𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, August 22, 2024
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Generated Fri 23 Aug 02:49:19 BST 2024
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2024/08/22/


╒═══════════════════ 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
QmZwah9nZHVvSzbJWEAMxumYDpanFPqTahnqoNP83tuZbx
QmQWSrGfeYwgf6HE9N3742DJrJwq8uNSCUAz469CnuUFGe
QmcgTTyseF5zFd4MLquM4PtJZzkFcBEqaUbqDe4eaUx6Na
QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu


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

⦿ Techrights  -  Always Remember Who Gave Microsoft the Power to Brick or Block Installations of GNU/Linux

⦿ Techrights  -  Countries Where Microsoft's Share in Search is as Minuscule as 0% This Month

⦿ Techrights  -  IBM is Firing Staff Everywhere, Not Just Offshoring

⦿ Techrights  -  IRC Proceedings: Wednesday, August 21, 2024

⦿ Techrights  -  [Meme] Microsoft Moles and 'Useful Idiots' of Microsoft

⦿ Techrights  -  Microsoft Cooking the Books to Hide the Losses and Disguise the Failure of Its Clown Computing Ventures

⦿ Techrights  -  Microsoft's $22,000,000,000 Bailout from President Biden is Now at Risk

⦿ Techrights  -  More Anti-Linux Spam by Brittany Day at linuxsecurity.com

⦿ Techrights  -  More on UEFI 'Secure Boot' Allowing Microsoft to Break PCs and Prevent People From Booting GNU/Linux

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  The World is Quitting Windows, Microsofters Try to Sabotage the Competition

⦿ Techrights  -  When You're 'Winning' You Become a 'Target'

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/08/22/Always_Remember_Who_Gave_Microsoft_the_Power_to_Brick_or_Block_.shtml
https://techrights.org/n/2024/08/22/Countries_Where_Microsoft_s_Share_in_Search_is_as_Minuscule_as_.shtml
https://techrights.org/n/2024/08/22/IBM_is_Firing_Staff_Everywhere_Not_Just_Offshoring.shtml
https://techrights.org/n/2024/08/22/IRC_Proceedings_Wednesday_August_21_2024.shtml
https://techrights.org/n/2024/08/22/Meme_Microsoft_Moles_and_Useful_Idiots_of_Microsoft.shtml
https://techrights.org/n/2024/08/22/Microsoft_Cooking_the_Books_to_Hide_the_Losses_and_Disguise_the.shtml
https://techrights.org/n/2024/08/22/Microsoft_s_22_000_000_000_Bailout_from_President_Biden_is_Now_.shtml
https://techrights.org/n/2024/08/22/More_Anti_Linux_Spam_by_Brittany_Day_at_linuxsecurity_com.shtml
https://techrights.org/n/2024/08/22/More_on_UEFI_Secure_Boot_Allowing_Microsoft_to_Break_PCs_and_Pr.shtml
https://techrights.org/n/2024/08/22/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/08/22/The_World_is_Quitting_Windows_Microsofters_Try_to_Sabotage_the_.shtml
https://techrights.org/n/2024/08/22/When_You_re_Winning_You_Become_a_Target.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/08/22/Gemini_Links_22_08_2024_Coking_Retro_and_More.shtml
https://techrights.org/n/2024/08/22/Gemini_Links_22_08_2024_Talos_Principle_2_and_Agate_Upgrade.shtml
https://techrights.org/n/2024/08/22/Links_22_08_2024_Misinformation_and_Surveillance_Ramped_Up_Fast.shtml
https://techrights.org/n/2024/08/22/Links_22_08_2024_Tension_Around_Taiwan_and_South_China_Sea_Auto.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 83

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/Always_Remember_Who_Gave_Microsoft_the_Power_to_Brick_or_Block_.shtml
    Gemini version at https://techrights.org/n/2024/08/22/Always_Remember_Who_Gave_Microsoft_the_Power_to_Brick_or_Block_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Always Remember Who Gave Microsoft the
Power to Brick or Block Installations of GNU/
Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


They say Linux is "too hard for grandpa". Whose fault is it?


Microsoft now tortures_old_people to protect_its_dying_monopoly:


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Note: Windows and Ubuntu are on separate SSD:s. I've seen
  some answers on the web, but I did not understand how to go further. I'm 74
years old with two strokes behind me so any explanations have to be simple. If
                              it's possible :-)⦈


Thanks_for_the_'help',_Ubuntu. Too_busy_sucking_up_to_Microsoft_and_gaslighting
users. This is what Microsoft bribes did to Canonical, which uses_slave_labour
and_causes_suicides.


         🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Hello? Support? 'Linux' stopped working⦈


       🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇You’ve been warned: But Linux is not a virus⦈


                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Windows Update⦈


               🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Linux is not secure to boot⦈




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

                    ䷩ 𝚕𝚒𝚗𝚎 1180

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/Countries_Where_Microsoft_s_Share_in_Search_is_as_Minuscule_as_.shtml
    Gemini version at https://techrights.org/n/2024/08/22/Countries_Where_Microsoft_s_Share_in_Search_is_as_Minuscule_as_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Countries Where Microsoft's Share in Search
is as Minuscule as 0% This Month⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇A_molecule⦈_


According to data from statCounter, Bing is measured at 0% right now (August
2024) in 18 countries:


Vietnam
Iran
Nigeria
Israel
Iraq
Syrian Arab Republic
Guinea
Montenegro
Belarus
Armenia
Sudan
Kyrgyz Republic
Turkmenistan
Norfolk Island
Tokelau
Svalbard & Jan Mayen Islands
Western Sahara
Christmas Island
Here is the sorted_data. It can be downloaded from here in case someone wishes
to reproduce. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣤⣄⡘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠝⠏⢀⠸⠀⣤⣴⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣈⠁⠀⠁⠐⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡇⢀⡄⠀⡀⡟⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠁⠀⠀⠀⢸⡇⠀⣤⠁⠀⠈⠀⠀⠀⠀⢸⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠏⠛⠃⠸⡆⠘⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡀⠀⢘⠀⣴⣿⣶⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠀⠈⠀⠀⠀⠀⠀⢸⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠀⠐⠀⣤⠄⢠⣶⣿⣿⣿⣄⠉⠙⣋⣸⡟⣿⣿⣿⡟⢁⣿⣿⣷⡆⠀⠀⠀⠁⡯⢨⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣧⣀⣄⣠⣀⣤⣀⣠⣄⣀⣀⣀⣀⣤⣀⣤⣄⣀⣴⣀⣀⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⠀⢠⣄⠀⠈⠛⠋⣽⣿⣟⠀⠀⣸⡟⠀⠛⠛⠋⠀⢸⣿⣿⡟⠁⢸⡄⢀⣤⣀⣸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⠀⠙⠃⣼⣿⣤⣄⡈⠉⢁⢴⣦⡈⠙⠾⠁⠂⠀⠀⠈⠙⠏⠁⢴⣿⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⠁⠀⣿⡟⠛⠛⠟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣃⠀⠀⠰⣿⣷⠄⠀⢰⠀⣀⣈⠉⠁⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣼⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⣴⣶⣄⠈⠁⣴⣶⣟⣠⣿⣿⡿⠀⠠⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣯⡀⠀⢸⣿⣿⣿⡿⣿⠇⢀⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣷⣈⢹⠟⣫⣶⣶⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢃⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣭⣭⣭⣛⡃⠛⠩⠅⢠⡝⠃⠻⠿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⠇⠀⠁⠀⠀⠀⠀⠀⢉⣀⠀⣛⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡉⣭⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢼⣿⣿⣿⣶⡝⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣄⣼⣄⣼⣤⣀⣴⣀⣤⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣿⣿⣶⣝⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣝⡻⣿⠏⣁⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⠿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⣫⣥⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⡏⠀⠀⢹⣟⠁⠀⣿⡏⠉⠙⠋⠙⠙⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⡀⠸⠆⠀⠄⢀⡀⠰⠞⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⡇⠀⠀⢸⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⣆⢦⡍⣁⣩⣴⡆⣴⣭⣭⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡌⢉⣇⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⡿⢂⢾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⠛⣫⣴⣿⣧⡙⠿⠿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣷⣾⣿⣿⣿⣿⣿⣶⣯⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⡿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⢷⣍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⢿⠿⣿⠿⢿⡿⠿⢿⡿⢿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⢃⣴⢾⠷⣦⡙⣿⣿⣿⠋⠀⠀⠀⠀⠙⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣇⢸⡇⠀⠀⢹⠇⣿⣿⣟⠀⠀⠀⠀⠀⠀⣼⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣦⣙⠒⠒⣊⣴⣿⣿⣿⣦⣀⠀⠀⢀⣴⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⣠⣀⣠⣄⣠⣀⣀⣠⣀⣄⣠⣀⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡟⠛⢻⣿⠛⠛⠟⠛⠿⠛⠻⠟⠛⠟⠛⠻⠛⠻⠟⠛⠿⠛⠻⠟⢿⡿⠿⢿⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣉⣉⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣆⣀⣀⠁⣀⣀⣄⣀⣠⣀⣀⣀⣀⣄⣀⣠⣀⣀⣀⣀⣄⣀⣠⣀⣸⣇⣀⣀⣀⣀⣀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⣿⣿⣷⣤⣤⣴⣾⣿⡿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⡖⠀⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡷⠶⠖⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⣬⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡿⠛⠛⠻⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠛⠿⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣷⣤⣤⣴⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 1275

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM is Firing Staff Everywhere, Not Just
Offshoring⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇IBM_logos⦈_


There are some anecdotal reports like these:


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I'm really sorry to hear that. That is also a bit shocking
  because I was RAed from Marketing and Communications and the reason we were
given is that our job in the U.S. no longer exists and is being moved overseas,
   to build a bigger presence in Brazil, Romania and India...So now they are
          laying off in those places? Good grief, it's all a ruse.⦈


Also a_day_ago:


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IBM is planning to lay off around 10,000 employees across
                                   Europe.⦈


There's also this_new_comment:


     This posting is at least 30 years late. IBM and other IT service
     companies were pioneers in outsourcing as early as the 1990s.
     Millions of jobs in all fields have been outsourced over the years to
     every possible country, so what is different about what's happening
     today?


     Well, what's happening today is the same old story...somebody's a**
     got canned who thought that job cuts only happened to the loser down
     the street. "Ha ha, get a job!" was followed by "Ha ha, learn to
     code!". Lawyers, accountants and managers laughed at happy hours over
     the fates of unemployed factory workers. Keyboard grunts working
     cushy IT jobs laughed at happy hours over the fates of their
     "lessers" who didn't understand the latest technological jargon, who
     didn't own the newest technological gadgets and who didn't subscribe
     to all the social media channels. Those people are the ones getting
     fired today, and all of them are complaining about their
     mistreatment. They were "educated" and "skilled", after all...getting
     fired wasn't supposed to happen to them.


     Life is full of irony. Irony is a great way to say "F*** YOU" to
     everybody. Enjoy the good times while they last, because they don't
     last forever...no matter what station you have in life.


Something will eventually appear in the media. Or_not. ("Many IBM Layoffs (in
Marketing), But the Media Is Not Mentioning Those Layoffs At All")




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣀⣀⠀⢀⣀⣀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⠀⢸⣯⠉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⠄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠛⠛⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⠀⡿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⣤⡤⢀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣴⡏⢩⠀⢈⠉⢳⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠀⠸⣿⠀⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠰⠀⠀⠆⠁⠈⠠⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣶⣶⡀⠈⠀⠸⠀⠈⡔⡒⢌⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣤⣤⠀⢰⣦⠀⣤⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡈⠀⠀⠈⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠿⠟⡁⢸⠀⠀⠱⣄⠲⠥⢂⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⣧⣤⡏⠠⠀⠠⠈⣤⣿⣷⣬⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⠔⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⠀⢠⣄⡙⠟⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣈⡙⠛⠢⠀⠠⠞⠛⠛⢋⣉⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⢉⠭⡉⡭⡍⡭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⢉⡭⡉⡭⡉⡭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⢉⡭⡉⣩⠉⡭⡍⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣛⠦⣟⡆⣓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣛⡎⣓⡇⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣓⡇⢸⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⢿⠛⠉⢠⠀⠀⠀⠈⡙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠁⠀⠀⡆⠘⠰⠀⠀⠀⠃⠐⡜⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⣿
⣿⣿⣿⣿⠁⠀⣀⠀⠰⠇⠀⠀⢠⠀⠀⡿⠇⠐⠄⢉⠻⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⢻⡏⠉⠉⠉⠉⠛⢿⡏⠉⠉⠉⢻⣿⡟⠉⠉⠉⢹⣿⣿⣀⡀⠀⢀⣐⣇⡀⠀⠀⣀⡀⠀⠙⣇⡀⠀⠀⠘⣿⡟⠀⠀⠀⣀⣿
⣿⣿⣿⣿⠀⢀⠀⠀⠁⠐⠃⠀⠘⠐⠀⠐⠀⠊⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⠀⠀⣾⠀⠀⢸⣿⠀⠀⠀⠈⣿⠁⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⠿⠇⠀⣠⣿⡇⠀⠀⠀⠹⠁⠀⠀⠀⣿⣿
⣿⣿⣿⣿⡆⢀⡀⠀⠀⠂⠐⡄⠀⠈⠀⢀⠀⠂⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⠈⠀⠀⢾⣿⠀⢰⠀⠀⠉⠀⡆⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⣀⡀⠈⢻⣿⡇⠀⠐⡄⠀⠀⡄⠀⠀⣿⣿
⣿⣿⣿⣿⣷⠈⠀⠀⡖⢐⠒⡖⡄⠀⠰⢲⢂⡐⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⣿⡇⠀⢘⣿⠀⢸⡇⠀⠀⢸⡇⠀⠀⣿⣿⣿⠛⠃⠀⠘⠻⡟⠃⠀⠀⠛⠃⠀⢀⡟⠃⠀⠀⣷⠀⢰⡇⠀⠀⠛⣿
⣿⣿⣿⣿⣿⣷⣄⠀⠃⢿⠀⠁⡇⠀⠀⠀⠠⢏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣹⣇⣀⣀⣀⣀⣀⣼⣇⣀⣀⣿⣀⣀⣿⣀⣀⣀⣹⣿⣿⣤⣤⣤⣤⣬⣧⣤⣤⣤⣤⣤⣤⣾⣇⣤⣤⣤⣿⣧⣿⣧⣤⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⡀⡇⡇⡄⣀⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠰⣙⡆⢋⠇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠰⣙⡆⣼⡇⡯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠰⣋⡆⠯⡅⡮⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⠀⠀⢀⠀⢀⣀⣘⣀⠒⢑⣓⣊⣙⣃⣀⡀⡀⠀⠀⣀⣀⣀⠀⣀⡀⠀⢀⣀⣀⣀⣀⠀⣀⣘⣐⣖⣉⣙⣃⣳⣃⣀⡀⢀⠀⠀⡀⠀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣒⣃⣲⣋⣳⣃⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⣿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣻⣛⣛⣛⣛⣛⣛⣿⣿⣛⣛⣛⣛⣿⣿⣟⣛⣛⣻⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⣈⣉⣉⣈⣿⣈⣉⣉⣉⣈⣙⣿⣈⣉⣁⣻⣿⣏⣉⣉⣁⣿⣿⣿⣿⣿⣯⣭⠭⠭⣭⣽⣭⡭⠭⢭⣭⡭⠭⢽⣭⠭⠭⠭⢽⣿⠭⠭⠭⣽⣿⣿⣿⡇⠀⠰⢶⡶⠆⠶⣶⡶⢶⣦⠰⢶⣶⡄⠀⣶⣶⠆⠀⠀⣿⣿
⣿⣿⣿⣁⣀⣿⣿⣿⣀⣘⣛⣃⣠⣿⣿⣀⣀⣈⣟⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣿⣿⣿⣓⣒⣛⣛⣓⣒⣿⣿⣓⣒⣒⣚⣛⣒⣒⣒⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⣿⣧⣼⡟⠀⢸⡿⣷⣼⢿⡇⠀⠀⠀⣿⣿
⣿⣿⣿⡋⢉⣿⣿⣿⢈⢩⣭⡍⠙⣿⣿⢉⢹⣏⠉⣹⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⣿⣿⣿⠧⠤⢤⣤⠤⠬⢿⣿⠧⠤⢷⠤⠤⢴⠦⠤⣿⣿⣿⣿⡇⠀⢀⣸⣇⡀⢀⣿⣇⣸⣿⢀⣸⡇⠸⡟⢸⣇⡀⠀⠀⣿⣿
⣿⣿⣍⣥⣤⣩⣿⣭⣤⣬⣭⣥⣤⣿⣭⣤⣼⣷⣤⣿⣥⣤⣭⣿⣿⣿⣿⣿⣟⣉⣉⣉⣉⣻⣉⣉⣉⣉⣉⣉⣉⣿⣉⣉⣉⣻⣏⣉⣿⣋⣉⣹⣿⣿⣿⡇⠀⠘⠛⠛⠃⠙⠛⠛⠛⠁⠘⠛⠃⠀⠁⠘⠛⠃⠀⠀⣿⣿
⣿⣿⣶⣶⣶⣶⣿⣶⣶⣶⣶⣾⣿⣿⣶⣶⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣾⣿⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⢉⢭⡉⡭⠍⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⢉⢭⡉⠭⡍⡭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠭⣍⡭⡍⣩⠉⡭⡍⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⣚⠟⣏⡆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⣒⠇⡼⠀⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡙⣇⠇⢸⠀⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⡭⢹⠟⡿⣹⣟⣟⠛⡟⠛⡛⢻⢛⢋⣟⢛⣟⣟⡟⣻⡟⣭⡏⢯⡝⣿⡏⢽⢛⢛⣟⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠦⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣾⣶⣽⣟⣼⣮⣯⣶⣷⣽⣾⣼⣯⣞⣼⣿⣷⣿⣷⣽⣷⣿⣵⣿⣷⣷⣾⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿
⣿⣿⣿⣿⣿⡶⢤⣿⣿⣿⡿⢿⡿⡿⢿⢿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡹⠏⣿⣿⣿⣬⣤⣤⣧⣬⣦⣽⣢⣤⣼⣥⣷⣤⣼⣹⣯⣾⣬⣿⣭⣿⣾⣦⣦⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣉⣹⣙⣉⣟⣍⣙⣿⣿⠀⣹⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢟⢿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣋⣺⣿⣶⣸⣺⣖⣘⣇⣇⣗⣨⣸⡗⣶⣰⣇⣮⣄⣰⣷⣶⣠⣕⣊⣌⣰⣁⣾⣵⣰⣆⣿⣐⣲⡇⣮⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣛⣛⣛⣛⣛⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿
⣿⣿⣿⣿⣿⢫⡝⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⡏⣝⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣽⣤⣼⣼⣤⣤⣄⣿⣤⣤⣽⣲⣯⣤⣯⣤⣥⣽⣯⣤⣬⣭⣯⣧⣤⣭⣯⣼⣤⣤⣬⣧⣼⣵⣭⣧⣭⣮⣮⣥⣤⣅⣸⣤⣤⣥⣤⣥⣤⣿⣿⣤⣤⣼⣵⣵⣥⣮⣿⣿⣿⣿⣓⣒⣚⣿⣿⣿
⣿⣿⣿⣿⣿⣭⣅⣿⣿⣿⣳⣏⣉⣉⣇⣑⣛⣅⣋⣛⣈⡙⢸⣛⣏⣺⣕⣛⣛⣟⣟⣛⣻⣋⣋⣃⣛⣋⣟⣹⣛⣋⣻⣟⣋⣹⣯⣉⣛⣉⣉⣹⣉⣏⣿⣭⣉⣉⣹⠁⣈⣍⣻⣟⣉⣟⣈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢳⡞⣿⣿⣿⠻⡻⢿⡟⠏⢿⠙⢻⠩⠟⢻⠹⡭⠹⡟⠛⢻⠿⠻⠿⡙⢻⡟⠟⠟⠻⠻⡿⢿⠿⡿⠛⡿⡛⠻⠿⢿⠟⠛⢟⡛⠻⢿⢟⠟⠛⡛⠛⠿⠻⡏⠛⡏⠛⠋⠙⢹⢿⡽⡻⠟⠛⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⡿⠿⠾⠿⠿⠿⣿⣿⣟⢻⢿⡿⡛⣿⠛⠿⠿⠿⡷⣿⣿⡿⠿⠟⡟⠿⠟⠻⢿⣿⠻⢿⠿⠿⠿⣾⡿⠿⠿⢿⠿⠿⣟⠿⠿⡿⣿⡻⣷⣛⣿⣿⣿⠿⠿⠿⢿⠿⠳⣶⠾⠿⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⢾⣶⣶⢶⣶⡶⣾⢾⣷⣶⣷⣶⣶⣼⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣶⣶⣾⣶⣶⣾⣶⣶⣿⣿⣶⣶⣦⣷⣶⣷⣷⣶⣼⣶⣦⣽⣶⣿⣷⣷⣷⣶⣶⣶⣾⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣤⣤⣤⣼⣉⣦⣤⣍⣯⣽⣼⣤⣭⣧⣧⣮⣥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⢫⡝⣿⣿⣿⣿⣿⠻⢿⠿⠿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣽⢿⣿⣿⣿⣿⣿⣿⣮⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣭⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣧⣼⣿⣿⢿⡿⠿⡿⡿⢿⢿⡿⠿⡿⣿⠿⠿⠿⠿⢿⠿⠿⠿⢿⢿⡿⢿⡿⠿⢿⢿⡿⢿⡿⣿⠿⠿⢿⠿⡿⢿⡿⠿⠿⠿⠿⢿⢿⢿⠿⠿⡿⠿⢿⢿⢿⡿⡿⡿⡿⢿⢿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢳⡟⣿⣿⣿⣧⣦⣼⣼⣤⣬⣭⣧⣭⣮⣷⣥⣤⣼⣽⣵⣭⣽⣯⣴⣽⣯⣵⣿⣦⣤⣽⣯⣥⣥⣿⣴⣤⣼⣭⣮⣾⣧⣤⣼⣽⣧⣴⣴⣽⣤⣶⣯⣤⣤⣼⣮⣵⣵⣧⣼⣧⣽⣯⣮⣦⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣃⣴⣂⣸⣗⣜⣖⣗⣝⣒⣗⣅⣕⣕⣀⣓⣚⣰⣊⣺⣞⣸⣕⣸⣁⣸⣈⣁⣇⣑⣷⣫⣠⣭⣁⣈⣨⣒⣂⣽⣐⣪⣺⣀⣀⣂⣽⣎⣰⣥⣨⣷⣪⣺⣀⣀⣯⣂⣖⣷⣪⣨⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⣟⣛⠍⡿⠟⠟⡟⠻⠛⠹⣯⠏⠟⢻⠛⡿⠉⠿⠿⢻⠝⢿⠛⠛⡏⠿⡛⣟⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⡛⡛⠻⢿⠿⢿⢿⡿⢿⡿⢻⣿⠿⣿⢿⡿⠿⡿⣿⠿⡿⠟⡟⡿⢿⡿⠿⣿⣛⡟⡛⡟⣿⠟⣿⡟⡿⢿⢿⢿⠿⡿⢛⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣿⣸⣸⣸⣇⣓⣋⣙⣘⣛⣿⣸⣇⣓⢊⠹⣈⣸⣸⣖⣃⣇⣇⣇⡇⠱⣿⣛⣇⣂⣇⣌⣆⣿⣇⣋⣸⡎⣾⣚⣸⣻⣸⣨⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⡟⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣤⣦⣤⣤⣧⣾⣦⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⢲⣹⣿⣿⣯⡏⣍⠩⠻⢹⡏⠛⣿⡛⣿⠟⢛⡟⣻⢙⣿⠛⣿⢹⣛⣿⡟⢛⢟⡟⡟⢉⣻⠿⡟⣛⣻⣟⣛⠛⡏⣯⠙⡏⡏⡟⢹⠋⡟⡟⢟⠛⣻⢛⠏⢻⠛⠛⢟⠛⡻⣿⣿⡰⢅⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠖⡛⣿⣿⣿⣷⣶⣶⣿⣾⣷⣶⣿⣴⣶⣶⣾⣶⣷⣶⣷⣴⣿⣶⣶⣿⣶⣮⣼⣷⣾⣾⣾⣶⣶⣷⣾⣶⣾⣾⣶⣿⣾⣾⣴⣾⣶⣷⣾⣷⣶⣶⣶⣴⣷⣶⣯⣿⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢓⣶⣿⣿⡏⢹⢯⢩⡹⡋⡩⢹⠯⢮⠏⢩⡹⡉⢿⠭⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣚⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠙⠟⢻⣛⡽⠻⠹⠛⠛⢻⡻⠛⠛⢿⠟⠻⡛⠻⢟⢟⡻⡍⡏⠉⢹⢩⠉⠹⡝⢿⡋⠻⣻⡟⠻⡿⠛⠛⣛⠉⢝⡛⠛⠹⠟⠟⢟⡛⠏⠟⣛⠙⣻⡋⠭⡋⠏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢟⡛⠿⡛⣛⢟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⢻⠛⣻⠻⠿⢿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣛⣛⣛⣛⣛⣛⣛⣛⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⡛⣿⡿⢿⠿⠿⢿⢻⢻⠿⡿⢿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣓⣽⣇⣧⣒⣟⣣⣸⣠⣒⣗⣹⣇⣺⣐⣗⣪⣹⣸⣇⣦⣻⣓⣜⣗⣺⣻⣗⣺⣃⣿⣻⣣⠞⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⢲⣹⣿⣿⡟⢻⢛⡛⣛⡛⡟⣛⡻⢛⠟⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡱⠌⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠶⢻⣿⣿⣷⣾⣾⣶⣾⣶⣿⣶⣶⣿⣿⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣾⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣚⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣘⣾⣿⣿⣇⣒⣅⣇⣺⣘⣐⣢⣪⣀⣹⣨⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣥⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣹⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣹⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1462

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/IRC_Proceedings_Wednesday_August_21_2024.shtml
    Gemini version at https://techrights.org/n/2024/08/22/IRC_Proceedings_Wednesday_August_21_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Wednesday, August 21,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣠⣤⣀⣀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⠋⠁⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣴⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠛⢳⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣶⣶⣤⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⣳⣈⡧⠟⡉⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠀⠀
⠀⢰⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡽⡶⡧⣻⡮⢗⠋⠁⢠⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠙⠛⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢲⣌⡾⢟⣩⣵⣾⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣋⣀⣀⡀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠽⠟⢛⣉⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⠛⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣶⣾⣷⡀⠘⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣶⣤⡀⠀⠉⠛⠿⢿⣧⠀⠀⠀⠀⠀⠹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⣤⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣿⣿⣿⣿⡆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1688

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/Meme_Microsoft_Moles_and_Useful_Idiots_of_Microsoft.shtml
    Gemini version at https://techrights.org/n/2024/08/22/Meme_Microsoft_Moles_and_Useful_Idiots_of_Microsoft.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Microsoft Moles and 'Useful Idiots'
of Microsoft⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I don't always shill for Microsoft. But when I do, I
                  concern-troll Linux and leading figures.⦈


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇You're a molly! @Microsoft github (no code, just mob)⦈


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇So your contribution to Free software is defaming the person
                             who started it all⦈


Based on a true story.




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

                    ䷩ 𝚕𝚒𝚗𝚎 2518

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/Microsoft_Cooking_the_Books_to_Hide_the_Losses_and_Disguise_the.shtml
    Gemini version at https://techrights.org/n/2024/08/22/Microsoft_Cooking_the_Books_to_Hide_the_Losses_and_Disguise_the.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Cooking the Books to Hide the
Losses and Disguise the Failure of Its Clown Computing
Ventures⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024,
updated Aug 22, 2024


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


Faking the numbers to fake growth, cook_the_books


Recent: Microsoft_Media_Operative,_Citing_Leaked_Document_From_Google:
"Google’s_Numbers_Also_Show_Azure_Had_a_Roughly_$3_Billion_Operating_Loss" |
Older: Poorly_Redacted_Documents_From_the_Court_Reveal_That_Microsoft_Has
Indeed_Defrauded_Shareholders_About_Azure


THIS incredible new_report_is_rather_revealing; it's not exactly shocking, but
at least it seems like someone in the media (AFP in this case) does actual
journalism. Sometimes...


From "Microsoft tweaks how it logs cloud [sic] revenue" (which can also end up
being less than the spendings, i.e. losses), as per reprinting in southeast
Asian media:


     Microsoft on Wednesday lowered its cloud computing unit revenue
     forecast in a bookkeeping move, shifting money to its "productivity"
     software business.


     The accounting change comes as investors are wary about whether the
     billions Microsoft and tech rivals are spending on artificial
     intelligence will help or hurt bottom lines.


     Contacted by AFP, Microsoft said the change is intended to more
     closely align earnings reports with how the company operates when it
     comes to cloud services tied to its business computing unit.


How can they get away with it? They not only mislead shareholders, they cheat
on their accounting to hide massive deficits. It's not even the first time they
do this.


Either way, the above comes to show they have financial problems. In fact, the
owe_more_money_than_they_have. █




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣷⠀⢠⣦⠀⢀⢀⣼⠀⠀⢀⣸⣿⣷⠀⢠⡀⠙⡁⡀⠀⠈⣷⠀⢠⣿⣿⠀⠀⣿⣿⡿⣀⡀⢹⣷⠀⠀⠀⢈⣯⠀⡐⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠧⠸⣿⡏⠷⠜⣿⡟⠃⣸⣿⠛⠒⠛⢸⣿⣟⣛⣒⣉⣴⣯⣓⣊⣠⣟⣛⣚⣃⣈⣚⡒⠛⢨⠛⠂⠚⠂⠋⠿⠔⡹⠆⠁⠮⠦⠎⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣿⡶⠟⠚⠒⠰⣭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⠟⣁⣀⡀⡀⠀⡀⢙⢯⣰⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣤⣀⡀⠀
⠀⢸⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⠡⣽⣿⣿⣿⣿⣿⣷⣠⡜⣿⣿⣢⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣴⣿⡟⢈⢟⣿⣿⣿⣿⣿⣿⠿⡇⢼⣿⣷⡂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠁⠀⠠⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣷⠡⣄⢹⣿⣩⣈⣹⣿⣁⣠⣀⢨⣿⣿⠓⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢸⣿⣿⣿⣿⡟⠋⠁⠀⠈⣙⣐⠀⠀⠙⡋⠉⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⢾⣷⠾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡿⣹⠀⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠈⣙⢀⠀⠀⠘⡛⠉⠀⠀⠉⣻⣿⣿⣿⣿⡇⠀
⠀⢸⣿⣿⣿⣿⣿⣷⣶⣤⣌⣛⣕⠰⠟⣠⣿⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠃⣄⣻⣿⣿⣯⣈⠋⡬⣿⣿⣿⠛⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣌⣛⡙⠥⠶⢀⣿⣥⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⡘⣻⣿⡯⣭⠭⢿⣻⣶⣿⣷⠖⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡿⣿⣿⣻⡇⠁⠀⠀⠀⢀⡀⢸⣿⣟⣫⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠺⣿⣿⢃⣷⣤⣤⣶⣾⡟⠁⠈⠻⠿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿⡇⠀
⠀⠘⠙⢉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⢄⢠⡀⠙⠋⠉⠉⣀⠄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣓⡢⠦⠤⠠⢔⣳⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠉⠉⠙⡏⡉⢉⣹⢉⠉⣉⡏⠉⣝⠉⠍⠉⡏⠉⡿⡏⢉⠻⡏⡉⠽⢿⣿⣏⠉⠍⢹⣍⠩⠉⡽⠉⠉⡉⢿⢍⠉⣉⠻⡏⠉⠉⡯⠉⢩⢩⡏⠉⠍⢹⣭⠉⢩⣽⣿⣧⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2601

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/Microsoft_s_22_000_000_000_Bailout_from_President_Biden_is_Now_.shtml
    Gemini version at https://techrights.org/n/2024/08/22/Microsoft_s_22_000_000_000_Bailout_from_President_Biden_is_Now_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft's $22,000,000,000 Bailout from
President Biden is Now at Risk⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Replica_of_skull⦈_


Recent: More_Microsoft_Bailouts_From_President_Biden's_Government_Before
Leaving_Office (Donald Trump also used to bail out Microsoft, several times in
fact; we're not picking on Biden in particular)


For the Redmond-based company it is a very bad day or week, hiding_the_losses
and reportedly losing_one_of_its_last_remaining_sources_of_income: the US
government, i.e. the US taxpayer (or national_debt).


Microsoft is no stranger to HoloLens controversy because it already fired all
its staff when I bought the company that had made it, there is sexual
misconduct_at_the_very_top, and in recent years distinguished people in the
military expressed unease - to put it politely - at the deal nobody really
consulted them about, trying to imposed HoloLens on troops. Some who tried it
said it worsened their performance, made them feel sick, and basically got in
their way.


We now learn that "Microsoft could lose its $22 billion IVAS US Army contract,
as 80 competitors look to take the HoloLens' place". To quote:


     Recently, the US Army announced that it would be considering new XR
     hardware partners for its Integrated Visual Augmentation System
     (IVAS) initiative roadmap to create an MR headset for in-the-field
     armed forces. Over the past few years, the US Army has worked with
     Microsoft and its HoloLens division to create a bespoke headset
     purpose-built to boost military tactics and awareness.


     However, recent reports highlight how the US Army may turn to a new
     XR hardware partner to develop IVAS: Next, the sophomore iteration of
     the military immersive head-mounted device.


     According to the reports, US Army officials and decision-makers are
     busy exploring new partner options for the IVAS: Next, including a
     significant contract. For Microsoft, the US Army IVAS contract
     reached an estimated $22 billion, a substantial figure for any
     headset vendor.


     At the same time, Microsoft’s HoloLens and Mixed Reality divisions
     took significant hits over the past year as Microsoft proactively
     downsized its focus on XR. Despite a reduced emphasis on immersive
     technologies, Microsoft is not keen to let the US Army contract go.


Is HoloLens dead? If this deal falls through, then it might be. █




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣬⣅⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠃⠈⣈⣉⡙⢻⠟⠡⣽⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⢀⣼⡛⣋⣽⣧⠤⠾⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠡⠀⠀⠀⠿⠿⠟⠿⠿⠏⠀⡀⢠⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⡀⣀⣤⠠⠀⠀⠀⠀⠀⣴⣯⣽⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣻⣵⣿⠿⠿⠿⣿⣿⣿⣿⣇⡐⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⢢⡹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠒⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⣶⠀⠈⣿⣿⣿⣯⡠⠅⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣾⣿⠀⠀⢿⣿⣿⣿⣿⣶⣏⠁⠄⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣊⣸⣿⡟⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣶⣴⣄⡀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣤⣀⡀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⣠⢸⣿⡛⠋⠉⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣏⡘⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣻⣿⠋⠉⠉⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣰⣿⠇⠉⠀⣡⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⠿⠃⠀⠆⠀⠀⠀⠈⣿⣿⣿⡷⠀⠀⠀⣿⠋⠀⠀⠀⣿⣿⣴⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣩⣯⡝⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⡿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⡛⠿⣿⣿⣷⣿⣟⣿⡿⠿⣿⣿⣿⣿⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣼⡿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣷⣿⣙⣿⣿⣿⠀⠀⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢤⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠴⠋⠀⠀⠈⠁⠀⠰⠏⠀⠀⠀⠒⠒⢾⠿⡿⠁⠆⠂⠀⡩⠻⣿⣿⣿⡿⠿⠻⠻⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣹⣿⣿⣧⡵⠼⣿⠀⠙⢀⠄⠑⠃⠁⠀⠀⠀⠁⣠⣧⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣻⣤⣄⣀⣀⡀⣿⣿⡶⡀⡿⡟⠉⣾⣷⣋⠛⠻⠿⣿⣷⣦⣄⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠘⡳⣄⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2699

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/More_Anti_Linux_Spam_by_Brittany_Day_at_linuxsecurity_com.shtml
    Gemini version at https://techrights.org/n/2024/08/22/More_Anti_Linux_Spam_by_Brittany_Day_at_linuxsecurity_com.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ More Anti-Linux Spam by Brittany Day at
linuxsecurity.com⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024,
updated Aug 22, 2024


Anti-Linux splog/spam operations carry on.


Latest:


     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Navigating the Linux Kernel's Latest DMA Security
                                Vulnerability⦈


100% chatbot spew:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇⁤The Linux operating system, widely acclaimed for its
robustness and security, recently received widespread media attention due to a
  significant kernel vulnerability, CVE-2024-43856. ⁤⁤The issue involves race
    conditions in the dmam_free_coherent() function, which could allow race
  condition-based attacks against various kernel versions. ⁤⁤In this article,
  I'll describe this flaw, its potential impacts, and various kernel vendors'
            attempts to address its risks with security patches.⁤⦈


This isn't just an attack on Linux but also on the Web. This site should be
ashamed of itself, deeply ashamed. Actual articles are being overridden by SEO
done and composed by bots, hiding actual information. █




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⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⢀⠀⠀⠀⠀⠈⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⠻⠿⢿⣿⣿⠶⣾⠟⠻⠿⢟⣟⣿⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⣀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠑⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣟⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠶⠦⠄⠂⠐⠂⠐⣶⡾⠿⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⣂⡴⢪⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠈⠛⢷⣦⡀⠀⡀⠀⠤⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠐⠻⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⢀⠠⠛⠛⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⣠⠀⢸⠀⠀⠀⢸⡇⠠⢤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣀⣀⣀⣸⣀⣀⣀⣸⣇⣈⣈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⢿⡿⢿⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⡿⡿⣿⡿⡿⣿⣿⣿⡟⣿⣿⠻⣿⢻⣿⣿⡿⣿⣿⡿⣿⠿⣟⢿⠿⣿⣿⢿⢿⣿⢿⣿⢿⠟⡿⢿⢿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢶⢶⣶⣶⣶⣶⢶⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣾⣷⣾⣿⣶⣶⣷⣿⣾⣷⣷⣾⣾⣶⣿⣾⣿⣷⣿⣾⣾⣾⣶⣶⣿⣿⣷⣷⣿⣷⣷⣾⣾⣾⣿⣿⣾⣿⣿⣿⣿⣶⣿⣾⣾⣾⣿⣿⣶⣿⣿⣷⣿⣿⣶⣾⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣴⣦⣷⣿⣼⣤⣿⣼⣷⣼⣷⣶⣤⣧⣷⣤⣤⣾⣯⣾⣤⣾⣾⣬⣧⣯⣧⣮⣽⣧⣼⣿⣧⣼⣤⣤⣦⣧⣼⣥⣤⣭⣯⣥⣧⣯⣥⣭⣾⣽⣾⣴⣷⣷⣧⣧⣾⣿⣯⣿⣯⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣷⣿⣷⣾⣾⣿⣿⣷⣷⣾⣿⣷⣾⣿⣷⣾⣷⣷⣿⣶⣿⣶⣾⣿⣷⣷⣿⣷⣾⣶⣿⣾⣶⣷⣾⣾⣶⣾⣶⣶⣾⣿⣿⣾⣿⣾⣿⣷⣿⣿⣴⣿⣿⣷⣾⣿⣾⣶⣷⣿⣷⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣽⣽⣿⣯⣭⣼⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡋⢹⢉⡍⡍⠝⠙⢉⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢻⣿⣧⣿⣿⣿⣿⣿⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⡙⠻⠿⠿⢿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣄⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡦⠴⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡁⠀⢸⣉⣉⣉⣹⣿⣿⣯⠀⠀⣹⣉⣉⣏⣩⣽⣿⣿⣇⠀⠀⣏⣉⣉⣉⣹⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣏⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠀
⣿⣿⣿⣿⣋⣉⢉⣉⣉⣉⡉⡉⢉⣉⣉⡋⣉⡉⣍⠉⣉⢉⣉⣉⣉⣉⡉⣉⢉⣉⠏⣉⣉⢉⣉⣹⣿⣿⣿⣿⣿⣿⡏⠢⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⡗⠒⠒⠒⠒⠲⠒⠒⠒⠒⢒⠒⠒⢶⡒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣼⣿⣿⣤⣭⣤⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⡯⠭⠭⢧⠭⠽⠭⠭⠭⠤⠯⠭⠬⢭⣭⣭⣬⣭⣭⣯⣬⣭⣭⣭⣭⣥⣬⣭⣭⣭⣬⣤⣥⣭⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣏⣙⣛⣻⣛⣉⣛⣛⣋⣙⣋⣉⣙⣙⣛⣛⣛⣿⣟⣟⣛⣛⣛⣋⣿⣿⣿⣿⠀⠀
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⣿⣿⣿⣧⠤⠤⠧⠤⠤⠧⠤⠤⠤⡤⠧⠤⠤⠤⠧⠤⠤⠤⠤⠧⣤⣤⣬⣤⣼⣤⣤⣤⣤⣤⣴⣤⣤⣤⣼⣿⣿⣿⡇⢀⡜⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣶⣶⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠴⠤⠴⣦⡤⠤⡴⠤⣤⡔⠤⠤⠧⣤⣴⣤⣤⣤⣦⣴⣤⣼⣤⣼⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⡏⢹⣟⣛⣛⣛⣻⣙⣛⣛⣉⣋⣛⡛⣛⣛⣛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠲⠶⠶⣶⣶⣶⡿⠶⠶⢲⣶⣶⣶⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⡛⣛⣛⣛⣛⣛⣛⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⣿⣿⣿⣿⣏⣙⣿⣿⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣺⠿⠭⠬⠭⠤⠽⠤⠿⢸⣿⣿⣿⣿⣿⣿⢓⠲⠒⠒⠒⠖⠖⠒⠛⣿⣿⣿⣿⣿⣿⢻⣶⣒⣒⣶⡯⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣭⣭⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2827

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/More_on_UEFI_Secure_Boot_Allowing_Microsoft_to_Break_PCs_and_Pr.shtml
    Gemini version at https://techrights.org/n/2024/08/22/More_on_UEFI_Secure_Boot_Allowing_Microsoft_to_Break_PCs_and_Pr.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ More on UEFI 'Secure Boot' Allowing
Microsoft to Break PCs and Prevent People From Booting GNU/
Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


First you can disable it... now you_can't! Like carrot_and_stick_for_a_donkey.


DAYS ago we pointed out that we_had_correctly_predicted_how_this_would_end_up.
Now even ZDNet (Microsoft_sponsored) admits it:


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Windows update breaks Linux dual boot - but there is a fix
                               for some users⦈


Remember this: The people who stood in the way of UEFI_'secure_boot' received
nothing but threats, including threats of violence and death. █


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Fake security person, User, Disable 'secure boot', 'secure
                  boot' mandated, broken by Windows Update⦈


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Encourages violence against people who disagree; Encourages
                        murder of people who disagree⦈




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⣿⣅⣀⡀⠀⢸⠀⣀⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠛⢻⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡟⠉⢹⣿
⣿⠉⠠⠤⠶⢾⠀⠿⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿
⣿⠂⠀⢰⡆⢸⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⣿⠀⢰⠀⠇⢸⠀⣉⣉⣹⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣷⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣾⣶⣶⣶⣶⣿⣿⣿⣿⣷⣷⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣷⣶⣷⣷⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣶⣿⣿
⣿⣤⣼⣧⣤⣼⣤⣤⣤⣤⣼⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣻⠻⠻⢟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣽⣯⣭⣭⣍⣯⣭⣭⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⡟⢻⡿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⣿⢿⣿⠻⣿⣿⣿⣿⢿⢻⣿⣿⣿⢻⡟⣿⢿⣿⣿⣿⣿⣿⢻⣿⣿⢿⢻⡟⣿⣿⣿⡿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣱⣱⣸⣰⣀⣂⣇⣂⣄⣄⣆⣸⣇⣃⢐⣢⣐⣸⣀⣀⣃⣁⣿⣐⣀⣦⣀⣄⣁⣠⣐⣀⣿⣘⣃⣇⣆⣘⣘⣀⣿⣐⣠⣋⣇⣁⣸⣇⣂⣅⣂⣐⣸⣸⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡼⢿⣿⠟⢿⣿⣿⣿⣟⢓⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⣻⣿⣿⢸⣿⡿⣫⣾⢫⣿⣿⣿⡿⢛⣛⡛⢿⣿⣿⣦⢀⢀⠀⠹⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⡛⢿⣿⣿⣿⣿⣿⣿⡿⠛⣛⣛⣛⣛⣩⣍⣭⣭⣭⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣮⣭⣭⣥⣥⣬⣭⠀⣿⣿⣿⢣⣾⣿⣿⣿⣷⣬⣭⣥⣈⢘⡤⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠿⠟⠛⠉⠉
⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⢈⣩⣭⣭⣍⣛⣛⠻⠿⣿⣿⣿⣿⣆⡻⠿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠕⣠⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢊⣥⢖⢛⣛⣛⣛⠿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢁⠆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⠢⣨⢱⢡⣿⡿⡿⠿⣷⡜⣿⠛⣩⣴⣄⠨⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠊⡆⡀⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠿⠛⣫⣵⣶⣾⣿⢢⣽⣿⡸⡼⣿⣓⣫⣵⡿⣁⣑⡑⣿⣏⡯⡆⢻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠠⡈⠘⢦⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢋⣭⣶⣿⣿⣿⣷⣯⡻⣿⣜⢱⣿⣿⣾⣤⣭⣭⣭⣾⣿⣭⣥⡻⠿⣿⠦⢀⢘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠢⠀⢬⠄⠀⣽⠿⠿⣛⡻⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣸⡎⣽⣿⡟⢭⣭⣽⣟⣻⡟⢿⣿⣿⡿⣶⣿⣿⣯⣝⢦⣝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠗⣴⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣷⣣⡻⣿⣿⣿⣶⣶⣾⣯⣭⣵⣂⣆⢶⣾⣯⣷⣬⣽⣾⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡘⣿⣿⣿⡸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⣿⣿⣿⣷⡻⣷⣤⣟⠛⠛⠿⠟⠿⢟⡴⣴⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣦⡙⠛⠛⣛⣛⣛⣛⣛⣉⣭⣭⣭⣭⣭⣥⡄⢰⣷⣝⡛⣋⣿⣬⣟⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣤⣀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⠥⠃⠀⡄⠀⠮⣻⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠗⠈⠻⢏⣾⣿⣿⡿⣟⣘⠃⠀⠀⠀⠀⠀⠀⠀
⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⣿⣿⠟⠛⠉⠉⠙⠻⣿⣸⣉⡷⠇⠟⠸⢼⣽⣿⣿⣿⣿⣿⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣰⣴⣶⡘⣿⣿⢯⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⢻⣿⣿⣿⣿⣿⢿⣻⣿⣧⡺⣿⠟⠁⡀⡀⢀⢀⠀⡀⡙⡛⢩⢃⠀⠀⡛⢛⢛⢛⠛⡛⡛⣛⢀⠀⣀⣤⡙⢿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⢟⣵⢟⣭⣷⣶⠒⠁⠀⢀⣊⣋⡛⠐⠂⢃⣃⣀⠘⢘⠃⠀⢒⣙⣙⣠⣘⣃⣒⣓⣔⠀⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⣯⡿⣡⣿⣿⣿⣿⣷⣤⣤⢈⢻⣿⣿⣶⣴⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠿⣿⣿⡿⠆⠹⣿⣿⣿⣿⣿⢟⡅⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠃⢿⣿⣿⣿⣟⡿⠿⢋⡜⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⣻⣿⣭⣷⢟⣁⡀⠻⢿⣿⣿⣿⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣝⣛⠛⣣⣬⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⡴⢒⣠⣭⣭⣽⣾⣿⣿⣿⢿⣶⠌⣿⣿⠀⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⡇⠀⡇⢔⡂⣔⣢⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⣿⣷⣜⣛⢕⢌⢻⣿⣟⠻⣿⡇⢰⣶⣿⣿⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠒⠁⠑⠂⠑⠊⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠦⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣷⣿⣆⠿⠇⠀⠈⣥⣾⣿⣿⣿⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣏⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣶⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⠛⠛⠛⠀⠸⢿⣁⣀⣀⣀⢀⣈⣓⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣾⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣴⣶⣶⣯⣛⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢟⣻⣽⣶⣶⣶⣾⡿⣿⣿⣷⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⣀⡀⢀⢀⣀⣙⣿⣿⣽⣿⣿⣿⣿⣿⢟⣫⣷⣾⣿⡸⣟⣧⣵⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣷⣶⣶⣶⣭⡻⣿⡏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣏⡠⠕⠠⡪⠺⠿⢿⣿⣿⣿⣿⣿⣿⣿⣥⣭⡽⣿⣿⣿⣿⣾⣭⣟⢛⣿
⣿⣿⣿⣿⣿⣿⣿⣫⣼⣿⣿⣿⣿⣿⣿⣧⣝⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢩⡹⡠⣔⠚⠁⣠⣶⣾⣿⣿⣿⣿⣿⠿⣟⣿⣯⣽⣿⣿⣿⣿⣿⣿⠿⢸⣿
⣿⣿⣿⣿⢿⣛⣗⣙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⡷⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⡿⣱⢙⢹⢫⠊⡀⠀⣛⣉⣓⣊⣉⣉⡉⣥⠭⣭⡍⢀⡄⢲⠶⠶⠶⠶⠶⠿⢸⣿
⠿⣿⣋⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⠿⠿⠿⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠩⣫⣇⣄⣟⣡⡾⠁⠈⣭⢩⣩⣍⣤⣡⣄⣤⣢⢐⡲⠈⢧⠀⢶⣶⣾⣿⣿⣿⣸⣿
⠿⣿⣟⠻⣿⣿⣿⡿⢿⣿⣛⣛⣛⣛⣯⣭⣭⣭⣭⣿⣼⣛⣛⣛⣿⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⢔⡖⢠⡦⢢⣿⣿⠇⠀⠀⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠈⣄⠘⣿⢹⢻⣿⣦⡞⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣌⠊⠔⢫⣶⡿⠛⠁⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠐⡆⠈⢸⢸⣿⣿⠇⠀
⠛⠛⠛⠛⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣛⣿⣭⡽⣕⣬⣭⣭⣭⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠛⠁⡊⠎⠸⣻⣾⠀⠀⠀⠀⠀⠸⣿⣿⡻⣟⣿⣿⣿⣿⣿⣿⡇⣧⠀⠘⣄⠸⢸⣻⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣛⣭⣷⣶⣾⣿⣿⠟⠵⠿⣩⢭⣭⡻⣿⠿⣓⡘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⢲⠈⣐⡬⠀⢀⣼⣿⣿⡆⠀⠀⠀⢸⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠁⣿⣦⠀⢠⣾⣿⣾⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣎⣿⠓⣷⣧⣾⡇⣵⢸⣝⣄⡎⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⠁⠀⠁⡸⠁⠀⠴⠿⣿⣛⣛⣃⣀⣀⡀⠈⢹⣽⣿⣯⣿⣿⣿⣿⣻⣿⡟⠆⢿⡏⣶⣿⢿⡾⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢾⣿⣶⣿⣷⡾⣶⡪⠭⠭⣾⣓⣍⠭⣭⣭⣭⣵⡶⢶⡀⠀⠀⠀⠙⠃⠴⠿⠿⠛⠛⠛⠛⠛⠛⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠱⢾⣷⡈⣾⣿⣿⣿⠃⠀⠀
⠀⠀⣸⡟⠀⠀⠘⣿⣿⣿⠿⣟⣸⠿⠛⢿⣿⣿⣮⢿⣿⣿⣿⣿⡿⣻⣽⣿⣿⣿⣿⣿⣶⣦⣤⠄⡾⣷⣦⠀⠀⠀⠀⢲⣶⣶⠚⠃⢠⠀⠛⢻⣿⠁⠀⠀⣯⣽⣛⠛⣛⣻⣿⡿⣿⣿⡭⠁⠀⢨⣭⣤⣻⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣟⣷⣿⣿⣅⡀⢰⣿⡿⢿⣿⠿⣾⠉⠉⡹⣶⣿⣿⢟⣿⣿⣿⣿⣿⣿⢹⢻⢸⡿⡣⠿⠿⢇⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡇⠛⢿⣾⣿⣭⣿⠿⠀⠀⢠⣾⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣝⡷⣫⣪⣾⣿⣿⣒⠶⠑⠐⠆⢰⣿⣿⣿⣗⠙⠿⣿⣿⣿⣿⣿⣞⠎⢰⣬⣛⣛⠋⠮⠍⠉⠉⣉⣉⣉⡉⠉⣿⣿⣿⠀⠀⠀⣿⡏⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⢨⣿⡿⡿⢃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⢹⢻⣟⠟⢻⡯⢹⢟⠟⠯⣠⣸⢿⠻⠟⢿⢰⣶⣶⣿⡝⠛⢻⠏⠀⠀⣭⠉⠉⢻⣿⣿⣿⡿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠃⣇⡸⣊⡴⣁⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⠩⢅⠈⠊⠀⠉⢨⡿⠾⠟⠃⠈⠙⢿⣿⣿⡇⠀⢸⣆⡀⠀⠀⠀⣠⣾⣿⡻⣱⣽⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⢸⣿⣿⠀⣶⣿⣿⡿⠿⢿⣿⣿⣿⠿⢿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣾⡶⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⠀⠈⠋⠀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠻⣿⣿⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⢀⣀⣀⢈⣾⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠛⣼⠃⠀⠀⠀⠀⠀⠀⠀⣸
⡄⢀⣀⡀⡀⣀⡀⣐⣛⣛⣛⣛⢛⣛⣛⡛⣛⣛⣛⢛⣛⣛⡛⣛⢛⡛⣛⢛⢛⢛⣛⣛⡛⢛⡛⣛⡛⣛⢛⣛⣛⣛⣛⣛⣛⢛⣛⣛⣛⣛⢛⣛⣀⢀⣀⢀⣀⣀⣈⣛⢛⣛⠛⣛⡛⡛⣛⣛⣛⢛⣛⣁⣀⣀⣀⣀⠀⠀
⡇⢸⣇⣿⡿⣯⣽⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣺⣾⠀⣿⣿⣿⣿⣿⣇⣗⣸⣿⣿⣭⣿⡂⣿⣧⣗⣇⣿⣿⣿⣿⣿⣾⢸⡇⢸⡟⣿⣺⣿⣿⡟⣼⣸⣗⢸⣿⣿⢻⣿⢸⣿⠀⣇⡇⣯⣿⣽⣿⣸⣿⣿⣿⣿⣺⣗⠀⠀
⣿⣦⣤⣤⣤⣤⣶⣤⣶⣤⣦⣤⣤⣤⣦⣤⣤⣶⣶⣶⣦⣶⣶⣶⣶⣴⣤⣶⣶⣶⣴⣦⣶⣤⣤⣦⣤⣴⣤⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⢠⣤⣶⣴⣶⣤⣴⣶⣶⣶⣶⣶⣴⣦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⣤⣤⣤⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠅⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠓⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣤⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣾⣿⣿
⠉⠁⠉⠉⢉⡉⣯⣷⣭⠉⠺⣟⠉⢛⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠻⣿⣿⡿⠟
⠀⠀⣤⣾⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣼⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠄⡀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠐⠀⡀⠠⡈⠠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢿⣿⣿⣿⣿
⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣀⣉⣈⣉⣉⣉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⡿⠏⠙⠛⠋⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠻⠛⠛⠛⠿⠛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⡿⠿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠛⠋⠀⠀⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2953

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2024/08/22/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Aug 22, 2024


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


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣟⣛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⡏⠒⠻⣾⣥⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠁⠡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠘⢻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⠿⣷⣾⣿⡿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣭⣯⣿⣿⣿⣯⣿⣯⣿⡿⠿⠻⠹⠟⠿⠿⠟⣻⠛⠛⠛⠛⠋⠉⠋⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠒⢦⣦⣶⡶⠵⠤⠽⠿⠿⠻⠿⠿⠿⠿⠿⠟⠛⠿⠛⠻⠛⠛⠛⠛⠟⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣬⣧⣴⣶
⠄⠂⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⡀⠀⠀⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣻⣗⣶⣿⣃⣀⣹⠄⠀⠀⣁⣐⣒⣲⣶⣶⣶⣾⣿⣷⣶⣷⣶⣶⣴⣾⣧⣶⣶⢖⣸⡵⣖⠀⠠⡸⠓⣫⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣧⣾⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠀⠀⠀⠀⠀⢠⣤⣄⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠋⠹⠭⠛⠙⠏⠻⠙⠛⠻⣻⣿⣿⣿⣿⣿⢿⠿⠙⢛⣛⣛⣛⣛⣛⣿⣛⣛⣛⣻⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠙⠉⣿⢿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⢿⠗⠄⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⡾⠿⠟⢩⠷⢾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣿⣷⠿⣿⣿⣿⣿⣿⡿⢟⠉⠉⠃⠈⠁⠀⠀⠐⢹⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠁⠠⢿⡿⠍⠉⠀⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⣟⣛⣛⣛⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡐⠈⡚⠻⣿⠿⠏⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⠉⠛⠛⣛⠿⠿⠿⠿⡛⣛⣿⢟⠻⠯⢵⠅⠚⠁⠀⠀⠀⠒⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠁⡈⠓⠸⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡉⠉⣉⣄⡤⠄⠁⢀⡀⡀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3286

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/08/22/The_World_is_Quitting_Windows_Microsofters_Try_to_Sabotage_the_.shtml
    Gemini version at https://techrights.org/n/2024/08/22/The_World_is_Quitting_Windows_Microsofters_Try_to_Sabotage_the_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The World is Quitting Windows, Microsofters
Try to Sabotage the Competition⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


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


Recent: Microsoft_Inside_Debian_is_Sabotaging_Debian_and_Its_Many_Hundreds_of
Derivatives_With_SystemD_(Microsoft/GitHub_Slopware_With_Catastrophic_Bugs_is
Hardly_a_New_Problem)


THIS month's statistics (global scope, based on Web usage) from statCounter
show both ChromeOS and GNU/Linux rising, of course at Windows' expense! There's
even some new coverage about it, e.g. "Linux_Market_Share_Reaches_New_Peak:
July_2024_Report" (published earlier this week). Microsoft meanwhile sabotages
dual-boot_systems, perhaps seeing that more and more people quit Windows
(people seem to be deleting Vista 11 in droves this summer) and I'm told Vista
11 is so bad that it does not even support PNG format - unlike operating
systems from the 1990s!


This is what's_happening_in_China_this_month. Aside from some noise 7 years
ago, what we have here is an all-time low for Windows:


           🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Operating System Market Share China⦈


Windows is basically a burning platform, but Microsoft moles like Miguel_de
Icaza and 'secure'_boot_charlatans (yes, they're friends and corresponding)
will try to sabotage GNU/Linux users' PCS and dethrone leading figures.
Microsoft has long used moles like these to get the "dirty jobs" done. At the
end it throws them under the bus. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⣾⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣀⣀⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣟⣛⠁⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⢿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠛⠛⠛⠂⠀⠀⢸⣿⣿⣿⣿⣿⠘⠻⠿⠿⣿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠛⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⢻⣿⣷⣶⣾⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⠛⠿⠿⠟⠛⠛⠛⠉⠉⢹⣿⣿⣿⣿⣿⢸⣿⡟⠛⠛⠛⠛⠛⡋⠉⠛⠋⠉⠉⠉⠉⡉⠛⠋
⢿⠷⠴⢿⡿⠃⠈⠙⠿⠿⢾⣿⣿⣿⣿⣿⡿⢷⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠛⠋⠀⠘⠿⡿⠛⠛⠂⠀⢸⣿⣿⣿⣿⣿⠘⣿⡇⠛⠛⠛⠛⠛⠛⠛⠁⠀⠈⠛⠛⠛⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠼⠿⠿⠉⠉⠛⠛⢿⣿⣿⣿⣿⣟⠉⢹⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣟⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠿⠋⢉⡉⠉⠛⠛⠛⠁⠘⠉⠉⠁⠬⠉⠉⠉⠉⠉⠉⠉⠉⢀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣻⣿⣏⣹⣿⣿⡇⠀⠀⠀⢀⣤⣶⣶⣾⣶⣶⣿⣶⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣀⡜⠛⢿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠄⢹⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠁⠀⢐⡚⠛⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠋⣸⢸⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣭⣿⣷⣶⣶⣶⣾⣿⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣷⠀⡟⣾⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡸⠿⣸⠶⣈⠤⠄⣶⠤⣇⢾⡇⣶⡇⠢⣿⠧⢝⡜⡤⠔⡶⡇⠤⣷⡆⡆⣿⣷⢋⣼⠣⢸⢰⣯⡺⠠⢄⢾⡷⠬⡁⣶⡟⠄⣧⣆⠤⣿⣗⠿⡇⣶⡇⣷⡆⡧⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⢿⣿⣿⣿⡿⢿⠿⡿⢿⠿⣿⣿⣷⠷⣿⣿⣿⣷⠿⠿⠿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣨⣅⣨⣒⣽⣏⣠⣛⣟⣻⣈⣼⣭⣟⣤⣛⣻⣀⢻⣋⣂⣃⣟⣸⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠻⡻⠛⠻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿
⣿⣿⣶⣶⣾⣶⣧⣴⣦⣤⣄⣉⠉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣄⡉⠛⠛⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣤⠀⠋⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣠⡀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣉⣩⣙⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡄⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠈⠻⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢸⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸
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                    ䷩ 𝚕𝚒𝚗𝚎 3400

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ When You're 'Winning' You Become a
'Target'⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇A_kiss_on_cheek⦈_


Microsoft is in_trouble. Don't believe the Wall Street schemes and bubbles. The
mass_layoffs_are_due_to_financial_problems, not just "greed".


Windows_is_in_disarray, Microsoft_tries_to_vandalise_Linux (because to Hell
with "Microsoft loves Linux" pretences), the government_bailouts_are_being
called_off, and Microsoft_fakes_its_finances_some_more (to hide the massive
losses).


So, what one should expect to happen is a lot more sabotage targeting whoever
brings about change. They_will_defame_Richard_Stallman (also Eben Moglen, Linus
Torvalds etc.) and they will disrupt_from_within, i.e. the usual. This is all
they have left. Is this going to work? Not really. Last night we showed that
the FSF_is_expanding (some time soon we'll have photos from the office in
Boston), so if they attack one person or one activist, many others will fill
the gap and come to replace or at least complement that person. See how the
assassination of Alexei Navalny backfired. Did that stop dissent or opposition
in Russia? Hell no! So now Putin goes after lawyers who represented Navalny,
charging them with "extremism" (even if in absentia). We put that in Daily
Links yesterday. It does not scale because assassinating an idea is
exceptionally hard; it makes martyrdom.


Movements like Navalny's exist because there is popular demand for them and
they don't go away with character assassination or actual assassination/s. In
the case of Free software, demand has long existed for it and it is in fact
growing because technology becomes more oppressive over time and more NGOs want
to do something about it, even if the way they formulate/express the issue may
not mention software freedom (they articulate similar ideas, albeit
differently).


Keep on fighting. Keep them on the retreat. █


           🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Goomba Whack-a-Mole: Microsoft mole⦈


"Everyone says corruption is everywhere, but for me it seems strange to say
that and then not try to put the people guilty of that corruption away."


                                                                -Alexei Navalny


"Consistency for me is everything."


                                                                -Alexei Navalny


"People don't believe in positive changes anymore."


                                                                -Alexei Navalny




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⠛⣋⣩⣥⣶⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠀⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢛⣻⣯⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⠉⠉⠙⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣶⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠸⣿⣿⣷⠄⠀⠀⠀⠀⠈⠙⠛⢻⡛⠛⠉⠹⠯⣹⣿⣿⢀⣜⢻⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣾⠔⢤⣤⣤⣠⣴⣦⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⠀⠀⠀⠀⠀⢰⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠋⠀⠀⠀⠀⠀⠀⢸⡄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⢿⣿⣿⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⢶⣶⣿⣿⣿⣿⣿⡿⠁⣼⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⣿⣿⣿⣿⣿⡿⠛⠉⠸⣿⣿⣿⡿⠋⠁⠀⣐⣿⠗⠀⣶⠀⢠⣀⣀⡀⢸⡧⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠠⣀⠀⠀⢀⣴⣿⠃⡐⠚⢧⡰⣮⣯⣍⣛⡻⣷⣼⣿⣿⣿⣿⡇⠀⠀⠀⠘⢻⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⣼⠀⣠⣤⣙⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⠏⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠁⣠⣶⣦⣵⡿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣷⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⠈⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⡟⠀⠀⠀⣴⣦⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣸⣿⠟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠈⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⡇⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢏⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠂⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⡿⣸⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣷⣿⣿⣿⣿⣿⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣷⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢻⠿⢿⣿⣷⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⠀
⢀⡀⠈⠛⠛⠋⠉⠉⠉⠙⠿⠟⠃⠀⠀⠈⠉⠻⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣤⣥⣤
⠙⠛⠀⠐⣀⣀⣀⣠⣤⠀⣴⣶⣶⣶⣶⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣟⡻⠁⠀⢀⣀⠀⠹⠛⠋⠉⠉⠉⠙⠿⠟⠃⢸⡏⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠈⠋⠃⠀⣀⣀⣰⣦⣤⢀⣶⣶⣾⠾⠷⠾⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠛⠋⠉⠉⠁⢸⣿⣿⣿⣿⣿⡟⠀⠁⠿⡿⡆⠈⠿⠿⠿⢿⣿⣉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⢀⡀⠀⠛⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠃⠀⠀⣀⣀⣀⠤⠤⠽⠿⠿⠿⠋⠀⠀⠀⠀⢀⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠘⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣯⣙⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣤⣤⣴⣶⣶⣿⢻⣩⢫⣏⡷⣦⡀⠀⢠⡄⡄⢩⢻⡯⢹⢫⣭⣹⡍⣿⠉⣩⠉⣝⠫⣍⣿⣿⣿⣿⣿⣿⣿⡀⠘⠋⠉⠀⠀⢤⣤⣤⣖⣒⣒⣚⣃⣀⣀⣀⣤⣭⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠸⠿⠰⠖⠅⠉⠁⠀⠀⠀⠁⠀⠈⠁⠀⠈⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⢿⣿
⣿⣿⣿⣿⣅⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⢁⣂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻
⣿⣿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣄⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⣠⣤⣤⣤⡄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣾⠀⢸⡆⢿⣿⡿⠛⠉⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⣿⡿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⡏⣁⣤⣝⠿⣿⣟⣼⣿⣶⣶⣶⣶⣿⣦⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⡼⢁⣤⡀⠀⠀⠀⠀⠀⠊⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⣷⣼⣿⣿⣿⣿⣿⠋⠀⠀⣟⡀⠀⠀⠈⠛⢹⣿⢷⣿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡻⡅⣿⢻⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⡄⠀⣴⣟⣃⠀⠀⢠⠆⢈⠛⠚⣛⣉⢥⠼⠠⠀⣽⣿⣿⣿⣿⣿⣿
⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣉⠀⠉⠭⡄⠆⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣶⣶⣶⣄⠉⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣤⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣨⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣺⡂⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏⠉⠀⠛⠛⠉⢩⢡⡿⠁⠀⢹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣠⡀⠠⠤⠤⠴⣴⣾⣶⠀⠀⠀⣀⡴⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⢛⣓⣶⣦⣤⣤⣤⡤⠤⠔⠒⠒⠚⢉⣁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠻⢷⣿⡇⢀⣀⣀⣂⣻⣿⠿⠶⠒⠋⣁⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3527

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 22/08/2024: Coking, Retro, and
More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇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⠀➾


                # ⚓ How_to_measure_⅚_cup_of_oil,_part_IV⠀⇛


                       My, it's amazing how a topic I wrote about twenty
                       years ago [1] has been popular over the past few
                       [2] years [3]. I just received an email from Jason
                       Arencibia about an even easier method of measuring
                       out ⅚ cup of oil: [...]


                # ⚓ 🔤SpellBinding_—_CEIUQRK_Wordo:_CRUST⠀⇛


                # ⚓ terms⠀⇛


                       ...as I see them


                       I read all of this - https://indieweb.org/small_web


                       and decided I would define, for myself, what each
                       thing "is".


                       So I'll begin:


                       Small Web/Smol Web: roughly a bare bones but not
                       more site on the WWW. Proper DOCTYPE heading, HTML
                       (CSS debatable), no video/music embeds. Not even
                       GeoCities level of media. Quick, unobtrusive.


                       Small/Smol net: the people of the Smol Web. Or,
                       small netWORKS of folks who read/comment amongst
                       small Web products. Email, forums, BBS. et al -
                       Just networks that are small.


          o § Politics and World Events⠀➾


                # ⚓ an_omen⠀⇛


                       today, the Australian government voted in a bill
                       that will massively hurt disabled people, which
                       disabled people have been arguing against, and they
                       rushed it through.


                       being a disabled person myself, i decided i was
                       going to ask my oracle dice (a divination tool,
                       like tarrot cards) about it, how it will effect me
                       etc. I get up to go get them and discover on the
                       floor one of the dice had managed to escape being
                       put away last night. the actions die. and the face
                       it had rolled was sacrifice.


          o § Technology and Free Software⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ retrocomputing_on_mastodon,_monkeys_and_rabbits,_loop
                        da_loop⠀⇛


                             My RSS feed, Feedbin, is slow these days,
                             too. 40+ Mastodon accounts, mostly
                             oldbytes.space and FOSStodon, of mostly
                             retrocomputing-oriented content, falls silent
                             as the projects and postings have settled
                             down greatly in the past year. New servers? A
                             likely case. I would have to investigate. And
                             so I shall go through and see who stays, who
                             goes. And then add some along the way.


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





                    ䷩ 𝚕𝚒𝚗𝚎 3649

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 22/08/2024: Talos Principle 2
and Agate Upgrade⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇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⠀➾


                # ⚓ DCE's_Tinylog⠀⇛


                       I keep seeing all of this injustice and corruption
                       everywhere I look. I always thought that I'd feel
                       better once I turned 18 and would be able to vote
                       and drink and stuff; but I still feel as powerless
                       as ever.


                # ⚓ Comradery⠀⇛


                       Comradery is an attempt to reinvent Patreon as a
                       cooperative that is focused more on the needs of
                       the creators on its platform and serving them
                       rather than investors. It's small and in alpha
                       currently but there are some cool people already on
                       there.


                # ⚓ ch01_-_exploration⠀⇛


                       had a chat with Pi.ai [1]. explained my situation:
                       desire to broaden/improve my skills for work in a
                       way that benefits my non-work life too, ideally


                       shared my resume, back-and-forthed in the morning,
                       before work. after mowing. had coffee.


                       [...]


                       - researched ai training versus inference,
                       especially as it relates to data centers. not
                       related to data analysis, just work. still lots to
                       read on this subject, but i'll get to it tomorrow.


          o § Politics and World Events⠀➾


                # ⚓ Where_insecurity_ends_and_I_begin⠀⇛


                       I recently read Polysecure, by Jessica Fern, a book
                       about attachment theory in the context of
                       polyamory. Attachment theory is fundamentally the
                       idea that the way we were loved (or not) during our
                       childhood creates insecurities in us, and what we
                       need to feel secure in our relationships with
                       others varies depending on our childhood
                       circumstances. I already knew some of my issues
                       with insecurity from prior therapy, but reading the
                       book and it's emphasis on personal security has
                       made me really inspect how it impacts me. There are
                       many areas in my life where different factors cause
                       pulls in separate directions.


          o § Technology and Free Software⠀➾


                # ⚓ Thoughts_on_The_Talos_Principle_2_(Non-Spoiler)⠀⇛


                       Just finished The Talos Principle 2! Overall I
                       liked it but there was a lot more I didn't like
                       than in the first game. I'd still highly recommend
                       it though, at the very least because there's always
                       a major dearth in nice Portal like 3D puzzle games.


                       Overall, at the very least they went for something
                       different and unique rather than “the same thing,
                       but again” which is what I was really really
                       worried about. They definitely went for a very
                       different story, looked at very different themes,
                       and the puzzle design (particularly the bonus/
                       hidden puzzles) felt subtly different (although the
                       latter point is not necessarily a positive).


                # § Internet/Gemini⠀➾


                      # ⚓ More_unintended_consequences_of_my_Apache
                        configuration⠀⇛


                             Now that mod_blog [1] supports conditional
                             requests [2], I thought of the next feature I
                             want to add—PUT support to upload posts.


                      # ⚓ The_Worst_People_You_Know_Have_to_Go_Somewhere:_On
                        the_Zynternet⠀⇛


                             The first time I was exposed to Hawk Tuah, it
                             was sideways, and I didn't get it. On r/
                             torontobluejays, which I browse occasionally
                             during the baseball season, someone posted a
                             picture of someone by the CN Tower with a
                             Blue Jays jersey personalized with HAWK-TUAH
                             / 69. Variations of eyeroll emojis, "classy"
                             remarks, and so on. I didn't get it, but 69,
                             the favourite number of the sort of person
                             for whom the ultimate life goal is a
                             threesome, was obviously a big clue. I
                             googled it. I got the context. I instantly
                             got dumber.


                      # ⚓ Emacs_Functions,_Agate_Upgrade⠀⇛


                             I've written around 100 elisp function in the
                             last two years or so. Most of them are not
                             functions that would be useful in a published
                             code library or package, but just functions
                             that save me time or otherwise provide some
                             automation useful in my particular life
                             circumstances. E.g., I've written code to
                             automatically send out e-mail reminders to
                             people each week; code to speed up my process
                             for making gemlog posts; code that launches a
                             gemipedia search; code that restarts system
                             daemons; and various other little things
                             perhaps not interesting enough to list out.


                             I suppose, as an ideal, it would be nice if
                             all our coding produced mostly code that
                             could easily be reused by others. But it is
                             very easy and quick to write code in elisp if
                             you are able to make a bunch of assumptions
                             specific only to your life and needs, such as
                             what file endings are involved, where you
                             want files to go, and so forth. I'm
                             interested in the idea of composing lots of
                             small functions, with super-powerful
                             combinators, but in practice the problem is
                             usually easily reduced to 5 or 10 steps that
                             can be represented as stateful function calls
                             combined with LET assignments to variables.


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





                    ䷩ 𝚕𝚒𝚗𝚎 3839

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 22/08/2024: Misinformation and
Surveillance Ramped Up Fast⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Yukinu ☛ Yukinu_is_back⠀⇛


                 I had gotten burnt out from updating my site, spending
                 too much time resolving technical paper cuts and getting
                 overwhelmed with too many half finished articles. At the
                 same time, I was also handling a lot of technical debt on
                 my dev machine (which is based on Debian 11 with a lot of
                 additional packages and custom configurations that need
                 cleaning up), further stalling progress on some of my
                 projects. So I decided to shelve my site for a bit of
                 time, think about the future of the site, and work on
                 other projects. In the end I've decided to scale back a
                 few site features, notably I will be archiving my
                 software forge and instead will be moving things back to
                 Codeberg for 3 reason: [...]


          o ⚓ Pete Brown ☛ Never_underestimate_greed_and_ignorance.⠀⇛


                 I kind of wonder if thinking about the world in this
                 way—that there is someone with a master plan—doesn’t make
                 it easier for people to go about their day-to-day lives,
                 even if that master plan is awful. If someone else is in
                 control, it gives you a either single point to attack or
                 a reason not to do anything.


          o ⚓ Jacky Alciné ☛ The_Wrong_Ideas_about_the_Wrong_Things⠀⇛


                 Is it me, then? Am I doing "too much"? Am I asking for
                 more than people can care about? Is it that it's too
                 dangerous to consider these ideas, even in semi-private
                 spaces? Regardless of the first question, I won't stop
                 working to close this gap and I'm hoping that I can join
                 other folks who've been doing this for longer - some of
                 which I'm lucky to lean on for support. This is hopefully
                 a way to give those on the fence or who've been confused
                 a peak inside my mind, where I'm at and why I won't stop
                 talking about the things that I do. We need to do better,
                 myself included.


          o ⚓ Barry Hess ☛ It’s_Been_Awhile⠀⇛


                 The fact is, twenty years is a long time to do things. So
                 long, in fact, that I didn’t do the things all twenty of
                 those years! Still, this here is the 469th post on the
                 blog, and that’s not nothing. Heck, I probably deleted
                 100 posts along the way (deeming them of questionable
                 value), so…more than 500 posts!


          o ⚓ Brandon ☛ Remodel_Underway_-_Site_Refresh_|_NOT_ALL_WHO_WANDER
            ARE_LOST⠀⇛


                 These past few days I've been thinking a lot about my
                 site design. I initially wrestled the base BearBlog theme
                 into something I was excited about, added some design
                 elements, brushed off my hands and moved on to writing.


          o ⚓ Anne Sturdivant ☛ Diving_into_indiewebify.me_&_microformats,_Part
            IX⠀⇛


                 Last week I decided I needed a new template for weblog.
                 The new post type has taken shape over the last few days
                 and I went with linklist for the name after putting up a
                 poll on Mastodon and made the decision before it was even
                 done. Turns out my choice ended up being the majority of
                 voters' choice as well.


                 I mocked up a test post with two different types of link
                 lists: a list of bookmarks or saved links for later, such
                 as a group of tabs from some research I'm doing; a
                 postroll that I publish as a blogroll spin, including
                 links for each new blog that I add. The main "subject" of
                 each of these links is a bit different, so the
                 microformats structure I came up with is different for
                 each. Let's take a look at what I came up with and my
                 thinking that went along with it.


          o § Science⠀➾


                # ⚓ Futurism ☛ Chinese_Scientists_Working_on_Magnetic_Launch
                  System_to_Fling_Cargo_From_Moon's_Surface_Back_to_Earth⠀⇛


                       And whoever comes on top, in terms of technology
                       and territory under its control, will most likely
                       set the rules of engagement in space for
                       generations to come. Extracting helium is just the
                       beginning, in other words.


                # ⚓ Jamie Zawinski ☛ Oops,_All_Crabs⠀⇛


          o § Education⠀➾


                # ⚓ teleSUR ☛ Most_Norwegian_Public_Schools_Adopt_Mobile_Phone
                  Restrictions_-_teleSUR_English⠀⇛


                       On Monday, Norway’s Ministry of Education announced
                       that a survey titled “Questions for Schools in
                       Norway” reveals that over 96 percent of primary
                       schools in Norway have implemented restrictions on
                       mobile phone use.


                # ⚓ Robert Birming ☛ Ditching_the_Desk_for_Dreams⠀⇛


                       Fast forward ten years, and here I am now. I love
                       my current job as a house inspector, even though I
                       still make less than I did back then.


                       And when it comes to IT, I'm more passionate about
                       it now that it's a hobby instead of a career. It's
                       fun again!


                # ⚓ Buttondown LLC ☛ An_idea_for_teaching_formal_methods
                  better⠀⇛


                       I was recently commissioned by a company to make a
                       bespoke TLA+ workshop with a strong emphasis on
                       reading specifications. I normally emphasize
                       writing specs, so this one will need a different
                       approach.


                # ⚓ Drew Breunig ☛ Domain_Expertise_is_the_Difference_Maker_for
                  Data_Scientists_|_Drew_Breunig⠀⇛


                       We over-index on the first two roles when
                       developing data scientists. Business decision
                       making? Well, that’s somebody else’s job: a product
                       manager or an exec views an analysis and makes the
                       call.


                       But domain knowledge in a company’s field is a
                       difference maker for data scientists.


                # ⚓ Crooked Timber ☛ 6_(or_more)_things_you_might_want_to_know
                  how_to_do_as_a_new_TA._—_Crooked_Timber⠀⇛


                       Note: all the strategies I describe here are to
                       some extent dependent on how the physical space of
                       your classroom is organized. If you have fixed
                       seats in rows, and the classroom is full, many of
                       these will be challenging. But to the extent that
                       students can be moved around the classroom so that
                       they can see each other, some will work better or
                       worse. (Structure Academic Controversy, for
                       example, can work even in a fixed seat room: I
                       recommend that you organize the A and B groups so
                       that they are in front of and behind each other,
                       not next to each other). One of the few joys of the
                       Humanities building is that many of the classrooms
                       have entirely moveable seating.


                       Also: you get to choose where your students sit.
                       They don’t. This isn’t a cafeteria, it’s a place of
                       work. Move them to optimize the learning
                       experience. You might think this seems
                       authoritarian: it isn’t and students don’t
                       experience it as such. They appreciate that someone
                       is thinking about their learning.


                # ⚓ The Guardian UK ☛ Afghan_women_arrive_in_Edinburgh_to
                  finish_medical_degrees_denied_under_Taliban⠀⇛


                       The foundation worked with UK and Scottish
                       government officials to arrange safe passage and
                       student visas for the women. They have been given
                       places at four medical schools after Scottish
                       ministers changed the law to treat them as home
                       students eligible for free tuition.


                # ⚓ Jeroen Sangers ☛ Jeroen_Sangers_◦_brain_tags_-_Speed_up
                  informative_videos⠀⇛


                       Speeding up informative videos can be an efficient
                       strategy to save time without significant loss of
                       understanding, as long as the speed stays within
                       certain limits. Research shows that increasing the
                       playback speed of videos up to 1.5x or 2x the
                       normal speed has minimal adverse effects on both
                       immediate and delayed (after a week) levels of
                       understanding. This means that viewers are able to
                       comprehend and remember the core content of the
                       videos, even when they are played at a faster pace.
                       However, it is important to note that performance
                       can significantly decrease at speeds above 2x.


                # ⚓ Lucidity ☛ Quitting_My_Job_For_The_Way_Of_Pain⠀⇛


                       But what I say instead is "I'm sure that you'll
                       find a better job eventually. Okay, clocking out
                       for the week, bye." How lightly I withhold the
                       opportunity for self-improvement, because I know
                       that they will take the news badly, and because I
                       do not believe that they have what it takes to
                       change. It's not that it's my job to be responsible
                       for all that, but withholding that information from
                       people that think of me as being honest with them
                       goes against my own values. And what standard is
                       there to hold myself to if not my own?


                       At the end of January 2025, I'll be leaving my
                       employer to focus full-time on my own business. It
                       doesn't currently make enough money to pay my rent.


                       Two helpings of suffering with a side of
                       principles, please.


          o § Hardware⠀➾


                # ⚓ Cyble Inc ☛ Widespread_Backdoor_Found_In_FM11RF08S_RFID
                  Smart_Cards⠀⇛


                       Security researchers have discovered a widespread
                       hardware backdoor in the FM11RF08S variant of the
                       MIFARE Classic RFID smart cards manufactured by the
                       Chinese chip company Shanghai Fudan
                       Microelectronics.


                       The backdoor allows instantaneous cloning of the
                       cards, posing a major security risk for businesses
                       and consumers using the affected cards. The variant
                       had been released around 2020 and touted as
                       resistant to all known ‘card-only’ attacks –
                       attacks that can be carried out on the card itself
                       without access to its reader.


                # ⚓ Ruben Schade ☛ Being_second_with_physical_media⠀⇛


                       The history of disks, chips, tapes, and cartridges
                       are filled with examples of companies getting this
                       right and wrong.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Science Alert ☛ Video_Games_Can_Boost_Your_Mental_Health_–
                  But_There's_a_Catch⠀⇛


                       A study of almost 100,000 people in Japan aged 10
                       to 69 found playing video games – or even owning a
                       console – can be good for mental health. But
                       playing too much each day can harm wellbeing.


                # ⚓ NPR ☛ She_was_on_the_surgical_table_just_once_but_was
                  billed_for_two_operations⠀⇛


                       Sabrina Corlette, co-director of Georgetown
                       University’s Center on Health Insurance Reforms,
                       said it was absurd for the surgery center to bill
                       for two operations and then refuse to back down
                       when the situation was explained. “It’s like a
                       Kafka novel,” she said.


                       Corlette said surgery center staffers should be
                       accustomed to such scenarios. “It is quite common,
                       I would think, for a surgeon to look inside
                       somebody and say, ‘Oh, there’s this other thing
                       going on. I’m going to deal with it while I’ve got
                       the patient on the operating table.’”


                # ⚓ American Psychological Association ☛ Fast-Forward_to
                  Boredom:_How_Switching_Behavior_on_Digital_Media_Makes_People
                  More_Bored⠀⇛


                       People often switch between videos and fast-forward
                       through them on platforms like YouTube, TikTok, and
                       Netflix. We show that people consume media this way
                       to avoid boredom. However, this switching behavior
                       makes people feel more bored, less satisfied, less
                       engaged, and less meaningful in some instances. Our
                       results provide valuable insights on how to consume
                       digital media in a more adaptive and enjoyable
                       manner in everyday life. Enjoyment may be better
                       attained by immersing oneself in videos rather than
                       swiping through them.


                # ⚓ Michael_Yeadon_turns_on_ivermectin,_and_hilarity_ensues⠀⇛


                       We’re now nearly four and a half years into the
                       global COVID-19 pandemic, and the longer it goes on
                       the more odd things happen in the contingent of
                       people, be they physicians, scientists, or lay
                       people, who have minimized the disease, peddled
                       unproven—and now disproven—repurposed drugs as
                       cures, claimed that SARS-CoV-2, the coronavirus
                       that causes COVID-19, was due to a “lab leak,” and
                       spread fear, uncertainty, and doubt about COVID-19
                       vaccines. Sure, there are the usual crank fights
                       (everyone versus Robert Malone, “inventor of mRNA
                       vaccines,” comes to mind). One blast from the past
                       whom I’ve seen resurfacing lately is Dr. Michael
                       Yeadon. Before the pandemic, Yeadon worked for
                       Pfizer in drug development for respiratory diseases
                       as a vice-president of of the company’s allergy and
                       respiratory research unit in Sandwich, Kent, and
                       later formed his own biotech company. However,
                       after the pandemic hit in 2020, he soon pivoted to
                       become of the earliest purveyors of the antivax lie
                       that COVID-19 vaccines cause infertility—in
                       December 2021, just as the vaccines were rolling
                       off the production lines for the first time in
                       large quantities at Pfizer!—and later expanded his
                       antivax fear mongering to claim that the vaccines
                       were not just causing infertility but
                       “depopulation.” Amazingly, it’s been over three
                       years since I last wrote about this particular
                       antivax crank, which is why his resurgence
                       interests me.


                # ⚓ Pro Publica ☛ Amid_Baby_Formula_Crisis,_U.S._Trade_Reps
                  Opposed_Lifting_Import_Tax⠀⇛


                       As U.S. parents struggled to find baby formula
                       during a nationwide shortage in May of 2022, the
                       Biden administration frantically sought ways to
                       restock empty store shelves. Among the options was
                       lifting steep tariffs on formula imported from
                       other countries.


                       But as White House lawyers drafted a proclamation
                       to remove the import tax, one federal agency
                       resisted: the Office of the United States Trade
                       Representative.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Popular Science ☛ AI_trained_on_AI_churns_out_gibberish
                  garbage⠀⇛


                       Large language models like those offered by OpenAI
                       and Google famously require vast troves of training
                       data to work. The latest versions of these models
                       have already scoured much of the existing internet
                       which has led some to fear there may not be enough
                       new data left to train future iterations. Some
                       prominent voices in the industry, like Meta CEO
                       Mark Zuckerberg have posited a solution to that
                       data dilemma: simply train new AI systems on old AI
                       outputs.


                       But new research suggests that cannibalizing of
                       past model outputs would quickly result in strings
                       of babbling AI gibberish and could eventually lead
                       to what’s being called “model collapse.” In one
                       example, researchers fed an AI a benign paragraph
                       about church architecture only to have it rapidly
                       degrade over generations. The final, most
                       “advanced” model simply repeated the phrase
                       “black@tailed jackrabbits” continuously.


                       A study published in Nature this week put that AI-
                       trained-on-AI scenario to the test. The researchers
                       made their own language model which they initially
                       fed original, human-generated text. They then made
                       nine more generations of models, each trained on
                       the text output generated by the model before it.
                       The end result in the final generation was
                       nonessential surrealist-sounding gibberish that had
                       essentially nothing to do with the original text.
                       Over time and successive generations, the
                       researchers say their model “becomes poisoned with
                       its own projection of reality.”


                # ⚓ Futurism ☛ Tech_CEO_Admits_That_He_“Really_F*cking_Hates”
                  Generative_AI⠀⇛


                       "I fucking hate generative AI," Procreate CEO James
                       Cuda said in a brief company video, posted
                       yesterday to Procreate's official X-formerly-
                       Twitter account.


                       "I don't like what's happening in the industry, and
                       I don't like what it's doing to artists," Cuda
                       continued. "We're not going to be introducing any
                       generative AI into our products."


                # ⚓ The Register UK ☛ Microsoft_unveils_unified_Teams_app⠀⇛


                       Teams has traditionally been the tool enterprises
                       impose on users as part of a Microsoft 365
                       subscription – at least until Microsoft was forced
                       to uncouple the collaboration software from its
                       productivity suite. However, it hasn't gained the
                       same traction with consumers.


                # ⚓ The Washington Post ☛ Investors_who_helped_Elon_Musk_buy
                  Twitter_revealed_after_judge’s_order⠀⇛


                       The filing lists nearly 100 entities with a stake
                       in X, although many appear to represent different
                       funds controlled by the same firm or person. Other
                       investors include venture capital firm Andreessen
                       Horowitz, Saudi Prince Alwaleed bin Talal al Saud;
                       Twitter founder and former CEO Jack Dorsey; and
                       8VC, a venture capital firm co-founded by Joe
                       Lonsdale, co-founder of intelligence contractor and
                       data analysis platform Palantir.


                # ⚓ Modern Diplomacy ☛ Publicizing_the_Bugs,_Malfunctions,
                  Failures,_and_Locations_of_Lethal_AWS_to_Avoid_Accidental
                  Escalations⠀⇛


                       Executive Summary: AI-lethal autonomous weapon
                       systems are likely to begin seeing the battlefield
                       or widespread adoption in the near future. However,
                       AWS possesses the major risk of an AWS failure
                       causing an accidental escalation or conflict, due
                       to their novelty, speed, and ambiguity. I recommend
                       that the U.S. begins publicizing instances of AWS
                       failures and their locations as a confidence-
                       building measure norm. While there are some
                       drawbacks to publishing AWS failures and locations,
                       the U.S. has previously demonstrated with nuclear
                       arms treaties that it is willing to make these
                       tradeoffs for the sake of stability and security.


                # ⚓ Security Week ☛ Thousands_of_Apps_Using_AWS_ALB_Exposed_to
                  Attacks_Due_to_Configuration_Issue⠀⇛


                       As many as 15,000 apps that use AWS’s Application
                       Load Balancer (ALB) for authentication could be
                       vulnerable to attacks, according to application
                       security company Miggo.


                # ⚓ Wired ☛ An_AWS_Configuration_Issue_Could_Expose_Thousands
                  of_Web_Apps⠀⇛


                       The researchers say that looking at publicly
                       reachable web applications, they have identified
                       more than 15,000 that appear to have vulnerable
                       configurations. AWS disputes this estimate, though,
                       and says that “a small fraction of a percent of AWS
                       customers have applications potentially
                       misconfigured in this way, significantly fewer than
                       the researchers' estimate.” The company also says
                       that it has contacted each customer on its shorter
                       list to recommend a more secure implementation. AWS
                       does not have access or visibility into its
                       clients' cloud environments, though, so any exact
                       number is just an estimate.


                # ⚓ Wired ☛ An_‘AI_Scientist’_Is_Inventing_and_Running_Its_Own
                  Experiments⠀⇛


                       The project demonstrates an early step toward what
                       might prove a revolutionary trick: letting AI learn
                       by inventing and exploring novel ideas. They’re
                       just not super novel at the moment. Several papers
                       describe tweaks for improving an image-generating
                       technique known as diffusion modeling; another
                       outlines an approach for speeding up learning in
                       deep neural networks.


                # ⚓ C4ISRNET ☛ Reliant_on_Starlink,_Army_eager_for_more_SATCOM
                  constellation_options⠀⇛


                       The Army is leaning heavily on SpaceX’s Starlink
                       satellite network for advanced command and control,
                       but service officials say they want to keep their
                       options open as new commercial megaconstellations
                       materialize.


                # ⚓ The Verge ☛ Telecom_will_pay_$1_million_over_deepfake_Joe
                  Biden_robocall⠀⇛


                       Lingo Telecom relayed a fake Biden message to New
                       Hampshire voters in January, urging them not to
                       turn out for the Democratic primary. The FCC
                       identified political consultant Steve Kramer as the
                       person behind the generative AI calls and
                       previously proposed Kramer pay a separate $6
                       million fine.


                       Under the new settlement with Lingo, the FCC said
                       the company will need to strictly adhere to its
                       caller ID authentication rules, including “know
                       your customer” principles. The FCC will also
                       require Lingo to “more thoroughly verify the
                       accuracy of the information provided by its
                       customers and upstream providers,” according to a
                       press release. A Lingo spokesperson did not
                       immediately respond to a request for comment.


                # ⚓ Deseret Media ☛ Company_that_sent_AI_calls_mimicking_Joe
                  Biden_to_voters_agrees_to_pay_$1M_fine⠀⇛


                       The case is seen by many as an unsettling early
                       example of how AI might be used to influence groups
                       of voters and democracy as a whole.


                       Meanwhile Steve Kramer, a political consultant who
                       orchestrated the calls, still faces a proposed $6
                       million FCC fine, as well as state criminal
                       charges.


                # ⚓ Security Week ☛ Microsoft_Copilot_Studio_Vulnerability_Led
                  to_Information_Disclosure⠀⇛


                       A vulnerability in Microsoft Copilot Studio could
                       be exploited to access sensitive information on the
                       internal infrastructure used by the service,
                       Tenable reports.


                # ⚓ The Washington Post ☛ How_to_get_back_into_a_hacked
                  Facebook_account⠀⇛


                       Bull-Humphries said she tried for six weeks to get
                       her account back, following the steps in Facebook’s
                       official account recovery process. She pored over
                       threads in the company’s community forums and even
                       sent a picture of her driver’s license to verify
                       her identity. Nothing worked.


                # ⚓ Macworld ☛ Microsoft_apps_on_the_Mac_have_a_security_hole
                  that_won't_get_fixed_soon⠀⇛


                       The apps affected are Microsoft Excel, OneNote,
                       Outlook, PowerPoint, Teams, and Word. Microsoft
                       runs an entitlement that disables macOS’s hardened
                       runtime, which provides security against
                       Dynamically Linked Library hacks. This can allow a
                       [attacker] to install malicious software into
                       Microsoft’s apps.


                # ⚓ Federal News Network ☛ Navy’s_journey_to_new_procurement
                  system_remains_in_peril⠀⇛


                       The Department of the Navy’s third attempt to
                       modernize its contract writing system and overall
                       electronic procurement system is on shaky ground.
                       The latest bid, which followed at least two
                       previous failures, is facing similar troubles as
                       earlier projects: incomplete planning, a technology
                       platform with questionable maturity and, maybe most
                       striking, the hubris of the leadership that their
                       current plan will be successful no matter what
                       evidence emerges that tells a different story.


                # ⚓ Los Angeles Times ☛ How_deepfakes_on_social_media_could
                  threaten_the_election⠀⇛


                       Deception has long played a part in politics, but
                       the rise of artificial intelligence tools that
                       allow people to rapidly generate fake images or
                       videos by typing out a phrase adds another complex
                       layer to a familiar problem on social media. Known
                       as deepfakes, these digitally-altered images and
                       videos can make it appear someone is saying or
                       doing something they aren’t.


                # § Games⠀➾


                      # ⚓ VOA News ☛ Burgeoning_Africa_gaming_industry_attracts
                        major_tech_firms⠀⇛


                             An Africa game industry report says the
                             number of gamers in sub-Saharan Africa has
                             grown from 77 million in 2015 to 186 million
                             in 2021. Ninety-five percent of gamers play
                             on their mobile phones.


                             According to survey company Geopoll, for the
                             majority, gaming is seen as a primary source
                             of entertainment, relaxation and a remedy for
                             boredom, with 73% playing for fun and 64% for
                             stress relief.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Ars Technica ☛ Your_TV_set_has_become_a_digital
                        billboard._And_it’s_only_getting_worse.⠀⇛


                             The TV business isn't just about selling TVs
                             anymore. Companies are increasingly seeing
                             viewers, not TV sets, as their most lucrative
                             asset.


                             Over the past few years, TV makers have seen
                             rising financial success from TV operating
                             systems that can show viewers ads and analyze
                             their responses. Rather than selling as many
                             TVs as possible, brands like LG, Samsung,
                             Roku, and Vizio are increasingly, if not
                             primarily, seeking recurring revenue from
                             already-sold TVs via ad sales and tracking.


                             How did we get here? And what implications
                             does an ad- and data-obsessed industry have
                             for the future of TVs and the people watching
                             them?


                      # ⚓ Privacy International ☛ Social_media_monitoring_in
                        the_UK:_the_invisible_surveillance_tool_increasingly
                        deployed_by_government⠀⇛


                             Privacy International presents how the use of
                             social media monitoring by governments and
                             companies is an increasingly prevalent one,
                             and as this article explores, largely
                             unregulated.


                      # ⚓ NYOB ☛ noyb_complaints_against_EU_Parliament_over
                        data_breach⠀⇛


                             In early May 2024, the European Parliament
                             informed its staff of a massive data breach
                             in the institution’s recruiting platform
                             (called “PEOPLE”). The breach affected the
                             personal data of more than 8,000 staff. This
                             included ID cards and passports, criminal
                             record extracts, residence documents and even
                             sensitive data such as marriage certificates
                             that reveal a person’s sexual orientation.
                             The Parliament only found out about the
                             breach months after it happened, and still
                             doesn’t seem to know the cause. This is
                             particularly worrying as the Parliament has
                             long been aware of vulnerabilities in its
                             cybersecurity system. EU institutions are
                             naturally high up on the list of hackers and
                             foreign adversaries. noyb has now lodged two
                             complaints with the European Data Protection
                             Supervisor on behalf of four parliament
                             employees.


                      # ⚓ Wired ☛ Stadiums_Are_Embracing_Face_Recognition.
                        Privacy_Advocates_Say_They_Should_Stick_to_Sports⠀⇛


                             Thousands of people lined up outside Citi
                             Field in Queens, New York, on Wednesday to
                             watch the Mets face off with the Orioles. But
                             outside the ticketing booth, a handful of
                             protesters handed out flyers. They were there
                             to protest a recent Major League Baseball
                             program, one that’s increasingly common in
                             professional sports: using facial recognition
                             on fans.


                             Facial recognition companies and their
                             customers argue that these systems save time,
                             and therefore money, by shortening lines at
                             stadium entrances. However, skeptics argue
                             that the surveillance tools are never totally
                             secure, make it easier for police to get
                             information about fans, and fuel “mission
                             creep” where surveillance technology becomes
                             more common or even required.


                      # ⚓ VOA News ☛ US_appeals_court_revives_Google_privacy
                        class_action_lawsuit⠀⇛


                             The 9th U.S. Circuit Court of Appeals in San
                             Francisco said the lower court judge who
                             dismissed the proposed class action should
                             have assessed whether reasonable Chrome users
                             consented to letting Google collect their
                             data when they browsed online.


                             Tuesday's 3-0 decision followed Google's
                             agreement last year to destroy billions of
                             records to settle a lawsuit claiming the
                             Alphabet unit tracked people who thought they
                             were browsing privately, including in
                             Chrome's "Incognito" mode.


                      # ⚓ Techdirt ☛ 84%_Of_Americans_Want_Tougher_Online
                        Privacy_Laws,_But_Congress_Is_Too_Corrupt_To_Follow
                        Through⠀⇛


                             As is the norm for U.S. journalism, the
                             outlet frames our failure to pass an internet
                             privacy law over the last 30 years as
                             something that just kind of happened without
                             meaningful cause. The “question” of whether
                             to have even baseline public privacy
                             protections has been left unanswered due to
                             some sort of ambiguous externality. Just
                             blame that pesky, ambiguous gridlock.


                             In reality, Congress hasn’t passed a privacy
                             law because it’s blisteringly, grotesquely
                             corrupt. U.S. policymakers have decided, time
                             and time and time again, that making gobs of
                             money is more important than consumer
                             welfare, public safety, market health, or
                             even national security (see: our obsession
                             with TikTok, while ignoring the national
                             security risks of unregulated data brokers).


                      # ⚓ The Register UK ☛ Slack_AI_can_leak_private_data_via
                        prompt_injection⠀⇛


                             The core problem identified by PromptArmor is
                             that Slack allows user queries to fetch data
                             from both public and private channels,
                             including public channels that the user has
                             not joined. According to the security vendor,
                             Slack considers this intended behavior – but
                             it's behavior that can be abused.


                      # ⚓ El País ☛ Canyon_Lake:_A_soda_and_9mm_ammo:_The_Texas
                        grocery_store_with_a_bullet_vending_machine⠀⇛


                             A blond man with long hair, cargo pants and a
                             loose shirt browses through the options while
                             holding a bag of food and a case of beer. The
                             vending machine has a touchscreen. Once
                             activated, it states that only people over 21
                             years of age with ID are permitted to use it.
                             And that it only accepts payments by card.
                             The man talks to his wife about the variety
                             of ammunition for sale, but doesn’t buy
                             anything. If he had wanted to buy some
                             bullets, he would have had to scan his face
                             and his official ID. Once he’s finished
                             seeing how it works, he leaves in a hurry,
                             not wanting to answer any questions. Another
                             woman in the same supermarket does want to
                             share her thoughts on the bullet vending
                             machine.


                # § Confidentiality⠀➾


                      # ⚓ 404 Media ☛ US_Feds_Are_Tapping_a_Half-Billion
                        Encrypted_Messaging_Goldmine⠀⇛


                             European cops hacked the encrypted phone
                             provider Sky in 2021. More and more cases in
                             the U.S. are using that mass of collected
                             messages.


                      # ⚓ Ruben Schade ☛ Generative_AI_is_a_security
                        vulnerability⠀⇛


                             None of this should be surprising, though I’m
                             glad it’s getting coverage. To be crystal
                             clear: there is no safe use for this tech
                             with proprietary or confidential information.
                             Data leaks aren’t merely an unavoidable or
                             inevitable byproduct, they’re intrinsic to
                             how these tools operate.


                      # ⚓ Dhole Moments ☛ Federated_Key_Transparency_Project
                        Update_-_Dhole_Moments⠀⇛


                             Earlier this year, I wrote about planned
                             effort to design a federated Key Transparency
                             proposal.


                             The end goal for this work was constrained to
                             building end-to-end encryption into a new
                             type of Direct Message on the Fediverse, with
                             other protocols and services being a stretch
                             goal rather than its primary purpose.


          o § Defence/Aggression⠀➾


                # ⚓ Atlantic Council ☛ How_a_‘Free_North’_strategy_can_ensure
                  Arctic_and_Baltic_security⠀⇛


                       From the United States to Finland, NATO allies
                       represent a contiguous northern flank. Finland and
                       Sweden’s NATO accessions have strengthened the
                       Alliance and repositioned its regional security
                       framework. Finland spans from the Arctic Circle to
                       the Baltic, so along with the United States, it is
                       optimally positioned to anchor a collective
                       commitment to a Free North. The Baltic Sea, which
                       is now nearly surrounded by NATO members, offers a
                       resolute coalition of reinforcements for Arctic
                       security.


                # ⚓ VOA News ☛ US_official_holds_talks_in_Africa_on_responsible
                  use_of_military_AI⠀⇛


                       Mallory Stewart, assistant secretary of state for
                       the Bureau of Arms Control, Deterrence and
                       Stability, said her two-day visit with Nigerian
                       officials from the regional bloc ECOWAS was part of
                       the United States’ commitment to deepen security
                       cooperation in Africa.


                       The U.S. government has been working with 55
                       nations, including African nations, “to agree upon
                       responsible uses of AI in the military context,
                       using AI in a manner consistent with international
                       laws [and] recognizing inherent human bias,”
                       Stewart told journalists Wednesday.


                # ⚓ C4ISRNET ☛ This_system_could_allow_small_Army_teams_to_hit
                  1,000_targets_per_hour⠀⇛


                       Since going through at least 10 iterations, with
                       more planned in the coming months and years, the
                       command has developed the Maven Smart System, a
                       combination of sensors and software that allows
                       users to quickly assess a battlespace, gather reams
                       of data and analyze that data using artificial
                       intelligence and machine learning to identify
                       targets and strike.


                # ⚓ New York Times ☛ U.S._Investigating_Americans_Who_Worked
                  With_Russian_State_Television⠀⇛


                       This month, F.B.I. agents searched the homes of two
                       prominent figures with connections to Russian state
                       media: Scott Ritter, a former United Nations
                       weapons inspector and critic of American foreign
                       policy, and Dimitri K. Simes, an adviser to former
                       President Donald J. Trump’s first presidential
                       campaign in 2016. Prosecutors have not announced
                       charges against either of the men.


                # ⚓ Sightline Media Group ☛ Commanders_find_new_ways_to
                  leverage_network_in_theater_and_training⠀⇛


                       The Army is employing diverse methods to keep its
                       network up, data flowing and signals passing
                       between units in a major field exercise as it
                       continues to build the next generation of command
                       and control.


                       Deployed brigades will need to establish their
                       networks quickly, work seamlessly with partner or
                       ally networks and toggle between multiple options —
                       from 5G to low-earth-orbit satellites — to maintain
                       connectivity, officials said.


                # ⚓ The Independent UK ☛ Taliban_bans_UN_special_rapporteur_who
                  sought_education_for_girls_from_entering_Afghanistan⠀⇛


                       Mr Bennett is based outside of Afghanistan but has
                       visited the country on multiple occasions since his
                       appointment in 2022 to research the human rights
                       situation on the ground.


                       He is yet to respond to the travel ban, although
                       The Independent understands his office is likely to
                       issue a statement later today.


                # ⚓ VOA News ☛ Taliban_block_UN_human_rights_investigator_from
                  visiting_Afghanistan⠀⇛


                       Bennett reports to the U.N. Human Rights Council
                       based in Geneva and has conducted several trips to
                       Kabul to investigate the Afghan human rights
                       situation since assuming duties in 2022 — a year
                       after the radical [sic] Taliban returned to power.


                # ⚓ The Guardian UK ☛ More_than_200_unexploded_second_world_war
                  shells_found_near_Solomon_Islands_school⠀⇛


                       On Tuesday, Inspector Clifford Tunuki said the
                       long-hidden weapons cache had been ferried away to
                       a safe location and was now “waiting for safe
                       destruction”.


                # ⚓ Deutsche Welle ☛ Iran_orders_closure_of_German_language
                  institute_in_Tehran⠀⇛


                       Another media outlet, Nournews, considered close to
                       Iran's state security apparatus, suggested that the
                       closures were a response to the closure of the
                       Hamburg Islamic Center (IZH) in Germany in July.


                       At the time, German Interior Minister Nancy Faeser
                       had described the IZH as an "important Iranian
                       propaganda center in Europe."


                # ⚓ The Moscow Times ☛ Moscow_Patriarchate_Condemns_Move_to_Ban
                  Ukrainian_Orthodox_Church_-_The_Moscow_Times⠀⇛


                       The Ukrainian Orthodox Church, which officially
                       broke ties with the Russian Orthodox Church in
                       2022, has been accused by some lawmakers of
                       maintaining covert connections with Russian clergy
                       despite the ongoing war.


                # ⚓ RTL ☛ Cutting_Moscow-aligned_ties:_Ukraine_MPs_vote_to_ban
                  Russia-linked_Orthodox_Church⠀⇛


                       Kyiv has been trying to curb spiritual links with
                       Russia for years -- a process accelerated by
                       Moscow's 2022 invasion, which the powerful Russian
                       Orthodox Church endorsed.


                       A majority of Ukrainian lawmakers approved the bill
                       outlawing religious organisations linked with
                       Russia, which will mostly affect the Moscow-linked
                       Ukrainian Orthodox Church (UOC).


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


                      # ⚓ Site36 ☛ German_Left_Party_Chairman_visits_Maja_T._in
                        Budapest:_Politicians_call_for_shift_in_policy_towards
                        Hungary⠀⇛


                             Two leading politicians from the Left Party
                             met Maja T., who is imprisoned in Budapest
                             waiting for an Antifa trial. One of their
                             demands is that the German judiciary should
                             organise her return.


          o § Environment⠀➾


                # ⚓ Futurism ☛ Tesla_Semi_Truck_Catches_Fire,_Prompting_Hazmat
                  Response_for_Toxic_Smoke⠀⇛


                       It took first responders many hours to put out the
                       big rig fire, highlighting just how challenging it
                       is to extinguish a lithium-ion battery blaze —
                       especially at the scale required to haul freight.


                # ⚓ CBS ☛ Tesla_semi-truck_fire_prompts_I-80_closure_in
                  California_as_hazmat_response_halts_Sierra_Nevada_freeway
                  traffic_-_CBS_Sacramento⠀⇛


                       First responders say that the batteries of the
                       electric big rig were still burning hours later.


                       Due to the situation surrounding the batteries,
                       people were being kept at least a half mile away
                       from the scene.


                # ⚓ MIT Technology Review ☛ This_rare_earth_metal_shows_us_the
                  future_of_our_planet’s_resources⠀⇛


                       If we extract, process, use, and discard these
                       metals, conceptually there must be some point in
                       the future when we run out of them. And as the
                       energy transition has gotten underway, plenty of
                       forecasts have attempted to understand which metals
                       we should worry about and when they might start to
                       be depleted. But experts say that understanding the
                       availability of resources in this sector is much
                       more complicated than picking out a single future
                       peak.


                # ⚓ University of Michigan ☛ It’s_time_for_Michigan_to_demand
                  climate_accountability⠀⇛


                       But, we also can’t ignore how we got into this
                       mess. Major fossil fuel companies have known for
                       decades that their products could lead to “dramatic
                       climatic changes” and require a shift away from oil
                       and gas. To protect their massive profits,
                       companies like ExxonMobil and others took a page
                       from the Big Tobacco playbook and ran ads insisting
                       the science was “unsettled” while they lobbied
                       against solutions. This deception stole precious
                       time in the fight against climate change, and now
                       Michiganders are paying the price.


                       No company should be allowed to sell a product they
                       know is harmful, lie about it and get away with it.
                       That’s why I’m glad that Michigan’s top law
                       enforcement official is now taking steps to hold
                       Big Oil accountable.


                # ⚓ Maine Morning Star ☛ PFAS-laden_firefighting_foam_spill
                  reinvigorates_calls_for_proactive_government_response⠀⇛


                       However, PFAS also make the material difficult to
                       dispose of. For instance, incineration risks
                       failing to break down all the chemical bonds or
                       creating harmful byproducts.


                       Brunswick Sewer System General Manager Rob Pontau
                       said now that the foam has gotten into the sewer
                       system, remediation options are limited. “We don’t
                       have a treatment technology to deal with it, and
                       that’s probably a long way out,” Pontau said.


                # ⚓ El País ☛ Bitcoin_mining_uses_the_same_amount_of_energy_as
                  Argentina,_while_laptops_need_a_ton_of_material⠀⇛


                       The trail left by an airplane is a small,
                       perceptible sample of the pollution generated by
                       air traffic. But digitalization does not leave
                       smoke, and its effects are less evident. However,
                       according to the UNCTAD report, the information and
                       communications technology sector’s carbon footprint
                       accounted for 1.5 to 3.2% of global greenhouse gas
                       emissions.


                # § Energy/Transportation⠀➾


                      # ⚓ FAIR ☛ ‘This_Is_a_Push_to_Pass_Laws_Criminalizing
                        Protest_of_Fossil_Fuel_Infrastructure’:_CounterSpin
                        interview_with_Emily_Sanders_on_criminalizing_pipeline
                        protest⠀⇛


                             Janine Jackson interviewed ExxonKnews‘ Emily
                             Sanders about criminalizing pipeline protests
                             for the August 16, 2024, episode of
                             CounterSpin. This is a lightly edited
                             transcript.


                      # ⚓ DeSmog ☛ BBC_Accused_of_Doing_PR_for_Major
                        Polluters⠀⇛


                      # ⚓ DeSmog ☛ How_U.S._governments_could_crack_down_on
                        greenwashing⠀⇛


                      # ⚓ The Record ☛ FAA_proposes_new_cybersecurity_rules_for
                        airplanes⠀⇛


                             The FAA believes the rules will “protect the
                             equipment, systems, and networks of transport
                             category airplanes, engines, and propellers
                             against intentional unauthorized electronic
                             interactions (IUEI) that could create safety
                             hazards.”


                             Applicants would be required to identify
                             cybersecurity deficiencies and develop
                             instructions for how pilots would continue
                             operating in the event of a cyber incident.


                      # ⚓ CNBC ☛ Ford_delays_new_EV_plant,_cancels_electric
                        three-row_SUV⠀⇛


                             Instead, Ford said it will prioritize the
                             development of hybrid models, as well as
                             electric commercial vehicles such as a new
                             electric commercial van in 2026, followed by
                             two EV pickup trucks in 2027.


                      # ⚓ Gannett ☛ Ford_shifts_EV_strategy,_dropping_plans_for
                        three-row_all-electric_SUV⠀⇛


                             Ford's announcement comes as other automakers
                             are also adjusting their strategies based on
                             slower U.S. EV adoption than predicted. EV
                             purchases are forecast to represent about
                             8.3% of new car sales, according to Cox
                             Automotive, a slight increase from last year
                             when EV's market share was 7.6%.


                      # ⚓ NPR ☛ Ford_scraps_all-electric_SUV_plan,_saying
                        drivers_want_hybrids⠀⇛


                             Ford, which is the No. 2 U.S. EV company, had
                             been working to produce an all-electric
                             three-row SUV. But it tapped the brakes on
                             that vehicle earlier this year, and now,
                             Lawler and Ford say, it’s stalled. Instead,
                             Ford will offer hybrid versions of the SUVs.
                             The next EVs in its pipeline are now pickup
                             trucks and commercial vans — areas where
                             Lawler sees a competitive edge.


                      # ⚓ Lewis Dale ☛ The_Raleigh_Refurb⠀⇛


                             Last year, I bought a Raleigh Randonneur
                             touring frame, which I used as my commuting
                             bike for work. For a while, it was brilliant,
                             but last winter was pretty hard on it, and
                             there were parts of the frame that weren’t
                             properly painted or protected from the
                             elements. So it got rusty, parts broke, and
                             at the start of this year I abandoned it in
                             favour of a NoLogo singlespeed.


                      # ⚓ Michigan News ☛ Michigan_reports_4-year_high_for
                        bicyclists,_pedestrians_struck_by_vehicles_-
                        mlive.com⠀⇛


                             In 2023, Michigan reported 2,114 vehicle
                             crashes involving pedestrians, and 1,480
                             involving bicyclists, according to state
                             police data released this summer. That’s 11%
                             more pedestrian-involved crashes and 10% more
                             bicyclist-involved crashes than in 2022.


                             Katie Bower, director of the Michigan Office
                             of Highway Safety Planning, voiced concern
                             over the surge in residents hit while biking
                             or on foot.


                # § Wildlife/Nature⠀➾


                      # ⚓ BBC ☛ Man_killed_by_XL_bully_dog_in_his_own_home⠀⇛


                             A man has been killed by his own XL bully dog
                             at his home in Lancashire, police have said.


                             David Daintree, 53, was attacked by the pet
                             in Ashley Court in Accrington and was found
                             dead at about 21:30 BST on Tuesday.


                             Lancashire Police said officers had “no
                             alternative” but to shoot the dog to “prevent
                             it from causing further injury”, the force
                             said.


                             Supt Marie Jackson said Mr Daintree's family
                             were being supported by specialist officers
                             after the "tragic incident".


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Wired ☛ The_US_Government_Wants_You—Yes,_You—to_Hunt_Down
                  Generative_AI_Flaws⠀⇛


                       At the 2023 Defcon hacker conference in Las Vegas,
                       prominent AI tech companies partnered with
                       algorithmic integrity and transparency groups to
                       sic thousands of attendees on generative AI
                       platforms and find weaknesses in these critical
                       systems. This “red-teaming” exercise, which also
                       had support from the US government, took a step in
                       opening these increasingly influential yet opaque
                       systems to scrutiny. Now, the ethical AI and
                       algorithmic assessment nonprofit Humane
                       Intelligence is taking this model one step further.
                       On Wednesday, the group announced a call for
                       participation with the US National Institute of
                       Standards and Technology, inviting any US resident
                       to participate in the qualifying round of a
                       nationwide red-teaming effort to evaluate AI office
                       productivity software.


                # ⚓ The Verge ☛ OpenAI_exec_says_California’s_AI_safety_bill
                  might_slow_progress⠀⇛


                       The letter is addressed to California State Senator
                       Scott Wiener, who originally introduced SB 1047,
                       also known as the Safe and Secure Innovation for
                       Frontier Artificial Intelligence Models Act.


                       According to proponents like Wiener, it establishes
                       standards ahead of the development of more powerful
                       AI models, requires precautions like pre-deployment
                       safety testing and other safeguards, adds
                       whistleblower protections for employees of AI labs,
                       gives California’s Attorney General power to take
                       legal action if AI models cause harm, and calls for
                       establishing a “public cloud computer cluster”
                       called CalCompute.


                # ⚓ Smithsonian Magazine ☛ British_Government_Places_Export_Ban
                  on_Alan_Turing's_World_War_II-Era_Notebooks_|_Smithsonian⠀⇛


                       The papers contain Turing’s notes related to the
                       Delilah project, a lesser-known endeavor to develop
                       a portable voice encryption system. Dating to the
                       mid-1940s, the notes “offer unique insights” into
                       Turing’s mind, as arts minister Chris Bryant says
                       in a statement from the British government.


                # ⚓ Deccan Chronicle ☛ SEBI_Issues_New_Cybersecurity_Framework
                  for_Regulated_Entities⠀⇛


                       The framework provides a structured methodology to
                       implement various solutions for cybersecurity and
                       cyber resiliency. In order to facilitate better
                       understanding and ease of compliance.


                # ⚓ India Times ☛ Big_Tech_wants_AI_to_be_regulated._Why_do
                  they_oppose_a_California_AI_bill?⠀⇛


                       Advanced by State Senator Scott Wiener, a Democrat,
                       the proposal would mandate safety testing for many
                       of the most advanced AI models that cost more than
                       $100 million to develop or those that require a
                       defined amount of computing power. Developers of AI
                       software operating in the state would also need to
                       outline methods for turning off the AI models if
                       they go awry, effectively a kill switch.


                # ⚓ Techdirt ☛ Dear_Taylor_Swift:_There_Are_Better_Ways_To
                  Respond_To_Trump’s_AI_Images_Of_You_Than_A_Lawsuit⠀⇛


                       Please don’t do this. First, it probably won’t
                       work. Suing via an untested law that is very likely
                       to run afoul of First Amendment protections is a
                       great way to waste money. Trump also didn’t create
                       the images, presumably, and is merely sharing or
                       re-truthing them. That’s going to make making him
                       liable for them a challenge.


                       But the larger point here is that all Swift really
                       has to do here is respond, if she chooses, with her
                       own political endorsement or thoughts. It’s not as
                       though she didn’t do so in the last election cycle.
                       If she’s annoyed at what Trump did and wants to
                       punish him, she can solve that with more speech:
                       her own. Hell, there aren’t a ton of people out
                       there who can command an audience that rivals
                       Donald Trump’s… but she almost certainly can!


                # ⚓ CNBC ☛ GM_lays_off_more_than_1,000_salaried_software_and
                  services_employees⠀⇛


                       The layoffs include roughly 600 jobs at General
                       Motors' tech campus near Detroit. The job cuts
                       represent about 1.3% of the company's global
                       salaried workforce of 76,000 as of the end of last
                       year.


                # ⚓ El País ☛ Donald_Trump_spreads_fake_images_of_electoral
                  support_from_Taylor_Swift⠀⇛


                       The superstar voiced her support for Joe Biden and
                       Kamala Harris in the 2020 presidential election,
                       but has not yet declared her preference this year


                # ⚓ Deutsche Welle ☛ EU_greenlights_new_chip_factory_in
                  Dresden⠀⇛


                       The European Commission on Tuesday said it had
                       approved a new silicon chip factory in Dresden as
                       Taiwanese semiconductor giant TSMC broke ground on
                       its first European factory.


                       European leaders are keen to avoid dependence on
                       other regions of the world for the supply of
                       semiconductors — indispensable in an array of
                       electronics from computers, to cars and and even
                       missiles.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Deutsche Welle ☛ Misinformation_targeting_Democratic
                        VP_candidate_Tim_Walz⠀⇛


                             Tim Walz, a 60-year-old veteran and former
                             geography teacher, has recently gained
                             national prominence after being chosen as the
                             vice-presidential running mate by Vice
                             President Kamala Harris in the 2024
                             Democratic presidential campaign. Prior to
                             this, Walz was not widely known outside the
                             state of Minnesota, where he serves as
                             governor.


                             Walz has been a critic of former President
                             Donald Trump, particularly regarding national
                             security, healthcare and social justice
                             issues. However, his ascent to the national
                             stage has also made him a target of
                             misinformation, much of it perpetuated by
                             Trump and his supporters.


                             DW has investigated a few of these claims:
                             [...]


                      # ⚓ The Washington Post ☛ Pakistani_police_charged_man
                        for_spreading_UK_riot_disinformation⠀⇛


                             Farhan Asif, 32, is accused of sharing fake
                             information that incited riots in the United
                             Kingdom, Pakistan’s Federal Investigation
                             Agency said Wednesday. He is accused of
                             amplifying misinformation about the identity
                             of the attacker who stabbed three children to
                             death July 29 in an article on the website
                             Channel3Now.


          o § Censorship/Free Speech⠀➾


                # ⚓ Meduza ☛ As_Telegram,_WhatsApp,_and_numerous_other_web
                  services_go_down_in_Russia,_Moscow_blames_attackers_while
                  activists_suspect_Kremlin_interference⠀⇛


                       Internet users in Russia reported outages affecting
                       a wide range of online services on Wednesday,
                       including Telegram, WhatsApp, and Skype. About an
                       hour after the issues began, Russia’s federal
                       censorship agency blamed the disruption on a
                       massive DDoS attack, but digital rights activists
                       said it bears all the hallmarks of an attempted
                       block by the authorities. Here’s what we know.


                # ⚓ [Repeat] France24 ☛ Nicaragua_outlaws_1,500_NGOs,_including
                  religious_charities⠀⇛


                       The government of Nicaragua's President Daniel
                       Ortega on Monday banned 1,500 non-governmental
                       organisations it views as hostile, most of them
                       religious charities. The move was part of an
                       ongoing crackdown on civil society groups seen as
                       opposing Ortega's rule.


                # ⚓ India Times ☛ How_a_law_that_shields_big_tech_is_now_being
                  used_against_it⠀⇛


                       Section 230, introduced in the internet's early
                       days, protects companies from liability related to
                       posts made by users on their sites, making it
                       nearly impossible to sue tech companies over
                       defamatory speech or extremist content.


                       Zuckerman has focused on a part of Section 230 that
                       spells out protection for blocking objectionable
                       material online. In 2021, after a developer
                       released software to purge users' Facebook feeds of
                       everyone they follow, Facebook threatened to shut
                       it down. But Section 230 says it is possible to
                       restrict access to obscene, excessively violent and
                       other problematic content. The language shields
                       companies from liability if they censor disturbing
                       content, but lawyers now say it could also be used
                       to justify scrubbing any content users don't want
                       to see.


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


                # ⚓ The Dissenter ☛ Chicago_Police_Arrest_Several_Journalists
                  While_Cracking_Down_On_DNC_Protest⠀⇛


                       During the Democratic National Convention, Chicago
                       police aggressively cracked down on a protest
                       outside of the Israeli consulate. Officers carried
                       out a mass arrest that included multiple members of
                       the press, according to several independent
                       reporters that were on the ground.


                       Josh Pacheco, a photojournalist from New York City,
                       and Olya Fedorova, a freelance photojournalist,
                       were singled out by police and arrested and charged
                       with “disorderly conduct.”


                       Police reportedly damaged Pacheco and Fedorova’s
                       camera equipment during their arrests, and they
                       were released from the Area 3 police station in the
                       early morning after being held in police custody
                       for nearly 10 hours.


                # ⚓ Defence_correspondents:_the_journalistic_wing_of_the
                  military?⠀⇛


                       An analysis of broadcasters’ online coverage of
                       defence spending and strategy since Keir Starmer
                       won the election shows that reporting is virtually
                       100% in line with the government’s own priorities.


                       Critical voices, where they are included, are
                       entirely from the right.


                       All 20 articles posted under ‘defence’ since 4 July
                       – 14 from Sky, 5 from the BBC and 1 from ITV –
                       faithfully reproduce the government’s agenda.


                       These include its proposals for a defence review,
                       its promise to increase military spending to 2.5%
                       of GDP, its commitment to Ukraine and NATO
                       (described on the BBC by foreign secretary David
                       Lammy as ‘part of Britain’s DNA’).


                # ⚓ RFA ☛ Hong_Kong_journalists_say_press_freedom_declines
                  further⠀⇛


                       Press freedom in Hong Kong has fallen to its lowest
                       point since an annual survey of the city’s
                       journalists began 11 years ago amid fears it will
                       weaken still further in the wake of Article 23
                       security legislation passed in March.


                       More than half of journalists who responded to the
                       latest Hong Kong Journalists' Association survey
                       said press freedom had declined over the past year,
                       with more than 90% of respondents saying that press
                       freedom had declined overall for the fifth year in
                       a row.


                # ⚓ VOA News ☛ RFE/RL_journalist_marks_1,000_days_jailed_in
                  Belarus_on_charges_viewed_as_bogus⠀⇛


                       Kuznechyk is one of several journalists and
                       activists who have been jailed in Belarus since
                       2020, when President Aleksander Lukashenko, in
                       power since 1994, claimed yet another victory in a
                       contested presidential election. Massive protests
                       against the disputed election were met with a
                       severe government crackdown.


                # ⚓ VOA News ☛ 5_journalists_killed,_dozens_injured_covering
                  Bangladesh_protests⠀⇛


                       During the mass protest movement in Bangladesh that
                       drove former Prime Minister Sheikh Hasina from
                       office on August 5, dozens of journalists were
                       injured and at least five killed.


                # ⚓ VOA News ☛ Nevada_official_sent_angry_messages_to_reporter
                  before_his_murder,_Las_Vegas_court_told⠀⇛


                       They argued that Telles’ anger over the coverage
                       motivated him to kill the Las Vegas Review-Journal
                       reporter.


                # ⚓ CPJ ☛ Yet_again,_Zambian_journalist_Thomas_Allan_Zgambo
                  faces_prison_over_reporting⠀⇛


                       Zambian journalist Thomas Allan Zgambo is facing up
                       to seven years in prison for his reporting on
                       corruption and poor governance in the southern
                       African nation. It is at least the third time that
                       Zgambo has risked imprisonment for his online
                       journalism, a growing threat for journalists in
                       many African countries.


                # ⚓ CPJ ☛ In_Nigeria,_at_least_56_journalists_attacked_and
                  harassed_as_protests_roil_region⠀⇛


                       “He hit me with a gun butt,” Premium Times
                       newspaper reporter Yakubu Mohammed told the
                       Committee to Protect Journalists, recalling how he
                       was struck by a police officer while reporting on
                       cost-of-living protests in Nigeria’s capital of
                       Abuja on August 1. Two other officers beat him,
                       seized his phone, and threw him in a police van
                       despite his wearing a ”Press” vest and showing them
                       his press identification card.


                # ⚓ BIA Net ☛ Journalist_threatened_after_exposing_public
                  contracts_secured_by_holding⠀⇛


                       Demirdaş explained to bianet that his report,
                       titled “Veysel Demirci Wins Another Tender,” was
                       published on Aug 17. It detailed the 460 million
                       lira contract awarded to Demirci’s company for a
                       project in Adana and highlighted other government
                       contracts that Ziver Holding has secured.


                       The journalist emphasized that his report was based
                       on factual data obtained from the Electronic Public
                       Procurement Platform (EKAP) and contained no
                       falsehoods or insults.


                # ⚓ [Repeat] Hong Kong Free Press ☛ Hong_Kong_press_freedom
                  falls_further,_according_to_HKJA_survey⠀⇛


                       According to the results of the Hong Kong
                       Journalists Association’s (HKJA) annual press
                       freedom index, published on Tuesday, the rating
                       recorded by reporters was just 25 out of 100, the
                       lowest since the survey was first conducted in
                       2013.


                # ⚓ VOA News ☛ Investigation_sought_after_influential_Thai
                  general_hits_journalist⠀⇛


                       The ethics code for Thai parliamentarians states
                       members should respect the rights and liberty of
                       others and refrain from threats, showing malice or
                       use of force to harm others.


                       The incident happened on Friday moments after the
                       Pheu Thai Party's Paetongtarn Shinawatra won a vote
                       in parliament to become prime minister, Thailand's
                       third premier from the billionaire Shinawatra
                       family, with which Prawit has a bitter history.


                # ⚓ CPJ ☛ Iraqi_security_forces_assault_2_news_crews_covering
                  protests⠀⇛


                       On August 18, in Halabja, Sulaymaniyah province,
                       Iraqi Kurdistan Asayish security forces attacked
                       Zoom News TV reporter Avin Atta and cameraman Zhyar
                       Kamli while they were reporting on a demonstration
                       against the killing of a porter, known as a kolbar,
                       by Iraqi border forces in the Hawraman area.


                # ⚓ The Nation ☛ Real-Time_“Fact-Checking”_Is_the_Lowest_Form
                  of_Journalism⠀⇛


                       In practice, this vision of reporters as above-the-
                       fray priests of a higher empirical truth could not
                       be more ill suited to the Trumpified political age.
                       Indeed, the vision of our political press as a
                       performative fact-checking outlet functions as a
                       kind of learned institutional helplessness. As
                       Trump derides the canons of the Lügenpresse and
                       calls journalists “the enemy of the people,” and
                       MAGA elected officials discuss the lynching of
                       reporters, the whole enterprise of compulsively
                       calling out the movement’s empirical shortcomings
                       is a case study in self-undermining futility. It
                       seems a lot like pointing out that your mugger’s
                       shoe is untied while you’re pinned against the wall
                       with a knife at your throat.


                # ⚓ Semafor Inc ☛ Burkina_Faso_jihadist_attacks_expose_Ibrahim
                  Traoré's_problems⠀⇛


                       Civilians who have displeased the regime, including
                       judges and journalists, have been forcibly drafted
                       into front-line combat. Those drafted include the
                       popular radio journalist Alain Traoré, known to his
                       audience as Alain Alain, who was reported “killed
                       in action” on Aug. 17.


          o § Civil Rights/Policing⠀➾


                # ⚓ EFF ☛ Geofence_Warrants_Are_'Categorically'
                  Unconstitutional_|_EFFector_36.11⠀⇛


                       If you'd like future lessons about the fight for
                       digital freedoms, you're in luck! We've got you
                       covered with our EFFector newsletter. You can read
                       the full issue here, or subscribe to get the next
                       one in your inbox automatically. You can also
                       listen to the audio version of the newsletter on
                       the Internet Archive, or by clicking the button
                       below:


                # ⚓ VOA News ☛ Senior_US_officials_meet_Dalai_Lama_in_New
                  York⠀⇛


                       China took control of Tibet in 1951 before the
                       Dalai Lama fled into exile in 1959.


                       Tibet had previously been largely autonomous,
                       following the fall of the Qing dynasty, which
                       lasted three centuries.


                # ⚓ JURIST ☛ Austria_agrees_to_ban_marriages_for_those_under
                  18⠀⇛


                       Austrian news outlet Kurier reported one of the
                       reasons for this reform is UNICEF’s worldwide call
                       for a minimum age of marriage of 18 years. The
                       European Union does not legislate on marriage,
                       leaving space for each member state to establish
                       rules on the matter. In this sense, all member
                       states require the legal age of marriage to be the
                       same as the age of majority, set at 18 for most
                       states. Despite this, most countries are free to
                       establish exceptions.


                # ⚓ RFERL ☛ Taliban_Bars_UN's_Human_Rights_Envoy_From_Entering
                  Afghanistan⠀⇛


                       Afghanistan's Taliban rulers have banned UN's
                       Special Rapporteur on Human Rights Richard Bennett
                       from entering the country, spokesman Zabihullah
                       Mujahid was quoted as saying by private Afghan
                       broadcaster Tolo. [...]


                # ⚓ ANF News ☛ Demonstration_for_Yazidi_women_in_front_of_the
                  UN_building_in_Beirut⠀⇛


                       The action was promoted by the Women's Life
                       Foundation, Newroz Community and Culture Foundation
                       and Werde Butrus-Equality for Women's Affairs
                       Association.


                       Lebanese and Palestinian women gathered in front of
                       the UN to express their support for the resistance
                       of Yazidi women and to call for the perpetrators of
                       the genocide attacks of 2014 to be held to account.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Jonathan Dowland ☛ Fediverse_and_feeds⠀⇛


                       The Fediverse (or the Mastodon-ish bits of it)
                       should avoid the fate of Twitter. JWZ puts it
                       better and more succinctly than I can.


                       The Fedi experience is, sadly, pretty clunky. So I
                       want to try and write a bit from time to time with
                       tips and tricks that might improve people's
                       experiences.


                       First up, something I discovered only today about
                       Mastodon instances. As JWZ noted, "If you are
                       worried about picking the "right" Mastodon
                       instance, don't. Just spin the wheel.". You can
                       spend too much time trying to guess a good answer
                       to this. Better to just get started.


                # ⚓ Inside Towers ☛ Democratic_Platform_Highlights_Broadband
                  Infrastructure_Investments_-_Inside_Towers⠀⇛


                       The platform for the Democratic National Convention
                       happening in Chicago this week links together
                       investments in broadband infrastructure with
                       policies promoting semiconductors and easing supply
                       chain woes. Broadband infrastructure is featured
                       beginning on page two of the 92-page platform,
                       stating the Bipartisan Infrastructure Law is
                       breaking ground on over 57,000 projects across
                       4,500 communities.


                # ⚓ The Conversation ☛ Avalanches_can_grow_100_times_larger
                  under_the_sea_than_on_land_–_here’s_why_they’re_a_risk_to_the
                  internet⠀⇛


                       My new study of an ancient underwater avalanche
                       challenges our understanding of how underwater
                       avalanches develop and may change the way
                       geologists assess their risk potential.


                       It is estimated that there are now over 550 active
                       seafloor cables around the world with a combined
                       length of 1.4 millionkm – enough to wrap around the
                       circumference of the Earth 35 times.


                # ⚓ US News And World Report ☛ Russia_Says_It_Records_Mass
                  Disruption_in_Telegram,_Whatsapp_Apps⠀⇛


                       It did not say what could have caused the
                       disruptions.


                # ⚓ Tech Central (South Africa) ☛ Internet_giants_must_'pay_to
                  play'_in_South_Africa⠀⇛


                       According to ACT’s white paper, the only OTT
                       players regulated in South Africa are voice-over-IP
                       service providers. Streaming services for music and
                       video and messaging platforms are not regulated,
                       and ACT believes telecoms policy needs to be
                       updated to include these companies in the
                       regulatory regime.


                       Central to ACT’s argument is the concept of “Fair
                       Share”: the idea that OTT service providers, as
                       high-bandwidth users of broadband networks, should
                       pay network operators for the capacity they take up
                       on the networks so that they, the operators, have
                       more capital to maintain and upgrade their
                       infrastructure.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Matt Birchler ☛ Netflix_is_more_serious_about_games_than
                  you_might_expect⠀⇛


                       It’s a good get for Netflix, and a reminder that
                       they have been developing a pretty impressive
                       library of games over the last year or two. Out of
                       curiosity, I checked out the full list of game they
                       currently have available to subscribers, and it’s
                       pretty good! It’s similar to Apple Arcade, but what
                       stands out to me is that it has more of the sorts
                       of games that appeal to me. Below are some
                       standouts, some of which are on Apple Arcade as
                       well, and some that were game-of-the-year
                       contenders in the larger gaming space outside of
                       iOS.


      § Monopolies/Monopsonies⠀➾


          o ⚓ Silicon Angle ☛ UK_antitrust_watchdog_closes_Google,_Apple_probes
            to_revise_regulatory_approach⠀⇛


                 The U.K.’s antitrust regulator, the Competition and
                 Markets Authority, has closed two parallel probes into
                 Google LLC and Apple Inc. that focused on their business
                 practices in the mobile market.


                 Officials announced the decision today. The development
                 relates to a new piece of legislation, the DMCC Act, that
                 became law in the U.K. this past May. The CMA signaled
                 that it could resume its scrutiny of Apple and Google in
                 a new form to make use of the additional regulatory tools
                 that the DMCC Act puts at its disposal.


          o ⚓ India Times ☛ The_case_against_Microsoft_that_"personally
            wounded"_Bill_Gates⠀⇛


                 However, the book's claims have not gone unchallenged. A
                 spokesperson for Bill Gates told Business Insider that
                 the book includes "highly sensationalised allegations and
                 outright falsehoods that ignore the actual documented
                 facts our office provided to the author on numerous
                 occasions."


          o ⚓ PC World ☛ Sick_of_Google?_Try_one_of_these_5_search_engines
            instead⠀⇛


                 You don't have to use Google to search the internet. Here
                 are five contenders you don't want to miss.


          o § Copyrights⠀➾


                # ⚓ Walled Culture ☛ OCLC_says_“what_is_known_must_be_shared”,
                  but_sues_Anna’s_Archive_to_stop_it_sharing_knowledge⠀⇛


                       The current lawsuit will probably be the first of
                       many, just as happened with Sci-Hub. How Anna’s
                       Archive will respond is not yet clear. But an
                       interesting post on the latter site points out that
                       the continuing rapid fall in storage costs means
                       that in a few years’ time it will be possible to
                       mirror the entirety of even expanded versions of
                       Anna’s Archive for a few thousand dollars. When
                       that happens, there won’t be one or two backups of
                       the site – and hence most human knowledge – but
                       thousands, possibly millions of copies: [...]


                # ⚓ The Register UK ☛ AI_copilots_are_getting_sidelined_over
                  data_governance⠀⇛


                       Microsoft positions its Copilot tool as a way to
                       make users more creative and productive by
                       capturing all the human labor latent in the data
                       used to train its AI models and reselling it.


                       But technology reached the market far ahead of
                       safety and security. It was only two years ago that
                       generative AI services started to appear and
                       there's still some work to be done.


                # ⚓ India Times ☛ OpenAI_signs_content_deal_with_Condé_Nast⠀⇛


                       News and digital media have faced steep challenges
                       over the last decade as many technology companies
                       eroded publishers' ability to monetize content,
                       Roger Lynch, CEO of Conde Nast, said in a memo to
                       employees.


                # ⚓ Torrent Freak ☛ Unofficial_M3U8_Playlists_For_Pluto_TV,
                  Samsung_&_Plex,_Shut_Down_By_Warner⠀⇛


                       Offering movies and TV shows at no cost to the
                       consumer has seen 'FAST' services like Pluto TV
                       attract tens of millions of users. Consumption is
                       also thriving via unofficial methods, including
                       M3U8 playlists that are versatile despite their
                       simplicity. During the past 24 hours, the most
                       popular unofficial playlists were taken offline by
                       Warner Bros, succeeding where earlier attempts
                       failed.


                # ⚓ Torrent Freak ☛ Webtoon_Targets_170+_Pirate_Domains_Through
                  DMCA_Subpoena⠀⇛


                       In June, Webtoon Entertainment celebrated going
                       public by sounding the closing bell at the Nasdaq
                       exchange. Thus far, early investors haven't been
                       rewarded, but the company itself sees a bright
                       future ahead. By targeting roughly 170 pirate site
                       domains though a DMCA subpoena, it hopes to unmask
                       their rogue operators and clear the path for future
                       growth.


                # ⚓ Torrent Freak ☛ Kakao_Reveals_Anti-Piracy_Successes,_Legal
                  Action_Against_Major_Manga_Sites⠀⇛


                       Kakao Entertainment's pursuit of pirates
                       distributing the company's 'webtoon' comics has
                       been controversial at times, yet appears to be
                       delivering results. Earlier this year the company's
                       P.Cok anti-piracy unit offered rewards for webtoon
                       fans to snitch on pirates. With the release of
                       Kakao's fifth anti-piracy report, the company
                       details its successes and reveals legal action
                       targeting three major manga sites.





                    ䷩ 𝚕𝚒𝚗𝚎 5968

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 22/08/2024: Tension Around Taiwan and
South China Sea, Automobile Market's
Oversupply⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Aug 22, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Integrity/Availability/Authenticity
          o Defence/Aggression
          o Environment
                # Energy/Transportation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Ruben Schade ☛ “Your_experience_with_$FOO”_spam⠀⇛


                 I’ve noticed more people trying to engage by sending spam
                 in the form of a question. Then, when they inevitably
                 don’t get a response, they’ll send a follow-up with
                 another question:


                 It would be great to chat about your pipeline. We work
                 with many game studios, maybe we can learn from each
                 other?


                 Are you using Perforce? What do you like about it, what
                 not?


          o ⚓ AccessNow ☛ The_Ministry_of_Digital_Affairs_welcomes_RightsCon_to
            Taiwan⠀⇛


                 The Ministry of Digital Affairs, Taiwan, witnessed by
                 Vice Premier Cheng Li-chiun of Executive Yuan, signed a
                 Letter of Intent with Access Now.


          o ⚓ New York Times ☛ A_Woman’s_Family_Reported_Her_Missing._Her_Body
            Was_in_Hospital_Storage,_Lawsuit_Says.⠀⇛


                 Jessie Peterson, 31, died at a hospital in April 2023.
                 Her family members, who filed a missing persons report,
                 were not told that she had died until a year later,
                 according to a negligence lawsuit.


          o § Standards/Consortia⠀➾


                # ⚓ Paul Boyd ☛ What_is_UDP?_-_pboyd.io⠀⇛


                       If you’ve heard anything about UDP, you’ve probably
                       heard it described as connectionless and
                       unreliable. That’s true, but it’s like describing
                       Elon Musk as a wingless human: technically
                       accurate, yet completely unhelpful. We usually
                       define things by what they are, not what they
                       aren’t. So, what’s UDP? Well, not much, it turns
                       out. You can read RFC 768 for yourself, but to
                       summarize, UDP is layered on IP and adds port
                       numbers: [...]


                # ⚓ Zimbabwe ☛ Google_says_disable_2G_on_your_phone_and_yet_Zim
                  mobile_operators_still_rely_on_2G_to_an_extent⠀⇛


                       So, the march towards 5G continues and I’m properly
                       whelmed by it now, as you should be too. The
                       reality is that 4G/LTE will remain important in
                       Zimbabwe for the foreseeable future, and even 3G
                       will still be relevant.


                       However, we have no business being dependent on 2G/
                       Edge and yet we still are, to an extent.


                # ⚓ Hackaday ☛ Supercon_2023:_Soft_Actuators_As_Assistive
                  Tech⠀⇛


                       When we think of assistive prostheses or braces, we
                       often think of hard and rigid contraptions. After
                       all, it wasn’t that long ago that prosthetic limbs
                       were still being made out of wood. Even devices
                       made of more modern materials tend to have a
                       robotic quality that inevitably limits their
                       dexterity. However, advancements in soft robotics
                       could allow for assistive devices that more closely
                       mimic their organic counterparts.


          o § Licensing / Legal⠀➾


                # ⚓ VOA News ☛ Shein_sues_Temu_over_copyright_infringements_as
                  legal_feud_heats_up⠀⇛


                       Online fast-fashion giant Shein has filed another
                       lawsuit against competitor Temu, accusing the
                       China-founded shopping platform of stealing its
                       designs, copying its product images and engaging in
                       other types of fraud.


                       The complaint filed in a Washington federal court
                       this week alleges that Temu, which has grown in
                       popularity in the United States, has subsidized its
                       low prices by encouraging sellers to offer
                       counterfeited items, stolen designs and substandard
                       products.


                # ⚓ Axios ☛ Disney+_lawsuit:_How_Americans_signed_away_their
                  right_to_take_a_company_to_court⠀⇛


                       Disney denied any wrongdoing and argued that
                       Piccolo had waived his right to sue twice when he
                       signed up for a Disney+ streaming account in 2019
                       and when he used the Disney World website in 2023,
                       according to a court filing from the company. "This
                       argument borders on the surreal," per Piccolo's
                       court filing.


          o § Science⠀➾


                # ⚓ New York Times ☛ A_‘Speedy_Little_Star’_May_Be_on_Course_to
                  Escape_Our_Galaxy⠀⇛


                       The so-called hypervelocity object, which is either
                       a low-mass star or a brown dwarf, is traveling
                       through the Milky Way at around a million miles an
                       hour.


                # ⚓ MIT Technology Review ☛ A_new_system_lets_robots_sense
                  human_touch_without_artificial_skin⠀⇛


                       Even the most capable robots aren’t great at
                       sensing human touch; you typically need a computer
                       science degree or at least a tablet to interact
                       with them effectively. That may change, thanks to
                       robots that can now sense and interpret touch
                       without being covered in high-tech artificial skin.


                # ⚓ Science Alert ☛ Streetlights_Could_Be_Causing_Insects_to
                  Starve,_Scientists_Warn⠀⇛


                       This might impact entire ecosystems.


                # ⚓ Science Alert ☛ Your_Nose_Can_Reveal_Serious_Hidden_Health
                  Issues⠀⇛


                       Don't ignore it like your brain does.


          o § Hardware⠀➾


                # ⚓ Tom's Hardware ☛ AMD_updates_Zen_5_Ryzen_9000_benchmark
                  comparisons_to_defective_chip_maker_Intel_chips_—_details
                  'Admin'_boost_coming_to_backdoored_Windows_11,_chipset_driver
                  fix⠀⇛


                       AMD penned a blog post today to clarify Zen 5's
                       gaming performance after withering criticism in the
                       wake of its turbulent Ryzen 9000 launch.


                # ⚓ Hackaday ☛ Farewell_Magnetic_Stripe⠀⇛


                       For decades, the magnetic stripe has been
                       ubiquitous on everything from credit cards to
                       tickets to ID badges. But the BBC reports —
                       unsurprisingly — that the mag stripe’s days are
                       numbered. Between smartphones, QR codes, and RFID,
                       there’s just less demand for the venerable
                       technology.


                # ⚓ CNX Software ☛ xMEMS_XMC-2400_is_a_1mm-thin_solid-state
                  micro_cooling_fan-on-a-chip_for_ultrathin_devices_and_SSDs⠀⇛


                       xMEMS Labs XMC-2400 is a vibration-free, solid-
                       state micro cooling fan-on-a-chip that’s just 1mm
                       thin and designed to cool the processor, other
                       chips, and batteries on space-constraints devices
                       such as smartphones, tablets, extended reality
                       headsets, laptops, as well as SSDs. The XMC-2400
                       can deliver up to 39cc/sec airflow and up to
                       1,000Pa back pressure per instance while remaining
                       inaudible and only consuming an estimated 30mW.


                # ⚓ Hackaday ☛ The_First_Mass_Produced_DRAM_Of_The_Soviet
                  Union⠀⇛


                       Although the benefits of semiconductor technology
                       were undeniable during the second half the 20th
                       century, there was a clear divide between the two
                       sides of the Iron Curtain. Whilst the First World
                       had access to top-of-the-line semiconductor
                       foundries and engineers, the Second World was
                       having to get by with scraps. Unable to keep up
                       with the frantic pace of the USA’s developments in
                       particular, the USSR saw itself reduced to copying
                       Western designs and smuggling in machinery where
                       possible. A good example of this is the USSR’s
                       first mass-produced dynamic RAM (DRAM), the 565RU1,
                       as detailed by [The CPUShack Museum].


                # ⚓ Hackaday ☛ Tiny_’90s_Laptop_Gets_Modern_Power⠀⇛


                       The laptop to have here in the 2020s varies
                       depending on who you ask, perhaps a Framework, or
                       maybe a ThinkPad. Back in the 1990s the answer
                       might have included a now-forgotten contender,
                       because in that decade Toshiba made a range of
                       legendarily tough chunky grey machines. Of these
                       the smallest was the Libretto, a paperback book
                       sized clamshell design which was an object of
                       desire. It’s one of these that [Robert’s Retro] has
                       upgraded to use USB-C power instead of the original
                       power brick.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ BIA Net ☛ Turkey’s_health_minister_rules_out_extra_Mpox
                  measures_for_African_students⠀⇛


                       No Mpox cases have been detected in Turkey yet, the
                       minister has emphasized.


                # ⚓ Latvia ☛ Latvenergo_pledges_to_donate_to_cancer_patients⠀⇛


                       Latvenergo has pledged to donate funds to pay for
                       medicines needed by oncology patients, the charity
                       organization "Ziedot.lv" confirmed to Latvian
                       Television on August 19.


                # ⚓ RFA ☛ American_drug_firms_accused_of_clinical_trials_in
                  Uyghur_region⠀⇛


                       US lawmakers say biopharmaceutical companies are
                       conducting medical testing in China’s Xinjiang.


                # ⚓ Hong Kong Free Press ☛ Beijing_launches_probe_into_dairy
                  products_from_EU_after_bloc_announces_5-year_tariffs_on
                  Chinese_EVs⠀⇛


                       By Matthew Walsh Beijing on Wednesday launched a
                       probe into EU subsidies of some dairy products
                       imported into China, the day after the bloc said it
                       planned to impose five-year import duties of up to
                       36 percent on Chinese electric vehicles.


                # ⚓ New York Times ☛ Congress_Presses_Health_Insurance
                  Regulators_on_‘Troubling’_Billing_Tactics⠀⇛


                       Lawmakers are zeroing in on MultiPlan, a firm that
                       has helped insurers cut payments while sometimes
                       leaving patients with large bills.


                # ⚓ Science Alert ☛ Here_Are_All_The_Reasons_Why_You_Should
                  Enjoy_Your_Cup_of_Coffee⠀⇛


                       In moderation, of course.


                # ⚓ Mexico News Daily ☛ Government_reinforces_security_in
                  Michoacán_to_protect_lime_producers⠀⇛


                       Growers and packers say increased security is a
                       temporary solution, demanding more robust action
                       from authorities against extortion.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Major Hayden ☛ Rub_some_Hey_Hi_(AI)_on_it⠀⇛


                       Author’s note: This post is all about my personal
                       thoughts on artificial intelligence (AI) and they
                       don’t represent the views of any employer or group.


                       You can’t escape the clutches of Hey Hi (AI)
                       lately.


                       It’s in my smartphone nestled next to my text
                       messages. It’s in my work_chats. It’s reading_my
                       Spanish in Duolingo. It’s in my photo albums
                       retouching_my_images.


                       Sometimes we know that there’s Hey Hi (AI) involved
                       in something and sometimes we don’t.


                       However, it seems like so many are in a rush to
                       implement some kind of Hey Hi (AI) offering without
                       a full idea of why they’re doing it.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ WhichUK ☛ Which?_Shorts_podcast:_how_to_stop_phishing
                        attacks_on_your_own_computer⠀⇛


                             We look at the clever ways that scammers are
                             trying to get hold of our information by
                             hacking into our computers at home.


          o § Defence/Aggression⠀➾


                # ⚓ CS Monitor ☛ How_China-Philippines_tensions_are_bringing
                  South_China_Sea_conflict_to_new_brink⠀⇛


                       China’s expansions in the South China Sea are
                       shifting power dynamics in the valuable, disputed
                       waterways, complicating efforts to maintain peace.


                # ⚓ RFA ☛ China’s_‘growing_authoritarianism’_won’t_stop_with
                  Taiwan:_Lai_Ching-te⠀⇛


                       Taiwan’s president also warned of Beijing’s
                       ‘military expansionism’.


                # ⚓ Hong Kong Free Press ☛ Taiwan_is_‘not_only_target’_of
                  pressure_from_China,_island’s_leader_Lai_Ching-te_says⠀⇛


                       Taiwanese President Lai Ching-te warned Wednesday
                       that China’s “growing authoritarianism will not
                       stop with” the island and urged democratic
                       countries to unite to curb its expansion. China
                       claims Taiwan as part of its territory, and a
                       senior Chinese Communist Party official said
                       Tuesday that Beijing was confident of “complete
                       reunification” with the island.


                # ⚓ RFA ☛ Taiwan_denies_entry_to_asylum-seeking_Chinese
                  dissident_writer⠀⇛


                       Deng Liting and her family are denied entry,
                       leaving the democratic island less than 24 hours
                       after jumping plane.


                # ⚓ Atlantic Council ☛ How_quickly_can_Taiwan_integrate_US
                  weapon_systems?_Speed_is_essential_to_help_deter_China.⠀⇛


                       To better prepare Taiwan to defend itself, the
                       United States needs more transparency into Taipei’s
                       weapons integration challenges.


                # ⚓ RFA ☛ China’s_Pooh-tin_pledges_closer_ties_with_Fiji_for
                  ‘ocean_of_peace’⠀⇛


                       Sitiveni Rabuka is the latest Pacific island leader
                       to visit Beijing in recent months.


                # ⚓ New York Times ☛ Middle_East_Crisis:_Israel_and_Hezbollah
                  Exchange_Strikes_Amid_Fears_of_Escalation⠀⇛


                       The Israeli military said it had hit weapons
                       facilities, prompting Hezbollah to target an
                       Israeli base, as tit-for-tat strikes continued
                       across the Lebanese border.


                # ⚓ New York Times ☛ Israel_and_Hezbollah_Trade_Cross-Border
                  Strikes⠀⇛


                       The strikes, in eastern Lebanon and the Israeli-
                       controlled Golan Heights, underscored how months of
                       talks have failed to stop either the war in Gaza or
                       the related conflict along the Lebanese border.


                # ⚓ RFA ☛ Ads_on_Facebook,_Fentanylware_(TikTok)_target_Lao
                  women_for_marriage_with_Chinese_men⠀⇛


                       The ads promise money, gold and a new phone – but
                       the government warned of trafficking risk.


                # ⚓ RFA ☛ Lao_and_Chinese_security_forces_raid_call_centers_in
                  the_Golden_Triangle⠀⇛


                       All centers in the Chinese-run special economic
                       zone face a Sunday deadline to shut down their
                       operations.


                # ⚓ Defence Web ☛ Tunisia_looks_to_buy_more_Archangel_boats
                  from_the_US⠀⇛


                       The US State Department has approved a $110 million
                       sale to Tunisia of additional 65 foot Archangel
                       boats manufactured by Washington-based SAFE Boats
                       International.


                # ⚓ Defence Web ☛ Border_guards_nab_man_with_34_passports⠀⇛


                       A routine inspection by Border Management Authority
                       (BMA) border guards at the busy Lebombo port of
                       entry (PoE) this week netted no less than 34
                       passports in possession of a single person.


                # ⚓ Atlantic Council ☛ Negah_Angha:_It’s_crucial_to_understand
                  and_listen_to_diverse_MENA_voices⠀⇛


                       The Iranian-American foreign policy and national
                       security expert was interviewed by our MENASource
                       editor to discuss her views on Middle East policy,
                       social movements, and where the region is heading.


                # ⚓ Bruce Schneier ☛ Story_of_an_Undercover_CIA_Agent_who
                  Penetrated_Al_Qaeda⠀⇛


                       Rolling Stone has a long_investigative_story (non-
                       paywalled version here) about a CIA agent who spent
                       years posing as an Islamic radical.


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


                      # ⚓ RFERL ☛ German_Chancellor_Visits_Moldova_For_Talks_On
                        Ukraine,_EU_Enlargement,_And_Bilateral_Relations⠀⇛


                             German Chancellor Olaf Scholz told Moldovan
                             President Maia Sandu and Prime Minister Dorin
                             Recean in a meeting in Chisinsau on August 21
                             that Berlin will remain the biggest European
                             supporter of Ukraine.


                      # ⚓ RFERL ☛ Ukrainian_Lawmakers_Ratify_Rome_Statute,_The
                        ICC's_Founding_Treaty⠀⇛


                             Ukraine's parliament, the Verkhovna Rada, on
                             August 21 ratified the Rome Statute, the
                             founding treaty of the International Criminal
                             Court (ICC), lawmakers Yaroslav Zheleznyak
                             and Oleksiy Honcharenko reported.


                      # ⚓ New York Times ☛ Russia_Seeks_to_Turn_Humbling
                        Incursion_Into_Military_Gains⠀⇛


                             Two weeks after Ukraine launched its surprise
                             attack, Russian forces have recovered from
                             the initial shock and are trying to use the
                             expanding war to their battlefield advantage.


                      # ⚓ New York Times ☛ Russia_Said_It_Repelled_a_Large
                        Ukrainian_Drone_Attack_as_Offensive_Advances⠀⇛


                             The attack came as Kyiv presses on with a
                             cross-border offensive into western Russia
                             that has rattled the Kremlin.


                      # ⚓ New York Times ☛ Thursday_Briefing:_Russia_Says
                        Ukraine_Aimed_Drones_at_Moscow⠀⇛


                             Plus, China’s “road-trip auntie.”


                      # ⚓ Meduza ☛ ‘Heads_will_roll’:_Sources_say_Russian
                        officials’_corruption_and_negligence_made_Ukraine’s
                        incursion_possible_—_and_now_they_fear_the_consequences
                        —_Meduza⠀⇛


                      # ⚓ Meduza ☛ Kremlin_officials_think_Ukraine’s_Kursk
                        incursion_could_continue_for_months_—_and_they_want_to
                        convince_Russians_this_is_the_‘new_normal’_—_Meduza⠀⇛


                      # ⚓ Latvia ☛ Anti-mobility_obstacles_continue_to_be
                        placed_along_Latvian_border⠀⇛


                             The defense sector continues to work on
                             strengthening Latvia's eastern border and
                             implementing the anti-mobility plan. Together
                             with Colonel Andris Rieksts of the National
                             Armed Forces (NBS), Latvian Radio walked
                             through the area on the side of the A13
                             highway, near Kārsava, about 10 kilometers
                             from the Latvian-Russian border.


                      # ⚓ LRT ☛ Lithuanian_citizen_detained_in_Russia_for
                        spying,_didn’t_ask_for_assistance_–_ministry⠀⇛


                             Lithuania’s Foreign Ministry has confirmed
                             that Aleksandr Poliackov, a Lithuanian
                             citizen, has been arrested in Russia on
                             espionage charges but has not requested legal
                             assistance.


                      # ⚓ RFERL ☛ Russian_Ex-Deputy_Defense_Minister_Held_On
                        Corruption_Charges_Loses_Appeal⠀⇛


                             A former Russian defense official held in
                             pretrial detention on corruption charges will
                             remain behind bars, a Moscow court decided on
                             August 21.


                      # ⚓ RFERL ☛ Kyrgyz_Banks_Suspend_Transactions_To_Major
                        Russian_Banks⠀⇛


                             The Keremet Bank in Kyrgyzstan said on August
                             20 it suspended money transactions to several
                             major Russian banks. Last week, another bank
                             in the Central Asian nation, MBank, made a
                             similar statement.


                      # ⚓ New York Times ☛ Wilmer_Puello-Mota,_Ex-U.S._Airman
                        Charged_With_Child_Pornography,_Appears_in_Russian
                        Video⠀⇛


                             “I don’t consider myself a traitor,” said
                             Wilmer Puello-Mota, who has enlisted in the
                             Russian military.


                      # ⚓ Meduza ☛ Why_Russia’s_state_censor_is_full_of_baloney
                        when_it_blames_‘DDoS_attacks’_for_widespread
                        disruptions_to_social_network_access_—_Meduza⠀⇛


                      # ⚓ RFERL ☛ Belarusian_Embassy_In_Yerevan_Pelted_With
                        Eggs_And_Tomatoes_After_Lukashenka_Statements⠀⇛


                             Protesters in Yerevan pelted the Belarusian
                             Embassy with eggs and other produce and
                             demanded that diplomatic ties with Minsk be
                             cut over statements made by authoritarian
                             leader Alyaksandr Lukashenka about Armenia's
                             shift westward.


                      # ⚓ RFERL ☛ RFE/RL_Journalist_Andrey_Kuznechyk_Marks
                        1,000_Days_In_Belarusian_Prison⠀⇛


                             Journalist Andrey Kuznechyk of RFE/RL's
                             Belarusian Service, known locally as Radio
                             Svaboda, on August 21, marked the 1,000th day
                             in prison on charges, he, his employer, and
                             human rights organizations call politically
                             motivated.


                      # ⚓ RFERL ☛ Russia_Postpones_Local_Elections_In_Districts
                        Under_Ukrainian_Armed_Forces'_Control⠀⇛


                             The Russian Central Election Commission
                             (TsIK) said on August 21 that it postponed
                             local elections scheduled for September in
                             seven districts of the Kursk region, parts of
                             which have been under the control of
                             Ukrainian armed forces since early August.


                      # ⚓ RFERL ☛ Russia_Says_Head_Of_UN_Atomic_Watchdog_To
                        Visit_Kursk_Nuclear_Plant⠀⇛


                             Rafael Grossi, head of the International
                             Atomic Energy Agency (IAEA), has confirmed he
                             is ready to visit the Kursk nuclear power
                             plant in Russia at the end of August, Russian
                             Foreign Ministry spokeswoman Maria Zakharova
                             said on August 21.


                      # ⚓ RFERL ☛ Russian_Opposition_Politician_Dmitry_Gudkov
                        Sentenced_To_8_Years_In_Absentia⠀⇛


                             A Russian court on August 21 sentenced exiled
                             opposition politician and former
                             parliamentary deputy Dmitry Gudkov to eight
                             years in prison in absentia for his criticism
                             of Russia's military offensive in Ukraine.


                      # ⚓ RFERL ☛ Zelenskiy_Says_Solution_Needed_For_Loan
                        Secured_By_Frozen_Russian_Assets⠀⇛


                             Ukraine needs a real mechanism that will
                             enable the use of Russia's frozen assets to
                             work for the country in the coming months,
                             President of Ukraine Volodymyr Zelenskiy
                             said.


                      # ⚓ RFERL ☛ Ukraine_Reports_Intense_Fighting_Near
                        Pokrovsk_As_Russian_Forces_Press_For_Breakthrough⠀⇛


                             Ukraine's military said its forces came under
                             repeated attack on August 21 around the town
                             of Pokrovsk in the Donetsk region, where
                             Russian forces are pressing for a
                             breakthrough.


                      # ⚓ LRT ☛ Lithuania_extends_Ukrainian_refugees’
                        protection_for_a_year⠀⇛


                             The Lithuanian cabinet on Wednesday extended
                             temporary residence permits for war refugees
                             from Ukraine for another year.


                      # ⚓ JURIST ☛ Ukraine_parliament_approves_ban_on_religious
                        organisations_tied_to_Russia⠀⇛


                             Verkhovna Rada of Ukraine, the Ukrainian
                             parliament, approved the Law on Amendments to
                             Certain Laws of Ukraine on the Activities of
                             Religious Organizations in Ukraine (No.
                             8371), which bans religious organisations
                             affiliated with Russia in Ukraine on Tuesday.


                      # ⚓ France24 ☛ 🔴_Live:_Ukraine_says_it_hit_pontoon
                        bridges_in_Kursk_offensive_as_Russia_claims_Donbas
                        gains⠀⇛


                             Ukraine said on Wednesday it had destroyed
                             Russian pontoon bridges with US-made weapons
                             to defend its incursion into Russia's Kursk
                             region as Moscow claimed its forces had
                             halted Kyiv's advance in the region and
                             gained ground in eastern Ukraine.


                      # ⚓ France24 ☛ Humanity,_not_sympathy:_How_Ukraine_treats
                        Russian_POWs_in_its_'exchange_fund'⠀⇛


                             Ukraine’s surprise attack on the Kursk region
                             in Russia has allowed the country’s forces to
                             take hundreds of enemy prisoners, who Kyiv
                             hopes to exchange for Ukrainian prisoners of
                             war (POWs) held in Russia. Our special
                             correspondent was able to speak with several
                             of these Russian POWs in the prison where
                             they are being held in Ukraine.


                      # ⚓ The Strategist ☛ Territorial_integrity_is_the_base_of
                        European_security⠀⇛


                             Since 2014, Russia has brazenly violated
                             Ukraine’s territorial integrity with
                             incursions, illegal annexations and a full-
                             scale invasion. And now Ukraine is violating
                             Russia’s territorial integrity with its own
                             incursion into the Kursk region.


                      # ⚓ The Straits Times ☛ Russia-China_partnership
                        ‘yielding_results’,_Putin_says⠀⇛


                             The two sides agreed to optimise trade
                             structure, grow bilateral trade volume and
                             promote development of e-commerce.


                      # ⚓ Atlantic Council ☛ Invasion?_What_invasion?_Putin_is
                        downplaying_Ukraine’s_Kursk_offensive⠀⇛


                             Vladimir Putin's efforts to downplay
                             Ukraine's invasion of Russia have severely
                             dented his strongman image and make a mockery
                             of the West's escalation fears, writes Peter
                             Dickinson.


          o § Environment⠀➾


                # § Energy/Transportation⠀➾


                      # ⚓ Defence Web ☛ Chinese_satellite_tracking_ship_Yuan
                        Wang_7_visiting_Durban⠀⇛


                             Over the years people observing the ship
                             movements at the port of Durban have become
                             used to seeing the impressive Chinese
                             tracking ships of the Yuan Wang class
                             arriving in port for a visit lasting several
                             days.


                      # ⚓ Defence Web ☛ Chinese_hospital_ship_on_goodwill_visit
                        to_Cape_Town⠀⇛


                             A Chinese PLA Navy hospital ship, Peace Ark,
                             has sailed from Maputo and can be expected to
                             arrive in Cape Town on Thursday 22 August for
                             a goodwill visit to South Africa’s ‘Mother
                             City’.


                      # ⚓ Atlantic Council ☛ McCue_co-authors_chapter_in_edited
                        volume_on_US_and_Indian_approaches_to_nuclear_security
                        challenges⠀⇛


                             On August 13, 2024, Forward Defense Visiting
                             Senior Fellow Lieutenant Colonel James McCue
                             co-authored a chapter in a new book published
                             by Springer titled The Challenges of Nuclear
                             Security: U.S. and Indian Perspectives.


                      # ⚓ Latvia ☛ New_car_market_in_Latvia_sees_oversupply⠀⇛


                             After the pandemic and the Russian war
                             crises, the new car market has finally
                             recovered and there is even an oversupply of
                             cars on the market. But Latvians are buying
                             fewer and fewer new cars, Latvian Radio
                             reported on August 21.


          o § Finance⠀➾


                # ⚓ Breach Media ☛ Montreal’s_model_for_resisting_culture
                  vulture_capitalism⠀⇛


                       Toronto’s arts scene is cratering under the
                       imperatives of corporate profit.


                # ⚓ BIA Net ☛ Diyarbakır_farmers_say_'interest_rates_more
                  lucrative_than_agriculture'⠀⇛


                       "The economy minister says they will reduce
                       inflation. Are they planning to do this by
                       impoverishing farmers?” says a farmer.


                # ⚓ LRT ☛ Germany’s_Commerzbank_to_open_office_in_Lithuania_by
                  end_of_year⠀⇛


                       Commerzbank, one of Germany’s largest banks, will
                       open its representative office in Lithuania in
                       December, the bank announced on Wednesday.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ New Yorker ☛ How_the_Harris_Campaign_Beat_Trump_at_Being
                  Online⠀⇛


                       Trump has always drawn ideas from the darker
                       corners of the Internet, but his new opponent has
                       found a different kind of traction by embracing the
                       Web’s native formats.


                # ⚓ CS Monitor ☛ Michelle_Obama_raised_a_big_tent_–_and_brought
                  down_the_house_–_at_the_DNC⠀⇛


                       Michelle Obama electrified the Democratic National
                       Convention with a speech that went beyond the “Yes,
                       we can!” of yesteryear, our cultural commentator
                       writes.


                # ⚓ New York Times ☛ Democrats_Use_the_Convention_to_Try_to
                  Define_Trump_as_a_Self-Interested_Fraud⠀⇛


                       Speeches and videos seek to shrink Donald Trump in
                       order to rise above him, as Kamala Harris and her
                       allies work to minimize him and disengage from him.


                # ⚓ New York Times ☛ Michelle_Obama_Absolutely_Takes_Apart
                  Donald_Trump⠀⇛


                       No doublespeak, no metaphors — just straight talk.


                # ⚓ New York Times ☛ ‘Keyboard_Warriors’_Who_Stoked_UK_Riots
                  Test_the_Limits_of_Free_Speech⠀⇛


                       As hundreds of people appear in court for their
                       role in recent anti-immigrant riots in Britain,
                       several are accused of fueling disorder through
                       online posts, raising questions about the limits of
                       free speech.


                # ⚓ Off Guardian ☛ Fascism_2.0_–_The_changing_face_of_social
                  control_media_censorship⠀⇛


                       Facebook make only about £34 a year from the
                       average customer in the UK – a little under £3 a
                       month (and that’s before costs) so clearly there is
                       no head-room or motivation, for a human level of
                       customer service or attention.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ TwinCities Pioneer Press ☛ Company_that_sent_Hey_Hi_
                        (AI)_calls_mimicking_Joe_Biden_to_New_Hampshire_voters
                        agrees_to_pay_$1_million_fine⠀⇛


                             By NICK PERRY MEREDITH, N.H. (AP) — A company
                             that sent deceptive calls to New Hampshire
                             voters using artificial intelligence to mimic
                             President Joe Biden’s voice agreed Wednesday
                             to pay a $1 million fine, federal regulators
                             said.


          o § Censorship/Free Speech⠀➾


                # ⚓ RFERL ☛ Kyrgyz_Activist_Loses_Appeal_Against_Prison_Term
                  Handed_Down_Over_Facebook_(Farcebook)_Post⠀⇛


                       Kyrgyzstan's Supreme Court on August 21 rejected an
                       appeal filed by activist Kanykei Aranova against a
                       42-month prison term she was handed in June over a
                       Facebook (Farcebook) post.


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


                # ⚓ Press Gazette ☛ Evening_Standard_‘legend’_Diane_Chanteau:
                  ‘Bold,_brash,_brilliant_and_ballsy’⠀⇛


                       Chanteau left journalism after the closure of the
                       London Evening News and practised criminal law.


                # ⚓ Press Gazette ☛ Weekly_Evening_Standard_to_be_distributed
                  on_Thursdays_as_‘The_London_Standard’⠀⇛


                       The last edition of the Evening Standard will be
                       distributed on Thursday 19 September.


                # ⚓ Press Gazette ☛ Independent_local_publisher_The_Lincolnite
                  closes_with_nine_jobs_lost⠀⇛


                       Attempts to "secure the future of the business"
                       have failed.


          o § Civil Rights/Policing⠀➾


                # ⚓ RFERL ☛ Romanian_Police_Search_Tate_Brothers'_Residence_In
                  Fresh_Human_Trafficking_Case⠀⇛


                       Romanian investigators carried out four fresh
                       searches on August 21 at residences of divisive
                       Internet influencer Andrew Tate, 37, and his
                       brother Tristan, 36, who are awaiting trial on
                       charges of human trafficking, rape, and forming a
                       criminal gang to sexually exploit women.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Dennis Crouch/Patently-O ☛ Deference_to_District_Courts:
                  Federal_Circuit’s_New_Approach_to_Venue_Transfer_Petitions⠀⇛


                       In a recent order, the Federal Circuit denied
                       Apple’s petition for a writ of mandamus seeking yet
                       again to transfer a patent monopoly infringement
                       case from the Western District of Texas (Judge
                       Albright) to the Northern District of California.
                       In re Fashion Company Apple Inc., 24-129 (Fed. Cir.
                       2024).


                # ⚓ Dennis Crouch/Patently-O ☛ Emphasizing_Context_in_Claim
                  Construction⠀⇛


                       In Neonode Smartphone LLC v. Samsung Electronics
                       Co., Ltd., the Federal Circuit has reversed Judge
                       Albright’s holding that claims of Neonode’s
                       US8095879 are invalid as indefinite.  No. 2023-2304
                       (Fed. Cir. Aug. 20, 2024) (non-precedential). The
                       appellate panel concluded that Albright failed to
                       properly consider the full context of the intrinsic
                       record, particularly the prosecution history.


                       The ‘879 patent monopoly describes a touch-
                       sensitive interface where functions are activated
                       by a multi-step operation involving touching a
                       representation of a function and then gliding away
                       from it.  Disputed claim 1 is directed to software
                       for making this happen.  In patent monopoly speak,
                       this is claimed as a “non-transitory computer
                       readable medium storing a computer program with
                       computer program code …”


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ UPC_Court_of_Appeal_says_Ireland_is_not_a
                        contracting_member_state [Ed: UPC is illegal and not
                        constitutional; these sites that got funded by the
                        litigation 'industry' are willing to ignore it and lie
                        about it still]⠀⇛


                             The Court of Appeal has temporarily suspended
                             a PI with effect for Ireland. In late June,
                             the local division The Hague issued two
                             opposing rulings in the dispute over
                             continuous glucose-monitoring devices (CGM)
                             between market leader Abbott and the Chinese
                             newcomer SiBio and the latter’s distribution
                             partner Umedwings.


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ TTAB_Reverses_Section_2(d)_Refusal_of_NAMASTE
                  COUTURE_BY_APRIL_STOLF_over_NAMASTE_for_Jewelry⠀⇛


                       The Board reversed a Section 2(d) refusal of the
                       mark NAMASTE COUTURE BY APRIL STOLF, finding
                       confusion unlikely with the registered mark
                       NAMASTE, both for jewelry. The Board found the
                       registered mark to be weak in view of numerous
                       third-party uses, and the two marks more dissimilar
                       than similar. However, it upheld the Office's
                       requirement that the applicant disclaim the word
                       COUTURE. In_re_Namaste_Couture_LLC, Serial No.
                       97652794 (August 19, 2024) [not precedential]
                       (Opinion by Judge Peter W. Cataldo).


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Kakaobank_Acquires_15%_Stake_in_PLAM
                  Owner_Naivy_for_$680,000⠀⇛


                       South Korea’s Kakaobank acquires a 15% stake in
                       music streaming startup PLAM owner Naivy for
                       $680,000. South Korea’s largest online-only bank,
                       Kakaobank, has acquired a 15% stake in financial
                       technology startup Naivy, in a deal worth $680,000
                       (908 million KRW.)


                # ⚓ Federal News Network ☛ A_first_snippet_of_the_implications
                  of_artificial_intelligence_when_it_comes_to_copyright
                  monopoly_law⠀⇛


                       The U.S. Copyright Office has just produced the
                       first report on AI, which addresses deepfakes.




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