𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, November 30, 2024
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Generated Sun 1 Dec 02:49:18 GMT 2024
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2024/11/30/


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

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


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

⦿ Techrights  -  Apache Software Foundation, Already Infiltrated by Microsoft for Well Over a Decade, Still Controlled by Proprietary Giants With Openwashing Agents

⦿ Techrights  -  Daniel Pocock Moved Up Two Spots in the Political Battles

⦿ Techrights  -  IBM and Microsoft Fake Headcount in Exactly the Same Way (While Mass Layoffs Persist and Real Revenue Falls, Not Just Compared to Inflation Rates)

⦿ Techrights  -  IBM is More Than 60 Billion Dollars in Debt (Which It Cannot Pay Back)

⦿ Techrights  -  In Case Undersea Cables Are Cut...

⦿ Techrights  -  IRC Proceedings: Friday, November 29, 2024

⦿ Techrights  -  [Meme] Growing Up and Becoming Sceptical

⦿ Techrights  -  [Meme] The Internet is More Fragile Than They Are Willing to Admit

⦿ Techrights  -  [Meme] The Word Security Has Been Redefined

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Proving Yet Again That Techrights Was Right About UEFI 'Secure Boot' All Along (Since 2012)

⦿ Techrights  -  Reporting Information and Facts at Times of War (and Information Wars), Dissent of Merit and Scepticism//Critical Skills Impermissible

⦿ Techrights  -  Stable at Over 4% and 400+ Days' Uptime

⦿ Techrights  -  The Irish Have Voted, We'll Soon Know How Many Voted for a Debian Developer and Free Software Specialist

⦿ Techrights  -  Tux Machines Turning Twenty a Half

⦿ Techrights  -  Two Years Later Sirius Open Source is Basically Dead (With a Zombie Web Site)

⦿ Techrights  -  Understanding Irish general election 2024 results Dublin Bay South

⦿ Techrights  -  With a Month Left to Raise Money the Free Software Foundation (FSF) Has Already Raised 56,000 Dollars

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/11/30/Apache_Software_Foundation_Already_Infiltrated_by_Microsoft_for.shtml
https://techrights.org/n/2024/11/30/Daniel_Pocock_Moved_Up_Two_Spots_in_the_Political_Battles.shtml
https://techrights.org/n/2024/11/30/IBM_and_Microsoft_Fake_Headcount_in_Exactly_the_Same_Way_While_.shtml
https://techrights.org/n/2024/11/30/IBM_is_More_Than_60_Billion_Dollars_in_Debt_Which_It_Cannot_Pay.shtml
https://techrights.org/n/2024/11/30/In_Case_Undersea_Cables_Are_Cut.shtml
https://techrights.org/n/2024/11/30/IRC_Proceedings_Friday_November_29_2024.shtml
https://techrights.org/n/2024/11/30/Meme_Growing_Up_and_Becoming_Sceptical.shtml
https://techrights.org/n/2024/11/30/Meme_The_Internet_is_More_Fragile_Than_They_Are_Willing_to_Admi.shtml
https://techrights.org/n/2024/11/30/Meme_The_Word_Security_Has_Been_Redefined.shtml
https://techrights.org/n/2024/11/30/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/11/30/Proving_Yet_Again_That_Techrights_Was_Right_About_UEFI_Secure_B.shtml
https://techrights.org/n/2024/11/30/Reporting_Information_and_Facts_at_Times_of_War_and_Information.shtml
https://techrights.org/n/2024/11/30/Stable_at_Over_4_and_400_Days_Uptime.shtml
https://techrights.org/n/2024/11/30/The_Irish_Have_Voted_We_ll_Soon_Know_How_Many_Voted_for_a_Debia.shtml
https://techrights.org/n/2024/11/30/Tux_Machines_Turning_Twenty_a_Half.shtml
https://techrights.org/n/2024/11/30/Two_Years_Later_Sirius_Open_Source_is_Basically_Dead_With_a_Zom.shtml
https://techrights.org/n/2024/11/30/Understanding_Irish_general_election_2024_results_Dublin_Bay_So.shtml
https://techrights.org/n/2024/11/30/With_a_Month_Left_to_Raise_Money_the_Free_Software_Foundation_F.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/11/30/Gemini_Links_30_11_2024_SIGINT_Foo_and_Hooking_Up_an_Old_Serial.shtml
https://techrights.org/n/2024/11/30/Links_30_11_2024_Cable_Cuts_Under_Investigation_America_s_Cemet.shtml
https://techrights.org/n/2024/11/30/Links_30_11_2024_More_Threats_to_Taiwan_Ananda_Krishnan_is_Dead.shtml
https://techrights.org/n/2024/11/30/Links_30_11_2024_Social_Control_Media_Under_Growing_Scrutiny_Pa.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 101

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Apache_Software_Foundation_Already_Infiltrated_by_Microsoft_for.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Apache_Software_Foundation_Already_Infiltrated_by_Microsoft_for.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Apache Software Foundation, Already
Infiltrated by Microsoft for Well Over a Decade, Still Controlled by
Proprietary Giants With Openwashing Agents⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


No wonder things get outsourced to Microsoft's proprietary prison (GitHub). It
is all about money.


This is the latest:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Apache_Software_Foundation’s_New_President,_Ruth_Suehle,_to
                       Focus_on_Security_and_Community⦈_


Yes, everything is "open"; even_proprietary_is_somehow..._"open"... proprietary
with some job role to do the openwashing (PR).


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Her_current_position_is_interesting,_considering_that_SAS
 isn’t_known_for_being_an_open-source_company_—_in_fact,_it’s_proprietary_all
                            the_way_to_the_bone.⦈_


See our_wiki preceded by these introductory words: "Apache is a Free software
pioneer. At times, however, Microsoft has been trying to take over it or steer
it towards Windows, Azure, GitHub and so on. The stories below documented
various affairs over the years."


Apache's founder also shows clear overlaps (fiscal) with the Linux_Foundation,
another group infiltrated_and_controlled_by_Microsofters.


We're losing the battle for Software Freedom or surrendering if we let
ourselves be controlled or publicly represented by those whom we always sought
to replace.


Some people get paid a lot of money to defect and attack their village. It's a
big problem. █




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
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⣿⡿⢻⣿⠿⢿⡿⠿⣿⠿⢯⠹⢿⣿⠿⣿⣿⢻⣛⡿⠿⡿⠫⠙⠿⢿⢿⠿⡿⢿⡿⡿⡿⠿⣿⣿⢻⣻⡿⢿⡿⣿⢿⠿⠿⣿⠿⠍⡿⠿⡿⠻⡏⣿⠿⣿⠿⠿⣿⢻⠿⢿⣿⡟⢿⣛⣿⠿⡿⢿⢿⠿⣿⣿⣿⣿⣿⣿
⣿⢡⡄⢿⠰⠇⡗⠅⢇⠺⢾⢸⠆⡇⠥⣼⣿⢲⢌⡑⡷⣸⢸⡇⢿⡘⡌⢹⠪⠅⠇⣶⡁⠥⣿⡿⢸⣼⠸⠇⡇⠿⠸⠀⡇⢇⠺⠃⡇⠅⢿⠸⡇⡇⢾⢨⠇⡇⢹⣿⠬⢺⣿⠿⣦⢹⡇⠥⣵⢉⡘⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⢛⡛⣿⣿⣿⣿⣿⣿⣟⣿⣿⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣿⣿⣿⣿⡟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢨⣥⡆⣶⡡⠥⡧⡑⡇⣏⠸⠸⡁⠥⣷⢰⠈⡇⢿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⢸⠆⣿⡇⣭⣿⢸⠆⡁⠷⡆⠷⠸⢌⢺⣿⠰⡇⡅⢰⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢬⠙⠁⣂⡇⣶⡇⢿⢸⡆⣶⢸⡆⣶⡘⢣⣿⠇⡂⣷⢰⠘⠡⡆⣿⣿⠸⣿⠏⣶⠌⡆⡆⣴⢸⠀⡆⣶⢸⢸⡆⡇⣴⢸⡆⡇⢰⣆⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣇⣀⣾⣒⣐⣀⣠⣰⣢⣀⣇⣈⣁⣚⣗⣅⣸⣀⣂⣴⣐⣁⣀⣀⣸⣀⣼⣂⣒⣈⣇⣗⣅⣑⣁⣢⣐⣘⣑⣆⣢⣀⣸⣉⣀⣀⣇⣄⣕⣠⣘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣖⣉⣿⣌⣈⣉⣉⣉⡩⠛⣟⣣⣉⣹⣣⣏⣉⣉⣡⣉⣹⣄⣉⣀⣍⣉⣉⣍⣹⣠⣉⣙⣩⣋⣌⣁⣋⣉⣭⣏⣍⣉⣉⣉⣫⣍⣉⣉⣡⣇⣈⣉⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠟⠿⠿⠿⠟⡟⡻⠿⠿⠻⢻⠻⠻⠟⡻⠿⣿⠿⠿⡿⠻⡿⡿⠻⢿⠿⠿⠻⠿⠟⠿⠿⡟⢿⠿⠿⠿⠿⡿⡻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣷⣿⣶⣶⣾⣾⣶⣷⣷⣶⣾⣶⣾⣶⣷⣶⣶⣯⣾⣶⣷⣷⣶⣾⣧⣾⣶⣿⣶⣶⣾⣷⣶⣶⣿⣾⣴⣾⣿⣶⣶⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣷⣿⣶⣾⣷⣶⣷⣿⣶⣿⣶⣶⣶⣾⣾⣶⣾⣾⣷⣷⣶⣿⣾⣶⣶⣿⣷⣶⣷⣾⣾⣶⣶⣷⣾⣶⣷⣷⣶⣿⣿⣾⣶⣶⣾⣿⣶⣷⣿⣾⣾⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠠⠠⢀⢤⠀⢤⠀⠠⠠⢠⢄⠄⡤⠀⢠⢤⠄⠀⠀⠀⠀⢄⠤⠀⠀⠀⣦⠄⠄⠀⢀⠄⠀⠀⠀⠀⠠⠄⠀⡠⠠⠢⠠⠀⠠⡀⠄⠀⠀⠄⢄⢠⠀⡀⠀⢄⡀⠤⡄⣄⠀⠄⣦⡠⡦⠄⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣋⣅⣀⣀⣀⣐⣋⣁⣀⣃⣀⣀⣀⣀⣐⣟⣚⣃⣐⣀⣀⣀⣚⣁⣀⣀⣀⣀⣘⣃⣀⣨⣀⣈⣻⣁⣐⣋⣃⣀⣨⣁⣀⣛⣈⣀⣒⣀⣒⣀⣐⣀⣘⣁⣁⣐⣊⣈⣛⣙⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⡿⡿⣿⢿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣬⣵⣷⣽⣴⣿⣦⣤⣼⣤⣧⣾⣴⣿⣤⣴⣧⣾⣿⣄⣾⣤⣠⣴⣴⣿⣤⣤⣤⣶⣴⣿⣷⣴⣷⣦⣠⣤⣴⣮⣿⣿⣿⣤⣧⣬⣧⣾⣼⣴⣷⣤⣧⣮⣴⣥⣾⣴⣲⣤⣶⣼⣧⣴⣼⣷⣴⣴⣧⣤⣾⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 187

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Daniel_Pocock_Moved_Up_Two_Spots_in_the_Political_Battles.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Daniel_Pocock_Moved_Up_Two_Spots_in_the_Political_Battles.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Daniel Pocock Moved Up Two Spots in the
Political Battles⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


This year's European elections (Ireland is in the EU) were the first time Mr.
Pocock presented himself as a politician. Pocock_finished_last ("European
Election results – Midlands-North-West, Dublin, and Ireland South
constituencies"). That's more or less expected from new entrants with no prior
recognition or experience or connections in the political scene, including
local media.


European election in Ireland (June 2024):


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇European_Election_results_–_Midlands-North-West,_Dublin,_and
                        Ireland_South_constituencies⦈_


Irish election (this past week):


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Election_2024:_Dublin_Bay_South_results⦈_


That's progress.


He has made_a_statement_about_it. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⡀⢴⢠⡄⠀⠀⠉⠙⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣀⣉⣉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣟⠉⡉⠉⠀⠂⠘⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⢸⣿⢻⠃⠀⠀⠀⠀⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠓⡒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀⠂⠀⠀⠀
⠀⠀⠀⠿⠷⠶⠄⠐⠂⠄⠤⠠⣤⣄⣀⣼⣋⣛⣓⢘⠈⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⢋⣉⠤⠍⠀⠀⠀⠈⠀⠀⠀
⠦⡄⢀⠀⢀⣀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠂⠐⠀⠛⠉⠙⠀⠀⠀⠤⠤⠤⢤⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠊⠤⠀⠒⠉⠉⠁⠦⠈⠐⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣷⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠠⠤⠤⣤⣄⣀⣀⣀⣀⣀⣠⣠⣀⣀⣀⡀⠀⠀⠀
⠀⡀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⣛⣿⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠭⢿⣿⣿⣷⠖⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣠⣤⡤⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠽⠿⠿⠿⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠉⠁⠒⠒⠒⠒⠂⠒⠲⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠉⠛⠋⠉⢻⠙⠉⠛⠛⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⠀⣿⣿⣿⣿⠉⠏⡉⡉⢻⣿⣿⣿⣿⣿⣿⠹⢍⣽⢹⣿⣿⣿⣿⣿⣿⡋⠯⡉⢉⣿⣿⣿⣿⣿⣿⣟⠹⢉⠉⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠷⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⣿⣿⣿⣿⡟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣤⣤⣤⣤⣻⣤⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⠀⣿⣿⣿⣿⣤⣧⣥⣦⣽⣿⣿⣿⣿⣿⣿⣌⣬⣤⣬⣿⣿⣿⣿⣿⣿⣥⣣⣭⣤⣽⣿⣿⣿⣿⣿⣯⣜⣬⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⣿⣿⣿⣿⡏⠉⠉⠉⠉⢹⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⣿⣿⣿⣿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣀⣀⣀⣀⣸⣶⣶⣶⣶⣶⣽⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⣿⣿⣿⣿⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣽⣷⣶⣿⣿⣿⣿⣿⣿⣷⣮⣾⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠉⡉⠙⠛⠙⠻⡏⢛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⠀⣿⣿⣿⣿⠉⠏⠉⡋⢿⣿⣿⣿⣿⣿⣿⠹⠉⠉⠹⣿⣿⣿⣿⣿⣿⣏⠏⠉⠉⣽⣿⣿⣿⣿⣿⣿⠹⠝⠩⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠤⠤⠤⠤⠼⠿⠿⠿⠷⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣀⣉⣉⣉⣁⣁⡉⣟⣈⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣇⣼⣿⠀⣿⣿⣿⣿⣀⣣⣦⣆⣹⣿⣿⣿⣿⣿⣿⣘⣂⣀⣾⣿⣿⣿⣿⣿⣿⣆⣓⣂⣠⣿⣿⣿⣿⣿⣿⣷⣘⣀⣨⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⠉⠉⠉⢹⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⠿⠿⢿⣿⠀⣿⣿⣿⣿⠿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣀⣀⣀⣀⣸⣶⣶⣦⣴⣶⣶⣽⣶⣶⣶⣴⣶⣶⣾⣶⣶⣶⣶⣦⣶⣶⣿⠀⣿⣿⣿⣿⣶⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣮⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣵⣶⣶⣿⣿⣿⣿⣿⣿⣷⣮⣶⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⣿⠛⢻⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⠀⣿⣿⣿⣿⠛⠟⠟⠟⢿⣿⣿⣿⣿⣿⣿⢻⠛⣻⠻⣿⣿⣿⣿⣿⣿⠛⡟⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡧⠤⠤⠤⠤⠼⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣀⣉⣁⣉⣉⡙⣇⣀⣉⢉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣇⣹⣿⠀⣿⣿⣿⣿⣀⣃⣇⣅⣻⣿⣿⣿⣿⣿⣿⡸⣀⣢⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣗⣒⣒⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⠛⠛⠛⢻⠿⣿⣿⣿⣿⣿⡿⠿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⣿⣿⣿⣿⠿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣤⣤⣤⣤⣤⣬⣯⣥⣤⣴⣤⣤⣤⣿⣿⣿⣿⣿⣿⣧⣾⣿⠀⣿⣿⣿⣿⣤⣥⣧⣦⣼⣿⣿⣿⣿⣿⣿⣬⣿⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠛⠿⠿⠿⠟⢿⣟⠿⠿⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⠀⣿⣿⣿⣿⠛⣟⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣤⣤⣤⣤⣼⣾⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⣿⣿⣿⣿⣶⣶⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⢸⡟⠛⠿⡿⠿⠿⠿⠿⠛⢻⣿⠛⠻⠿⢻⠿⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⠛⢟⠛⠛⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠅⠀⠀⠀⠀⢸⣇⣤⣆⣀⣀⣀⣀⣀⣀⡘⢻⣀⣀⣰⡀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣌⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣂⣫⣀⣌⣼⣦⣀⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⠘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠻⠿⠿⠟⠻⠿⣿⠟⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠛⡿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⢸⣧⣤⣤⣤⣤⣤⣄⡀⣩⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣤⣥⣦⣤⣤⣥⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢠⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠩⠉⠛⠛⠛⠛⢻⣿⠉⠋⠙⠛⠛⠛⠛⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⢹⣿⠉⠉⡍⡉⠩⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⣤⣶⣶⣶⣆⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇⠆⠉⠍⠉⠁⠈⠉⠉⣹⡇⢀⡈⠉⠀⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠠⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠆⢿⠀⠀⠆⡄⠐⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⢸⡿⠿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠂⠀⠀⠀⢸⡇⠂⡀⠀⠀⡀⡁⠈⢿⠀⠋⠀⠀⠀⢠⠀⠀⡀⢈⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⡐⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠃⢟⠃⡀⢀⣆⠀⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠿⢿⠿⠿⠿⠿⠟⠻⣿⡟⠛⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⣿⠛⢛⠛⠛⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠂⠀⠀⠀⢸⣇⣤⣆⣀⣀⣀⣀⣀⣀⣀⢛⣇⣁⣄⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣁⣫⣈⣌⣼⣦⣀⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣙⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⠻⠙⠛⠉⠻⠛⠛⢻⣿⡏⠛⠻⠙⠛⠛⡟⢉⠹⠛⠛⠛⠻⠙⠛⠉⠛⢻⣿⣿⣿⣿⣿⡙⢋⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⡉⣿⢉⠛⠹⠉⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⢸⣧⣦⣤⣴⣄⣀⣤⣤⣤⣤⣉⣧⣤⣦⣤⣤⣤⣤⣧⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣴⣦⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣥⣵⣤⣦⣤⣷⣤⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇⠛⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⡇⠈⠙⠛⠛⠁⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠩⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⡌⣿⢠⠙⠹⡁⠩⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣼⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣾⣾⣷⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

                    ䷩ 𝚕𝚒𝚗𝚎 328

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/IBM_and_Microsoft_Fake_Headcount_in_Exactly_the_Same_Way_While_.shtml
    Gemini version at https://techrights.org/n/2024/11/30/IBM_and_Microsoft_Fake_Headcount_in_Exactly_the_Same_Way_While_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM and Microsoft Fake Headcount in Exactly
the Same Way (While Mass Layoffs Persist and Real Revenue Falls, Not Just
Compared to Inflation Rates)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


They convert profits into fake 'growth' instead of cashing in (so debt
continues_to_soar), in effect gaming_the_system based on misleading metrics


EARLIER this month we said_that_"Microsoft's_Acquisition_of_Activision_(to_Fake
Revenue_Growth_by_Buying_Revenue)_Was_a_Failure", citing what we wrote 1.5
years earlier ("Why_Microsoft_Was_Trying_to_Buy_Activision_and_'Look_Big'_in
2022"). It seems apparent that Microsoft continues to lie about the wellbeing
of XBox by pretending it "grew" (because Activision's revenue got added to it).
In reality, XBox sales fell by more than 50%, based on Microsoft itself.


But it seems like IBM has resorted to similar tricks by buying some mid-sized
company every other month or so, i.e. adding revenue and people from somewhere
else. IBM continues to lay off tens of thousands of people, but then it uses
what's left of the profits to just buy companies (to fake revenue growth...
theirs, not IBM's). Then IBM can pretend headcount is unchanged, as this_hours-
old_article_from_Nigeria_put_it: "One of the largest global technology firms,
IBM, announced a second round of job cuts targeting senior programmers, sales
staff, and support personnel under its “workforce rebalancing” strategy.
Although the company aims to downsize a small percentage of its global
workforce, it expects to end the year with a workforce size similar to its
beginning."


Well, yes, as it keeps buying companies. But its debt grows. It cannot pay back
its debt. All that money is used to fake revenue growth and pay interest on the
debt. It's a really bad strategy, an unsustainable mess, but Wall Street likes
it that way. Incomplete metrics being optimised for will doom a lot of
companies, rendering them little but a pile of debt chasing the government for
bailouts. They offload_all_the_risk_to_taxpayers. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠉⠛⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠤⣿⠀⠀⠤⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠛⠿⠋⠙⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⢀⡤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠙⠉⠻⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠐⠛⠀⠀⡼⡄⣻⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠸⠇⠀⠰⣿⠧⠀⠛⠛⠋⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣻⣿⣿⡟⠉⠉⠉⠙⠉⠀⠈⠁⠁⠈⠁⠀⠀⠀⢀⢄⣠⣿⣼⣿⣷
⣹⡯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣦⡀⠀⡀⠀⠈⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣰⣶⡄⠬⠤⠤⠁⠠⠀⠀⠀⢀⠀⣿⣿⣿⣼⠍⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠲⠄⠘⣿⣽⣿⢿⣿⣇
⣿⣦⣴⣦⣤⢸⡅⠐⠠⢤⠄⢠⣤⣶⣶⣤⣶⢤⣶⣾⠛⣳⡒⢰⢁⣍⣄⣤⡀⣀⣀⣼⡄⣨⣭⣨⣭⠭⢹⣿⣿⣥⣥⠀⣡⣄⠀⢼⣾⣿⣿⠾⣿⣿⣿⣷⣤⣤⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣐⣿⢿⣿⣞⣿⣇
⠿⠙⢻⠟⡏⡈⢙⢛⣏⣛⢘⢿⠿⠿⠎⠿⢛⢛⠃⣙⣀⣉⣠⣈⣨⣩⣉⣭⣍⣅⣬⡩⣥⣭⣩⣭⣍⣬⣽⠿⠿⠿⠿⠿⠯⠭⣭⣭⢭⢍⣁⣀⣛⣛⣛⣛⠛⠻⡿⠶⠤⢤⣠⡄⠀⣬⣣⣦⣶⣿⡛⢻⠩⠛⢳⣿⠻⢟
⠀⠀⠀⠀⣂⡙⡛⠉⢉⣹⣶⣶⣿⣿⣿⠿⠿⠟⠛⠛⠉⣉⠉⠉⠉⠁⠉⠈⠰⠻⠺⠀⠉⠈⠙⠋⠉⠛⢿⠟⠀⠃⠀⠀⠀⠀⠀⠀⠸⡿⠿⢿⣍⣉⣙⡛⠛⠁⠇⠆⢸⣵⢰⢒⣖⡌⡈⢛⠛⠛⠋⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⣿⡿⣶⣟⣻⠭⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣾⣿⣶⣿⣿⣿⣀⣦⡀⠛⢀⡀⡀⡀⢸⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠈⠈⠚⠁⠁⠆⡞⡰⢠⢆⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣠⣶⠀⠀⣼⣿⣿⣿⣿⢹⠛⠉⣽⣿⣿⣿⡇⠀⢸⡏⠉⠉⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣯⣍⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⢠⡦⠆⠀⡌⠀⣾⣿⡇⠙⠟⠀⠀⠈⡿⠿⢻⡿⠀⠀⠀⢸⣿⣿⣿⣧⣴⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣼⣿⠏⠀⠀⠀⠀⠀⠀⠶⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣶⣶⣤⣄⣿⣷⠀⣿⣿⢸⣿⠻⣷⠃⠀⠀⡟⠀⠀⠀⠀⠀⠀⣁⣠⣿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⡿⣶⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣀⣍⢀⡀⠀⠁⠀⠀⠀⣀⣤⣴⣿⣿⣿⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣤⣶⣶⣶⣿⣿⣿⠆⠃⠛⠙⠙⠻⠃⠀⠀⠀⠀⠀
⣷⡄⠿⢿⣿⣿⣿⣿⡇⠉⠛⡟⠿⢻⠿⠋⢿⣿⡿⠿⠿⠻⠿⠺⠓⠂⠇⠾⢿⡿⣿⢿⢿⣿⢄⣤⠀⠀⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠻⠟⠿⠿⠿⠿⠟⠿⠿⠟⠿⠿⡿⠟⠛⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣰
⣿⠇⠀⢸⣿⣿⣿⠿⠁⠀⠀⠁⢠⠀⠀⠀⠘⣿⣧⣶⣴⣦⡆⢠⢠⣤⣤⣤⣬⣥⣤⣤⠀⠈⠀⠀⢠⠀⠈⠉⣭⣿⣿⣤⣭⣯⣧⣤⣬⣤⣄⢀⣶⣶⣾⣿⣿⣿⣾⣷⣿⣿⣿⣆⣀⣤⣰⣶⡇⠀⠀⠀⡄⠀⠈⠀⠀⢻
⠋⠀⠀⠘⣿⡿⠃⠀⠀⠀⡀⢀⣠⣤⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣾⣿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣆⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣴⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⠀⢀⡀⠀
⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠈⡇⠀
⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⡿⠛⠉⠉⠉

                    ䷩ 𝚕𝚒𝚗𝚎 408

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM is More Than 60 Billion Dollars in Debt
(Which It Cannot Pay Back)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


IBM debt is growing. Paying back the debt (not just paying interest on the
debt) is_hard_to_pay_back_when_you're_busy_faking_"growth".


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


A drop in the bucket?


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


Approaching 103 trillion dollars in debt if you also count personal
("household") debt and business debt. █




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣤⣬⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠛⠟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠻⡟⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠁⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠋⠁⠀⣤⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠀⠉⠻⣿⣿⣿⣇⠀⠀⢔⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⢀⣤⣤⣄⣄⠉⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣤⡄⠀⣰⣿⣿⣿⣿⣆⣀⢾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⢠⣾⣿⣿⣿⣿⣷⠀⠀⡾⠛⣷⣦⣤⣶⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣤⣤⣵⣿⣯⣠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⠄⠀⢳⠀⢹⣿⡿⢿⣿⣷⣄⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⡻⣿⣿⣿⡿⢋⣀⣤⡄⠠⢸⡿⠄⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣀⣭⣵⣿⣿⣿⣿⣿⡀⠀⢿⢤⣤⣅⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⣡⣾⡽⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠙⠛⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⡿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢉⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣀⣠⡴⣾⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢋⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⡔⠏⠂⠀⠁⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠊⣤⠈⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣤⣤⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⠙⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢠⣤⣄⡀⣤⣄⣀⣀⣀⣀⣠⣀⣤⣄⢠⣤⣤⣠⣤⣤⣿⣇⣴⣶⣦⣶⣶⣶⠀⠀
⠀⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⣀⢀⡀⣀⣀⠀⠀⣀⣀⡀⣠⣤⣶⣦⣤⣤⣤⣤⣤⣦⣿⣿⣿⣧⣶⣶⣶⣶⣶⣿⠀⢸⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡟⢻⣿⣿⣛⣿⣿⣝⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⡀⢸⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣟⣛⣿⡏⢹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠀⠸⣿⣿⡏⠿⠿⠟⠿⠿⠟⠻⠷⣿⡟⠛⠛⠃⠘⠛⠛⠈⠛⠋⠈⠉⠉⠉⠉⠈⠉⠁⠈⠁⠀⠀⠀
⠀⢸⣿⡇⠸⣿⠿⠿⠿⠿⠿⠻⠿⠏⠻⠿⠃⠀⠛⠛⠋⠛⠃⠘⠛⠻⠟⠋⠘⠛⠉⠈⠉⠈⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀
⣠⠤⠀⠀⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⡶⠶⠟⠛⠻⠻⠿⢿⣿⣿⡿⠿⠿⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣷⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣾⠿⠟⠛⠛⠉⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠏⠀⠀⠀⠙⠛⠹⣻⣫⣝⠍⠛⢟⣿⡿⣿⣟⠿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⠃⢀⠜⠁⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣷⣶⡍⠅⠁⡞⠣⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠋⠃⠀⢸⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠒⣒⣒⣒⣒⣚⡛⠇⠄⠀⠀⠄⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⣴⣾⣿⣿⣿⣿⢿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⡰⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠛⠛⠛⠛⠫⠭⠆⠀⠀⠀⠁⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠈⠿⣿⡿⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠉⠉⠛⣿⣽⣿⡟⠀⠀⠀⠀⠀⠚⠻⠻⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⠘⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠀⠀⠀⢠⣾⢀⡀⠁⠀⠀⠀⠀⠘⠻⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⠀⠘⠿⠆⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢠⣦⣙⠸⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠘⢿⣿⣿⣿⠉⠛⠻⣧⣄⠀⠀⠀⢿⣿⠸⡆⠀⠀⢻⠓⢀⠀⠀⠀⠈⠁⡀⢀⡈⠀⠀⠀⢸⣿⠃⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡄⢻⣿⣿⡇⠀⠀⣿⣿⣷⣤⡀⠘⣿⣌⠁⠀⠸⠈⠀⠨⠿⣿⣧⢻⣿⣿⣿⣿⣿⢠⡶⡹⠿⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠻⣶⣤⣤⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣶⣿⡓⠂⠀⠀⠀⢀⣰⣶⣶⣶⣦⣶⣶⠶⣶⣴⣶⣶⡃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⡀⢀⡀⢶⡾⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣴⠟⠉⠀⠙⠻⢭⣷⣾⣷⣿⣿⠟⠙⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀
⣿⣿⣿⣿⠟⢻⡟⠛⢻⣿⢿⠻⡟⣻⣿⣿⠿⣛⣿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡛⣿⢿⠋⠛⢿⠿⠿⡟⣽⡟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⡿⣿⢹⣿⠛⠛⣿⠽⡿⣿⠟⣿⢿⡛⠛⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣮⣾⣿⣼⣮⣥⣾⣮⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣵⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣏⣻⣏⣋⣭⣙⣹⣏⣏⣙⣍⣉⡉⢹⣏⣫⣋⣏⣿⣟⣹⣹⣟⣹⣏⣻⣻⣛⣻⣿⣻⣍⣻⣏⣻⣛⣛⣫⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣽⣧⣵⣵⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣿⣿⣿⣾⣧⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢦⣼⣿⣿⣿⣿⣯⣍⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣻⡻⡛⡟⣿⢟⣟⣿⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣿⣿⣷⣾⣿⣿⣭⣭⣭⣿⣿⣟⣛⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣾⣾⣶⣷⣿⣷⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⣶⠶⢿⣿⣯⣭⣽⣹⣿⣿⠀
⣿⣿⣿⢽⢍⠍⣋⣿⡫⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⡝⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣟⠿⢷⣿⠶⠶⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣾⣿⣿⣿⣿⣿⣭⣭⣭⣭⣿⣿⣛⣿⣿⣛⣛⠻⢿⣿⠀
⣿⣿⣿⣽⣧⣦⣥⣯⣽⣿⣬⣽⣤⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣽⣿⣧⣿⣿⣿⣿⣿⣮⣷⣿⣿⣿⣿⣿⣿⣿⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣾⣿⣿⣭⣭⣍⣹⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠻⠟⠛⠏⠛⠻⣿⣿⣿⡏⢡⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⢠⡤⡤⠤⡤⠤⡤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾
⣿⣿⡇⢀⣤⣤⣥⡥⠤⠤⠬⠤⠤⠤⠤⠤⠤⠶⠶⠶⠖⠒⣲⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⡶⣶⣶⣶⣶⡆⢠⠄⣤⣤⡄⠀⣤⣤⡄⡀⢀⢴⣦⣤⣤⣤⢤⣤⣤⠀⢀⡀⠀⠀⢀⣀⢀⢀⢠⣤⣤⣤⡄⢹
⣿⣿⡇⠀⡿⣫⣿⣥⣼⣧⣵⣽⣤⣭⣬⣬⣿⣥⣭⣬⣤⣤⣨⣿⣟⣇⢤⣶⣶⣾⣴⣬⣬⣶⢿⠿⠿⢿⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠌⢹⡟⢠⣴⢶⠿⣶⣾⣮⣶⣦⠘⠿⠿⠿⠃⢸
⣿⣿⡇⠀⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣤⠽⠿⠿⠿⠿⠿⠿⠿⠸⠀⠀⢠⡏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣇⡘⠛⠚⠚⠚⠛⠓⠚⠛⠀⠀⠀⠀⠀⢸
⣿⣿⡇⠀⠛⠶⠶⢲⢒⢲⢶⢲⡶⠒⠒⣖⠲⢲⠒⢲⢰⣶⣶⡶⠶⢯⢒⠖⢶⣲⡶⠶⢶⣖⠖⡆⠀⠀⠉⢙⣿⡁⠀⠀⣈⣀⣀⣀⣀⣛⣓⣈⣙⣛⣛⣃⣘⣛⣿⣟⣿⣿⣿⣦⡸⢄⣿⣭⣿⣇⣽⣄⣿⡾⠀⠀⠀⢸
⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸
⣿⣿⡇⢀⣀⣀⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⡁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⡄⢀⢀⣀⣀⡀⠀⠀⠀⠀⠈⠙⣿⣟⣁⣀⣀⠀⢀⣀⣀⣀⡀⢸
⣿⣿⡇⠀⣿⣿⡿⠿⠿⢟⣿⣧⣴⣿⣼⣮⣤⣿⣴⣧⣾⣧⣤⣥⣀⣤⣤⡀⠉⣥⣥⣼⣥⣼⣿⣧⣤⡔⠀⠀⣠⣭⣤⣼⣶⣧⣥⣯⣦⣿⣧⣤⣯⣀⣀⣤⣤⡔⠉⣠⣭⣬⣼⣾⣯⣥⣬⠁⠀⠈⠁⠀⠐⠁⠈⠀⠀⢸
⣿⣿⡇⠀⠀⠐⠄⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠁⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠉⠾⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⡇⠠⡤⠤⠤⢤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⣤⣤⣤⣾

                    ䷩ 𝚕𝚒𝚗𝚎 515

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/In_Case_Undersea_Cables_Are_Cut.shtml
    Gemini version at https://techrights.org/n/2024/11/30/In_Case_Undersea_Cables_Are_Cut.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ In Case Undersea Cables Are
Cut...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024,
updated Nov 30, 2024


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


Undersea cables are a bit of an "elephant in the room..."


This isn't new technology and by now there are many such cables. There are also
maps of these ("open-source intelligence"), however incomplete and inaccurate
(or outdated intentionally, leaving out critical fallbacks). Publishing those
maps is essential to prevent damage from ship anchors, among other physical
threats, irrespective of the flag the ship bears. It's a case of collective
responsibility at a global scale, albeit it relies on universal solidarity and
respect for the world's communication facilities.


We all knew (all along) that reconnaissance by submarines had been done to map
cables of "rival" blocs and we all knew that in case of war/s not only gas
pipes and energy facilities would be targeted. Ask freezing Ukrainians this
month what this means to them.


Between 2012 and 2022 I worked (indirectly) for a company that helped protect
undersea cables and other 'deepwater' assets (the word "assets" gets thrown
around a lot; it's almost always cables). We supported JBoss, PostgreSQL, GNU/
Linux etc. for them. Tomorrow night marks exactly 2 years since I sent my
letter of resignation and started focusing more on this site.


Recently, in our_IRC_network, we had a number of discussions about undersea
cables and what it would mean if China (and its ally Russia) turned out to be
systematically dragging anchors on the sea/ocean floor to vandalise key
infrastructure. Almost all of the world's Internet traffic goes through
undersea cables and almost all means of communication (even landlines) got
offloaded to the Internet. The Baltic sea got the most attention for vandalism
by Chinese vessels, with British waters being closely watched and guarded for
movement of Russian vessels. They might be preparing a list of assets
(intelligence) ahead of an actual attack, which can target many cables all at
the same time. The way the Net was built, if one cable is cut (or even 10), an
alternative routes for transmission of packets would get chosen, albeit speeds
would decrease, as would latency (due to throughput limits and capacity
issues). But each country has a finite number of "fat pipes" going in and out
of it (consider what happened to Georgia when some metal digger hit a crucial
cable over a decade ago) and satellites cannot cope with millions of
simultaneous Net users, especially if they transmit large files or stream DRM
garbage over Netflix.


I am neither an optimist nor a pessimist, probably just somewhere in the
middle, but it seems likely that in the coming months or years we'll hear a lot
more about severed undersea cables. For some countries this will mean either no
connection or much slower connections (and sessions arbitrarily reset; this is
fatal for some software). That means that sites which are low in complexity and
bandwidth (such as ours) will become more accessible. Our Gemini capsule has
very small footprint in terms of bandwidth. It's basically just the text of
pages, nothing else. "Remember that Techrights and Tux Machines can still be
accessed using Netscape 4," Ryan has just said in IRC. "It will look a bit
wrong, but you can still read everything. The links to other sites won't work
(SSL/TLS). The code to handle a basic web site was there over 25 years ago. A
user-centric web with no copyright laws would be a dramatically different
place. Browsers wouldn't have changed much since the 1990s. BitTorrent would be
how things got moved around. People would have built exactly what they need and
nothing more. The reason for total lack of security in the modern world is
corporations coming and blowing it all sky high and starting over with
overdesigned specifications meant to control what your computer is up to at all
times. I was one of the first users of BitTorrent. Because I was one of the
first users of every file sharing protocol, even back to Napster. The fake news
media has re-defined what "digital native" means, and says that people who sit
there all day looking at a phone are the first "digital natives". They act as
if it wasn't the PC boom of the 90s and rampant "piracy" and hacker culture.
They act like it only started when Apple gave it to the equivalent of the next
wave Eternal September crowd, the iPhone user. As soon as iPhones got more and
more widespread, I said to myself "Get these people off the goddamned
Internet!" But it's a problem that's not going away. It brought in two things,
I think. Boomers who took their property line disputes to "social media" and a
bunch of barely educated children and young adults. And the noise drowned out
everyone in between. Interestingly, CNN is behind a paywall now, mostly,
because why not. But accessing CNN with 100 M/bit sec cable internet and no ad
blocker on takes just as long as it did in 1998 over dial up. They used static
pages back then. You signed in, there was a picture, you know, some text. Even
in the early 2000s. The space shuttle broke up, here's what happened."


The demise of the Web is a subject we often revisit here in Techrights; back in
the 90s people warned about how the Web would cause information loss (by
'replacing' physical archives that can last centuries) and how making sites too
bloated would further exacerbate the matter.


But anyway, let's go back to basics. The Internet is a lot more precarious than
people are led to assume. Their skinnerboxes would not operate without it.


Undersea cables are an issue and not a new issue. Monitoring undersea cables is
nearly impossible at a scale that can detect/prevent sabotage because the
cables are very long and are placed very deep (where only submarines or high-
intensity sonar can see what's going on).


The issue has been somewhat of a taboo - mostly overlooked or entirely ignored
at times of peace. This is likely to change. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣯⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣷⣿⣿⣯⣽⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠛⢿⡙⢛
⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⢛⡴⠾⣱⡈
⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⢀⣐⣤⡆⡉⠀
⠿⢿⣿⢉⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣯⣭⣿⣿⣿⣿⠛⡿⠿⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣀⣴⣿
⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣙⣋⣛⣇⣅⣻⣯
⣿⡿⢟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠑⠾⠻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠐⠲⢿⠿⣉⠝⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⡍⢁⣶⣶⣮⡉⠊⠗⢠⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣻
⣆⠚⠉⢭⡟⠄⠁⣀⣀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⠟⢻⣛⣿⣿⣟⡿⢿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠛⠙⢻⣿⣿
⠀⠀⠈⡻⣷⡀⡈⣽⣿⡿⣾⣹⣶⣿⡻⠿⠟⠻⠯⢛⣯⣿⣶⢞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⢃⣈⡦⡁⣈⠟⣏⣁⣬⣇⣼⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠻⣶⣦⣴⣤⠜⠛⠋
⠄⠐⢺⣻⠌⣽⡇⠍⠐⠢⢾⣿⣿⣷⢉⣀⠀⠀⢀⣬⣽⠛⠀⣭⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⡿⣿⣿⣿⡏⠹⠟⣿⡦⠙⠁⠉⠁⠀⠀⠠
⣀⣄⣨⣗⣤⠀⠀⠀⠀⠠⢄⠀⣿⣿⣿⣿⣀⠁⠈⠈⠁⠀⠀⢸⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠟⡙⢟⣿⣿⠿⣟⣻⣿⣿⣿⣿⣿⡧⣷⠿⢦⠶⠖⠠⠄⠀⠈⠍
⣤⣾⣿⣿⣿⣐⠶⠀⠀⠀⢠⣑⣻⣿⣽⣿⣿⣧⣤⣰⣤⣠⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⠛⣻⣿⣿⣿⣿⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣳⣯⣿⣦⣆⠙⣿⣿⣿⢾⣿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣛⣿⣍⠐⠋⢱⣄⣀⣠⠀⠄⠁⠀⠐⢷⡈⢀⠏⠉⣫⣿⣿⡟⠻⣿⣿⣿⣿⣿⣷⢂⣷⡿⢟⣻⣷⣂⣷⣞⡿⠋⠈⠓⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠀⠈⠿⡑⠛⣁⠀⠌⣭⣼⣾⡿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⡟⠓⠂⠀⢨⠅⡹⠻⢄⢄⠠⢀⡀⠰⠛⢗⢀⣶⣿⣿⣿⡃⠐⢿⣿⢿⣿⣿⡿⠿⡑⠀⡀⠈⠀⠁⠊⠙⠁⠀⠀⠀⠀⠀⠀⠀⢀⢈⠙⠉⠉⢿⣯⣻⠣⡄⣿⣶⣽⣷⣿⣯⣽⣿⣷⡯⣂⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀
⢞⠋⢆⠀⠀⠀⠀⠩⣤⣴⣯⡧⣤⣠⣖⣠⢠⣿⠟⠛⣿⠋⡀⣸⣟⣥⣽⡟⠛⢻⠋⡀⠠⢠⡄⠀⢼⢶⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠰⣟⣵⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⣷⢉⡋⣤⣶⣤⠀⠀⠀⠀⠀⠀
⠀⣄⠀⠀⠀⠀⠀⠌⠙⠋⠀⠠⠼⠋⠀⠈⠁⢁⣸⣿⣿⣀⣈⣿⣿⣿⡿⠮⡹⢪⢷⠒⢶⠁⢀⠀⠀⠙⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⢽⢿⠿⠿⡏⣽⣿⣿⣷⣿⣦⠻⣿⣿⣯⣙⣿⣿⣅⢀⡀⠀⠀⠀⠀
⣤⠹⡗⠢⠒⠀⠀⠀⠈⠁⠀⠀⠝⣀⡀⠀⢀⣾⣿⣿⣿⣿⣿⠟⣿⣿⠈⠂⠀⠁⠀⠀⠂⢠⠌⠁⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⠀⠀⠀⠈⠀⠀⠼⠊⠀⠀⢫⠙⠯⣿⣿⣟⢙⣿⣟⣿⣿⣟⣩⣆⠀⠀⠀⠀
⠀⢘⡡⣇⣨⣶⣠⠀⠀⠀⠀⠀⠉⠈⠐⠀⢸⣿⣿⣿⣛⣻⡑⠈⠋⡫⠅⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠈⢠⡀⠀⠀⠀⠠⣤⢔⡻⣫⣴⣀⠁⣹⣿⣿⣿⣯⣿⣯⣿⣟⣉⠻⠓⠀⠀⠀
⡂⢉⣹⡿⠿⣋⣽⣄⡀⠀⣀⡀⣀⣀⣴⣀⣤⣝⣿⣾⠁⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠯⠉⠐⠘⢕⣿⣿⣿⣿⣿⣿⣿⣿⢧⣤⣽⣥⡄⠄⢀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 664

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/IRC_Proceedings_Friday_November_29_2024.shtml
    Gemini version at https://techrights.org/n/2024/11/30/IRC_Proceedings_Friday_November_29_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Friday, November 29,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇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 888

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Meme_Growing_Up_and_Becoming_Sceptical.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Meme_Growing_Up_and_Becoming_Sceptical.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Growing Up and Becoming
Sceptical⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024,
updated Nov 30, 2024


Social control media is a toxic weapon against what's true [1, 2]


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




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡦⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⠗⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣤⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⣞⣁⡀⠉⢻⣿⠛⣉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⢿⣿⣿⣿⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣽⣿⣿⣿⣿⣿⡏⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠒⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⣠⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡋⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨⣶⡄⠀⠀⠀⣼⣿⣿⠣⣤⣤⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠁⠀⠀⠀⠀⢸⣿⣿⢨⣿⣯⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢰⣒⣒⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⣶⣶⠈⠿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⣷⡿⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢘⢿⠟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠏⢸⣿⣿⠀⠠⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠦⣤⢘⣟⣿⠀⡤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣘⠻⢿⣿⠿⠿⠟⠡⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⣋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣿⣿⣿⣿⣷⡀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣙⣛⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢀⣾⣿⣿⣿⣿⡿⣟⢟⣿⡟⠻⣿⣿⡄⣿⡟⠳⠦⡻⡻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⠛⡙⣿⣿⣆⣽⡿⠀⢸⣇⡠⣿⣉⣸⠜⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⣤⣴⠂⠀⠀⠀⠀
⠀⣼⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⣿⣿⣿⠛⠈⠙⠉⣁⢀⣼⡉⢹⣧⢀⣉⣿⠚⢇⠘⣿⣿⣿⡇⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠉⠙⠿⢿⡇⠻⠿⠃⢠⡶⠘⢿⣧⠙⣷⣼⠏⠀⠉⠀⣠⠼⠂⠀⠙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠀⠀⠀⠀⢀⣿⡇⠀⠠⣶⣸⣇⣀⣈⠻⠇⠈⠉⢀⡤⠖⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠀⠀⠀⠠⣿⣿⡇⠀⠀⠙⢿⡍⠉⠉⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠁⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣱⣿⣿⣿⣿⣿⣿⣄⢤⣆⠀⠠
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠿⠻⣿⣿⣿⣯⠀⣿⣿⣦
⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣤⣤⣄⣀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠰⠿⣿⠁⠀⠀⠻⣿⣿⡏⠀⢹⠻⣿
⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠾⡿⠿⠿⠿⠨⠏⠀⠈⠉⠀⠁⠀⠁⠀⠀⠙⠛⣿⣿⡾⠁⠀⣴⣿⣦⣤⣀⠀⠈⠻⣷⢰⡄⠃⠈
⣿⣿⣿⣧⠁⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⡤⢄⣀⣀⠀⠀⢀⠶⢆⡀⠀⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢵⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡘⢿⡶⠟
⣿⣿⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⣿⣿⣿⣿⣧⣄⣀⠈⠉⠛⠻⠿⣿⠀⠀⠈⠉⠁⠒⠛⠛⠻⠿⠿⠿⠶⣂⣀⣀⣀⣀⣀⣀⠀⠀⠀⠴⠶⠶⠾⠛⠛⠋⠉⢀⣼⣿⣿⣿⣿⣄⣾⣇⠀
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠂⠤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⠏⠉⠉⠀
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣹⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⢠⡄⠀⠈⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣤⣤⣤⣀⡀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷

                    ䷩ 𝚕𝚒𝚗𝚎 988

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] The Internet is More Fragile Than
They Are Willing to Admit⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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⣿⣿⣿⣿⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣤⣥⣭⣯⣩⣧⣽⣤⣧⣤⣼⣼⣤⣬⣼⣯⣤⣼⣭⣭⣥⣧⣭⣯⣭⣭⣯⣍⣥⣭⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡛⠛⢻⡛⠛⣛⠛⠛⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣍⣉⣩⣭⣉⣉⣉⣉⣉⣉⣍⣍⣙⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣦⣤⣴⣦⣶⣥⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣸⣇⡀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣦⣤⣬⣤⣴⣥⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣤⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠇
⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⣿⣿⣿⣿⠀⠀⠀⠸⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1064

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Meme_The_Word_Security_Has_Been_Redefined.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Meme_The_Word_Security_Has_Been_Redefined.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] The Word Security Has Been
Redefined⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


Context: Proving_Yet_Again_That_Techrights_Was_Right_About_UEFI_'Secure_Boot'
All_Along_(Since_2012)




⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⠰⣀⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⡀⣴⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣿⣷⣶⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢲⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠂⢸⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⡀⠉⢾⣷⡟⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⠉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡟⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡏⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠂⣿⣿⣷⣍⠻⣿⡇⠀⠼⣯⡤⠚⠿⠷⠶⢶⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣯⢈⡀⠉⠀⣠⣤⣤⣤⣤⣤⣌⣛⠟⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡶⢒⡟⠙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡆⠀⢸⡇⢈⡃⠀⣷⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠘⠁⠀⠙⠀⠈⠟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⡤⠆⢻⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠯⠿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠁⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⢠⣍⡁⠀⠚⠛⠂⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⡟⠁⠀⠀⠉⠛⢦⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⣿⡿⠀⡇⢸⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⣿⣿⣿⣦⣹⡈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠼⢿⣿⠃⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⡙⠛⢿⠏⠀⡈⠣⠀⠠⡝⡁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣦⣤⣄⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣾⣿⡿⠿⠿⠻⠟⠛⠻⠿⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢚⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠋⡒⠪⢉⢁⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⣀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣀⡀⣀⣀⣈⣋⢹⢫⠹⢛⢋⢛⡻⢟⣛⣛⣛⡛⡛⡋⡍⣙⢛⢋⢹⠹⠺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡶⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠦⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠅⠧⠜⠬⠵⠣⠼⠸⠸⣄⡸⠸⢸⣇⣘⠤⠜⠤⠇⠇⠇⠧⠇⠰⠤⠸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣾⣷⣶⣖⠒⠶⠶⣄⡀⣴⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣿⣷⣶⠀⠀⡀⠀⠐⠒⢶⡶⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢼⣿⡀⠉⢶⣿⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠃⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠻⣿⡇⠀⠼⣯⡤⠚⠿⠷⠶⢶⡄⠀⡀⠀⠐⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⡀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⠣⠀⢠⡶⢒⠟⢙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡅⠀⠸⡇⢐⠇⠀⣷⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠐⠂⠀⠙⠀⠈⠍⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠬⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠭⠿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠁⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣷⡀⠀⢠⣍⡀⠀⠚⠛⠀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⠟⠁⠀⠀⠉⠙⢤⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡿⠀⡇⢰⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⢿⣿⣿⣦⣸⡈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣬⡙⠛⢿⠏⠀⡈⠣⠀⠠⠝⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣦⣤⣄⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣾⣿⣿⠿⠿⠟⠛⠛⠿⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠊⠋⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⡒⠪⢉⢁⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣀⡀⣀⣀⢈⣋⢹⢫⠻⢛⢛⢛⡻⢟⣛⣛⣛⡛⡛⡋⡍⣛⢛⢋⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡷⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠦⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠅⠧⠜⠬⠵⠣⠼⠸⠸⣄⡸⠸⢸⣇⣘⠤⠜⠤⠇⢇⠇⠧⠇⠰⠤⠸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣦⣤⣤⣤⠄⢠⡀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⡀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢴⣶⣀⣤⣤⣴⣶⡆⠀⠀⢰⣿⣷⣖⠀⠀⡀⠀⠐⠒⢶⡶⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡂⢻⣿⠛⠋⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠉⢶⣶⡟⠋⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣠⣿⣿⣿⠟⠋⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡨⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠿⣿⡇⠀⠼⣯⡄⠚⠿⠶⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⠀⡀⠉⠀⣠⣤⣤⣤⣤⣤⣀⣛⠟⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⠆⠀⢠⡶⢒⡛⠙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠘⡇⢀⡇⠀⣷⠉⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠁⠀⠀⠀⠘⠀⠈⠉⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠤⠆⢸⣿⣿⣿⣿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠭⠽⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯⣧⠀⠀⢠⣅⡀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⠋⠀⠀⠀⠉⠑⢤⠀⠀⠀⠧⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡿⠀⠇⢠⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠃⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢿⣿⣿⣦⣸⡈⢇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢬⡙⠛⢿⠏⠀⠈⠢⠀⠀⠝⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣶⣤⣄⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣶⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⡒⠪⢉⢁⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣀⡀⣀⣀⣙⣋⢹⢫⠻⢛⢛⢛⡻⢟⣛⣛⣛⡛⡛⡋⡍⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠅⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣧⣘⠤⠜⠤⠇⣇⠇⠧⠇⠰⠤⠸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣦⣤⣤⣤⣴⣦⣤⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢀⣠⣤⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠰⠀⠰⡀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡦⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡶⢲⣄⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡂⢹⣿⠙⠋⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⡈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣼⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡨⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⡇⠀⠼⣧⡄⠚⠿⠶⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠉⠀⣠⣤⣤⣤⣤⣤⣀⣛⠟⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢹⣿⣿⣿⣿⣿⠞⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⣿⡩⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣤⣿⣿⣾⢡⠀⠀⢠⡖⠒⡃⠙⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣷⡄⠀⠘⡇⠀⠄⠀⣗⠉⢿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⣆⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⠁⠀⣸⠃⠀⠀⠀⠘⠀⠀⠑⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠭⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡆⠀⠀⣤⣄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⠏⠀⠀⠀⠀⠈⠒⢤⠀⠀⠀⠧⠀⢴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡿⠀⠃⢠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠁⠀⠀⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢾⣿⣿⣦⣰⡈⢇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠘⠻⠟⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⡉⠛⢿⠏⠀⠀⠢⠀⠀⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣦⣄⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶⣶⣿⡿⠿⠛⠛⠛⠛⠛⠛⠻⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⡓⠫⢉⢁⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣀⡀⣀⣈⣛⣛⢹⢫⠻⢟⢛⢛⡿⢿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠄⠧⠜⠬⠵⠣⠼⠸⠸⣤⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣤⣤⣤⣴⣶⣶⣤⣤⡀⠀⠈⠁⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⢀⣠⣤⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠰⠀⠐⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡶⢒⣄⠀⠀⢰⣶⣾⣿⣿⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣀⣶⣾⣷⣶⣾⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣸⡀⢹⣿⠙⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢴⣶⡞⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⡈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠆⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠨⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡆⠀⠈⠙⠿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⢋⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠜⣯⡄⠒⠿⠶⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠉⠀⣠⣤⣤⣤⣤⣤⣀⣛⠟⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠂⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⣿⠜⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⣿⡈⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣤⣿⣿⣶⠀⠀⠀⢀⡖⠒⠃⠙⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣷⡄⠀⠘⡇⠀⠀⠀⣧⠈⢿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠿⣆⠀⠀⠀⠀⢀⠀⢘⣿⣿⣿⣿⣿⠁⠀⣰⠁⠀⠀⠀⠘⠀⠀⠈⡟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠥⠽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠝⠀⠀⠐⣦⣄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⡿⠀⠃⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⢾⣿⣿⣦⣰⠈⢇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠌⠉⠛⢿⠋⠀⠀⠢⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣦⣄⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⡿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶⣾⣿⠿⠛⠉⠉⠉⠊⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⡓⠪⢉⢉⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⡀⡀⣀⣘⣛⣛⢹⢫⠻⢟⢛⢛⣿⢿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠴⠄⠧⠜⠬⠵⠣⠼⠸⠸⣤⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣶⣶⣦⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠚⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⠰⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⢒⣀⠀⠀⢰⣶⣾⣿⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢿⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⢻⠀⣀⣶⣾⣷⣶⣶⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣷⠐⣤⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣸⡀⢻⣿⠙⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢴⢶⡞⠉⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⡈⠇⢙⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣴⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡆⠀⠈⠙⠿⠓⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⢋⣉⣹⡿⠿⠿⠴⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠸⣧⡄⠒⠿⠶⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠉⠀⣠⣤⣤⣤⣤⣤⣀⣛⠟⠀⠀⠀⠀⠀⠀⠸⠷⡄⠀⠀⠀⠀⠀⠀⢶⣺⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⡿⠜⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⢻⣿⣠⣿⣿⣦⠁⠀⠀⢀⡔⠒⠃⠐⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡⣿⣿⣿⣿⣆⡄⠀⠘⡇⠀⠀⠀⡇⠈⢿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠿⣆⠀⠀⠀⠀⢀⠀⠐⣿⣿⣿⣿⣿⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠆⢠⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡉⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡂⠁⠀⠀⠰⢶⡄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠇⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⠀⠇⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡿⠀⠃⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⢾⣿⣿⣦⣰⠈⢇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠘⣿⠷⣤⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⢿⠋⠀⠀⠢⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣦⣄⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⡿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣴⣾⣿⡟⠛⠉⠉⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⡒⠪⢉⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣀⡀⣙⣛⣛⣛⢹⢫⠻⢛⢛⢛⢿⢿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠤⠝⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠀⠮⠥⠂⠀⠘⠆⠇⠟⠤⠤⠄⠧⠜⠬⠵⠣⠼⠸⠸⣄⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣴⣶⣦⣤⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠶⠒⢀⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⠰⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⢒⣀⠀⠀⢰⣶⣾⣿⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢿⠀⣀⣶⣾⣷⣶⣶⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣷⠐⣦⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢺⡀⠹⣿⠙⠋⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢘⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⠴⣶⡎⠉⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⡈⠇⢙⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣴⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⡿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⢋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣧⡄⠒⠿⠶⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠉⠀⣠⣤⣤⣤⣤⣤⣀⣛⠟⠀⠀⠀⠀⠀⠀⠸⠷⡄⠀⠀⠀⠀⠀⠀⢶⢾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠂⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⡿⠜⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⢓⠈⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⢻⡿⣠⣿⣿⣦⠀⠀⠀⢀⡔⠂⠂⠑⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⣿⣿⣿⣿⣆⡄⠀⠘⡇⠀⠀⠀⣗⠈⢿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⢹⠿⣆⠀⠀⠀⠀⢀⠀⠐⣿⣿⣿⣿⣿⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠄⢠⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⠁⠀⠀⠀⠻⠦⡀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠃⠀⣴⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⡿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢾⣿⣿⣦⣐⠈⢇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠻⠿⢶⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⢿⠋⠀⠀⠢⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣤⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⢀⣀⣠⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣀⣤⣴⣾⣿⡿⢻⠻⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣴⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⡒⠢⢉⢉⢉⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣀⡙⣛⣛⣛⣛⢹⢫⠻⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠩⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡷⠤⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠅⠧⠜⠬⠵⠣⠼⠸⠸⣄⡸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⣤⣄⡄⠀⠀⠀⠈⠁⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣶⠶⠂⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⠰⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⢒⣀⠀⠀⢰⣶⣾⣿⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⢿⠀⣀⣶⣾⣷⣶⣾⣾⠀⢰⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣷⠐⣦⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⡀⠹⡿⠙⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢘⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢴⢶⡞⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⡈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⡿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠻⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⢋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣧⡄⠒⠿⠶⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠉⠀⣠⣤⣤⣤⣤⣤⣀⣛⠟⠀⠀⠀⠀⠀⠀⠸⢷⠄⠀⠀⠀⠀⠀⠀⢶⢾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢸⣿⣿⣿⣿⣿⠜⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⢗⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⢻⡿⣠⣿⣿⣦⠀⠀⠀⠠⡔⠂⠂⠐⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡⣿⣿⣿⣿⣆⡄⠀⠘⡇⠀⠂⠀⣇⠈⢿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣆⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠁⠀⠀⠀⠈⠀⠀⠈⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠆⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⡇⠀⠀⠀⠀⠛⠢⡀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠃⠀⢴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⠀⠸⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⢾⣿⣿⣦⣰⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⢿⠃⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣤⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⣀⣠⣤⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣀⣤⣴⣶⣿⡿⠿⢛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⡿⡉⠉⠁⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⡒⠢⢀⢈⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⡈⡛⣛⣛⣛⣛⢹⢫⠻⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠩⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⠤⠝⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠅⠧⠜⠬⠵⠣⠼⠸⠸⣄⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣴⣦⡤⠄⠀⠀⠀⠈⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡶⠶⠀⢀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⠰⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⠒⣀⠀⠀⢰⣶⣾⣿⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢿⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢻⠀⣀⣶⣾⣷⣶⣾⡷⠀⢰⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⢤⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣺⡀⢹⣿⠙⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢘⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣷⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢴⣶⠎⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⡈⠇⢉⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠆⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣯⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⠄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠄⠀⠈⠙⠻⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⢋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠸⣧⡄⠒⠿⠶⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠉⠀⣠⣤⣤⣤⣤⣤⡀⠛⠛⠀⠀⠀⠀⠀⠀⠸⠷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⡿⠜⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⠓⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⢻⣿⣠⣿⣿⣦⠀⠀⠀⢠⡔⠂⠂⠐⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⣿⣿⣿⣿⣆⡄⠀⠘⡇⠀⠂⠀⡇⠈⢿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣆⠀⠀⠀⠀⢀⠀⠐⣿⣿⣿⣿⣿⠁⠀⢰⠁⠀⠀⠀⠐⠀⠀⠀⡟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠆⢰⣻⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡅⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⠀⠀⠀⠀⠈⠛⢢⡀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠀⢴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⣾⡿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⢺⣿⣿⣦⣰⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⢿⠋⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣦⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⣠⣴⣶⣿⣿⢿⢟⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠝⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⡒⠢⢀⢉⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⡙⣛⣛⣛⣛⣋⢹⢫⠻⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠩⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡑⠤⠝⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠅⠧⠜⠬⠵⠣⠼⠸⠸⣤⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣄⣤⣤⣤⣤⣴⣤⢠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⠗⠀⢀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡀⠐⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠒⢶⡖⢒⣀⠀⠀⢰⣶⣾⣿⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢮⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢾⠀⣀⣶⣾⣷⣶⣶⡾⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣷⠐⣦⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⡀⠹⣿⠙⠉⢹⣿⠹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣷⣿⠂⣸⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⠀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢴⣶⠎⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⡈⠇⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⡿⠛⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣯⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡆⠀⠈⠙⠻⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⢋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣧⡄⠒⠻⠶⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠉⠀⣠⡤⠄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠸⠷⡄⠀⠀⠀⠀⠀⠀⢶⢾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⡿⠜⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⢓⡈⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⢻⣿⣠⣿⣿⣦⠀⠀⠀⢀⡆⠂⠆⠐⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢁⣿⣿⣿⣿⣆⡄⠀⠘⡇⠀⠀⠀⡇⠈⢿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣆⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠁⠀⠀⠀⠘⠀⠀⠀⠟⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠀⠀⣤⡀⠀⠀⠠⠆⢠⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣿⡿⠀⠀⠀⠀⠀⠉⠛⠦⠀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⠀⠀⠀⠃⠀⢴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⡿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⢺⣿⣿⣦⣰⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⢿⠃⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠆⣀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣤⣴⣾⣿⠿⠟⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠍⠁⠉⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠋⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡈⣛⣛⣛⣛⣛⣛⢹⢫⠻⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢻⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠐⠤⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠮⠥⠂⠀⠘⠆⠇⠟⠤⠼⠄⠧⠜⠬⠵⠣⠼⠸⠸⣤⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣄⣤⣤⣤⣤⣤⡄⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣾⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠰⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⢒⣀⠀⠀⢰⣶⣾⣿⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⢿⠀⣀⣶⣾⣷⣶⣶⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⢦⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⡀⢹⣿⠙⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢘⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢴⣶⡎⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⡈⡇⢙⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⡿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⠄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠻⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⢋⣉⣹⡿⠿⠿⠴⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣯⡄⠒⠿⠶⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠷⡄⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⣿⠜⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⠗⠈⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣠⣿⣿⣦⠀⠀⠀⢀⡔⠒⠂⠐⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢁⣿⣿⣿⣿⣦⡄⠀⠘⡇⠀⠀⠀⣗⠈⢿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣆⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⠁⠀⢰⠁⠀⠀⠀⠈⠀⠀⠀⠟⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⣸⠃⠀⠀⣤⡀⠀⠀⠀⠆⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣾⣿⠇⠀⠀⠀⠀⠀⠈⠑⠦⠀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠃⠀⢴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⣾⡿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⢾⣿⣿⣦⣰⠈⠇⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢂⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣤⣶⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡉⣛⣛⣛⣛⣛⣛⢹⢫⠻⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠯⠐⠤⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠮⠥⠂⠀⠘⠆⠇⠟⠤⠼⠄⠧⠜⠬⠵⠣⠼⠸⠸⣤⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣣⣤⣄⣤⣤⣤⣤⣤⢤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠰⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⢒⣄⠀⠀⢰⣶⣶⣾⣾⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢿⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢻⠀⣀⣶⣾⣷⣶⣶⣾⠀⢸⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣷⠐⢆⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⡀⢹⣿⠙⠋⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢴⢶⠞⠉⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⡈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣴⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⡿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡆⠀⠈⠙⠻⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⢋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣧⡄⠚⠿⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣺⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⣿⠜⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⢻⡿⣤⣿⣿⣦⠀⠀⠀⢠⡔⠒⠂⠐⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣧⡄⠀⠘⡇⠀⠀⠀⣗⠉⢿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⠁⠀⢰⠁⠀⠀⠀⠈⠀⠀⠈⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⢠⢿⡇⠀⠀⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣑⡀⠀⠀⢰⣦⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⡟⠀⠀⠀⠀⠀⠀⠉⠃⠰⠄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠣⠀⢴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢺⣿⣿⣦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠌⠉⠛⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣃⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣶⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡙⣛⣛⣛⣛⣛⣛⢹⢫⠛⢛⢛⢛⡿⢿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠤⠝⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠄⠫⠭⠪⠽⠸⠀⠮⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣄⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠰⠀⠀⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⢒⡄⠀⠀⢰⣶⣶⣶⣾⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢿⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⢿⠀⣀⣶⣾⣷⣶⣿⡾⠀⢸⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⣹⡀⢹⣿⠙⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠉⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⡈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⡿⠛⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠨⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠿⠃⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⣋⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣧⡄⠚⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⡿⠝⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣤⣿⣿⣮⢀⠀⠀⢀⡖⠒⠃⠙⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣧⡄⠀⠘⡇⠀⠀⠀⣇⠈⢿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⠁⠀⢰⠁⠀⠀⠀⠘⠀⠀⠀⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠸⣿⡏⠀⠀⣦⡀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠀⢰⣤⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠙⠃⠰⠄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⣿⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⣾⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠻⠆⡣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡙⣛⣛⣛⣛⣛⣛⢹⢫⠛⢛⢛⢛⠿⢿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢻⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠤⠝⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠠⠫⠭⠪⠽⠸⠀⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⣸⢸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣠⣤⣄⣤⡄⠀⠄⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡆⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⠰⠀⠰⡀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣾⣿⣾⣷⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣾⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣻⡆⢻⣿⠛⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡨⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡆⠀⠈⠙⠿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠤⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢘⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⡇⠀⠘⠧⠄⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢻⣿⣿⣿⣿⡿⠜⣿⣿⣿⢿⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣯⠀⣿⣿⣿⢜⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣤⣿⣿⣮⣶⠀⠀⢠⡖⠒⡃⠙⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠘⡇⠐⠃⠀⣧⠉⢿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⠁⠀⣸⠁⠀⠀⠀⠘⠀⠈⠉⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠼⣿⡏⠀⠀⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡷⠀⠀⠀⠀⣤⣤⡘⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠈⠹⡄⠰⠄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣶⡷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠀⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡛⣛⣛⣛⣛⣛⣛⢹⢫⠛⢛⢛⢛⣿⢿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢻⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠯⠐⠤⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⣇⠧⠜⠬⠵⠣⠼⠸⠸⣤⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⠇⠰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣠⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⣠⣴⣦⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢃⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⢰⠀⠰⡀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡦⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡶⢲⣄⠀⠀⢰⣶⣶⣿⣿⣷⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣻⡆⢹⣿⠙⠋⢽⣿⣹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⡇⠀⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠀⢶⢾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢻⣿⣿⣿⣿⣿⠝⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣯⠀⣿⣿⣿⡼⠄⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣾⠱⠀⠀⢠⡖⠒⡇⠘⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣯⡄⠀⠘⡇⠐⠂⠀⣷⠉⢿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⠁⠀⣸⠃⠀⠀⠀⠘⠀⠀⠈⢟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⡏⠀⠀⣦⡀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⠀⠀⠀⢰⣤⣤⡹⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠊⠀⠀⠀⠀⠀⠉⢣⡀⠰⠄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠧⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢨⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠀⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡛⣛⣛⣛⣛⣛⣛⢹⢫⠻⢛⢛⢛⠿⢟⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢻⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠐⠬⠝⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⣇⠧⠜⠬⠵⠣⠼⠸⠸⣄⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⢇⡰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣣⣤⣄⣤⣤⣤⣤⣤⠀⠀⢠⣦⣶⣦⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⡀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⣰⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣾⣷⣦⠀⠀⡀⠀⠐⠒⢶⡶⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠂⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢶⣿⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⢿⣿⠇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⠄⠀⢠⡖⠒⡗⢙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠸⡇⢐⡇⠀⣷⠉⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠀⠀⠀⠘⠀⠀⠋⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⣦⡀⠀⠀⠤⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⣠⣤⡈⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠄⠀⠀⠀⠉⠉⠻⣿⠀⠰⠄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡛⣛⣛⣛⣛⣛⣋⢹⢪⠻⢛⢛⢛⣿⢿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⣇⠧⠜⠬⠵⠣⠼⠸⠸⢄⡸⠸⢸⣧⣜⠤⠜⠤⠇⣇⡇⠧⢇⡰⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣿⣣⣤⣄⣤⣤⣤⣤⣴⣤⣦⣶⣶⣦⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⢰⠂⠰⡀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢴⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣿⣷⡆⠀⠀⡀⠀⠐⠒⢶⡶⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠙⠋⢽⣿⣹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠋⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡟⢿⣿⣿⣿⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠿⣿⠇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠈⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣏⠄⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣼⠀⠀⢠⡖⠒⡇⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠘⡇⠀⠁⠀⣷⠉⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠀⠀⠀⠘⠀⠈⠁⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡏⠀⠀⣦⡀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣀⣄⠹⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠉⠙⢳⡟⠀⠰⠄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡉⣛⣛⣛⣛⣛⣋⢱⢪⠻⢛⢛⢛⣿⢿⣛⣛⣛⡛⡛⡛⡝⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⣇⠧⠜⠬⠵⠣⠼⠸⠸⢄⣸⠸⣸⣧⣜⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣿⣣⣤⣄⣤⣤⢤⣤⣴⣤⣶⣶⣶⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⣄⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢴⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣾⣷⣶⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢶⣷⡟⠋⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⢉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠻⠿⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠈⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢠⡶⠒⡟⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠘⡇⠀⡇⠀⣷⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠀⠃⠀⠘⠀⠀⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠤⠆⢸⣿⣿⣿⣿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣉⠙⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠛⠛⠷⡀⣸⠀⠰⠄⠀⠀⠘⠛⠂⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡈⣛⣛⣛⣛⣛⣋⢹⢫⠻⢛⢛⢛⣿⢿⣛⣛⣛⡛⡛⡛⡏⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⢄⡸⠸⣸⣧⣘⠤⠜⠤⢇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣿⣀⣤⣄⣤⣤⣤⣤⣴⣦⣶⣶⣦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⡀⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣾⣷⣶⣖⠒⠶⠶⣄⠀⣶⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣿⣷⣦⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠂⢸⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠙⠋⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢽⣿⡀⠉⢶⣿⡟⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠿⠿⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢠⡶⠒⡟⢙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⠘⡇⠈⡇⠀⣷⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⢼⠃⠈⠁⠀⠘⠀⠈⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⡤⠆⢸⣿⣿⣿⣿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠊⠛⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⠀⠀⠰⠿⠿⢧⠀⢸⠀⠰⡄⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡏⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡒⠢⢀⢀⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡈⣛⣛⣛⣛⣛⣋⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡝⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠤⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣧⣘⠤⠜⠤⠇⣇⡇⠧⢇⡰⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣿⣀⣤⣄⣤⣤⣤⣤⣶⣶⣶⣶⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⡀⣶⣶⣀⣤⣤⣴⣶⡦⠀⠀⢸⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢲⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢽⣿⡀⠉⢾⣿⡟⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣌⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣠⣾⣿⣿⡟⠋⢉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⣏⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠉⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡣⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡡⠀⢰⡶⢒⡟⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢘⡇⠀⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠈⠁⠀⠙⠀⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⡤⠆⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⣠⣶⣶⡀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠨⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀⠹⡄⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡖⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⣛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠴⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⢇⠧⠜⠬⠵⠣⠼⠸⠸⣄⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⣶⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣷⣷⣶⣖⠒⠶⠶⣄⡀⣶⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠂⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢿⣿⡀⠉⢶⣿⡟⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣈⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣠⣿⣿⣿⡟⢋⢉⠉⠁⣿⢸⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⣏⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠛⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⣗⠀⢰⡶⢒⡟⠙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡅⠀⢸⡇⠘⡇⠀⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠀⠀⠹⠀⠈⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⡤⠆⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠿⠿⣿⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠉⠉⠈⢣⡀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡒⠢⢀⢈⢉⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣧⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⣦⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⡀⢴⣶⣀⣤⣤⣴⣶⡦⠀⠀⢸⣿⣷⣶⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠉⢾⣿⡿⠋⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡟⠋⠉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡏⠀⠀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⠀⠀⢠⡶⠒⡛⢹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢈⡇⠀⣷⠙⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠐⠃⠀⠘⠀⠈⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠈⣦⡀⠀⠀⡤⠆⢺⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠈⠙⠉⠻⣄⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⡒⠢⢀⢉⢉⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣘⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⣆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⠰⣀⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣷⣿⣶⣖⠒⠶⠶⣄⡀⣴⣶⣀⣤⣤⣴⣶⣦⠀⠀⢸⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡷⣲⣄⠀⠀⢲⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠂⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢽⣿⠀⠉⢾⣿⡟⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣾⣿⣿⠟⠋⣉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⠧⠀⢰⡶⠒⡟⢙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⠘⡇⢘⡃⠀⣷⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠘⠃⠀⠙⠀⠈⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⡤⠆⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⡆⠀⠀⠘⠛⠂⠀⠀⠀⠨⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠈⠛⠋⠳⡄⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⠀⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⡒⠢⢀⢉⢉⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣘⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠆⠰⣂⢶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⡀⣶⣶⣀⣤⣤⣴⣶⣦⠀⠀⢸⣿⣿⣶⠀⠀⣀⠀⠐⠖⢶⡷⢲⣄⠀⠀⢲⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢽⣿⡀⠋⢾⣿⡟⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣌⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠻⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡧⠀⠀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡶⢲⡟⢙⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⠘⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠁⠀⠙⠀⠈⠟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠠⡤⠦⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠨⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠘⠛⠋⠳⡄⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⠀⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠗⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣶⣦⣤⣤⣤⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⡖⠢⢈⢉⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣙⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⢇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣴⣤⣤⣤⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠆⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⡀⣶⣶⣀⣤⣤⣴⣶⣦⠀⠀⢸⣿⣿⣶⠀⠀⡀⠀⠐⠖⢶⡷⢲⣄⠀⠀⢲⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢿⣿⡀⠉⢾⣿⡿⠟⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣌⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠿⠃⠀⠀⣤⣿⣿⣿⠟⠛⢛⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⣏⠀⠀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡯⠀⢰⡶⢲⣟⢙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢘⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠂⠀⠙⠀⠈⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠠⡤⠆⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠘⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠘⠛⠋⠳⡀⠀⠘⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⠀⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⡖⠢⢈⢉⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣙⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠴⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⢇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣰⠆⠰⣤⢶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣖⡒⠶⠶⣄⠀⢶⣶⣀⣤⣤⣴⣶⣦⠀⠀⢸⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢲⣶⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⡀⠉⢾⣿⡿⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣍⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠸⠿⠧⠀⠛⠻⠃⠀⠀⣤⣿⣿⣿⠟⠛⣉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡏⠀⠀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡶⢲⣟⢹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⠘⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠈⠃⠀⠹⠀⠈⠟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠠⡤⠦⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠸⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠘⠛⠛⠳⡄⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⠀⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣿⣶⣦⣤⣤⣤⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⡒⠢⢈⢉⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠆⠰⣤⢶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣶⣖⡒⠶⠶⣄⡀⢶⣶⣀⣤⣤⣴⣶⣦⠀⠀⢸⣿⣿⣶⠀⠀⣀⠀⠐⠲⢶⡷⢲⣄⠀⠀⢲⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠰⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⡛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢽⣿⠀⠉⢾⣿⡟⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣌⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠸⠿⠧⠀⠻⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⠉⠉⠁⣿⢸⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⣇⠀⠀⣀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠉⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡗⠀⢰⡶⢲⡟⢹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢘⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠀⠁⠀⠙⠀⠈⠟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠠⡤⠆⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠄⠀⠀⠘⠛⠂⠀⠀⠀⠸⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠘⠛⠋⠳⡄⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⠀⠀⠠⠶⠆⠀⠀⠸⠿⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⡖⠢⢈⢁⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⣛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠴⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣸⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⠆⠰⣀⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⡀⣴⣶⣀⣤⣤⣴⣶⣦⠀⠀⢸⣿⣿⣶⠀⠀⡀⠀⠐⠖⢶⡷⢲⣄⠀⠀⢲⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⣿⠀⣠⣾⣾⣷⣿⣿⣿⠂⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢿⣿⠀⠉⢾⣿⡿⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡟⠋⢉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠗⠰⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡶⠒⡟⢙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢘⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠀⠀⠀⠙⠀⠈⠟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⡤⠆⢹⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠸⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠘⠛⠋⠳⡄⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡗⠀⠀⠠⠶⠆⠀⠀⠺⠿⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣿⣶⣦⣤⣤⣄⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⡒⠢⢈⢉⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⣛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠴⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⢇⣇⡇⠧⢇⡸⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣰⠆⢰⣤⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⡀⣶⣶⣀⣤⣤⣴⣶⣦⠀⠀⢸⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢲⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣿⣿⣿⠂⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⡛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢽⣿⡀⠉⢾⣿⡞⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣌⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠗⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣛⣉⣻⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠂⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡷⠀⢰⡶⢒⡟⢙⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢘⡇⢘⡇⠀⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠈⠁⠀⠙⠀⠈⠟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⡤⠆⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠸⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀⠀⠘⠛⠋⠳⡄⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡗⠀⠀⠠⠶⠆⠀⠀⠺⠿⠶⠶⠟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣶⣦⣤⣤⣄⣨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⡖⠢⢀⢉⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡀⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠷⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠴⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⢰⣦⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⣦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠰⣶⢴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠋⢾⣿⣿⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣌⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡿⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⠃⠀⠀⠀⣶⣶⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠂⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡈⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣶⣿⣿⣿⣿⣟⠀⢰⡶⠲⣿⢹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢸⡇⠀⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠃⠀⠙⠀⠈⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⡴⠆⢻⣿⣿⣿⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠘⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠈⠉⠉⠻⡄⠀⠘⠀⠀⠀⠀⢰⠀⠀⠀⢧⠀⣶⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⠠⠶⠆⠀⠀⠺⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⡖⠢⢈⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⣀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣛⢹⢫⠹⢟⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⣛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠴⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣰⠂⢰⣦⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡗⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠻⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⣿⠀⣠⣾⣾⣿⣾⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡀⠋⢾⣿⣿⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠄⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢋⠉⠀⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠔⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡇⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠂⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡟⠀⢰⡶⢲⣟⠹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢠⡇⠀⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠃⠀⠙⠀⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⡴⠆⢹⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠘⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠘⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⠠⠶⠆⠀⠀⠺⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⣛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠴⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⢰⣦⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⠀⣶⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⣀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢢⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡀⠋⢾⣿⣿⠟⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣈⡇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠷⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡿⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠓⠴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡗⠀⢰⡶⢲⣟⠹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢸⡇⠀⣷⠉⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠂⠀⠙⠀⠈⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⡴⠆⢺⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠉⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠘⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⠠⠶⠆⠀⠀⠺⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⡖⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣛⢹⢫⠹⢟⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⣛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠯⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⢰⣦⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣾⣷⣶⣖⠒⠶⠶⣄⠀⣶⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣿⣷⣶⠀⠀⡀⠀⠐⠒⢶⡗⢲⣄⠀⠀⢰⣶⣾⣿⣿⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢿⣿⣹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠉⢾⣿⡿⠋⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣈⡇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠄⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡟⠉⢉⠉⠁⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⠇⠀⢰⡶⠲⡟⢙⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡆⠀⢸⡇⢨⡇⠀⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠘⠃⠀⠙⠀⠈⠝⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⠠⠶⠆⠀⠀⠺⠷⠶⠶⠟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡈⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⣛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠸⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⢇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠆⠰⣦⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣖⠒⠶⠶⣄⠀⣶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⣀⠀⠐⠒⢶⡷⢲⣄⠀⠀⢰⣶⣾⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⡤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢿⣿⡀⠉⢾⣿⣿⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣌⡇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠷⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣶⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠓⠔⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡟⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⠛⠀⢰⡶⢲⡟⠙⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢈⡇⠀⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠃⠀⠙⠀⠈⠍⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⡤⠆⢺⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠘⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠈⠉⠉⠻⡄⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⠠⠶⠆⠀⠀⠺⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣛⢹⢫⠹⢟⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⣛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠯⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⢇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠆⠰⣆⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣾⣷⣶⣖⠒⠶⠶⣄⠀⣶⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣿⣷⣶⠀⠀⡀⠀⠐⠒⢶⡗⢲⣄⠀⠀⢰⣶⣾⣿⣿⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠙⢾⣿⣿⠋⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣈⡏⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠉⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡶⠲⡟⢹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢰⡇⠀⣷⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠈⠃⠀⠘⠀⠈⠟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠰⠆⢺⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣋⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⡸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⠰⣤⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡂⠀⠐⠲⢶⡖⢲⣄⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠛⢿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠛⢿⣿⣿⠏⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣈⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡿⠋⠉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⡼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⡇⠘⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡖⢲⣿⢹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢘⡇⢸⡃⠀⣿⠙⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⢼⠇⠈⠂⠀⠘⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠁⣦⡀⠀⠀⠴⠆⢻⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠨⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⢠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⡖⠢⢈⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⠰⣤⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡶⢲⣄⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠛⢿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠛⢾⣿⣿⠏⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣌⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠄⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡟⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢿⠃⠀⠀⠀⣶⣦⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡇⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡟⠀⠀⣀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡃⠀⢰⡖⢒⡟⢹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢘⡇⢘⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠀⠀⠹⠀⠀⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⠴⠆⢻⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠀⠀⢠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⡒⠢⢈⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⣤⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣾⣷⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠛⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠘⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡀⠛⢾⣿⣿⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠂⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢻⠃⠀⠀⠀⣶⣦⣤⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣹⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣿⣟⡇⠀⢰⡖⢒⡏⢹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⠘⡇⢸⠃⠀⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠘⠀⠀⠘⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠁⣦⣀⠀⠀⠰⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⢠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⡒⠢⢈⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡟⣛⢛⢛⢹⠹⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⠂⢰⣆⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣿⣶⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⣀⠀⠐⠒⢶⡶⢲⣄⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠻⢿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠰⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠋⢾⣿⣿⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣍⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡿⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⡼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠰⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡇⠘⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠇⠀⠈⠉⠀⠘⠛⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠁⠈⠟⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡗⠀⢰⡶⢒⣿⢹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡅⠀⢸⡇⢸⡃⠀⣿⠙⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⢼⠇⠘⠂⠀⠸⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⠴⠆⢻⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠂⠀⠀⠀⠹⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⢠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⡒⠢⢀⢉⢀⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡘⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡝⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣠⣤⣄⣤⣤⣤⣤⣶⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⢰⣤⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠻⢿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠘⣶⢶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠛⢾⣿⣿⠟⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣌⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡟⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢹⠃⠀⠀⠀⣶⣦⣤⡼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡇⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⣷⠀⢰⡶⢒⡿⢹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢸⠇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⢼⠇⠘⠀⠀⠘⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠁⣦⣀⠀⠀⠤⠆⢻⣿⣿⣿⣿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠸⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠀⠀⢠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⡒⠢⢈⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡙⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡝⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⣇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣁⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣿⣶⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠻⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠰⣶⢶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠛⢾⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡟⠋⢉⠉⠀⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢹⠃⠀⠀⠀⣶⣦⣤⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⡀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠇⠀⠈⠉⠀⠘⠛⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡏⠀⢰⡶⢒⡿⢹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢹⡇⢸⡃⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⢼⠇⠘⠁⠀⠘⠀⠈⡙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⠰⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠀⠈⠉⠉⠻⡄⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡷⠀⠀⢠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⣀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡙⣛⣛⣛⣛⣛⣛⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡝⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠴⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⣇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣁⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⣤⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣶⣖⠒⠶⠶⣄⠀⢲⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣿⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠻⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢿⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠋⢶⣿⡿⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣈⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⠃⠀⠀⠀⣶⣦⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡇⠀⠀⣀⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠃⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡖⢒⡟⢹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢸⡃⠀⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⢼⠇⠘⠁⠀⠘⠀⠀⠙⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠰⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠈⠉⠉⠹⣄⠀⠘⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠀⠀⠠⠶⠆⠀⠀⠺⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡙⣛⣛⣛⣛⣛⣋⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣶⣷⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣿⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠰⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠛⢶⣿⡿⠛⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣌⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠧⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⢇⠀⢰⡖⢒⣟⢹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡆⠀⢸⡇⢸⠇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠇⠘⠁⠀⠘⠀⠈⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⠠⠆⢺⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠈⠉⠉⠻⣄⠀⠐⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣦⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡙⣛⣛⣛⣛⣛⣋⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡝⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⠸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣠⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣶⣖⠒⠶⠶⣄⠀⢶⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣿⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠻⢿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠛⢶⣿⡿⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣉⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⠃⠀⠀⠀⣶⣶⣤⡼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧⡇⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⠿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡶⢲⡟⢹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⡇⢸⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⢼⠃⠘⠁⠀⠘⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠁⣦⣀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠸⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠈⠉⠉⠻⣄⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⢠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡙⣛⣛⣛⣛⣛⣋⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣶⣖⠒⠶⠶⣄⠀⢲⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣿⣶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣿⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢽⣿⡀⠛⢾⣿⡿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣌⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠗⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠀⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢼⠃⠀⠀⠀⣶⣶⣤⡬⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⡰⡄⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⢿⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⡇⠀⢰⡶⢒⡟⢹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡅⠀⢸⡇⢸⠇⠀⣿⠙⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⢼⠃⠈⠀⠀⠘⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠈⠉⠉⠻⣄⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣶⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢠⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⡒⠢⢀⢈⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡛⣛⣛⣛⣛⣛⣋⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡍⣛⢛⢛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⠸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣰⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣰⠂⠰⣄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣶⣖⠒⠶⠶⣄⠀⢲⣶⣂⣤⣤⣴⣶⡦⠀⠀⢰⣿⣷⣶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣿⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠹⢿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣾⣾⣷⣾⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢽⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠓⢾⣿⣿⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠋⢉⠉⠀⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢽⠃⠀⠀⠀⣶⣶⣤⡼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡰⡆⠀⠈⠙⠿⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣋⣉⣻⣿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠄⣿⣿⣷⣝⠿⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠟⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣿⣿⠇⠀⢰⡖⠲⡟⢹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⠘⡇⢸⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠁⠀⣼⠃⠘⠁⠀⠘⠀⠀⠘⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠩⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠈⠉⠉⠻⣄⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠧⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠀⠀⠠⠶⠆⠀⠀⠺⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣦⣄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⡒⠢⢀⢉⢁⣀⢀⢀⢀⡀⡂⣄⠀⡀⠀⡀⡀⡀⣀⣀⢀⢀⢀⢀⢀⢀⠀⠀⡆⢠⡆⡂⣀⣀⡛⣛⣛⣛⣛⣛⣋⢹⢫⠹⢛⢛⢛⣿⣿⣛⣛⣛⡛⡛⡛⡝⣛⢛⣛⢹⠹⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠧⠐⠬⠽⠫⠭⠸⠤⠸⠼⠸⠀⠇⠇⢳⠁⠀⠇⠇⠤⠫⠭⠪⠽⠼⠠⠯⠥⠂⠀⠘⠆⠇⠟⠤⠼⠇⠧⠜⠬⠵⠣⠼⠸⠸⣤⡸⠸⢸⣇⣘⠤⠜⠤⠇⣇⡇⠧⢇⣸⠤⢸⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣤⣤⣤⣤⣶⣶⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⠰⠂⠐⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣴⣶⡦⠀⠀⢰⣶⣶⡖⠀⠀⡀⠀⠐⠒⢶⡖⠲⣄⠀⠀⢰⣶⣿⣶⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣠⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢹⣿⠙⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣤⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠻⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠿⠿⠇⠀⠈⠉⠀⠐⠚⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣤⣿⣿⣮⣸⠀⠀⢠⡖⠒⡇⠘⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣧⡄⠀⠘⡇⢠⠂⠀⣷⠈⠿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠃⠀⠀⠀⠘⠀⠀⠀⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠀⠆⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⠉⠉⠑⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡷⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣤⣀⣤⡄⡬⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠰⠀⠐⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣂⣤⣤⣤⣶⡦⠀⠀⢰⣶⣶⡖⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣿⣶⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢴⣾⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠻⠃⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⠿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣴⣿⣿⣿⣟⠀⠀⢰⡖⠒⡃⠹⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠈⡇⢰⠂⠀⣷⠈⢿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⢘⣿⣿⣿⣿⣿⠁⠀⢸⠃⠀⠀⠀⠈⠀⠀⠀⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⣀⠀⠀⠀⠆⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠀⠀⠀⠀⠈⠉⠉⠙⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡷⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣄⣬⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⠰⠀⠐⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣂⣤⣤⣤⣶⡦⠀⠀⢰⣶⣶⣖⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣿⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⢾⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣀⣾⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠙⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢴⣶⡟⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠚⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠻⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⢹⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣴⣿⣿⣿⣗⠄⠀⢰⡖⠂⠃⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠈⡇⢰⠇⠀⣗⠈⢿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⡿⠁⠀⢸⠁⠀⠀⠀⠈⠀⠀⠀⢟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠀⠆⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀⠀⠈⠉⠉⠑⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡷⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣄⣬⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⠰⠀⠐⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡦⠀⠀⢰⣶⣶⣖⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣿⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡟⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡆⠀⠈⠙⠿⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣴⣿⣿⣿⣷⠀⠀⢠⡖⠒⡇⠙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠘⡇⠸⠇⠀⣷⠉⢿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⢘⣿⣿⣿⣿⡿⠁⠀⢸⠃⠀⠀⠀⠘⠀⠀⠀⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⠀⠈⠉⠉⠑⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡗⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣬⣀⣤⣄⣤⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⠰⠀⠐⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣂⣤⣤⣤⣶⡦⠀⠀⢰⣶⣶⣖⠀⠀⡀⠀⠐⠒⢶⡖⠲⣀⠀⠀⢰⣶⣿⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣀⣾⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢴⣶⡟⠉⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⣿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡆⠀⠈⠙⠻⠓⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣴⣿⣿⣿⣵⠀⠀⢰⡖⠂⡃⢹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠈⡇⠸⠇⠀⣗⠉⠿⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⢘⣿⣿⣿⣿⣿⠁⠀⢸⠃⠀⠀⠀⠘⠀⠀⠀⡟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠠⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⠀⠀⠀⠀⠈⠉⠉⠑⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡷⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣄⣬⣤⣤⣤⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⠰⠂⠰⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠐⠒⢶⡖⢲⣀⠀⠀⢰⣶⣾⣿⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢹⣿⠛⠋⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢶⣶⡟⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠻⠓⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠈⢻⣿⣿⣿⣿⡿⠟⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⢋⡐⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣤⣿⣿⣮⡔⠀⠀⢠⡖⠂⡃⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣧⡄⠀⠘⡇⠰⠃⠀⣗⠈⢿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠁⠀⠀⠀⠘⠀⠀⠀⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠉⠉⠙⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡗⠀⠀⢠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣦⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣎⣀⣤⣀⣬⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⡰⠂⠰⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡶⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⢾⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⢀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢴⣶⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡄⠀⠈⠙⠻⠃⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠴⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠿⡿⠇⠀⠈⠉⠀⠐⠚⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⢹⣿⣿⣿⣿⡿⠟⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⢏⡀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣴⣿⣿⣦⡖⠀⠀⢠⡖⠂⡆⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣧⡄⠀⠘⡇⠐⠃⠀⣗⠈⠿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⣸⠁⠀⠀⠀⠈⠀⠀⠀⡟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠉⠉⠙⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡗⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⣀⣤⣀⣬⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⠰⠂⠐⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣴⣶⠆⠀⠀⢰⣾⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⢾⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⢀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢹⣿⠛⠋⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢶⣶⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠻⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠿⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⢹⣿⣿⣿⣿⡿⠟⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣷⠀⣿⣿⡛⡀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣯⡆⠀⠀⢰⡖⠒⠇⢹⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣷⡄⠀⠘⡇⠰⠇⠀⣷⠉⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠁⠀⠀⠀⠘⠀⠀⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠈⠉⠉⠙⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡗⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣆⣀⣤⣄⣤⣤⣤⣤⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠰⠂⠐⠀⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣴⣶⠆⠀⠀⢰⣾⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⢲⣀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⢾⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠋⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠁⢴⣶⡞⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⡇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣶⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⡄⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠈⠙⠻⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢸⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠿⡿⠇⠀⠈⠉⠀⠐⠚⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢹⣿⣿⣿⣿⡿⠟⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣷⠀⣿⣿⢓⡂⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣴⣿⣿⣮⠌⠀⠀⢰⡖⠒⡇⢹⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣧⡄⠀⠈⡇⢰⠃⠀⣷⠈⢿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠸⣿⣿⣿⣿⡿⠁⠀⢸⠃⠀⠀⠀⠘⠀⠀⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠈⠉⠉⠙⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣖⣀⣤⣀⣼⣤⣤⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠰⠀⠐⠄⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣴⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⢲⣀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⢾⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣽⡆⢻⣿⠙⠋⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡟⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣤⣤⠤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⡄⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⡄⠀⠈⠙⠻⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣋⣉⣹⡿⠿⠿⠤⠄⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢨⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠿⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⡿⠟⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣷⠀⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣮⢆⠀⠀⢠⡖⠒⡆⢹⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣧⡀⠀⠈⡇⢰⠃⠀⣗⠈⢿⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠁⠀⠀⠀⠘⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠈⠉⠉⠙⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠠⠶⠆⠀⠀⠸⠷⠶⠶⠗⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⢄⣨⣤⣤⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠰⠂⠰⠄⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⢲⠀⠀⠀⢰⣶⣾⣿⣶⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠀⣦⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣹⡆⢻⣿⠙⠉⢽⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣶⡞⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠓⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢸⣿⣿⣿⣿⡿⠟⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣤⣿⣿⣶⠂⠀⠀⢠⡖⠲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣇⡄⠀⠈⡇⠸⠃⠀⢷⠈⢿⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⠁⠀⢼⠃⠀⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠉⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠈⠉⠉⠙⢆⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡛⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣄⣬⣤⣤⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠰⠂⠐⠄⠲⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⢒⣀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣶⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢿⡆⢻⣿⠙⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠀⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣶⡏⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠓⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢘⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠀⢲⣺⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢻⣿⣿⣿⣿⡿⠟⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣤⣿⣿⣧⣀⠀⠀⢠⡖⠒⡆⢹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣇⡄⠀⠘⡇⢰⠃⠀⣗⠈⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠃⠀⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠈⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠉⠀⠉⢆⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡟⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣶⣀⣤⣀⣬⣤⣤⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠰⠀⠐⠄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣷⡆⠀⠀⡀⠀⠐⠒⢶⡖⢲⡀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠙⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡟⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠓⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢘⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⢲⢺⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢻⣿⣿⣿⣿⡿⠟⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣟⠡⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣤⣿⣿⣦⣀⠀⠀⢠⡖⠲⡆⢹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣏⡆⠀⠈⡇⢸⠃⠀⣗⠈⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢼⠁⠀⠀⠀⠘⠀⠈⠀⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠁⣦⡀⠀⠀⡄⠆⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠀⠀⠀⠀⠉⠀⠙⢆⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡿⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⡀⢤⣄⣬⣤⣤⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣂⠰⠀⠐⠠⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣾⣶⣶⣖⠒⠲⠶⣄⠀⣰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⢲⣀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢺⡆⢻⣿⠉⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣶⡿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣤⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠻⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡷⡄⠀⠁⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⡿⠛⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⡵⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣧⣥⠀⠀⢠⡖⢒⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢙⣿⣿⣿⣿⣟⡄⠀⠘⡇⢸⠃⠀⣿⠉⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢼⠃⠀⠀⠀⠘⠀⠈⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢉⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠀⠀⠀⠀⠉⠀⠙⢦⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠣⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡟⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⢀⣬⣤⣤⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠰⠀⠐⠠⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣾⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⢒⣀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢿⡆⢻⣿⠉⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣶⡟⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢻⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠟⠇⠀⠚⠛⠃⠀⠀⣤⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡄⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⡿⠟⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⡿⡋⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣤⣿⣿⣯⣃⠀⠀⢠⡖⢲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣟⡄⠀⠘⡇⢸⠃⠀⣷⠉⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢼⠃⠀⠀⠀⠘⠀⠈⠀⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢉⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠉⠀⠉⢦⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠣⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡟⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣀⣬⣤⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡂⠰⠀⠐⠠⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣾⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⢲⣀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢺⡆⢻⣿⠉⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣾⡟⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⠻⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢻⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⣟⡹⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣧⣦⠀⠀⢠⡖⢲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⠘⡇⢸⠃⠀⣷⠈⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢼⠃⠀⠀⠀⠘⠀⠈⠀⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢉⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠉⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠉⠀⠉⢦⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡟⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⡤⢀⣼⣤⣤⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠰⠀⠰⠠⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣾⣶⣶⣖⠒⠲⠶⣄⠀⣰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⢲⣀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢾⡆⢻⣿⠉⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣶⡞⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢻⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣾⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠰⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠛⠛⠛⢛⣉⣉⣽⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡷⡄⠀⠁⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢻⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⠿⡣⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣯⣃⠄⠀⢠⡖⢲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢩⣿⣿⣿⣿⣿⡄⠀⠘⡇⢸⠃⠀⣷⠉⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢼⠃⠀⠀⠀⠘⠀⠀⠀⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢉⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠉⠀⠉⢦⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣄⣼⣤⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡂⠰⠀⠰⠄⠴⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠐⠒⢶⡖⠒⡀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⡆⢻⣿⠛⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠀⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡎⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠰⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠻⠓⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⣮⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠉⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⠝⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣷⣁⠀⠀⢠⡖⠲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣟⡄⠀⠘⡇⢸⠃⠀⣷⠉⣿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢼⠁⠈⠀⠀⠘⠀⠈⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠉⣦⡀⠀⠀⠄⠆⢰⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠉⠀⠉⢣⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠧⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡿⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣬⣤⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣶⡀⠰⠀⠰⠄⠴⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠶⣄⠀⢰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣾⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⠀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣴⣰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⡆⢻⣿⠉⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠟⠇⠀⠘⠛⠃⠀⠀⣤⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⡿⠟⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⡟⡯⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣧⢧⠀⠀⢠⡖⠲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣟⡄⠀⠘⡇⢸⡇⠀⣷⠉⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠀⠀⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠁⣦⡀⠀⠀⡄⠆⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣴⣄⠀⠀⢸⠀⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡆⠀⠀⠀⠀⠉⠀⠉⢦⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⢀⡬⣤⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⠰⠀⠰⠤⠰⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢰⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣻⡆⢻⣿⠙⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣶⡞⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢻⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢻⣿⣿⣿⣿⣿⠟⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⠿⡳⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣯⣡⠀⠀⢠⡶⠲⡆⢹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢩⣿⣿⣿⣿⣿⡄⠀⠘⡇⢸⡇⠀⣷⠉⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠈⠀⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠁⣦⡀⠀⠀⡄⠆⢰⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠹⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠁⠀⠈⠣⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⢤⡀⢬⣠⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⠰⠀⠰⡤⠔⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣻⡆⢻⣿⠉⠉⢽⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣶⡮⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣉⠇⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢻⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣷⠀⣿⣿⡿⡕⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣷⣁⠀⠀⢠⡖⢲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢩⣿⣿⣿⣿⣟⡄⠀⠘⡇⢸⡇⠀⣷⠉⢿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠁⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠣⠀⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⠀⠬⣤⣤⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⠰⠀⠰⠄⠒⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⣀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⡀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣶⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢾⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡎⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⣀⣀⣀⣠⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢺⣿⣿⣿⣿⡿⠛⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⣏⠋⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣧⠌⠀⠀⢠⡖⢲⡆⠹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢙⣿⣿⣿⣿⣗⡆⠀⠈⡇⢸⡇⠀⣷⠈⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠀⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⢁⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠁⠀⠈⢣⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣄⣬⣤⣤⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⠰⠀⠰⠄⠐⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⢒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⡀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣶⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢼⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢺⣿⣿⣿⣿⡿⠛⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣯⠄⠀⠀⢠⡖⠲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣇⡄⠀⠈⡇⢸⡇⠀⣷⠈⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⢉⣦⡀⠀⠀⠄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠂⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠣⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡟⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣀⡬⣤⣤⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣠⠰⠀⠰⠄⠴⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢲⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⢒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢾⡆⢻⣿⠋⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣽⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣼⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠉⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢺⣿⣿⣿⣿⡿⠛⣿⣿⣿⣟⠅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣧⡄⠀⠀⢠⡶⠒⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣇⡆⠀⠈⡇⢸⠇⠀⣷⠉⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢠⠃⠈⠀⠀⠘⠀⠈⠀⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠁⣦⡀⠀⠀⡀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠂⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⢢⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠣⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣶⣀⡤⣀⣼⣤⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠰⠀⠰⠄⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢲⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢺⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡎⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠚⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠰⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡆⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣺⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢺⣿⣿⣿⣿⡿⠟⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⡟⡈⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣯⠤⠀⠀⢠⡶⢲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢩⣿⣿⣿⣿⣟⡆⠀⠈⡇⢸⠇⠀⣷⠉⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠈⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⢁⣦⡀⠀⠀⠄⠆⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⢢⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⣀⣤⣀⡼⣤⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⠰⠀⠰⠄⠐⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⣰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢄⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢾⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠤⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢺⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⡫⠂⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣧⢄⠀⠀⢠⡶⠒⡆⠹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢩⣿⣿⣿⣿⣏⡄⠀⠈⡇⢸⠇⠀⣷⠈⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠈⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢈⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣶⣀⣤⣀⣬⣤⣤⣤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⠰⠀⠰⠤⠒⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⣰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢾⡆⢹⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡎⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡆⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢺⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⡟⠎⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣴⣿⣿⣯⠆⠀⠀⢀⡶⠒⡆⠹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣏⡄⠀⠈⡇⢸⡇⠀⣷⠈⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠀⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⢁⣦⡀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠣⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣮⣀⣤⣀⣬⣤⣤⣤⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠰⠀⠰⠄⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⣰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣾⣷⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⡀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣶⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢿⡆⢻⡿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠚⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢺⣿⣿⣿⣿⡿⠟⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣓⠏⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣯⢂⠀⠀⢠⡶⢲⡆⠹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢉⣿⣿⣿⣿⣇⡄⠀⠈⡇⢸⠇⠀⣷⠉⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢸⠃⠈⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⢁⣦⡀⠀⠀⡤⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⣀⣤⣀⣬⣤⣤⣤⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⠰⠀⠰⠄⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢲⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣷⡆⠀⠀⡀⠀⠐⠒⢶⡖⢒⣀⠀⠀⢰⣶⣶⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⡀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡎⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢻⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠚⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣺⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢻⣿⣿⣿⣿⣿⠛⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⠿⡈⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣧⠄⠀⠀⢠⡶⠒⡆⠹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢉⣿⣿⣿⣿⣏⡄⠀⠈⡇⢸⠇⠀⣷⠉⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢸⠃⠈⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢉⣦⡀⠀⠀⠄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⢸⠀⠲⠄⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠳⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⣀⣤⣀⣼⣤⣤⣤⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣠⠰⠀⠰⠄⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣶⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢾⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⠞⠋⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢻⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠚⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⠻⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⡝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠘⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢺⣿⣿⣿⣿⣿⠛⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⡿⡉⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠻⣿⣴⣿⣿⣧⡂⠀⠀⢠⡶⠒⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢙⣿⣿⣿⣿⣟⡆⠀⠈⡇⢸⠇⠀⣷⠈⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢠⠃⠈⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢀⣦⡀⠀⠀⢄⠆⢰⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠩⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠇⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⣀⠤⠀⡌⣤⣤⣤⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠰⠀⠰⠄⠐⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⠀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣶⣾⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣗⠀⠀⢺⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⠇⣧⢻⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡆⠀⠀⠙⠿⠓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠐⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⢷⡄⠀⠁⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢺⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⣿⣿⠏⡈⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠻⣿⣴⣿⣿⣷⠠⠀⠀⢠⡶⠒⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢱⣿⣿⣿⣿⣎⡄⠀⠈⡇⢸⠇⠀⣷⠈⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠃⠀⠀⠀⠘⠀⠀⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⢁⣦⡀⠀⠀⢄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠀⠀⠠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⣀⢀⣀⣼⢤⣠⣤⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣀⠰⠀⠰⠄⠲⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⣰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⢒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣶⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⢺⡆⢻⡿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⣀⣀⣀⣠⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡆⠀⠀⠙⠻⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⡄⠀⠁⠀⠀⠀⠀⢲⣺⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢹⣿⣿⣿⣿⡿⠛⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠻⣿⣤⣿⣿⣧⠀⠀⠀⢠⡖⠲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣏⡄⠀⠈⡇⢸⡇⠀⣷⠉⢿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠃⠈⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢁⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠱⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠣⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡾⠀⠀⠀⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣆⣀⢄⡀⠠⣠⡄⣤⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣀⠰⠀⠰⠀⠒⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣾⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣶⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣤⢄⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⢸⡆⢻⡿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡞⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⠇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠉⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢻⣿⣿⣿⣿⡿⠛⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣋⠈⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⡿⣤⣿⣿⣯⠄⠀⠀⢠⡶⢒⡆⠹⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠉⣿⣿⣿⣿⣆⡄⠀⠈⡇⢸⠃⠀⣷⠈⢿⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠃⠀⠀⠀⠘⠀⠀⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⢈⣦⡀⠀⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠿⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣠⡾⢶⡀⠀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⠀⠀⠀⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⣀⠤⠀⠐⢠⡤⣤⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⠰⠀⠰⠤⠶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣾⣶⣶⣖⠒⠲⠶⣄⠀⣲⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣷⡆⠀⠀⡂⠀⠐⠒⢶⡖⢒⣀⠀⠀⢰⣶⣾⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠉⢶⣾⡾⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢼⠃⠀⠀⠀⣶⣶⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠿⠓⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠘⣻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠈⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢺⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⡿⡯⠂⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣾⡗⠀⠀⢠⡖⢲⡖⢹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣿⡄⠀⢘⡇⢸⠃⠀⣷⠉⢿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠃⠈⠀⠀⠘⠀⠈⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡏⠀⢉⣦⣀⠀⠀⡄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠹⠿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠐⠚⠛⢧⡀⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡃⠀⠠⡶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣶⣄⣀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢖⡒⢀⠤⡀⠤⡄⠀⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢹⠩⢿⠿⢻⢍⠭⡁⣶⢩⠽⢿⢿⠛⡏⠭⡹⠒⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡀⠢⠼⠘⠭⠋⠭⠃⠀⠻⠸⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⢝⡡⠼⠸⠪⣽⣤⡼⠜⠭⠃⠿⠰⠽⣢⣜⣤⣗⣭⣇⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣦⣀⣤⣄⣬⣤⣤⣤⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⠰⠀⠰⠤⠒⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣾⣶⣶⣖⠒⠲⠶⣄⠀⢶⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⡀⠀⠀⢰⣶⣾⣿⣷⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢾⣶⡞⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣤⣾⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⡻⠿⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠘⣻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⢻⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⣟⡯⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢻⣿⣴⣿⣿⣷⣇⠀⠀⢠⡖⢒⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣟⡄⠀⠘⡇⢸⠃⠀⣷⠉⣿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠃⠈⠀⠀⠘⠀⠈⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⡏⠀⢈⣦⡀⠀⠀⢤⠆⢰⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄⠻⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠉⠉⠙⢆⢸⠀⠲⠆⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠠⡶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣦⣄⣄⣀⣀⡀⠀⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢖⡒⢀⠤⡀⠤⡄⠀⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢸⠩⢿⠿⢻⢍⠭⡉⣶⢩⠽⠿⢿⠛⡏⠭⡹⠒⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡀⠢⠼⠘⠭⠋⠭⠃⠀⠻⠰⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⢝⡡⠼⠸⠪⢽⣤⣼⠜⠭⠃⠿⡰⢽⣢⣼⣤⣗⣭⣧⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣀⣤⣄⣼⣤⣤⣤⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡠⠰⠀⠰⠤⠖⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣾⣶⣶⣖⠒⠲⠶⣄⠀⣲⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⠒⡀⠀⠀⢰⣶⣾⣿⣿⣶⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⣀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⡆⢻⡿⠋⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢾⣶⡞⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠄⠀⠁⠀⠀⠀⠀⢰⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⢻⣿⣿⣿⣿⡿⠛⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠻⣿⣤⣿⣿⣯⣶⠀⠀⢠⡶⠲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣟⡄⠀⢘⡇⢸⠃⠀⣷⠉⣿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣇⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢸⠃⠈⠀⠀⠘⠀⠈⠀⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢿⡏⠀⠈⣦⡀⠀⠀⢄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⣶⣎⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠰⠆⠀⠀⠘⠛⠀⠀⠀⠀⠸⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠇⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠆⠀⠀⠨⠷⠶⠶⠟⠂⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⣤⣤⣄⣀⣀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢖⡒⢀⠤⡀⠤⡄⠀⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢸⠩⢽⠻⢻⢍⠭⡁⣶⢩⠽⢿⢿⠛⡟⠭⡹⠒⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡀⠢⠼⠘⠭⠋⠭⠃⠀⠻⠰⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠪⠽⣤⣼⡜⠭⣃⣿⠰⢽⣢⣼⣤⣗⣭⣧⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣿⣃⣤⢄⣼⢤⣤⣤⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⠰⠂⠰⠤⠒⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣾⣶⣶⣖⠒⠲⠦⣄⠀⣲⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⠒⡀⠀⠀⢰⣶⣿⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠀⣀⣴⣾⣷⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⣠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⡆⢻⣿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡾⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣧⢻⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠙⠛⠃⠀⠀⣤⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⢿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠃⠀⠀⠀⣶⣦⣤⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣝⢿⣿⣿⣿⡇⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠆⠀⠁⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢻⣿⣿⣿⣿⣿⠛⣿⣿⣿⢿⡂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⡿⡳⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠻⣿⣤⣿⣿⣿⠥⠀⠀⢠⡶⠒⡆⠹⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣿⣿⣏⡄⠀⠘⡇⢸⠃⠀⣷⠉⣿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣇⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⡿⠁⠀⢰⠃⠀⠀⠀⠘⠀⠀⠀⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠉⣦⡀⠀⠀⢄⠆⢸⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⣆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⠀⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠀⠀⠀⠃⠀⣴⣦⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⡙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠆⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣤⣤⣤⣄⣀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⡏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢖⡒⢀⠤⡀⠤⡄⠀⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠩⢽⠻⢻⢍⠭⡉⣶⢩⠽⢿⢿⠛⡟⠭⡹⠒⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡀⠢⠼⠘⠭⠋⠭⠇⠀⠻⠰⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠪⠽⣤⣼⣜⢭⣃⣿⣰⢽⣢⣼⣤⣗⣭⣣⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣿⣃⣤⣄⣬⢤⣤⣤⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⠰⠀⠰⡤⠒⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠶⠦⣄⠀⣰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⠒⠀⠀⠀⢰⣶⣿⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⡀⠀⠀⢲⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢺⠀⣀⣴⣾⣷⣶⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣶⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠀⠀⢼⡆⢹⡿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡎⠉⠀⠈⣻⣿⣿⣿⣿⣿⣿⠇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣴⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣽⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣦⡄⢿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢾⠃⠀⠀⠀⣶⣦⣤⠰⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⠻⠃⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢲⣺⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠉⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢸⣿⣿⣿⣿⡿⠛⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⡿⣏⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠻⡿⣤⣿⣿⣧⠄⠀⠀⢀⡖⠒⡂⠰⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⣿⣿⣿⣿⣏⡄⠀⠈⡇⢰⠀⠀⡷⠈⢿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢰⠃⠀⠀⠀⠀⠀⠈⠀⢟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣦⡀⠀⠀⢀⠄⢸⣻⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢆⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠃⠀⣰⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⠙⠛⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⣤⣤⣤⣠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣠⣤⣶⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢖⡒⢀⠤⡀⠤⡄⠀⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢽⠛⢻⢍⠭⡉⣶⢩⠽⠻⢿⠛⡏⠭⡹⠒⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠢⠼⠘⠭⠋⠭⠇⠀⠻⠰⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⣄⣸⣜⢭⣃⣿⣰⢽⣢⣼⣤⣗⣭⣃⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣿⣣⣤⣄⠬⡤⡤⠀⢲⣶⣶⣶⣶⣾⣶⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⠰⠀⠰⡄⠒⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢲⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠐⠒⢶⡖⠒⠀⠀⠀⢰⣶⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠑⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⠀⣀⣴⣾⣷⣶⣷⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣴⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠀⠀⢼⡆⢹⡿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡎⠉⠀⠈⣻⣿⣿⣿⣿⣿⣿⠇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣴⠇⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣽⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣦⡄⢿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣄⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠻⠃⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⣬⣙⢿⣿⣿⣿⡇⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣾⡇⠀⠘⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣺⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⠃⠀⠀⠙⠉⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢹⣿⣿⣿⣿⡿⠛⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⣿⣇⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠻⡟⣤⣿⣿⣦⠀⠀⠀⢀⡖⠲⠀⠐⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢡⣿⣿⣿⣿⣇⡄⠀⠈⡇⢰⠀⠀⢷⠈⢿⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠐⣿⣿⣿⣿⡿⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄⢸⣻⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢆⠀⠀⡀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠃⠀⣰⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⢸⣿⣿⣦⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠙⠛⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⣤⣤⣤⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣤⣴⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢖⡒⢀⠤⡀⠤⡄⠀⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢬⠛⢹⢍⠭⡉⣷⢩⠽⠻⢿⠛⡏⠭⡹⠒⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠢⠼⠘⠭⠋⠭⠇⠀⠻⠰⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⣤⣸⡜⢭⣃⣿⣰⢽⣢⣜⣤⣗⣭⣃⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣣⣤⣄⣼⢄⣀⠀⡐⠶⣶⣶⣶⣶⣶⣾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⠰⠀⠐⣄⠐⣶⣶⣶⣶⣶⣶⠖⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣶⣶⡆⠀⠀⡀⠀⠀⠒⢶⡖⠒⠀⠀⠀⢰⣶⣶⣶⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠑⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢼⠀⣀⣰⣾⣷⣶⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣦⢠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠀⠀⢼⡆⢹⡿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢴⣶⠎⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⠆⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣆⣈⠏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣼⠃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⡤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣦⡄⢿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⠃⠀⠀⠀⣶⣦⣄⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⠻⠃⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⠛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⣬⣙⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣧⡄⠚⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣺⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⠃⠀⠀⠙⠉⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠙⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠻⡟⣤⣿⣿⣦⠀⠀⠀⢀⡖⠒⠂⠐⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡⣿⣿⣿⣿⣇⡄⠀⠈⡇⢰⠀⠀⠷⠈⢿⠉⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⡿⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢸⣻⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢷⠀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠨⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⢸⣿⣿⣦⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠙⠛⢿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣶⣤⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢖⡒⢀⠤⡀⠤⡄⠀⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢹⢍⠭⡉⣾⢩⠽⠻⢻⠛⡏⠭⡹⠒⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠢⠼⠘⠭⠋⠭⠇⠀⠻⠰⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⢄⣸⠜⠭⣃⣿⣰⢽⣢⣜⠤⢗⣭⣃⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣣⣴⣤⣼⡤⠀⢀⠰⡶⣶⣶⣶⣶⣶⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⠰⠀⠐⠀⠐⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⢰⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠒⢶⡖⠒⠀⠀⠀⢰⣶⣾⣾⣶⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⠀⣀⣴⣾⣷⣶⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣴⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢺⡆⢹⡿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣷⣿⠂⣸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣷⠀⠁⢶⢶⠎⠉⠀⠈⣻⣿⣿⣿⣿⣿⣿⠇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣆⣈⠇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣴⠃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠘⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⡄⢿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠼⠃⠀⠀⠀⣶⣦⣄⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⠻⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠘⠛⠛⠛⠛⣉⣉⣹⡿⠿⠿⠴⠀⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⣬⡙⢿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⢧⡄⠒⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠘⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠙⣿⣿⡿⡛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠻⡟⣤⣿⣿⣦⠀⠀⠀⢀⡖⠲⠀⠐⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⣿⣿⣿⣿⣇⡄⠀⠈⡇⢰⠀⠀⠧⠈⢿⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⡿⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡉⠩⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡆⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⢸⣿⣿⣦⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠙⠛⢿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⣿⡗⡹⠶⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢖⡒⢀⠤⡀⠤⡄⠀⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢌⠭⡉⣶⢩⠽⠻⢻⠛⡏⠭⠹⠒⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⡏⠀⠢⠼⠘⠭⠋⠭⠇⠀⠻⠰⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠸⠜⠭⣃⣿⣰⣽⣢⣜⠤⢗⣭⣃⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣻⣼⣤⣼⣤⣤⣄⠄⠒⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠰⠀⠰⣄⠐⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠶⠦⣄⠀⣶⣶⣀⣤⣤⣤⣶⠆⠀⠀⢰⣶⣶⡆⠀⠀⡄⠀⠐⠒⢶⡖⠒⠀⠀⠀⢰⣾⣾⣿⣷⣶⣖⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡄⡀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠙⢾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣾⠀⣀⣴⣾⣷⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⢸⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⠐⣴⢠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⠙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢹⡿⠉⠉⢹⣿⢹⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⠀⠁⢶⣶⡎⠉⠀⠈⣻⣿⣿⣿⣿⣿⣿⠇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣈⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣼⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠚⠛⠃⠀⠀⣠⣼⣿⣿⠟⠉⠉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⡄⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢺⠃⠀⠀⠀⣶⣦⣤⠰⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⡄⠀⠀⠙⠿⠓⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠛⠛⠛⢛⣉⣉⣹⡿⠿⠿⠴⠔⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠘⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣧⡄⠚⠿⠷⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⣀⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⣄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⠙⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣷⠀⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣟⣇⠀⠀⠀⠀⠀⠹⣿⣤⣿⣿⣮⠦⠀⠀⢠⡖⠲⠆⠸⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣏⡄⠀⠘⡇⢸⠀⠀⣷⠈⢿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠷⢶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡋⠩⠭⠽⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠨⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⠀⠀⢀⣠⣤⣾⣿⣿⠀⠀⠀⠀⠀⢰⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣅⠀⠈⠙⠛⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⢸⣿⣿⣦⡀⠈⢆⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⡙⠛⢿⠃⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢖⡒⢀⠤⡀⠤⡌⠁⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢨⠽⢿⢿⠛⡏⠭⡹⠒⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠢⠼⠘⠭⠋⠭⠇⠀⠻⠰⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⣿⣰⣽⣢⣼⡤⠗⢭⣃⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣼⣤⣤⣤⣾⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣢⣦⡤⢒⡶⣶⢲⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⢰⠂⢲⣤⡶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⡒⠶⠦⣄⠀⣶⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣷⡦⠀⠀⡄⠀⠐⠒⢶⡖⢒⣀⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⠀⣀⣶⣾⣷⣾⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢹⣿⠉⠋⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢀⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⠀⠙⢿⣷⡿⠋⠀⠈⣻⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢾⠃⠀⠀⠀⣶⣶⣤⠰⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡏⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⡠⡆⠀⠀⠙⠿⠓⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠟⠛⠛⢛⣉⣉⣿⡿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢘⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣧⡄⠚⠿⠷⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⣠⣤⣤⣤⣤⣄⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣦⣀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠘⠿⠟⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠆⠀⢰⡖⠲⡆⠹⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠘⡇⢸⡃⠀⣷⠉⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⢸⠃⠈⠀⠀⠘⠀⠈⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠭⠭⠽⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠛⠟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⣤⣤⣤⣴⣿⣿⡇⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠇⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣏⠉⠙⠻⠿⠿⡿⠏⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢸⣿⣿⣦⡐⠈⢆⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⡙⠛⢿⠃⠀⠀⠃⠀⠀⠉⠁⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢖⡒⢀⠤⡀⠤⡌⠉⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢠⠬⢿⢿⠛⡏⠭⡹⠒⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠢⠼⠘⠭⠋⠭⠇⠀⠻⠸⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⠿⠰⢽⣢⣼⡤⣗⣭⣃⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣴⣤⣤⣾⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⠆⢲⣤⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⡲⠶⠶⣄⠀⣶⣶⣂⣤⣤⣴⣷⡦⠀⠀⢰⣿⣿⣶⠀⠀⡆⠀⠐⠲⢶⡗⢲⣄⠀⠀⢰⣿⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠉⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⢿⠋⠉⠉⠁⠀⠀⡀⠀⢸⢸⣿⣿⣿⠀⠀⣿⠀⣀⣶⣾⣷⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⢄⣠⠄⠀⠀⠀⢸⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢀⡿⠷⠀⠀⣿⣞⠁⠀⠀⠀⠘⢸⣿⣿⣿⠀⠀⢿⣿⡀⠛⣿⣿⣿⠏⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣉⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠸⠿⠇⠀⠻⠛⠓⠀⠀⣤⣿⣿⣿⡿⠋⣛⡉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡀⠀⢀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢾⠃⠀⠀⠀⣶⣶⣦⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡢⡖⠀⠈⠙⠿⠗⢴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠛⠛⢛⣋⣉⣿⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠆⣮⣟⢿⣿⣿⣿⡟⠀⠀⣀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢸⡄⠀⠀⠀⠀⠀⠃⣿⣿⣷⣍⠻⣿⡇⠀⠘⣷⡴⠺⠿⠷⠶⢶⡤⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⠋⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠉⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠹⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣗⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡃⠀⠀⠀⠀⠰⣿⣿⡆⠄⢰⡶⣶⣯⢹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠀⢸⣿⣯⡆⠀⢹⡧⢸⡇⠀⣿⠙⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⣼⠇⠈⠃⠀⠹⠀⠘⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠽⠽⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠛⠟⢳⡄⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣤⣤⣤⣤⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠇⢠⠀⠀⠀⠀⢀⠐⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣏⠛⠻⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢺⣿⣿⣦⣰⠈⣆⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠇⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢬⣛⠛⢿⠋⠀⠀⠃⠀⠀⠉⠁⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣂⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⡿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢖⡒⢀⠤⡉⠤⡌⠉⡅⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡉⠁⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢨⠛⡏⠭⡹⠒⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⡀⠻⠸⠁⠇⠇⠯⠳⠣⠀⠸⠸⠀⠘⠭⢃⡀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⠻⠰⠽⣂⣼⣤⣗⣭⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣶⣷⣶⣿⣶⣿⣿⣿⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⠆⢶⣤⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣶⣷⣶⣖⡲⠶⢶⣄⠀⣶⣶⣂⣤⣤⣴⣿⡦⠀⠀⢰⣿⣿⣶⠀⠀⡆⠀⠐⠲⢶⡟⢲⣆⠀⠀⢰⣿⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⣿⡋⠉⠉⠁⠀⠀⠀⠀⢺⢸⣿⣿⣿⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠸⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⢷⣤⡀⢀⠤⢤⣤⠀⠀⠃⠀⣿⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢠⡿⠷⠀⢴⣿⣿⡋⠀⠁⠀⠿⢸⣿⣿⣿⡂⠀⣿⣿⡀⠻⣾⣿⣿⠏⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣍⡏⣻⣿⣿⣿⣿⣿⣿⠂⠀⠀⡆⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢸⠿⠗⠀⠿⠛⠗⠀⠀⣤⣿⣿⣿⡿⢛⣛⡉⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢾⠃⠀⠀⠀⣶⣶⣦⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⢹⡟⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡢⡖⠀⠈⠙⠿⠗⢴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠛⠛⢛⣋⣉⣿⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠂⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠆⣮⣟⢿⣿⣿⣿⡷⠀⠀⣀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣄⢸⣄⠀⠀⠀⠀⠀⠁⣿⣿⣷⣝⠻⣿⡏⠀⠘⣷⡶⠾⠿⠷⠶⢶⡤⠀⡀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠉⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠈⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠇⠀⠀⠀⠘⣿⣟⠅⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣏⠀⠀⠀⠀⠀⢨⡵⠈⣰⡾⢿⣿⢻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠀⠀⠀⣭⡧⠀⢻⣇⢻⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣼⠇⠘⠃⠀⠹⠀⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠻⠀⠀⠂⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠿⠽⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠃⠀⠀⠀⠉⠛⠟⢳⡄⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣤⣤⣤⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⡇⢠⠀⠀⠀⠀⢀⠰⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠛⠻⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢻⣿⣿⣦⣰⠈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠇⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣛⠿⢿⠋⠀⠈⠣⠀⠀⠙⠁⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣂⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢖⡒⢀⠤⡉⠤⡍⠉⡍⡅⡄⡦⡄⡠⠄⡤⠀⢴⢰⢤⢀⠤⡉⠋⡥⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢠⠘⣟⠭⡹⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⡀⠻⠸⠁⠇⠇⠯⠻⠣⠀⠸⠸⠀⠘⠭⢃⡀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⠿⠰⠽⢂⣘⣤⣗⣭⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⠆⢲⣦⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣷⣷⣶⣖⡲⠶⢶⣄⡀⣶⣶⣂⣤⣤⣴⣿⡦⠀⡠⢸⣿⣿⣶⠀⠀⣆⠀⠐⠲⢶⡟⢲⣆⠀⠀⢰⣿⣿⣿⣿⣿⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡄⠀⠉⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⣿⠋⠉⠉⠉⠀⠀⠀⠈⣳⢸⣿⣿⣿⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⠇⢻⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠹⣶⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⣷⣤⡀⢀⠤⣞⣺⣽⠀⡇⠀⣿⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣼⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇⣹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠀⡁⠀⠀⢀⠴⠀⠈⠉⠉⠁⠀⢠⡿⠿⠘⢾⣿⣯⠏⠀⠃⠀⠿⢸⣿⣿⣿⡇⠀⣿⣿⡀⠻⣿⣿⣿⠟⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣍⡏⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡆⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢸⠿⠗⠀⠿⠻⠛⠀⠀⣤⣿⣿⣿⡿⠛⣛⡛⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⠃⠀⠀⠀⣶⣶⣦⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⢹⡟⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡢⡶⠀⠈⠙⠿⠓⢰⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠟⠛⢛⣋⣉⣿⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠆⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠇⠈⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⡆⣮⣟⢿⣿⣿⣿⡿⠀⠀⣀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⢸⡄⠀⠀⠀⠀⠀⠃⣿⣿⣷⣝⣿⣿⡏⠀⠘⣷⡶⠾⠿⠷⠶⣶⡤⠀⡀⠀⠀⠀⠀⠀⠉⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠉⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠏⠀⠀⠙⠋⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡆⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡏⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣟⠁⠀⠀⠀⠀⠲⡌⢶⡾⣿⣿⢹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠀⠀⠀⣤⠀⢻⣇⢻⡇⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣽⠇⠸⠇⠀⠹⠀⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠆⠀⠀⠀⠀⠁⠘⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠿⠽⢿⣿⣿⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠈⠛⠟⢳⡄⠠⣶⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣦⣀⣀⣤⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⣿⣿⠀⡇⢰⠀⠀⠀⠀⢀⠰⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠛⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢻⣿⣿⣦⣰⠈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠷⠀⠀⠙⠛⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⣻⠻⢿⠋⠀⠈⠣⠀⠀⠙⠁⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢖⡒⢀⠤⡈⠤⡍⠉⡍⡅⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡉⠋⡭⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢠⠀⣝⠿⡹⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⡀⠻⠸⠁⠇⠇⠯⠻⠣⠀⠸⠸⠀⠘⠭⢃⡀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⠿⠰⠽⠂⡘⠤⣗⣭⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣾⣷⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⠆⢲⣦⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣶⡲⠶⣶⣄⡀⣶⣶⣂⣤⣤⣴⣿⡦⠀⡠⢼⣿⣿⣶⠀⠀⣆⠀⠐⠶⢶⡟⢲⣆⡀⠀⢰⣿⣿⣿⣿⣿⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡄⠈⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⣿⡋⠉⠉⡉⠀⠀⡀⠀⣻⢸⣿⣿⣿⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠹⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⣷⣦⡀⢠⣬⣷⣸⡅⠀⡇⠀⣿⢼⣿⣿⣿⠀⠀⣿⡇⢻⣿⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⡁⠀⠀⢀⡴⠀⠈⠉⠉⠁⠀⢠⡿⠿⠘⢿⣿⣿⢙⠂⡇⠀⠻⢹⣿⣿⣿⡇⠀⣿⣿⡈⠟⣿⣿⣿⠟⠁⠉⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣍⡏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡆⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢹⠿⠗⠀⠿⠻⠟⠀⠀⣤⣿⣿⣿⡿⣛⣛⡛⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣷⡿⢰⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⠃⠀⠀⠀⣶⣶⣦⠼⠄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⢹⡿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡶⠀⠈⠙⠿⠓⢴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠟⠛⣛⣋⣉⣿⣿⠿⠿⠶⠶⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠆⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠇⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⡆⣮⣟⢿⣿⣿⣿⣿⠀⠀⣀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⢸⣄⠀⠀⠀⠀⠀⠃⣿⣿⣷⣝⣿⣿⡏⠀⠘⣷⡶⠾⠿⠷⠶⣶⡤⠀⡀⠀⠀⠀⠀⠀⠉⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠉⠈⠟⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠏⠀⠀⠙⢻⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⡃⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⠁⠀⠀⠀⠀⠻⢜⢲⡾⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠀⠀⠀⣄⠀⣿⣇⢹⡇⠀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⠇⠸⠇⠀⠹⠀⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⡅⠀⠀⠀⠀⠁⠘⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠃⠁⠀⠀⠀⠈⠛⠟⢳⡄⠀⣶⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣄⣀⣀⣠⣾⣿⣿⡣⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⣿⣿⠀⡇⢰⠀⠀⠀⠀⢀⠰⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠻⠿⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢻⣿⣿⣦⣱⠈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠷⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⠻⢿⠋⠀⠈⠣⠀⠀⠙⠁⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣂⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢖⡒⢀⠤⡉⠭⡍⠉⡍⡅⡄⡦⡄⡠⠄⡤⠀⢴⢰⢤⢀⠤⡉⠉⡭⡥⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢠⠀⣝⡿⡹⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⡀⠻⠸⠁⠇⠇⠯⠻⠣⠀⠸⠸⠐⠘⠭⠃⣀⠇⠇⠀⠫⠝⠡⠼⠸⠪⠽⠄⠘⠜⠭⠃⠿⠰⠽⠂⠘⠤⣗⣭⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣿⣷⣶⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⠆⢲⣦⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⣀⣤⣶⣶⣷⣷⣶⣶⡲⠶⣶⣄⡀⣶⣶⣂⣤⣤⣴⣿⡦⠀⡠⢸⣿⣿⣶⠀⠀⣆⠀⠐⠶⢶⡟⢲⣆⠀⠀⢲⣿⣿⣿⣿⣿⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡄⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⣿⡋⠉⠉⠁⠀⠀⡀⠀⣻⢸⣿⣿⣿⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠹⣶⣶⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⢷⣤⡀⠀⣄⣧⣤⡂⠀⡇⠀⣿⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠈⠀⡁⠀⠀⢀⠴⠀⠈⠉⠉⠁⠀⢠⣿⠿⠘⢱⣿⣯⠻⠀⠇⠀⠟⢸⣿⣿⣿⡇⠀⣿⣿⡈⠻⣿⣿⣿⠏⠁⠉⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣉⡏⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡆⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢹⠿⠗⠀⠿⠻⠟⠀⠀⣤⣿⣿⣿⡿⢛⣛⡹⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡀⠀⢀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⠃⠀⠀⠀⣶⣶⣦⠼⠤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⢹⡿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡢⡶⠀⠈⠙⠿⠗⢴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠛⠛⢛⣋⣉⣿⣿⠿⠿⠶⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠃⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⡆⣮⣟⢿⣿⣿⣿⣿⠀⠀⣀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⢸⣄⠀⠀⠀⠀⠀⠇⣿⣿⣷⣍⣿⣿⡏⠀⠘⣷⡶⠾⠿⠷⠶⢶⡤⠀⡀⠀⠀⠀⠀⠀⠉⠃⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠋⠈⠟⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣶⡄⠈⠻⣿⣿⣿⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀⠘⢿⡿⡇⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁⠀⠀⠀⠸⢻⠃⣲⡿⣿⣿⢻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⡄⠀⠀⠀⡈⠀⢿⣇⢹⡇⠈⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⠇⠸⡇⠀⠹⠀⠘⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠀⠀⠀⠀⠁⠙⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠉⠛⠟⢳⡄⠀⣶⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⠀⠀⠀⠀⣠⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⣿⣿⠀⡇⢠⠀⠀⠀⠀⢀⠰⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠶⢴⣶⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢻⣿⣿⣦⣱⠈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⠀⠈⠉⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣻⠛⢿⠋⠀⠈⠣⠀⠀⠙⠁⣄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢖⡒⢀⠤⡉⠭⡍⠉⡍⡅⡄⡦⡌⡠⠄⡤⠀⢴⢰⠤⢀⠤⡉⠋⡭⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢠⠀⣝⠯⡹⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⡀⠻⠸⠁⠇⠇⠯⠻⠣⠀⠸⠸⠐⠘⠭⠃⡀⠇⠇⠀⠫⠝⠡⠼⠸⠪⠽⠄⠘⠜⠭⠃⠿⠰⠽⠂⠘⢤⣗⣭⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣶⣿⣷⣶⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⠆⢲⣦⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣷⣷⣶⣖⡲⠶⣶⣄⠀⣶⣶⣂⣤⣤⣴⣿⡦⠀⠠⢸⣿⣿⣶⠀⠀⣆⠀⠐⠶⢶⡟⢲⣆⠀⠀⢲⣿⣿⣿⣿⣿⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡄⠈⠉⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⣿⡋⠉⠉⠉⠀⠀⡀⠀⣺⢸⣿⣿⣿⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⠇⣺⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠹⣶⣶⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⣷⣦⡀⢀⠄⣱⣶⣁⠀⡇⠀⣿⢸⣿⣿⣿⠀⠀⣿⡇⢻⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠀⡁⠀⠀⢀⡴⠀⠈⠉⠉⠁⠀⢠⡿⠿⠈⢼⣿⢯⣟⠀⡁⠀⠟⢸⣿⣿⣿⡇⠀⣿⣿⡈⠻⣿⣿⣿⠟⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣉⡏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡆⣾⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢹⠿⠗⠀⠿⠻⠟⠀⠀⣤⣿⣿⣿⡿⣛⣛⡙⠁⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡀⠀⢀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⠃⠀⠀⠀⣶⣶⣦⠼⠤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⢹⡟⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡶⠀⠈⠙⠿⠓⢴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠛⠛⢛⣋⣉⣿⣿⠿⠿⠶⠖⠒⠚⠛⠃⠀⠘⠇⣿⣿⣿
⠇⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡇⠈⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⡆⣮⣟⢿⣿⣿⣿⣿⠀⠀⣀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⢸⣄⠀⠀⠀⠀⠀⠇⣿⣿⣷⣝⣿⣿⡏⠀⠘⣷⡶⠾⠿⠿⠶⣶⡤⠀⡀⠀⠀⠀⠀⠀⠉⠃⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠉⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⠫⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦⣄⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⠀⠀⠀⢿⡻⠂⣴⡿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣦⣄⠀⠀⠀⢀⡇⠀⣻⣧⢻⡇⠀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠁⠀⣿⠇⠸⡇⠀⠹⠀⠸⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠻⠀⠀⠇⠀⠀⠀⠀⠁⠙⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠉⠛⠟⢷⡄⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⣿⣿⠀⡇⢰⠀⠀⠀⠀⢀⠰⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡆⣤⣤⣴⣿⣿⣿⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢻⣿⣿⣦⣰⠈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⡀⠀⠉⠛⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠟⢿⠋⠀⠈⠣⠀⠀⠙⠁⣄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣂⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣖⡒⢀⠤⡉⠬⡍⠉⡍⡅⡄⡦⡄⡠⢄⡤⠀⢴⢰⠤⢀⠤⡉⠋⡥⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢠⠀⣟⠯⡹⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⡀⠻⠸⠁⠇⠇⠯⠻⠣⠀⠸⠸⠐⠘⠭⢃⣀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⠿⠰⠽⠂⡘⢤⣗⣭⣧⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣷⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⠆⢲⣤⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⡲⠶⢶⣄⡀⣶⣶⣂⣤⣤⣴⣷⡦⠀⠀⢰⣿⣿⣶⠀⠀⡆⠀⠐⠲⢶⡟⢲⣄⠀⠀⢰⣿⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠉⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⢿⠋⠉⠉⠁⠀⠀⠀⠀⣸⢸⣿⣿⣿⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⠇⢹⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠰⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⡿⢷⣤⡀⠀⠀⢰⡤⠄⠀⠁⠀⣾⢸⣿⣿⣿⠀⠀⣿⡆⢻⣿⠛⠛⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢠⡿⠷⠀⢲⣗⡿⠻⠀⠁⠀⠛⢸⣿⣿⣿⠁⠀⢿⣿⡈⠛⢿⣿⣿⠋⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡏⣹⣿⣿⣿⣿⣿⣿⠁⠀⠀⡆⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⢸⠿⠇⠀⠻⠛⠟⠀⠀⣤⣿⣿⣿⡿⠋⣛⠉⠀⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣼⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢾⠃⠀⠀⠀⣶⣶⣦⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡢⡖⠀⠈⠙⠿⠓⢴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠛⠛⢛⣋⣉⣿⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠂⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡇⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⡆⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⢸⡄⠀⠀⠀⠀⠀⠁⣿⣿⣷⣝⢻⣿⡇⠀⠘⣷⡶⠾⠿⠿⠶⣶⡤⠀⡀⠀⠀⠀⠀⠀⠉⠃⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⠋⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠇⠀⠀⠀⢠⣿⣿⡀⠀⢰⡶⣷⣿⢹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣏⠀⠀⠀⠀⢸⣿⣿⡆⠀⢻⣇⢹⡇⠀⣿⠙⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⢸⣿⡿⠁⠀⣾⠇⠘⠃⠀⠹⠀⠘⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠿⠽⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠛⠟⢳⡄⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⡇⢠⠀⠀⠀⠀⢀⠰⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⠀⠀⢀⣠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢻⣿⣿⣦⣰⠈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡉⠉⠙⠿⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣛⠛⢿⠋⠀⠈⠣⠀⠀⠙⠁⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠆⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢖⡒⢀⠤⡉⠤⡌⠉⡍⡅⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡉⠋⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢠⠛⡟⠭⡹⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⡀⠻⠸⠁⠇⠇⠯⠻⠣⠀⠸⠸⠠⠘⠭⢃⡀⠇⠇⠀⠫⠝⠡⠼⠸⠪⠽⠄⠘⠜⠭⠃⠻⠰⠽⠂⣘⣤⣗⢭⣧⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣶⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⠆⢲⣤⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⡲⠶⢶⣄⠀⣶⣶⣂⣤⣤⣴⣷⣦⠀⠀⢰⣿⣿⣶⠀⠀⣆⠀⠐⠲⢶⡟⢲⣄⠀⠀⢰⣿⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠉⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⢿⠋⠉⠉⠁⠀⠀⠀⠀⢸⢸⣿⣿⣿⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⠿⢷⣤⡀⠀⠀⡠⢠⠀⠀⠃⠀⣿⢸⣿⣿⣿⠀⠀⣿⡆⢹⣿⠙⠛⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢠⡿⠷⠀⢲⡾⡫⠒⠀⠂⠀⠛⢸⣿⣿⣿⠂⠀⢽⣿⡀⠛⣿⣿⣿⠋⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡏⣹⣿⣿⣿⣿⣿⣿⠁⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⢸⠿⠇⠀⠻⠛⠛⠀⠀⣤⣿⣿⣿⡿⢛⣋⠉⠀⣿⢹⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⠃⠀⠀⠀⣶⣶⣤⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡢⡖⠀⠈⠙⠿⠓⢴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠛⠛⢛⣋⣉⣿⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠂⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡇⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠆⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣄⢸⡄⠀⠀⠀⠀⠀⠁⣿⣿⣷⣍⠻⣿⡇⠀⠘⣷⡴⠺⠿⠷⠶⣶⡄⠀⡀⠀⠀⠀⠀⠀⠉⠃⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⠋⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠘⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡷⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣷⠔⠀⢰⡶⣶⣿⢹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⢹⡇⢸⡇⠀⣿⠙⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠄⠀⠀⣿⣿⡿⠁⠀⣼⠇⠈⠂⠀⠹⠀⠈⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠹⠀⠀⠄⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠽⠽⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠛⠟⢳⡄⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠇⢠⠀⠀⠀⠀⢀⠰⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⢀⣠⣴⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢻⣿⣿⣦⣰⠈⣇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠐⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡚⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢨⣛⠛⢿⠋⠀⠈⠣⠀⠀⠉⠁⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣷⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠆⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢖⡒⢀⠤⡀⠤⡌⠉⡍⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠬⡉⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢠⠛⡟⠭⡹⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⡀⠻⠸⠁⠇⠇⠯⠳⠣⠀⠸⠸⠀⠘⠭⢃⡀⠇⠇⠀⠫⠝⠡⠼⠸⠪⠽⠄⠘⠜⠭⠃⠻⠐⠽⢂⣸⣤⡗⢭⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣾⣿⣶⣿⣶⣿⣿⣷⣶⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⢰⠆⢲⣤⡶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⡒⠶⠶⣄⠀⣶⣶⣀⣤⣤⣤⣷⡆⠀⠀⢰⣿⣿⣶⠀⠀⡄⠀⠐⠲⢶⡞⠒⣄⠀⠀⢰⣿⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠉⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠹⢿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠈⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢹⣿⠙⠋⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠈⠀⠁⠀⠀⢀⠤⠀⠈⠉⠉⠁⠀⢠⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡀⠛⢿⣿⣿⠋⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⣧⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠸⠿⠇⠀⠻⠛⠃⠀⠀⣤⣿⣿⣿⡿⠋⣉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢾⠃⠀⠀⠀⣶⣶⣦⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡖⠀⠈⠙⠿⠓⠰⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⢸⠿⠛⠛⢛⣋⣉⣿⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡇⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⡄⣮⣟⢿⣿⣿⣿⡇⠀⠀⣀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⢘⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⡇⠀⠘⣷⡔⠺⠿⠷⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠃⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠟⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣻⠂⠀⢰⡶⢲⡯⢹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⠺⡇⢸⡇⠀⣿⠙⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢀⣀⡀⠀⠀⠀⣿⣿⣿⡿⠁⠀⣸⠃⠘⠁⠀⠘⠀⠈⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠽⠽⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠛⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⡇⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢸⣿⣿⣦⣰⠈⢆⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠠⣴⣾⣿⣿⣿⠄⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢨⡙⠛⢿⠃⠀⠀⠃⠀⠀⠉⠁⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠉⠛⠻⠋⠁⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠆⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⢿⣿⡿⠿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢖⡒⢀⠤⡀⠤⡍⠉⡅⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢺⠛⡟⠭⡹⠒⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⠀⠻⠸⠁⠇⠇⠯⠳⠣⠀⠸⠸⠀⠘⠭⢃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⠻⠰⠽⣢⣼⡤⠗⣭⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣿⣿⣬⣶⣿⣷⣶⣶⣶⣶⣶⣿⣿⣷⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⢰⠆⢲⣤⡶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣖⠒⠶⠶⣄⠀⣶⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣿⡦⠀⠀⡄⠀⠐⠒⢶⡖⢲⣄⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠹⢾⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣠⣶⣾⣷⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠐⣶⣦⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢹⣿⠙⠋⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢠⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠙⢾⣿⣿⠋⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⣿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡏⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠂⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⡿⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢾⠃⠀⠀⠀⣶⣶⣤⠸⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡆⠀⠈⠙⠿⠓⠠⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠿⠛⠛⢛⣋⣉⣽⡿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢘⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣍⠻⣿⡇⠀⠘⣷⡔⠚⠿⠷⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠋⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣦⡄⠀⠀⠈⠁⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠁⠀⠀⠀⠀⣴⣿⣿⣿⣣⠀⠀⢠⡶⢲⡏⢹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣯⡆⠀⠘⡇⢸⡇⠀⣿⠙⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⢸⠃⠘⠀⠀⠘⠀⠈⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠽⠽⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠛⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⡇⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢸⣿⣿⣦⣰⠈⢆⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢀⣠⣶⣿⣿⡆⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢨⡙⠛⢿⠃⠀⠀⠃⠀⠀⠙⠁⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠂⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⢿⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢖⡒⢀⠤⡀⠤⡌⠉⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⠀⢿⠛⡏⠭⡹⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠢⠼⠘⠭⠋⠭⠇⠀⠻⠸⠁⠇⠇⠯⠳⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⠛⠰⠽⣢⣼⡤⢗⣭⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣿⣥⣤⣦⣿⣷⣶⣶⣶⣶⣶⣾⣿⣷⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⢴⠆⢲⣤⡶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣖⠒⠲⠦⣄⠀⣶⣶⣀⣤⣤⣤⣶⡆⠀⠀⢰⣾⣷⡆⠀⠀⡄⠀⠐⠒⢶⡖⢒⣀⠀⠀⢰⣾⣿⣿⣿⣷⣶⢰⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠙⢾⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣀⣶⣾⣷⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⢸⡎⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠐⣶⣦⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠟⡙⠋⠁⠀⠙⠿⣿⣿⣿⣿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⡆⢹⣿⠙⠋⢿⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿
⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠁⠀⠀⢀⠄⠀⠈⠉⠉⠁⠀⢠⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⡀⠛⢾⣿⣾⠋⠀⠈⣻⣿⣿⣿⣿⣿⣿⡇⣧⢿⣿⣿⣿
⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣉⡏⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣾⠇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠸⠿⠇⠀⠛⠛⠃⠀⠀⣤⣿⣿⣿⠟⠉⢉⠉⠀⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⡿⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⣿⢸⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢾⠃⠀⠀⠀⣶⣶⣄⠼⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⢸⡟⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡖⠀⠈⠙⠿⠓⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠸⠿⠛⠛⢛⣋⣉⣽⣿⠿⠿⠴⠖⠒⠒⠛⠃⠀⠘⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣮⣟⢿⣿⣿⣿⡏⠀⠀⣀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⣿⡇⠀⠘⣷⡔⠺⠿⠷⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⣠⣤⣤⣤⣤⣤⣈⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠋⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠙⣿⣿⣿⡿⡅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⣤⡄⠀⠀⠈⢿⡏⠀⣿⣿⡿⡏⠅⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠈⠁⣰⣿⣿⣯⠅⠀⠀⢠⡶⢲⡇⢹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡄⠀⠈⡇⢸⡇⠀⣷⠉⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⢸⠃⠈⠀⠀⠘⠀⠈⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠂⠀⠀⠀⣹⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠭⠭⠽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠁⠀⠀⠀⠀⠛⠟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⢸⣿⣿⣦⣰⠈⢇⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⣠⣴⣾⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⡙⠛⢿⠃⠀⠀⠃⠀⠀⠙⠁⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⠀⠀⠀⠙⠿⠿⠟⠉⠁⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢂⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢖⡒⢀⠤⡀⠤⡌⠉⡄⡄⡄⡦⡄⡠⠄⡤⠀⢴⢰⠤⢀⠤⡀⠀⡤⡤⠄⡠⢄⠠⢴⢰⠠⢤⠀⢰⢄⠤⡀⣶⢀⠤⢸⢿⠛⡏⠭⡹⠒⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠢⠼⠘⠭⠋⠭⠇⠀⠻⠸⠁⠇⠇⠯⠣⠣⠀⠸⠸⠀⠘⠭⠃⠀⠇⠇⠀⠫⠝⠡⠼⠸⠨⠽⠄⠘⠜⠭⠃⠛⠰⢽⣲⣼⡤⢗⣭⣧⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣼⣤⣬⣦⣿⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣾⣷⣶⣶⣶⣶⣶⣦⣶⣶⣾⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4689

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Nov 30, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Microsoft_Partners_Help_Microsoft_Spread_Fear,_Uncertainty,_Doubt/Fear-
      mongering/Dramatisation_About_"Linux"_(as_Usual)⠀⇛


           More FUD


   2. ⚓ Mozilla_Announce_Smaller,_Faster_Firefox_Downloads_For_Linux⠀⇛


           Firefox fans on Linux will enjoy smaller download sizes and
           faster decompressing when using the official binary builds from
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      ⚓  New⠀⇛


   3. ⚓ Open_Hardware/Modding:_Olimex,_Raspberry_Pi,_ESP_and_More⠀⇛


           hardware with hacking slant


   4. ⚓ Red_Hat_Leftovers⠀⇛


           some of it promotional chaff


   5. ⚓ today's_howtos⠀⇛


           modest sized batch


   6. ⚓ Microsoft_Interference,_Free,_Libre,_and_Open_Source_Software_(FLOSS),
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           Misc. FOSS links


   7. ⚓ Windows_TCO_and_Security_Leftovers⠀⇛


           Security picks


   8. ⚓ Monopoly_Abuse_by_Microsoft⠀⇛


           Microsoft under probe


   9. ⚓ Games:_Raw_Fury_Humble_Bundle,_Selaco,_17,000_Games_for_Steam_Deck_
      (Arch_Linux)⠀⇛


           half a dozen GamingOnLinux articles


  10. ⚓ Ubuntu_Touch_OTA-7_Released_for_Linux_Phones_with_PulseAudio_Security
      Fixes⠀⇛


           The UBports Foundation announced today the release of Ubuntu
           Touch OTA-7 as the seventh stable update based on Ubuntu 20.04
           LTS (Focal Fossa) bringing important security fixes and other
           changes.


  11. ⚓ GNU/Linux_Leftovers⠀⇛


           Ubuntu and more


  12. ⚓ Programming_Leftovers⠀⇛


           Development picks


  13. ⚓ Open_Hardware:_Raspberry_Pi_and_Arduino⠀⇛


           Modding and gadgetry


  14. ⚓ Free/Libre_Applications:_Cambalache,_Kdenlive,_and_More⠀⇛


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      493 /n/2024/11/25/today_s_leftovers.shtml




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⣾⣿⣿⣧⣿⣿⣿⣿⣿⢰⡿⣾⡟⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠸⡿⣷⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣽⣾⣿⣿⣟⠀⢙⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿
⣿⠻⣿⢛⣿⣿⡿⢻⡿⣿⣿⣿⣿⣿⣿⠀⡿⠟⣻⣿⡿⣉⠉⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠟⠋⠻⣿⣿⣿⡇⠀⢸⣧⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⢸⣿⢸⣿⣿⣿⣿⡟⠛⠋⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿
⣿⠀⣷⣿⣾⣿⣸⣼⡇⣿⣿⣿⣿⣿⣿⠀⠏⠉⠉⣿⡿⠌⠀⠈⠃⠒⣿⣿⣿⣿⣿⣿⡟⠡⠀⠀⠹⠁⠎⠀⠀⠿⣿⠉⠁⠀⠈⠛⢹⡇⣿⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⠈⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠁⠀⢀⣠⡄⠀⠈⢀⢀⡀⠀⠀⡀⠀⠀⠺⠇⢃⡀⠈⠲⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢰⠀⠰⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⠀⣿⣿⣿⣿⣿⣿⣗⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⡀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣏⠀⠀⠀⣾⣿⣧⢸⠣⠃⠀⠀⠀⠈⠀⠀⠘⣀⣾⡏⣹⣶⠟⡛⠒⠀⠀⣾⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⠛⠛⠚⠛⠛⠻⠿⠾⠿⠷⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣯⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢬⡁⣽⡇⠁⠤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢠⣤⣤⣆⣰⣶⣶⣶⠤⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣠⣾⢦⣤⣆⣶⢻⣿⣿⣿⣿⣿⡿⠀⡿⠿⠆⣿⣿⣿⣿⣿⣿⣿⠷⠄⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠉⠙⣛⡋⠉⠛⠐⠒⠒⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠅⠹⠈⠉⠋⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢀⡀⠠⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⠀⠙⠻⢿⣃⣀⣆⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠉⠉⠛⠛⠛⠀⠀⠉⠉⠉⠉⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⠶⢶⣿⣷⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠑⠐⠀⡀⠀⠀⣿⣿⣿⣿⡿⡉⢪⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⠠⠒⠁⠀⠀⡀⠀⣀⣤⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⣿⣿⣿⣿⡷⢏⡎⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⢀⣠⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣴⣾⣿⣿⣿⢿⠟⠉⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⢼⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⢀⣠⣶⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⠀⣠⣴⣾⣿⡵⠷⡈⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠐⠒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣷⣖⡁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠿⣏⠁⢠⣄⡀⣀⠀⠀⠀⠀⠾⣟⣏⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⡇⠀⣀⣀⣀⣀⣀⣀⣴⣶⣿⣧⠈⠋⠛⠟⣄⣈⣴⣞⠀⠀⢻⣿⣷⣿⢿⣿⣿⣿⣿⠿⠛⠁⠀⠀⣼⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 4875

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Proving_Yet_Again_That_Techrights_Was_Right_About_UEFI_Secure_B.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Proving_Yet_Again_That_Techrights_Was_Right_About_UEFI_Secure_B.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Proving Yet Again That Techrights Was Right
About UEFI 'Secure Boot' All Along (Since
2012)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


'Secure Boot' or 'secure' boot is about anything but security


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇You_said_it_was_secure!_No,_I_said_'secure_boot',_totally
                              different_thing!⦈_


A LOT of articles that you saw in recent days about "Linux" and "security" are
wrong. Yes, there's some_"grain_of_truth"_in_them, but UEFI is not Linux,
'secure' boot isn't about security (it's about Microsoft being in control of
physical computers irrespective of what operating system they run), and for
merely having the audacity to point this out - as we've done for nearly 13
years already - you'd receive constant harassment and abuse by Microsofters
(eventually we had to sue them for this harassment [1, 2], on top of many
police reports we had filed).


To avoid replicating or spreading the latest FUD, we've carefully offloaded all
of it to this_page_that's_still_being_updated, containing more than a dozen
pieces about it - FUD pieces that have become visible as "news" with "Linux" in
their headline. Singling out this_one_example, an associate emphasises that
"UEFI is /not/ Linux", so it would be wrong to frame it like that. Even the
British media did_this, so the associate thought it was time for an I-told-you-
so style article and bibliographic review of warnings. Remember_that_months_ago
'secure'_boot_was_deliberately_or_inadvertently_weaponised_by_Microsoft_to
prevent_PCs_that_ran_GNU/Linux_from_even_booting. We very well know who's
responsible for this, i.e. who helped promote this and still_does_so.


The British publisher says "the finding suggests work is being done to target a
broader set of potential targets and dispels the previous thinking that UEFI
bootkits are designed for Windows systems only."


That's missing the point entirely! They cite a Microsoft partner and promote
the talking point that whatever security problems Windows has, Linux has those
too.


Pushers of UEFI 'secure' boot have long promoted this lie and they're
Microsofters. The serial strangler from Microsoft calls one of them "former
Microsoft researcher" (in his latest blog post) and they work together to
silence and terrorise critics of UEFI 'secure' boot. Just follow the money;
they are swimming with the Microsoft shark.


Regarding security, I recently said that Microsoft "ALWAYS has holes, even
after patching [and] it's in Snowden docs" (also citing cautionary_tales_from
2016).


CALEA_and_CALEA2 then came up. The insecurity is part of the actual design. Put
another way, insecurity is the goal, so they have compromised everything, now
they blame Russia, China etc. Yes, they made insecurity the "standard" and real
security a "relative" thing. Then, as the associate put it, "the 'Microsoft
effect' [is] where all computers are insecure at one level or another so
therefore one must stay with Microsoft (ignoring the difference in the scale
and scope of the holes)." That's what ESET is trying to tell us right now. █


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




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⠀⢸⣿⣿⣿⡇⠀⠸⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠁⠁⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠁⠀⢀⣿⣿⣿⣿⣿⠀⠀⣤⡄⢀⣤⣤⢠⣴⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⠀⠀⠀⠀⠀⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⣿⡇⡜⢿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠹⠷⣿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⡼⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠿⣿⣿⣿⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣀⡀⣄⣀⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣶⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣧⣿⣿⣁⡀⠀⠀⣉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣴⣿⣻⣈⡛⠋⣁⣀⣈⣈⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠻⢿⣿⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣄⠀⠀⣶⣶⣾⣿⣾⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣽⠿⠿⣿⠟⠃⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠽⠑⡇⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠈⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠐⠓⣆⠻⣿⣿⣿⡼⣿⠻⣿⣿⣿⣿⣿⡿⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣧⣤⣠⣤⣿⣿⣿⣿⣿⣿⠃⣀⣒⣚⡛⠓⠀⠀⠀⠘⢿⣿⣿⡿⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣄⣼⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠉⠁⠀⠀⠀⠀⢜⡻⣿⠁⠀⠘⠀⠀⠀⠀⠀⢴⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠿⣿⣿⡟⣿⣿⠟⠉⠻⡿⠁⠀⠀⠀⠐⠂⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⠿⠿⠇⠿⠄⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠁⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⢻⣿⡇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿
⠀⠀⠀⢰⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣤⣤⣤⣼⣬⣥⣼⣭⡝⠀⠈⠀⠑⠀⠀⠑⠃⠛⠀⠀⠂⠋⠉⠘⣮⣿⣾⣧⣇⣤⣵⣥⣧⣬⣤⣴⣼⣴⣧⣤⣬⣦⣬⣦⣭⣤⣮⣷⣬⣮⣌⣧⣵⣤⣬⣥⣵⣬⣾⣴⣥⣼⣤⣧⣬⣆⣨⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣴⣤⣔⣏⣑⣀⣀⣑⣈⣁⣉⣚⣈⣐⣚⣈⣀⣁⣂⣁⣀⣓⣈⣠⣧⣵⣼⣥⣬⣼⣴⣭⣧⣤⣌⣰⣤⣴⣤⣷⣼⣴⣦⣶⣴⣼⣬⣼⣦⣵⣬⣽⣤⣬⣤⣔⣥⣮⣦⣭⣤⣭⣼⣦⣭⣮⣽⣿⣿⣿⣿⣿⣿⡿

                    ䷩ 𝚕𝚒𝚗𝚎 4991

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Reporting Information and Facts at Times of
War (and Information Wars), Dissent of Merit and Scepticism//Critical Skills
Impermissible⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇SF_and_FG_almost_level_at_21.1%_and_21%,_FF_on_19.5%_-_Exit
                                    Poll_⦈_


POLITICIANS are generally corrupt. Some of the most "successful" ones are
extremely reliant on corruption ("nice guys finish last") and it seems like a
universal truism, globally or internationally applicable because cheating (or
taking bribes from the rich) gets "results"*.


Some time today_(in_the_afternoon) we'll probably know who got cast aside as
"RTÉ_announces_unrivalled_General_Election_2024_Results_coverage_across_all
platforms" and at_the_moment it says: "It indicates Green Party first
preference support stands at 4%; Labour at 5%; the Social Democrats at 5.8%;
Aontú at 3.6%; People Before Profit-Solidarity at 3.1%; Independents at 12.7%,
Independent Ireland at 2.2%, with others on 1.9%."


So in Ireland, TikTok (which is operated by and for the Communist Party of
China) didn't quite prop up non-establishment candidates like in Romania [1,
2]. Romania is a priority if Putin wants the Soviet Union back.


"As an independent candidate," Daniel Pocock explained some hours ago, "I'm not
expecting to get too many votes. Ireland is a country where traditions are very
strong and people gravitate to the parties and candidates they grew up with. On
top of that, my campaign was subject to distortion and obfuscation in Google
search results. I will be happy if I get more than 5 votes but even that is not
certain. In the last election, some independent candidates only got 23 votes
each."


The reason we reproduce what Pocock has to say is that he has long covered a
number of suppressed topics. He also has access to a lot of evidence, more so
as a former insider.


The world needs more reporting, not jingoism. The world is full of white-collar
crime, so the more people report, the better.


There's_a_SLAPP_crisis_in_the_UK and this new report says "Lords slam
government inaction on SLAPPs, calling for action by summer [...] Lords say
financial penalties for lawyers pursuing slaps should be 10,000 times
higher..." █


_____


* Consider this new_article_from_Daily_Links. The US falls_into_insane_levels
of_debt (approaching_103_trillion_dollars_in_debt if folks also count personal
("household") debt and business debt, not just national_debt) while bailing out
Microsoft and letting_Microsoft_control_the_government. The latest article
shows that Pelosi_profits_from_this_corruption and this is how she stays at the
top. "Pelosi Sells 5K Microsoft Shares Ahead Of FTC Antitrust Probe, Marking
Her Largest Sell In Years," says the latest headline. An associate says that it
is a problem (among many others) worthy of revisiting at intervals. But it's
tiring. It's happening all the time. The political systems are very badly
compromised. In more transparent countries with free press it becomes more
visible more quickly. Microsoft bribes everybody, even_its_opposition.




⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡇⣍⢾⢸⡨⢿⣿⣽⣽⣯⣽⣿⣏⣭⣭⣭⣽⣿⣏⣭⣿⣹⣽⣯⣿⣽⣭⣩⣽⣿⣿⣩⣯⣹⣯⣏⣭⣹⣿⣟⣩⣏⣯⣿⣭⣋⣿⣿⣫⣯⣿⣭⣽⣹⣿⣯⣽⣽⣍⣯⣿⣿⣭⣽⣿⣭⣽⣫⣿⣽⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠂⠘⠃⠀⠐⠀⠘⠀⠀⠀⠀⠈⠐⠘⠀⠂⠀⠀⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠫⣻⠩⢽⣿⠿⢿⢿⢿⢿⢹⣿⠩⢽⢫⣙⣿⢿⢿⢹⠿⠿⠿⡿⠿⠿⢿⢻⣿⢹⠿⢿⢿⢿⢿⢿⢹⣿⡿⡟⢻⣿⣫⢻⡋⣿⣿⣋⢹⠫⠻⣻⣿⡿⠿⡿⡿⡿⡏⣿⣟⡝⣟⠙⡟⠝⢏⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣝⣼⣸⣿⣿⣰⣸⣸⣸⣼⣸⣿⣸⣿⣜⣅⣿⣔⣼⣜⣼⣤⣧⣮⣧⣕⣼⣜⣿⣜⣔⣴⣎⣼⣔⣼⣸⣯⣢⣻⣸⣿⣑⣻⣃⣻⣽⣟⣘⣟⣼⣤⣿⣇⣆⣇⣇⣧⣇⣿⣏⣚⣟⣀⣿⣣⣧⣼⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠩⢽⠩⢽⡿⢛⢿⢛⢿⣟⡍⡟⠭⢻⣿⠩⢽⠩⡛⠽⣿⡿⣿⡏⠭⣟⠟⡏⡏⣻⡏⠭⠹⢛⢿⢹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣼⣿⣼⣿⣷⣭⣼⣼⣼⣿⣥⣽⣯⣾⣽⣭⣼⣯⣾⣥⣿⣷⣿⣧⣭⣯⣮⣧⣧⣽⣧⣿⣷⣭⣼⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⠻⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⢀⣿⡀⠀⢀⣇⠰⠰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⡀⣄⠀⠀⡄⢀⢀⡀⠠⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠉⠀⠁⠁⠉⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⡿⣿⡿⠿⣿⣿⠿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣪⣂⣇⣺⣇⣵⣐⣸⣀⣓⣿⣸⣇⣷⣧⣸⣸⣇⣷⣷⣥⣸⣨⣄⣇⣇⣼⣰⣉⣖⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⢛⣛⢻⡏⠉⠉⠩⢹⡏⠉⠩⠭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠥⠬⠤⢼⣿⠉⠁⠉⢹⣿⢭⣥⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠦⠖⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⠰⠴⠲⢸⣿⠈⠀⠀⢸⣿⠤⠄⠤⢤⣿⠉⠉⠉⠉⣿⠀⠀⠀⠀⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⠛⠛⣛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠹⠿⠟⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠉⠁⠈⢹⣿⠉⠉⠉⢹⣿⠒⠒⠒⠒⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⢸⡇⠀⡀⠀⢸⡇⠀⢠⡀⢸⣿⠀⡀⠄⢸⣿⢠⠠⢠⢸⣿⠀⡀⡀⠀⣿⠀⠀⠀⠀⣿⠀⣀⠠⠀⣿⠀⢀⡄⠀⣿⠀⡠⣄⠄⣿⠀⡀⠠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣼⣧⣤⣤⣤⣼⣷⣤⣤⣤⣼⣿⣶⣶⣶⣾⣿⣤⣤⣤⣼⣿⣤⣤⣤⣴⣿⣤⣤⣤⣤⣿⣤⣤⣤⣤⣿⣤⣤⣤⣤⣿⣶⣶⣶⣶⣿⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣹⣻⣹⣿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⢿⣿⣿⠿⡿⣿⣿⡿⣿⡿⢿⣿⣿⣿⢿⢿⠿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠄⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣧⣦⣿⣿⣿⣾⣿⣾⣶⣶⣿⣶⣷⣾⣶⣾⣾⣿⣿⣬⣥⣤⣤⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣷⣼⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5104

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Stable_at_Over_4_and_400_Days_Uptime.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Stable_at_Over_4_and_400_Days_Uptime.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Stable at Over 4% and 400+ Days'
Uptime⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


TODAY is the last day of November and statCounter still_sees GNU/Linux at 4+
percent on desktops/laptops (or 6.31 percent if one adds ChromeOS).


Windows looks like this:


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


Thankfully we never had Windows in our home. None, nada. Our 7 laptops all run
GNU/Linux. They're cheap laptops (the latest_one_cost_79_pounds; we got rid of
2 Raspberry Pi machines - apparently_a_trend - and one is still stuck at Dutch
customs), but despite their cost they're reliable and stable. On my main laptop
my uptime is almost 420 days, the second laptop has been running for almost a
year, and my wife's laptop was last rebooted 278 days ago. I've just made her
Plasma desktop a bit faster and added some new effects.


Hopefully some time this weekend we'll find enough time to upload party photos
(this site turning 18). █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣗⣠⣤⣄⣤⢀⣀⣐⣂⣒⡒⠒⠒⠒⠶⢺⣟⣿⣿⣿⣿⣿⡏⠛⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠛⠛⣿⣿⡿⣿⣿⣿⣿⡇⠉⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠸⢶⣶⣶⣶⣤⣴⢶⣶⣶⣶⡶⣆⢒⣐⣂⣒⠀⣷⣶⣶⣾⣿⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⣉⣉⣉⣉⣉⡉⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢠⣤⠀⣤⣌⢉⠉⡉⠁⣉⣉⠉⠻⠿⡻⡋⠫⡛⠛⠛⢸⣧⣠⣠⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢨⣿⠀⠈⠀⠒⠒⠛⠻⠤⢤⣴⠿⣿⣟⣉⣩⣥⣶⠶⣸⡧⠤⠭⠽⣦⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠗⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠃⣶⣦⣤⣤⣤⣤⣂⣀⣀⡀⢀⠐⠲⠶⠶⢤⣤⢤⣤⣤⣀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣬⣥⣄⣚⣁⣀⡀⠀⠠⠶⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦
⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⣙⣉⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⢰⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⡈⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⢂⣀⠤⠭⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣧⠸⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⢸⣿⣿⣿⣷⣶⣴⣴⣤⣤⣤⣄⣀⡀⠀⠀⠀⠈⠉⢉⣉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢺⣶⣭⣴⣤⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⣿⣿⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣐⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣷⣥⣌⡙⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠿⣿⣿⡏⠀⠀
⣽⣾⣿⣿⢴⣦⡠⠀⢆⣤⣔⣂⣣⣶⣼⡾⠁⠀⠀⠨⡋⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣄⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠁⠀⠀
⣿⣿⣿⣷⣿⡿⠿⠜⠟⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠛⠻⠿⠇⠀⠀⠀⠀⠬⡿⢿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣿⣷⣦⣄⡈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣟⣛⣛⣉⣡⣀⡀⠈⠉⡀⠒⠀⠀⠀⠠⢴⠄⠆⢀⠠⠐⢈⠄⠔⢆⠀⠠⠤⣀⣀⠀⢰⣋⠀⠀⠀⠀⠈⠀⠌⠀⠘⡛⢿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⠚⠁⠀⠀⠀⠨⡀⡐⡨⠤⠂⣡⠔⢊⠀⠠⢂⠈⠐⢀⠁⡁⠐⢄⠐⡛⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠐⢌⡟⢿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀
⣿⣟⣋⣙⣿⣿⣿⡆⠀⠀⢀⠌⠌⢂⠢⠨⡈⠙⠐⠀⠀⢌⢀⠰⠶⡧⠀⠀⠠⠈⠂⠈⠠⣀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠂⢈⠘⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠈⠙⠻⠿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣁⠁⣠⣀⠐⠌⠄⠂⠊⠈⢂⢂⠡⢑⢀⠀⠢⠁⢀⠂⠀⠄⢀⠀⠀⠀⠀⠈⠳⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡿⣿⣿⣿⣿⣿⣾⡒⠣⠯⡺⠶⣦⣀⣈⠀⠀⠀⠄⠂⠠⠀⠀⠀⠀⠀⠐⡐⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠊⢿⣾⣿⣿⣽⣟⣿⠟⢷⠂⠀⠀⠀⠀⠉⠸⠑⠣⠆⡤⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢵⡀⡠⠀⢩⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠘⣿⣿⣿⣿⣇⠉⠙⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣶⣶⣦⡀⡀⠀⠀⠀⠀⠀⠀⠑⢼⣆⢐⠄⠀⠙⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣬⣙⡜⣿⣿⣿⣿⡆⠀⠘⢻⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡀⠀⠀⠀⠀⠙⢿⣿⢿⣻⣽⣮⡂⡀⠀⠀⠀⠀⠀⠀⠈⠫⣱⠀⡂⠀⠈⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠹⣿⣿⣿⣿⡀⠀⠈⣆⣼⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠐⠀⠙⣮⡻⣿⣿⣿⣦⡂⡀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡂⢀⢄⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡆⠀⠀⢹⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣏⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠳⣮⣻⣿⣯⣼⣮⡢⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀
⢿⠁⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⢻⠁⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀
⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠛⠛⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡏⠉⠉⠙⢻⢿⣿⢹⠛⠛⠻⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡏⠁⠙⠻⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⢻⡿⠙⠙⠙⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣍⣿⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡃⡃⠀⠀⠀⢘⢸⢸⢸⠈⠁⠀⠀⠀⠀⠀⡃⠀⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢻⢸⢸⢸⢹⢹⠉⠙⠛⢿⣿⠿⡿⢿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠛⠀⡇⠀⠀⠀⠈⢿⣿⣿⣿⠿⠙⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⢻⢻⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢻⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣷⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⠀⢰⢰⢰⢰⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⠀⢰⢰⢰⢰⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⢰⢰⢰⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢰⢰⢰⢰⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣯⣿⣭⣽⣯⣭⣽⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣟⠀⠀⠀⠀⠀⠀⡃⡃⠀⠀⠀⢘⢘⢘⢘⠀⠀⠀⠀⠀⠀⡃⡃⠀⠀⠀⢘⢘⢘⢘⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢘⢘⢘⢘⢘⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢘⢘⢘⢘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣦⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⢸⢸⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣀⣀⣀⣀⣀⣀⣇⣇⣀⣀⣀⣸⣸⣸⣸⣀⣀⣀⣀⣀⣀⣇⣇⣀⣀⣀⣸⣸⣸⣸⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣸⣸⣸⣸⣸⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣸⣸⣸⣸⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⢻⣿⢛⣿⢛⣿⢋⣿⡋⣻⡫⣿⡋⣻⡋⣿⡟⣿⡟⣻⡟⣿⡟⣻⡟⢹⡟⢽⡟⢹⡟⢽⡟⢹⣟⢹⣟⢻⣿⢻⣿⢻⣿⢛⣿⢻⣿⢛⣿⢛⣿⡫⣿⡋⣻⡫⣿⡋⣻⡫⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢛⣶⣻⣶⣻⣾⣻⣾⣫⣷⡋⣣⡋⣫⡋⣫⡋⣫⡟⣯⡞⣯⡞⣯⡞⣧⣞⢽⣟⢹⣟⢹⣟⢹⣞⢹⣜⢙⣜⢙⣔⢛⣜⢛⣴⣻⣴⣻⣴⣻⣼⣻⣴⡋⣦⡋⣪⡋⣢⡋⣢⡋⣢⡟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5207

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/The_Irish_Have_Voted_We_ll_Soon_Know_How_Many_Voted_for_a_Debia.shtml
    Gemini version at https://techrights.org/n/2024/11/30/The_Irish_Have_Voted_We_ll_Soon_Know_How_Many_Voted_for_a_Debia.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Irish Have Voted, We'll Soon Know How
Many Voted for a Debian Developer and Free Software
Specialist⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


Results due in the weekend [1, 2].


Dublin Bay South results:


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


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Election_2024:_Dublin_Bay_South_results⦈_




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⣿⣿⣿⡇⡓⣼⠀⡇⢾⣿⣿⣙⣿⣟⣩⣟⣿⣿⣝⣩⣙⣟⣍⣿⣿⣿⣯⣉⣏⣏⣹⣏⣋⣯⣉⣽⣿⣍⣿⣿⣿⣉⣹⣿⣏⣙⣿⣿⣿⣿⣿⣿⣹⣿⣿⣟⣹⣹⣹⣿⣿⣏⣿⣏⣹⣉⣿⣫⣹⣿⣿⣩⣹⣉⣭⣹⣉⣿
⠿⠿⠿⠷⠿⠶⠶⠿⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢭⣤⣤⣤⣤⣤⣤⣤⣤⡭⢻⣉⠉⣉⡉⢹⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⣉⠛⣿⣿⡿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⠀⠛⠛⣿⡇⢸⡟⢉⣤⣌⠹⡟⢉⣤⣌⣹⡅⢨⣽⡍⢹⡟⢉⣤⣌⠙⣯⠉⢋⣤⡈⢻⣿⣶⣿⠟⢠⣿⠏⣴⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⢸⣿⠀⣿⣿⠿⡇⢸⣇⠰⣶⣶⢶⡄⠸⣿⡿⢿⡇⢸⣿⡇⢸⡄⠸⣿⡿⠀⣼⠀⣿⣿⡇⢸⣿⠟⣡⣾⡟⣧⣬⣭⡅⢨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠹⣿⣿⠋⠀⣀⣤⣾⣿⣶⣶⣶⣶⣷⣶⣿⣶⣤⣴⣾⣿⣶⣤⣴⣾⣿⣶⣼⣷⣶⣿⣶⣤⣴⣾⣿⣶⣿⣿⣷⣶⣿⣶⣶⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠻⣿⡏⠉⢹⣿⣿⠉⢹⣿⠉⠉⠉⠉⠉⢻⣿⠉⠉⣿⣿⣿⡏⠉⠉⠉⣿⠉⠉⠻⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡆⠀⢹⡇⠀⢸⣿⣿⠀⢸⣿⠀⠀⠿⠿⠀⣸⣿⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⠹⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣇⠀⢸⣿⣿⠀⢸⣿⠀⠀⣤⣤⠀⠈⣿⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⣧⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⢀⣠⣿⣿⣄⠀⠉⠁⣀⣼⣿⠀⠀⠉⠉⢀⣠⣿⠀⠀⠉⠉⢹⡏⠁⠀⠉⣿⠀⠀⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠟⠿⠿⠻⠿⠿⠿⠿⠟⠿⠛⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠈⠁⠈⠁⠉⠁⠉⠈⠉⠋⠉⠉⠉⠋⠙⢎⣉⣉⠩⠭⠝⠛⠛⠉⠁⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⡀⡄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢸⠀⡇⡗⢱⠀⡇⡇⢸⢹⠀⠀⡗⢺⢀⠭⡆⢇⡜⠀⠘⠒⡄⡎⢱⢸⠀⡇⡏⢸⠊⡇⠀⠤⠄⠀⢇⡌⡔⢱⢸⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠉⠉⠀⠁⠁⠈⠈⠀⠀⠉⠉⠈⠉⠁⠼⠁⠀⠈⠉⠀⠈⠁⠈⠁⠁⠈⠈⠀⠁⠀⠀⠀⠀⠼⠀⠈⠉⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⢠⠤⢀⠤⡀⡤⢤⢠⠤⠠⡦⢨⠠⠄⡄⢠⢀⠤⡄⡤⢤⢀⠤⠄⡄⡀⠀⢠⢠⠀⡤⢄⢠⠄⡇⠤⠄⢰⠄⡠⢄⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠘⠔⠘⠤⠃⠇⠸⠐⠝⠀⠧⠸⠀⠄⠱⠸⠈⠫⠃⠇⠸⠘⠤⠂⢱⠁⠀⠸⠸⠀⡇⠞⠘⠄⠇⠫⠣⠘⠄⠫⠍⠐⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⣶⡶⢹⡍⢭⡍⡿⡿⡿⢿⠟⢻⢽⠿⡿⡿⢿⢿⣯⡭⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢻⡿⠁⣸⣇⣛⣇⣇⣒⣦⣛⣻⣘⣘⣜⣋⣄⣿⣘⣏⣚⣷⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⠈⡏⢻⠉⡇⢈⠙⡇⢸⠀⡏⢉⠙⣿⣿⠐⠂⢸⣋⡉⢻⠹⡏⣽⣿⡐⠲⢾⢋⡉⢻⢹⡏⢻⠀⣹⢘⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣉⣴⣧⣘⣀⣇⣘⣠⣧⣸⣀⣇⣸⣀⣿⣿⣈⣉⣼⣄⣢⣸⡆⢰⣿⣿⣍⣁⣼⣌⣃⣼⣈⣁⣸⣄⣻⣸⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⣻⣿⣿⣹⣯⣫⣉⣻⣿⣙⣙⣉⣹⣋⣹⣝⣉⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡂⠀⢸⣿⣏⣟⣏⣯⣏⣿⣏⣟⣉⣹⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡀⠀⢼⣿⣿⣝⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣾⣿⣿⣟⣿⣿⣻⣿⣟⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣼⣼⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣓⢈⣿⣿⣠⣯⣿⣍⣉⣹⣿⣀⣘⣃⣃⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣇⣽⣟⣹⣿⣿⣏⣺⣅⣘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠠⠾⣿⣿⣽⣿⣹⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣟⣫⣹⣩⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⠛⠃⠸⣿⣿⣨⣈⣻⣝⣿⣐⣄⣀⣃⣸⣅⣣⣁⣡⣰⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣻⣿⣇⣬⣹⣟⣽⣿⣇⣨⣢⣐⣅⣃⣰⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠀⢸⣿⣿⣮⣿⣿⣫⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠰⢿⣿⣧⣿⣿⣝⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣦⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠁⠸⣿⣿⣼⣤⣬⣴⣼⣧⣧⣽⣧⣧⣼⣤⣦⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣧⣥⣤⣤⣵⣿⣽⣿⣼⣼⣴⣤⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⠀⠀⠀⠀⢸⣧⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⡙⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⡿⠿⢿⠿⣿⠿⢿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⡿⣿⢿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠍⠅⣸⣿⣿⣥⣥⣴⣿⣿⣿⣿⣤⣧⣤⣵⣤⣷⣤⣼⣥⣵⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⠬⠠⢀⣿⣿⣧⣦⣤⣴⣿⣧⣾⣤⣦⣧⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡀⣀⠿⣿⣿⣾⣿⣾⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠌⠻⢿⣧⣯⣾⣧⣿⣽⣾⣿⣬⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣉⣉⠻⣿⣿⡿⣿⣿⣿⣿⢿⠿⢿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣙⢻⣿⣿⡿⢿⣿⣿⣿⣿⡿⡿⠿⢿⠿⣿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡩⠅⢐⣿⣿⣴⣿⣬⣧⣿⣴⣤⣬⣦⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠁⢸⣿⣿⡧⣽⣼⣽⣮⣿⣧⣦⣤⣴⣤⣾⣤⣥⣧⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⠀⣾⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠈⠛⢿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⣿⡿⠿⠿⢿⡿⣿⢿⣿⠿⡿⡿⡿⣿⡿⢿⣿⢿⣿⣿⣿⣿⡟⣩⣄⠙⣿⣿⣿⠿⠿⢿⣿⠿⠿⣿⠿⣿⣿⡿⠿⣿⠿⡿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢴⢺⣿⣿⣷⣾⣾⣿⣿⣷⣶⣾⢿⣿⣿⣿⣿⣶⣷⣷⣷⣾⣷⣾⣷⣾⣿⣿⣿⣿⣷⣯⡍⠀⣿⣿⣿⣶⣶⣾⣿⣶⣷⣷⣶⣿⣿⣷⣶⣷⣾⣷⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠈⠁⠙⠻⣿⣶⣾⣿⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⣝⠂⠚⠻⣿⣿⣷⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⠀⢹⣿⣿⠻⣿⣿⠿⣿⢟⢛⢟⣟⠛⠟⠻⠛⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⡟⣻⣿⡿⣿⠟⣿⠛⠟⣻⣛⢛⠟⡛⢟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⢰⣿⣿⡾⣿⣷⠶⣿⣷⣾⢶⣷⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣾⣿⡷⢾⣿⠷⣷⢷⣿⠾⣷⣾⣶⣶⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠹⣿⣾⣷⣷⣾⣾⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⣠⠄⢹⣿⣷⣿⣾⣷⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⢻⣿⠿⠻⠟⣿⡟⠛⡟⠛⢟⡛⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⡂⠀⣿⣿⢒⡿⣶⢶⣶⣿⣗⣿⣾⡖⣷⣷⣶⣖⣾⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⠣⣿⢸⡀⢭⣿⢰⣝⢘⢙⢹⠋⠙⡏⡫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣾⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
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⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⣿⠿⡿⢿⣿⣿⣿⡿⠿⣿⣿⡿⢿⣿⢿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣙⣉⣉⣩⣏⣉⣍⣏⣉⣩⣩⣿⣉⣉⣻⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⠀⢸⠀⡇⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡟⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣯⣉⣉⣩⣉⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠤⠤⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠭⠍⠭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⠤⠤⠤⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5367

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Tux_Machines_Turning_Twenty_a_Half.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Tux_Machines_Turning_Twenty_a_Half.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Tux Machines Turning Twenty a
Half⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


Crossposted_from_Tux_Machines


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

                    ䷩ 𝚕𝚒𝚗𝚎 5495

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/Two_Years_Later_Sirius_Open_Source_is_Basically_Dead_With_a_Zom.shtml
    Gemini version at https://techrights.org/n/2024/11/30/Two_Years_Later_Sirius_Open_Source_is_Basically_Dead_With_a_Zom.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Two Years Later Sirius Open Source is
Basically Dead (With a Zombie Web Site)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


1 day from now it's exactly 2 years since Rianne and I resigned (at 1am and
only a_few_minutes_apart). Life has been a lot better since then. Below it's
the two of us last week, enjoying life in spite of crimes_and_abuses_directed
at_us because we run/lead important sites. Rianne's site turns_20.5_very_soon.


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


AS mentioned about_an_hour_ago, tomorrow is the anniversary of my (and also my
wife's) resignation from Sirius_Open_Source. For her it was after more than 9
years of good service for the company, for me it was nearly 12 years. I hadn't
yet known about the crimes_the_company_committed_against_my_colleagues_and_I.


The decision to leave was definitely the right one. It had also been
premeditated. Our sites have thrived since then (steadily over 1.2M requests
per day) and the company we left has been sinking since the day we left. After
we left many colleagues left as well. That had a lot to do with our own
resignations. Colleagues and esteemed buddies used to tell me that the CEO used
me as a recruitment card because of my qualifications and online reputation.


Checking official files from the British government (without taking screenshots
this time around, just examining the underlying text), Sirius is basically dead
now; they sort of killed off the companies - yes, plural! - and all that's left
is no financial activity, only a mountain_of_debt (not worth obsessing or
boasting about though). For the original company it says 1 employee (for the
second year in a row, that's the CEO who stole money from staff; his ex-wife
got in contact with us, expressing support for us). This one is 143.5k in debt;
he (the perpetrator of pension fraud) later created a_new_shell and the other
shell is half a million pounds in debt (so in total about 650k in debt).


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇I_pay_your_company_under_an_NDA,_weeks_later_you_and_your
wife_receive_humiliating_treatment,_only_to_be_acquitted⦈_


Sirius Open Source is basically finished. All the key people who knew how to
run the systems (or serve the clients) left for good and the company's chief
hides in the US after he took money from Bill Gates under_an_NDA. We'll
probably never know what exactly happened there. Was this sabotage?


Do not mind the Web site of the company. 90% (or more) of the people named as
staff don't work there and some haven't worked there for over half a decade
already!


We now know that some of the people who committed crimes against my family also
contacted Sirius Open Source. They admit this.


Finding_or_fully_attaining_justice_for_pension_fraud would be too expensive to
be worth it (we explored crowdfunding with ex-colleagues; their lawyers said
legal fees would exceed what can be recovered and the company would formally
shut down to avoid compliance with court rulings), but for other things it's
worth every penny [1, 2].


Life is full of surprises and elaborate scams (bringing_that_up_apparently
killed_the_linuxjobs_mailing_lists_more_than_a_year_ago). Sirius Open Source
taught me not_to_trust_payslips, even if formally issued by certified
accountants in London. It also taught me that the British system is willing to
cover up white-collar crimes instead of helping victims of it. I escalated to
my MP, the police, London Town Hall (our former biggest client)... to no avail.
They do not want to acknowledge their role in pension fraud, even if they know
about it. █




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

                    ䷩ 𝚕𝚒𝚗𝚎 5650

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Understanding Irish general election 2024
results Dublin Bay South⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


Reprinted with permission from Daniel_Pocock.


Counting staff have conducted initial tallies of the ballot papers and these
confirm my predictions from the_blog_post_yesterday.


Personally, I'm not in contention to win a place in the Dáil. The big positive
outcome for my campaign is the increased interest in my blogs about the adverse
impact of social control media and some of the other things that are going
wrong at the intersection of technology and society. Unlike last time I ran for
public office, it does not look like a finished last again.


Yesterday I commented_on_one_of_the_minor_candidates_from_the_communist-
trotskyist_PBP. Many people were amused that I frustrated the campaign of a
communist. Nonetheless, that was not my intention. My only intention was to
demonstrate the hypocrisy of communists using social control media platforms
that enrich billionaires in a foreign country. Nonetheless, it is interesting
to see that the communist increased her share of the votes from three percent
to four percent. At the same time, the Green party vote fell as they were
running with a different candidate. In general, the left votes were divided and
fighting against each other and none of them appear to be able win a seat. That
is a loss for the left as one seat was previously held by the Greens.


Kate O'Connell previously served as a local representative for the party Fine
Gael and this time she ran as an independent. The media showed a big interest
in her campaign. Her previous status and her media profile haven't helped her
attain the number of first preference votes required to be in contention for
one of the four seats.


Nonetheless, Kate achieved about 4.5% of the vote and this demonstrates how
much harder it was for other independents who have little or no public profile
at all.


Many people have commented on my €17,000 electricity bill. This is the type of
scandal that is so unusual that it would normally appear in a news report even
if there was not an election in progress. The media have known about the bill
for a week but chosen not to report on it. This adds to the perception of many
people that the media has been very selective in reporting on the existing
political parties and not providing any space for new candidates and the issues
we raise.


One of the issues people raised with me during the campaign was the status of
the Sandymount Baths. Despite Dublin's incredible shoreline, the Baths have
been derelict for over 100 years. Coincidentally, many people comment that the
same two parties have taken turns to govern Ireland over the same period of 100
years.


The only independent candidate who did get significant media attention for free
is the high profile bank robber Gerry Hutch. He is in fourth position after the
first tally and this means there is a real possibility that he will win a seat.
He could miss out on the seat if the preference transfers from other candidates
all work against him to help one of the candidates in fifth or sixth positions
to rise up into the fourth position and displace him. If that happens, he may
miss out on the seat by a very slim margin. It may come down to just one
hundred votes. People who acquired Gerry_'The_Monk'_Hutch domain names may
share some of the responsibility if he misses out on a seat by such a small
margin.


The election created a huge interest in my blog posts about inconvenient truths
in the days before voting. It is interesting to see that the heightened
interest in my blog has continued in the time since the polls closed. █





                    ䷩ 𝚕𝚒𝚗𝚎 5738

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/30/With_a_Month_Left_to_Raise_Money_the_Free_Software_Foundation_F.shtml
    Gemini version at https://techrights.org/n/2024/11/30/With_a_Month_Left_to_Raise_Money_the_Free_Software_Foundation_F.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ With a Month Left to Raise Money the Free
Software Foundation (FSF) Has Already Raised 56,000
Dollars⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


December starts tomorrow.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Free_Software_Foundation_(FSF)_at_56,000_dollars;_Come_build
                           a_better_world_with_us!⦈_


The FSF "is a 501(c)(3) nonprofit organization based in Boston, MA, USA." It
probably cannot get to $400,000 next month (we've already said it's an
overambitious target), but the more, the merrier.


Miriam_Bastian did some_good_advocacy_this_month.


Unlike_the_fake (identity_thief), the FSF does not take Microsoft bribes. It
blasts Microsoft:


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇_Free_software_is_vital_for_the_public_and_state-run
                      infrastructure_of_a_free_society_⦈_


Microsoft has since then censored_or_watered_down_that_report. █




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣢⣶⣴⢲⢲⢴⣦⢸⣲⢴⣰⣿⣧⣶⡇⣔⣶⢸⣲⢴⣦⣷⣾⣴⡦⡖⢰⡴⡴⣖⣶⡖⣷⣺⡇⣶⣶⢺⣿⣿⢦⢰⣶⣶⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⢀⣀⢀⣀⣀⢀⢀⢀⣀⢤⢀⣀⣀⡀⣠⢀⢀⢀⣀⡄⡄⢀⣄⠀⣄⣤⣀⠄⣀⡀⣄⣀⣀⡀⡀⣄⡀⡀⡀⣤⢀⣀⢀⢀⢠⣀⣠⢠⣀⡀⣀⣀⢀⣠⣠⢀⣀⣤⡄⡀⣄⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠉⠉⠉⠈⠁⠉⠉⠈⠈⠉⠉⠉⠈⠘⠉⠉⠉⠁⠉⠈⠉⠁⠈⠁⠉⠈⠈⠁⠉⠉⠈⠀⠁⠉⠉⠁⠉⠉⠈⠛⠈⠉⠈⠉⠉⠉⠉⠁⠈⠉⠁⠈⠉⠀⠉⠉⠁⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠘⠗⠝⠹⠞⠫⠿⠻⠂⠇⠊⠾⠹⠇⠏⠖⠜⠵⠄⠇⠝⠯⠪⠷⠃⠱⠖⠗⠨⠿⠿⠅⠻⠿⠉⠖⠕⠾⠇⠸⠣⠮⠺⠕⠕⠹⠄⠫⠛⠿⠟⠰⠛⠿⠟⠘⠖⠕⠼⠇⠏⠺⠂⠝⠸⠝⠅⠱⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢰⡦⣄⡄⠆⣆⠆⣄⢤⣤⣴⣦⢠⣠⣤⢰⣄⡄⣤⣤⢰⡠⣤⡄⣤⣤⡤⣤⣤⡄⡄⣠⣤⢤⡠⢄⣴⢠⡄⡄⣤⣤⡄⣤⢰⣤⣤⡆⣤⣦⣠⣶⣤⡆⣤⣤⣄⡤⣠⣤⢴⢰⡢⣤⣤⣤⣄⣤⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⣀⣀⠀⢀⡀⢀⢀⢀⢀⢀⡀⣀⡀⡀⢀⡀⡀⣀⡀⡀⡀⡀⣀⣀⡀⣀⢀⢀⣀⡉⣀⣀⣀⠀⡀⢉⢀⡀⡀⡀⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⠈⠛⠛⠗⠁⠚⠃⠀⠛⠓⠓⠘⠃⠛⠘⠛⠸⠏⠊⠚⠃⠚⠃⠑⠙⠙⠃⠚⠉⠐⠙⠓⠛⠛⠑⠁⠚⠍⠘⠊⠋⠒⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⣶⣶⣶⡲⠲⠖⣶⠖⣖⢖⡐⣶⠒⠒⡖⡒⢲⣶⠒⣶⠖⣶⣲⠲⢰⣆⢖⠖⣲⣒⢐⡖⢲⡖⣲⢲⣖⣲⣶⢒⣶⠒⣖⠲⡂⣶⢲⢲⠲⣒⠖⡶⣖⢲⠒⣲⣶⣖⢒⡐⡒⢲⢲⢲⣲⡖⢖⣖⣶⠒⡲⢲⡶⡲⢰⣶⣶⣶
⣿⣿⣿⣿⢶⣶⣿⣶⣷⣾⣷⣷⡾⣶⡷⣷⣾⣿⣶⣿⣾⣿⣶⣶⣾⣿⣶⣶⣿⣷⣾⣷⣾⣧⣾⣶⣷⣾⣿⣶⣿⣶⣿⣶⣶⣿⣶⣾⣶⣷⣶⣿⣿⣶⣶⣿⣿⣿⣾⣷⣷⣾⣾⣾⣿⣶⣶⣷⣷⣶⣷⣾⣷⣾⣾⣿⣿⣿
⣿⣯⣋⣿⣆⣧⣺⣒⣿⣨⣔⣗⣂⣕⣢⡣⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⡿⣟⣿⣿⣛⣻⣟⣿⣿⣿⣟⣿⣿⣛⣿⣿⣿⣻⣟⣿⣻⣿⣿⣻⣿⣻⣿⣿⣿⣿⣛⣿⣟⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠻⢿⡟⣿⡿⢻⡟⠿⠿⣿⠿⣿⠛⠻⠿⠿⠿⡿⠿⠿⢿⠿⠿⠟⠿⠟⡟⠿⣿⠿⠿⡟⠟⠿⠿⡿⠿⠿⢿⣿⠛⠿⢿⠛⡛⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⣿⡻⡟⠿⠟⡟⢿⡿⠿⠿⢿⡟⠻⠿⢻⢛⡿⠿⢿⣿⣿
⣿⡷⠿⠟⠺⠷⠷⠿⢷⠺⣿⠷⢷⢷⣶⡺⠷⡞⠳⠷⡗⠶⠳⡷⡿⢲⠾⠶⣿⠿⠿⢿⠾⢻⠶⡖⠶⠿⢿⠿⠾⢾⠶⢾⢾⣷⣷⣿⣾⣾⣿⣷⣶⣶⣾⣶⣶⣿⣷⣿⣷⣷⣿⣷⣿⣾⣷⣿⣷⣶⣶⣾⣿⣷⣷⣿⣿⣿
⣿⣷⣶⣷⣾⣶⣶⣶⣾⣶⣿⣾⣷⣾⣿⣷⣿⣷⣶⣷⣷⣶⣶⣷⣷⣾⣷⣶⣷⣶⣶⣾⣶⣾⣶⣷⣾⣾⣾⣶⣶⣾⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣥⣿⣼⣖⣽⣶⣵⣾⣇⣭⣭⣬⣧⣼⣥⣷⣼⣼⣺⣤⣧⣵⣵⣴⣬⣾⣭⣾⣷⣬⣄⣵⣤⣼⣮⣮⣧⣵⣤⣭⣭⣬⣽⣦⣷⣥⣼⣮⣾⣬⣼⣷⣬⣥⣷⣾⣮⣮⣯⣾⣵⣬⣾⣷⣼⣯⣥⣦⣵⣿⣿⣿⣿⣿⣿
⣿⣇⣉⣉⣍⣻⣟⣍⣟⣵⣎⣽⣍⣹⣟⣿⣡⣈⣯⣫⣧⣫⣭⣝⣏⣹⣻⣉⣿⣿⣁⣩⣹⣫⣿⣭⣟⣻⣋⣙⣿⣟⣟⣏⣉⣈⣏⣹⣏⣩⣁⣟⣹⣍⣽⣩⣽⣩⣽⣫⣉⣙⣟⣽⣏⣀⣭⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣉⣝⣍⣉⣉⣭⣋⣍⣏⣹⣁⣩⣫⣉⣉⣟⣭⣹⣉⣽⣿⣉⣍⣾⣻⣻⣹⣋⣩⣽⣉⣍⣻⣸⣏⣹⣙⣋⣿⣻⣉⣸⣫⣉⣻⣃⣉⣻⣏⣉⣹⣻⣭⣉⣉⣽⣍⣻⣿⣭⣹⣹⣋⣍⣻⣉⣉⣉⣿⣟⣹⣉⣭⣿⣿⣿
⣿⣯⣩⣭⣍⣭⣯⣽⣩⣏⣹⣫⣍⣙⣋⣹⣍⣩⣉⣩⢉⣻⣉⢩⣏⣉⣹⣏⣉⣍⡯⣿⣉⣉⣽⣝⣿⣍⣻⣭⣹⠲⠶⠀⠖⠔⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣰⣨⣉⣍⣿⣍⣉⣉⡍⣫⣁⣅⣏⣉⣍⣿⣉⣏⣍⣹⣉⣍⢩⣁⣏⣽⣿⣇⣅⣩⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣽⣩⣉⣏⣩⣉⣍⣿⣉⣿⣉⣍⣩⣉⣍⣩⡉⣉⣉⣇⡝⣽⣸⣩⣿⣿⣿⣿⣿
⣿⣿⠏⣏⢽⡟⡛⢛⠛⢟⠛⡟⡛⢻⠛⡛⠛⠟⣻⢙⡟⣻⠛⡟⠻⠛⢛⡛⡟⢻⢛⢻⠛⡋⡋⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣷⣾⣿⣴⣷⣿⣾⣷⣷⣷⣾⣶⣷⣷⣷⣿⣶⣿⣾⣼⣷⣾⣾⣾⣷⣿⣾⣶⣷⣶⣷⣷⣷⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣏⣉⣏⣉⣍⣯⣭⣉⣟⣙⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣉⣉⣩⣹⣹⣉⣍⣹⣫⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⠙⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣏⣉⣛⣫⣉⣉⣝⣍⣍⣏⣹⣭⣹⣽⣉⣉⣻⣏⣹⣉⣉⣏⣟⡝⣯⣫⣩⣫⣫⣻⣽⣝⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⠓⠀⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣻⣭⣟⣛⣿⣻⣏⣙⣫⣻⣽⣟⣋⣟⣿⣿⣿⣟⣿⣻⣹⣻⣟⣛⣿⣟⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣄⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣏⣟⣟⣛⣻⣿⣛⢻⢻⣿⢛⣻⡟⡟⣛⣛⢛⢛⣹⠿⣿⢟⣻⡽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣟⢋⡟⡛⢻⠟⡋⣛⣿⠛⠛⡛⢻⣿⣿⠋⡏⠛⡿⡟⠛⢻⢟⢻⠹⡿⡟⢻⢿⠙⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⠐⠀⣛⠀⣀⠀⣀⠘⠂⠀⠂⠐⠇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡿⢛⡿⣟⠛⣟⣟⣿⣿⣛⣻⣿⣻⣻⣟⣟⢻⣻⣛⣟⠛⡿⣟⡟⢛⣿⣻⡛⡟⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠈⠋⠀⠘⠓⠓⢛⣋⡉⠉⣉⠉⠉⠉⠉⠀⠀⠚⠛⠚⠚⠓⠚⠓⠙⠛⠀⠀⠀⠀⠀⣿⣿
⣿⣟⢿⣻⣻⣟⣿⠟⡿⣟⣟⢿⣿⡻⣻⢿⣿⡻⣻⡿⠛⡻⣻⣛⡛⣻⡛⣻⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡟⢿⠿⡿⠿⢿⣟⠿⢿⣿⣿⡿⡿⢿⣿⣿⢿⠿⠻⡿⠛⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⡦⠀⣧⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣧⣬⣈⣯⣹⣩⣉⣉⣻⣯⣍⣩⣽⣋⣉⣹⣏⣹⣓⣩⣯⣉⣍⣉⣻⣽⣉⣸⣉⣯⣉⣛⣉⣝⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢻⠛⢣⠂⠂⠀⠀⠀⠰⡀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣏⣝⣉⣍⣉⣍⣹⣹⣏⣉⣋⣉⣝⣏⣯⣉⣏⣏⣉⣻⣟⣹⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣯⣍⣙⢛⣝⣋⣿⣿⣉⣏⣯⣏⣉⣋⣯⣫⣛⣽⣿⣝⣉⣏⣙⣹⡫⣛⣫⣉⣭⣙⣋⣯⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣯⣿⣛⣛⣟⣟⣛⣿⣻⣻⣿⣻⣿⣛⣟⣻⣻⣟⣛⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣯⣏⣛⣫⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⢛⣛⣻⢿⣟⢻⡹⡟⣿⣻⣿⣟⣟⣛⡿⣛⣛⢟⢛⢏⣻⣿⢏⣙⣛⡟⣟⣻⢛⡛⡻⣏⣹⣛⢛⢻⢟⣛⡻⡛⣛⡛⣟⡛⣟⣙⣻⢻⣛⣿⢻⡹⣛⣛⡻⣿⣿⣿⣿⣿⣿⣿⡿⢟⣟⡛⣿⣋⣹⣿⣻⣛⣻⣿⣿⣿
⣿⡟⢋⡿⢻⢻⠻⢻⣛⠛⠛⣿⢻⢻⠛⡛⠛⡿⠻⠟⡿⠛⣿⠛⠿⣟⢻⢻⣛⣻⢿⢛⡛⣿⣿⢛⠛⣻⢿⠛⠛⣛⡿⠛⡻⢿⠟⣟⠛⢻⡿⣻⢻⢛⠛⢻⣻⣿⠛⡟⣟⠋⢛⢻⡟⢻⠛⠟⢻⡛⠛⢻⡟⠛⢻⣿⣿⣿
⣿⡟⠛⢻⠛⠛⣿⠛⠻⣟⠛⡛⠛⢻⡛⡟⠟⡟⢻⡟⡟⢛⠟⠛⣿⣿⣿⣿⣿⣿⣿⣛⣟⠛⣛⡛⢛⣟⣻⠛⡟⠛⠛⣟⣻⠻⠟⠛⡟⠛⡟⠛⣿⣻⠟⠛⣿⡛⠛⢟⣟⢛⣿⠛⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⢛⣻⠿⡟⢺⠿⠛⢿⢻⢿⣻⢛⢻⡟⢻⠿⢿⢿⢿⠻⡷⠿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣻⣿⡻⢿⣿⣛⢿⠿⣻⣿⣿⠿⠿⢿⠿⠿⡷⠟⣟⢻⢿⠟⡿⢿⠻⠿⣿⣿⢻⢿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿
⣿⡿⣿⡿⣿⠿⡿⢿⠿⠿⢿⢻⠿⢿⠿⠟⣿⠿⣿⣿⠿⡿⠿⡿⢿⣿⠿⢷⡞⡿⢿⡿⣿⠿⣿⠻⡿⠻⣿⢿⠻⢿⡟⢿⣿⠿⣷⡟⠿⡿⠿⠿⣿⠿⣿⠿⣾⠿⢿⡿⠿⢿⣿⣻⣿⠿⢿⢿⠿⡿⡿⣿⢿⡟⠻⠿⣿⣿
⣿⡿⣿⢿⡟⣿⡾⠿⠟⣿⠿⣿⣿⢿⠿⢿⣿⠿⡿⣿⠿⡿⣿⡷⡿⣿⠛⡿⣿⠻⢿⡟⠻⠷⣿⢿⠿⡿⣿⢿⣿⣾⠛⠿⣿⡿⢿⡿⠿⢿⣿⣿⣿⣿⠿⢿⣿⠿⠿⢿⣻⢿⢿⢿⣿⣿⠻⠷⠿⡿⠳⢿⢿⠿⣿⣿⣿⣿
⣿⣿⢾⣾⢾⣾⠷⢿⣶⣷⠿⠾⢷⣾⠷⡿⢾⢷⠿⣿⠾⣾⣿⡿⡾⠾⣷⣷⡿⠶⢷⠿⡿⣿⡷⣿⡾⠿⠾⢾⡿⢾⢾⣷⢿⢿⢿⠿⢾⣿⢿⡷⠾⡿⢷⡾⠿⢷⢷⢿⠷⢿⣷⠾⠿⣾⣶⣾⣷⣷⣿⣾⣷⣷⣷⣷⣿⣿
⣿⣷⣶⣶⣶⣿⣿⣾⣾⣿⣶⣶⣾⣿⣶⣿⣾⣶⣶⣿⣶⣷⣿⣷⣶⣾⣿⣿⣷⣶⣾⣶⣷⣷⣶⣶⣷⣶⣶⣾⣿⣷⣶⣿⣷⣿⣾⣿⣾⣾⣾⣷⣶⣿⣾⣷⣾⣾⣿⣾⣶⣾⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5836

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 30/11/2024: SIGINT Foo and
Hooking Up an Old Serial Terminal to a NetBSD Machine Over
USB⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Humanity_is_done⠀⇛


                       I strongly believe that humanity as we know it will
                       be a thing of the past within my lifetime.


                       In 2010 the average global temperature was 1.0°C
                       above that from before the industrial revolution.


                       In 2024 we've crossed 1.5°C. Yes, we have just
                       passed the symbolic mark of the Paris Climate
                       Convention. In just under fifteen years the global
                       average has risen by 0.5°C.


                # ⚓ 🔤SpellBinding:_PHIMNOE_Wordo:_LOOKS⠀⇛


                # ⚓ A_MONTH_OFF⠀⇛


                       I was planning to take the last couple of months of
                       the year off, or half-off, just not working on new
                       products to sell. As usual it didn't quite work out
                       because everything drags on too long, but I pretty
                       much reached the point yesterday.


                       But then it's not quite time off because it's
                       really time for doing all the non-profitable jobs
                       I've been optimistically listing for completion on
                       weekends. I've got to attempt bodywork on my car
                       (inc. learning MIG welding), solar power for my
                       house, paint all the wood on the house where the
                       old paint has flaked off, finish that backup
                       gravity-fed water supply and satellite dish 4G
                       antenna platform (the modem's signal has been
                       dropping out from time to time since the 3G turn-
                       off, though not too bad yet), and the eternal job
                       of trying to make the rusty guttering on the house
                       and shed work. Oh and fix the potholes in the
                       (long) driveway _again_, fix the shed where my
                       parts car lives, get rid of the bees that are
                       spreading through the roof of my house again, and
                       the ones in my parts car now. Fix the instrument
                       panel in the ute again because my last effort
                       failed - the intermittent short must be in the fuse
                       box itself. etc. etc.


          o § Politics and World Events⠀➾


                # ⚓ Trump_is_God⠀⇛


                       People voted Trump like they believe in god. Not a
                       lot, they mostly don't think about it.


                # ⚓ Diary_of_an_Unemployed_Citizen_004⠀⇛


                       This morning, I was informed by the automated
                       dispatch messaging bot that, due to my not
                       accepting today's assignment within the sixty
                       minute window (I was still sleeping), my dispatch
                       offer had expired. I thought little of it. An
                       unexpected day off meant working on some
                       applications for decent jobs and even a hike with
                       my mother. How so silly I can be.


                       Not silly of me to be flexible regarding temp
                       assignments as 'easy come, easy go'. Rather, silly
                       to have assumed that such an automated system would
                       be at all competent at its job. Sure enough, as the
                       meet time came and passed, I received multiple
                       phone calls asking me where I was.


                       "Ah, well, I will be there in an hour's time, then"


                       And my day's plans reverted. Such is a commonality
                       of the modern temp job.


          o § Science⠀➾


                # ⚓ Stargazing_2024-11-29:_Beehive_Cluster_(publ._2024-11-29)⠀⇛


                       After a long cloudy, warm spell, the temperature
                       dropped down to around -27 deg F and the skies
                       began to clear up. Last night (2024-11-28) the
                       skies were very clear, but we were busy with
                       Thanksgiving festivities, and I couldn't stay up
                       any later after we got home.


                       This morning, the skies were still mostly clear,
                       except a few wispy Cirrus clouds. I was able to
                       manage about 30 minutes of stargazing before
                       needing to head off to work. Temps were still very
                       cold but I put on my thermal insulated pants, a
                       sweater, my winter boots, two coats, a scarf, a
                       hat, and my electric heated gloves, and I was able
                       to stay warm. Thankfully, my binoculars didn't
                       frost over, which can happen due to my having to
                       breath near them.


          o § Technology and Free Software⠀➾


                # ⚓ Yet_More_SIGINT_Foo⠀⇛


                       There are various misunderstandings of what happens
                       when control+c is mashed in a unix terminal, this
                       time when a shell runs a pipeline. The claim is
                       that the SIGINT goes to the last process in a
                       pipeline, and the other processes get a SIGPIPE.


                # ⚓ Hooking_Up_an_Old_Serial_Terminal_to_a_NetBSD_Machine_over
                  USB⠀⇛


                       I recently purchased an old Wyse WY-55 dumb
                       terminal on a whim, and I've been experimenting
                       with different things I can do with it. I wanted to
                       try hooking up the terminal to a NetBSD machine. I
                       figured it would be pretty simple since NetBSD is
                       among the most "Unix-y" of the modern Unix-likes,
                       and it should still have good support for these
                       types of serial terminals. As it turns out, the
                       process *is* simple. The main complicating factor
                       was that the computer I run NetBSD on does not have
                       a serial port, so I had to use a USB serial
                       adapter. Figuring out how to get NetBSD to
                       communicate via the USB adapter wasn't very hard
                       either, but I figured I would still document the
                       process in case someone finds it interesting or
                       useful.


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





                    ䷩ 𝚕𝚒𝚗𝚎 6027

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Investigation, America’s Cemeteries Are Rewilding, Panda Protection Money
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posted by Roy Schestowitz on Nov 30, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Meat_cleaver⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Standards/Consortia
    * § Leftovers⠀➾


          o § Standards/Consortia⠀➾


                # ⚓ The Conversation ☛ Why_timekeeping_is_now_on_the_verge_of_a
                  giant_leap_forward_in_accuracy⠀⇛


                       Time is vital to the functioning of our everyday
                       lives: from the watches on our wrists to the GPS
                       systems in our phones. Communication systems, power
                       grids, and financial transactions all rely on
                       precision timing. Seconds are the vital units of
                       measurement in timekeeping.


                       Surprisingly, there is still debate over the
                       definition of the second. But recent advances in
                       the world’s most accurate forms of timekeeping may
                       have just changed the game.


                # § Science⠀➾


                      # ⚓ Latvia ☛ Latvian-Swiss_research_project_could_pave
                        the_way_for_the_future_of_asphalt⠀⇛


                             Riga Technical University (RTU), in
                             collaboration with the Swiss Federal
                             Laboratories for Materials Science and
                             Technology (Empa), is launching an ambitious
                             research project, LACHMAT, aimed at
                             developing advanced concrete and asphalt
                             materials and technologies, reports Labs of
                             Latvia.


                      # ⚓ France24 ☛ How_to_carry_out_a_visual_detox:_Ways_to
                        sharpen_our_visual_critical_thinking⠀⇛


                             With the advent of social control media, our
                             brains are receiving a constant stream of
                             images. So how can we undergo a visual detox?
                             Annette Young speaks to Marine Tanguy who has
                             written a book on how to do just that. Also
                             as we face a global epidemic of domestic
                             violence, a novel approach in southern Italy
                             offers survivors the opportunity to rebuild
                             their lives by providing training and
                             accommodation. Plus a female theatre group in
                             the Balkans stage the ancient Greek play
                             which condemns women's suffering in war while
                             celebrating our capacity to resist.


                      # ⚓ Science Alert ☛ Almost_30%_of_Microplastics_Come_From
                        a_Hugely_Overlooked_Source⠀⇛


                             We urgently need to fix this.


                      # ⚓ Science Alert ☛ Mysterious_Network_of_Canals_From
                        4,000_Years_Ago_Predates_The_Maya⠀⇛


                             Who built this?


                      # ⚓ Science Alert ☛ NASA_Discovers_Secret_Army_Base
                        Buried_Under_Decades_of_Ice⠀⇛


                             “We didn’t know what it was at first.”


                      # ⚓ Science Alert ☛ Incredible_Fossil_Preserves_a
                        Crocodile_From_12_Million_Years_Ago⠀⇛


                             A stunning creature unearthed in Peru.


                      # ⚓ Science Alert ☛ The_World's_Rarest_Mineral_Is_So_Rare
                        It's_Only_Ever_Been_Found_Once⠀⇛


                             You're looking at it.


                      # ⚓ Science Alert ☛ Are_Asteroids_Really_Worth_a_Fortune?
                        Here's_What_We_Know.⠀⇛


                             A goldrush in space could happen, but it's
                             complicated.


                      # ⚓ The Conversation ☛ 2024-11-20_[Older]_It’s_100_years
                        since_we_learned_the_Milky_Way_is_not_the_only_galaxy⠀⇛


                      # ⚓ The Conversation ☛ 2024-11-21_[Older]_‘Deep_inside,
                        something_told_me_I_had_found_the_earliest_human
                        ancestor;_I_went_numb’_–_Yohannes_Haile-Selassie_on_his
                        lifetime_quest_to_discover_ancient_humanity⠀⇛


                      # ⚓ The Conversation ☛ 2024-11-25_[Older]_The_whole_story
                        of_human_evolution_–_from_ancient_apes_via_Lucy_to_us_–
                        in_one_long_read⠀⇛


                # § Career/Education⠀➾


                      # ⚓ University of Michigan ☛ Lawsuit_alleges_UMich_owes
                        back_pay_to_about_3,600_professors⠀⇛


                             A lawsuit filed in the Michigan Court of
                             Claims Tuesday claims the University of
                             Michigan owes back pay to about 3,600 U-
                             M professors after systematically underpaying
                             them by delaying pay raises.


                      # ⚓ The Conversation ☛ 2024-11-22_[Older]_The_peer_review
                        system_no_longer_works_to_guarantee_academic_rigour_-_a
                        different_approach_is_needed⠀⇛


                # § Hardware⠀➾


                      # ⚓ CNX Software ☛ Picade_Max_USB_Controller_board
                        supports_two_joysticks_and_up_to_30_arcade_buttons⠀⇛


                             Pimoroni Picade Max USB Controller is a
                             Raspberry Pi RP2040 board designed for arcade
                             game consoles with support for two joysticks
                             and up to 30 buttons through standard DuPont
                             socket connectors and one Plasma button
                             connector. The board comes with a 2MB QSPI
                             flash for the firmware, a USB-C port for
                             power and programming, one of DuPont socket
                             connectors exposes three ADC inputs, 3.3V,
                             and GND, and there’s also a Qwicc/Qt STEMMA
                             connector for I2C module expansion, plus BOOT
                             and RESET buttons for programming.


                      # ⚓ Tom's Hardware ☛ Taiwan_ready_to_discuss_2nm_transfer
                        to_U.S._following_Trump's_comments⠀⇛


                             The National Science and Technology Council
                             Minister says the country could discuss the
                             possibility of transferring 2 nm to TSMC's
                             fabs in the U.S. after mass production is
                             initiated in Taiwan.


                      # ⚓ Hackaday ☛ Fully_Submerge_This_Modernized_PH_Sensor⠀⇛


                             There’s a school of thought that says you
                             shouldn’t mess around with a solution that’s
                             already working, but that’s never seemed to
                             stop anyone in this community. When [Skye]
                             was looking at the current state of connected
                             pH meters they realized there was incredible
                             room for improvement.


                      # ⚓ Hackaday ☛ Simple_Pen_Plotter_Rolls_On_The_Table⠀⇛


                             Pen plotters are popular builds amongst DIY
                             CNC enthusiasts. They’re a great way to learn
                             the fundamentals of motion control and make
                             something useful along the way. In that vein,
                             [Maker101] has created a neat barebones
                             plotter for tabletop use. 


                      # ⚓ Hackaday ☛ Building_A_Generator_That_Runs_Off_Hose
                        Power⠀⇛


                             [Paul Junkin] bought a curious product off
                             the Internet. It was supposed to generate
                             electricity when hooked up to a running hose.
                             Only, it didn’t do a very good job. His
                             solution was straightforward—he built his own
                             hose-powered generator that actually worked.


                # § Health/Nutrition/Agriculture⠀➾


                      # ⚓ JURIST ☛ Canada_top_court_rules_multi-crown
                        litigation_provision_constitutional_in_opioid_class
                        action⠀⇛


                             The Supreme Court of Canada ruled on Friday
                             that the province of British Columbia (BC)
                             may bring a class action on behalf of
                             multiple governments in Canada for harm
                             caused by opioids.


                      # ⚓ Latvia ☛ Medicine_prices_should_fall_noticeably_next
                        year_in_Latvia⠀⇛


                             As of next year, the price of medicines
                             costing more than €5 should fall by 15-20%,
                             and the price of expensive prescription
                             medicines should fall significantly. However,
                             a charge will be introduced for each
                             prescription, Latvian Television reported on
                             November 28.


                      # ⚓ The Straits Times ☛ UN_talks_struggle_for
                        breakthrough_on_plastics_treaty_as_deadline_looms⠀⇛


                             The chairman of talks aiming for an
                             international treaty to rein in pollution
                             from plastics issued a document on Friday
                             outlining measures that could furnish the
                             basis of a pact, in an attempt to spur
                             discussions as a Dec. 1 deadline approaches.


                      # ⚓ New York Times ☛ UK_Lawmakers_Vote_to_Legalize
                        Assisted_Dying_After_Emotional_Debate⠀⇛


                             After an emotional debate, Parliament voted
                             on Friday in favor of allowing assisted
                             suicide for some terminally ill people in
                             England and Wales.


                      # ⚓ MIT Technology Review ☛ The_risk_of_a_bird_flu
                        pandemic_is_rising⠀⇛


                             This article first appeared in The
                             Checkup, MIT Technology Review’s weekly
                             biotech newsletter. To receive it in your
                             inbox every Thursday, and read articles like
                             this first, sign up here. How worried should
                             we be about bird flu? It’s a question that
                             I’ve been asked by friends and colleagues
                             several times over the last couple of weeks.


                      # ⚓ New York Times ☛ A_Bird_Flu_Pandemic_Would_Be_One_of
                        the_Most_Foreseeable_Catastrophes_in_History⠀⇛


                             It’s not too late for President Biden to give
                             the U.S. a life-changing gift.


                      # ⚓ Science Alert ☛ Warnings_Issued_in_California_After
                        Bird_Flu_Confirmed_in_Raw_Milk⠀⇛


                             "We are in a soup of virus."


                # § Proprietary/Artificial Intelligence (AI)⠀➾


                      # ⚓ Dhole Moments ☛ Imagining_Private_Airspaces_for
                        Bluesky [Ed: Bluesky is a spying company; nothing is
                        private]⠀⇛


                             Recently, I shared my thoughts on the Ex-
                             Twitter Exodus.


                      # ⚓ Press Gazette ☛ Bluesky_already_delivering_more
                        referral_traffic_than_X_for_some_publishers [Ed: Those
                        publishers make themselves dependent on men in the
                        middle; dumb decision-making, encourage use of RSS]⠀⇛


                             The Boston Globe and Guardian have both
                             reported seeing more traffic from Bluesky
                             than Threads.


                      # ⚓ Bryan Lunduke ☛ Google_Accuses_Abusive_Monopolist
                        Microsoft_of_"Dark_Patterns"_with_Edge_Browser_on
                        Windows⠀⇛


                             To make this case, they've formed the
                             "Browser Choice Alliance" with Opera &
                             Vivaldi.


                      # ⚓ Bruce Schneier ☛ Race_Condition_Attacks_against
                        LLMs⠀⇛


                             These are two_attacks against the system
                             components surrounding LLMs:


                                  We propose that LLM Flowbreaking,
                                  following jailbreaking and prompt
                                  injection, joins as the third on
                                  the growing list of LLM attack
                                  types. Flowbreaking is less about
                                  whether prompt or response
                                  guardrails can be bypassed, and
                                  more about whether user inputs and
                                  generated model outputs can
                                  adversely affect these other
                                  components in the broader
                                  implemented system.


                # § Security⠀➾


                      # § Privacy/Surveillance⠀➾


                            # ⚓ JURIST ☛ WhatsApp_challenges_data_protection
                              fine_at_EU_top_court⠀⇛


                                   WhatsApp Ireland Ltd has appealed a
                                   €225 million ($236 million) fine to the
                                   Court of Justice of the European Union
                                   (CJEU) on Tuesday, the European Union’s
                                   highest court of appeal.


                # § Defence/Aggression⠀➾


                      # ⚓ France24 ☛ Returning_Lebanese_find_destroyed_homes
                        and_razed_neighbourhoods_among_rubble⠀⇛


                             In Lebanon, thousands of displaced people
                             began returning to their homes this week
                             after a ceasefire was announced between
                             Israel and the Hezbollah militant group. Many
                             found their homes reduced to rubble after
                             intense Israeli airstrikes over the past two
                             months leveled entire neighbourhoods in
                             eastern and southern Lebanon, as well as the
                             southern suburbs of Beirut. Nearly 1.2
                             million people have been displaced.


                      # ⚓ The Conversation ☛ 2024-11-22_[Older]_Why_some
                        countries_are_more_likely_to_believe_nuclear_war_won’t
                        happen_to_them⠀⇛


                      # ⚓ New York Times ☛ Chad_Ends_Longtime_Military
                        Partnership_With_France⠀⇛


                             The decision by Chad is another blow to what
                             remained of France’s military influence in
                             the troubled stretch of countries below the
                             Sahara, where Russia’s influence has been
                             growing.


                      # ⚓ France24 ☛ Jihadists_and_allies_breach_Syria's_second
                        largest_city⠀⇛


                             Jihadists and their Turkish-backed allies
                             reached Syria's second city of Aleppo Friday,
                             as they pressed a lightning offensive against
                             forces of the Iranian- and Russian-backed
                             government. The fighting is some of the
                             deadliest in years, with 255 people killed,
                             according to the Syrian Observatory for Human
                             Rights. Most of the dead have been combatants
                             but the toll also includes 24 civilians, most
                             killed in Russian air strikes.


                      # ⚓ The Straits Times ☛ South_Korea_completes_missile
                        interceptor_to_counter_threat_from_North⠀⇛


                             It is designed to intercept incoming
                             ballistic missiles or aircraft at altitudes
                             higher than 40km.


                      # ⚓ Seoul_to_counter_North_Korean_threats_with_new
                        missile_system⠀⇛


                             A homegrown Long-range Surface-to-Air Missile
                             is designed to intercept ballistic missiles
                             at high altitudes.


                      # ⚓ The Straits Times ☛ S’pore_needs_to_work_extra_hard
                        to_maintain_valuable_ties_with_China_amid_global
                        uncertainty:_SM_Lee⠀⇛


                             SM Lee's remarks come in a week when Trump
                             has declared extra 10% and 25% tariffs for
                             China.


                      # ⚓ The Straits Times ☛ China_urges_‘utmost_caution’_by
                        US_ahead_of_Taiwan_president’s_Hawaii_trip⠀⇛


                             Taiwan's president will make a stopover in
                             Hawaii during a week-long trip beginning on
                             Nov 30.


                      # ⚓ China_debuted_a_new_fighter_plane._How_does_it
                        compare_to_the_F-35?⠀⇛


                             The J-31 fighter, also known as the Falcon
                             Hawk, is designed for stealth and speed.


                      # ⚓ Beijing_tests_bilateral_waters_with_US_prisoner
                        exchange⠀⇛


                             Return of three U.S. prisoners for
                             Thanksgiving sends message to the incoming
                             Trump administration, experts say.


                      # ⚓ China_probes_top_military_official_for_‘serious
                        violations’⠀⇛


                             Defense ministry says top military official
                             Miao Hua is suspended, denies minister Dong
                             Jun under investigation.


                      # ⚓ Chinese_military_conducts_patrol_near_disputed
                        Scarborough_shoal⠀⇛


                             China’s air-and-sea patrol took place as a
                             U.S. carrier strike group entered the South
                             China Sea.


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


                            # ⚓ LRT ☛ Lithuania_expels_three_staff_members_of
                              Chinese_mission⠀⇛


                                   Lithuania has declared three staff
                                   members of China’s diplomatic mission
                                   persona non grata and handed a
                                   diplomatic note to Beijing.


                            # ⚓ The Straits Times ☛ Trump_may_thwart_Kim-Putin
                              ambition_on_economic_ties,_says_study⠀⇛


                                   If the war ends in any form, the needs
                                   of both countries for each other may
                                   change.


                            # ⚓ The Straits Times ☛ ICC_turns_down_appeal
                              request_from_Mongolia_over_failure_to_arrest
                              Russia’s_Putin⠀⇛


                                   ICC member Mongolia failed to arrest
                                   Russian President Vladimir Putin during
                                   a visit in September.


                            # ⚓ LRT ☛ Poland’s_former_president:_Frozen
                              conflict_would_be_terrible_for_Ukraine_–
                              interview⠀⇛


                                   A frozen conflict in Ukraine would only
                                   benefit Vladimir Putin, former Polish
                                   President Aleksander Kwaśniewski tells
                                   LRT in an exclusive interview.


                            # ⚓ France24 ☛ Lebanon’s_uneasy_truce,
                              Trumponomics,_Merkel’s_Memoir,_Sudan_‘The
                              Invisible_Crisis’⠀⇛


                                   This week, the guests gathered around
                                   Gavin LEE discuss the fragile ceasefire
                                   that was agreed between Israel and
                                   Lebanese Hezbollah; how Donald Trump
                                   plans on launching a new tariff war
                                   with America's neighbours; and what is
                                   happening in Sudan, where war is still
                                   raging, despite focus being displaced
                                   towards Ukraine and the Middle East.
                                   And as a Black Friday special deal, our
                                   set of experts also dive into Angela
                                   Merkel's legacy book.


                            # ⚓ France24 ☛ Russia_targets_Ukraine's_energy
                              infrastructure_ahead_of_winter⠀⇛


                                   Russia launched more than a hundred
                                   drones at Ukraine overnight and early
                                   Friday, killing one person and wounding
                                   eight others, officials said. The
                                   nearly three-year war has seen a sharp
                                   escalation in recent days, with Moscow
                                   pummelling Ukraine's energy
                                   infrastructure ahead of the winter.


                            # ⚓ LRT ☛ Belarusian_orgs_plead_for_‘more_humane’
                              treatment_from_Lithuanian_authorities⠀⇛


                                   Belarusian organisations in Lithuania
                                   are calling on the government and the
                                   public to protect Belarusian nationals
                                   who fought for Ukraine. The plea comes
                                   in response to the case of Vasil
                                   Verameichyk, who was extradited to
                                   Belarus after being denied residence in
                                   Lithuania.


                            # ⚓ RFERL ☛ Jailed_Former_Moscow_Anti-War_Lawmaker
                              Gorinov_Handed_New_Prison_Sentence⠀⇛


                                   Imprisoned former Moscow municipal
                                   deputy Aleksei Gorinov, known for his
                                   outspoken criticism of Russia's war
                                   against Ukraine, has been handed a new
                                   three-year prison sentence for
                                   "justifying terrorism."


                            # ⚓ RFERL ☛ Ukraine_Says_It_Struck_Russian_Oil
                              Depot,_Radar_Station⠀⇛


                                   Ukraine said it struck an oil depot and
                                   an air-defense radar inside Russia
                                   early on November 29 amid an escalation
                                   of attacks by both Moscow and Kyiv
                                   ahead U.S. President-elect Donald
                                   Trump's return to the White House.


                            # ⚓ The Straits Times ☛ North_Korea_leader_Kim:
                              Russia_has_right_to_exercise_self_defence_against
                              Ukraine⠀⇛


                                   SEOUL - North Korean leader Kim Jong Un
                                   told Russian defence minister Ukraine's
                                   use of long-range weapons is the result
                                   of direct military intervention by the
                                   United States and Moscow is entitled to
                                   take action in self-defence, state
                                   media said on Saturday.


                            # ⚓ New York Times ☛ Russia_Moves_to_Cut_Off
                              Ukraine’s_Nuclear_Power_Plants⠀⇛


                                   Moscow has increasingly hit critical
                                   substations linked to nuclear power
                                   plants in an effort to disconnect them.
                                   At the same time, Ukraine replaced the
                                   commander of its ground forces.


                            # ⚓ Meduza ☛ Life_without_light_As_Russian_strikes
                              on_Ukraine’s_power_grid_bring_blackouts,_Kyiv
                              residents_carry_on_in_the_dark_—_Meduza⠀⇛


                            # ⚓ Meduza ☛ Kyiv_prepared_to_end_war’s_‘hot_phase’
                              in_return_for_‘NATO_umbrella’_over_Ukrainian-
                              controlled_territories,_Zelensky_says_—_Meduza⠀⇛


                            # ⚓ New York Times ☛ Ukraine’s_River_of_Anguish⠀⇛


                                   Amphibious operations across the Dnipro
                                   River at Kherson illustrated the
                                   suffering and endurance of Ukrainian
                                   forces. A team of Times journalists
                                   observed the perilous movements.


                            # ⚓ RFERL ☛ U.K._Prosecutor_Says_Bulgarian_Accused
                              Of_Spying_For_Russia_Discussed_Killing_Journalist
                              Grozev⠀⇛


                                   A Bulgarian accused of spying for
                                   Russia in Britain discussed in text
                                   messages the possibility of kidnapping
                                   or murdering investigative journalist
                                   Christo Grozev, British prosecutors
                                   said during the trial of members of an
                                   alleged spy ring.


                            # ⚓ The Straits Times ☛ China,_Russia_militaries
                              conduct_joint_air_patrol_over_Sea_of_Japan⠀⇛


                                   BEIJING - Chinese and Russian
                                   militaries have organised and carried
                                   out the ninth joint strategic air
                                   patrol in "relevant airspace" over the
                                   Sea of Japan on Friday, Chinese state
                                   broadcaster CCTV said.


                            # ⚓ The Straits Times ☛ Chinese,_Russian_military
                              planes_enter_South_Korea’s_air_defence_zone,
                              Seoul_says⠀⇛


                                   The aircraft all exited without
                                   incident or intruding South Korea's
                                   airspace.


                            # ⚓ The Straits Times ☛ China_says_‘willing_to
                              work’_with_countries_in_severed_Baltic_Sea_cables
                              probe⠀⇛


                                   China says it is maintaining close
                                   communication with Sweden on the issue


                            # ⚓ Latvia ☛ Latvian_Security_Service_asks_for
                              prosecution_of_potential_terrorist⠀⇛


                                   On November 22, the State Security
                                   Service (VDD) asked the Prosecutor's
                                   Office to prosecute a Latvian citizen
                                   for allegedly preparing for terrorist
                                   attacks and propagandizing terrorism,
                                   the VDD said in a statement.


                # § Environment⠀➾


                      # ⚓ The Straits Times ☛ Indonesian_rescuers_search_for
                        missing_in_buried_cars_and_bus_after_landslide_in
                        Sumatra⠀⇛


                             Torrential rain for the past week in the
                             province has triggered flash floods and
                             landslides in four districts.


                      # ⚓ The Straits Times ☛ 3_dead,_thousands_displaced_as
                        Malaysia_warns_of_worst_floods_in_a_decade⠀⇛


                             Over 80,000 people had been evacuated to 467
                             temporary shelters in seven states.


                      # ⚓ The Straits Times ☛ China_completes_3,000-km_green
                        belt_around_its_biggest_desert,_state_media_says⠀⇛


                             It is part of efforts to curb the sandstorms
                             that plague parts of China during the spring.


                      # § Energy/Transportation/Mining⠀➾


                            # ⚓ The Straits Times ☛ South_Korean_firefighter
                              holds_on_to_truck_driver_for_45_minutes_to_save
                              him_from_falling_off_bridge⠀⇛


                                   He saved the driver from an 11-metre
                                   fall.


                            # ⚓ Hong Kong Free Press ☛ Flight_operations_take
                              off_at_Hong_Kong_third_runway,_clearing_way_for
                              airport_capacity_increase⠀⇛


                                   Hong Kong started flight operations on
                                   its third runway on Thursday, with
                                   officials saying it will keep the
                                   city’s airport competitive as an
                                   aviation hub despite its lagging post-
                                   pandemic recovery.


                            # ⚓ Science Alert ☛ World's_Largest_Gold_Deposit
                              Found,_Worth_Over_US$80_Billion⠀⇛


                                   The most lucrative jackpot ever?


                            # ⚓ Hackaday ☛ Swapping_Batteries_Has_Never_Looked
                              This_Cool⠀⇛


                                   We don’t know much more than what we
                                   see with [Kounotori_DIY]’s battery
                                   loader design (video embedded below)
                                   but it just looks so cool we had to
                                   share. Watch it in action, it’ll
                                   explain itself.


                      # § Wildlife/Nature⠀➾


                            # ⚓ New York Times ☛ Life_After_Death:_America’s
                              Cemeteries_Are_Rewilding⠀⇛


                                   More burial sites are forgoing pristine
                                   lawns for drought resistant plants and
                                   wildflowers that help wildlife. Efforts
                                   picked up in the pandemic.


                            # ⚓ New York Times ☛ Here_Are_the_Risks_When_Zoos
                              Pay_for_Endangered_Species⠀⇛


                                   We tracked $86 million in U.S. money
                                   that was supposed to go toward panda
                                   conservation in China.


                            # ⚓ New York Times ☛ Millions_of_Dollars_to_Protect
                              Pandas_Was_Spent_by_China_on_Roads_and
                              Buildings⠀⇛


                                   A Times investigation found that zoos
                                   knew conservation money went toward
                                   apartment buildings and roads. But they
                                   wanted to keep displaying pandas, so
                                   nobody looked too closely.


                            # ⚓ Science Alert ☛ Orcas_Have_a_Killer_Technique
                              to_Hunt_The_Biggest_Fish_in_The_Ocean⠀⇛


                                   They really are scarily intelligent.


                      # § Overpopulation⠀➾


                            # ⚓ The Straits Times ☛ Seoul_to_explore_supporting
                              children_born_outside_of_marriage⠀⇛


                                   Children born outside of marriage made
                                   up 4.7 per cent of all births in South
                                   Korea in 2023.


                            # ⚓ The Straits Times ☛ South_Korea’s_birth_rate
                              catches_Elon_Musk’s_attention,_again⠀⇛


                                   Mr Musk's stand has made him a poster
                                   child of the pro-natalist movement.


                            # ⚓ The Straits Times ☛ Divorces_in_China_on_the
                              rise_again_despite_mandatory_cooling-off_period⠀⇛


                                   Data for 2023 showed that 3.6 million
                                   couples finalised their divorces, up
                                   from the 2.88 million in 2022. 


                # § Finance⠀➾


                      # ⚓ Science Alert ☛ An_Expert_Reveals_What_Black_Friday
                        Is_Doing_to_Your_Brain⠀⇛


                             The thrill of the hunt.


                # § AstroTurf/Lobbying/Politics⠀➾


                      # ⚓ The Straits Times ☛ Japan’s_Ishiba,_leading_a
                        minority_government,_must_find_political_nous_to
                        survive_and_thrive⠀⇛


                             TOKYO – Japanese Prime Minister Shigeru
                             Ishiba, held hostage to the whims and demands
                             of the opposition as he heads a minority
                             government, began and ended his second policy
                             speech to Parliament by quoting a man who
                             lasted just 65 days as premier.


                      # ⚓ France24 ☛ Replay:_President_Macron_speaks_at_Notre-
                        Dame_Cathedral⠀⇛


                             Watch French President Emmanuel Macron's
                             speech during his visit Friday to Paris's
                             Notre Dame Cathedral ahead of its scheduled
                             reopening on December 7.


                      # ⚓ Hong Kong Free Press ☛ Hong_Kong’s_John_Lee_‘proud’
                        of_city’s_prosecutors_amid_US_calls_for_sanctions_over
                        national_security_cases⠀⇛


                             Hong Kong’s leader has praised the city’s
                             prosecutors for what he termed their
                             integrity, professionalism and passion,
                             following US threats of sanctions in response
                             to the jailing of dozens of democrats in a
                             national security case.


                      # ⚓ The Straits Times ☛ TikTok,_Meta_brace_for_fallout
                        from_Australia’s_social_control_media_ban⠀⇛


                             Australia's new law bars under-16s from
                             social control media.


                      # ⚓ RFERL ☛ Romania_Begins_Ballot_Recount_Amid
                        Accusations_Of_Social_Media_Violations⠀⇛


                             Romania's Central Election Bureau has begun a
                             court-ordered recount of all ballots cast in
                             the first round of the presidential election
                             as accusations swirled that surprise winner
                             Calin Georgescu illegally used Fentanylware
                             (TikTok) to boost his campaign.


                      # ⚓ Marcy Wheeler ☛ Ball_of_Thread:_Rudy’s_Hunter_Biden
                        Witch_Hunt⠀⇛


                             This Ball of Thread episode lays out Rudy
                             Giuliani's effort to frame Joe Biden.


                # § Censorship/Free Speech⠀➾


                      # ⚓ JURIST ☛ Saudi_Arabia_detentions_spark_international
                        concerns_over_freedom_of_expression⠀⇛


                             Amnesty International urged Saudi Arabia on
                             Thursday to release individuals who have been
                             detained “solely for exercising their right
                             to freedom of expression online.” Amnesty
                             International stated that the releases must
                             occur before the United Nations Internet
                             Governance Forum (IGF), which Saudi Arabia
                             will host from December 15 to 19.


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


                      # ⚓ Press Gazette ☛ Lord_Kinnock_joins_chorus_of_concern
                        for_future_of_The_Observer⠀⇛


                             Former Labour leader tells Press Gazette: "I
                             can’t be sure that Tortoise has the capacity
                             or the inclination to sustain The Observer."


                      # ⚓ Press Gazette ☛ Sardegna_Live_chooses_MyType_to
                        transform_digital_journalism_in_Sardinia⠀⇛


                             Atex has announced its partnership with
                             Sardegna Live, a prominent Sardinian news
                             outlet and video production company. MyType
                             brings cutting-edge digital content
                             management (CMS) capabilities to Sardegna
                             Live, enabling them to amplify their reach,
                             enhance content creation, and foster deeper
                             connections with their audience.


                # § Civil Rights/Policing⠀➾


                      # ⚓ The Straits Times ☛ S._Korea_faces_increasing
                        complaints_of_abuse_from_migrant_workers_even_as
                        reliance_on_them_grows⠀⇛


                             South Korea is in desperate need of migrant
                             workers but abuse of such workers is rampant.


                      # ⚓ The Straits Times ☛ China_court_jails_journalist_Dong
                        Yuyu_for_7_years_on_spy_charges,_family_says⠀⇛


                             Dong Yuyu, 62, was detained by police in
                             Beijing in February 2022.


                      # ⚓ Hong Kong Free Press ☛ China_jails_journalist_Dong
                        Yuyu_for_7_years_on_spy_charges,_family_says⠀⇛


                             A Beijing court on Friday sentenced veteran
                             Chinese state media journalist Dong Yuyu to
                             seven years in prison on espionage charges,
                             his family said.


                      # ⚓ The Straits Times ☛ China_resumes_multiple-entry
                        visas_for_Shenzhen_to_Hong_Kong⠀⇛


                             This allows unlimited visits within a year,
                             instead of the previous one-trip-per-week
                             limit. 


                      # ⚓ JURIST ☛ Ontario_judge_dismisses_lawsuit_accusing
                        Canada_company_of_human_rights_abuses_in_Tanzania⠀⇛


                             Ontario Superior Court Justice Edward Morgan
                             on Wednesday dismissed a lawsuit accusing
                             Canadian company Barrick Gold of committing
                             human rights abuses against Tanzanian mine
                             workers.


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]_These
                        Peruvian_Women_Left_the_Amazon,_but_Their_Homeland
                        Still_Inspires_Their_Songs_and_Crafts⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-25_[Older]_As
                        Amazon_Expands_Use_of_Warehouse_Robots,_What_Will_It
                        Mean_for_Workers?⠀⇛


                # § Internet Policy/Net Neutrality⠀➾


                      # ⚓ Medevel ☛ Keeping_Your_Kids_Safe_Online:_How_DNS
                        Servers_Can_Help?_Using_DNS_Servers_Apps_As_Parental
                        Controls,_Benefits_and_Limitations⠀⇛


                             As a parent in today's digital age, I
                             understand the constant worry about what our
                             children might encounter online. While the
                             internet offers incredible educational
                             opportunities, it can also expose our kids to
                             inappropriate content.


            § Monopolies/Monopsonies⠀➾


                # ⚓ New York Times ☛ Canada_Accuses_Surveillance_Giant_Google
                  of_Creating_Advertising_Tech_Monopoly⠀⇛


                       The case largely echoes an antitrust action in the
                       United States and seeks to force Surveillance Giant
                       Google to sell off sections of its online ad
                       business.


                # ⚓ Silicon Angle ☛ Canada’s_Competition_Bureau_seeks_to_force
                  Surveillance_Giant_Google_to_divest_ad_tech_tools_in
                  antitrust_suit⠀⇛


                       Canada’s Competition Bureau, the country’s
                       antitrust watchdog, took legal action against
                       Surveillance Giant Google LLC today, alleging that
                       it’s engaging in anticompetitive conduct in its
                       online advertising technology services within
                       Canada, and it’s seeking to force the company to
                       divest some of its advertising technology tools.


                # ⚓ Cloudbooklet ☛ Google_Faces_Canada_Lawsuit_Over_Online_Ad
                  Monopoly⠀⇛


                       Discover how Surveillance Giant Google faces Canada
                       lawsuit for abusing ad dominance and unfair
                       practices in the digital market


                # § Trademarks⠀➾


                      # ⚓ TTAB Blog ☛ November_2024_Update_of_TMEP_Now
                        Available⠀⇛


                # § Copyrights⠀➾


                      # ⚓ New York Times ☛ Major_Canadian_News_Outlets_Sue
                        Proprietary_Chaffbot_Company_In_New_Copyright_Case⠀⇛


                             A coalition of some of Canada’s biggest media
                             companies is seeking billions of dollars in
                             compensation for what they say is copyright
                             monopoly infringement on their work through
                             ChatGPT.


                # § Gemini* and Gopher⠀➾


                      # § Personal/Opinions⠀➾


                            # ⚓ Life,_Health,_and_Laptops⠀⇛


                                   Well, it's been a couple of months
                                   since I last posted an update here and
                                   that's because life got quite chaotic
                                   very quickly. Time for an update and to
                                   re-cap the last two months of my life.


                                   [...]


                                   I was weighing up which OS and desktop
                                   environment I should go with for my new
                                   setup. In the end, I decided to go with
                                   Fedora's Sway Atomic rpm-ostree based
                                   release. I spent awhile customising my
                                   Sway and Waybar setup and eventually
                                   came up with this config for my laptop
                                   [2]:


                            # ⚓ Org-journal_with_prompts⠀⇛


                                   Although I have made several attempts,
                                   I never got into the habit of
                                   journaling.


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


                            # ⚓ Witchcraft_as_Transgression⠀⇛


                                   To me, the word and idea of
                                   "witchcraft" is fundamentally about
                                   transgression, which is the big
                                   difference that sets it apart from
                                   "magic" in general—there are as many
                                   laws against witchcraft specifically as
                                   there are against fortune-telling and
                                   divination or other practices out
                                   there. If you're not willing to
                                   transgress those…well, what are you
                                   actually willing to do then that's
                                   witchy? (Yes, I know there are many
                                   different opinions on what witchcraft
                                   is, this is just my approach to
                                   understanding the words "witchcraft"
                                   and "witch".)


                                   There's lots of kinds of magic out
                                   there, none of which has ever really
                                   been socially acceptable on a broad
                                   scale when it comes to cultural norms
                                   in general. In that light, all magic
                                   can be considered transgressive in some
                                   sense or another, but this isn't the
                                   same kind of transgressive as what I
                                   consider witchcraft to be. When I
                                   consider witchcraft, I think of the
                                   witches of Thessaly who drew down the
                                   Moon not to commune with her but to
                                   operate in complete darkness to work
                                   when the skies weren't right; I think
                                   of the various coercive spells of the
                                   Greek Magical Papyri where one
                                   threatens to bind, abuse, even murder
                                   the gods themselves so as to get one's
                                   aim done; I think of spells that don't
                                   seek to fall under the protection of a
                                   god, but to become a god greater than
                                   the gods. In other words, if there's a
                                   cosmic order of things—a hierarchy of
                                   powers that be—then witchcraft is magic
                                   that transgresses that cosmic order,
                                   and works only within their own order
                                   to institute their own order by
                                   toppling the existing grander one
                                   already at play.


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





                    ䷩ 𝚕𝚒𝚗𝚎 7245

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 30/11/2024: More Strongarming and
Threats to Taiwan, Ananda Krishnan is Dead⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Hackaday ☛ Minichord_Wants_To_Help_You_Find_Rad_Chord
            Progressions⠀⇛


                 If you’re good at music theory, you can probably find all
                 the chords and progressions you need just by using your
                 fingers and a suitable instrument. For a lot of
                 musicians, though, remembering huge banks of chords can
                 be difficult, and experimenting with combinations can
                 quickly become tedious and tiring. Enter the minichord, a
                 tiny version of the Omnichord synth designed by
                 [Benjamin] that offers to help out by putting all the
                 chords you need a mere button press away.


          o ⚓ Hackaday ☛ UFO_50_Inspired_LX_System_Looks_Straight_Out_Of_A
            Video_Game⠀⇛


                 They simply don’t make them like they used to, and in the
                 case of this retro LX system build, they only make what
                 never existed in the first place. Earlier this year the
                 long awaited video game UFO 50 released to widespread
                 critical acclaim. The conceit of the game is an
                 interactive anthology of a faux 1980’s game console
                 constructed by a large group of actual indie game
                 developers. Leave it to [Luke], who admitted to UFO 50 to
                 taking over his life, to bring the LX system from the
                 digital screen to the real world.


          o § Standards/Consortia⠀➾


                # ⚓ India Times ☛ Interoperability_in_net_banking_payments
                  soon⠀⇛


                       The National Payments Corporation of India (NPCI)
                       is in the process of integration with a group of
                       five or six banks to go live with interoperability
                       in netbanking and mobile banking payments, three
                       people in the know said.


                       While the date for the launch of the first phase of
                       the project has not been decided with the banks, it
                       should happen within the next few months, they
                       said. Other banks will be integrated in later
                       phases.


          o § SaaS/Back End⠀➾


                # ⚓ [Old] Niels Cautaerts ☛ We_have_cloud_at_home⠀⇛


                       Still, it means paying for yet another subscription
                       in a world where the concept of true ownership is
                       continuously being eroded. As one inevitably
                       collects ever more data over the years it becomes
                       increasingly difficult to exit the platform,
                       ensuring one becomes locked in to the subscription.
                       While subscriptions are annoying, the money is only
                       a minor concern. Managed cloud services are
                       extremely convenient, but over-reliance on
                       platforms you don't control also carries risk.
                       Anyone whose YouTube account was randomly banned
                       and whose content simply evaporated can probably
                       attest to that. Platforms maintain the discretion
                       to deny service to users who they deem are breaking
                       their rules. What if that happened to your Google
                       account and all your memories in Google photos just
                       disappeared one day? It may be rare, but it does
                       happen.


          o § Science⠀➾


                # ⚓ New York Times ☛ Footprints_Suggest_Different_Human
                  Relatives_Lived_Alongside_One_Another⠀⇛


                       A discovery in northern Kenya hints that two
                       extinct species that were our ancient relatives
                       shared the same habitat and possibly interacted.


                # ⚓ Science Alert ☛ NASA_Just_Released_a_Fireplace_Video_For
                  The_Holidays,_And_It's_Hilarious⠀⇛


                       Enjoy the warm glow!


                # ⚓ Science Alert ☛ Mysterious_Bad_Odor_Prompts_Space_Station
                  to_Seal_Off_Module⠀⇛


                       This is serious.


                # ⚓ Science Alert ☛ Man_Keeps_a_Rock_For_Years_Hoping_It's
                  Gold._It_Turns_Out_to_Be_Far_More_Valuable.⠀⇛


                       No wonder he couldn't crack it open!


          o § Career/Education⠀➾


                # ⚓ University of Michigan ☛ U-M_Dearborn_faces_course_cuts,
                  faculty_layoffs_amid_budgetary_challenges⠀⇛


                       University of Michigan-Dearborn students and
                       faculty at the College of Arts, Sciences and
                       Letters will see class size increases, course cuts
                       and section consolidations for the winter 2025
                       semester, according to a Tuesday morning press
                       release from the Lecturers’ Employers Organization.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ GPS_Enabled_Pumpkin_Spice_Sprayer_Knows_When
                  It’s_PSL_Season⠀⇛


                       Pumpkin spice, also known as allspice with better
                       marketing, has found its way into a seemingly
                       endless amount of products over the years. It goes
                       beyond the obvious foodstuffs of pies and cakes;
                       because there are plenty of candles, deodorants,
                       and air fresheners ready to add a little more spice
                       to your world. One such autumnal smell enthusiast,
                       YouTube user [J-Knows], sought to automate the
                       delivery mechanism with his 3D printed pumpkin
                       spice aerosol sprayer.


                # ⚓ Hackaday ☛ The_Japanese_Console_You_Maybe_Haven’t_Heard
                  Of⠀⇛


                       The games consoles which came out of Japan in the
                       1980s are the stuff of legend, with the offerings
                       from Nintendo and Sega weaving themselves into
                       global popular culture. Most of us can recite a
                       list of the main players in the market, but how
                       many of us would have Epoch and their Super
                       Cassette Vision on that list? [Nicole Express] is
                       here with a look at this forgotten machine which
                       tried so hard and yet missed the target when
                       competing with the NES or Master System.


                # ⚓ Tom's Hardware ☛ New_U.S._restrictions_will_hit_Chinese
                  chipmaking_tool_companies_—_sanctions_aim_to_slow_development
                  of_domestic_chipmaking_tools_to_replace_ASML,_others⠀⇛


                       The new U.S. sanctions against China are meant to
                       hit developers of chipmaking gear rather than
                       chipmakers itself.


                # ⚓ Hackaday ☛ Chocolate-Coating_Machine_Mk._2:_The_Merry-Go-
                  Round⠀⇛


                       This holiday season, [Chaz] wanted to continue his
                       family’s tradition of enrobing a little bit of
                       everything in dark chocolate, and built an
                       improved, rotating chocolate-coating machine.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ Chinese_Women_Mobilize_Against_Subpar
                  Sanitary_Pads⠀⇛


                       An online campaign has prompted major pad
                       manufacturers to apologize. Regulators said they
                       would consider women’s criticisms when writing new
                       standards.


                # ⚓ Science Alert ☛ A_Toxic_Synergy_Arises_When_'Forever
                  Chemicals'_Merge_With_Microplastics⠀⇛


                       Disturbing new evidence.


                # ⚓ Science Alert ☛ Ozempic_vs_Supplements:_Dietitian_Reveals
                  Truth_About_GLP-1_Imitations⠀⇛


                       Do they really work?


                # ⚓ Science Alert ☛ Young_American_Deaths_From_Cervical_Cancer
                  Fall_Sharply_After_HPV_Vaccine⠀⇛


                       An incredible result.


                # ⚓ Science Alert ☛ An_Expert_Explains_The_Real_Dangers_of
                  Microplastics_to_Human_Health⠀⇛


                       We need to act urgently.


                # ⚓ Science Alert ☛ A_Cheap_Daily_Supplement_Seems_to_Boost
                  Brain_Function_in_Older_People⠀⇛


                       The effect can be seen within weeks.


                # ⚓ Stanford University ☛ Medicine_professor_Jay_Bhattacharya,
                  COVID_lockdown_critic,_selected_to_lead_NIH⠀⇛


                       The Stanford professor was appointed Tuesday to
                       lead the National Institutes of Health.
                       Bhattacharya has previously made controversial
                       critiques of lockdowns and vaccine mandates during
                       the COVID-19 pandemic.


                # ⚓ Mexico News Daily ☛ At_overflowing_Veracruz_landfill,
                  Greenpeace_Mexico_demands_anti-plastic_laws⠀⇛


                       The activists called for enforcement of existing
                       plastic bans and management of unregulated dump
                       sites.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ WhichUK ☛ 5_ways_Hey_Hi_(AI)_is_being_misused_to_fuel
                  online_shopping_scams⠀⇛


                       Artificial intelligence is increasingly being used
                       by fraudsters in shopping scams online


                # ⚓ Medevel ☛ ChatGPT_as_a_Doctor?_Why_You_Should_NOT_Trust_AI,
                  Even_if_You’re_a_Prompt_Engineer⠀⇛


                       The Promise and Peril of Hey Hi (AI) in Medical
                       Decision-Making: A Critical Analysis


                # ⚓ Medevel ☛ Mom_Discovers_Son’s_Rare_Diagnosis_with_ChatGPT,
                  Experts_Warn_Against_Self-Diagnosis_with_AI⠀⇛


                       A recent news story highlights how a determined
                       mother used ChatGPT, an Hey Hi (AI) chatbot, to
                       identify a rare condition in her son after doctors
                       failed to pinpoint the cause of his chronic pain.
                       While this success story has drawn attention to the
                       potential of Hey Hi (AI) in healthcare, experts
                       caution against


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Hong Kong Free Press ☛ 4_visa_applicants_and
                        immigration_consultancy_charged_over_Hong_Kong
                        investment_visa_fraud⠀⇛


                             Hong Kong’s anti-graft watchdog has charged
                             four people and the head of an immigration
                             consultancy with conspiracy to defraud over
                             applications for investment visas.


                      # ⚓ France24 ☛ Mazan_rapes:_Fake_profiles,_sites_are
                        pretending_to_be_Gisèle_Pélicot_for_money⠀⇛


                             It's confirmed she's not on social control
                             media…but X and Instagram profiles under the
                             name of Gisèle Pélicot have been sharing and
                             interacting with content as if it’s the 71
                             year old rape survivor herself. Additionally,
                             a website exists in her name sharing articles
                             about the Avignon trial, but it’s evidently
                             AI-generated, with not one photo of the real
                             Gisèle. It’s creator was traced to India, and
                             admits to using the site to bulk up his
                             income. Vedika Bahl explains in Truth or
                             Fake.


                # § Privacy/Surveillance⠀➾


                      # ⚓ China_plans_big_data_warning_system_to_prevent_public
                        killings⠀⇛


                             Leaders call for mining of 'rich seams' of
                             political, legal data to stop violence before
                             it happens.


                      # ⚓ The Strategist ☛ To_pre-empt_extremist_violence,_we
                        need_real-time_social_control_media_data_sharing⠀⇛


                             Law enforcement and social control media
                             platforms must implement real-time data
                             sharing to stop online extremism before it
                             leads to violence. Using appropriate
                             safeguards, we can achieve this without
                             raising concerns about creating a
                             surveillance state.


                      # ⚓ Press Gazette ☛ The_Swedish_regional_newsbrand
                        driving_subscriptions_via_Surveillance_Giant_Google
                        Discover⠀⇛


                             VK Media says it has grown revenue with a
                             tool that predicts when a story is about to
                             go viral on Surveillance Giant Google
                             Discover.


                      # ⚓ JURIST ☛ WhatsApp_challenges_data_protection_fine_at
                        EU’s_top_court⠀⇛


                             WhatsApp Ireland Ltd has appealed a €225
                             million ($236 million) fine to the Court of
                             Justice of the European Union (CJEU) on
                             Tuesday, the European Union’s highest court
                             of appeal.


          o § Defence/Aggression⠀➾


                # ⚓ France24 ☛ Report_on_2022_coup_plot_in_Brazil_'very
                  methodical,_detailed_and_loaded_with_evidence'⠀⇛


                       Brazil’s former far-right President Jair Bolsonaro
                       was fully aware of and actively participated in a
                       coup plot to remain in office after his defeat in
                       the 2022 election, according to a newly unsealed
                       Federal Police report. For in-depth analysis and a
                       deeper perspective, FRANCE 24 is joined by Anthony
                       Pereira, Professor of Political Science and
                       Director of the Kimberly Green Latin American and
                       Caribbean Center at Florida International
                       University.


                # ⚓ New York Times ☛ Syrian_Rebel_Groups_Launch_Largest
                  Offensive_in_Years⠀⇛


                       Scores of people were killed after forces opposed
                       to the government of President Bashar al-Assad
                       overtook a Syrian military base, a monitoring group
                       reported.


                # ⚓ The Strategist ☛ 6.5_million_on_the_move:_across_the_world,
                  migration_is_surging⠀⇛


                       Global migration flows have risen to record levels
                       since the pandemic, driven by economic opportunity
                       and conflict, and are facing a widespread policy
                       backlash. A record 6.5 million people made new
                       homes in advanced nations ...


                # ⚓ Defence Web ☛ Djibouti_maritime_forces_benefit_from_EU
                  supported_exercise⠀⇛


                       The recently finished Exercise Doraleh in Djibouti
                       is a further example of capacity building and
                       improving training for the Djiboutian Navy and
                       Coast Guard.


                # ⚓ Defence Web ☛ Stilfontein_zama_zamas_likely_have_Improvised
                  Explosive_Devices_(IEDs)_to_resist_take-down⠀⇛


                       A hellish picture worthy of a Tolkien fantasy novel
                       is emerging of the Stilfontein zama zama crisis –
                       including improvised explosive booby-traps illegal
                       miners could likely manufacture right there and use
                       to resist a forcible take-down by Police and the SA
                       National Defence Force.


                # ⚓ RFERL ☛ Former_British_Soldier_Found_Guilty_Of_Spying_For
                  Iran⠀⇛


                       A former British soldier, whose prison escape
                       sparked a massive manhunt in 2023, has been found
                       guilty of passing on sensitive information to the
                       Iranian intelligence service.


                # ⚓ New York Times ☛ A_Top_Military_Official_in_China_Is
                  Suspended_Under_Suspicion_of_Corruption⠀⇛


                       The case of Adm. Miao Hua suggests the persistence
                       of graft at high levels of the military, despite
                       the efforts by Pooh-tin Jinping to stamp out
                       corruption.


                # ⚓ Hong Kong Free Press ☛ China_says_military_official_Miao
                  Hua_suspended_and_under_investigation,_but_denies_reports_of
                  Dong_Jun’s_removal⠀⇛


                       By Ludovic Ehret and Oliver Hotham A top Chinese
                       military official has been removed from office and
                       is suspected of “serious violations of discipline”,
                       Beijing said Thursday, the latest senior
                       apparatchik to fall in a sweeping crackdown on
                       graft in the country’s armed forces.


                # ⚓ The Straits Times ☛ Latest_graft_probe_on_China_defence
                  minister_Dong_Jun_a_blow_to_foreign_engagement⠀⇛


                       Admiral Dong Jun, the international face of the
                       PLA, has been in the job for just 11 months.


                # ⚓ The Straits Times ☛ China_says_top_military_official_Miao
                  Hua_suspended,_under_investigation⠀⇛


                       He had been removed from office and was suspected
                       of “serious violations of discipline”.


                # ⚓ Taiwan_leader_to_visit_Hawaii_as_part_of_visit_to_Pacific:
                  report⠀⇛


                       The islands’s foreign minister declined to say if
                       President Lai would visit Hawaii on his Pacific
                       trip.


                # ⚓ Hong Kong Free Press ☛ As_Taiwan’s_Lai_Ching-te_prepares
                  Pacific_nation_visits,_China_vows_to_‘resolutely_crush’_any
                  attempts_at_independence⠀⇛


                       China on Thursday vowed to “resolutely crush” any
                       attempts for Taiwan independence, as the self-ruled
                       island’s President Lai Ching-te is set to embark on
                       an overseas trip. Beijing claims Taiwan as its own
                       territory and baulks at any official contact Taipei
                       has with other countries.


                # ⚓ The Straits Times ☛ Taiwan_holds_air_defence_drill_ahead_of
                  President_Lai’s_Pacific_trip⠀⇛


                       China is also likely to launch military drills in
                       the coming days near Taiwan.


                # ⚓ The Straits Times ☛ Ahead_of_Taiwan_president’s_Hawaii
                  trip,_China_says_it_will_defeat_secessionism⠀⇛


                       China' military also urged the US not to send the
                       wrong signals on Taiwan independence.


                # ⚓ The Straits Times ☛ China_criticises_Trump_tariff_threat,
                  says_it_won’t_solve_America’s_problems⠀⇛


                       Trump’s comments fired the starting gun for what
                       analysts expect to be a four-year trade war.


                # ⚓ The Straits Times ☛ China_warns_of_'necessary_actions'_if
                  US_escalates_chip_curbs⠀⇛


                       China warned on Thursday it would take \"necessary
                       actions\" to protect Chinese firms if the U.S.
                       escalated chip control measures, following reports
                       that the Biden administration could unveil new
                       export restrictions as soon as this week.


                # ⚓ Explained:_What_is_America’s_‘blacklist’-_and_does_it
                  really_work_against_China?⠀⇛


                       A U.S. government list intended to restrict
                       business with objectionable foreign companies grows
                       longer.


                # ⚓ New York Times ☛ With_Trump_Returning_and_Hezbollah
                  Weakened,_Iran_Strikes_a_Conciliatory_Tone⠀⇛


                       As Iran faces domestic and foreign challenges, its
                       bellicose rhetoric on the United States and Israel
                       has given way to signs that it wants less
                       confrontation.


                # ⚓ New York Times ☛ Lebanon_Cease-Fire_Appears_to_Hold_Despite
                  Israeli_Strike⠀⇛


                       Israel said it had targeted militants headed to a
                       rocket facility, but neither Israel nor Hezbollah
                       seemed keen to immediately return to full-scale
                       fighting.


                # ⚓ TwinCities Pioneer Press ☛ Catherine_Thorbecke:_China’s
                  dystopian_tech_influence_grows_in_Vietnam⠀⇛


                       Over the years, internet freedoms in Vietnam have
                       been severely beaten back.


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


                      # ⚓ New York Times ☛ E.U._Vessels_Surround_Anchored
                        Chinese_Ship_After_Cables_Are_Severed_in_Baltic_Sea⠀⇛


                             Multiple countries are investigating and the
                             authorities in Europe say they have not ruled
                             out sabotage. But U.S. intelligence officials
                             have assessed that the cables were not cut
                             deliberately.


                      # ⚓ LRT ☛ Lithuania,_Finland,_Sweden_set_up_team_to_probe
                        Baltic_Sea_cable_damage⠀⇛


                             The top prosecutors and the heads of law
                             enforcement agencies of Lithuania, Finland,
                             and Sweden have set up a joint investigation
                             group to investigate the recent incidents
                             when internet cables on the Baltic Sea bed
                             were damaged.


                      # ⚓ JURIST ☛ Russian_court_orders_arrest_of_French
                        journalist_for_crossing_Kursk_border_illegally⠀⇛


                             The Leninsky District Court of Kursk issued
                             an in absentia arrest order for France 24
                             journalist Catherine Norris Trent and several
                             other unidentified individuals on Tuesday. In
                             a statement issued on Telegram, the court
                             alleges that the group crossed into the
                             Sudzhansky District of Kursk illegally while
                             filming a report with Ukrainian armed forces.


                      # ⚓ North_Korea_doesn’t_deny_reports_of_troop_deployment
                        to_Russia⠀⇛


                             North will ‘fulfill obligations’ under a June
                             defense pact with Russia, North’s UN envoy
                             said.


                      # ⚓ RFERL ☛ More_Than_1_Million_Ukrainians_Left_Without
                        Electricity_After_Latest_Russian_Attack⠀⇛


                             Russia unleashed a "massive" attack on
                             Ukraine’s infrastructure on November 28,
                             leaving more than 1 million people without
                             power in freezing temperatures across the
                             country.


                      # ⚓ RFERL ☛ Trump_Nominates_Defense_Adviser_Kellogg_As
                        Special_Envoy_For_Ukraine,_Russia⠀⇛


                             U.S. President-elect Donald Trump on November
                             27 tapped Keith Kellogg, a retired Army
                             lieutenant general who has long served as a
                             top adviser to Trump on defense issues, as
                             his nominee to be special envoy for Ukraine
                             and Russia.


                      # ⚓ Meduza ☛ ‘His_tool_is_blackmail’_How_Ukrainian_media
                        reacted_to_Trump’s_appointment_of_Keith_Kellogg_as
                        Ukraine-Russia_envoy_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Ukraine_confirms_it_discussed_lowering_draft
                        age_with_allies,_says_issue_not_a_‘point_of
                        disagreement_or_tension’_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ More_than_80,000_Russian_servicemen
                        confirmed_killed_in_Ukraine,_majority_of_whom_were
                        civilians_before_full-scale_war_—_BBC_and_Mediazona_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ U.S._pressuring_Ukraine_to_lower_draft_age
                        to_18_amid_troop_shortage_—_Financial_Times_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia_launches_massive_attack_on_Ukraine’s
                        energy_infrastructure_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Biden_administration_preparing_$725_million
                        military_aid_package_for_Ukraine_—_Reuters_—_Meduza⠀⇛


                      # ⚓ France24 ☛ Chronic_inflation_hits_Russia_as_huge_pay
                        increases_fuel_rising_prices⠀⇛


                             Inflation has again spiked in Russia in
                             recent months, fuelled by massive public
                             spending on the Ukraine war and big wage
                             increases in many sectors of the economy. To
                             counter this, the Central Bank raised its
                             benchmark interest rate to a record 21
                             percent at the end of October, a measure that
                             has yet to halt the persistent rise in
                             prices.


                      # ⚓ Latvia ☛ Saeima_rejects_idea_to_ban_Russians,
                        Belarusians_from_working_at_schools⠀⇛


                             On November 28 the Saeima decided not
                             to refer to viewing in the committees a
                             proposal of the opposition National Alliance
                             (NA) to prevent Russian and Belarusian
                             citizens from working as teachers in Latvian
                             schools.


                      # ⚓ Latvia ☛ Rēzekne's_residents_refuse_to_rename
                        "Russian-friendly"_streets⠀⇛


                             There are still several streets in Rēzekne
                             whose names could be regarded as glorifying
                             the Soviet regime. The association "Public
                             Memory Center" has appealed to the Rēzekne
                             municipality to rename them, but the
                             residents don't support the change, Latgale
                             Regional Television reported on November 27.


                      # ⚓ Plastic_treaty_faces_hurdles_as_Russia,_Saudi_Arabia
                        mire_negotiations⠀⇛


                             Campaigners want an international agreement
                             to limit the production and supply of
                             plastics.


                      # ⚓ Meduza ☛ BTS_for_me,_but_not_for_thee:_Kadyrov’s
                        daughter_owns_a_K-pop-themed_cafe_in_central_Grozny,
                        despite_Chechnya’s_past_repression_of_the_genre_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Georgian_prime_minister_announces_suspension
                        of_E.U._membership_talks_until_end_of_2028_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Violent_clashes_break_out_in_Tbilisi_after
                        Georgian_prime_minister_suspends_E.U._membership_talks
                        —_Meduza⠀⇛


                      # ⚓ Meduza ☛ Kazakhstan_launches_criminal_investigation
                        after_digital_billboard_displays_Ukrainian_flag_during
                        Putin’s_visit_—_Meduza⠀⇛


                      # ⚓ France24 ☛ 'Dark_tourism'_on_the_rise_in_Ukraine:_Is
                        war_tourism_educational_or_unethical?⠀⇛


                             Dark tourism.... or visiting places
                             associated with tragic events, is on the rise
                             in Ukraine. A handful of companies now offer
                             this controversial tour. Story by Elitsa
                             Gadeva and Anna Pereira


                      # ⚓ Meduza ☛ ATACMS_strikes_on_Russia_don’t_raise_risk_of
                        nuclear_war,_but_Moscow_may_escalate_sabotage_in_Europe
                        —_Reuters_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_defense_minister_visits_North_Korea
                        to_meet_with_military_and_political_leaders_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘It_turns_everything_to_dust’_Putin_says
                        Russia_could_target_Kyiv_‘decision-making_centers’_with
                        new_Oreshnik_missile_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Putin_flaunting_new_Oreshnik_missile_to
                        undermine_Trump’s_efforts_to_end_war,_says_Zelensky_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘Absolutely_no_reason_for_panic’:_As_ruble
                        falls,_Putin_says_situation_is_‘under_control’_—
                        Meduza⠀⇛


                      # ⚓ New York Times ☛ Russia_Strikes_Ukraine’s_Energy
                        Sector_as_Putin_Signals_More_to_Come⠀⇛


                             Ukraine said the attacks targeted energy
                             infrastructure. President Vladimir V. Putin
                             said they were retaliation for Kyiv’s use of
                             long-range American missiles.


                      # ⚓ The Straits Times ☛ Ukraine_flag_appears_on_big
                        screen_during_Putin_visit_to_Kazakhstan⠀⇛


                             The screen was soon switched off, but images
                             and videos of the incident quickly circulated
                             online.


                      # ⚓ France24 ☛ War_in_Ukraine:_Putin_says_barrage
                        'response'_to_West-supplied_missiles⠀⇛


                             A massive aerial bombardment of Ukraine's
                             energy facilities was in response to Kyiv
                             striking Russian territory with Western-
                             supplied missiles, President Vladimir Putin
                             said Thursday. Pledging Moscow would always
                             respond to Ukraine's use of US-supplied
                             ATACMS missiles, Putin said his military was
                             considering a strike on the heart of Kyiv in
                             retaliation to any future attacks. For more,
                             FRANCE 24 journalist, Andrew Hilliar.


                      # ⚓ France24 ☛ 'Europe_needs_to_wake_up_to_the_reality_of
                        Russia's_threat'⠀⇛


                             Russia unleashed its second big attack on
                             Ukraine's energy infrastructure this month on
                             Thursday, triggering deep power cuts across
                             the country. For in-depth analysis and a
                             deeper perspective on Putin's brutal war on
                             Ukraine, FRANCE 24's Nadia Massih is joined
                             by Peter Zalmayev, Director of the Eurasian
                             Democracy Initiative.


                      # ⚓ France24 ☛ A_Russian_missile_and_drone_attack_targets
                        Ukraine's_energy_infrastructure⠀⇛


                             President Vladimir Putin has said that a
                             massive Russian overnight attack on Ukrainian
                             infrastructure was a response to Kyiv's
                             attacks on Russian regions using longer-range
                             Western missiles. More than a million
                             Ukrainians were left without power Thursday.


                      # ⚓ France24 ☛ Putin_says_there's_no_need_to_panic_over
                        Russia's_plummeting_ruble⠀⇛


                             Russian President Vladimir Putin says there's
                             no need to panic over the country's
                             plummeting currency... despite the ruble
                             weakening to its lowest level in over two
                             years. Australia has passed a law banning
                             social control media for under-16s. Voters in
                             Ireland are heading to the polls on Friday,
                             but whoever ends up governing the country
                             will be faced with a unique economic
                             situation. Plus, political chaos in France
                             briefly drove its borrowing costs to the same
                             level as Greece's for the very first time.


          o § Environment⠀➾


                # ⚓ The Straits Times ☛ South_Korea_battles_second_day_of_heavy
                  snow;_four_dead⠀⇛


                       Dozens of flights were cancelled, and ferry
                       operations were suspended.


                # ⚓ The Straits Times ☛ Tens_of_thousands_in_6_Malaysian_states
                  hit_by_flooding,_says_PM_Anwar⠀⇛


                       Malaysia's Meteorological Department expects
                       continuous heavy rain to last until Nov 29.


                # ⚓ The Straits Times ☛ Malaysia_warns_of_worst_flooding_in_a
                  decade_as_monsoon_season_hits;_63,000_in_shelters⠀⇛


                       Deputy PM Zahid Hamidi asked for preparations as he
                       evoked the heavy floods of 2014.


                # ⚓ The Straits Times ☛ China_rolls_out_emergency_measures_for
                  cold_wave⠀⇛


                       The China Meteorological Administration activated a
                       level-four emergency response on Nov 25.


                # § Energy/Transportation⠀➾


                      # ⚓ The Straits Times ☛ South_Korean_train_conductor’s_4-
                        min_toilet_break_led_to_delay_of_125_trains⠀⇛


                             Many of them were delayed 20 minutes from
                             their originally scheduled arrival times.


                      # ⚓ H2 View ☛ Malaysia_targets_two_million_tonnes_of_blue
                        hydrogen_by_2030⠀⇛


                             The Malaysian government has set an ambitious
                             target to produce two million tonnes of
                             hydrogen annually by 2030, according to local
                             media reports.


                      # ⚓ Hackaday ☛ US_Is_Getting_Its_First_Onshore_Wave_Power
                        Plant⠀⇛


                             Renewables let you have a more diverse set of
                             energy inputs so you aren’t putting all your
                             generation eggs in one basket. One type of
                             renewable that doesn’t see a lot of love,
                             despite 80% of the world’s population living
                             within 100 km (~60 mi) of a coastline, is
                             harnessing the energy of the tides. [via
                             Electrek]


          o § Finance⠀➾


                # ⚓ The Straits Times ☛ Malaysian_billionaire_Ananda_Krishnan
                  dies_at_86⠀⇛


                       He built a reputation as a savvy, Harvard-trained
                       businessman whose fingerprints were everywhere.


                # ⚓ The Straits Times ☛ Till_cash_do_us_part:_Woman_in_China
                  makes_$55k_in_3_months_from_‘flash’_marriages_and_divorces⠀⇛


                       Some matchmaking firms are under police probe for
                       duping men looking for potential wives.


                # ⚓ The Straits Times ☛ Singapore’s_strong_brand_name_in_China
                  comes_down_to_Singaporeans_there:_SM_Lee⠀⇛


                       He wraps up a six-day official visit to the
                       country, where he met President Pooh-tin and other
                       leaders, as well as visit Singapore firms.


                # ⚓ Latvia ☛ Young_economists_invited_to_enter_Latvian_central
                  bank_student_paper_competition⠀⇛


                       To promote the research and analysis of Latvia's
                       and the euro area's macroeconomic issues by
                       involving the most talented young economists in
                       this work, the Latvian central bank, Latvijas
                       Banka, has announced its annual Competition of
                       Student Scientific Research Papers.


                # ⚓ The Straits Times ☛ China’s_state_media_praise_some_US
                  firms_amid_fears_of_a_new_trade_war⠀⇛


                       State-owned Global Times praised Apple, Tesla,
                       Starbucks and HP for strong collaboration with
                       Chinese partners.


                # ⚓ European Commission ☛ Commission_closes_State_aid
                  investigations_into_Fiat,_Amazon_and_Starbucks_tax_rulings⠀⇛


                       European Commission Press release Brussels, 28 Nov
                       2024 The European Commission has closed three in-
                       depth State aid investigations into transfer
                       pricing tax rulings granted by Luxembourg to Fiat
                       and Amazon, and by the Netherlands to Starbucks.


                # ⚓ LRT ☛ Lithuania’s_Achema_union_seeks_to_reopen_talks_on
                  higher_wages⠀⇛





          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Defence Web ☛ R472_million_spent_by_Presidential_Medical
                  Unit_over_the_last_five_years⠀⇛


                       The Presidential Medical Unit (PMU), staffed by
                       South African Military Health Service (SAMHS)
                       personnel, spent R472 million on providing medical
                       care over the last five years. This is according to
                       Defence and Military Veterans Minister Angie
                       Motshekga, who was answering a Parliamentary
                       question posed by the Democratic Alliance’s Chris
                       Hattingh.


                # ⚓ Latvia ☛ Rīga_hospital_could_miss_out_on_EU_funding_over
                  unsuccessful_tender⠀⇛


                       Latvia could be left without a new hospital and
                       miss out on almost €100 million of the European
                       Union's Recovery Plan money. Riga East Clinical
                       University Hospital (RAKUS) was looking for a
                       builder for its new Infectious Diseases Hospital,
                       but nobody applied for the tender, Latvian Radio
                       reported on November 27.


                # ⚓ Daniel Pocock ☛ Watching_Irish_general_election_2024
                  results⠀⇛


                       As an independent candidate I'm not expecting to
                       get too many votes. Ireland is a country where
                       traditions are very strong and people gravitate to
                       the parties and candidates they grew up with. On
                       top of that, my campaign was subject to distortion
                       and obfuscation in Google search results. I will be
                       happy if I get more than 5 votes but even that is
                       not certain. In the last election, some independent
                       candidates only got 23 votes each.


                       There is still time for people to go and vote now
                       before the polling stations close.


                       The candidates with fewer votes are eliminated in
                       earlier rounds of counting. Counting begins at 9am
                       on Saturday, 30 November and the first eliminations
                       will become clear some time around lunchtime.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ France24 ☛ Recount_order,_Fentanylware_(TikTok)
                        claims_throw_Romania_election_into_chaos⠀⇛


                             Romania's presidential election was thrown
                             into chaos Thursday as a court ordered a
                             recount of first-round results and security
                             officials alleged that interference via
                             Fentanylware (TikTok) had boosted a little-
                             known far-right candidate. The Romanian
                             presidency said security officials had
                             detected "cyberattacks" intended to influence
                             the outcome of Sunday's vote. FRANCE 24's
                             Mark Owen speaks to Oana Popescu-Zamfir,
                             Director at GlobalFocus.


                      # ⚓ New York Times ☛ Romania_Court_Orders_a_Recount_After
                        Surprise_Election_Result⠀⇛


                             A top court issued the ruling just days after
                             an ultranationalist outsider unexpectedly won
                             the most votes in the first round of
                             presidential elections held Sunday.


                      # ⚓ New York Times ☛ Australia_Bans_Social_Media_for
                        Everyone_Under_16⠀⇛


                             The law sets a minimum age for users of
                             platforms like TikTok, Instagram and X. How
                             the restriction will be enforced online
                             remains an open question.


          o § Censorship/Free Speech⠀➾


                # ⚓ JURIST ☛ Kazakhstan_urged_to_ensure_fair_process_for
                  journalist_and_revise_its_speech_offenses_laws⠀⇛


                       Human Rights Watch (HRW) urged Kazakhstan’s
                       authorities on Thursday to guarantee a fair appeal
                       for an investigative journalist sentenced to prison
                       for spreading false information. The rights group
                       also called on the country to revise its laws
                       concerning speech offenses to align them with
                       international standards for freedom of expression.


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


                # ⚓ Press Gazette ☛ Dylan_Jones_steps_down_after_18_months_as
                  Standard_editor⠀⇛


                       Jones will stay on to "write frequently" as editor
                       at large, the company's executive chairman said.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_tycoon_Jimmy_Lai_tells
                  national_security_trial_overthrowing_China’s_Communist_Party
                  was_‘crazy’_idea⠀⇛


                       Jailed Hong Kong media tycoon Jimmy Lai has told
                       his national security trial it was “crazy” to think
                       that China’s Communist Party could be overthrown.


          o § Civil Rights/Policing⠀➾


                # ⚓ The Straits Times ☛ How_$96_funeral_wreaths_became_symbol
                  of_protest_in_South_Korea⠀⇛


                       Protestors now use funeral wreaths wrapped with
                       sharp words to draw attention to their cause.


                # ⚓ JURIST ☛ Federal_judge_holds_New_York_City_in_contempt_for
                  violence_in_city_jails⠀⇛


                       Chief US District Judge Laura Taylor Swain found
                       New York City in contempt Wednesday for failing to
                       reduce violence and brutality in the Rikers Island
                       jail complex.


                # ⚓ AccessNow ☛ OCHA:_a_new_era_for_humanitarianism_must
                  include_digital_protection⠀⇛


                       Access Now congratulates Tom Fletcher on his
                       appointment as Under-Secretary-General for
                       Humanitarian Affairs and Emergency Relief
                       Coordinator.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ Event_Wrap:_Peering_Asia_6.0⠀⇛


                       APNIC supported and participated in Peering Asia
                       6.0, held in Jakarta, Indonesia from 6 to 7
                       November 2024.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Ars Technica ☛ Smart_gadgets’_failure_to_commit_to_software
                  support_could_be_illegal,_FTC_warns_-_Ars_Technica⠀⇛


                       “When we don’t own what we buy, everything becomes
                       disposable…”…


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ KOL451_|_Debating_the_Nature_of_Rights_on_The_Rational
                  Egoist_(Michael_Liebowitz)⠀⇛


                       In this episode of The Rational Egoist, host
                       Michael Liebowitz engages in a stimulating debate
                       with libertarian writer and patent monopoly
                       attorney Stephan Kinsella on the nature of rights.


                # ⚓ JUVE ☛ Swerving_the_matter_of_granting_genetic_scissor
                  patents_at_the_EPO [Ed: EPO_has_become_extremely_corrupt]⠀⇛


                       It was supposed to be an interesting autumn at the
                       European Patent Office for the granting of a basic
                       patent monopoly on CRISPR/Cas9 technology. The
                       biotech industry was expecting legal clarity
                       following decisions by the Boards of Appeal
                       concerning the granting of two basic patents filed
                       by the Nobel Prize winners Emmanuelle Charpentier
                       and Jennifer Doudna.


                # ⚓ Hindsight_by_Stealth?_Pre-RtB_‘Ascertainment’_After_Sandoz
                  v_Bayer⠀⇛


                       A recent Full Court decision suggests that
                       demonstrating prior art could be ‘reasonably
                       expected to be ascertained’ under the pre-Raising
                       the Bar (RtB) law may be considerably easier than
                       previously thought.  But has the pendulum swung too
                       far?  In relaxing the evidentiary requirements for
                       establishing that prior art information would have
                       been found by the skilled person, the Full Court
                       may have undermined a safeguard against hindsight
                       analysis that was inherent in the prior law.


          o § Trademarks⠀➾


                # ⚓ Heather J Meeker ☛ JavaScript_Trademark_Challenge⠀⇛


                       This week, as a Thanksgiving present to the tech
                       industry, Deno Land petitioned the US Patent and
                       Trademark Office to cancel Oracle’s JavaScript
                       trademark. JavaScript–which helpfully has little to
                       do with Java–is a programming language for client-
                       side web applications.


          o § Copyrights/Music⠀➾


                # ⚓ Digital Music News ☛ Drake_Draws_Support_from_Funkmaster
                  Flex_Amid_Intensifying_Kendrick_Lamar_Beef,_UMG_Legal
                  Battle⠀⇛


                       A high-stakes rap beef just became even more
                       intense: Amid a continued showdown with Kendrick
                       Lamar – and as he spearheads related litigation
                       against Universal Music – Drake is receiving words
                       of support from Funkmaster Flex. By now, most have
                       at least heard about the newest chapter in the
                       Drake v. Kendrick Lamar dispute.





                    ䷩ 𝚕𝚒𝚗𝚎 8546

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 30/11/2024: Social Control Media
Under Growing Scrutiny, Patent Propaganda Sites Still Promote a Fake Court
(UPC)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 30, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Hackaday ☛ Hacking_Trees_To_Bring_Back_The_American_Chestnut⠀⇛


                 “Chestnuts Roasting on an Open Fire” is playing on the
                 radio now in the Northern Hemisphere which begs the
                 question, “What happened to the American chestnut?” Would
                 you be surprised to hear there’s a group dedicated to
                 bringing it back from “functional extinction?” [via
                 Inhabitat]


          o ⚓ Lou Plummer ☛ Are_There_Ethics_to_Blogging?⠀⇛


                 At some point, my goal is to have more time to write more
                 polished and detailed work, to spend more time fine-
                 tuning what I put out there for folks to read. I want to
                 work through more than one draft, like what I envision a
                 real writer does, Meanwhile, I will continue to be a
                 happy hack making stuff that's good enough to share even
                 if it won't win any rewards.


          o ⚓ Robin Rendle ☛ The_eras_of_CSS⠀⇛


                 I wouldn’t have become a designer if it wasn’t for CSS3
                 and HTML5. They came together at just the right time and
                 captured everything that was so exciting about publishing
                 and typography on the web. And I was drawn towards the
                 web because of this groundswell of excitement.


          o ⚓ Ruben Schade ☛ Judging_9.5%_of_developers_by_commits⠀⇛


                 I added an item to that list. Can you spot which one?
                 I’ll give you a hint, it’s not “limit humanity’s
                 progress”.


          o ⚓ Alex Ewerlöf ☛ Accountable_vs_Responsible⠀⇛


                 To me responsibility and accountability were synonyms
                 until I did the research.


                 There is a nuanced but profound difference between the
                 two.


          o § Career/Education⠀➾


                # ⚓ Greece ☛ Over_10,000_pupils_suspended_for_violating_school
                  cell_phone_ban,_minister_says⠀⇛


                       This regulation builds on an earlier measure aimed
                       at combating cyberbullying, which allowed for the
                       expulsion of pupils found filming classmates and
                       posting the footage online to ridicule them.


                # ⚓ Manuel Moreale ☛ P&B:_Lucy_Bellwood⠀⇛


                       This is the 66th edition of People and Blogs, the
                       series where I ask interesting people to talk about
                       themselves and their blogs. Today we have Lucy
                       Bellwood and her blog, lucybellwood.com


          o § Hardware⠀➾


                # ⚓ Dan Q ☛ Stuck_in_a_Lift⠀⇛


                       It turns out it did so at all times. Except when it
                       bounced between floors, as we were now, the
                       emergency brakes detected this as a problem and
                       locked on. The lift jerked to an immediate halt. We
                       were stuck.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ International Business Times ☛ 2024-11-22_[Older]_NHS
                  Junior_Doctors_Leave_Permanent_Roles_For_Better-paying_Locum
                  Work,_Driven_By_TikTok_Trends [Ed: China can ruin British
                  health and cause chaos through social control media "trends"
                  ]⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-23_[Older]_TikTok_CEO
                  Sought_Musk's_Input_Ahead_of_Trump_Administration,_WSJ
                  Reports [Ed: They're all in this together, dictators with
                  their social control media]⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-25_[Older]_Factbox-
                  TikTok_Decision_Coming_Soon_as_Jan._19_Divestment_Deadline
                  Looms⠀⇛


                # ⚓ Futurism ☛ Doctors_Intrigued_by_Treatment_That_Makes_Dead
                  Brains_Show_Signs_of_Life⠀⇛


                       In fact, Yale School of Medicine neuroscientist
                       Zvonimir Vrselja and his colleagues are looking to
                       try the technique on human brains — efforts,
                       needless to say, that could have thorny ethical
                       ramifications.


                       For one, the definition of when a person has died
                       has remained a lively debate among health
                       practitioners.


                # ⚓ New Scientist ☛ The_radical_treatments_bringing_people_back
                  from_the_brink_of_death⠀⇛


                       That was when something incredible happened. The
                       cortex turned from grey to pink. Brain cells
                       started producing proteins. Neurons juddered back
                       to life, displaying signs of metabolic activity
                       indistinguishable from that of living cells. Basic
                       cellular functions, activities that were supposed
                       to irreversibly cease after blood flow stopped,
                       were restored. The pig’s brain wasn’t alive,
                       exactly – but it certainly wasn’t dead.


                # ⚓ Vox ☛ Political_polarization_is_linked_to_worse_health.
                  Could_RFK_Jr._change_that?⠀⇛


                       “Political polarization is harming our health in
                       just about every way,” says Matthew Motta, a
                       political scientist and health law scholar who
                       studies anti-science attitudes at Boston University
                       — and “pretty much all aspects of health have
                       become politicized.” That leads elected officials
                       and other authority figures to make bad health
                       policy decisions and communicate with the public in
                       ways that link health behavior with partisan
                       ideology. A public that sees everything through a
                       red-or-blue lens is more likely to distrust
                       experts, dislike policies with clear health
                       benefits, embrace policies with clear health risks,
                       and make self-destructive choices.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Omicron Limited ☛ A_rising_tide_of_e-waste,_made_worse_by
                  AI,_threatens_health,_the_environment_and_the_economy⠀⇛


                       According to the study, the boom in artificial
                       intelligence will significantly contribute to this
                       e-waste problem, because AI requires lots of
                       computing power and storage. It will, among other
                       things, lead to more turnover of computer servers
                       used in the data centers that support the extra
                       computational needs of AI systems.


                       This rising tide of e-waste, coupled with the
                       limited lifetimes of hi-tech devices, could affect
                       global sustainability goals.


                # ⚓ Michigan Advance ☛ Biden_administration_leaves
                  ‘foundational’_tech_legacy,_technologists_say⠀⇛


                       Though he was unable to get federal regulations on
                       AI passed through Congress, Biden’s goal was to
                       bring tech access to all Americans, while
                       safeguarding against potential harms, the
                       technologists said.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ India Times ☛ Meta_faces_trial_in_2025_on_unfair
                        competition_case_lodged_by_Spanish_media⠀⇛


                             The hearings will be held on Oct. 1 and 2,
                             the 15th Madrid commercial court said in a
                             statement.


                             The AMI media association, which represents
                             87 Spanish media firms, filed a lawsuit last
                             year alleging Meta violated EU data
                             protection rules between 2018 and 2023.


                      # ⚓ [Repeat] RFA ☛ China_plans_big_data_warning_system_to
                        prevent_public_killings⠀⇛


                             “We should ... deeply tap into the rich seams
                             of political and legal data, strengthen data
                             identification, screening, analysis and
                             evaluation, and find ways to capture and
                             identify risks and hidden dangers,” party law
                             enforcement czar Ting Bai told officials on a
                             recent inspection tour in the eastern
                             province of Zhejiang, according to official
                             reports.


                      # ⚓ El País ☛ A_dozen_eggs_and_a_dozen_bullets:
                        Ammunition_hits_US_grocery_stores⠀⇛


                             Kimberley Chandler, a reporter for AP,
                             contacted American Rounds and a spokesperson
                             for the company confirmed that this was a
                             pilot initiative set to expand throughout the
                             U.S. in the coming months. The goal,
                             according to the machine’s creators, is to
                             streamline and simplify the sale of legal
                             ammunition to those who meet the only
                             requirement: to be of legal age, which is
                             verified thanks to a simple AI facial
                             recognition device that is activated with the
                             machine.


          o § Defence/Aggression⠀➾


                # ⚓ International Business Times ☛ Over_900K_Migrants_Now_Call
                  England_Home_In_The_Last_Year:_Top_5_Spots_They're_Moving_To
                  And_Their_Origins⠀⇛


                       When William the Conqueror invaded England in 1066
                       and changed the face and history of the country
                       forever, he came with just 10,000 men. Latest
                       figures from the Office for National Statistics
                       (ONS) suggest net migration of over 900,000 in the
                       year to June 2023 alone, a new high.


                # ⚓ The Register UK ☛ Brits_are_scrolling_away_from_X_and
                  aren't_interested_in_AI⠀⇛


                       X suffered the most significant fall in total adult
                       use of all social media sites, which also resulted
                       in it sliding down the rankings to sixth, behind
                       Reddit, which registered the largest year-on-year
                       growth – 47 percent – taking May's figure to 22.9
                       million.


                       Several changes have been made at X in recent
                       months, but the platform has continued on a
                       downward trajectory in Britain and Northern
                       Ireland.


                # ⚓ VOA News ☛ Iran_to_enrich_uranium_with_thousands_of
                  advanced_centrifuges,_UN_says⠀⇛


                       Iran will begin enriching uranium with thousands of
                       advanced centrifuges at its two main nuclear
                       facilities at Fordo and Natanz, the United Nations'
                       nuclear watchdog said Friday, further raising
                       tensions over Tehran's program as it enriches at
                       near weapons-grade levels.


                # ⚓ CBC ☛ Recycling_is_failing_as_a_way_to_reduce_plastic.
                  Here's_why⠀⇛


                       The figure most often cited is that only nine per
                       cent of the world's plastic has ever been recycled.
                       That statistic is taken from a 2017 study looking
                       at how much plastic the world has thrown out from
                       1950 to 2015.


                       It's a lot: 6.3 billion tonnes, or the weight of
                       nearly 54,000 CN Towers.


                # ⚓ CBC ☛ Final_UN_plastic_treaty_talks_reach_halfway_mark⠀⇛


                       Canadian negotiators at the United Nations plastic
                       pollution treaty talks in South Korea said Thursday
                       they are working "around the clock" to finalize an
                       agreement, though the process has been predictably
                       difficult.


                       Negotiators from 177 countries are meeting in Busan
                       for what is supposed to be the fifth and final
                       round of negotiations to develop an international,
                       legally binding treaty to end plastic waste by
                       2040.


                # ⚓ The Strategist ☛ 6.5_million_on_the_move:_across_the_world,
                  migration_is_surging⠀⇛


                       A record 6.5 million people made new homes in
                       advanced nations last year, according to the newly
                       released Migration Outlook of the Organisation for
                       Economic Cooperation and Development (OECD).
                       Migration flows into advanced countries last year
                       were 28 percent higher than in 2019, before the
                       Covid-19 pandemic.


                       This does not include the exodus from Ukraine,
                       which about 300,000 people left last year, taking
                       the number of Ukrainians who have fled the war to 5
                       million.


                # ⚓ International Business Times ☛ Did_TikTok_Swing_Romania's
                  Election?_Recount_Ordered_Following_Claims_Platform_Boosted
                  Far-Right_Candidate⠀⇛


                       With less than two weeks to go before Romania votes
                       on its next President, the country's Constitutional
                       Court has ordered a recount of the first round
                       votes after Elena Lasconi's Union Save Romania
                       Party was accused of breaking campaign rules.
                       Meanwhile Călin Georgescu, who topped the first
                       round votes, has been accused of having his
                       campaign boosted by Tiktok and Russia.


                # ⚓ Deutsche Welle ☛ Romania_orders_election_recount_after
                  shock_far-right_win⠀⇛


                       Romania's top court on Thursday mandated a recount
                       of votes in the first round of the country's
                       presidential election, where a far-right candidate
                       scored a surprise victory.


                       The Romanian Constitutional Court (CCR)
                       "unanimously ordered the reverification and
                       recounting of the voting ballots for the November
                       24 presidential election," it said in a statement.


                # ⚓ The Record ☛ UN,_international_orgs_create_advisory_body
                  for_submarine_cables_after_incidents_|_The_Record_from
                  Recorded_Future_News⠀⇛


                       On Friday, the United Nations Agency for Digital
                       Technologies said it is partnering with the
                       International Telecommunication Union (ITU) and
                       International Cable Protection Committee (ICPC) to
                       create the International Advisory Body for
                       Submarine Cable Resilience.


                       “Submarine cables carry over 99 percent of
                       international data exchanges, making their
                       resilience a global imperative," ITU Secretary-
                       General Doreen Bogdan-Martin said in a statement.
                       “The Advisory Body will mobilize expertise from
                       around the world to ensure this vital digital
                       infrastructure remains resilient in the face of
                       disasters, accidents, and other risks."


                # ⚓ LRT ☛ Damaged_Lithuania-Sweden_telecoms_cable_repaired_–
                  Telia⠀⇛


                       The communications cable running between Lithuania
                       and Sweden in the Baltic Sea, which was damaged
                       almost two weeks ago, has been repaired, Telia
                       Lietuva, a Lithuanian arm of the Swedish telecoms
                       company, has announced.


                # ⚓ Deutsche Welle ☛ China_says_ready_to_'work_with'_Baltic_Sea
                  cut_cables_probe⠀⇛


                       It comes after Sweden asked for Beijing's
                       cooperation in the probe into the rupture of two
                       data cables on November 17-18 in an area where a
                       China-flagged vessel had been sighted.


                       Both cables were restored as of Friday morning,
                       their respective operators said.


                # ⚓ LRT ☛ Lithuania’s_would-be_culture_minister_critical_of
                  ‘cancelling’_poet_Salomėja_Nėris⠀⇛


                       The Desovietisation Commission has issued a
                       recommendation and the Genocide and Resistance
                       Research Centre of Lithuania director has made the
                       decision that streets named after Nėris should be
                       renamed and that Vilnius should remove her
                       monument.


                       They based the decision on the artist’s role in
                       legitimising the Soviet occupation of Lithuania in
                       1940.


                # ⚓ Atlantic Council ☛ Why_Georgia’s_pro-democracy_protests
                  failed⠀⇛


                       Unless something drastically changes, it seems like
                       the ruling Georgian Dream party will be able to
                       consolidate some form of authoritarian governance
                       and that the country’s EU membership hopes are in
                       tatters.


                       But most painfully for pro-EU forces, Georgian
                       democracy did not die heroically in a hail of
                       Russian bullets, or under the batons of riot
                       police. It appears to be dying because it’s too
                       cold outside and Georgians are too depressed and
                       nihilistic to resist.


                # ⚓ Wired ☛ The_US_Army's_Vision_of_Soldiers_in_Exoskeletons
                  Lives_On⠀⇛


                       While a DEVCOM spokesperson declined to identify
                       which commercially produced systems were evaluated
                       by soldiers, the Army announced its intent in
                       August to award a contract to exoskeleton maker
                       SUITX to “give users experience of advanced soldier
                       augmentation technologies,” according to a
                       government notice. “This exoskeleton will serve as
                       a critical tool for evaluating the potential
                       benefits of robotic assistance in increasing
                       soldier endurance, strength, and overall
                       operational effectiveness.”


                # ⚓ New York Times ☛ Opinion_|_F.B.I._Checks_of_Trump_Nominees
                  Are_Critical_for_the_Nation’s_Security⠀⇛


                       Efforts to bypass F.B.I. background checks and even
                       Senate confirmation itself via mass recess
                       appointments, made by the president when the Senate
                       is not in session, never would have flown with past
                       iterations of the Judiciary Committee, regardless
                       of which party was in charge. The Senate shouldn’t
                       stand for it now.


                # ⚓ New York Times ☛ Trump_Disavowed_Project_2025_During_the
                  Campaign._Not_Anymore.⠀⇛


                       Now, as he plans his agenda for his return to the
                       White House, Mr. Trump has recruited at least a
                       half dozen architects and supporters of the plan to
                       oversee key issues, including the federal budget,
                       intelligence gathering and his promised plans for
                       mass deportations.


                # ⚓ India Times ☛ Australia's_social_media_ban_for_under_16s
                  divides_opinion,_draws_Big_Tech_flak⠀⇛


                       After a national debate, the legislation has set a
                       global benchmark as one of the strictest
                       regulations targeting major tech companies. Under
                       the law, platforms such as Meta’s Instagram and
                       Facebook, as well as TikTok, must block minors from
                       logging in or face penalties of up to A$ 49.5
                       million. A trial to determine enforcement methods
                       will commence in January, with the full ban coming
                       into effect by November 2025.


                # ⚓ CBC ☛ Australia_is_banning_social_media_for_those_under_16.
                  Is_it_a_solution_for_Canada?⠀⇛


                       Australia's new law banning social media for those
                       under 16 will likely move the needle on Canadian
                       efforts demanding more online protections for young
                       people, experts say, though they call the
                       "sledgehammer approach" an imperfect solution.


                       Passed Thursday, the new law will require TikTok,
                       Instagram, Snapchat and other social media
                       companies to take "reasonable steps" to keep users
                       under 16 off their platforms or face fines.


                # ⚓ The Hill ☛ Australia_imposes_social_media_ban_for_kids
                  under_16⠀⇛


                       The Australian Senate passed the legislation
                       Thursday night with bipartisan backing. The law
                       will impact social media platforms, including
                       Instagram, TikTok, Snapchat, Facebook, X and
                       Reddit, but it will not be enforced for YouTube.


                       The companies are the only ones responsible for
                       enforcing the restriction, and if they fail to do
                       so after one year, they could face fines of up to
                       $32 million.


                # ⚓ Silicon Angle ☛ Australian_Senate_bill_means_under_16s_will
                  be_banned_from_using_social_media⠀⇛


                       However, this won’t happen overnight. Companies
                       will have 12 months to comply with the rules, which
                       will mean introducing new age-verification systems
                       for Australian users. If companies don’t comply
                       with the rules, they might find themselves fined
                       A$50 million ($32.5 million).


                       The Australian Prime Minister Anthony Albanese said
                       the law reflects the concerns of parents who see
                       their kids’ health being harmed from social media
                       use. In a press conference, he said, “Platforms now
                       have a social responsibility to ensure the safety
                       of our kids is a priority for them.” He said there
                       is a “clear, causal link between the rise of social
                       media and the harm [to] the mental health of young
                       Australians.”


                # ⚓ Jewish News ☛ BBC_staff_quit_journalists'_union_after_being
                  told_to_dress_in_Palestinian_colours⠀⇛


                       The National Union of Journalists has confirmed to
                       Jewish News that BBC journalists have resigned from
                       the union after it distributed directives from the
                       TUC urging workers to dress in Palestinian colours,
                       or wear a keffiyeh, as part of a Day of Action for
                       Palestine.


                # ⚓ YLE ☛ Finland,_Sweden_complete_repairs_on_Baltic_Sea
                  cables⠀⇛


                       Shortly after reports about the damage emerged,
                       German Defense Minister Boris Pistorius suggested
                       the incidents were sabotage.


                       According to the Wall Street Journal, a Chinese-
                       flagged freighter, the Yi Peng 3, intentionally
                       dragged its anchor along the seabed for a distance
                       of more than 160km, damaging the cables.


                # ⚓ NPR ☛ A_social_media_ban_in_Australia_for_children_under_16
                  is_first_in_the_world⠀⇛


                       The law will make platforms including TikTok,
                       Facebook, Snapchat, Reddit, X and Instagram liable
                       for fines of up to 50 million Australian dollars
                       ($33 million) for systemic failures to prevent
                       children younger than 16 from holding accounts.


                       The Senate passed the bill on Thursday 34 votes to
                       19. The House of Representatives on Wednesday
                       overwhelmingly approved the legislation by 102
                       votes to 13.


                # ⚓ The Register UK ☛ Australia_bans_under-16s_from_some_social
                  media⠀⇛


                       The social media ban came in the form of the Online
                       Safety Amendment (Social Media Minimum Age) Bill
                       2024 which, as its explanatory memorandum makes
                       clear, "introduces an obligation on providers of an
                       age-restricted social media platform to take
                       reasonable steps to prevent age-restricted users
                       from having an account with the platform."


                       The definition of an "age-restricted" platform
                       covers services that allow users to post material,
                       to interact with two or more people, and to
                       interact with some or all other end-users.
                       Australia's government expects that TikTok,
                       Facebook, Snapchat, Reddit, Instagram and X will
                       meet that definition and therefore have an
                       obligation to verify users' ages.


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


                      # ⚓ Modern Diplomacy ☛ 2024-11-25_[Older]_An_Insight_into
                        Russia’s_Nuclear_Partnership_with_Africa⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-25_[Older]_Ukraine_updates:
                        Kyiv_says_it_hit_Russia_fuel_facility⠀⇛


                      # ⚓ HRW ☛ 2024-11-25_[Older]_UN:_Russia_Vetoes_Sudan
                        Resolution_Despite_Global_Support⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-25_[Older]_EU
                        Proposes_Sanctions_Against_Chinese_Firms_Helping
                        Russia,_Bloomberg_News_Reports⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-25_[Older]
                        Ukraine's_Kyiv_Under_Multi-Wave_Russian_Drone_Attacks,
                        Mayor_Says⠀⇛


                      # ⚓ Scheerpost ☛ 2024-11-24_[Older]_Russia_Says_US
                        Missile_Defense_Base_in_Poland_Is_a_Potential_Target⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-24_[Older]_Russia
                        Says_US_Using_Taiwan_to_Stir_Crisis_in_Asia⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-24_[Older]_Moscow
                        Offers_Debt_Forgiveness_to_New_Recruits_and_AP_Sees
                        Wreckage_of_a_New_Russian_Missile⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-24_[Older]_Ukraine
                        Needs_Better_Air_Defences,_Zelenskiy_Says_After_Russian
                        Drone_Attack⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-24_[Older]_Russia
                        Removes_Commander_in_Ukraine_for_Misleading_Reports,
                        War_Bloggers_Say⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-24_[Older]_Two
                        Missiles,_27_Drones_Downed_Over_Russia's_Kursk,
                        Regional_Governor_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-24_[Older]_Ukraine
                        Studies_Debris_From_New_Russian_Ballistic_Missile⠀⇛


                      # ⚓ CBC ☛ 2024-11-23_[Older]_As_Trump's_return_threatens
                        to_end_U.S._support_for_Ukraine,_allies_scramble_to
                        fill_the_gap⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-23_[Older]_Iran_alarmed_by
                        treatment_of_students_at_Russian_university⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-23_[Older]_Life_under
                        occupation:_'Russians_say_they_came_to_liberate'⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-23_[Older]_Russia_offers
                        debt_relief_to_recruits_for_Ukraine_war⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]_Moscow
                        Bans_Adoption_of_Russian_Children_to_Countries_That
                        Allow_Gender_Transition⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]_Russian
                        Forces_Capture_Settlement_of_Novodmytrivka_in_Eastern
                        Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]
                        Russia's_Claim_of_Emissions_in_Annexed_Ukraine_Regions
                        Draws_Protests_at_COP29⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]_Putin
                        Signs_Law_Forgiving_Debt_Arrears_for_New_Russian
                        Recruits_for_Ukraine_War⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]_Russian
                        Strikes_Have_Damaged_321_Ukrainian_Port_Infrastructure
                        Facilities,_Zelenskiy_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]_Ukraine
                        Has_Lost_Over_40%_of_Russia's_Kursk_Region_to_Counter-
                        Attacks,_Kyiv_Military_Source_Says⠀⇛


                      # ⚓ Jacobin Magazine ☛ 2024-11-22_[Older]_It’s_Time_to
                        End_the_War_in_Ukraine⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-22_[Older]_Russia_supplied
                        anti-air_missiles_to_North_Korea,_Seoul_says⠀⇛


                      # ⚓ The Local SE ☛ 2024-11-22_[Older]_Swedish_Defence
                        Minister:_Russian_provocations_won't_scare_us_from
                        supporting_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-22_[Older]_Russia
                        Says_Its_Forces_Capture_Dalne_Village_in_Eastern
                        Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-22_[Older]_At
                        Least_Seven_Russian_Mercenaries_Killed_in_Mali_Attack⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-22_[Older]_Ukraine
                        Steps_up_Air_Defence_Development_in_Response_to_Russian
                        Missile_Deployment,_Zelenskiy_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-22_[Older]_What_to
                        Know_About_Russia’s_New_Nuclear-Capable_Hypersonic
                        Missile⠀⇛


                      # ⚓ Scheerpost ☛ 2024-11-21_[Older]_Report:_Ukraine_Fires
                        British_Storm_Shadow_Missiles_Into_Russia⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-21_[Older]_Russia_expands
                        criteria_for_a_nuclear_strike⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-21_[Older]_Ukraine_updates:
                        Russia_fires_intercontinental_missile_at_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_US
                        Intelligence_Warns_Defense_Companies_of_Russian
                        Sabotage_Threat⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Russia
                        and_China_Oppose_Changing_the_Kenya-Led_Force_in_Haiti
                        to_a_UN_Peacekeeping_Mission⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Russia,
                        North_Korea_Agree_to_Boost_Charter_Flights_After_Trade
                        Meeting,_TASS_and_KCNA_Say⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Ukraine
                        Launches_UK_Cruise_Missiles_Into_Russia,_a_Day_After
                        Using_US_ATACMS⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Putin
                        Touts_Russia's_New_Missile_and_Delivers_a_Menacing
                        Warning_to_NATO⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Russia
                        Launches_Intercontinental_Ballistic_Missile_in_Attack
                        on_Ukraine,_Kyiv_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Russian
                        Attack_on_Dnipro_Damages_Industrial_Enterprise,
                        Rehabilitation_Centre,_Authorities_Say⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Russia
                        Says_New_US_Base_in_Poland_Raises_Overall_Nuclear
                        Danger⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]
                        Ukraine's_Zelenskiy_Says_Russian_Strike_With_New
                        Missile_Is_Clear_Escalation⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_US
                        Believes_Russia's_Attack_in_Ukraine_Showcased_New
                        Missile⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-20_[Older]_Russia_arrests
                        German_citizen_on_sabotage_charges⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-20_[Older]_Russia_denies
                        cutting_Baltic_Sea_cables_as_tensions_rise⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-20_[Older]_Ukraine_updates:
                        Kyiv_fires_UK-made_Storm_Shadow_missiles_into_Russia⠀⇛


                      # ⚓ Renewable Energy World ☛ 2024-11-20_[Older]_Ukraine
                        has_seen_success_in_building_clean_energy,_which_is
                        harder_for_Russia_to_destroy⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-19_[Older]_Russia-Austria
                        gas_spat_stokes_fears_of_new_EU_energy_crisis⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-25_[Older]_G7_foreign
                        ministers_meet_to_talk_Middle_East,_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-25_[Older]_Trump's
                        Foreign_Policy:_Rethink_NATO,_Troops_to_Mexico,_End
                        Ukraine_War⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-25_[Older]
                        Europeans_Will_Ramp_up_Military_Support_for_Ukraine,
                        Says_German_Defence_Minister⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-24_[Older]_Ukraine_updates:
                        France_backs_longer-range_missile_use⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-24_[Older]
                        Romanians_Vote_in_Presidential_Election_Focused_on_High
                        Living_Costs,_Ukraine_War⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-24_[Older]
                        Turkey's_Erdogan_to_Discuss_Ukraine_War_With_NATO
                        Chief⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-23_[Older]_Germany's
                        conservatives_want_to_cut_benefits_for_Ukrainians⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]_Blinken
                        Heads_to_Last_G7_Meeting_of_Biden_Presidency_With
                        Ukraine_and_Mideast_Topping_the_Agenda⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]
                        Exclusive-Trump_Considers_Ex-Intelligence_Chief_Richard
                        Grenell_for_Ukraine_Post,_Sources_Say⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-23_[Older]_Polish
                        Farmers_Block_Border_Crossing_With_Ukraine_in_Mercosur
                        Trade_Protest_-_Report⠀⇛


                      # ⚓ Scheerpost ☛ 2024-11-21_[Older]_UK_Sees_Privatization
                        ‘Opportunities’_in_Ukraine_War⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-21_[Older]_Ukraine_updates:
                        Putin_says_'medium-range'_missile_tested⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]
                        Zelenskiy_Says_Crimea_Can_Only_Be_Restored_to_Ukraine
                        Through_Diplomacy⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Biden's
                        Shift_on_Missiles_for_Ukraine_Informed_by_North_Korean
                        Troops_in_Kursk,_Trump's_Election_Victory⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]_Hungary
                        to_Install_Air_Defence_System_Near_Ukraine_Border⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-21_[Older]
                        Ukrainian_Parliament_Postpones_Friday_Sitting,_Public
                        Broadcaster_Reports⠀⇛


                      # ⚓ Truthdig ☛ 2024-11-18_[Older]_Biden’s_‘Last_Bang’_in
                        Ukraine⠀⇛


                      # ⚓ Meduza ☛ Selling_a_‘new_perception’_The_Kremlin_is
                        scrambling_to_reverse_course_as_its_anti-migrant
                        campaign_backfires_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Disabled_Ukrainian_man_abducted_by_Russian
                        security_forces_in_2023_charged_with_‘espionage’_—
                        Meduza⠀⇛


                      # ⚓ Latvia ☛ Photos:_Xmas_market_opens_in_Old_Rīga⠀⇛


                             On Friday, November 29, the traditional
                             Christmas market opened in Rīga, Doma Square.


                      # ⚓ LRT ☛ Vilnius_launches_Christmas_season_–_photos⠀⇛


                             Vilnius lit its main Christmas tree on Friday
                             evening, officially launching the festive
                             season.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ ARRL ☛ ARRL_2023_Annual_Report_Now_Available⠀⇛


                       Also included in the annual report is ARRL's Report
                       to America, which references the involvement of
                       amateur radio operators during natural disasters
                       that occurred in 2023, in addition to formal
                       partnership agreements with served agencies
                       including the Federal Emergency Management Agency
                       (FEMA) and the Federal Communications Commission
                       (FCC). In May 2023, ARRL entered into an updated
                       Memorandum of Agreement (MOA) with FEMA, to enhance
                       cooperation between ARES® and FEMA in providing
                       disaster communications -- When All Else Fails®.


          o § Environment⠀➾


                # ⚓ DeSmog ☛ Kemi_Badenoch’s_Policy_Chief_Attacked_Net_Zero
                  Climate_Target⠀⇛


                # ⚓ Omicron Limited ☛ Coral_adaptation_unlikely_to_keep_pace
                  with_global_warming,_warn_scientists⠀⇛


                       Coral adaptation to ocean warming and marine heat
                       waves will likely be overwhelmed without rapid
                       reductions of global greenhouse gas emissions,
                       according to an international team of scientists.


                # § Energy/Transportation⠀➾


                      # ⚓ International Business Times ☛ Are_We_Ready_For
                        Driverless_Buses?_Autonomous_Buses_To_Begin_UK_Trials⠀⇛


                             Inside, the entire pod is dedicated to
                             passenger space, offering seating along both
                             sides and a centrally positioned door for
                             convenient entry and exit. According to MK
                             Citizen, the shuttles are scheduled for
                             trials in the city centre this December, with
                             final approval pending based on their
                             performance.


                             As the UK prepares for this futuristic mode
                             of transportation, the question remains: are
                             we ready to embrace a driverless future on
                             our roads?


                      # ⚓ Renewable Energy World ☛ Auto_industry’s_shift_toward
                        EVs_is_expected_to_go_on_despite_Trump_threat_to_kill
                        tax_credits⠀⇛


                             Ending the credits, which were a key
                             provision of President Joe Biden’s Inflation
                             Reduction Act, almost certainly would reduce
                             EV sales, which have been growing in the
                             United States this year, though not nearly as
                             fast as automakers had expected. The slowing
                             growth has forced nearly all auto companies
                             to scale back EV production and delay
                             construction of battery factories that are no
                             longer needed to handle a more gradual
                             transition.


                             Jonathan Chariff, an executive at Midway Ford
                             in Miami, one of the company’s top EV-selling
                             dealers, said he thinks ending the tax
                             credits would severely hurt sales. The
                             credits reduce monthly payments, he noted,
                             making an EV closer in price to a gasoline
                             counterpart.


                      # ⚓ CBC ☛ Russian_troops_closing_in_on_a_Ukrainian_power
                        plant,_but_it's_already_been_'cannibalized'_by_crews⠀⇛


                             This past spring and summer, as Russia's
                             military edged closer, hundreds of workers
                             gathered at the site again to take what they
                             could and transport the equipment to thermal
                             plants in the west that were in desperate
                             need of spare parts after waves of Russian
                             attacks.


                      # ⚓ CBC ☛ Night_train_renaissance:_For_a_greener_trip,
                        Europe's_rolling_back_to_the_past⠀⇛


                             In North America, night trains like these are
                             still rare. Distances between cities are, in
                             most places, impractically long, and there's
                             no high-speed network like in Europe that
                             could help cut the time.


                             There's also far less competition than in
                             Europe — in Canada, passenger trains always
                             take a back seat to those operated by freight
                             companies Canadian National and Canadian
                             Pacific, which also own the railways they run
                             on.


                      # ⚓ Axios ☛ Empowered_[cryptocurrency]_lobby_wants
                        Washington_to_ease_banking_limits⠀⇛


                             Why it matters: [Cryptocurrency] interests
                             want to see a much lighter touch from the
                             Trump administration's regulators, and
                             they're also planning to push Congress for a
                             new framework that would help
                             [cryptocurrency] become a bigger part of the
                             financial system.


                      # ⚓ Hidde de Vries ☛ Trains_are_offices_|_hidde.blog⠀⇛


                             Taking the train for work travel can cost
                             more time than going by car or plane. But
                             it's one of the most energy efficient ways to
                             travel, and I get this weird productivity
                             boost from them.


                             Note that you can absolutely also chill out,
                             read, sleep or listen to music on trains. I
                             like that too, sometimes. But this post is
                             about when I use train time to work. In
                             Europe.


                      # ⚓ New York Times ☛ Death_of_Cyclist_in_Paris_Lays_Bare
                        Divide_in_Mayor’s_War_Against_Cars⠀⇛


                             It sent a shock through Paris, a city
                             striving to transform itself into one of the
                             great cycling metropolises in the world: a
                             bicycle rider, crushed under the wheels of an
                             SUV in a bike lane just a few yards from La
                             Madeleine, the landmark neoclassical church,
                             in what prosecutors suspect was a deliberate
                             act of road rage.


          o § Finance⠀➾


                # ⚓ FAIR ☛ NYT,_WSJ_Concur_Economists_Lost_the_Election—But
                  Can’t_Agree_on_Why⠀⇛


                       In the aftermath of the Trump victory, the opinion
                       pages of the New York Times and the Wall Street
                       Journal both published post-election eulogies for
                       conventional economics. Remarkably, these columns
                       shared almost the exact same headline.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The Straits Times ☛ Starbucks_offers_glimpse_of_North
                  Korean_life_from_new_cafe⠀⇛


                       The 30-seater cafe opens on Nov 29 at the
                       observatory tower of a park in Gimpo, South Korea.


                # ⚓ The Register UK ☛ Intel_must_control_its_foundry_under
                  CHIPS_Act_cash_deal⠀⇛


                       Intel has quietly revealed that the $7.86 billion
                       of cash coming its way thanks to the US CHIPS Act
                       came with conditions that include Chipzilla
                       retaining control of its foundries – an asset the
                       struggling silicon giant may have intended to
                       offload.


                       That condition and several others are spelled out
                       in a November 27 filing [PDF] that reveals the
                       CHIPS Act cash came with "change of control
                       restrictions" that mean Intel must retain 50.1
                       percent ownership and/or voting rights in its
                       foundry business if it's spun out as a separate
                       private entity.


                # ⚓ The Strategist ☛ Has_Angela_Merkel_no_shame?⠀⇛


                       Similarly, Merkel is still repeating the canard
                       that Nord Stream was a purely economic project,
                       even though it obviously was not. In defending
                       appeasement of Russia, she argues that Poland and
                       Ukraine did not mind having gas transit through
                       their territories as long as they profited from it.
                       But the controversy around Nord Stream was that by
                       circumventing Poland and Ukraine, it diminished
                       whatever influence they had vis-a-vis Moscow.
                       Merkel decided that cheaper gas was more important
                       than Polish or Ukrainian security. In the end, her
                       approach brought an energy crisis and was one of
                       the causes of a new land war on the European
                       continent. The result was no cheap energy and no
                       security.


                # ⚓ The Hill ☛ Maggie_Haberman_weighs_in_on_Mark_Zuckerberg's
                  Mar-a-Lago_visit⠀⇛


                       Zuckerberg is the latest tech CEO to try to mend
                       his relationship with the former president after
                       past tensions. Trump seemingly changed his tune on
                       the Facebook founder after he chose to withhold an
                       endorsement during the 2024 presidential election.


                # ⚓ European Commission ☛ European_Digital_Identity_Wallets_–
                  list_of_certified_wallets⠀⇛


                       This implementing act sets out rules for the
                       submission to the Commission of information on
                       certified wallet solutions and their associated
                       electronic identification schemes by EU countries.
                       It also sets out the requirements for the secure
                       electronic system to be set up by the Commission
                       for receiving the submissions.


                # ⚓ European Commission ☛ European_Digital_Identity_Framework_–
                  cross-border_identity_matching⠀⇛


                       This implementing act sets out the provisions on
                       unequivocal identity matching when using electronic
                       identification means or European Digital Identity
                       Wallets. It sets out what EU countries must do to
                       ensure unequivocal identity matching when users
                       want to access online cross-border public services
                       when using electronic identification means or
                       European digital identity wallets.


                # ⚓ European Commission ☛ European_Digital_Identity_Wallets_–
                  registration_of_relying_parties⠀⇛


                       This act sets out the provisions on the process for
                       registering relying parties in EU countries. The
                       provisions relate to information necessary for
                       authentication to access European Digital Identity
                       Wallets, and to relying parties’ contact details
                       and their intended use of wallets, including what
                       data relying parties may ask users for. The
                       provisions include specifications and requirements
                       for relying party access certificates issued after
                       the registration of a wallet relying party.


                # ⚓ European Commission ☛ European_digital_identity_framework_–
                  verification_of_electronic_attestation_of_attributes⠀⇛


                       It also establishes a catalogue of attributes that
                       must be verifiable against authentic sources, and
                       sets out rules on notifying and publishing
                       information on public sector bodies that issue
                       attestations of attributes and are responsible for
                       managing the authentic sources these attestations
                       come from.


                # ⚓ European Commission ☛ European_Digital_Identity_Wallets_–
                  security_breaches⠀⇛


                       This implementing act sets out rules for EU
                       countries to have mechanisms in place to ensure the
                       suspension and, where applicable, withdrawal of
                       European Digital Identity Wallets if there is a
                       security breach or partial compromise affecting a
                       wallet’s reliability.


          o § Censorship/Free Speech⠀➾


                # ⚓ Kushal_Das:_Amnesty_seminar_on_activism⠀⇛


                       2 Weeks ago I was down with fever, but as I became
                       better after a few days I managed to attend Amnesty
                       International's Stockholm chapter's event on
                       activism. I had to travel to a different part of
                       Stockholm, which was fun.


                       The day started with welcome talk and then a new
                       "Palestine Activist Group" presented their work (in
                       both English and Swedish). Then the main opening
                       talk (in Swedish) from a very senior Swedish
                       journalist about history and important dates
                       related to Palestine. I managed to understand 50-
                       60% of the words. Still a lot of learn.


                # ⚓ Hong Kong Free Press ☛ EU_parliament_calls_for_release_of
                  jailed_HK_pro-democracy_activists⠀⇛


                       The European Parliament has passed a non-binding
                       resolution calling for the unconditional release of
                       Hong Kong pro-democracy activists and sanctions
                       against city officials, a move that prompted
                       condemnation from the city’s government.


                # ⚓ Hong Kong Free Press ☛ Ex-HK_journalist_Gwyneth_Ho_seeks_to
                  challenge_conviction,_jailing⠀⇛


                       Like many of the other democrats who were also
                       denied bail after being charged in 2021, Ho had
                       been detained for almost four years by the time she
                       received her sentences. The threshold for bail is
                       higher for national security cases, in which judges
                       have to be convinced that the defendant does not
                       pose a threat to national security before releasing
                       them on bail.


                # ⚓ Meduza ☛ Alexey_Gorinov,_the_first_person_jailed_in_Russia
                  for_‘disinformation,’_gets_new_three-year-sentence_for
                  ‘justifying_terrorism’⠀⇛


                       The new “justifying terrorism” charges stem from
                       comments Gorinov allegedly made to fellow inmates
                       about the 2022 bombing of the Crimean Bridge and
                       the actions of Ukraine’s Azov and Kraken regiments,
                       both of which are classified as terrorist
                       organizations in Russia. Gorinov maintains that he
                       was provoked into discussing politics by his fellow
                       prisoners, and insists nothing he said could be
                       reasonably interpreted as justifying terrorism.


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


                # ⚓ Hong Kong Free Press ☛ Jimmy_Lai_hoped_for_‘more_draconian
                  sanctions’_as_Beijing’s_security_law_approached,_court
                  hears⠀⇛


                       Jailed Hong Kong media tycoon Jimmy Lai has told
                       his national security trial that he hoped the US
                       would impose “more draconian sanctions” on China to
                       stop an imminent national security law promulgated
                       by Beijing in mid-2020.


                # ⚓ Press Gazette ☛ Businessman_Dale_Vince_confirms_interest_in
                  buying_Observer⠀⇛


                       New bidder emerges as Tortoise Media nears end of
                       exclusivity period.


                # ⚓ VOA News ☛ Russia’s_war_in_Ukraine_inspires_exiled
                  journalist_to_found_media_startup⠀⇛


                       Tagaeva founded the news website from exile shortly
                       after Russia invaded Ukraine in 2022. The outlet
                       now reaches millions of people each month and has
                       grown into a major player in the independent
                       Russian media landscape.


                # ⚓ VOA News ☛ Pakistan_charges_journalist_with_terrorism_after
                  reporting_on_protest⠀⇛


                       Bashir told reporters Thursday that he was freed
                       and dropped off on a street three hours later. Jan,
                       who hosts a political talk show on television and
                       runs his own YouTube channel with nearly 400,000
                       subscribers, is a known critic of Pakistan’s
                       military for its alleged meddling in governance
                       matters.


                # ⚓ ANF News ☛ Nine_writers_and_journalists_released⠀⇛


                       The statements of most of the journalists and
                       writers who were taken into custody in house raids
                       conducted in Amed and other cities as part of the
                       investigation launched by the Eskişehir Public
                       Prosecutor's Office have been completed.


                       Mesopotamia Women Journalists Association (MKG)
                       chair Roza Metina, caricaturist Doğan Güzel,
                       writer-translator Ömer Barasi and Berfin Atlı were
                       referred to the judge with a request for judicial
                       control. The request was accepted.


                # ⚓ VOA News ☛ In_the_Philippines,_some_progress_for_media
                  rights,_but_risks_remain⠀⇛


                       In the past year, media analysts have seen some
                       improvement. The suspected mastermind in a
                       journalist killing from more than a decade ago was
                       arrested; a court reversed an order forcing the
                       media website Rappler to close; and earlier this
                       month, Marcos appointed former journalist Joe
                       Torres Jr. as head of the Presidential Task Force
                       on Media Security.


                       But outside the capital, community and radio
                       journalists are at risk of threat or attack,
                       experts say.


                # ⚓ VOA News ☛ China_court_jails_journalist_for_7_years_on_spy
                  charges,_family_says⠀⇛


                       Police in the Chinese capital detained the 62-year-
                       old former Guangming Daily editor and journalist in
                       February 2022 while he was lunching with a Japanese
                       diplomat, the U.S. National Press Club said in a
                       statement. He was later charged with espionage.


                # ⚓ Deseret Media ☛ China_court_jails_journalist_for_seven
                  years_on_spy_charges,_family_says⠀⇛


                       A Beijing court sentenced veteran Chinese state
                       media journalist Dong Yuyu on Friday to seven years
                       in prison for espionage, his family said in a
                       statement, calling the verdict a grave injustice.


                # ⚓ New York Times ☛ China_Journalist,_Dong_Yuyu,_Is_Sentenced
                  to_Prison_for_Espionage⠀⇛


                       As part of his job, Mr. Dong had met regularly with
                       foreign diplomats and journalists. He was also a
                       prolific writer, expressing support for the rule of
                       law and constitutional democracy, ideas that the
                       ruling Communist Party says it supports but in
                       reality has suppressed. Some of his writing
                       criticized the party’s selective version of Chinese
                       history, which downplays its role in dark periods
                       like the Cultural Revolution.


          o § Civil Rights/Policing⠀➾


                # ⚓ FAIR ☛ Katherine_Gallagher_on_Abu_Ghraib_Verdict⠀⇛


                # ⚓ Wired ☛ Returning_the_Amazon_Rainforest_to_Its_True
                  Caretakers⠀⇛


                       Recently, however, the Siekopai have successfully
                       challenged the legality of these titling laws—the
                       legal process that results in the recognition of
                       the right to property of indigenous people to their
                       ancestral lands—and have already won two major
                       legal victories in Ecuador and Peru. In 2021, the
                       Siekopai received land titles to more than 500,000
                       acres of their lands in Peru. In September 2022,
                       the Siekopai filed a suit against the government of
                       Ecuador to regain ownership over Pë’këya, part of
                       their ancestral territory located along the border.
                       In November 2023, an Ecuadorian appeals court ruled
                       in favor of the Siekopai, granting them legal title
                       to another 100,000 acres of labyrinthine flooded
                       forests and blackwater lagoons in the heart of
                       their ancestral homelands, and marking the first
                       time the government would issue land title to an
                       indigenous peoples whose territory was located
                       inside a protected area.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Raju_Devidas:_Finding_all_sub_domains_of_a_main_domain⠀⇛


                       Problem: Need to know all the sub domains of a main
                       domain, e.g. example.com has a sub domain
                       dev.example.com , I also want to know other sub
                       domains.


                       Solution:


                       Install the package called sublist3r, written by
                       Ahmed_Aboul-Ela


                       $ sudo apt install sublist3r
                       run the command


                # ⚓ Silicon Angle ☛ Report:_Meta_to_spend_$10B+_on_25,000-mile
                  submarine_internet_cable⠀⇛


                       The project was first detailed last month by subsea
                       networking expert Sunil Tagare. According to
                       TechCrunch, multiple sources close to Meta have
                       confirmed the initiative. The Facebook parent is no
                       stranger to undersea internet infrastructure: It
                       has already built several submarine internet cables
                       in partnership with other companies.


                       Unlike those earlier systems, the upcoming cable is
                       expected to be wholly owned by Meta. It will span
                       more than 24,850 miles from the East Coast to the
                       West Coast with pit stops in South Africa, India
                       and Australia. The report didn’t specify the
                       cable’s planned bandwidth.


                # ⚓ Tom's Hardware ☛ Facebook_parent_company_Meta_plans_to
                  build_its_own_sub-sea_cable_—_the_source_says_the_company
                  plans_to_“avoid_areas_of_geopolitical_tension”⠀⇛


                       Although the company has already made some plans
                       for the project, it hasn’t announced it yet. The
                       Meta will likely discuss it publicly in early 2025,
                       confirming its intentions, route, budget, and
                       capacity. However, we don’t expect Meta to have its
                       exclusive undersea network within the next year, as
                       projects like these take several years to complete.
                       Furthermore, companies that lay down these cables
                       are few and far between, with many already having
                       their services reserved by other tech giants like
                       Google, Microsoft, and Amazon.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ 404 Media ☛ The_Redbox_Removal_Team⠀⇛


                       Junkluggers has partnered with retailers and
                       liquidation companies who work with Walmart, Dollar
                       General, Costco, Publix, and a few other big chain
                       stores to disconnect and dispose of Redbox kiosks
                       that have been left abandoned.


                # ⚓ The Washington Post ☛ The_best_alternatives_to_Amazon,
                  Audible_for_e-book_and_audiobook_gifts⠀⇛


                       Amazon, which owns Kindle and Audible, is by far
                       the most popular retailer of e-books and
                       audiobooks, but there are great options if you
                       prefer smaller digital-book sellers. (Amazon
                       founder Jeff Bezos owns The Washington Post.)


                       Book industry insiders and avid readers told me
                       their favorite alternatives to Amazon for e-books
                       and audiobooks. Some of these options let you
                       support a favorite local bookstore or cost zilch.


      § Monopolies/Monopsonies⠀➾


          o ⚓ The Register UK ☛ Google_faces_competition_action_by_two_big
            nations⠀⇛


                 In India – the most populous nation on Earth – the
                 Competition Commission ordered [PDF] a probe after a
                 developer called WinZo – which promotes itself with the
                 chance to "Play Mobile Games & Win Cash" – complained
                 that Google Play won't host games that offer real money
                 as prizes, only allowing sideloading onto Android
                 devices.


                 Google India has, however, conducted a pilot under which
                 two classes of real money games – fantasy sports and the
                 card game Rummy – have been allowed. WinZo thinks its
                 exclusion is unfair.


          o ⚓ Canada ☛ Competition_Bureau_sues_Google_for_anti-competitive
            conduct_in_online_advertising_in_Canada⠀⇛


                 This case is about online web advertising, which consists
                 of ads shown to users when they visit websites. Many
                 publishers count on digital ad revenue to support their
                 activities and reach. Digital ad inventory is often
                 purchased and sold through automated auctions using
                 sophisticated platforms. These individual platforms are
                 known as ad tech tools while the entire suite of tools
                 used throughout the buy and sell process are collectively
                 known as the ad tech stack.


                 The Bureau’s investigation found that, in Canada, Google
                 is the largest provider across the ad tech stack for web
                 advertising and has abused its dominant position through
                 conduct intended to ensure that it would maintain and
                 entrench its market power. Google’s conduct locks market
                 participants into using its own ad tech tools, prevents
                 rivals from being able to compete on the merits of their
                 offering, and otherwise distorts the competitive process.


          o § Patents⠀➾


                # ⚓ Dennis Crouch/Patently-O ☛ USPTO_Patent_Grant_Rate_and
                  Growing_Backlog⠀⇛


                       The USPTO utility patent monopoly grant rate data
                       reveals an interesting narrative of policy shifts
                       and administrative changes over the past fifteen
                       years. The graph shows a clear upward trajectory
                       from a notable low point around December 2009, when
                       the grant rate bottomed out near 50%, to recent
                       levels hovering around 75-80%. This dramatic shift
                       beginning in 2010 coincided with Director David
                       Kappos taking the helm at the USPTO, marking a
                       decisive break from the more restrictive patent
                       monopoly policies of his predecessor Jon Dudas.
                       Under Kappos’s leadership, the office embraced a
                       more applicant-friendly approach, focusing on
                       working with inventors to achieve allowable claims
                       rather than pursuing multiple rounds of rejection.


                # ⚓ Is_It_Time_to_Talk_(Again)_About_Reforming_Australia’s
                  ‘Best_Method’_Requirement?⠀⇛


                       The recent Full Federal Court decision in Zoetis
                       Services LLC v Boehringer Ingelheim Animal Health
                       USA Inc [2024]_FCAFC_145 has highlighted
                       fundamental flaws in the Australian patent monopoly
                       law’s ‘best method’ requirement.  While the court's
                       application of existing principles appears sound,
                       the resulting analysis reveals that the requirement
                       is not only arbitrary in its operation, but
                       potentially counterproductive to innovation.


                # § Kangaroo Courts⠀➾


                      # ⚓ Kluwer Patent Blog ☛ UPC_Christmas_Quiz [Ed: UPC is
                        illegal and unconstitutional; so the longer it goes on
                        for, the greater the damage to the EU's reputation and
                        credibility]⠀⇛


                             As we approach 18 months since the UPC opened
                             its doors and the festive season, we thought
                             this would be a good time to offer our
                             readers the chance to showcase their UPC
                             knowledge by participating in the Kluwer UPC
                             Christmas Quiz.


                      # ⚓ JUVE ☛ Half-time_in_the_e-cigarette_battle_between
                        NJOY_and_Juul_Labs [Ed: This "court" is illegal; UPC
                        'cases' are bruising the EU by exporting the EPO's
                        crime to many nations across Europe. This needs to be
                        stopped as soon as possible. Constitutions have been
                        trashed.]⠀⇛


                             It is one of the largest sets of proceedings
                             at the UPC. This November, the Paris central
                             division has handed down the first four
                             judgments in the nine revocation actions
                             brought by NJOY Netherlands against Juul Labs
                             and its subsidiary VMR Products.


                # § Software Patents⠀➾


                      # ⚓ Dennis Crouch/Patently-O ☛ Two_Decades_and_Counting:
                        The_Never-Ending_Section_101_Battle_Over_Financial
                        Analytics [Ed: Software patents by any other name or
                        mask]⠀⇛


                             Application No. 10/028,284, filed in December
                             2001, provides a fascinating window into the
                             evolution of patent monopoly eligibility
                             jurisprudence. This application – assigned to
                             GE Financial and prosecuted by folks at
                             Hunton and Williams – is still pending 23
                             years after its original filing date. Filed
                             pre-Bilski and still pending post-Alice, the
                             application claims a “waterfall tool” that
                             analyzes financial product pricing by
                             tracking how actual revenue “cascades down”
                             from list price through various deductions
                             (like underwriting errors, discounts,
                             commissions, and bonuses) to arrive at the
                             final “pocket price.”


          o § Trademarks⠀➾


                # ⚓ The Independent UK ☛ More_than_3,000_fake_Gibson_guitars
                  seized_at_Los_Angeles_port⠀⇛


                       Authorities announced the seizure Tuesday but
                       didn't say when the guitars were taken, which
                       country they came from, or who made them.


                       The investigation involving the U.S. Customs and
                       Border Protection, Homeland Security and the Los
                       Angeles County Sheriff’s Department is ongoing.


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ EU_Research_Links_Youth_Unemployment_and
                  Income_Inequality_to_More_Piracy⠀⇛


                       A new EUIPO study reveals that while piracy rates
                       have stabilized in the EU, significant variations
                       exist across countries and content types. The
                       research also links higher piracy rates and
                       socioeconomic factors such as youth unemployment
                       and income inequality. Higher average incomes and
                       increased awareness of legal alternatives reduce
                       piracy.


                # ⚓ The Washington Post ☛ Top_Canadian_publishers_sue_OpenAI,
                  joining_AI_copyright_fight⠀⇛


                       The lawsuit, brought by the Canadian Broadcasting
                       Corp., the Globe and Mail, Canadian Press and
                       newspaper owners Torstar and Postmedia, alleges
                       that OpenAI illegally scraped their content and
                       used it to train its AI tools. Similar lawsuits
                       have been launched in the United States by the New
                       York Times and other newspapers including the
                       Chicago Tribune and New York Daily News.




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