𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, March 25, 2025
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Generated Wed 26 Mar 02:49:23 GMT 2025
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2025/03/25/


╒═══════════════════ 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  -  After US Government Funding Cuts the Centralisation of the Web (Especially Certificate Authority Let's Encrypt) is at Risk

⦿ Techrights  -  Anticipated in 2018: Lilie James & Location tracking, Googlists complained

⦿ Techrights  -  European Patent Office (EPO) Illegally Turning to Slop Behind Closed Doors, Staff Objects to This Hidden Catastrophe

⦿ Techrights  -  Free Software Community Folks Are Closer Together Than the Cliques and Opportunists Rallying Around "Open Source" (Openwashing, Marketing, Conniving)

⦿ Techrights  -  Growing Poverty Rates in the United States of America (or Elsewhere) Beneficial to GNU/Linux Adoption

⦿ Techrights  -  IBM Layoffs in the United Kingdom (UK) in 2025

⦿ Techrights  -  IRC Proceedings: Monday, March 24, 2025

⦿ Techrights  -  Let Them Eat 'Apps'

⦿ Techrights  -  Linux Runs Almost Everything, But They Almost Never Tell You This (No Marketing Budget)

⦿ Techrights  -  Martinique: Windows Down to All-Time Low

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Roku Will 'Lead' Attempts to Abolish the Illegal and Unconstitutional Unified Patent Court (UPC), Which Represents EPO Corruption and Lobbyism Spreading Upwards Inside the EU

⦿ Techrights  -  The Open Source Initiative (OSI) Might Get 'Forked' Soon

⦿ Techrights  -  When Microsoft Folks Who Literally Strangle Women Try to Strangle Microsoft Critics

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2025/03/25/After_US_Government_Funding_Cuts_the_Centralisation_of_the_Web_.shtml
https://techrights.org/n/2025/03/25/Anticipated_in_2018_Lilie_James_Location_tracking_Googlists_com.shtml
https://techrights.org/n/2025/03/25/European_Patent_Office_EPO_Illegally_Turning_to_Slop_Behind_Clo.shtml
https://techrights.org/n/2025/03/25/Free_Software_Community_Folks_Are_Closer_Together_Than_the_Cliq.shtml
https://techrights.org/n/2025/03/25/Growing_Poverty_Rates_in_the_United_States_of_America_or_Elsewh.shtml
https://techrights.org/n/2025/03/25/IBM_Layoffs_in_the_United_Kingdom_UK_in_2025.shtml
https://techrights.org/n/2025/03/25/IRC_Proceedings_Monday_March_24_2025.shtml
https://techrights.org/n/2025/03/25/Let_Them_Eat_Apps.shtml
https://techrights.org/n/2025/03/25/Linux_Runs_Almost_Everything_But_They_Almost_Never_Tell_You_Thi.shtml
https://techrights.org/n/2025/03/25/Martinique_Windows_Down_to_All_Time_Low.shtml
https://techrights.org/n/2025/03/25/Over_at_Tux_Machines.shtml
https://techrights.org/n/2025/03/25/Roku_Will_Lead_Attempts_to_Abolish_the_Illegal_and_Unconstituti.shtml
https://techrights.org/n/2025/03/25/The_Open_Source_Initiative_OSI_Might_Get_Forked_Soon.shtml
https://techrights.org/n/2025/03/25/When_Microsoft_Folks_Who_Literally_Strangle_Women_Try_to_Strang.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2025/03/25/Gemini_Links_25_03_2025_Relaxation_Literary_Movements_and_Gemin.shtml
https://techrights.org/n/2025/03/25/Links_25_03_2025_Clownflare_s_Slop_and_Bounties_on_Fake_Patents.shtml
https://techrights.org/n/2025/03/25/Links_25_03_2025_Putin_Sends_Children_to_Battle_23andMe_Drowns_.shtml
https://techrights.org/n/2025/03/25/Links_25_03_2025_Terrace_Workbench_and_Spellcheck_in_LibreOffic.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 89

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/After_US_Government_Funding_Cuts_the_Centralisation_of_the_Web_.shtml
    Gemini version at https://techrights.org/n/2025/03/25/After_US_Government_Funding_Cuts_the_Centralisation_of_the_Web_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ After US Government Funding Cuts the
Centralisation of the Web (Especially Certificate Authority Let's Encrypt) is
at Risk⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


Related: (earlier this_year)


    * Moving_Away_From_Certificate_Authorities_(CAs)_Like_Let's_Encrypt_Means
      Taking_Away_From_the_US_Government_the_Power_to_'Censor'_Sites_by
      Revoking_Certificates
    * The_Linux_Foundation's_Certificate_Authority_(CA)_Let's_Encrypt_Hits_New
      Lows_in_Geminispace
    * Certificate_Authority_Let's_Encrypt_Falls_to_Only_0.4%_of_the_Total_in
      Geminispace
"Tor-backer OTF sues to save its funding from Trump cuts," the British news
site The_Register_reported_a_couple_of_hours_ago. Make no mistake about it,
this isn't about Tor per se. It's about a bunch of things and also about the
Linux_Foundation's Certificate Authority (CA) Let's Encrypt. What if it went
offline? What would happen to the Web and other services that rely on CAs (even
most of the_networks_for_IRC_in_2025)? As an associate put it, "what happens
when the plug is pulled on Let's Encrypt? It's not like Web browsers even allow
self-signed certificates any more. Centralization bites..."


Well, yes, and moreover, it was always that way. It started that way and over
time Web browsers became more hostile towards sites that do not 1) have
certificates AND 2) get certificates from particular vendors (a cabal of so-
called "trust"; trust us, you cannot truly trust them). Set aside clock-related
issues and other malarkey. It's a faulty "trust model" which is also flaky and
tends to cause more downtime than it saves people from scams (lots of false
alarms, little net gain). We've warned about it all along. Now they_try_to_do
the_same_to_software. Someone has told me: "I can no longer log into IRC
because there are no free clients available anymore."


Another person has just told me (in IRC): "for some reason IRC is blocked at my
dad's, so I need to use a web client there..."


They try to pull the plug on open protocols with decent encryption available
(unless it is outsourced to third parties, usually American or intelligence
allies of the US). It's_all_about_control_over_users. Do not assume that
because Let's Encrypt is here today (issuing certificates and sending out E-
mails) it'll also be here tomorrow. Let's Encrypt can die as fast as Voice of
America (VOA) or RFA. "The VOA site is now devoid of content," an associate
notes. "The void shall be filled_by_RT_et_al." was my reply. On the Web, many
sites are considered to be "liberal", so MElon and the Cheetos stand to gain
from disrupting everything. The anti-media rhetoric grew louder in recent
weeks, both in Hungary and in the US (also Turkey and Maharlika). █


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Elon_Musk_vs_Trump's_Son;_Certificate_for_Techrights
revoked;_When_he_realises_Gemini_doesn't_have_strict_enforcement_of_centralised
                                     CAs⦈_


    * Anticipated_in_2018:_Lilie_James_&_Location_tracking,_Googlists
      complained
    * Martinique:_Windows_Down_to_All-Time_Low


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⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼
⣿⣿⣦⣀⠀⠀⠀⣠⣴⣿⣿⡋⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣾
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣄⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣶⣤⣶⣤⡀⠀⠀⠀⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣶⣷⣿⡅⠀⢀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡂⠀⠀⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠭⣽⣿⣿⣿⣍⣿⣿⣿⣿⣧⣼⣿⣿⣿⡿⣶⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡿⢿⣿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⡿⠇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠉⣛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⠿⠿⠟⠛⠛⢿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⢠⡞⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣤⡀⠀⠀⠀⠀⢰
⠀⠀⠈⣿⣦⣤⣤⣄⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣸
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠃⠈⠛⠿⣶⣄⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⡿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⡿⠋⠁⠐⢺⣿⣿⣿⣿
⠀⢀⠀⠿⠟⠋⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠀⠘⠛⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢸⣟⡍⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣰⣾⣿⣿⣿⣿
⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⢀⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼
⣿⣿⣦⣀⠀⠀⠀⢀⣠⣾⣿⠿⠃⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣾
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣦⣀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣷⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣿⣶⣴⣶⣤⡀⠀⠀⠀⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣾⣷⣿⣇⠀⠀⣠⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠭⣽⣿⣿⣿⣍⣿⣿⣿⣿⣧⣼⣾⣿⣿⡿⣶⣿⣿⣿⣿⣿⣿⣶⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⡿⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠉⢛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⠿⠿⠟⠛⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⢀⡎⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⣾⣿⣿⣷⣽⣿⣿⣿⣿⣧⣤⣤⡀⠀⠀⠀⠀⣼
⠀⠀⠈⣿⣦⣤⣤⣄⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠙⠻⠿⣶⣄⣹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⡿⠛⠁⠐⢺⣿⣿⣿⣿
⠀⢀⠠⠿⠟⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠘⠛⠿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣟⠉⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰⣾⣿⣿⣿⣿
⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴
⣿⣿⣦⣀⠀⠀⠀⠀⢀⣠⣶⣶⠖⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣷⣦⡀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣿⣧⣴⣶⣤⡀⠀⠀⠀⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣾⣷⣿⣧⠀⠀⣠⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠭⣽⣿⣿⣿⣍⣿⣿⣿⣿⣧⣼⣾⣿⣿⡿⣶⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣟⠋⢛⣿⣿⡿⠿⢿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⠿⠿⠟⠛⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⣼
⠀⠀⠘⣿⣦⣤⣤⣄⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣽
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠙⠻⠿⣆⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⠟⠁⠀⠺⣿⣿⣿⣿
⠀⢀⠠⠿⠟⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢸⣟⡍⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⢠⣾⣿⣿⣿⣿
⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠀⢀⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠂⠀⣴⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼
⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣴⣦⡴⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⣿
⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣦⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⡚⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣍⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠈⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢀⣾⣿⣿⣿⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣠⣴⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⣽⣿⣿⣿⣭⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠟⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⡋⢙⣿⣿⡿⠿⢿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀
⠀⠙⠿⠿⢿⠟⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⣛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⢿⣷⣿⣿⣿⣮⣷⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⣼
⠀⠀⠘⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣿
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠻⢿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⠟⠁⠀⠚⣿⣿⣿⣿
⠀⢀⠠⠿⠟⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⢠⣾⣿⣿⣿⣿
⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⢀⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⣶⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴
⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣾
⣿⣿⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣭⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡘⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣅⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠘⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣿⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣆⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⠙⣻⣿⡿⠿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀
⠀⠙⢿⠿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣷⣿⣿⣿⣦⣶⣾⣿⣿⣿⢠⣤⣀⠀⠀⠀⠀⣸
⠀⠀⢘⣿⣦⣤⣄⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣀⠀⠸⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣽
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠛⠻⠿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠟⠋⠀⠚⣿⣿⣿⣿
⠀⢀⠰⠿⠟⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⠉⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⢠⣾⣿⣿⣿⣿
⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠁⠀⢀⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴
⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢯⣶
⣿⣿⣿⣿⣿⣷⣦⣤⣠⣴⣾⣿⣟⡁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⡜⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣅⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠘⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣿⡄⠀⢀⣤⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣠⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⣽⣿⣿⣿⣭⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⢧⣾⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⣛⠛⢻⣿⣿⠿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀
⠀⠻⢿⡿⢿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣾⣷⣿⣿⣿⣦⣴⣾⣿⣿⣿⢠⣤⣀⠀⠀⠀⠀⢸
⠀⠀⢘⣷⣦⣤⣄⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣀⣀⠀⠸⣷⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸
⠀⠀⠈⣿⣿⣿⣽⣿⠿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠻⠿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⠿⠋⠀⠚⣿⣿⣿⣾
⠀⢀⠰⠿⠟⠋⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣟⠉⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⢀⣾⣿⣿⣿⣿
⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⣀⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴
⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢯⣿
⣿⣿⣿⣿⣿⣶⣦⣄⣀⣠⣴⣾⡿⠟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢳⡜⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣍⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣄⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣬⣽⣿⣿⣿⣿⣦⣦⣶⣤⡀⠀⠀⠘⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣤⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣿⡄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⢧⣶⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢣⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠯⠛⠛⠻⣿⣿⡿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀
⠀⠻⢿⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⡟⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣷⣾⣿⣿⣦⣴⣶⣿⣿⣿⠁⢀⣀⠀⠀⠀⠀⢰
⠀⠀⢘⣷⣤⣤⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⣀⣀⠀⠸⣾⣿⣿⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠃⠀⠀⠀⢸
⠀⠀⠈⣿⣿⠻⣭⣾⠿⠋⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⡇⠈⠛⠿⢿⣆⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⠛⠁⠒⢷⣷⣿⣾
⠀⢀⠰⠿⠟⠃⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠉⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⣶⣿⣿⣿⣿
⣔⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⣈⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⣿⡿⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣾⣿⣧⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠯⣧
⣿⣿⣿⣿⣿⣾⣭⣌⣉⠙⣛⣿⣿⡿⣿⣿⣿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⡜⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣅⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣄⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣬⣿⣿⣿⣿⣿⣤⣴⣶⣦⡀⠀⠀⠘⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣿⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⣠⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣼⣾⣿⣿⣿⢧⣶⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡾⢿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠇⠀⠀⠀⠀⢷⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠻⠉⠛⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀
⠀⠻⢿⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣿⣾⣿⣿⣶⣴⣶⣿⣿⣿⠁⣀⣀⠀⠀⠀⠀⢰
⠀⠀⢘⣷⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠇⠀⠀⠀⠸
⠀⠀⠈⣿⣿⣯⣭⣿⠿⠋⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠇⠈⠛⠿⢿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⠟⠁⠐⢶⣷⣶⡾
⠀⢀⠰⠿⠟⠋⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠉⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⠀⠀⣴⣿⣿⣿⣧
⣔⡿⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⣈⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⢠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢸⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣿⣿⣧⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠿⣧
⣿⣿⣿⣿⣿⣾⣭⣌⣉⠙⢛⣻⣿⣯⣿⣿⣿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⣠⣦⣄⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣄⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣼⣿⣿⣿⣿⣿⣦⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣀⣴⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡠⢿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠻⢯⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀
⠀⠹⣿⠿⠿⠿⠟⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠸⠉⠟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣿⣶⣿⣿⣷⣤⣦⣼⣿⣿⡏⢀⣀⠀⠀⠀⠀⢰
⠀⠀⢐⣶⣄⣠⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⣀⣀⠀⠸⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠏⠀⠀⠀⢸
⠀⠀⠀⣿⣿⣋⣵⣿⠿⠃⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠃⠈⠛⠿⢿⣤⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⠟⠋⠐⢺⣿⣿⡿
⠀⠀⣐⠿⠛⠋⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⠀⠀⣰⣾⣿⣿⣧
⣀⡿⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⣀⣨⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠀⠀⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢹⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣿⣿⣥⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣣
⣿⣿⣿⣿⣿⣾⣭⣌⣉⠙⠛⢛⣛⡯⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⡅⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣟⣁⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣼⣿⣿⣿⣿⣷⣤⣶⣶⣦⡀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣇⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢀⣴⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣴⣦⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀
⠀⠙⣿⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⠉⠟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣿⣶⣿⣿⣷⣤⣶⣼⣿⣿⡟⠀⣀⡀⠀⠀⠀⢰
⠀⠀⠐⣶⣄⣠⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣀⡉⠀⠸⣷⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠀⠀⠀⢸
⠀⠀⠀⣿⣿⣩⣵⣿⠿⠃⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠁⠈⠛⠿⠷⣤⣤⡹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⠿⠋⠀⢺⣿⣿⡿
⠀⠀⣐⠻⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠐⠚⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⠀⢰⣾⣿⣿⣧
⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣆⣀⣨⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢻⣿⣿⣿⡋⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⡟⠛⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠿⣣
⣿⣿⣿⣿⣿⣾⣯⣌⣉⠙⠛⣛⣿⠋⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣽⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⡁⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠤⣿⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣿⣿⣿⣧⢀⢲⣿⣿⣿⣿⣾⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀
⠿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⢟⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣿⠈⠟⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⣧⣷⣾⣿⣿⣦⣐⣬⣿⣿⣿⠃⢀⡀⠀⠀⠀⢰
⠀⠀⠀⣤⣀⣀⣀⢠⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⡠⢿⠀⠸⣶⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠁⠀⠀⠸
⠀⠀⠀⢻⣍⠉⣥⣾⠿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠿⠆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⡿⠟⠁⠒⣿⣿⡿
⠀⠀⠠⠿⠛⠀⠉⠀⠀⠀⣿⣿⣿⠿⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠀⠀⢠⣾⣿⣿⣷
⣆⣼⠉⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣆⣀⣴⣿⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢹⣿⣿⣿⡉⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣾⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠿⣫
⣿⣿⣿⣿⣿⣾⣯⣌⣉⠙⢛⣿⣟⣫⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣦⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⡁⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣢⣾⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠬⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣿⣿⣿⣷⢀⡶⣷⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⢻⣿⣿⣟⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⢯⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠈⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⢰⣶⠀⠟⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⣧⣼⣾⣿⣿⣦⣐⣬⣿⣿⣿⠏⢀⡀⠀⠀⠀⠀
⠀⠀⠀⢈⠁⣀⣀⢀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡄⣀⣀⡈⡃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠓⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠇⠀⠀⠠
⠀⠀⠀⢻⡛⠋⣹⣮⠻⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠛⠷⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠘⠿⠿⣿⣿⣿⣿⣿⠟⠃⠰⢿⣿⡿
⡄⠀⠀⠾⠟⠀⠉⠀⠀⠀⣿⣿⡿⠿⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠻⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠂⠀⠀⣴⣿⣿⣿
⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣆⣀⣴⣿⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿
⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⢈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿
⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢹⣿⣿⣿⡉⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⣶⣿⣾⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠿⣿
⣿⣿⣿⣿⣿⣾⣯⣌⣩⣽⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣶⣤⣈⡁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠉⠛⢻⡷⠟⠋⠉⠉⠿⡿⢿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣦⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⡃⠀⠀⡀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⠤⣿⣿⣿⣯⣽⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⢀⣾⣷⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀
⠻⣟⣛⣿⣿⣿⣭⣭⣿⣿⣿⡿⣿⡿⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠟⢟⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⡄⠀⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⡧⢸⣶⣿⣿⣷⣄⣠⣭⣿⣿⡟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢩⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⣈⡃⠀⠸⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠃⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡟⠀⠀⠀
⠀⠀⠀⢸⡟⠛⢛⣵⠹⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠛⠷⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⡿⠋⠠⢾⣾⣶
⡆⠀⠀⠼⠟⠁⠉⠀⠀⠀⣿⣿⡿⠿⠟⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⢠⣾⣿⣿
⡧⢠⠆⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣆⣀⣴⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⢰⣾⣿⡟⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿
⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿
⡿⠇⠀⠀⠀⢀⣾⣦⠀⠀⣼⠃⠀⠀⢸⣿⣿⣿⣿⣭⣭⣭⡛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣧⠀⢀⣤⣴⣾⣿⠟⠀⠀⠈⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣿⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣺⣿⣶⡶⣿⣶⣿⣿⣤⣶⣭⣿⢛⣛⣟⣛⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡿⣿
⣿⣿⣿⣿⣿⣿⣯⣌⡉⠙⠛⠛⠛⠋⣿⣿⠿⠿⢿⢿⡿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢧⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⣿⣿⣿⣿⣿⡿⠛⠻⠃⠀⠀⠀⠀⠈⣽⣿⣿⣿⣦⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠋⠁⣤⢰⠃⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣍⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣦⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡀⢠⣾⣿⣿⡇⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⠤⣽⣿⣿⣮⣽⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⢀⣾⢷⣶⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀
⠻⢟⣛⣿⣿⣿⣭⣭⣿⣿⣿⡟⣻⣿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⢟⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⡄⠀⢟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣧⢠⣷⣿⣿⣿⣆⣀⣍⣿⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣈⡃⠀⠘⣷⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡿⠀⠀⠀
⠀⠀⠀⠸⣟⠛⢋⣥⠹⠃⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⠷⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠑⠻⠿⣿⣿⣿⣿⣿⡿⠛⠠⢶⣿⡶
⡆⠀⠀⠸⠟⠀⠉⠀⠀⠀⢿⣿⡿⠟⠛⠻⣿⣿⣿⡿⢀⣤⡄⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡯⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡏⠀⠀⢠⣾⣿⣿
⣷⢀⡎⣼⣦⠀⠀⠀⠀⠀⢸⣯⣶⡆⣠⣶⣿⣿⣿⣇⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿
⣿⣿⣠⣿⣿⠁⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⢈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠃⠀⠀⠸⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣟⡟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣥⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠻⠇⠀⠉⠛⠉⢻⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⣿⣿⣿⣇⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⢘⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡿⢿
⣿⣿⣿⣿⣿⣾⣭⣌⡉⠙⠛⠛⠛⠋⣿⣿⠿⠿⢿⢿⡿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢧⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠻⣿⠟⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣍⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣳⣦⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣼⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣿⣷⣿⣷⠀⠀⢀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣾⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣠⣿⣿⣿⣧⣼⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣆⣼⠿⣶⣾⣿⣿⣷⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⢿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀
⠻⢿⣛⣻⣿⣿⣯⣭⣿⣿⣿⣿⢟⣛⢿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⠛⡀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣷⠀⣷⣾⣿⣿⣦⣀⣤⣹⣿⣿⠃⢀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣈⣃⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠁⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⠂⠀⠀
⠀⠀⠀⠀⣟⠙⠛⣥⠙⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠁⠒⠿⢿⣿⣿⣿⣿⡿⠟⠁⠶⣿⣿
⡧⠀⠀⠰⠛⠀⠁⠀⠀⠀⢹⣿⠟⠛⠛⠛⣿⣿⣿⡿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢯⠉⠉⠛⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠀⠀⢀⣴⣿⣿
⣿⠀⡬⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡆⣠⣾⣿⣿⣿⣇⣀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣄⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣾⣿⣿⣿
⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣾⡏⢻⣿⣿⣦⡀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿
⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⣿⣿⣷⣄⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡾⢏
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⣾⣿⣷⣦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣆⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢟⣻⣿⣿⣿⣿⡄⢠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⣿⣿⣿⣷⣼⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣇⣼⡿⣶⣾⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⡿⠿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠛⢿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠛⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢶⣷⠀⣾⣾⣿⣿⣦⣄⣤⣹⣿⣿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡉⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠁⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠆⠀⠀
⠀⠀⠀⠀⣟⠛⠛⣡⠘⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⠿⢅⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⠒⠿⠿⣿⣿⣿⣿⣿⠟⠃⠴⣾⣿
⣷⠀⠀⠠⠛⠀⠀⠀⠀⠀⢹⣿⠟⠛⠛⠙⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠉⠉⠙⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠀⣴⣿⣿
⣿⠀⡴⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣆⣠⣾⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣾⣿⣿⣿
⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⡀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣷⣄⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡾⢟
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⠳⡸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣦⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⢶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⡆⠠⣾⣷⣿⣿⡀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣿⣇⣾⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⣽⣿⣿⣧⣼⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣇⣴⡿⣶⣶⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠛⡀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢤⣷⠀⣸⣮⣿⣿⣧⣀⣬⣹⣿⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠋⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⣀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⡆⠀⠀
⠀⠀⠀⠀⢲⠲⠲⢃⡜⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⠿⣿⡅⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠽⠿⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣿⣿⣿⡿⠋⢰⣶⣶
⣷⠀⠀⠀⠞⠃⠈⠉⠀⠀⢹⣿⡿⠛⠛⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠍⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠇⠀⠀⣠⣾⣿
⣿⡆⣠⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣆⣀⣴⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⣶⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⣶⣿⣿⣿
⣿⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣗⣶⡆⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠸⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣄⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣾⣿⣥⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣯⣿⢿
⣿⣿⣿⣿⣿⣾⣯⣌⡉⠙⠛⠛⠛⠋⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠀⢶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⡆⠀⣾⣷⣿⣿⡄⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣿⡇⣴⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣽⣿⣿⣧⣼⣿⣿⣿⣿⣧⣾⣿⣿⢿⣿⣇⣴⣿⢲⣶⣿⣿⣷⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⠟⡇⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⡃⠀⠀⠀⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢤⣿⠀⢸⣮⣿⣿⣧⣄⣬⣹⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠋⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣀⣀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⡖⠀⠀
⡀⠀⠀⠀⢸⠶⠶⢛⣜⠋⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣅⠀⠀⠈⠿⣿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣿⣿⡿⠟⢡⣶⣶
⣷⠀⠀⠀⠼⠓⠈⠉⠁⠀⢻⣿⡿⠛⠛⠛⢿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠷⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡍⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡇⠀⠀⢀⣼⣿
⣿⡆⢠⠂⠀⠀⠀⠀⠀⠀⠘⣿⣶⣆⣀⣴⣿⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⣴⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠠⣴⣿⣿⣿
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⢹⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣄⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣥⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣯⣌⡉⠙⠛⠛⠛⠋⣿⡿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣷⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣶⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠀⢰⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡇⠀⣶⣿⣿⣿⡄⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⢂⣼⣿⣿⣷⣾⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣇⣰⣿⢢⣶⣾⣿⣿⣾⣶⣤⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣸⣿⣿⣿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀
⠻⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠿⡇⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⡆⢠⣷⣿⣿⣷⣄⣠⣽⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢉⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣷⠀⠀
⡄⠀⠀⠀⢸⡟⠛⢛⣥⠛⣿⣿⣍⡛⢿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣧⠀⠀⠀⠻⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠶⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠳⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁⣴⣶
⣿⡄⠀⠀⠸⠿⠶⠛⠋⠀⢿⣿⡿⠟⠛⠛⢿⣿⣿⡟⠀⠀⠉⠙⠛⠀⠀⠀⠠⠿⣯⣀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡏⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡟⠀⠀⢀⣴⣿
⣾⡇⢀⡂⠀⠀⠀⠀⠀⠀⠈⣿⣶⣆⣀⣴⣿⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢴⣾⣿⣿
⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⡟⠛⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣆⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣶⣿⣧⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣯⣌⡉⠙⠛⠛⠛⠋⣿⡿⣿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⢀⣠⣀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣤⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⣶⣾⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡇⠀⣶⣿⣾⣿⡄⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣿⡇⣠⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢓⣂⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⡇⣰⣿⢇⣶⣾⣿⣿⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀
⠻⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⠿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠿⠇⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⢿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⣾⡆⢀⣷⣿⣿⣿⣤⣢⣬⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢡⣈⡀⢀⠀⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣷⠀⠀
⣄⠀⠀⠀⠘⡏⠉⢉⣵⠉⣿⣿⣭⡉⢿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣧⣴⣶⣦⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠴⠞⢋⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠓⠾⠿⣿⣿⣿⣿⣿⣿⠟⠁⣴⣶
⣿⡆⠀⠀⠸⠿⠓⠙⠉⠀⢿⣿⣿⠿⠛⠛⢿⣿⣿⡿⠀⠈⠉⠛⠛⠛⠻⠿⠿⢿⣯⣁⣐⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡍⠉⠛⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠀⠀⢀⣤⣿
⣾⣷⢀⡆⠀⠀⠀⠀⠀⠀⠈⢿⣷⣆⣀⣴⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢤⣾⣿⣿
⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿
⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣧⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⡿⢿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⢉⣻⣿⣿⣦⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣴⣶⣾⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⡛⠻⣿⣿⣿⣿⣧⠀⣾⣿⣾⣿⡅⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣾⣿⣿⣷⣷⣿⣿⣿⣿⣿⣼⣿⣿⣏⣿⣧⣠⣾⠇⣴⣾⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀
⠻⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣛⡻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⠿⣧⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⠿⣿⣿⣿⣤⣶⣦⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣾⡇⠀⣷⣾⣿⣿⣦⣰⣬⣿⣿⣿⠃⢀⠀⠀⠀
⠁⠀⠀⠀⠠⣌⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠆⠀
⣦⠀⠀⠀⠀⣿⡋⢉⣡⡎⢿⣿⣿⣛⢻⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣀⣀⢠⣼⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠡⠖⠊⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠑⠺⠿⢿⣿⣿⣿⣿⣿⠿⠋⢠⣶
⢿⣧⠀⠀⠀⠿⠓⠘⠛⠀⢸⣿⣿⡿⠿⠿⢿⣿⣿⣿⠇⠈⠛⠛⠻⠿⠿⠿⣿⣿⣿⠋⠉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⡏⠉⠙⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠀⠀⠀⣠⣾
⣼⣿⠀⡔⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⣀⣀⣴⣿⣿⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣴⣿⣿⠇⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠠⣶⣿⣿
⣿⣟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿
⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⣿⣿⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣿⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⡿⢿⡿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⢀⣴⣶⣤⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣧⠀⣾⣿⣾⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢳⣂⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣼⣿⣿⣟⣿⣧⢀⣾⡇⣴⣶⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀
⠻⠿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⢿⠀⠀⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣇⠀⣴⣼⣿⣿⣦⣐⣬⣿⣿⣿⠋⠀⡀⠀⠀
⡁⠀⠀⠀⠈⣌⡁⠀⠀⢹⣿⣿⣿⣯⣽⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠃⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⡆⠀
⣧⡀⠀⠀⠀⣿⠉⠉⣩⡌⢹⣿⣿⣛⢛⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠛⠉⠉⠡⠴⠊⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠑⠺⠿⢿⣿⣿⣿⣿⣿⡿⠋⢠⣶
⣾⣷⠀⠀⠀⠿⠓⠚⠛⠁⠸⣿⣿⣿⠿⠿⢿⣿⣿⣿⡇⠈⠛⠻⠿⠷⠀⠀⠀⣿⣿⠟⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡫⠉⠙⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠀⠀⠀⣠⣼
⣼⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⣀⣀⣴⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⣶⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣴⣿⣿⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⣴⣿⣿
⣿⣟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿
⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⠏⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⡟⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣿⣷⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⡿⠿⣿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣤⣄⣠⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣡⣄⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣷⠀⣴⣿⣿⣿⡅⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⣂⣰⣿⣿⣷⣶⣿⣿⣿⣿⣿⣼⣿⣿⡟⣿⣿⢀⣾⡇⣠⣶⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀
⠻⠿⣿⣿⣛⣿⣿⣿⣻⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⠯⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣭⣨⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣧⠀⢸⣾⣿⣿⣦⣔⣦⣽⣿⣿⡏⠀⡀⠀⠀
⡄⠀⠀⠀⠘⡉⠋⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡆⠀
⣷⡄⠀⠀⠀⣿⠶⠖⢲⡌⠻⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠛⠉⠉⡡⠤⠎⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠙⠾⠿⢿⣿⣿⣿⣿⣿⡿⠋⢠⣴
⠿⣿⠀⠀⠀⣿⠷⠔⠟⠃⠀⣿⣿⣿⡷⠿⠿⣿⣿⣿⡿⠀⠙⠻⠿⠿⠀⠀⠀⣹⣿⣿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡫⠉⠙⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡅⠀⠀⢀⣼
⣾⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣠⣾⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⣤⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⣴⣾⣿⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠠⣤⣾⣿
⣿⣟⣶⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠿
⡿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣿⣿⡏⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣿⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣔⣶
⣿⣿⣿⣿⣿⣿⣯⣬⣉⠙⠛⠛⠛⠋⣿⡿⠿⣿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣣⣆⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣷⠀⣴⣿⣿⣿⣇⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣂⣸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣼⣿⣿⡟⣿⣿⢀⣾⡇⢠⣶⣿⣿⣷⣷⣶⣄⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀
⠻⠿⣿⡿⢿⣿⣿⣟⣛⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⢿⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣭⣬⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣧⠀⢸⣾⣿⣿⣶⣔⣶⣽⣿⣿⡏⠀⡀⠀⠀
⡄⠀⠀⠀⠘⡛⠋⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡗⠀
⢿⣄⠀⠀⠀⢾⢶⠶⠶⣘⠻⣿⣿⡻⠿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠛⠋⢉⣥⠴⠎⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠙⠾⠿⢿⣿⣿⣿⣿⣿⡿⠋⢠⣴
⠿⣿⠄⠀⠀⣼⠧⠀⠟⠋⠀⣿⣿⣿⡷⠾⠿⣿⣿⣿⣿⠀⠙⠛⠿⠿⠀⠀⠀⣹⣿⣿⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣿⡫⠉⠙⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡟⡁⠀⠀⢀⣼
⣶⣿⡇⣠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣠⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢤⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⣴⣾⣿⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢤⣾⣿
⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣼⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣿⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣬⣿
⣿⣿⣿⣿⣿⣿⣯⣬⣉⠙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣎
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣴⣶⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⡏⠽⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣧⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠱⣀⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⡟⣿⣿⣀⣾⡟⢰⣶⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⢀⣟⣻⣿⣿⣿⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⢿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠛⠿⣿⣿⣛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⢟⠀⠀⠘⠛⢿⣿⡿⠿⣿⣿⣿⣿⣿⠟⠃⠀⠀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣭⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣧⠀⢸⣶⣿⣿⣷⣤⣶⣾⣿⣿⡏⠀⣀⠀⠀
⣦⠀⠀⠀⠈⣉⠉⠀⠁⠈⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡟⠀
⣻⣦⠀⠀⠀⢾⡷⠶⠞⣜⠛⣿⣿⣟⡛⣻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠋⠉⣩⠵⠖⠋⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠑⠺⠿⢿⣿⣿⣿⣿⣿⠿⠋⠠⣶
⠋⣿⡇⠀⠀⠼⠗⠀⠚⠋⠀⢿⣿⣿⠿⠿⠟⢿⣿⣿⣿⠀⠈⠛⠛⠛⠻⠿⢿⣿⣿⡿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⣿⡯⠉⠙⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠁⠀⠀⢀⣴
⣿⣿⡇⣰⠀⠀⠀⠀⠀⠀⠀⢨⣿⣇⣀⣀⣠⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣴⣿⣿⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⢴⣾⣿
⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠻
⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣬⣉⡙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⡀⠀⠀⠀⠻⢿⣿⣷⣆⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠐⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣀⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⡍⠽⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣧⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⣿⣿⣤⣾⡟⢰⣶⣿⣿⣷⣾⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣟⣛⣿⣿⣿⡿⠿⢿⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⠿⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠻⠿⣿⣟⣛⣿⣿⣿⣭⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⠛⡀⠀⠘⠛⢿⣿⡿⠿⣿⣿⣿⣿⣿⠟⠃⠀⠀
⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣤⣤⣦⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣷⠀⢸⣾⣿⣿⣷⣤⣶⣾⣿⣿⡏⠀⣀⠀⠀
⣦⠀⠀⠀⠈⡈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡏⠀
⣻⣧⠀⠀⠀⢾⡷⠶⠟⣬⠋⣿⣿⣿⡛⣻⣿⣿⣿⣿⣿⡏⢿⣿⣿⣆⠀⣶⣼⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠋⢉⡭⠷⠒⠃⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠑⠺⠿⢿⣿⣿⣿⣿⣿⠿⠋⠠⢶
⠈⣿⡇⠀⠀⠼⠃⠀⠉⠉⠀⢻⣿⣿⠿⠛⠛⢿⣿⣿⣿⠀⠈⠉⠛⠛⠛⠻⠿⠿⣿⡿⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⡏⠉⠙⢛⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⠁⠀⠀⢠⣴
⣿⣿⠇⣰⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣀⣀⣠⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣴⣿⣿⡏⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⢴⣾⣿
⣿⣟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠻
⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣼⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣬⣍⡙⠛⠛⠛⠋⣷⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣴⣶⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⢠⣶⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⡿⠿⢿⣿⣿⡍⠿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣷⠀⠀⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢫⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣦⣾⡟⣰⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣟⣛⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠿⠟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠻⠿⣿⣟⣻⣿⣿⣿⣭⣿⣿⣿⣿⢿⣻⡻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⢻⠀⠀⠘⠛⣿⣿⡿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣤⣶⣦⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠠⣾⣧⠀⣸⣾⣿⣿⣶⣤⣶⣿⣿⣿⡇⢀⣀⠀⠀
⣆⠀⠀⠀⠈⡉⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀
⣻⣦⠀⠀⠀⣿⡷⠶⢿⣌⠋⣿⣿⣿⡏⢽⣿⣿⣿⣿⣿⡏⢿⣿⣿⣷⣦⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢋⣭⡿⠿⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠑⠻⠿⢿⣿⣿⣿⣿⣿⠟⠋⠠⢶
⠉⣿⡄⠀⠀⠟⠋⠁⠉⠁⠀⢻⣿⣿⠟⠛⠛⢿⣿⣿⣿⠀⠀⠉⠉⠉⠛⠀⠈⠻⣿⠛⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡿⡍⠉⠙⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢛⡁⠀⠀⢠⣾
⣿⣿⠇⣴⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣀⣀⣴⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣶⣿⣿⠇⠀⠀⠀⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢶⣿⣿
⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠻
⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣟
⣿⣿⣿⣿⣿⣿⣿⣬⣉⡙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠣⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⢀⣾⣿⣶⣄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣯⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⡀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸⡿⠿⣿⣿⣿⡭⢿⣿⣿⣿⣿⡇⢐⣿⣿⣿⣿⣧⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢋⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢷⣿⣿⣄⣾⡇⣴⣶⣿⣿⣷⣷⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣞⣛⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣸⣿⣿⢿⠟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠻⠿⣿⣟⣻⣿⣿⣯⣭⣿⣿⣿⣿⢿⣛⡻⢿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠿⠀⠀⠘⠛⣿⣿⡿⠿⢿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣴⣶⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⡇⠀⣸⣾⣿⣿⣶⣤⣶⣿⣿⣿⡇⢀⣀⠀⠀
⡆⠀⠀⠀⠉⡉⠁⠈⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⠀
⣿⣆⠀⠀⠀⣷⡶⠶⣧⣜⠋⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⠇⢻⣿⣿⣆⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⣻⣿⡿⠛⠊⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⡿⠟⠋⠰⢶
⠉⣿⠀⠀⠀⠛⠀⠈⠉⠀⠀⢻⣿⡿⠛⠛⠛⢻⣿⣿⣿⠀⠀⠀⠉⠉⠁⠀⠈⠻⠿⠛⠹⣿⣿⣿⣿⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡿⡍⠉⠙⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⣏⠀⠀⠀⢠⣾
⣿⣿⠀⣴⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣀⣀⣴⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣴⣿⣿⠇⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢴⣿⣿
⣿⣯⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⢰⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠻
⡿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣬⣉⠙⠛⠛⠛⠋⣷⡿⠿⢿⣿⢿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠣⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⠀⠀⣠⣾⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡏⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣶⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⣿⡭⢿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣧⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢠⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢃⣀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⢳⣿⣿⣄⣾⡟⣴⣾⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⣿⣿⠿⠿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⢿⠟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀
⠻⠿⣿⢿⣿⣿⣿⣛⣿⣿⣿⣿⣿⠿⠿⠿⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⠀⠀⠙⢛⣿⣿⠿⠿⢿⣿⣿⣿⣿⠛⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠠⣾⡇⠀⣾⣾⣿⣿⣶⣤⣶⣽⣿⣿⠃⢀⡀⠀⠀
⡄⠀⠀⠀⠙⠋⠉⠁⠈⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡄⣀⣀⣀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠃⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠇⠀
⢷⡄⠀⠀⠀⡤⠴⠶⣆⠛⠃⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡇⠙⠿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⡿⠟⠁⠰⣶
⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠋⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠜⠁⠋⠁⠀⠀⠀⢸⣿⡍⠉⠛⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣋⠀⠀⠀⣠⣾
⣾⣿⢀⡴⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⡀⣴⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣴⣿⣿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠠⢶⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⢠⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠙⠻
⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⢻⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⢫
⣿⣿⣿⣿⣿⣿⣿⣬⣉⡙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣾⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠄⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⢻⠛⣛⠻⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⠀⠀⠀⢀⣠⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣶⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣿⠭⢿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⢇⣀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⢳⣿⣿⣆⣼⡗⣶⣾⣿⣿⣿⣶⣶⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⢿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀
⠻⢿⣿⢿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣋⣿⣿⣛⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⢿⠀⠀⠙⢛⣿⣿⠿⠿⢿⣿⣿⣿⣿⠛⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⣼⡇⠀⣿⣾⣿⣿⣷⣤⣶⣿⣿⣿⠁⢀⡀⠀⠀
⡀⠀⠀⠀⠛⠋⠉⠁⠉⣿⣿⢿⣿⣟⢛⣛⣿⣿⣿⣿⣿⡇⢀⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠃⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠃⠀
⢷⡀⠀⠀⠀⢤⢶⠶⠾⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢀⣴⣿⣯⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠰⣶
⠻⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣿⡿⠛⠉⠉⢙⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠫⠞⠋⠁⠀⠀⠀⢸⣿⠉⠉⠛⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠋⠀⠀⠀⣠⣾
⣾⣿⢀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣀⣀⣴⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣧⡘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⣴⣿⣿⠇⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⢶⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⣿⣿⣿⣿⣿⣎⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠙⠻
⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⣿⣿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠘⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣧⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⢋
⣿⣿⣿⣿⣿⣿⣿⣬⣉⠙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠄⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⢛⣟⣻⠿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⢠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⠭⢿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⢇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢳⣾⣿⣇⣰⣿⣶⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣼⣛⣻⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀
⠻⢿⡿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⠿⠀⠀⠙⢛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠛⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⡄⠀⠀⣿⡿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⣼⣧⠀⣷⣾⣿⣿⣶⣬⣶⣿⣿⣿⠁⣀⡀⠀⠀
⠀⠀⠀⠀⢛⠉⠉⠀⢸⣿⣿⡟⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣠⣤⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠃⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣧⡀⠀⠀⠐⡶⠞⠛⠚⠋⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣠⣾⣿⣽⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠴⣶
⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠛⠛⠛⢿⣿⣿⡏⢻⣿⣿⣿⣿⣿⠀⠈⠉⠙⠻⢿⣿⣿⣿⠀⠀⠀⠜⠴⠛⠋⠁⠀⠀⢁⢸⣟⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⣋⠀⠀⠀⣤⣿
⣾⣿⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢠⣾⣿⣿⣿⠀⠈⠉⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⣶⣿⣿⠃⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠠⣶⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠸⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠙⠻
⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣗⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣋
⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠛⣿⣿⣿⣿⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣇⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢳⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢱⣾⣿⣇⣰⣿⣶⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⣼⣛⣻⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀
⠻⠿⠟⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡟⠁⠀⠛⢛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠛⠀⠀⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣼⣧⠀⣷⣾⣿⣿⣷⣼⣶⣿⣿⣿⠁⣤⡀⠀⠀
⠀⠀⠀⠀⢿⡁⠈⠀⢸⣿⣿⡟⣻⣿⣿⣿⣯⣽⣿⣿⣿⣿⣆⣄⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠃⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⣦⠀⠀⠀⢸⣿⡟⠻⠘⠋⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⠤⠄⠀⢨⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⢀⣴⣾⣿⣝⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠁⢴⣶
⢻⣧⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⠀⠀⢀⢎⠴⠛⠋⠁⠀⠀⢁⢸⣟⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠁⠀⠀⠀⣤⣿
⣼⣿⢀⣴⣿⣿⣯⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⢀⣶⣿⣿⠃⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠠⣶⣿⣿
⣿⣯⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣿⣿⣿⣿⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠛⠻
⡿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⢻⣿⣿⡇⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣗⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠙⢻⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣹⡟⣃
⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣶⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣏⠩⢿⣿⣿⣿⣿⠀⢰⣿⣷⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣆⣠⣾⣿⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣱⣶⣿⡇⣠⡞⣤⣶⣿⣷⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⣸⣛⣻⣿⣿⣿⡿⢿⣯⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡿⣿⣿⣷⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀
⠿⠿⢟⣻⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⠟⠛⠀⠀⠛⠛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠛⠀⠀⠀
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⡿⣿⣿⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣠⣦⠀⣷⣾⣿⣿⣦⣴⣶⣿⣿⣟⠁⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠀⣹⣿⣿⡛⠋⢸⣿⢿⣿⣿⣿⣿⣿⠿⢋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀
⡄⠀⠀⠀⠘⠛⢟⣣⡝⠿⠋⠋⠀⢸⣿⣦⣀⢈⣤⣤⣶⣿⣿⡇⠻⢧⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣋⠀⠀⠀⣠⡴⡲⡉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠙⠳⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣤⣶
⢝⠆⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⣡⠴⠛⠉⠀⠀⠀⠀⢸⢟⠉⠙⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠀⠀⠀⠀⣠⣿
⣠⣧⠀⡀⠀⠀⠀⠀⢠⣄⡀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡾⠀⢠⣶⣿⣿⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠠⣴⣿⣿
⣿⣏⡾⠁⠀⠀⢀⣀⣼⣿⣧⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢉⣃⠀⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠹⠀⠀⠈⠛⢿
⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠰⡿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣃⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠠⢾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣇⠀⠀⠀⠘⣿⣿⣿⣿⠿⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣦⡀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣹⣿⣁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⡇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠻⠃⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⢰⠁⢿⣿⣿⣧⣿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢰⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⡿⠿⣿⣿⣏⠩⢿⣿⣿⣿⣿⠀⢰⣿⣷⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣂⣰⣿⣿⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣰⣾⣿⣇⣠⣞⣤⣴⣾⣷⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣛⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡿⣿⣿⣿⡯⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀
⠿⠿⢿⣻⣿⣿⣯⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⠿⠛⠁⠀⠛⠛⢿⣿⠿⠿⣿⣿⣿⣿⡿⠛⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠟⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⠁⣠⣦⠀⣷⣾⣿⣿⣦⣴⣦⣿⣿⡿⠁⢀⠀⠀⠀
⠀⠀⠀⠈⠋⠁⠁⠈⣿⣿⣿⡛⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠻⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀
⡀⠀⠀⠀⠐⢞⡛⣧⠟⣿⣿⠿⠇⠀⣼⣏⡛⠿⠿⠿⠟⠛⢉⣴⠹⣧⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⣏⡀⠀⢀⣠⠔⢚⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣤⣶
⢽⣆⠀⠀⠀⠈⠟⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⣶⣶⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⢚⣤⠾⠛⠁⠀⠀⠀⠀⢸⢟⠙⠙⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡿⠏⠁⠀⠀⠀⣠⣿
⣠⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣾⣾⡾⠀⢠⣾⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠄⠠⣴⣿⣿
⣿⠏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⣠⣽⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣉⢉⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠟⠀⠀⠈⠻⢿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⠀⢾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣇⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣸⡛⣁
⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⣿⣿⣿⡟⠻⣿⣿⣿⣿⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣦⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠻⠃⢸⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠙⢿⣿⣿⣷⣦⣤⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢠⣶⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠈⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣏⠩⢿⣿⣿⣿⣿⠀⢰⣿⣷⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣴⣾⣿⡇⣰⢞⣤⣴⣾⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣛⣻⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⡿⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀
⠿⡿⠿⣿⣿⣛⣛⣻⣿⣿⣿⣶⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⠻⠛⠀⠀⠛⠻⢿⣿⡿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡤⠀⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠀⣠⣆⠀⣦⣽⣿⣿⣦⣲⣦⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠈⠋⠉⠀⠙⣿⣿⣿⠛⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢿⣿⣿⣿⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⣀⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣷⠀⠀
⡀⠀⠀⠀⠰⠶⡶⣜⢻⣿⣳⣾⠆⠀⠀⠘⣿⣿⣿⣿⣿⣷⣾⣿⣿⠎⠁⠀⠀⢈⣿⣿⣿⣿⣿⡿⣋⠀⠀⢀⡤⣒⠛⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⢶⣾⡿⣿⣿⣿⣿⣿⡿⠟⠁⣴⣶
⣛⠄⠀⠀⠀⠸⠿⠋⠊⠙⠙⠋⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠟⢋⣵⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠐⢡⣴⠾⠛⠀⠀⠀⠀⠀⢸⡟⠙⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⠋⠁⠀⠀⠀⣠⣿
⣨⣧⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⣠⣴⣾⣿⡟⠀⠀⠀⠀⠙⠻⣿⣿⡿⣿⣿⡏⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⣾⡗⠀⢠⣾⣿⡿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣦⠀⢠⣾⣿⣿
⣿⢏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠛⠻⣿⣿⣿⡿⠁⠀⠀⠀⣀⣀⣀⣀⣉⠀⣈⢙⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣘⣿⣿⢃⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠟⠀⠀⠙⠻⢿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⣠⣴⣿⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣿⣇⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢪⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣿⣦⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⠛⣐
⣿⣿⣿⣿⣿⣶⣦⣄⡀⣽⣿⣿⣿⣿⣿⣿⣿⡀⣾⡏⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠿⠂⢾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢠⣶⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡿⣭⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⣡⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠈⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣏⠩⢿⣿⣿⣿⣷⠀⢰⣿⣿⢿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣂⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣴⣾⣿⡇⣠⢎⣤⣴⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢈⡛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⡻⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀
⠿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣴⡂⠀⠀⢰⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⠿⠛⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠇⣠⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⣠⣆⠀⣶⣯⣾⣿⣤⣶⣤⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠙⠉⢻⣿⣿⡟⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁⢿⣿⣿⣿⣿⣶⣾⣿⠇⠀⠀⠀⠀⠀⢀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡷⠀⢠
⡀⠀⠀⠀⠠⠴⢶⡸⢿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣷⣿⣿⣿⣟⣻⣯⣍⢻⣧⢶⣌⣿⣿⡿⢿⣿⡿⣋⠀⠀⢀⣤⣒⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⢴⣾⡿⣿⣿⣿⣿⣿⡿⠟⠁⣤⡶
⣻⠄⠀⠀⠀⢰⡿⠓⠉⠙⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣱⠄⠙⢿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠐⢡⣴⠿⠛⠀⠀⠀⠀⠀⣸⡟⠙⠛⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠁⠀⠀⢀⣼⣿
⣨⣧⠀⡴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⣋⣥⣶⣿⡏⠀⠀⠀⠈⠻⠿⠿⠿⣿⣿⡏⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⠀⢠⣾⣿⡿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣦⠀⢤⣾⣿⣿
⣿⣏⡾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠻⠖⣿⣿⣿⣿⡏⠀⠀⠀⣀⣀⣀⣀⣁⠀⣈⢙⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⢣⣀⣘⢿⣿⢃⡀⠀⣀⣉⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠟⠀⠀⠙⠻⢿
⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⣼⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢪⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣤⡀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⢋⣠
⣿⣿⣿⣿⣿⣶⣦⣄⡀⢺⣿⣿⣿⣿⣿⣿⣿⠀⣸⡟⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣀⢮⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡿⠁⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢸⣿⣨⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠴⠀⠀⠀⢰⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣯⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣂⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣶⣾⣿⡇⠰⢮⣤⣶⣾⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣧⣶⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣯⣼⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡿⡿⠋⠀⠘⠛⠻⣿⣿⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣽⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⢀⣤⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠁⣠⣆⢀⣦⣽⣿⣷⣦⣶⣤⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠛⠙⢻⣿⣿⡟⠋⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡟⠀⢸
⠀⠀⠀⠀⠠⠶⣖⡸⣿⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣟⣛⣿⣯⣼⠉⠀⣼⣿⣿⡿⢿⣿⡿⢋⠀⠀⢀⣤⣒⡻⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠛⢴⣾⡿⣿⣿⣿⣿⣿⡿⠛⠠⣴⡮
⡳⡄⠀⠀⡀⣿⡿⠃⠋⠛⠛⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⢋⣼⠁⠐⠿⣿⣿⣿⣿⣿⣿⣿⠀⡐⣡⣶⠾⠛⠀⠀⠀⠀⠀⣿⡟⠛⠛⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠁⠀⠀⢀⣼⣷
⣨⣦⢀⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⣛⣉⣴⣾⣿⠋⠀⠀⠀⠈⠙⢿⢿⣿⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣶⣿⡗⠀⢠⣾⣿⡿⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠀⢤⣾⣿⣿
⣿⢏⣞⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠙⠛⢻⣿⣿⣿⣿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣉⢛⣀⡀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣡⣀⣸⣿⣿⢁⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠏⠀⠀⠙⠻⢿
⣿⣿⠏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣠⣴⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢃⣧⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡄⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣦⣄⡀⣶⣾⣿⣿⣿⣿⣿⡆⠀⢸⡿⠁⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣴⣢⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠿⠀⠏⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⠁⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣧⣸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣠⣖⣸⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠘⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣏⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣂⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡟⣶⣾⣿⡇⣠⢮⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡸⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡂⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣯⣴⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⠿⠛⠀⠘⠛⠻⣿⣿⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣶⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⣠⣆⢀⣦⣥⣿⣷⣦⣒⣤⣿⣿⡟⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠛⠙⠉⢻⣿⣿⡟⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⢸
⠀⠀⠀⠀⢰⠶⣶⣸⢿⣿⣿⣷⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣽⣿⣷⠆⡍⠀⢈⣿⣿⣿⣿⣿⡿⢋⠀⠀⢀⣤⣶⣋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠛⢶⣾⡿⣿⣿⣿⣿⣿⠿⠋⠠⣴⡮
⡳⡄⠀⠀⢀⢾⡿⠏⠉⠛⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠟⣡⣾⠃⠀⠸⢿⣿⣿⣿⣿⣿⣿⠀⡐⣩⡴⠾⠓⠀⠀⠀⠀⠀⣿⡟⠛⠛⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠋⠀⠀⠀⢀⣼⣷
⣸⣦⢀⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⣉⣭⣤⣾⣿⣿⠋⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣶⣿⡇⠀⢠⣾⣿⡟⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠀⢤⣾⣿⣿
⣿⢏⣞⠨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠹⣿⣿⣿⡿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣉⢛⣁⡀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣠⣀⣸⣿⣿⢁⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠏⠀⠀⠙⠻⢿
⣿⣿⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⣶⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣽⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⡀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⡛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣦⣄⣠⣶⣿⣿⣿⣿⣿⣿⡄⠀⢸⡿⠁⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣩⣿⣶⡦⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠿⠀⠏⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⠁⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣧⣸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡧⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣠⣖⣸⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣽⣡⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠘⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⢿⡿⢿⣿⣿⣏⠩⢿⣿⣿⣿⣷⠀⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡟⣶⣾⣿⡇⡠⢮⣤⣶⣷⣶⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣟⣻⣿⣿⣿⣟⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢈⡿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⠿⡿⢿⣟⣿⣿⣛⣛⣻⣿⣿⣧⣖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣼⣿⣿⣿⣿⣿⣯⣭⣽⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⡟⠟⠀⠘⠛⠻⣿⣿⠿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⣠⣦⢰⣦⣥⣿⣷⣦⣖⣮⣿⣿⡏⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠙⠉⠉⠀⢹⣿⣿⠛⠁⠀⠀⠈⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⡟⠁⢿⣿⣿⣿⣷⣮⣽⣿⡇⠀⠀⠀⠀⠀⠀⢀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⢸
⠀⠀⠀⠀⢲⠞⠛⣣⡟⣿⢿⣾⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⡗⠀⢨⣿⣿⠿⢿⣿⣿⣏⠀⠀⢀⣠⠴⠊⠉⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠙⠑⣶⣿⡿⣿⣿⣿⣿⣿⠿⠋⠠⣴⡮
⡳⡄⠀⠀⠼⠓⠛⠛⠀⠁⠘⠁⠀⠀⠀⠀⠀⢈⣿⠛⠛⢛⣉⣤⣶⣿⣿⠃⠀⠈⠙⠿⣿⣿⣿⣿⣿⠀⡰⢋⡵⠞⠓⠀⠀⠀⠀⠀⣿⡛⠛⠛⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠟⠃⠀⠀⠀⢀⣼⣷
⣸⡄⢀⢺⣷⡤⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣶⣷⡇⠀⣠⣾⣿⡟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠀⢴⣾⣿⣿
⣿⢏⡞⢸⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠘⣿⣿⣿⠟⠀⠀⠀⣀⣀⣀⣀⣀⠀⣈⢉⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣠⣀⣸⣿⡿⢁⡀⠀⣀⣉⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠏⠀⠀⠙⠻⣿
⣿⣿⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣻⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠈⠉⣿⠉⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣿⣾⠇⠀⠀⠀⠀⣀⣴⣿⣿⣿⣄⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣻⠟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣉⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⣼⠏⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡈⣿⣤⣏⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠏⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣡⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⢿⠿⢿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡟⣶⣾⣿⡇⡠⢮⣤⣶⣶⣶⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣟⣛⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢈⡿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡄⠀⠀⠀
⠿⣿⣿⣛⣻⣿⣯⣿⣛⣿⣿⣿⣴⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣶⣿⣿⣿⣿⣿⣿⣿⣭⣽⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⡻⠛⠀⠘⠛⠻⣿⣿⠿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⣠⣦⢰⣦⣥⣿⣷⣦⣶⣦⣿⣿⡏⠀⡀⠀⠀⢠
⠀⠀⠀⠘⢉⠉⠁⠈⠀⣹⣿⡟⠋⠀⠀⠸⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣉⣥⠀⢿⣿⣿⣿⣷⣦⣽⣿⡇⠀⠀⠀⠀⠀⠀⣀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⢸
⠀⠀⠀⠀⢻⣟⠛⢚⣢⠛⣿⣷⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠛⠋⢰⣿⡿⠀⠈⣿⣿⡿⠿⣿⣿⣟⠀⠀⢀⣠⠴⠺⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠲⣶⣿⠿⣿⣿⣿⣿⣿⠿⠋⠠⣶⡮
⡳⡄⠀⠀⣼⠗⠐⠛⠋⠀⠀⠁⠀⠀⠀⠀⠀⠉⣯⣉⢉⣠⣴⣶⣿⣿⡿⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⠀⠠⢋⡡⠟⠋⠀⠀⠀⠀⠀⣿⡛⠛⠛⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠟⠃⠀⠀⠀⢀⣼⣷
⣸⡆⢀⢺⣷⡤⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣶⣷⡇⠀⣠⣾⣿⡟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⠀⢴⣾⣿⣿
⣿⢇⡏⠀⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢉⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣠⣀⣸⣿⣿⢁⡀⠀⣀⣉⢀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠏⠀⠀⠙⠻⣿
⣷⣿⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⢻⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣿⠉⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣿⣼⠁⠀⠀⠀⢀⣤⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⠟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣍⣿⣋⣸
⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⠃⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⠟⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⠃⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣲⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣣⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠘⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⢿⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣂⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣶⣶⣿⡇⡀⢮⣴⣶⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣤⡄⠀⣾⡻⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⣷⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣭⣽⣿⣯⣭⣝⣻⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣍⣹⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⠟⠛⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀
⠀⠈⠙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⣠⣦⢰⣤⣥⣿⣷⣤⣒⣬⣿⣿⡏⠀⠀⠀⠀⢠
⠀⠀⠀⠸⣿⣯⣄⠉⠀⠀⢀⣧⣿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⡆⢻⣿⣾⣿⣿⣯⣽⣿⡟⠀⠀⠀⠀⠀⠀⢀⣈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠘⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⢸
⠀⠀⠀⠀⣿⣿⣿⠉⠉⢁⡌⣻⠟⠀⠀⠸⢿⢿⡿⠿⠿⣿⣿⣷⣿⣿⣿⣿⠃⠀⢿⣿⣿⡿⣿⣿⠟⠀⠀⠀⣠⡴⠞⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠙⠙⣶⣾⠿⣿⣿⣿⣿⣿⠿⠋⢠⣴⣮
⡳⡀⠀⠀⣼⠿⠟⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠙⢻⣿⣿⣿⣿⠀⢀⠞⡩⠞⠊⠀⠀⠀⠈⠀⣿⡛⠛⠛⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠛⠉⠀⠀⠀⢠⣾⣷
⣹⡄⢀⠀⣿⣷⠤⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⡇⠀⣠⣾⣿⡟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠀⢴⣿⣿⣿
⣿⢳⡏⠀⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢈⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣠⣀⣸⣿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠇⠀⠀⠙⠿⣿
⣿⣿⠆⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣰⣇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠈⠉⣽⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⡀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣿⣄⣦⠀⠀⣤⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣻⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡟⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⠟⠄⢮⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣦⡀⠘⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣲⣆⣼⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣣⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠐⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀⠀⠀⠀⢿⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣶⣾⣿⡇⡠⢮⣤⣶⣷⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢨⣿⣿⣿⣿⣿⣿⣿⣿⡷⣐⣤⣤⣤⠀⠀⣾⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⣷⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣯⣭⣽⣿⣏⣍⣛⣻⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣛⣛⣇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⠟⠛⠃⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⣠⣦⢰⣤⣥⣿⣷⣦⣒⣬⣿⣿⡏⠀⠀⠀⠀⢠
⠀⠀⠀⠹⣿⣿⣯⡄⠉⠀⠀⢈⣥⡾⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⢹⣿⣾⣿⣿⣯⣽⣿⡟⠀⠀⠀⠀⠀⠀⢀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠇⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣏⠉⠉⣡⢘⡿⠂⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⣀⣤⡶⠯⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠙⠫⣶⣾⠿⣿⣿⣿⣿⣿⠿⠋⠠⣴⣯
⡳⠀⠀⠀⢸⡿⠿⠟⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢠⣝⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠼⡋⠖⠛⠉⠀⠀⠀⠀⣿⡟⠛⠛⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠟⠉⠀⠀⠀⢠⣾⣷
⣽⡄⢀⠀⢸⣿⡦⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⡇⠀⣠⣾⣿⡟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠀⢴⣿⣿⣿
⣿⢳⠇⠀⣼⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢈⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣠⣀⣸⣿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠇⠀⠀⠙⠿⣿
⣿⡿⠄⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣰⣇⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣽⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣄⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣿⣄⣶⡆⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣻⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⠏⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⠟⠀⠯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣦⡀⠈⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣲⣎⣨⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣹⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡆⠀⠀⢠⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣵⣣⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠐⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⡀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢀⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣶⡄⠀⠀⠀⢿⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣶⣶⣿⣇⠀⣤⣤⣾⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣦⠀⠀⠀⣰⡿⢿⣿⣿⣿⡿⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣛⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⠛⠛⠃⠚⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠁⣀⣦⢰⣤⣴⣿⣧⣄⣒⣌⣿⣿⠏⠀⠀⠀⠀⢀
⠀⠀⠀⠹⣿⣿⣿⣿⣤⠈⠁⠀⠀⣍⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⣿⣿⣿⣿⣯⣩⣿⣿⠀⠀⠀⠀⠀⠀⠀⣈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠘⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠇⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠁⠁⡈⣻⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣠⡴⡪⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠙⠫⣵⣾⠿⣿⣿⣿⣿⣿⠟⠋⠠⣶⣯
⡷⠀⠀⠀⠉⣽⡙⠿⠟⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⢠⠋⠓⠊⠉⠀⠀⠀⠀⣿⡟⠛⠛⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠟⠁⠀⠀⠀⣤⣿⣷
⣼⡄⢀⠀⠀⣿⣿⠦⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡇⠀⢠⣾⣿⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠀⢶⣿⣿⣿
⣿⢳⡇⠀⢀⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣡⣀⣸⣿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠃⠀⠀⠙⠻⣿
⣷⡿⠁⠀⣸⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣸⡇⠀⠀⠟⠀⠀⢀⣤⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣷⣄⢀⡾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣿⢋⣠
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⠀⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣼⣢⣤⣴⡆⢠⣿⣴⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⡿⣂⢾⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣧⣸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣤⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠺⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣧⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⣄⠀⠀⠀⢻⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣿⡀⢰⣿⣿⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣶⣾⣿⣇⢀⣤⣤⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠀⠀⠀⣰⣟⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⡿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣟⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣛⣻⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡾⠻⠛⠃⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⠁⣀⣦⢠⣤⣴⣿⣧⣄⣠⣈⣿⣿⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠨⣿⣿⣿⣿⣿⣤⠉⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣯⣭⣿⣿⠂⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⠃⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠉⠀⢀⠘⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣠⡴⡺⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠙⠫⢵⣿⢿⣿⣿⣿⣿⣿⠟⠁⠰⣶⣞
⡧⠀⠀⠀⠉⢸⣿⠛⠿⠏⠀⠐⠉⠀⠀⠀⠀⠀⠈⡽⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⠆⠀⠠⠊⠓⠂⠁⠀⠀⠀⠀⣿⡟⠛⠛⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠟⠀⠀⠀⠀⣴⣿⣷
⣽⡄⢐⠀⠀⢸⣿⡷⢤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡇⠀⢠⣾⣿⡿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⢾⣿⣿⣿
⡿⣱⠇⡀⠀⣾⣏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣡⣀⣸⣿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠃⠀⠀⠙⠻⢿
⢷⡿⠉⠁⢀⡟⠁⠀⣀⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣸⡄⠀⠀⠸⢀⣴⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣷⣄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⡛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣉⣿⠋⣀
⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣄⡀⠈⠀⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣻⣦⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⡿⠂⢼⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣧⣸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣦⣶⣠⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣏⣤⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣦⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⡀⠀⢀⣾⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣄⠀⠀⠀⢹⡿⠿⣿⣿⣯⠭⠿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡠⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣆⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣾⣿⡇⠀⣤⣤⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣿⡻⢿⣿⣿⡿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣛⣛⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡿⠛⠛⠁⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠁⢀⣶⣦⣤⣶⣿⣧⣀⣠⣙⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠡⣽⣿⣿⣿⣿⣿⣤⠈⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣍⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⠀⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠐⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⡴⠒⠉⠁⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠙⠻⢽⣿⣿⣿⣿⣿⣿⣿⠟⠁⠴⣶⣾
⢧⠀⠀⠀⠉⠉⣹⣿⠛⠿⠛⠀⠀⠈⠀⠁⠀⠀⠀⠹⠟⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣇⠀⠠⠚⠑⠊⠀⠀⠀⠀⠀⣿⡟⠛⠛⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠛⠁⠀⠀⠀⣴⣿⣷
⣿⡀⣐⠀⠀⠀⣿⣿⠗⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡗⠀⢠⣾⣿⡿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠰⢾⣿⣿⣿
⡿⣰⡷⠀⠀⢰⣿⣇⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⢣⣀⣘⢿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠃⠀⠈⠛⠻⣿
⢿⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣸⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣷⣄⢸⡿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣦⡀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣿⡛⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠈⠙⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⡿⠂⢸⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣦⣶⣠⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣇⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣀⣀⡀⠀⢀⣾⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣄⠀⠀⠀⢹⡿⠿⣿⣿⣿⠭⠿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣆⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣾⣿⡇⠀⣤⣤⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣿⡻⢿⣿⣿⡿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣛⣻⡃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡿⠛⠛⠁⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠁⢀⣶⣦⣤⣦⣿⣧⣀⣠⣙⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠨⣥⣿⣿⣿⣿⣿⣤⠈⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣍⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⠀⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠐⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⣠⠴⠒⠉⠁⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠉⠹⢭⣿⣿⣿⣿⣿⣿⣿⠟⠁⠴⣶⣾
⢧⠀⠀⠀⠉⠉⣹⣿⠙⠻⠛⠀⠀⠈⠀⠀⠀⠀⠀⠹⠟⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣇⠀⠠⠛⠑⠂⠁⠀⠀⠀⠀⣿⡟⠛⠛⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠁⠀⠀⠀⣴⣿⣷
⣵⡀⣐⠀⠀⠀⣿⣿⠗⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡗⠀⢠⣾⣿⡿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠰⣾⣿⣿⣿
⡟⣰⡷⠀⠀⢰⣿⣇⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣘⢿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠃⠀⠈⠛⠻⣿
⢿⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣸⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠈⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣷⣄⢸⡿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣦⡀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣿⡋⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠈⠙⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⡿⠂⢸⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢿⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣦⣶⣠⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣎⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⣀⠀⠀⣴⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⣴⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⢹⣿⠿⣿⣿⣿⡉⠽⣿⣿⣿⣿⡆⢠⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣌⠄⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢗⣂⣬⣿⣿⣿⣷⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⡇⠀⣤⣤⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆⠀⠀⠀⢀⣾⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣛⣻⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡿⠛⠛⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⣠⣦⣦⣐⣮⣿⣍⡈⣍⣹⣿⡿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠡⣿⣿⣿⣿⣿⣟⣷⣤⠈⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣍⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⡿⠀⠀⢸
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡍⠉⠀⡀⢺⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⠴⠖⠉⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠛⠛⣭⣿⣿⣿⣿⣿⣿⣿⠟⠁⢶⣶⣞
⠆⠀⠀⠀⠉⠉⢉⣿⣟⣻⠟⠃⠀⠀⠁⠈⠀⠀⠈⢻⠿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠰⠋⠁⠋⠁⠀⠀⠀⠀⣾⡟⠛⠛⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⠟⠁⠀⠀⠀⣶⣿⣷
⣷⠀⡐⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⠀⢠⣶⣿⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠰⣾⣿⣿⣿
⡟⣾⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣘⢿⣿⢃⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠁⠀⠈⠛⠿⣿
⢿⡿⠀⠀⢀⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣾⡄⠀⠀⣼⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣧⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠈⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣧⠀⠀⢸⣿⣿⣷⣶⠾⠄⠘⣿⣿⣿⣿⣧⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣷⣀⠸⣻⣿⣿⣶⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⢺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣿⡛⣀
⣿⣿⣿⣿⣿⣿⣯⣅⣀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⣿⣁⢸⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣧⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣞⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣾⣿⣿⣿⣿⣶⣾⣷⣶⡄⠀⠀⠀⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣀⠀⠀⣠⣶⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠸⣿⠿⣿⣿⣿⡋⡽⣿⣿⣿⣿⡆⢠⣾⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢗⣂⣨⣿⣿⣷⣷⣿⣿⣿⣿⣧⣾⣾⣿⢷⣿⣿⠀⠀⣠⣤⣶⣤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⢀⣾⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⣛⣻⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠿⠛⠛⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⣠⣦⣄⣐⣽⣿⣉⠉⢉⣻⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠩⣻⣿⣿⣿⣿⣟⣻⣤⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⣷⣿⣿⣯⣝⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣔⣷⠀⠀⢸
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡏⠉⠑⠂⠸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢻⣿⣿⣿⣿⣿⠟⠀⠀⢀⣠⠴⠖⠈⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠉⠛⠛⣫⣿⣿⣿⣿⣿⣿⣿⠟⠁⢴⣶⣞
⠆⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⣶⣶⡁⠈⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢶⣾⣿⣿⡇⠀⡰⠋⠅⠚⠁⠀⠀⠀⠀⢸⡟⠛⠛⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⠟⠉⠀⠀⢠⣴⣿⣿
⣶⠀⣐⠀⠀⠀⢰⣿⡿⠛⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠰⣾⣿⣿⣿
⡟⣼⠋⠀⠀⣀⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⡀⠀⠀⠀⢰⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣘⢿⣿⢃⡀⠀⣀⣉⢃⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠁⠀⠈⠻⠿⣿
⢿⡿⠀⣠⣿⣿⣿⣿⡃⠀⠀⠀⠰⣿⣿⣿⣇⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣾⡀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣇⠈⢿⣿⣿⣾⣿⠗⠀⠀⠀⠀⠻⣿⣿⣿⣷⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣷⡈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣹⡛⣀
⣿⣿⣿⣿⣿⣿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠋⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⣷⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠸⣿⡿⠋⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣞⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣶⣷⣶⣶⣦⡀⠀⠀⠀⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣀⠀⠀⣠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡛⣽⣿⣿⣿⣿⡆⠀⣶⣷⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢓⢂⣨⣿⣿⣷⣷⣿⣿⣿⣿⣧⣼⣿⣿⢿⣿⣿⠀⢀⣄⣠⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣆⠀⠀⠀⢀⡾⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣾⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⣛⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⡿⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⣴⣆⣄⣠⣽⣿⣋⠉⠛⢻⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣦⠈⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣿⣿⣯⣛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⢿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⡷⠀⠀⢰
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣉⣐⣂⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣠⠴⡖⠈⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠛⠻⢛⣿⣿⣿⣿⣿⣿⣿⠟⠁⠰⣴⣾
⡄⠀⠀⠈⠉⠉⠉⣿⣟⠛⠿⠛⢿⣿⣿⣿⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠻⣶⣿⣿⣿⡇⠀⠐⡋⠥⠚⠁⠀⠀⠀⠀⢸⣟⠛⠛⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠟⠉⠀⠀⢠⣾⣿⣿
⣤⠀⡀⠀⠀⠀⢰⣿⡿⠳⣶⠖⠂⠹⣿⣿⣦⠀⠀⠈⠀⠀⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣾⠀⢀⣴⣿⣿⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡆⠰⣿⣿⣿⣿
⡏⣾⠁⣿⡇⠀⣸⣟⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣈⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣈⢿⣿⢇⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠁⠀⠈⠻⠿⣿
⣿⣿⣿⣿⣷⠀⡟⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣾⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⣹⡟⣁
⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠟⠁⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠇⠰⣙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢐⣴⣃⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣶⣶⣶⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣜⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣾⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⡀⠀⣠⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣷⣠⣴⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⣽⣿⣿⣿⣿⡆⠀⣶⣷⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⡀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢓⢂⣨⣿⣿⣷⣷⣿⣿⣿⣿⣷⣼⣿⣿⢿⣿⣷⠀⢀⡄⣤⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣦⠀⠀⠀⢀⡾⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣾⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⡀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣛⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠿⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣴⣆⣄⣀⣹⣿⣉⠉⡙⢻⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣻⣦⠈⠁⠈⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣭⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠿⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡷⠀⠀⢠
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠂⠸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢿⣿⣿⣿⣿⣿⢋⠀⠀⣀⡤⠴⠀⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠙⠻⢛⣿⣿⣿⣿⣿⣿⣿⠟⠁⠰⣶⣾
⠄⠀⠀⠈⠉⠉⠉⣿⣿⣿⣿⣿⣷⡄⠉⠀⠀⠀⠈⢛⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠻⢿⣿⣿⣿⡇⢀⠞⡉⠔⠛⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠉⠀⠀⢠⣾⣿⣿
⣧⢀⡄⠀⠀⣀⣰⣿⡿⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣾⠀⢀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⢏⣾⣀⣤⣾⣿⣿⣿⡄⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣈⢿⣿⢇⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠉⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣦⡀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣾⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣧⡀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⣹⡟⣁
⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⠇⠰⣝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢒⣴⣇⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣜⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣿⣷⣶⡄⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣀⣀⡀⠀⣴⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣧⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣦⠀⠀⠀⠀⠘⣿⠿⣿⣿⣿⡏⠽⢿⣿⣿⣿⡇⠀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢓⣂⣠⣿⣿⣷⣷⣿⣿⣿⣿⣷⣼⣿⣿⢿⣿⡇⠀⢠⣤⣤⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣷⠀⠀⢠⡻⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣺⣿⣷⠀⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣯⣍⣻⣇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡻⠟⠃⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣴⡆⣄⣐⣽⣿⣉⠉⣉⣻⣿⡟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣻⣷⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣭⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⡟⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⢀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠘⢿⣿⣿⣿⣿⢿⡃⠀⢀⣠⠤⢲⠈⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠉⠉⠛⠯⣿⣿⣿⣿⣿⣿⡿⠛⠀⢰⣶⣶
⠆⠀⠀⠈⠁⠀⠀⣾⣿⣙⣛⠛⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⡠⢋⡡⠞⠃⠀⠀⠀⠀⠀⢸⢟⠙⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠋⠉⠀⠀⢠⣾⣿⣿
⣦⢀⡄⠀⠀⢶⣤⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠰⣿⣿⣿⣿
⢇⣟⡀⠀⠛⣿⢿⣿⣿⣿⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠇⠉⠂⣨⠁⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣶⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⣿⣿⣤⡀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣧⣀⢀⣤⣾⣿⣿⠁⠈⠿⣿⣿⣿⣿⣦⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⡿⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠏⡀⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣹⣿⡿⠁⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢶⣴⣆⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣀⠀⣴⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣧⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⠿⢿⣿⣿⡏⠽⢿⣿⣿⣿⣇⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣠⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢳⣂⣰⣿⣿⣷⣷⣿⣿⣿⣿⣿⣼⣿⣿⢿⣿⡇⠀⣠⣤⣴⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆⠀⣰⡻⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣸⣿⣷⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣯⣍⣻⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠿⠛⠃⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠹⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣼⡆⣄⣒⣽⣿⣍⡉⣉⣻⣿⡟⠁⢀⠀⠀⠀⠀
⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣻⣷⣂⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⡟⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢁⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢿⣿⣿⣿⣿⣟⣃⠀⢀⣠⡴⠒⠈⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠛⢫⣿⣿⣿⣿⣿⣿⡿⠛⠀⢰⣶⣶
⡆⠀⠀⠈⠀⠀⠀⣾⣿⣛⡛⠛⠀⠀⠉⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⡴⢙⡵⠟⠓⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠉⠀⠀⢠⣾⣿⣿
⣧⢀⡆⠀⢤⣶⣶⣿⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠁⠀⢀⣻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠰⣿⣿⣿⣿
⣇⡟⠀⠀⢠⡿⢽⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠇⠀⠀⣌⢀⡾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣧⠀⠀⠀⠈⠛⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⠇⢿⣿⣿⣿⣷⣄⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣦⡀⣀⣴⣿⣿⣿⠉⠀⠀⠙⢿⣿⣿⣿⣷⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢩⣵⣿⢃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠹⣿⣿⣿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠟⡀⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠐⣿⡟⠁⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢰⣶⣆⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⣣⣄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣀⡰⢯⣤⣴⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⣘⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣿⣿⣿⣿⣿⣭⣭⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⠛⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣤⣿⡄⣤⣐⣼⣿⣥⣀⣈⣹⣿⡿⠀⢀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣯⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⡟⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣠⢀⡠⢈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠹⣿⣿⣿⣿⣿⢿⡁⠀⣀⡤⡶⠌⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠻⢽⣿⣿⣿⣿⣿⣿⡿⠟⠀⢰⣶⣶
⡆⠀⠀⠈⠁⠀⠀⣾⣿⣿⠿⢿⣿⣏⠀⠀⠀⠀⢠⡷⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠙⠻⣿⣿⣿⣧⣞⣩⡾⠟⠒⠀⠀⠀⠀⠀⢸⣟⠛⠛⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⢠⣾⣿⣿
⡧⢀⣤⡀⢀⣴⣿⣿⣿⣟⡁⠀⢹⣿⣶⡄⠀⠀⡜⠀⠀⢀⣽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡁⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣣⣿⠋⠀⢸⣿⣿⣿⣿⠛⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⡁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠇⠀⠀⢸⣿⣿⣿⣡⣴⠇⠀⠈⣿⣿⣿⣇⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠈⣿⣿⣿⡿⠃⠀⠀⠀⢻⣿⣿⣿⣆⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⠉⣿⣿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣇⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣦⣀⣸⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡿⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⣵⡿⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣹⠿⠀⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣾⣶⣾⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣴⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠹⣂⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⣿⢀⡴⢏⣤⣴⣶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⠀⣘⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣽⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣭⣭⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⠻⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣄⡀⢸⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣤⣾⡄⣤⣤⣾⣿⣥⣀⣈⣹⣿⡟⠁⢀⠀⠀⠀⠀
⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⡿⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⡄⠉⠛⠙⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠻⣿⣿⣿⣿⣿⣟⡀⠀⣠⠤⡶⠈⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉⠛⢽⣿⣿⣿⣿⣿⣿⡿⠟⠀⢶⣶⣶
⡆⠀⠀⠈⠁⠈⠀⣾⣿⡛⠛⠉⠙⣿⣧⠀⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⢚⣡⡾⠟⠒⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠯⠁⠀⠀⢠⣾⣿⣿
⡇⢠⣤⣠⣴⣦⣴⣿⠟⠋⠀⠀⠀⣿⣿⣷⡀⠀⠏⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡁⠊⠁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⠂⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣣⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⣾⣿⣿⠟⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⡁⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠇⠙⣿⣿⣿⡏⢀⡤⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⣿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣆⠀⠀⢿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣦⣀⣸⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡿⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣭⡾⢋
⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⢼⣿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣽⡿⠀⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣾⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠰⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢀⣀⣀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢿⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣷⠀⢴⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣂⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣴⣿⣿⡿⣇⣀⡾⢯⣤⣴⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡿⢀⣛⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣧⣽⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣬⣽⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⠃⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⢿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣾⣿⡄⣦⣄⣾⣿⣥⣀⣈⣙⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣻⣷⣆⣀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠛⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡿⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣡⠈⠽⠉⠉⣍⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢿⣿⣿⣿⣿⣿⣫⡀⢀⣠⠴⠦⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⢭⣿⣿⣿⣿⣿⣿⡿⠟⠀⢶⣶⣶
⠆⠀⠀⠋⠉⠈⠁⣿⣟⣛⡛⠀⠀⠁⠀⠀⠀⠀⣿⠿⠿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⢋⣥⡿⠟⠒⠀⠀⠀⠀⠀⢸⣿⠋⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠉⠀⠀⢠⣾⣿⣿
⡇⢠⠀⠀⠀⣠⣤⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⠸⠁⠀⢀⣬⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⠃⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣱⡇⢠⡖⠀⠸⣿⣿⣿⣿⣿⣿⣽⣿⠆⠀⠀⠀⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⡃⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⡿⠂⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣋⡀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⠀⠀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⣿⠉⠉⠉⢉⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⠀⠀⠀⠄⢀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣦⡀⢀⣠⣾⣿⣿⡟⠁⠈⠻⣿⣿⣿⣷⣦⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡿⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⣩⣾⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⠀⠀⠘⢿⣿⣿⣿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣸⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⢲⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣯⠩⢿⣿⣿⣿⣷⠀⣴⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣀⣰⣽⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⡿⡇⣠⡾⢇⣠⣴⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡿⢀⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾⣿⣿⣿⣿⣿⣭⣽⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⠃⡀⠰⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣾⣿⠀⣦⣔⣾⣿⣥⣀⣈⣹⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣷⣀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣷⣿⣿⣶⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡟⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣡⠈⡟⠁⠉⣍⣹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣋⡀⢀⣠⠴⠶⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠭⣿⣿⣿⣿⣿⣿⡿⠛⠀⢶⣶⣶
⠇⠀⠀⠋⠉⠉⠁⣿⣝⣻⣟⣥⠑⠉⠀⠀⠀⢸⡿⠿⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⡷⢋⣵⡿⠗⠒⠀⠀⠀⠀⠀⢸⣿⠋⠛⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠉⠀⠀⢠⣾⣿⣿
⡧⣠⠀⠀⠀⠠⢴⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠸⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⠃⠀⣴⣿⣿⠇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣱⡇⠀⣠⣴⣶⡟⢻⣿⣿⣿⣿⣷⣶⠶⠀⠀⠀⠀⠰⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣈⡃⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⡿⠂⠀⠁⠀⠀⠃⢸⣿⣿⣿⣿⣿⣤⡦⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⠀⠀⠀⢠⡀⠀⢸⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⣿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣷⣄⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣦⡀⠀⣠⣾⣿⣿⣟⠁⠀⠙⠻⣿⣿⣿⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡿⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢮⣻⣴⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣨⠿⠃⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢾⣿⠏⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⣿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⢲⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⣀⣤⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⣯⠭⢿⣿⣿⣿⣧⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣀⡄⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢹⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣀⣰⡾⢣⣤⣴⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⢐⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣯⣬⣽⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣯⣭⣽⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⢁⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣼⣷⠀⣦⣤⣾⣿⣥⣀⣈⣹⣿⣿⠁⢀⠀⠀⠀⠀
⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⢠⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣷⣿⣿⣶⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡟⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⡡⠈⠭⠀⢰⣦⣼⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠿⣿⣿⣿⣿⣿⣯⡄⢀⣤⢶⠆⠉⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠽⣿⣿⣿⣿⣿⣿⡿⠟⠀⢶⣶⣶
⡂⠀⠀⠋⠉⠉⠁⣿⣟⣻⣿⣦⣉⡀⠀⠀⠀⣼⠟⠿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡗⣋⣶⡿⠗⠂⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⠀⠀⢠⣾⣿⣿
⡇⡰⠀⠀⠀⠰⠚⢻⣿⣿⣿⣿⣿⣋⠀⠀⠀⠏⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡴⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣽⠃⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⢰⠀⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣘⡁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⡿⠀⠀⠀⠘⠃⠀⣿⣿⣿⣯⣴⣿⣿⣿⡀⠈⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠦⠀⠀⣿⣿⣿⣿⡏⢹⣿⣿⣿⣄⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⣸⣿⣿⣿⡿⠀⠀⠻⣿⣿⣿⣷⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⣆⡀⢀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣝⣦⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣠⡽⠋⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⢳⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣀⣀⣤⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⣿⡿⢿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⡄⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢱⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡟⣀⣴⡿⢡⣤⣴⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⢰⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣾⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⡟⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣯⣭⣽⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢀⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣿⣷⠀⣦⣤⣾⣿⣥⣄⣀⣙⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣶⣀⡀⠀⢠⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢿⣷⣿⣿⣶⣽⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⡟⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣏⣀⣉⣡⠈⠯⠀⢹⣦⣠⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠿⣿⣿⣿⣿⣿⣏⡀⢀⡤⠴⡆⠉⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠽⣾⣿⣿⣿⣿⣿⡿⠛⠠⢶⣶⣶
⡀⠀⠐⠋⠉⠉⠁⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⠟⠛⠛⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡟⣫⣼⡿⠗⠂⠀⠀⠀⠀⠀⢸⣟⠋⠋⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠀⠀⠀⢠⣾⣿⣿
⡇⡴⠀⠀⠀⢠⣾⣿⣿⣿⡿⣋⣹⣿⣶⡄⢀⡇⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣴⣿⣿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠲⣿⣿⣿⣿
⣼⠃⠀⠀⢀⣼⣿⣿⣿⣿⡿⠛⢛⣿⣿⣧⢸⠃⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣘⠁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⡿⠀⠀⠀⠸⣿⣿⣿⣿⣋⣴⡾⠋⣿⣿⣿⣏⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠈⠆⢸⣿⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⣧⡀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣦⣀⣀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣝⣦⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢴⣿⡿⠋⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣠⡽⠟⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⡿⣵⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣠⣤⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⡿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣀⠄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠹⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡏⣠⣾⡿⢀⣤⣴⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠇⢸⠿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢰⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣮⣽⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠏⠀⣿⣿⣿⣿⣿⣿⣭⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⢀⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣧⠀⣦⣤⣾⣿⣥⣄⣀⣙⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⡀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡟⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⡎⠝⠁⣸⣭⣀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠻⣿⣿⣿⣿⣿⣿⣫⡀⢀⣠⠴⠂⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠋⠽⣿⣿⣿⣿⣿⣿⡿⠛⠠⢶⣶⣶
⠀⠀⠘⠋⠉⠉⠁⣿⣏⡛⠋⠉⢿⣿⣧⠀⠀⣿⠿⠻⠛⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⡶⣫⣵⡿⠗⠂⠀⠀⠀⠀⠀⢸⣟⠉⠋⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⢠⣾⣿⣿
⡇⡄⢀⠀⢠⣤⣀⠛⠁⠀⠀⠀⢸⣿⣿⡆⠀⡏⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠲⣿⣿⣿⣿
⣼⢵⠟⢡⣾⣿⣿⣿⠿⠀⠀⠀⠀⢻⣿⣿⣰⠇⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣘⡁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⠟⠀⠀⢌⢻⣿⣿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠈⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⢿⣿⣿⣷⣄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⣄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⣆⡀⣉⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⣯⣶⡼
⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠟⠁⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⢻⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣾⣿⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣀⣠⣤⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣴⣿⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⡄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠸⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡏⣠⣾⡿⢠⣤⣴⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠇⢸⠿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⣄⠀⠐⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣄⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣧⠀⣦⣤⣾⣿⣧⣄⣀⣩⣿⣿⠁⢀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣿⣿⣿⣿⣾⣽⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡟⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⠈⠟⠁⣸⣍⣉⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣯⡀⢀⣠⠴⠖⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠛⠷⣿⢿⣿⣿⣿⣿⡿⠛⠠⣶⣶⣶
⠀⠀⠘⠋⠉⠉⠁⣿⣿⣿⣿⣀⡈⠀⠀⠀⠀⣿⡿⠿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡶⢫⣵⡿⠗⠂⠀⠀⠀⠀⠀⢸⣟⠉⠋⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⢠⣾⣿⣿
⡇⣴⠆⠀⠀⠀⠐⠿⣿⣿⣿⣿⣷⣶⠶⠀⠀⡏⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡔⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣼⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⠖⠀⡇⠀⢸⣿⣿⡟⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣈⠁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⠟⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡶⠘⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠐⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⣤⠀⠀⢠⣿⣿⣿⣿⡟⢻⣿⣿⣿⣦⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠒⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⣆⡀⠁⢀⣴⣿⣿⣿⡟⠉⠀⠀⠹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢯⣲⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠙⣿⣿⣿⡿⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠿⣯⠟⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠘⢿⣿⠋⠁⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣶⣟⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣀⣠⣄⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⠄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠹⣨⣱⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣏⣾⣿⡇⢠⣴⣴⣾⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠇⢸⠿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣾⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣣⡄⠀⠐⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⣦⣤⣴⣿⣧⣄⣀⣨⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣶⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡟⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠠⠌⠋⠁⢹⣭⣉⣹⣿⣿⣿⣿⣿⡿⠁⠀⠘⣿⣿⣿⣿⣿⣿⣯⠀⠀⣠⡤⡶⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠛⠶⣿⢿⣿⣿⣿⣿⡿⠟⠠⣶⣶⣶
⠀⠀⠜⠛⠋⠉⠁⣿⡟⠛⠛⣇⣀⡀⠀⠀⠀⣸⡿⠿⠿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⢀⠞⣑⠼⠛⠂⠀⠀⠀⠀⠀⢸⣟⠉⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⠋⠀⠀⢠⣾⣿⣿
⢄⡄⠀⠀⠀⢀⣰⣿⣶⣾⣷⣿⣿⣿⣶⡶⠀⣟⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡁⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣶⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠲⣿⣿⣿⣿
⣾⢸⠏⠀⠀⠙⠛⠋⠉⣽⣿⣿⣿⣿⣷⡾⠗⡏⠀⠐⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⠟⠀⠀⡄⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣤⡶⠁⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⠁⠸⣿⣿⣿⣦⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣷⣄⡀⠀⢀⣤⣾⣿⣿⣿⠋⠁⠀⠀⠘⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣳⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀⠀⢘⣿⣿⣿⡏⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣦⣬⠟⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⢿⠟⠋⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡂⠀⢀⣀⣤⣄⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⡄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠸⣩⣱⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣏⣾⣿⠇⢠⣄⣴⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠏⢸⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⡿⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣽⣿⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣳⣆⠀⠐⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⣶⣤⣵⣿⣧⣤⣀⣬⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⢍⣿⣾⣿⣿⣿⣿⣿⣶⣄⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣷⣿⣿⣶⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡟⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠠⠌⠉⠁⢰⣯⣄⣺⣿⣿⣿⣿⣿⣿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿⡀⠀⣀⡤⠖⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠛⠷⣿⢿⣿⣿⣿⣿⡿⠟⠠⣶⣶⣶
⠀⠀⠞⠛⠋⠉⠁⣿⠟⠛⠋⢱⣄⠀⠀⠀⠀⢸⣿⠿⠿⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⢆⠞⣩⠾⠛⠀⠀⠀⠀⠀⠠⢸⢿⠉⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠋⠀⠀⢠⣾⣿⣿
⢀⡆⠀⠀⠀⠀⢼⣿⣿⣿⣿⣾⣿⣧⣤⡦⠀⢸⠁⠀⢀⣤⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠲⣿⣿⣿⣿
⡿⠀⡾⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⠆⡾⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⠗⠀⠀⣀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠟⣿⣿⣄⠃⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠘⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⠿⣿⣿⣦⡀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠁⠀⠻⣿⣿⣿⣦⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⡀⠀⢀⣤⣿⣿⣿⡿⠛⠁⠀⠀⠀⠘⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣳⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣦⣬⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣡⣄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣾⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣤⣤⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢹⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠀⢠⣤⣴⣾⣷⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠸⠟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣭⣭⣯⡿⣾⣿⣿⠿⣿⣿⣿⣿⣿⠿⠏⠀⣿⣿⣿⣿⣿⣷⣬⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣷⡆⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣯⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⣶⣦⣵⣿⣷⣤⣀⣌⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⣷⣯⣿⣿⣿⣿⣿⢿⣷⣄⡀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣷⣿⣿⣷⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠡⢬⡉⠁⠀⣤⣄⣼⣿⣿⣿⣿⣿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⣟⡀⠀⣀⡤⠴⠊⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠙⠲⢾⡿⣿⣿⣿⣿⡿⠟⠡⢶⣶⣶
⠀⠀⠞⠛⠋⠉⠁⠿⠉⢋⣿⣿⣿⢿⣿⣿⡄⠀⣿⡿⠿⠿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠚⠿⣿⣿⣿⣯⠞⡩⠜⠛⠀⠀⠀⠀⠀⠀⢸⢿⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠀⠀⢠⣾⣿⣿
⢀⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣶⣯⠀⠀⣀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠰⣿⣿⣿⣿
⡟⠀⠀⠀⡶⠀⣿⣷⣶⣧⣤⡤⠀⠈⢿⣿⣿⣿⡇⠀⠸⣿⣿⣿⠃⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠙⠻⢿
⠇⠀⠀⣀⠀⢰⣿⣿⣿⣿⣫⣴⡖⠀⠈⣿⣿⣿⣷⡀⠀⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠘⠀⢸⣿⣿⣿⣿⠟⢁⣠⠄⠀⠙⢿⣿⣿⣷⣄⣿⠃⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⡀⠀⠀⠀⠘⣿⣿⣿⣷⣶⠿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣀⠀⢀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣳⡾
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡿⠋⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣶⣼⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⣤⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⣯⠽⢿⣿⣿⣿⣧⠀⣾⣿⣆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣤⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢹⣩⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⠀⠀⣤⣴⣾⣿⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢹⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠼⠟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣭⣭⣯⡿⣾⣿⣿⢿⣿⣿⣿⣿⣿⠿⠟⠁⣿⣿⣿⣿⣿⣷⣤⣽⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣵⡆⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠙⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡆⠀⣷⣦⣽⣿⣷⣦⣀⣠⣽⣿⠃⠀⠀⠀⠀⠀
⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⢿⣷⣿⣿⣷⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣁⠆⢩⡉⠁⢠⣄⣻⣿⣿⣿⣿⣿⣿⣿⠃⠈⢻⣿⣿⣿⣿⣿⣯⡀⠀⣀⡤⠴⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢾⡿⣿⣿⣿⣿⡿⠟⠡⢶⣶⣶
⠀⠀⠞⠛⠋⠉⠁⠿⠉⠉⠻⠿⠿⠿⣿⣿⣷⡀⣸⡿⠿⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠚⠿⣿⣿⣿⣿⡞⠹⠞⠋⠀⠀⠀⠀⠀⠠⢸⢿⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠟⠀⠀⢠⣾⣿⣿
⢠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⠀⠀⢀⣤⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠰⣿⣿⣿⣿
⡟⠀⠀⠀⢠⠴⣿⣆⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⣿⣿⢃⡀⠀⣀⣀⢀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠙⠻⢿
⠃⠀⠀⣀⠀⣠⣿⣿⣿⣿⢏⡀⠀⠀⠀⣿⣿⣿⣷⡀⠀⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠈⠀⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⠿⣿⣿⣷⣀⣿⠏⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠘⣿⣿⣿⣯⣴⡿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⡀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣳⣾
⣿⣿⣿⣿⣿⣶⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣶⣬⠟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⡿⢭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣵⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡂⠀⣀⣀⣤⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣾⣿⣆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣤⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢹⣨⣱⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⠇⠀⠀⣤⣦⣾⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⢓⠻⢿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠸⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣯⣭⣭⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣷⣤⣽⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡀⠀⠀⠛⠛⠻⣿⣿⠿⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⣿⡽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⢹⣶⣾⣿⣿⣦⣄⣤⣽⣿⡏⠀⠀⠀⠀⠀
⠀⠀⣰⣽⣿⣿⣿⣿⣿⣿⣷⣆⣀⡀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠄⠙⠁⠈⢡⣌⣻⣿⣿⣿⣿⣿⣿⣿⡟⠈⢻⣿⣿⣿⣿⣿⣿⡀⠀⣀⡤⠴⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢾⡿⣿⣿⣿⣿⡿⠟⠁⢶⣶⣶
⠀⠀⠛⠛⠉⠉⠁⠾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠉⠻⢿⣿⣿⣿⡇⡴⠋⠘⠉⠀⠀⠀⠀⠀⢠⢸⢿⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠀⠀⢠⣾⣿⣿
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣦⣦⠀⣀⠀⢸⡁⠀⠀⣠⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⢿⣿⣿⣿
⡏⠀⠀⠐⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⣼⠁⠀⣾⣿⣿⡿⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⢣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠙⠻⢿
⠃⠀⠐⣦⡄⠀⠀⠻⠿⠏⣿⣿⣿⣿⣿⣷⡾⠿⠃⠀⠀⢸⣿⡟⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⡖⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠿⢻⣿⣷⣄⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠛⠀⠙⣿⣿⣿⣷⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣱⡼
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣏⣤⠀⠀⠀⠘⣿⣿⣿⣿⣿⠁⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣽⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣶⣬⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣼⣿⣿⣿⠟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣵⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡁⠀⣀⣠⣤⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣠⣤⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⣨⣡⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⠃⠀⠀⣴⣶⣾⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢃⡛⢿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣾⣭⣍⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣷⣤⣽⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡀⠀⠀⠛⠛⠻⣿⣿⠿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⡀⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⢸⣶⣾⣿⣿⣦⣄⣤⣽⣿⡏⠀⠀⠀⠀⠀
⠀⠀⣐⣿⣿⣿⣿⣿⣿⡿⣷⣦⣀⣀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣿⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣏⠀⠀⠔⠉⠁⠈⢉⣉⣹⣿⣿⣿⣿⣿⣿⣿⡿⠈⢻⣿⣿⣿⣿⣿⣿⡀⠀⢀⡤⠴⠀⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢾⡿⣿⣿⣿⣿⡿⠟⠁⢶⣶⣶
⠀⠠⠟⠛⠋⠉⠁⠾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠚⢿⣿⣿⣿⡇⡰⠋⠐⠉⠁⠀⠀⠀⠀⢀⢸⢿⠉⠉⠛⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠀⠀⠀⣾⣿⣿
⢠⠀⣠⡄⠀⠀⠀⠀⢀⣀⣀⣿⣼⣷⣾⣆⣤⡄⢸⡇⠀⠀⣠⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⣿⣿⣿⣿
⡏⢠⣏⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⡿⣋⣡⣼⠁⠀⢾⣿⣿⡿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠻⢿
⠃⠀⠹⣷⠀⠀⠀⠙⠛⠉⣿⣿⣿⣿⣿⣿⡟⢋⣃⠀⠀⢸⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢸⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⢫⣾⣿⣷⣄⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣸⠀⠀⢀⣴⣾⣿⣿⣿⠿⠋⠁⠈⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣱⡼
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡗⢛⣟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠸⣿⣿⣿⠟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣵⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣠⣤⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣷⠀⣴⣿⣦⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢀⣠⣤⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣨⣡⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⡿⠀⠀⠀⣤⣶⣾⣿⣷⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⢂⡛⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡘⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⠄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣼⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣷⣤⣽⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣷⡀⠀⠀⠛⠛⠻⢿⣿⠿⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⡀⣿⡽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠀⢸⣶⣾⣿⣿⣶⣤⣤⣽⣿⡏⠀⠀⠀⠀⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⠀⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠉⠉⠄⠉⠁⠉⢉⣉⢿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢿⣿⣿⣿⣿⣿⣿⡀⠀⢀⡠⠴⠆⠁⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢿⣿⣿⣿⣿⣿⡿⠟⠁⢶⣶⣶
⠀⠰⠟⠛⠋⠉⠁⠿⠋⢉⣉⣀⣀⡀⢰⣆⠀⠀⢸⣿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠘⠿⣿⣿⣿⡇⡰⠏⠚⠋⠁⠀⠀⠀⠀⢀⣸⢿⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠀⠀⠀⣼⣿⣿
⣠⣴⡆⠀⠀⠀⠀⠀⠀⢿⣟⣻⣿⣿⣿⣿⣦⠀⢸⡇⠀⠀⣠⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⣾⣿⣿⣿
⠇⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⣸⠁⠀⢾⣿⣿⡿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⢿
⠃⠀⠹⣆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢟⣿⣷⡋⠀⠀⢸⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣿⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡿⢿⣿⣷⡀⠀⢸⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠋⠀⠸⣿⣿⣿⣦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣸⠀⠀⢀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠘⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣯⣲⡼
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡞⢻⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣠⣤⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠩⠿⣿⣿⣿⣷⠀⣴⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣠⣤⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⣨⣡⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⡿⠀⠀⠀⣤⣶⣶⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢂⠛⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡘⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣭⣭⣩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣦⣽⣷⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣷⡀⠀⠀⠘⠛⠛⢿⣿⡿⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⡀⣿⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡷⠀⠀⢸⣶⣾⣿⣿⣶⣤⣤⣽⣿⡟⠀⡀⠀⠀⠀
⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⠃⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠉⠉⠄⠙⡉⠉⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⡟⠈⢻⣿⣿⣿⣿⣿⣿⡅⠀⢀⣠⠴⠆⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢿⡿⣿⣿⣿⣿⡿⠟⠁⢶⣶⣶
⠀⠰⠟⠛⠋⠉⠁⠿⠋⠉⢩⣷⣶⣶⣤⣼⣷⠀⢸⣿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠛⠿⣿⣿⣿⡇⡰⠋⠙⠉⠁⠀⠀⠀⠀⢀⣸⢯⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠀⠀⠀⣼⣿⣿
⣠⠀⣀⠀⠀⠀⠀⠀⣶⡀⣀⣴⣦⣠⣬⣿⣿⣇⣸⡅⠀⠀⣠⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠁⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠰⢾⣿⣿⣿
⠇⢸⣏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠁⠀⢾⣿⣿⡿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠙⠻⢿
⠃⠀⠹⣆⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⢉⣽⣿⣿⣿⡀⠀⢸⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⠁⠀⠀⠀⣿⣿⣿⣿⣧⣴⡿⠛⢿⣿⣿⣷⡀⢸⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠃⠀⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠹⣿⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣀⠀⠀⢀⣼⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣯⣲⡼
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣥⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣭⢟⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠈⠻⡿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣽⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣠⣄⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣏⠩⠿⣿⣿⣿⣷⠀⣾⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⣄⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣨⣱⣽⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⠟⠀⠀⠀⣠⣴⣶⣿⣶⣶⣦⣤⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢀⠻⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡊⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣭⣝⣛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣦⣽⣷⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣧⡀⠀⠀⠘⠛⠛⢿⣿⡿⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣄⡀⣿⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠀⠀⢸⣶⣦⣿⣿⣶⣤⣠⣼⣿⡏⠀⠀⠀⠀⠀
⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣧⡈⠁⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣾⣿⠛⠈⠀⠌⠋⠉⠉⢉⣉⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⣿⣿⣿⣿⣄⠀⢀⣠⡴⠆⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠛⠷⢾⣿⣿⣿⣿⣿⡿⠿⠋⢴⣶⣶
⠀⠰⠟⠛⠋⠉⠁⣾⠉⢛⣋⣁⠀⠀⢀⠀⠀⠀⢸⣿⠿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⡷⠛⠑⠉⠀⠀⠀⠀⠀⢀⣸⢯⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠟⠁⠀⠀⣴⣿⣿
⡠⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡆⠀⠀⢼⡁⠀⠀⣠⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠐⢾⣿⣿⣿
⠇⠀⠀⠰⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⠀⠀⣾⣿⣿⡿⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠂⠈⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⠀⠃⠀⠀⢸⣿⡟⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠈⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠋⠉⣿⣿⣷⣄⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣷⣄⣀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃⠀⠀⠹⣿⣿⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣟⣦⠾
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣦⣽⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣽⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡂⠀⣀⣠⣄⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣏⠭⢿⣿⣿⣿⣧⠀⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⢄⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣩⣱⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⢿⠏⠀⠀⠀⣠⣴⣶⣿⣷⣶⣶⣤⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢀⡻⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡊⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣯⣭⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣦⣽⣷⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣇⡀⠀⠀⠘⠛⠛⢿⣿⡿⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣀⠀⣿⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⢸⣶⣶⣿⣿⣶⣤⣠⣼⣿⡟⠀⠀⠀⠀⠀
⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⢠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣿⣿⣷⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣾⣿⠋⠉⠁⠄⠙⠛⠉⢉⡉⣩⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣿⡁⠀⢀⣠⢴⠆⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠛⠷⢾⡿⣿⣿⣿⣿⣿⠿⠋⢴⣶⣶
⠀⠰⠟⠛⠋⠉⠁⣾⠝⠛⠋⠁⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠚⢿⣿⣿⣿⣷⡿⠟⠙⠋⠁⠀⠀⠀⠀⢀⣼⢯⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠋⠁⠀⠀⣴⣿⣿
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣀⣶⣴⣶⠀⠀⣿⠁⠀⢀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠐⢾⣿⣿⣿
⠇⠀⠀⠀⣴⠆⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡿⠃⡿⠀⠀⣿⣿⣿⡟⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣡⣀⣈⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠂⠀⠀⣀⠀⠀⠀⠀⢰⡿⣹⣿⣿⣿⣿⣿⣶⠶⠃⠀⠀⢿⣿⡟⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⣦⡀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁⢿⣿⣿⣿⣦⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣝⣦⢿
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡆⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣦⡽⠟⢼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢈⣿⣿⣿⣿⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⠿⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣵⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠂⠀⣀⣠⣤⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠩⠿⢿⣿⣿⣷⠀⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣨⣁⣽⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⠃⠀⠀⠀⣠⣴⣶⣿⣷⣶⣶⣤⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⡿⢀⣛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⣷⣤⣭⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣆⠀⠀⠀⠘⠛⠛⢿⣿⡿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⡀⠀⣿⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⢸⣶⣾⣿⣿⣦⣤⣦⣼⣿⡟⠀⠀⠀⠀⠀
⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣟⣥⣿⣿⣿⠀⢸⣷⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠋⠉⠡⠌⠛⠁⠉⣍⡉⢙⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⢀⣠⢴⠖⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠷⣿⡿⣿⣿⣿⣿⣿⠟⠋⠴⣶⣶
⠀⠰⠛⠛⠉⠉⠀⣾⠟⠛⠋⠁⠀⡀⠀⠀⠀⠀⣿⡿⠿⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠉⠛⠻⣿⣿⣿⡇⡰⠋⠓⠉⠀⠀⠀⠀⠀⠀⣸⢯⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠉⠀⠀⠀⣴⣿⣿
⣠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣤⣴⣿⣿⣧⣶⣴⣟⠀⠀⢀⣬⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠐⢾⣿⣿⣿
⡇⠀⠀⠀⢠⠆⠀⠘⠛⢉⣽⣿⣿⣿⣿⣿⣷⣾⡏⠀⠰⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠃⠀⠀⣀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣧⣼⡅⠀⠀⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⢸⣿⣿⣷⣤⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠉⠀⠀⠙⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣕⣤⠿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣡⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣽⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣤⡿⠋⢆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⠿⣽⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣠⣤⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠈⣿⡿⢿⣿⣿⣿⣫⠿⣿⣿⣿⣿⠀⣴⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣒⣄⣽⣿⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⡿⠃⠀⠀⠀⣠⣴⣶⣿⣷⣶⣶⣤⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⢀⡛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⣷⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠘⠛⠻⢿⣿⡿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠙⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⡀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⢸⣶⣼⣿⣿⣦⣤⣦⣼⣿⡏⠀⠀⠀⠀⠀
⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣧⠀⢸⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠋⠉⠡⠌⠛⠁⢨⣭⡉⢙⣿⣿⣿⣿⣿⣿⡟⠀⠀⢻⣿⡿⣿⣿⣿⣿⡄⠀⢀⣠⣴⠖⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⠷⣾⡿⣿⣿⣿⣿⡿⠟⠋⠴⣶⣶
⠀⠠⠛⠛⠉⠉⠁⣾⠝⠛⠛⠁⠀⢠⣦⠀⠀⢠⣿⡿⠿⠿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡇⢰⠟⠟⠋⠁⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠉⠁⠀⠀⣴⣿⣿
⣠⠁⠀⠀⠀⠀⠀⠀⣴⡟⣻⣿⣿⣿⣿⣷⠀⢸⡏⠀⠀⣀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⢠⣾⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠐⢾⣿⣿⣿
⡇⠀⠀⠺⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣸⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠃⠀⠠⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⢋⣽⣿⣿⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣶⡿⠛⣿⣿⣧⡀⠀⣿⠇⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠏⠀⠀⠹⣿⣿⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⢀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣱⣼⠯
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⡿⠋⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⢿⡿⠃⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣯⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⣡⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡅⢀⣀⣠⣄⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣛⣽⣿⣿⣿⣿⠀⢰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣒⣄⣼⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⠁⠀⠀⠀⣠⣶⣶⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⢀⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣷⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣆⠀⠀⠀⠘⠛⠻⣿⣿⡿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣆⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⢸⣶⣽⣿⣿⣦⣴⣦⣽⣿⡏⠀⠀⠀⠀⠀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣋⣷⣿⣿⡇⠀⢹⣿⣿⣿⣷⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠋⠉⠠⠌⣻⠀⢸⣭⡉⢙⣿⣿⣿⣿⣿⣿⠃⠀⠤⣿⣿⠿⢿⣿⣿⣿⡀⠀⠀⣀⡤⠖⠈⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠷⣾⡿⣿⣿⣿⣿⡿⠟⠋⠰⣶⣶
⠀⠠⠛⠛⠋⠉⠁⣾⡟⠿⠿⠿⠛⠿⣶⣿⣇⢸⣿⠿⠿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⡇⢠⠞⠛⠋⠁⠀⠀⠀⠀⠀⢸⢿⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⠋⠁⠀⠀⣴⣿⣿
⢠⣷⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⡃⠀⠀⣠⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠠⣶⣿⣿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠐⢾⣿⣿⣿
⣿⣿⡄⠀⠀⠀⢻⣷⣤⣄⣤⡄⠀⠀⣿⣿⣿⣿⠃⠀⢸⣿⣿⡿⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠃⠈⠻⣆⠀⠀⣾⣿⣿⣿⣟⣥⡄⠀⠘⣿⣿⣿⣧⠀⠸⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠁⠀⠀⢻⣿⣿⣿⡿⠋⣠⡀⠀⠿⣿⣿⣿⣧⣀⣿⠃⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⢀⡄⠀⠘⣿⣿⣿⣴⡾⠋⠀⠀⠀⠈⠛⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣈⠁⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣼⢏
⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣥⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣡⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠆⢀⣀⣠⣄⣀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣛⣿⣿⣿⣿⣿⠀⢰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣒⣄⣨⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⠁⠀⠀⠀⢠⣶⣶⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡇⢀⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣦⣭⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣭⣽⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣿⣁⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣽⣿⣿⣦⣐⣤⣽⣿⡟⠀⠀⠀⠀⠀
⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣾⡄⠀⢹⣿⣿⣿⣷⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⡇⠀⠀
⠀⠀⢻⣿⣿⣿⡿⣿⣿⣿⣿⠋⠁⣠⠝⠛⠀⣼⣍⡉⣙⣿⣿⣿⣿⣿⣿⠁⠀⠀⣻⣿⣿⢿⣿⣿⣿⡄⠀⠀⣀⣤⡶⠊⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠛⢷⣾⡿⣿⣿⣿⣿⡿⠟⠋⠰⣶⣶
⠀⠀⠟⠛⠋⠉⠁⣾⣟⣿⣿⣀⣀⣀⠀⠀⠀⣹⣿⡿⠿⢿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⡇⢠⠞⠙⠊⠀⠀⠀⠀⠀⠀⣸⢟⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠋⠀⠀⠀⣴⣿⣿
⢀⣤⡤⠀⠀⠀⠀⠉⣿⣿⠿⣿⣿⣿⣷⡀⠀⣿⡁⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠠⣾⣿⣿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠐⢾⣿⣿⣿
⡟⣹⡁⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣧⡀⣿⠁⠀⣾⣿⣿⡟⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠃⠈⢻⣆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣿⣧⠏⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠁⠘⣿⣿⣿⣦⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠀⠀⠀⠘⢿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣢⣾⣏
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣡⢄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⣿⣿⣿⣿⣿⣶⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣠⣀⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣛⣽⣿⣿⣿⣿⠀⢰⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣒⣄⣬⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⡿⠁⠀⠀⠀⢠⣦⣶⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣷⠀⢀⡿⠿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣤⣭⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⣿⣿⣿⣿⣿⣭⣭⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣷⣾⣿⣿⣶⣶⣿⣿⣿⣏⡁⠀⠀⣻⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣦⣽⣾⣿⣤⣀⣄⣹⣿⡟⠀⠀⠀⠀⠀
⠀⠀⢡⣻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣟⣩⣿⣧⠀⠀⢸⣿⣾⣿⣷⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠉⠁⣤⠻⠋⠀⣮⡉⠉⣙⣿⣿⣿⣿⣿⡟⠀⠀⠀⣻⣿⠿⢿⣿⣿⣿⡅⠀⠀⣀⣤⡔⠊⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⠿⣶⡿⢿⣿⣿⣿⣿⠿⠋⠰⢶⣶
⠀⠀⠞⠛⠋⠉⠁⣿⡻⠿⠟⠀⠉⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⡇⢠⠞⠛⠂⠀⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠀⠀⢠⣾⣿
⢀⠄⠀⠀⠀⠀⠀⠉⠀⢀⣶⣤⣿⣾⣿⣴⣶⡟⠀⠀⢀⣬⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⢶⣿⣿⣿
⣾⠀⠰⠏⠀⠀⢀⣤⠾⠿⣹⣿⣿⣿⣿⣯⣴⡿⠀⠰⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠏⠀⠀⠙⠻⢿
⠟⠀⢪⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣷⠆⠀⢿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⣾⣿⣿⣦⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠉⠀⠈⢻⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣦⣿⢏
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⢿⣿⣿⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⠈⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣡⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⣿⣿⣿⣿⣿⣷⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⣤⣄⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣛⣽⣿⣿⣿⣿⠀⢰⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣖⣄⣨⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⡿⠁⠀⠀⠀⢠⣴⣶⣾⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣷⠀⢀⡾⠿⣿⣿⣿⣻⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣦⣭⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣯⣭⣿⡄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣯⡁⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣶⣽⣿⣿⣤⣀⣄⣹⣿⡟⠁⠀⠀⠀⠀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣷⣇⠀⠀⢸⣿⣾⣿⣷⣶⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⡇⠀⠀
⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣟⠉⠉⣤⠻⠃⠂⣮⡉⠉⣉⣿⣿⣿⣿⣿⠏⠀⠀⠀⣻⣿⡿⠿⣿⣿⣿⡅⠀⠀⣀⣤⡔⠊⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠿⣶⡿⢿⣿⣿⣿⣿⠿⠋⠰⢶⣶
⠀⠀⠘⠛⠋⠉⠁⣿⡻⠿⠟⠀⢁⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣧⠞⠛⠊⠁⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠉⠀⠀⠀⢠⣾⣿
⠀⡌⠀⠀⠀⠀⠀⠉⢀⣰⣤⣤⣾⣿⣿⣶⣶⡟⠀⠀⢀⣬⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⢶⣿⣿⣿
⣼⡆⠀⢴⠇⠀⠀⠛⠋⢩⣽⣿⣿⣿⣿⣷⣾⡟⠀⠰⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠏⠀⠀⠙⠻⢿
⠟⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣼⡷⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⢿⣿⣦⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⣿⣿⣦⣀⠀⠀⠀⣠⣿⣿⣿⡿⠛⠁⠀⠀⠉⢿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣕⣤⡿⣏
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡽⠉⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠻⣿⡟⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣶⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣶⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣄⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡄⢰⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣗⣖⣨⣿⣿⣿⣷⣾⣿⣿⣿⣧⣾⣿⡿⠀⠀⠀⠀⠀⣴⣴⣾⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⠂⠀⣜⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣭⣽⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠟⠿⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⠁⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣦⣴⣾⣿⣥⣀⣤⣙⣿⣿⠃⠀⠀⠀⠀
⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⠀⠀⢸⣿⣾⣿⣿⣶⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣷⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣟⠉⢩⣤⣹⠏⢸⣿⣍⠉⣉⣿⣿⣿⣿⣿⠇⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣴⠚⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠛⢿⣵⡿⣿⣿⣿⣿⣿⡿⠛⠁⢶⣶
⠀⠀⠐⠋⠉⠉⠁⣿⡻⣿⣿⣷⣭⣤⣽⣧⢸⣿⣿⡿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⡇⢠⠾⠛⠊⠁⠀⠀⠀⠀⠀⢸⢟⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡟⠉⠁⠀⠀⢠⣾⣿
⡄⡰⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⢺⣿⣿⣿⣟⠀⠀⢀⣬⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠲⣿⣿⣿
⣽⠇⠀⢀⠄⠀⣿⣦⣶⣿⣷⡿⣃⣼⣿⣿⣿⣿⠀⠐⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⡟⠀⠀⠈⠻⠿
⡿⠂⢀⣌⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣆⠀⢿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⠀⠀⠁⠀⠀⣿⣿⣿⣿⡟⢁⣴⠟⠙⢿⣿⣿⣿⣦⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠢⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣿⣦⣀⠀⠀⢸⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣴⡽⢃
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⠋⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣽⠟⢡⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⢀⣀⣤⣄⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⡗⣒⣨⣿⣿⣿⣷⣶⣿⣿⣿⣧⣾⣿⡿⠀⠀⠀⠀⠀⣴⣤⣾⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⠃⠀⣼⡻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠋⠀⢰⣿⣿⣿⣿⣿⣿⣭⣽⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀
⠈⠹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⢿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣿⠁⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⣤⣾⣿⣧⣀⣬⣙⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠐⣽⣿⣿⣿⣿⣿⣿⣆⡀⠀⢰⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⣯⣷⡇⠀⠀⠸⣿⣿⣿⣿⣶⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣷⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣉⢩⣤⡹⡏⢸⣿⣍⡉⣉⣿⣿⣿⣿⣿⠇⠀⠀⠀⣹⣿⣿⢿⣿⣿⣿⣇⠀⠀⢀⣠⣴⠚⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠛⢯⣽⣿⣿⣿⣿⣿⣿⣿⠟⠁⢴⣶
⡀⠀⠐⠋⠉⠉⢁⣿⡻⠿⣿⠿⠿⢶⣶⣿⣼⣿⣿⡿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⡇⢀⠾⠛⠊⠁⠀⠀⠀⠀⠀⢸⣟⠉⠋⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⡿⠏⠁⠀⠀⢀⣴⣿
⡆⣠⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣟⠀⠀⢀⣬⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠂⠀⣴⣿⣿⠇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄⠰⣾⣿⣿
⣵⠇⠀⠟⠁⢴⣤⢀⠀⢀⡀⠀⠀⠐⣿⣿⣿⣿⠀⠰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠿⠀⠀⠈⠻⠿
⡿⠃⢰⣤⠀⢸⣿⣿⣷⣿⢇⡀⠀⠀⢹⣿⣿⣿⣆⠀⢿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠁⠀⢸⣿⣿⣿⣿⡿⢋⠀⠀⠘⣿⣿⣿⣿⣦⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⣿⠉⠉⠉⢉⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣆⠀⠀⠀⠈⣿⣿⣿⣏⣴⡿⠁⠀⠀⠀⠉⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⣿⣿⣦⣀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣴⡽⣣
⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣥⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠟⢤⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣶⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣶⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣄⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣗⣒⢀⣿⣿⣿⣷⣴⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⣠⣤⣶⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⠁⠀⣸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣿⣿⣿⣿⣿⣿⣭⣭⣯⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣟⠁⠀⠀⢸⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣤⣶⣿⣯⣀⣩⣉⣿⣿⡏⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣗⠀⠀⠀⢰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣼⡆⠀⠀⠸⣿⣿⣿⣿⣷⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⠆⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡋⠙⣩⣴⠹⠋⢸⣶⣍⡉⣉⣿⣿⣿⣿⣿⠃⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⡧⠀⠀⢀⣠⣴⠚⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠙⠻⢿⣭⣿⣿⣿⣿⣿⡿⣿⠿⠋⠰⣶
⠄⠀⠀⠚⠉⠉⢩⣟⠻⠿⠟⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉⠚⠻⢿⣿⣿⡇⢀⠴⠋⠓⠈⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⠛⠁⠀⠀⠀⣴⣿
⣦⢠⠅⠀⠀⠀⠘⠋⠁⠀⣤⣄⣤⣤⠀⣀⣸⠏⠀⠀⢀⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠰⣾⣿⣿
⣧⣿⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⠟⣹⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢿⠃⠀⠈⠛⠿
⣿⠏⢳⡄⠀⠀⠀⠰⡿⢹⣿⣿⣿⣿⣿⡿⢻⠁⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢉⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣇⠀⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢻⣿⣿⣦⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣾⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⣿⣿⣧⣛⠀⠀⠀⢀⣼⣿⣿⣿⣿⠗⠸⢿⣿⣿⣿⣾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣱⣼⡿⣣
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣟⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠟⢄⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢈⣿⣿⣿⣿⠃⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡧⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣶⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⣶⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣤⣄⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣗⣒⣀⣿⣿⣿⣷⣴⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⢠⣤⣶⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⠇⠀⣸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣭⣭⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⠁⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣤⣶⣿⣯⣉⢩⣉⣻⣿⡟⠁⠀⠀⠀
⠀⠀⠀⣞⣿⣿⣿⣿⣿⡛⠀⠀⠀⢰⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣯⣼⡆⠀⠀⠈⣿⣷⣿⣿⣷⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣺⡆⢀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠛⢋⣼⠹⠋⢸⣶⣍⡉⣉⣿⣿⣿⣿⣿⠇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⡴⠒⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⠻⠿⣯⣽⣿⣿⣿⣿⣯⢼⡿⠋⠰⢾
⠄⠀⠀⠚⠉⠉⢹⣟⠻⠿⠏⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⡇⢀⠴⠛⠓⠁⠀⠀⠀⠀⠀⢸⣟⠉⠛⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢿⣿⠟⠁⠀⠀⠀⢠⣾
⣦⢀⠆⠀⠀⠀⠘⠉⠀⠀⢰⣄⣶⣶⣄⣠⣼⡏⠀⠀⢀⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠀⢶⣿⣿
⣯⣿⡀⠀⠀⠀⢀⣠⣼⡿⣿⣿⣿⣿⣿⣟⣽⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢿⠏⠀⠀⠛⠿
⣿⠟⢳⡄⠀⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣹⡅⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⣷⡀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⣿⣿⣿⣦⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣾⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠
⣿⣿⣷⣌⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⠀⠙⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣵⣼⡿⣡
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⠟⠄⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⣷⣿⣿⣿⣷⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⣀⣀⣤⣄⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⣗⣒⣠⣿⣿⣿⣶⣴⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⠆⠀⣰⡿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣯⣭⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡉⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣦⣴⣿⣿⣉⢉⣉⣻⣿⡿⠁⠀⠀⠀
⠀⠀⠀⢘⣿⣿⣿⣿⣿⡖⠀⠀⠀⢠⣿⣟⢙⣿⣿⣿⣿⣿⣿⣿⣫⣴⣇⠀⠀⠀⣿⣿⣿⣿⣿⣯⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣰⡶⢠
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡋⠋⢡⡌⠽⠃⠀⣷⣮⡉⣉⣹⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣤⠒⠛⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠛⠿⣯⣽⣿⣿⣿⣿⣿⡼⡿⠛⠁⢾
⠀⠀⠀⠘⠉⠉⢹⣟⠻⠿⠃⠀⠁⢠⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⡿⠀⡴⠛⠃⠉⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢾⣿⡟⠉⠀⠀⠀⢠⣼
⣶⠀⣄⠀⠀⠀⠘⠉⢰⣾⠛⣻⣿⣿⣿⣧⢰⡟⠁⠀⢀⣨⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⣠⠀⢴⣾⣿
⣏⣿⠿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⢯⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢿⡿⠀⠀⠙⠿
⢿⠿⢨⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀
⣾⡄⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣠⣿⣿⣿⣿⣧⡀⣻⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠁⠀⠙⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠
⣿⣿⣷⣄⠀⠀⠀⣰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣼⡿⣡
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣿⣦⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠙⢿⡿⠉⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⢠⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣴⣶⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⣗⣒⣲⣿⣿⣿⣷⣼⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⡆⠀⢰⣟⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣾⣿⣿⣿⡿⢿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣯⣭⣽⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀
⠀⠈⢻⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡋⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣦⣴⣾⣿⣍⡉⣍⣻⣿⣿⠋⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡀⠀⠀⢠⣿⡟⢙⣿⣿⣿⣿⣿⣿⡿⣋⣵⣧⠀⠀⠀⢿⣿⣿⣿⣿⣮⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣐⣶⢠
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡯⢏⣥⡎⠽⢁⠀⣿⣦⣉⣉⣹⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⡿⠀⠀⢀⣠⣤⠒⠛⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⠿⣿⣭⣿⣿⣿⣿⣿⣡⣿⠟⠁⢼
⠆⠀⠀⠘⠉⠉⢹⣛⠻⠿⣷⡾⠷⣶⣶⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⢀⡴⠟⠃⠉⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢾⣿⡿⠁⠀⠀⠀⠀⣼
⣾⠀⡤⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠁⠀⢀⣨⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣤⣠⡄⠰⣾⣿
⡿⣾⠃⡾⠀⠀⠈⣿⣧⣶⣿⣷⡿⣓⣿⣿⣿⣿⡄⠠⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣿⡿⠁⠀⠙⠿
⢿⡿⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠹⣿⣿⣿⣷⠀⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀
⣺⡆⠀⠁⠀⠀⠀⣿⣿⣿⣿⠟⢁⣴⠞⠻⣿⣿⣿⣷⣽⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣾⠟⠁⠀⠀⠈⠙⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠢⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⣀⣀⣠
⣿⣿⣷⣄⠀⠀⢀⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣼⡿⣡
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⣿⣿⠛⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣠⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣦⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⡆⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⣗⣒⣠⣿⣿⣿⣾⣴⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡆⠀⢠⣿⣛⣿⣿⣿⣟⣿⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣭⣭⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠿⡿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡋⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣴⣶⣿⣯⣁⢉⢙⣿⣿⡟⠁⠀⠀
⠀⠀⠀⢰⣻⣿⣿⣿⣿⣶⣀⣀⣀⢀⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⢛⣠⣧⠀⠀⠀⢹⣿⣿⣿⣿⣷⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣲⣶
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢡⣴⡖⠿⠁⠀⣿⣦⣍⢉⣡⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⠁⠀⠀⣠⣤⡖⠋⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⠿⣿⣭⣽⣿⣿⣿⣿⡅⢼⡿⠋⢸
⠦⠀⠀⠀⠉⠉⢹⣏⢛⣿⣷⣦⣄⣠⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠀⡴⠛⠃⠉⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⡿⠋⠀⠀⠀⠀⢸
⣶⡄⡴⠀⠀⠀⠈⢁⡈⠉⠉⢻⣿⣿⣿⡆⠀⣟⠁⠀⠀⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣀⡄⠠⣴⣿
⣟⣼⠇⢠⠖⠀⠀⢸⣿⣦⣶⣿⣿⣿⣿⣿⣴⡿⠀⠠⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢿⣿⢃⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣿⣿⠇⠀⠈⢻
⣿⡿⢂⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⠋⠀⠀⠀⠈
⣸⣦⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⢟⣩⣿⢿⣿⣷⣄⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠁⠈⠻⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⣀⣀⣤
⣿⣿⣿⣦⠀⠀⠀⣸⣿⣿⣿⣿⡅⠀⠀⠀⠀⠹⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣢⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡈⠛⠻⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠺⣿⣿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣤⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣶⣿⣿⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⢀⣀⣤⣄⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⡆⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣗⣒⣠⣿⣿⣿⣶⣴⣿⣿⣿⣧⣼⣿⡿⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡆⠀⢀⣾⣛⣻⣿⣿⣿⣻⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣯⣭⡧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡋⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣤⣶⣿⣯⣅⢉⣉⣿⣿⡟⠁⠀⠀
⠀⠀⠀⢠⣸⣿⣿⣿⣻⣶⣄⣀⣀⠀⣿⡟⢉⣿⣿⣿⣿⣿⣿⣿⢋⣡⣇⠀⠀⠀⢸⣿⣿⣿⣿⣷⣭⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⣶
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡗⠁⣴⡶⠽⠁⠀⣿⣦⣉⢉⣡⣾⣿⣿⣿⡟⠀⠰⡄⢠⣿⣿⣿⡿⣿⣿⣿⠅⠀⠀⣀⣤⡒⠋⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⠿⢿⣯⣽⣿⣿⣿⣿⡏⢸⡿⠋⢸
⠂⠀⠀⠀⠉⠉⢹⣍⠙⠛⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⠀⡰⠟⠃⠈⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣿⣿⠋⠀⠀⠀⠀⢸
⣶⡄⣰⢀⠀⠀⠈⠁⠀⣀⣰⣆⣰⣶⡶⢆⣠⡟⠁⠀⢀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣠⣄⣠⠀⢴⣿
⣿⣽⡿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢻⣏⠀⢰⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⢯⣀⣀⢿⣿⢋⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣽⣿⠏⠀⠈⢻
⡿⡿⢧⣄⠀⠀⠀⠀⠿⢡⣿⣿⣿⣿⣿⣿⢿⠟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⠏⠀⠀⠀⠘
⣰⣦⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⣆⡀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣀⡤
⣿⣿⣿⣦⡀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠀⣿⣿⣿⣿⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠆⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠋⢄⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢘⣿⣿⣿⡿⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣷⣶⣯⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠈⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣶⣿⣿⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣄⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⡄⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⡗⣒⣈⣿⣿⣷⣧⣼⣿⣿⣿⣧⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣦⣄⣠⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⡆⠀⠀⣼⣟⣛⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀
⢿⣿⣿⣿⣻⣿⣿⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⢿⣿⣷⣾⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣭⣽⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⡟⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣦⣰⣾⣿⣉⠉⡉⢻⣿⣿⠃⠀⠀
⠀⠀⠀⠠⣿⣿⣿⣿⣻⣿⣤⣄⣀⠀⣾⣿⢉⣿⣿⣿⣿⣿⣿⣿⣛⣡⣇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⢀⣶
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣗⠂⣤⡶⠽⠃⠀⣿⣦⣉⢉⣡⣾⣿⣿⣿⡟⠀⠀⢠⣤⣿⣿⣿⠿⢿⣿⣿⠃⠀⠀⢀⣠⣴⡚⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⢿⠿⣿⣭⣿⣿⣿⣿⡏⠀⣺⠟⢻
⡷⠀⠀⠀⠉⠉⢹⣇⠉⠛⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⠀⠀⠞⠋⠀⠁⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣾⣿⠏⠀⠀⠀⠀⢸
⣶⡄⣠⠀⠀⠀⠈⠁⠀⣀⣰⣧⣀⣿⣶⣿⣷⣿⡅⠀⢀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⡀⢀⠀⢠⣾
⣿⣱⡏⠀⠀⠀⠀⠰⠾⠿⣟⣿⣿⣿⣿⣿⣿⣿⡶⢰⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢏⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢹
⡿⡿⢧⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣁⣤⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⡟⠀⠀⠀⠘
⣁⣷⡀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⢻⣿⣿⣦⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⣀⣀⡤
⣿⣿⣿⣧⡀⠀⢀⣤⣾⣿⣿⣿⠿⠛⠁⠘⢻⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣢⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠋⠄⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣗⣶⣯⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢇⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣾⣿⣿⣿⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣤⣄⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⣛⣿⣿⣿⣿⡀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⡗⡒⣸⣿⣿⣿⣧⣾⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⡆⠀⠀⣼⣟⣛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀
⢿⣿⣿⣿⣻⣿⣿⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⢿⣿⣷⣾⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣯⣭⣽⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡟⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣤⣰⣾⣿⣉⠉⣉⢻⣿⣿⠋⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣧⣄⣀⠀⣾⣿⢋⣿⣿⣿⣿⣿⣿⡿⣛⣤⣇⠀⠀⠀⠈⣿⣿⣿⣿⣷⣮⣽⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠀⣶
⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠂⢤⡶⠽⠃⠀⣿⣦⡉⣉⣡⣶⣿⣿⣿⡟⠀⠀⠀⢀⣿⣿⣿⡿⢿⣿⣿⡏⠀⠀⢀⣠⣴⡚⠛⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⠿⣿⣭⣿⣿⣿⣿⡏⠀⢻⠟⢻
⡗⠀⠀⠀⠉⠉⢹⣏⠉⠛⠛⠉⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⠀⠀⠴⠛⠁⠁⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣿⠟⠀⠀⠀⠀⢸
⣿⡆⣠⠀⠀⠀⠈⠁⢠⣶⣶⣦⣤⣾⣿⣷⣴⡿⠁⠀⢀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⡀⢀⡀⢠⣾
⣿⣱⡟⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⡷⠀⢰⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣾⣿⡿⠁⠀⢹
⡿⡿⢧⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣿⣅⡀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⡿⠁⠀⠀⠘
⣃⣷⡀⠇⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣷⣾⣿⣿⡀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣧⣡⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⣿⣿⣿⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⡤
⣿⣿⣿⣧⡀⠀⢀⣤⣿⣿⣿⣿⠿⠋⠀⠀⠙⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣲⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣽⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠛⢄⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢾⣿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣟⣷⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣴⣼⣿⣿⣿⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣠⣤⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⡀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡧⡀⣝⣿⣿⣯⣧⣿⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣦⣤⣤⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⡆⠀⠀⢠⣿⣛⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⠀
⢿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣿⣿⣧⣭⣭⣿⣿⡿⢿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣍⣙⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣽⠁⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣀⣮⣿⣏⠉⢉⠛⣿⣿⠏⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⣴⣿⢛⣿⣿⣿⣿⣿⣿⡿⣋⣵⣇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣭⣽⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢰
⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠈⢥⡴⠹⠃⠀⣿⣦⣉⣉⣥⣾⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣤⣶⠛⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠐⢿⠿⣿⣫⣽⣿⣿⣿⣿⠁⢘⠿⢻
⣿⠀⠀⠀⠉⠉⢹⣇⠙⠛⠋⣀⣀⣀⣀⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡇⠀⠀⠊⠁⠀⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣿⡿⠁⠀⠀⠀⢸
⣿⡧⢠⠇⠀⠀⢈⣉⠀⠀⠘⠛⠛⠛⢻⣿⣿⡟⠁⠀⠀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⢀⠀⡀⠀⣼
⣿⣣⡟⠀⠀⠀⠘⣿⣧⣾⣿⣶⡿⢀⣾⣿⣿⣷⡀⢰⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣶⣿⣿⠃⠀⢸
⡿⣿⢷⠀⠀⠀⢰⣿⣿⣿⣿⣿⡾⠋⠹⣿⣿⣿⡇⠘⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⡿⠃⠀⠀⠘
⣇⣷⡌⠃⠀⠀⢸⣿⣿⣿⡿⠋⢀⣴⠾⣿⣿⣿⣿⡄⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⣿⣿⣷⠀⠀⠀⠈⣿⣿⣿⣿⣾⠟⠁⠀⠉⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣀⣠⣤
⣿⣿⣿⣷⡀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣰⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣥⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣽⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡈⡿⠛⢧⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣼⣿⣿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣠⣤⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡀⠀⠈⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡇⡀⣘⣿⣿⣯⣧⣿⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣄⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⡄⠀⠀⢀⣿⣛⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣬⣭⣿⣿⡿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣍⣙⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡟⣻⠃⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣄⣾⣿⣏⡉⢉⠙⣿⣿⡟⠁⠀
⠀⠀⠀⠐⣾⣿⣿⣿⣟⣷⣖⣀⣀⠀⢸⣾⠛⣿⣿⣿⣿⣿⣿⣿⣃⣽⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣏⣽⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢰
⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠍⢉⡴⠨⠋⢠⣷⣄⣉⣉⣠⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣀⣤⣶⠛⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠐⢻⡿⢿⣫⣽⣿⣿⣿⣿⠁⠐⠿⢻
⢿⡂⠀⠀⠉⠉⢹⣏⠙⠛⠛⣀⣀⣀⢀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⠀⠀⠊⠉⠀⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣿⡿⠁⠀⠀⠀⢸
⣿⡧⢠⠇⠀⠀⠚⠉⠀⠀⠿⠛⠛⢻⣿⣿⣾⡟⠁⠀⢀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⡀⠀⣼
⣿⣣⣿⠁⠀⠀⣿⣦⣀⠀⣀⠀⠀⠠⣿⣿⣿⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣶⣿⣿⠇⠀⢸
⣿⢿⢿⡀⠀⠀⣿⣿⣿⣿⢟⣡⡀⠀⢿⣿⣿⣇⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⠋⠀⠀⠀
⣇⣲⡄⠃⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⡆⠀⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀
⣿⣿⣿⡀⠀⠀⢹⣿⣿⣿⣡⣾⠟⠀⠈⠿⣿⣿⣿⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⢀⣠⡤
⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣴⣾⠿⢁
⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣦⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⣿⣿⡻⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢼⣿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣾⣿⣿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀⣠⣤⣀⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣶⡄⠀⠈⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⡀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⡇⡀⣜⣿⣿⣯⣧⣿⣿⣿⣿⣧⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣤⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣶⠀⠀⠀⠀⣼⣟⣛⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⣭⣿⣿⡿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣯⣙⣛⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣹⠏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠸⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣄⣲⣿⣿⡉⠉⡙⢿⣿⡿⠃⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣻⣶⣂⣀⠀⢀⣾⣻⣿⣿⣿⣿⣿⣿⢟⣡⣼⡝⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣩⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠
⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡗⠉⣡⠌⠟⢸⣷⣤⣀⣠⣼⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⢀⣠⣴⠟⠋⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠐⢺⡿⠿⣟⣭⣿⣿⣿⡿⠁⠀⠻⢿
⢿⡇⠀⠀⠈⠁⢰⣧⣈⠛⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⡇⠀⠀⠐⠉⠀⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣿⠇⠀⠀⠀⢠
⣿⣿⢠⡇⠀⠀⠘⠋⠁⠀⣠⡀⠀⠀⠀⠀⣸⠏⠀⠀⢈⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⢀⠀⣼
⣿⣇⣿⠗⠀⠀⠀⠀⣤⣤⣿⣷⣶⣶⣠⣤⣿⠁⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢃⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣴⣯⣾⡟⠀⠘
⣿⠿⢿⣀⠀⠀⠀⢾⡟⣻⣿⣿⣿⣿⣟⣁⣟⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀
⣇⣻⡄⠋⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣋⡉⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣤⢀⣠⡤
⣿⣿⣿⣷⡄⠀⠀⢀⣾⣿⣿⣿⣿⢫⣿⣿⣿⣤⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣰⣾⠿⢁
⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⠁⠀⠛⢿⣿⣿⣿⣷⣦⣄⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⣽⠟⠳⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣾⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣴⣼⣿⣿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⣤⣄⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣶⣄⠀⠈⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⠀⢰⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡓⡀⣹⣿⣿⣿⣧⣿⣿⣿⣿⣦⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣤⣤⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣦⠀⠀⠀⠀⣼⣟⣛⣿⣿⣿⡿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣧⣼⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣙⣻⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣋⣿⡏⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣽⣿⣉⠉⡙⠻⣿⣿⠋⠀
⠀⠀⠀⠀⣬⣿⣿⣿⣿⣻⣷⣆⣀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢟⣠⣾⡹⠃⠀⠀⠀⢸⣿⣿⣿⣿⣯⣭⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠈⣉⡆⠍⢹⣷⣄⣀⣠⣾⣿⣿⣿⡿⠁⠐⠶⣶⣶⣸⣿⣿⣿⡿⢿⣿⣿⠃⠀⠀⠀⣠⣴⠞⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠐⢺⡿⠿⣟⣭⣿⣿⣿⣿⠉⠀⠠⢿
⢻⡂⠀⠀⠈⠀⢸⣿⣄⠙⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠋⠁⠀⠀⠀⠀⣸⢟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣿⣷⣿⣿⠏⠀⠀⠀⢸
⣿⣿⢠⡇⠀⠀⠘⠋⠁⠀⣄⠀⠀⠀⠀⠀⣾⠋⠀⠀⣈⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⢀⠀⢼
⣿⣧⣿⠃⠀⠀⠀⣀⣤⣤⣿⣿⣿⣷⣴⣶⣿⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣤⣮⣾⡿⠀⠘
⣿⠿⢿⡀⠀⠀⠙⠉⠉⣽⣿⣿⣿⣿⣯⣶⡿⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀
⣇⣺⡄⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣭⡤⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢿⣿⣦⡀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⢀⣠⡤
⣿⣿⣿⣷⡄⠀⠀⢀⣾⣿⣿⣿⣿⠃⢸⣿⣿⣷⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⣾⠿⢁
⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠛⠁⠀⠈⠛⣿⣿⣿⣿⣾⣦⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣽⣿⣄⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣴⣾⣿⣿⣷⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⣤⣤⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣷⠀⣰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡁⡂⣹⣿⣿⣿⣤⣿⣿⣿⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣀⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡆⠀⠀⠀⠀⢰⣿⣛⣿⣿⣿⣿⣿⣿⡏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣾⣿⣿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣥⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣛⣻⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣏⣿⡟⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣮⣿⣏⡉⢉⠛⣿⣿⠟⠀
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⣿⣦⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣋⣴⣿⠹⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣭⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠊⢀⠤⠉⣿⣦⣄⣀⣤⣴⣿⣿⣿⡿⠀⠀⠀⣰⣦⣤⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣤⠶⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠲⣿⠿⣿⣫⣿⣿⣿⣿⠋⠀⠘⠽
⢻⡅⠀⠀⠈⠉⢰⣿⣦⡉⠛⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⢟⠙⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢿⣿⣾⣿⡟⠀⠀⠀⢠
⣾⣿⢀⠇⠀⠀⠘⠋⣡⣤⣶⣦⣴⣿⡄⠀⡿⠋⠀⠀⣙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢀⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠁⠀⠀⠀⢸
⣿⣏⣿⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣤⣿⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣠⣾⣵⡿⠁⠈
⣿⢻⠟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⡿⠁⠀⠀
⣇⣺⡆⠃⠀⠀⠀⢸⣿⣿⣿⡟⢁⣴⣿⣿⣿⡄⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀
⣿⣿⣿⣄⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠁⢿⣿⣿⣆⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⣠⡤
⣿⣿⣿⣿⣄⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠘⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣢⣾⡿⣁
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡽⠟⢤⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣴⣿⣿⣿⣷⣶⣴⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣠⣄⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣿⣧⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣆⠀⢹⠡⠀⣽⣿⣿⣽⣭⣿⣿⣿⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣤⣀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⡄⠀⠀⠀⠀⢰⣿⣛⣿⣿⣿⣿⣿⣿⡿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣵⡶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣛⣻⡃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣿⡿⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣾⣿⣏⡉⢉⠛⢿⣿⠟⠁
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⣿⣶⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣉⣴⣿⠙⠃⠀⠀⠀⠘⣿⣿⣿⣿⣯⣍⣿⣿⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠱⠘⣿⣤⣄⣠⣴⣾⣿⣿⣿⡟⠀⠐⠲⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣠⠴⠞⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠒⣿⠿⢿⣫⣽⣿⣿⣿⠏⠀⠐⢼
⢿⡁⠀⠀⠈⠉⢁⣿⣯⡙⠛⣋⣁⠀⣠⡀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⢟⠛⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢿⣿⣾⣿⡿⠀⠀⠀⢀
⣾⣿⢠⡇⠀⠀⠘⠋⠉⠀⠛⠋⠛⢻⣿⣷⡿⠉⠀⠀⣙⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢠⣴⣿⣿⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠁⠀⠀⡀⢸
⣿⣏⣿⠀⠀⠰⣿⣦⣤⣤⣤⠄⠀⠀⣿⣿⣿⡄⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣾⣵⣾⠁⠀
⣿⢻⠟⠀⠀⢰⣿⣿⣿⣿⣿⡶⠂⠀⢿⣿⣿⣇⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀
⣇⣸⡆⠂⠀⢸⣿⣿⣿⣿⠋⢀⣤⠀⢾⣿⣿⣿⡄⢹⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀
⣿⣿⣿⡀⠀⠘⣿⣿⣿⣧⣶⡟⠁⠀⠘⠻⣿⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⣠⣤
⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣾⡿⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣽⠟⢤⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⢧⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⣿⣿⣿⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣧⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⠡⠀⣻⣿⣿⣽⣭⣿⣿⣿⣿⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣤⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⡄⠀⠀⠀⠀⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⡿⠂⠀⠀⣾⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣩⣿⡿⠁⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣶⣿⣿⡉⠉⡙⢻⣿⡿⠁
⠀⠀⠀⠀⣴⣼⣿⣿⣿⣿⣿⣦⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣛⣴⣯⠋⠁⠀⠀⠀⠘⣿⣿⣿⣿⣯⣙⣿⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠉⡠⠛⣿⣦⣈⣁⣴⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠⠴⠶⠊⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⡿⢿⣿⣭⣿⣿⣿⡟⠀⠀⠲
⢿⠆⠀⠀⠈⠉⢉⣿⣏⠙⠿⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⠛⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣿⡿⠀⠀⠀⠀
⣾⣿⢀⡆⠀⠀⠸⣟⣿⣷⣶⣤⣤⡄⠀⠀⡿⠁⠀⠀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠀⢠⣴⣿⡿⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⡀⢠
⣿⣏⣾⠀⠀⠀⠘⣿⣄⣉⣿⣿⣿⣿⡀⢠⡇⠀⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣔⣷⣾⠃⠀
⣿⢿⢿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢸⠇⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀
⣟⣺⣎⠋⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⣿⣏⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿⣿⣷⣾⠿⣿⣿⣧⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡄⣀⣤
⣿⣿⣿⣿⣄⠀⠀⣾⣿⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣰⣾⡿⢏
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣭⠟⢠⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⢧⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣴⣿⣿⣿⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣄⠀⠘⣿⣿⣿⣿⣿⡿⢟⣻⣿⣿⣿⣧⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⢡⠀⣹⣿⣿⣽⣭⣿⣿⣿⣿⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣄⣀⡀⠀⠀⠀
⣿⣟⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣦⠀⢀⣀⠀⠀⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⡛⠻⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠿⣹⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣶⣿⣿⣉⠉⡙⢻⣿⡿⠃
⠀⠀⠀⠀⣦⣾⣿⣿⣿⡿⣿⣶⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣣⣼⡏⢁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣻⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠉⣠⠛⣷⣄⣈⣠⣤⣿⣿⣿⣿⠇⠀⠓⠂⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠⠴⠶⠚⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⡿⢿⣯⣭⣿⣿⣿⡟⠀⠀⠳
⢿⡆⠀⠀⠈⠉⠉⣿⣏⡛⠿⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣶⣿⣿⠁⠀⠀⠀
⣾⣿⢀⡆⠀⠀⠸⠟⠋⢀⡀⢀⠀⠀⠀⢀⡟⠁⠀⢀⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⠀⢠⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⡀⢠
⣿⣏⣾⠁⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣀⣬⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣖⣷⣾⠃⠀
⣿⢻⢿⣆⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣟⣹⡁⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀
⣿⣸⣆⠋⠀⠀⠀⠘⢣⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡃⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⡄⣀⣤
⣿⣿⣿⣿⣄⠀⠀⢠⣿⣿⣿⣿⣿⢋⣿⣿⣷⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣔⣾⡿⢏
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠛⠁⠀⠙⣿⣿⣿⣿⣿⣶⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⠟⢠⡘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣯⣾⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣷⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣀⣀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣇⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢫⢥⠬⢿⣿⣿⣽⣭⣿⣿⣿⣿⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣦⣤⣄⣀⠀⠀⠀
⣿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣿⠇⠀⢀⣾⡟⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⣿⣷⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⡛⠻⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠻⢿⠁⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣅⠬⡍⣻⣿⡿⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⣿⡇⢠⣾⡀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣻⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠉⣀⠘⣷⣤⣀⣤⣾⣿⣿⣿⣿⠃⠀⠙⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢠⠴⠶⠚⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⡿⢿⣯⣽⣿⣿⣿⡟⠀⠀⠵
⢿⣆⠀⠀⠈⠁⠀⣿⣿⡛⠿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣿⡿⠀⠀⠀⠀
⣾⣿⢀⡬⠀⠀⠠⠟⠛⢡⣀⢰⣦⣤⡄⣠⡟⠁⠀⢈⣻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠁⠀⠀⡀⢠
⣿⣏⣾⡿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢃⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣾⣷⣿⠃⠀
⣿⢻⢿⣇⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠉⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⡿⠃⠀⠀
⣿⣸⣆⠙⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠈⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀
⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⢫⣿⣿⣦⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡄⣀⣤
⣿⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⣿⠿⠀⠘⢻⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠀⠛⢂⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣮⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⢾⣿⣧⣜
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⣿⠟⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣴⣿⣿⣿⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⢿⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣇⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⣀⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢫⢥⠬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣦⣤⣄⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣾⣿⣿⠏⠀⢀⣾⡻⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⡛⠻⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣷⣿⣿⣿⣷⣿⣿⡿⢏⠀⠈⠉⠁⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣶⣾⣿⣄⣤⣍⣹⣿⡿⠁
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡆⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣥⣿⡇⢤⡾⠀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣻⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀
⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠘⣧⣄⣀⣴⣴⣿⣿⣿⣿⠃⠀⠁⠰⣿⣾⣦⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⡤⠶⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠒⠲⣿⡟⢻⣭⣿⢿⣿⣿⡏⠀⠀⠿
⢯⣇⠀⠀⠀⠁⠀⣿⣿⡛⠿⠟⢃⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣿⡿⠀⠀⠀⠀
⣼⣿⢀⡬⠀⠀⠀⢿⣿⣿⣶⣶⣾⣿⣆⢠⡟⠁⠀⢈⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⡀⢠
⣿⡟⣾⠟⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣾⡆⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢃⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣾⣷⣿⠁⠀
⣿⢿⢿⣧⡀⠀⠀⢠⣿⣿⣿⣿⣿⠿⣿⣿⣇⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀
⣿⣸⣆⠙⠁⠀⠀⢸⣿⣿⣿⣿⣁⣴⣿⣿⣿⣆⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀
⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⣀⣠
⣿⣿⣿⣿⣄⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠻⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠀⠛⢂⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢕⣦⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡏⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⣿⣧⡔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠺⣿⡿⠋⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢸⣿⣷⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣬⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣤⡀⠸⣿⣿⣿⣿⣿⡿⣛⣿⣿⣿⣿⡆⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡇⠀⠀⣀⣠⣤⣤⠄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢯⠴⢮⣿⣿⣿⣭⣿⣿⣿⣿⣷⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⡿⠀⢀⣾⣛⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡿⠛⠿⢿⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣏⠀⠀⢀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⣮⣽⣿⣿⣤⣐⣄⣹⣿⡟⠁
⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣖⡀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣵⣿⡆⢾⡿⠀⠀⠀⠀⣿⣿⣿⣿⣯⣙⣿⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡀
⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠒⢂⣸⣦⣉⣉⣠⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡤⠶⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⡟⣿⣷⣾⠿⣿⣿⠏⠀⢘⠟
⠽⣣⠀⠀⠀⠀⠀⣸⣿⣛⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡟⠀⠀⠀⠀
⣴⣿⠀⡼⠀⠀⠀⠿⠟⠋⠁⠀⠀⠹⣿⣿⣏⠁⠀⢈⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠀⡀⢀⠀⢠
⣿⣟⣾⠃⠰⣶⣀⡀⢀⡀⠀⠀⠀⠀⣿⣿⣿⡆⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢰⣿⣾⡿⠀⠀
⣿⢿⣿⠀⢀⣿⣿⣿⡿⣃⣄⠀⠀⠀⢹⣿⣿⣧⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀
⣿⣸⣦⠇⢸⣿⣿⣿⣿⠟⢁⠀⠀⠀⢺⣿⣿⣿⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀
⣿⣿⣿⡇⠘⣿⣿⣿⣏⣴⠟⠀⠀⠀⠀⠙⢻⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣤
⣿⣿⣿⣿⣄⣸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢕⣦⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡿⠁⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣼⡿⢣⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢨⣠⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣰⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣿⣿⣿⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣄⠀⠸⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⡆⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⢀⣀⣤⣤⣤⠄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢯⠄⣬⣿⣿⣿⣭⣿⣿⣿⣿⣧⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣤⣤⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⡟⠀⢀⣾⡛⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣉⠀⠀⣀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣽⣿⣿⣤⣀⣄⣹⣿⠟⠀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⠿⠀⠀⠀⠀⣿⣿⣿⣿⣯⣙⣿⣿⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⢰⣌⣉⣉⣭⣿⣿⣿⣿⡿⠀⠀⠀⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣤⠶⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⣛⣻⣷⣾⠿⣿⣿⠏⠀⠘⠟
⠽⣷⠀⠀⠀⠁⠉⢸⣿⣿⣿⣿⣋⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡟⠀⠀⠀⠀
⣴⣿⠄⡼⠀⠀⠀⡿⠿⠛⠿⣿⣿⣿⡄⢸⠏⠉⠀⢈⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⢀⠀⢠
⣿⡟⣼⠃⠀⠀⣿⣧⣀⣠⣀⣹⣿⣿⣷⣼⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢰⣯⣾⡟⠀⠈
⣿⢿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⡟⠁⠀⠀
⣿⣸⣮⡤⠀⠀⢻⣿⣿⣿⣿⠟⢉⣿⣿⣿⣷⡄⢈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣷⡿⠋⠁⠙⢿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣠
⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣦⣿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⠿⠣⡐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠰⣿⣿⠟⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢸⣷⣾⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣄⠀⠸⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡆⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣠⣤⣴⣶⠄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠿⠖⣾⣿⣿⣷⣶⣿⣿⣿⣿⣧⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣶⣤⣤⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡾⣿⣿⣿⣿⡟⠀⢀⣾⡿⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠉⠙⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣛⢻⡇⠀⠈⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⣿⣿⣿⣶⣿⣿⣿⣿⡁⠀⢀⣀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣽⣿⣿⣤⣒⣄⣹⣿⠟⠀
⠀⠀⠀⠀⠠⣮⣿⣿⣿⣿⡿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣿⣿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀
⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠓⠂⢤⣍⡉⣩⣽⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⡤⠴⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠺⣿⡛⣿⣷⣾⢿⣿⣿⠋⠀⠸⠟
⠭⣗⠀⠀⠀⠁⠉⢸⣿⣛⠿⠿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣶⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠏⠀⠀⠀⠀
⣤⣿⡆⣰⠀⠀⠀⣿⠿⢫⣤⣀⢀⣀⠀⢸⠋⠈⠀⣙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⣀⠀⣤
⣿⡿⣹⠇⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⡀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠈
⣿⣿⣿⠂⠀⠀⢴⣿⠿⣾⣿⣿⣿⣿⣿⡿⠛⠀⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀
⣿⣰⣶⡇⠀⠀⠈⠁⢠⣿⣿⣿⣿⣿⣿⣶⠇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣻⣿⣦⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⣤
⣿⣿⣿⣿⣦⡀⠀⣠⣿⣿⣿⣿⡿⠁⢿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢂⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢕⣦⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⠿⠫⡔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣹⣿⣿⡿⠃⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣿⣾⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟

                    ䷩ 𝚕𝚒𝚗𝚎 2363

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/Anticipated_in_2018_Lilie_James_Location_tracking_Googlists_com.shtml
    Gemini version at https://techrights.org/n/2025/03/25/Anticipated_in_2018_Lilie_James_Location_tracking_Googlists_com.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Anticipated in 2018: Lilie James & Location
tracking, Googlists complained⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025


Reprinted with permission from Daniel_Pocock.


The ABC published a summary of the Lilie James inquest with a focus_on_the
Location_Tracking_issues. The coroner hasn't completed their official report
yet and these news reports are only summaries of the evidence. (See my previous
blog about what_people_hide_from_coroners).


In the winter 2017/2018 round of Outreachy, I selected Renata D'Avila from
Brazil to be an intern for Debian Debian_official_announcement and Outreachy
project_list).


During the application process, we ask each applicant to do a small programming
task and submit the results. I was startled to see Renata giving help to the
women she was competing against. It turns out that while tech industry
diversity programs try to attract interns who are fresh out of university,
Renata had already worked as a schoolteacher for a number of years and helping
the other women was just part of her nature.


In the middle of the program, Renata published a blog post with the title The
right_to_be_included_in_the_conversation. Renata's blog post features a
screenshot of Google Maps with lines marked on it showing how Googlists have
tracked her movements around Porto Alegre, here it is again, along with some
analysis:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Google,_Stalking,_Harassment,_women,_interns,_Outreachy⦈_


 


Renata's blog opens with a quote from Pierre-Joseph Proudhon that anticipates
the prospect of being clubbed to death:


     To be GOVERNED is to be watched, inspected, spied upon, directed, ...
     then, at the slightest resistance, the first word of complaint, to be
     repressed, fined, vilified, harassed, hunted down, abused, clubbed,
     disarmed, bound, choked, imprisoned, judged, condemned, shot,
     deported, sacrificed, sold, betrayed; and to crown all, mocked,
     ridiculed, derided, outraged, dishonored.


The ABC report mimics the quote chosen by Renata:


     The inquest examining Ms James's death at St Andrew's Cathedral
     School in 2023, heard she had tried to set boundaries with Thijssen
     the weekend before.


Creepy. But it gets worse.


The Googlists couldn't stand this. Google is one of the companies that
contributes money to these diversity internships. When women are selected for
the program, their blog posts are syndicated into various web sites where they
are seen by many Google employees and their followers. It was really shocking
for them when this blog about how creepy they are suddenly appeared all over
the open source eco-system.


Various rumors appeared. They created rumors about "behavior", rumours about
"harassment" and rumors about "abuse". They created rumors that I was dating an
intern.


They sent threats to Renata, which she didn't tell me about until a few months
later. I published_some_of_those_communications.


     Debian "Community Team" (political police) to Renata, private email
     of 13 June 2018: Reinforcing positive attitudes and steps that you
     see in Debian towards women inclusion can also motivate yourself, the
     other Debian contributors, and possible newcomers, to go on working
     in that strategy and foster diversity in Debian. This does not mean
     to avoid criticism or hiding problems, but providing a more accurate
     vision of how the Brazilian Debian community works towards our common
     goals.


In other words, we can tell fairy tales but nobody is allowed to speculate
about the negative risks associated with location tracking or anything else
that comes from Googlists. Because now that it actually happened to a location
tracking victim, we can all say I chose the right woman for the internship.


Please watch_Renata_speaking_in_this_video. They continue spending vast sums of
money on "diversity" internships but diversity of thought is not welcome.


Related: the Code_of_Conduct_gaslighting in open-source software hobbyist
groups may violate_the_new_coercive_control_laws too.


Even more scary are the predictions I made when_Donald_Trump_was_elected_for
the_first_time.


Googlists have spent_over_US$130,000 to try and discredit me, to stop women
telling me stuff and to stop us making predictions that are uncomfortably close
to the truth. █


§ RIP Lilie James⠀➾


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


    * Over_at_Tux_Machines...
    * After_US_Government_Funding_Cuts_the_Centralisation_of_the_Web_
      (Especially_Certificate_Authority_Let's_Encrypt)_is_at_Risk


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⣿⣿⣿⡆⠀⠹⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠃⠀⠐⢁⠀⢠⣿⣿⠀⣼⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡟⢏⡱⡀⠓⢒⠛⣟⣻⣿⣿⣟⣙⣻⣉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
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⠤⠼⠿⠿⠿⠿⡆⠀⣿⡿⠿⣿⣿⣿⠃⠀⠀⠈⠉⠃⠀⠀⠀⢻⡿⠿⠏⡐⢟⣤⣼⣿⣦⣰⣷⣶⣌⣤⣾⣿⣿⡿⡻⣿⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿
⢊⣴⣦⣶⣶⣶⣿⡀⠙⣷⠄⠈⠉⢋⡶⢶⡀⠀⠀⠀⠤⢴⢀⠜⠅⢠⡖⠔⠚⠛⡛⣻⢻⣿⣿⣿⣿⣿⣾⣿⣷⡗⡁⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣚⣝⣃⣉⣇⣌⣻⣕⣁⠀⠛⠄⠀⣠⠄⠉⢰⣾⣿⣟⣿⡟⡛⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣶⣶⣷⣿⡇⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠟⠛⢉⣿⣿⣿⡟⠀⠀⠀⢨⣿⢀⠀⠘⡋⠍⣿⣿⣷⣶⣿⡻⣿⠁⢈⠥⠜⢯⠉⣲⣞⣷⣿⣟⣿⡾⣻⣿⣟⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⢀⣼⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣷⣾⡿⣿⣿⣽⣿⣯⣟⢛⢻⣿⣿⣯⣄⠀⢐⢸⣿⣷⣿⣿⣟⣯⣿⣻⣿⡟⢻⡿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣭⣉⣝⣙⣉⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠾⠉⠙⠋⣏⣍⣏⣟⣿⠍⠛⡓⢿⣶⣾⣿⣿⡾⣓⠒⣾⣿⣿⣿⣿⣟⣿⣿⣧⣿⣿⣿⣮⣷⣷⣻⣶⣾⣤⣷⣥⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠐⠙⣻⣿⢙⢳⣄⣁⣥⣾⡛⡉⢽⣿⣽⣿⣯⣿⣽⣻⣯⣾⣿⣿⡟⠨⢹⣿⣿⣿⣿⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣮⢿⣷⣾⣿⣷⣴⣷⣿⣿⣷⣿⠿⣿⣽⣿⣼⣻⢻⣿⣿⣟⢿⠛⢿⣿⣿⣿⣿⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣽⡽⡿⣿⣿⣿⣿⣻⣧⣀⣼⣿⣽⣟⡕⠪⠭⠵⣢⢷⣄⣼⣟⠻⠻⢿⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣾⣿⣿⣿⣿⣿⣿⢿⢷⣿⢿⢿⣿⣿⢿⠻⣿⡯⡷⣧⣴⣿⣿⣿⣿⣾⣿⣿⣞⡿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠅⠁⠀⠀⠀⠀⠀⠀⢠⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣯⣖⣶⣿⡿⣖⣷⣟⣿⣿⣿⣯⣤⣾⣨⣫⣙⢃⢂⣽⣯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠐⠀⣠⢀⡀⢀⢀⠀⣀⡀⣼⣧⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⡿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣷⣽⣶⣷⣈⣑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣌⣉⣉⣉⣹⣁⣉⣿⣿⣿
⣿⣿⣏⢡⡗⠃⠳⢄⠵⠵⠜⠿⢬⣴⣧⣬⣦⣷⣮⣬⣦⣬⣬⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⢿⢿⣿⣿⢿⣿⣽⣿⣿⣿⣿⣷⣟⣿⣿⣟⣿⡷⣾⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣩⣠⣺⣬⣺⣿⣿⣿⣿
⣿⣿⡗⢸⡗⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣞⣟⡿⣿⣿⣿⣾⣿⢿⣿⣿⣿⡮⣳⡽⣿⣝⡻⣿⣿⣿⣶⣿⣿⣽⣿⢿⣏⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠻⢦⣏⣀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣽⣿⣳⣽⣿⣿⣿⣻⣿⣿⣮⡻⣯⢝⣾⡽⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠆⠖⢡⡅⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣯⢿⣿⣿⣿⣿⣿⣷⣯⣯⢿⣽⣿⣷⣿⣿⢿⣷⢷⡾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿
⠻⠊⠁⠘⠀⠀⠀⠀⠀⢸⣿⣯⣉⣩⣯⣙⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣞⣿⣿⣿⣷⣿⣷⣽⣷⣿⣞⣿⣿⣿⣿⣿⣿⠿⢿⣧⠀⠉⠘⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠽⡿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣢⢺⣵⠀⣴⡆⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⣲⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣯⣿⣿⣿⣿⣿⣿⢿⣝⠡⢻⢁⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣧⣾⣼⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⡿⢽⡿⡿⠾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣌⡠⣿⣧⣀⢼⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡽⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠷⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣧⣷⡿⣻⢿⣟⣿⠾⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢾⣿⣿⣻⣿⣷⣝⣻⣌⣤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣷⣿⣿⣿⣿⣿⣮⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠻⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⢷⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣡⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠡⠠⢤⣥⣮⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡉⣻⣿⣿⣿⣿⣿⣷⣺⣿⣿⣿⣿⣿⣿⣟⡎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠙⢿⣿⣿⣿⣿⣷⣪⣿⣿⣿⣯⣿⡞⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢚⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣉⣱⣀⣝⣋⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣛⣛⣋⣡⣾⣿⣿⣿⣿
⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡯⢿⣽⣿⢏⡻⣿⣟⣿⣿⣟⣿⢿⣟⣙⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿
⡷⢯⣺⣵⣯⣽⣫⣿⣿⣿⣿⣷⣣⣯⣯⣿⣿⢿⣿⣿⣜⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣫⣷⣾⣿⢿⣿⣿⣿⣷⣿⣿⣵⣟⣿⣿⡾⢿⣻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡽⣿⣿⣾⣾⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣾⡿⢿⣟⣗⣿⣿⣿⣭⣷⣥⣿⣿⣿⣿⣾⠯⣿⣿⣏⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣺⣟⣿⣿⣿⣿⣟⣿⣿⡷⣣⣿⡛⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⣶⣯⢟⣿⡿⣯⣯⣿⣿⣿⣿⢿⣿⡯⣾⣿⣿⣞⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⣿⣷⣾⣿⣿⣻⢟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣟⡿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣕⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣗⠿⣽⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⢛⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣷⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2563

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/European_Patent_Office_EPO_Illegally_Turning_to_Slop_Behind_Clo.shtml
    Gemini version at https://techrights.org/n/2025/03/25/European_Patent_Office_EPO_Illegally_Turning_to_Slop_Behind_Clo.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ European Patent Office (EPO) Illegally
Turning to Slop Behind Closed Doors, Staff Objects to This Hidden
Catastrophe⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


This is what happens when Europe's second-largest institution gets stacked or
stuffed with white-collar criminals who lack_any_grasp_of_science and lack
respect for truth/facts


Slop - or sometimes LLM slop (basically nonsense spewed out by models that lack
actual comprehension of both inputs and outputs) - is practically_worthless
hype_and_a_bubble, just like many that came before it and continue to re-emerge
[1, 2] to reinvigorate and deceive. Remember 4IR? Or IOT/IoT? How about
"Metaverse"?


Nowadays almost everything that MBAs touch is being re-labeled "hey hi" (AI).
It's not new, so they use terms and redundant adjectives like "advanced" or
"generative" or "agentic" or "superintelligent" "AI". They have marketing
slogans with terms like "era" or "arms race". There's hardly any use case for
it... to date, except gimmicks or harder-to-detect_plagiarism. To give a new
example of what we're dealing with, yesterday_we_said_that_Planet_Ubuntu_(or
Ubuntu_Planet)_is_LLM_slop because it aggregates Serial Sloppers or bots. Today
too we saw another example of it, again with the same culprit in Planet Ubuntu
(or Ubuntu Planet):


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Fixed_Release_vs._Rolling_Release_Distributions:_Which
                            One_is_Right_for_You?⦈_


Slop as usual.


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_distributions_come_in_two_main_release_models:_fixed
   release_and_rolling_release._Each_has_its_own_advantages_and_drawbacks⦈_


Now, imagine dealing with serious legal issues (with a lot of money at stake)
using slop. What sane person would do this? Probably these_corrupt_people who
do illegal things behind back doors and closed doors. They conspire to break
the law and/or harm people. Such people must never be in positions of power at
all.


Thankfully, the illegal EPO policy ("Internal use only") has_been_leaked:


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_AI_POLICY:_It's_not_legal,_keep_quiet_about_it⦈_


Hiding one's illegalities behind a veil of secrecy might be expected from rogue
and illegal (unconstitutional) pseudo-agencies like "DOGE" [sic]. The EPO is no
better, except this is happening in Europe and it almost directly discredits
the EU.


Thankfully the EPO's Central Staff Committee has already analysed it and
politely explained what's happening here. To quote:


     Dear Colleagues,

     Staff of the EPO and their representation discovered in the news item
     of 5 March 2025 that the EPO has adopted an AI policy. The document
     was adopted without consultation of any stakeholder and has far-
     reaching consequences which should have been subject to an open
     debate.

     First, the EPO AI policy is not bound by international texts such as
     the Council of Europe Framework_Convention_on_Artificial_Intelligence
     and_Human_Rights,_Democracy,_and_the_Rule_of_Law of 17 May 2024, and
     the EU_AI_Act.

     Second, the EPO AI policy lacks boundary between AI "assistance" and
     "decision-making". While the policy presents as key principle a
     “human-centric approach” promising that “final decisions will be
     taken by humans at the EPO”, the document nevertheless advocates the
     implementation of AI in pre-search, machine translation, pre-
     classification, re-classification and “to potentially automate
     considerable parts of the search” [and] "to automate repetitive
     tasks, leading to increased efficiency and productivity in various
     areas ? including the examination process”.

     In the already implemented AI-based automatic closing of circulation
     of patent applications for the purpose of classification, the
     classification decision is done without the final input of the
     relevant classifiers and gérants in the field who are simply
     supplanted by AI.

     Third, the EPO AI policy acknowledges that “the automation of tasks
     through AI may lead to job displacement and the need for reskilling
     programmes to support affected individuals” and hence directly
     acknowledges an impact on working conditions. Further far-reaching
     changes on adverse decision-making on employee rights and benefits
     are foreseen via AI systems which are classified as high-risk.

     In this open letter, we request that the present EPO AI policy is
     submitted to an open and transparent debate with all stakeholders and
     to statutory consultation.


Here's the full open letter as GemText, HTML, and plain text:


     European Patent Office
     80298 Munich
     Germany


     Central Staff Committee
     Comité central du personnel
     Zentraler Personalausschuss


     centralSTCOM@epo.org


     Reference: sc25022cl


     Date: 21/03/2025


     European Patent Office | 80298 MUNICH | GERMANY


     To:
     Mr António Campinos
     (President of the EPO)


     By email:
     president@epo.org


     § OPEN LETTER⠀➾


     § EPO AI policy: A policy requiring open debate and consultation of
     stakeholders⠀➾


     Dear Mr President,


     Staff of the EPO and their representation discovered in the news
     item1 of 5 March 2025 that the EPO has adopted an AI policy2. The
     document was adopted without consultation of the staff
     representation, without any decision from the Administration Council
     and is classified for “internal use only”, thereby suggesting that
     there is no intent to make it available to the public. This policy
     has far-reaching consequences which should have been subject to an
     open debate.


     The EPO AI policy is not bound by international texts
     First, the policy states that the EPO just takes note of initiatives
     such as the Council of Europe Framework Convention on Artificial
     Intelligence and Human Rights, Democracy, and the Rule of Law of 17
     May 2024, and the EU AI Act. However, further into the document, the
     EPO hides behind its administrative autonomy under Article 4(1) EPC
     to consider these texts as not legally binding3. We note that the
     same approach was adopted by the EPO to argue that it was not bound
     by the European Convention on Human Rights. This led our Organisation
     to several breaches of the right to freedom of association (incl. the
     right to strike


     _______


     1 “New EPO AI Policy adopted”, News item of 5 March 2025


     2 EPO AI Policy: Policy on the use of artificial intelligence systems


     3 page 5, par. b


     =====================================================================
     and the right to freedom of communication). We believe our
     organisation should take utmost care to learn from the past and
     explicitly recognise international texts, and in particular when it
     comes to AI.4


     Lack of boundary between “assistance” and “decision-making”
     Second, the policy presents as key principle a “human-centric
     approach”5 defined as “the combination of human + AI providing better
     result in terms of quality and efficiency than either of them alone”
     while “final decisions will be taken by humans at the EPO”. The
     document also recognises that AI “may even supplant decision-making
     processes”6 and “[i]n public administration this may pose certain
     legal questions relating to due process”. However, the document
     advocates the implementation of AI in pre-search, machine
     translation, pre-classification, re-classification7 and “to
     potentially automate considerable parts of the search” [and] "to
     automate repetitive tasks, leading to increased efficiency and
     productivity in various areas ‒ including the examination process”8.


     There is already an area where AI has started to supplant EPO
     officials and that is for the classification of patent applications.
     The reason provided is consistency9 : “AI can ensure consistent
     practice and administration, e.g. by categorising applications into
     relevant classes and subclasses, improving the accuracy and
     consistency of patent classification.” In practice since June 2024,
     the EPO has put in place an AI-based automatic closing of circulation
     of patent applications. Allocated classes by third-parties can be
     marked by the AI as final without any confirmation from classifiers
     and gérants in the relevant fields. The classification decision is
     done without the final input of the relevant experts who are simply
     supplanted by AI but remain, according to this policy10, subject to
     “principles and rules relating to the responsibility and
     accountability of EPO employees laid down in the Service Regulations
     and other internal rules”. The feedback we gathered from classifiers
     and gérants is for the vast majority negative about the quality of
     the AI-based automated classification when currently 46.7% of the
     classification tasks are automated. We are deeply concerned that the
     Office wants to continue to leverage AI in classification under these
     conditions and reach by 202811 a target proportion of 90% of
     classification tasks that no longer require human intellectual
     classification.


     ______


     4 page 5, paragraph b


     5 page 2, last paragraph


     6 page 6, section C. 1. paragraph 1


     7 page 3, paragraph 2


     8 page 3, section 2. bullets 1 and 5 bullet


     9 page 3, section 2. bullet 4


     10 page 9, section 4. paragraph 3


     11 Strategic Plan 2028 Progress Dashboard


     =====================================================================
     Impact on working conditions
     Third, the policy acknowledges that “the automation of tasks through
     AI may lead to job displacement and the need for reskilling
     programmes to support affected individuals” and hence directly
     acknowledges an impact on working conditions. Further far-reaching
     changes on adverse decision-making on employee rights and benefits
     are foreseen via AI systems which are classified as high-risk. They
     are defined as such if they are intended to be used12:


     • “to evaluate the eligibility of individuals for essential benefits
     and services, including coverage under healthcare insurance provided
     or paid by the EPO, as well as to grant, reduce, revoke, or reclaim
     such benefits”


     • “for assessing the likelihood that an individual will engage in
     misconduct not solely based on the profiling of individuals as
     referred to in Article 3(1)(d) EPO DPR or to assess personality
     traits and characteristics or past behaviour of individuals or
     groups”


     • “for the profiling of individuals as referred to in Article 3(1)(d)
     EPO DPR in the course of the detection or investigation of
     misconduct”


     While such AI systems are classified as high-risk, their
     implementation or use is nevertheless considered if individual and
     overall residual risks “are deemed acceptable” and provided that AI
     is used for its intended purpose and with the promise that they will
     be trained, tested and validated with the “data sets that meet the
     highest quality criteria and are subject to appropriate data
     governance and management practices”13. This is clearly insufficient
     to reassure staff.


     The EPO AI policy has triggered many discussions among concerned EPO
     staff.


     We request that the present EPO AI policy is submitted to an open and
     transparent debate with all stakeholders and to statutory
     consultation.


     Sincerely yours,


     Derek Kelly
     Chairman of the Central Staff Committee


     ______


     12 page 12


     13 page 13


The only room/capacity for slop at the EPO should be none, zero. People don't
pay for bots to pretend to do work, the EPC didn't see member states
reconvening on the matter.


Benoît_Battistelli used to ride all sort of buzzwords (vague mumbo-jumbo for
voodoo science) to justify granting loads of European_software_patents - i.e.
patents which are both illegal and undesirable. António_Campinos has done the
same with "blockchain" hype and now "hey hi". Since Campinos has no background
in science, name-dropping buzzwords is the best he can ever do. We did some
video rebuttals to his laughable name-dropping. Is this clown the best Europe
has to offer in its biggest patent office? Highly concerning!


The EPO's crises deepens the financial crisis in Europe and contaminates_the_EU
with_corruption. Who stands to gain from all this and at whose expense? █


    * Gemini_Links_25/03/2025:_Relaxation,_Literary_"Movements",_and_Gemini
      Mentions
    * Growing_Poverty_Rates_in_the_United_States_of_America_(or_Elsewhere)
      Beneficial_to_GNU/Linux_Adoption


⣏⣩⣍⣙⣉⣉⣻⣉⣩⣉⣉⣍⣉⣋⣉⣉⣍⣋⣉⣉⣙⣏⣉⣉⣩⣙⣍⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣏⣿⣙⣩⣹⣟⣹⣙⣛⣏⣹⣉⣉⣿⣉⣏⣙⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⡇⠿⠈⣽⠉⠏⢹⡇⣴⠍⠉⠉⡩⢸⡇⡠⠉⡁⡉⡉⢹⠉⠉⣿⡝⡍⠙⣿⢀⢈⢍⢸⡇⢩⠉⠍⣿⠀⠍⢉⠈⢙⠉⠍⡉⢹⡇⢂⣵⠉⢨⢩⠀⠍⠹⠁⣵⠉⡋⠹⠉⢹⣧⢡⢡⢨⠁⡋⠁⢹⣿⣿⣿⣿⣿⡇⠀⠀
⡿⠿⢿⣿⣿⣿⢿⣿⡿⠿⢿⣿⡟⣿⢿⡟⣿⣿⣿⡿⡿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣧⣉⣄⣆⣀⣽⣸⣠⣇⣄⣻⠀⣇⣰⣸⣇⣄⣄⣾⣿⣸⣀⣏⣸⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠹⣿⣿⣿⣿⣿⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣦⡀⣹⣿⣿⡿⠀⣷⣶⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⢿⣿⣷⠀⠉⠈⠀⢀⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡇⠀⠀
⣿⣿⣿⡿⣿⢿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀
⡿⠶⢾⠶⠶⠶⠲⢶⠾⣶⠶⠶⠾⠶⢶⠶⠞⠶⠶⠶⢷⠶⢶⡶⢷⠶⠶⣷⢶⠶⢾⠶⠾⢶⠶⠦⡷⠶⡶⠶⡿⠶⠷⠷⠾⡶⠳⡶⠷⡷⠶⠶⠴⡾⠶⠶⢶⠶⠶⡶⠾⠶⢶⢦⠷⠶⢷⠶⠶⠶⢶⣶⣶⣿⣿⡇⠀⠀
⡷⠶⠾⠶⢾⢶⠶⠟⢶⠷⢶⠶⠶⠶⢾⠶⠺⡾⢲⢶⢾⠲⢾⠶⠾⠶⢶⠾⢾⠶⠾⣶⣶⣾⣾⣷⣷⣷⣷⣶⣷⣶⣶⣾⣾⣷⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣾⣿⣶⣶⣾⣾⣶⣶⣾⣶⣾⣶⣾⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣏⣼⣇⣈⣈⣁⣿⣅⣎⣁⣉⣩⢩⣏⣡⣇⣃⣉⣉⣉⣇⣈⣁⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣹⣯⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠍⠭⠭⠭⠭⠭⠭⠭⠭⠭⠉⠭⠭⠭⠭⠍⠭⠭⠭⠭⠭⠭⠯⠭⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⣯⣭⡛⣿⣿⣹⣛⣛⣛⣟⣛⣛⣛⣻⣉⣉⣉⣹⣿⣿⣿⣿⣿
⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣽⡟⣼⣿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⢿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣛⣛⣛⡏⠙⠛⠛⠛⢋⣛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣭⣽⣭⣭⣭⣭⣽⣭⣯⣭⣽⣯⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠿⢿⠿⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠒⠒⠒⢶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣦⣶⣶⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠛⠛⢻⡖⢻⣿⣿⣿⠛⠛⠛⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⣶⠶⠆⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⡒⣒⣒⣒⣒⣒⣒⣒⣒⡒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⢒⣒⡒⣲⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⣲⣶⣾⣿⣿⣿⣿⣿⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠭⠹⠭⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⢔⢲⠲⠤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠂⠀⠤⡠⠄⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣥⣤⣬⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢐⣒⡇⣒⡍⣴⡎⣿⡟⠌⢿⢸⣿⢐⣸⢱⣶⢹⢸⣿⢸⢰⡾⣧⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣶⣾⣿⣶⣿⣾⣾⣿⣾⣿⣷⣶⣿⣶⣾⣾⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⡿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣸⣮⣪⣸⣀⣺⢌⣿⣐⣅⣾⣇⣇⣾⣀⣿⣃⣇⣨⣸⣯⣪⣸⣇⣸⣰⣂⣇⣿⣐⣿⣀⣇⣿⣇⣾⣸⣀⣿⣀⡗⢸⣀⣷⣨⣒⣅⣿⣇⡧⣹⣀⣗⣅⣅⣶⣸⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⡿⢿⣻⡟⣿⣿⣿⣿⣿⣿⠟⣿⡻⣿⣿⢻⣿⠟⢻⣿⣻⣿⣿⣻⣿⣿⣻⣿⣿⡿⣿⣿⢻⠟⣻⣿⣿⣿⢿⡿⢛⣟⣿⣿⣿⣿⣿⣻⠿⢿⣟⣿⢿⣻⣿⢿⣿⣻⣻⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⡿⣿⣿⣻⡟⣟⣿⣿⡿⢿⣿⠿⢿⣿⣻⢿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⢿⣿⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢟⣿⢛⡿⣿⣿⡟⢻⢿⣻⣿⣿⣻⣿⣿⣿⢻⣿⣿⡛⣿⣟⢻⣿⣿⡟⣿⣿⣻⣿⣿⡛⣿⣿⣛⢿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣛⣿⡛⢿⣟⣿⣿⡿⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣟⣿⣻⢻⣻⠟⣻⡟⣿⣻⣛⣿⣻⣿⠿⣻⣻⣟⠿⣿⣛⣟⠛⣿⣻⣿⢿⣟⠿⣿⢻⣿⣿⡿⣻⢻⣻⣿⣿⡻⢟⣿⣟⡿⣿⣿⣻⡿⣿⣿⡻⣿⣛⠻⣟⢻⠿⣟⣟⡿⣻⠿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⡿⡿⣿⣿⣿⣿⡿⣿⢿⡟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⡿⣿⡿⣿⣿⡿⣿⡿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⡿⢿⣿⡿⣿⡿⣿⠿⣿⣿⢿⢿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⡿⣿⡿⢿⣿⡿⣷⣿⣿⣿⣿⠿⢿⣿⡿⣿⣿⣿⣿⡿⢿⣿⢿⡿⡿⣾⡿⢿⣿⡿⠿⣿⡿⢿⣿⣿⢷⣿⡿⢿⣿⣿⡿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣾⡾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢷⣾⣿⣿⡷⣿⣷⣾⣿⣾⣿⣿⣷⣿⣷⣿⣿⣷⣿⣿⣾⣷⣶⣿⣷⣾⣿⣷⣿⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⠟⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⢿⣿⣿⠿⢿⢿⢿⡿⠿⡿⣿⣿⣻⣿⣿⣿⢿⣿⡟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⢿⡿⣿⣿⡿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⢿⣿⢿⣿⣿⣿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⠿⣿⡿⣷⡿⢷⣿⣶⠿⣷⣿⣿⣾⢷⣿⡷⡶⣿⡿⣷⣾⢿⣷⣾⢿⣿⡿⣿⣾⣿⣾⣿⣿⡿⣾⣶⡶⢿⣷⣾⡷⣾⣷⢷⣿⣿⡿⣾⡿⣿⣿⣷⣷⣷⣿⣿⣿⣾⣿⡿⢷⣾⢿⡶⢿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⣶⣿⣷⣾⣿⡿⣷⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⢿⡾⣿⣶⡿⣿⣿⣿⣷⣿⣷⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⢿⣿⣿⢿⣿⣿⢿⣿⡟⣻⢿⣿⡿⣿⣿⣿⠛⡿⣿⣿⣿⣟⣟⣻⣿⣿⣿⣻⢻⡻⢿⣿⡿⣿⣿⢿⣿⢿⣿⡿⣿⣿⠿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⢿⣿⢿⣿⡿⢿⣿⢿⣿⣿⣿⣿⡿⣿⡿⢿⣿⠿⣿⡿⢿⣿⣿⢿⣿⢿⣿⠿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣶⡿⣿⡿⣿⣿⣿⢿⣿⣾⣿⣿⣿⡿⣿⡷⣿⡿⣿⣿⠿⣿⣷⢾⣿⣿⡿⣷⣿⣿⣿⣶⣿⣿⠿⣾⡿⢿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⡿⢿⡿⣿⣷⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⡿⣾⡿⣾⣿⣿⢿⣿⣷⣿⣷⣿⣷⣿⣿⣶⣶⠿⣾⣿⣾⣶⣿⡿⣿⣷⣿⣿⣿⣶⣾⣷⣾⣿⡿⣶⣿⣷⣿⣿⣿⡿⣿⣿⡿⣿⣷⣿⣿⣿⣾⣷⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣾⣿⣿⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣼⣿⣦⣿⣷⣿⣿⣿⣷⣼⣿⣶⣿⣧⣿⣧⣿⣿⣿⣼⣿⣧⣿⣧⣿⣶⣿⣿⣿⣧⣽⣿⣥⣽⣼⣿⣽⣿⣧⣿⣧⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣧⣼⣿⣧⣬⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3022

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/Free_Software_Community_Folks_Are_Closer_Together_Than_the_Cliq.shtml
    Gemini version at https://techrights.org/n/2025/03/25/Free_Software_Community_Folks_Are_Closer_Together_Than_the_Cliq.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Free Software Community Folks Are Closer
Together Than the Cliques and Opportunists Rallying Around "Open Source"
(Openwashing, Marketing, Conniving)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


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


I've been heavily and persistently involved in the Free software community for
well_over_20_years (at technical capacity and advocacy) and one thing that
almost always amazes me is the dedication of the people or the devotion towards
the goal, which is Freedom (as in, Software Freedom). This devotion extends to
my wife and I. We don't use proprietary things. We also carefully assess the
impact of using one piece of software over another and we're not alone. The
community is not a corporation. The Free software community does not get to
choose who enters (no "job interview"), but it can repel bad actors. And so it
does. The same goes for projects.


That's why there were - and still are - stern reflexive reactions to Red Hat/
IBM (now Microsoft) projects like systemd. People can rightly smell that the
true motivation isn't greater control or choice by_the_users; it's monolithic
and restricted. The aim isn't to foster freedom but actually limit it.
Sociopaths_in_management make the calls (or call the shots); they can also
control what_the_media_says, hence or thereby manipulating (e.g. censoring)
public discourse.


There are people in the "Open Source" crowd (like Red Hat/IBM) who say they
value rather than devalue freedom, but upon closer inspection one can see they
don't walk the walk, they just "talk" or merely namedrop words like "free".
They'd even promote DRM and TPM while saying how it's "free". In the case of
today's FSF, there's no mention of the founder, the office is being shut down,
assets are being sold in auctions, documents are belatedly published using
Microsoft tools [1, 2, 3], and there_seems_to_be_no_awareness_that_C#_is
Microsoft (or perhaps a lack of awareness of how vicious Microsoft is).


At the end of the day, however, in my personal experience (decades already)
those who 'fake' being into Software Freedom lose their status in the community
and gradually perish away, just like Bruce Byfield and this other phony that
attacks my family [1, 2] (one day he might have to face, in court, the people
whom he attacked online for many years).


Generally speaking, freedom-loving geeks learn to reject morbid elements and
trolls, who end up expelled, or implicitly ostracised. This is a protection
mechanism.


For the record, my laptops run Free software and my main laptop will have an
uptime of 1.5 years in two weeks from now. Free software is stable and
predictable. Prior to 2010 I occasionally had system crashes due to the GPU
driver, which was proprietary.


Never make concessions or agreements with people who threaten to stab people or
'joke' about killing people with an axe. The Free software community is a
pacifist one; we do not tolerate violence. █


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇inheritance⦈_


    * The_Open_Source_Initiative_(OSI)_Might_Get_'Forked'_Soon
    * Linux_Runs_Almost_Everything,_But_They_Almost_Never_Tell_You_This_(No
      Marketing_Budget)


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

                    ䷩ 𝚕𝚒𝚗𝚎 3184

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/Growing_Poverty_Rates_in_the_United_States_of_America_or_Elsewh.shtml
    Gemini version at https://techrights.org/n/2025/03/25/Growing_Poverty_Rates_in_the_United_States_of_America_or_Elsewh.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Growing Poverty Rates in the United States
of America (or Elsewhere) Beneficial to GNU/Linux
Adoption⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


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


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Just_stop_worrying_and_sell_vapourware_or_false_promises
                                  like_'AI'⦈_


This year in the US GNU/Linux_rose_to_new_or_unprecedented_(record)_usage
levels judging by the data from statCounter. Let's suppose that what we care
about are trends rather than absolute values; in that case, GNU/Linux is
certainly rising in terms of adoption. It has had a couple of very strong years
and that probably doesn't even count Steam Deck and all sorts of Linux (or
Android) devices.


Some days ago an article was published under the headline "How_Linux_Took_Over
the_World_(Without_Anyone_Noticing)". Nope, many of us did notice...


The mainstream media has been busy producing LLM slop and sponsored puff pieces
(product marketing) wrapped up as "news". Which one is worse? Hard to decide.


Toxic politics around the world, including the US, may mean weaker economies.
In turn, this means that fewer people will buy a Windows licence (permission to
merely rent a copy of Windows) even if it's marketed as something like "hey hi
PC", i.e. pure hype and no underlying substance. █


    * European_Patent_Office_(EPO)_Illegally_Turning_to_Slop_Behind_Closed
      Doors,_Staff_Objects_to_This_Hidden_Catastrophe
    * Roku_Will_'Lead'_Attempts_to_Abolish_the_Illegal_and_Unconstitutional
      Unified_Patent_Court_(UPC),_Which_Represents_EPO_Corruption_and_Lobbyism
      Spreading_Upwards_Inside_the_EU


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⠄⣼⠿⠿⢿⣿⣠⣀⡀⠀⢂⡏⠙⠉⡟⠛⠻⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⣀⣀⣁⠀⢸⠉⠋⠏⠛⠓⡶⠲⠧⠧⣤⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠂⢻⣿⣿⣿⣿⣿⣿⣶⣶⣮⣤⣧⣬⣀⣀⡀⢀⠐⠉⠍⡉⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⢿⣿⣏⣠⣄⣄⣤⣦⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡾⠁⠀⠀⠀⠀⢐⣻⣿⣿⣿⣿⣟⣛⠛⠛⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣋⣰⣴⣶⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠐⣲⣿⣿⣿⣿⣯⣭⣤⣆⣀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢛⣫⣿⣿⣿⣿⠃⠼⠛⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠉⢿⣿⣿⣿⣿⠿⠿⣿⣿⣧⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣍⠁⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡜⢿⣿⣿⡽⠟⠛⢛⣿⣿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⢠⣿⣿⣿⠉⢹⣷⣿⣿⣿⠃⢰⣾⣿⢿⠟⠃⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢿⣿⣿⣿⣟⣵⣶⣶⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⠶⠀⠀⠀⠀⢸⣿⣿⣿⣧⠛⠻⠛⢿⣅⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠿⠿⠿⢿⣿⣿⣿⣿⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠰⣤⡀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⠟⠀⠀⢀⠂⠀⢹⣿⡿⠁⠀⣩⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⡠⠁⠀⠀⠀⣿⣿⣷⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠁⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠗⠀⠀⠔⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣠⣤⣤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⣾⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣻⢾⡵⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣽⣛⣧⣟⣚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⢛⣿⢋⠁⢺⢩⣀⠅⠀⠸⡇⠀⠀⣴⡿⠅⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣖⢾⣳⣶⢫⡶⣾⢱⡖⣾⡟⣾⣶⣧⣾⣵⣶⡏⣶⣲⣶⣶⣶⢰⣶⡆⣶⢰⣆⣶⣴⣶⣦⠀⠀⠀⡈⠳⢶⣄⢸⣿⣿⢰⠀⢘⡿⠀⡐⣟⣠⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢫⣝⣷⢹⣿⣸⣇⣿⢸⡏⣽⣷⣿⡿⣿⡟⣿⣿⡇⣿⢹⣾⣿⣿⠀⣿⠁⣿⢸⣿⣿⣿⣿⣷⠀⠀⢰⠦⣤⣽⠋⠈⢿⣿⣷⡦⠛⠁⢶⢾⡿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠙⠿⢿⣷⣿⣿⣾⣿⣿⣿⢿⡷⣿⣿⣾⡿⣷⡿⣾⣿⢿⣿⣷⣿⣶⣿⣾⣷⣿⣾⣭⣭⣤⣴⣯⡼⣯⣷⣖⣷⣶⣿⣿⣿⣿⣿⣿⣿⣦⡉⠿⠻⠟⢋⢻⣷⡄⢰⣀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⢸⣿⡇⣿⣾⡇⣿⣿⡿⠹⣯⡛⣿⣯⢸⡇⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣄⣀⡚⠿⠃⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣷⣿⢻⡇⣿⡿⠇⠸⣯⡿⢿⣧⢸⣧⢸⣧⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠄⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿
⠀⠀⠀⣤⣤⣤⣤⣤⢠⣤⣄⣠⣤⡄⣤⢠⡄⣤⣤⢠⡄⣤⢠⡄⣤⣄⢠⣤⣄⣤⣤⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⡏⣿⣿⣸⣿⠿⣿⣿⡇⣿⢸⡇⣿⣿⣹⣷⣿⣾⣧⣿⣿⢸⡷⣏⣿⡷⠀⠀⠀⢠⡶⣶⣷⣾⣽⢟⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠃⠛⠙⠛⠛⠀⠙⠛⠃⠛⠚⠃⠛⠛⠋⠛⠛⠛⠙⠛⠛⠚⠃⠛⠛⠛⠀⠀⠀⢸⣿⣿⣿⣿⣸⣉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⢰⢢⣄⣦⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡛⠟⠀⠀⠀⠀⠠⣼⣿⡟⠟⠉⠙⠛⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣦⠀⣠⣴⣶⣶⣦⡀⠀⠀⠛⠛⠃⠘⣘⣛⡋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⣀⢠⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⡖⣶⣶⢲⣶⣗⣶⣶⣶⣶⡀⣷⣿⣷⣶⡆⢁⣿⣼⠉⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣽⣷⣭⠈⠉⠉⠁⣩⣬⣵⣿⣶⣭⣭⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣄⡀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣵⣯⢿⣿⣿⣿⣏⣁⢠⣤⡄⠈⣿⣿⡿⠀⠀⠀⠀⣠⣶⠃⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⡟⠉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⢺⣿⢿⠃⠀⠀⢀⣴⣿⣿⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀
⢻⣿⣿⠀⠀⣸⣿⣿⣧⣤⣤⣄⠀⠀⠰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣫⣿⣿⡛⢻⡿⡶⠀⣠⣶⣿⣿⣿⣿⣿⣷⣤⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀
⣼⣿⣿⡄⢀⣿⡿⠿⠛⣿⣿⣿⠂⠀⠀⠹⣿⣿⣿⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢹⣿⣿⠈⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠙⢿⠟⠉⢹⣿⣿⣿⠃⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠀⡀⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣿⠀⠑⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡃⠀⠀⠀⣸⣿⣿
⠈⠙⢿⣿⡿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠟⢿⣿⣟⣿⣿⣿⣦⠀⣾⣿⣿⡄⠀⠀⠀⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠖⠀⠘⣿⡄⢨⣿⣿⣿⣧⠹⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠐⢻⣿⣾⡏⣻⠃⠀⢀⢙⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠈⠄⠙⣿⣤⡀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⢸⣿⢛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3286

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/IBM_Layoffs_in_the_United_Kingdom_UK_in_2025.shtml
    Gemini version at https://techrights.org/n/2025/03/25/IBM_Layoffs_in_the_United_Kingdom_UK_in_2025.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM Layoffs in the United Kingdom (UK) in
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025


Yesterday: IBM_(and_Red_Hat)_on_a_Fast_Train_to_Nowhere | Press_Reports_Say
Almost_10,000_Western_IBMers_Laid_Off


Hours ago:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇In_past_years,_the_US_gets_hit_first,_and_then_in_the_week
                or_two_after,_the_rest_of_the_world_gets_hit.⦈_


Threads like the_one_above are more than we can count; we saw all sorts of
countries being mentioned for IBM layoffs this month. It does not look like any
country is spared, some say not even India (people claim IBM also laid off
there). Of course thousands got laid off in China, even very recently (almost
2,000_workers).


Since IBM refuses to be transparent, and it's_not_a_new_issue_by_the_way,
almost nobody can keep a tally. All one can say is, IBM is losing government
contracts and removes loads of stuff to "puff up" the stock, even if that means
no actual future for the company. Then_it_floats_bogus_figures,_including
"headcount". Anyone who protests what's happening is presumed_racist.


A lot of the numbers we see and hear can only ever qualify as "Gossip" or
"Hearsay" because IBM almost always refuses to comment.


Should Free software people trust such a secretive company? Can they? █


    * Roku_Will_'Lead'_Attempts_to_Abolish_the_Illegal_and_Unconstitutional
      Unified_Patent_Court_(UPC),_Which_Represents_EPO_Corruption_and_Lobbyism
      Spreading_Upwards_Inside_the_EU
    * The_Open_Source_Initiative_(OSI)_Might_Get_'Forked'_Soon


⣿⣿⣯⣭⣭⠭⣭⣭⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⠉⣉⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⠇⣽⣿⢸⡏⢙⠉⢋⢿⢿⠟⢛⢿⠟⢹⢹⣏⠏⡟⠛⡟⢿⡝⡯⠫⠉⣯⠟⡟⡏⢛⠙⢻⡟⠟⠙⣿⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣒⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⡋⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⡟⢿⣿⢸⠝⢻⠛⠛⠛⡛⠛⠛⡛⢟⠙⠛⡯⠉⢿⠛⠛⢻⠙⠛⠋⢛⠛⢿⠛⠛⢟⠛⠛⠛⠛⢻⠋⠛⣟⢛⠛⠛⡟⠛⡟⠛⠛⡟⢋⠛⠛⡟⠙⢻⠛⠛⠻⠛⢹⠋⠛⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣾⣿⢸⡿⢿⢾⢟⡿⠻⢻⢿⣟⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⠿⠷⠿⠶⢷⠶⠷⠾⡶⢷⠿⠿⢿⢿⠿⠿⡿⡿⢿⠿⠿⡿⠿⠿⠿⢿⢿⠿⠿⠿⡿⠿⠿⠿⢿⠿⠿⠿⠿⣿⣿⡿⢿⢿⢿⠿⠿⠿⢿⠿⠿⠿⣿⠿⠿⢿⣿⢿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣶⣶⣶⣿⣷⣷⣶⣷⣶⣿⣶⣶⣿⣶⣶⣷⣿⣾⣾⣷⣷⣶⣶⣶⣷⣼⣶⣿⣾⣷⣶⣶⣷⣾⣶⣿⣶⣷⣿⣿⣾⣾⣷⣾⣶⣷⣶⣾⣾⣵⣶⣾⣤⣶⣿⣾⣶⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣦⣤⣬⣶⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣯⣅⣁⣴⣤⣇⣸⣠⣦⣼⣢⣤⣬⣺⣤⣼⣧⣠⣇⣴⣤⣸⣤⣬⣄⣮⣠⣥⣯⣴⣤⣻⣲⣔⣜⣤⣸⣮⣺⣄⣤⣨⣇⣴⣅⣇⣥⣴⣦⣧⣥⣤⣼⣠⣥⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⣭⣭⣭⣭⡭⣭⣭⣭⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⣼⣧⣤⣥⣤⣾⢿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⡛⣿⠿⡿⢿⠿⣟⡟⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣑⣿⣸⣇⣻⢘⣘⣃⣇⣻⣀⣿⢐⣂⣈⣊⣀⣐⣇⣆⣈⣂⣀⣲⣀⣺⣐⣇⣺⣗⣑⡁⡪⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⡆⣹⣿⢸⡛⡟⠻⠟⣟⣿⠛⠿⢟⡟⢛⡻⣿⠻⠟⢿⠿⠿⡿⣿⠟⠿⠿⢿⣿⢛⢛⡛⣿⡻⡿⠿⠿⡿⠿⡻⠿⡿⠿⢻⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡏⠦⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠖⢿⣿⢸⣾⣾⣶⣶⣷⣾⣶⣶⣾⣾⣶⣶⣾⣾⣶⣶⣶⣶⣷⣾⣶⣶⣶⣶⣷⣾⣷⣶⣾⣾⣶⣶⣶⣿⣷⣷⣶⣶⣶⣾⣶⣾⣶⣿⣶⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣬⣭⣭⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡓⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣓⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡯⠭⠭⠭⠭⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣛⢿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⡒⢲⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣥⣿⣿⢸⣧⣤⣄⣔⣤⣤⣤⣤⣀⣧⣤⣠⣤⣤⣤⣤⣤⣦⣤⣤⣭⣤⣼⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣀⣚⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣿⣿⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠦⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣛⣛⣚⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3372

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Monday, March 24,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Door_Handle⦈_


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


    * IBM_(and_Red_Hat)_on_a_Fast_Train_to_Nowhere
    * Over_at_Tux_Machines...


⠛⠃⢸⢸⣿⡄⠀⠀⠀⠀⠀⢸⠀⠀⣿⣧⣿⣿⡇⠀⠀⢸⣧⢀⠀⠙⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣼⣿⡿⠀⠀⠀⠀⠀
⡇⢀⣈⣼⣮⠁⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⢿⣿⡇⠀⠀⢸⣿⡄⢆⠀⠀⣀⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣧⠀⠀⠀⠀⠀
⡇⢸⣿⣏⣾⠄⠀⠀⠀⠀⠀⢀⠀⠀⠋⢹⣿⣿⡇⠀⠀⢸⣿⣿⣤⣅⣀⣤⣼⣿⣿⣿⣿⡿⣿⣿⣿⡏⢻⡅⠀⠀⠀⡿⠀⠀⠉⠉⠉⢉⣭⣩⣩⣉⣍⣉⣛⣙⣋⣙⣛⣛⣛⣛⣛⣛⣛⣛⢋⠛⠚⠛⠻⠆⠀⠐⠀⠀
⣷⣿⡿⣷⣿⡖⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠉⠛⠽⠹⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠟⠟⠰⠗⠒⠃⠂⠀⠐⠂
⣿⣿⣧⠃⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⡇⠀⠀⠘⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣤⢀⣀⣀⣀⠀⣂⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠻⠟⠉⢘⡃⠁⠀⠀⠀⠀⠀⠀⠀⠘⢸⣯⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⡇⣿⢼⠀⢸⡋⣿⠀⠀⠀⠘⡟⠌⡀⢘⣿⣿⢿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣯⣉⣱⣷⣶⣦⣥⣤⣨
⣿⡃⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀⢸⡇⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⡖⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⠇⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⢿⢹⣿⣿⠀⢸⠇⡼⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠻⠿⣿⣿⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⣿⡆⠀⠀⠀⣿⣿⡟⠛⡉⡛⣿⣿⢸⡟⣿⡄⢸⠀⢠⠄⠀⠀⠀⢠⠀⢀⠀⣒⢀⡈⠉⠀⠶⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⠸⣯⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⣷⣶⡇⣿⡎⣿⣿⠁⣿⠀⢸⠀⢸⠀⠀⠀⢀⠀⠀⠈⠈⠙⠛⠃⠀⠉⠀⠶⠿⠿⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢰⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⡇⠀⠀⢰⣟⠿⠿⢿⣿⣿⣴⣿⣿⢸⣿⠀⢸⣶⣷⣶⣆⢀⠄⠒⠶⢾⣭⣄⡀⠀⢀⠙⢛⣻⣿⠋⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣸⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠈⢿⣆⡐⠉⠛⣿⣿⣿⣏⠀⡟⣼⣿⣿⣿⣿⣿⣆⣤⠏⠅⣀⠤⠤⠙⠻⠿⣦⣬⡉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠀⠀⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢲⣮⣸⣿⣶⢶⣿⣿⣿⣿⠁⣷⣿⡟⢯⣩⣍⢾⠖⠒⠩⡉⠀⠠⠤⠤⠤⠤⠴⠬⠴⠶⠶⠾⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣛⣫⣤⣬⣭⣹⣿⣿⣇⣼⣺⣖⢿⣢⡿⠃⡀⠀⢰⠀⠀⠐⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣞⣿⣷⣿⠙⠻⠛⠋⢿⡟⢻⢿⡽⣿⣮⣁⢡⣁⡇⢠⣿⠀⠀⠒⢠⣶⡶⢶⢶⠶⢶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⡿⣿⣿⣿⠹⠧⠢⠀⠀⠁⠚⠀⠂⠑⢀⠀⠀⢸⣿⡇⢸⣿⠀⣈⣉⣉⣉⣙⣙⣛⣛⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠱⢿⢚⣰⠄⠀⠀⡠⡜⠀⣶⣷⠀⠀⠀⠀⠀⢸⣿⠁⠸⢻⠀⠛⠛⡿⠿⢛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡇⠀⠀⠀⠀⢠⣾⣷⠠⡷⠀⠀⣰⣿⡿⡄⠀⠀⠀⠀⠈⠁⠀⠀⣾⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⢞⠿⢸⣄⣰⣿⣿⣿⠁⣿⠀⢸⡀⠀⠀⠀⠀⠀⠟⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⡟⣇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⠀⠀⠀⠀⠀⠐⣐⢋⣭⣕⣿⣿⠁⡧⣿⣇⣿⡟⠀⠀⠀⠀⠀⣆⠀⠈⠱⢿⣿⣿⣿⡿⣿⢧⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⢿⠀⡇⣿⣿⣿⡗⠀⠚⠀⠀⢰⡟⠀⠀⠐⢒⠂⠀⠀⣠⣼⣿⣻⣇⠀⣰⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡳⣴
⠀⢻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢀⡆⣿⣿⡟⠛⢓⢠⡇⣿⣟⣿⡇⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⠉⠀⠀⠀⠈⢙⣿⣯⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄
⠀⣸⣿⣇⡆⠄⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣷⠙⠻⠿⠃⡔⢀⡇⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠃⣤⠀⠀⠈⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣻
⡀⡏⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠲⠒⠀⠚⠀⠀⠨⠭⠭⠿⠽⠙⠻⠿⠛⠿⠿⠿⠿⠿⠛⠛⠿⠟⠛⠛⠛⠛⠋
⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣸⡇⣿⣾⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⢻⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠒⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3600

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/Let_Them_Eat_Apps.shtml
    Gemini version at https://techrights.org/n/2025/03/25/Let_Them_Eat_Apps.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Let Them Eat
'Apps'⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇about:blank⦈_


THIS morning Ryan linked to this_page (US government site) and then quoted:
"The payment site is designed to work with all mobile and desktop browsers. If
you have a technical issue related to browser compatibility, we recommend
downloading the latest version of Google Chrome. If you still have problems,
you may request technical support within your account from the help page."


I am familiar with this phenomenon and wrote about it in 2021 [1, 2], then made
a formal complaint that was handled by the Council.


I told Ryan "it is a chrome webapp, proprietary on proprietary" (both Chrome
and the "app", probably the operating system too). It's not very user-friendly
and if you somehow manage to install this malware (with a "recent" enough so-
called 'phone'; old versions won't be supported anymore), then you have no
actual person to speak to; they tend to say, "you can go to our site to run our
malware on your malware" (browser), but there too there's no actual person who
can help. They want people to struggle with finger strokes and unfamiliar (to
be learned and used only once in a lifetime) interfaces. They're basically
cheapening the service... making it cheaper only to themselves (while you pay
with your time, angst and so on).


I joked with Ryan that "you must be a humanoid with "apps"... otherwise, [it's]
either hard or persona_non_grata". I told him that "for accessibility reasons
they tend to have paper-based fallbacks" (they always exist but are also well
hidden; they'd even lie to some people about the existence of such options, not
for technical reasons but because of the above-mentioned cheapening).


"It costs more to file using paper," he says. Yes, they try to punish people
one way or another, like today's U.S. Patent and Trademark Office (USPTO)
penalising people financially if they do not use Microsoft's proprietary
formats.


I told Ryan, "it also costs more to eat well, but you don't want to live on
just bread and butter..."


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Feed_me!!_Or_I_will_need_feed_your_social_control_media
                          notifications_addiction!!⦈_


The latest_article_by_Dr._Andy_Farnell speaks about this. He said: "My family
and I have been free from BigTech for many years and refuse to use Microsoft,
Google or other US services for security reasons. That has sometimes made life
difficult, to say the least. But we are resolute and insistent. Despite
relentless, cloying propaganda claiming it's "impossible" to be free of US
behemoths, we've been happily and more safely living that simple reality for a
long time."


'Apps' aren't fast and they typically don't save time considering how much
maintenance (set aside costs) a modern "phone" demands. It's like having a pet
inside your pocket or purse. It's just an extra responsibility, no matter where
one goes. A wristwatch didn't demand battery changes (or charges) every day and
you didn't need to constantly upgrade it, worry about bloat, viruses etc.


Go Appless. Not Apples. Appless. █


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


You feed him data any second it's turned on.


    * Linux_Runs_Almost_Everything,_But_They_Almost_Never_Tell_You_This_(No
      Marketing_Budget)
    * Links_25/03/2025:_Terrace_Workbench_and_Spellcheck_in_LibreOffice_on
      FreeBSD


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

                    ䷩ 𝚕𝚒𝚗𝚎 4851

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/Linux_Runs_Almost_Everything_But_They_Almost_Never_Tell_You_Thi.shtml
    Gemini version at https://techrights.org/n/2025/03/25/Linux_Runs_Almost_Everything_But_They_Almost_Never_Tell_You_Thi.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux Runs Almost Everything, But They
Almost Never Tell You This (No Marketing
Budget)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


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


Only about 1% (or at_most_2%) of the Linux Foundation's budget goes to or gets
spent towards Linux goals; a lot is routed towards Bill Gates and Microsoft
promotion


Next week (April 1) will be exactly one year since we started our ritual (so-
called 'ritual') of going out for coffee every week. We chat for 3+ hours and
then get back home. We just find it refreshing, especially on sunny days.


Yesterday we went out for coffee and when the machine was doing some advanced
maintenance and probably a reboot cycle (not a mere self-wash cycle) I noticed
that it ran Android and thus Linux. "How cool is that?" I thought... Linux was
making our drinks.


Cool? Meh. It's 2025. It was maybe exciting in 2005. Now? More of the same.


That point could be expanded, a friend has told me, as some readers aren't "old
enough to remember" (as the banter/saying goes). In 2006 Novell colluded with
Microsoft around software patents and many of us were truly worried about the
very survival of GNU/Linux as a free platform; remember it was the same year as
Windows Vista (after XP had become very dominant) and only a few years after
the SCO_case_began. Oracle 'forked' or decided to stick a 'soft fork' (dagger?)
in Red Hat around the same time. Many of us were in the mindset of fighting for
the survival of Free software, especially echoing Richard_Stallman's_concerns
about_Microsoft,_Novell,_and_software_patents. We no longer write about Novell,
but we're still writing a lot about software patents. The problem did not go
away.


Linux, as pointed_out_earlier_today, basically runs the world now. Well, the
digital stuff in the world (but a lot of stuff is digital now, even planes and
cars).


Mind you, more things becoming "digital" is not necessarily a good thing, but
that's a subject for another post. Jeff Geerling has_just_published "I won't
connect my dishwasher to your stupid cloud"; he says: "If you have a cloud app,
that means there's a cloud service that has to be running. That costs money to
maintain."


My mom still uses the same dishwasher she got 35 years ago. What sort of
"cloud" or "app" lasts this long?


Years ago I noticed that even the parcels we send are managed by Linux. The
label-printing machine runs Android and the back end is GNU/Linux. Yes, GNU;
unless or until the British Army in "Ubuntu" clothing changes_that.


Those sorts of things are hardly even worth mentioning anymore. They're
considered almost banal. Maybe that's a good thing, but why does the Linux
Foundation not devote any money to promotion of what it is called_after? Why
did it kill the site Linux.com and turn it into its own spamfarm*? See below. █


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Bill_Gates_PR_and_SPAM:_Drive_your_career_forward_with
        sitewide_savings_of_40%_on_courses,_certifications_and_more!⦈_


_____


* Someone has said "it'd be good to also mention the activities which the Linux
Foundation should be engaged in doing instead of spamfarming", so here's a list
of options:


    * Sponsor git hosting or VPS, as FreeDesktop.org was desperate for it
      lately (it wasn't alone) because of Equinix Metal sunsetting
    * Advertise the fact that GNU/Linux as a desktop (or laptop) platform is
      worth trying
    * Work with OEMs to make GNU/Linux more readily available from store
      shelves
    * Support distros financially
    * Rehire Linux.com writer and editors to make more original stories about
      GNU/Linux
    * Speak out about why Microsoft and Windows are bad; the media almost quit
      talking about that (Microsoft pays advertising money to keep it that way)
    * Free_Software_Community_Folks_Are_Closer_Together_Than_the_Cliques_and
      Opportunists_Rallying_Around_"Open_Source"_(Openwashing,_Marketing,
      Conniving)
    * Let_Them_Eat_'Apps'


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

                    ䷩ 𝚕𝚒𝚗𝚎 5042

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/Martinique_Windows_Down_to_All_Time_Low.shtml
    Gemini version at https://techrights.org/n/2025/03/25/Martinique_Windows_Down_to_All_Time_Low.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Martinique: Windows Down to All-Time
Low⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


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


Martinique is an island with_about_350,000_inhabitants. That's a population
large enough for statistics and smooth curves, unlike say in Antarctica or the
Vatican. The statCounter_data_looks_like_this in March:


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


The sharp increase in favour of Android (Linux) can be explained by examining
device_type_trends:


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


This means that we cannot expect Windows to ever recover. It's down globally.
It is a business_models_catastrophe for Microsoft. █


    * After_US_Government_Funding_Cuts_the_Centralisation_of_the_Web_
      (Especially_Certificate_Authority_Let's_Encrypt)_is_at_Risk
    * When_Microsoft_Folks_Who_Literally_Strangle_Women_Try_to_Strangle
      Microsoft_Critics


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠲⠖⠆⣲⣖⢲⣒⣖⣲⠖⣶⣶⡖⡖⡖⠟⣻⣿⠛⡟⡛⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣮⣥⣽⣧⣼⣮⣧⣼⣵⣿⣿⣿⣼⣯⣤⣿⣥⣵⣵⣬⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣤⣬⣦⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡇
⣿⣿⣿⣿⣿⣷⡈⠉⠙⠻⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣦⡈⠋⠙⠛⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣆⢀⣀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⡏⡫⣙⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⡀⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⣿⣿⡿⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠻⣿⡟⠉⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⣿⣿⣷⣶⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⠀⠀⠀⠀⡽⠀⠚⠀⢠⠈⠛⠙⡿⠛⡿⠛⠟⢻⢻⠛⠻⠋⠻⠛⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⡇
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⠿⠀⠀⠀⡀⠁⣀⣀⣄⣉⡀⠸⣘⣂⣉⣆⣁⣤⣈⣸⣸⣀⣄⣡⡐⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢸⣿⡇
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⢁⣠⣿⣿⣿⣿⣿⡄⠉⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⢧
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠻⡿⢿⣿⣿⣿⣿⡟⠀⠘⠋⢹⣿⣿⣿⣿⠛⠿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⣿
⣿⣿⣏⣉⣍⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣇⠀⠈⠘⢁⠘⠿⠇⢸⣧⣶⠈⢈⣀⡉⠋⢠⣀⣠⣴⣤⠘⠉⠿⣿⣿⣿⡿⠿⠀⠀⣿⢸⣷⡇
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠟⠛⠀⢀⢀⠘⠄⢀⠀⢿⣿⣿⠆⠺⠛⠇⠐⠟⠹⢿⣿⣿⣄⡄⡀⠁⠀⠀⠀⠀⠀⠀⣿⢸⣼⡁
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⡀⠈⢿⣿⣿⣿⣿⡿⠿⠁⡀⠀⣷⣇⣸⣿⠀⠀⣿⡇⠈⠉⠉⢠⣤⣤⣴⡀⠀⣀⣄⢁⡈⢀⠁⠀⢀⣄⣤⣄⣀⠀⠀⣏⣤⣿⡇
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣧⣼⣿⣇⠸⣿⣿⣿⡏⠁⣤⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣼⣶⣾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣦⠀⠙⢸⢟⡆
⣿⣿⡟⢛⠛⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠼⠿⠿⠿⠿⠀⠿⠿⠿⠃⠼⠿⠿⠿⠿⠿⠿⠿⠿⠧⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠙⠉⠙⠛⠋⠀⠀⢨⣿⡇
⣿⣿⣷⣶⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⣿⣿⣿⣿⣧⣈⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⡿⠛⠁⠙⠋⠉⢉⣀⣾⣿⣿⣿⣶⣶⣦⡀⠀⡿⢸⣿⡇
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⡿⠿⠿⡿⠛⠟⠁⠈⠻⠿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠄⢴⣶⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⢸⣿⡇
⣿⣿⣿⣿⣿⡇⣿⣿⣿⠿⠟⠻⡿⠛⠛⠛⠛⠙⠙⠙⠛⠛⠋⠀⠤⠿⠿⠿⠛⠉⠉⠙⠛⠋⠡⠀⠀⠀⡀⢀⣄⢀⣤⣤⣦⣴⣦⡆⢰⣤⣶⣦⣴⣷⣶⣶⣀⣦⣤⡈⢉⠉⠙⠋⣁⣉⡈⠁⠉⠙⠛⠛⠛⠙⢿⢸⣿⡇
⣿⣿⣿⣿⣿⡇⠉⢉⣀⠴⡾⠦⠤⠾⠶⠿⠿⠗⠒⠒⠈⠉⠀⡄⡠⠤⠤⠴⠔⠐⠀⠊⠐⠺⠓⠚⠙⠋⢁⠘⠟⠛⠿⠿⠿⠿⠿⠀⠀⠘⠋⠙⠿⠿⠿⠿⠿⠿⠛⠛⠿⠻⠷⠿⠿⠿⠃⠀⠿⣿⠶⠿⠲⠲⠤⢸⣿⡇
⣿⣿⣿⣤⣤⣥⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣤⢤⣄⣠⣄⣄⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡛⡟⠛⢛⢟⠛⠛⠛⣿⣿⣿⣿⣿⡿⢻⢻⠟⠛⠛⠛⠛⡛⣿⣿⣿⣿⣿⣿⡟⡛⢿⡛⠛⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⢟⡻⡟⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⡷⡷⠾⠷⡶⠶⠶⢿⣿⣿⣿⣿⡿⠷⢿⢾⠶⢶⠶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠾⢿⠶⠶⠾⠾⡿⠿⠿⠿⠿⠿⣿⣿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣵⣧⣤⣤⣼⣬⣤⣼⣼⣿⣿⣿⣿⣷⣮⣾⣬⣤⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣤⣤⣤⣤⣧⣥⣥⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣇⣼⣤⣯⣲⣆⣖⣗⣾⣷⣳⣤⣿⣰⣳⣇⣖⣗⣾⣀⣧⣼⣯⣳⣄⣿⣿⣣⣸⣶⣿⣠⣀⣾⣞⣴⣼⣿⣻⣗⣆⣷⣾⣔⣰⣺⣇⣬⣿⣿⡇⠀⢠⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡿⣹⡛⣟⡋⢿⡛⣟⣿⡩⡍⣛⣟⢻⣛⢛⣿⣟⡟⣟⡛⣟⣛⣿⣛⡏⢟⣻⣿⡟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣥⣿⣧⣾⣭⣯⣿⣭⣦⣿⣮⣼⣿⣭⣿⣿⣼⣧⣥⣿⣯⣿⣿⣧⣮⣽⣭⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡎⢹⠍⡿⠺⠰⡷⢠⢾⣟⣿⡜⣼⢹⢩⡷⢸⠖⠖⡧⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣮⣤⣼⡉⠉⣉⡉⠉⠉⠉⠭⠭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣄⣤⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⢉⠉⢹⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣂⣂⠉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡓⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⣾⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⢿⣿⣿⡟⢠⣄⣁⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⢿⠁⣾⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⠛⠛⢻⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠤⠤⠀⠀⠀⠀⠸⠛⠋⠛⠓⠂⠈⠛⠛⠟⠛⠟⠟⠟⠀⠏⠙⠛⠻⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠠⠆⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠛⠀⠀⣠⣰⣯⣤⣧⣭⣤⣼⣬⡄⠅⠠⠥⣧⣥⡇⠀⣧⣬⡄⢨⣼⣿⣿⣿⣿⡿⠛⣿⣿⠻⠿⠁⠉⡟⢻⠟⠿⡿⠏⢸⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⣄⠋⠁⠁⣤⠈⠛⠃⡀⠀⠘⢿⠛⢿⠃⠀⠁⣤⣴⣤⣤⣴⣀⠀⢠⣄⡀⠀⢸⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⠀⢰⣾⣿⣤⡆⠸⡿⠿⠀⠀⠰⠀⠠⣿⣿⣿⣿⣿⣿⣿⠿⠃⢻⣿⠷⠀⢸⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⠿⠿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⠀⠈⠙⣿⠁⢁⡄⢀⡀⢠⣾⣴⣶⡄⠀⢀⠛⠿⠋⠋⠉⡀⢀⠀⠁⠀⠀⢸⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣼⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠂⠀⣶⣦⡆⠀⣠⣴⣦⣴⣶⣶⣶⣶⣶⣶⣤⣶⣶⣤⣶⣦⣤⣶⣶⣶⣶⣶⣶⢰⡆⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡆⢰⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣁⠉⢻⣿⣿⣿⡿⠇⢀⣼⣷⣾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡀⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣧⠈⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣼⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⣬⣭⣭⣭⣄⠨⠉⣌⣠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢀⠁⠔⢉⣁⣈⣠⣬⣉⠛⠿⠿⠿⠿⠟⠿⠟⠻⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠋⠛⠋⠉⠁⢈⣠⣴⣶⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣧⣴⣦⣶⣄⣤⣤⣁⣁⠈⠛⠿⠏⠙⠛⠛⠛⠛⠛⠛⠋⠙⠛⠿⠿⠿⠿⡿⠟⠟⠹⡿⠃⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣹⠀⠈⠉⠉⠉⠉⠀⠐⠂⠐⠂⠒⠚⠂⢀⣉⣉⣉⣉⣉⢉⠛⠛⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣈⣁⠐⠒⠛⠓⠚⠛⠉⣉⠛⠛⠛⠓⠒⠒⢀⠀⠐⠀⠒⠂⠀⠀⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⡟⠛⠛⠛⣛⢛⣿⣿⢛⢻⠻⠛⢛⠛⠻⣿⡿⣛⢟⠛⢛⠛⢛⣿⡿⢛⢿⢛⡛⡛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣿⣿⣷⣿⣶⣶⣶⣶⣶⣿⣿⣶⣿⣶⣶⣶⣶⣿⣿⣷⣿⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5180

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2025/03/25/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Mar 25, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Cars_Chevrolet_3100_Series_Pickup_1946⦈_


⚓  Updated This Past Day⠀⇛


   1. ⚓ Linux_6.14_Released⠀⇛


           original and LWN


      ⚓  New⠀⇛


   2. ⚓ GIMP_3.0.2_Image_Editor_Improves_the_Flatpak_Bundle_and_Fixes_Various
      Issues⠀⇛


           The GIMP (GNU Image Manipulation Program) project released
           today GIMP 3.0.2 as the first maintenance update to the latest
           and greatest GIMP 3.0 series of this powerful, free, open-
           source, and cross-platform image editor.


   3. ⚓ This_Week_in_KDE_Apps:_Stability_improvements_in_KDE_PIM-land,_and
      polls_in_NeoChat⠀⇛


           Every week we cover as much as possible of what's happening in
           the world of KDE apps


   4. ⚓ Raspberry_Pi_rpi-image-gen_and_Raspberry_Pi_Add_PoE⠀⇛


           The tool builds on concepts from Raspberry Pi's previous pi-gen


   5. ⚓ GNU/Linux_Leftovers⠀⇛


           some more on GNU/Linux


   6. ⚓ Free,_Libre,_and_Open_Source_Software_Leftovers⠀⇛


           FOSS picks


   7. ⚓ DragonFly_BSD_Digest_and_BSDs_in_2025⠀⇛


           BSD picks


   8. ⚓ Programming_Leftovers⠀⇛


           Development picks


   9. ⚓ Open_Hardware:_Flipper_Zero,_Raspberry_Pi,_and_More⠀⇛


           hardware picks


  10. ⚓ Open_Source_Initiative_Election_Shenanigans,_LINUX_Unplugged,_and_This
      Week_in_Linux⠀⇛


           new episodes


  11. ⚓ today's_howtos⠀⇛


           mostly idroot


  12. ⚓ Red_Hat:_"IBM_to_Slash_Nearly_9,000_Jobs_in_US"_and_Fedora_42,_SCaLE22x
      Etc.⠀⇛


           Red Hat picks


  13. ⚓ Enable_3/4_Finger_Dragging_in_Ubuntu_via_Libinput_2.18.0⠀⇛


           Libinput released version 1.28.0 today


  14. ⚓ Linux-Assistant_is_a_Tool_You_Didn't_Know_You_Needed!⠀⇛


           Tired of managing your Linux installation? Linux-Assistant
           helps simplify common maintenance tasks


  15. ⚓ 9to5Linux_Weekly_Roundup:_March_23rd,_2025⠀⇛


           The 232nd installment of the 9to5Linux Weekly Roundup is here
           for the week ending on March 23rd, 2025.


  16. ⚓ Android_Leftovers⠀⇛


           Nothing and Pixel prove that stock Android is a thing of the
           past


  17. ⚓ scooter_is_an_interactive_find-and-replace_terminal_UI_app⠀⇛


           This is free and open source software


  18. ⚓ Hyprland_Celebrates_Its_Third_Birthday_with_v0.48⠀⇛


           Hyprland 0.48 tiling Wayland compositor is out with major
           improvements


  19. ⚓ Security_Leftovers_and_Windows_TCO⠀⇛


           Security picks


  20. ⚓ 10_Tricks_You_Can_Do_With_FFmpeg_on_Linux⠀⇛


           Want to do more with the Linux terminal? You might not
           instinctively put videos and the command line together


  21. ⚓ today's_leftovers⠀⇛


           GNU/Linux and more


  22. ⚓ Free_and_Open_Source_Software⠀⇛


           This is free and open source software


  23. ⚓ Review:_Bazzite_41⠀⇛


           Bazzite In mid-to-late January 2025, I finally broke my OS


  24. ⚓ Videos:_GNU/Linux,_Free_Software,_and_HowTos/Demos⠀⇛


           via Invidious


  25. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


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


                          Span from 2025-03-18 to 2025-03-24
      1002 /n/2025/03/17/
           GIMP_3_0_Image_Editor_Is_Now_Available_for_Download_Here_s_What.shtml


      975  /n/2025/03/19/
           GNOME_48_Bengaluru_Desktop_Environment_Officially_Released_This.shtml


    * IRC_Proceedings:_Monday,_March_24,_2025
    * Anticipated_in_2018:_Lilie_James_&_Location_tracking,_Googlists
      complained


⠀⠀⠀⢀⣴⣾⣿⢽⣿⣿⣿⡿⢛⠁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⡂⠆⠋⠛⡾⡿⢿⡟⢁⢆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣶⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢾⣶⣿⡿⢦⠀⢄⠞⠀⡎⣼⣿⣅⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿⣿⣿⣶⣶⣭⣽⣟⣻⣿⣿⣶⣶⣤⣤⣤⣶⣾⣿⣿⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠚⠊⠠⠞⠀⣰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡍⠋⢿⣿⣘⠹⢿⣿⣿⣿⢻⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣚⣉⣉⠉⠉⠙⠋⠛⠛⠿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣽⣿⣿⣿⣷⣤⣌⣿⣿⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣾⣿⣿⡿⢿⣦⣿⡿⠃⡸⠘⣿⣶⣦⣄⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠐⠂⠠⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠒⠿⠿⠿⠶⢶⠆⠬⠭⠍⠙⢛⣛⠛⠻⠟⠻⠾⢭⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⠾⣿⡿⠳⢾⡇⠀⣿⣿⣿⣿⡗⠁⠀⠁⠀⣀⠀
⠀⢀⡀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⡒⢠⣶⣤⣤⣴⣆⢀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢶⣶⣶⣶⣤⣤⣤⣄⡀⠀⠀⠉⠀
⣶⠀⠀⠉⠙⠒⠲⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀
⡗⠢⠤⣀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⣿⣶⣶⣶⣶⣶⣶⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⢸⣿⡆⠀⣁⢀⡀⠀⠀⠀⢀⣤⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠙⠋⣯⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣭⣛⣓⣿⠿⠣⠀⠁⠀⠀⢀⣤⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣤⣄⠀⠉⠛⠻⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⣿⣛⣛⣛⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣽⣛⣛⣛⣻⣛⡶⠟⣛⣉⣭⣉⣛⠻⢿⣿⣿⣷⢄⣻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣙⡻⢿⣿⣶⡞⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⢛⣿⣿⠛⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣾⣿⣿⣿⣿⣿⣷⣄⠹⠟⣄⠀⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⢰⡆⠉⠉⠙⠛⠛⠛⣻⡟⠛⢻⣿⡟⠉⣽⣿⠇⢀⣾⣿⠃⢠⣿⡿⠃⣴⣿⠟⢀⣼⣿⠋⢿⣿⣿⣿⣿⣿⡏⢰⣿⠟⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡏⠀⣸⠃⠀⠀⠀⠀⠀⢰⣿⡇⠀⣾⣿⠁⢰⣿⡟⠀⣼⣿⠇⠀⣾⣿⠃⣼⣿⠏⢀⣾⣿⠃⢀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣯⣿⣿⣿⣾⣿⣿⣽⡇⠀⢀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⠀⣿⠀⠀⠀⠀⠀⠀⣸⣿⠀⢠⣿⡏⠀⣾⣿⠃⢀⣿⡿⠀⢸⣿⠇⢸⣿⡟⠀⣼⣿⠇⠀⣾⣿⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⡛⡿⡿⣿⡛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠀⠀⡎⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⠇⢀⣿⡿⠀⢸⣿⡇⠀⣿⣿⠀⣿⣿⠁⢰⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠿⢿⣷⣿⡿⠟⠁⠀⢰⣿⣿⣿⣏⢙⢧⠽⡿⠩⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⢠⣿⠇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢰⣿⡇⢰⣿⡟⠀⣾⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⣿⣉⠌⠓⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⡇⠀⣾⣿⠀⢀⣿⡇⠀⣸⣿⠁⣸⣿⠃⢀⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⠉⣿⠠⠃⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⣿⠃⠀⣿⡟⠀⢸⣿⠁⠀⣿⣿⠀⣿⣿⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣸⣿⠀⢰⣿⡇⠀⣾⡿⠀⢰⣿⡇⢠⣿⡏⠀⣼⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⢸⣿⠁⠀⣿⡇⠀⢸⣿⠁⢸⣿⠁⠀⣿⡿⠀⢀⣿⣿⣿⣿⣿⣯⢉⣡⣿⣿⣿⣿⣿⣿⣿⡟⣿⣫⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣿⠃⠀⣸⣿⠀⢰⣿⠃⠀⣾⡿⠀⣸⣿⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣇⠀⣾⡿⠛⢻⣻⣿⣿⣻⣿⣿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣿⠇⠀⢸⣿⠀⠀⣿⡃⠀⣿⡋⠀⢸⣿⠁⠀⢸⡿⢸⣿⣷⣰⣤⣟⣿⡿⣿⠟⢐⣿⣿⠐⠌⡉⣿⣯⣯⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢸⡏⠀⠀⣿⠁⠀⣿⠂⠀⢸⣯⠀⠀⡷⢳⣿⣿⣿⡟⢣⣤⢿⠃⢹⠦⡿⠻⠁⠀⠀⠀⠘⠻⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠞⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠀⠀⠿⠀⠀⠸⠛⠀⢀⣴⣿⣿⣛⢿⠟⠏⠘⠚⡠⠚⠲⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠐⠺⠣⠿⠟⠋⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 5412

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/Roku_Will_Lead_Attempts_to_Abolish_the_Illegal_and_Unconstituti.shtml
    Gemini version at https://techrights.org/n/2025/03/25/Roku_Will_Lead_Attempts_to_Abolish_the_Illegal_and_Unconstituti.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Roku Will 'Lead' Attempts to Abolish the
Illegal and Unconstitutional Unified Patent Court (UPC), Which Represents EPO
Corruption and Lobbyism Spreading Upwards Inside the
EU⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Roku_demo⦈_


When bribery buys policies and courts, even illegal_policies and courts


Related: An_Article_Techrights_Contributed_to_Exposes_Corruption_in_Europe's
Largest_Institutions,_Including_the_EPO_and_EUIPO


At last it's happening.


Roku challenges the legality of the_UPC! It all along seemed like this was just
a matter of time, only a matter of which heavy- or deep-pocketed company does
this first.


One can hope those who decide on the matter aren't political or, yet worse, in
the pockets of Team UPC, i.e. profiteers of a_system_they_themselves_created_in
order_to_profit_more (at others' expense).


As one person put_it_this_month: "Roku is challenging the compatibility of the
Unified Patent Court Agreement with EU law, and has been allowed to appeal that
question to the CoA."


Some further quotes: "Roku challenging the legality of the Unified Patent Court
[...] According to Roku, it's insufficient that the Brussels I bis Regulation
(secondary law) treats the UPC as the equivalent of a court of an EU Member
State [National Court]"


"The judgment is in German," someone has told us, but based on those who "made
some LLM automated translation to English, it basically says art267tfeu is for
national courts. Changing how EU Law works would have required a change of the
EU treaties."


"Roku is appealing to UPC in Luxembourg," we're told, and there's "doubt they
will ask the question to the CJEU."


Eventually it needs to go to the highest courts (not kangaroo ones), ending the
UPC and probably removing all "unitary effect" from all European Patents.


This was a very dark episode in EU history; when they pushed the UPC despite
knowing it was impossible (unless they promote what's impossible, i.e. the
illegal and unconstitutional) they signalled that the EU quit caring about the
Rule of Law and instead did whatever lobbyists demanded.


A lot of the media quit writing about EPO corruption (the EPO sends SLAPPs to
reporters), but it remains a serious problem that even EPO stakeholders talk
about and campaign around. Patent applicants too are upset. We_can_relate_to
that.


For the sake of their hard-earned reputation and perceived legitimacy (respect
from the public) courts of law do not wish to entertain and generally prefer to
avoid violent criminals (e.g. Texans from Microsoft) whose goal is to gag their
victims and/or people who report on abhorrent behaviour. Similarly, patent
courts can reject EPO rubbish to avoid getting stereotyped like Texan patent
courts. █


    * Growing_Poverty_Rates_in_the_United_States_of_America_(or_Elsewhere)
      Beneficial_to_GNU/Linux_Adoption
    * IBM_Layoffs_in_the_United_Kingdom_(UK)_in_2025


⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⡿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣯⣀⣀⣀⣀⣀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠇⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⣿⣿⣿⣿⣿⣿⣿⣿⠆⠆⢸⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣳⣚⣉⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠘⠁⠛⠙⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠰⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣦⣶⣴⣶⣶⣶⡶⢶⣴⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣙⣙⣙⣙⣙⣉⣛⣙⣙⣁⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠙⠲⠒⠒⠖⠘⠓⠖⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⢟⣋⣙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⢠⣧⢺⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣇⠻⣿⣿⠇⣿⣿⣿⣿⣿⣿⠀⠀⢨⣿⣿⣿⣿⣥⣥⢭⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠃⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣦⣭⣭⣾⣿⣿⣿⣿⣿⣿⠀⠀⢨⣭⠭⠟⠫⠭⠭⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠘⣿⣿⣿⣷⡆⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣟⠋⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣄⣀⣠⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣏⢠⠈⣷⠗⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢶⡶⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣦⠀⠋⠀⢀⠀⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠗⠈⣁⠀⠄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢠⣶⣶⣶⣶⣶⣶⣶⣦⣁⣀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣟⠁⡀⢀⣀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣯⠀⣴⠶⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⠉⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢈⣛⢉⠹⡿⢿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⡆⠀⠠⠀⠀⠀⠀⢀⣀⣀⣀⣀⣒⣀⣀⣀⣀⡀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 5531

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/The_Open_Source_Initiative_OSI_Might_Get_Forked_Soon.shtml
    Gemini version at https://techrights.org/n/2025/03/25/The_Open_Source_Initiative_OSI_Might_Get_Forked_Soon.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Open Source Initiative (OSI) Might Get
'Forked' Soon⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Garden_Hand_Fork⦈_


Someone who read our series has already taken a leading role


We shall soon resume the series about the OSI. It'll be very long.


It seems like some people have read the previous_chapter and decided to do
something about the Open Source Initiative's (OSI) series of unforced_errors.
How do we know this? Well, days later Bradley Kuhn (SFC) wrote two angry blog
posts about the OSI and days ago he decided to speak to this_right-wing_fanatic
from_Microsoft_about_"Open_Source_Initiative_Election_Shenanigans". To quote
the outline:


     The "Hacker-in-Residence" of the Software Freedom Conservancy (and
     past Executive Director of the Free Software Foundation) talks about
     Open Source Initiative election rigging.


We'll be covering the "Open Source Initiative election rigging" (correct words
used there) next month.


So what will happen to the OSI and the Open Source Definition, which is
possibly not even controlled by the OSI and was never controlled by the OSI -
more so after its co-founder Bruce Perens had left in protest? Perens is the
one who wrote this definition or wrote the DFSG and thus - inter alia - the
Open Source Definition.


"Here’s the response from Bruce is the Debian free software guidelines a free
doc," one reader told us. "Because of the we hope other projects take on this
as a model." (We suggested this weeks ago).


"I do plan to modify," she said, "but just the name so we can have a new
definition to work from. But the Debian project isn’t exactly A great player
these days, so Let’s see how this goes!!!!"


She_wrote_to_Debian. "There was some talk about a flaw," she said, but "I need
to dive down that rabbit hole cause that seems very interesting. No consensus,
yet on the gladly granting me permissions!"


The message:


     Hi. My name is Marcia Wilbur. I have a few projects I contribute to,
     Including a remaster tool, Technical writing tools, and a few fun
     things having to do with open computer vision.


     Bruce Perens in the Debian Free Software Guidelines announce states:


     We hope that other software projects,


     including other Linux distributions, will use this document as a
     model.


     We will gladly grant permission for any such use.


     https://lists.debian.org/debian-announce/1997/msg00017.html


     I would like to use the Debian Free Software Guidelines document as a
     model for my projects as well as promote DFSG or a derivative as a
     model for other projects.


     At this point in time, the only thing I would modify is the name.


     Thank you,


     Marcia Wilbur


     Linux respin


Requests to use DFSG as a model were granted by Perens, who said: "I hope
you're doing well. If you're not going to modify it, I think you could just
cite the document at its current location. If you are, just for formality sake
you should ask the Debian folks. I've not been on that project for some years -
just too many things to do."


So it looks like it's actually underway already, with the implicit blessing of
the originator of the DFSG and the Open Source Definition (he co-founded the
OSI and no longer trusts the OSI).


Expect the OSI to issue many more face-saving work soups. There's not much the
OSI can do to salvage its reputation at this point. █


    * IBM_Layoffs_in_the_United_Kingdom_(UK)_in_2025
    * Free_Software_Community_Folks_Are_Closer_Together_Than_the_Cliques_and
      Opportunists_Rallying_Around_"Open_Source"_(Openwashing,_Marketing,
      Conniving)


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣉⣙⢟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠈⠈⠉⠀⠑⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠷⠋⠀⠀⠀⠀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡜⣵⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⠢⠍⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣋⣎⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠹⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⢀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣛⠻⣿⣿⢿⠿⢟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠐⠃⠁⠈⠉⠀⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣕⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡆⠭⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⣐⣭⠡⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠩⠁⠀⠀⠀⠀⠀⠀⢀⠀⢜⢵⣷⣷⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡟⠻⠀⠀⠀⠀⠀⠀⠀⢠⣦⣿⣼⣵⣝⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⣿⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⡇⠃⠀⠀⠀⠀⠀⢠⣲⣪⣿⣿⣿⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣑⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⡂⠁⠀⠀⢀⡠⠀⢡⢻⣿⣿⣿⣿⣿⠨⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠲⣅⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⢊⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣌⢆⣀⣠⣰⣿⣿⣿⣿⣿⣿⣿⡯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⡿⣝⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣷⣷⣿⣿⣿⣿⣿⡿⣋⡩⠀⠀⠀⠀⠀⠀⠀⠀⡰⣲⣶⣿⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠆⠀⠀⠀⠀⠀⠀⣠⢖⣴⣵⣟⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⡒⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣀⣤⣁⣗⣵⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⢀⠔⣤⣡⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⡶⢶⣿⣿⣿⣿⣿⢹⠂⠀⠀⠀⠀⠀⠀⢀⢤⣽⡩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 5696

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/25/When_Microsoft_Folks_Who_Literally_Strangle_Women_Try_to_Strang.shtml
    Gemini version at https://techrights.org/n/2025/03/25/When_Microsoft_Folks_Who_Literally_Strangle_Women_Try_to_Strang.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ When Microsoft Folks Who Literally Strangle
Women Try to Strangle Microsoft Critics⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


Speaking to Court staff yesterday, they too are shocked about those SLAPPs [1,
2]


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


Daniel Pocock has just_said that "Googlists have spent over US$130,000 to try
and discredit me, to stop women telling me stuff and to stop us making
predictions that are uncomfortably close to the truth."


The word "discredit" may be an understatement when they go out of their way to
defame_people and incite dangerous mobs against them. We took necessary action
[1, 2].


Microsofters have spent more than this (more than US$130,000) trying to silence
this site (and my wife's site, which merely advocates GNU/Linux and Free
software; boo hoo) and one must be aware of the motivations, which go years
back_and_overlap_attacks_on_other_people_who_speak_about_Software_Freedom_and
against_Microsoft's_monopoly_abuse. All this stuff is connected; the aim is to
turn the FSF from an organisation that promotes its founder's talks (and
message) into a C#_booster that authors_in_Microsoft_tools and keeps_a_distance
from_its_chief_visionary. That's what they already did to the OSI.


The most horrible thing is, they try to go after me for doing the right thing
and opposing violence against women. One_is_connected_to_the_other.


“He refers to MJG as "former Microsoft researcher" (in his own site),” I said
last year, and then provided_evidence_yesterday. He tried_to_censor_stories (by
begging), then tried_with_threats sent via_another_continent by some
disrespectful broke_firm that does_"reputation_management" for anyone_willing
to_pay (money_from_Microsoft, they repeatedly_refuse_to_talk_about_this). █


    * Martinique:_Windows_Down_to_All-Time_Low
    * Links_25/03/2025:_Putin_Sends_Children_to_Battle,_23andMe_Drowns_as
      People's_Highly_Personal_DNA_Data_Floats


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⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠗⣉⣭⣵⣶⣦⣄⣀⡀⠀⢀⣀⣼⣦⣤⡤⠀⢿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡁⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠟⣛⣛⣛⣛⡋⠉⠉⠉⠀⣴⣴⣶⣾⣿⣿⣷⣿⣷⣶⣦⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣷⡤⠉⠿⠿⠿⠿⠿⣿⠁⠿⠿⠛⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠏⠀⣠⣿⣶⣶⣦⡆⠀⢰⣶⣿⣿⠿⠿⠿⠟⠛⠛⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⠙⠛⠛⠻⠿⠛⠛⠉⠙⠻⠆⢰⣶⣿⣿⣿⣿⣿⣷⣦⠠⣿⣿⣿⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠯⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠛⠀⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⢄⣽⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 5785

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 25/03/2025: Relaxation,
Literary "Movements", and Gemini Mentions⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Relaxation⠀⇛


                       Long day. Biked to work, after that I visited a
                       friend on the way. I went to have a good workout,
                       and got some groceries on the way home. At home, I
                       heated up the sauna and had great time finally
                       relaxing. One final burst of activity to get my
                       things ready for tomorrow, and then I had some
                       food.


                # ⚓ literature,_history,_and_literary_"movements"⠀⇛


                       In it, I note that World Book got one thing more
                       right than my four years of undergrad did: it
                       acknowledges that "literary movements" aren't
                       monolithic, easily-defined things. Labeling any
                       author or work a "Transcendentalist" or a
                       "Romantic" or a "Modernist" is, at best,
                       simplistic. This is even true of writers who
                       intentionally and aggressively stuck to a single
                       movement or set of ideas as it developed - like
                       Ralph Waldo Emerson or Bronson Alcott.


                       Rather, every writer at every point in history is
                       in conversation - with their own work, with other
                       writers, with current events, with history itself.
                       Those conversations interweave and interact.


                       Also, some "movements" are either so aggressively
                       American or so well-adapted to commentary on the
                       American experiment that they never really die. I
                       mean Realism in the former case and Modernism in
                       the latter. I'd even go so far as to argue that
                       were it not for the influence of the CIA, "post-
                       modernism" would not exist.


                # ⚓ Experimenting_with_vegan_milk_kefir⠀⇛


                       I have a small culture of water kefir grains, which
                       I use to make… water kefir. Recently, I wondered if
                       I could make something similar to milk kefir using
                       soy milk and my grains. I tried:


                       * Putting kefir grains in soy milk * Putting
                       already-made water kefir (which also contains
                       ferments) in soy milk


                       Both methods produced kind of the same result,
                       which was a separation of curd and "water". The
                       grains' result was much faster and impressive, but
                       the grains were really hard to remove (unlike in
                       water, you can't really sieve them, since the curd
                       itself will not pass the sieve). I tried skimming
                       the result for various amounts of time, which made
                       :


          o § Politics and World Events⠀➾


                # ⚓ The_alleged_flaws_in_LAFRA_2024⠀⇛


                       The Conservatives' Leasehold & Freehold Reform Bill
                       of 2024 passed its last stage in the House of Lords
                       on the final sitting day of Parliament before the
                       general election. It quickly received royal assent
                       and became enacted as LAFRA 2024.


                       Under its own terms, only a few of its provisions
                       came into force that day. The rest are subject to
                       secondary legislation for "commencement". The
                       government announced in November a timetable for
                       some of the measures to be commenced. But that
                       statement blamed "flaws" in legislation for the
                       inablity to commence some of it.


          o § Technology and Free Software⠀➾


                # ⚓ Updates⠀⇛


                       I'm learning Spanish, not very fast and not very
                       good but it takes some my time.


                       Also, I was dived deeply in my some projects for
                       Agons:


                       - port of CP/M 2.2 - ZINC(ZINC Is Not CP/M) - CP/
                       M compatibility layer for Agon Light and
                       compatible. It similar to WINE for UN*X -
                       translating API calls from CP/M to Agon MOS


                       - I've updated SNAIL and made it really good - I've
                       created my own compiler that works directly on Agon
                       - BSimple. It's B- or C-like programming language
                       that compiles to assembly.


                       Mostly typeless(one data type - machine word) and
                       have very simple semantic.


                       Currently, I'm working on iteration of BSimple
                       development [...]


                # § Internet/Gemini⠀➾


                      # ⚓ Gemini_mentions⠀⇛


                             In Geminispace there are a lot of creative
                             geminauts :) There are incredible decisions
                             and ideas. One of my following geminauts are
                             Becardi55 and one his idea gemini-mentions[1]
                             was something what I was thinking about, too.


                             Some kind of socialization is needful for all
                             people and I am one of them. And Becardi55
                             created RFC for Gemini Mentions[2]. Also he
                             wrote example in Golang[3].


                # § Programming⠀➾


                      # ⚓ Devlog_14⠀⇛


                             Okay, so I went away and did some reading and
                             I've concluded the following:


                             * Yes: server-side rendering is a much better
                             approach


                             * HTMX is awesome


                             * I much prefer Java to Go


                             That last one might surprise some of you, but
                             I was able to pretty much implement the
                             entirety of what I've done with Vue/ Go over
                             the last couple of months with Spring, HTMX,
                             and Thymeleaf in a morning. I'm just more
                             efficient with Java. My first real love.


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


    * Links_25/03/2025:_Putin_Sends_Children_to_Battle,_23andMe_Drowns_as
      People's_Highly_Personal_DNA_Data_Floats
    * European_Patent_Office_(EPO)_Illegally_Turning_to_Slop_Behind_Closed
      Doors,_Staff_Objects_to_This_Hidden_Catastrophe



                    ䷩ 𝚕𝚒𝚗𝚎 5998

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 25/03/2025: Clownflare’s Slop and
Bounties on Fake Patents⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025,
updated Mar 25, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Science⠀➾


                # ⚓ Jim Nielsen ☛ Book_Notes:_“The_Order_of_Time”_by_Carlo
                  Rovelli⠀⇛


                       When we do science, we want to describe the world
                       in the most objective way possible. We try to
                       eliminate distortions and optical illusions
                       deriving from our point of view. Science aspires to
                       objectivity, to a shared point of view about which
                       it is possible to be in agreement.


                       This is admirable, but we need to be wary about
                       what we lose by ignoring the point of view from
                       which we do the observing. In its anxious pursuit
                       of objectivity, science must not forget that our
                       experience of the world comes from within. Every
                       glance that we cast toward the world is made from a
                       particular perspective.


                       I love this idea. Constantly striving for complete
                       and total objectivity is like trying to erase
                       yourself from existence.


                       As Einstein showed, point of view is everything in
                       a measurement. Your frame of reference is important
                       because it’s yours, however subjective, and you
                       cannot escape it.


                       What we call “objectivity” may merely be the
                       interplay between different subjective
                       perspectives.


                # ⚓ New York Times ☛ You_Can_Make_Amber_Fossils_in_24_Hours,
                  Instead_of_Millions_of_Years⠀⇛


                       Paleontologists hope that an amber-like material,
                       made with living tree resin, will shed light on the
                       prehistoric fossilization of the real stuff.


                # ⚓ University of Michigan ☛ Life_Sciences_Orchestra_blends
                  science_and_music_for_25_years⠀⇛


                       The U-M Life Sciences Orchestra is celebrating its
                       25th season of blending science and music by
                       featuring amateur musicians of the medical and
                       science community.


                # ⚓ Science Alert ☛ 'Red_Princess':_Mysterious_Skeleton_With
                  Dyed_Teeth_Is_a_Scientific_First⠀⇛


                       We've never seen this before.


                # ⚓ Science Alert ☛ Mysterious_Golden_Orb_Found_at_The_Bottom
                  of_The_Ocean⠀⇛


                       "It's like the beginning of a horror movie."


                # ⚓ Science Alert ☛ Mysterious_'Death_Star'_on_The_Verge_of
                  Exploding_Is_Hiding_a_Secret⠀⇛


                       We don't know how this happens.


                # ⚓ Science Alert ☛ Largest_Carbon_Molecules_Found_on_Mars
                  Build_The_Case_For_Ancient_Life⠀⇛


                       What made them?


                # ⚓ Science Alert ☛ Your_Brain_Might_Start_'Eating_Itself'
                  During_Strenuous_Endurance_Exercise⠀⇛


                       Don't worry, it's reversible.


                # ⚓ Chronicle Of Higher Education ☛ Dihydroxyacetone_Man
                  Policies_Could_Send_International_Talent_Elsewhere,_Hobbling
                  U.S._Science⠀⇛


                       Funding cuts and immigration concerns might cast a
                       long shadow.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Wearable_Computing_Goes_Woven,_Wireless,_And
                  Washable⠀⇛


                       Sometimes we come across a wild idea that really
                       tries to re-imagine things, and re-conceiving
                       wearable computing as a distributed system of
                       “fiber computers” embedded into textiles is
                       definitely that. The research paper presents fully-
                       functional fiber computers and sensors that are
                       washable, weave-able, wireless, and resist both
                       stretching and bending.


                # ⚓ Tom's Hardware ☛ U.S._asks_Malaysia_to_'monitor_every
                  shipment'_to_close_the_flow_of_restricted_GPUs_to_China⠀⇛


                       Malaysia to tighten GPU exports oversight amid U.S.
                       pressure over Nvidia shipments to China.


                # ⚓ Tom's Hardware ☛ Ant_Group_reportedly_reduces_Hey_Hi_(AI)
                  costs_20%_with_Chinese_chips⠀⇛


                       Ant Group is utilizing Chinese semiconductors to
                       enhance the efficiency of its artificial
                       intelligence development.


                # ⚓ Hackaday ☛ PPS_Is_The_Hottest_USB-C_Feature_You_Didn’t_Know
                  About⠀⇛


                       USB Power Delivery is widely considered to be
                       a good thing. It’s become relatively standard, and
                       is a popular way for makers to easily power their
                       projects at a number of specific, useful voltages.
                       However, what you may not know is that it’s
                       possible to get much more variable voltages out of
                       some USB chargers out there. As [GreatScott!]
                       explains, you’ll want to meet USB-C PPS.


                # ⚓ RealtimeKit_and_CPU_Scheduling⠀⇛


                       Take a look at your process tree, it’s likely that
                       you might notice a new service: rtkit-daemon, the
                       RealtimeKit Daemon. It seems nobody on the internet
                       is talking about it, so let’s explain what it’s
                       about in this article.


                       § A Refresher on Multitasking


                       First, let’s refresh our minds about multitasking
                       OSes.
                       In a multitasking OS, we have many “tasks” that
                       share the same resources. One of these resources is
                       the CPU bandwidth, aka time; We call that time-
                       sharing. The OS CPU scheduler is the piece of
                       software that dictates the scheduling policy: it
                       selects which task runs at what time, for how long,
                       and how the CPU should be relinquished to allow
                       switching to another task. It goes to say that this
                       program is one of the most important in the OS,
                       without it nothing happens. Furthermore, this has
                       to be calibrated properly since switching between
                       tasks can be quite expensive, it requires the whole
                       execution context to be loaded again each time.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ FDA_Approved_Artificial_Blood_Vessel
                  Despite_Warnings⠀⇛


                       The agency OK’d an artificial vessel to restore
                       blood flow in patients, even though its own
                       scientists flagged questionable study results and
                       potentially fatal ruptures of the product.


                # ⚓ New York Times ☛ West_Virginia_Bans_7_Artificial_Food_Dyes,
                  Citing_Health_Concerns⠀⇛


                       At least 20 other states are considering bills
                       restricting the use of certain food dyes and
                       additives.


                # ⚓ University of Michigan ☛ Center_for_Global_Health_Equity
                  names_new_director⠀⇛


                       Akbar K. Waljee has been appointed the Leslie D.
                       Yamada and Tachi Yamada M.D. Director of the Center
                       for Global Health Equity at U-M, replacing
                       inaugural center director Joseph C. Kolars.


                # ⚓ New Yorker ☛ Medical_Benchmarks_and_the_Myth_of_the
                  Universal_Patient⠀⇛


                       From growth charts to anemia thresholds, clinical
                       standards assume a single human prototype. Why are
                       we still using one-size-fits-all health metrics?


                # ⚓ Anti-coup_medical_workers_under_attack_while_tackling
                  Myanmar’s_health_care_gap⠀⇛


                       They risk arrest and worse at the hands of junta
                       authorities.


                # ⚓ Latvia ☛ Latvia_among_highest_death_rates_in_EU_for
                  circulatory_diseases_and_cancer⠀⇛


                       Eurostat data published March 21 shows Latvia among
                       the European Union countries with the highest rates
                       of deaths from circulatory diseases and cancer, but
                       it does better on respiratory disease deaths.


                # ⚓ The Straits Times ☛ Married_Malaysian_couple_nabbed_with
                  over_$360,000_worth_of_drugs_disguised_as_health_drinks⠀⇛


                       A total of about 37,331ml of liquid methamphetamine
                       was seized.


                # ⚓ Science Alert ☛ Men_And_Women_May_Respond_Differently_to
                  Latest_Alzheimer's_Drugs⠀⇛


                       We need more research.


                # ⚓ Science Alert ☛ A_Simple_Mistake_Might_Have_Encouraged_Sick
                  People_to_Eat_The_Dead⠀⇛


                       Mummy will help.


                # ⚓ Science Alert ☛ 'Wild_Swimming'_Does_Something_Amazing_to
                  Your_Mind,_Study_Reveals⠀⇛


                       Here's why.


                # ⚓ European Commission ☛ Opening_Remarks_by_Commissioner_Kadis
                  at_the_Agriculture_and_Fisheries_Council:_Launch_of_the_EU-
                  wide_Communication_Campaign_on_Aquaculture⠀⇛


                # ⚓ European Commission ☛ Opening_Remarks_by_Commissioner_Kadis
                  at_the_Agriculture_and_Fisheries_Council:_Implementation_of
                  the_provisions_of_Article_14_of_the_Fisheries_Control
                  regulation⠀⇛


                  >
                # ⚓ European Commission ☛ Opening_Remarks_by_Commissioner_Kadis
                  at_the_Agriculture_and_Fisheries_Council:_Future_support_to
                  the_Aquaculture_and_Fisheries_sector⠀⇛


                       Thank you for raising the issue of financial
                       support for EU fisheries.


          o § Proprietary⠀➾


                # § Artificial Intelligence (AI) or Just Slop⠀➾


                      # ⚓ Hackaday ☛ Cloudflare’s_AI_Labyrinth_Wants_Bad_Bots
                        To_Get_Endlessly_Lost [Ed: SLOP "Labyrinth"; this is
                        Clownflare trying to hop on the hype and buzzwords
                        wave]⠀⇛


                             Cloudflare has gotten more active in its
                             efforts to identify and block unauthorized
                             bots and AI crawlers that don’t respect
                             boundaries. Their solution? AI Labyrinth,
                             which uses generative AI to efficiently
                             create a diverse maze of data as a defensive
                             measure.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ The Straits Times ☛ Sabah_man_loses_nearly_$9,000_in
                        alleged_hypnosis_incident⠀⇛


                             The case gained attention after the victim’s
                             child shared the story on social control
                             media.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Silicon Angle ☛ Once_valued_at_$3.5B,_23andMe_files
                        for_Chapter_11_bankruptcy [Ed: Shows how fake, phony,
                        even fraudulent those "valuations" really are; some
                        people who participate in this merely defraud
                        everybody, so it's a form of white-collar crime]⠀⇛


                             Four years after going public at a $3.5
                             billion valuation, 23andMe Holding Co. today
                             filed for bankruptcy. The company, which
                             sells saliva-based genetic testing kits for
                             consumers, will continue operating during the
                             Chapter 11 proceedings. It plans to take out
                             a $35 million loan to finance day-to-day
                             activities.


          o § Defence/Aggression⠀➾


                # ⚓ The Straits Times ☛ Taiwan_President’s_gambit:_Time_for_a
                  tougher_stance_on_China⠀⇛


                       Mr Lai Ching-te has been accused of being a
                       separatist by China.


                # ⚓ Taiwan_accuses_China_of_60_incursions_into_restricted
                  waters⠀⇛


                       Taipei says China’s coastguard keeps moving into
                       seas close to the Taiwan-held Kinmen islands


                # ⚓ The Straits Times ☛ Japan_protests_Chinese_government
                  statement_it_says_misquoted_PM_Ishiba⠀⇛


                       China’s foreign ministry on March 21 had said Mr
                       Ishiba had said Japan 'respects' the positions of
                       the Chinese side.


                # ⚓ The Straits Times ☛ Japan_aims_to_make_military_more_potent
                  with_new_joint_command⠀⇛


                       The joint operations command would ensure
                       coordination between Japan's air, land, sea and
                       other forces.


                # ⚓ Hong Kong Free Press ☛ Chinese_premier_calls_for_‘dialogue’
                  with_Washington_as_US_senator_visits_Beijing⠀⇛


                       By Peter Catterall China’s number two leader on
                       Sunday called for “dialogue” with Washington,
                       during a meeting in Beijing attended by prominent
                       US business executives and a key congressional ally
                       of President The Insurrectionist.


                # ⚓ Atlantic Council ☛ Is_China_or_the_US_the_‘wolf_warrior’_in
                  Latin_America_now?⠀⇛


                       The United States’ harsh rhetoric toward Latin
                       American nations has given China an opportunity to
                       falsely present itself as a more altruistic partner
                       to the region.


                # ⚓ Silicon Angle ☛ Security_sloppiness_at_the_White_House:
                  Yemen_war_plans_shared_with_Atlantic_editor_over_Signal⠀⇛


                       The National Security Council today said it’s
                       reviewing an incident in which The Atlantic Editor-
                       in-Chief Jeffrey Goldberg was accidentally added to
                       a Signal chat in which top White House officials
                       discussed operational war plans against the Houthis
                       in Yemen.


                # ⚓ Atlantic Council ☛ How_Beijing_uses_inducements_as_a_tool
                  of_economic_statecraft⠀⇛


                       As strategic competition between the United States
                       and China intensifies, Washington and Beijing seek
                       every possible advantage to gain an edge. In this
                       environment, both countries are increasingly
                       turning to economic statecraft—the use of economic
                       coercion or inducement to pursue strategic goals—to
                       advance their interests.


                # ⚓ The Strategist ☛ It’s_time_for_the_ADF_to_train_in_Asia-
                  Pacific_languages⠀⇛


                       The proposed negotiation of an Australia–Papua New
                       Guinea defence treaty will falter unless the
                       Australian Defence Force embraces cultural
                       intelligence and starts being more strategic with
                       teaching languages—starting with Tok Pisin, the
                       most widely spoken language [...]


                # ⚓ Latvia ☛ Questions_asked_after_massive_heroin_shipment_made
                  it_from_Latvia_to_Germany⠀⇛


                       Latvian Television's 'De facto' investigative
                       strand reported March 23 on how a huge shipment of
                       heroin was able to be transported from Latvia to
                       Germany even though advance intelligence suggested
                       such a shipment was likely to happen.


                # ⚓ New York Times ☛ Hegseth_Disclosed_Secret_War_Plans_in
                  Group_Chat_With_Atlantic_Journalist⠀⇛


                       The conversation among the defense secretary and
                       other national security officials on a commercial
                       messaging app mistakenly included the editor in
                       chief of The Atlantic, Jeffrey Goldberg.


                # ⚓ The Straits Times ☛ Australia_to_speed_up_$840_million_in
                  defence_spending_in_budget,_says_defence_minister⠀⇛


                       Australia and other US security allies are under
                       pressure from The Insurrectionist to increase
                       defence spending.


                # ⚓ France24 ☛ Greenland_PM_denounces_US_'foreign_interference'
                  ahead_of_visit⠀⇛


                       Greenland's prime minister, Mute Egede, accused
                       Washington on Monday of interfering in its
                       political affairs by sending a US delegation to the
                       Danish territory, which is coveted by US President
                       The Insurrectionist. Egede said US National
                       Security Adviser Mike Waltz would visit Greenland
                       this week, along with Usha Vance, the wife of US
                       Vice President JD Vance. FRANCE 24's August
                       Hakansson reports.


                # ⚓ Defence Web ☛ Police_Committee_Chairperson_raises_alarm
                  over_illegal_land_grabs_in_Eastern_Cape⠀⇛


                       The Chairperson of the Portfolio Committee on
                       Police, Ian Cameron, expressed grave concern over
                       reports indicating that illegal land grabs have
                       resurfaced in Fort Jackson, a region within the
                       Buffalo City Municipality near East London in the
                       Eastern Cape.


                # ⚓ Defence Web ☛ Developing_and_keeping_talent_important_for
                  the_SA_defence_industry⠀⇛


                       In the wake of the Public Private Partnerships for
                       Defence and Security 2025 conference earlier this
                       month, an appeal has been made for “strategic
                       approach to talent retention and development within
                       the South African defence industry (SADI)”.


                # ⚓ The Straits Times ☛ S._Korean_PM_Han_reinstated,_but_split
                  verdict_hints_at_greater_impasse_for_Yoon’s_case⠀⇛


                       The split verdict may mean a bigger divide among
                       the same judges deliberating President Yoon's
                       impeachment, say analysts.


                # ⚓ JURIST ☛ South_Korea_Constitutional_Court_reinstates
                  impeached_Prime_Minister_Han_as_acting_president⠀⇛


                       The South Korean Constitutional Court ruled on
                       Monday that the impeachment of Prime Minister Han
                       Duck-soo was Illegitimate as his conduct, while
                       partially unconstitutional, did not constitute a
                       “betrayal of public trust”. The decision
                       effectively reinstates Duck-soo as acting
                       president.


          o § Environment⠀➾


                # ⚓ Pro Publica ☛ NIH_Ends_Funding_to_Study_the_Health_Effects
                  of_Climate_Change⠀⇛


                       The National Institutes of Health will no longer be
                       funding work on the health effects of climate
                       change, according to internal records reviewed by
                       ProPublica.


                       The guidance, which was distributed to several
                       staffers last week, comes on the back of multiple
                       new directives to cut off NIH funding to grants
                       that are focused on subjects that are viewed as
                       conflicting with the Trump administration’s
                       priorities, such as gender identity, LGBTQ+ issues,
                       vaccine hesitancy, and diversity, equity and
                       inclusion.


                # § Energy/Transportation⠀➾


                      # ⚓ The Straits Times ☛ Body_of_motorcyclist_buried_in
                        Seoul_sinkhole_found⠀⇛


                             Rescue operations resumed at 7am on March 25.


                      # ⚓ Hong_Kong,_China_hit_out_at_sale_of_CK_Hutchison
                        ports_to_BlackRock⠀⇛


                             State-backed media says Lee Ka-shing's firm
                             should 'think again,' and consider the
                             Chinese national interest.


                      # ⚓ Hong Kong Free Press ☛ Chinese_EV_giant_BYD_surpasses
                        US_rival_Tesla_with_record_2024_revenue⠀⇛


                             By Peter Catterall Chinese carmaker BYD saw a
                             surge in revenue last year, a stock filing
                             showed Monday, surpassing the US$100 billion
                             mark and beating rival Tesla as the electric
                             vehicle giant accelerates its overseas
                             expansion.


                      # ⚓ Science Alert ☛ Researchers_Disprove_Their_Own_Work
                        by_Producing_Power_From_Earth's_Rotation⠀⇛


                             Is it really possible?


                      # ⚓ Pro Publica ☛ The_Doublespeak_of_Energy_Secretary
                        Chris_Wright⠀⇛


                             For Chris Wright, there may be no simple
                             truths. At his Senate confirmation hearing on
                             Jan. 15, the man poised to take control of
                             the U.S. Department of Energy and its vast
                             apparatus of technological research and
                             development sat behind a walnut desk wearing
                             a gray suit and a crisply knotted red tie.
                             Wright, the founder and CEO of Liberty
                             Energy, a $3 billion natural gas fracking
                             company, harkened back to his days as a solar
                             energy researcher and offered lawmakers a
                             vision of open-mindedness and innovation.
                             Climate change is an urgent challenge, he
                             reassured them, and he would address it.


                             “It is a global issue. It is a real issue.
                             It’s a challenging issue. And the solution to
                             climate change is to evolve our energy
                             system,” he told the Senate Committee on
                             Energy and Natural Resources. “I am for
                             improving all energy technologies that can
                             better human lives and reduce emissions.”


                      # ⚓ The Straits Times ☛ Malaysia_eyes_trade_boost_with
                        China_and_Thailand_via_new_inland_port_and_rail_links⠀⇛


                             Upcoming Perlis Inland Port aims to draw
                             trade from the north by enhancing regional
                             rail connectivity.


                      # ⚓ France24 ☛ BYD’s_2024_sales_surpass_the_$100bn_mark,
                        overtaking_rival_Tesla⠀⇛


                             BYD has reported a record leap in sales,
                             surpassing the $100bn mark for 2024 and
                             beating rival Tesla. Meanwhile MElon’s EV
                             company has been targeted with a series of
                             attacks and vandalism, as well as weekly
                             demonstrations outside its Tesla showrooms
                             over MElon’s role in the Convicted Felon
                             administration. Plus, Twitter’s iconic bird
                             logo sold for $35 000 at an auction.


                # § Wildlife/Nature⠀➾


                      # ⚓ New York Times ☛ Lessons_from_a_Lost-Pet_Detective
                        Named_Kat⠀⇛


                             Recovering missing animals requires
                             understanding both animal and human behavior.


                      # ⚓ The Straits Times ☛ South_Korea_authorities_deploy
                        choppers,_troops_to_battle_wildfire⠀⇛


                             Officials warned that high winds and rising
                             temperatures were hindering efforts to put
                             out the blazes.


                      # ⚓ The Straits Times ☛ South_Korean_wildfires_spread,
                        three_more_disaster_zones_named⠀⇛


                             Deadly wildfires spread further across South
                             Korea on Monday as authorities designated
                             three more counties 'special disaster zones'.


                      # ⚓ The Straits Times ☛ South_Korea_struggles_to_contain
                        deadly_wildfires⠀⇛


                             Dry, windy weather is hampering efforts to
                             contain one of the country’s worst-ever fire
                             outbreaks.


                      # ⚓ North_Korea_checks_civil_defense_armories_after
                        weapons_used_for_wild_boar_hunt⠀⇛


                             The matter is being treated seriously as
                             threat to the country’s leadership.


          o § Finance⠀➾


                # ⚓ The Straits Times ☛ South_Korea_to_probe_‘made_in_Korea’
                  violations_ahead_of_US_tariffs⠀⇛


                       Dihydroxyacetone Man administration said it would
                       prepare reciprocal tariffs against major trading
                       partners by April 2.


                # ⚓ New York Times ☛ On_Fighting_Oligarchy_Tour,_Bernie_Sanders
                  Channels_the_Grateful_Dead⠀⇛


                       An aging star playing to massive crowds of
                       supporters in head-to-toe merch? It’s not the
                       Grateful Dead, it’s the Fighting Oligarchy tour.


                # ⚓ Mexico News Daily ☛ Mexico’s_inflation_rate_decelerates_as
                  central_bank_prepares_for_a_rate_cut⠀⇛


                       Mexican consumers are getting a break on prices so
                       far in March, according to the national statistics
                       agency's mid-month report.


                # ⚓ Xi_Jinping’s_family_wealth_persists_despite_anti-corruption
                  drive:_US_report⠀⇛


                       They may have benefited from connections to
                       political power, said the US intelligence report.


                # ⚓ New York Times ☛ Social_Security,_Buffeted_by_Turmoil,
                  Awaits_a_New_Leader [Ed: US Cheeto implementing eugenics
                  already: kill the old and the poor. And the vets who fought
                  for the country. VA no more?]⠀⇛


                       The billionaire MElon has become fixated on finding
                       fraud inside the agency, which provides retirement,
                       survivor and disability payments to 73 million
                       Americans each month.


                # ⚓ New Yorker ☛ Don’t_Believe_Convicted_Felon’s_Promises_About
                  Protecting_the_Social_Safety_Net⠀⇛


                       The Social Security Administration is shuttering
                       offices, and the Republicans’ own math suggests
                       that they are planning big cuts to Medicaid and
                       SNAP.


                # ⚓ JURIST ☛ HRW:_Germany’s_social_security_system_violates
                  women’s_rights⠀⇛


                       HRW reported Monday that Germany’s social security
                       system inadequately protects women from poverty,
                       breaching the state’s constitutional obligation to
                       ensure that taxpayers can afford to pay for
                       “necessary living expenses.” According to HRW,
                       women in Germany are overrepresented among the
                       population that is at risk of poverty.


                # ⚓ The Strategist ☛ Economic_security_and_geostrategic
                  competition:_tariffs_don’t_equal_coercion⠀⇛


                       The Forrest Dump administration’s decision to
                       impose tariffs on Australian aluminium and steel
                       has surprised the country. This has caused some to
                       question the logic of the Australia-United States
                       alliance and risks legitimising China’s economic
                       coercion.


                # ⚓ The Straits Times ☛ China_rolls_out_new_rules_to_step_up
                  countermeasures_to_foreign_sanctions⠀⇛


                       China has grappled with trade and investment curbs
                       from major Western markets, including those from
                       the US.


                # ⚓ New York Times ☛ Layoffs_and_Unemployment_Grow_Among
                  College_Graduates_/_Has_the_Decline_of_Knowledge_Work
                  Begun?⠀⇛


                       The unemployment rate for college graduates has
                       risen faster than for other workers over the past
                       few years. How worried should they be?


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ ACLU ☛ Anniversary_of_‘Bloody_Sunday’_Marks_Continued_Fight
                  for_Voting_Rights⠀⇛


                       Sixty years ago, on March 7, 1965, hundreds of
                       civil rights activists, also known as foot
                       soldiers, marched from Selma to Montgomery, Alabama
                       to fight for the right to vote for Black people. As
                       they marched across the Edmund Pettus Bridge,
                       Alabama State Troopers brutally beat them. The
                       violence these activists endured became synonymous
                       with the struggle for Black enfranchisement.


                       The Edmund Pettus Bridge march, alongside three
                       other marches in Alabama, helped Congress recognize
                       the urgency with which it must pass voting rights
                       legislation. Mere weeks after the Edmund Pettus
                       march, the Voting_Rights_Act_of_1965 was presented
                       to Congress on March 17, 1965. President Johnson
                       signed the bill into law on August 6, 1965.


          o § Censorship/Free Speech⠀➾


                # ⚓ Vietnam_investigates_Chinese_tea_brand_over_controversial
                  ocean_map⠀⇛


                       Chagee is accused of displaying the ‘nine-dash
                       line’ on its mobile app.


                # ⚓ NYPost ☛ Columbia_student,_21,_arrested_during_anti-Israel
                  protest_faces_deportation_by_Convicted_Felon_admin:_lawsuit⠀⇛


                       Chung’s legal team argued the actions by the
                       Convicted Felon administration is an attempt to
                       “chill” her free speech. The student has called the
                       US home since she was 7 years old and is a legal
                       permanent resident.


                # ⚓ Hong Kong Free Press ☛ HKU_talk_by_CEO_of_Anti-Defamation
                  League,_which_defended_MElon_‘Nazi’_salute,_listed_as
                  cancelled_after_backlash⠀⇛


                       A talk by Anti-Defamation League (ADL) chief
                       Jonathan Greenblatt set to take place at the
                       University of Hong Kong on Tuesday has been listed
                       as “cancelled” following a backlash.


                # ⚓ Hong Kong Free Press ☛ Petition_urges_HKU_to_axe_talk_by
                  Anti-Defamation_League_CEO_who_said_‘anti-Zionism is
                  antisemitism’⠀⇛


                       Petitioners have urged the University of Hong Kong
                       (HKU) to withdraw an invitation for the CEO of the
                       Anti-Defamation League (ADL) Jonathan Greenblatt to
                       speak on campus this Tuesday.


                # ⚓ BIA Net ☛ Turkish_court_orders_blocking_of_bianet’s_X
                  account⠀⇛


                       The order comes amid a wave of online censorship
                       targeting hundreds of accounts covering the
                       protests following the İstanbul mayor's arrest.


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


                # ⚓ Press Gazette ☛ Former_CNN_correspondent_says_she_‘lost_the
                  support’_of_broadcaster_after_disability⠀⇛


                       Disability Journalism Forum hears how disabled
                       people are being failed by media.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_security_chief_slams
                  ‘smearing_remarks’_in_Guardian_article_about_Jimmy_Lai_top
                  court_ruling⠀⇛


                       Hong Kong’s security chief has lashed out at
                       British newspaper The Guardian over an article
                       citing experts criticising a top court ruling on
                       media mogul Jimmy Lai’s appeal as “another cut on
                       the city’s once revered legal system.”


          o § Civil Rights/Policing⠀➾


                # ⚓ New York Times ☛ China_Releases_Mintz_Employees_After_2-
                  Year_Detention⠀⇛


                       The release of the five employees, detained during
                       a crackdown on foreign due diligence, comes as
                       Beijing is trying to bring back overseas
                       investment.


                # ⚓ The Straits Times ☛ China_frees_US_firm_Mintz_staff_in_move
                  to_soothe_foreign_sentiment⠀⇛


                       Chinese authorities detained five local staff in
                       the March 2023 raid.


                # ⚓ Pro Publica ☛ DOJ_Launches_Probe_Into_Illinois’_Treatment
                  of_People_With_Disabilities⠀⇛


                # ⚓ RFERL ☛ Tate_Brothers_Check_In_At_Police_Station_To_Comply
                  With_Romanian_Legal_Measures⠀⇛


                       Facing multiple charges of sex trafficking and
                       exploitation in the United States and Romania,
                       controversial internet personalities Andrew and
                       Tristan Tate have appeared at a police station in
                       Romania to fulfill their monthly judicial control
                       obligations.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ The Strategist ☛ China’s_shadow_fleet_threatens_Indo-
                  Pacific_communications⠀⇛


                       China is using increasingly sophisticated grey-zone
                       tactics against subsea cables in the waters around
                       Taiwan, using a shadow-fleet playbook that could be
                       expanded across the Indo-Pacific.


      § Monopolies/Monopsonies⠀➾


          o ⚓ Digital Music News ☛ Live_Nation_Settles_Investor_Class_Action
            for_$20M_As_DOJ_Action_Lumbers_Onward⠀⇛


                 Live Nation settles a lawsuit filed by investors claiming
                 the company failed to warn them about its antitrust
                 activity that led to the DOJ’s case. Live Nation has
                 agreed to pay $20 million to settle the dispute, which
                 alleged the company misled investors about its
                 “compliance with antitrust laws.”


          o ⚓ The_Significant_Economic_Mistakes_of_the_FTC’s_Case_Against
            Amazon⠀⇛


                 As the Federal Trade Commission (FTC) continues its
                 monopolization case against Amazon in anticipation of
                 next year’s trial [...]


          o § Patents⠀➾


                # ⚓ Unified Patents ☛ $3,000_awarded_for_IngenioSpec_eyeware
                  patents_prior_art⠀⇛


                       Unified is pleased to announce PATROLL
                       crowdsourcing contest winners below totaling $3,000
                       in cash prizes. The patents are owned by
                       IngenioSpec_LLC, an NPE. The patents generally
                       relate to smart eyewear. They have been asserted
                       against Samsung, Bose_Corporation, Sony, and LG.


                       We would also like to thank the dozens of other
                       high-quality submissions that were made on this
                       patent.


                # ⚓ Unified Patents ☛ $6,000_for_Polaris_Innovations_memory
                  patents_prior_art⠀⇛


                       Unified Patents added three new PATROLL contests,
                       each with a $2,000 cash prize, seeking prior art on
                       the list below. The patents are owned by Polaris
                       Innovations Limited, an NPE and entity of Owlpoint
                       IP Opportunities JVF I LP. The patents generally
                       relate to various semiconductor memory
                       technologies.


                # ⚓ JUVE ☛ Juul_Labs_ahead_in_battle_with_NJOY_but_fight
                  continues_at_Court_of_Appeal⠀⇛


                       NJOY wants the Unified Patent Court to remove nine
                       patents protecting Juul Labs’ vaporizer technology
                       from the market. For this reason, the company filed
                       revocation actions in September 2023 at the Paris
                       central division. In the meantime, the first
                       instance court has ruled on all nine cases.


                # ⚓ KOL455_|_Haman_Nature_Hn_109:_Philosophy,_Rights,
                  Libertarian_and_Legal_Careers⠀⇛


                       Adam interviews patent monopoly attorney,
                       philosopher, legal theorist and libertarian
                       anarchist Stephan Kinsella about his life, his
                       works, and what's next for the great man!


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ CAFC_Affirms_TTAB's_MONEY_MART_Decision,
                  Confirming_that_Zone_of_Natural_Expansion_Doctrine_Applies
                  Only_Defensively⠀⇛


                       The CAFC upheld the Board's latest decision (on
                       remand) in this long-running dispute over Dollar
                       Financial Group's registrations for the mark MONEY
                       MART, in standard character and design form, for
                       loan financing and check cashing services. The
                       appellate court ruled that the Board "correctly
                       determined that DFG may not rely on the zone of
                       natural expansion doctrine to establish priority
                       and that confusion was likely with respect to DFG’s
                       recited pawn brokerage and pawn shop services."
                       [TTAB opinion here]. Therefore, the Board properly
                       ordered that "pawn brokerage and pawn shops" be
                       deleted from DFG's registrations.


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Lydia_Harris’_$107_Million_Death_Row
                  Records_Lawsuit_Is_Moving_Forward_—_Pretrial_Conference
                  Officially_Scheduled⠀⇛


                       Lydia Harris is officially proceeding with her more
                       than $100 million lawsuit against Snoop Dogg, Suge
                       Knight, Jimmy lovine, Lucian Grainge, and others.
                       The presiding judge just recently put the case’s
                       scheduling wheels in motion, after Lydia Harris
                       (who was previously married to Death Row co-founder
                       Michael Harris) submitted the pro se action last
                       week.


                # ⚓ Dennis Crouch/Patently-O ☛ Sheet_Music_v._Sound_Waves:_When
                  Old_Copyright_Law_Meets_Modern_Music⠀⇛


                       The copyright monopoly dispute over Ed Sheeran's
                       song "Thinking Out Loud" has made its way to the
                       Supreme Court's doorstep.  The petition raises
                       questions about judicial deference to
                       administrative interpretations and the scope of
                       copyright monopoly protection for musical
                       compositions under the 1909 Copyright Act.  In the
                       case, the Second Circuit had sided with Sheeran -
                       - affirming dismissal of the infringement claim
                       based largely on a technical limitation of pre-1976
                       copyright monopoly law.  Structured Asset Sales,
                       LLC v. Sheeran.


                # ⚓ Michael Geist ☛ The_Law_Bytes_Podcast,_Episode_229:_My
                  Digital_Access_Day_Keynote_–_Assessing_the_Canadian_Digital
                  Policy_Record⠀⇛


                       With a federal election just called and the
                       campaign now underway, the focus will turn - at
                       least in very small part - to party policies. It is
                       certainly possible that digital issues such as Hey
                       Hi (AI) regulation, online harms, and the fate of
                       Internet laws will merit a mention.


    * Links_25/03/2025:_Terrace_Workbench_and_Spellcheck_in_LibreOffice_on
      FreeBSD
    * next



                    ䷩ 𝚕𝚒𝚗𝚎 7149

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 25/03/2025: Putin Sends Children to
Battle, 23andMe Drowns as People's Highly Personal DNA Data
Floats⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ The Nation ☛ The_Time_George_Foreman_Sang_Me_Some_Dylan⠀⇛


                 I wanted to hear about 1968, but also about his life
                 leading up to Mexico City. I asked him when he was first
                 aware of the Black freedom struggle. He started by
                 talking about the extreme poverty of his youth, when even
                 a school lunch was out of his reach. “Growing up poor, I
                 didn’t even have a lunch to take to school,” he recalled
                 “Lunch was 26 cents, and we didn’t even know what 26
                 cents looked like.” Life was survival. That changed when
                 he was hired at a public works jobs program as a 16-year-
                 old, and a “young Anglo-Saxon boy from Tacoma,
                 Washington,” introduced him to Bob Dylan. I asked him
                 what Dylan song opened his mind about the state of the
                 world. I thought he’d say “The Times They Are A-Changin’”
                 or “Blowin’ in the Wind.” Instead, he invoked “Rainy Day
                 Women Number #12 and 35”—the first track on the 1966
                 album Blonde On Blonde. “Do you know that one?” Foreman
                 asked. Before I could answer, he started to sing. In a
                 voice richer and deeper than I had expected, he crooned,
                 “Well, they’ll stone ya when you’re walkin’ ’long the
                 street. They’ll stone ya when you’re tryin’ to keep your
                 seat. They’ll stone ya when you’re walkin’ on the floor.
                 They’ll stone ya when you’re walkin’ to the door. But I
                 would not feel so all alone. Everybody must get stoned.”
                 When he’d finished, he asked me if I understood what
                 Dylan was trying to say. Taken off guard, I said, “I
                 think he’s singing about weed?”


          o ⚓ Smithsonian Magazine ☛ This_Dusty_Painting_Turned_Out_to_Be
            Gustav_Klimt's_Long-Lost_Portrait_of_an_African_Prince⠀⇛


                 Though unsigned, the two-foot-tall portrait is stamped
                 with a symbol indicating that it’s “almost certainly from
                 the estate of Gustav Klimt,” as Weidinger says in a
                 statement, per the Washington Post. The artwork had been
                 auctioned off in 1923—five years after Klimt’s
                 death—before changing hands several times. Since the
                 1950s, it’s been part of a private collection.


          o ⚓ Android Police ☛ Spotify's_podcast_porn_problem_is_currently
            topping_the_charts⠀⇛


                 Erotic audio content also violated terms, but remains
                 undetected due to listener ratings and other tricks.


          o ⚓ Lou Plummer ☛ No,_I'm_Not_in_a_Bubble⠀⇛


                 Needless to say, I think these people are full of shit.
                 MAGA has been running the country for less than 100 days
                 and already ABC, CBS, and Meta have settled frivolous
                 lawsuits initiated by the US president rather than stand
                 their ground in the face of his threats. A good part of
                 my upbringing occurred while my step-father worked as a
                 journalist. I have long supported and admired the
                 underpaid and overworked people who bring us the news,
                 but that feeling is ebbing in the modern era. The
                 industry hasn't handled the way the country has been
                 reshaped. It's still in the habit of framing arguments as
                 if both sides have merit, even when one of those sides is
                 batshit crazy, racist, misogynistic and incoherent. The
                 word "sanewashing" had to be invented to describe what
                 once respected outlets like the New York Times does to
                 present Donald Trump as if he weren't a crazy person.
                 Even Fox News cuts away from his live speeches to keep
                 from showing the nonsensical, incoherent imbecile that he
                 truly is.


          o ⚓ Hong Kong Free Press ☛ HKFP_Lens:_HK's_bamboo_scaffolding_through
            the_years⠀⇛


                 Hong Kong is among the last remaining cities that use
                 bamboo scaffolding in modern construction and maintenance
                 projects.


          o ⚓ Wired ☛ The_Weight_of_the_Internet_Will_Shock_You⠀⇛


                 But a lot has happened since 2006—Instagram, iPhones, and
                 the AI boom, to name a few. (By Seitz’s logic, the
                 [Internet] would now weigh as much as a potato.) There’s
                 also the fact that, around the time of Seitz’s
                 calculation, Discover magazine proposed a different
                 method. Information on the [Internet] is written in bits,
                 so what if you looked at the weight of the electrons
                 needed to encode those bits? Using all [Internet]
                 traffic—then estimated to be 40 petabytes—Discover put
                 the [Internet]’s weight at a tiny fraction (5 millionths)
                 of a gram. So, more like a squeeze of strawberry juice.
                 WIRED thought it was time to investigate for ourselves.


          o § Science⠀➾


                # ⚓ CS Monitor ☛ What_will_happen_to_grad_school?_Research
                  universities_face_tough_choices.⠀⇛


                       “American higher education is the absolute envy of
                       the world. And America’s elite institutions of
                       higher education contribute so much, to not just
                       American society but to the world, that it’s really
                       a self-inflicted wound for the federal government
                       to be going after these kinds of institutions,”
                       says Morgan Polikoff, professor of education at the
                       University of Southern California’s Rossier School
                       of Education.


                       Universities and students have three choices, Dr.
                       Polikoff says. They can file lawsuits, capitulate
                       to government demands for changes, or resist,
                       protest, and vote.


                # ⚓ Wired ☛ A_Math_Couple_Solves_a_Major_Group_Theory
                  Problem—After_20_Years_of_Work⠀⇛


                       The problem that absorbed them takes a key theme in
                       mathematics and turns it into a concrete tool for
                       group theorists. Math is full of enormously
                       complicated abstract objects that are impossible to
                       study in their entirety. But often, mathematicians
                       have discovered, it’s enough to look at a small
                       fragment of such an object to understand its
                       broader properties. In the third century BC, for
                       instance, the ancient Greek mathematician
                       Eratosthenes estimated the circumference of the
                       Earth—roughly 25,000 miles—by measuring shadows
                       cast by the sun in just two cities about 500 miles
                       apart. Similarly, when mathematicians want to
                       understand an impossibly convoluted function, they
                       might only need to look at how it behaves for a
                       small subset of possible inputs. That can be enough
                       to tell them what the function does for all
                       possible inputs.


                # ⚓ Wired ☛ The_Chaos_of_NIH_Cuts_Has_Left_Early-Career
                  Scientists_Scrambling⠀⇛


                       During the lifespan of a scientist, there are
                       several critical steps. For many, the first is to
                       gain research experience during college—whether
                       through working in a university laboratory or
                       through summer research programs. From there, some
                       take gap years (with the NIH postbaccalaureate
                       program previously a popular option) to pursue even
                       more research. Then comes an application to
                       graduate school, completing graduate school, and
                       possibly doing a postdoctoral fellowship. After all
                       of that, only some end up as research faculty at
                       institutions—where they embark on a decades-long
                       saga of grant applications, many of which are for
                       federal funding from the NIH or National Science
                       Foundation (NSF).


          o § Career/Education⠀➾


                # ⚓ YLE ☛ Foreign_students_increasingly_relying_on_food_banks,
                  church_says⠀⇛


                       Volunteers at the Evangelical Free Church (EFC) in
                       Helsinki fill plastic bags with bread, vegetables,
                       fruit, meat and other food items collected by the
                       congregation throughout the week.


          o § Hardware⠀➾


                # ⚓ The New Stack ☛ When_Do_Retry,_Backoff,_and_Jitter_Work?⠀⇛


                       But what surprised me was that many folks felt that
                       these retries, backoffs, and jitters are perfect
                       antidotes for reliably handling increased load on
                       servers. While retries, backoffs, and jitters are
                       amazing and cheap solutions to handle situations of
                       bursty load, there is an important distinction to
                       understand before assuming this is a universal
                       cure.


                       It would be better to understand how and why these
                       work and then use that knowledge to apply and
                       validate if they work in different situations.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ The Telegraph UK ☛ There’s_a_big_difference_between_genetic
                  ADHD_and_when_it’s_caused_by_constant_stimulation_from_tech⠀⇛


                       Dr Sabine Donnai worries that technology has killed
                       our brain’s ability to switch off, which could
                       explain the surge in ADHD diagnoses


          o § Proprietary⠀➾


                # ⚓ The Register UK ☛ Microsoft_tastes_the_consequences_of
                  tariffs_on_time_•_The_Register⠀⇛


                # ⚓ Techdirt ☛ Max_Streaming_‘Enshittifies’_Further,_Removes
                  Classic_Looney_Tunes⠀⇛


                       And the hits keep on coming. Last week users began
                       grumbling after Max executives decided to delete
                       the entire 1930-1969 run of classic Looney Tunes
                       shorts from the streaming company’s catalog.
                       Because kids’ programming doesn’t sell quite as
                       well as homogenized reality TV dogshit, executives
                       have decided that these old classics are no longer
                       relevant to the public interest.


                # ⚓ Wired ☛ Trump’s_Aggression_Sours_Europe_on_US_Cloud
                  Giants⠀⇛


                       There are early signs that some European companies
                       and governments are souring on their use of
                       American cloud services provided by the three so-
                       called hyperscalers. Between them, Google Cloud,
                       Microsoft Azure, and Amazon Web Services (AWS) host
                       vast swathes of the internet and keep thousands of
                       businesses running. However, some organizations
                       appear to be reconsidering their use of these
                       companies’ cloud services—including servers,
                       storage, and databases—citing uncertainties around
                       privacy and data access fears under the Trump
                       administration.


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ India Times ☛ OpenAI_finds_own_product_ChatGPT_linked
                        to_more_loneliness,_social_isolation⠀⇛


                             Researchers analysed millions of text-based
                             conversations and thousands of audio
                             interactions, identifying a small group of
                             “power users” who showed a strong correlation
                             between intensive ChatGPT usage and increased
                             feelings of loneliness, dependence, and
                             reduced socialisation.


                      # ⚓ The New Stack ☛ AI_Agents_Are_a_Security_Ticking_Time
                        Bomb⠀⇛


                             The most significant risk we face in the era
                             of computer use of AI agents is their
                             susceptibility to external manipulation, such
                             as prompt injections that can exploit
                             vulnerabilities in their decision-making
                             processes. These agents can access users’
                             browsers, files, email, and applications to
                             autonomously complete tasks, presenting a
                             large attack surface that leaves users’
                             systems vulnerable from multiple angles.
                             Potential impacts range from annoyances, like
                             making the agent click on ads on a website,
                             to serious threats, like allowing a hacker to
                             take over the user’s account or download
                             malicious files that compromise the user’s
                             system.


                      # ⚓ MIT Technology Review ☛ Why_handing_over_total
                        control_to_AI_agents_would_be_a_huge_mistake⠀⇛


                             This core issue lies at the heart of what’s
                             most exciting about AI agents: The more
                             autonomous an AI system is, the more we cede
                             human control. AI agents are developed to be
                             flexible, capable of completing a diverse
                             array of tasks that don’t have to be directly
                             programmed.


                             For many systems, this flexibility is made
                             possible because they’re built on large
                             language models, which are unpredictable and
                             prone to significant (and sometimes comical)
                             errors. When an LLM generates text in a chat
                             interface, any errors stay confined to that
                             conversation. But when a system can act
                             independently and with access to multiple
                             applications, it may perform actions we
                             didn’t intend, such as manipulating files,
                             impersonating users, or making unauthorized
                             transactions. The very feature being
                             sold—reduced human oversight—is the primary
                             vulnerability.


                      # ⚓ India Times ☛ What_are_AI_hallucinations?_Why_AIs
                        sometimes_make_things_up⠀⇛


                             When an algorithmic system generates
                             information that seems plausible but is
                             actually inaccurate or misleading, computer
                             scientists call it an AI hallucination.


                             Researchers have found these behaviors in
                             different types of AI systems, from chatbots
                             such as ChatGPT to image generators such as
                             Dall-E to autonomous vehicles. We are
                             information science researchers who have
                             studied hallucinations in AI speech
                             recognition systems.


                # § Social Control Media⠀➾


                      # ⚓ US Navy Times ☛ US_Navy_reiterates_social_media
                        limits_for_sailors_and_Marines⠀⇛


                             “Service Members may not engage in partisan
                             political activity while on duty and should
                             avoid inferences that their personal
                             political activities imply, or appear to
                             imply, official sponsorship, approval, or
                             endorsement by the [Department of the Navy]
                             or [Defense Department],” the memo stated.


                             Service members are allowed to operate
                             personal accounts, the memo reads, so long as
                             they do not conduct official DOD
                             communications on social media platforms or
                             misrepresent the armed forces in their online
                             activity.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Scoop News Group ☛ Judge_says_Treasury,_Education,
                        OPM_can’t_share_personal_information_with_DOGE⠀⇛


                             “Enacted 50 years ago, the Privacy Act
                             protects from unauthorized disclosure the
                             massive amounts of personal information that
                             the federal government collects from large
                             swaths of the public,” Boardman wrote.
                             “Congress’s concern back then was that ‘every
                             detail of our personal lives can be assembled
                             instantly for use by a single bureaucrat or
                             institution’ and that ‘a bureaucrat in
                             Washington or Chicago or Los Angeles can use
                             his organization’s computer facilities to
                             assemble a complete dossier of all known
                             information about an individual.’”


                             The lawsuit was filed by the American
                             Federation of Teachers, the International
                             Association of Machinists and Aerospace
                             Workers, the International Federation of
                             Professional and Technical Engineers, the
                             National Active and Retired Federal Employees
                             Association, the National Federation of
                             Federal Employees, and six military veterans.


                      # ⚓ Wired ☛ How_to_Enter_the_US_With_Your_Digital_Privacy
                        Intact⠀⇛


                             When Ryan Lackey has traveled to countries
                             like Russia or China, he has taken certain
                             precautions: Instead of his usual gear, the
                             Seattle-based security researcher and chief
                             security officer of a cryptocurrency
                             insurance firm brings a locked-down
                             Chromebook and an iPhone that's set up to
                             sync with a separate, nonsensitive Apple
                             account. He wipes both before every trip and
                             loads only the minimum data he'll need.
                             Lackey has gone so far as to keep separate
                             travel sets for each country, so that he can
                             forensically analyze the devices when he gets
                             home to check for signs of each country's
                             tampering.


                      # ⚓ International Business Times ☛ Facebook_May_Start
                        Charging_in_the_UK_—_Here's_Why_Brits_Could_Soon_Face_a
                        Shocking_New_Subscription_Fee⠀⇛


                             Tanya O'Carroll took legal action against
                             Facebook, arguing the company utilised her
                             private information for direct marketing. The
                             ICO confirmed her ability to challenge this
                             based on GDPR. Tanya, who called the ads'
                             surveillance ads,' celebrated her 'victory'
                             and said she thinks this sets a precedent for
                             people to fight against such advertising
                             online.


                      # ⚓ International Business Times ☛ 'Should_I_Delete_My
                        23andMe_Data?':_What_Happens_If_You_Don't_and_Why_The
                        Company's_Gone_Bankrupt⠀⇛


                             On Sunday, 23andMe announced it had filed for
                             Chapter 11 bankruptcy protection in the
                             United States, aiming to facilitate a court-
                             supervised sale process. The filing follows
                             years of financial turmoil, strategic
                             missteps, and a massive data breach that
                             exposed the personal information of nearly 7
                             million users.


                      # ⚓ 404 Media ☛ DNA_of_15_Million_People_for_Sale_in
                        23andMe_Bankruptcy⠀⇛


                             There is no way to know what a buyer will
                             want to do with the reams of genetic
                             information it has collected. Customers,
                             meanwhile, still have no way to change their
                             underlying genetic data.


                      # ⚓ Wired ☛ How_to_Delete_Your_Data_From_23andMe⠀⇛


                             California attorney general Rob Bonta
                             reminded consumers in an alert on Friday that
                             Californians have a legal right to ask that
                             an organization delete their data. 23andMe
                             customers in other states and countries
                             largely do not have the same protections,
                             though there is also a right to deletion for
                             health data in Washington state’s My Health
                             My Data Act and the European Union’s General
                             Data Protection Regulation. Regardless of
                             residency, all 23andMe customers should
                             consider downloading anything they want to
                             keep from the service and should then attempt
                             to delete their information.


                      # ⚓ Scoop News Group ☛ As_23andMe_declares_bankruptcy,
                        privacy_advocates_sound_alarm_about_DNA_data⠀⇛


                             23andMe, which was once valued at $6 billion,
                             has been experiencing financial distress and
                             declining profits since going public in 2021.


                      # ⚓ The Register UK ☛ 23andMe_files_for_bankruptcy
                        protection⠀⇛


                             It said that Chapter 11 proceedings were
                             initiated in the US Bankruptcy Court for the
                             Eastern District of Missouri on Sunday, and
                             the court will oversee 23andMe's attempted
                             sale of its assets.


                             Companies file for bankruptcy protection when
                             they can no longer meet their obligations to
                             creditors. The court will now oversee the
                             sale of 23andMe's assets and ensure they're
                             distributed among creditors.


                      # ⚓ Jeff Geerling ☛ I_won't_connect_my_dishwasher_to_your
                        stupid_cloud⠀⇛


                             If you have a cloud app, that means there's a
                             cloud service that has to be running. That
                             costs money to maintain.


                             And if there's no subscription fee right now,
                             that means one of two things:


                             1. They could be selling our data already.


                             2. At some point, they'll either close the
                             service because it's a cost center (so the
                             rinse cycle and eco mode on all these
                             dishwashers just goes "POOF!"), or they're
                             going move to a subscription model.


                             All of a sudden, if you want to run the self-
                             cleaning cycle, you better start paying five
                             bucks to Bosch every month. Forever. That's
                             insane.


                      # ⚓ The Washington Post ☛ Delete_your_DNA_data_from
                        genetics_company_23andMe_right_now⠀⇛


                             “I remind Californians to consider invoking
                             their rights and directing 23andMe to delete
                             their data and destroy any samples of genetic
                             material held by the company,” he said in a
                             statement.


                      # ⚓ The Verge ☛ 23andMe_files_for_bankruptcy_as_CEO_steps
                        down_|_The_Verge⠀⇛


                             Once valued at $6 billion, executives have
                             yet to find a bidder for the $50 million gene
                             testing company that has never turned a
                             profit.


                      # ⚓ Bruce Schneier ☛ More_Countries_are_Demanding_Back-
                        Doors_to_Encrypted_Apps⠀⇛


                      # ⚓ La Quadature Du Net ☛ All-out_mobilization_against
                        the_French_“war-on-drugs”_law⠀⇛


                             In the midst of the media uproar over drug
                             trafficking, a law on “drug trafficking” is
                             passing through Parliament. In reality, this
                             text does not only apply to the sale of
                             narcotics and leads to a heavy reinforcement
                             of the surveillance capacities of the
                             intelligence and judicial police. It is one
                             of the most repressive and dangerous texts of
                             recent years. This law could notably give
                             even more powers to repress activism.


                             This bill was adopted unanimously in the
                             Senate, with the support of the Socialists,
                             the Ecologists and the Communists, and will
                             now be discussed in the National Assembly. La
                             Quadrature du Net is calling for urgent
                             mobilization to raise awareness of the
                             dangers of this text and to push left-wing
                             parties to reject it.


                             On this page, you will find a set of
                             resources and tools to help you understand
                             this law and convince your elected
                             representatives to mobilize: [...]


                # § Confidentiality⠀➾


                      # ⚓ The Register UK ☛ Tor-backer_OTF_sues_to_save_its
                        funding_from_Trump_cuts⠀⇛


                             The Open Technology Fund (OTF) backs projects
                             including the nonprofit certificate authority
                             Let's Encrypt and the Tor anonymizing
                             network, among other things designed to
                             improve online privacy, promote democracy,
                             and thwart repression around the world. Tor
                             and Let's Encrypt each have or have had
                             numerous sponsors besides the OTF, from big
                             names in tech to European governments, for
                             what it's worth.


                      # ⚓ BoingBoing ☛ Crypto_developer_faces_40_years_in
                        prison_for_creating_privacy_software⠀⇛


                             A cryptocurrency mixer, also known as a
                             tumbler, allows people to send bitcoins to an
                             address, where they are mixed with other
                             people's coins, effectively breaking the
                             audit trail. The mixing service returns the
                             same amount of bitcoin back to each
                             participant, after it taking a cut for
                             performing the service.


                      # ⚓ Wired ☛ The_Quantum_Apocalypse_Is_Coming._Be_Very
                        Afraid⠀⇛


                             Cybersecurity analysts call this Q-Day—the
                             day someone builds a quantum computer that
                             can crack the most widely used forms of
                             encryption. These math problems have kept
                             humanity’s intimate data safe for decades,
                             but on Q-Day, everything could become
                             vulnerable, for everyone: emails, text
                             messages, anonymous posts, location
                             histories, bitcoin wallets, police reports,
                             hospital records, power stations, the entire
                             global financial system.


          o § Defence/Aggression⠀➾


                # ⚓ Site36 ☛ Germany_keeps_third_country_report_under_wraps:
                  Experts_see_high_hurdles_for_outsourced_asylum_procedures⠀⇛


                # ⚓ RFERL ☛ Islamic_State_Is_Evolving,_But_Has_The_World_Taken
                  Its_Eyes_Off_The_Ball?⠀⇛


                       A diversified array of IS branches has emerged in
                       recent years throughout the world, particularly in
                       regions where there is little ability to counter
                       extremism.


                       Colin Clarke, director of policy and research at
                       the New York-based Soufan Group consultancy, said
                       IS has become a group for which the sum of its
                       parts is greater than the whole.


                       “IS might be even more challenging as a
                       decentralized organization than it was as a proto-
                       state. When it was running a proto-state, it was a
                       big target,” Clarke told RFE/RL.


                # ⚓ Air Force Times ☛ One_of_last_surviving_Tuskegee_Airmen
                  criticizes_Trump’s_DEI_purge⠀⇛


                       Col. James H. Harvey III, 101, is among the last
                       few airmen and support crew who proved that a Black
                       unit — the 332nd Fighter Group of the Tuskegee
                       Airmen — could fight as well as any other in World
                       War II and the years after.


                # ⚓ Techdirt ☛ How_Does_This_End?⠀⇛


                       We are witnessing the answer in real time:
                       institutional capture, norm erosion, and the
                       systematic dismantling of accountability
                       mechanisms. The Department of Justice, Department
                       of Homeland Security, and significant portions of
                       federal agencies are being transformed into
                       instruments of personal power rather than
                       constitutional governance. Meanwhile, DOGE stands
                       as a parallel government structure, implementing
                       radical changes without congressional oversight or
                       judicial review.


                       A particularly dangerous dynamic is now in motion:
                       the “point of no return” for key figures in the
                       administration. As Elon Musk, Trump family members,
                       and others become increasingly implicated in
                       potentially illegal activities, their incentive to
                       preserve democratic processes diminishes
                       proportionally. The more their personal legal and
                       financial survival depends on maintaining power,
                       the more willing they become to take extraordinary
                       measures to keep it.


                # ⚓ Pete Warden ☛ Join_me_at_the_Tesla_Protests_on_Saturday⠀⇛


                       I’ve been writing this blog for nineteen years, and
                       in over 1,100 posts I’ve never once brought up
                       politics, but I can’t ignore what’s happening in
                       our country. We’re facing such a profound crisis
                       right now in the US that not speaking up at this
                       point would be breaking the oath I took in 2014,
                       when I became a proud citizen, to “defend the
                       constitution” … “against all enemies, foreign and
                       domestic“. I won’t repeat all the ways that the
                       executive branch is destroying fundamental rights
                       like habeas corpus and the rule of law. If you’re
                       happy with what’s going on, I don’t know how to
                       even reach you, so feel free to stop reading.


                # ⚓ Wired ☛ Using_Starlink_Wi-Fi_in_the_White_House_Is_a
                  Slippery_Slope_for_US_Federal_IT⠀⇛


                       “The only reason they'd need Starlink would be to
                       bypass existing security controls that are in place
                       from WHCA,” claims former NSA hacker Jake Williams.
                       “The biggest issues would be: First, if they don't
                       have full monitoring of the Starlink connection.
                       And second, if it allows remote management tools,
                       so they could get remote access back into the White
                       House networks. Obviously anyone could abuse that
                       access.”


                # ⚓ Mike Brock ☛ The_Collapse_of_Republican_Seriousness_-_by
                  Mike_Brock⠀⇛


                       This statement deserves to be examined not merely
                       as one senator's gaffe but as a window into the
                       complete collapse of serious thought within a once-
                       substantive political movement.


                # ⚓ Site36 ☛ 15_corpses_have_been_discovered_on_beaches_of_the
                  Balearic_Islands,_and_Alarm_Phone_indicates_more_to_come⠀⇛


                       The Balearic Islands have become the second largest
                       hotspot for migration to Spain after the Canary
                       Islands. According to official government figures,
                       at least 5,846 migrants on board 347 boats reached
                       the Balearic Islands in 2024 – more than twice as
                       many as in the previous year. Refugee organisations
                       and the International Organisation for Migration
                       (IOM) assume that the number of unreported cases is
                       higher. According to the UN organisation, 2,600
                       people have already died or gone missing crossing
                       the Mediterranean in 2024 alone.


                # ⚓ McSweeney’s ☛ Lest_We_Forget_the_Horrors:_An_Unending
                  Catalog_of_Trump’s_Cruelties,_Collusions,_Corruptions,_and
                  Crimes⠀⇛


                       Early in President Trump’s first term, McSweeney’s
                       editors began to catalog the head-spinning number
                       of misdeeds coming from his administration. We
                       called this list a collection of Trump’s cruelties,
                       collusions, corruptions, and crimes, and it felt
                       urgent to track them, to ensure these
                       horrors—happening almost daily—would not be
                       forgotten. Now that Trump has returned to office,
                       amid civil rights, humanitarian, economic, and
                       constitutional crises, we felt it critical to make
                       an inventory of this new round of horrors. This
                       list will be updated monthly between now and the
                       end of Donald Trump’s second term.


                # ⚓ El País ☛ Trump’s_authoritarian_drift_pushes_the_US_towards
                  a_constitutional_crisis⠀⇛


                       Donald Trump declared during his campaign that if
                       he won the election, he would be a dictator on day
                       one. Since his triumphant return to the White
                       House, the U.S. president has focused on straining
                       the executive branch, encroaching on legislative
                       powers with a flood of executive orders, and
                       defying judicial rulings. His authoritarian drift
                       threatens to trigger a constitutional crisis and
                       jeopardizes the system of checks and balances that
                       has defined American democracy for nearly 250
                       years. The clash between branches of government has
                       intensified over the past week, after the president
                       invoked an 18th-century law, applicable in times of
                       war, to deport immigrants without legal guarantees
                       — just as he had promised to do.


                # ⚓ The Atlantic ☛ The_Trump_Administration_Accidentally_Texted
                  Me_Its_War_Plans⠀⇛


                       I, however, knew two hours before the first bombs
                       exploded that the attack might be coming. The
                       reason I knew this is that Pete Hegseth, the
                       secretary of defense, had texted me the war plan at
                       11:44 a.m. The plan included precise information
                       about weapons packages, targets, and timing.


                       This is going to require some explaining.


                # ⚓ RTL ☛ Trump_admin_sent_journalist_classified_US_plan_for
                  Yemen_strikes⠀⇛


                       Hegseth, a former Fox News host with no experience
                       running a huge organization like the Pentagon, took
                       no responsibility for the security breach as he
                       spoke to reporters late Monday.


                # ⚓ The Register UK ☛ Trump_officials_leak_plans_for_US
                  airstrikes_in_Signal_SNAFU⠀⇛


                       “By using Signal for such a sensitive issue, the
                       participants demonstrate a cavalier attitude to
                       operational security,” he wrote Tuesday, Australian
                       time. “For a Secretary of Defense who allegedly
                       values a war-fighting ethos, this shortfall in
                       security is appalling. In normal times, this would
                       see people sacked. I don’t expect that in this case
                       though because these are not normal times.”


                       “Why aren’t they using more secure communications
                       that are assured by the NSA or another government
                       communications agency?” he added. The Register
                       understands chat tools used by those agencies
                       include features that prevent, say, journalists
                       from participating in group chats.


                       Another question worth asking is why the group’s
                       members used Signal, and why they set at least some
                       of the messages to auto-delete, which may be a
                       violation of federal records-keeping laws.


                # ⚓ The Atlantic ☛ A_Conversation_With_Jeffrey_Goldberg_About
                  His_Extraordinary_Scoop⠀⇛


                       Even President Donald Trump seemed unaware of the
                       breach. “You’re saying that they had what?” he
                       replied when asked about the news. Trump added that
                       he is “not a big fan of The Atlantic,” something
                       he’s previously made clear, and which makes the
                       unintentional leak all the more remarkable. A
                       spokesperson for the National Security Council
                       said, “This appears to be an authentic message
                       chain, and we are reviewing how an inadvertent
                       number was added to the chain.”


                       I called Goldberg this afternoon to learn more
                       about how the story came about and what the
                       disclosure reveals about the Trump administration.
                       This interview has been condensed and edited.


                # ⚓ Task And Purpose ☛ '100%_OPSEC'_apparently_means_texting
                  military_plans_to_a_reporter⠀⇛


                       Although defense officials have repeatedly stressed
                       they are committed to being the “most transparent”
                       in history, it is unlikely that this is what they
                       meant.


                # ⚓ US News And World Report ☛ White_House_Mistakenly_Shares
                  Yemen_War_Plans_With_a_Journalist_at_the_Atlantic⠀⇛


                       Democratic lawmakers swiftly blasted the misstep,
                       saying it was a breach of U.S. national security
                       and a violation of law that must be investigated by
                       Congress.


                # ⚓ Spiegel ☛ Harvard_Professor_Steven_Levitsky:_"Right_Now,
                  the_U.S._Is_Ceasing_to_Be_a_Democracy"⠀⇛


                       Donald Trump is currently transforming the U.S.
                       into an authoritarian state, argues Harvard
                       Professor Steven Levitsky, author of "How
                       Democracies Die." And he is using an unexpected
                       twist in the authoritarian playbook to do so.


                # ⚓ Futurism ☛ What_Kids_Are_Actually_Using_Phones_for_in
                  School_Is_So_Pathetic_That_We_May_Need_to_Take_a_Quick_Walk
                  for_Mental_Health_Purposes⠀⇛


                       One would think that the kids themselves would be
                       more opposed to having their phones taken away all
                       day — but as educators have found in schools and
                       districts where phones have been locked up, they
                       cope just fine.


                       Their parents, on the other hand, have been a
                       harder nut to crack because some of them are
                       extremely resistant to not being able to get in
                       touch with — or not being able to monitor — their
                       offspring.


                # ⚓ New York Times ☛ Who’s_Against_Banning_Cellphones_in
                  Schools?⠀⇛


                       “We found a transformative environment,” he told me
                       recently. “We expected kids to be in tears,
                       breaking down. Immediately we saw them talking to
                       each other, engaged in conversation in the
                       lunchroom.”


                       One unanticipated outcome was that students flooded
                       counselors’ offices looking for help on how to
                       resolve conflicts that were now happening in
                       person. Previously, if they found themselves in
                       some sort of fight with someone online, they would
                       have called or texted a parent for advice on how to
                       deal with it, Mr. Blanchard told me. “Now students
                       were realizing that their friends were right there
                       in front of them and not the people on social, a
                       few towns away, that they had never met.”
                       Enrollment in elective classes also went up when
                       the option to scroll your way through a 40-minute
                       free period was eliminated.


                # ⚓ Security Week ☛ Despite_Rip-and-Replace_Efforts,_FCC
                  Suspects_Banned_Chinese_Telecom_Providers_Still_Active_in
                  US⠀⇛


                       The Federal Communications Commission (FCC)
                       announced last week that it’s conducting an
                       investigation into whether Chinese
                       telecommunication providers whose devices and
                       services are believed to pose a risk to national
                       security are still doing business in the United
                       States.


                # ⚓ Hong Kong Free Press ☛ Japan,_China_in_new_spat_after_3-way
                  talks_involving_South_Korea⠀⇛


                       Japan and China became embroiled in a new spat on
                       Monday with Tokyo accusing Beijing of
                       misrepresenting its position after high-level
                       weekend talks also involving South Korea.


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


                      # ⚓ RFERL ☛ Russian_Strike_On_Sumy_Injures_94_As_US,
                        Russia_Hold_Talks_In_Saudi_Arabia⠀⇛


                             A Russian missile attack hit the Ukrainian
                             city of Sumy, injuring more than 90 people as
                             talks aimed at reaching a partial cease-fire
                             in the conflict took place between US and
                             Russian negotiators in Saudi Arabia.


                      # ⚓ Meduza ☛ Russian_strike_on_Ukraine’s_Sumy_injures_at
                        least_88,_including_17_children_—_Meduza⠀⇛


                      # ⚓ RFERL ☛ Russian_Forces_Intensify_Attacks_Near
                        Pokrovsk_As_Cease-Fire_Talks_Begin_In_Riyadh⠀⇛


                             As Russian and Ukrainian delegations meet for
                             cease-fire discussions with US officials in
                             the Saudi capital, Riyadh, Moscow's troops
                             are intensifying their attacks on Kyiv's
                             positions on the front line near the city of
                             Pokrovsk, Ukrainian soldiers in the area told
                             Current Time.


                      # ⚓ RFERL ☛ War_In_Ukraine_Rages_On_As_US,_Russia_Hold
                        Daylong_Talks_In_Saudi_Arabia⠀⇛


                             US and Russian officials are holding talks in
                             Saudi Arabia aimed at reaching a partial
                             cease-fire in Ukraine to end the largest and
                             deadliest conflict in Europe since World War
                             II.


                      # ⚓ New York Times ☛ Russia_and_Ukraine_Hold_U.S.-
                        Mediated_Talks_in_Riyadh:_What_to_Know⠀⇛


                             American envoys talked with Russian officials
                             on Monday, a day after meeting with a
                             Ukrainian delegation. The initial discussions
                             were expected to focus on halting attacks on
                             energy facilities.


                      # ⚓ New York Times ☛ Is_Russia_an_Adversary_or_a_Future
                        Partner?_Convicted_Felon’s_Aides_May_Have_to_Decide.⠀⇛


                             On Tuesday, America’s top intelligence
                             officials will release their current
                             assessment of Russia. They are caught between
                             what their analysts say and what Hell Toupée
                             wants to hear.


                      # ⚓ LRT ☛ MoD_moves_to_ban_Russian,_Belarusian,_Chinese
                        citizens_from_Lithuanian_Military_Academy⠀⇛


                             The Defence Ministry has proposed that
                             Lithuanian citizens who also hold Russian,
                             Belarusian or Chinese passports be barred
                             from enrolling in the country’s main officer
                             school, the General Jonas Žemaitis Military
                             Academy of Lithuania.


                      # ⚓ LRT ☛ How_Russians_adapt_in_exile_in_Lithuania:_‘It’s
                        not_shameful_to_work_with_your_hands’⠀⇛


                             Every weekday in Lithuania, Russian emigre
                             Mikhail Benyash, a well-known former lawyer
                             and activist, rises at 6:30 local time, dons
                             a helmet, and picks up a hammer.


                      # ⚓ North_Korean_troops_sent_to_Russia_included_relatives
                        of_defectors:_report⠀⇛


                             Family members of North Korean defectors
                             often face severe penalties imposed by
                             Pyongyang.


                      # ⚓ Meduza ☛ Russian_region_to_give_$1,200_to_pregnant
                        schoolgirls⠀⇛


                      # ⚓ Meduza ☛ Photos:_aftermath_of_Russian_drone_attack
                        that_killed_child_in_Kyiv⠀⇛


                      # ⚓ Meduza ☛ Journalists_report_first_known_combat_death
                        of_Russian_soldier_born_in_2007_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_and_U.S._delegations_conclude_talks
                        in_Riyadh_after_12_hours_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Kids_pay_the_price_as_Russia_swaps_proven
                        cystic_fibrosis_drug_for_untested_one⠀⇛


                      # ⚓ Latvia ☛ Drone_Coalition_to_send_'several_hundred'
                        tactical_drones_to_Ukraine⠀⇛


                             The member states of the Drone Coalition will
                             allocate 20 million euros from their common
                             fund to purchase 'several hundred tactical-
                             level reconnaissance drones for the Ukrainian
                             Armed Forces in an extraordinary, accelerated
                             procedure' it was announced March 24.


                      # ⚓ France24 ☛ ‘Unspeakable’:_Ukraine_breaks_the_silence
                        surrounding_wartime_sexual_violence⠀⇛


                             Growing numbers of Ukrainian women in areas
                             recaptured from Russian occupation are
                             starting to speak about the sexual violence
                             they experienced at the hands of Russian
                             soldiers. The watershed moment comes from the
                             amplitude and nature of the crimes, says Inna
                             Shevchenko, a Ukrainian feminist activist and
                             author of “A Letter from the East”.


                      # ⚓ France24 ☛ 'My_Undesirable_Friends':_Documentary
                        profiles_Russian_journalists_prior_to_fleeing_country⠀⇛


                             A Russian-American filmmaker has spoken to
                             FRANCE 24 about how her new film captures the
                             last days of resistance to the regime in
                             Russia before the invasion of Ukraine. Julia
                             Loktev, who was born in what was then
                             Leningrad, grew up in the United States. Her
                             film "My Undesirable Friends: Part I — Last
                             Air in Moscow" follows the staff of the
                             television channel TV Rain, which aims to
                             tell the truth about the Russian regime.
                             Since the documentary was filmed, TV Rain has
                             been forced to close in Russia and has set up
                             home in Amsterdam, from where it now
                             broadcasts. She spoke to us in Perspective.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Marcy Wheeler ☛ The_Classified_Information_John_Ratcliffe,
                  Pete_Hegseth,_and_Mike_Waltz_Sent_to_Journalist_Jeffrey
                  Goldberg⠀⇛


                       If you’re like me, you’ll keep checking when
                       reading this story about how Mike Waltz added
                       journalist Jeffrey Goldberg to a Signal chat of top
                       Trump officials planning war strikes on Yemen to
                       see if it’s the Onion.


                       But it’s not.


                       It’s real.


                # ⚓ Federal News Network ☛ Pentagon_is_the_latest_agency_to
                  announce_a_leak_investigation_that_could_include_polygraphs⠀⇛


                       At the Homeland Security Department, Secretary
                       Kristi Noem pledged this month to step up lie
                       detector tests on employees in an effort to
                       identify those who may be leaking information about
                       operations to the media.


          o § Environment⠀➾


                # ⚓ The Hindu ☛ As_ice_frozen_for_millennia_thaws,_Kashmir
                  wakes_up_to_new_risks⠀⇛


                       The stability of permafrost in the Indian Himalaya
                       is thus of great concern.


                       The new study, published in Remote Sensing
                       Applications: Society and Environment, was
                       coauthored by researchers from the University of
                       Kashmir and IIT-Bombay.


                       According to the study, permafrost covers 64.8% of
                       the total geographic area of Jammu & Kashmir (J&K)
                       and Ladakh. Of this 26.7% is continuous permafrost
                       (most of the soil is frozen), 23.8% is
                       discontinuous (more than half of the soil is
                       frozen), and 14.3% is sporadic (intermittent
                       patches of frozen soil).


                # ⚓ New York Times ☛ Supreme_Court_Will_Not_Hear_Appeal_in
                  ‘Juliana’_Climate_Case⠀⇛


                       Juliana v. United States argued that the government
                       had violated the constitutional rights of the
                       plaintiffs with policies that encouraged the use of
                       fossil fuels. But it was dismissed by the United
                       States Court of Appeals for the Ninth Circuit,
                       where the judges ruled that courts were not the
                       right venue to address climate change.


                # ⚓ Southern California Public Radio ☛ Is_planting_trees_'DEI'?
                  Trump_administration_cuts_nationwide_tree-planting_effort⠀⇛


                       Trees are proven to reduce heat in cities, take up
                       stormwater when it rains and improve air quality —
                       all important needs in New Orleans as climate
                       change intensifies storms and raises temperatures.


                # ⚓ EcoWatch ☛ Freshwater_Lakes_Are_Losing_Vital_Surface_Oxygen
                  as_Global_Heating_Continues:_Study⠀⇛


                       The researchers quantified the impacts of
                       continuous global heating and intensified heat
                       waves on surface DO levels, a press release from
                       the Chinese Academy of Sciences said.


                       “The persistent decline in dissolved oxygen (DO)
                       concentrations, observed across diverse aquatic
                       ecosystems since the mid-20th century, has prompted
                       substantial concern. Global observations
                       demonstrate a widespread decline (2%) in DO
                       concentrations across the open oceans, leading to
                       the proliferation of ‘dead zones,’ areas
                       characterized by very low DO,” the authors of the
                       findings wrote.


                # § Energy/Transportation⠀➾


                      # ⚓ The Register UK ☛ Raspberry_Pi_announces_a_Power-
                        over-Ethernet_Injector⠀⇛


                             The problem comes with the switch – something
                             capable of supporting Power-over-Ethernet
                             (PoE) is required. Where that's not possible,
                             there is the Raspberry Pi PoE+ Injector,
                             which supports IEEE 802.3af (PoE, 13 W) and
                             IEEE 802.11at (PoE+, 25 W) standards, and
                             mains voltages between 100 V and 240 V. Plug
                             in a mains lead (not included) and some RJ45
                             connectors, and away you go.


                      # ⚓ Pivot to AI ☛ AI_data_centers:_Microsoft_steps_on_the
                        gas⠀⇛


                             Microsoft said last year how its data center
                             buildout already meant it was just blowing
                             through all its carbon commitments and that
                             Microsoft increased its CO2 output by about
                             30% in the last five years.


                             But Microsoft wants to use even more natural
                             gas. Bobby Hollis, Microsoft VP for Energy,
                             talked up using more gas and mumbled
                             something about carbon capture and storage at
                             the CERAWeek energy conference this month.


                      # ⚓ India Times ☛ The_AI_Boom_and_Its_Data_Center
                        Imperative⠀⇛


                             According to McKinsey, global demand for data
                             center capacity is projected to grow annually
                             by 19-22% from 2023 to 2030, potentially
                             reaching 171 to 219 gigawatts. This surge is
                             driven by the escalating requirements of AI
                             workloads, particularly in terms of power,
                             cooling, and scalability. For India, the AI
                             revolution presents a unique opportunity to
                             establish itself as a global AI powerhouse by
                             building sovereign, high-performance, and
                             sustainable AI-ready data center
                             infrastructure.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Call_for_Submissions:_Save_This
                        Species⠀⇛


                      # ⚓ The Revelator ☛ Save_This_Species:_Sumatran
                        Orangutans⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Stuart Schechter ☛ Difficult_Truths_for_our_Harsh_Times_—
                  Have_security_&_privacy_research,_and_the_students_we_have
                  trained,_actually_made_the_world_a_better_place?_|_Mildly-
                  Aggrieved_(not_mad!)_Scientist⠀⇛


                       Not everyone will miss Ross Anderson.


                       Ross was not afraid to speak truths that made
                       people uncomfortable. His ideas and arguments
                       threatened the beliefs, status, power, ego, and
                       bank balances of others — often those with power.
                       His writings and talks undermined proponents of
                       hardware attestation, chip-and-pin authentication,
                       and surveillance, to name just a few. Many of those
                       threatened by what Ross had to say professed to be
                       faithfully working to serve the public. Many likely
                       believed they were.


                # ⚓ Truthdig ☛ The_Spread_of_Schoolyard_Astroturf⠀⇛


                       These astroturf operations have been proliferating,
                       resulting in serious negative impacts. Consider the
                       havoc wreaked on some school boards by Moms for
                       Liberty (M4L). M4L even got into presidential
                       politics in 2024, boosting Donald Trump, at the
                       behest of the donors, who co-founder Tina Descovich
                       termed as M4L’s “investors.”


                # ⚓ Deccan Chronicle ☛ US_Travel_Risks_Grow_for_Indian_H-1B,_F-
                  1_Visa_Holders⠀⇛


                       Amid rising uncertainty surrounding US immigration
                       policies, legal experts are urging visa
                       holders—including H-1B workers, international
                       students (F-1), and even green card holders—to
                       carefully reconsider any travel outside the
                       country. Although India is not included in the US's
                       proposed travel ban list, returning to the US has
                       become increasingly challenging due to stricter
                       inspections, extended visa processing times, and
                       intensified scrutiny at consulates.


                # ⚓ Scoop News Group ☛ Despite_challenges,_the_CVE_program_is_a
                  public-private_partnership_that_has_shown_resilience⠀⇛


                       Twenty-five years later, the CVE program, which
                       assigns a unique record to each reported
                       vulnerability, is in its fifth iteration. It has
                       become a highly valued and integral aspect of how
                       cybersecurity defenders can consistently share
                       information about vulnerabilities and achieve
                       interoperability across threat databases. There are
                       now 413 organizations from over 40 countries
                       reporting CVEs, with new reported vulnerabilities
                       soaring to over 40,000, and total CVE records
                       climbing to 270,768 in 2024.


                # ⚓ 404 Media ☛ Mozilla_Foundation_Calls_on_Tech_Industry_to
                  Block_ICE_Contractor⠀⇛


                       The Mozilla Foundation says 30 companies should
                       block web scrapers from ShadowDragon, an ICE
                       contractor.


                # ⚓ Connor Tumbleson ☛ Nation_State_Threat_Model⠀⇛


                       If some nation blew up some random consumer car -
                       there would be an outrage and probably a swift
                       response from our military to the affected nation.
                       Yet when you move that focus into the digital world
                       - it more resembles the wild west. You can have a
                       nation with entire teams/lives funded and dedicated
                       to finding a flaw in something. More often than not
                       they succeed and the wider community might laugh
                       with - "wow, increase your security." or even worse
                       it goes entirely unnoticed.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ 404 Media ☛ Viral_Audio_of_JD_Vance_Badmouthing_Elon
                        Musk_Is_Fake,_Just_the_Tip_of_the_AI_Iceberg⠀⇛


                             While we don’t know which specific piece of
                             software was used to create the audio,
                             deepfake and AI-generated disinformation firm
                             Reality Defender’s software detected the
                             audio as “likely fake.”


                             "We ran it through multiple audio detection
                             models and discovered it to be a likely
                             fake,” a Reality Defender spokesperson told
                             me in a statement. “The background noise and
                             reverb were also likely added to deliberately
                             mask the quality of the actual deepfaked
                             audio for further obfuscation."


          o § Censorship/Free Speech⠀➾


                # ⚓ New Eastern Europe ☛ History_rhymes:_intellectual
                  resistance_and_state_repression_in_Georgia⠀⇛


                       The concept of relentless resistance against
                       Russian interference is nothing new for Georgians,
                       least of all for students and intellectuals. In
                       fact, intellectual resistance has always been
                       central to Georgia’s resilience against Russia.
                       After the collapse of the Russian Empire in 1917,
                       Ivane Javakhishvili, a prominent Georgian
                       historian, scholar and public intellectual whose
                       work significantly shaped modern Georgian
                       historiography and consciousness, along with a
                       group of Georgian intellectuals, pushed for the
                       revival of national identity and the restoration of
                       statehood. These efforts materialized through the
                       establishment of the first university in the
                       Caucasus, Tbilisi State University (TSU), in 1918,
                       and just months later, Georgia’s declaration of
                       independence on May 26th 1918.


                # ⚓ Hindustan Times ☛ Journalist_booked_for_anti-Shivaji
                  Maharaj_remarks_held_from_Telangana⠀⇛


                       Koratkar was booked on February 26 under the
                       Bharatiya Nyaya Sanhita (BNS) provisions for
                       promoting hatred or enmity among groups on the
                       basis of an audio conversation between him and
                       Kolhapur-based historian Indrajeet Sawant


                # ⚓ India Times ☛ Free_speech_champion_Elon_Musk’s_X_suspends
                  Turkey_opposition_accounts_amid_nationwide_protests⠀⇛


                       Elon Musk's platform X has suspended several
                       opposition accounts in Turkey amid protests over
                       the arrest of Istanbul mayor Ekrem İmamoğlu.
                       Despite a four-day government ban on gatherings,
                       protests continue. X complied with 86% of content
                       removal requests during the second half of 2024.
                       Musk's stance on free speech is being questioned
                       following these actions.


                # ⚓ Rolling Stone ☛ 'Careless_People':_Memoir_About_Facebook_Is
                  Now_a_Bestseller⠀⇛


                       Meta won a ruling blocking Sarah Wynn-Williams from
                       promoting her book, which likely helped it shoot to
                       the top of the New York Times bestseller list


                # ⚓ EFF ☛ 230_Protects_Users,_Not_Big_Tech⠀⇛


                       Once again, several Senators appear poised to gut
                       one of the most important laws protecting internet
                       users - Section 230 (47 U.S.C. § 230).


                       Don’t be fooled - many of Section 230’s detractors
                       claim that this critical law only protects big
                       tech. The reality is that Section 230 provides
                       limited protection for all platforms, though the
                       biggest beneficiaries are small platforms and
                       users. Why else would some of the biggest platforms
                       be willing to endorse a bill that guts the law? In
                       fact, repealing Section 230 would only cement the
                       status of Big Tech monopolies.


                # ⚓ CPJ ☛ Prominent_Turkish_journalist_İsmail_Saymaz_under
                  house_arrest_for_2013_interviews⠀⇛


                       Saymaz’s lawyer said the journalist was questioned
                       while in custody about his journalistic activity,
                       contacts, and social media activity while reporting
                       on the Gezi protests, including his communication
                       with some of those convicted on charges of
                       organizing the unrest, such as businessman Osman
                       Kavala, lawyer Can Atalay, film producer Çiğdem
                       Mater, and architect Mücella Yapıcı


                # ⚓ Truthdig ☛ Trump’s_War_on_Lawyers_is_Just_Starting⠀⇛


                       In a series of moves that seem culled from the
                       authoritarian playbooks of Tayyip Erdogan, Vladimir
                       Putin and Viktor Orban abroad, and that harken back
                       to the dark days of McCarthyism and the second Red
                       Scare here at home, Trump has slapped three
                       prominent private law firms with longstanding ties
                       to the Democratic Party with executive orders
                       designed to impose crippling sanctions on their
                       operations. The orders charge the law offices with
                       “weaponizing the judicial process” against Trump,
                       and call for terminating their federal contracts;
                       suspending the security clearances of at least some
                       of their attorneys; and limiting their access to
                       federal government buildings, presumably including
                       courtrooms.


                # ⚓ Greece ☛ Turkey_detains_journalists_as_protests_over_the
                  jailing_of_Imamoglu_rock_the_country⠀⇛


                       In an apparent escalation of the government’s
                       response to the growing protests, the Disk-Basin-Is
                       union said at least eight reporters and
                       photojournalists were detained in what it said was
                       an “attack on press freedoms and the people’s right
                       to learn the truth.”


                       “You cannot hide the truth by silencing
                       journalists!” the union wrote on the social media
                       platform X, calling for their immediate release.


                # ⚓ France24 ☛ Turkey_detains_1,100_protesters_and_several
                  journalists_after_Erdogan_rival_arrested⠀⇛


                       Police have detained more than 1,100 people,
                       officials said Monday – including journalists –
                       since the arrest of President Recep Tayyip
                       Erdogan's main rival triggered some of Turkey's
                       worst unrest in years.


                       The demonstrations began in Istanbul after Ekrem
                       Imamoglu's arrest last week and have since spread
                       to more than 55 of Turkey's 81 provinces, sparking
                       clashes with riot police and drawing international
                       condemnation.


                # ⚓ The Hindu ☛ Journalist_booked_for_anti-Shivaji_Maharaj
                  remarks_held_from_Telangana⠀⇛


                       A case was filed against Mr. Koratkar for making
                       derogatory remarks about 17th-century Maratha ruler
                       Chhatrapati Shivaji Maharaj and his son,
                       Chhatrapati Sambhaji.


                       Mr. Koratkar was booked on February 26 under
                       Bharatiya Nyaya Sanhita provisions for promoting
                       hatred or enmity among groups on the basis of an
                       audio conversation between Mr. Koratkar and
                       Kolhapur-based historian Indrajeet Sawant.


                # ⚓ The Economist ☛ Erdogan_arrests_the_candidate_who_could
                  beat_him⠀⇛


                # ⚓ The Telegraph UK ☛ Istanbul_mayor_arrested_despite_massive
                  protests_against_president_Erdogan⠀⇛


                       Ekrem Imamoglu’s detention is largely seen as an
                       attempt by Recep Tayyip Erdogan, the president of
                       Turkey, to block him from power and has led to the
                       country’s worst street protests in over a decade.


                       The arrest came as voters cast their ballots in a
                       primary to name Mr Imamoglu the opposition CHP
                       party’s candidate for the 2028 presidential race.


                # ⚓ BBC ☛ Fierce_protests_after_Turkish_President_Erdogan's
                  main_rival_Imamoglu_jailed⠀⇛


                       In response to his arrest, Sunday night saw a
                       ramping up of the worst unrest the country has seen
                       in more than a decade - with protesters fired upon
                       with tear gas and rubber bullets.


                # ⚓ Associated Press ☛ Turkey_court_orders_formal_arrest_of
                  Istanbul_mayor⠀⇛


                       Earlier Sunday, a court formally arrested Mayor
                       Ekrem Imamoglu and ordered him jailed pending the
                       outcome of a trial on corruption charges. His
                       detention Wednesday morning sparked the largest
                       wave of street demonstrations in Turkey in more
                       than a decade, with large crowds gathering outside
                       city hall for the fifth night in a row. It also
                       deepened concerns over democracy and rule of law in
                       Turkey. His imprisonment is widely regarded as a
                       political move to remove a major contender from the
                       next presidential race, currently scheduled for
                       2028. Government officials reject the accusations
                       and insist that Turkey’s courts operate
                       independently. “If you weren’t here today, if you
                       hadn’t rushed here since the first day, if you had
                       yielded to tear gas and barricades, if you had
                       gotten scared and remained at home, then today a
                       caretaker appointed by Tayyip Erdogan would be
                       residing here in this building,” said Ozgur Ozel
                       Sunday night, pointing at city hall as he spoke to
                       the massive crowd chanting anti-government slogans.
                       Ozel is the head of the Republican People’s Party,
                       or CHP, to which Imamoglu belongs.


                # ⚓ Jerusalem Post ☛ Turkey_in_turmoil:_Erdogan_cracks_down_on
                  protests,_mayor_arrested_-_The_Jerusalem_Post⠀⇛


                       An Istanbul court on Sunday solidified the arrest
                       of Istanbul Mayor Ekrem Imamoglu. He was detained
                       last week alongside dozens of others in a large
                       police raid. The arrest has sparked massive
                       protests in Turkey. The arrest is seen as
                       politically motivated and another step on the
                       authoritarian road in Turkey.


                # ⚓ The Telegraph UK ☛ ‘I_condemned_the_Oct_7_massacre._It_cost
                  me_my_job’⠀⇛


                       A sewage worker was sacked after condemning the Oct
                       7 massacre, The Telegraph can reveal.


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


                # ⚓ CPJ ☛ Several_journalists_hurt,_detained_by_police_amid
                  Turkey_protests⠀⇛


                       Police in Istanbul took at least five
                       photojournalists into custody while raiding their
                       homes on Monday morning: Yasin Akgül of Agence
                       France-Presse (AFP) and Ali Onur Tosun of NOW
                       Haber, along with freelancers Bülent Kılıç, Zeynep
                       Kuray, and Hayri Tunç. Another freelance
                       photojournalist, Murat Kocabaş, was also detained
                       by the police in Izmir on Monday.


                # ⚓ CPJ ☛ Ghanaian_journalists_attacked_by_military,_illegal
                  miners_in_separate_incidents⠀⇛


                       “It is concerning that military officers accused of
                       attacking journalists have not been held to
                       account,” said Angela Quintal, CPJ’s Africa
                       regional director, from New York. “Authorities must
                       act to reverse impunity when security forces attack
                       the press, and deliver funds allocated as payment
                       for items damaged in the attack against the press.”


                       The five journalists, all of whom work for
                       privately owned broadcasters, include: [...]


                # ⚓ RFERL ☛ US_Court_Set_To_Hear_Radio_Free_Europe_Case_Against
                  USAGM_Over_'Harmful'_Cuts⠀⇛


                       The lawsuit argues that denying access to funds
                       appropriated by Congress for RFE/RL violates
                       federal laws and the US Constitution, which gives
                       Congress the ultimate authority over federal
                       spending. It also asks the court to grant a
                       temporary restraining order (TRO) to release the
                       March funds to limit damaging the broadcaster.


          o § Civil Rights/Policing⠀➾


                # ⚓ The Register UK ☛ 2_in_5_techies_quit_over_inflexible
                  workplace_policies⠀⇛


                       Two in five techies quit in the past year because
                       their employer didn't offer requisite flexibility
                       with respect to hours, location and the "intensity
                       of work."


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Inside Towers ☛ Carr_Asks_Congress_to_Restore_FCC’s
                  Spectrum_Auction_Authority⠀⇛


                       The FCC lost its spectrum auction authority three
                       years ago, when Congress let it lapse. “Since then,
                       America has been falling behind China and many
                       other nations when it comes to the amount of prime,
                       mid-band spectrum necessary to power new
                       innovations,” the agency Chair states. “This puts
                       America at a significant disadvantage to China and
                       harms U.S. consumers.”


                # ⚓ Inside Towers ☛ FCC_Security_Council_Probes_Covered_List
                  Entities⠀⇛


                       The Commission says despite being on this list,
                       some or all of those companies may still be
                       operating in the U.S.—either because they do not
                       believe the FCC’s Covered List prohibits particular
                       types of operations or otherwise. The Covered List
                       entities targeted are: Huawei Technologies Company,
                       ZTE Corporation, Hytera Communications Corporation,
                       Hangzhou Hikvision Digital Technology Company,
                       Dahua Technology Company, China Mobile
                       International USA Inc., China Telecom (Americas)
                       Corp., Pacifica Networks Corp./ComNet (USA) LLC,
                       and China Unicom (Americas) Operations Ltd.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ PC World ☛ HP_printer_class_action_lawsuit_ends_in
                  disappointment⠀⇛


                       Models made before the year 2016 are also covered…
                       but that will be a relatively small slice of
                       printers still in service almost a decade later. HP
                       has begun at least nominally warning customers that
                       its new printers include “Dynamic Security” that
                       blocks ink cartridges that don’t use HP’s
                       proprietary verification system. HP has apparently
                       dropped its more overt attempts to “make printing a
                       subscription,” but it’s still heavily invested into
                       locking customers into its expensive ink system.


                # ⚓ Ars Technica ☛ HP_avoids_monetary_damages_over_bricked
                  printers_in_class-action_settlement_-_Ars_Technica⠀⇛


                       In December 2020, Mobile Emergency Housing Corp.
                       and a company called Performance Automotive & Tire
                       Center filed a class-action complaint against HP
                       [PDF], alleging that the company “wrongfully
                       compels users of its printers to buy and use only
                       HP ink and toner supplies by transmitting firmware
                       updates without authorization to HP printers over
                       the Internet that lock out its competitors’ ink and
                       toner supply cartridges.” The complaint centered on
                       a firmware update issued in November 2020; it
                       sought a court ruling that HP’s actions broke the
                       law, an injunction against the firmware updates,
                       and monetary and punitive damages.


                # ⚓ Static Media ☛ Max_Removing_The_Original_Looney_Tunes
                  Shorts_Is_An_Act_Of_Cultural_Vandalism⠀⇛


                       As it currently stands, if you want to watch
                       classic Looney Tunes, your only option is physical
                       media. Warner Bros. Discovery says this is because
                       children's entertainment doesn't drive
                       subscriptions (it gave the same excuse for nuking
                       "Sesame Street"), which is obviously a lie given
                       that a good chunk of the new Looney Tunes cartoons,
                       much of which is explicitly aimed at children, is
                       still streaming. That the library was removed the
                       same weekend "The Day the Earth Blew Up: A Looney
                       Tunes Movie" was released to theaters by
                       independent distributor Ketchup Entertainment reeks
                       of trademark Zaslav pettiness. The man has no
                       business running Warner Bros. Where's an Acme anvil
                       when you need one?


      § Monopolies/Monopsonies⠀➾


          o ⚓ CoryDoctorow ☛ Pluralistic:_Trump_loves_Big_Tech⠀⇛


                 These billionaires transferred millions from their
                 personal accounts to Trump's "inauguration fund," a kind
                 of presidential tip jar that Trump rattled under the
                 noses of any convenient industry leaders hoping for
                 preferential treatment from his regime. It paid off
                 handsomely.


                 Just days before the inauguration, Trump flew to Davos
                 where he told the world's leaders – especially in the EU
                 – that he would not tolerate attempts to regulate US Big
                 Tech companies, such as the EU's groundbreaking Digital
                 Markets Act and Digital Services Act: [...]


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ France_Mulls_Instant_IPTV_Blocks,_€750K
                  Fines_&_New_Piracy_Crime_of_'Incitement'⠀⇛


                       Senators Michel Savin and Laurent Lafon presented a
                       bill last week aimed at reforming professional
                       football through recommendations spanning how the
                       sport is organized, managed and financed. With
                       sharp observations on remuneration at the top of
                       the game, and suggestions of conflicts of interest,
                       also at the top of the game, the senators appear
                       unrestrained.


                # ⚓ D.C._Circuit_Upholds_Human_Authorship_Requirement_in_Thaler
                  v._Perlmutter⠀⇛


                       Last Tuesday, the U.S. Court of Appeals for the
                       D.C. Circuit issued an opinion in Thaler v.
                       Perlmutter affirming the denial of a copyright
                       monopoly application filed by artificial
                       intelligence (AI) developer Dr. Stephen Thaler to
                       an image created by one of Thaler’s generative Hey
                       Hi (AI) systems. Although the appellate court did
                       not categorically reject registrability of all AI-
                       generated works, the D.C. Circuit agreed with the
                       agency that the Copyright Act of 1976 requires all
                       eligible work to be authored in the first instance
                       by a human being.


    * When_Microsoft_Folks_Who_Literally_Strangle_Women_Try_to_Strangle
      Microsoft_Critics
    * Gemini_Links_25/03/2025:_Relaxation,_Literary_"Movements",_and_Gemini
      Mentions



                    ䷩ 𝚕𝚒𝚗𝚎 9090

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 25/03/2025: Terrace Workbench and
Spellcheck in LibreOffice on FreeBSD⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 25, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Twelve:_Play⠀⇛


                       From 2008 through around 2015, my preferred medium
                       for tabletop roleplay was the 4th Edition of
                       Dungeons & Dragons. At the start, I loved the
                       modular and (comparatively) stripped-down approach
                       from the bloat of what 3.0 and 3.5 amassed and
                       appended in attempt to unify a fractured hobby in
                       the protracted edition mess of BX, BECMI, and AD&D.
                       In previous editions, I always felt like I had
                       catching up to do, like I couldn't adequately
                       approach the game as a player or a referee without
                       total knowledge of the options available in the
                       officially-sanctioned modules and rulesets. This
                       was often reinforced in the games I played (always
                       as a PC in those days, never as a ref) where my
                       approach to character creation stemmed from fairly
                       mundane thoughts like "what if I had a couple of
                       hand crossbows where I had different sets of
                       magical bolts, and I could be a sort of trick-shot
                       alchemist" that mechanically translated to a Very
                       Bad multiclass mish-mash, while the others who had
                       system expertise seemed to get their ideas from how
                       to squeeze the most juice out of the rules. These
                       were my very first introductions to the concept of
                       TTRP from the table itself. When 4e came out, clean
                       slate, I wanted to become the expert and, as it
                       happened, nobody else in my group wanted to
                       referee.


                # ⚓ 🔤SpellBinding_—_BDHIMRO_Wordo:_TRESS⠀⇛


                # ⚓ Terrace_Workbench⠀⇛


                       Rex Krueger published a video many years ago on how
                       to build a $30 workbench, essentially a version of
                       the "roman workbench" but using materials which are
                       easily available today.


          o § Politics and World Events⠀➾


                # ⚓ Down_down_down⠀⇛


                       Fanscesca Albanese is saying all the right things
                       but people keep arming and Israel.


          o § Technology and Free Software⠀➾


                # ⚓ Spellcheck_in_LibreOffice_on_FreeBSD⠀⇛


                       From the `note-to-self' department:


                       After a fresh install of FreeBSD on my Thinkpad
                       X270, the spell checking in LibreOffice for the
                       Dutch language didn't work.


                       Installing the package `nl-libreoffice' which
                       contains the "nl language pack for libreoffice"
                       didn't help.


                       Installing aspell and nl-aspell also didn't help.


                       After installing the packages `hunspell' and `nl-
                       hunspell', the spell checking in LibreOffice works
                       ;)


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


    * Let_Them_Eat_'Apps'
    * Links_25/03/2025:_Clownflare’s_Slop_and_Bounties_on_Fake_Patents


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