𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, May 31, 2024
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Generated Sat 1 Jun 02:49:23 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/2024/05/31/


╒═══════════════════ 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  -  In Many Countries Vista 11's Market Share Goes Down, Not Up (Even Microsoft-Funded Mainstream Media Admits This)

⦿ Techrights  -  In Spite of Boot-locking (Trying to Make It Hard If Not Impossible to Install BSDs and GNU/Linux on New PCs) Microsoft's Grip is Rapidly Slipping

⦿ Techrights  -  "I once preached peaceful coexistence with Windows. You may laugh at my expense -- I deserve it." -Be's CEO Jean-Louis Gassée

⦿ Techrights  -  IRC Proceedings: Thursday, May 30, 2024

⦿ Techrights  -  [Meme] Never "Missing Out" in FOSS Conferences

⦿ Techrights  -  Microsoft's Problem in Puerto Rico

⦿ Techrights  -  Microsoft's Share of Physical Web Servers Fell From 9.14% to 9.04% in One Month

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Racism, Ageism, and Ableism at IBM/Red Hat and Kyndryl

⦿ Techrights  -  The War on Free Software Reporters - Part II - Antisocial Mobs

⦿ Techrights  -  The War on Free Software Reporters - Part I - Why Techrights Cannot be Censored (and Won't be Censored)

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/05/31/In_Many_Countries_Vista_11_s_Market_Share_Goes_Down_Not_Up_Even.shtml
https://techrights.org/n/2024/05/31/In_Spite_of_Boot_locking_Trying_to_Make_It_Hard_If_Not_Impossib.shtml
https://techrights.org/n/2024/05/31/I_once_preached_peaceful_coexistence_with_Windows_You_may_laugh.shtml
https://techrights.org/n/2024/05/31/IRC_Proceedings_Thursday_May_30_2024.shtml
https://techrights.org/n/2024/05/31/Meme_Never_Missing_Out_in_FOSS_Conferences.shtml
https://techrights.org/n/2024/05/31/Microsoft_s_Problem_in_Puerto_Rico.shtml
https://techrights.org/n/2024/05/31/Microsoft_s_Share_of_Physical_Web_Servers_Fell_From_9_14_to_9_0.shtml
https://techrights.org/n/2024/05/31/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/05/31/Racism_Ageism_and_Ableism_at_IBM_Red_Hat_and_Kyndryl.shtml
https://techrights.org/n/2024/05/31/The_War_on_Free_Software_Reporters_Part_II_Antisocial_Mobs.shtml
https://techrights.org/n/2024/05/31/The_War_on_Free_Software_Reporters_Part_I_Why_Techrights_Cannot.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/05/31/Gemini_Links_31_05_2024_MNT_Pocket_Reform_and_Benben_v0_5_0.shtml
https://techrights.org/n/2024/05/31/Links_31_05_2024_Escalations_in_Ukraine_and_Russia_National_Rep.shtml
https://techrights.org/n/2024/05/31/Links_31_05_2024_Generating_and_Using_Identifiers_Why_Unicode.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 79

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/In_Many_Countries_Vista_11_s_Market_Share_Goes_Down_Not_Up_Even.shtml
    Gemini version at https://techrights.org/n/2024/05/31/In_Many_Countries_Vista_11_s_Market_Share_Goes_Down_Not_Up_Even.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ In Many Countries Vista 11's Market Share
Goes Down, Not Up (Even Microsoft-Funded Mainstream Media Admits
This)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Silver_kangaroo⦈_


Here's the_land_of_the_kangaroo: (where_GNU/Linux_grows)


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Desktop Windows Version Market Share Australia: Feb 2009 -
                                  May 2024⦈


Hardly the exception!


In the news this week:


     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Microsoft’s Windows 11 upgrade pleas get even more
                                  desperate⦈


More people are moving to GNU/Linux. █




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

                    ䷩ 𝚕𝚒𝚗𝚎 223

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/In_Spite_of_Boot_locking_Trying_to_Make_It_Hard_If_Not_Impossib.shtml
    Gemini version at https://techrights.org/n/2024/05/31/In_Spite_of_Boot_locking_Trying_to_Make_It_Hard_If_Not_Impossib.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ In Spite of Boot-locking (Trying to Make It
Hard If Not Impossible to Install BSDs and GNU/Linux on New PCs) Microsoft's
Grip is Rapidly Slipping⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


Escaping the Microsoft prison


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I tried to turn off 'secure' boot. They don't let you do
                            that with newer PCs.⦈


"There are a lot of market share posts," someone has told me, so "perhaps it is
a time for a round-up with a proper analysis of the global, significant shift
away from Microsoft and what that means in regards to the end of monopoly
rents."


Well, a more detailed market share analysis is overdue and I want to cover this
today. Last night I mentioned Puerto Rico and said "Android has climbed to its
highest level in 4 years this month." In the morning I said "Africa is "lost
territory" for Microsoft colonialism." In the case of Africa, the retreat from
Microsoft monoculture is very rapid and there_are_mass_layoffs_this_month.


In order for Microsoft to charge a significant fee for Windows licences (not
from users; Microsoft bypasses the users by colluding with OEMs and then
imposing those fees on users whether they like it or not) it needs to have
virtually no competition. With Chromebooks being more widely available in more
countries, running the Gentoo-based ChromeOS, Microsoft cannot charge much for
Windows. In the US and the UK, for instance, many buy Chromebooks (they're more
widely available too), so in order to compete Microsoft might as well charge
nothing for Windows, at least initially. And regardless, Windows loses relative
market share very quickly while its Windows-associated revenue falls, both
because total sales volume (units) goes down and the price per unit goes down.


Remember that ChromeOS (or Android for that matter) isn't the destination.
However, anything other than Windows helps end the monopoly rents, which in
turn compels Microsoft to invent some "fictional" future direction like "Hey
Hi" hype and "clown computing", even if those mean deep losses rather than
profits. Microsoft already_cooks_the_books while openly admitting that Windows
revenue is down sharply, XBox sales are down sharply, and debt has soared.


We expect that Microsoft will try to tighten the screws some more with UEFI
'secure'_boot, in effect coming up with "innovative" ways to lock GNU/Linux and
BSDs out of the market, under the false cover of "security" of course...
meddling with these plans or resisting has been spun as opposition to security,
but nothing could be further from the truth. UEFI 'secure' boot is itself a
cluster of security problems and booting Windows means instantiating a large
bunch of security holes connected to the Internet.


Microsoft won't go away easily. Microsoft won't stop committing competition
crimes in an effort to salvage what's left of Windows. So we must remain
vigilant. █




⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣠⣴⣶⡆⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠟⠛⠛⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠆⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠙⢿⣿⡇⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠧⠀⠀⠀⢀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢠⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠀⠀⠀⢸⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠾⢆⡀⠀⠀⠸⠿⠿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣐⠂⢀⣤⡀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠿⠿⠃⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠐⠗⠀⠀⠀⠀⠀⣜⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠐⠓⠒⠂⠀⠀⢰⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣎⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠉⠀⠀⠀⢰⣿⣿⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣤⡦⠀⣀⣈
⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣼⣿⣿⠨⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣽⣿⣷⠀⣿⣿
⠀⠀⠀⣀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣄⠚⣿⣣⣿⣿⣿⣿⣿⡿⢸⡟⣿⠀⠀⠀⠀⢠⢻⣿⣷⠀⣿⣿
⢀⣠⣾⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣆⣿⠙⣿⣿⣿⣿⣿⣟⢸⣇⣿⠃⠀⠀⠀⢸⢼⣿⣿⠀⣿⣿
⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⣣⡙⠫⠸⣿⣏⠀⠉⣿⠉⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀⢿⢸⣿⡏⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣏⠻⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⡇⠘⣿⣿⣿⣾⡇⣿⣻⡆⣿⣸⡇⢰⣿⣿⢸⣿⠃⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡇⠀⣿⣿⣿⣿⡇⣿⢹⡆⣿⣿⡇⢸⣿⣿⢸⡏⠁⣿⠉⠛⠃⠨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠳⠀⠉⠉⠿⠛⠁⠉⠈⠁⠉⠈⠁⠀⠉⠁⠈⠁⠀⠉⢸⣿⡇⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢸⡇⣿⣹⢾⣿⡁⠇⠀⣿⣹⠆⣿⢿⡶⣿⣿⠈⣿⠋⠘⠻⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠹⣿⣿⣶⡆⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣸⡇⣿⢹⣿⣿⡁⢠⡀⣿⣹⡇⣿⣸⠇⣷⣿⠀⣿⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢙⣛⡋⠀⠀⠀⠀⠛⠛⠛⢛⣛⣉⣁⣀⣉⣀⣀⣁⣀⣀⣀⣀⣉⣁⣈⣁⣉⣁⣀⣀⣁⣀⣈⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠉⠧⢠⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠈⣉⣉⣉⣉⣉⣉⣛⣟⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠈⣉⣻⣦⣥⣤⣤⣵⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠃⢀⣈⡛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣆⠀⠀⠀⠀⠀⠴⢶⣶⣤⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⡀⠀⠀⠀⠀⢠⣬⣧⣾⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢀⣜⣡⣤⣜⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣤⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣤⣶⣾⠛⢿⣿⣿⣇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣽⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢷⣄⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣈⣶⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⡃⣿⡇⣿⡇⣿⡟⠋⣿⣼⡿⠀⢸⣿⢻⣿⠀⣿⣻⣿⠀⣿⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⣿⡿⣿⡇⣿⣟⣃⣿⣿⣿⣿⢹⣿⢸⣿⢠⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣧⡿⠇⠿⠗⢿⣿⣿⣿⣿⠛⠁⠸⠿⠾⠿⠉⠿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⣀⡀⣀⣀⡀⠀⢀⣀⣀⠀⠈⣈⣉⣿⣿⣇⢀⣀⠀⣀⣀⡈⣉⣀⣀⠀⢀⣀⢀⣀⠀⣀⣉⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣟⣿⡆⣿⡏⣿⡆⠀⠛⣿⡟⢹⣿⣸⣿⠀⣿⢿⡇⢹⣿⠋⠀⢸⣿⢸⣿⣤⣿⢹⣿⠘⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠉⠛⠛⣿⡏⣿⡇⣿⡇⣿⣿⣶⠀⣿⣇⢸⣿⢻⣿⢸⣿⣸⣷⢸⣿⠀⠀⠘⣿⣾⢻⣿⣿⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠿⠷⠿⠁⠻⠷⠟⠛⠁⠀⣿⡿⠸⠿⠸⠿⠸⠿⠹⠿⠸⠿⠀⠀⠀⠿⠿⠘⠿⠏⠸⠿⠀⠸⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 338

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/I_once_preached_peaceful_coexistence_with_Windows_You_may_laugh.shtml
    Gemini version at https://techrights.org/n/2024/05/31/I_once_preached_peaceful_coexistence_with_Windows_You_may_laugh.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ "I once preached peaceful coexistence with
Windows. You may laugh at my expense -- I deserve it." -Be's CEO Jean-Louis
Gassée⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Execution of Red Hat: But I helped promote Azure and .NET⦈


Latest comments on the Web [1, 2]:


     Of course they [Red Hat] would lie like a rug they have a mass exit
     with no more support


     Looks a bit like the boneheaded management decisions on CentOS a
     couple of years ago really did kill off RHEL future growth prospects?
     Or maybe this is completely unrelated...


     Oh well, in any case time to cut R&D to the bone and milk the
     existing customer base for a decade or two in the finest Big Blue
     tradition


     [...]


     Did they really retain McKinsey & Company, or did they actually bring
     William Hill on-board?


     Personally I don’t rate the odds on the gambles being taken here and
     elsewhere. Risky strategies based on unverifiable incantations.


     Whatever next? The Nostradamus LLM?


Related: Canonical_and_Red_Hat_Are_Not_Competing_With_Microsoft_Anymore




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⡟⠛⡛⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢁⣠⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿
⣿⣿⣿⣿⣿⣿⣷⡯⢵⡵⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣂⣇⣠⣇⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣛⣿⣽⣿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠠⠀⡩⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⢹⠩⠉⡏⢝⠩⡏⠙⡏⠍⠉⢹⢩⠉⠙⢹⢩⢩⢩⠉⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡃⢀⠨⠨⠏⠀⠈⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⣬⣤⣥⣿⣬⣧⣴⣧⣿⣤⣼⣬⣦⣦⣼⣬⣾⣼⣤⣽⣿⣿⡟⣿⣿⣿⣿⠠⣿⢠⣿⣿⣿⣿
⠿⢿⣿⣿⠋⠻⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢂⠀⢸⢐⠀⢐⡇⠌⠀⢸⢰⢸⣿⠀⠀⣲⠀⣿⣿⣿⡿⠁⢿⣿⠿⠿⢸⣿⣾⣿⣍⣿⣿
⠀⡉⠑⠠⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣾⣶⣶⣷⣷⣾⣾⣶⣾⣾⣶⣶⣾⣶⣿⣿⣿⣡⡤⠶⠋⠀⠈⠙⠿⠿⣿⢿⢿⣿
⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿
⠀⠀⠀⢃⡌⠭⠀⠀⠀⠀⠀⣰⣿⣿⠿⢿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⡆⠩⠁⠀⠀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠁⠇⢁⠀⠀⠀⢸⣾⣿⣿⢀⣾⣿⣿⣿⠷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢿⢃⣠⡤⢴⡿⠿⢾⡆⠉⠢⠈⠙⡿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣴
⣤⣤⡀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣜⠃⣿⣿⣿⠀⠈⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣰⣷⣼⣿⣿⣧⣿⡇⠂⢸⢁⣷⣤⠶⣾⣷⣄⡹⠀⠀⠀⣿⣿⡿⣭⣿⡫⠭⡄⠀⣼⣿
⣛⣻⠿⠀⠀⠀⠀⣤⣸⣿⣿⣿⢿⡿⠿⣷⡿⠛⠁⢀⠜⢠⡏⣽⣿⣿⣿⣿⣽⣭⣟⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⠖⠋⠿⠻⠯⢿⣿⣿⣿⣿⣆⡄⠀⢿⣿⣿⠿⠿⣿⣿⣷⣷⣿⣿
⣫⡿⠆⠀⠀⠀⠐⢋⣨⣩⣥⣐⣄⣤⡤⠈⣇⠀⠀⡂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡶⠶⣶⣿⣿⣿⣿⣿⣿⢿⡧⠀⠀⠈⠛⠛⠒⠾⢉⣽⣿⣿⣿
⠁⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣽⣵⣴⣥⣄⣀⠙⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢴⣾⣿⣿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⠿⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠖⣹⣿⠿⠛⡛⡇⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠁⠀⠀⠹⣿⢦⣍⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢉⣉⠡⠤⠖⢊⣡⣶⣾⣿⣶⣶⣿⡿⠁⡢⠅⠇⠃⠀⠊⠈⢰⡇⡄⠀⠀⠠⠀⠀⠀⠀⠄⢈⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠁⠀⠀⠀⠀⠀⠈⢡⣞⡈⣿⣿⣿⣿⢿⣿⡿⠕⠀⠩⠫⠉⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⢠⣤⣄⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠄⠁⠀⠀⠨⠈
⡿⠏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠠⠋⠻⠛⠁⢀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⡙⠻⠿⠇⠀⢰⣀⣶⠠⡀⣤⠀⡤⢄⠀⠀⠀⢀⠀
⠁⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⢿⣻⣿⣿⡿⠿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⢶⡶⠾⠇⠘⠀⠃⠛⠃⠳⠈⠏⠯⠿⠗⢎⣹⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠈⠵⠖⠂⠀⠴⠒⠶⠶⣶⣟⣟⡁⠀⠀⠀⠀⠀⢠⣄⣤⣦⡆⠀⠀⡀⠀⢩⡄⠀⠖⠊⠁⠐⠤⠔⠂⠀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⢈⢁⠀⡄⠀⠐⠀⢀⠤⠲⠁⠀⢀⣠⠴⠃⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⠏⠉⠉⠉⠉⠉⠁⠈⠉⢉⡉⠁⠤⠖⠂⠀⠀⠀⠂⠘⠉⠀⠀⠀⠛⠉⠁⠠⠀⠀⠋⠀⠀⡤⠄⠀⢀
⠀⠀⠀⠀⠘⠿⠟⠿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠞⠋⠁⠀⢀⣀⣀⣠⣤⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣀⡀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠲⠄⠰⠀⠀⡂⠀⠀⠀⠀⣐⠀⠀⠠⠁⡀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠁⠈⢉⣉⣿⠿⠿⣿⣛⣿⣿⣿⣿⣿⡟⠛⠛⠿⢿⡿⠿⢿⢿⣟⢟⡀⠠⡏⠉⡉⠉⠀⡉⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠈⠹⠿⠟⠃⠴⠿⠛⠉⢀⣙⠻⣿⣇⣀⣹⣷⣶⣴⣦⣾⣿⣿⡇⡆⠇⠀⠃⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣻⠒⠂⢄⠃⠐⣒⡂⠐⠀⢰⠀⠀⠀⠠⠆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡶⠉⠁⠈⠁⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠈⠀⣠⠎⠀⠀⡇⠁⠈⠀⠈⠈⠀⠀⠀⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠟⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠠⢠⠏⠀⠀⠀⡇⡅⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⣄⣄⣠⣀⣀⠀⠀⠀⠘⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣯⣵⣟⢿⠚⣿⣳⣀⠰⠀⠺⠁⠀⠀⠀⠓⠂⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⣿
⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⣿⣿⣿⣿⣿⣦⣤⡀⢀⡀⠀⠀⠉⠻⣿⣿⣿⣿⣾⣽⡷⣶⡢⠋⠋⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣿

                    ䷩ 𝚕𝚒𝚗𝚎 423

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/IRC_Proceedings_Thursday_May_30_2024.shtml
    Gemini version at https://techrights.org/n/2024/05/31/IRC_Proceedings_Thursday_May_30_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Thursday, May 30,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣶⣄⣠⣤⣀⣀⡀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣾⣷⣦⣀⣀⣀⣤⣤⣤⡤⢤⣴⣿⣷⡆⠀⣶⡀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⡁⠉⢿⣿⡿⠛⣿⣿⣿⣿⠟⣿⠁⢈⣤⠈⣿⣿⣿⡇⠀⣿⡇⠁⢸⣿⣿⣿⣿⣷⣴⣶⣶⣦⣀⠀⣀⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡟⣡⣶⠀⢸⣿⣾⠟⠘⣷⡀⢠⣿⣰⣿⠿⣦⠼⣿⣿⣗⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡌⢛⣛⠍⢉⡉⠑⠼⠿⠇⠀⡟⠙⡟⠈⠁⠟⢁⣠⣾⣄⠘⣿⣷⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⠢⠷⠄⠈⠅⠀⠀⠀⠀⠀⠀⣤⡘⠀⠀⣴⣿⣿⣿⣿⣆⠘⣿⠀⣿⠀⢸⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⡴⠀⠀⣾⣿⡇⣠⡀⠸⣿⣿⣿⣿⣿⣆⠀⠀⠿⠀⢸⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣰⣿⡆⣿⣿⢱⣿⣷⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⡮⢻⣿⣿⣿⣿⣿⣿⣷⡀⢰⣿⣿⣿⣿⢧⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⣦⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⡻⣿⣿⡿⣼⠟⡿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⢟⣾⣿⣿⣿⣇⠀⠸⣿⣿⣿⠉⢻⠀⠀⠀⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⣙⡻⢿⡿⢸⣟⢸⢱⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣼⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⠦⠾⡀⣿⡄⠸⣿⣧⢸⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣶⣦⣤⡙⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠘⣿⡇⢻⣿⣿⣿⣿⣿⣇⠀⠀⢿⣯⠀⠀⠀⢿⣿⡆⢹⣿⡄⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣗⠸⠃⡄⢸⣿⣿⣿⣿⡿⠃⠿⣿⣿⡏⠀⢿⡇⣼⣿⣿⣿⣿⣿⣿⡄⠀⠘⣿⡆⢀⠀⢸⣿⣿⡾⢛⣇⠀⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠟⠿⠿⠃⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⠑⡲⠁⠙⢿⣿⣿⡼⠧⠀⠐⣿⣿⣾⡿⠘⢨⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢻⢡⡞⠀⠈⣿⠇⡄⠈⣿⠀⢻⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠀⣀⠀⠀⠀⠀⠐⣿⣿⣿⠟⠛⠛⠟⠿⢿⣿⣿⣿⣿⣿⣀⣴⠂⠉⠃⠈⠢⠙⠻⡇⠀⢁⠐⣿⣿⠟⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣾⡇⠈⠀⣰⠾⠛⠀⠘⡇⠸⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⠟⠀⠀⠀⢀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣤⣴⣤⣄⠀⠀⠳⠄⠀⠈⢦⡘⠏⠀⢀⠀⢸⣿⣿⣿⣿⣿⠛⠻⣿⣿⡀⠀⠈⠀⠀⢀⣵⣿⣷⣷⡄⠀⠀⢻⣿⣿⣷⡹⣿⣿⣿⣿⣿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⣀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠛⠛⡿⠟⠾⢿⡆⠀⢀⡀⠉⠀⠃⣸⣇⠸⣿⡟⠻⠿⠃⠀⠀⠙⢻⢃⡀⡠⠊⣶⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣮⣿⣿⢳⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠿⣿⣿⠀⠀⠀⠉⠉⣹⣿⣿⠛⠁⠀⢀⠀⠻⣶⣶⣦⣁⠀⠸⣿⣷⠀⠀⠻⠟⡀⣿⣧⣄⠀⠀⢀⣤⡄⠞⢼⣿⣄⠀⢿⣿⣿⣿⡟⠉⣹⣆⠀⠀⢹⢿⣿⣿⣿⣷⣝⢸⡿⢸⣿⡿⢻
⠀⠀⠀⣀⣀⠸⣿⣿⠀⠀⣰⣶⣶⣿⣿⣤⣀⠀⢀⣴⣿⣿⣿⣦⡀⠀⠘⠀⠀⠀⠸⠿⢿⣷⣄⠹⡇⠀⠀⣿⣶⡄⠹⡿⢿⣇⠀⠈⢿⡟⣀⠘⠻⡇⠀⠀⣼⣿⣿⡇⠀⢿⣿⣦⡀⠈⣄⢈⣿⣿⣿⣿⡄⠃⠈⣿⣿⢀
⠀⠈⢻⣿⣿⣦⠀⠀⠀⢰⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⢀⣿⣿⡷⣈⠀⠀⡘⣿⡇⠀⢻⠂⠁⠀⠀⠌⣸⣿⣦⡀⠀⠀⠀⠙⠿⠟⠀⠀⠀⣿⣿⡇⠀⣿⣿⣿⣿⠀⠙⠁⠀⢀⣿⠇⠘
⠀⠀⠀⠙⠻⣿⣷⣶⡄⠘⣿⣿⣿⠀⠙⠿⣿⡟⠙⣿⣿⡿⠿⠟⠋⠙⣿⣿⣿⠇⢠⣄⣠⣿⣿⢿⣿⡆⠀⠁⠙⣣⡀⠀⣴⣶⣶⣦⣴⣿⣿⣿⣿⡇⠀⠀⢠⣾⣷⡀⠀⠀⠉⢻⣷⠀⠻⣿⣿⣇⣀⠀⠀⡂⢸⠃⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 649

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Never "Missing Out" in FOSS
Conferences⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


               🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I am a self-described 'SJW'⦈


The sexists who objectify women and bully women are going to FOSS events in
pursuit of sex, according to themselves.




⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣶⡆⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣿⡇⣿⣈⡁⠀⠀⠀⠀⠐⣠⣦⣤⡄⠀⠀⠀⠄⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠠⠂⠔⡠⢺⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡿⠃⠉⠉⠓⠠⢀⠀⠀⠈⢸⣿⣿⡇⢀⠐⠀⠂⠀⠀⠀⠀⠀⠀⡁⢈⠀⡡⢊⠐⡡⢊⠔⠱⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⡇⠀⠋⠀⠀⣤⣤⣤⣤⣤⣄⠀⠀⢼⣿⣿⡕⠀⠀⠀⢀⠐⠀⠂⠐⡠⠊⠔⠡⠊⠐⡡⠊⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠠⢾⣿⣻⡆⠠⠀⠄⠠⠈⠄⠁⠈⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡄⣼⣯⣄⣠⣿⣅⣨⣀⠀⢺⣿⡿⢎⠀⡄⠀⠐⠀⠢⡐⢀⠂⡀⢀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣄⡀⠀⠀⠀⠀⡈⠁⣿⣿⣿⣟⣻⣻⣿⠫⠐⣿⣿⣿⣇⠐⠄⠢⡐⢠⣮⠄⠀⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢱⡇⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣿⣿⣉⡉⣹⠇⠀⠀⣺⣿⣿⡧⡀⠔⠡⢊⠂⡁⠈⠀⠁⠈⠀⠀⠀⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿
⣿⣿⣿⣿⠻⣿⣿⣿⣿⡇⢸⡇⢿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠻⣿⣿⡏⠢⠤⣌⣰⣿⣿⡗⠈⠂⠐⢄⠂⡀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡟⠓⠙⠂⠀⠚⠛⠿⠿⡇⢸⠇⢸⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠨⣿⡏⠆⠀⠀⠁⠈⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠁⠁⠀⠀⠀⠀⠀⠁⠈⡇⢸⠀⠘⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢀⣠⡽⣧⠀⠀⠀⠀⠀⠀⢳⠀⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠘⣿⣿⢹⣿⣸⣿⠀⢸⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣇⢴⣿⣿⣼⡟⣿⣿⠀⢸⡿⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣫⠻⣮⣍⣁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣴⣶⣶⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⡇⣿⣻⠆⣿⡃⣿⢻⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⢀⠤⢤⡀⣴⠶⣄⢰⢠⡄⣤⡐⡆⠻
⠀⡹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢾⣇⣸⡏⠙⠛⢸⣿⣿⣼⣿⣿⣿⣿⣻⣗⣿⢸⣿⣿⣿⣧⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠘⣧⣠⡤⢻⣄⣿⠸⣇⣧⢻⡙⢷⠀
⠀⠛⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠈⠁⠀⠀⠀⠉⢿⣿⡟⠚⣉⡀⢰⣾⡀⢨⣿⣿⣿⣿⣿⠁⠀⠈⡠⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠈⠁⠈⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⡆⣺⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣿⡇⣿⣉⡁⠀⠀⠀⠀⠐⡠⣢⣤⣤⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⡠⢂⠔⡠⢂⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡿⠃⠉⠉⠃⠠⢄⠀⠀⠀⢰⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⡡⢈⠔⡁⢊⠐⡁⠊⠐⠡⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⡏⠀⠋⠀⠀⣤⣤⣤⣤⣤⣄⠀⠀⢼⣿⣿⡇⠀⠀⠀⠂⠐⠀⠂⠐⠡⠊⠐⠁⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣿⣿⣿⣿⣿⣿⠄⠀⢼⣿⣛⡄⠠⠀⠄⠡⠈⠀⠁⠈⠀⠑⠌⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡄⢸⣯⣤⣠⣽⣥⣨⣄⡀⢺⣿⣿⣏⠀⠄⠂⠀⠀⠠⡀⢀⠀⡀⢀⠐⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣤⡀⠀⠀⠀⠀⠈⠃⣼⣿⣿⣿⣛⣻⣿⠿⠀⢾⣿⣿⣇⠐⠄⠢⡐⢠⣮⠄⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢻⣿⣏⣉⣽⡟⠀⠀⢺⣿⣿⡧⡈⢔⠱⢊⠂⠁⠈⠀⠁⠀⠀⠀⠀⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣟⠑⣿⣿⣿⣿⡇⢸⠀⢸⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠙⢿⣿⣿⠢⣀⣀⣢⣿⣿⡗⠈⠂⠐⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠿⠟⠽⠛⠀⠈⠋⡝⠻⠇⢸⠀⢸⠇⠀⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⢸⣿⣷⡈⢠⣼⣟⠆⠀⠈⠙⠉⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠒⠂⠀⠀⠀⠀⠀⠉⠀⡄⢸⠀⠘⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢃⢀⡹⣿⠁⠀⠀⠀⠀⠀⢫⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⣿⣿⢹⣿⣼⣿⠀⢸⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⢠⣿⣿⣼⡟⣿⣿⠀⣸⡿⣷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⢎⢹⣯⣉⡁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣿⣾⣿⣷⣿⣿⣿⢻⣿⣷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⡠⠤⡄⢠⡶⣤⢰⡄⡄⣤⣀⣦⠻
⠀⡹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⣼⣿⣿⣿⣿⣻⣇⣿⣾⣿⣿⣿⣇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⢷⣀⣤⠸⣇⣼⠏⣧⣻⢹⡟⢿⠀
⠀⠛⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠈⠉⣿⣿⡿⠿⢋⢁⢹⣯⡈⠙⣿⣿⣿⠀⣿⠁⠀⠀⣁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠈⠉⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣺⡆⣺⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣿⡇⣿⣉⡁⠀⠀⠀⠀⠀⡠⣦⣤⡄⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⡠⢂⠔⡠⢊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣹⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡿⠃⠉⠙⠓⠠⢄⠀⠀⠀⢰⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⡠⠀⠀⡁⢊⠔⡁⢊⠐⡁⢊⠐⠡⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⡏⠀⠋⠀⠀⣤⣤⣤⣤⣤⣄⠀⠀⢼⣿⣿⡇⠀⠀⠀⠂⠐⠀⢂⠐⠡⠊⠐⠡⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⢾⣿⣻⡄⠠⠀⠄⠁⠈⠀⠁⠈⠀⠁⠌⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡆⢸⣯⣶⣀⣼⣯⣨⣅⡀⢺⣿⣿⢎⠀⠄⠀⠐⢀⠢⡀⢀⠀⡀⢂⠐⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⣄⣤⡀⠀⠀⠀⠀⠈⠃⣸⣿⣿⣿⣛⣿⣿⠿⠄⢸⣿⣿⡧⠐⠄⠢⡐⢠⣮⠄⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠹⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⡧⡈⠄⠱⢊⠂⠁⠈⠀⠀⠀⠀⠀⠀⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⢈⣿⣿⣿⣿⡇⢸⠀⢸⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⡉⠻⡿⣟⠥⣀⣀⡰⣿⣿⡗⠈⠂⡐⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⣟⠾⠿⣁⠀⠒⠿⣮⣟⡇⢸⠀⢸⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⢸⣿⣷⡈⢀⣽⣿⢆⠀⠉⠙⠉⢻⡗⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠓⠂⠀⠈⠀⠈⠀⠈⠀⠃⢸⠀⠘⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢯⠀⡻⣿⠁⠀⠀⠀⠀⠀⢫⠀⠁⢈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠤⣿⣿⢽⣿⣼⣿⠀⢸⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢠⣿⣿⣼⡟⣿⣿⠀⢸⡿⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠎⢻⣏⡉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣶⣶⣤⣤⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⣼⣿⣷⣿⣟⣿⢿⣿⣷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⣠⠤⣤⢠⡶⢦⡰⡆⣄⣤⣄⣦⠻
⠀⡹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⣸⣿⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⢻⣄⣤⠜⣧⣸⡇⢷⣹⢸⡟⢿⠀
⠀⠛⢻⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠀⠉⣿⣿⡿⠿⠟⢝⢻⣿⣿⣮⡗⠛⠻⠈⣿⠁⠀⠈⣁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠈⠉⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⡆⢺⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⣾⣿⡇⣿⣉⡁⠀⠀⠀⠀⠐⢠⣢⣤⣤⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⠄⡠⢂⠔⡠⢂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⠇⠉⠛⠓⠠⢄⠀⠀⠀⣸⣿⣿⡧⠀⠐⠀⠀⠀⠀⠀⡠⢀⠀⡡⢊⠔⡁⢊⠐⡡⠊⡐⠡⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⡏⠀⠟⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⢼⣿⣿⡇⠀⠀⠀⠂⠐⠁⠂⠐⠠⠊⠀⠡⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⢾⣿⣋⡔⠠⠀⠄⠀⠈⠀⠁⠈⠀⠁⠌⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣿⣶⣀⣼⣏⣉⣇⡀⢺⣿⣿⢎⠐⠄⠀⠀⢀⠠⡀⢀⠀⡀⢂⠐⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣤⡀⠀⠀⠀⠀⢈⠃⢸⣿⣿⣿⣟⣟⣿⠿⠀⢺⣿⣿⣧⠐⠄⠢⡀⠠⣮⠄⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠸⣿⣿⡧⡈⠀⠱⢎⠂⡁⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⠛⣿⣿⣿⣿⡇⢸⠀⢸⣿⠁⢂⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠉⠻⡿⣿⠇⡀⢄⠰⣿⣿⡗⠈⠀⡀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿
⣿⠾⠧⡗⠀⠘⠛⣿⠟⡇⢸⠀⢸⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⢸⣿⣷⡈⠂⣵⣿⢆⠈⠉⠙⠉⢻⡗⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠟⠃⠀⠀⠀⠀⠁⠀⠁⠁⢸⠀⠘⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢟⠈⡻⣿⠀⠀⠀⠀⠀⠀⢫⠀⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠠⣿⣿⢿⣿⣸⣿⠀⢸⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢢⣿⣿⣼⡟⣿⣿⠀⢸⡿⣷⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡞⢻⣏⠉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣶⣶⣶⣴⣦⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⣼⣿⣿⣾⣟⣿⢿⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⢠⠤⢤⠀⡶⢦⡄⡆⣄⢠⣄⣶⠚
⠀⡙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⣸⣿⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣇⣿⣹⡇⣿⣁⣿⣼⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠸⣆⣠⡄⢷⣨⡗⢻⣸⠘⡟⢿⠀
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠈⠉⣿⣿⡿⡿⠟⢿⢫⣍⡀⠈⠓⠟⢛⠉⣿⠀⠀⠈⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠉⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢲⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⡗⣿⣋⡁⠀⠀⠀⠀⠐⣠⣦⣤⣤⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⠄⠠⢂⠔⡠⢂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⠇⠛⠛⠓⠠⠀⠀⠀⠀⣰⣿⣿⡧⠀⠐⠀⠀⠀⠈⠀⡀⢈⠐⡁⢊⠔⡁⢊⠐⡁⠊⠐⠁⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⡏⠀⠟⠁⠀⢠⣤⣤⣤⣀⣄⠀⠀⢼⣿⣿⡇⠀⠀⠀⠂⠐⠀⠂⠔⠡⠈⠄⠡⠀⠌⢠⠘⠁⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⢼⣿⣻⡔⠠⠀⠀⠁⠈⠀⠁⠌⠠⠁⠄⠠⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⢰⣿⣕⣀⣸⣟⣉⣅⡀⢺⣿⣿⢎⠀⠄⠀⡀⢀⠠⡀⢀⠐⡀⢂⠐⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣤⡄⠀⠀⠀⠀⢈⠋⢸⣿⣿⣿⣟⢟⣿⡟⠀⢺⣿⣿⣧⠐⠄⠀⡀⠠⣾⠌⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠈⠻⣿⣿⣉⣻⣿⠁⠀⠸⣿⣿⡷⠈⠢⡑⢌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⠻⣿⣿⣿⣿⡇⢸⠈⢸⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠉⠻⣿⣿⠇⡀⠀⠰⣿⣿⡷⢌⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⢯⡾⠟⠀⠙⠛⢿⣿⡇⢸⢀⢸⡏⠀⠐⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠂⣨⣿⢆⠈⠛⠛⠛⢻⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠛⡊⠁⠀⠀⠀⠀⠁⠉⡃⢸⢨⠘⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠈⠻⣿⡌⠄⠀⠀⠀⠀⢫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⣿⣿⣿⣼⣿⠀⢸⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢲⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠘⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡼⢻⣟⠉⠁⠁⠉⠀⠉⠁⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣶⣶⣦⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⣸⣿⣿⣽⡟⣿⣿⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⢀⠤⠦⡄⣴⠶⣄⣦⢤⢠⣄⢲⠒
⠀⡙⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣿⣿⣿⣿⣿⣟⣿⢸⣿⣿⣿⡇⣿⣹⡇⣿⣁⣿⣼⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠘⢧⣠⡤⢻⣄⣿⢸⣸⡎⣟⢻⡀
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠁⣿⣿⣿⣿⡿⣿⢓⣍⡊⠘⠓⠿⢿⠙⣿⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠉⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⡷⣿⣉⡁⠀⠀⠀⠀⠀⣠⣤⣤⣤⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⠔⠠⠂⠔⡠⢂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡟⠛⠛⠓⠤⠀⠀⠀⠀⣱⣿⣿⡿⠀⠀⠀⠀⠀⠈⠄⡠⢈⠐⡁⢊⠐⡁⢊⠐⡁⠊⡐⠁⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡟⠀⠿⠁⠀⢀⣤⣤⣤⣀⣀⠀⠀⢰⣿⣿⡟⠀⠀⠀⢂⠐⠁⠊⠀⠀⠀⠄⠢⠐⠄⢢⠘⠀⠁⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢼⣿⣛⣔⠠⠀⠀⠁⠈⠀⠀⠄⠠⠀⠄⠠⠈⢔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢆⢰⣿⣕⣀⣹⣟⣉⣅⡀⢺⣿⣿⢏⠀⠀⠂⡀⢀⠠⡀⢂⠐⡀⢂⠐⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣤⠄⠀⠀⠀⠀⢸⠋⢸⣿⣿⣿⣟⢿⣿⡟⠀⢺⣿⣿⣧⠐⠄⠀⡈⠠⣿⠌⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠻⣿⣿⣛⣋⣿⠃⠀⠻⣿⣿⡿⠈⠢⡑⢌⠂⠁⠀⠀⠀⠀⠀⠀⠀⠰⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿
⣿⣿⣿⣿⠹⢛⣿⣿⣿⡇⢸⢘⢸⣿⠁⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣄⠀⠙⢿⣿⣿⢇⡀⠀⠰⣿⣿⡗⢌⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣟⠿⠗⠀⠐⠃⠻⣻⡇⢸⢸⢸⡏⠀⠈⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡈⠢⣙⣿⢂⠈⠛⠛⠟⢻⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠋⠃⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠻⣿⡍⠀⠀⠀⠀⠀⢫⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⣿⣻⣿⣼⣿⠀⢸⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠘⠀⠀⠀⠀⠁⠀⠀⣀⠄⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣼⢻⡿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣶⣦⣶⣦⣤⣤⣴⣴⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⣸⣿⣿⣽⡟⣿⣿⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⠀⡤⠶⡄⢰⠶⣄⢰⢠⢠⣄⢲⠐
⠀⡘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣿⣿⣿⣿⣿⣟⣿⢸⣿⣿⣿⡇⣿⣹⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⢷⣀⡤⠸⣇⣽⠸⣎⡇⣏⢻⡂
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠁⣾⣿⣿⣿⣿⡟⢓⣊⠀⠘⠳⠿⢿⠙⣯⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠉⠁⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⡷⣿⣉⡁⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⠂⠔⡠⠂⠔⡠⢂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡗⠛⠛⠓⠤⠀⠀⠀⠀⡡⣿⣿⡷⠀⠀⠀⠀⠀⢈⠄⡀⢈⠐⡁⢊⠐⡁⢊⠐⡁⠊⠐⠁⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⠟⠀⠸⠋⠀⢀⣤⣤⣤⣀⣀⠀⠀⠼⣿⣿⡇⠀⠀⠀⢂⠐⠁⠊⠀⠠⠀⠄⠢⠐⠌⢢⠘⠁⠁⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢾⣷⣻⣖⠠⠈⠀⠁⠈⠀⠀⢄⠠⠀⠄⠠⠈⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢆⢀⣿⣕⣂⣸⣟⣉⣅⡀⢺⣿⣿⢏⠐⠀⠀⡀⢀⠠⡀⢂⠐⡀⢂⠐⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣤⡀⠀⠀⠀⠀⢸⠛⢰⣿⣿⣿⣟⠿⣿⡟⠁⢺⣿⣿⣧⠐⠄⠀⡀⠠⣿⠌⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⣿⣿⣛⣋⣿⠃⠀⠻⣿⣿⡷⠈⠢⡑⢌⠢⠁⠄⠀⠀⠀⠀⠀⠀⢰⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿
⣿⣿⣿⣿⠟⣿⣿⣿⣿⡇⢸⢸⢸⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣌⠀⠉⢿⣿⣿⠇⠀⠀⠱⣿⣾⡗⢌⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⣿⣿⠿⠟⠀⠘⠛⢿⠿⡇⢸⢸⢸⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡀⠢⢙⣿⢆⠉⠳⠓⠟⢻⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠛⠃⠀⠀⠀⠀⠀⠀⠀⠆⢸⠠⠘⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡐⢻⣿⡏⠄⠀⠀⠀⠀⢯⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⣿⣿⣻⣿⣼⣿⠀⢸⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢘⠀⠀⠀⠀⠁⠀⠀⢀⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡼⢻⡿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣦⣶⣴⣤⣤⣤⣴⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣿⣿⣽⡟⣿⣾⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⠀⡤⠲⢄⢰⡶⣦⢰⢠⣠⣄⢲⠐
⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣿⣿⣿⣿⣿⣟⣿⢹⣿⣿⣿⡇⣿⣹⡇⣿⣁⣿⣼⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⢻⣄⣴⠸⣧⣼⠚⣎⡇⣯⢻⡂
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠈⠉⣶⣿⣿⣿⣿⡛⢙⡈⠀⠘⠷⠿⠿⠛⣦⠀⠀⠀⠀⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⡷⣾⣋⡁⠀⠀⠀⠀⠀⣠⣦⣤⣄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⡠⠂⠄⠠⠂⠔⠠⠂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡧⠀⣿⣿⡟⠛⠻⠿⠄⠀⠀⠀⠀⡡⣿⣿⡿⠀⠐⠀⠀⠀⢈⠄⡁⢊⠐⡁⢊⠐⡀⢊⠐⢁⠎⠰⠁⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠟⠀⠹⠋⠀⢀⣤⣤⣤⣀⣀⠀⠀⢐⣿⣿⡇⠀⠀⠀⠂⠐⠀⠀⠀⠠⠀⠄⠢⠐⠀⢂⠔⠁⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢼⣿⣟⣔⠠⠀⠀⠁⠈⠀⠀⠄⠠⠀⠄⠠⠈⠔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢆⠀⣿⣝⣂⣈⣿⣉⣅⡀⢺⣿⣿⡏⠐⠄⠀⡀⢀⠠⡀⢂⠐⡀⢂⠐⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣠⣤⡄⠀⠀⠀⠀⢸⠛⢠⣿⣿⣿⣟⡿⣿⡟⠀⢲⣿⣿⣦⠐⠄⠀⡈⠠⣷⠌⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⣿⣿⣛⣋⣿⠃⠀⠻⣿⣿⡷⠈⠢⡑⢌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⠫⢻⢿⣿⣿⡇⢸⢸⢸⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡄⠀⠙⢿⣿⣿⡇⠀⠀⠱⣿⣿⡗⢌⠀⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⠿⠇⠀⠐⠓⠿⢻⡇⢸⢸⢸⡏⠀⠈⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⣿⣷⣌⠶⢙⣿⣆⠉⠲⠒⠟⢻⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠝⡃⠈⠀⠀⠀⠀⠀⠀⠄⢸⢸⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢾⣿⡏⠄⠀⠀⠀⠁⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⣿⣿⣿⣿⣸⣿⠀⢸⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⢲⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠘⠀⠀⠀⠀⠁⠀⠀⢀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡬⢻⡿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣶⣶⣦⣤⣴⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣿⣿⣽⡟⣷⣾⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⠀⡤⠶⢄⢰⡶⣦⢰⢠⣠⣄⢲⡐
⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣿⣿⣿⣿⣿⣟⣿⢹⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⢻⣀⣤⠸⣧⣼⠞⣏⡇⣯⢻⡇
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠉⣴⣿⣿⣿⣿⠟⢽⡉⠈⠸⠷⢿⣿⠳⣦⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠈⠁⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⣷⣾⣉⡁⠀⠀⠀⠀⠐⣢⣤⣤⣄⠀⠠⠀⠄⠀⠀⠀⠀⠀⠠⠀⠄⡠⠂⠔⠠⠂⠔⠠⠂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⣹⣿⡟⠟⠻⠿⠀⠀⠀⠀⠀⡠⣿⣿⡷⠀⠀⠀⠀⠀⢈⠄⡁⢈⠐⡁⢊⠐⡁⢊⠐⠁⠎⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠟⠀⢹⠋⠀⢀⣠⣤⣤⣀⣀⠀⠀⠰⣿⣿⡇⢀⠀⡀⠂⠐⠁⠀⠀⠠⠀⠄⠢⠐⠌⢂⠔⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⢼⡷⣛⡔⠠⠈⠀⠁⠈⠀⠀⢄⠠⡀⠄⠠⢈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⠀⣿⣝⣂⣈⣿⣉⣅⡀⢺⢿⣿⢎⠀⢀⠀⡀⢀⠰⡀⢂⠐⡀⢂⠐⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⣤⡄⠀⠀⠀⠀⢘⠿⢰⣿⣿⣿⣿⣻⣿⡟⠁⢺⣿⣿⣧⡐⠀⠀⠈⠠⣿⠍⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⢸⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠻⣿⣿⣛⣛⣿⠃⠀⠹⣿⣿⣷⠈⠢⡑⢌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡻⣿⣿⣿⣿⡇⢸⢸⢸⣿⠃⢀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⣄⠀⠙⢿⣿⣿⡯⠀⠀⠑⣿⣿⡗⢌⠀⡀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⢝⠏⢿⠀⠘⠛⣿⣿⡇⢸⢸⢸⡏⠀⠐⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⣿⣶⣌⠢⡙⣿⣆⠉⠲⠖⠿⠿⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⣿⠑⠀⠀⠀⠀⠀⠁⠈⠁⢸⢸⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⢾⣿⡏⠄⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⣿⣿⣻⣿⣼⣿⠀⢸⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⢰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠘⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡨⢿⡿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠄⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣶⣶⣤⣴⣦⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣿⣿⣹⡟⣷⣾⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⡤⠦⡄⢰⠶⣄⢰⢠⢠⣄⢲⠐
⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣿⣿⣿⣿⣿⣗⣿⢹⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣼⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⢿⣀⡤⠸⣆⣽⠸⣎⡇⣏⢻⡇
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠈⠉⣴⣾⣿⣿⡿⠟⠿⡉⠀⠚⠷⣿⡿⢲⣄⠀⠀⠈⠁⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⣷⣾⣉⡁⠀⠀⠀⠀⠐⣠⣦⣤⣤⠄⠠⠀⠄⠀⠀⠀⠀⠀⠠⠀⠄⡠⠂⠔⠠⠂⠔⠠⠂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡧⠀⣽⣿⡟⠿⠻⠿⠀⠀⠀⠀⠀⡱⣿⣿⡿⠀⠀⠀⠀⠀⢈⠔⡁⢊⠐⡁⢊⠐⡀⠂⠐⢀⠆⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠟⠀⢸⠏⠁⢀⣀⣤⣄⣀⣀⠀⠀⠸⣿⣿⡏⢀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠄⠢⠐⠈⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⢼⡳⣛⠖⠠⠈⠀⠁⠀⠠⠀⠄⠠⡀⠄⠡⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⠀⣾⣿⣋⣉⣿⡉⣹⡀⢺⣿⣿⡎⠀⠀⠀⡀⢀⠰⡀⢂⠐⡀⢂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣄⣤⡄⠀⠀⠀⠀⢸⠿⠀⣿⣿⣿⣿⡿⣿⡿⠁⢺⣿⣿⣧⠐⠄⠀⠌⠠⣷⠌⠠⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⣿⣿⣛⠛⣿⠇⠀⠪⣿⣿⣷⠈⠢⡑⢌⠢⠀⠄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿
⣿⣿⣿⣿⠛⣿⣿⣿⣿⡇⢸⢸⢸⣿⠃⠀⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⣄⠀⠉⠿⣿⣿⡿⠀⠀⠱⣿⣾⡷⢌⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⡿⠿⠟⠀⠘⠋⢿⣿⡇⢸⢸⢸⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⣿⣷⣄⠢⡙⣿⣇⠙⠲⡶⢿⢿⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿
⠛⠃⠀⠀⠀⠀⠀⠁⠉⠁⢸⢸⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠅⢾⣿⡟⠄⠀⠈⠀⠁⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⣿⣿⣻⣿⣸⣿⠀⢸⣿⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⢰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠘⠀⠀⠀⠀⠁⠀⠀⢀⠄⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡨⢿⡿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣶⣶⣤⣶⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣿⠿⣹⡟⣷⣼⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⢀⡤⢤⡀⣴⠶⣄⣦⣤⢠⣔⣦⠻
⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠋⢸⣿⣿⢸⣟⣿⣿⣿⣿⣗⣿⢹⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣺⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠘⢧⣀⡄⢻⣄⣿⢸⣸⠘⡟⢿⠀
⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠉⣴⣾⣿⣿⡿⠟⠽⠉⠈⠘⢿⣿⣿⢲⣄⠀⠀⠈⢁⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠉⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⣿⣷⣾⣃⡁⠀⠀⠀⠀⠀⢠⣄⣤⣤⠄⠀⠀⠀⠀⠀⠀⢀⠄⡠⢀⠄⡠⠂⠄⠠⠀⠄⠠⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⢽⣿⡟⠿⠻⠿⠀⠀⠀⠀⠐⡡⣿⣿⡿⠀⠀⢀⠀⡀⢈⠔⡁⢊⠐⡁⢊⠀⠀⠂⠀⢀⠆⠀⠀⠁⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡿⠀⢸⠟⠁⠀⣀⣀⣀⣀⣀⠀⠀⠰⣿⣿⡯⢀⠐⠁⠊⠀⠁⠀⠀⠀⠐⠀⠢⠐⡀⢂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠼⣿⣟⣶⠁⠈⠀⠀⠄⠠⠀⢄⠠⠈⠄⠡⢈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⠀⣾⣯⣋⣉⣿⡋⣹⡀⢸⣿⣿⠏⡀⢀⠀⡀⢀⠰⡀⢂⠐⠀⠂⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣄⣤⡄⠀⠀⠀⠀⢘⠾⠀⣿⣿⣿⣿⡿⣿⣿⠁⢺⣿⣿⣿⠐⠀⠀⠌⠢⣵⠍⠠⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠻⣿⣿⣟⠋⣹⡏⠀⠡⣿⣿⣿⠈⠢⡑⢌⠠⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿
⣿⣿⣿⣿⠏⢿⣿⣿⣿⡇⢸⢸⢸⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢡⣄⠀⠙⠿⣿⣿⡿⠀⠀⠑⣿⣿⣿⢄⠀⡀⠀⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿
⣿⣿⡿⢿⠀⠈⠙⠿⣿⡇⢸⢸⢸⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⣿⣷⣤⡦⡈⣿⣇⠑⠲⡼⢿⢿⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿
⠛⠋⠀⠀⠀⠀⠀⠀⠙⠁⢸⢸⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡅⢼⣿⡏⠆⠀⠈⠀⠁⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⣿⣿⣻⣿⣸⣿⠀⢸⣿⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠄⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⢰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣨⢿⣿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣶⣶⣦⣤⣤⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣿⠿⣻⡟⣷⣼⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⣀⠤⣤⢠⡶⢦⡰⡤⡄⣄⣲⡜⢻
⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣯⣿⣿⣿⣿⣗⣿⢻⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠻⣆⣠⠌⣷⣸⡇⢇⡇⢛⠻⡇⠈
⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠁⣴⣾⣿⣿⣿⠿⠿⠉⠈⠺⢿⣿⣿⢢⣌⠀⠀⠈⢀⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢸⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡗⠀⣼⣿⣷⣾⣋⣁⠀⠀⠀⠀⠐⣲⣦⣤⣄⠄⠠⠀⠀⠀⠀⠠⢀⠄⡠⢀⠄⡠⠂⠔⠠⠀⠄⠠⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⣹⣿⣟⡿⠻⠿⠀⠀⠀⠀⠀⣱⣿⣿⣿⠀⠀⢀⠀⡠⢈⠔⡁⢊⠐⡁⢊⠐⠀⠂⠀⢀⠄⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡿⠀⢸⠟⠁⠀⣀⣀⣀⣀⣀⠀⠀⢰⣿⣿⣯⢀⠔⠁⠊⠀⠁⠀⠀⠢⠐⠄⠢⠐⡀⢂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣧⢀⢜⣿⣛⢖⠁⠈⠀⠁⠄⠠⠀⢄⠡⡈⠄⡡⢊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⣾⣯⡉⢉⣿⡋⢹⡁⢺⣿⣿⡷⡀⢀⠐⡀⢀⠰⡀⢂⠑⠈⠂⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣤⣄⠀⠀⠀⠀⢸⢾⡀⣿⣿⣿⣿⡿⣿⣿⠉⢺⣿⣿⣿⡔⢀⠀⢌⠢⣽⠅⠠⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠻⣿⣿⣟⡉⣹⡏⠄⢹⣿⣿⣿⢈⠢⡑⢌⠢⢈⠄⠡⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⣿⣿⣿
⣿⣿⣿⣿⡟⢿⣿⣿⣿⡏⢸⢸⢸⣿⠃⢐⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢫⣏⠀⠙⠿⣿⣿⡿⡀⠀⠱⣿⣿⡿⢄⠀⡀⠂⠐⢈⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⣿
⣿⠿⡿⣿⠁⠸⠻⣿⣿⡇⢸⢸⢸⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⣿⣷⣬⣦⡼⣿⡏⠐⠲⡼⢿⢿⡟⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠁⠅⠁⠀⠀⠀⠈⠁⠉⠅⢸⢸⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡍⢼⣿⡏⠆⠀⠈⠀⠁⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⣿⣿⣻⣿⣸⣿⠀⢸⣿⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠄⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢘⠀⠀⠀⠀⠀⠈⠀⣀⠤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣨⢽⣿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣶⣶⣶⣦⣶⣤⣦⣶⣦⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣿⡿⣻⡟⣷⣼⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⢀⡠⢤⡀⣴⢶⣄⢦⢤⢠⡐⣆⠻⡟
⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⢸⣯⣿⣿⣿⣿⣗⣿⢻⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠸⣧⢀⡄⢻⣄⣿⠸⣸⠈⠛⣿⠀⢿
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠁⣤⣾⣿⣿⣿⠿⠿⠙⠈⠺⣿⣿⣿⣤⣌⠀⠀⠈⢀⣉⡉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢸⢸⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡗⠀⣾⣿⣷⣿⣃⣁⠀⠀⠀⠀⠐⢰⣦⣤⣦⠄⠀⠀⠀⠀⠀⠀⢀⠄⡠⢀⠄⡠⠂⠔⠠⠂⠄⠠⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠂⢽⣿⡿⣿⠻⠿⠀⠀⠀⠀⠐⡨⣿⣿⣿⠀⠀⢀⠀⡠⢊⠔⡁⢊⠐⡁⢂⠐⠀⠂⠐⢀⠂⠁⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡿⠀⢸⡟⠋⠀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿⣿⢀⠔⡡⠊⠄⠁⠀⠀⠠⠐⠄⠢⠐⡀⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⣿⣿⣿⣿⣿⣧⢀⢼⣣⣛⣖⠁⠊⠀⠁⠄⠠⠀⢄⠡⠈⠔⡡⢊⠔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⢼⣿⢭⢉⣿⣏⢹⡡⢺⣿⣯⢿⡀⢀⠤⡠⢂⠐⡄⠂⠐⠀⠂⠐⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣤⣄⠀⠀⠀⠀⢸⣷⡂⣿⣿⣿⣿⡿⣿⣿⠈⢺⣿⣿⣿⡔⠡⠘⢌⠢⣿⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠹⣿⣿⣿⢈⠢⡁⢄⠠⢈⠀⠁⠈⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠻⣿⣿
⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⢸⢸⢸⣿⠃⢠⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣏⠀⠙⠿⣿⣿⡿⠁⠀⠑⣿⣿⣿⢄⠀⡀⠂⠐⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠿⡯⠿⡋⠀⠒⠻⠿⣿⡯⢸⢸⢸⡟⠀⠈⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⣿⣷⣤⣲⣼⢿⣇⠐⠦⣼⣿⢿⡟⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣮⠁⡀⠃⠀⠀⠀⠀⠐⠆⢸⢸⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡍⢽⣿⡟⠆⠀⠈⠀⠁⢏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣿⣿⣻⣿⣸⣿⠀⢸⣿⡏⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠄⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢘⠀⠀⠀⠀⠀⠈⠀⣡⠤⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣨⢽⣿⠋⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣶⣶⣦⣶⣦⣶⣦⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣷⣼⣟⡷⣿⡇⣿⣻⠆⣿⡣⣿⣿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⣀⣀⡀⢀⣤⣄⢠⡄⡀⠀⣄⠰⣶⡶
⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣯⣾⣿⣿⣿⣇⣿⢻⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠰⣇⠀⣁⢸⡅⢹⡏⡇⠃⠸⣾⡆⢸⡇
⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡉⠀⠁⠀⠀⠈⠁⣤⣾⣿⣿⣿⠿⢛⠙⠈⠸⣿⣿⣷⢤⡄⠁⠀⠈⣁⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠛⠃⠈⠙⠋⠀⠘⠋⠀⠈⠁⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡗⠀⣾⣿⣷⣿⣃⣁⠀⠀⠀⠀⠰⣴⣤⣤⣦⠄⠠⠀⠄⠀⠀⠠⢀⠄⡠⢀⠄⡠⢂⠔⠠⠂⠄⠠⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⠻⠿⠀⠀⠀⠀⠐⡩⣿⣿⣿⠂⠀⢀⠀⡀⢊⠔⡁⢊⠐⡁⢂⠐⠀⠂⠐⠈⠂⠑⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡿⠀⢸⡿⠋⠀⢀⣀⣀⣀⠐⠀⠈⢸⣿⣿⣿⢂⠔⡡⢊⠄⠡⠀⠀⠠⠐⢄⠢⠐⡀⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⣿⣿⣿⣿⣿⣧⢀⢼⣿⣛⣗⠁⠊⠠⠁⠄⠠⠀⢄⠡⢈⠔⡡⢊⠔⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣼⣿⢭⢉⣿⠏⢿⡡⢺⣿⣯⢯⡀⢄⠶⡠⢂⠰⡄⠂⠐⠡⠂⠐⠅⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣠⣤⣄⠀⠀⠀⠀⢸⣷⡆⣿⣿⣿⣿⡿⣿⣿⠉⢺⣿⣿⣿⡔⠡⠚⢌⠢⣿⠅⠠⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣻⣿⣿⣿⣿⣿⡿⢄⠹⣿⣿⣿⢈⠢⡁⢄⠠⢈⠄⠁⠈⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢿⣿
⣿⣿⣿⣿⣙⢿⣿⣿⣿⣿⢸⢸⢸⣿⠃⢠⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣞⠁⠙⢿⣿⣿⡿⡁⠀⡑⣿⣿⣿⢄⠀⡀⠂⠐⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣻⢛⠉⠺⣻⣿⡿⣿⢸⢸⢸⡟⠀⠘⢹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⣿⣷⣤⣶⣞⢿⣇⠘⠦⣼⣿⣿⣿⠠⠐⠄⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⡟⠛⡯⠀⠀⠐⠋⠳⠇⢸⢸⠸⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡝⣽⣿⣟⠆⠀⠈⠀⠁⢯⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣿⣿⣻⣿⣼⣿⠀⢸⣿⡏⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠤⡠⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢸⠄⠀⠀⠀⠀⠈⠀⣡⡮⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢨⢽⣿⠋⠁⠁⠉⠀⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣦⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢹⣟⣷⣿⡟⣷⣼⣟⡷⣿⡇⣿⣻⠆⣿⡣⣿⣿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⢀⣀⠀⢀⣤⣀⢠⡄⡀⠀⢀⢠⣤⡶
⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣯⣾⣿⣿⣿⣇⣿⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⢰⡏⠈⠁⢸⡇⢹⡏⣧⢹⠘⢾⡄⠘⣇
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡉⠀⠁⠀⠀⠈⠈⣠⣶⣿⣿⣿⡿⣟⠙⠉⠺⣿⣿⣷⢤⡌⠁⠀⠈⣁⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠾⠋⠈⠛⠛⠁⠙⠛⠀⠈⠃⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡗⠀⣼⣿⣷⣿⣃⣁⠀⠀⠀⠀⠐⢰⣦⣤⣤⠀⠀⠀⠄⠀⠀⠀⠀⠄⡠⢀⠄⡠⢂⠔⠠⠂⠔⡠⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⣿⣿⠻⡿⠀⠀⠀⠀⠀⣠⣿⣿⣿⠂⠀⢀⠀⡠⢈⠔⡁⢊⠐⡁⢂⠐⠀⠊⠐⠀⠂⠐⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡿⠀⢸⡿⠋⠀⢀⣀⣀⣀⠐⠀⠀⢸⣿⣿⡿⢀⠔⡠⢊⠔⠡⠀⠄⠠⠐⢄⠢⠐⠄⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⣿⣿⣿⣿⣿⣧⠀⢴⣫⣟⡖⠡⠊⠀⠁⠌⠠⠀⢄⠠⠈⠄⡡⢈⠄⡡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⢸⡿⢯⠍⣿⣟⢻⡡⢪⣿⣯⣿⡐⢀⠢⡀⢂⠰⡄⠂⠑⡠⠂⠐⠅⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣤⣤⣄⠀⠀⠀⠀⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⠍⢺⣿⣿⣿⡐⠡⠐⠌⠢⣿⠅⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢻⣿⣿⣿⣿⣿⣿⢄⠱⣿⣿⣿⢈⠢⡑⢄⠠⢈⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠿
⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⢸⢸⢸⣿⠃⢠⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣟⠁⠙⢿⣿⣿⡿⡁⠀⠑⣿⣿⡿⢄⠀⡀⠂⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⡟⡟⠁⠸⠻⢿⣿⣇⢸⢸⢸⡟⠀⠈⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣿⣷⣤⣶⣜⣿⣇⠒⢦⣼⣿⣿⡟⠠⠀⠄⠠⠀⠀⠁⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡑⢮⠋⡂⠀⠀⠈⠀⠻⠁⢸⢸⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡝⣼⣿⣿⠆⠀⠈⠀⠁⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣿⣿⣻⣿⣸⣿⠀⢸⣿⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠤⠠⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢸⠀⠀⠀⠀⠀⠀⠀⣀⡬⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⢽⣿⠋⠁⠁⠉⠀⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣷⣸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⣻⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⢀⠀⠀⢀⣀⠀⣀⢀⠀⠀⡀⣤⣤
⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⣾⣿⣿⣿⣇⣿⢻⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⣾⠉⠙⠀⣿⠉⣷⢹⡈⡇⢳⣧⠀⢻
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡉⠀⠁⠀⠀⠈⠁⣠⣼⣿⣿⣿⡿⢟⠙⠉⢾⣿⣿⣷⢤⡈⠁⠀⠈⣁⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠷⠾⠁⠛⠶⠋⠈⠳⠃⠀⠙⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢸⢸⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡗⠀⣼⣿⣷⣿⣃⣁⠀⠀⠀⠀⠐⣲⣦⣤⣦⠄⠀⠀⠄⠀⠀⠀⠀⠄⡠⢀⠄⡠⢂⠔⡠⢂⠔⡠⠊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣯⠀⣽⣿⡿⣿⠻⡟⠀⠀⠀⠀⠐⡩⣿⣿⣿⠂⠀⢀⠀⡠⢈⠔⡁⢊⠐⡁⢊⠐⠁⠊⠑⠈⠂⠐⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡿⠀⢽⡿⠋⠀⢀⣀⣀⣀⠐⠀⠈⢸⣿⣿⣿⢂⠔⡠⢂⠔⠡⠈⠄⠠⠀⢄⠢⠐⠄⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⣿⣿⣿⣿⣿⣧⠀⢼⣿⣛⣗⠡⠊⠀⡁⠄⠠⠀⢄⠡⢈⠄⡡⢊⠄⡡⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⢸⣿⢯⠭⣿⣟⠻⡱⢺⣿⣯⡿⡐⢀⠀⡀⢂⠐⡌⢂⠐⡠⠂⠔⠅⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣤⣄⠀⠀⠀⠀⢸⣯⡆⣾⣿⣿⣿⡿⣿⣿⠇⢻⣿⣿⣿⡜⠡⠑⢜⡢⣿⠄⠠⠈⠄⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣁⢿⣿⣿⣿⣿⣿⣿⢄⠹⣿⣿⣿⢎⠢⡁⢌⠁⢈⠀⠁⠈⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⠃⢹⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⡁⠙⠿⣿⣿⣿⠃⠀⡑⣿⣿⣿⢀⠀⠀⠂⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠉⠙⢿⣿⣿⣿⢸⢸⢸⡟⠀⢘⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⣿⣷⣤⣶⣮⣿⣗⠚⢦⣼⣿⣿⣟⠢⠀⠄⠠⠀⠀⠁⠈⠀⠁⠈⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢮⣿⠿⡩⠀⠀⠜⡉⠙⠃⢸⢸⠸⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⣿⣿⣷⡝⣭⣿⣿⠆⠀⠈⠀⠁⢯⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⡃⠀⠀⠀⠀⠀⠀⠀⠃⢸⢸⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⣿⣿⣻⣿⣸⣿⠀⢸⣿⡏⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠤⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢸⠀⠀⠀⠀⠀⠈⠀⡀⢀⢴⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⡆⠀⠸⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⢽⣿⠏⠁⠁⠉⠀⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢹⣟⣷⣿⡟⣿⣼⣟⡷⣿⡇⣿⣻⠆⣿⡣⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⣀
⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⣿⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣾⣿⣿⣿⣇⣿⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⣞⠉⠓⢰⡏⢹⣧⣿⠘⠀⢷⣇⠈
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢐⢸⣿⣿⣿⣿⣿⡉⠀⠁⠀⠀⠈⠁⣠⣼⣿⣿⣿⣿⣟⠛⠉⠾⣿⣿⣷⣤⡈⠁⠀⠉⣑⣉⣉⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠀⠻⠾⠋⠘⠶⠃⠈⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢸⢸⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡗⠀⣾⣿⣷⣿⣣⣁⠀⠀⠀⠀⠐⣲⣦⣤⣦⠄⠀⠀⠄⠀⠀⠀⠀⠄⠠⢀⠄⡠⢂⠔⡠⢂⠔⡠⠊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣯⠀⣽⣿⡿⣿⠻⡿⠀⠀⠀⠀⠀⣩⣿⣿⣿⠂⠐⢀⠀⡠⢈⠔⡡⢊⠔⡁⢊⠔⠁⠊⠑⠈⠊⠐⠀⠁⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡿⠁⢸⡿⠋⠄⢀⣀⣀⡀⠐⠀⠈⢸⣿⣿⣿⢂⠔⡠⢊⠔⠡⠈⠄⠡⠐⢄⠢⠐⠄⠂⠐⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣿⣿⣿⣿⣿⣧⢀⢼⣿⣟⣗⠡⢊⠂⡁⠄⠠⠀⢄⠡⢈⠄⡡⢊⠄⡡⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⢰⣿⣿⠟⣻⣟⠻⡥⢺⣿⣿⢿⡐⢀⠀⡀⢂⠰⡤⠂⠐⡡⠂⠔⠥⠊⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⣤⣤⣄⠀⠀⠀⠀⢸⣯⡆⢾⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⠜⠣⠑⢜⡢⣿⠄⠡⠈⠄⠁⠈⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡊⢁⢻⣿⣿⣿⣟⣻⣿⢄⠹⣿⣿⣿⢌⠢⡁⢌⠁⢈⠀⠁⠈⠀⠀⠀⠀⡠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⢸⢸⢸⣿⠃⢀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⡁⠙⠿⣿⣿⣿⡏⠀⡑⣿⣿⣿⢀⠀⠀⠂⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⢿⠈⠟⣿⣿⣿⣯⢸⢸⢸⡟⠀⠘⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⣿⣷⣦⣶⣿⣿⣗⠚⠦⣼⣿⣿⣟⠢⠐⠄⠠⠊⠀⠁⠈⠀⠁⠈⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢭⡿⠿⠳⠀⠀⠇⠉⢻⠇⢸⢸⠸⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⣿⣿⣷⡟⣩⣿⣿⠆⠀⠈⠀⠁⢯⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠁⠀⠅⠀⠀⠀⠀⠀⠂⢸⢸⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⣿⣿⣻⣿⣼⣿⠀⢸⣿⡏⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠁⠁⠀⠀⠀⠀⠀⠀⠀⠘⡬⠤⣠⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢸⠀⠀⠀⠀⠀⠀⠀⡀⢂⣤⠴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠰⢀⠀⠸⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⢹⣿⠏⠁⠁⠉⠀⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣦⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣿⣼⣟⡷⣿⡇⣿⣻⠆⣿⡣⣿⣿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⣸⣿⣿⢸⣏⣾⣿⣿⣿⣇⣿⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⣖⠉⠒⢰⡏⢻⡆⣷⢸⠀⣾⣇
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⣿⡉⠀⠁⠀⠀⠈⠉⣠⣼⣿⣿⣿⣿⣟⠛⠉⢾⣿⣿⣷⣤⣈⠁⠀⢉⣑⣉⣉⣀⣀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠖⠈⠷⠼⠇⠹⣾⠀⠈⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡷⠀⣾⣿⣷⣿⣃⣁⠀⠀⠀⠀⠐⣲⣦⣤⣦⠄⠀⢀⠄⠀⠀⠀⠀⠄⡠⢀⠔⡠⢂⠔⡠⢂⠔⡠⠊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣯⠀⣿⣿⡟⣿⠻⡟⠀⠀⠀⠀⠐⣩⣿⣿⣿⠂⠀⢀⠀⡠⢈⠔⡡⢊⠔⡡⢊⠔⠁⠊⠐⡉⠊⠐⠁⠟⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠀⢻⡿⠏⠈⠀⠀⡀⠀⠐⠀⠈⢼⣿⣿⣿⢀⠔⡡⢊⠔⠡⠈⢄⠡⠐⢄⠢⠐⠄⠂⠐⠀⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⣿⣿⣿⣿⣧⢀⢼⣿⣿⣷⡡⢊⠐⡁⠄⠠⠀⢄⠡⢈⠄⡡⢈⠄⡡⢈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢠⣿⣟⠟⣻⣿⠻⡧⢺⣿⣿⣿⡐⢀⠀⡀⢂⠰⡄⢂⠐⡠⢂⠔⠥⠊⠐⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣤⣤⠀⠀⠀⠀⢸⣯⡇⢸⣿⣿⣾⣿⣿⣾⡿⢻⣿⣿⣿⡜⠣⠑⢜⡢⣿⠄⠡⠈⠄⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢁⢻⣿⣿⣿⡿⠚⣿⢇⠹⣿⣿⣿⢌⠢⡁⢌⠁⠈⠀⠁⠈⠀⠀⠀⠀⠠⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⡁⠙⢿⣿⣿⣿⡏⠠⡑⣿⣿⣿⢀⠀⡀⠂⠑⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠙⢿⣿⣿⣿⣿⢸⢸⢸⡟⠀⠘⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠠⠒⠀⠀⠀⣿⣷⣤⣷⣮⣿⣿⠚⠦⣼⣿⣿⣿⠢⠐⠄⠡⠊⠀⠁⠈⠀⠁⠈⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡟⢿⠛⠈⠉⠗⢻⢻⠇⢸⢸⠸⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠐⠂⠁⠈⠀⠀⠀⠀⠀⣿⣿⣷⡝⣩⣾⣿⢆⠀⠈⠂⠁⢯⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢁⠄⠉⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⣿⣿⣻⣿⣼⣿⠀⢸⣿⡏⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠌⠅⠀⠀⠀⠀⠀⠀⠐⢀⠸⡬⠤⣤⠄⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢸⠀⠀⠀⠀⠁⠈⠀⡁⢀⠀⡀⡠⠴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠰⠂⠄⠸⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢹⣿⠏⠁⠁⠉⠀⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢹⣟⣷⣿⡟⣿⣸⣿⡷⣿⡇⣿⣻⠆⣿⡣⣿⣿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣿⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⢀⡴⠲⠄⣰⠗⣦⢰⡆⡆⢦
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⢸⣿⣿⣿⣿⣿⡉⠀⠁⠀⠀⠈⠁⣠⣼⣿⣿⣿⣿⢟⠙⠉⢿⣿⣿⣦⣤⣈⠁⢀⢉⣑⣉⣉⣀⣀⣀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⡄⢸⣄⣿⠙⣧⡇⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡗⠀⣾⣿⣷⣿⣁⣁⠀⠀⠀⠀⠐⣰⣦⣤⣤⠄⠀⢀⠄⠀⠀⠀⠀⠄⡠⢀⠄⡠⢂⠔⡠⢂⠔⡠⠊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⣽⣿⡟⣿⠻⡟⠀⠀⠀⠀⠐⡩⣿⣿⣯⠂⠐⢀⠀⡠⢈⠔⡡⢊⠐⡡⢊⠔⠁⠊⠐⡁⠊⠐⠀⠿⠛⠉⠉⠉⠛⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠁⢸⣿⠏⠈⠁⠀⠀⠀⠀⠀⠈⢰⣿⣿⣿⢀⠔⡠⢊⠔⠡⠈⠄⠠⠀⢄⠢⠐⠄⠂⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⣿⣿⣿⣿⣧⠀⢸⣿⣛⢗⠡⢊⠀⡁⠌⠠⠀⢄⠠⢈⠄⡡⢈⠄⡡⢈⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢠⣿⣛⠛⣻⡿⠻⡧⢺⣿⣯⢾⡐⢀⠀⡀⢂⠰⡌⢂⠐⡠⠂⠔⠥⠊⠐⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣤⣄⠀⠀⠀⠀⢸⣧⡇⢸⣿⣿⣾⣿⣿⣾⡏⢻⣿⣿⣿⡜⠣⠑⢌⠢⣿⠅⠠⠈⠄⠁⠈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁⢻⣿⣿⣿⡿⠿⣿⢇⠹⣿⣿⣿⢌⠢⡑⢌⠡⠈⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢽⡿⣿⣿⣿⡇⢸⢸⢸⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⣾⠁⠙⠿⣿⣿⣿⡟⠀⠑⣿⣿⣿⢀⠀⡀⠂⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⣛⠍⠀⠀⠛⠿⣿⡇⢸⢸⢸⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⣿⣷⣄⣲⣨⣻⣿⠋⢦⣼⣿⣿⣟⠠⠁⠄⠠⠀⠀⠁⠈⠀⠁⠈⠀⠀⠂⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠮⢕⠒⠀⠀⠀⠁⠍⢸⠆⢸⢸⠸⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣷⡟⣩⣾⣿⢆⠀⠈⠀⠁⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⢻⣿⣸⣿⠀⢸⣿⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠤⢤⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢘⠀⠀⠀⠀⠁⠈⠀⡀⢀⠀⠀⢀⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢹⣿⠏⠁⠁⠉⠀⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣿⣸⣟⡷⣿⡇⣿⣻⠆⣿⡣⣿⢿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣾⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⢠⠤⢤⠀⣴⢶⡄⣶⢰⠠
⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠁⣀⣤⣿⣿⣿⡿⢟⠙⠉⠻⣿⣿⣦⣤⡈⠁⠀⢉⣑⣉⣉⣀⣀⣀⡀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⠄⣧⣠⡿⢻⣈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⣷⣿⣁⣁⠀⠀⠀⠀⠐⣲⣦⣤⣤⠀⠀⠀⠄⠀⠀⠀⠀⠄⠠⢀⠄⡠⢂⠔⡠⢂⠔⡠⠊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⣿⣟⣿⠻⡟⠀⠀⠀⠀⠀⣨⣿⣿⣿⠂⠀⢀⠀⡀⢈⠄⡡⢊⠔⡡⢊⠔⡁⠊⠐⡁⠊⠐⠁⡿⠟⠋⠉⠛⠛⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⠿⠀⢹⣿⠏⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠔⡠⢊⠔⠡⠂⠄⠡⠈⢄⠣⠐⠄⠢⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣾⣿⣿⣿⣿⣧⢀⢼⣿⣛⣟⠡⢊⠀⡁⠄⠠⡁⢄⠠⡈⠄⠡⢈⠄⡡⢈⠄⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢠⣿⣟⠛⣻⣿⠻⡿⢺⣿⣭⢾⡐⢀⠀⡀⢀⠰⡄⢂⠐⡨⠂⠐⠅⠊⠐⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⣤⣤⣄⠀⠀⠀⠀⢸⣧⡇⢸⣿⣿⣶⣿⣿⣾⡇⢻⣿⣿⣿⡐⠡⠐⢜⠢⣿⠄⠠⠈⠄⠁⠈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁⢻⣿⣿⣿⡿⠿⣿⢇⠹⣿⣿⣿⢊⠢⡁⢌⠡⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢛⠻⣿⣿⣿⡇⢸⢸⢸⣿⠃⢠⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⣾⡀⠙⢿⣿⣿⣿⡟⠀⠑⣿⣿⣿⢀⠀⡀⠂⠑⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⢿⡛⠃⠐⠫⣻⡿⣯⡇⢸⢸⢸⡏⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⣿⣷⣦⣲⣜⣿⣿⠛⢦⣼⣿⣿⣟⠠⠀⠄⠠⠀⠀⠁⠈⠀⠁⠈⠀⠀⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡵⠅⡓⡀⠀⠀⠈⠉⠡⠂⢸⢸⠘⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⣿⣷⡟⢫⣾⣿⢆⠀⠈⠀⠁⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⢻⣿⣼⣿⠀⢸⣿⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡤⢤⡤⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢘⠀⠀⠀⠀⠁⠈⠀⡀⢀⠀⡀⠀⣀⢤⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢹⣿⠏⠁⠁⠉⠀⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣶⣶⣦⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣿⣸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣾⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⡤⢤⡀⢠⡶⣤⢰⡄⡄
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡉⠀⠁⠀⠀⠈⠁⣀⣤⣿⣿⣿⣿⣟⠙⠙⢻⣿⣿⣦⣄⡈⠁⠀⢉⣑⣉⣉⣀⣀⣀⣄⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⡤⢸⣄⣽⠞⣇⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⣷⣿⣃⡁⠀⠀⠀⠀⠐⣲⣦⣤⣤⠄⠀⢀⠔⠀⠀⠀⠀⠀⠠⢀⠄⡠⢀⠔⡠⢂⠔⡠⢊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⣿⡟⣿⠻⡟⠀⠀⠀⠀⠀⣩⣿⣿⣿⠊⠐⠀⠂⡀⢈⠄⡠⢂⠔⡡⢊⠔⡁⢊⠐⡁⢊⠐⡁⡿⠿⠛⠉⠛⠛⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠟⠀⢻⣿⠏⠉⠁⠁⠈⠀⠀⠀⢀⢼⣿⣿⣿⠀⠐⡠⢊⠔⠡⠀⠄⠠⠈⢄⠣⠐⠄⠢⠐⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⣾⣿⣿⣿⣿⣦⢀⢼⣿⣻⣿⠡⠊⠀⡁⢌⠀⡁⢄⠠⣀⠄⡡⢈⠄⡡⢈⠄⡡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢠⣿⣟⡛⣻⣿⠿⡧⢺⣿⣿⣮⠐⢄⠂⡀⢀⠰⡄⢂⠐⡠⢂⠔⠤⠊⠐⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣤⣤⣄⠀⠀⠀⠀⢸⣾⡇⢸⣿⣿⣶⣿⣿⣶⡇⢻⣿⣿⣿⡔⠡⢑⢜⠣⣿⠄⠠⠈⠄⠡⠈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢺⣿⣿⣿⡿⠿⣿⠇⠹⣿⣿⣿⢈⠢⡁⢌⠡⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢽⢻⣿⣿⣿⡇⢸⢸⢸⣿⠁⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣾⡄⠙⢿⣿⣿⣶⡟⠀⠱⣿⣿⡿⢄⠀⠀⠂⠑⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣉⠒⠉⢛⣿⣿⡇⢸⢸⢸⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⣿⣷⣤⣲⡭⣿⣿⠋⢦⣼⣿⣿⡟⠠⠀⠄⠠⠀⠀⠁⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⡎⠁⠊⠀⠀⠂⠉⠳⠇⢸⢸⠘⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⣿⣿⣿⡟⣉⣾⣿⢆⠀⠈⠀⠁⢏⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⢻⣿⣸⣿⠀⢸⣿⡏⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠤⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢸⠀⠀⠀⠀⠁⠈⠀⡁⢀⠀⡀⠀⢀⣠⣤⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢹⣿⠏⠁⠁⠉⠀⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣶⣶⣶⣦⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣿⣸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣾⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣺⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⣴⣦⡀⡄⢠
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⡈⠁⣀⣬⣿⣿⣿⣿⢟⠙⠙⢺⣿⣿⣦⣄⡈⠁⠀⢉⣑⣉⣉⣀⣀⣀⣄⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⠐⣇⣸⡇⢿⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣶⡆⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡧⣿⣉⡁⠀⠀⠀⠀⠐⣠⣦⣴⣤⠀⠀⠀⠄⡀⢀⠄⠀⠀⠀⠀⠀⠠⠀⠄⠠⢀⠄⡠⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⣟⠻⡇⠀⠀⠀⠀⠊⢸⣿⣿⡧⢀⠐⡁⠊⠀⠀⠂⡀⢀⠀⡠⢂⠔⡡⢊⠔⡡⢊⠔⡡⣿⠿⠟⠋⠛⠛⠻⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⠏⠀⣿⣿⠇⡉⠈⠁⠀⠀⠀⠀⠀⢼⣿⣿⡗⠠⠈⠀⠀⠐⠠⢂⠄⡡⢊⠜⠣⠊⠜⠡⠊⠔⠡⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢽⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣾⣿⣿⣿⣶⣦⠡⣺⣿⣻⢟⠠⠊⠀⡡⢊⠐⡁⢎⠢⡁⢌⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⢠⣿⣿⣻⣿⡿⠿⡷⢺⣿⣿⣏⠐⠀⠂⡐⢄⠢⡀⢀⠀⡀⢂⠐⡀⠂⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⣤⣤⡤⠀⠀⠀⠀⢸⣞⡄⢸⣿⣷⣶⣿⣿⣶⡇⣻⣿⣿⡧⡘⠄⠀⡌⡢⣿⠌⠠⠀⠄⠠⠈⠄⠠⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠃⢺⣿⣿⣿⡿⠿⣿⠇⢻⣿⣿⡧⠈⠂⡑⢎⠆⡀⢀⠐⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣻⢿⣿⣿⣿⡇⢸⠀⢸⣿⠁⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⣮⠀⠻⢿⣿⣷⣶⡟⢀⠹⣿⣿⡗⢀⠂⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⡟⠻⠃⠉⠘⣛⣻⣿⡇⢸⠀⢸⠇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⣿⣷⣄⣢⣝⣿⣿⠫⢦⣽⣿⣿⡟⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣗⡗⡘⡎⠀⠐⠐⠋⢻⠆⢸⠀⠘⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣟⣿⣿⢄⠀⠈⠀⠉⢏⠀⡁⢀⠀⡀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⢻⣿⣸⣿⠀⢸⣿⡟⡀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠄⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⢹⣿⠏⠁⠁⠉⠀⠉⠁⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣿⣸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣾⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣻⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢠⣤⡄⢠⠀
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠉⣀⣬⣿⣿⣿⣿⢿⠫⠛⢺⣿⣿⣮⣀⡀⠁⡀⢉⣑⣉⣉⣀⣀⣀⣀⡁⠀⠁⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣆⢀⡁⢻⡀⣿⢸⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⡇⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣿⡷⣿⣩⡀⠀⠀⠀⠀⠔⣰⣦⣴⡤⠀⠀⠀⠄⡠⠀⠔⡀⠀⠄⠀⠀⠀⠀⠄⠠⠀⠄⡠⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣻⡇⠀⣿⣿⡏⣟⠻⡇⠀⠀⠀⠀⠊⢸⣿⣿⡗⢀⠐⡠⠊⠐⠁⠂⡀⢀⠀⡀⢈⠐⡠⢊⠐⡡⢊⠔⡡⣿⠿⠟⠋⠙⠛⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⠏⠀⣿⣿⠇⠋⠈⠉⠀⠀⠠⠀⠀⣼⣿⣿⡗⠠⠈⠄⠀⠐⠠⢂⠔⡠⢊⠜⡣⠊⠔⡡⠊⠔⠡⠊⠐⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣾⣿⣿⣷⣶⣦⠁⢺⣿⣿⢏⠠⠉⠄⡠⢈⠐⡁⢎⠠⡁⢌⠠⡁⠈⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢠⣿⣿⣿⣿⣿⠿⡶⢿⣿⣿⢏⠐⡀⠂⡐⢄⠢⡐⢀⠀⡀⢀⠐⡀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡤⣤⣤⡤⠀⠀⠀⠀⣻⣞⡄⢸⣿⣶⣶⣿⣷⣶⡇⣻⣿⣿⡧⡘⢄⠀⡈⡠⣿⠌⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡍⠃⢺⣿⣿⣿⣿⠽⣿⠏⠺⣿⣿⡷⠈⠄⠑⢎⠆⡁⢈⠀⡁⠂⠐⠀⠂⠄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⢸⠇⢻⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠹⣮⠀⠻⢿⣿⣷⣶⡟⢀⠻⣿⣿⡗⠈⠢⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡯⣿⡋⠸⢉⠿⡿⣿⡇⢸⠃⢸⠇⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠠⠔⠂⠀⠀⣿⣷⣈⢢⣟⣿⣿⠡⢦⣽⣿⣿⡏⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠃⠋⠂⠀⠀⢐⠐⠸⠃⢸⠀⠘⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⢄⠀⠉⠀⠉⢏⠀⠁⢀⠀⡀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⢻⣿⣼⣿⠀⢸⣿⡟⡀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠄⠤⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣠⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠂⠀⠁⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⢹⣿⠏⠁⠁⠉⠀⠉⠁⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣿⣸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣾⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣿⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢠⣤⣄⢠⡀
⠀⠛⢻⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠈⠁⣀⣬⣿⣿⣿⣿⢟⠫⠛⢺⣿⣿⣮⣀⣈⠁⡀⢉⣑⣉⣉⣀⣀⣀⣀⡁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣁⢸⡀⣹⠸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⡇⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣿⡧⣿⣀⡀⠀⠀⠀⠀⠐⣦⣦⣴⡤⠀⠀⠀⠄⠠⢀⠄⡠⢂⠄⠀⢀⠄⠀⠈⠠⠁⠄⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣻⡇⠀⣿⣿⡏⡟⢻⠇⠀⠀⠀⠀⢂⢼⣿⣿⡗⢀⠀⡀⢊⠐⡡⠊⠐⠀⠂⡀⢈⠂⡀⢈⠀⡡⢊⠄⣹⣿⡿⠟⠋⠉⠛⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⠇⠀⣿⣿⠇⡋⠈⠁⠀⠀⠠⠀⠀⣼⣿⣿⡗⡠⢈⠄⠁⠐⠀⠀⠀⣀⢂⠜⡡⢊⠔⡡⢊⠔⡡⢊⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣶⣿⣿⣶⣶⣆⠠⣛⣿⣿⣏⠠⠁⠄⠠⠈⠀⡁⢊⠔⡱⢈⠐⡁⢈⠀⡁⢈⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢠⣿⣿⡿⢿⡿⠿⡶⣿⣿⣿⣇⠔⡀⠂⡐⢄⠪⡐⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣤⣤⡤⠀⠀⠀⠀⣽⣞⡄⢸⣿⣿⣶⣾⣷⣶⡟⣿⣿⣿⡧⠘⢄⠠⡘⡠⣧⠌⠠⠁⠄⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡉⠃⢸⣿⣿⣿⣿⢿⣿⠏⢺⣿⣿⡧⠈⠄⠑⢎⠆⡁⢈⠐⡁⠀⠐⡀⠂⠔⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠻⣿⣿⣿⣿⡇⢸⡇⢻⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠹⣶⠈⠻⣿⣿⣷⢶⡟⢀⠹⣿⣿⡗⠈⠂⠐⠀⠂⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⡏⠘⠊⡿⠿⠿⡇⢸⠇⢸⠇⠀⠨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠠⠔⠂⠀⠀⣿⣷⣀⢢⣝⣿⣿⠫⣤⣽⣿⣿⡏⠄⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣩⡞⡃⠀⠀⠐⠋⠑⡆⢸⠆⠘⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⣿⣿⣿⡿⣟⣿⣿⢄⠀⠉⠀⠉⡏⠀⠁⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⢻⣿⣼⣿⠀⢸⣿⡟⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠤⡠⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢰⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⢹⣿⠏⠁⠁⠉⠀⠉⠁⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣿⣸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣾⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣺⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣤⣄⢠⡄
⠀⠛⢻⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠈⠁⠀⠀⠈⠁⣀⣬⣿⣿⣿⣿⠿⠫⠛⢺⣷⣿⣬⣀⢀⠁⡀⢉⣑⣉⣉⣀⣀⣀⣀⡅⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣁⢸⡇⢹⡞⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⡇⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⣺⡆⠀⣿⣿⣷⣿⣌⡀⠀⠀⠀⠀⠐⣤⣦⣴⡤⠀⠀⠀⠄⠠⢀⠄⡠⢀⠄⡠⠀⠄⠡⠈⠀⠁⠈⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣏⡟⢻⠇⠀⠀⠀⠀⢊⣽⣿⣿⡗⢀⠐⡠⢊⠐⡩⠊⠐⠀⠂⡐⢀⠂⡀⢈⠀⡁⢈⠀⣸⣿⡿⠟⠋⠉⠙⠛⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⠇⠀⣿⣿⠧⠋⠈⠁⠀⠀⠀⠀⢀⣾⣿⣿⡗⡠⢈⠄⠡⠘⠄⠀⠀⣠⢂⡐⡡⢊⠔⡡⢊⠔⡡⢊⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣶⣶⣶⣶⣶⣆⠀⣿⣿⣿⣏⠠⠁⠀⠠⠈⠄⡁⢊⠖⡱⢊⠐⡡⢈⠐⡁⢊⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⣿⠿⣿⣿⠿⡶⣿⣿⣿⣇⠔⡀⠂⠐⢄⢢⡐⢅⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡯⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⣤⣤⡤⠀⠀⠀⠀⣿⣟⡄⢸⣿⣷⣴⣾⣷⣴⡗⣿⣿⣿⡧⠘⢄⠢⡘⢤⣧⠈⠀⠁⠌⠠⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡗⡇⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡙⠃⢸⣿⣿⣿⣿⣿⣿⠏⢺⣿⣿⡷⡀⠄⠑⢊⠆⡁⢈⠀⡁⢂⠐⡀⢂⠄⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡗⡇⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠳⣦⠈⠻⣿⣿⣷⢶⡟⢌⢺⣿⣿⡗⠈⠂⠐⠠⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣻⢨⣹⣿⣿⣿⡇⠣⡇⢼⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⢠⠔⠀⠀⠀⣿⣷⣈⣢⡝⣿⣿⠥⣤⣹⣿⣿⡏⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⣷⠣⠁⠀⠑⢭⠋⠹⡁⠰⡇⠘⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣿⣿⣿⡻⣟⣷⣿⡄⠀⠉⠈⠉⡏⠀⠁⢀⠀⡀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢻⣿⣼⣿⠀⢸⣿⡟⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠤⡤⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢹⡟⢱⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠃⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⢹⣿⠋⠁⠁⠉⠀⠉⠁⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣿⡟⣿⣸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⢿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢾⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣿⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣾⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢀⣤⣄⢠⡄
⠘⠛⢻⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠈⠁⠀⠀⠀⠁⣀⣬⣿⣿⣿⣿⠿⠫⠛⢾⣷⣿⣌⣀⢀⠀⡀⢉⣓⣈⣉⣀⣀⣀⣀⡥⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣁⢸⡇⢹⡎⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⣺⡆⠀⣿⣿⣷⣿⣌⡀⠀⠀⠀⠀⠒⣴⣤⣴⡤⠀⠀⡀⠀⠀⠀⠄⡠⢀⠔⡠⢀⠄⠡⠈⠄⠡⠈⠄⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣯⡟⢻⠇⠀⠀⠀⠀⢀⣽⣿⣿⡗⠀⠀⡀⢂⠐⡩⠊⠐⠁⠊⡐⢀⠂⡐⢄⠂⡑⢈⠂⢸⣿⡿⠛⠋⠉⠙⠛⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⠇⠀⣿⣿⠧⠛⠚⠁⠀⠀⠀⠀⠀⣾⣿⣿⡇⡠⠀⠔⠡⠈⠄⠀⡀⢀⢀⡐⡡⢂⠔⡠⢂⠔⡠⢊⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⣶⣶⣶⣶⣶⣄⠠⣿⣿⣿⣏⠰⡁⠀⠠⠀⠄⡡⢈⠖⡱⢊⠔⡡⢈⠄⡁⢊⠔⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⡿⠿⢿⣿⢿⡔⣿⣿⣿⣇⠀⡀⢂⠐⠄⢢⡐⢅⠂⠐⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣤⣤⡄⠀⠀⠀⠀⣿⣽⡄⢸⣿⣿⣴⣾⣷⣴⡗⣿⣿⣿⡧⠙⢄⠢⡘⢤⡯⠈⠀⠁⠈⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡙⠃⢼⣿⣿⣿⣯⣿⣿⠉⢺⣿⣿⡷⡁⢄⠑⢈⠆⡁⢈⠀⡁⢀⠀⡀⢀⠄⡀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⡿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⣄⠌⠻⣿⣿⣷⢶⡟⢌⢺⣿⣿⡗⡈⠂⠐⡬⠂⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣻⠕⠹⢹⡽⡿⣿⡇⡇⡇⣿⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠤⠂⠀⠀⣿⣦⡔⢢⣙⣿⣿⠥⣄⣹⣿⣿⡇⠄⠠⠈⠀⠁⠈⠀⠁⠈⠀⠀⠀⠐⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠷⣿⠔⠃⠀⠀⠑⠐⠐⠂⠃⡇⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⣿⣿⣯⡿⣟⣿⣿⡌⠀⠉⠉⠙⡇⠀⠀⠈⠂⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢻⣿⣼⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠠⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢡⣿⣿⣿⡿⣿⣿⠀⣸⡿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⢾⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⣷⢿⣿⣿⢸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⣿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢾⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣴⣿⣿⣿⣇⣿⣿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣺⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣤⣄⢠⡄
⠐⠛⢿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠈⠁⠀⠀⠀⠉⣀⣬⣿⣿⣿⣿⠿⠫⠛⢾⣿⣿⣌⣀⠁⠀⡀⢉⣃⣉⣉⣀⣀⣠⣀⡅⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣁⢸⡅⢹⡎⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡇⡇⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⠂⢰⣿⣿⣾⣏⣈⡀⠀⠀⠀⠀⢒⣶⣤⣴⡄⠀⠀⡠⢂⠀⠀⠀⠀⠀⠄⡠⢀⠔⡠⢂⠔⡠⢂⠔⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡅⢸⣿⣿⣿⡟⢿⠇⠀⠀⠀⠀⢀⣿⣿⣿⡗⠀⠂⡀⢀⠀⡡⢂⠔⡡⢊⠔⡁⢊⠐⠁⢊⠐⡁⠊⢸⣿⡿⠛⠛⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⠏⠠⣿⣿⡿⠛⠚⠂⠀⠀⢀⠀⡡⣿⣿⣿⡇⡠⢀⠔⡡⠊⠔⠡⠈⢄⠡⡈⠄⠢⠐⠄⠀⠐⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠋⠀⢀⣴⣶⣶⣦⣤⡄⡤⣿⣿⣿⣏⠴⡁⢈⠠⡁⢌⠠⡀⠆⠱⢈⠆⡡⢈⠄⡡⢊⠔⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⣿⡿⡿⣿⣿⣿⠔⣿⣿⣿⣇⠠⡀⢀⠀⡈⢢⠑⡈⢂⠔⠁⠊⠔⠁⠂⠐⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣤⣤⣤⡄⠀⠀⠀⠀⣿⡵⡀⣼⣿⣽⣥⣿⣷⣼⡝⣿⣿⣿⡧⢛⠌⡢⣙⢴⡯⠈⠄⠡⠈⠄⠡⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠇⣿⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⡷⡑⢌⠐⡉⠄⠀⠈⠂⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣻⣿⣿⣿⣿⠇⡇⡇⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡷⣶⠘⣿⣿⣿⣷⣼⡟⠌⢻⣿⣿⡇⡈⢀⠐⡌⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡻⡽⣭⢯⣿⣿⠆⡇⡇⣿⠃⠀⢩⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠤⠀⠁⠐⣿⣧⡀⢩⣛⣿⡿⣕⣄⣻⣿⣿⡇⠄⠠⠈⠄⠁⠈⠀⠁⠈⠀⠁⠀⠐⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣫⣷⡃⠀⠩⢓⣺⡜⠀⡇⡇⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⣿⣿⣿⡿⣟⣽⣷⡀⠈⠙⠉⠛⡅⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣽⠐⠁⠀⠀⠀⠀⠁⠀⡇⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⣿⣿⢿⣿⣽⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠁⠈⠀⠀⠀⠀⠀⠀⠀⢧⠤⢤⠄⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢡⣿⣿⣾⡿⣿⣿⠀⣸⡿⣷⡂⠀⠀⠀⠈⠁⠁⢈⠀⠀⠀⠀⠀⢀⡀⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡈⣽⣿⠉⠁⠁⠉⠀⠉⠁⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢲⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡇⢸⣟⡃⠀⢺⣿⣷⢸⣟⢸⣿⠷⢽⣿⣿⢸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⣿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣾⣿⣿⣾⣇⣿⣿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣿⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣤⣄⢠⡀
⠘⠛⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣎⠉⠈⠁⠀⠀⠈⠈⢀⣨⣿⣿⣿⣿⡿⠟⠻⣿⣿⣷⣈⡀⠉⢀⡀⣉⣃⣉⣉⣀⣄⣠⣀⠅⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣁⢸⡇⢹⡾⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣷⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⠂⢰⣿⣿⣾⣏⣈⠀⠀⠀⠀⠀⢂⣶⣤⣦⡄⠀⠀⡠⠂⠄⡀⠀⠀⠀⠀⠀⠀⠄⠠⢀⠄⡠⢀⠔⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡄⢸⣿⣿⣻⡟⢿⠃⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠊⠐⠀⠀⡑⢀⠀⡀⢂⠔⡡⢂⠔⡡⢊⠔⡡⢊⢼⣿⡿⠛⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡏⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠿⠃⢸⣿⣿⠸⠗⠚⠀⠀⠀⠀⠀⠠⣿⣿⣿⠂⠀⠀⠀⠀⢊⠔⠡⢊⠔⡡⠈⠄⠡⠈⠄⠡⠈⠄⠁⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠋⠀⢀⣤⣴⣶⣤⣤⡈⠰⣿⣿⡻⡃⠔⡁⢈⠄⡁⢈⠠⡁⢊⠠⠀⠄⠠⠈⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣷⠜⣿⣿⣽⡁⠢⡐⢀⠀⡀⢆⠐⡈⢂⠐⡀⢂⠔⠀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⡇⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⢤⣤⣤⡄⠀⠀⠀⠀⣿⣶⠀⣾⣿⣦⣠⣿⣅⣼⢻⣿⣿⣿⣇⠁⠀⡠⣑⢼⡧⠀⠄⠠⠈⠄⠡⠈⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡇⡇⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠻⠇⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⠇⡑⢌⠲⡁⢀⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣿⣿⠀⡇⠇⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡧⣀⠙⣿⣿⣿⣭⣽⡟⠈⢻⣿⣿⠣⡀⢀⠀⠌⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣹⠇⠏⢩⣿⣿⣿⠀⡇⠀⣿⠁⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠤⠀⠁⢰⣿⣦⡀⣌⢻⣿⡿⣑⣄⣻⣿⣿⠁⠈⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⡏⠃⠀⠀⠈⠂⠉⠟⠀⡇⠀⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠈⣿⣿⣿⠿⣗⣽⣷⡀⠉⠙⠉⠻⡁⢀⠀⠀⠂⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣼⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠤⠄⠄⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢱⣿⣿⣾⣿⣿⣿⠀⣸⡿⣿⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡈⣿⣿⠉⠁⠁⠉⠀⠉⠁⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡇⢸⣟⡃⠀⢺⣿⣷⢸⣟⢸⣟⢷⢸⣿⣷⢸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⢻⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢺⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣻⣯⣿⣾⣏⣿⣿⣿⣷⣿⡇⣿⣽⡇⣿⣁⣿⣽⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣤⣀⢠⡀
⠘⠛⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡎⠉⠈⠁⠀⠀⠈⠈⢀⣈⣿⣿⣿⣿⡟⠝⠿⣾⣿⣧⣈⠀⠉⠀⠀⣉⣃⣉⣉⣀⣀⣠⣀⠅⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⣁⢸⡁⢹⢼⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⣷⢰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⢺⣇⣬⠀⠀⠀⠀⠀⢂⢶⣤⣦⡄⠀⠀⡠⠀⠄⡠⠀⠔⠠⠀⠀⠀⠀⠠⠀⠄⡠⢀⠄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⣿⢹⡟⢿⠀⠀⠀⠀⠐⢀⣿⣿⣿⠆⡠⠂⠔⠀⢂⠑⢀⠀⡀⢀⠀⡡⢀⠔⡡⢊⠔⡡⢊⢼⣿⠿⠛⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠿⠃⢸⣿⣿⠸⠷⠟⠀⠀⠀⠀⠀⠠⣿⣿⣿⠂⠄⠡⠀⠀⠂⠔⡠⢋⠔⡡⢚⠔⠡⠊⠔⠡⠊⠔⠡⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⢀⣤⣤⣤⣤⣤⡈⠰⣿⣿⡿⡁⠔⠁⢈⠄⡁⢊⠰⡁⢊⠠⡁⢊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⢸⣿⣿⣿⣿⣿⣧⠾⣿⣿⣿⡁⠢⠐⢀⠂⡀⢄⠀⡀⠂⠐⠀⠂⠐⠀⠂⠐⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣤⣤⣤⡄⠀⠀⠀⢠⣗⡢⠀⣿⣿⣖⣠⣿⣅⣹⢸⣿⣿⣿⢄⠣⠀⢠⢑⢼⡧⠁⠄⠠⠀⠄⠡⠀⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⠀⣿⣿⣿⣿⣿⣿⣿⠐⢿⣿⣿⠆⡑⢈⠲⡱⢊⠀⡁⢊⠐⠀⠂⠐⠠⠂⠐⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣟⣿⣿⣿⣿⣿⠀⡇⠀⣿⡏⠀⢼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡦⡀⠻⣿⣿⣿⣭⣽⡿⡈⣿⣿⣿⠢⡐⢀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣟⠛⡅⠌⣸⣿⣿⣿⠀⡇⠀⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢸⣿⠆⡁⢝⠻⣿⡿⣑⣄⣿⣿⣿⠁⠈⠠⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⡏⠉⠀⠀⠁⠡⢾⠍⠀⡇⠀⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠘⣿⣷⣿⢾⣗⣿⡧⡈⠙⠛⠙⠻⡁⢈⠀⡀⢂⠀⡀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠤⠤⠄⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢱⣿⣿⣾⣿⣿⣿⠀⣸⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⠂⠀⠁⠀⠈⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⣿⣿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢲⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢼⣟⢷⢹⣿⣷⢸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⣻⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢺⣇⣸⡏⠙⠛⢸⣿⣿⢸⣿⣷⣯⣿⣿⣏⣿⣼⣯⣷⣿⡇⣿⣹⡇⣿⣁⣿⣽⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣤⡀⢠⡀
⠘⠛⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡎⠉⠈⠁⠐⠀⠈⠈⢀⣈⣿⣿⣿⣿⡿⡹⠿⣾⣿⣇⣈⠀⡉⢁⠀⣩⣃⣉⣉⣀⣀⣀⣀⠁⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⣁⢸⡀⣻⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⣷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⢺⣏⣬⠀⠀⠀⠀⠀⢂⢶⣤⣶⡄⠀⠀⠀⢀⠄⡠⢀⠔⡠⠀⠀⠀⢀⠠⠀⠄⡠⢀⠄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠄⢸⣿⣿⢹⡟⢿⠀⠀⠀⠀⠐⣁⣿⣿⣿⠄⡀⢊⠔⠁⢊⠑⢀⠀⡀⢀⠀⡡⢂⠔⡡⢊⠔⡡⢊⢼⣿⠿⠛⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠿⠃⢸⣿⣿⣸⠷⠿⠠⠀⠀⠀⠀⢰⣿⣿⣿⢊⢄⠡⠀⠀⢂⠄⡠⢈⠔⡡⢛⠔⠡⢊⠔⡡⠊⠔⡡⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⢀⣤⣤⣤⣀⣀⢈⢰⣿⣿⣿⡁⠔⡡⢈⠄⡡⢈⠰⡁⢊⠐⡁⢊⠀⠁⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⢸⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⡡⢢⠔⢅⠂⡀⢆⠀⡈⠂⠑⠀⢢⠐⠀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣤⣤⣤⠄⠀⠀⠀⠠⣗⣤⠀⣾⣿⣛⣩⣿⣋⣹⢻⣿⣿⣿⢖⠣⡀⢠⠑⢼⡧⠁⠄⠠⠀⠄⡣⠀⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⠀⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠀⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⡆⡑⢈⠲⡱⢊⠐⡁⢊⠐⠀⠂⠐⠠⠂⠐⠀⠂⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⡏⠀⢺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣄⡤⢿⣿⣿⣿⣿⣿⡿⡈⣿⣿⣿⠢⡐⢀⠀⡌⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠋⠛⣩⣿⢿⣿⠀⡇⠀⡿⠀⠐⢼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⢰⣟⡆⡙⣝⠿⣿⡿⣑⢌⣿⣿⣿⠁⠈⠢⠑⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⡖⡫⠀⠀⠊⠙⠫⠾⠀⡇⠀⠃⠀⠈⣨⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠘⣿⣿⣟⣾⡿⣿⡧⠈⠛⠛⠛⢿⡁⢀⠀⡀⢀⠐⡀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣁⠁⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠤⠤⠄⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢱⣿⣿⣾⣿⣿⣿⠀⣸⡿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠈⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⣿⣿⠉⠁⠁⠉⠀⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢲⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣿⣼⣟⢷⣹⣿⣷⢸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⣻⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⣻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢺⣇⣸⡏⠙⠛⢸⣿⣿⢸⣿⣷⣏⣿⣿⣟⣿⣼⣯⣷⣿⡇⣿⣹⡇⣿⣁⣿⣽⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⡀⢠⡀
⠘⠛⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡎⠉⠈⠁⠀⠀⠈⠈⠀⣈⣿⣿⣿⣿⡿⡻⣿⣾⣿⣇⢈⠀⡉⢀⠀⣩⣃⣉⣉⣀⣀⣠⣀⠁⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣁⢸⡀⣻⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣾⢰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣷⠀⢸⣿⣿⢾⣧⣄⠀⠀⠀⠀⠀⢂⣶⣤⣦⠄⠀⠀⠀⠀⠀⡠⢀⠄⡠⢀⠀⡡⢀⠀⠀⢈⠀⠁⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⣿⣹⠛⠿⠀⠀⠀⠀⠐⡁⣿⣿⣿⠀⡀⢂⠐⠀⢊⠕⠁⠊⠐⢀⠂⡐⢀⠀⡀⢈⠔⡡⢂⣿⣿⠟⠛⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠿⠀⢸⣿⣿⢼⣷⡿⠀⢀⠀⠀⠀⢰⣿⣿⣿⢂⠄⠡⠈⠄⠣⠀⠀⢁⠄⡠⢙⠔⡠⢊⠔⡡⢊⠔⠡⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⣀⣀⣀⣀⣀⢈⢰⣿⣿⣿⡁⠂⠀⠈⠄⡡⢈⠴⡱⢎⠔⡡⢊⠔⡁⢊⠐⡡⢊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣆⢮⣿⣿⢾⡀⢂⠔⢀⠢⡐⣄⠊⡐⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠤⣤⣤⣤⡄⠀⠀⠀⢰⡧⣄⠀⣾⣿⡍⣉⣿⡋⣻⢸⣿⣿⣿⢔⠣⡈⢄⠁⢼⡦⠁⠌⠠⠁⠄⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢸⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣶⠀⣿⣿⣿⣿⢿⣿⣿⡑⣿⣿⣿⢆⠑⠈⠲⡱⢈⠀⡀⢂⠀⡀⢂⠐⡠⠂⠐⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠈⣿⠇⠈⢼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡈⡸⢿⣿⣿⣿⣛⣿⡿⡘⣿⣿⣿⠢⡑⠀⠊⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡿⢟⠉⢬⢉⣽⣿⣿⠀⡏⠀⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⢹⡗⣀⡙⢿⣿⣿⣿⠁⢌⣿⣿⣿⠡⠈⠀⠑⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⡥⠄⠀⠀⠁⠉⠋⡙⠀⡿⠀⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⢘⣿⣧⣿⣾⡿⣿⡇⠙⠿⠛⠻⢿⠁⠈⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠄⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢱⣿⣿⣽⡟⣿⣿⠀⣸⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⠈⣿⣿⠉⠁⠁⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢿⡇⢸⣟⡃⠀⢸⣿⣷⢸⣿⣼⣟⠷⢸⣿⣷⢸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⣻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢺⣇⣸⡏⠙⠛⢸⣿⣿⢸⣿⣷⣏⣿⣿⣟⣿⣸⣏⣷⣿⡇⣿⣹⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⡀⢠⠀
⠘⠛⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡎⠉⠈⠁⠀⠀⠈⠈⠀⣨⣿⣿⣿⣿⢟⠿⣿⣿⣿⣅⠈⠀⡉⢁⠀⣹⣁⣉⣍⣠⣀⣤⣠⠁⠀⠁⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⡁⣿⠀⣿⢸⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣷⠀⢸⣿⣿⣾⣧⣄⠀⠀⠀⠀⠐⣰⣦⣴⣦⠀⠀⢂⠔⠀⠀⠀⠀⠀⡀⢀⠄⡠⢊⠔⡡⢊⠔⡡⢊⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⢼⣿⣿⣿⠛⡿⠀⠀⠀⠀⠐⡠⣿⣿⣿⠂⠀⠀⠀⡀⢈⠕⡠⢂⠔⡡⢊⡔⢁⠊⡐⠁⠊⠐⠁⣿⣿⠿⠛⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⠀⢸⣿⣿⣼⣷⣿⠀⠀⠀⠀⠀⢴⣿⣿⣿⢀⠄⡠⢊⠔⡣⠈⢄⠡⡈⠄⠡⠈⠀⠁⠈⠀⠁⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠈⠉⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⡡⠊⠀⡁⠀⠀⠈⠀⡑⢌⠂⡑⢈⠀⡡⢈⠀⡡⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣿⣿⣿⣿⣿⡄⢺⣿⣿⣿⡄⢀⠐⢀⠢⡐⣄⠢⡐⡡⠊⠔⡡⠂⠔⠡⠊⠔⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣤⣤⡤⠄⠀⠀⠀⢸⣇⡀⠀⣾⣟⡛⢻⣿⠛⣷⢻⣿⣿⣿⢜⠣⡐⢄⡣⣾⠄⠡⠈⠀⠁⠈⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⠰⣿⣿⣷⣿⣿⣷⣿⡱⣿⣿⣿⢎⠐⡈⠊⡑⢀⠂⡐⢀⠀⡀⠀⠀⠠⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⠇⠨⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡙⡰⣿⣿⣿⣿⣾⣿⡯⡐⣿⣿⣿⠢⠑⠄⢢⡐⢀⠀⠀⠀⠀⠄⠠⠀⠀⠠⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣿⠻⢹⣿⣿⣿⣿⢸⢸⢸⡟⠀⠐⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠘⠘⢱⡍⢍⡛⣿⣿⣿⣿⠁⢘⣿⣿⣟⠢⠈⠄⠁⢈⠀⠁⢀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡿⣷⠀⠀⠉⡛⣿⣻⢸⢸⠘⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠄⠒⠈⠀⠀⠀⢸⣿⣦⣝⣿⣿⣿⡏⠳⢾⠿⡿⣿⠐⠀⠂⠐⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠉⠈⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⡬⠤⡤⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⡟⢹⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠀⠁⠈⠀⠀⢀⠀⠀⠂⠀⡀⠀⠀⢀⡤⠶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠐⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢸⣿⣿⠉⠃⠁⠉⠀⠉⠁⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢾⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⠷⢸⣿⣷⢸⣟⡷⣿⡇⣿⣻⠆⣿⡃⣿⣻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢺⣇⣸⡏⠙⠛⢺⣿⣿⢸⣿⣿⣏⣿⣾⣗⣶⣸⣿⣷⣿⡇⣿⣽⡇⣿⣁⣿⣽⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⣤⡀⢠⢀
⠘⠻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡎⠉⠈⠁⠀⠀⠈⠉⢀⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⡁⠈⠀⡉⣁⣀⣹⣡⣉⣍⣠⣀⣤⣠⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡄⢈⡀⣿⠀⣿⢸⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣷⠀⣸⣿⣿⣾⣧⣄⠀⠀⠀⠀⠐⡰⣦⣴⣦⠀⠀⢀⠔⡀⠀⠀⠀⠀⠀⢀⠄⡠⢀⠔⡠⢊⠔⡡⢂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⠛⡟⠀⠀⠀⠀⠀⣰⣿⣿⣿⠂⠐⢀⠀⡀⢈⠄⡠⢂⠔⡠⢊⠔⡁⠊⡐⠁⠊⠐⠁⣿⣿⠿⠛⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠁⢸⣿⣿⣾⣷⣟⠀⠀⠀⠀⠀⢼⣿⣿⣿⢀⠄⡠⠂⠄⠣⠊⢄⠡⡊⢄⠡⠈⠀⠁⠈⠀⠁⠈⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠈⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⢿⡡⢊⠀⡁⢀⠀⡀⠀⠑⢌⠢⡑⢈⠂⡁⢈⠀⡁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣿⣿⣿⣿⣿⡄⢺⣿⣿⣿⠀⢀⠐⠀⠢⡐⣄⠢⡐⠀⠂⠔⠡⠊⠔⡠⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢤⢤⡤⣤⠄⠀⠀⠀⢸⣇⡀⠀⣼⣿⡛⢻⣿⠟⢷⢻⣿⣿⣿⠌⠢⣀⢄⡣⣾⠄⠡⠈⠀⠁⠈⠀⠁⠈⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⠰⣿⣿⣷⣿⣿⣷⣾⠹⣿⣿⣿⢎⠐⡈⠊⡑⢀⠂⠐⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣟⣿⣿⣿⣿⣿⢸⢸⢸⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡉⡸⣿⣿⣿⣿⣾⣿⡯⡐⣿⣿⣿⠠⠑⠀⢢⡀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠘⢜⣯⣿⣿⣿⢸⢸⢸⡟⠀⠀⣻⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠘⠘⢹⡑⢌⠛⣿⣿⣿⣿⠃⢈⣿⣿⣿⠠⠀⠄⠱⠈⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡚⠊⡓⠀⠈⠉⠀⠉⠁⢸⢸⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠄⠂⠈⠀⠀⠀⢸⣿⣦⣝⣼⡿⣿⡎⠳⢾⠿⡿⣿⠀⠀⠂⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠤⠤⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢹⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⢀⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠅⢸⣿⣿⠉⠃⠁⠉⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢼⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⠷⢸⣿⣷⢸⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⣻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣯⣿⣯⣿⣼⣗⣶⣸⣿⣷⣿⡇⣿⣽⡇⣿⣁⣿⣽⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⣤⡀⣤⢀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡈⠉⠈⠁⠀⠀⠈⠉⣀⣸⣿⣿⣿⣿⠿⢿⣿⣿⣿⡁⠈⠀⡁⣁⣀⣉⣁⣉⣍⣠⣀⣄⣠⠁⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡄⢈⡀⣿⠈⣷⢸⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡷⠀⣾⣿⣷⣾⣤⣄⠀⠀⠀⠀⠐⡠⣦⣴⣦⠀⠀⢀⠔⡀⢀⠀⡀⢀⠀⠀⠀⠠⢀⠄⡠⢀⠄⡠⢂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣷⠀⣽⣿⣿⣿⠻⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⠂⠐⠀⠊⠀⠈⠀⡀⢂⠐⡠⢂⠔⡠⢊⠔⡡⢊⠔⡁⣿⣿⠟⠛⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠀⢿⣿⣧⣾⣿⣗⣀⠀⠀⠀⠀⢼⣿⣿⣿⠀⠈⠀⠀⠄⠠⢀⢄⡡⣊⢔⠡⠊⠄⠡⠈⠄⠡⠈⠄⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠈⠀⠀⠀⠀⠀⠂⠀⢼⣿⣿⣿⡁⢈⠄⡡⢈⠐⡁⢊⠑⠈⠂⠑⠈⠂⠑⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⡆⢺⣿⣿⣯⠐⢠⠀⠀⠀⠑⣄⠢⠐⠀⠂⠐⠀⢂⠐⡀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⠤⣤⡤⠀⠀⠀⠀⢸⡧⡀⠀⣾⣟⡛⢻⣿⠛⢻⣻⣿⣿⣿⠈⠢⣐⢌⡢⣾⠄⠡⠈⠄⠡⢈⠄⠁⠈⠄⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⢰⣿⣿⣷⣿⣿⣷⣿⠹⣿⣿⣿⢌⠢⡉⢊⠕⡀⠂⠐⠀⠂⠐⠀⠂⠐⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡻⣿⣿⣿⣿⡇⢸⢸⢸⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⡈⡸⣿⣿⣿⣿⣿⣿⡯⠑⣿⣿⡿⠀⠁⠄⠢⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡿⡏⠊⠝⣿⣿⣿⡇⢸⢸⢸⡏⠀⠀⢽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠠⠈⠈⢸⡃⢈⢻⣿⣿⣿⣿⠃⣘⣿⣿⣟⠠⠁⠄⠡⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⠃⠀⠈⠀⠉⠙⡁⢸⢘⠘⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⢸⣿⣦⣱⣿⢷⣿⡆⠙⢾⠿⡿⢏⠀⠀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣿⣿⣿⣿⣼⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠤⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⣿⣿⣿⡟⣿⣿⠀⣸⡿⣷⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠃⢸⣿⡿⠉⠁⠁⠉⠀⠈⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣟⢷⢸⣿⣷⢸⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⣻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣯⣿⣿⣿⣿⣏⣷⣸⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⣤⡀⣤⢀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡈⠉⠈⠁⠀⠀⠈⢉⣠⣬⣿⣿⣿⠿⢛⢿⣿⣿⣿⣇⠈⢀⡁⣁⣀⣉⣁⣉⣍⣠⣀⣤⡤⠁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡄⢈⡀⣏⠈⣷⢻⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢶⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⣷⣿⣤⣄⠀⠀⠀⠀⠀⡰⣦⣴⣶⠀⠀⢀⠀⡀⢀⠐⡀⢂⠀⠀⠀⠀⠀⠀⡠⢀⠄⡠⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⣿⡟⣿⠻⡟⠀⠀⠀⠀⠈⢸⣿⣿⣿⠀⠐⡠⠊⠐⡁⠂⠀⠀⠀⡀⢂⠕⡠⢂⠔⡡⢊⠔⡡⣿⣿⠟⠛⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠟⠀⢽⣿⣧⡾⠟⠓⠀⠤⠀⠀⠀⢼⣿⣿⣟⠡⠈⠀⠁⠈⠢⢀⠄⡠⣂⢔⡡⢊⠔⡡⠊⠔⡡⢊⠔⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢀⣤⣤⣤⣀⣠⡀⢾⣿⣿⢿⠐⠈⠄⡡⢊⠐⡁⢊⠔⠁⠂⠐⠀⠂⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣧⢻⣿⣿⣯⠐⡠⠀⠀⠠⠑⡄⠢⠑⠄⠂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⢤⡤⠤⠀⠀⠀⠀⢸⣟⢆⠀⣾⣿⣍⣩⣿⣋⣹⢹⣿⣿⣿⠈⠢⢑⢌⡢⣿⠄⠡⠈⠄⠡⢈⠄⡁⢈⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⢸⢸⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⠿⠀⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣷⢌⠢⡉⢊⠕⡀⠂⠐⠀⠂⠐⠀⠂⠐⠀⠂⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣟⣿⣿⣿⣿⡇⢸⢸⢸⣿⠁⢉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⢢⡀⢻⣿⣿⣿⣿⣿⡯⡑⣿⣿⡟⠀⠁⠄⠢⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡟⡋⠈⠪⣭⡭⢿⡇⢸⢸⢸⡏⠀⠐⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠤⠒⠒⠀⠀⠀⢸⣅⢄⠨⣽⣿⣿⠟⢠⣸⣿⣿⣏⠠⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢃⠀⠃⠀⠀⠀⠉⠲⠃⢸⢈⠘⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡵⢍⣷⣿⡇⠀⠉⠋⠙⢋⠀⡀⠂⠐⠉⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⡃⣿⣿⣿⣿⣼⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠤⠤⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡇⢼⣿⣿⣽⡟⣿⣿⠀⣸⡿⣷⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⣿⣿⠉⢁⠁⠉⠀⠈⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣿⠷⢺⡟⣷⢸⣿⡷⣿⡇⣿⣻⠆⣿⡃⣿⣻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣯⣿⣿⣿⣿⣇⣿⢿⣿⣷⣿⡇⣿⣹⡇⣿⣁⣿⣼⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣠⣤⡀⣤⢀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠈⠉⠈⠁⠀⠀⠀⠉⣤⣾⣿⣿⠿⠟⠋⠚⢿⣾⣿⣿⣮⣀⣁⣀⣀⣈⣁⣋⣍⣤⣠⣤⡤⠁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡀⢈⡀⣇⠈⣷⢻⠘
⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾⡆⢾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⡗⣿⣤⡄⠀⠀⠀⠀⠀⣰⣦⣴⡦⠀⠀⠀⠂⡀⢀⠀⡀⢂⠄⡠⢂⠐⡀⢀⠀⡀⢀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣇⠀⣿⣿⡏⣿⠻⠟⣀⠀⠀⠀⠊⢼⣿⣿⡟⠀⠀⡠⠂⠐⡉⠊⠐⠀⠀⡀⢀⠑⡀⠂⠐⡀⢂⠔⡠⣿⣿⠟⠛⠉⠉⠉⠙⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠏⠀⣿⣿⡇⠋⠀⠀⠀⠁⠈⠀⠀⢼⣿⣿⣇⠠⣈⠐⠁⠈⠠⠁⢌⠠⣀⢄⡡⢊⠔⡡⢊⠔⡡⢊⠔⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣶⣿⣶⣶⣶⣇⢺⣿⣿⢏⠐⠁⠀⡀⢌⠐⡡⢊⠔⡡⢊⠔⡁⠊⠔⠁⢊⠔⡁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡄⠀⣸⡿⠿⠿⣿⣿⣿⢸⣿⣿⣧⡐⡤⠂⡄⠠⠑⡌⠢⠑⠌⠠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⢤⠤⠤⠄⠀⠀⠀⢸⣿⣷⠀⣿⣾⣧⣬⣿⣧⣼⣻⣿⣿⣷⠊⠂⡑⢌⠢⣷⠄⠠⠀⠄⠀⠈⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠂⢸⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠌⠰⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣷⢌⠢⡑⢌⠅⡀⠀⠐⡀⠂⠐⠀⠂⠔⠀⠂⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⠀⢄⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢺⡀⠘⠻⣿⣿⣿⣿⠃⣹⣿⣿⡟⠀⠀⠄⠢⠁⠄⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡛⣟⡗⠘⣼⣭⣯⢿⡇⢸⠀⢸⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡠⢌⣻⣿⠅⠀⠙⠟⠻⢏⠂⡁⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⡇⠉⠀⠁⠐⠙⠛⡇⢸⠀⠘⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡃⠈⢿⣿⠀⠀⠀⠀⠀⠀⢢⠀⠂⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠐⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⡠⣿⣿⢿⣿⣼⣿⠀⢸⣿⡟⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠠⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢠⣿⣿⣼⡟⣿⣿⠀⣸⡿⣷⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠶⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡅⢨⠹⣿⠉⢹⡅⠉⠀⠉⠁⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣾⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣻⠆⣿⡃⣿⣿⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢙⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣇⣸⡏⠉⠛⢸⣿⣿⣼⣿⣿⣿⣿⢿⣏⣿⢸⣿⣿⣿⣇⣿⣹⡇⣿⣁⣿⣿⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⢀⠠⣀⠀⣤⣤⡀⣤⢠
⠘⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠈⠉⠘⠁⠀⠀⠈⠉⠸⣿⣿⠊⠉⠀⣀⡈⠀⠈⠓⢻⣿⣏⣹⣿⣀⣉⣁⣉⣭⣤⣤⣤⡤⠁⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⢶⡀⢈⡀⣇⢈⡇⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾⣖⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⣗⣿⣤⠄⠀⢀⡀⠀⠠⣰⣦⣶⡦⠀⠐⠀⠂⠀⢀⠀⡀⢂⠔⡠⢂⠔⡠⢂⠐⡀⢂⠐⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣺⣗⠀⣿⣿⡏⠋⠁⠀⠀⠀⠀⠡⠀⢸⣿⣿⡗⠀⠐⡠⢂⠔⡉⠊⠔⠡⠊⠄⠡⠑⠀⠂⠐⠄⠂⠐⡰⣿⣿⠟⠛⠉⠉⠉⠙⠛⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⠏⠀⣿⣿⡇⠀⠀⣤⣤⣤⣀⣀⣤⢸⣿⣿⣟⡠⢊⠐⠁⠈⠀⠁⢌⠠⣀⢄⠢⣀⢄⡡⢊⠔⡡⢊⠔⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣇⢺⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⢤⣿⣿⣯⠐⠁⠀⡀⢄⠀⡠⢊⠔⡡⢊⠔⡁⢊⠔⡡⢊⠔⡡⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⣿⡉⡉⠙⣿⠛⣹⢺⣿⣿⣧⡀⣤⠂⡔⠠⢛⡌⠢⠙⠄⠡⠐⠄⠡⠈⠄⠠⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⠤⠴⠤⣄⣤⠤⠀⠈⠉⢰⠠⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⡿⢊⠂⡑⢌⠲⣷⢄⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠆⢸⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣆⠙⢿⣿⣷⣿⣿⠋⠿⣿⣿⣗⢌⠂⡑⢈⠅⡀⠂⠐⠀⠂⠐⠀⠂⠔⠀⠂⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⠀⡀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠙⢿⣿⠋⠠⠐⢀⠂⠐⠠⢁⠄⡣⠃⢄⠠⠀⠄⠠⠀⠄⠁⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣟⠐⠻⣿⡿⣿⡇⢸⠀⢸⠇⠀⡂⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠁⠀⠀⠸⣿⠀⠠⠈⠀⠁⠈⠀⠱⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢟⡟⠦⠀⠀⠚⠈⢿⠇⢸⠀⠘⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⠲⡁⢸⣶⣿⠀⠀⠀⠂⠀⠀⠀⠀⠻⣗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠆⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⣿⣿⣿⣿⣼⣿⠀⢸⣿⡇⠀⠀⠈⢴⡀⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣼⣟⣿⣿⣷⣼⡿⣷⠀⠀⠀⠀⠐⡄⠀⠐⠀⠀⠀⠀⠀⣠⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣧⣉⣀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣾⣿⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⡃⠀⢸⣿⣷⢻⣿⣿⣟⢷⣽⣿⣿⣸⣿⡿⣿⣿⣿⣿⠟⣿⣷⣿⣻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣲⣏⣿⣿⣟⣿⣽⣏⣷⣿⡇⣿⣹⣇⣿⣟⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⢀⠤⣄⠀⣤⣤⡀⣤⢠
⠘⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠈⠉⠈⠁⠀⠀⠀⠉⠀⠸⠋⠀⠈⣿⣿⣿⣿⣏⠀⠁⣈⢀⣉⣉⣀⣉⣁⣩⣍⣤⣤⣤⡄⠁⠀⠁⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⢷⡀⣈⡐⣇⢘⡇⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢶⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⣷⣿⠤⠀⠀⠀⠠⢀⠐⡰⣦⣶⣦⠀⠀⢀⠐⡀⢂⠐⡀⢂⠀⠀⠀⠀⠀⠄⡠⢀⠄⡠⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣗⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠇⠸⣿⣿⣿⠂⠐⠠⠊⠐⠉⠂⠀⢀⠀⡠⢂⠔⡠⢊⠔⡡⢊⠔⡡⣿⣿⠿⠻⠋⠉⠉⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠟⠀⣿⣿⡇⠀⢀⣤⣤⣤⣤⣤⣦⠘⣿⣿⣟⠡⠈⠀⠀⠌⠠⠀⢄⡠⣊⠔⡡⢊⠔⠡⠊⠔⠡⠊⠔⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⣸⣿⣿⣿⣿⣿⣿⢲⣿⣿⢯⠀⢈⠀⡁⢌⠀⡁⢊⠐⡀⠂⠐⠈⠂⠐⠀⠂⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠗⠀⣿⣄⣀⣙⣿⣉⣼⢿⣿⣿⣯⡔⢠⠀⡀⠠⠑⡌⠢⠑⡀⠂⠐⡀⠂⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⡤⠀⠀⠉⠙⠋⠉⠀⠀⠀⡇⢿⣿⣿⠿⣿⣿⣿⣹⣿⣿⣿⠈⠠⡑⢌⡢⣿⠄⠡⠈⠄⠡⠈⠄⠡⠈⠄⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⠻⣿⣿⣿⡿⠁⠈⠉⠻⡛⢞⠦⡙⢎⠕⡀⠂⠐⠀⠂⠐⠀⠂⠐⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠯⣻⣿⣿⣿⡇⢸⢸⢸⣿⠁⠠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠙⢻⣿⠁⠀⠑⢄⠂⠐⠀⠘⣄⠢⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡿⠃⠐⠨⢻⠹⣻⡇⢸⢸⢸⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⢨⣿⡄⠀⠀⠀⠁⠀⠀⠀⠜⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠃⠁⠀⠀⠉⠉⡝⡅⢸⢨⠘⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡍⠓⢌⡘⣿⣿⣄⢀⠀⠀⠀⠀⠀⠀⠘⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣦⣼⣿⡇⠀⠀⠀⠀⠙⢓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠄⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⣵⠀⠀⠀⠀⠀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠿⠿⢿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⡿⢿⣷⣦⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⠀⢸⣿⣿⢻⣿⢿⣟⣿⣿⣿⣿⣻⣿⡿⣿⡟⣿⣻⠟⣿⣣⣿⣿⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢙⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠉⠛⢸⣿⣿⢻⣏⣰⣏⣿⣿⣿⣿⣽⣿⣷⣿⡇⣿⣹⡇⣿⣑⣿⣼⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⣠⣤⡀⣤⢀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⠈⠉⠈⠁⠀⠀⠀⠉⠀⠈⠉⠀⣸⣿⣿⣿⣿⣿⣿⣇⡈⠀⠉⣁⣀⣉⣁⣉⣍⣠⣀⣄⡠⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⢈⡀⣇⢈⣷⢿⢸
⣿⣿⣿⣿⣿⣿⣿⣶⣶⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣷⠀⢺⣿⣷⣾⠗⠁⠀⠀⠐⢄⡠⢒⣔⣠⣄⠀⠀⠀⡀⠂⠐⠀⠀⠀⠀⠀⠀⢀⠀⡀⢂⠐⡀⢂⠔⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠂⢀⣿⣿⣿⠀⠀⠊⠀⠀⠀⠀⠀⠀⠠⠀⠄⡠⠀⠔⡠⢊⠔⡡⠊⣿⣿⣿⢿⠿⠛⠛⠻⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⠀⢹⣿⡇⠀⢠⣶⣤⣤⣤⣴⣷⠀⣿⣿⣿⠀⠀⠀⠀⡀⢀⠄⡁⢈⠐⡡⢊⠐⡁⢊⠐⡁⢊⠐⠁⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣸⣿⣿⣟⠀⠔⠀⠀⠀⠀⠀⠀⠠⠈⠄⠢⠐⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⢸⣿⠇⠀⣧⣀⣀⣹⣯⣥⣾⢿⣿⣿⣟⠁⠈⠀⠁⠈⠠⡁⢌⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠻⣿⣿⢿⣿⣿⡿⢼⣿⣿⣿⡐⢀⠀⡡⢆⣴⡁⢂⠐⡀⠂⠐⠀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠛⣿⣿⣿⡟⠁⠀⠉⠉⠫⡙⠹⠂⡜⠁⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣻⣿⣿⡇⢸⢸⢸⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡀⠈⢹⣿⡇⠀⠠⠀⠄⠀⠈⠀⠱⣌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢛⠓⠂⠀⣛⠹⠿⡇⢸⢸⢸⡟⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣎⠀⠀⢀⣿⣿⡄⠀⠈⠂⠀⠀⠀⠈⠉⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠃⠁⠀⠀⠀⠀⠀⠂⢸⢸⠸⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⣈⠱⣴⣦⣝⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣤⡀⢀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⣀⠤⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⠿⢛⣭⣭⣍⡻⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⡿⠹⣿⣷⡊⠀⠀⠉⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢼⡇⢸⣟⡃⠀⢸⣿⣿⢺⣟⢹⣿⣿⣿⣿⣿⣻⣿⣷⣿⡏⣿⣻⠏⣿⡃⣿⣿⡟⠃⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⣰⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⣿⣹⡇⣿⣁⣿⣻⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⣀⢀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠈⠀⠁⠀⠀⠈⠀⠀⠈⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⠁⠀⠁⢁⠈⠉⢀⠀⡀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠀⣟⠉⣧⢻⠘
⣿⣿⣿⣿⣿⣿⣷⣶⣆⢸⣰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡄⠀⣾⣿⣷⡾⠓⠀⠀⠀⠀⢀⠀⠴⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠔⡠⢂⠐⡠⢂⠔⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⣷⣿⡗⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠄⠠⠈⠄⠡⠈⠄⠡⠈⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⢿⣿⡇⠀⢠⣤⣤⣤⣤⣶⣧⠀⣿⣿⡏⠀⠀⠀⠁⠀⠀⡁⠈⠀⠀⠀⠐⢀⠀⡁⢈⠀⡁⠈⠐⣿⣿⠋⠙⠁⠀⠀⠀⠉⠻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⢨⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⣿⠇⠀⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠀⠂⠐⠀⠂⠔⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸⣿⡇⠀⣄⡀⠈⣹⣏⣩⣾⠸⣾⣼⡣⠀⠀⠀⠀⠠⠀⠄⠠⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣿⡇⢸⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢨⣿⡿⢿⣿⣿⣿⣸⣿⣿⡷⠀⠀⠀⢀⠐⣈⠆⠐⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠙⠿⣿⣿⣿⠱⠀⠉⠛⠛⢛⠓⢦⢢⠐⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠻⣿⣿⣿⣿⡇⢸⠀⢸⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠈⢻⣿⣿⡀⠀⠀⠀⠀⠀⠁⠀⣣⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠋⠀⠐⠓⢻⣿⡇⢸⠀⢸⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⡇⠙⠀⠠⣿⣿⣧⠀⠀⠁⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠅⢸⠐⢸⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣤⡥⢀⣵⣷⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠋⣉⣴⣶⣶⣆⣭⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⢿⣶⡖⠀⠀⠀⠁⠀⠀⠀⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⠀⢾⣿⣷⢸⣟⣼⣿⣿⣿⣿⣿⣻⣿⣷⣿⡟⣿⣻⠟⣿⡃⣿⢿⣿⡿⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⣿⣹⡇⣿⣁⣿⣻⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠦⠀⡶⢲⡄⣶⢰
⣿⣿⣿⣿⣿⣿⣷⣶⡆⢸⡖⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡷⣿⠗⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⢀⠔⡠⢂⠔⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠨⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⠁⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⠀⢀⣀⣀⣀⣠⣴⣆⠀⣿⣿⡧⠀⠀⠀⠀⠁⠈⠄⠁⠈⠀⠁⠈⠀⠁⠌⠠⠁⠈⠀⢸⣿⣿⣿⢿⠿⠛⠛⠻⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡷⠀⢻⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢈⠀⡠⢈⠀⡁⢈⠀⢸⡿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠄⠉⠉⢻⣟⣉⣿⡾⡽⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠠⠀⠄⠠⠂⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢀⢈⣷⣶⢿⣿⣿⣿⢹⣷⣥⠎⠠⠀⠀⠀⠈⠀⡁⠈⠀⠁⠈⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⠿⣾⣿⣿⡏⢏⠙⠛⠿⠶⡦⢦⡐⢀⣦⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣟⢟⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠹⣿⣿⣧⠀⠀⠄⠀⠀⠀⠂⢹⡄⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⢿⠏⠀⠘⠻⢿⣿⡇⢸⠀⢸⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠘⠻⠋⠙⠂⠀⣹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠌⠁⠀⠀⠀⠀⠈⠢⠃⢸⠀⢸⠏⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⣤⡒⠁⢠⣴⣾⣮⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢘⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠋⡀⣴⣶⣶⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣦⣤⠤⠠⠀⠤⠀⠀⠀⠀⠀⠤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⢃⠾⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⡟⣿⣻⠿⣿⡿⣿⣿⣿⣿⡏⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣹⡇⣿⣁⣿⣸⡏⠏⠀⣾⣹⣇⣿⠸⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠀⡀⢀
⣿⣿⣿⣿⣿⣿⣷⣦⡄⢸⠐⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠧⠔⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⢀⠄⠠⠀⠀⠀⠀⠄⠀⠀⠰⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⡋⠃⢸⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡡⢀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⣀⣀⣀⣤⣶⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠔⡠⢂⠔⡡⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⡇⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⡁⢈⠄⡁⢈⠀⡁⢈⠔⢹⣿⣿⡿⠟⠟⠛⠛⠛⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⣽⣿⡇⡀⠀⠈⠙⠻⡟⢛⣽⣷⣿⣿⡇⠀⠀⠀⠀⠐⠀⠂⠀⠀⠂⠀⠀⠀⡀⢀⠀⠀⠀⠂⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠈⠲⣶⣺⣿⣿⣿⡿⡷⣛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠄⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣿⣿⣿⣿⣿⣯⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠛⢰⣿⣿⣿⡄⢫⡉⢒⠶⣦⠴⡤⡀⠠⡀⢈⠀⡀⢀⠀⡀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡇⠀⠀⢻⣿⣿⣷⠀⠁⢂⠐⠀⠀⡐⢈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⢹⢿⣿⣿⣿⡇⢸⠀⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠿⢿⠋⠙⠃⠃⢨⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠫⡫⠀⠀⠀⠋⠋⠉⡁⢸⠀⢸⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⣴⣚⣁⣀⣴⣶⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠁⠀⣦⣦⣶⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⣣⠶⢻⣿⣷⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⠟⣿⡋⣿⢿⡇⢉⣿⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡇⣿⣁⣿⣸⡇⠾⠋⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣷⣿⡟⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⡆⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠂⠄⠀⠀⠀⠀⠐⢀⠄⡀⢂⠔⡠⠂⠀⠀⠀⡀⢀⠀⡠⢂⠔⡠⢊⠔⡁⢂⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠁⠀⠀⠀⠄⠠⢂⠔⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⢘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡆⠀⣿⣿⡇⡀⠀⣀⣀⣤⣤⣴⣿⡆⢠⣁⡀⠀⠀⠀⡁⢈⠀⠀⠀⠀⠀⠀⠀⢀⠄⡡⢈⠄⡡⢊⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣧⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠔⡁⢊⠔⡡⢊⠔⡡⢺⣿⣿⣿⡿⡿⠿⠻⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⢧⣀⣿⣿⡇⣤⠀⠀⠉⢙⣿⣉⣼⣿⣿⣿⡇⠀⠀⠀⠀⠠⠂⠄⠡⠈⠄⠁⠊⠄⠁⠈⠀⠡⠈⠀⢩⣿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿
⣿⣿⣿⣿⣿⣿⣿⣿⡷⢸⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢶⠼⣿⣿⣿⡟⢿⠿⡳⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⡁⢈⠂⡀⢀⠀⡀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣟⣿⡇⢸⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠠⣿⣿⣿⣷⠈⢦⡄⠉⠋⠛⠋⠑⣄⠂⠐⠀⠂⠐⠀⠂⠐⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣾⣿⣟⡀⠀⠙⣿⣿⣿⣧⠀⠈⠠⠁⢄⠠⡀⢐⡁⠈⠀⠁⠈⠀⡁⠈⠀⠁⠈⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢯⢿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⢛⣹⠃⠀⢉⢁⣠⣾⣿⣿⣿⣇⠀⠀⠀⠂⠑⠀⠊⢷⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⢟⠲⠀⠑⠛⠿⣻⡃⢸⠀⢸⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣾⣿⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠙⠁⢸⠀⢸⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠃⢀⣶⣶⡶⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠟⢿⣿⠓⠁⠈⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⣬⢿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⡃⣿⢻⡇⢀⣟⣿⡻⠆⣿⢸⡇⣿⣾⡯⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣁⣿⣸⡇⠉⠃⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣘⣿⣿⣿⣛⣿⣃⣛⡛⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⢒⡂⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢀⠄⠠⠂⠀⠀⠀⠀⠀⠀⡠⢀⠄⡠⢂⠔⡠⢊⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⠝⡃⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⢀⠀⡠⢊⠐⡡⢊⠐⡁⢊⠐⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣆⢸⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡆⠀⣿⣿⡇⠆⠀⣤⣤⣶⣶⣿⣿⡆⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢊⠄⠡⠀⠄⠠⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⡄⠀⠻⣿⣿⣿⣿⠿⣿⢸⣿⡇⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠠⠀⠄⡠⠈⠄⡡⠈⢼⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠢⠿⠿⠇⠧⠀⠀⠀⢨⣷⣤⣾⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⡀⢊⠐⡁⢊⠐⡡⢚⣿⠿⠋⠀⠁⠀⠀⠀⠀⠉⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⠚⣿⣿⣿⣿⠘⣟⠣⠤⣤⣠⢤⡠⠀⠄⠠⠀⠄⠠⠈⠄⠡⠈⠀⠁⠀⠄⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣿⣿⣿⡿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣦⡀⠀⣿⣿⣿⣿⣇⠘⠁⢀⠀⡁⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⣿⠿⠟⢦⠠⠈⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠐⠈⢆⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠻⢿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⢁⡤⡶⠁⣀⣠⣤⣶⣿⣿⣿⣿⣿⡄⠀⠀⠄⠠⠀⠀⠁⢫⡄⠀⠈⠀⠁⠈⠀⠀⠀⠀⢠⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⡿⠂⠈⠘⠻⠛⠿⡇⢸⠀⢸⣿⠏⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⢸⡟⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣏⡛⠛⠛⠛⣛⡋⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⣤⣤⠀⠠⠌⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⢤⣿⠟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣓⠙⠻⠿⠿⠿⠿⠉⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⠠⣾⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⡃⣿⢻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡏⠟⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣟⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⣛⣻⣿⣛⣻⣃⣛⡛⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡶⡆⢸⢰⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠔⠠⠀⠀⠀⠀⠠⢀⠔⠠⠊⠔⠠⠂⠀⠀⠀⡀⢀⠐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⠗⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⡀⠀⠀⠠⢀⠄⡡⠊⠔⠁⠊⠀⠁⠀⠠⠀⠄⡠⢂⠔⡡⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣅⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡄⠀⣿⣿⡟⡇⠀⣶⣶⣾⣿⣿⣿⣇⢸⡇⠀⠀⠐⠁⠊⠀⠀⠀⡀⢀⠀⡀⢂⠔⡡⢊⠔⡡⢊⠔⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⣇⠀⠙⠿⢿⡿⠿⢛⣿⣼⣿⡗⠀⠀⠀⠀⠀⡠⠀⠔⠡⢊⠔⠡⠊⠔⠠⠀⠄⠡⠊⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⢋⠀⠀⢀⢠⣿⣶⣿⣿⠿⣿⠇⠀⠀⠀⠀⢈⠄⡁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣿⠟⠉⠊⠀⠀⠀⠈⠙⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠉⣻⣿⣿⣿⣆⠱⣎⠑⠻⠚⠔⠃⠂⡀⠀⠐⠀⠂⠐⠠⠂⠔⠀⢂⠔⡠⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡄⠀⠹⣿⣿⣿⣿⣄⠈⠘⠀⠀⠀⠠⠀⢄⠠⠀⠄⠡⠈⠄⠡⠈⠄⡡⠈⠔⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⣿⣿⣿⣿⣷⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⡠⠿⣛⠋⠙⠗⠊⣨⣿⣿⣿⣿⡄⠀⠀⡁⢀⠀⠀⠈⢷⡀⠂⠐⠀⠂⠀⠀⠂⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣄⣔⣿⣥⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣄⢀⠀⠀⠐⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢿⣋⠉⠹⠿⢿⣿⡇⢸⠀⢸⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠈⠆⡀⠈⠀⠀⠀⠀⢸⣿⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠈⠀⠀⠀⠀⠀⠻⠇⢸⠀⢸⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⠀⠀⢑⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⢷⠈⠉⡉⣉⡩⣕⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⡇⠁⠈⠂⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡰⡿⠛⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠈⠉⠉⠋⠙⠋⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⡃⣿⢻⡇⠀⠟⣿⡻⠆⣿⢸⡇⣿⣾⡏⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠉⠋⢸⣿⣿⢸⣏⣻⣿⣿⣿⣟⣿⢹⣿⣿⣿⣿⣿⣿⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⣛⣻⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡶⠆⢰⡆⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡠⠂⠄⠀⠀⠀⠀⠐⠀⢂⠔⡠⠂⠐⠠⠂⠐⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⠛⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢀⣠⣾⣷⡀⢠⡆⠁⠈⠀⠀⠀⠠⢊⠔⡡⠊⠐⠁⠈⠀⠁⠈⠠⠀⠄⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⡅⢸⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡄⠀⣿⣿⡇⡇⠀⢺⣿⣿⣿⣿⣿⣷⢸⡇⠀⠀⠐⠁⠊⠐⠁⠀⠀⠀⠀⠀⢀⠀⡠⢊⠔⡁⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⢇⣀⣿⣿⡇⣿⡀⠈⠛⠻⣟⢉⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠄⠠⢂⠔⡡⠊⠔⠡⠊⠔⠡⢊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⣿⣿⣿⡇⢻⠃⠠⣤⢤⡤⢬⠄⡁⢊⠀⡁⢈⠀⡁⢈⠀⡁⠈⠀⠁⢸⣿⣿⠟⠉⠊⠀⠀⠀⠈⠙⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢽⣿⣿⣿⣿⡀⠋⠔⡁⠊⠐⠁⠂⠀⠀⠀⡀⢀⠀⡀⢀⠐⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣶⣿⣆⡀⡈⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⣦⠐⠄⠠⠀⠄⡠⠈⠄⠠⠀⠔⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣾⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠄⣋⡭⠁⠀⣉⣡⣼⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⡀⢀⠀⠣⢀⠐⡀⠂⠀⠀⠂⠐⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣬⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⢀⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠫⠀⠙⠯⠿⠿⠇⢸⠀⢸⣿⠏⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠱⠆⠀⠀⠀⠀⣸⣿⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠑⠋⠁⠀⠀⠀⠈⠉⠃⢸⠀⢸⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⠂⠐⠡⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠛⠄⠀⢠⣠⣴⠞⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⠿⠿⣿⣿⣿⣿⡟⠁⢹⣿⠀⠈⠀⠀⠀⠀⢰⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠞⠟⠉⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠠⠜⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡃⣿⢻⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡏⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣟⢸⣇⣸⡏⠉⠋⢸⣿⣿⢸⣏⣸⣿⣿⣻⣟⣿⢹⣿⣿⣿⣿⣿⣿⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⣛⣻⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡒⠂⡇⡆⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⠀⠀⠀⢀⣴⣶⡀⠀⣰⡆⠠⠂⠄⠀⠀⠀⠀⠀⠠⠀⠔⠠⠀⠄⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⠻⠃⡇⡇⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⡀⠀⣤⣶⣿⣿⣿⣿⡄⣿⡇⠀⠀⠀⡠⢀⠀⡁⢊⠀⠁⠈⠀⠀⠀⠠⢀⠔⡠⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⡄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⠀⠀⣿⣿⣿⡇⠀⠸⢿⣿⠟⢛⣿⣿⡏⠀⠀⠀⠊⠐⠁⠀⠀⠀⠀⠀⢀⠐⡀⢂⠔⡡⢊⠔⡡⢊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠉⠚⠛⠛⠛⠓⠆⠀⠀⢸⣷⣾⣿⣿⡟⢻⠆⢀⣀⣀⣠⣀⢄⡠⠀⠄⠡⠊⠔⠡⠊⠔⠡⠈⠔⠡⢺⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣻⣿⣿⣿⣿⡄⢁⡔⡀⢀⠐⡁⠊⠐⠀⠂⠐⠀⠂⡐⢈⠀⡀⠀⠀⠀⢸⣿⡿⠋⠁⠉⠀⠀⠀⠈⠙⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡦⠀⠘⠿⣿⣿⣿⣷⡄⠈⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠄⠠⠂⠐⠀⠂⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⢿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⡾⠿⡛⠀⠻⠖⣰⣝⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠱⢎⠀⡁⢈⠀⡁⢈⠀⡁⠂⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣾⣿⠇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢃⠠⣖⣯⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠐⠀⠂⠀⠀⠉⠱⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣿⠁⡇⡇⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⣠⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡷⠢⠀⠉⢍⢯⢟⠀⡇⡃⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⢤⣤⠆⠀⡹⠀⠀⠀⠀⣿⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠈⠁⠀⡇⡅⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⢇⠉⠛⠛⠙⢈⣫⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠊⢻⡇⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠠⡜⠟⠋⣁⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⠈⠉⠙⠛⠋⠉⠉⠁⢀⠜⠁⠁⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢹⣟⢿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠆⣿⡃⣿⢻⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠋⢸⣿⣿⢸⣏⢰⣏⣿⣻⣟⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣈⣛⡻⠿⡛⠻⢃⠛⠛⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣯⣾⣿⢿⣾⣾⣷⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡷⠶⠂⡇⡆⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣠⣾⣦⡀⠀⣾⡆⠀⠀⡠⠀⠔⠠⠂⠄⠀⠀⠀⠀⠀⡀⢂⠔⡠⢂⠔⡠⢺⣶⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣟⠻⠂⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠠⣶⣿⣿⣿⣿⣷⡄⣿⠇⠀⠀⠔⠁⠈⠀⠀⠀⠠⠀⠄⠠⠊⠔⠡⠊⠔⠡⠊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣤⡀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠀⠀⣿⣿⣿⣇⠀⠘⠿⣟⠛⢩⣿⣿⣧⠀⠀⠀⠀⠀⢀⠀⡁⢈⠀⡡⠈⠀⠁⠀⠀⠀⠀⠀⠀⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⠀⠙⠛⠛⠛⠓⡂⠀⠀⣿⣿⣿⣿⣿⣿⠹⡆⠤⢄⣤⡤⢤⠤⡀⠀⠀⠀⠀⡀⠂⠐⡀⢂⠔⡠⢂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢽⣿⣿⣿⣿⣦⠈⢐⠀⠊⠀⠀⠀⠀⠂⠄⠠⠈⠔⠡⠈⠔⠡⢈⠔⡡⢺⣿⣿⠏⠉⠋⠁⠀⠉⠉⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣧⠀⠈⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠐⠰⣂⠐⠀⠂⠐⠀⠂⠐⠀⠂⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣼⠿⡛⠁⠛⠟⣹⣮⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠋⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣼⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢋⠈⢴⣛⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢌⠀⡁⠈⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⢿⣿⣿⣿⣿⠁⡇⡇⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣄⣀⠀⠀⠀⠀⠀⠀⠈⣂⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢟⡀⠈⠹⠿⢿⢿⠀⡇⠇⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣤⡂⠐⠹⠀⠀⠀⠀⣿⣯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⣿⠇⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⠇⠉⠛⠋⠀⠉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⣧⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠠⡶⠟⠋⣑⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⠙⠛⠛⠛⠛⠛⠉⠉⢀⠔⠁⠁⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢹⣟⢿⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⠇⣿⡃⣿⢻⡇⠀⠏⣿⡻⠆⣿⢸⡇⣿⣾⡯⣟⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠋⢸⣿⣿⢸⣏⢰⣏⣿⣻⣏⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣁⣿⣸⡇⠀⠈⣾⣹⣇⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠛⠻⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣽⢿⣟⣵⣾⣷⣿⣿⣿⣿⠁⠀⠀⠁⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣶⢶⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⢀⣶⣷⡄⠀⢰⣿⡤⠀⠀⠀⠄⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠐⡀⢂⠔⡠⢂⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⡷⢶⠄⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⣠⣾⣿⣿⣿⣿⣶⣸⡿⠃⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⡀⢀⠔⡡⢊⠔⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⡆⠀⠿⡿⡛⠋⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠁⠊⠐⠁⠀⠀⠀⠂⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠇⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠚⠛⠿⠿⠧⠄⠀⠐⣿⣿⣿⣿⣿⣿⠲⡤⠀⣀⣠⣠⠤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⠄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠁⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣆⠈⠀⠀⠐⠁⠈⠀⠈⠀⡀⢀⠀⡁⢊⠐⡁⢊⠐⡁⢊⢼⣿⣿⡿⠛⠟⠛⠉⠛⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡅⡇⡇⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣆⠀⠘⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠄⠀⠀⠐⠀⠊⠐⠀⢺⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠅⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣿⠿⠃⠾⡿⢻⣝⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣼⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣤⠶⢁⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠄⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⠟⠙⠂⠛⡛⠛⠿⠀⡇⠀⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣠⣤⣄⠄⠠⠊⠀⠀⠀⠀⣿⣟⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⣿⡏⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⠁⠛⠛⠉⠀⠸⢿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⠽⣇⠐⠁⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⢀⢤⠶⠖⡂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⠿⠿⠿⠿⠿⠿⠛⠛⠀⠐⠃⠂⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢹⣟⢿⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⡏⣿⡃⣿⢻⡇⠀⠏⣿⡹⠆⣿⢸⡇⣿⣼⡏⣟⣿⠼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⢰⣏⣿⢻⣏⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣷⣻⣫⣾⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣶⣶⣦⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⣴⣶⣄⠀⠀⣼⣦⠀⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣲⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣽⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢀⣴⣾⣿⣿⣿⣶⣄⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠩⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢲⠀⠹⣿⠿⠛⢻⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡀⢊⠐⡀⢊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡂⡇⠁⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⠀⢸⣿⣿⣿⣇⠀⠀⢿⣶⣾⣿⣿⣿⣿⢤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠠⠂⠀⠘⢻⣿⣿⣿⣿⣿⡆⠉⠈⠉⠉⠙⠩⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡂⡇⡀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠸⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⣽⣿⠟⠃⠀⠁⠀⠀⠀⠀⠉⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠅⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠟⣥⣴⢾⡻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠄⠁⠀⠀⠁⠈⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣿⣿⣿⣟⢻⣿⠁⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠘⣩⠅⠀⢈⣡⣶⣿⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⡀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣴⣴⣯⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⡏⣟⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⡀⠀⠈⡃⠀⠀⠀⠀⣴⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠀⠊⠛⢻⣿⠀⡇⠀⣿⡟⠉⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⠛⢿⠟⠛⠉⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡄⠊⠀⠀⠀⠀⠀⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⣿⠁⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⡀⠀⠀⣀⣀⣀⠕⣸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢉⠇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠠⢰⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢽⣟⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⢻⡇⠀⠏⣿⡹⠆⣿⢸⡇⣿⣾⡏⣟⣿⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⢰⣏⣿⢻⣏⣿⢹⣿⣿⣿⣿⣿⣿⡏⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡷⠏⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣮⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⡀⠶⠶⢖⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣷⣶⣤⣀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢀⣴⣿⣿⣦⡀⠀⣼⣿⡆⠀⢈⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠰⣿⣿⣿⣿⣿⣿⣦⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⠙⠁⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠘⠛⣉⢁⣺⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠔⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⡄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⠀⢸⣿⣿⢹⡆⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⡿⠀⠀⠉⠉⠉⠁⠀⠈⠸⢿⣿⣿⣿⣿⣿⡄⠉⠁⠙⠛⠛⠋⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⡆⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠛⠛⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣻⣿⣿⠟⠋⠙⠉⠁⠉⠉⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠂⡇⠇⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⣠⣤⡾⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢚⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣻⣿⣿⣿⣿⣿⢻⣿⠁⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠼⢛⠋⠀⠙⣉⣬⣦⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡽⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⡁⢠⡔⣃⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣽⠃⠉⠿⠿⠿⠿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⢿⣿⣿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⣷⡄⠀⠁⠀⠀⠀⠀⣿⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠃⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠛⠂⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠊⡇⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢰⣟⢿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⢻⡟⠛⠟⣿⡹⠆⣿⢸⡇⣿⣼⡏⢿⣿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠉⢸⣿⣿⢸⣏⣸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣿⣸⡇⠀⠀⣾⣹⣇⣿⠘⣿⡟⣿⡇⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠿⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣶⣶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣤⣤⣤⣤⣀⡀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣆⠀⠀⠀⣴⣄⠋⠙⢫⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣾⣿⣿⣿⣷⣄⠘⣿⣿⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⢤⠄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠙⡿⡿⠛⢻⣿⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣀⠂⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣄⠀⢸⣶⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠨⣿⣿⠼⠆⠘⠛⣿⣿⣿⣿⣿⣿⣿⠦⢄⠀⣀⣀⣠⣠⠄⡀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⢀⣸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠃⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⢫⣶⡾⠏⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠡⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⡜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣽⣿⣿⣿⣿⣯⣸⣿⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠟⡉⠁⠀⢉⣤⣾⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠿⢿⣿⣿⣿⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⣄⣠⣾⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠁⠀⢺⠿⠿⠿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡿⠉⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡾⠻⠿⠻⠋⠻⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⢿⠧⠀⠀⠀⠀⠀⠀⣿⠿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠃⠀⢸⣿⣷⢸⣟⢸⣟⣷⣽⡿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⣟⣿⡻⠆⣿⢸⡇⣿⣾⡏⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠉⢸⣿⣿⢸⣏⣰⣟⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣁⣿⣹⡇⠉⠁⣾⣹⣇⣿⠘⣿⡟⣿⡇⣸⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠟⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⣶⣶⣶⠖⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠀⠀⠀⠀⣀⠰⣿⠿⣻⢋⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣤⣀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣆⠀⢸⣿⣧⠁⠈⠔⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣛⠁⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠘⣿⣿⠿⠿⣿⣿⣷⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠐⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠙⠁⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠈⠠⣦⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⡄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⠀⠠⣿⣿⢇⠀⠿⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠟⠀⠘⠛⠛⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠉⠑⠀⠒⠲⠚⠓⠃⠒⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠁⠈⠀⡁⠀⢼⣿⣿⣿⠿⠛⠿⠟⠛⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⠖⣦⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻
⢿⣿⣿⣿⣿⡟⢻⣿⡇⡇⠁⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⡿⠋⠸⠿⠏⣁⡙⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠄⢤⡀⠀⠀⠀⠀⠀⣫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣾⣿⡅⡇⡆⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⣻⡇⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠈⢻⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣦⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⠿⢿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⣠⣶⣾⡿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡶⣶⣆⠀⠀⠀⠀⠀⠀⣿⣿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡏⠀⠘⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⡇⠉⢸⣿⣷⢸⣟⢹⣟⢿⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡿⠾⣿⢸⡇⣿⣼⡏⢟⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⡚⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⢰⣯⣿⣻⣏⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⡇⡿⠟⣿⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⡟⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⡉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⠚⠀⠀⠀⠀⠀⠀⠀⡆⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂⠀⠠⢲⣶⣶⣶⡶⢂⠔⡠⠂⠀⠀⠀⠀⢀⠔⡠⢂⠔⠠⠂⠄⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⠀⠀⢡⢿⣿⣿⠕⡁⠊⠀⠀⠀⡀⢀⠔⡡⢊⠀⠁⠈⠀⠀⠄⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣷⣶⣦⣤⣄⡀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣧⣀⠀⣾⣿⡆⠊⠔⠡⠊⡀⢀⠐⡠⠊⠄⠁⠀⠀⠀⠀⡀⢂⠔⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠻⠃⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢻⣿⠿⠛⣿⣿⣿⣆⣻⣿⡇⠁⠀⠀⠈⠔⠁⠈⠀⠀⠀⠀⠀⠄⡠⢊⠔⡡⠊⠔⡡⠊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣀⠀⣶⣦⣼⣿⣿⣿⣿⣿⣇⠀⠂⠀⠀⠀⠀⢀⠀⡀⢀⠐⠀⢊⠐⠁⠊⠐⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⡄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⠀⠈⣿⣿⡄⠻⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⡀⢂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⠠⠴⠿⠿⠓⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠳⠂⠐⠤⢤⡴⠲⠖⠠⠀⠀⠀⠀⠄⡡⢊⠔⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠊⠐⠡⠂⠐⠀⠊⠐⠀⠂⠐⠀⠊⠐⣹⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣶⣬⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣌⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠙⢿
⢿⣿⣿⣿⣿⣿⢻⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣩⣶⡶⠋⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠑⡑⢌⠀⡀⢀⠀⡀⠀⢼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣾⣿⠇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠐⢿⡏⠀⣿⣿⣼⣿⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⠀⠄⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠋⢻⣿⣿⣿⠀⡇⠃⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⢀⣰⣻⣧⣶⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠍⠁⠀⠀⠀⠀⠹⠋⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⣶⣾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡿⠀⠘⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⡟⠟⢹⣿⣷⢸⣿⢾⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣸⡇⣿⣾⡏⠟⣿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⢰⣏⣿⣿⣟⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇⣿⣿⣿⣿⣇⣿⠘⣿⡟⣿⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⡛⠃⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠨⠻⠑⠊⡉⢰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠂⠠⢲⣶⣶⣶⡶⢂⠔⡠⠂⠀⠀⠀⠀⢀⠔⡠⢂⠔⠠⠂⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣄⠀⠀⠀⢀⡀⢑⣿⣿⢯⠕⡡⠊⠀⠀⠀⡀⢊⠔⡡⠊⠐⠁⠀⠀⠀⠀⠠⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣤⣀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡌⠰⣿⣿⡄⠊⠔⠡⠊⠀⢀⠐⡠⠊⠄⠁⠀⠀⠀⠀⡀⢂⠔⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⡛⠃⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠿⢛⡉⠻⣿⣿⣿⣾⣿⣿⡃⠀⠀⠀⠈⠄⠁⠈⠀⠀⠀⠀⠀⠄⡠⢈⠔⡡⠊⠔⠡⠊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠙⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠂⠀⠀⠀⠀⢀⠀⡀⢀⠐⠀⢊⠐⠁⠊⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⡄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⠀⠈⣿⣿⡈⠑⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠐⡀⢂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠟⠀⠔⠛⠛⠒⠀⠰⢿⣿⡿⣿⣿⣿⣿⣟⠳⠒⠐⠶⢶⠶⠒⠒⠢⠀⠀⠀⢀⠄⡡⢊⠔⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠊⠀⠡⠂⠐⠀⠊⠐⠀⠂⠐⠀⠊⠐⢹⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣶⣶⣽⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠈⠙⢿
⢿⣿⣿⣿⣿⡿⢻⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣩⣤⡶⠋⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡑⢈⠐⡑⢆⡀⡀⢀⠀⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣾⣿⠇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠰⢿⡏⠀⣿⣿⣼⣿⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠄⠠⠀⠄⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠋⠹⣿⣿⣿⠀⡇⠃⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠀⠠⢺⣧⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠈⠉⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣤⣄⣴⣶⣦⡀⠀⠀⠀⠀⠀⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡿⠀⠈⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠛⠟⢻⣿⣿⢹⣿⢽⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣸⡇⣿⣼⡏⠟⣿⠟⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⠻⠁⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⢰⣏⣿⣿⣟⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇⣿⣟⣿⣹⣇⣿⠘⣿⡟⣿⡇⢰⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⡛⠃⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⠻⠀⠊⡙⢰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣆⠀⠀⠀⠀⠀⠐⠰⣾⣶⣷⠖⡠⢂⠔⠠⠂⠀⠀⠀⡀⢂⠔⡠⢂⠔⠁⠂⠀⠀⢺⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣤⣤⣤⣄⣀⠀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡀⠂⣠⣤⣄⠐⢛⠟⡡⢊⠔⠁⠀⠀⠀⠄⠠⠀⠔⠡⠊⠄⠁⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣷⣦⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠽⣿⣿⣿⣄⣿⣿⣿⠀⠡⠊⠐⢁⠀⠀⢀⠄⡁⢊⠀⠁⠈⠀⠀⠀⡀⢀⠔⡠⢂⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⢦⡄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠔⠠⢊⠔⡡⢊⠔⡡⠊⢼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡝⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠈⠄⠁⠈⠀⠁⠈⠀⠁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⠐⣻⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⢀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠐⠊⠉⠁⠀⠈⠙⠋⠉⢿⣿⣿⣿⣿⣏⠀⠀⠈⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠂⠔⠠⠂⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⠀⢀⡁⢈⠀⡁⢈⠀⡁⢈⠄⡁⠈⢼⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠷⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⡷⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠹
⣽⣿⣿⣿⣿⣯⣸⣿⠃⡇⠁⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⡋⢡⡶⠞⠃⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠖⠠⠀⠀⠀⠀⠄⠀⢺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠻⢿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⢿⡏⠀⣿⣿⣼⣿⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠕⠀⠂⠐⠀⠂⠀⠡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠀⠀⠀⠻⠿⢿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⡞⠋⠀⠀⢺⣧⣶⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⡄⣀⠀⣀⣀⡀⠀⣠⣤⡠⡈⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⠿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⣿⠯⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡟⠀⠈⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠻⠛⢻⣿⣿⢹⣿⢽⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⣟⣿⡻⡏⣿⢸⡇⣿⣼⡏⢟⣿⠑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⢸⣯⣿⣿⣏⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣽⡇⠛⠋⣾⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠙⠂⠀⡘⢀⣿⣿⣝⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⣿⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣆⠀⠀⠀⠀⠀⠐⠰⣾⣶⣷⡖⡠⢂⠔⠠⠂⠀⠀⠀⡀⢀⠔⡠⢂⠔⡠⠂⠐⠀⢺⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣤⣤⣤⣤⣀⣀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⡀⢀⣠⣦⡄⠐⢛⠟⡣⢊⠔⠁⠈⠀⠀⠄⠠⢀⠔⡡⠊⠔⠁⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣶⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠛⠉⢿⣿⣿⣷⣠⣿⣿⡇⠀⡡⢊⠐⢁⠀⡀⢀⠐⡡⢊⠀⠁⠈⠀⠀⠀⡀⢀⠄⡠⢂⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡧⢶⠆⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠠⢊⠔⡡⢊⠔⡡⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⠊⠔⠡⠈⠄⠁⠈⠀⠁⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣷⠐⣺⣿⣿⣿⣿⣿⣿⣿⣧⣀⣄⣀⠀⣀⣀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠐⠛⠐⠊⠉⠁⠀⠈⠙⠋⠉⢿⣿⣿⣿⣿⣏⠐⠀⠈⠝⠁⠊⠀⠁⠀⠀⠀⠀⠀⠀⠄⠠⠀⠔⠠⠂⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠄⡁⢈⠀⡁⢈⠀⡡⢊⠄⡁⠈⢼⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠷⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻
⣿⣿⣿⣿⣿⣧⣼⣿⠃⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡉⢠⡶⠞⠃⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢫⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠛⢿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⢿⡏⠁⣿⣿⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠀⠀⠈⠙⠻⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁⠠⢸⣇⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⡄⣀⠀⣀⣀⣀⢀⣠⣄⡠⠀⠀⠀⠀⠀⠀⢀⢔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⠿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⠀⠀⠀⠀⠀⠀⣿⡻⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡏⠀⠸⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠿⠟⢻⣿⣿⢹⣿⢽⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣟⣿⡻⠏⣿⢸⡇⣿⣼⡏⢟⣿⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣏⢸⣯⣿⣿⣏⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣹⡇⠛⠉⣾⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠐⠊⠓⠈⢑⠂⣾⣿⣝⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⣿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠐⠰⣶⣶⣶⠖⡠⠂⠔⠀⠀⠀⢀⠀⡠⢂⠔⡀⠂⠐⠀⠀⠀⠀⢼⣶⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣤⣤⣤⣤⣄⣀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣄⠀⢀⣠⣤⡀⠠⢛⠟⡱⢊⠔⠀⠀⠀⢀⠔⠠⠊⠐⠁⠀⠀⠀⠀⡀⠀⠔⡠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢷⠄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⢋⢿⣿⣿⣷⢠⣿⣿⡇⠀⠁⠈⠀⢁⠄⡁⢈⠀⠁⠈⠀⠀⠀⠀⢀⠔⡡⢊⠔⡡⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡧⢶⠆⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣶⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⡠⢂⠔⡡⠊⠔⠡⠊⠔⠁⠊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⡀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⠫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠈⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣧⠄⣺⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⡡⢈⠄⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠠⠟⠀⠒⠋⠉⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⣏⠐⠀⠉⠙⠋⠉⠀⠁⠄⠀⠂⠐⠀⠂⠐⠠⠂⠔⠠⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⢼⣿⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠅⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡷⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻
⣿⣿⣿⣿⣿⣷⣼⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣁⡶⡶⠋⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠈⠱⡄⠄⠠⠀⠄⠀⠀⠄⠀⢪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠛⠛⠟⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣿⡇⠁⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⠆⠀⠀⠀⠀⠀⠀⠀⡡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠀⠀⠀⠁⢙⠛⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⠁⠁⢼⣇⣠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⡄⡀⠀⣀⣀⡀⢀⣀⣠⡁⠀⠀⠀⠀⠀⠀⠀⢔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⠀⠀⠀⠀⠀⠀⣿⣻⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡟⠀⠸⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⢿⡿⣻⣿⣷⢻⣟⢽⣿⠿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣟⣿⡻⠏⣿⢸⡇⣿⣼⡏⢟⣿⠡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣟⢲⣏⣿⣿⣟⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣻⡇⠛⠉⣾⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠁⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠠⠘⠐⠈⠩⠆⣼⣮⣟⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠒⠔⢠⣶⣶⣶⡖⡠⠂⠀⢀⠀⡀⢀⠔⡠⢂⠐⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣦⣤⣤⣤⣤⣀⡀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⡄⠀⢀⣠⣄⠀⠠⢊⠝⡫⠞⠀⠀⠔⡠⠂⠔⠀⠀⠀⠀⠀⠀⢀⠔⡠⢂⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠷⠄⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⢛⣿⣿⣿⣧⢸⣿⣿⡇⠀⡁⠀⠠⢂⠔⠁⠈⠀⠁⠀⠀⠀⠄⡠⢊⠔⡡⢊⠔⡡⠊⠄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠷⠆⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠂⠀⠁⠀⠀⠀⠀⡠⢀⠐⡀⢊⠔⠁⠊⠐⠀⠂⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣀⡀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠐⡠⢂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠐⣿⣧⠩⢽⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠡⢈⠔⡡⢈⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⠤⠔⠛⠉⠀⠙⠻⠿⠛⣿⣿⣿⣿⣿⣟⠉⠉⠚⠻⢋⠉⡁⠂⠐⠀⠂⠐⠀⠊⠐⠀⠂⠐⠀⠊⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢈⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⠁⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣮⣹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢦⡀⢈⠀⡁⢀⠀⡀⢀⠀⡀⠀⢼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠉⠻
⣾⣿⣿⣿⣿⣷⣼⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⢁⣤⡷⠎⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⠐⢠⠀⠀⠀⠈⠄⠀⠀⠄⠀⢊⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠉⠹⢿⢿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡗⠃⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠁⠈⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⠀⠀⠀⠀⢙⡻⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠃⢀⣹⡇⣠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⡀⡀⠀⢀⡀⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢔⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣾⠟⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡟⠀⠸⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⣿⣿⣿⣿⣷⢺⣿⣻⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣟⣿⡻⡟⣿⢸⡇⣿⣼⡏⢟⣿⠃⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣟⢲⣟⣿⣿⣟⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣕⣿⣿⡇⠟⠋⣿⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠟⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠠⠔⠆⠚⢡⡄⣸⣿⣻⣿⣿⣾⣿⣷⣟⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠐⠀⠒⠤⢢⣶⣶⣖⡴⠀⠀⡠⢂⠔⠠⠂⠀⠀⠀⠀⢀⠄⡠⢀⠄⡠⢂⢴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣶⣶⣶⣦⣤⣄⣀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡄⠀⡄⢀⣀⠀⠁⠊⠟⢛⠔⡡⠊⠔⠀⠂⠀⠀⠀⡀⢂⠔⡡⢊⠔⡡⢊⠐⠁⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠷⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⣿⣿⣿⣦⢈⣿⣿⡇⠀⢋⠔⠡⠊⠄⠀⠀⠀⢀⠀⡠⢊⠔⠡⠊⠔⠁⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡗⠷⠆⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣤⣼⣿⣿⣿⣷⣿⣿⣇⠀⠠⠂⠀⠀⠀⡀⢈⠄⡁⠊⠀⠁⠀⠀⠀⠀⠠⢀⠄⡠⢂⠔⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣄⡀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⡠⢊⠔⡡⢊⠔⡡⢊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣦⡉⢽⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⠡⠀⠄⠡⠈⠄⠡⠈⠄⠡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⠿⠤⠬⠛⠛⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⡏⠩⠐⠲⠶⢒⠒⠢⢂⠀⠀⠀⠀⠀⠀⠀⢀⠂⡀⠀⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡁⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢘⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠐⠀⠂⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⡿⣿⣿⠁⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣦⣭⣻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠠⠈⡄⠡⠊⠀⠁⠈⠐⡁⢈⠄⡁⠈⢼⣿⡿⠟⠋⠁⠀⠁⠀⠀⠉⠛⢿
⣾⣿⣿⣿⣿⣷⣼⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⢋⣥⣽⠟⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠫⠐⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠉⠛⠿⢿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡗⠋⣿⣿⣹⣿⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠈⠀⠈⠙⠛⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠆⠀⣹⡇⢠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣯⣤⣤⣤⣬⣵⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡟⠀⢹⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⣿⣿⢿⣿⣿⢿⣿⢿⣟⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⡟⣿⢸⡇⣿⣼⡏⢟⣿⠂⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣯⢽⣟⣿⣿⣟⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⡇⠿⠟⣿⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠟⠃⠁⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⢀⢠⠠⠌⢁⡄⣸⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠐⠲⠒⠖⣀⢐⣶⣶⢖⡠⠂⠀⢀⠀⡠⢂⠔⠠⠂⠐⠀⠀⡀⢀⠀⡀⢀⠄⣰⣶⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣶⣶⣶⣦⣤⣀⡀⠀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡄⠀⠀⠀⠀⠀⠈⠜⠹⠎⡠⠀⠄⡡⠊⠄⠁⠈⠀⠀⠄⡠⢂⠔⡡⢊⠔⡡⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠷⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⢿⣿⣷⣦⠐⣾⣿⣧⠀⠀⡀⢈⠔⡁⠊⠀⠀⠀⠀⢀⠀⡡⢊⠔⡡⢊⠀⠁⠈⠀⠁⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠳⠂⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣤⣄⣩⣿⣿⣿⣾⣿⣿⣿⠀⠊⠀⠀⠀⠀⠀⠀⠠⠀⠐⠡⠂⠐⠀⠀⠀⠀⠀⠀⢀⠄⡠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣄⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠀⢸⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠀⠀⠀⠀⢀⠄⡠⢀⠔⡡⢊⠔⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⡂⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣦⢋⣻⣿⣿⣿⣿⣿⣿⣿⣇⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠐⡡⢊⠐⡡⢊⠔⡡⢊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡆⡇⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣀⡸⠿⠿⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠀⢤⣤⠤⡤⢄⠔⠀⠀⠀⠀⠀⠄⠀⠀⠄⠠⠀⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠅⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡀⠀⠀⠁⠈⠐⠀⠈⠀⠀⠀⠀⠀⠄⠀⢀⠀⠡⠀⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⣬⣞⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⠐⡀⠂⠐⠀⠂⠐⠀⠂⠐⠠⠂⠐⣹⣿⡿⠟⠻⠛⠉⠙⠛⠻⢿⣿⣿
⣾⣿⣿⣿⣿⣷⣾⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⣋⣛⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢶⠠⠀⠀⠡⠈⠀⠁⠈⠀⠡⠈⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⠏⠉⠹⠻⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⠖⣿⣿⢻⣿⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠉⠉⠋⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠌⢻⡇⢀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠂⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣏⣁⣀⣀⣈⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣴⣶⣦⣴⣶⣿⡄⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣿⣷⣿⣾⣿⣿⣿⣿⢿⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣾⡏⠟⣿⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⣿⠃⠀⠈⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣟⣻⣯⣿⣿⣟⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣓⣿⣿⡏⣿⠿⣿⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠻⠿⠛⠻⠃⠛⠛⡟⠃⠁⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠀⡈⠌⢉⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠰⠒⠂⢀⠔⣶⣶⡖⡠⠂⡀⢀⠔⡠⠂⠐⠀⠀⠀⢀⠀⡠⢀⠔⡠⢂⠄⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣶⣶⣶⣶⣦⣤⣀⡀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣄⠀⠀⠀⠀⠀⠈⠙⠉⠟⡡⢊⠄⠡⠊⠀⠀⠀⠀⢂⠔⡠⢊⠔⠡⠊⠐⠀⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣮⠐⣾⣿⣧⠀⠐⡡⢊⠔⠁⠀⠀⠀⠀⡠⢈⠄⠡⠊⠀⠁⠈⠀⠀⠀⡀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠻⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣡⣄⣩⣿⣿⣿⣾⣿⣿⣿⠀⠂⠀⠀⠀⠀⠂⠔⠠⠂⠐⠀⠀⠀⠀⠀⡀⢀⠀⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣧⣤⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣄⠀⢸⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠔⡡⢊⠔⡡⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣦⠛⣻⣿⣿⣿⣿⣿⣿⣿⣇⣤⣠⠀⠀⠀⠀⠀⠀⠠⢀⠄⠁⠈⠀⠁⠈⠀⠁⠈⠀⡁⠊⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣀⣸⠿⠿⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠠⢤⣤⡤⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⠀⡀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡁⠀⠄⠁⠀⠀⠀⠀⠠⠀⠄⠠⠀⠄⠠⠈⠄⠠⠈⠄⡠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⡿⢿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣴⣬⣚⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠐⠀⢂⠐⡀⠂⠐⠀⢊⠐⣹⣿⡿⠿⠿⠟⠛⠟⠿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣷⣾⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⣋⣓⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿
⣿⣿⠏⠉⠻⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠖⣿⣿⢻⣿⣹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠀⠀⠀⠀⠈⠻⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠌⢺⡇⢀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣋⣁⣀⣀⣈⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤⣶⣤⣤⣶⣷⡆⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣿⣷⣿⣿⣿⣿⣽⣿⢽⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣾⡏⠟⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣟⣻⣯⣿⣻⣿⣿⢸⣯⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⡏⣿⡿⣿⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠅⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⢀⡈⠌⢉⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠒⠲⠒⠒⢄⠔⣶⣶⡖⡠⠂⡀⢀⠔⡀⠂⠐⠀⠀⠀⢀⠀⡠⢀⠔⡠⢂⠄⣰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣶⣶⣶⣦⣀⡀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣄⠀⡀⠀⣀⠀⠈⠙⠉⠞⡠⢊⠔⠡⠊⠀⠀⠀⠀⠂⠔⡠⢊⠔⠡⠊⠐⠀⠂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⠛⠀⡇⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣮⠀⣾⣿⣷⠀⠐⡡⢊⠔⠁⠀⠀⠀⠀⡠⢈⠄⠡⠊⠀⠁⠈⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠛⠀⡇⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢡⣄⣨⣿⣿⣿⣮⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⠐⠀⠂⠀⠀⠀⡀⢀⠀⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⣿⣿⣿⣿⣿⣿⣷⣤⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⠀⢸⣷⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢂⠔⡡⢊⠔⡡⢊⠔⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣧⢈⣩⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⠀⠀⠀⠀⠀⠀⡀⠈⠄⠁⠈⠀⠁⠈⠀⠁⠈⠀⡁⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣀⡸⠿⠟⠀⠺⢿⣿⡿⣿⣿⣿⣿⣿⡿⢛⡀⠤⣤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢿⣿⣿⣿⣿⡀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠄⠠⠈⠄⡡⢈⠄⡠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⡿⢻⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣬⣞⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠐⠀⢂⠐⡀⠂⠐⡁⢂⠐⣹⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⣋⣻⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿
⣿⣿⠋⠁⠙⣻⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠆⣿⣿⢻⣿⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠈⠝⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠈⢻⡇⢠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣏⣁⣀⣈⣈⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤⣶⣦⣤⣶⣿⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⣷⣿⣿⣿⣿⣽⣿⢿⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣾⡏⢟⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠇⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣻⣯⣿⣿⣟⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⡇⣿⠟⣿⣹⣇⣿⠘⣿⡟⣿⡇⢸⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠻⠿⠛⠻⠃⠛⠛⠟⠃⠁⠀⠀⠈⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⢀⠀⠜⢁⠀⣬⣻⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠒⠲⠂⠒⢄⠔⣲⣶⡖⡠⠂⡀⢀⠔⡀⠂⠐⠀⠀⠀⢀⠀⡠⢀⠔⡠⢂⠄⣰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣶⣦⣤⣀⠀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣆⠀⠀⠀⣀⡀⠈⠔⠉⠎⡠⢂⠄⠡⠊⠀⠀⠀⠀⠂⠔⡠⢊⠔⠡⠊⠐⠀⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣋⠀⡇⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⣾⣿⣷⠀⠐⡠⠊⠔⠁⠀⠀⠀⠀⡠⢈⠄⠡⠊⠀⠁⠈⠀⠁⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠙⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢡⣤⣨⣿⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠔⠠⠂⠐⠀⠀⠀⠀⠀⡀⢀⠀⡠⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⠀⢸⣷⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢀⠔⡡⢊⠔⡡⢊⠔⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣷⢈⣩⣽⣿⣿⣿⣿⣿⣿⣷⣤⣦⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠈⠐⠁⠈⠀⠁⠈⠀⡁⠊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣀⠸⠿⠟⠀⠺⢿⡿⠿⣿⣿⣿⣿⣿⡿⢛⠀⡤⣤⠤⡤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠄⠠⠈⠄⡠⠀⠄⠠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢿⣿⣿⣿⣿⡟⢻⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣤⣟⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠐⠀⢂⠐⠀⠂⠐⠁⢂⠐⣩⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⣉⣻⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⠀⠁⠀⠀⠀⠈⠙⠿⣿⣿
⣿⣿⠃⠀⠉⠻⢿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡧⠆⣿⣿⢻⣿⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠛⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠈⢻⡇⢀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢚⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣍⣁⣠⣤⣈⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣶⣶⣤⣶⣿⣇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⣷⣿⣾⣿⣿⣽⣿⢿⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣾⡏⢟⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠁⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣹⣯⣿⣽⣟⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣓⣿⣿⡇⣿⠟⣿⣹⣏⣿⠘⣿⡟⣿⡇⢸⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠉⠀⠀⠈⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⢀⢠⠀⠌⢁⠀⣨⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⢀⣀⠀⠐⠲⠊⠒⢀⠔⣲⣶⡖⠠⠂⡀⢀⠔⡀⠂⠀⠀⠀⡀⢀⠄⡠⢂⠔⡠⢂⠄⣰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣶⣶⣤⣄⠀⡇⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣆⠀⠀⠀⣀⠀⠈⠐⠉⠞⡠⠊⠔⠁⠀⠀⠀⠀⠀⢂⠔⡠⠊⠔⠡⠊⠐⠀⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣉⠀⡇⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣮⠀⣽⣿⣷⠀⠐⡡⢊⠔⠁⠀⠀⠀⠄⡡⢈⠄⠡⠈⠀⠁⠀⠀⠀⠀⡠⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠉⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢡⣤⣨⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⡠⠀⠔⠠⠂⠐⠀⠀⠀⢀⠀⡀⢈⠔⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⠀⢸⣷⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡡⢊⠔⡡⢊⠔⡡⠊⠔⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣷⢈⣩⣽⣿⣿⣿⣿⣿⣿⣿⣴⣶⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠈⠀⠁⠈⠀⠁⠀⠠⡁⠊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⢀⡸⠿⠟⠀⠺⢿⡿⡿⣿⣿⣿⣿⣿⣿⢋⠀⡤⣤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⡀⢂⠐⡀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠡⠀⠄⠠⠀⠄⠠⠈⠄⠡⠈⠄⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢿⣿⣿⣿⣿⣏⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣮⣞⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠐⠀⢂⠐⡀⠂⠐⡀⢊⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠛⣋⣻⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠟⠉⠀⠁⠀⠀⠈⠉⠻⢿⣿⣿
⣿⠿⠁⠀⠈⠹⠿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡧⠖⣿⣿⢻⣿⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠴⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠈⢻⡇⢀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣏⣉⣀⣀⣈⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣠⣶⣦⣤⣶⣿⣇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣿⣷⣿⣿⣿⣿⣽⣿⢿⣟⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣾⡏⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠄⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣟⣻⣯⣿⣽⣟⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣓⣿⣿⡇⣿⠟⣿⣹⣏⣿⠘⣿⡟⣿⡇⢸⡇⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠟⠃⠍⠀⠀⠈⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⢀⠀⡀⠬⢋⡀⣨⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠖⠒⠀⠀⠀⠴⠶⠒⠤⢆⠐⢶⣶⣶⢂⠔⠀⠂⠀⢀⠀⠠⢀⠔⠠⠀⠀⠀⠀⠀⠀⠀⡀⢲⣶⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦
⣿⣿⣿⣿⣿⣶⣦⣤⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣄⠀⠀⠀⠀⠀⠐⡡⠊⠕⠁⠀⠀⢀⠔⡀⠂⠐⠁⠂⠀⢀⠀⡠⢀⠔⡡⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣭⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣎⠀⣴⣿⣷⠀⠀⠁⠐⡠⢊⠔⠁⠈⠀⠀⠀⠀⢀⠔⡠⢊⠔⡡⢊⠔⠡⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠈⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢋⣉⣘⣿⣿⣿⣦⣿⣿⣿⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠠⢈⠔⠡⠊⠄⠁⠈⠀⠁⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⠀⢸⣷⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠐⠁⠂⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⢀⠔⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣧⠘⣛⣻⣿⣿⣿⣿⣿⣿⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⠡⢊⠔⡡⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⠀⢸⣿⠿⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢀⣀⣠⢀⠄⡁⠀⠀⠁⢈⠐⡁⢈⠀⡁⢊⠐⡁⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄⠀⠀⠊⠀⠡⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣟⣹⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣬⣾⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⢗⡻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠀⠰⢆⠀⠀⢊⠀⠀⢂⠐⠀⠂⠀⡹⠟⠉⠀⠁⠀⠀⠀⠉⠻⢿⣿⣿
⣿⠟⠃⠀⠁⠂⠋⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡅⣿⣿⢿⣿⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠀⠘⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢿⡇⢀⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣟⠛⠁⣀⡈⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣀⣤⣤⣀⣤⣶⡗⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣟⣧⣼⣿⣿⣿⣹⣿⣽⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣼⡏⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠆⠀⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣟⣺⣟⣿⣻⣿⣿⢸⣯⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⡏⣿⣟⣿⣻⣟⣿⠘⣿⡟⣿⡇⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠍⠀⠀⠈⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠑⠀⠀⠀⠀⠀⣘⠍⠈⢩⡾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡗⠚⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⠀⠀⠀⠀⠀⡇⡆⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠒⠂⠀⠀⠠⠶⠒⠤⢀⡠⢲⣶⡶⢂⠐⠀⠀⡠⢀⠔⠠⠂⠀⠀⠀⠀⢀⠐⡀⢀⠄⡠⢒⣴⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦
⣿⣿⣿⣿⣿⣷⣶⣤⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣄⠀⠀⠀⠀⠀⠐⠁⠊⠀⢀⠀⡀⢊⠐⠁⠀⠀⠀⠀⠠⢈⠔⡡⢊⠔⡁⠊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡯⣤⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣄⠀⣴⣿⣷⠀⠀⢀⠐⡡⠊⠀⠀⠀⠀⢀⠐⡀⢊⠔⡡⠊⠐⠀⠂⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠈⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢋⣉⢙⣿⣿⣿⣆⣿⣿⣿⠀⠀⠁⠈⠀⠀⠀⠠⢀⠄⠡⠊⠀⠁⠀⠀⠀⠀⠀⢀⠄⡠⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⠀⢸⣷⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⢈⠐⡡⢊⠔⡡⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣇⠙⢛⣻⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠡⠊⠔⠡⠂⠔⠁⠂⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⠀⢈⣿⡿⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣀⣀⣀⡀⡁⠈⠀⠀⠈⠀⠁⠈⠠⠀⠈⠠⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁⠁⠹⣿⣿⣿⣿⣿⡌⠅⠁⠋⠀⠀⠀⠀⢂⠀⡀⢀⠀⡀⢀⠐⡀⢂⠀⡀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⡏⣹⣿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄⣶⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠄⠠⠀⠄⠀⢚⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⢽⣧⠀⠘⡿⠿⣿⢿⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠟⢶⣻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠠⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⠋⠁⠀⠁⠀⠀⠀⠉⠻⢿⣿⣿
⠞⠈⠀⠀⠂⠘⠺⠎⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡡⣿⣿⢿⣿⣹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⡇⢀⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣶⡞⠛⠁⠀⠈⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣤⣀⣀⣤⣶⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣟⣧⣴⣿⣿⣿⣻⣟⣿⣿⣿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣼⡏⠟⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⠏⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢹⣯⢻⣟⣿⣻⣿⣿⢸⡯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣏⣿⣿⣿⣻⣟⣿⠘⣿⡟⣿⡇⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠁⠍⠀⠀⠘⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⢚⠋⠉⢉⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⠚⠛⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣄⣀⣠⣄⣀⠀⠀⠀⠀⣶⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠒⠂⠀⠀⠠⠶⠒⠤⢀⠰⢶⠶⡶⢂⠐⠀⠀⡠⠀⠔⠠⠂⠀⠀⠀⠀⢀⠀⡠⢀⠄⡠⢒⢴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣷⣤⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣄⠀⠀⠀⠀⠀⠐⡡⠊⠀⢁⠐⡀⠊⠐⠁⠂⠀⠀⠀⠠⢈⠔⡡⢊⠔⡡⠊⠔⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣤⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣄⠀⣴⣿⣧⠀⠀⠀⠔⡡⠊⠀⠀⠀⠀⢀⠐⡀⢊⠔⠡⠊⠐⠁⠂⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠈⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢏⡉⢙⣿⣿⣿⣦⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠡⠈⠀⠁⠀⠀⠀⠀⠀⢀⠄⡠⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠀⡡⢊⠔⡡⢊⠔⡡⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣆⠙⢛⣻⣿⣿⣿⣿⣿⣿⣷⣾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠡⠊⠔⠁⠂⠔⠁⠊⠔⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⠀⢘⣿⡿⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣀⣀⣀⡀⡁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠄⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠹⣿⣿⣿⣿⣿⡌⠀⠁⠊⠀⠀⠀⠀⢀⠀⡀⢀⠀⡀⢀⠐⡀⢂⠀⡀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣿⣿⣏⣽⣿⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣐⡴⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠄⠠⠀⠄⠡⠀⠄⠀⢪⣿⣿⡿⣿⠿⢿⢿⣿⣿⣿⣿⣿
⣿⠶⠘⠽⡿⡿⣿⢿⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠟⢾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠠⢱⢌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣟
⠉⠀⠀⠀⠀⠙⠉⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡡⣿⣿⢿⣿⣹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⡏⢀⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶⡾⠛⠁⠀⠊⢁⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣠⣀⣀⣤⣮⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣟⣣⣴⣾⣿⣿⢻⣿⣿⣿⣿⣿⡿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣼⡏⢟⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠛⠛⢸⣿⣿⢹⣯⢿⣿⣿⣻⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣏⣿⣿⣿⣻⣟⣿⠘⣿⡟⣿⡇⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠁⠍⠀⠀⢘⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠉⠀⢚⠛⠋⢉⢾⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⡷⠚⠛⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣤⣤⣤⣄⣀⠀⠀⠀⠀⣶⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠒⠀⠀⠀⠠⠶⠒⠤⠀⠰⢲⠶⡶⢂⠐⠀⠀⠀⠀⠄⠠⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⡀⢒⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣷⣦⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣄⠀⠀⠀⠀⠀⠐⡡⠊⠐⢁⠀⡀⢂⠔⡁⠊⠀⠀⠀⠀⢀⠄⡡⢊⠔⡡⢊⠔⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡷⢶⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣅⠀⣴⣿⣧⠀⠀⢀⠔⡡⠊⠀⠁⠀⠀⠀⠀⡀⢂⠔⡡⢊⠔⠡⠊⠐⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⢸⡛⢋⣉⢙⣿⣿⣿⣆⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠠⠀⠄⠡⠈⠄⠡⠈⠀⠁⠈⠀⠀⠀⡀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⡠⢊⠔⡡⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣇⠙⢛⣻⣿⣿⣿⣿⣿⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠊⠄⠡⠊⠔⠡⠊⠔⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⠀⢸⣿⡿⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣀⣀⣀⣀⣔⡁⠈⠀⠁⠈⠀⠁⢈⠀⡁⢈⠀⠁⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎
⣿⣿⣿⣿⣿⣿⣿⣿⠀⡯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠹⣿⣿⣿⣿⣿⡈⠁⠁⠊⠀⠀⠀⠀⢂⠀⠀⢀⠀⡀⠀⠀⡀⢀⠀⡀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⡿⣿⣿⣧⣽⣿⠀⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣔⡴⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠄⠠⠀⠄⠀⢺⣿⡿⠿⠿⠟⠻⠿⢿⣿⣿⣿⣿
⡾⡶⠀⠘⠝⡿⣿⢿⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠟⢾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠠⢱⢌⠀⡁⢈⠀⠀⠀⠀⠁⢀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟
⠀⠀⠀⠀⠘⠀⠋⠚⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡡⣿⣿⢿⣿⣹⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢻⡏⢀⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣶⡾⠛⠁⠀⠊⢁⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣤⣀⣀⣤⣮⡆⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣟⣣⣴⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣼⡏⢟⣷⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠹⠛⢸⣿⣿⢹⣯⢿⣿⣿⣻⣿⣿⢸⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣻⣟⣿⠘⣿⡟⣿⡇⢸⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠁⠍⠀⠀⢘⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠈⠀⢚⠛⠋⢉⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⠚⠛⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⣤⣤⣤⣀⠀⠀⠀⣶⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠟⠒⠀⠀⠀⠤⠶⠒⠤⢆⠐⢲⠶⡶⢂⠔⠀⠂⠀⠀⠀⡠⢀⠔⠠⠊⠄⠀⠀⠀⠀⠀⠀⢒⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⠶⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣄⠀⠀⠀⠀⠀⠐⡠⠊⠐⠁⠀⠀⢀⠔⡀⠂⠐⠀⠈⠀⠀⠀⡠⢀⠔⡠⢊⠔⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡗⠶⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣌⠀⣴⣿⣷⠀⠀⠀⠀⡠⢈⠀⠁⠈⠀⠀⠀⠀⢀⠐⡠⢊⠔⡡⢊⠔⠡⠊⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⢸⡏⢫⣉⣙⣿⣿⣿⣆⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠠⢈⠄⡡⠈⠐⠁⠈⠀⠁⠈⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣷⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⢀⠄⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣇⠙⣛⣻⣿⣿⣿⣿⣿⣿⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠊⠔⠡⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠀⢨⣿⠿⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣀⣠⣀⠄⡀⠀⠀⠁⢈⠐⡁⢈⠀⡁⢊⠀⡁⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠹⣿⣿⣿⣿⣿⡄⠁⠀⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣧⣼⣿⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣌⡶⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠄⠀⠀⠄⠀⢺⣿⣿⠟⠛⠿⠛⠛⠻⠿⣿⣿⣿
⢿⠿⠐⠙⢾⣿⣿⢿⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⢾⣻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠀⣰⢄⠀⡀⢈⠀⠀⠂⠐⠀⠂⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟
⠁⠁⠀⠀⠈⠉⠈⠹⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡡⣿⣿⢿⣿⣹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⡇⢀⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣶⡾⠛⠁⠀⠊⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣤⣀⣀⣤⣦⡆⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣟⣣⣴⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣾⡏⢟⣿⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠹⠛⢸⣿⣿⢹⣯⢻⣿⣿⣻⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣏⣿⣿⣿⣿⣟⣿⠘⣿⡟⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠃⠛⠛⠛⠁⠍⠀⠀⠘⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠈⠀⢚⠛⠋⢉⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⠚⠛⠘⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣤⣄⡀⢰⣶⢰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠛⠀⢀⣀⠀⠐⠂⠀⠒⠤⠀⡠⢂⠔⡠⠂⠀⠀⠀⡀⢀⠔⡠⢂⠐⠀⠀⠀⢀⠀⡀⢀⠀⣠⣲⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡶
⣿⣿⣿⣿⣿⣿⣟⣛⢨⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣾⣿⣿⣦⠀⠀⠀⢀⠀⠈⠔⠁⠈⠀⠀⠄⡠⠊⠔⠁⠈⠀⠀⠀⠠⢀⠔⡠⢊⠔⡡⠊⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠹⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⣾⣿⣷⠀⠀⠀⢀⠔⡁⠈⠀⠀⠀⠀⢀⠀⡠⢊⠔⡡⢊⠐⡡⠊⠐⠁⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⠀⢸⡍⣡⣤⣨⣿⣿⣿⣦⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠡⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠸⢸⠸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣷⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⢀⠄⡠⢊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣆⠈⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠔⡁⢊⠔⡡⢊⠔⡡⢊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠰⢸⢀⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⢸⠿⠏⠀⠻⢿⣿⠿⣿⣿⣿⣿⣿⡿⢃⡀⠤⢤⠤⡤⢦⠄⠀⠀⠀⠠⠀⠄⠠⠀⠄⠠⠀⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⢿⣿⣿⣿⣿⡟⣿⣿⠐⢸⠈⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⢀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣍⠉⢿⡿⣷⣿⣿⠀⢸⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣬⣞⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⠀⠂⠐⠀⠂⠐⠀⠂⠀⣹⣿⡿⠟⠋⠁⠀⠉⠁⠉⠙⠻⢿
⠛⠉⠀⠀⠹⠽⢳⠹⠀⢸⢀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⣋⣗⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠐⢰⡠⠀⠄⠁⠀⠄⠀⠈⠀⠁⠈⠔⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠔⣿⣿⢻⣿⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠀⠂⠀⠀⠊⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⡈⢽⡇⢀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣰⣾⣛⣋⣀⣀⣈⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣠⣤⣤⣠⣤⣵⡆⠀⠀⠀⠀⠀⠀⣾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⢿⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣿⣧⣼⣿⣿⣿⣹⣿⢽⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣾⡏⢿⣿⡿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣟⣺⣏⣿⣽⣟⣿⣸⣏⣿⣿⣿⣿⣿⣿⣿⣓⣿⣿⡇⣿⣟⣿⣹⣏⣿⠘⣿⡟⣿⡇⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠑⠀⠀⠀⠁⠀⣈⠍⠈⢨⣺⣿⣿⣾⣿⣷⣟⣿⣿⣿⣿⣿⣿⡟⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣦⣄⢰⣶⢰⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠀⣀⣤⠀⠂⠀⠀⠐⠠⢂⠔⡠⠒⠀⢀⠄⡠⠀⠄⠀⠀⠀⠀⠀⡠⢂⠔⡠⢂⠔⠠⠀⢴⣲⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣯⣭⢸⢽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡷⠀⠀⡀⣀⡀⠀⠀⠠⢈⠔⡁⠂⠀⠀⠀⠀⢀⠀⡡⢊⠐⡁⠊⠐⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠉⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣷⠀⣾⣿⣿⠀⠀⠄⠁⠀⠀⠀⠀⡀⠂⠐⠁⠈⠀⠀⠀⠀⠀⠐⡀⢀⠔⡠⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⢸⢸⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⠀⢸⡆⣱⣦⣴⣿⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⡠⢀⠄⡡⢊⠔⡡⢊⠔⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣴⣦⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⢂⠐⡁⢊⠐⡁⠊⠐⠁⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⠈⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⣿⠀⢸⣿⣆⠨⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢨⢸⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⡸⠟⠋⠀⠛⠿⠿⠿⣿⣿⣿⣿⣿⡿⡃⠂⠤⠤⠖⠐⠒⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⡡⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣻⣿⣿⣿⣿⡏⣻⣿⠈⢸⠀⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠛⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠠⢀⠐⡀⠂⠐⠀⠂⠐⠀⠂⠔⠁⠂⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⣿⣿⣿⠀⢸⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣮⣟⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⢼⣿⠟⠋⠋⠀⠀⠈⠁⠀⠉⠛⠿
⡿⠟⠁⠀⠉⠛⡿⣿⠀⢸⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⣉⣫⡿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡧⠆⣿⣿⢻⣿⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠈⢻⡇⢠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢡⠈⠀⠁⢀⠀⠀⠀⠀⡡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣰⣿⣏⣉⣀⣀⣈⣡⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣤⣶⣦⣤⣶⣿⡄⠀⠀⠀⠀⠀⠀⣿⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⢻⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣿⣧⣾⣿⣿⣿⣻⣿⢽⣟⢿⣿⣿⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣾⡏⢟⣿⡿⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣟⣻⣯⣿⣽⣿⣿⣸⣯⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⡇⣿⣟⣿⣹⣇⣿⠘⣿⡟⣿⡇⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠁⠁⠀⠀⢸⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠀⢀⠨⠉⡀⢨⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣶⣾⣶⣶⣶⡦⢰⢸⢰⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣠⣤⡀⠀⠀⠀⠀⠐⠀⠂⡀⢂⠔⡠⠂⠀⠀⠀⡀⢀⠀⡠⢂⠔⡡⠂⠀⠀⠀⠀⠀⢴⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣖
⣿⣿⣿⣿⣿⣿⡧⣤⢸⢸⢸⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣾⣿⣿⣿⣷⠀⠀⢀⣠⡀⠀⠊⠔⠁⠊⠀⠀⠀⠀⠂⠔⠠⠊⠀⠀⠀⠀⠀⠀⡠⠂⠔⡠⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⡘⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡿⠿⢿⣿⣿⣷⡀⣾⣿⣿⠀⠀⠀⠀⢀⠀⡡⠈⠀⠁⠈⠀⠀⠀⠠⢀⠔⡡⢊⠔⡡⢊⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡄⣼⣶⣶⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠔⠁⠊⠐⠁⠊⠐⠁⠊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠙⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠿⠀⢸⣿⣇⠀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⢈⠄⡡⢈⠄⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠸⠛⠃⠀⠙⠛⠛⠛⣿⣿⣿⣿⣿⣎⠄⠀⠒⠶⠒⠒⡢⢂⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣇⣿⣿⢸⢸⠰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠙⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⠀⠐⠠⠀⠄⠀⠀⠀⠀⠈⠀⠁⠈⠀⠁⠀⢼⣿⣿⣿⣿⡿⠿⣿⡿⢿⣿⣿⣿
⣿⣿⡟⠿⣿⣿⣿⣿⠘⢸⢠⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢞⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻
⡿⠋⠀⠀⠉⠙⠛⢿⠀⢸⠨⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⣥⣭⠟⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⠊⣿⣿⣹⣿⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠈⠀⠀⠀⠀⡩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠆⠀⢹⡇⢠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣼⣿⣭⣡⣤⣬⣬⣵⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⣶⣶⣶⣿⡄⠀⠀⠀⠀⠀⠀⣿⣺⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣿⢷⣿⣿⣿⣿⢽⣿⢿⣟⣿⣿⣿⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡿⣿⣟⣿⣿⣿⣿⢸⡇⣿⣼⡏⢿⣿⡝⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣽⣯⣿⣿⣟⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣕⣿⣻⡇⡿⠏⣿⣹⣇⣿⠘⣿⡟⣿⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠁⠁⠀⠀⢸⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠀⡀⠬⢂⡀⢸⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣶⣾⣿⣶⡶⠦⢰⢸⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⣶⡄⠀⠀⠀⠀⠐⠠⢂⠔⠠⠂⠀⠀⠀⡀⠀⠔⠠⠀⠀⠀⠀⠀⢀⠔⡠⢂⠔⡠⢺⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦
⣿⣿⣿⣿⣿⣿⡷⢶⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣿⣿⣿⣿⡀⠀⢄⣤⣄⠀⠁⠀⠀⢀⠄⡡⠊⠐⠁⠀⠀⠀⠀⠠⢈⠔⡡⢊⠔⡡⢊⠄⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣈⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⢸⠿⡿⠛⠻⣿⣿⣿⡀⣾⣿⣿⠀⠀⠀⠐⠁⠀⠀⢀⠀⡀⢀⠐⡁⢊⠐⠁⠊⠐⠁⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣄⣾⣷⣾⣿⣿⣿⣷⣿⣿⣿⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡠⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⠉⠺⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⡡⢈⠔⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠟⠀⢸⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠐⠠⠂⠐⠀⠂⠐⠀⠂⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠜⠋⠁⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣟⠁⡀⢒⠖⠋⠋⠑⠠⠀⠀⠀⠈⠀⠁⠈⠀⠁⠈⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣧⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢄⣙⣿⣿⣿⣿⣿⡌⠔⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁⢀⠀⡁⢈⠀⡁⠀⢼⣿⣿⣿⣿⠿⠿⢿⡿⠿⣿⣿⣿
⣿⣿⠟⠿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣯⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠐⠀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣪⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠟⠋⠀⠀⠀⠉⠉⠟⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⢉⣤⡷⠟⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠹⠈⡀⠁⠈⠀⠁⠈⠀⠁⠈⠀⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠃⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡕⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠆⠂⣹⡇⢠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠆⠀⠀⠀⠀⠀⢀⣾⣿⣧⣤⣤⣤⣬⣵⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣿⣿⣶⣿⣿⡄⠠⠀⠀⠀⠀⠀⣿⢳⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠈⢹⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⣷⣿⢾⣿⣿⢾⣿⢿⣟⣿⣿⣿⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣟⣿⡿⡿⣿⢸⡇⣿⣼⡏⢿⣿⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠐⠀⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣯⢽⣟⣿⣿⣟⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣻⡇⠿⠟⣿⣹⣇⣿⠘⣿⡟⣿⡇⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠁⠀⠀⠀⠀⠠⠐⢁⡄⢸⣽⣻⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣷⣾⣿⣶⡶⠒⢸⢸⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡆⠀⠀⠀⠀⠀⠐⢀⠀⡠⢂⠔⠀⠀⠀⠀⠀⡀⠀⠔⡠⠊⠔⠡⠀⠄⠀⠀⠀⢰⣶⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦
⣿⣿⣿⣿⣿⣿⡗⠳⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡀⠀⢂⣤⣄⠀⡁⠊⠐⠁⠂⠀⠀⠀⡠⢊⠐⠀⠊⠀⠀⠀⠀⢀⠄⡀⢀⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣤⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⠀⢸⠻⢟⠛⠻⣿⣿⣿⡄⣼⣿⣿⠀⠀⠀⠀⡀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠐⡀⢂⠔⡡⢊⠔⡡⢊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣆⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⢀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠊⠔⠡⠊⠔⠁⠊⠀⠁⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⠀⢸⣿⠈⠺⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠊⠐⠀⠊⠐⠀⠀⠀⢀⠀⡀⢀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠋⠀⢸⣿⡇⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⢛⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠂⠔⠠⠂⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠤⠄⠈⠉⠁⠀⠈⠉⠋⠛⣿⣿⣿⣿⣿⣗⠂⠈⠉⠛⠉⠉⠁⠡⠀⠀⠀⢈⠀⡁⢊⠐⡁⢊⠐⡡⢊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣙⣿⣿⣿⣿⣿⣄⠀⡁⠀⠀⠀⠀⠐⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠟⠛⠿⠟⠿⠿⣿⣿
⣿⣿⠟⠻⢿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠏⠁⠀⠀⠀⠀⠀⠃⠰⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢛⣡⣤⡶⠛⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠹⢀⡄⡀⢀⠀⡀⢀⠀⡀⢀⠀⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠁⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠠⠀⠀⠀⠀⡔⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠃⢀⢹⡇⢠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⣠⢏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡾⣿⣧⣤⣴⣶⣾⣷⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣾⣿⣿⣾⣿⣿⡄⠠⠀⠀⠀⠀⠀⣿⣳⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⢹⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣟⢿⣿⢿⣿⣿⢽⣿⣿⣟⢿⣿⣿⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡿⣿⣟⣿⡿⡿⣿⢸⡇⣿⣾⡏⢿⣿⠜⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣯⢾⣟⣿⣿⣟⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣽⡇⠿⠛⣿⣹⣇⣿⠘⣿⡟⣿⡇⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⠁⠀⠀⠀⠁⠀⠀⠀⠀⠤⠘⢁⡄⢸⣯⣻⢿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣶⣿⣿⣶⡖⡂⢸⢸⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣆⠀⠀⠀⠀⠀⠂⡠⢂⠔⡠⠂⠀⠀⠀⡀⢀⠔⡀⠊⠐⠀⠀⠀⢀⠀⡀⢀⠄⡰⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣿⣿⡟⠛⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣯⣄⠀⢠⣶⣦⠀⠔⠁⠀⠀⠀⠄⠠⠂⠀⠁⠀⠀⠀⠀⠀⢀⠔⡡⢊⠔⡡⢊⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡦⠀⢸⠙⢟⡉⢙⣿⣿⣿⡄⣾⣿⣿⠀⠀⠀⠀⠔⠁⠈⠀⠀⠀⠀⢀⠀⡡⢊⠔⡡⠊⠐⡡⢊⠐⠁⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣇⠀⢸⣆⣾⢿⣟⣿⣿⣿⣿⣿⣿⣿⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⢀⠀⡀⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡂⠀⠀⠀⠀⠀⠰⣿⠀⢸⣿⡀⠙⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠠⢀⠔⡠⢂⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⡇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡫⣉⠀⠀⢀⣀⣀⡀⠀⠀⠀⡠⢈⠔⡁⢈⠔⡁⢊⠔⡡⢊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⡿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠄⠀⠀⠀⠀⠀⠄⠀⠒⠊⠁⠀⠀⠀⠈⠉⠉⣽⣿⣿⣿⣿⣇⠐⠀⡉⠉⠐⠁⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⣢⣙⣿⣿⣿⣿⣿⣄⠊⠄⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣫⣿⣿⣿⠿⠛⠛⠻⠛⠛⠻⢿⣿
⣿⡿⠋⠙⠛⠿⢿⡿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢷⡽⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠀⣁⢀⠀⡀⢂⠀⠀⠂⠐⠀⠂⠀⡵⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠀⠀⠀⠈⠀⠀⢨⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⡉⢴⡶⡟⡉⢻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⠁⠄⠀⠀⠀⠄⠠⠀⠄⠠⠀⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣺⡏⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣎⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠁⠁⢼⡇⣠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⡀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⣴⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⠿⣿⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⣶⣶⣶⣾⣿⣻⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢆⠐⠀⠀⠀⠀⢀⣿⢽⠇⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⢿⢿⢿⣿⣿⢺⣿⣿⣿⠿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⣟⣿⡻⡟⣿⢸⡇⣿⣾⡏⢿⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⢸⡏⠉⠛⢸⣿⣿⢸⣟⢲⣏⣿⣿⣯⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⡇⠛⠋⣿⣹⣇⣿⠘⣿⡟⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠻⢿⣛⠻⠃⠛⠛⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⠅⠀⠀⠀⠁⠀⠀⠀⠐⠐⠊⠨⠆⣸⣾⣝⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣶⣿⣿⣷⣆⣀⢸⢰⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣦⠀⠀⠀⠀⠀⠂⠀⠀⠄⡠⠂⠀⠀⠀⠀⠀⠀⠀⢂⠔⡠⠂⠔⠀⠂⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡶
⣿⣿⣿⣿⣿⣿⡏⠉⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄⠀⣠⣶⣦⠀⠄⠁⠊⠀⠁⠀⠠⠀⠄⠡⠈⠄⠡⠈⠀⠁⠀⠀⠀⠀⡠⢀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡦⠀⢸⠙⢫⣉⢙⣿⣿⣿⡆⣿⣿⣿⠀⠀⠀⠀⠀⡀⢂⠐⠀⠀⠀⠀⠀⠀⢀⠀⡀⢊⠔⡡⢊⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⣇⠀⢸⣧⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⠊⠔⠡⠊⠔⠡⠊⠔⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡄⠀⠀⠀⠀⠀⠐⣿⠀⢸⣿⡀⠙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠄⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠃⢀⣀⣀⣀⣀⣀⠀⠀⠀⡀⢀⠀⡀⢀⠐⡀⢂⠀⡀⢀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⡏⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠅⠀⠀⠀⠀⠀⠐⠒⠒⠈⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠠⠀⠄⠠⠀⠄⠡⠂⠔⠠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⢜⣿⣿⣿⣿⣿⣆⠁⠄⠀⠀⠀⠀⢈⠠⡁⢈⠀⡁⠈⠀⠀⠀⠀⡀⢈⠀⡹⣿⣿⡿⠟⠛⠉⠛⠛⠛⠛⢿⣿
⣿⠟⠁⠈⠛⠻⠿⣿⢸⢸⠸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠷⠽⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠀⠀⠀⠀⠀⠁⢰⢸⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⡁⢴⡶⠟⣉⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢾⡏⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠂⠐⠀⠀⠀⠀⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⠶⠟⠁⠠⢺⣇⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣀⣀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣶⣳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣿⡿⠿⣿⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⢠⣿⢵⠇⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣿⣿⣿⣟⣿⣟⢸⡇⢸⣟⠿⠿⢻⣿⣿⢺⣿⢿⣿⢿⣿⣿⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡟⣿⣟⣿⡻⡟⣿⢸⡇⣿⣼⡏⢿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣟⢺⣏⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣺⡇⠋⠉⣾⣹⣇⣿⠘⣿⡟⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢛⣻⢿⢛⣻⡃⠛⠛⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠨⠆⣸⣶⣽⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣿⣿⣾⣦⣄⢸⢰⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣦⠀⠀⠀⠀⠀⠂⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠔⡠⠂⠔⠠⠂⢰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣿⣿⡏⠉⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄⠀⢡⣾⣦⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠠⢀⠔⡡⢊⠐⠁⠈⠀⠁⠀⠀⠀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⡶⠀⢸⠉⢫⣍⣙⣿⣿⣿⣆⣾⣿⣿⠀⠀⠀⠀⠀⠀⠂⠐⡀⠀⠀⠁⠀⠀⠀⠀⡀⢀⠀⡠⢂⠔⡠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⣇⠀⢸⣧⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⢀⠔⠠⠊⠔⡡⠊⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⠀⢸⣿⡀⠘⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠁⢀⠀⡀⢈⠐⡁⢊⠀⡁⢈⠐⠁⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡕⠂⢀⣀⣀⣀⣀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣
⣿⣿⣿⣿⣿⡏⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣇⠀⠀⠀⠁⠈⠀⠀⠈⠂⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣰⣈⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢈⠀⡀⢀⠐⡀⠊⠐⠀⠂⠐⠀⠊⠀⡹⣿⣿⡿⠟⠋⠉⠛⠋⠙⠛⢿⣿
⣿⠟⠁⠈⠛⠛⢿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠿⢾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠀⠀⠀⠀⠀⠁⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢛⡥⢼⣿⢟⣁⡻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⠟⠁⠠⢸⣇⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣄⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⣶⡷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢿⣿⣿⣧⣿⣿⣿⠅⠀⠀⠀⠀⣀⣰⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠠⣿⢸⠇⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠿⠿⢻⣿⣿⢻⣿⢿⣿⢷⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡟⣿⣟⣿⡻⡟⣿⢸⡇⣿⣼⡏⢿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣟⢻⣏⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣓⣿⣺⡇⠉⠉⣾⣹⣇⣿⠘⣿⡟⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠛⣻⣿⣛⣻⡃⠛⠛⠛⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠘⠆⣸⣷⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣿⣿⣿⣦⣄⢸⢰⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣦⠀⠀⠀⠀⠀⠂⠔⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⡠⢂⠔⡠⠂⠔⠠⠂⢰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣿⣿⠏⠉⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⠀⢡⣾⣦⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠠⢀⠔⡡⠊⠐⠁⠈⠀⠁⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⡶⠀⢸⠍⢻⣍⣙⣿⣿⣿⣆⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠁⠀⠀⠀⠀⡀⢀⠀⡠⢂⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣧⠀⢸⣧⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⢀⠔⠡⢊⠔⡡⢊⠔⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⡿⠀⢸⣿⡀⠈⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠁⢀⠀⡀⢈⠀⡁⢊⠀⡁⢊⠐⠁⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⡕⠂⠀⣀⣀⣀⣀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⡏⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠇⠀⠀⠀⠀⠀⠐⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⠁⢂⠀⠁⠈⠀⠀⠈⠂⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣠⣌⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢈⠀⡀⢀⠀⡀⠂⠐⠀⠂⠐⡀⠂⠀⡱⣿⣿⠿⠛⠋⠙⠛⠉⠛⠛⢿⣿
⣿⠟⠁⠀⠋⠻⠿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠿⢾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠠⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⡥⠼⣟⠏⣄⡹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⠀⠀⠀⠀⠀⠀⠀⣇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠁⠠⢸⣇⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣤⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⣶⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢿⣿⣿⣧⣿⣿⣿⠅⠀⠀⠀⠀⢀⣠⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠈⠀⠀⠀⠀⠠⣿⢹⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠿⠿⢻⣿⣿⢹⣿⢿⣿⢷⣿⣿⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡟⣿⣟⣿⡻⡟⣿⢸⡇⣿⣼⡏⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣟⢻⣏⣿⣻⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣺⡇⠉⠉⣾⣹⣇⣿⠘⣿⡟⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣛⣻⣿⣛⡻⡃⡛⠛⠛⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠈⠆⣸⣷⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣿⣿⣶⣆⣄⢸⢰⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣧⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⡠⢂⠔⡠⠂⠔⠠⠂⢴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶
⣿⣿⣿⣿⣿⣿⠏⠉⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⠀⢡⣾⣦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⢀⠔⡡⠊⠐⠁⠈⠀⠁⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣖⠀⢸⡏⢹⣍⣉⣿⣿⣿⣇⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠁⠀⠀⠀⠀⡀⢀⠐⡠⢂⠔⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⣧⠀⢸⣧⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣦⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⢀⠔⠠⢊⠔⡡⠊⠔⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⡿⠀⢸⣿⡄⠈⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠁⢀⠀⡀⢈⠀⡁⢈⠀⡁⠊⠐⠁⠊⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⡁⠂⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⡏⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠇⠀⠀⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣇⠀⢀⠀⠁⠈⠀⠀⠈⠀⠀⠄⠠⠀⠄⠠⠀⠄⡠⠀⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⣿⣿⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣠⣬⣿⣿⣿⣿⣿⣦⠁⠀⠀⠀⠀⠀⢈⠀⡀⢀⠀⡀⠂⠐⠀⠂⠐⡀⠊⠀⣹⣿⣿⠟⠛⠉⠙⠛⠙⠛⠻⣿⣿
⡿⠛⠀⠀⠋⠛⢻⣿⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠿⢾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⡥⠴⣟⠏⣀⡹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠃⠀⢼⡇⣠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣄⣀⡀⣀⣠⡆⠀⠀⠀⠀⠀⠀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡿⠿⣿⣿⣿⣧⣿⣿⣿⠅⠀⠀⠀⠀⠀⣠⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡀⠀⠀⠀⠀⠠⣿⡿⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣟⢸⡇⢸⣟⠿⠟⢻⣿⣿⢻⣿⢿⣿⢷⣿⣿⣷⢸⣟⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡟⣿⣟⣿⡻⡟⣿⢸⡇⣿⣼⡏⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢸⣇⣸⡏⠉⠛⢸⣿⣿⢸⣟⢺⣏⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣺⡇⠉⠉⣿⣹⣇⣿⠘⣿⡟⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⢛⣻⣿⣛⡻⣃⡛⠛⠛⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠆⢸⣷⣭⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⢀⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠟⠟⠋⠍⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⠛⢁⡀⠁⣀⣀⠀⠐⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠢⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣷⡀⠀⠀⠀⠀⢰⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣷⠀⢀⢴⣂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⡟⠻⢿⣟⣷⣶⣷⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢸⣿⣼⣿⠉⢸⣿⣿⡇⠀⠙⠋⠈⢿⣿⣿⣿⢿⣿⣿⣣⣄⡈⠀⠀⠀⠊⠙⠉⣜⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣿⡟⣿⣿⣶⣻⣿⣿⣿⡘⢧⠀⠀⠈⢿⠛⣿⣾⣿⣿⣿⡿⠣⠀⠀⠀⠀⡀⠺⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⢡⣿⣿⡿⢿⣿⣿⣿⡧⠸⡄⠀⠀⠈⠙⢿⣿⣿⣿⠿⠧⠀⠀⠀⠀⠰⠇⠀⠀⠋⠀⠊⠀⢉⠿⠿⡝⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⣼⣿⣷⢸⣟⢸⣟⠷⢸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡇⠀⠟⣿⡻⢿⣿⣻⣇⣿⣿⡿⠟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢻⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣁⣿⣿⡇⠀⠀⣾⣹⣿⣿⠻⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠛⠑⠽⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⠈⣡⣿⣿⣿⣿⡿⠋⢉⠑⠉⣏⠔⠀⠠⠈⠁⠹⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠟⠟⠛⠍⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠛⢀⠀⠁⣀⡀⠀⠐⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠛⠂⣸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⡀⠀⠀⠀⠀⢰⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣽⣿⣿⣿⣷⠀⢀⢴⢆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢆⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⡟⠻⢿⣛⣷⣶⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢸⣿⣼⣿⠉⢸⣿⣿⡇⠀⠙⠋⠈⢿⣿⣿⣿⣿⣿⣿⣧⣤⡙⠀⠀⠠⠊⠙⠉⢝⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣾⡟⣿⣿⣶⣿⣿⣿⣿⠘⣧⠀⠀⠈⢿⠛⣿⣿⣿⣿⣿⣟⠣⠀⠀⠀⠀⡀⡾⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⢱⣿⣿⣿⢻⣿⣿⣿⡦⠘⡄⠀⠀⠈⠙⢿⣿⣿⣿⠿⠧⠉⠀⠀⠀⡸⢇⠀⠀⠋⠀⠃⠀⢉⠿⠿⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⣿⣿⣷⢸⣟⢸⣟⠷⢸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡇⠀⠟⣿⡻⢿⣿⣻⣇⣿⣿⡿⠟⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢿⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⡇⠀⠀⣾⣹⣿⣿⠻⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠛⠑⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⠈⣡⣿⣿⣿⣿⣿⠋⢉⠑⠉⣏⠔⠀⠠⠀⠁⠹⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠿⠻⠋⠍⠉⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠝⠛⢁⠀⠀⢀⣀⠀⠐⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠔⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⡀⠀⠀⠀⠀⢐⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣷⠀⢀⣴⢢⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠖⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⡏⠹⢿⣟⣿⣴⣿⣽⣿⣿⣿⣿⡿⠇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢸⣿⣼⣿⠉⢸⣿⣿⡇⠀⠙⠁⠈⢿⣿⣿⣿⣿⣿⣿⣷⣤⡚⠀⠀⠀⠊⠙⢉⢝⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣾⡟⣿⣿⣶⣿⣿⣿⣷⠘⣧⠀⠀⠈⢻⣛⣿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⡀⠾⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠱⣿⣿⡿⣿⣿⣿⣿⣤⠺⠀⠀⠀⠈⠙⢿⣿⣿⣿⢿⠧⠀⠀⠀⠀⠐⠇⠀⠀⠊⠀⠂⠀⢉⠿⠿⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⣾⣿⣷⢸⣟⢸⣟⠷⢸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⡇⠀⠟⣿⡻⢿⣿⣿⣏⣿⣿⡿⠟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢻⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⡇⠀⠀⣾⣹⣿⣿⠻⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠑⠽⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⠈⣵⣿⣿⣿⣿⡿⠋⢉⠑⠉⣏⠔⠀⠀⠀⠁⠹⠉⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠀⠀⣠⡶⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠿⠻⡛⠩⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡙⠛⠁⡀⠈⢀⣀⠀⠐⠁⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠢⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣄⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⠀⢀⣴⣢⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠖⠠⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢄⠞⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣦⣮⣭⣿⣿⣿⣿⣿⠗⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢸⣿⣼⣿⠉⣿⣿⣿⠀⠃⠋⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧⣤⡆⠀⠀⠀⠌⠙⠋⡽⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣾⡟⣿⣿⣶⣿⣿⣿⡄⣿⠀⠀⠀⠈⢹⡟⣿⣿⣿⣷⣿⡟⠡⠀⠀⠀⠀⠀⠸⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠁⢿⣿⣿⣿⣿⣿⣧⡼⡏⠀⠀⠀⠈⠛⢿⣿⣿⣿⠿⠧⠂⠀⠀⠀⠠⠟⠀⠔⠋⠀⠁⠀⠉⠽⠿⢟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⢾⣿⣷⢸⣟⢸⣟⠷⢸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⡇⠀⠟⣿⣻⣿⣿⣻⣇⣿⣿⡿⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢻⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⡟⣿⣁⣿⣿⡇⠀⠀⣾⣹⣿⣿⠻⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠑⠽⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⢈⣽⣿⣿⣿⣿⡫⠊⢉⠑⢩⢉⠔⠁⠀⠀⠁⠸⠉⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠂⠀⢀⣔⠆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢀⣼⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⡋⠐⠀⠁⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣁⣀⣈⣀⣤⣄⠀⠁⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡄⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⡇⢀⡴⣿⣦⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠟⢅⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⠿⠿⣿⣿⣿⣿⣿⡿⠠⠎⠉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠃⣠⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢸⣿⣼⣿⢙⣸⣿⣿⡄⣡⠀⠀⠈⠹⣿⣿⣿⣿⣿⡿⣫⣤⡎⠀⠀⠀⠀⠈⠁⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣾⡟⣿⣿⣾⣿⣿⣿⣇⢸⡅⡠⠀⠀⠘⡟⣻⣿⣿⣷⣿⠟⢁⠀⠀⠀⠀⣠⠘⠛⣻⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠑⣿⣿⣿⣿⣿⣿⣯⠾⠇⠀⠀⠀⠀⠀⢛⣿⠿⣿⢿⠂⠀⠀⠀⠀⠐⢋⠀⠚⠉⠀⠀⠀⠈⠻⠟⢏⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠷⣿⣟⢸⡇⢸⣟⡃⠀⣾⣿⣷⢸⣟⢸⣟⠷⣸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⡇⠀⠟⣿⡻⣷⣿⣿⣇⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢻⣿⣿⢸⣏⣰⣏⣿⢹⣇⣶⢸⣿⣿⣿⣿⣿⣿⡇⣿⣋⣿⣿⡇⠀⠀⣾⣹⣿⣿⠹⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠑⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⣸⣿⣿⣿⣿⡟⡉⠊⠉⡹⠋⢉⠔⠁⠀⠀⠁⠈⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⣀⣶⡖⣠⡖⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣽⡿⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠍⠉⠉⠐⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣋⣁⣠⣄⣠⣤⣄⠀⠁⠰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠐⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠼⣿⣦⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⡻⠆⠌⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⡇⠀⠖⠏⠁⢙⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⢸⣿⣼⣿⢛⣽⣿⣿⣧⠀⢶⠀⠀⠀⢿⣿⣿⣿⣿⡟⣶⣤⠐⠀⠀⠀⠈⠈⢡⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⣿⣼⡜⡇⠀⠀⠀⠋⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣤⠘⠛⣻⠿⣿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠹⣿⣿⣿⣿⣿⣿⡿⠿⠀⡇⠀⠀⠀⠀⠈⣙⠿⠿⠟⠂⠀⠀⠀⠀⠈⠩⠸⠋⠁⠀⠁⠀⠈⠟⠛⢟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠷⣿⣟⢸⡇⢸⣟⡃⠀⣼⣿⣷⢸⣟⢸⣟⠷⣼⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⡇⠀⠟⣿⡻⣶⣿⢿⣇⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢿⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⡇⣿⣃⣿⣿⡇⠀⠀⣾⣹⣿⣿⠸⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⣼⣿⣿⣿⣿⡟⡁⠊⠉⡡⡋⢉⠔⠁⢀⠄⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠂⢰⣶⣶⢂⡰⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠄⠀⢾⡿⢁⠊⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠉⠍⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠐⡾⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣤⣤⣤⣤⣤⣤⠀⠁⠐⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⣖⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡾⣯⣦⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣏⣛⣻⣿⣿⣿⣿⣿⡟⠆⠈⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠟⣿⣿⣿⣿⣿⡇⠀⠊⠋⠁⢩⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢸⣿⣼⣿⣻⣽⣿⣿⡇⠀⢷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣤⠆⠀⠀⠀⠀⠈⢡⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⣷⣴⠙⡇⠀⠀⠈⠁⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣤⠜⢛⣻⠟⢻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⢻⣿⣿⣿⣿⣿⣿⡿⠋⠄⡇⠀⠀⠀⠀⠈⢹⠿⠿⠫⠀⠀⠀⠀⠀⠀⠩⠐⠋⠁⠀⠀⠀⠈⠛⠛⢟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⠷⣸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⡇⠀⠟⣿⡻⣦⣿⢿⣇⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣏⢸⣇⣸⡏⠙⠛⣻⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⡇⣿⣃⣿⣿⡇⠀⠀⣾⣹⣿⣿⠸⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠓⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⢀⣼⣿⣿⣿⣿⠏⠁⠈⠉⡡⠋⣋⠔⠁⢀⠄⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⢀⡖⢀⣶⣲⠖⣰⢶⢶⠰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡘⣡⣿⣿⠏⣐⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠉⠍⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⢸⢿⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣴⣦⠀⠁⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⢀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠼⣯⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢢⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⡀⠘⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⣿⣿⣿⣿⣿⡇⠀⠔⠽⠁⠸⣽⣿⣿⣿⣿⣿⡿⢄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢸⣿⣼⣿⣻⣽⣿⣿⡇⠀⢰⡄⠀⠀⢻⣿⣿⣿⣿⡿⣦⣤⠆⠀⠀⠀⠀⠈⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⣧⣾⡆⢷⠀⠀⠈⠃⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣤⠞⣛⣿⠿⠻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⣿⣿⣿⣿⣿⣿⣿⡿⠟⠄⠸⠀⠀⠀⠀⠸⢿⢿⠿⠯⠂⠀⠀⠀⠀⠀⠩⠐⠋⠁⠀⠀⠀⠈⠛⠛⣟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⢼⣿⣷⢸⣟⢸⣟⠷⢸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⡇⠀⠟⣿⡻⣮⣿⢿⣇⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢻⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⡇⣿⣁⣿⣿⡇⠀⠀⣾⣹⣿⣿⠸⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠘⠛⠙⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⢀⣾⣿⣿⣿⣿⠏⠁⠐⠉⡡⠋⢹⡠⠀⢀⠔⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢲⠂⣰⠖⣰⣶⡶⢠⡆⢒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⢠⠏⣶⣿⡿⢁⡎⠈⢋⠌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⠉⠉⠁⠐⠀⠀⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢀⣷⡿⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣄⣤⣄⣠⣤⣄⠀⠁⠺⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠀⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠔⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⢠⠾⣽⣼⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣧⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣾⣿⣛⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⠁⢀⠜⠿⠃⢉⣿⣿⣿⣿⣿⣿⣛⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⢸⣿⣼⣿⣻⣿⣿⣇⡀⠀⢠⡀⠀⠀⢿⣿⣿⣿⣟⣻⣂⣤⠆⠀⠀⠀⠀⠈⢰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⠈⢶⠀⠀⠸⠂⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣦⠏⣛⣿⠟⠻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⣿⣿⣿⣿⣿⣿⣿⡿⠋⠄⠈⡆⠀⠀⠀⠙⢻⢿⠿⠓⠀⠀⠀⠀⠀⠈⠡⠐⠋⠁⠀⠁⠀⠈⠛⠛⢝⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⠷⢸⡟⣷⢸⣿⣿⣿⣿⣿⣿⢟⣿⡃⣿⣿⡇⠀⠟⣿⣻⢧⣿⢻⣇⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣏⢸⣇⣸⡏⠙⠛⢿⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⡏⣿⣁⣿⣿⡇⠀⠀⣾⣹⣿⣿⠸⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠘⠛⠛⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⣼⣿⣿⣿⡟⠉⠁⠐⠉⡡⠋⠉⡰⠀⢀⠄⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠀⠀⡶⢴⡶⡲⠀⡄⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠆⠀⡊⣹⣤⡾⠃⡈⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠛⠛⠁⠀⠈⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⢑⢻⠟⢁⡎⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣘⣈⣀⣀⣀⣀⣄⡀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢚⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠈⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡷⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣦⠀⠀⠀⠀⢰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⣾⣣⣼⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢸⣿⣿⣿⣿⣇⣿⣿⣿⣿⡃⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⢟⡗⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⠿⠿⢿⣿⣿⣿⣿⣿⠟⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠚⠻⠿⣿⣿⣿⣿⣿⠁⠈⣩⠟⠋⣛⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢸⣿⣼⣿⢿⣿⣿⣿⠀⠀⣀⠀⠀⠘⣿⣿⣿⣿⠿⡧⠀⣀⠂⠀⠀⠀⠀⠉⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣼⡟⣿⣿⣿⣿⣿⣿⢀⡀⢻⡄⠀⠀⠱⠙⣿⣿⣿⣧⡔⠃⠀⠀⠀⠀⢠⡄⠛⣛⡿⠛⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠍⣵⣿⣿⣿⣿⣿⣿⢾⠟⠀⠀⠀⠀⠀⠀⠻⢿⠿⠟⠃⠀⠀⠀⠀⠀⠈⠅⠘⠋⠀⠀⠀⠀⠈⠛⠙⡙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⢸⣿⣷⢸⣟⢸⣟⠷⣸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⡇⠀⠟⣿⡻⣮⣿⢸⣇⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢸⣿⣿⢸⣏⣰⣏⣿⢹⣇⣶⢸⣿⣿⣿⣿⣿⣿⡏⣿⣑⣿⣾⡇⠀⠀⣾⣹⣿⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⢨⣿⣿⣿⣿⠏⠁⠔⠉⢁⠋⠉⡠⠀⠀⠀⠁⠀⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡰⠂⢀⡖⢶⠆⡶⢰⠂⠒⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠂⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⢸⠇⢀⡏⡹⢂⡽⠁⠚⣨⠰⠄⠀⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠟⠻⠋⠍⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠀⠫⣴⣕⡟⢁⠌⠑⠇⠂⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠙⠁⠀⠀⠀⣀⠀⠐⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠈⣿⠟⢡⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡄⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠋⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⡷⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⠀⢀⣴⢢⣼⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⣿⣿⣿⣿⣣⣿⣿⣿⡿⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣆⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢇⠜⠿⡿⣿⣿⣿⣿⡿⠉⠩⣿⡿⠟⠲⢶⣾⣿⣿⣿⣿⠏⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⢺⣿⣼⣿⣿⣿⣿⡇⠀⠈⠁⠀⠀⠀⣿⣿⣿⡿⣿⡷⠀⢀⠀⠀⠀⠀⠉⠋⣡⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣼⡟⣿⣿⣿⣿⣿⣷⣤⡄⢙⣧⡀⠀⢫⡙⣿⣷⣿⣦⡼⠃⠀⠀⠀⠀⢀⡄⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⢉⣵⣿⣿⣿⣿⣿⣿⣿⠇⠉⠉⠃⠀⠀⠫⠿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠚⡃⠰⠛⠁⠀⠀⠈⠹⠿⠻⡛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠗⣿⣟⢸⡇⢸⣟⡃⠀⢺⣿⣷⢸⣟⢸⣟⠷⢸⡟⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⢿⡇⠀⠟⣿⡻⣟⣿⢽⣇⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈
⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⣏⢸⣇⣸⡏⠙⠛⢻⣿⣿⢸⣏⣰⣏⣿⢸⣇⣶⢸⣿⣿⣿⣿⣿⣿⡏⣿⣑⣿⣿⡇⠀⠀⣾⣹⣿⣿⠘⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠘⠛⠻⠿⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠉⠈⠁⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠈⠀⠈⣿⣿⣿⣿⠋⠁⠐⠉⢁⠜⠉⡀⠂⠀⠀⠁⠁⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2129

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/Microsoft_s_Problem_in_Puerto_Rico.shtml
    Gemini version at https://techrights.org/n/2024/05/31/Microsoft_s_Problem_in_Puerto_Rico.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft's Problem in Puerto
Rico⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Puerto_Rico_Flag⦈_


A year ago: Kevin_Shockey's_Presentation_on_Puerto_Rico_and_FSF


LOOKING at desktop and general market share in Puerto Rico (based on
statCounter), it's clear that Microsoft is no longer "in charge". Vista_11_is
down_over_there,_not_up. Heck, Windows is down as a whole. statCounter used to
measure it at 94% and it's down to just a quarter (of observed Web requests).


Notice how much Windows has fallen. Android has climbed to its highest_level_in
4_years this month. █


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Operating System Market Share Puerto Rico: Feb 2009 - May
                                    2024⦈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⣀⡀⢀⣀⣀⣀⣀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⠀⠀⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢟⣭⡹⡿⣛⡿⣛⢿⢟⣟⡻⣛⣻⡟⣛⢿⢟⢻⣿⠩⣽⢿⣟⢛⣛⣛⢟⡻⡿⡛⣛⢿⣿⡹⣿⢻⣟⡻⡿⣻⢹⢻⢛⢟⢙⣿⡫⢭⡏⣛⣿⣛⢿⢟⡿⡻⣿⡏⣭⢹⣿⣿⢟⡻⡿⣛⢙⠟⡻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣎⣛⣡⣏⣛⣤⣒⣺⣿⣕⣂⣏⣻⣇⣿⡸⣐⣺⣿⣛⣢⡎⣼⣒⣸⣛⣔⣒⣿⣿⣿⣸⣿⣷⣡⣿⣕⣂⣿⣿⣰⣡⣒⣺⣘⣿⣛⣃⣇⣿⣯⣒⣸⣸⣇⣒⣿⣇⣶⣿⣙⣹⣔⣒⣿⣿⣘⣜⣋⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣛⣟⡿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣆⢿⣇⠿⣗⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⡟⣿⣿⠿⢿⠿⢿⠿⡿⠿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⠿⣿⠿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣽⠤⡅⠶⣿⠟⢽⡸⢺⠿⡠⠍⣿⣯⣿⣷⢣⢸⠤⣯⢳⣿⠫⢇⠿⡟⠵⣑⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣗⣔⣆⣸⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⡈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣑⣅⣺⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣀⡀⠙⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠈⠿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠋⠉⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⡀⠀⠀⠀⣹⡿⠿⠟⠻⠿⢿⠛⢿⠿⢿⠿⢿⢿⠿⠿⠿⠟⠿⠮⠙⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢢⠀⠓⠀⠀⠀⣽⡇⠀⡆⢘⠀⠀⡀⢂⠐⣂⠒⣨⠘⠀⠀⡆⡆⢊⡀⢀⢀⡘⢿⣿⣟⣝⣿⣾⣿⢿⣾⣯⢿⣿⣞⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⠋⠉⡉⠹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⣻⣿⣿⣿⣷⢿⣿⣿⣯⢿⣿⣞⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣄⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⣟⣿⣾⣿⣿⣿⣯⢿⣿⣞⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣻⣷⣦⡹⢿⣿⣿⣿⣿⣿⣯⢿⣿⣞⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⠫⢹⣿⣿⣿⣦⡹⢿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣸⢸⣿⣿⣿⣿
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⣿⣿⣿⠟⠛⠛⠻⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠰⠿⠶⠄⠸⠿⠿⠿⠟⠛⠿⠿⠿⠿⠿⠇⠈⡛⠃⠀⠁⠠⠇⠸⠿⠿⠿⠿⠿⠿⠿⠦⠙⠿⠿⠷⠝⠿⣿⡿⢸⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣷⣶⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⡇⠈⠀⠹⠿⠀⡆⠘⠃⠀⠹⡿⠁⣀⠠⢰⣦⣴⣿⡇⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣮⣻⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡇⠀⠐⠈⠀⠰⣿⠦⣠⣶⡀⠁⢠⣿⣷⣾⣿⣿⣿⡇⠀⠀⠘⠿⣿⠀⠉⠛⠿⠿⠿⣿⣦⠙⠛⠛⠛⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⡿⠛⠃⢀⣶⣦⣶⡀⠁⢠⠀⠟⢀⡄⠈⢿⣿⣿⣿⣿⣿⡇⠀⠼⠀⠈⠈⠀⠠⠀⠀⠀⠄⠈⠈⠀⠀⢀⡀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠀⢠⣴⣶⣿⣿⣿⣿⣿⣶⣿⠀⠀⣾⣿⡆⠘⠋⠉⠉⠙⠋⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠀⣠⣴⡆⠀⠀⠐⠉⢸⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣸⣷⣿⣿⣿⠛⣿⣿⣿⡿⠟⠿⠀⠘⠟⠻⠓⠒⠀⡆⠀⠀⠀⡆⠀⠒⠀⣿⣦⣴⣶⣿⣷⣦⣀⢀⠄⣴⣿⣤⣴⢸⣿⣿⣿⣿
⣿⣿⣿⣥⣦⣦⣴⡇⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⠀⡴⠒⢲⣶⠶⠆⠀⠐⠀⠀⢀⣤⣤⣴⣶⣤⣀⣴⣤⣤⣄⣠⣀⠀⠂⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⢀⣠⣴⠀⠁⡀⠀⣰⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⢻⣿⡿⢀⡀⠀⡆⠀⣿⠏⠻⣿⣿⡿⠻⠿⠟⠉⢿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⠿⠇⠂⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠟⠋⢉⡀⣀⠈⠀⠀⡀⠘⠀⠀⠁⢰⣷⣀⠉⢀⠀⠉⠉⠁⢠⣴⣶⣆⠈⠛⠛⠻⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⠛⠛⠋⠉⢁⣀⣠⣤⡤⠀⠀⣀⣀⣤⣤⣤⣄⣀⣤⣄⡈⠉⢉⣉⠉⢀⠈⠉⠉⠁⢀⣀⣴⣀⣸⣿⣿⣷⠞⢻⣷⣶⣾⣦⣄⣸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡿⠷⣶⣶⣤⢸⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⢿⡆⠤⠴⠶⠶⠗⠛⠛⠛⠋⠉⠀⠀⠰⠾⠿⠿⠿⠿⠛⠿⠛⠛⠿⠓⠒⠺⠛⠛⠋⠀⠀⠴⣦⠀⠛⠻⠿⠿⠿⠿⠿⠀⡀⠘⠉⠙⠿⠿⠿⠛⠛⠟⠋⠉⠋⠙⠛⠉⠩⠉⠀⠀⠛⠛⠛⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣬⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣄⣀⣀⣠⣄⣠⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡅⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣾⣧⣦⣤⣷⣥⣬⣦⣬⣼⣿⣿⣿⣿⣿⣿⣿⣦⣭⣾⣴⣤⣴⣥⣴⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣾⣼⣬⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2234

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/Microsoft_s_Share_of_Physical_Web_Servers_Fell_From_9_14_to_9_0.shtml
    Gemini version at https://techrights.org/n/2024/05/31/Microsoft_s_Share_of_Physical_Web_Servers_Fell_From_9_14_to_9_0.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft's Share of Physical Web Servers
Fell From 9.14% to 9.04% in One Month⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Microsoft down⦈


THE May_2024_Web_Server_Survey is out and it sees an increase in domains, for a
change:


     In the May 2024 survey we received responses from 1,097,398,145 sites
     across 268,137,699 domains and 12,898,459 web-facing computers. This
     reflects an increase of 4.4 million sites, 202,938 domains, and
     26,168 web-facing computers.


What's interesting to us is how Microsoft continues moving down in everything
measured. It has been like this for a number of years already. █




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡷⣉⢩⢋⠉⣟⠍⠩⡏⠉⣽⣿⣿⣿⡟⡘⠩⣯⣿⣿⠠⡱⡗⢍⢸⣿⣿⣿⡇⣸⢉⢹⠭⠉⢩⡏⣿⣿⣿⣿⢈⡁⠉⡝⣽⠪⡱⡗⢍⢸⣿⣿⣿⡇⣉⢹⢩⢽⠉⢩⡍⣿⣿⣿⣿⠴⢨⡏⠉⡍⠉⡉⣿⣿⣿⣿
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⣿⣛⡿⣻⡟⢟⣋⠹⢻⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⢻⢻⣟⣛⣿⡻⣿⣿⣿⣿⣟⢛⢻⣟⣛⣛⠛⣿⣿⣿⣿⣿⣿⡟⣟⠛⢻⣟⣟⠛⣻⣿⣿⣿⣿⣟⣛⢻⡿⣟⡟⢟⣿⣿⣿⣿⣿⣿⣿⣟⢻⣛⢟⣿⣿⣿
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⣿⣧⣀⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣭⣼⣧⣤⣼⣽⣿⣿⣿⣿⣯⣤⣽⣧⣤⣴⣤⣿⣿⣿⣿⣿⣿⣯⣯⣤⣭⣯⣥⣬⣼⣿⣿⣿⣿⣯⣤⣽⣭⣭⣴⣴⣿⣿⣿⣿⣿⣿⣷⣮⣬⣿⣥⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣯⣯⣉⣅⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣨⣾⣧⣈⣼⣼⣿⣿⣿⣿⣷⣧⣸⣷⣀⣠⣀⣿⣿⣿⣿⣿⣿⣇⣧⣰⣼⣷⣡⣘⣸⣿⣿⣿⣿⣷⣧⣸⣧⣳⣠⣡⣿⣿⣿⣿⣿⣿⣿⣷⣹⣾⣡⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠹⣹⢟⣟⢛⡟⣟⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣽⣯⢍⣽⣽⣿⣿⣿⣿⣿⡿⢹⣿⢝⣝⠋⣿⣿⣿⣿⣿⣿⣿⡟⠙⣽⡟⢯⡙⣽⣿⣿⣿⣿⣿⡿⢹⣯⢯⢍⢯⣿⣿⣿⣿⣿⣿⡿⢯⢻⣝⡏⣿⣿⣿
⡿⠷⠿⠷⠿⠷⠷⠷⠷⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠾⠷⠶⠾⠾⠿⠿⠿⠿⠿⠿⠿⠷⠶⠾⠷⠿⠿⠿⠿⠿⠿⠿⠿⠾⠾⠿⠷⠿⠾⠿⠿⠿⠿⠿⠿⠾⠷⠷⠿⠷⠿⠿⠿⠿⠿⠿⠿⠷⠷⠶⠷⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⡟⠛⣛⠛⡟⢛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⡛⡟⢻⠛⠛⠛⢟⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡟⢿⠻⣿⠿⡿⠿⠻⠿⢿⠿⠿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣰⣄⣶⣿⣰⣇⣠⣌⣌⣸⣦⣀⣇⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣌⣭⣿⣭⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡯⠭⠭⠭⠭⠭⠟⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣭⣭⣽⣥⣭⣭⣭⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠿⠭⠭⠽⠛⠛⠭⠝⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣦⣴⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠮⠭⠝⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠭⠭⠭⠭⠯⠭⠭⠭⠶⠾⠭⠭⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣓⣊⣙⣛⣛⣛⣛⣛⣛⣉⡹⠦⠶⠶⠶⠿⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣝⣛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣝⣉⣋⣋⣋⣿⣿⣿⣿⡇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣛⡻⠿⢿⣿⡿⡃⣿⢬⡦⠤⠴⠤⠧⣤⠤⢿⡇⣤⣶⡮⠭⣽⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⢻⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢛⣃⣂⣉⡃⣿⢺⠒⢒⠖⡖⢓⢳⣶⣾⡇⣀⣐⣚⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢛⣉⣒⣛⣛⣛⠛⠃⣿⣹⣩⣝⣫⣏⣉⣙⣿⣿⡇⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣙⣻⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⣉⣉⣉⣉⣉⡉⠉⣉⣉⣙⣒⣒⣉⣉⣛⣒⣒⣓⣛⣓⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣉⣙⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣛⣛⣭⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣹⣯⣭⣭⣭⣭⣭⣭⣥⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣝⡾⡋⣉⢼⠋⣣⢜⢫⣡⣟⢉⡫⡟⣭⡮⡋⣙⢼⢋⣹⢝⢫⣡⣟⢩⣪⡟⣍⡼⡋⣑⢽⢋⣱⢝⢫⡡⣟⢙⡠⡟⣝⣮⡋⣙⢼⢋⣷⢝⢉⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⣠⣤⣿⣧⣶⣿⣤⣿⣥⣴⣾⣧⣴⣿⣥⣴⣿⣤⣾⣷⣥⣿⣗⣴⣾⣭⣴⣿⣤⣶⣯⣤⣾⣇⣤⣼⣿⣴⣾⣧⣴⣯⣥⣦⣿⣤⣾⣯⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⡿⡿⢿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⡿⣿⣿⣿⠿⠿⡿⢿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣴⣥⣤⣯⣤⣰⣧⣤⣾⣿⣿⣿⣯⣬⣰⣷⣿⣿⣵⣼⣯⣦⣼⣿⣿⣿⣧⣾⣤⣼⣤⣤⣴⣧⣿⣿⣿⣿⣤⣤⣤⣎⣾⣵⣬⣭⣦⣼⣿⣿⣿⣧⣦⣼⣴⣦⣤⣴⣦⣿⣿⣿⣿⣭⣴⣧⣤⣦⣀⣤⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿
⣿⡍⠉⣿⡝⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⡟⡉⠹⢻⡿⠹⢻⢻⣿⣿⣿⣿⡿⠉⢻⡿⣭⣯⡉⣿⣿⣿⣿⣟⣹⡟⡟⢩⣿⡿⡻⠋⢻⣿⣿⣿⣿⡿⠉⢹⡟⡿⢉⡻⣿⣿⣿⣿⣿⣿⣟⡻⡹⠯⡏⣿⣿⣿
⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠻⣟⡟⠿⡛⣻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣟⡟⢻⢻⣟⡛⢿⣻⣿⣿⣿⣿⣟⠻⣻⣿⡛⢛⠛⣿⣿⣿⣿⣟⢻⡿⣟⠛⣻⣿⡛⢟⢻⣿⣿⣿⣿⣟⡻⢻⡿⣟⡟⢟⣿⣿⣿⣿⣿⣿⣿⣟⢻⣛⡛⣿⣿⣿
⣿⣿⣷⣷⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣾⣾⣷⣶⣾⣿⣿⣿⣿⣿⣷⣾⣿⣷⣷⣾⣶⣿⣿⣿⣿⣷⣮⣷⣷⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣷⣾⣾⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣿⣿⣿
⣿⢿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⢿⢿⡿⠿⢿⠿⣿⣿⣿⣿⣿⡿⢿⡿⣿⠿⠿⣿⣿⣿⣿⡿⣿⡿⡿⠿⢿⡿⡿⠿⢿⣿⣿⣿⣿⣿⡿⢿⡿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⡿⣿⣿⣿
⣿⣮⣾⣬⣿⣬⣯⣯⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣶⣼⣧⣬⣼⣽⣿⣿⣿⣿⣿⣧⣼⣿⣧⣴⣤⣿⣿⣿⣿⣿⣟⣧⣧⣤⣼⣧⣬⣴⣼⣿⣿⣿⣿⣿⣧⣼⣯⣦⣵⣴⣿⣿⣿⣿⣿⣿⣷⣮⣬⣿⣮⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2309

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2024/05/31/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on May 31, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Unknown_Factor_in_the_Democratic_Republic_of_the_Congo [original]⠀⇛


           If it was Windows, it would not be classified as "unknown"


   2. ⚓ Tux_Machines_Party_(and_Protecting_Women_From_Bullies) [original]⠀⇛


           The community must collectively fight back, uniting to end this
           "cancel mob"


      ⚓  New⠀⇛


   3. ⚓ Kernel:_Linux_6.10,_GitLab,_and_2024_Linux_Storage,_Filesystem,_Memory-
      Management_and_BPF_Summit⠀⇛


           New in LWN, no paywall today


   4. ⚓ Trinity_keeps_KDE_3_on_life_support⠀⇛


           As the shiny new KDE Plasma 6 desktop makes its way into
           distribution releases, a small group of developers is still
           trying to preserve the KDE experience circa 2008


   5. ⚓ today's_leftovers⠀⇛


           openwashing and more


   6. ⚓ Software_and_Distro_Development⠀⇛


           Programming leftovers


   7. ⚓ Red_Hat_/_Fedora_/_IBM_Leftovers⠀⇛


           only 3 stories for now


   8. ⚓ Open_Hardware_or_Linux_Devices⠀⇛


           some hardware leftovers


   9. ⚓ Security_Leftovers⠀⇛


           Security links


  10. ⚓ today's_howtos⠀⇛


           many howtos for today


  11. ⚓ Ruby_3.1.6,_Datadog,_and_More_Ruby_Programming⠀⇛


           Some Ruby news


  12. ⚓ System76’s_Darter_Pro_Linux_Laptop_Gets_16:10_Display,_Intel_Core_Ultra
      CPUs⠀⇛


           Linux hardware vendor System76 unveiled today the latest
           generation of the Darter Pro Linux-powered ultrabook featuring
           Intel Core Ultra processors with Intel Arc graphics.


  13. ⚓ Canonical_Announces_Availability_of_Real-Time_Kernel_for_Ubuntu_24.04
      LTS⠀⇛


           Ubuntu maker Canonical today announced the general availability
           of an enterprise-grade real-time Ubuntu kernel for Ubuntu 24.04
           LTS (Noble Numbat) operating systems.


  14. ⚓ GNOME_46.2_Released_with_Various_Improvements_and_Bug_Fixes⠀⇛


           The GNOME Project released today GNOME 46.2 as the second
           maintenance update to the latest GNOME 46 “Kathmandu” desktop
           environment series bringing more bug fixes and small
           improvements.


  15. ⚓ Programming_Leftovers⠀⇛


           Programming related links, mostly Python today


  16. ⚓ today's_leftovers⠀⇛


           Openwashing and more


  17. ⚓ Open_Hardware,_Modding,_and_Linux_Devices⠀⇛


           half a dozen hardware picks


  18. ⚓ today's_howtos⠀⇛


           a bunch of howtos for this afternoon


  19. ⚓ Results_from_the_2024_FreeBSD_Community_Survey_Report⠀⇛


           Original and LWN


  20. ⚓ Linux_Kernel_6.8_Reaches_End_of_Life,_Users_Should_Upgrade_to_Linux
      Kernel_6.9⠀⇛


           This is your friendly reminder that the Linux 6.8 kernel series
           is now marked as EOL (End of Life) on the kernel.org website,
           so you should consider upgrading to Linux kernel 6.9 as soon as
           possible.


  21. ⚓ Windows_Total_Cost_of_Ownership_(TCO)_and_High-Profile_Data_Breach⠀⇛


           true TCO


  22. ⚓ Android_Leftovers⠀⇛


           Dusun DSGW-130 smart home controller fits into an 86-type
           junction box


  23. ⚓ Ochin_V2_tiny_Raspberry_Pi_CM4_robotics_carrier_board_gets_micro_HDMI
      port,_Fast_Ethernet_support⠀⇛


           Like its predecessor, the Ochin V2 board is partially open-
           source with the KiCad PDF


  24. ⚓ Games:_SteamVR_for_GNU/Linux,_Steam_Deck,_Doors_of_Trithius,_and_More⠀⇛


           Latest 10 articles from gamingonlinux


  25. ⚓ Best_Free_and_Open_Source_Software⠀⇛


           All of these tools are released under a freely distributable
           license. Here’s our verdict


  26. ⚓ Slackel_–_Linux_distribution_based_on_Slackware⠀⇛


           Slackel is a Linux distribution based on Slackware and includes
           tools from Salix


  27. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


  28. ⚓ Transmission_4.0.6_Open-Source_BitTorrent_Client_Released_with_Various
      Fixes⠀⇛


           Transmission 4.0.6 open-source, free, and cross-platform
           BitTorrent client is out today as a bugfix-only release in the
           4.0.x series addressing various issues reported by users from
           previous versions.


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


                         Span from 2024-05-24 to 2024-05-30
      903 /n/2024/05/25/
          Switch_from_Windows_11_to_Linux_this_Memorial_Day_with_Ultramar.shtml


      863 /n/2024/05/24/Qualcomm_s_ARM_Laptops_Matter_Because_Of_Linux.shtml


      823 /n/2024/05/27/today_s_howtos.shtml


      783 /n/2024/05/24/
          Releases_GCompris_4_1_Stratus_Redundant_Linux_SRL_3_0_Rufus_4_5.shtml


      782 /n/2024/05/24/
          KDE_Plasma_6_1_Beta_Released_with_Explicit_Sync_Support_on_Wayl.shtml


      761 /n/2024/05/22/Alpine_Linux_3_20_0_Released.shtml


      761 /n/2024/05/24/today_s_howtos.shtml


      754 /n/2024/05/30/
          Tux_Machines_Party_and_Protecting_Women_From_Bullies.shtml


      735 /n/2024/05/28/
          Canonical_releases_Ubuntu_24_04_Server_image_for_Milk_V_Mars_RI.shtml


      734 /n/2024/05/26/today_s_leftovers.shtml


      730 /n/2024/05/26/today_s_howtos.shtml


      715 /n/2024/05/26/Practical_differences_between_FreeBSD_and_Linux.shtml


      701 /n/2024/05/23/
          Meet_TUXEDO_Stellaris_Slim_15_Gen6_a_Thin_and_Light_Linux_Gamin.shtml


      695 /n/2024/05/25/today_s_howtos.shtml


      693 /n/2024/05/26/today_s_howtos.1.shtml




⣿⣿⣿⣿⣿⣿⠡⠀⡙⡶⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⠀⡗⢰⣿⣿⣿⣷⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀
⠿⠟⠿⠿⠛⠛⠛⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀
⢀⡀⣠⡄⢤⣄⠲⠶⠂⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣯⣽⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀
⠉⠙⠈⠉⠉⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣷⣷⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⠀⠀⠀
⣦⣿⣶⣿⣂⡸⢹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠈⠻⢿⣧⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣭⣽⣭⣥⣤⣜⣂⣠⡀⠀⠀⠀⠀⢸⣿⡀⠀⠀
⣿⣯⡟⠉⢿⣯⠄⢻⣿⣭⣾⣻⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⠄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢓⠆⠀⠀
⣭⣛⡟⠠⡄⢻⣞⠿⣋⡙⢿⡿⢻⣿⡿⢿⣿⣎⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⠀⠀
⣿⠾⣤⣤⡵⣿⠨⠟⣿⡟⢸⣿⣠⣴⣘⠀⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠀⠀
⠹⣷⡎⠿⣷⡀⠀⠂⠀⠀⠀⡘⡹⢸⣏⠀⠸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠂⢠⠆⠲⠉⣁⠀⠀⠀⠀⠀⠀⠰⠀⢉⡔⠀⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠺⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠻⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣾⡄⠀⠀⠀⠀
⠀⠀⠀⠈⠀⣿⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠈⠂⠀⠐⠍⠛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠺⠷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠨⠿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠶⠜⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠨⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠼⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠻⠿⡿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⣿⣿⣿⠯⣂⠀⠀⠀⠠⢼⣿⠿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⣄⠀⠰⢼⠀⠈⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2615

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/Racism_Ageism_and_Ableism_at_IBM_Red_Hat_and_Kyndryl.shtml
    Gemini version at https://techrights.org/n/2024/05/31/Racism_Ageism_and_Ableism_at_IBM_Red_Hat_and_Kyndryl.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Racism, Ageism, and Ableism at IBM/Red Hat
and Kyndryl⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Kyndryl⦈_


THERE is a new report (past 24 hours) that says "Big Tech Layoffs Are Hitting
Diversity and Inclusion Jobs Hard" and IBM's Kyndryl is now accused of "racial,
age, disability discrimination", according to The Register [2], one of the few
remaining online publishers that scrutinise IBM and habitually write about Red
Hat's impending layoffs.


Earlier this month we saw_the_report "IBM's Red Hat SUED over culling 21 white
men employees as CEO vowed to punish managers who missed DEI targets" along
with about 20 other bits of coverage (we mentioned this here only in passing
because the press had politicised it).


No matter where you stand on politics, it's clear that IBM_is_imperialistic_and
still_very_racist (this goes_back_to_the_company's_roots). One must be open-
minded and consider the fact that PR campaigns like "inclusive language" (IBM
still uses the word "master" quite a lot) are a shallow/thin_smokescreen.


As we've shown here throughout_the_month, the former Red Hat staff who kept
pushing UEFI_'secure'_boot (for Microsoft) claims to be supporting women, but
he's actually very sexist. One person wrote to tell me this morning: "I forgot
to add that Matt's list of crimes against you two probably can be considered to
contain also sexual harassment." █


___________


   1. ⚓ Big_Tech_Layoffs_Are_Hitting_Diversity_and_Inclusion_Jobs_Hard⠀⇛


   2. ⚓ Kyndryl_accused_of_racial,_age,_disability_discrimination_•_The
      Register⠀⇛


           Kyndryl, the IT services firm spun out of IBM, has been accused
           by multiple employees within its CISO Defense security group of
           discrimination on the basis of age, race, and disability, in
           both internal complaints and formal charges filed with the US
           Equal Employment Opportunity Commission (EEOC).


           The Register has reviewed documents supporting allegations that
           include discrimination and retaliation against staff.


           These files describe a years-long saga of staff allegedly being
           axed, moved, or demoted for taking time off work for health
           reasons, for being from India or non-White, and for other
           alleged unfair reasons.


           It's a saga of a team experiencing an influx of workers from
           another company, sparking tensions over pay and performance.
           All of which will have to be probed and resolved by the
           employment commission.




⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠄⠙⢿⡟⢃⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢣⣟⣿⣞⡇⢿⣿⣧⣿⣇⠸⡾⣿⣿⣿⣧⠁⠀⡇⢻⡆⠸⣧⢹⡄⠸⡄⠀⡁⡎⣷⣿⣟⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⡿⡇⢸⣿⣿⣸⣿⣷⣇⣏⣿⡏⣿⡄⠀⢳⢸⣧⠀⢻⡜⣷⠀⢷⠀⢷⠄⠘⣧⠱⠸⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡷⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣧⡿⢠⠉⠛⠛⠿⢿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣸⣿⡏⣿⣷⣿⣦⢸⣼⠸⣷⠀⢹⠁⠀⠹⡝⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣯⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⠀⠀⠀⠀⠀⠤⡀⠈⠙⠛⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⡆⢸⠀⠀⡀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣛⢟⠛⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣉⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣧⠀⡇⢀⠀⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣩⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠯⢽⣶⣶⣤⣌⢉⣙⠛⠻⠿⠿⣿⣿⣿⣿⣷⣿⡇⣷⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣎⣥⠢⢠⠀⠀⠀⠀⠀⠀⢀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣽⣯⣉⣿⠜⢻⣿⡅⢀⣶⣤⡌⠉⠉⠛⠛⠷⢿⣿⣧⡀⡂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣗⣽⠫⡼⠀⠀⠇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⣾⣿⡤⢤⣿⣟⠛⣷⡀⢸⣿⣿⣼⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠸⠃⠆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠻⠿⠿⠂⣺⣿⠐⣛⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⡆⠀⠈⠀⠀⠀⠀⠀⡀⢠⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⣗⠀⢀⠀⠀⠀⠀⠄⡇⠀⢃⣿⣿⣿⣿⢿⣿⡿⣽⣟⠀⣇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠄⣰⣟⡄⠀⠀⢰⠀⣸⣷⠁⠀⠈⢹⣿⢟⣵⣿⣿⣿⣿⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡗⢰⣿⣿⣧⠀⠀⠀⣰⣿⣿⠀⠀⠀⢘⣡⣾⣿⡿⣭⣿⣿⣯⢀⡷⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣌⢿⣿⣿⡦⠀⠰⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⢠⡿⠶⠤⠄⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡇⢀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠹⡍⠞⢛⠉⢇⠀⠀⠛⠿⡏⠀⣸⣿⣿⣿⣵⣿⣿⡿⣻⣾⣿⢸⣟⡛⠒⠤⠄⢀⣄⡀⠀⠄⠀⠀⠀⠀⢘⡇⠩⡀⠀⣇⠀⡾⠘⡗⠒⢦⠀⣠⠤⣸⡀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠰⣿⡄⠀⠀⠀⠀⠀⠀⠐⠃⠸⢿⣿⣶⣿⣿⡿⢋⣼⣿⢿⡧⢸⣟⠛⠓⠦⠤⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠀⠸⢶⠃⠀⡇⠀⢸⠘⡇⠀⠘⡇⢹⠉⠐⡄⠀⣤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⡿⢋⣴⣿⣿⣿⣿⡦⢸⡟⠋⠡⠄⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠈⠀⠘⠂⠘⠇⠸⠀⠀⢱⣰⠇⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢃⣴⣿⣿⣿⢛⣽⣿⠏⢸⣟⠒⠶⠆⠀⠀⡀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⡇⣿⡿⣿⡖⠲⠂⠀⠀⣿⡿⠋⣿⣿⣿⣿⣿⢛⣼⣿⣿⣿⠧⢸⣟⣛⠛⠳⠶⠀⣀⡀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣉⠐⠀⠀⠀⠰⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⣃⣿⠁⢈⣙⡁⠈⠀⠀⠁⣠⣶⣿⣿⣿⣫⣽⣿⣿⣿⠟⣿⡇⢺⣟⣛⡛⠋⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠔⠒⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2714

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/The_War_on_Free_Software_Reporters_Part_II_Antisocial_Mobs.shtml
    Gemini version at https://techrights.org/n/2024/05/31/The_War_on_Free_Software_Reporters_Part_II_Antisocial_Mobs.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The War on Free Software Reporters - Part
II - Antisocial Mobs⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


                  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇OMG Corrupt Microsoft⦈


IN this relatively short series we wish to discuss how various GNU/Linux
bloggers got "canceled" over the years. We know them, we saw what happened to
them, but we'd rather not name them. It's not the names that matter but the
modus operandi.


In Part_I ("Why Techrights Cannot be Censored (and Won't be Censored)") we
focused on DDoS attacks, i.e. on technical attacks, not social or legal
attacks.


Today we focus on social methods, social engineering, and of course social
control media.


Some people who used to run sites about GNU/Linux got "canceled" and vanished.
In 2020 I identified some_of_the_culprits, which are antisocial despite their
label. It's not just social control media, which is low quality and where it is
too easy to take things out of context. Later in the same year I started making
videos every day because I realised videos, unlike text, are a bit harder to
take out of context or isolate from subtle cues, nuance, body language, tone
and so on.


There are also social engineering-type attacks and we covered some of them
before. Microsoft is an "expert" at those. In my case, consider this meme about
how I feel about it.


                  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Y U hatin' Microsoft?⦈


As a reminder, Microsoft kept chasing me both online and offline. In fact,
after they contacted my university and phoned my employer Bill Gates bribed
them and then they tried to 'bribe' my webhost, they sent_trolls_to_IRC etc.
They just won't leave me alone; anything like blog comments, some social
control networks and even our own IRC network would be leveraged to smear,
intimidate, misrepresent, and incite.


What company other than Microsoft behaves like this??? █




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

                    ䷩ 𝚕𝚒𝚗𝚎 3562

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/05/31/The_War_on_Free_Software_Reporters_Part_I_Why_Techrights_Cannot.shtml
    Gemini version at https://techrights.org/n/2024/05/31/The_War_on_Free_Software_Reporters_Part_I_Why_Techrights_Cannot.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The War on Free Software Reporters - Part I
- Why Techrights Cannot be Censored (and Won't be
Censored)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024,
updated May 31, 2024


Microsoft remains by far the biggest culprit, every single time...


                  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇OMG Corrupt Microsoft⦈


IN nearly 18 years we've suffered many DDoS attacks. As far as I can recall,
the first very major DDoS attack, which forced us off of shared hosting, was in
2008 (it continued_afterwards). Tracy began hosting the site - a task he'd do
until 2018 when he dissolved his hosting business altogether. Tracy is still in
our IRC network, even right now.


DDoS attacks generally increased the cost of hosting and complicated the
"logistics".


Throughout the years we've used all sorts of tools to combat DDoS attacks. We
wrote our own programs to respond to DDoS attacks (we didn't outsource the
traffic), we used Varnish for caching, and we also optimised WordPress in a
number of ways. Ever since we abandoned WordPress - as we had planned since
2013 - we suffered no DDoS attacks at all. It would take an enormous amount of
traffic to slow down the site, perhaps as much as 1,000 requests per second
(which would encumber and over-stress throughput capacities, not CPU or RAM).


As far as DDoS attacks are concerned, we're quite safe now. We hardly ever
worry about load spikes.


In recent years we've been subjected to new forms of attacks: doxing and
bullying (even of women and elderly people like our parents). It is vicious and
utterly disgusting. Some of it is outright criminal, so we've opened several
cases at the police. Some involve actual cybercrimes (cracking attempts, not
just social engineering or Denial of Service).


Can we withstand those attacks? Yes, definitely! It's just unfair that the
dignity_of_our_families - i.e. people who have nothing to do with this site -
is being compromised.


If only readers knew how much abuse we've been subjected to, presumably for the
'audacity' to report news about Microsoft and Free software.


In the next part we'll shed more light on some of the latest attack tactics and
how we respond to the nuisance. We've already dealt with much worse abuse in
the past (2009 was probably the worst; we repeatedly defended RMS from the
first cancel mob that year), so we're not worried, our sole aim is to reduce
time-wasting. We have many stories left to release/report on because people
send us material of relevance.


This site was always difficult to suppress because it does not bother with
third parties like social control media or oppressive CDNs such as Clownflare.
It also runs its own IRC network, so speech policing isn't done by some
arbitrary third party. █




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⠋⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3678

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 31/05/2024: MNT Pocket Reform
and Benben v0.5.0⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Hello_again⠀⇛


                       I did the 10k. I think I signed up this year just
                       to show I'm still alive and still going. I didn't
                       train for this. It felt like I was going fast, but
                       it was my worst time yet, besides the first.


                       Next year at this time, I will do the marathon. For
                       now that doesn't mean anything except to runa
                       little bit more often.


                # ⚓ Under_the_weather⠀⇛


                       Feeling a bit sick today. Thinking about skipping
                       out of work early and getting looked at. I thought
                       maybe it was just a seasonal thing, like I get
                       sinus issues a couple times a year usually.


                # ⚓ Typhoon_#1⠀⇛


                       Looking on windy.com, Typhoon #1 is still down by
                       Taiwan, but Tokyo is getting a lashing. The wind is
                       howling outside and the rain is coming down in
                       sheets. It's also terribly muggy.


                       The weather report says it's going to be sunny
                       tomorrow. I'll believe it when I see it.


                # ⚓ A_nice,_sunny_day⠀⇛


                       So the weather was right: today was a nice, hot and
                       sunny day with puffy clouds floating lazily across
                       the sky. Typhoon #1 is still making its way here
                       though, and it'll be just south-west of Tokyo on
                       the 31st, which means rain. And high winds again.


                # ⚓ Being_social_is_hard_when_everything_you_do_is_evil⠀⇛


                       I occasionally reference that I have pretty bad
                       scruples OCD. When I'm not careful it means that
                       I'll end up getting stuck in long periods of being
                       convinced that I'm the most evil person in
                       existence, an absolute monster who should be put
                       down like a rabid animal.


                       The way I mostly handle the scruples obsessions is
                       to live by a lot of restrictive moral rules.
                       Sometimes my strong need for deeply interrogating
                       the ethics of my own actions is good: I think it's
                       a good thing that I'm vegan and have been extremely
                       careful of what kinds of jobs I've taken even when
                       it means I've been very poor. At least I wasn't
                       doing formal methods work for the military, y'know?


          o § Science⠀➾


                # ⚓ Soldering⠀⇛


                       I'm terrible at soldering. And, I ruined two
                       soldering iron tips on my small project this week.


                       I did collect some useful information while
                       researching. But, I don't have a complete set of
                       advice that works.


          o § Technology and Free Software⠀➾


                # ⚓ Roses_are_red...and_orange,_and_blue,_and⠀⇛


                       We went to the "international rose test garden"
                       today that's downtown and then on a long walk
                       through the giant forest to see the big stand of
                       redwoods.


                       I may be, as people say, a Professional Computer
                       Toucher but I never feel as at home as when I'm in
                       the woods.


                       I don't feel like these are contradictory.
                       Computation---at its best---is an extension of mind
                       and body, a way to extend our ability to think and
                       communicate and observe the world around us.


                # ⚓ Linux_II:_The_(not)Linuxing_of_the_Dell⠀⇛


                       So, I spent most of my day trying to deal with my
                       Dell Inspiron E6430. Turns out, the GPU driver---
                       nvidia-legacy 390---isn't available for Fedora
                       anymore. In fact, it's not available for Debian 12,
                       either. Instead, I'd have to put Debian Bullseye on
                       the poor thing and pin the kernel and driver, or
                       find some sort of alternative driver that'll work
                       with latest somehow. Bleh...


                       I mostly wanted to throw Trinity onto it to see if
                       I could live in there for the most part. I may
                       still be able to, but it's going to take some time
                       and effort that I don't exactly have access to at
                       the moment. Mostly to install Debian Bullseye and
                       start updating from there.


                # ⚓ Low-powered_Computing_[Thoughtstream]⠀⇛


                       I'm writing this not long after my previous entry
                       [0], mostly because the more I sat here at my desk,
                       the more my mind dwelled on it.


                       The experience and disappointment with my Dell
                       Latitude's GPU no longer being supported actually
                       made me start wanting to go back to the terminal
                       apps I was using on Linux, and do things with low-
                       powered computers instead of the more modern
                       systems that most develop for these days[^0].


                # ⚓ MNT_Pocket_Reform⠀⇛


                       I think this is my last "new" computer for a long
                       time. It arrived two days ago and now is (mostly)
                       ready for use. The machine is new (from the batch
                       of the first 18 machines shipped to customers) and
                       still are some software details what need to be
                       polished - suspend does not work in default setup
                       (she suspend script refuses to work with the
                       installed CPU and I didn't dare to try suspend it
                       directly, yet; the NVME migration script does
                       strange things).


                # ⚓ Desk_changes⠀⇛


                       I have decided to re-organise my desk.For a few
                       years (~5) I had one shared keyboard for "all" my
                       machines but two LCDs - one for most of systems and
                       one just for the SGI O2 (the O2 works best with the
                       special SGI 1600SW screen - a special 17" 1600x1024
                       device with a non-standard connector).


                # ⚓ ..._and_shoot_them_into_the_Sun⠀⇛


                       This, alas, while perhaps being a psychologically
                       satisfactory outcome to those held in low regard by
                       the one who wants to depose of the others into (or
                       near enough to) the Sun, the task of getting stuff
                       to the Sun is non-trivial. Now, I am not a rocket
                       scientist, nor have I ever played Kerbal Space
                       Program, but the gist of the problem is the Earth
                       falls (and, luckily for us, so far) continues to
                       miss the Sun at some velocity, roughly 7,170 rods/
                       microfortnight. That's fast! The velocity covers
                       something like 200 cricket fields set end-to-end
                       per second, though why there are cricket fields set
                       out end-to-end in space is left as an exercise to
                       the reader.


                # ⚓ Benben_v0.5.0_Now_in_Soft_Feature_Freeze,_Release_Date
                  Set⠀⇛


                       WOO! Benben v0.5.0 is now basically "finished",
                       minus testing bug fixes. I've placed it into a soft
                       feature freeze, with a hard feature freeze
                       scheduled for 17 June 2024, and a tentative release
                       date scheduled for 29 July 2024. The soft freeze is
                       just in case I forgot to add something I really
                       wanted, or deem something so easy that it's trivial
                       to add. So basically, it's all testing from here on
                       out. I've given myself extra time just because
                       there's SO MUCH to test in this release.


                # ⚓ The_Revolution_Will_Not_Be_In_Proportional_Width_Font⠀⇛


                       In the above link you will find what I believe to
                       be a completely counterproductive and silly
                       approach to thinking about terminals and ASCII.


                       1. List a set of problems in an unserious way. 2.
                       Propose a vague solution (paraphrase: "something
                       other than a terminal").


                       This approach to text will lead to the following
                       behavior: Not taking the terminal seriously, and
                       not solving problems for the terminal. Or, waiting
                       for the fancy new solution to arrive. (It will
                       never arrive.) Need I remind anyone that the Gemini
                       protocol was designed with the terminal in mind?


                # § Programming⠀➾


                      # ⚓ Git_Super_-_a_tiny_script_for_the_stacked_diff
                        workflow⠀⇛


                             Huya, I discovered today that the git
                             workflow I've been using for years have a
                             name. Some folks on the internet call this:
                             The stacked diff workflow


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





                    ䷩ 𝚕𝚒𝚗𝚎 3954

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 31/05/2024: Escalations in Ukraine
and Russia, National Reporter's Shield Law in
US⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Dhole Moments ☛ Furries_Are_Losing_the_Battle_Against_Scale_-
            Dhole_Moments⠀⇛


                 Many of the most annoying and pervasive problems with the
                 furry fandom–from the cyclical nature of Twitter
                 discourse to the increasingly frustrating issue of furry
                 convention main hotel registrations selling out
                 immediately after opening–are entirely predictable if you
                 know even a little bit of mathematics.


                 And it’s going to get worse. If you don’t believe me,
                 read on.


          o ⚓ Chloé Vulquin ☛ My_Thoughts_On_Notes⠀⇛


                 This has led to my note output to multiply. I need to
                 take notes about what I do in a given day, comments on
                 what I find, what needs to be done, and more.
                 Additionally, the notes are heterogenous in nature, such
                 that if I was to group them “logically”, they would
                 quickly become a pain to search. Being already familiar
                 with Luhmann’s Zettelkasten, I figured I would go over
                 the software available for organising notes, since I
                 don’t exactly have the space needed to do a physical note
                 cabinet.


                 Instead of focusing on terminology, I’ll try to express
                 the trends I found in more practical terms. To this end,
                 I should first describe what the conclusions (i.e
                 consequences) of what I’d want are first.


          o ⚓ Lou Plummer ☛ I_Like_Your_Blog_If...⠀⇛


                 As I spend less and less time on commercial websites and
                 more time exploring the blogs on IndieWeb platforms, I am
                 developing a type and preferences. There's plenty to
                 choose from.


          o ⚓ Gregory Hammond ☛ China_WeChat:_could_a_competitor_exist_outside?
            -_Gregory_Hammond⠀⇛


                 Using one app could make it easier for many people,
                 especially those who are often overwhelmed with
                 technology, or don’t use it often. How could it make life
                 easier? One example is instead of needing to buy packages
                 from your cell phone company for calling minutes and
                 texting, you may just need the one for data. In some
                 places in the world, data on a cell phone is the most
                 expensive package.


                 You could go into the app to contact a delivery company
                 about an upcoming package, or view details about that
                 package without having to leave the app. WeChat also has
                 the ability to have an account where you can post like
                 social media. What about being able to pay using it just
                 by scanning a code and using the app, and that includes
                 paying a friend. While being able to chat with family and
                 friends. This seems like so many features rolled all into
                 one app, and that’s kind of what WeChat currently is.


          o ⚓ Lykolux ☛ Small_blog_changes⠀⇛


                 It is satisfying to tinker with CSS and get results after
                 a short amount of time. If you have any ideas for
                 improvments, feel free to reach me out!


          o ⚓ Lykolux ☛ Nothing_but_work⠀⇛


                 I worked a lot today, because there was a lot to do,
                 quickly. Work-Life balance is sometimes hard, but the
                 most important is this balance is balanced most of the
                 time. So I’m writing a quick one tonight, because I’m
                 beat.


          o § Licensing / Legal⠀➾


                # ⚓ 404 Media ☛ Watch_Man_Park_His_Car_On_Zoom_While_Appearing
                  Before_a_Judge_For_Suspended_License_Trial⠀⇛


                       A Michigan man stunned a court into silence when he
                       logged into Zoom to attend his own suspended
                       license hearing while driving a car.


                       Corey Harris joined the Zoom call to appear before
                       District Judge Cedric Simpson in Ann Arbor,
                       Michigan on May 15 in the middle of pulling up to
                       his doctor’s office, he said in the livestream. The
                       full day of hearings were streamed on YouTube as
                       part of Simpson's criminal docket proceedings.


          o § Science⠀➾


                # ⚓ NPR ☛ What_is_Manhattanhenge?_Here's_when_and_where_you_can
                  see_the_phenomenon⠀⇛


                       Even though Tyson likened Manhattanhenge to the
                       sunset views at solstice in Stonehenge, England,
                       city planners did not intentionally build Manhattan
                       for the purpose of having epic sunsets.


                       “When we had people building the grid of Manhattan
                       in the early 19th century, they didn't realize that
                       when the sun was going to arc at a certain time of
                       year, we'd be seeing the sun right down the streets
                       of Manhattan,” he shared.


          o § Education⠀➾


                # ⚓ Anne Sturdivant ☛ Brag_for_yourself.⠀⇛


                       I just read Melanie Richard's Coping with imposter
                       syndrome yesterday and was reminded of a "brag
                       document" (more here) which is a great thing to
                       have for your staff manager, to keep a log for
                       doing quarterly or yearly reviews, or for merit
                       increase/promotion requests. It got me thinking
                       this might be something I want to have on my weblog
                       at /brag (yay! another slash page!).


                # ⚓ Phil Eaton ☛ How_I_run_a_software_book_club⠀⇛


                       This post is for folks who are interested in
                       running their own book club. None of these ideas
                       are novel. I co-opted the best parts I saw from
                       other people running similar things. And hopefully
                       you'll improve on my experience too, should you
                       try.


                       Despite the length of this post running a book club
                       takes almost no noticeable effort, other than when
                       I need to select and confirm discussion leaders. It
                       is the limited-effort-required to thank that I've
                       kept up the book clubs so consistently.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Can_You_Hear_Me_Now?_Try_These_Headphones⠀⇛


                       When you are young, you take it for granted that
                       you can pick out a voice in a crowded room or a
                       factory floor. But as you get older, your hearing
                       often gets to the point where a noisy room merges
                       into a mishmash of sounds. University of Washington
                       researchers have developed what they call Target
                       Speech Hearing. In plain English, it is an AI-
                       powered headphone that lets you look at someone and
                       pull their voice out of the chatter. For best
                       results, however, have to enroll their voice first,
                       so it wouldn’t make a great eavesdropping device.


                # ⚓ CNX Software ☛ Arm_unveils_Cortex-X925_and_Cortex-A725
                  CPUs,_Immortalis-G925_GPU,_Kleidi_Hey_Hi_(AI)_software⠀⇛


                       Arm has just announced new Armv9 CPUs and
                       Immortalis GPUs for mobile SoCs, as well as the
                       Kleidi Hey Hi (AI) software optimized for Arm CPUs
                       from Armv7 to Armv9 architectures. New Armv9.2 CPU
                       cores include the Cortex-X925 “Blackhawk” core with
                       significant CPU and Hey Hi (AI) performance
                       improvements, the Cortex-A725 with improved
                       efficiency, and a refreshed version of the Cortex-
                       A520 providing 15 percent efficiency improvements.


                # ⚓ Rob Knight ☛ The_Converse_Experiment:_Report_One⠀⇛


                       The day after I just put them on because the
                       wedding was over and they could just go into the
                       normal shoe rotation. Then a month went by and I
                       realised I had worn them every day which gave me a
                       data point I wish I'd done for the many other pairs
                       of Converse I've bought over the years: how long
                       does a pair actually last? I had a vague idea but
                       nothing concrete.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Democracy Now ☛ PFAS_Cover-Up:_How_3M_Hid_Risks_of_Forever
                  Chemicals_&_“Gaslit”_Scientist_Who_Tried_to_Sound_Alarm⠀⇛


                       As public concern grows about the health and
                       environmental impacts of so-called forever
                       chemicals, a new investigation by ProPublica and
                       The New Yorker reveals that 3M, the American
                       manufacturing giant, discovered and concealed the
                       risks of these toxic substances for decades. PFAS
                       are used in everyday products, from nonstick
                       cookware to food packaging, but take decades or
                       longer to break down in the body and environment.
                       They have been found in the blood of almost every
                       person in the United States and are linked to
                       serious health effects.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Wisconsin Public Radio ☛ ‘Wall_Street_Journal’_layoffs
                  continue,_despite_lucrative_AI_deal_and_record_profits⠀⇛


                       The Wall Street Journal has laid off even more
                       journalists, despite a surge in paid subscribers,
                       strong profits at its parent company, and a new
                       nine-figure licensing deal with OpenAI.


                       The union representing the newsroom –- the
                       International Association of Publishers’ Employees
                       –- staged an hour-long walkout Thursday to object
                       to the job cuts. Staffers stuck Post-it notes
                       protesting the move on the glass walls of the
                       office of Editor in Chief Emma Tucker, whose vision
                       for the paper has come under fire.


                       The layoffs of at least eight reporters who covered
                       national and breaking news follow double-digit cuts
                       to staff in Washington and abroad, although the
                       paper has added some positions back in recent
                       months. The union tabulation only covers those
                       represented by the local; others have been laid off
                       as well.


                # ⚓ IT Pro Today ☛ Amazon_Workers_Walk_Out_Amid_Layoffs,_Citing
                  Concerns_for_Climate⠀⇛


                       Hundreds of Amazon staff members walked off the job
                       on Wednesday afternoon demanding a flexible remote
                       work policy and renewed commitments to reducing
                       carbon emissions to zero.


                       The walkout is a collaboration between Amazon
                       Employees for Climate Justice and an informal group
                       of employees who oppose Amazon's mandated return to
                       office. Employees say recent layoffs and the
                       mandate - which increases emissions as workers
                       commute - have left them questioning whether Amazon
                       executives are leading the company in the right
                       direction.


                       "It's definitely concerning how low the morale is,"
                       said a Seattle-based Amazon employee who walked out
                       and spoke on the condition of anonymity out of fear
                       of retaliation. "There's a lot of distrust in
                       leadership right now."


                # ⚓ Andy Bell ☛ How_I’m_using_“AI”⠀⇛


                       I put “AI” in quotes in my writing because the
                       current iteration of “AI” is hardly intelligent.
                       But, whether I like it or not, it is the colloquial
                       term right now.


                       I don’t think it’s a surprise to anyone that I am
                       certifiably Not A Fan™ of “AI” either. I don’t like
                       art and culture being diluted into unseasoned slop
                       and I certainly don’t like “AI” being a cause of
                       mass-layoffs and putting people in real danger in a
                       lot of cases.


                # ⚓ uni Oxford ☛ What_does_the_public_in_six_countries_think_of
                  generative_AI_in_news?⠀⇛


                       Based on an online survey focused on understanding
                       if and how people use generative artificial
                       intelligence (AI), and what they think about its
                       application in journalism and other areas of work
                       and life across six countries (Argentina, Denmark,
                       France, Japan, the UK, and the USA), we present the
                       following findings.


                # ⚓ The Register UK ☛ MIT_professor_hoses_down_predictions_AI
                  will_boost_GDP⠀⇛


                       Acemoglu goes on to argue that AI is unlikely to
                       significantly improve wages and that even if the
                       technology improves the productivity of low-end and
                       middle-performing workers, it may not reduce
                       inequality.


                       "I estimate that AI will not reduce inequality and
                       is likely to have a negative effect on the real
                       earnings of low-education women (especially white,
                       native-born low-education women)," he asserts in
                       his paper. His findings also suggest that "AI will
                       further expand the gap between capital and labor
                       income as a whole."


                # ⚓ Wired ☛ Chatbots_Are_Entering_Their_Stone_Age⠀⇛


                       Anthropic, a competitor to OpenAI, announced a
                       major new product today that attempts to prove the
                       thesis that tool use is needed for AI’s next leap
                       in usefulness. The startup is allowing developers
                       to direct its chatbot Claude to access outside
                       services and software in order to perform more
                       useful tasks. Claude can, for instance, use a
                       calculator to solve the kinds of math problems that
                       vex large language models; be required to access a
                       database containing customer information; or be
                       compelled to make use of other programs on a user’s
                       computer when it would help.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Latvia ☛ Company_reportedly_fell_victim_to_million-
                        euro_phone_fraud⠀⇛


                             Cases of fraud on the Internet and over the
                             phone have become so commonplace that almost
                             everyone has come across attempts by
                             fraudsters to steal data or money.
                             One particular case was experienced this
                             year, when a million euros were defrauded
                             from a company at one time through the
                             company's accountant, reported Latvian
                             Television May 28.


                # § Privacy/Surveillance⠀➾


                      # ⚓ The Record ☛ Senate_Intel_Committee_approves_changes
                        narrowing_scope_of_Section_702_surveillance_law⠀⇛


                             U.S. senators want to tweak a recently
                             renewed surveillance authority in an attempt
                             to honor a pledge to narrow which entities
                             the federal government can compel to hand
                             over communications.


                             The Senate Intelligence Committee last week
                             unanimously approved legislation that would
                             amend a bill that reauthorized Section 702 of
                             the Foreign Intelligence Surveillance Act.
                             The statute allows the National Security
                             Agency to vacuum up the content of calls,
                             emails and other electronic information of
                             overseas targets from U.S. technology
                             providers. It also sweeps up the personal
                             data of an unknown number of Americans.


                      # ⚓ Cyble Inc ☛ 7_New_Pegasus_Spyware_Infections_Spotted
                        In_Europe⠀⇛


                             Seven Russian and Belarusian-speaking
                             independent journalists and opposition
                             activists based in Europe were targeted or
                             infected with NSO Group’s proprietary Pegasus
                             spyware.


                             A joint investigation by Citizen Lab and
                             Access Now detailed incidents from August
                             2020 to January 2023 and concluded that a
                             single NSO Group customer might be
                             responsible for at least five of these cases.


                      # ⚓ The Verge ☛ Google_Home_adds_a_Favorites_Widget_to
                        Android⠀⇛


                             Quick access to smart home devices is coming
                             to Android in the form of a new Google Home
                             Favorites widget. This will let you control
                             devices, actions, and automations directly
                             from the homescreen of your phone. There’s
                             also a new Favorites tile and complication
                             coming to Wear OS for accessing frequently
                             used devices right from your wrist.


                      # ⚓ Meduza ☛ Pegasus_spyware_was_used_to_target_seven
                        more_journalists_and_activists_in_the_E.U.⠀⇛


                      # ⚓ Citizen Lab ☛ By_Whose_Authority?_Pegasus_targeting
                        of_Russian_&_Belarusian-speaking_opposition_activists
                        and_independent_media_in_Europe⠀⇛


                             In a joint investigation with Access Now, we
                             found that seven Russian and Belarusian-
                             speaking independent journalists and
                             opposition activists based in Europe were
                             targeted and/or infected with NSO Group’s
                             Pegasus mercenary spyware.


                      # ⚓ AccessNow ☛ Exiled,_then_spied_on:_Civil_society_in
                        Latvia,_Lithuania,_and_Poland_targeted_with_Pegasus
                        spyware⠀⇛


                             At least seven more Russian, Belarusian,
                             Latvian, and Israeli journalists and
                             activists have been targeted with Pegasus
                             within the EU.


                # § Confidentiality⠀➾


                      # ⚓ The Register UK ☛ Indian_stock_exchange_finally
                        encrypting_all_trader_messages⠀⇛


                             India's Bombay Stock Exchange (BSE) has told
                             market participants they need to adopt
                             encryption – which, shockingly, isn't already
                             implemented – for certain messages sent to
                             its trading platforms when using its Enhanced
                             Trading Interface (ETI).


                             ETI is the bourse's interface for traders,
                             and sent out its directive last Monday.


          o § Defence/Aggression⠀➾


                # ⚓ The Record ☛ All_democracies_'struggling’_with_foreign
                  manipulation,_warns_Estonian_president⠀⇛


                       “The cyber world allows our adversaries to cheaply
                       and covertly subvert our society. Cyber attackers
                       are becoming more and more unpredictable and
                       crafty,” he said in a keynote speech at the
                       International Conference on Cyber Conflict (CyCon),
                       adding that the number of high-impact cyber
                       incidents in Estonia had increased by 25% in 2023.


                # ⚓ Wired ☛ The_Unusual_Espionage_Act_Case_Against_a_Drone
                  Photographer⠀⇛


                       On January 5, 2024, Fengyun Shi flew to Virginia
                       while on leave from his graduate studies at the
                       University of Minnesota and rented a Tesla at the
                       airport. His research focused on using AI to detect
                       signs of crop disease in photos. Shi’s subject that
                       week wasn’t plants, however, but allegedly the
                       local shipyards—the only ones manufacturing the
                       latest generation of Navy carrier ships in the
                       country, and nuclear submarines as well.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_national_security_police
                  make_7th_arrest_under_new_security_law⠀⇛


                       A 53-year-old woman was arrested by Hong Kong
                       national security police on Wednesday over
                       “seditious” online posts, becoming the seventh
                       person apprehended under the new law in a case
                       linked to jailed human rights activist Chow Hang-
                       tung.


                # ⚓ The Straits Times ☛ China_wants_ties_with_Arab_states_that
                  will_be_model_for_world_peace⠀⇛


                       BEIJING - China wants to build up its relations
                       with Arab states as a benchmark for maintaining
                       world peace and stability, President Pooh-tin
                       Jinping said in a speech on Thursday that also
                       addressed the Gaza crisis.


                # ⚓ France24 ☛ Trump's_former_UN_ambassador_Nikki_Haley_writes
                  'Finish_Them'_on_Israeli_shell⠀⇛


                       Former US presidential hopeful Nikki Haley has been
                       photographed writing "Finish Them" on an Israeli
                       shell as she toured sites near the northern border
                       with Lebanon.


                # ⚓ JURIST ☛ Netherlands_public_prosecution_service_prosecutes
                  teen_boy_for_assaulting_politician_Thierry_Baudet⠀⇛


                       A 16-year-old boy who assaulted a politician will
                       be prosecuted by the public prosecution service on
                       charges of attempted serious assault, local media
                       said on Monday. The boy, who was 15 at that time,
                       assaulted Thierry Baudet, the leader of Forum voor
                       Democratie, in Groningen last year.


                # ⚓ EDRI ☛ La_Quadrature_du_Net_takes_legal_action_against_the
                  French_government’s_censorship_of_Fentanylware_(TikTok)_in
                  New_Caledonia [Ed: "censorship of Fentanylware (TikTok) in
                  New Caledonia" as in preventing China riling up violent
                  riots?]⠀⇛


                       Through an emergency proceeding (reféré-liberté)
                       filed last week, La Quadrature du Net asked the
                       Conseil d’État (Council of State) to suspend French
                       Prime Minister Gabriel Attal’s decision to block
                       the Fentanylware (TikTok) platform in New
                       Caledonia.


                # ⚓ EDRI ☛ EDRi-gram,_29_May_2024⠀⇛


                       EDRi member La Quadrature du Net is taking legal
                       action against the French prime minister’s decision
                       to block Fentanylware (TikTok) in New Caledonia.
                       The French government is resorting to the tried-
                       and-tested authoritarian reflexes of obstructing
                       people’s freedom of expression as tensions in the
                       archipelago reach new heights.


                # ⚓ France24 ☛ TikTok_ban_lifted_on_French_overseas_territory
                  of_New_Caledonia⠀⇛


                       French authorities on Wednesday said they had
                       lifted a ban in New Caledonia on TikTok, which they
                       suspect of fuelling recent unrest in the French
                       Pacific territory.


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


                      # ⚓ Latvia ☛ Sale_of_Rīga's_'Moscow_House'_will_raise
                        funds_for_Kyiv⠀⇛


                             The sale of a former Russian political and
                             cultural hub in Rīga will raise thousands of
                             euros for Ukraine, following a decision of
                             the Latvian parliament, the Saeima, on May
                             30.


                      # ⚓ NYPost ☛ Biden_gives_Ukraine_permission_to_use_US
                        weapons_to_attack_Russia_—_marking_shift_in_long-
                        standing_policy⠀⇛


                             A US official noted, however, that Ukraine
                             will not be allowed to use long-range US
                             weapons to hit military targets deep inside
                             Russian territory.


                      # ⚓ France24 ☛ Biden_allows_Ukraine_to_hit_Russia_with_US
                        weapons_to_defend_Kharkiv⠀⇛


                             President Joe Biden has lifted restrictions
                             on Ukraine using weapons supplied by the
                             United States against targets on Russian
                             territory, but only to defend the under-fire
                             Kharkiv region, a senior US official said
                             Thursday.


                      # ⚓ France24 ☛ NATO_chief_Stoltenberg_pushes_alliance_to
                        let_Ukraine_strike_targets_inside_Russia⠀⇛


                             NATO chief Jens Stoltenberg pushed at the
                             start of a meeting of the alliance's foreign
                             ministers on Thursday to let Ukraine use
                             Western weapons to strike inside Russia, a
                             move sought by Kyiv but opposed for now by
                             its chief backer Washington.


                      # ⚓ LRT ☛ Former_US_ambassador_to_NATO:_Inviting_Ukraine
                        to_join_would_be_meaningless⠀⇛


                             The US administration believes that inviting
                             Ukraine to join NATO is meaningless and will
                             therefore not be taken at the Washington
                             summit in July. “Much better to say under
                             what conditions we will all agree to move
                             forward,” Ivo H. Daalder, head of the Chicago
                             Council on Global Affairs, told LRT.lt in an
                             exclusive interview.


                      # ⚓ RFERL ☛ One_Dead,_12_Wounded_In_Russian_Shelling_Of
                        5-Story_Building_In_Kharkiv⠀⇛


                             Russian forces hit a five-story residential
                             building in the northeastern city of Kharkiv,
                             causing a fire and possibly trapping people
                             in the burning rubble, Oleh Synyehubov, the
                             governor of the Kharkiv region, said after
                             the attack that occurred around midnight
                             local time on May 30.


                      # ⚓ RFERL ☛ Moldovan_Parliament_Denounces_Russian
                        'Genocide'_In_Ukraine⠀⇛


                             Moldova's parliament denounced Russia's
                             invasion of Ukraine as "genocide" in
                             connection with Moscow's treatment of
                             children in occupied areas, but the
                             assembly's Moscow-friendly opposition parties
                             refused to take part in the vote.


                      # ⚓ RFERL ☛ Biden_Partially_Lifts_Ban_On_Ukraine_Using
                        U.S._Weapons_In_Strikes_Inside_Russia:_Reports⠀⇛


                             U.S. President Joe Biden has given Ukraine
                             the go-ahead to use U.S. weapons to strike
                             inside Russia for the limited purpose of
                             defending the eastern city of Kharkiv,
                             according to media reports quoting
                             unidentified sources.


                      # ⚓ RFERL ☛ Russia_Not_Invited_To_D-Day_80th_Anniversary,
                        French_Presidency_Says⠀⇛


                             Russia will not be invited to events marking
                             the 80th anniversary of the D-Day landings
                             next week given its war of aggression against
                             Ukraine, the French Presidency said on May
                             30.


                      # ⚓ RFERL ☛ Germany_Pledges_New_$542_Million_Arms_Package
                        To_Ukraine⠀⇛


                             German Defense Minister Boris Pistorius on
                             May 30 announced a new German arms package
                             worth 500 million euros ($542 million) to
                             support Ukraine.


                      # ⚓ RFERL ☛ Sri_Lanka_Tightens_Controls_To_Stop_Men_From
                        Being_Duped_Into_Fighting_In_Ukraine⠀⇛


                             Sri Lanka will tighten controls to try to
                             stop its men being lured to Russia to fight
                             in Ukraine with often false promises of
                             salaries and benefits.


                      # ⚓ RFERL ☛ Ukraine_Says_Naval_Drones_Destroy_Two_Russian
                        Boats_In_Crimea⠀⇛


                             The Ukrainian Defense Ministry's Main
                             Intelligence Directorate (HUR) has said its
                             naval drones destroyed two Russian "Tunets"
                             boats in Crimea.


                      # ⚓ RFERL ☛ Russian_Jailed_For_13_Years_For_Urging
                        Russian_Troops_To_Surrender⠀⇛


                             A military court has sentenced a resident of
                             the western Russian region of Chelyabinsk to
                             13 years in a maximum-security prison and
                             fined him 200,000 rubles ($2,245) on a charge
                             of high treason for calling on those
                             mobilized to the military to surrender to
                             Ukrainian forces.


                      # ⚓ RFERL ☛ Stoltenberg_Floats_Talks_On_Lifting_Of
                        Weapons_Restrictions_As_NATO_Meets_In_Prague⠀⇛


                             Ukraine can prevail in its battle to repel
                             Russian forces with the "robust support" of
                             its allies, NATO chief Jens Stoltenberg said,
                             as foreign ministers from the military
                             alliance's 32 member countries gathered in
                             Prague to discuss a fresh military aid
                             framework for Kyiv.


                      # ⚓ The Straits Times ☛ Debris_analysis_shows_Russia
                        using_North_Korean_missiles_in_Ukraine,_US_military
                        says⠀⇛


                             WASHINGTON - A Pentagon intelligence agency
                             says analysis of debris imagery confirms that
                             Russia has fielded North Korean missiles in
                             its war in Ukraine, according to a report
                             summary released in an unclassified form on
                             Thursday.


                      # ⚓ The Straits Times ☛ US_officials_meet_China’s_vice
                        foreign_minister_after_sanctions_warning⠀⇛


                             The meeting comes a day after US accused
                             China of supporting Russia's war in Ukraine.


                      # ⚓ CS Monitor ☛ How_a_lethal_Ukrainian_sea_drone_is
                        protecting_the_global_food_supply⠀⇛


                             One lesson of the Russia-Ukraine war is that
                             Ukrainian farmers’ prosperity and the world’s
                             food security are very much linked. Now, in
                             David-and-Goliath fashion, a Ukrainian sea
                             drone has been deployed in the Black Sea to
                             help keep the grain flowing.


                      # ⚓ New York Times ☛ Under_Pressure,_Biden_Allows_Ukraine
                        to_Use_U.S._Weapons_to_Strike_Inside_Russia⠀⇛


                             White House officials said the president’s
                             major policy shift extended only to what they
                             characterized as acts of self-defense so that
                             Ukraine could protect Kharkiv, its second-
                             largest city.


                      # ⚓ New York Times ☛ Ukrainian_Drone_Strikes_Target
                        Russian_Nuclear_Radar_Stations⠀⇛


                             A radar facility more than 1,100 miles into
                             Russia was damaged, satellite imagery showed.
                             The attacks have drawn concern from U.S.
                             officials.


                      # ⚓ New York Times ☛ Trump_Is_Guilty_on_All_Counts⠀⇛


                             Also, Biden will allow Ukraine to use U.S.
                             weapons in Russia. Here’s the latest at the
                             end of Thursday.


                      # ⚓ New York Times ☛ Taking_the_Fight_to_Russia:_The_West
                        Weighs_Ukraine’s_Use_of_Its_Weapons⠀⇛


                             More NATO allies are backing Kyiv’s pleas to
                             allow its forces to conduct strikes in
                             Russian territory with Western weapons.


                      # ⚓ New York Times ☛ Ukraine_Warns_of_Deepening_Russian
                        Threat_in_the_North⠀⇛


                             Analysts say an offensive in the Kharkiv or
                             Sumy regions could stretch Ukrainian troops
                             to the breaking point and allow Moscow to
                             punch through.


                      # ⚓ Meduza ☛ In_their_own_words,_Kharkiv_residents
                        describe_life_under_constant_Russian_bombardment⠀⇛


                      # ⚓ Meduza ☛ Kremlin_spokesman_blames_West_for
                        ‘provoking’_Ukraine_into_continuing_‘senseless_war’⠀⇛


                      # ⚓ JURIST ☛ EU_Parliament_probe:_police_raid_targets
                        suspected_in_alleged_Russian_interference_operations
                        ahead_of_elections⠀⇛


                             Belgian Police conducted raids on Wednesday
                             in an investigation into alleged Russian
                             interference within the European Parliament,
                             particularly focusing on accusations that
                             Members of the European Parliament (MEPs)
                             were paid to promote Russian propaganda via
                             the Voice of Europe website.


                      # ⚓ LRT ☛ Four_suspects_in_Lithuania‘s_probe_into
                        Vičiūnai_Group‘s_exports_to_Russia⠀⇛


                             Lithuania’s law enforcement authorities
                             investigating the possible export of
                             sanctioned goods to Russia by a company owned
                             by Vičiūnai Group have identified four
                             suspects, the LRT Investigation Team reports.


                      # ⚓ RFERL ☛ Leak_Suggests_Bulgarian_PM_Tried_To_Pull
                        Support_For_Srebrenica_Genocide_Resolution_At_UN⠀⇛


                             Leaked documents of a back-and-forth between
                             Sofia and its UN envoy have sparked
                             accusations that caretaker Prime Minister
                             Dimitar Glavchev succumbed to “external
                             pressure” over a widely followed UN vote in
                             an effort to appease neighboring Serbia or
                             Russia.


                      # ⚓ RFERL ☛ Large_Fire_Breaks_Out_In_Eastern_Moscow⠀⇛


                             A large fire broke out early on May 30 in the
                             eastern part of Moscow in a production
                             building and a warehouse, Russia's
                             Emergencies Ministry said.


                      # ⚓ New York Times ☛ OpenAI_Says_Russia_and_China_Used
                        Its_Hey_Hi_(AI)_in_Covert_Campaigns⠀⇛


                             Iran and an Israeli company also exploited
                             the tools in online influence efforts, but
                             none gained much traction, an Proprietary
                             Chaffbot Company report said.


                      # ⚓ New York Times ☛ Europe_Banned_Russia’s_RT_Network.
                        Its_Content_Is_Still_Spreading.⠀⇛


                             A study found that hundreds of sites, many
                             without obvious Kremlin links, copied Russian
                             propaganda and spread it to unsuspecting
                             audiences ahead of the E.U. election.


                      # ⚓ Atlantic Council ☛ Panikoff_quoted_in_The_Independent
                        on_Russia_using_Iranian_drones_to_bomb_Ukranian
                        civilians⠀⇛


                      # ⚓ JURIST ☛ Poland_to_further_fortify_border_with
                        Belarus_after_migrant_stabs_soldier⠀⇛


                             Polish Prime Minister Donald Tusk announced
                             on Wednesday that Poland will further fortify
                             its border with Belarus following an incident
                             where a Polish soldier was injured by a
                             migrant. “We will defend our border with all
                             available means,” Donald Tusk said after the
                             attack occurred.


                      # ⚓ LRT ☛ Minsk-linked_Lithuanian_company_to_produce
                        passports_for_Belarusian_opposition⠀⇛


                             Garsų Pasaulis, a Lithuanian company that
                             used to have links with an oligarch close to
                             the Minsk regime, will produce alternative
                             passports designed by the Belarusian
                             opposition, the 15min news website reports on
                             Thursday.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Rohan Kumar ☛ Takeaways_from_the_Google_Content_Warehouse
                  API_documentation_leak⠀⇛


                       In March, the official Elixir client for Google
                       APIs received an accidental commit for internal
                       non-public APIs. The commit added support for
                       Google’s Content Warehouse API, which includes
                       Google’s 14,000+ search ranking factors. Oops! Some
                       people noticed this after its redaction earlier
                       this month, and the news broke on May 28. You can
                       read through the Content Warehouse API reference on
                       HexDocs. I skimmed through these and read some blog
                       posts by others who looked more deeply.


                       In particular, I referenced Secrets from the
                       Algorithm: Google Search’s Internal Engineering
                       Documentation Has Leaked by Mike King. Note that
                       Mike King’s article doubles as an advertisement for
                       his company’s services and for the legitimacy of
                       search engine optimization (SEO) companies in
                       general. I don’t endorse that message. I disagree
                       with some of its claims, and elaborate on them in
                       the coming sections. That said, I found the article
                       well-researched. It cross-references information
                       against other leaks, too.


                # ⚓ New Yorker ☛ Piecing_Together_the_Secrets_of_the_Stasi⠀⇛


                       East Germans all seem to know a few stories like
                       Genin’s. They tell them about their neighbors and
                       co-workers and best friend’s cousins. They watch
                       “The Lives of Others”—the 2006 film about a Stasi
                       agent who spies on a playwright and his
                       girlfriend—and shake their heads, saying, “They
                       should have made it about my Tante Hilda.” The
                       sheer number and surreal specificity of Stasi
                       stories are proof of the agency’s insidious reach,
                       of how deeply it infiltrated every corner of East
                       German society. But they also show how thoroughly
                       its secrets were later exposed. In January, 1992,
                       the newly unified German government made almost the
                       entire archive of Stasi reports available to the
                       public: a hundred and eleven kilometres of files,
                       divided into some nine thousand index headings,
                       covering half a century of surveillance. It was the
                       most radical release of state secrets in history:
                       WikiLeaks on a vast scale.


                       The Stasi files offer an astonishingly granular
                       picture of life in a dictatorship—how ordinary
                       people act under suspicious eyes. Nearly three
                       hundred thousand East Germans were working for the
                       Stasi by the time the Wall fell, in 1989, including
                       some two hundred thousand inoffizielle Mitarbeiter,
                       or unofficial collaborators, like Genin. In a
                       population of sixteen million, that was one spy for
                       every fifty to sixty people. In the years since the
                       files were made public, their revelations have
                       derailed political campaigns, tarnished artistic
                       legacies, and exonerated countless citizens who
                       were wrongly accused or imprisoned. Yet some of the
                       files that the Stasi most wanted to hide were never
                       released. In the weeks before the Wall fell, agents
                       destroyed as many documents as they could. Many
                       were pulped, shredded, or burned, and lost forever.
                       But between forty and fifty-five million pages were
                       just torn up, and later stuffed in paper sacks.


          o § Environment⠀➾


                # ⚓ Kansas Reflector ☛ Environmentalists_dodge_wetlands_threat,
                  but_larger_floodplain_development_lurches_ahead⠀⇛


                       About half of New Boston Crossing’s site rests in
                       the floodplain, but the company’s attorneys and
                       consultants have sought to navigate through
                       objections raised at the city, county and federal
                       levels. The Wichita-based company’s idea has been
                       to gain consent for fill-and-build construction on
                       ground elevated by rock and soil to —
                       hypothetically — rise above inevitable flooding.
                       The elevation material would come from digging an
                       18-acre pond.


                # ⚓ New York Times ☛ The_Right_Kind_of_Tipping_Point⠀⇛


                       For centuries, the burning of coal, oil and gas has
                       produced huge volumes of planet-warming gasses. As
                       a result, global temperatures rose by an average of
                       1.5 degrees Celsius higher than at the dawn of the
                       industrial age, and extreme weather is becoming
                       more frequent.


                       But we now appear to be living through the precise
                       moment when the emissions that are responsible for
                       climate change are starting to fall, according to
                       new data by BloombergNEF, a research firm. This
                       projection is in roughly in line with other
                       estimates, including a recent report from Climate
                       Analytics.


                # § Energy/Transportation⠀➾


                      # ⚓ DeSmog ☛ GB_News_Gives_Dozens_of_Appearances_to_UK’s
                        Main_Climate_Denial_Group⠀⇛


                      # ⚓ DeSmog ☛ Occidental_Petroleum’s_net-zero_strategy_is
                        a_‘license_to_pollute,’_critics_say⠀⇛


                      # ⚓ Nebraska Examiner ☛ 21_states_join_Biden
                        administration_in_bid_to_modernize_nation’s_aging
                        grid⠀⇛


                             Twenty-one states are joining a push by the
                             Biden administration to modernize America’s
                             aging electric grid, which is under pressure
                             from growing demand, severe weather and a
                             changing power generation mix that includes
                             lots of wind and solar.


                             The administration, which has set a goal of a
                             carbon-free power sector by 2035, announced
                             Tuesday that the states had joined what it
                             called the “Federal-State Modern Grid
                             Deployment Initiative,” which is intended to
                             “help drive grid adaptation quickly and cost-
                             effectively to meet the challenges and
                             opportunities that the power sector faces.”


                      # ⚓ David Rosenthal ☛ One_Heck_Of_A_Halvening⠀⇛


                             The fundamental idea behind Bitcoin is that,
                             if you restrict the supply of something, its
                             price will rise. That is why the system
                             arranges that there will only ever be 21
                             million Bitcoin by halving the reward paid
                             for mining the next block every 210,000
                             blocks (about every four years), an event
                             called the "halvening" (or more recently just
                             the halving). It is an article of faith among
                             the crypto-bros that, after the halvening,
                             the price will rise. For example: [...]


                # § Wildlife/Nature⠀➾


                      # ⚓ Latvia ☛ Latvian_municipalities_failing_in_felling
                        and_forest_management⠀⇛


                             Municipalities do not deal effectively with
                             the forest resources under their possession,
                             and by not properly managing forests,
                             municipalities reduce the future value of the
                             forest and the possibility to earn thousands
                             of euros in revenue, according to a new
                             report from the State Audit Office (Valsts
                             Kontrole, VK).


                # § Overpopulation⠀➾


                      # ⚓ Omicron Limited ☛ Scientists_predict_high_groundwater
                        depletion_risk_in_South_Korea_by_2080⠀⇛


                             Groundwater forms when precipitation such as
                             rain and snow seeps into the soil,
                             replenishing rivers and lakes. This resource
                             supplies drinking water. However, a recent
                             study has alarmed the scientific community by
                             predicting that approximately three million
                             people in currently untapped areas of Korea
                             could face groundwater depletion by 2080.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ New York Times ☛ Former_Intelligence_Chief_Tapped_as_Next
                  Dutch_Prime_Minister⠀⇛


                       Dick Schoof is poised to be the country’s first new
                       leader in over 13 years. His selection came as a
                       relative surprise, after more than six months of
                       negotiations to form a governing coalition.


                # ⚓ The Washington Post ☛ America’s_best_decade,_according_to
                  data⠀⇛


                       We did spot some peaks: When asked which decade had
                       the most moral society, the happiest families or
                       the closest-knit communities, White people and
                       Republicans were about twice as likely as Black
                       people and Democrats to point to the 1950s. The
                       difference probably depends on whether you remember
                       that particular decade for “Leave it to Beaver,”
                       drive-in theaters and “12 Angry Men” — or the Red
                       Scare, the murder of Emmett Till and massive
                       resistance to school integration.


                       “This was a time when Repubs were pretty much
                       running the show and had reason to be happy,”
                       pioneering nostalgia researcher Morris Holbrook
                       told us via email. “Apparently, you could argue
                       that nostalgia is colored by political preferences.
                       Surprise, surprise.”


                # ⚓ Hamilton Nolan ☛ Behold_The_Terrors_of_the_Texas_Republican
                  Platform⠀⇛


                       I have pulled out just a few notable parts of the
                       50-page platform below. In order to avoid this
                       turning into a long ass Wikipedia-style entry, let
                       me stipulate up front: The Texas Republicans love
                       guns and hate gays and hate taxes and love Jesus
                       and hate public schools and love oil and hate
                       immigrants. I’m not writing a comprehensive survey
                       here but you should understand that basically the
                       entire national Republican platform is in here,
                       sometimes in bitterly concentrated form. What makes
                       the Texan Republicans stand out to me is how boldly
                       open they are about their derangements, in a major
                       state, where they do in fact wield total political
                       control.


                # ⚓ [Repeat] Michael Lynch ☛ I_Sold_TinyPilot,_My_First
                  Successful_Business⠀⇛


                       When you sell a business at TinyPilot’s scale,
                       there’s no deposit. You can invest hundreds of
                       hours into preparing reports for due diligence,
                       reveal all your confidential business secrets, and
                       spend thousands of dollars negotiating legal
                       documents and still walk away with nothing if the
                       buyer backs out.


                       As due diligence stretched on, my negotiating
                       position became markedly weaker. Before signing the
                       LOI, I could easily move on to the next buyer. By
                       month two of due diligence, walking away from the
                       deal meant restarting this costly and time-
                       consuming process from zero. I’d also risk
                       TinyPilot’s sales slipping after so many months
                       being distracted from the business.


                # ⚓ Scoop News Group ☛ EPA_says_it’s_‘on_target’_to_complete
                  process_for_cybersecurity_risk_assessment⠀⇛


                       The Environmental Protection Agency said it is “on
                       target” to establish a process to conduct
                       organization-wide cybersecurity risk assessments
                       within the next six months, putting a hard timeline
                       on its long-awaited response to a watchdog report
                       critical of the agency’s cyber posture.


                # ⚓ The Verge ☛ Elon_Musk_finally_agrees_to_testify_in_the
                  SEC’s_Twitter_investigation⠀⇛


                       This means Musk will have to appear at one of the
                       SEC’s offices for an up to five-hour interview. The
                       document says Musk and the SEC have already agreed
                       to a date, but it’s not disclosed “for
                       confidentiality purposes.”


                       In 2022, the SEC opened an investigation into
                       Musk’s failure to properly disclose his stake in
                       Twitter. But the SEC filed a lawsuit against Musk
                       last October after he refused to testify in the
                       agency’s probe. The SEC claims Musk “abruptly
                       notified the SEC staff that he would not appear”
                       two days before his scheduled deposition and
                       refused to testify at a later date. Earlier this
                       year, the SEC accused Musk of trying to delay the
                       investigation.


                # ⚓ The Verge ☛ Microsoft_needs_Windows_developers_like_never
                  before⠀⇛


                       It failed miserably. Developers didn’t flock to
                       universal Windows apps, and Microsoft eventually
                       abandoned its touch-friendly UI in favor of a more
                       traditional desktop in Windows 10. The cross-
                       platform dream of the Windows 8 era didn’t last
                       very long.


                # ⚓ The Nation ☛ Young_People_See_“a_Dying_Empire”_Because
                  They’re_Paying_Attention⠀⇛


                       Not surprisingly, a corollary belief stemming from
                       this glum appraisal is that elections aren’t very
                       consequential; 48 percent of respondents agreed
                       with the statement that “it doesn’t matter who wins
                       elections, nothing changes,” with just 30 percent
                       disagreeing. (A sizable cohort of 26 percent said
                       they neither disagreed nor agreed, which still
                       lands far short of a ringing endorsement of the
                       prospect of reform through the ballot box.)


                # ⚓ Semafor Inc ☛ ‘A_dying_empire_led_by_bad_people’:_Poll
                  finds_young_voters_despairing_over_US_politics_|_Semafor⠀⇛


                       As part of the online poll of 943 18-30-year-old
                       registered voters, Blueprint asked participants to
                       respond to a series of questions about the American
                       political system: 49% agreed to some extent that
                       elections in the country don’t represent people
                       like them; 51% agreed to some extent that the
                       political system in the US “doesn’t work for people
                       like me;” and 64% backed the statement that
                       “America is in decline.” A whopping 65% agreed
                       either strongly or somewhat that “nearly all
                       politicians are corrupt, and make money from their
                       political power” — only 7% disagreed.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Los Angeles Times ☛ Inside_the_anti-Biden_‘wildfire’
                        from_TikTok_influencers_ahead_of_the_election⠀⇛


                             The larger group is less interested in
                             politics but sees TikTok as their main source
                             of news, entertainment, relationships and
                             education around certain topics, said Darr,
                             who shared his findings with the Los Angeles
                             Times.


                             A White House spokesperson notes that the
                             bipartisan TikTok law had been in the works
                             before the Israel-Hamas war started and said
                             that the chief concern is over the Chinese
                             government’s ability to access users’
                             sensitive data and to manipulate the
                             company’s secret algorithms, which control
                             what videos go viral.


                      # ⚓ Science Alert ☛ One_Action_Has_Made_a_Significant
                        Impact_on_How_Misinformation_Spreads_Online⠀⇛


                             There are two types of 'superspreaders' of
                             online misinformation: the intentional and
                             organized spreaders of falsehoods or
                             misleading claims, and those who unwittingly
                             share information they didn't know was false.


                             We've seen some of the fatal consequences of
                             their combined effect running rife during the
                             COVID-19 pandemic, but have far less detail
                             on how eyeing such misinformation on social
                             media changes people's behavior, particularly
                             around vaccination.


                             Researchers at Massachusetts Institute of
                             Technology (MIT) and the University of
                             Pennsylvania set out to connect the dots to
                             show cause and effect, analyzing the impact
                             of more than 13,000 headlines on vaccination
                             intentions among roughly 233 million US-based
                             Facebook users – a pool equivalent to nearly
                             70 percent of the country's population.


          o § Censorship/Free Speech⠀➾


                # ⚓ Reason ☛ $1.1M_Libel_Award_to_Drag_Performer_Who_Had_Been
                  Accused_of_Exposing_Himself⠀⇛


                       From the Couer D'Alene/Post Falls Press (Kaye
                       Thornbrugh) yesterday: The jury found that blogger
                       Summer Bushnell defamed Post Falls resident Eric
                       Posey when she accused him of exposing himself to
                       the crowd while he performed in drag at the Coeur
                       d'Alene City Park bandshell in June 2022….


                # ⚓ RFA ☛ Police_probe_singer_for_video_showing_South
                  Vietnamese_flag⠀⇛


                       The tiny flag appeared in the background of a house
                       in the US, but online critics bashed her.


                # ⚓ Reason ☛ The_Alito_Flag_Flap,_Snyder_v._Phelps,_and
                  Chaplinsky_v._New_Hampshire⠀⇛


                       The latest reporting from the New York Times
                       intersections with Free Speech cases.


                # ⚓ JURIST ☛ Digital_rights_and_civil_society_groups_urge
                  YouTube_and_Google_to_resist_Russia_censorship⠀⇛


                       Digital rights group Access Now, alongside over 20
                       Russian and international civil society
                       organizations, sent an open letter on Tuesday to
                       YouTube and its parent company Google calling on
                       them to cease aiding the Kremlin in censoring
                       independent media and human rights organizations in
                       Russia. The letter, entitled “Open letter to
                       YouTube and Google: Stop helping Roskomnadzor
                       censor Runet,” demands that YouTube and Google
                       assess all blocking orders against international
                       human rights standards and challenge any that
                       unduly restrict access to protected expression.


                # ⚓ Variety ☛ Trump_Hits_'The_Apprentice'_Movie_With_Cease_and
                  Desist_Letter⠀⇛


                       The movie, which was independently produced, stars
                       Sebastian Stan as Trump and Jeremy Strong as Cohn.
                       It presents a damning portrait of the former
                       president as an ethically compromised, philanderer
                       who stiffs contractors and cuts deals with the mob
                       to get his buildings completed. It includes other
                       controversial details, including a scene where
                       Trump rapes his first wife, Ivana, and depicts him
                       abusing amphetamines to lose weight, as well as
                       undergoing liposuction and plastic surgery.


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


                # ⚓ Press Gazette ☛ Independent_UK_news_publishers_see_falls_in
                  revenue,_audience_and_staff⠀⇛


                       Non-profits have seen a dramatic fall in revenue
                       since last year, according to 2024's annual PINF
                       index.


                # ⚓ Press Gazette ☛ Memberships_making_up_40%_of_revenue_for
                  South_Africa’s_Daily_Maverick⠀⇛


                       The publisher has 30,000 active members and is
                       pleased with a churn rate of 4.65%.


                # ⚓ Press Gazette ☛ Evening_Standard_set_to_go_from_daily_to
                  weekly_print_edition⠀⇛


                       Standard journalists are to be consulted on "any
                       impact on staffing".


                # ⚓ The Dissenter ☛ Newspaper_In_Kansas_That_Faced_Illegal
                  Police_Raid_Backs_National_Reporter's_Shield_Law⠀⇛


                # ⚓ [Repeat] Reason ☛ This_Journalist_Was_Arrested,_Strip-
                  Searched,_and_Jailed_for_Filming_Police._Will_He_Get
                  Justice?⠀⇛


                       The Fort Bend County Sheriff's Office (FBSCO) has
                       allegedly been vexed by his audacity. In July 2021,
                       Pulliam was expelled by police from a press
                       conference because they alleged he did not qualify
                       as media, and in December of that same year, he was
                       arrested for videoing police at a mental health
                       call, despite that he had stationed himself about
                       130 feet away from the interaction. Officer Taylor
                       Rollins demanded Pulliam move back even further,
                       and he obliged, although he continued to film the
                       deputy speaking to other bystanders at the scene
                       (none of whom were arrested).


                       That didn't end well for Pulliam, who was charged
                       with interfering with police duties. (According to
                       his complaint, Officer Ricky Rodriguez, who
                       assisted with the arrest, told another cop at the
                       jail that the ordeal would teach Pulliam a lesson
                       "for fucking with us.") In April 2023, a jury was
                       not able to reach a verdict in the case, with five
                       jurors wanting to acquit and one urging to convict.
                       It took law enforcement more than a year to decide
                       not to pursue the case further.


          o § Civil Rights/Policing⠀➾


                # ⚓ The Register UK ☛ IT_worker_sued_over_‘vengeful’_cyber
                  harassment_of_policeman⠀⇛


                       In an ongoing civil lawsuit, an IT worker is
                       accused of launching a "destructive cyber campaign
                       of hate and revenge" against a police officer and
                       his family after being issued a ticket for
                       jaywalking.


                       The allegations against John Christopher Spatafore
                       – who at the time worked for the US city of
                       Fresno's Community Hospitals of Regional Central
                       California (CHCC) – are broad. They include digital
                       harassment, sextortion, invasion of privacy,
                       infliction of emotional distress, and defamation
                       against the unidentified officer's family. The
                       family is seeking $16.5 million in damages and
                       fees.


                # ⚓ TMZ ☛ Trump_Accused_of_Saying_N-Word_on_Season_1_of
                  'Apprentice'_About_Black_Contestant⠀⇛


                       Rumblings about Donald Trump allegedly saying the
                       n-word have circulated for years -- but now, an ex-
                       producer on "The Apprentice" is definitively
                       claiming ... yeah, he said it.


                # ⚓ EDRI ☛ Be_scanned_-_or_get_banned!⠀⇛


                       Belgium – currently holding the unenviable role of
                       trying to broker a compromise between European
                       Union (EU) Member States – claimed earlier this
                       year that they had found a “more proportionate” way
                       forward on this controversial law. Governments of
                       countries including Germany, Austria, France,
                       Poland, the Netherlands, Italy, Estonia and Finland
                       have reportedly raised concerns throughout the
                       process. However, they are now under even more
                       extreme pressure to reach a Council deal on the CSA
                       Regulation, even if they have to give up on digital
                       rights and technical reality in the process.


                       Now, a proposed Council text dated 28 May (9093/24)
                       reveals a harshly different reality from Belgium’s
                       promise of a human rights-respecting CSA
                       Regulation. This new draft text carries over the
                       many issues we’ve recently warned about (such as a
                       shocking misunderstanding of statistics when images
                       are wrongly flagged, a failure to respect vital
                       end-to-end encryption, and a risk categorisation
                       methodology that punishes secure and privacy-
                       respecting services whilst rewarding those that
                       systematically violate people’s privacy). It also
                       adds two new major problems in addition:


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ [Podcast]_We_don’t_need_subnets_any_more⠀⇛


                       Nets and subnets — do we actually need the idea of
                       a subnet in the IP addressing architecture?


                # ⚓ APNIC ☛ The_LUCI_project_—_connecting_the_remote_Chini_Lake
                  area,_Malaysia⠀⇛


                       Guest Post: Hybrid LoRaWAN technology brings
                       Internet access to Orang Asli villages.


      § Monopolies/Monopsonies⠀➾


          o ⚓ Barry Sampson ☛ Value_For_Money?⠀⇛


                 I know that a lot of people don't understand why, but I'm
                 still really annoyed about the iPad Pro advert where they
                 crushed a bunch of creative tools. In the advert, towards
                 the left was something that most people probably wouldn't
                 recognise - a brown rectangle, on which there's a black
                 disc, with a smaller white rectangle inside it. That is a
                 traditional animation disc.


                 And that got me thinking. Do I want to give £2,000 to the
                 richest company on the planet for a piece of technology
                 that will last maybe five years, and at best always be a
                 shallow imitation of the real world? Or do I want to give
                 £900 to a small business for a piece of hardware that
                 should outlast me?


                 What would you do?


          o ⚓ 404 Media ☛ The_Monopoly_Case_Against_Ticketmaster,_Explained⠀⇛


                 The key thing you need to know about this 124-page
                 lawsuit, and about Live Nation as an entity, is what this
                 vertical integration means for anyone touching the live
                 music industry and anyone who wants to see a concert
                 anywhere in the U.S. The Justice Department’s lawsuit,
                 filed last week, paints a vivid picture of this
                 vertically-integrated monopoly and explains all of the
                 harms it has led to.


                 In simple terms, Live Nation, which owns Ticketmaster, is
                 not just selling fans tickets on Ticketmaster.com. It
                 owns, operates, or has exclusive contracts with the vast
                 majority of midsized and large concert venues, and a
                 supermajority of all outdoor pavilions and amphitheaters.
                 And it has a concert promotion and artist agent arm,
                 meaning major bands and artists are signed to Live Nation
                 promoters. For all but the smallest bands playing tiny
                 indie venues, it is nearly impossible to book and perform
                 a tour in the United States without touching Live Nation
                 or Ticketmaster at some point. And this omnipresence over
                 the whole industry means that Live Nation has a huge
                 amount of control and power over how much bands are paid,
                 how much tickets cost, and which venues they play at.


          o ⚓ Silicon Angle ☛ ShinyHunters_lists_560M_stolen_Ticketmaster_user
            records_for_sale_following_BreachForums_resurgence⠀⇛


                 The post on BreachForums claims that the data includes
                 names, addresses, emails, phone numbers, ticket sale
                 information, event information and order details. In
                 addition, ShinyHunters claims to have credit card details
                 but only the last four numbers of cards and expiration
                 dates.


                 The full stolen database is being offered for sale by
                 ShinyHunters for $500,000.


          o ⚓ Digital Music News ☛ Ticketmaster_Hack_Reportedly_Compromises_560
            Million_Accounts⠀⇛


                 Stemming the tide of related criticism could prove a
                 different story. Justified or not, the Eras Tour pre-sale
                 fiasco spurred all manner of customer qualms, which then
                 translated into, among other things, enhanced scrutiny
                 from federal lawmakers. On social media, many are already
                 weighing in on the reported Ticketmaster hack.


          o § Copyrights⠀➾


                # ⚓ Press Gazette ☛ Media_manifestos_2024:_Publishers_urge
                  action_to_control_generative_AI⠀⇛


                       News Media Association sets out policy priorities
                       for next UK government.


                # ⚓ Torrent Freak ☛ Court_Denies_Filmmakers'_Renewed_Attempt_to
                  Get_Redditors'_IP_Addresses⠀⇛


                       Reddit is not required to hand over to filmmakers
                       the IP-addresses of several Redditors who made
                       piracy-related comments. A California federal court
                       denied the filmmakers' request for a 'de novo'
                       review, after turning down their initial request in
                       February. While this is bad news for the movie
                       companies, a viable alternative appeared recently.


                # ⚓ Torrent Freak ☛ FBI_Carries_Out_Fresh_Round_of_Z-Library
                  Domain_Name_Seizures⠀⇛


                       The U.S. Government's crackdown against Z-Library
                       continues. The FBI just carried out a new round of
                       seizures affecting several of the site's key domain
                       names, including Z-Library.se. These efforts have
                       also taken out the shadow library's main email
                       domain but, thus far, its servers appear to be
                       unaffected.





                    ䷩ 𝚕𝚒𝚗𝚎 5698

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Identifiers, Why Unicode⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on May 31, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ 🔤SpellBinding:_ACNOPYU_Wordo:_JOKER⠀⇛


                # ⚓ small_coloured_bricks_and_small_wobbly_plans⠀⇛


                       I've turned into a critter-writing machine but
                       that's okie, lol. I used some inspiration prompts
                       I've been hauling around for literal years and I
                       enjoyed doing it, so it's all good --


                       Next is some dragon adaptations, probably. Also I
                       saw some nice prompts for Kaijune this year so
                       maybe even /more/ critters ...


          o § Technology and Free Software⠀➾


                # ⚓ How_to_keep_clean_your_Docker_bind-mounts_files
                  permissions?⠀⇛


                       Very similar situations are produced with a PHP
                       project, on `vendor/` or `var/` folders by example.


                       We all tried to do some kind of manual user ID
                       mapping. If the user "www-data", from inside our
                       containers, use the same user ID than our host
                       user, the process should produce inodes that our
                       regular user have access to. Mhh?


                       Also, maybe it is possible, somehow, to configure
                       our projects, or Docker itself, to keep clean our
                       host filesystem. Can we configure docker with this
                       "user-namespace"? Or better, could we run Docker as
                       rootless? What about Podman?


                # ⚓ Generating_and_Using_Identifiers⠀⇛


                       Over the last few months, I've had a number of
                       conversations about unique identifiers. For
                       starters, I get pulled into a periodic meeting to
                       justify decisions we made about six years ago for
                       my day job. Then there was a conversation on fedi
                       [1] (not a link to the conversation, it was too
                       long ago and I auto-delete my posts).


                # ⚓ Profile_results_are_as_expected_as_the_Spanish
                  Inquisition⠀⇛


                       I'm not upset at rewriting the code that handles
                       the network buffering [1] as it needed work, but
                       I'm still seeing a disporportionate amount of CPU
                       (Central Processing Unit) time accumluate on the
                       supposedly simpler protocol gopher. The most
                       popular requests of both my gopher server [2] and
                       Gemini server [3] are entries from my blog, so I
                       take a look at the code that handles such requests
                       for both servers. Yes, the gohper server has a bit
                       more code dealing with links than the Gemini server
                       (because gopher URL (Uniform Resource Location)s
                       are almost, but not entirely, like http URLs—and
                       the small differences are annoying), but I'm not
                       seeing anything that stands out. Yes, the code is
                       not quite twice as much, but the CPU utilization is
                       more than three times as much (as of writing this).


                # § Internet/Gemini⠀➾


                      # ⚓ Alternative_view_on_embeded_media_in_gemini⠀⇛


                             There have been many talks about embeded
                             media in gemtext. How it is needed, how it is
                             unneeded, how it is it could be implemented,
                             how it could set gemini on slippery slope
                             that is HTML. I think I have a compromise
                             that will satisfy all parties.


                # § Programming⠀➾


                      # ⚓ Unicode._Why_did_it_have_to_be_Unicode?⠀⇛


                             For each line of code executed, we get the
                             filename, the function name and the line of
                             code that's executing, turn that into a key,
                             and use that to count the number of times
                             that line of code is executed. Easy.




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