberation. I
                       specifically say libre, as opposed to "open source"
                       because indeed in the energy we put into using
                       those types of tools, we ascribe solidarity,
                       openness, equality in some shape or form, and
                       resistance towards oppressive and predatory
                       practices that surround our everyday use of digital
                       tools. If I say "we", it's because I too do this,
                       and firmly believe in it.


                       The oft-quoted Audrey Lorde sentence is "The
                       master's tools will never dismantle the master's
                       house." We've heard it being applied to the digital
                       realm as well, and I have to agree to some extent,
                       while cautioning that the context in which it was
                       written is very different from that of libre
                       software. Besides, maybe a fuller look at the quote
                       should include the sentence following it. "They may
                       allow us temporarily to beat him at his own game,
                       but they will never enable us to bring about
                       genuine change."


                # ⚓ Four_questions:_tech⠀⇛


                       Ben Colliver invited me to answer these questions.
                       Every month I miss the five questions Christina
                       used to ask us gopher scribblers. It's nice to have
                       a shared prompt!


                       1. When did you first get interested in technology?


                       I learned to type, made zines on copy machines and
                       an offset press, wrote a website for my zine in the
                       '90s on my dad's desktop, but I wasn't interested
                       in the tech, just using it.


                       2011-ish my win xp netbook broke. The new one came
                       with win 7 starter edition, which was just an ad
                       for an os. I wiped it, installed my first linux
                       (crunchbang, openbox on debian), and learned how to
                       use it.


                       I had fun with basic phreaking learned from text
                       files when I was a girl. Stole long distance with a
                       homemade lineman's handset to chatter with my
                       penpal and map what houses wires served, called
                       ranges of 800 numbers to explore. Penpal and I sent
                       mail art that tested the postal service's limits.


                       2. What's your favorite technology?


                       Hard to say. Sundial? Offset press? Dip pen with
                       steno nib? Wristwatch? Boots? Playing cards?
                       Bicycle? Train? Sewing needle? Photo- copier? Slide
                       rule? Books? Inter-library loan? The postal
                       service?


                # ⚓ Take_4⠀⇛


                       Make your writing accessible: concise, bland and
                       simple. Write enough -don't avoid explaining. The
                       aim is to convey a message and there is a
                       difference between avoiding clutter and lack of
                       clarity. The former helps, the latter doesnt.


                       There must be flexibility when writing the first
                       draft. Even if it looks and sounds childish and
                       makes you hate yourself for having written it. This
                       is essential to enable a flow state and make sure
                       that every idea is laid on paper. Some of the
                       apparently bad ideas might turn out great. Also,
                       everything written can be revised and most of it
                       must be revised.


                # § Internet/Gemini⠀➾


                      # ⚓ Hello_geminauts!⠀⇛


                             I am very excited to write this first post on
                             my fresh, new gemlog. A bit late to the
                             party, I know. I've been meaning to set up a
                             capsule for a while now but the list of
                             things I've been meaning to do was (and still
                             is) long. But apparently, the time was ripe,
                             and I installed vger and stunnel on my server
                             infrastructure and voila, here I am!


                             It sure feels refreshing to be here. A refuge
                             from the surveillance and abuse on the world-
                             wide web. Exploring this space will be fun,
                             and I hope to find my place within it.


                             [...]


                             This capsule is hosted on a FreeBSD server.
                             Incoming connections are handled within a
                             jail, where an stunnel daemon terminates the
                             SSL connection and forwards it to vger, a
                             simplistic Gemini server that supports
                             virtual hosting. Together with the SNI
                             (Server Name Indication) capability of
                             stunnel, this allows me to host multiple
                             capsules on different domain names. For now,
                             there is only this one, but I have plans to
                             convert many of my web sites to capsules as
                             well.


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


    * You_Should_Probably_Self-Host_Your_E-mail_and_Never_Use_a_Web_Browser_for
      Mail
    * Confirming_IBM_Shutdowns_and_Layoffs_Today



                    ䷩ 𝚕𝚒𝚗𝚎 6241

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 16/04/2025: Cliff Lynch RIP, More
Attacks on Science (NASA)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 16, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
                # Desktop/Laptop
          o Proprietary
          o Linux_Foundation
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          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 ⚓ Mike Brock ☛ There_Are_Only_Twenty-Four_Hours_in_a_Day⠀⇛


                 The center must be held—not because it is easy, but
                 because it is ours to hold. And holding it begins with
                 this recognition: there are twenty-four hours in a day,
                 and how we allocate our attention within them may
                 determine whether our republic survives this moment of
                 peril.


          o ⚓ Michael Burkhardt ☛ What’s_in_a_Name?⠀⇛


                 Generally, yes. Michael was the most popular male baby
                 name in the US from every year (except 1960) from 1954 to
                 1998. 4,350,425 of us were named Michael in the 100 years
                 ending 2023. Because of that, I didn’t love being one of
                 five or six Michaels all through grade school. But that
                 wore off and I’ve come to inhabit the name comfortably.


          o ⚓ Austin Kleon ☛ I_can’t_stop_printing_-_Austin_Kleon⠀⇛


                 I’m getting many “what are you going to do with all these
                 prints?!?” questions… so that might be the subject of
                 next week’s newsletter…


          o ⚓ David Rosenthal ☛ Cliff_Lynch_RIP⠀⇛


                 Last Tuesday Cliff Lynch delivered an abbreviated version
                 of his traditional closing summary and bon voyage to
                 CNI's 2025 Spring Membership Meeting via Zoom from his
                 sick-bed. Last Thursday night he died, still serving as
                 Executive Director. CNI has posted In Memoriam: Clifford
                 Lynch.


                 Cliff impacted a wide range of areas. The best overview
                 is Mike Ashenfelder's 2013 profile of Cliff Lynch in the
                 Library of Congress' Digital Preservation Pioneer series,
                 which starts: [...]


          o ⚓ [Old] LOC ☛ Digital_Preservation_Pioneer:_Clifford_Lynch_|_The
            Signal⠀⇛


                 Clifford Lynch is widely regarded as an oracle in the
                 culture of networked information. Lynch monitors the
                 global information ecosystem for cultural trends and
                 technological developments. He ponders their variables,
                 interdependencies and influencing factors. He confers
                 with colleagues and draws conclusions. Then he reports
                 his observations through lectures, conference
                 presentations and writings. People who know about Lynch
                 pay close attention to what he has to say.


                 Lynch is a soft-spoken man whose work, for more than
                 thirty years, has had an impact — directly or indirectly
                 — on the computer, information and library science
                 communities.


          o ⚓ AJ Bourg ☛ Greenhouse!⠀⇛


                 They’re enclosed, so even on windy days it’s nice to be
                 outside (helps keep it a bit warmer too when the wind has
                 a bite)


          o § Science⠀➾


                # ⚓ The Register UK ☛ Politicians_protest_proposed_cuts_to_NASA
                  science⠀⇛


                       The proposed cuts to NASA's budget are drawing
                       sharp criticism from US lawmakers, with one saying:
                       "If you cut this budget, you cut into the heart of
                       America's leadership when it comes to space
                       exploration."


                # ⚓ Wired ☛ Proposed_NASA_Budget_Cuts_‘Would_Decimate_American
                  Leadership_in_Space’⠀⇛


                       The approximate 20 percent budget cut could force
                       the closure of the Goddard Space Flight Center and
                       would see projects such as the Nancy Grace Roman
                       Space Telescope scrapped.


                # § IBM⠀➾


                      # ⚓ Jonathan Dowland ☛ [IBM's]_Jonathan_Dowland's_Weblog:
                        submitted [Ed: He worked for Red Hat (IBM) at the same
                        time. Hard to see what a PhD, if he gets it, will get
                        him inside IBM. IBM does not value "Expensive" staff.
                        It looks for ways to REPLACE them.]⠀⇛


                             Today I submitted my PhD thesis, 8 years
                             since I started (give or take). Next step,
                             Viva.


          o § Career/Education⠀➾


                # ⚓ Associated Press ☛ Canadian_university_teachers_warned
                  against_traveling_to_the_United_States⠀⇛


                       Reports of foreigners being sent to detention or
                       processing centers for more than seven days,
                       including Canadian Jasmine Mooney, a pair of German
                       tourists, and a backpacker from Wales, have been
                       making headlines since Trump took office in
                       January.


                # ⚓ CBC ☛ Canadian_university_teachers_warned_against
                  travelling_to_the_United_States⠀⇛


                       The Canadian Association of University Teachers
                       says it released updated travel advice Tuesday due
                       to the "political landscape" created by the Trump
                       administration and reports of some Canadians
                       encountering difficulties while crossing the
                       border.


                # ⚓ Mira Welner ☛ How_I_got_a_Job_in_March_of_2025⠀⇛


                       I want to preface this by saying that this is NOT a
                       guide on how to get a job. This is a recounting of
                       my own personal experience in the job market in
                       2025 as a recent (2022) computer science and
                       engineering graduate. This is what happened to me,
                       a white 24-year-old living in Pittsburgh, PA. If
                       these are not your demographics, your mileage may
                       vary. And honestly, even if those are your
                       demographics, your mileage may still vary; the
                       market is a fiasco right now.


                # ⚓ Justin Searls ☛ The_Best_Programmers⠀⇛


                       Matthias Endler wrote up a list of traits he sees
                       in great developers, which I read because Jerod
                       linked to it in Changelog's newsletter. In his
                       blurb, Jerod called back to the conversation he had
                       with yours truly on a recent podcast episode, which
                       is also the first thing I thought of when I read
                       the post.


                       As lists go, these traits are all great things to
                       look for in developers, even if a lot of it is
                       advice you've seen repeated countless times before.
                       This one on bugs stands out: [...]


                # ⚓ Robert Birming ☛ The_value_of_a_firm_"No"⠀⇛


                       That is one of the advantages of getting older: I
                       feel secure in declining things. It's a great
                       feeling!


          o § Hardware⠀➾


                # § Desktop/Laptop⠀➾


                      # ⚓ Russell Coker ☛ What_Desktop_PCs_Need⠀⇛


                             It seems to me that we haven’t had much
                             change in the overall design of desktop PCs
                             since floppy drives were removed, and modern
                             PCs still have bays the size of 5.25″ floppy
                             drives despite having nothing modern that can
                             fit in such spaces other than DVD drives
                             (which aren’t really modern) and carriers for
                             4*2.5″ drives both of which most people don’t
                             use. We had the PC System Design Guide [1]
                             which was last updated in 2001 which should
                             have been updated more recently to address
                             some of these issues, the thing that most
                             people will find familiar in that standard is
                             the colours for audio ports.


                             [...]


                             Here are some of the things that I think
                             should be in a modern PC System Design Guide.


                             [...]


                             For restricting noise of PCs we have
                             industrial relations legislation that seems
                             to basically require that workers not be
                             exposed to noise louder than a blender, so if
                             a PC is quieter than that then it’s OK. For
                             name brand PCs there are specs about how much
                             noise is produced but there are usually
                             caveats like “under typical load” or “with a
                             typical feature set” that excuse them from
                             liability if the noise is louder than
                             expected. It doesn’t seem possible for
                             someone to own a PC, determine that the noise
                             from it is what is acceptable, and then buy
                             another that is close to the same.


                             We need regulations about this, and the EU
                             seems the best jurisdiction for it as they
                             cover the purchase of a lot of computer
                             equipment that is also sold without change in
                             other countries. The regulations need to also
                             cover updates, for example I have a Dell T630
                             which is unreasonably loud and Dell support
                             doesn’t have much incentive to be
                             particularly helpful about it. BIOS updates
                             routinely tweak things like fan speeds
                             without the developers having an incentive to
                             keep it as quiet as it was when it was sold.


                      # ⚓ Russell Coker ☛ Storage_Trends_2025⠀⇛


                             It’s been almost 15 months since I blogged
                             about Storage Trends 2024 [1]. There hasn’t
                             been much change in this time (in Australia
                             at least – I’m not tracking prices in other
                             countries). The change was so small I had to
                             check how the Australian dollar has performed
                             against other currencies to see if changes to
                             currencies had countered changes to storage
                             prices, but there has been little overall
                             change when compared to the Chinese Yuan and
                             the Australian dollar is only about 11% worse
                             against the US dollar when compared to a year
                             ago. Generally there’s a trend of computer
                             parts decreasing in price by significantly
                             more than 11% per annum.


                             § Small Storage


                             The cheapest storage device from MSY now is a
                             Patriot P210 128G SATA SSD for $19, cheaper
                             than the $24 last year and the same price as
                             the year before. So over the last 2 years
                             there has been no change to the cheapest
                             storage device on sale. It would almost never
                             make sense to buy that as a 256G SATA SSD
                             (also Patriot P210) is $25 and has twice the
                             lifetime (120TBW vs 60TBW). There are also
                             256G NVMe devices for $29 and $30 which would
                             be better options if the system has a NVMe
                             socket built in.


                             The cheapest 500G devices are $42.50 for a
                             512G SATA SSD and $45 for a 500G NVMe. Last
                             year the prices were $33 for SATA and $36 for
                             NVMe in that size so there’s been a
                             significant increase in price there. The
                             difference is enough that if someone was on a
                             tight budget they might reasonably decide to
                             use smaller storage than they might have used
                             last year!


          o § Proprietary⠀➾


                # ⚓ India Times ☛ Google_layoffs_may_hit_these_teams_in_India⠀⇛


                # ⚓ The Register UK ☛ OneDrive_clients_for_Windows,_Mac_still
                  broken_10_months_on⠀⇛


                       OneDrive users on both OSes complained that their
                       shared folders no longer appeared in their local
                       OneDrive directories and had instead been replaced
                       with .url files linking to OneDrive's web
                       interface. The change effectively broke offline
                       access and syncing, with users reporting the issue
                       to Microsoft through community forums and support
                       channels.


                # ⚓ The Register UK ☛ Fresh_Classic_Mac_OS_and_PowerPC_apps_in
                  2025⠀⇛


                       The first Intel-based Mac was 19 years ago, but new
                       versions of apps for both Classic Mac OS and
                       PowerPC Mac OS X still occasionally appear, and we
                       are here for it.


                # ⚓ Wired ☛ China_Secretly_(and_Weirdly)_Admits_It_Hacked_US
                  Infrastructure⠀⇛


                       In public and private meetings, Chinese officials
                       are typically firm in their denials about any and
                       all accusations of offensive hacking. This makes it
                       all the more unusual that the Chinese delegation
                       specifically confirmed that years of attacks on US
                       water utilities, ports, and other targets are the
                       result of the US's policy support of Taiwan.
                       Security researchers refer to the collective
                       activity as having been perpetrated by the actor
                       “Volt Typhoon.”


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ International Business Times ☛ Tesla_Ordered_To
                        Replace_Faulty_'Self-Driving'_Computers_In_4_Million
                        Cars_Or_Pay_Up⠀⇛


                             Tesla, the electric vehicle titan, faces a
                             monumental challenge that could reshape its
                             future. A recent ruling mandates the company
                             to replace the 'self-driving' computers in
                             approximately 4 million vehicles or
                             compensate their owners, following admissions
                             that the hardware falls short of promised
                             autonomous capabilities.


                             This development, reported on 14 April 2025,
                             has sent ripples through the automotive
                             world, raising questions about Tesla's
                             ambitious vision.


                      # ⚓ Cyble Inc ☛ New_GenAI_Supply_Chain_Threat:_Code
                        Package_Hallucinations⠀⇛


                             “An adversary can exploit package
                             hallucinations, especially if they are
                             repeated, by publishing a package to an open-
                             source repository with the same name as the
                             hallucinated or fictitious package and
                             containing some malicious code/
                             functionality,” they said. “As other
                             unsuspecting and trusting LLM users are
                             subsequently recommended the same fictitious
                             package in their generated code, they end up
                             downloading the adversary-created malicious
                             package, resulting in a successful
                             compromise. This compromise can then spread
                             through an entire codebase or software
                             dependency chain, infecting any code that
                             relies on the malicious package.”


                      # ⚓ arXiv ☛ We_Have_a_Package_for_You!_A_Comprehensive
                        Analysis_of_Package_Hallucinations_by_Code_Generating
                        LLMs⠀⇛


                             In this work, we focus on a specific type of
                             hallucination during code generation called
                             package hallucination. Package hallucination
                             occurs when an LLM generates code that
                             recommends or contains a reference to a
                             package that does not actually exist. An
                             adversary can exploit package hallucinations,
                             especially if they are repeated, by
                             publishing a package to an open-source
                             repository with the same name as the
                             hallucinated or fictitious package and
                             containing some malicious code/functionality.
                             As other unsuspecting and trusting LLM users
                             are subsequently recommended the same
                             fictitious package in their generated code,
                             they end up downloading the adversary-created
                             malicious package, resulting in a successful
                             compromise. This compromise can then spread
                             through an entire codebase or software
                             dependency chain, infecting any code that
                             relies on the malicious package. This is a
                             variation of the classical package confusion
                             attack that has been enabled by code-
                             generating LLMs


                      # ⚓ Pivot to AI ☛ H&M’s_‘AI_models’_campaign_makes
                        impossible_claims⠀⇛


                             H&M is making some big promises with this
                             pitch. But is any of this … real? It’s
                             certainly not plausible. Think for one moment
                             about these claims.


                             Fashion images — or any ad for a particular
                             object — have to be accurate to the object. I
                             cannot overstate how important this is. The
                             clothes, the belt, the watch, have to be
                             represented accurately. You can’t use
                             whatever approximation the diffusion model
                             thinks is a bit like the object.


                      # ⚓ Futurism ☛ Called_Out_for_AI_Slop,_Andrew_Cuomo
                        Blames_One-Armed_Man⠀⇛


                             The excuse also doesn't quite add up. There's
                             nothing wrong with using dictation software,
                             but why would that cause blatant spelling
                             errors or a reference to ChatGPT? And why
                             wasn't someone else reviewing the document
                             before pushing it out? All told, it sounds a
                             lot like a fictional explanation crafted by a
                             political campaign to deter critics by
                             throwing a man with a disability under the
                             bus.


                      # ⚓ Society for Scholarly Publishing ☛ Guest_Post_-_The
                        Open_Access_–_AI_Conundrum:_Does_Free_to_Read_Mean_Free
                        to_Train?_-_The_Scholarly_Kitchen⠀⇛


                             When the Open Access (OA) movement gained
                             momentum in the early 2000s, its proponents
                             envisioned a world where research findings
                             would be freely available to all readers —
                             breaking down paywalls that limited knowledge
                             dissemination and hindered scientific
                             progress. By the 2010s, an increasing number
                             of countries began to mandate open access
                             publications, arguing that publicly funded
                             research should be freely available to the
                             public. The readers envisaged by proponents
                             of OA were obviously human (academics as well
                             as the wider public). While text mining had
                             been considered as one potential application,
                             they could not foresee the development of
                             large language models (LLMs) which would
                             begin to rapaciously ingest large amounts of
                             text. OA literature has become particularly
                             attractive for AI training precisely because
                             it lacks the legal and technical barriers
                             that might protect traditionally published
                             content.


                      # ⚓ Quanta Magazine ☛ To_Make_Language_Models_Work
                        Better,_Researchers_Sidestep_Language⠀⇛


                             Here’s how these models typically work. When
                             a user queries an LLM, an algorithm breaks
                             that input text into a sequence of tokens.
                             The model then converts each token into a
                             string of numbers called an embedding, fodder
                             for the underlying mathematical machinery. An
                             input of 10 tokens results in 10 embeddings,
                             for example. The transformer then processes
                             these embeddings through its various
                             components, called layers. Each layer feeds
                             its results into the next layer, gradually
                             connecting each embedding to every other
                             embedding. The final layer puts all this
                             information together to generate one final
                             set of embeddings. The last embedding in this
                             sequence is called a hidden state — “hidden”
                             because it’s not exposed to the outside
                             world. This hidden state contains all the
                             relevant information needed for the model to
                             predict the most likely next token, or word,
                             to follow the initial input sequence of
                             tokens.


                      # ⚓ Bruce Schneier ☛ Slopsquatting_-_Schneier_on
                        Security⠀⇛


                      # ⚓ Hidde de Vries ☛ Is_“ethical_AI”_an_oxymoron?_|
                        hidde.blog⠀⇛


                             It depends who you ask. But the current wave
                             of generative AI has unpleasant side effects
                             that are hard to ignore: large-scale
                             copyright infringements, environmental impact
                             and bias.


                # § Social Control Media⠀➾


                      # ⚓ Futurism ☛ Zuckerberg_Encourages_Theatergoers_to_Use
                        Their_Phones_While_Movie_Is_Playing⠀⇛


                             Using chatbot technology that Meta refers to
                             as "Movie Mate" — a new spin, perhaps, on
                             Zuckerberg's cringey push to get his
                             subordinates to refer to each other as "Meta
                             Mates" back when he was all-in on virtual
                             reality — fans will be able to talk to an AI
                             version of the iconic robot.


                      # ⚓ Variety ☛ Meta_Launching_Second_Screen_Theater_Tech
                        With_'M3GAN'_Rerelease⠀⇛


                             The “M3GAN” screening will also allow fans to
                             communicate with the evil doll herself via a
                             M3GAN chatbot. Meta is launching its Movie
                             Mate technology with the screening, allowing
                             moviegoers to second screen during the film
                             to access exclusive content, trivia and
                             behind-the-scenes info in real-time.


                      # ⚓ The Atlantic ☛ How Social-Media_Sites_Can_Fight_Hate
                        Without_Censorship⠀⇛


                             All of these ideas are free-speech friendly.
                             They do not involve top-down censorship, but
                             bottom-up user choice. Letting people police
                             the content on their own pages and feeds is
                             the natural next step for platforms that want
                             to empower users rather than constantly
                             surveil and censor them. Such features are
                             also just common sense. No one has an
                             inherent right to graffiti another person’s
                             real-world home; they shouldn’t have a right
                             to vandalize a virtual one.


          o § Linux Foundation⠀➾


                # ⚓ I Programmer ☛ Linux_Foundation_Mentorship_Program [Ed: PR
                  slush funds]⠀⇛


                       Applications are now open for Summer 2025
                       participation in the Linux Foundation Mentorship
                       Program, a program that provides structured
                       guidance and opportunities for newcomers to
                       contribute to the Linux kernel and other open-
                       source projects.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ India Times ☛ Whistleblower_org_says_DOGE_[sic]_may
                        have_caused_'significant_cyber_breach'_at_US_labor
                        watchdog⠀⇛


                             A whistleblower alleges Elon Musk's tech team
                             caused a major cybersecurity breach at the
                             NLRB, compromising sensitive labor case
                             files. IT staffer Daniel Berulis claims
                             unauthorized access, data exfiltration, and
                             attempted Russian logins occurred. Efforts to
                             alert authorities were blocked, and Berulis
                             faced intimidation. Musk’s team has not
                             commented.


                      # ⚓ The Register UK ☛ Meta_set_to_resume_training_AI
                        models_on_EU_user_posts⠀⇛


                             At the request of the DPC, the European Data
                             Protection Board (EDPB) in December published
                             an opinion about how the fundamental data
                             protection rights recognized under Europe's
                             General Data Protection Regulation (GDPR) can
                             be reconciled with AI models and how they get
                             trained.


                             The decision looks at: The circumstances
                             under which an AI model can be considered
                             anonymous, how data controllers can show they
                             have a legitimate interest in data as it
                             applies to AI model training and deployment,
                             and what are the consequences when an AI
                             model is deemed to have unlawfully processed
                             personal data.


                      # ⚓ The Register UK ☛ Report:_EC_issues_burner_phones_for
                        visits_to_US⠀⇛


                             The European Commission is giving staffers
                             visiting the US on official business burner
                             laptops and phones to avoid espionage
                             attempts, according to the Financial Times.


                             The use of clean and locked-down hardware is
                             common practice for anyone visiting China,
                             Russia, and other states where aggressive
                             electronic surveillance is expected.
                             Apparently the European Union has added the
                             United States to that list.


                      # ⚓ The Record ☛ EU_confirms_issuing_‘burner_phones’_to
                        top_officials_but_denies_practice_caused_by_Trump⠀⇛


                             A spokesperson for the European Commission
                             confirmed on Tuesday that it does provide
                             “burner phones” to top officials, but denied
                             a report that the practice was new and
                             connected to a recent security appraisal of
                             the risks when visiting the United States.


                      # ⚓ Wired ☛ Suspected_4chan_Hack_Could_Expose_Longtime,
                        Anonymous_Admins⠀⇛


                             “4chan is an anonymous message board that
                             enables often offensive and hateful content.
                             The content leaked, if genuine, would remove
                             some of the anonymity from 4chan
                             administrators, moderators, and janitors,”
                             says Ian Gray, director of analysis and
                             research at the security firm Flashpoint. The
                             image board’s billing as an “anonymous”
                             platform may have given users a “false sense
                             of security,” Gray says. “Some users may have
                             registered their email addresses years ago
                             when they were less aware or concerned about
                             their operational security.”


                      # ⚓ 404 Media ☛ 4chan_Is_Down_Following_What_Looks_to_Be
                        a_Major_Hack_Spurred_By_Meme_War⠀⇛


                             Hackers claim to have obtained 4chan's code,
                             emails of moderators, and internal
                             communications.


                      # ⚓ EPIC ☛ EPIC_Feedback_to_House_Energy_&_Commerce
                        Majority_Privacy_Working_Group⠀⇛


                             The Electronic Privacy Information Center
                             (EPIC) appreciates the opportunity to provide
                             feedback to the Privacy Working Group led by
                             the Majority Leadership of the House
                             Committee on Energy and Commerce. Federal
                             privacy legislation must limit the collection
                             and use of Americans’ personal data with
                             rules that respect our human right to
                             privacy, limit harmful discrimination and
                             targeting, and support the beneficial
                             evolution of the technologies and systems we
                             rely on in our everyday lives. EPIC has long
                             advocated for strong privacy laws at the
                             federal and state levels and is ready and
                             willing to be a resource to the Privacy
                             Working Group as it seeks to provide
                             comprehensive privacy protections to all
                             Americans.


                      # ⚓ EDRI ☛ Civil_society_files_DSA_complaint_against_Meta
                        for_toxic_feeds⠀⇛


                             Today, Bits of Freedom, EDRi, Gesellschaft
                             für Freiheitsrechte, and Convocation Design +
                             Research are filing a complaint under the
                             Digital Services Act (DSA) against Meta, the
                             company behind Facebook and Instagram.
                             According to the complaint, Meta violates the
                             DSA’s user protections by not offering easily
                             accessible news feed options on its platforms
                             that are not based on profiling of users.


                             This alternative news feed must be directly
                             and easily accessible for users.


                      # ⚓ EFF ☛ Privacy_on_the_Map:_How_States_Are_Fighting
                        Location_Surveillance⠀⇛


                             Last year, we sounded the alarm, urging
                             lawmakers to protect individuals from the
                             growing threats of location tracking
                             tools—tools that are increasingly being used
                             to target and criminalize people seeking
                             essential reproductive healthcare.


                             The good news? Lawmakers in California,
                             Massachusetts, Illinois and elsewhere are
                             stepping up, leading the way to protect
                             privacy and ensure that healthcare access and
                             other exercise of our rights remain safe from
                             invasive surveillance.


                      # ⚓ The Atlantic ☛ Would_You_Give_PornHub_Your_ID?⠀⇛


                             A new study by researchers at Stanford, NYU,
                             the University of Georgia, and Georgia State
                             followed the implementation of a law in
                             Louisiana that required any website
                             publishing a substantial amount of
                             pornographic content to take reasonable steps
                             to verify the age of users before giving them
                             access. The researchers found that while
                             search traffic to Pornhub—which complied with
                             the law—dropped by 51 percent, traffic to its
                             noncompliant rival, XVideos, rose by 48.1
                             percent. This is a classic tale of tech
                             regulation: lots of friction while the
                             primary aim remains unfulfilled.


                             But one of the researchers, Zeve Sanderson,
                             the executive director of NYU’s Center for
                             Social Media and Politics, isn’t resigned to
                             defeat. On today’s episode of Good on Paper,
                             we discuss what governments can even do to
                             regulate the internet on behalf of minors and
                             what doing so might cost the rest of us.
                             Also, he explains, Louisiana’s legislation
                             shows that writing a law can be the
                             beginning, not the end, of a policy process.


                      # ⚓ The Record ☛ 23andMe_bankruptcy_draws_investigation
                        from_House_panel_over_data_concerns⠀⇛


                             The company’s bankruptcy filing “raises
                             significant concerns regarding potential
                             transfers of customers’ and family members’
                             sensitive personal data to various interested
                             entities,” including China’s government, says
                             committee Chairman James Comer (R-KY) in a
                             letter to Anne Wojcicki, who initiated
                             23andMe’s bankruptcy proceedings in March and
                             resigned as chief executive soon afterward.


                      # ⚓ The Register UK ☛ Hertz_says_personal,_sensitive_data
                        stolen_in_Cleo_attacks⠀⇛


                             A smaller subset of customers may also have
                             had more sensitive data stolen, including
                             Social Security or other government
                             identification numbers, passport information,
                             Medicare or Medicaid ID, or injury-related
                             information associated with vehicle accident
                             claims.


          o § Defence/Aggression⠀➾


                # ⚓ The Hindu ☛ Bengal_govt_must_stop_attacks_on_Hindus_over
                  Waqf_Act_protests:_VHP⠀⇛


                       Mr. Parande said the fleeing of Bengali Hindus from
                       their homes in Dhulian area of Murshidabad district
                       and taking shelter in adjacent Malda district to
                       escape attack from “jihadi marauders”, is
                       reminiscent of “the exodus of Kashmiri pandits from
                       Jammu and Kashmir in the past”.


                # ⚓ Techdirt ☛ Another_IRS_Commissioner_Steps_Down_After_Being
                  Forced_To_Share_Immigrant_Tax_Records_With_The_DHS⠀⇛


                       One acting commissioner — one with 38 years
                       experience — has already resigned because of the
                       DHS’s desire to use tax records as a migrant-
                       hunting database. What began as a request for
                       “only” 700,000 records has ballooned to a demand
                       for seven million tax records — a number that would
                       encompass nearly two-thirds of the eleven million
                       immigrants currently living in the United States.


                       Acting commissioner Melanie Krause has chosen to
                       walk, rather than be a part of this horrific mass
                       vanishing of migrants, despite initially showing
                       some willingness to cooperate with the Trump
                       administration’s demands.


                # ⚓ Task And Purpose ☛ Russia_continues_to_throw_troops_into_a
                  meat_grinder_in_Ukraine⠀⇛


                       “Since 2022, Russia has suffered more than 700,000
                       casualties in Ukraine,” former Secretary of Defense
                       Lloyd Austin said in January. “Now, that’s more
                       than Moscow has endured in all of its conflicts
                       since World War II — combined. Russian casualties
                       in Ukraine now surpass two-thirds of the total
                       strength of the Russian military at the start of
                       Putin’s war of choice. In November 2024 alone,
                       Russia lost nearly 1,500 troops a day.”


                # ⚓ The Atlantic ☛ How_the_Trump_Administration_Is_Taxing_the
                  IRS⠀⇛


                       Sabotaging the agency’s work amounts to an
                       inducement for the ultra-rich to treat taxes as a
                       voluntary contribution.


                # ⚓ The Atlantic ☛ What_the_Courts_Can_Still_Do_to_Constrain
                  Trump⠀⇛


                       More accurately, the administration is defying the
                       spirit, rather than the letter, of the Supreme
                       Court ruling. What’s indisputable, though, is that
                       it's daring the federal courts to take much more
                       aggressive steps to block its immigration policies.


                # ⚓ MIT Technology Review ☛ Phase_two_of_military_AI_has
                  arrived⠀⇛


                       But the complexity of AI systems, which pull from
                       thousands of pieces of data, make that a herculean
                       task for humans, says Heidy Khlaaf, who is chief AI
                       scientist at the AI Now Institute, a research
                       organization, and previously led safety audits for
                       AI-powered systems.


                       “‘Human in the loop’ is not always a meaningful
                       mitigation,” she says. When an AI model relies on
                       thousands of data points to draw conclusions, “it
                       wouldn’t really be possible for a human to sift
                       through that amount of information to determine if
                       the AI output was erroneous.” As AI systems rely on
                       more and more data, this problem scales up.


                # ⚓ Axios ☛ How_judges_can_hold_Trump_admin_accountable_for
                  defying_court_orders⠀⇛


                       Some legal scholars are warning that Trump
                       administration's reluctance — or outright refusal —
                       to comply with court orders is setting the stage
                       for a full-blown constitutional crisis.


                # ⚓ New Eastern Europe ☛ American-Russian_rapprochement_as_a
                  threat_to_Europe⠀⇛


                       Analyzing long-term trends, we will see many
                       reasons for the US-Russian rapprochement, which
                       should make Europeans worry, because, after all,
                       such a shift will occur at the expense of Europe.


                # ⚓ ANF News ☛ Yazidi_youngster_kidnapped_by_ISIS_from_Shengal
                  in_2014_freed_by_the_SDF⠀⇛


                       In a statement about the operation, the SDF Press
                       Center said: “Our forces succeeded in rescuing the
                       kidnapped Yazidi man, “Othman Khairu Khodi Da”,
                       from the grip of the terrorist organization after
                       more than eleven years of his abduction. Othman is
                       originally from the village of “Al-Wardiya” in the
                       Shengal region, which witnessed large-scale
                       massacres committed by ISIS, where thousands of
                       men, youngsters, and elderly were killed, and more
                       than seven thousand women and girls were abducted.
                       Othman was one of the victims of that massacre.”


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ USMC ☛ Pentagon_senior_adviser_Dan_Caldwell_ousted_in_probe
                  into_leaks⠀⇛


                       Caldwell, who served in the Marine Corps, was one
                       of several senior advisers who worked closely with
                       Hegseth. Caldwell’s ties to the secretary go back
                       to Hegseth’s time as the head of Concerned Veterans
                       for America, a nonprofit that fell into financial
                       difficulty during his time there. Caldwell worked
                       at CVA beginning in 2013 as policy director and
                       later as executive director.


                # ⚓ Wired ☛ Here’s_What_Happened_to_Those_SignalGate_Messages⠀⇛


                       Attorneys suing the United States government over
                       its use of vanishing Signal messages to coordinate
                       military strikes last month in Yemen allege that
                       new court filings by the government reveal a
                       “calculated strategy” by Trump administration
                       officials to evade transparency laws through the
                       illegal destruction of government records.


                # ⚓ The Verge ☛ Meta’s_antitrust_trial_slide_redactions_aren’t
                  actually_hiding_anything⠀⇛


                       A PDF of Meta’s opening statement slides in its FTC
                       antitrust hearing yesterday contains easy-to-remove
                       redactions that make it possible to see everything
                       the company didn’t want made public, The Verge has
                       discovered.


                       Thanks to the poor redactions, we can see sections
                       comparing the use of Apple’s Messages app to Meta
                       apps like Instagram and WhatsApp. The original
                       slide displayed only a quote from Apple director of
                       product marketing Ronak Shah describing an iMessage
                       “core use case” allegedly similar to Facebook’s.
                       Another, labeled “Snapchat in 2020: Competitors Are
                       Succeeding and Not Just Meta Apps,” says that
                       “Tiktok, Insta, FB, Messengers and YouTube” are
                       “thriving.”


                # ⚓ Nick Heer ☛ Meta’s_Poor_Prebuttal_to_“Careless_People”⠀⇛


                       It must have been a surprise as Meta’s preemptive
                       response came in the form of a barely formatted PDF
                       sent to Semafor, and it seems pretty clear the
                       company did not have an advance copy of the book
                       because all of its rebuttals are made in broad
                       strokes against the general outline reported by the
                       Post. Now that I have read the book, I thought it
                       would be fun and educational to compare Meta’s
                       arguments against the actual claims Wynn-Williams
                       makes. I was only half right — reading about the
                       company’s role in the genocide in Myanmar remains a
                       chilling exercise.


          o § Environment⠀➾


                # ⚓ Reuters ☛ Trump_exempts_dozens_of_coal_plants_from_mercury,
                  air_toxics_limits⠀⇛


                       The Trump administration has exempted 47 companies
                       from regulations to curb mercury and air toxics for
                       their coal-fired power plants for two years,
                       according to a list of facilities published by the
                       Environmental Protection Agency on Tuesday.


                # ⚓ Seattle Times ☛ Trump_exempts_nearly_70_coal_plants_from
                  Biden-era_rule_on_mercury_and_other_toxic_air_pollution⠀⇛


                       A list quietly posted as of Tuesday on the
                       Environmental Protection Agency’s website lists 47
                       power providers — which operate at least 66 coal-
                       fired plants — that are receiving exemptions from
                       the Biden-era rules under the Clean Air Act,
                       including a regulation limiting air pollution from
                       mercury and other toxins. The actions follow an
                       executive order last week by President Donald Trump
                       aimed at boosting the struggling coal industry, a
                       reliable but polluting energy source that’s long
                       been in decline.


                # ⚓ Associated Press ☛ EPA_offers_industrial_polluters_a_way_to
                  avoid_rules_on_toxic_chemicals⠀⇛


                       Environmental groups denounced the administration’s
                       offer, calling the email address a “polluters’
                       portal” that could allow hundreds of companies to
                       evade laws meant to protect the environment and
                       public health. Exemptions would be allowed for nine
                       EPA rules issued by the Biden administration,
                       including limits on mercury, ethylene oxide and
                       other hazardous air pollutants. Mercury exposure
                       can cause brain damage, especially in children.
                       Fetuses are vulnerable to birth defects via
                       exposure in a mother’s womb.


                # ⚓ Brattleboro Reformer, Vermont ☛ Letter_to_the_Editor:
                  Honoring_Earth_Day_has_never_been_so_urgent_|_Opinion⠀⇛


                       And, so goes Vermont. Or not. Don’t despair! There
                       are two ways many of us can change this tragic
                       trajectory. First action: join your regional land
                       trust. They are an express-train solution to save
                       all our flowers, ferns, critters, forests, fields
                       and streams in one fell swoop. Immediate,
                       strategic, large scale land conservation can
                       preserve southeastern Vermont’s natural beauty,
                       drinking water, wildlife, agriculture, recreation,
                       history, real estate values and the all-important
                       flood/drought/fire resilience.


                # ⚓ The Nature Conservancy ☛ Earth_Day_is_April_22,_2025_|
                  Ideas_to_celebrate_and_take_action⠀⇛


                       Every Earth Month and Earth Day action is
                       meaningful and momentous. Here are four things you
                       can do.


                # ⚓ UN ☛ International_Mother_Earth_Day_2025⠀⇛


                       The United Nations General Assembly proclaimed 22
                       April as International Mother Earth Day through a
                       resolution adopted in 2009. The Day recognizes the
                       Earth and its ecosystems as humanity's common home
                       and the need to protect her to enhance people’s
                       livelihoods, counteract climate change, and stop
                       the collapse of biodiversity.


                # ⚓ International Earth Day Network ☛ Earth_Day_Poster_-_2025_-
                  Earth_Day⠀⇛


                       EARTHDAY.ORG is thrilled to announce that renowned
                       artist Alexis Rockman has created the official
                       Earth Day 2025 poster, marking our 55th
                       anniversary.


                # ⚓ Gannett ☛ When_is_Earth_Day_2025?_See_the_history_of_the
                  annual_celebration⠀⇛


                       While it may seem strange to think of a world
                       without ecological awareness, there was once a time
                       when Americans were even less aware of their
                       consumption's impacts on Earth.


                       Following the publication of "Silent Spring" by
                       Rachel Carson in 1962, public concern began to grow
                       for the environment and the links between pollution
                       and health.


                # § Energy/Transportation⠀➾


                      # ⚓ International Earth Day Network ☛ Earth_Day_2025_-
                        Our_Power,_Our_Planet⠀⇛


                             As we approach this milestone, we celebrate a
                             transformative reality: we already possess
                             the solutions we need to create clean,
                             inexpensive, and unlimited energy for the
                             entire planet through renewable solar, wind
                             and other technologies.


                             This Earth Day 2025, let us commit to
                             harnessing renewable energy to build a
                             healthy, sustainable, equitable and
                             prosperous future for us all, let us commit
                             to Renewable Energy Now.


                      # ⚓ The Verge ☛ Google’s_geothermal_energy_ambitions_are
                        growing⠀⇛


                             Google is working toward climate goals of
                             cutting the company’s planet-heating
                             emissions in half and matching its
                             electricity use with carbon-free energy
                             purchases around-the-clock by 2030.
                             Geothermal energy comes from heat emanating
                             from within Earth, making it a renewable
                             source of electricity that can help eliminate
                             the fossil fuel pollution causing climate
                             change.


                # § Wildlife/Nature⠀➾


                      # ⚓ 404 Media ☛ The_Ocean_Spectacle_that_Has_Entranced
                        Sailors_for_Centuries⠀⇛


                             Milky seas are produced by bioluminescent
                             bacteria that can transform the nighttime
                             ocean into a glowing white veneer. For
                             centuries, seafarers have marvelled at the
                             eerie beauty of these surreal displays, which
                             sometimes last for months and can cover areas
                             of 100,000 square kilometers (about the size
                             of Iceland).


                # § Overpopulation⠀➾


                      # ⚓ The Moscow Times ☛ Russia’s_Birth_Rate_Plunges_to
                        200-Year_Low⠀⇛


                             The decline was even steeper in February
                             alone, with births falling 7.6% year-over-
                             year to 90,500 — 7,400 fewer than in the same
                             month last year.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The Dissenter ☛ The_Trump_Administration's_Lie_Detector
                  Dragnet⠀⇛


                # ⚓ Papers Please ☛ Withdrawal_from_REAL-ID_gets_a_hearing_in
                  Maine⠀⇛


                       A bipartisan proposal to withdraw the state of
                       Maine from compliance with the Federal REAL-ID Act
                       of 2005 had its first hearing today (archived
                       video) before the Joint Standing Committee on
                       Transportation of the Maine State Legislature.


                       The REAL-ID withdrawal bill, LD 160, was presented
                       to the Transportation Committee by state Rep.
                       Laurel Libby (R-Auburn) and state Sen. Nicole
                       Grohowski (D-Ellsworth), two of the six co-
                       sponsors.


                # ⚓ FAIR ☛ ‘They’re_Doing_Their_Best_to_Turn_People_Who_Have
                  Not_Committed_Any_Crime_Into_Criminals’:_CounterSpin
                  interview_with_Dara_Lind_on_criminalizing_immigrants⠀⇛


                       Janine Jackson interviewed the American Immigration
                       Council’s Dara Lind about the criminalization of
                       immigrants for the April 11, 2025, episode of
                       CounterSpin. This is a lightly edited transcript.


                # ⚓ The Independent UK ☛ Hong_Kong_post_office_to_stop_shipping
                  parcels_to_the_US_after_Trump’s_tariffs⠀⇛


                       A government statement said Hongkong Post would not
                       collect tariffs on behalf of Washington, and will
                       suspend accepting non-airmail parcels containing
                       goods destined for the U.S. on Wednesday, since
                       items shipped by sea take more time. It will accept
                       airmail parcels until Apr. 27.


                # ⚓ The Strategist ☛ Australia_can_learn_from_Britain_on_cyber
                  governance⠀⇛


                       Australia needs to reevaluate its security
                       priorities and establish a more dynamic regulatory
                       framework for cybersecurity. To advance in this
                       area, it can learn from Britain’s Cyber Security
                       and Resilience Bill, which presents a compelling
                       model for reforming our own cyber governance and
                       standards.


                # ⚓ Scoop News Group ☛ Chinese_law_enforcement_places_NSA
                  operatives_on_wanted_list_over_alleged_cyberattacks⠀⇛


                       China has in recent years begun pointing the finger
                       back at the United States, which has accused
                       Beijing of backing a litany of cyberattack, but
                       Tuesday’s allegations were more specific and
                       aggressive than usual. Relations have soured
                       further between China and the United States under
                       the Trump administration as both nations escalate
                       tariffs.


                # ⚓ The Verge ☛ OpenAI_names_new_nonprofit_‘advisors’_|_The
                  Verge⠀⇛


                       OpenAI has revealed the “advisors” for its new
                       nonprofit commission: Dolores Huerta, Monica
                       Lozano, Dr. Robert K. Ross, and Jack Oliver. The
                       company says the four advisors will help “inform
                       OpenAI’s philanthropic efforts,” according to an
                       announcement on Tuesday.


                # ⚓ Mike Brock ☛ The_Surrender_to_China⠀⇛


                       Make no mistake: this is how World War III is being
                       lost—not with missiles and tanks, but with
                       spreadsheets and trade policies. While we've been
                       distracted by regional conflicts and culture wars,
                       China has been methodically building alternative
                       financial infrastructure, technological
                       capabilities, and diplomatic relationships
                       precisely to capitalize on this kind of American
                       self-destruction.


                       The truth is stark but must be faced: electing
                       Trump was effectively surrendering to China. Every
                       day this administration remains in power,
                       irreversible damage occurs to America's economic
                       foundations, diplomatic standing, and global
                       influence. The Chinese Communist Party couldn't
                       have designed a more effective strategy for
                       American collapse if they had installed it
                       themselves.


                       This is why obsessing over Harris' Iran policy or
                       other Middle East concerns ultimately missed the
                       central geopolitical reality of our time. The
                       Middle East, while important, is not the arena
                       where global hegemony will be decided. That battle
                       is economic and technological—and we're voluntarily
                       conceding it.


                # ⚓ Krebs On Security ☛ Funding_Expires_for_Key_Cyber
                  Vulnerability_Database⠀⇛


                       A critical resource that cybersecurity
                       professionals worldwide rely on to identify,
                       mitigate and fix security vulnerabilities in
                       software and hardware is in danger of breaking
                       down. The federally funded, non-profit research and
                       development organization MITRE warned today that
                       its contract to maintain the Common Vulnerabilities
                       and Exposures (CVE) program — which is
                       traditionally funded each year by the Department of
                       Homeland Security — expires on April 16.


                # ⚓ The Register UK ☛ Homeland_Security_funding_for_CVE_program
                  expires⠀⇛


                       While the whole world's vulnerability management
                       efforts aren't going to descend into chaos
                       overnight, there is a concern that in a month or
                       two they may. The lack of US government funding
                       means that, unless someone else steps in to fill
                       the gap, this standardized system for naming and
                       tracking vulnerabilities may falter or shut down,
                       new CVEs may no longer be published, and the
                       program's website may go offline.


                       Not-for-profit outfit MITRE has a contract with the
                       US Department of Homeland Security to operate the
                       CVE program, and on Tuesday the group confirmed
                       this arrangement has not been renewed. This comes
                       as the Trump administration scours around the
                       federal government for costs to trim.


                # ⚓ The Record ☛ MITRE_warns_of_lapse_with_CVE_program_as
                  contract_with_US_set_to_expire⠀⇛


                       The MITRE Corporation said on Tuesday that its
                       stewardship of the CVE program — which catalogs all
                       public cybersecurity vulnerabilities — may be
                       ending this week because the federal government has
                       decided not to renew its contract with the
                       nonprofit.


                # ⚓ Security Week ☛ MITRE_Warns_CVE_Program_Faces_Disruption
                  Amid_US_Funding_Uncertainty⠀⇛


                       In a letter to the CVE board, VP and Director at
                       MITRE’s Center for Securing the Homeland Yosry
                       Barsoum said the contract with the US government to
                       manage the program will expire on April 16 and
                       there’s no word on funding moving forward.


                # ⚓ LWN ☛ MITRE_Warns_CVE_Program_Faces_Disruption_(Security
                  Week)⠀⇛


                       Security Week is one of several outlets reporting


                       that the funding for the CVE program at MITRE
                       disappears as of


                       April 16.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Techdirt ☛ DeepSeek_Is_Already_Being_Applied_Widely
                        Across_China’s_Industries,_And_Used_For_Government
                        Surveillance_And_Propaganda⠀⇛


                             An article by Valentin Weber in the Journal
                             of Democracy predicts that the “next step in
                             the evolution of China’s surveillance state
                             will be to integrate generative-AI models
                             like DeepSeek into urban surveillance
                             infrastructures.” Weber also warns that the
                             rise of AI agents, recently discussed here on
                             Techdirt, is likely to provide the Chinese
                             authorities with even tighter control of
                             their citizens: [...]


                      # ⚓ The Strategist ☛ To_counter_anti-democratic
                        propaganda,_step_up_funding_for_ABC_International⠀⇛


                             The ABC’s international media channels and
                             the bespoke content we create, distribute and
                             share with our media partners showcase an
                             Australian society that is diverse, free and
                             equal, with an independent media that holds
                             power to account.


          o § Censorship/Free Speech⠀➾


                # ⚓ Harvard University ☛ ‘This_is_weakening_the_United
                  States.’⠀⇛


                       The funding, more than $2 billion of which was
                       frozen hours after Harvard responded to the
                       demands, supports research that “has led to
                       groundbreaking innovations across a wide range of
                       medical, engineering, and scientific fields,”
                       according to a message President Alan Garber sent
                       to the Harvard community Monday afternoon.


                # ⚓ Reuters ☛ Students_sue_US_Defense_Department_schools_for
                  book_removals⠀⇛


                       A dozen students in U.S. Defense Department schools
                       sued, opens new tab the department and Defense
                       Secretary Pete Hegseth on Tuesday for book removals
                       and curriculum changes following executive orders
                       from President Donald Trump, an advocacy group
                       said.


                # ⚓ ACLU ☛ Students_Sue_Department_of_Defense_Schools_Over
                  Curriculum_Changes,_Book_Bans_|_American_Civil_Liberties
                  Union⠀⇛


                       Students in Department of Defense Education
                       Activity (DoDEA) schools on military bases sued
                       today, arguing that DoDEA’s book removals and
                       curricular changes following several executive
                       orders from President Donald Trump violate their
                       First Amendment rights. DoDEA operates 161 schools
                       across 11 countries, seven states, Guam, and Puerto
                       Rico.


                # ⚓ ACLU ☛ Students_Sue_Department_of_Defense_Schools_Over
                  Curriculum_Changes,_Book_Bans⠀⇛


                       “Learning is a sacred and foundational right that
                       is now being limited for students in DoDEA
                       schools,” said Natalie Tolley, a plaintiff on
                       behalf of her three children in DoDEA schools. “The
                       implementation of these EOs, without any due
                       process or parental or professional input, is a
                       violation of our children's right to access
                       information that prevents them from learning about
                       their own histories, bodies, and identities. I have
                       three daughters, and they, like all children,
                       deserve access to books that both mirror their own
                       life experiences and that act as windows that
                       expose them to greater diversity. The
                       administration has now made that verboten in DoDEA
                       schools.”


                # ⚓ New Yorker ☛ Why_Harvard_Decided_to_Challenge_Donald
                  Trump⠀⇛


                       The First Amendment protects speech we might hate,
                       including racist, sexist, and antisemitic language.
                       That is a cost of free expression in a free
                       country. Consistent with that principle, Trump, in
                       his first term, issued an executive order
                       instructing agencies to insure that universities
                       receiving federal grants “promote free inquiry”
                       consistent with the First Amendment. But there is
                       apparently an exception to the Trump
                       Administration’s commitment to free speech: a broad
                       category of ideas and expression that it has
                       classified as antisemitic. A month before the 2024
                       Presidential election, on the anniversary of
                       October 7th, the Heritage Foundation, which
                       produced Project 2025, published Project Esther, “a
                       blueprint to counter antisemitism,” to be deployed
                       “when a willing Administration occupies the White
                       House.” As my Harvard colleagues Jesse Hoffnung-
                       Garskof and Daphna Renan explained last month, in
                       The Chronicle of Higher Education, Project Esther
                       aims to render pro-Palestinian ideas, expression,
                       and activity unacceptable, by convincing the public
                       that they are equivalent to support for terrorism
                       by Hamas. The document is explicit about the
                       project’s goals: to make Jews feel that such
                       expression is “a threat to their safety,” similar
                       to how, when “most Americans hear ‘Klan,’ they
                       immediately associate this homegrown American hate
                       group with ‘bad.’ ”


                # ⚓ Vox ☛ Trump_vs_Harvard:_What_the_administration_demanded⠀⇛


                       Today I’m focusing on the Trump administration’s
                       battle with Harvard University, in which a powerful
                       university targeted by the president is pushing
                       back.


                       What’s the latest? The Trump administration last
                       night froze $2.2 billion in federal funding for
                       Harvard, punishment after the university said
                       Monday it would not comply with the
                       administration’s demands.


                # ⚓ The Moscow Times ☛ St._Petersburg_Woman_Jailed_Over_Army
                  Criticism_After_Neighbor’s_Denunciation⠀⇛


                       Saint Petersburg’s Pushkinsky District Court
                       sentenced her to five years and two months in
                       prison and banned her from using social media for
                       three additional years, the court’s press service
                       said on Telegram.


                # ⚓ Hindustan Times ☛ Harvard's_challenge_to_Trump
                  administration_could_test_limits_of_government_power⠀⇛


                       On Monday, Harvard become the first university to
                       openly defy the Trump administration as it demands
                       sweeping changes to limit activism on campus. The
                       university frames the government’s demands as a
                       threat not only to the Ivy League school but to the
                       autonomy that the Supreme Court has long granted
                       American universities.


                       “The university will not surrender its independence
                       or relinquish its constitutional rights,” the
                       university’s lawyers wrote Monday to the
                       government. “Neither Harvard nor any other private
                       university can allow itself to be taken over by the
                       federal government.”


                # ⚓ The Atlantic ☛ What_Harvard_Learned_From_Columbia’s
                  Mistake⠀⇛


                       Earlier this month, the Trump administration
                       threatened to revoke $9 billion in federal grants
                       and contracts if Harvard did not agree to a long
                       list of demands, including screening foreign
                       applicants “hostile to the American values and
                       institutions” and allowing an external body to
                       audit university departments for viewpoint
                       diversity. (How screening international students
                       for their beliefs would contribute to viewpoint
                       diversity was not specified.) Today, Harvard
                       announced that it would not agree to the Trump
                       administration’s terms. “Neither Harvard nor any
                       other private university can allow itself to be
                       taken over by the federal government,” the
                       university’s lawyers wrote in a letter to
                       administration officials. “Accordingly, Harvard
                       will not accept the government’s terms as an
                       agreement in principle.”


                       In making this decision, Harvard appears to have
                       learned a lesson from the Trump administration’s
                       tangle with another Ivy League school—just not the
                       lesson the government intended.


                # ⚓ US News And World Report ☛ Don't_Like_a_Columnist's
                  Opinion?_Los_Angeles_Times_Offers_an_AI-Generated_Opposing
                  Viewpoint⠀⇛


                       Soon-Shiong, a medical innovator who bought the
                       Times in 2018, blocked his newspaper from endorsing
                       Democrat Kamala Harris for president last fall and
                       said he wanted to overhaul its editorial board,
                       which is responsible for researching and writing
                       Times editorials.


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


                # ⚓ The Moscow Times ☛ Russia_Sentences_Journalists_to_5.5
                  Years_in_Navalny_'Extremism'_Case_-_The_Moscow_Times⠀⇛


                       Antonina Favorskaya, Artyom Kriger, Konstantin
                       Gabov and Sergei Karelin were detained last year on
                       accusations of gathering material and preparing and
                       editing videos for Navalny’s Anti-Corruption
                       Foundation (FBK) and the NavalnyLIVE YouTube
                       channel. All four have maintained their innocence,
                       saying they were being prosecuted for their work as
                       journalists.


                       [...]


                       The court also handed the journalists a three-year
                       ban on administering websites.


                # ⚓ RTL ☛ Sent_to_penal_colony:_Russia_jails_four_journalists
                  who_covered_Navalny⠀⇛


                       Russia sentenced four journalists linked to late
                       opposition leader Alexei Navalny to five and a half
                       years in a penal colony on Tuesday, deepening its
                       crackdown on dissent and press freedom amid the
                       ongoing war in Ukraine.


                # ⚓ Court House News ☛ Four_journalists_who_were_accused_of
                  working_for_Kremlin_foe_Navalny_are_convicted_of_extremism⠀⇛


                       Antonina Favorskaya, Kostantin Gabov, Sergey
                       Karelin and Artyom Kriger were found guilty of
                       involvement with a group that had been labeled as
                       extremist. All four had maintained their innocence,
                       arguing they were being prosecuted for doing their
                       jobs as journalists.


                       The closed-door trial was part of an unrelenting
                       crackdown on dissent that has reached an
                       unprecedented scale after Moscow sent troops into
                       Ukraine in February 2022.


                # ⚓ The Nation ☛ We_Must_Save_Public_Media_to_Change_It⠀⇛


                       Government attacks on public media are as old as
                       Big Bird. Ever since Richard Nixon feuded with
                       public broadcasting during its earliest days, every
                       Republican administration, except Gerald Ford’s,
                       has tried to cut public media funding. But the
                       severity of today’s attacks is different. The
                       ruthless savagery that Donald Trump and Elon Musk
                       are inflicting against what’s left of the US public
                       sector suggests that this time they might succeed
                       where previous efforts fell short.


                       With these existential threats looming, now is an
                       opportune moment to reflect on why we created
                       public media in the first place—and why it’s still
                       needed today. Interrogating the history of US
                       public media also brings into focus the structural
                       problems that were present since its inception:
                       Because we never provided it with adequate,
                       permanent, and insulated funding, the US public
                       media system has always been politically and
                       economically vulnerable. This is a fixable problem
                       that we must confront—after defending what we still
                       have against trumped-up charges.


                # ⚓ ANF News ☛ Released_journalist:_We_will_continue_to_amplify
                  women’s_voices⠀⇛


                       Following a decision made during a hearing at
                       Istanbul’s 23rd High Criminal Court, journalist
                       Necla Demir Arvas was released from Bakırköy Closed
                       Prison on Monday.


          o § Civil Rights/Policing⠀➾


                # ⚓ The Telegraph UK ☛ Trans_women_are_not_legally_women,
                  Supreme_Court_rules⠀⇛


                # ⚓ BBC ☛ UK_Supreme_Court_rules_legal_definition_of_a_woman_is
                  based_on_biological_sex⠀⇛


                       The LGB Alliance charity, which provided a combined
                       written submission in the case along with several
                       other groups, says they are “delighted” with the
                       ruling.


                       "The ruling confirms that the words ‘gay’ and
                       ‘lesbian’ refer to same-sex sexual orientation and
                       makes it absolutely clear that lesbians wishing to
                       form associations of any size are lawfully entitled
                       to exclude men – whether or not they possess a GRC
                       (gender recognition certificate)," chief executive
                       Kate Barker says.


                       "It is difficult to express the significance of
                       this ruling: it marks a watershed for women and, in
                       particular, lesbians who have seen their rights and
                       identities steadily stolen from them over the last
                       decade."


                       She adds: “This is a victory for biology, for
                       common sense, for reality."


                       [...]


                       UK Conservative Party leader Kemi Badenoch has
                       congratulated For Women Scotland and says the
                       ruling is a "victory".


                       She says: "Saying 'trans women are women' was never
                       true in fact, and now isn't true in law either.


                       "This is a victory for all of the women who faced
                       personal abuse or lost their jobs for stating the
                       obvious.


                       "Women are women and men are men: you cannot change
                       your biological sex."


                # ⚓ The Verge ☛ The_Columbia_student_arrested_at_his_USCIS
                  interview_knew_it_was_coming⠀⇛


                       It’s unusual — though not unheard of — for
                       immigrants to be arrested during USCIS interviews.
                       Matt Cameron, a Boston-based immigration attorney,
                       says it has happened to a couple clients of his,
                       but “always because they have previous immigration
                       or criminal history which makes them deportable.”
                       Mahdawi’s attorneys say he has no criminal record
                       and is a “committed Buddhist” who “believes in non-
                       violence and empathy as a central tenet of his
                       religion.” He doesn’t appear to have violated
                       immigration law. But Mahdawi, who was born in the
                       West Bank, was involved in Columbia University’s
                       student protests against Israel’s ongoing war in
                       Gaza. He knew about the Trump administration’s
                       efforts to deport any noncitizens — even those with
                       green cards and visas — for their involvement in
                       pro-Palestine activism under the auspices of a
                       McCarthy-era immigration law.


                # ⚓ The Atlantic ☛ What_Porn_Taught_a_Generation_of_Women⠀⇛


                       What did growing up against this particular
                       cultural backdrop do to me? What did it do to all
                       of us? I didn’t start trying to process this
                       particular initiation into adulthood until two
                       decades later. A few months into the coronavirus
                       pandemic, I gave birth to twins, and becoming a
                       parent in almost complete isolation triggered a
                       kind of identity crisis. I was too exhausted to
                       read; I could no more sit through an entire movie
                       than I could sprout wings and fly. When I went back
                       to work, the #MeToo movement had many women parsing
                       their own historical experiences of assault and
                       abuse. All of the subjects I wrote about seemed to
                       be circling the same theme: an environment that had
                       been set up against women from the beginning.


                # ⚓ Hamilton Nolan ☛ Not_Just_Unions;_Strike-Ready_Unions._-_by
                  Hamilton_Nolan⠀⇛


                       This is even more true in the public sector, which
                       represents about half of union membership in
                       America today. Millions of federal, state, and
                       local government workers are legally prohibited
                       from striking. Their unions are primarily
                       administrative entities that negotiate and oversee
                       contracts. These unions, to varying degrees, are
                       the embodiment of the premise that organized labor
                       power can exist in the absence of the strike—that
                       laws, contracts, and regulations are enough to
                       guarantee workers their rights.


                       That premise turns out to be false. We are now
                       living through a brutal demonstration of its
                       emptiness. The Trump administration, which cares
                       only about power and not at all about the
                       traditional niceties of law and public relations,
                       has begun simply throwing union contracts in the
                       trash and declaring that existing federal unions do
                       not exist after all, because the boss says so. This
                       is the worst thing that a boss could possibly do to
                       a union. It should prompt the strongest response.
                       If anything should cause a union to strike, it is
                       this. Yet the unions in question have not struck.
                       Why? On a surface level, because they are not
                       legally allowed to strike. But on a more basic
                       level, because they have been built from the ground
                       up as entities that do not consider strikes to be
                       within their purview. The law, in other words, is
                       not their deepest weakness; their deepest weakness
                       is the fact that they do not imagine themselves to
                       be capable of striking and therefore have not done
                       the constant organizing work that would enable them
                       to strike and therefore have little capability of
                       carrying out a strike even if they wanted to. This
                       is true not just of AFGE, the federal union that
                       has absorbed the brunt of Trump’s attacks so far,
                       but of most (not all) public sector unions in most
                       (not all) red states. It is also true of many major
                       private sector unions that have leadership that is
                       lazy and/ or unimaginative, who have accepted that
                       their power rests mostly in politics and lawyers,
                       and who, because of this, likewise fail to do the
                       internal organizing and training and education and
                       mobilization work necessary to create strike-ready
                       unions.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ ARRL ☛ ARRL_Files_Comments_on_FCC⠀⇛


                       In response to ARRL’s request, over 200 members
                       submitted suggestions that were reviewed when
                       considering what rules should be deleted or
                       modified. ARRL will continue to engage with members
                       and advocate for the Amateur Radio Service.


                       In its filing, ARRL asked the FCC to delete or
                       amend the following rules: [...]


      § Monopolies/Monopsonies⠀➾


          o ⚓ Techdirt ☛ With_3-0_GOP_Majority_And_All_Democrats_Fired,_The_FTC
            Is_Now_A_Total_Trump_Puppet_Agency_Pretending_To_Care_About
            ‘Antitrust_Reform’⠀⇛


                 Back in March Trump illegally fired the Federal Trade
                 Commission’s two Democratic Commissioners. With a
                 captured Supreme Court and a 3-2 agency majority,
                 Trumpism could have already done whatever it wanted at
                 the FTC, so firing the two Democratic Commissioners was
                 just scorched Earth; like applying napalm on the site of
                 a nuclear strike. Real sociopath shit.


                 With everything going on, the firings were about a four
                 hour news cycle. But the two fired Commissioners (Rebecca
                 Kelly Slaughter and Alvaro Bedoya) sued Trump, noting
                 (quite correctly) that the firings were illegal under the
                 precedent of Humphrey’s Executor, the 1935 Supreme Court
                 case stating FTC commissioners can only be fired for
                 clear cause. Not for simply… existing.


          o ⚓ India Times ☛ What_if_Mark_Zuckerberg_had_not_bought_Instagram_&
            WhatsApp?⠀⇛


                 No one knew how these deals would turn out. But
                 hindsight, it seems, is 20/20. On Monday, the government
                 argued in a landmark antitrust trial that both
                 acquisitions - now considered among the greatest in
                 Silicon Valley history - were the actions of a monopolist
                 guarding his turf. Zuckerberg, who was called as the
                 first witness in the trial, has previously denied that
                 buying Instagram and WhatsApp hurt competition.


          o ⚓ Silicon Angle ☛ Mark_Zuckerberg_tried_to_negotiate_settlement
            with_FTC_in_landmark_antitrust_trial_but_failed⠀⇛


                 It seems the FTC wasn’t moved by Zuckerberg’s
                 counteroffer of $1 billion, hoping the number might be
                 closer to $18 billion. Meta has done everything in its
                 power to avoid the trial, but here we are. The company is
                 currently fighting to save its social media empire, which
                 is valued at $1.3 trillion.


                 Today, FTC lawyers asked Zuckerberg the simple question:
                 Did you need to buy Instagram, and why didn’t you just
                 build your own Instagram-type app? “I’m sure we could
                 have built an app,” Zuckerberg replied. “Whether it would
                 have succeeded or not I think is a matter of
                 speculation.”


          o ⚓ New York Times ☛ At_Trial,_Mark_Zuckerberg_Avoids_Explaining
            Takeovers_of_Instagram_and_WhatsApp⠀⇛


                 In his second day on the stand in a landmark antitrust
                 trial, Mark Zuckerberg, the chief executive of Meta, on
                 Tuesday defended the social media company’s 2012
                 acquisition of Instagram, describing the transaction as
                 business as usual for a tech company.


                 Businesses weigh the benefits and costs of developing new
                 products themselves against buying start-ups with
                 products they want to add, he said.


          o ⚓ The Verge ☛ Mark_Zuckerberg_once_suggested_wiping_all_Facebook
            friends_lists_to_boost_usage⠀⇛


                 Meta CEO Mark Zuckerberg had a “potentially crazy idea”
                 in 2022 to get people using Facebook more: deleting
                 everyone’s friends’ lists. The possibility was discussed
                 on Monday via internal emails shown by the FTC as
                 Zuckerberg testified during Meta’s antitrust trial.


          o ⚓ The Verge ☛ Zuckerberg_defends_his_empire_during_FTC_antitrust
            trial⠀⇛


                 Zuckerberg has so far testified for roughly nine hours.
                 He’s expected to continue testifying on Wednesday,
                 followed by Sheryl Sandberg. So far, the FTC has prodded
                 him to confirm its theory of the market and understand
                 his motivation for acquiring nascent rivals.


                 The FTC’s theory of the case is that Meta gobbled up
                 newer competitors by buying Instagram and WhatsApp in the
                 early 2010s, when it feared they would grow to challenge
                 its dominance. The agency is trying to show that Meta has
                 monopoly power in a market it calls personal social
                 networking services, which is focused on connecting with
                 friends and family and includes the apps Snapchat and
                 MeWe.


          o ⚓ Nick Heer ☛ The_Acquisition_of_Instagram_Made_Sense_to_Facebook
            Even_at_the_Time⠀⇛


                 While Stewart’s bit remains funny, I must again note that
                 many people with actual expertise in this area treated
                 the acquisition as a reasonable cost to neutralize a
                 surging competitor.


          o ⚓ Axios ☛ Meta's_copycat_strategy_targeted_in_court⠀⇛


                 Meta has a long history of acquiring or building copycat
                 apps and features that have ultimately failed and
                 shuttered in less than a few years.


                 But the unprecedented success of two of its biggest bets
                 have regulators concerned its tactics are
                 anticompetitive.


          o ⚓ India Times ☛ ETtech_Explainer:_Why_the_US_government_wants_to
            break_up_Meta⠀⇛


                 Back in 2020, the FTC sued Meta (then known as Facebook),
                 arguing that it had illegally maintained monopoly power
                 by acquiring competitors before they could grow. Meta has
                 strongly denied the allegations. Its lawyers argue that
                 the FTC approved the Instagram and WhatsApp deals more
                 than a decade ago, and trying to undo them now is both
                 legally shaky and bad for business.


          o ⚓ The Independent UK ☛ Japan_orders_Google_to_stop_pushing
            smartphone_makers_to_install_its_apps⠀⇛


                 The Japan Fair Trade Commission said on Tuesday Google
                 had unfairly hindered competition by asking for
                 preferential treatment for its search and browser from
                 smartphone makers in violation of the country’s anti-
                 monopoly law.


                 The antitrust watchdog said Google, as far back as July
                 2020, had asked at least six Android smartphone
                 manufacturers to preinstall its apps when they signed the
                 licence for the American tech giant’s app store, Nikkei
                 Asia reported.


          o ⚓ India Times ☛ Japan's_anti-monopoly_watchdog_accuses_Google_of
            violations_in_smartphones⠀⇛


                 Japanese regulators on Tuesday accused US tech giant
                 Google of violating anti-monopoly laws, echoing similar
                 moves in the US and Europe. Google Japan said in a
                 statement that it found the action "regrettable." It said
                 it has invested in Japan significantly to promote
                 innovation as a technology leader.


                 It's unclear if Google, a subsidiary of Alphabet Inc.,
                 based in Mountain View in the Silicon Valley, will take
                 legal action to fight the order.


          o ⚓ India Times ☛ Meta_chief_Mark_Zuckerberg_testifying_again_in_US
            antitrust_trial⠀⇛


                 Social media titan Mark Zuckerberg took the stand for a
                 second day Tuesday in a landmark US antitrust trial where
                 his conglomerate Meta is accused of taking over Instagram
                 and WhatsApp before they could become competitors.


          o ⚓ India Times ☛ At_US_antitrust_trial,_Meta's_Mark_Zuckerberg
            admits_he_bought_Instagram_because_it_was_'better'⠀⇛


                 Meta CEO Mark Zuckerberg made a key concession at a US
                 antitrust trial on Tuesday, saying he bought Instagram
                 because it had a "better" camera than the one his company
                 was trying to build for flagship app Facebook at the
                 time.


          o ⚓ The Verge ☛ Google_must_stop_favoring_Search_and_Chrome_on
            Android_in_Japan⠀⇛


                 Japan’s Fair Trade Commission (JFTC) has ordered Google
                 to stop making deals that give preference to Google
                 Search and Chrome on Android devices. Nikkei Asia says
                 that it’s the first time the regulator has issued a cease
                 and desist order to a major tech company.


                 The regulator found that Google had asked at least six
                 different Android phone makers for such deals since July
                 2020, according to Nikkei. The article says the deals
                 included Google sharing revenue with “five business
                 partners”, with the condition that Chrome and Google
                 Search services be “placed on the initial screen” and
                 that other companies’ similar services not be installed
                 at all.


          o ⚓ Baldur Bjarnason ☛ We're_in_for_a_rough_ride_as_an_industry⠀⇛


                 There’s the not so small issue of the tech industry being
                 quite invested in turning the US into an authoritarian
                 dictatorship and seemingly succeeding. But even if you
                 assume that the US will come out of this in four years’
                 time as a recovering democracy (an extremely unsafe
                 assumption, I think), the web is likely to suffer as an
                 industry either way.


                 We have monopolies or oligopolies who control much of the
                 software market and, of particular concern to the web
                 sector, they control how people discover websites.


          o ⚓ Baldur Bjarnason ☛ An_aside_on_proposed_anti-trust_remedies
            against_Google⠀⇛


                 The Democrats love to build or reinforce the mechanisms
                 of authoritarianism, which they mistakenly think they can
                 apply for good and moral purposes, but then become major
                 building blocks for an authoritarian state.


                 If the dominance of Chrome is a problem, then that won’t
                 be solved by shifting it over to an equally large
                 competitor. That solution only makes sense if your goal
                 is to maintain the current oligopoly dynamic and that the
                 biggest threat from Google isn’t their threat to the free
                 market – none of these people seem to care about the
                 actual economy – but Google’s size making them harder to
                 control. They want to make Google more controllable,
                 which is already problematic for a democracy, but a
                 controllable Google is an outright gift to the rising
                 fascists.


          o ⚓ India Times ☛ Google's_spam_policy_hit_by_EU_antitrust_complaint
            from_German_media_company⠀⇛


                 A German media company has complained to EU antitrust
                 regulators following Alphabet unit Google's crackdown
                 against companies gaming its search algorithm to push up
                 rankings for other sites.


                 In its complaint to the European Commission, Hamburg-
                 based Meraki Group GmbH urged immediate action against
                 the policy, saying it penalises websites.


          o § Copyrights⠀➾


                # ⚓ EFF ☛ EFF_Urges_Court_to_Avoid_Fair_Use_Shortcuts_in_Kadrey
                  v._Meta_Platforms⠀⇛


                       Kadrey, however, attempts to side-step fair use.
                       The plaintiffs—including Sarah Silverman and other
                       authors—sued Meta for allegedly using BitTorrent to
                       download “pirated” copies of their books to train
                       Llama, a large language model. In other words,
                       their legal claims challenge how Meta obtained the
                       training materials, not what it did with them.


                # ⚓ Torrent Freak ☛ Nhentai_Operators_Ordered_to_Expose
                  Themselves_in_U.S._Copyright_Lawsuit⠀⇛


                       The operators of Nhentai.net, a popular adult site
                       with dozens of millions of monthly visits, have
                       been ordered to identify themselves in a California
                       court. Recent court rulings denied both the site's
                       bid to dismiss the case early, and its request for
                       a protective order to hide the identities of its
                       operators. The case will now move forward, with all
                       copyright claims intact.


                # ⚓ Digital Music News ☛ Jack_Dorsey_Says_We_Should_'Delete_All
                  IP_[sic]_Law,'_Elon_Musk_Agrees⠀⇛


                       These responses touched on not only the income
                       fallout for creatives, but differences between
                       various types of (and protections for) IP [sic],
                       the potential effect on medical research, and a
                       whole lot else.


    * StatCounter_Shows_the_Market_Share_of_Vista_11_is_Decreasing_in_Ukraine
      This_Year
    * You_Should_Probably_Self-Host_Your_E-mail_and_Never_Use_a_Web_Browser_for
      Mail


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