𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, February 21, 2025
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Sat 22 Feb 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/2025/02/21/


╒═══════════════════ 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  -  Before Trying Censorship by Extortion the Serial Strangler From Microsoft Literally Begged Us to Delete Pages

⦿ Techrights  -  Free University of Bozen-Bolzano Proud to Host Free Software Talk by Richard Stallman

⦿ Techrights  -  Hype Watch: Weeks After Microsoft Disappointed Investors With "Hey Hi" It's Trying Some "Quantum" Hype (Adding Impractical Vapourware to Accompany This Hype and Even LLM Slop in 'News' Clothing)

⦿ Techrights  -  IRC Proceedings: Thursday, February 20, 2025

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Report About February Mass Layoffs at Microsoft (Third Wave of Microsoft Layoffs in 2025) Comes Back From the Dead

⦿ Techrights  -  Richard Stallman 'Only' Founded the FSF

⦿ Techrights  -  Slopwatch: Anti-Linux Machine-Generated FUD (LLM Slop) From GBHackers, CybersecurityNews, and Guardian Digital, Inc (Google News Promotes Slop Plagiarism, Misinformation)

⦿ Techrights  -  Techrights Disconnected From the United States Two Years Ago

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2025/02/21/Before_Trying_Censorship_by_Extortion_the_Serial_Strangler_From.shtml
https://techrights.org/n/2025/02/21/Free_University_of_Bozen_Bolzano_Proud_to_Host_Free_Software_Ta.shtml
https://techrights.org/n/2025/02/21/Hype_Watch_Weeks_After_Microsoft_Disappointed_Investors_With_He.shtml
https://techrights.org/n/2025/02/21/IRC_Proceedings_Thursday_February_20_2025.shtml
https://techrights.org/n/2025/02/21/Over_at_Tux_Machines.shtml
https://techrights.org/n/2025/02/21/Report_About_February_Mass_Layoffs_at_Microsoft_Third_Wave_of_M.shtml
https://techrights.org/n/2025/02/21/Richard_Stallman_Only_Founded_the_FSF.shtml
https://techrights.org/n/2025/02/21/Slopwatch_Anti_Linux_Machine_Generated_FUD_LLM_Slop_From_GBHack.shtml
https://techrights.org/n/2025/02/21/Techrights_Disconnected_From_the_United_States_Two_Years_Ago.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2025/02/21/Gemini_Links_21_02_2025_Web_Browsers_Mechanical_Shortcuts_and_I.shtml
https://techrights.org/n/2025/02/21/Links_21_02_2025_Doomscrolling_and_European_Ham_Radio_Show.shtml
https://techrights.org/n/2025/02/21/Links_21_02_2025_Linux_Foundation_Openwashing_Microsoft_Copilot.shtml
https://techrights.org/n/2025/02/21/Links_21_02_2025_Myanmar_Scam_Centre_and_Disruptions_at_USPTO.shtml
https://techrights.org/n/2025/02/21/Links_21_02_2025_TikTok_Layoffs_WebOS_Software_Patents_in_Bad_H.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 75

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/Before_Trying_Censorship_by_Extortion_the_Serial_Strangler_From.shtml
    Gemini version at https://techrights.org/n/2025/02/21/Before_Trying_Censorship_by_Extortion_the_Serial_Strangler_From.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Before Trying Censorship by Extortion the
Serial Strangler From Microsoft Literally Begged Us to Delete
Pages⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


YESTERDAY morning we wrote about Microsofters misusing_British_law_firms_as
"guns_for_hire" (as the British anti-SLAPP coalition put it; it's a good
description of what some people with a licence to practice law have become). In
the case of Microsofters, they and their lawyers are openly referring to their
own threats as "threats" (yes, they use the term directly!).


We've had many threats sent to us by them and even others were being
threatened. This is very clearly just a broad campaign of intimidation,
striving to terrorise people who 'touch' particular topics. The only way to
deal with such intimidation is to not capitulate but to persist. That's what
we've been doing when dealing with the EPO (same_tactics_were_used) and that's
what we've been doing with Microsoft for several years already.


What we've been subjected to isn't too common; this one is unique because of
the SLAPP-chaining (one SLAPP comes to a dead end [1, 2], so another SLAPP gets
initiated, not only using the same lawyer and same law firm but also an
associate of the first SLAPPer).


We're not at_all surprised that they're reaching out and scraping the very
bottom of the barrel in pursuit of "guns for hire" in London. Both are
Americans, but they're 'litigation_tourists' who export_US_fascism (greater
hostility than ever towards the press) to here. Their "guns for hire" got
blasted in the press for "ambulance chasing" and covering up tax crimes and
facilitators of such crimes [1-3], so they have a history of doing very
unethical things and even standing for - fighting for - really bad people. It
should be noted a small law firm in Manchester said these "guns for hire" in
London made this reputation for themselves by choosing such bad clients. If
some tiny law firm knows "BRETT WILSON LLP" (small firm in_debt) just for being
the worst or most notorious out there, then that must mean something. See [1-3]
below for a taste of it.


There's no lack of other examples. They're giving a whole new meaning to terms
like "criminal lawyers". Assisting people who commit crimes is no occupation to
be proud of; one might argue no such occupation should even exist or be
permitted. The other day we gave an example of lawyers like these working from
London on behalf of Russian war criminals, whose crimes_against_humanity_can_be
explored_by_looking_up_"Bucha".


Months ago the general public was shocked to learn of hundreds of victims of
Al-Fayed realising they are not alone and were never alone. Al-Fayed - with
help from his staffers - kept his victims isolated, just like recipients of
"threats" (the word used by the above-mentioned "guns for hire"!). Victims or
recipients might not realise just how many other threats get sent out to
journalists.


Either way, we'll discuss the similarity to the Al-Fayed case some time in the
future as there is a striking resemblance.


Here are messages I received 3 years ago: (I never responded to this person,
ever)


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Hello_Roy,_you've_published_upwards_of_20_articles_about_me.
  I'm_writing_to_beg_you_to_take_them_down_and_give_me_my_life_back._(Before
                       BRETT_WILSON_LLP_SLAPP_action)⦈_


His solicitor (Rick Cofer, Partner) later wrote to me to admit there were
charges against him. It turns out Cofer was also a "donor" of those who call
the shots [1, 2] - hardly unexpected given what_we've_seen_in_US_courts. It was
a crooked system even before the election got bought by MElon (Elon Musk).


Just to be perfectly clear about this, or in case he reads this, I didn't ruin
your life, sir, you ruined your own and you ruined your victims' lives too. I
merely reported on what had happened. Egoistic and narcissistic people view
everyone else as disposable. You cannot keep your victims gagged forever.


What we can conclude from all this is, there's no merit or real substance in a
legal case; but if begging does not work, then find some "guns for hire"
(unscrupulous lawyers) in another continent. Maybe some bottom-feeding
misogynists can be hired to send what they themselves call "threats",
constantly harassing someone who merely reported crimes/wrongdoing/corruption
in order for the general public to be aware.


A doctor who reads this site told me that this is "certainly crazy stuff."


"...but I do wonder whether it is worth wasting your time on all these non-
technical issues, given there are only so many hours in a day. surely there are
better ways to use your in-depth knowledge of open source and programming...."


"Their objective is to stop me using my knowledge," I replied, and "I explained
yesterday that ignoring them completely is not an option."


As a matter of simple observation and generally speaking, many people nowadays
can code and can talk about "open source" (not Free software), but far fewer
experienced the sort of abuse we're subjected too and thus they cannot uncover
how it works and how to confront such abuse. We do our best to explain who's
doing it, how it's done, and how to tackle it.


If people who spent years viciously attacking me and my family (yes, if you are
thin-skinned the attacks are enough, but if_not_then_they_attack_the_family)
'drown'_in_transparency, then so be it. The_public_deserves_to_know_who_the
real_abuser_is_and_who_the_victim_is or who the victims are. "The_Truth_is
About_to_Prevail". █


______


   1. A_Law_Firm_Is_Promoting_Itself_On_Facebook_To_People_Whose_HIV_Status_Was
      Leaked (yes, that's "BRETT WILSON LLP")
   2. SLAPPed_by_tax_avoidance_firm_“Property118” (yes, that's "BRETT WILSON
      LLP")
   3. HMRC_is_likely_investigating_the_two_big_landlord_tax_avoidance_firms.
      What_should_their_clients_do? (again, that's "BRETT WILSON LLP")


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⣤⠤⡤⠤⣤⢤⡤⣤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⡤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀
⠀⠀⠀⣿⣿⣶⣶⣾⣿⣶⣶⣾⣶⣷⣆⣀⣀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣉⣿⣀⣀⣉⣈⣉⣉⣉⣁⣉⣋⣉⣉⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣯⣩⣯⣉⣉⣋⣫⣏⣉⣯⡇⠀⠀⠀
⠀⠀⠀⡟⠿⠛⠛⠛⢿⠛⠛⡟⠙⠛⠛⢻⠛⠛⠛⠙⠛⠛⠛⠋⠛⢻⠛⠛⡿⠿⢿⣿⣟⠛⠻⠿⠭⠉⢛⣛⣒⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣏⠹⠿⠭⢉⣛⣓⣂⣀⣭⣭⣥⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀
⠀⠀⠀⣏⣟⣏⣉⡛⢽⣩⣭⣏⣝⣉⢉⢉⣝⡄⡍⣈⣉⣏⣙⣯⣙⣛⣹⣉⣙⣛⣉⣏⣉⣉⡏⣝⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⡏⠋⠛⠻⠻⡿⢟⠟⢛⠙⢛⠻⢻⡻⢻⠿⡭⡫⠏⠍⡋⠩⣝⢝⣹⡽⡻⡿⠋⠋⠻⡻⣿⢿⡿⣟⠛⢿⢿⡻⡿⡛⠙⡻⡟⠋⠛⢿⢿⢿⠛⠛⢹⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡿⢿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⡿⢿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⢷⣬⢅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⣿⣧⣤⣤⣮⣦⣦⣕⣾⣲⣤⣥⣦⣤⣯⣮⣮⣦⣬⣷⣤⣼⣤⣠⣤⣥⣴⣥⣼⣵⣯⣴⣼⣤⣦⣤⣥⣤⣭⣤⣤⣤⣤⣧⣤⣤⣯⣧⣤⣧⣤⣷⣥⣇⣸⣤⣼⣤⣤⣡⣢⣤⣤⣯⣥⣯⣤⣤⣼⣿⣿⣿⠀⠀⠀
⠀⠀⠀⣿⣧⣤⣤⣦⣭⣮⣦⣤⣮⣧⣴⣤⣇⣠⣥⣼⣤⣤⣼⣶⣎⣧⣴⣬⣴⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 236

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/Free_University_of_Bozen_Bolzano_Proud_to_Host_Free_Software_Ta.shtml
    Gemini version at https://techrights.org/n/2025/02/21/Free_University_of_Bozen_Bolzano_Proud_to_Host_Free_Software_Ta.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Free University of Bozen-Bolzano Proud to
Host Free Software Talk by Richard Stallman⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025,
updated Feb 21, 2025


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


The official account of the Free University of Bozen-Bolzano posted this 13
hours ago ahead of Monday's talk: [1, 2]


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Free_University_of_Bozen-Bolzano_on_Monday,_February_24,
                                    2025⦈_


A non-Microsoft_page_explains_more:


     There are many threats to freedom in the digital society. They
     include nonfree software, massive surveillance, and censorship.


     Nonfree programs are often designed to restrict users, control users
     or manipulate users. The War on Sharing aims to stop users from
     sharing copies of published works. Computers for voting make election
     results untrustworthy.


     Other threats come from use of web services, implemented by companies
     that can impose any conditions whatsoever.


     Finally, most internet activities (aside from those which existed
     before 2000) are precarious, dependent on permission from one
     company.


     All of these threats originate more or less in the use of nonfree
     software. That is why free software is the first battle in the
     liberation of the digital society.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Meet_Dr._Richard_Stallman,_the_Founder_of_the_Free_Software
   Foundation,_Founder_and_development_leader_of_the_GNU_operating_system⦈_


That's the same Richard Stallman (RMS) photo as used_a_week_earlier_or_earlier
this_month_in_Torino.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Dr._Richard_Stallman_launched_the_free_software_movement_in
        1983_and_started_the_development_of_the_GNU_operating_system⦈_


The photos at the bottom are new. They were added only after the talk, i.e.
some time this week. Here is RMS in the "deck":


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


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


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


Many people attended in person:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Dr._Richard_Stallman_talk:_crowd⦈_


Those crowds show that 'cancel culture' failed, history_will_be_told, and
innocence_matters. In India the crowds that the Richard Stallman's talks
attracted were even bigger. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠉⠉⠛⠛⠻⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠼⠿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣤⣤⣈⠙⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⡶⠶⠾⠛⢿⣿⣿⡿⠟⠉⠉⡉⠙⠉⠁⠀⠀⣤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠤⢲⢀⣿⣿⡇⠘⣥⣉⣧⣶⣶⡧⠀⣀⣘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣿⠃⢸⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⠀⣸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⢠⠉⠻⠛⠁⠤⠶⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠘⠛⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⢠⣶⣯⣿⣶⣷⡶⣿⣂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠉⠉⠈⠉⠉⠀⠀⠩⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣦⣤⣤⣴⣾⣧⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠠⠤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠐⠛⢛⣛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢥⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣩⣿⣛⣿⣿⣻⣿⣿⣿⣫⣿⣻⣿⣿⣟⣿⣏⣿⣻⣹⣟⣿⣿⣿⣿⣿⣽⣿⣟⣿⣟⣽⣯⣩⡏⣿⣹⣹⣟⣻⣿⣿⣻⣿⣿⣻⣿⣛⣹⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⢻⢻⣻⣿⡿⣿⣿⣟⢿⣿⣿⣿⡿⣿⣟⡿⣿⣿⠻⣿⣿⠿⣿⣿⣻⠿⣿⡿⠟⢿⣿⡿⣿⣻⡟⣿⣿⡟⣿⣿⣿⣿⢻⡿⣿⡿⢿⣿⣿⢿⣿⢻⣿⣿⣿⣿⢻⣿⡟⢿⣿⣿⡿⢿⣿⣿⣿⢿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣷⣿⣿⣶⣿⣿⣶⣿⣿⣶⣿⣿⣷⣶⣿⣷⣶⣾⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣾⣷⣾⣿⣿⣷⣾⣿⣿⣷⣷⣶⣾⣿⣿⣿
⣿⣿⣿⣯⣾⣼⣿⣼⣷⣅⣾⣼⣿⣵⣿⣷⣴⣧⣿⣿⣷⣿⣿⣿⣿⣿⣾⣯⣯⣧⣿⣧⣷⣯⣬⣾⣧⣯⣷⣿⣯⣾⣿⣧⣿⣾⣼⣦⣾⣷⣧⣥⣿⣷⣽⣾⣽⣷⣿⣿⣽⣾⣿⣧⣟⣿⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⠟⣿⣿⢟⢻⣿⠛⣿⣿⣿⡏⣻⡿⡛⣿⣿⡙⣿⡿⡿⡛⣿⣿⢿⢿⣿⣯⡏⣻⣟⢿⢟⢻⣿⠉⣿⣿⢿⣿⣛⣿⣿⣻⣟⣿⡿⠛⣿⣿⡛⡛⣿⢻⣿⣿⢹⡟⢻⠟⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⣿⠾⢿⡿⡿⡿⡿⢿⡿⢿⣿⢿⢿⢿⢿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣾⣿⣾⣷⣷⣿⣷⣿⣿⣷⣾⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣽⢛⢿⡻⢛⢛⣿⡟⢟⣟⠟⡻⣻⡻⢟⣿⣿⣻⡛⢛⡟⠟⣟⢟⡿⡻⢻⣿⣿⣿⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⠿⣿⣿⣿⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣿⣯⣦⣿⣼⣼⣭⣵⣽⣿⣯⣼⣽⣯⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⣩⣻⣝⣩⣹⣽⣿⣿⣋⣹⣫⣿⣝⣿⣉⣽⣿⣏⣿⣰⣹⣿⣽⣟⣿⣍⣙⣍⣍⣿⣿⡟⣽⣍⣹⣷⣋⣽⣍⣍⣿⣧⣝⣿⣯⣻⣯⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢛⣿⡿⡿⢻⡿⣿⣿⣿⢿⣿⣿⡟⠿⣿⣿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣾⣿⣾⣷⣶⣿⣷⣾⣿⣿⣷⣷⣿⣶⣶⣷⣷⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣧⣼⣿⣧⣿⣿⣴⣬⣿⣿⣥⣿⣿⣿⣿⣱⣧⣵⣽⣴⣮⣧⣿⣧⣶⣮⣶⣿⣇⣧⣿⣷⣽⣿⣿⣮⣷⣼⣿⣿⣵⣤⣮⣤⣿⣧⣧⣼⣼⣷⣦⣦⣿⣯⣦⣿⣿⣿⣵⣿⣧⣴⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⢹⣿⢟⠻⣿⣛⢫⡿⣿⡿⣿⢟⢿⡯⣛⢻⣻⣟⣻⣻⡟⡟⣟⢿⣟⡛⡻⣿⢟⢿⣿⣿⣟⡋⢿⡻⡻⣿⡋⣻⢟⠹⡿⣛⣿⠏⣟⣻⣿⣿⡛⠻⡿⣿⠟⢙⢻⡿⡛⡟⣛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠻⣿⠿⡿⡿⡿⣿⢿⢿⢿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⠿⢾⠿⢿⣿⣿⡿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠷⣿⣷⣿⣶⣶⣷⣷⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣾⣿⣿⣾⣾⣾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣒⣾⣿⣼⣏⣿⣷⣭⣮⣭⣿⣫⣭⣷⣽⣿⣭⣽⣿⣿⣙⣾⣟⣽⣮⣭⣧⣿⣯⣍⣍⣯⣇⣿⣿⣽⣙⣿⣭⣭⣭⣽⣿⣧⣼⣯⣽⣬⣯⣭⣽⣽⣿⣥⣿⣥⣻⣯⣬⣝⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⣿⡟⠙⠛⡻⢹⣿⣿⢹⢛⡛⢻⡏⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⡿⢿⣿⢿⣿⡿⣿⠿⢿⢿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢿⢿⢿⢿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⠿⣿⡿⣿⢿⣿⣿⢿⣿⣿⢿⣿⡿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣷⣿⣿⣾⣾⣶⣿⣿⣶⣿⣷⣷⣶⣧⣿⣷⣷⣼⣷⣷⣯⣿⣿⣿⣿⣿⣶⣶⣿⣾⣷⣾⣾⣿⣿⣾⣾⣿⣿⣾⣿⣿⣷⣶⣿⣿⣿⣧⣾⣿⣿⣶⣿⣶⣿⣿⣶⣶⣿⣽⣿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣿⣉⣭⣋⣽⣨⣫⣛⣉⣯⣻⣝⣹⣿⣯⣹⣹⣏⣉⣿⣻⣋⣝⣉⣿⣿⣯⣉⣿⣿⣈⣿⣝⣽⣝⣋⣹⣟⣭⣏⣹⣿⣿⣫⣉⣿⣿⣯⣟⣁⣋⣈⣿⣟⣻⣏⢫⣇⣹⣯⣩⣯⣋⣉⣿⣫⣽⣉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⡿⡟⣟⡟⢿⠻⢛⣻⣻⠛⢛⠟⣿⡻⢻⢟⡟⣟⠟⢟⣟⡟⣿⣟⢿⢻⣻⢻⡟⠻⣻⡻⢻⣻⡻⢻⡟⡿⣻⣟⡿⢻⣿⡟⣟⢿⢿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣀⣽⣩⣻⣝⣩⣯⣿⣝⣹⣽⣙⣩⣿⣍⣩⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⢿⣿⡿⢿⡿⡿⢿⣿⠿⣿⣿⣿⠿⢿⢻⣿⡿⣿⢿⢿⡟⡿⡿⣿⢟⢿⣿⣿⢿⣿⡿⣿⣿⡟⣿⣿⣿⢻⣿⣿⣿⡿⡟⠿⣿⣿⣿⡿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣾⣿⣾⣷⣷⣿⣶⣾⣴⣶⣾⣿⣿⣾⣾⣷⣮⣿⣾⣿⣾⣿⣿⣿⣾⣷⣷⣿⣿⣿⣾⣷⣷⣷⣷⣾⣿⣶⣿⣾⣷⣶⣿⣿⣿⣷⣷⣶⣾⣿⣾⣷⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣧⣴⣰⣷⣷⣾⣦⣬⣾⣾⣾⣵⣿⣯⣾⣶⣽⣥⣷⣷⣿⣮⣯⣼⣧⣼⣮⣴⣷⣷⣴⣷⣿⣦⣼⣿⣷⣥⣷⣥⣷⣷⣽⣿⣿⣷⣷⣬⣾⣿⣿⣬⣾⣦⣷⣮⣟⣷⣷⣤⣾⣼⣤⣾⣧⣴⣧⣿⣾⣾⣾⣿⣿⣿
⣿⣿⣿⣟⠟⢻⢟⠟⠻⣿⠏⡻⠟⡛⢻⣿⠉⡿⣿⢻⢿⡟⠻⣿⠏⠻⣿⠿⢿⣿⣿⠟⢻⡻⣿⠏⣿⢿⣟⡿⡿⡿⠋⢹⢿⡻⣿⡏⠟⣿⢿⣿⢛⢛⢿⡟⢻⡿⣿⠟⢹⡿⡟⡻⣿⣻⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⡿⠿⡿⣿⢾⠿⡿⠿⣿⡿⣟⡟⢿⣿⣿⣿⢿⡿⣻⠿⢿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣾⣿⣶⣿⣿⣶⣾⣾⣾⣿⣷⣷⣿⣿⣿⣷⣷⣷⣷⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢟⣿⢟⠛⣿⣿⠉⡿⡟⣿⣿⡛⣿⣯⣿⠟⠙⢻⣿⡿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⠿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⡿⣿⢿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣽⣽⣾⣾⣧⣾⣷⣽⣿⣾⣿⣴⣷⣾⣴⣶⣧⣿⣿⣯⣴⣮⣤⣧⣾⣧⣷⣽⣽⣴⣧⣷⣼⣿⣽⣦⣿⣿⣧⣶⣾⣬⣿⣽⣯⣴⣦⣾⣿⣿⣼⣾⣧⣯⣧⣿⣵⣬⣦⣯⣾⣴⣿⣴⣿⣼⣿⣯⣾⣿⣿⣿⣿
⣿⣿⣿⣏⣿⣏⣩⣹⣿⣏⣹⣿⣿⣿⢻⣿⣏⣍⣹⣿⣿⣍⣩⣿⣿⣏⣝⣯⣿⣿⣻⣿⣻⣿⣇⣏⣽⣿⣏⣙⣿⣏⣉⣿⣿⣿⣟⣻⣿⣝⣿⣿⣿⣿⣋⣿⣏⣩⣿⣿⡍⣏⣿⣉⣽⣫⣷⣇⣳⣯⣖⣹⣿⣽⣿⣿⣿⣿
⣿⣿⣿⡟⡟⢿⣿⣿⠿⠿⣿⠿⡿⣿⢿⡿⣻⣟⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⡿⢿⢿⣿⡟⣿⢿⠿⠿⣿⣿⠿⢿⢿⣿⡿⠿⣿⣟⠿⣿⠿⣿⡿⣿⢿⣿⠿⡿⣿⠿⡿⣿⡿⣿⡻⣿⡿⠟⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣽⣻⣹⣿⣛⣽⣽⣿⣫⣿⣹⣻⣹⣽⣏⣿⣟⣹⣛⣿⣟⣛⣟⣽⣟⢻⣫⣿⣹⣟⣻⣫⡿⣿⣝⣿⡋⣿⣯⢻⣙⣽⣙⣟⣫⣋⣩⣿⣝⣹⣋⣿⣝⣹⣹⣟⣛⡟⣽⣫⣿⣛⣛⢹⣽⣿⣟⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⡻⢿⣿⣿⠻⠿⣿⣿⡿⢿⣿⣿⡿⣿⣿⣿⣿⠿⢿⣟⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⢿⣿⣿⣻⣿⡿⢻⣿⣿⡿⣿⣻⢟⣻⣻⡿⣛⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣶⣶⣿⣿⣿⣾⣿⣿⣶⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣶⣿⣷⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣶⣿⣼⣿⣿⣿⣿⣷⣶⣿⣿⣷⣿⣷⣷⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣿⠟⣿⣿⠻⣿⣿⣿⣿⣟⢻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⢿⣿⢾⣿⣿⢿⠿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣻⣻⡻⢛⣿⣛⡿⣟⣿⣟⣿⣻⢻⠛⣻⣻⡛⣻⣟⣿⠛⣟⣟⣿⢛⣿⠛⢟⣿⣻⣻⣿⣿⣟⣟⣟⠻⣻⣿⢻⡿⣿⣻⣟⣟⣟⡟⣟⣟⠟⣟⡟⠛⣛⣟⠟⣻⣟⡟⣿⡿⡿⣿⣟⣻⣿⣿⡟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⡀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠙⠋⠛⠛⠋⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣷⣶⡟⠷⠒⠷⡶⠻⢶⡶⠺⠶⡖⠷⠶⣶⣶⣶⣾⣿⣿⣿
⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣓⣛⣟⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⡿⠿⠯⠿⡿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠹⠿⠛⠛⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⢿⣿⢿⣯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣾⣧⣷⣧⣮⣯⣿⣯⣿⣽⣯⣽⣽⣿⣽⣽⣿⣿⣽⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⣸⣿⡗⠤⠤⠴⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⣫⣛⣛⣽⣭⣭⣽⣿⣯⣯⣽⣽⣭⠽⣽⣽⣭⣯⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⠿⣿⡻⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡢⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣭⣽⣽⣽⣯⣎⣫⣩⣍⣽⣩⣭⣽⣿⡿⠐⢃⠘⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⢿⠛⣟⠟⢟⢿⠻⡿⢿⡟⡟⢻⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠀⣄⠀⠀⠀⠰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣾⣿⣷⣿⣿⣿⣃⣀⣂⣀⣀⣈⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢾⣾⣾⣾⣷⣷⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣷⢾⣿⣿⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠒⠂⠢⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣉⣉⣙⣛⠛⠿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣴⠾⠋⣉⣉⡉⠙⢿⣷⣦⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣾⣿⠏⠀⣺⣿⣿⠗⠀⠀⠙⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⡿⠀⠀⠀⢹⠁⣁⣀⠀⠀⠸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⣽⣽⣿⣿⣽⡏⢸⣿⣿⠀⠀⠀⠟⠈⠀⠛⠿⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡶⣿⣿⣟⣿⣾⣾⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣉⣉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⣿⣿⠿⡿⠻⢿⣿⣿⣿⡿⠿⡿⣿⣿⣿⣟⡿⢿⠿⣿⣿⣿⣟⣿⢿⡟⠿⣿⣿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠑⠈⠙⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢉⣿⢛⢛⣻⢿⡿⣿⡛⡟⠟⠋⣿⠻⡟⣿⢛⡿⢛⠛⢹⠙⡿⡟⡛⠙⡛⠛⡟⢛⣏⣿⡿⣿⢿⡿⣿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠻⠛⠻⠙⠋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣶⣿⣿⡆⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠐⠻⣿⠛⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣿⢿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⡿⣾⣾⣾⣿⢾⣾⣿⡿⢿⣿⣿⣶⣾⣿⣿⣷⣷⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⣠⢀⣤⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣷⣷⣷⣿⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠿⠁⠉⠀⠉⢻⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⣀⣀⣀⣁⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠐⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠐⠂⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠑⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣷⣶⣶⣶⣶⣶
⣿⣿⣿⢮⡿⢼⣶⠧⣴⣷⡾⢦⣤⣼⢴⠤⣴⣴⢶⣷⣧⢦⣧⣾⣦⣤⣿⣾⣵⣼⣵⣧⣧⣾⣦⣶⣶⣦⣧⣴⣤⣦⣦⣿⣴⣧⣽⣼⣴⣦⣧⣴⣦⣧⣶⣤⣴⣼⣦⣷⣼⣴⣦⣷⣴⣦⣧⣴⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣶⣾⣶⣶⣾⣶⣶⣶⣷⣾⣶⣶⣷⣶⣿⣶⣾⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣤⣦⣺⣶⣄⣤⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⠿⠿⢿⠿⠿⠿⠿⠿⢿⠿⢿⠿⠿⠿⡿⠿⢿⡿⠿⡿⠿⠿⠿⡿⣿⢿⢿⠿⠿⠿⢿⡿⣿⡿⢿⢿⢿⠿⡿⠿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠾⣿⡟⡿⠶⢿⡞⣿⢖⣷⡿⣶⡛⠳⣿⡷⢿⡶⢻⣿⣾⠿⠖⢷⢿⣿⢷⢿⡿⡿⡶⡿⣿⣾⢿⠟⣿⣶⣿⠚⠞⣷⠳⠗⢿⠿⡞⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠠⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⡛⢛⢛⢛⣟⣛⢛⢛⣛⣻⣟⣛⣿⢛⣛⣟⡛⢛⡓⣛⣿⣛⣟⣛⠛⣿⣻⡟⣛⢻⠛⣻⢻⣛⢛⣛⢻⡻⣿⣛⢛⣿⢛⣟⣛⣟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣿⣟⣿⣻⣯⣟⣿⣍⣹⣋⣻⣛⣻⣛⣿⣻⣟⣿⣛⣛⣟⣻⣻⣿⣻⣉⣹⣿⣛⣻⣛⣝⣟⣿⣛⣋⣟⣻⣛⣿⣿⣏⣟⣿⣟⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣍⣯⣍⣿⣍⣟⣩⣍⣏⣽⣯⣭⣹⣭⣯⣍⣯⣩⣽⣏⣽⣋⣩⣩⣋⣩⣹⣉⣭⣉⣻⣯⣋⣯⣽⣩⣯⣏⣹⣍⣩⣭⣍⣹⣩⣭⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣯⣯⣿⣤⣯⣭⣯⣿⣬⣭⣿⣼⣯⣯⣼⣿⣽⣿⣭⣦⣼⣷⣽⣬⣭⣭⣿⣯⣯⣿⣦⣭⣬⣭⣭⣿⣬⣭⣽⣿⣯⣿⣤⣭⣧⣥⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⣾⡦⣧⡵⣶⣷⣴⡶⣶⣷⢧⣿⡵⠼⣼⣶⣭⣷⣶⡼⣶⢼⣮⣶⣿⢦⣵⣦⣼⣦⢾⣾⣷⣷⣶⣦⣾⣦⣤⢤⣿⣼⣦⣷⣾⣼⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠶⠷⣾⠷⠶⡶⠾⡷⠾⠿⡶⠶⠷⠿⠶⢶⠷⢷⠾⠷⡶⢷⠾⠶⢿⢾⢷⡷⢷⠾⠾⠷⣿⣿⣾⣾⣾⣶⣶⣶⣶⣿⣷⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⣶⣾⣾⣷⣿⣶⣷⣿⣾⣷⣷⣷⣶⣾⣾⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⠿⠿⠿⢿⠿⢿⡿⢿⠿⡿⣿⠿⡿⠿⣿⠿⢿⠿⢿⢿⡿⣿⡿⢿⡿⠿⠿⢿⡿⡿⢿⠿⡿⠿⡿⢿⡿⢿⡿⡿⡿⠿⢿⢿⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣿⣷⣿⣶⣾⣾⣶⣷⣷⣶⣷⣶⣶⣷⣶⣷⣶⣾⣶⣶⣶⣾⣶⣷⣷⣷⣷⣷⣶⣶⣾⣾⣾⣿⣾⣶⣶⣿⣶⣾⣷⣷⣶⣾⣷⣾⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣦⣶⣵⣽⣤⣿⣽⣼⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⢿⠿⢿⠿⣿⣿⡿⢿⢿⠿⠿⢿⠿⣿⢿⠿⢿⠿⠿⠿⡿⢿⠿⡿⠿⠿⠿⠿⠿⣿⣿⢿⢿⠿⢿⠿⣿⠿⢿⠿⢿⢿⠿⠿⠿⠿⠿⣿⢿⢿⠿⡿⡿⢿⢿⢿⣿⡿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣶⢾⢶⣷⡾⣿⣷⠶⢾⣷⣶⣷⣾⣶⣶⣾⣷⣶⣶⣾⣶⣷⣾⣶⣶⣶⣶⣶⣶⣾⣾⣿⣶⣶⣶⣾⣶⣷⣶⣾⣾⣶⣾⣶⣿⣷⣷⣶⣷⣾⣾⣶⣾⣷⣾⣿⣶⣾⣶⣾⣷⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⡿⢿⢿⡿⡿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣤⣾⣿⣽⣯⣧⣤⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⢻⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠙⠛⠛⠛⠛⠃⠨⠿⢿⣿⣿⣿⠈⣿⣿⣿⣿⠿⠿⡿⠾⢿⡿⣿⣻⣿⠿⠿⠻⠛⠛⠛⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢸⣿⠂⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠈⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡨⠊⣢⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠉⠈⡏⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢶⣧⣶⣿⣶⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⠀⠀⠀⠙⠻⣿⣿⣛⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣯⣿⣶⣅⠤⠤⠀⠀⠀⠈⠀⠀⠸⣷⣄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣞⢿⣟⣦⣶⡄⠀⠀⢀⣶⡦⠀⢻⣿⣷⡁⠀⠊⠁⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣻⢿⢿⣿⣿⣯⣥⡿⣶⢶⠈⠉⡾⢿⣿⡇⠀⢉⣭⠆⠀⠀⠀⠀⠀⠀⠰⣻⣭⣯⣓⠂⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢉⣹⣿⣿⣿⡟⠃⡍⠘⡆⠀⣧⣸⣿⣿⢰⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⢀⠀⢀⠀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡿⠣⣁⠄⢻⣴⢿⡿⣿⣿⢸⣿⣿⠀⣠⠔⢲⣶⠶⢤⡀⠀⠉⠁⠀⢸⠟⠋⠻⡆⠀⠀⣿⣿⣿⣿⣶⣶⣶⠂⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠀⠀⢿⣿⣿⣿⣦⣽⣃⢸⡿⠿⣷⡿⠿⢾⢟⡟⠀⣿⣿⣿⣷⣶⣿⠇⠀⠤⠄⠀⠷⠔⠲⠶⠃⠀⢠⣿⣿⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣧⣤⣴⣧⣇⣀⣀⡇⢸⠿⠇⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠟⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣰⡶⠐⣆⠑⡂⠐⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣉⣛⣚⣋⣉⣁⣀⣉⣙⣛⣾⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡽⠛⠿⠛⠛⠛⠿⠟⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠏⠑⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠁⠉⠉⠙⠛⣉⣭⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠟⠿⠄⠙⡯⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣿⣿⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⣿⣿⣽⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⢻⣿⣶⡄⠢⡀⢀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⡹⣿⡿⠦⠈⠀⠲⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠽⡻⠌⢿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⣠⠄⠀⠀⢀⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠇⣀⣀⣀⣒⣐⣋⣀⣿⣿⣿⣬⣬⣤⣤⣶⣿⣷⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⡄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⢛⣹⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠻⣿⣿⣿⣿⣿⣿⢿⣿⠻⣿⣿⢿⣽⣿⡿⡦⡵⢾⣿⢿⣿⣿⣿⡿⣿⡿⣿⡻⣿⠟⢿⣷⢙⣿⣟⣟⢿⣾⣿⣿⣥⣤⣹⣿⣿⣿⣷⢽⣿⣿⣿⣿⣿⣿⣿⣿
⣛⠈⣩⢿⡏⠉⢻⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢆⠟⠛⠿⣿⡿⣿⢟⣉⣈⠟⠑⢷⣿⣽⡁⠀⠀⢈⣻⣧⡙⠙⠀⠀⠻⠃⠙⠁⠀⡀⠛⢊⠘⣹⣿⡿⣳⡯⢹⠇⠛⡘⠕⠤⣶⣻⡿⠙⢿⣿⣛⠙⣿⣿⣙⣏
⢛⡢⠿⠿⣗⡀⡬⠤⡄⠀⠈⣟⠛⢟⠟⢿⣿⡛⣫⡍⠡⠦⣟⣳⡀⠈⣧⣤⡈⠋⢀⡘⠓⠺⢿⡆⠙⠒⠶⠴⡛⠉⠛⡠⣤⡤⠤⠀⢠⢤⡰⠿⢆⣀⣾⣿⣿⣿⠿⣳⡀⣤⣀⡙⠋⠈⠀⠆⠐⣶⣸⡿⠿⢾⣿⡿⢿⣿
⣿⣿⡿⢚⡛⢖⣜⠟⠛⡋⠀⣆⣺⡎⢔⡚⠋⠉⠀⠀⠀⠀⠸⠿⢏⠂⠉⡃⠀⢰⣾⣿⣆⠀⠈⡧⡞⢻⡆⠀⠀⣾⣸⣡⣤⣀⠀⣙⠛⠋⠁⠀⠈⣾⣿⣷⣶⡤⠸⢀⠀⠀⠀⠉⠫⢄⢀⣳⣶⣟⠉⣀⣢⣤⣖⡲⡀⠀
⣿⣿⢤⣢⠿⠫⠛⠀⠈⠁⢀⡈⠀⠁⡋⣴⠀⠀⠀⠀⠀⠀⠀⣐⠿⢷⠀⠀⠀⠈⠿⠛⠋⠁⠀⠿⠽⡿⠃⠐⠀⣿⣿⡷⣤⣬⢀⡿⠿⠂⠀⠀⠀⢸⣧⣀⣀⠠⠀⠻⠷⠀⠀⠀⣰⣿⣿⡿⠿⠿⣷⣄⠀⠁⠉⠀⠀⠀
⣦⣁⢉⡶⠂⢀⣖⢤⠄⠀⠀⠀⣸⣣⡇⠋⠁⠀⠀⠀⠀⠀⠈⠏⠿⠒⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠰⠷⠸⣟⠁⠘⡟⠷⠺⢑⣷⠃⠀⠀⢀⣼⣿⣿⣿⡏⢽⠃⢀⠀⢀⠼⠿⣿⠟⠀⠀⠀⠈⠛⠆⠀⠀⠀⠀⠀
⣙⣿⣿⣶⣦⣤⣭⣯⠤⠀⢀⣀⣼⣿⡇⠐⠰⠅⠀⠀⠀⠀⣠⣴⠶⠂⠲⠒⠄⠀⢀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠿⠀⠀⠠⠉⠀⠀⠀⢘⣿⣿⠿⠋⠀⡴⠄⠀⠀⢰⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠛⠻⢿⡿⣿⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠰⠿⠦⣤⠿⠛⠏⠀⠀⠀⢀⣿⠂⢀⣠⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⢰⣿⠿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢂⡼⡟⢻⠅⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⣿⣿⣀⣠⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠌⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠠⡀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⡀⠄⠐⢅⣹⡷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡄⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡾⠃⠀⢡⣤⡶⠒⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣯⣽⠿⢊⡻⣿⣿⠿⠛⠟⠷⣀⣀⣂⠐⠀⢠⡆⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣳⠃⢠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⢂⣾⣿⣿⠋⣠⠖⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡾⣿⠾⣶⣶⣶⣄⣀⠀⢙⣹⣿⣛⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠶⠾⠷⠀⢼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠠⢡⣾⣿⡿⠁⡴⠟⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠬⢉⣷⣾⣿⣿⣿⣽⣿⣿⣶⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣿⠇⡀⢀⣿⣿⡿⠁⠈⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⡈⠻⢻⣿⢿⣿⣿⣿⡿⠛⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠠⢥⠐⠒⠂⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣼⠋⠀⢀⣈⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠿⠿⠀⠤⠥⢤⣾⣷⣿⣽⣿⢿⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣀⣀⡾⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⡟⠸⠀⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 632

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/Hype_Watch_Weeks_After_Microsoft_Disappointed_Investors_With_He.shtml
    Gemini version at https://techrights.org/n/2025/02/21/Hype_Watch_Weeks_After_Microsoft_Disappointed_Investors_With_He.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Hype Watch: Weeks After Microsoft
Disappointed Investors With "Hey Hi" It's Trying Some "Quantum" Hype (Adding
Impractical Vapourware to Accompany This Hype and Even LLM Slop in 'News'
Clothing)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


Recent: When_You_Simply_Rebrand_Almost_Everything_as_"Hey_Hi"_("AI"),_"Hey_Hi
Workloads",_"Hey_Hi_Datacentres"_and_Whatnot | Rumour_of_IBM_'Bloodbath'_in
Clown_Computing


Latest hype_wave from Serial_Sloppers: (proofs of concept are decades old!)


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft’s_Majorana_1_quantum_chip_could_break_encryption
                       and_expose_your_data_to_hackers⦈_


SCIENTIFIC-sounding terms (that arouse intrigue or invoke "the unknown") - or
terms like "Quantum" - are often misused; Mozilla did that some years ago and
that didn't have anything to do with QC, it was just some buzzword that helped
created hype around performative overhaul in Firefox ("Quantum").


IBM has nothing to offer (in Clown_Computing it's mostly a reseller), so as
noted_2_days_ago IBM's lousy CEO starts name-dropping "Quantum". So does
Microsoft this week, maybe even Google (in recent weeks). Microsoft_is_bleeding
and it_tries_to_crush_media_that_talks_about_it. It needs to change the
subject, too.


I am no QC guru, but the consensus is that QC is mostly hype and NVIDIA says
its commercial potential is only or at least decades away, if not longer (if
science in Western civilisation or east Asia survive that long). Until then
it's more of a "lab experiment" or borderline "sci-fi" for geeky media which so
talks about "flying cars". Fantasies about the perceived impossibilities do
sell (not products but words).


"Quantum" is just some nonsense that "suits" tell to shareholders who rightly
express concerns and scepticism of "hey hi". They're begrudgingly coming to
recognise it's little_more_than_a_bubble that repurposes old_things but
compensates for a lack of novelty with purchased "media coverage" and
unprecedented brute force (read: total waste of power; no_returns_foreseen).


When these charlatans and liars are done telling us to wait a while longer for
actual sales/profits in "hey hi" they will move on to talking about the
"quantum arms race", the "quantum era", the "quantum revolution" et cetera
while paying some media to play along, worshipping naked emperors with new
(invisible) "quantum" clothes.


Remember "metaverse"? What happened to media hype about "blockchain" and "IoT"?
█




⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠡⠄⡠⠤⢠⠆⠤⡄⣤⢤⢀⡤⡄⡄⣠⢀⣄⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠠⠂⠯⠝⠸⠰⠩⠿⠇⠾⠸⠭⠏⠿⠻⠞⠰⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠤⠤⠀⠀⠀⠀⠀⠒⠄⠠⠆⠀⠀⠐⠰⠀⠀⠐⠀⠀⠀⠠⠰⠂⠀⠀⠂⠠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠂⠐⠆⠀⠀⠀⠀⠰⠄⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠙⠋⡗⡟⣟⢛⡟⡟⡿⢿⢻⢻⢱⢹⣽⠻⣿⡏⠻⣹⢻⢻⠚⣟⠛⣻⠛⡟⡟⡟⡟⣿⡍⣿⡿⣻⠛⣿⡟⡟⡟⡟⡏⡟⡟⡟⣛⣻⣿⢻⣻⣛⠗⡟⡟⣿⢟⣿⢻⢻⢻⢻⠸⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣷⣷⣶⣾⣷⣶⣷⣾⣶⣾⣾⣶⣿⣶⣿⣷⣷⣿⣶⣾⣼⣶⣷⣿⣶⣶⣷⣷⣶⣿⣶⣾⣿⣶⣼⣶⣷⣶⣷⣷⣷⣷⣶⣷⣿⣿⣿⣶⣾⣿⣶⣧⣶⣿⣷⣾⣶⣾⣶⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢨⢹⢩⢉⡹⡉⡇⡫⣿⢋⣹⢩⢹⢩⠏⣭⠛⡍⡍⡇⡍⡏⡍⡏⡍⣿⢏⢹⢩⢹⢩⢸⡟⣉⣯⣻⣭⢽⢩⢹⣉⠝⣉⣿⡟⢫⢫⢹⢹⢹⢩⣿⢩⢸⢉⢫⡽⡉⣿⡇⡏⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣵⣧⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢸⢙⢏⢏⠮⡇⡹⠱⢽⢹⠕⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢟⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡈⠋⠈⣿⣿⣿⢿⣿⣿⣿⣿⣻⣹⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣉⣐⣓⣁⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 717

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/IRC_Proceedings_Thursday_February_20_2025.shtml
    Gemini version at https://techrights.org/n/2025/02/21/IRC_Proceedings_Thursday_February_20_2025.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Thursday, February 20,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now




⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣾⢿⣼⣿⣿⡉⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠈⣿⠀⠀⠀⢀⣉⠒⠠⠠⣿⢟⣿⣿⣿⣻⡛⣻⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⢠⣿⠀⠀⠀⢸⡇⢸⣷⡖⣶⢠⢍⣐⠀⠠⠒⢶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠸⣿⠀⠀⠀⢸⣷⣿⣿⣇⣿⢰⠀⠈⢸⢹⣶⢶⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡔⢫⣽⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣷⣿⣼⣿⣸⣾⣽⣿⢿⣿⣿⣿⣿⢿⢿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡷⢾⣿⠀⠀⠀⢸⡇⣿⣿⠇⣿⠹⠹⠟⣿⢿⣿⣿⣿⣿⣿⣽⣛⡚⠓⢒⣒⡚⠋⠉⠀⠿⠷⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⢸⣿⠀⠀⠀⢸⣷⣿⣿⣿⣿⣸⣾⣇⣿⣼⣿⣸⣿⣿⣿⠏⠀⠀⡌⣀⣀⣀⠀⠀⠐⠆⠀⣀⠀⠀⣠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹
⣿⡇⢰⡟⠀⠀⠇⢼⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣶⠀⠭⠭⢉⡉⣉⡀⣄⣂⣀⣽⠁⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⢿⣿⣿⣿⣀⣃⡝⢺⣿⣿⣿⣿⡅⠀
⣿⣷⣾⡇⠀⠀⠀⣸⡄⣿⣷⠀⠀⠀⠀⠈⠈⢩⣟⢛⢻⠿⢿⣷⣿⣀⣤⡆⡇⠀⣿⡀⣿⣿⣄⠀⣘⠁⣨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠒⠒⠿⠿⡏⣀⣈⡁⠠⢼⣿⣿⣿⣿⡇⠀
⡄⠀⢉⡍⠀⠀⠀⢸⠁⣿⣿⢀⡇⠀⠀⠀⡶⢸⡯⢸⢸⢉⣿⠸⣿⢿⠿⠿⡿⣧⣿⠄⡇⢹⠄⢠⣤⡤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠙⠑⢃⠄⠀⠃⠁⠉⠀⠀⠀⠀⠀⠀⠈⠀⠁⠯⢿⡃⠀
⣧⡀⢸⡇⠀⠀⠀⢸⣰⣿⣿⣸⡇⣦⣤⣤⣧⣼⣇⣼⣾⣾⣿⣦⣿⠈⠉⡇⡏⠃⠍⠬⡇⢸⠀⢸⣿⠏⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⠶⢦⡄⡆⠀⠀⠀⠀
⣿⣽⣿⡇⠀⠀⠀⣾⣤⣾⣿⢤⡁⠉⠉⠉⠩⢼⣯⢼⢸⠀⠉⠀⣿⠒⠒⠒⡓⠂⡇⠀⢷⡶⠆⢸⣿⠁⣼⡹⠴⡦⣦⢀⣀⣄⣀⣨⠍⠍⠉⢱⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⣈⡉⠁⢀⠟⠀⠀⠀⠀⠀
⣿⠀⢸⡇⠀⠀⠀⡿⠁⢹⡇⢀⡄⢠⡄⠀⡇⢈⡁⢸⣾⣶⢱⠖⣿⣂⢠⣘⢿⠛⠟⠇⠀⣾⠀⠸⠟⠀⠟⠣⠀⠀⠁⠀⠙⣿⣿⣿⣦⣤⣤⣤⣬⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣿⡇⠀⡂⠀⠒⠀⢸⣿⢺⡏⡻⠇⠀⠋⢹⢏⢹⢻⡏⢠⠈⠻⠀⠘⠘⠀⠐⠐⠒⠚⠋⠛⠀⠀⢀⣀⣤⣤⣠⣶⡶⠋⠋⠉⠉⡉⠉⠉⠉⡛⠛⠛⠋⣹⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣐⣂⠀⠀⠀⠀⠀⠀⠀
⣭⠭⠿⠇⠀⠄⠀⠁⠀⠘⠛⠘⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⡿⠿⠈⠉⠉⠒⠐⠛⠀⠀⠘⠛⠋⢋⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣯⠀⢀⠀⠀⠀
⠂⠒⠒⠐⠂⠓⠀⠀⠀⠈⣋⣀⡀⣀⠀⠀⣤⣤⣤⣴⣶⣶⣶⣶⣯⣤⣤⣦⣴⣾⣿⣿⣿⣏⣩⠙⣿⠛⢟⡛⠻⠿⢿⢶⣦⣦⣤⣤⣶⣤⣤⣼⣿⣿⣿⣿⣿⣛⣛⣛⣟⣿⣿⣿⣿⣿⣿⣧⣘⣀⡄⢸⣿⠀⢸⣷⣶⠄
⣰⡶⣶⢶⣿⣽⣤⣿⠟⡛⠛⠳⣶⣿⡿⠟⡟⢿⣿⣿⣟⣻⣿⣿⣯⡷⠖⠺⣽⣿⣛⣻⡫⡁⠀⠀⠀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣏⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡀⡞⠀⢘⠦
⢉⣀⡬⠬⠟⠛⣛⣉⣵⣤⣤⣿⣿⣿⣿⡀⠀⢲⣟⣻⡿⣯⣭⣭⣥⣦⣮⣾⣿⣿⣿⣿⣭⣭⣍⣋⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠃⠀⠘⠛⠛⠃⠀⠛⠛
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⡿⠿⢿⣿⣿⠿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣫⣭⣿⣷⣶⣚⣿⣿⣻⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣟⢋⠛⢻⣿⣿⣿⠿⠿⠟⠛⠛⢛⣛⣋⣛⣿⣽⣿⣛⣻⣿⠭⠀⠀⠁⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢫⡽⠿⠟⠛⠛⠉⠋⠉⢛⣛⡿⢽⢛⣻⣿⣯⢝⣻⣯⣾⢿⣽⣿⡿⢅⣉⢭⠙⠿⠭⣱⣷⣯⡭⢷⠿⠻⠟⠛⠓⠲⠒⠚⠿⠾⣿⣿⣫⣭⣛⡿⢯⠉⠑⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠁⡂⡌⠙⠉⠉⠅⠍⠉⠄⠘⠛⠋⠙⠹⢍⠄⢀⠀⠠⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⡈⠚⠛⢬⠷⡯⠛⠻⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠴⠎⠤⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠔⡀⠏⠛⠘⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 944

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2025/02/21/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Feb 21, 2025


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Ubuntu_24.04.2_LTS_Is_Now_Available_for_Download_Powered_by_Linux
      Kernel_6.11⠀⇛


           After a week’s delay, Ubuntu 24.04.2 LTS was published today by
           Canonical for all official flavors as the second point release
           to the long-term supported Ubuntu 24.04 LTS (Noble Numbat)
           operating system series.


   2. ⚓ Open_Hardware/Modding:_Raspberry_Pi,_RISC-V,_and_Arduino⠀⇛


           Hardware news


   3. ⚓ The_secret_maze_of_Debian_images⠀⇛


           It's difficult to find the right Debian image


      ⚓  New⠀⇛


   4. ⚓ OpenSSH_Patched⠀⇛


           On Tuesday, the developers of OpenSSH, the popular open source
           implementation of the Secure Shell (SSH) protocol, rolled out
           patches for two vulnerabilities


   5. ⚓ Pi-hole_6_Is_Here⠀⇛


           New release


   6. ⚓ Programming_Leftovers⠀⇛


           Development news


   7. ⚓ Mozilla_Without_Mitchell_Baker_and_With_More_Buzzwords/Hype/Bubbles/
      Schemes⠀⇛


           Mozilla news/noise


   8. ⚓ 4_Ways_to_Search_the_Web_From_the_Linux_Terminal⠀⇛


           Whether you’re a confirmed command line-dweller, or just
           terminal-curious


   9. ⚓ Free_and_Open_Source_Software,_howtos_and_Installations⠀⇛


           Only the Raw edition is free and open source software


  10. ⚓ SME_Server_–_Linux_Server_distribution_for_small_to_medium_sized
      enterprises⠀⇛


           SME Server is billed as a complete, secure, stable and
           versatile Open Source Linux Server distribution for small to
           medium sized enterprises


  11. ⚓ today's_howtos⠀⇛


           Instructionals/Technical posts


  12. ⚓ LibreOffice_24.8.5_is_available_for_downloadLibreOffice_24.8.5_is
      available_for_download⠀⇛


           LibreOffice 24.8.5, the fifth minor release of the LibreOffice
           24.8


  13. ⚓ Wallpaper_Competition_for_Ubuntu_25.04_is_Open_Now!⠀⇛


           Wallpaper competition for the upcoming Ubuntu 25.04


  14. ⚓ Graphics_and_Games:_MemSed,_Mesa_25.0,_Proton_Experimental,_and_More⠀⇛


           gaming picks


  15. ⚓ Events/FOSDEM_Leftovers⠀⇛


           geeks who attended


  16. ⚓ Security_Leftovers⠀⇛


           patches and Windows TCO


  17. ⚓ Android_Leftovers⠀⇛


           Android 16 now lets you customize keyboard shortcuts — Here's
           how it works


  18. ⚓ Ubuntu_25.04_Features_and_Release_Date:_Here's_What_You_Need_to_Know⠀⇛


           Here are the best Ubuntu 25.04 features


  19. ⚓ Best_Free_and_Open_Source_Software⠀⇛


           This is free and open source software


  20. ⚓ Wireshark_on_Ubuntu:_Stay_Ahead_with_the_Latest_Releases_and_Nightly
      Builds⠀⇛


           Wireshark is an essential tool for network analysis


  21. ⚓ KDE_Snaps_are_broken,_sorry_lights_out_for_now⠀⇛


           All core22 KDE snaps are broken


  22. ⚓ LWN_on_Linux_and_Rust⠀⇛


           4 articles outside the paywall today


  23. ⚓ Whatever_Happened_to_Ubuntu_TV?_Where_Linux_Smart_TVs_Are_Now⠀⇛


           When Ubuntu Expanded Beyond Computers


  24. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


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


                         Span from 2025-02-14 to 2025-02-20
      860 /n/2025/02/14/More_About_Asahi_Issue.shtml


      777 /n/2025/02/04/
          Someone_got_Linux_running_inside_a_PDF_file_because_its_users_a.shtml


      757 /n/2025/02/13/openSUSE_Tumbleweed_Moves_to_SELinux.shtml


      651 /n/2025/02/17/Linux_6_14_rc3.shtml


      639 /n/2025/02/16/No_More_Snakes_Serpent_OS_Rebrands_as_AerynOS.shtml


      576 /n/2025/02/16/
          GNOME_48_Beta_Is_Now_Available_for_Public_Testing_with_Adwaita_.shtml


      561 /n/2025/02/14/Oreon_Mesa_and_More.shtml


      536 /n/2025/02/15/
          PostgreSQL_17_3_Siren_Call_of_SQLite_on_the_Server_and_More_on_.shtml


      532 /n/2025/02/14/today_s_howtos.shtml


      530 /n/2025/02/17/today_s_howtos.shtml


      526 /n/2025/02/16/today_s_howtos.shtml


      525 /n/2025/02/15/today_s_howtos.shtml


      517 /n/2025/02/15/
          Fedora_threatened_with_legal_action_from_OBS_Studio_due_to_thei.shtml


      515 /n/2025/02/17/
          Review_Rhino_Linux_2025_1_and_MX_Linux_23_5_with_Xfce_4_20.shtml


      504 /n/2025/02/18/today_s_leftovers.shtml




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣍⣛⠳⠶⣦⣄⣄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⢷⡿⢳⣶⣬⣉⣛⠿⢦⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠟⢫⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⡿⠟⠋⠙⠿⢿⣿⣿⣿⣿⡿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⣸⣽⣿⣾⣿⠻⣷⣦⣭⣝⡛⠷⣦⣆⣀⠀⠀⣠⡶⢾⢿⠾⡷⡿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⣿⣿⣧⠀⠀⠀⠀⠉⢺⣿⣿⡏⠀⠀⢀⠔⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣻⣶⢿⣿⣿⣿⡏⢸⣿⣿⣿⣿⢻⣿⣶⣦⣭⣙⡳⠶⣤⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣆⠰⣤⡀⠀⠀⠀⠀⢀⠀⢄⣬⣿⢿⣿⡿⣿⡯⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⢁⣊⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠻⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣸⣿⣿⣿⠋⣿⣯⣷⢶⣮⣭⣛⡻⠎⣿⣿⡿⣿⣿⣿⡠⢀⠀⠄⠐⠀⠁⢀⣠⣿⣿⣽⣾⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠤⠒⠃⡀⠀⠀⢐⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣴⣆⣤⡆⢉⡝⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⠿⠓⠛⢉⠉⣠⣤⡄⢸⡷⠋⡀⡝⠋⢺⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠅⠤⠤⢼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣿⣿⣿⡇⣼⣿⣾⡇⣰⣦⣤⠈⣉⠉⠛⠻⠿⠿⣿⣿⣿⣿⣟⠻⢿⡇⠠⣶⢶⢹⣾⢀⣿⡿⠓⠒⡚⠉⣤⣕⣲⣽⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠤⡆⢄⣰⣴⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣀⣿⣿⡇⣴⣦⡆⢠⣌⣍⡙⠛⠻⠶⠤⡀⠉⠁⠨⠅⠐⠂⠀⠀⡀⢀⣼⣧⡌⣙⢛⠛⣛⠛⠛⠳⠄⠀⠀⠀⠀⢀⣠⣀⡄⡴⠒⣟⣉⡉⢙⢙⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⡭⠉⠛⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣿⣿⣿⣿⣸⣷⡆⣦⡴⠰⠂⡆⢰⡇⢸⡇⣼⣇⢨⣿⣿⣷⣿⣷⡆⢩⣶⣥⡐⠻⡆⠀⢐⠴⡨⣿⣿⣧⣧⣹⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣥⣴⣽⣯⠄⢄⣹⣶⠊⠉⣭⡽⠛⢛⣿⠿⠿⣿⣿⣿⣿⣿⡿⣿⣿⠇⢺⣷⣷⢺⠷⠹⢿⠒⠀⠈⠹⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣅⣤⣦⣴⣤⣰⣼⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⣷⣾⣸⡏⠉⣆⣿⣆⣆⣿⠤⣼⣯⠉⢹⡿⠟⠀⢘⣰⣭⣤⠠⢤⠔⢀⠒⢰⢸⣿⢿⡿⣯⡟⣯⡝⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⠗⠟⢿⢻⢻⠻⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⠀⣷⣿⣾⣾⡇⢡⡀⢀⣸⡏⢱⣦⣶⢶⢻⣚⣾⣾⣿⣿⣶⣿⠛⢻⡟⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠻⢻⢷⢽⡇⣸⣿⣿⣮⣻⢸⢻⣿⣿⣿⣿⣿⣷⢨⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⢩⣩⣽⣩⣹⣹⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢙⣸⢘⣿⣿⣿⣟⣏⠩⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠉⠉⣈⣭⡽⣿⣿⣧⣿⣿⣿⠛⠿⠛⠛⠛⠉⠀⠁⠘⠻⣿⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⢸⢿⠀⠻⣿⡏⠏⣻⠁⣼⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⠀⢤⣥⡿⣧⡿⣯⣿⣿⣿⠆⠀⠀⠶⠆⠀⠀⡀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣯⣄⣘⣀⣀⣀⣋⣃⣀⣈⣀⣘⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠻⡿⣿⣿⠠⠀⠀⠀⠀⠀⢀⡋⠓⠢⠿⣧⣿⣿⣿⣿⣤⡄⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣛⣛⣛⣻⣟⣛⠛⠛⠻⠻⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⣿⡿⠿⠿⠛⠛⣛⡚⢗⠛⠛⠛⠛⠛⠒⠒⠚⠒⠓⠀⠀⠀⠀⠋⠛⠛⠐⠁⠀⠤⠄⠀⠁⠀⠀⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠅⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1211

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/Report_About_February_Mass_Layoffs_at_Microsoft_Third_Wave_of_M.shtml
    Gemini version at https://techrights.org/n/2025/02/21/Report_About_February_Mass_Layoffs_at_Microsoft_Third_Wave_of_M.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Report About February Mass Layoffs at
Microsoft (Third Wave of Microsoft Layoffs in 2025) Comes Back From the
Dead⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025,
updated Feb 21, 2025


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_Layoffs_Hit_Cloud_Solution_Architects,_Customer
                                    Roles⦈_


WHENEVER an article about Microsoft - one that is unflattering to Microsoft -
gets taken down, well... be_suspicious. Microsoft tends to bribe and blackmail
people. Many_articles_about_Microsoft_are_fake_and_paid_for_by_Microsoft.
Microsoft is generally a company that attracts many criminals to join its
ranks. It's the "work culture". That's how Microsoft treats the media too.


Yesterday we wrote about an article in CRN (reporting Microsoft layoffs) being
removed without any reasons specified.


It has finally been restored: Microsoft_Layoffs_Hit_Cloud_Solution_Architects,
Customer_Roles


It was taken down a day ago: Possibly_a_Third_Round_of_Mass_Layoffs_at
Microsoft_in_2025_("Cloud_Solution_Architects,_Customer_Roles"),_Report_Removed
or_Censored


Based on how Wade Tyler Millward puts it, it was likely taken down due to
pressure from Microsoft and now it contains face-saving quotes, starting with:
"'Organizational and workforce adjustments are a necessary and regular part of
managing our business,' a Microsoft spokesperson tells CRN." (That's how the
article starts, based on the wrong assumption Microsoft tells the truth)


Why are they starting this article with "a Microsoft spokesperson"? Because
they received some threats demanding that Microsoft's own PR precedes
everything?


Here is the 'beef' of the article:


     Former employees with the vendor saying they were let go on
     Microsoft-owned LinkedIn include:


     - A technical program manager with the company for about three years


     - A level two designer working on Azure Cloud and AI who was with the
     company for about three years


     - A senior research scientist for responsible AI with the company for
     about eight years


     - A customer experience manager with the company for about five years


     - A cloud solution architect with the company for about six years


     - A cloud solution architect with the company for about 10 years


     - A senior customer success account manager with the company for
     about six years


     - A level two program manager with the company for about 12 years


     - A medical documents writer with the company and its Nuance
     subsidiary for about four years


     - A quality documentation (QD) administrator with Microsoft and its
     Nuance subsidiary for about five years


A lot of the article is now "a Microsoft spokesperson". That probably explains
why the article was taken down yesterday. Typical_Microsoft.


Meanwhile there are also new_reports_of_IBM_layoffs in_'RTO'_clothing
(reporting by Thomas Claburn). █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣦⣴⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⢿⣿⣿⢿⣿⢿⠿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣿⣜⣆⣯⣓⣗⣻⣜⣼⣧⣻⣇⣛⣹⡱⣳⣜⣼⣸⣸⣫⣿⣰⣾⣸⣸⣧⣛⣇⣧⣣⣜⣸⣻⣿⣗⣪⣝⣾⣸⣣⣇⣧⣜⣼⣾⣿⣧⣍⣧⣧⣻⣸⣸⣇⣧⣻⣜⣧⣗⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⣻⢿⠿⣿⣿⢿⢿⢿⠿⡿⣿⢿⣿⢻⢻⢿⡟⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣮⣿⣾⣼⣵⣯⣮⣾⣼⣷⣿⣽⣼⣿⣿⣼⣯⣦⣯⣽⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1335

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/Richard_Stallman_Only_Founded_the_FSF.shtml
    Gemini version at https://techrights.org/n/2025/02/21/Richard_Stallman_Only_Founded_the_FSF.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Richard Stallman 'Only' Founded the
FSF⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Robert_J._Hansen_FAQ:_Inappropriate_pressure_from_RMS,_as
      well_as_to_protest_FSF's_decision_to_reappoint_him_to_the_Board.⦈_


The message shown above has a source and a URL (or message ID), but let's treat
it in isolation. RMS is short for Richard M. Stallman.


What this message (dated last night) says is that the FSF declining to shun its
own founder (who had committed no crimes) was such a big deal that some FAQ
will be abandoned. To me it seems like an excuse because the rest of the
message says: "I'm sick and tired, and tired and sick, of doing nothing as my
country tears itself apart. I can't do much but I can explain things well.
Maybe that will make GnuPG more useful to people who are deeply concerned about
the trend of Western democracies towards surveillance capitalism and
authoritarian rule."


So the person who RMS_calls_"wrecker" is the real source or the present source
of frustration, or so it seems anyway. And for the record, the person wrongly
linked to RMS was repeatedly_shunned_by_RMS_as_"rapist"_while_Bill_Gates_was
defending_this_rapist, having long_hung_out_with_him (that caused the Gates
divorce; his_wife_dumped_him_over_it).


For those of us not misled by Trump-connected media (Rupert Murdoch's
newspapers were quick to throw RMS under the MIT bus, distracting from what
Bill_Gates_had_done_in_MIT) there's no reason to be upset at the FSF for
keeping their founder in the Board. He's still scheduled to_give_a_public_talk
this_coming_Monday:


     ✐ Talk in Balzano, Italy Feb 24⠀✐


     § Free/Libre software and freedom in the digital society⠀➾


     Registration and program: fuss.bz.it


     Place:                    Free University of Bozen-Bolzano


     When:                     Feb 24, 18:00–20:00


     Language:                 English


                               Aula Magna (Room D0.01)
     Location:                 Free University of Bozen-Bolzano
                               Universitätsplatz 1, Piazza Università 1


Long live RMS. Censorship_attempts shall backfire. █




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⠋⢿⣿⣿⠉⣭⣹⠏⢻⣿⠛⣍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠇⣥⠘⢿⣿⠀⢶⡟⢬⠄⢻⡘⠿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⠿⢿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡒⡒⢶⡶⣶⠲⢶⡖⢶⣖⠲⡒⣶⢖⡒⡶⡲⣖⢲⡶⢲⢲⡾⣻⡛⢗⣖⣲⡒⣖⢒⢶⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣾⣷⣿⣿⣾⣿⣾⣷⣶⣿⣷⣿⣿⣿⣷⣿⣾⣿⣾⣾⣷⣷⣷⣿⣿⣿⣶⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣏⣔⣆⣨⣠⣸⣊⣐⣃⣻⣐⣊⣀⣇⣃⣀⡈⢲⣀⣿⣚⣂⢄⣿⣘⣂⣲⣀⣅⣀⣚⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣿⣏⢋⡝⣻⡛⠛⢟⠛⡟⢛⢛⢻⡛⠛⠛⢛⠹⢛⠛⢹⡏⡛⠛⢻⡏⣿⢻⣟⠋⠟⣻⡏⣿⣿⣿⣿⡟⡟⡿⣻⢻⣿⣿⡏⣿⡛⢻⡟⢻⣿⠛⣿⣿⡏⣿⣿⢟⡟⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣿⠛⣿⣟⠛⣛⢿⡟⢛⡟⢻⡿⣛⣿⣿⡛⣛⠛⠻⣿⠻⣻⡟⢛⡛⢛⣟⡟⣟⣟⣿⣛⠛⠛⣿⠻⢻⢻⢻⣻⡟⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠓⣿⣿⢹⡻⠚⠛⠛⡛⠛⢓⡏⠟⡛⠛⣿⠛⢛⠻⢻⢻⢿⡛⢻⣟⡙⡛⠛⣷⡏⢙⠫⣿⣿⠛⢻⣟⠟⢫⢯⣿⡟⠓⣶⡖⠖⣶⠒⣖⠒⣲⢲⢲⢺⣿⡙⠉⣹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⢳⠳⠟⠛⠟⢛⣿⡟⠛⣿⣟⠚⠛⢛⢻⢻⠟⢛⢿⡏⡟⠟⣿⡏⡟⣿⡻⠘⠛⣿⠹⢻⢻⡛⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1427

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/Slopwatch_Anti_Linux_Machine_Generated_FUD_LLM_Slop_From_GBHack.shtml
    Gemini version at https://techrights.org/n/2025/02/21/Slopwatch_Anti_Linux_Machine_Generated_FUD_LLM_Slop_From_GBHack.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Slopwatch: Anti-Linux Machine-Generated FUD
(LLM Slop) From GBHackers, CybersecurityNews, and Guardian Digital, Inc (Google
News Promotes Slop Plagiarism, Misinformation)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Feb 21, 2025,
updated Feb 21, 2025


ANOTHER day, another avalanche of LLM slop. Let's focus on LLM slop that
tarnishes the name of Linux and creates/accentuates false stigmas.


Consider the following fake 'article':


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


It's LLM slop:


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LLM_slop:_A_newly_discovered_vulnerability_in_the_Fedora
Linux_kernel,_identified_as_CVE-2025-1272,_has_raised_alarm_bells_in_the_open-
                              source_community.⦈_


Also in a site (slopfarm) that seems connected to the above [1, 2]: (both are
in Google News despite being 100% slop)


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


Meanwhile at Guardian Digital, Inc (linuxsecurity.com):


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇They_don't_even_check_what_they_post_anymore:_From_C_to
                Rust:_The_Evolution_of_Linux_Kernel_Security⦈_


LLM slop, as usual:


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Let's_examine_the_need_for_enhanced_kernel_security,_the
    benefits_and_challenges_of_this_transition,_and_the_road_ahead_for_Rust
                      integration_in_the_Linux_kernel.⦈_


They relay the Linux_Foundation's (GAFAM) lies. They rely on GAFAM LLMs, so
they perpetuate lies from bots controlled by the liars.


On the same day, this time by Serial Slopper Brittany Day: (still_trying_to
associate_ransomware_with_Linux, despite it being_a_Windows_problem)


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


The Web is getting really bad. Companies that lie try to drown out the signal
with falsehoods, hoping that some people will read those falsehoods and pass
them on, too (verbally or otherwise).


A strict stance against LLM slop is needed. Collective action would help.


LLMs are often painted in the media (or LLM slop pretending to be media) as an
amazing scientific advancement, whereas in practice LLMs help crush scientific
advancement by curbing quality. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣽⣿⣯⣝⣉⣩⣉⣍⣿⣿⣯⣍⣙⣍⣙⣉⣉⣉⣍⣿⣿⣏⣋⣉⣋⣉⣩⣙⣍⣹⣿⣿⣋⣋⣟⣩⣙⣉⣉⣏⣉⣽⣿⣏⣉⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⣻⣏⣙⣉⣝⣋⣛⣛⣋⣋⣙⣻⣏⣙⣛⣛⣻⣏⣛⣛⣏⣛⣟⣋⣏⣙⣛⣏⣛⣛⣛⣛⣏⣙⣛⣋⣙⣛⣉⣋⣛⣙⣛⣉⣙⣋⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠿⣿⠟⣿⢿⡿⢿⠿⣿⢻⡟⡿⢿⡿⡿⢿⢿⡟⡿⣿⢿⡿⠿⠿⣿⢿⢻⡿⠛⠛⡿⠿⢿⢿⢿⠟⠻⡿⡿⢿⡿⢿⡿⣿⠿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣦⣀⣄⣂⣅⣂⣇⣆⣂⣿⣘⣃⣇⣆⣇⣃⣃⣸⣇⣌⣇⣀⣇⣆⣆⣇⣀⣸⣇⣶⣀⣐⣸⣀⣀⣾⣐⣒⣀⡇⣂⣅⣂⣂⣠⣀⣄⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⢛⠟⠛⠿⠛⠉⠉⠉⠻⢻⠛⢿⡏⡙⠟⠛⡋⡛⡛⣿⠙⠟⠻⣿⠉⢟⢙⢙⠟⠛⢟⠋⠙⡻⡛⡟⠛⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣴⣬⣤⣼⣬⣤⣤⣤⣤⣦⣼⣬⣼⣧⣥⣦⣥⣧⣥⣥⣿⣬⣦⣴⣧⣶⣼⣼⣬⣬⣤⣬⣤⣤⣥⣥⣧⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⢛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣬⣤⣤⣤⣥⣤⣤⣬⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣋⣉⣉⣹⣙⣻⣉⣉⣹⣉⣉⣙⣋⣉⣹⣉⣻⣉⣉⣹⣿⣿⣏⣹⣫⣭⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣾⡿⠛⠋⠛⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣸⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠿⠿⢿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣦⣤⣤⣤⣤⣤⡤⢠⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⣀⡟⠁⣠⣀⠈⢻⡟⠁⢠⠀⠁⠨⡟⠁⣀⣀⠈⢻⡇⠈⣀⣠⠏⢁⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡅⠀⣤⣤⡤⢼⡄⠀⠸⠀⠀⠀⡇⠀⣿⣿⠇⢀⡇⠀⣿⣿⠀⢸⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⣷⣤⣀⣀⣠⣾⣷⣄⣈⣀⣄⣰⣷⣤⣀⣀⣠⣾⣇⣠⣿⣿⣧⣄⣀⣠⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⡿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣅⣟⣟⣜⣺⣘⣆⣼⣈⣆⣗⣹⣧⣛⣥⣃⣿⣸⣸⣧⣌⣜⣢⣓⣟⣻⣂⣟⣸⣇⣟⣣⣿⣊⣜⣹⣾⣐⣹⣠⣃⣞⣦⣃⣿⣘⣭⣛⣠⣣⣃⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣶⣿
⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⡇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡇⢸⣿⣿⡇⣿⣿⡿⠁⣠⣴⣶⣦⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣾⣿⡇⢸⣿⣿⡇⣿⣿⠀⢸⣿⣿⠻⢻⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡇⢸⣿⣿⡇⣿⣿⡀⠸⣿⣷⣷⣾⣿⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⣷⣄⠈⠛⠛⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⠿⠿⡿⠿⡿⠿⠿⢿⡿⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⣶⠶⠶⠶⠧⠤⠤⠤⣧⣤⣤⣤⣤⣤⣵⣶⣾⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⣤⣤⣤⣧⣤⣤⣤⣤⣤⣦⣼⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⠛⠿⠿⠿⠿⠿⠿⠿⠟⡟⠿⠟⠿⢿⠿⠿⠿⠿⡟⠻⠿⠿⠿⠟⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠍⠛⠛⠃⠘⠚⠛⠐⠀⠛⠰⠀⠙⠛⠛⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠠⠄⠠⠤⠀⠀⠄⠤⠤⠠⠄⠤⠠⠤⠤⠀⠀⠤⠤⠠⠠⠄⠤⡄⠀⠀⠤⠤⠤⢄⠀⠀⠀⠄⠠⠤⠠⠠⠤⠀⠀⢠⠤⠄⠤⠀⠠⠤⠠⠠⠀⠀⠀⠤⠠⠄⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣿⣾⣾⣾⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⡝⠻⢛⡟⡻⢛⠛⢿⣿⣿⡟⡻⢻⢛⢿⣿⠏⡟⢻⢻⢛⡟⢻⢹⡏⣏⢻⢻⡟⣻⠛⡟⡛⢻⢙⡏⣿⢙⣛⢟⣿⣿⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣷⣾⣶⡷⣾⣾⣶⣾⣷⣾⠷⣷⣶⢶⣿⣿⡷⣷⣾⣾⣾⣷⣾⣾⣿⣾⣷⣾⣷⠿⣶⣷⣷⣾⣶⢷⣿⣾⣾⣼⣿⠶⣷⣾⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣱⣲⣚⣈⣑⣇⣼⣀⣅⣆⣸⣧⣋⣇⣸⣸⣆⣿⣹⣹⣒⣕⣪⣀⣇⣓⣸⣷⣪⣂⣿⣚⣩⣈⣰⣘⣘⣸⣸⣧⣹⣀⣿⣘⣸⣀⣇⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⢻⢛⠛⠛⠻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⢸⠈⠆⢀⠃⡇⠀⠀⠐⢅⡈⠀⡇⠀⡎⠀⢱⠀⢰⠁⠈⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣴⣶⣶⣮⣤⡤⠀⠧⠤⠄⠸⠀⠘⠎⠀⠇⠀⠀⠠⠤⠼⠀⠇⠀⠣⠤⠜⠀⢘⠤⠤⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿⣿⡿⠛⡛⠻⣿⣦⠀⠀⠀⣤⠶⡤⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣀⠀⣘⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⡇⢸⣿⣤⣿⣿⡆⠀⢸⣧⣤⢀⣤⢤⣤⠀⢀⣤⣤⣤⣿⠀⣠⡴⣦⣝⠛⣿⣿⡦⢠⡴⣦⣄⠓⠀⠀⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠉⠉⠉⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠏⣠⣶⡇⢰⣾⣿⣿⣿⠇⠀⢸⡇⠀⢾⣥⡴⠞⠃⣾⠁⠀⠈⣿⢸⡇⠀⠀⢹⡆⣿⠀⠀⣤⡶⠶⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣧⣘⢛⣡⣾⣿⣿⣿⠏⠀⠀⠘⠇⠀⠈⠳⠶⠶⠃⠈⠳⠶⠞⠿⠀⠛⠶⠶⠋⠀⠿⠀⠀⠻⠶⠖⠿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠘⠻⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⢀⡀⡀⣀⢀⡀⡄⡄⡄⢀⢠⡀⣀⢀⣀⣀⡀⣀⢀⡄⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠁⠈⠀⠁⠘⠀⠊⠈⠁⠋⠂⠁⠑⠃⠈⠈⠃⠈⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⡿⡿⠿⣿⠿⢿⣿⣿⢿⢿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠄⠀⠠⠠⠠⠠⠠⠀⠠⠀⠇⠄⠀⠄⠀⠀⠢⠀⠄⠴⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⢿⡟⢻⡟⢻⡟⢛⡟⣻⢻⣿⢻⣟⣟⣛⡟⣟⢿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣝⣯⣙⣯⣫⣟⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣙⡛⠂⣿⡏⠟⡛⠛⢋⢿⠛⠟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣽⣿⣿⣿⣿⣽⣿⣽⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⣯⣽⣯⣿⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣽⣽⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣯⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢩⢽⢛⢟⢿⢛⢟⢿⡏⣭⣿⢻⢟⢻⡏⠍⡟⡟⡟⢻⢹⢿⣯⢩⡍⡛⡟⢻⣯⠩⡟⣟⢛⢯⡟⡟⡟⡏⡿⡻⡟⡻⣿⢛⠟⣩⡏⣿⡋⡛⢻⢻⢻⡻⣻⡏⢯⡿⠻⡛⡛⡟⡟⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣾⣾⣾⣾⣾⣾⣷⣿⣿⣾⣾⣾⣷⣷⣷⣷⣿⣾⣾⣾⣿⣾⣷⣷⣷⣿⣿⣾⣿⣾⣾⣾⣷⣷⣷⣷⣷⣷⣷⣷⣿⣾⣶⣿⣷⣿⣷⣷⣾⣾⣾⣶⣿⣷⣷⣷⣿⣿⣷⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⡟⣻⢻⡟⡟⡟⣻⠋⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣶⣷⣶⣷⣷⣾⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡟⡿⠛⢻⣿⢟⠛⣿⡿⠛⣿⡛⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣷⣿⣷⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠟⠛⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣧⣾⣿⣿⣿⣿⣿⣿⡯⡯⠭⣭⡿⣯⣭⣭⣽⠽⣭⢯⣭⠿⣿⡭⢽⣽⣭⣭⣭⢭⣯⢭⣭⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡿⣻⣿⣶⣶⣦⡀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣥⣄⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣦⣶⣄⡈⠛⠻⠿⣿⣋⣉⣉⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋
⣿⣿⣿⣿⡇⠀⠀⡐⣬⢭⣛⡛⣒⢶⡶⡚⠛⡟⡭⣇⣀⡀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣿⣷⣶⣿⣿⣾⣿⣿⣿⣷⣤⣤⡀⠀⠀⠋⠁⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⡇⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢛⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠟⠋⠉⠉⠀⠀⠀⠁⠚⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⡿⢿⡿⠷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⢿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣥⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣵⣬
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠷⢶⡤⠤⠄⠤⠤⠀⢤⣤⡿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣧⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠉⠉⠉
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⢐⣠⠖⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠃⠀⠙⠷⣦⡄⠀⢀⠀⠨⠝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠊⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⠀⠀⠀⡀⠜⠛⠷⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣗⢒⠲⡬
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣿⣿⣿⣿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡯⠘⠻⠟
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠐⠋⠛⠛⠛⠛⠛⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣤⣤
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠒⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠄⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡯⢉⣩⣽
⣿⣿⣿⣿⡟⠛⠛⢻⡟⠛⠛⠛⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿
⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⡇⠘⠭⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢀⣿
⣿⣿⣿⣿⣷⣶⣶⣾⣷⣶⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣯⣶⣷⣿⣷⣿⣶⣷⣿⣶⣾⣶⣷⣷⣿⣷⣷⣧⣾⣶⣶⣿⣶⣷⣿⣾⣿⣾⣦⣷⣿⣿⣷⣽⣷⣷⣾⣶⣶⣷⣾⣶⣾⣾⣿⣾⣾⣶⣾⣶⣾⣶⣾⣦⣿⣾⣶⣧⣶⣶⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀
⣿⣿⣿⣿⣯⣯⣼⣿⣯⣽⣽⣿⣭⣿⣽⣽⣿⣯⣯⣧⣿⣯⣽⣿⣽⣽⣭⣯⣿⣧⣯⣽⣭⣭⣿⣿⣯⣿⣿⣽⣽⣿⣿⣯⣭⣯⣯⣧⣼⣿⣿⣭⣿⣽⣿⣯⣯⣯⣿⣿⣽⣿⣭⣿⣽⣭⣽⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣻⣹⣽⣻⣽⣝⣏⣭⣯⣿⣯⣉⣯⣫⣹⣏⣿⣟⣽⣿⣙⣹⣽⣿⣯⣻⣻⣉⣛⣯⣹⣭⣟⣿⣿⣏⣛⣿⣹⣭⣉⣩⣿⣹⣟⣯⣯⣯⣿⣙⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣷⣾⣾⣶⣾⣾⣽⣶⣷⣿⣷⣿⣷⣷⣿⣷⣿⣶⣶⣽⣷⣶⣷⣾⣷⣷⣿⣶⣾⣽⣾⣷⣶⣷⣶⣾⣷⣷⣿⣾⣾⣴⣾⣾⣷⣶⣶⣷⣶⣾⣾⣾⣿⣿⣿⣾⣿⣶⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⡿⣟
⣿⣿⣿⣿⣯⣯⣽⣭⣟⣧⣯⣭⣿⣽⣯⣭⣯⣭⣽⣿⣭⣽⣽⣯⣯⣬⣿⣯⣯⣯⣯⣿⣯⣭⣯⣯⣯⣭⣯⣽⣽⣭⣽⣿⣽⣽⣿⣽⣽⣽⣿⣽⣯⣿⣯⣿⣽⣿⣭⣿⣯⣍⣯⣭⣯⣯⣽⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣶
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣤⣤⣤⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⡟⠟⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣶⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠛⠛⠋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⢿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣾⣶⣷⣾⣾⣿⣶⣶⣿⣾⣿⣾⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣤⣤⣤⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⠿⠿⠿⠿⢿⠿⡿⠿⠿⠿⠿⢿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣶⣾⣶⣾⣷⣷⣾⣿⣷⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣭⣩⣏⣿⣩⣍⣻⣽⣩⣽⣹⣿⣽⣉⣏⣩⣹⣯⣽⣹⣯⣩⣉⣉⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣼⣭⣭⣭⣯⣽⣼⣽⣭⣭⣭⣯⣽⣭⣽⣯⣭⣯⣭⣯⣽⣿⣿⣿⣿⣿
⣧⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣻⠳⣹⣿⢻⢿⠿⡿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢙⠽⣟⡟⢿⢹⣿⢹⡗⡟⡟⡟⡟⣟⢿⣿⢙⢽⠛⡟⣟⠹⣿⢻⢻⢻⢻⣏⡻⢻⢻⢸⢻⢻⢹⢻⣻⠟⡟⣟⢿⡟⡟⡟⣿⡏⣏⢻⡛⣿⡻⡟⣟⡟⣿⢻⣿⢹⡏⡟⢻⢹⢻⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣿⣾⣾⣷⣾⣷⣷⣷⣷⣷⣿⣾⣿⣾⣾⣶⣷⣾⣾⣾⣾⣾⣼⣿⣷⣿⣿⣾⣾⣾⣾⣾⣾⣶⣷⣷⣷⣾⣿⣾⣶⣿⣷⣿⣾⣷⣾⣷⣿⣾⣷⣶⣷⣿⣾⣾⣷⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢫⢽⣉⣏⢹⡇⡏⡏⣿⣟⡘⣿⡇⡫⢿⢹⢩⢹⡫⣫⢽⢹⢩⢹⢹⢫⢿⢹⢩⡋⣹⣿⣅⢿⢸⢸⢍⠛⣭⡇⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢁⡀⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣰⣦⣠⣼⣿⣷⣶⣶⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣛⡛⢛⣛⣛⣿⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣴⣿⣿⠃⣼⣿⣿⣆⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣓⣷⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠬⣽⣷⣾⡿⣿⣇⠸⣿⣿⠿⠐⠻⣷⣗⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣯⣿⣿⣿⣤⣿⣿⣭⣥⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⢀⢢⣄⢀⢠⢤⠀⡄⢂⠠⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣪⠂⢳⠀⡇⢠⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠄⣀⣒⣒⣒⠒⠠⠤⢕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⣇⣸⣤⣄⡐⢁⢔⡒⠒⠢⠤⠭⠭⠭⢉⣐⣒⣒⣒⡒⠀⠬⠭⢍⠢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠤⠤⠤⠤⠤⠐⢢⠀⠀⠀⠀⠀⠀⣿⠀⡸⣰⣿⠿⠛⠻⢿⣆⠢⠂⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠪⡢⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈⡁⢀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⣿⠀⢱⣿⠇⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠇⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠻⡐⢼⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢰⡧⢼⡇⢸⡧⠤⠀⠠⡀⡇⠀⠀⢰⠁⠀⣇⣸⣿⣤⣤⣤⣤⣤⣼⣿⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏

                    ䷩ 𝚕𝚒𝚗𝚎 1680

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/21/Techrights_Disconnected_From_the_United_States_Two_Years_Ago.shtml
    Gemini version at https://techrights.org/n/2025/02/21/Techrights_Disconnected_From_the_United_States_Two_Years_Ago.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Techrights Disconnected From the United
States Two Years Ago⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Recycling_Insecurity:_We_are_prone_to_recycling_messages_and
feelings_of_insecurity,_which_is_the_basis_of_much_needless_human_pain_and
suffering._Recognizing_the_forms_these_take_as_criticism_of_self_and_others_is
the_first_step_to_distancing_ourselves_from_them.⦈_


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


Yesterday I saw a foolish new comment which said: "The website is called tech
rights but isn’t even secured with HTTPS".


Actually, we support both HTTPS and HTTP (and even more than those two), but
people can choose. We don't impose HTTPS on people because HTTPS is an
accessibility problem (not limited to access by older devices) and some
bloggers explained this point only days/weeks ago. If you altogether shun HTTP,
then you give a helluva lot of control to the Oval Office and its_loyal
facilitators. So please do not do that.


Did people really need to wait for the US government to become this_hostile
towards_the_media before recognising the threat? The_term_"free_speech
absolutist"_is_just_a_slogan_of_the_archetype_neo-fascist. Don't_be_so
gullible.


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Elon_Musk_caught_following_X_account_posting_only_Nazi
                         content_and_soft-core_porn⦈_


Anyway, our hosting company is now in the EU and the server is in the UK. We've
not regretted this move, which goes_1.5_years_back.


"Scheduled maintenance is currently in progress," says the host today. It
started around 8AM this morning. Pages fetches are still relatively_fast and
traffic in the past two days was about 60% higher than usual (probably
Streisand Effect). Today is also the day my laptop accomplishes 500+ days in
uptime - an all-time record for me.


$ uptime
 12:54:36 up 500 days, 19:39, 41 users,  load average: 0.63, 0.65, 0.55
To be very clear, this site has nothing to do with MElon's administration. We
left the US in 2023 and 'litigation_tourists' have fantasies like the US being
in control of Europe. If anything, politically, Europe distances itself even
further from the US. Seeing the SLAPP culture, we welcome this transition. Keep
the thugs away from us [1, 2]. Free software demands digital sovereignty. █


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Elon_Musk_cuddles_his_pet_lap_dog_Trump:_We_cannot_censor
        sites_by_revoking_their_certificates_if_they_issue_their_own⦈_




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⢀⣀⡀⣀⢀⣀⡀⡀⠀⢀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⣶⣶⣦⡶⢄⠀⠉⠛⢿⣾⢺⢸⢍⣇⡯⣻⢸⢍⣫⣜⡏⢿⢹⣕⣿⣫⣼⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢹⢥⡆⣶⢸⢰⣖⣶⢆⣖⠀⠀⠘⢶⣻⣱⣅⣅⡚⡚⣗⣲⣓⣺⣖⣛⣓⡒⣂⡝⣒⣒⣲⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢳⣛⡎⣊⢹⣷⣿⢗⢽⢿⣟⣟⢗⠀⠀⠻⠿⣗⡇⡿⡇⣗⣿⣊⣽⣏⢸⢸⢧⡇⡿⡇⢸⢊⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡽⠛⠇⠧⠻⢮⡇⡞⠾⠤⠇⢰⡏⠿⠦⠀⠑⠖⠂⣌⣝⢶⢒⣒⣄⣭⣁⢑⣛⣛⡛⡙⢃⣓⣓⣒⢈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣟⢷⣮⠆⣔⣆⡆⣼⡇⡧⣖⢾⣦⢖⣏⣿⣳⣤⡀⠀⠤⣇⣿⣾⣸⢺⢸⡠⡾⡆⡗⡇⡇⡇⣻⡗⡇⣼⡞⠶⠆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠻⣧⣤⣟⢦⡧⢖⣧⣜⣧⢓⣦⣻⣟⣮⠏⣏⣿⣿⠗⠀⠐⢛⣋⡚⡺⠷⠿⠙⠱⠿⠿⢧⡇⠯⠭⠥⠧⠻⠷⢿⠟⠂⠠⢦⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⣾⣹⡞⡞⣯⡖⢮⣲⢟⣿⡒⣶⣱⢢⢶⢷⣶⠢⠶⠏⠀⠀⠀⠈⢿⢻⢷⢸⣧⡾⣼⢿⢸⣹⢎⣹⡿⡇⡿⣾⢸⢍⡷⡏⡏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⢻⣧⣏⣏⡇⡯⡟⢯⠟⣺⢏⣿⣽⡿⠻⢸⣤⣾⣯⡆⠀⠀⠀⠀⠀⠀⠀⢭⣾⣻⣭⡇⠉⠸⠾⠷⡾⡷⡵⠧⠵⠴⠿⠧⠵⣷⣥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢭⠭⠭⢴⠒⣬⢩⣝⠬⣩⣭⡶⣹⡿⡭⣍⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⡷⠄⣿⢸⢽⢾⢽⢘⢭⡇⣻⡯⡇⡯⠳⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠝⣒⣝⠸⠯⠒⠙⠱⠓⠛⠒⠋⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡛⠋⠛⠐⠼⢭⠮⠵⠬⠷⠧⠝⠽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢾⢿⣞⣟⣿⡚⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡗⡧⡏⣱⢧⡯⡷⡛⣹⢹⢩⡞⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣽⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠙⠻⠷⠛⠳⠿⠿⠾⠷⠯⠽⠾⠮⠦⠥⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠺⣶⣶⠾⣷⣴⡲⣬⢻⢫⠍⣭⢻⢿⢿⣌⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠩⣭⡼⣴⣝⣫⣿⡆⣽⢾⢘⣴⣼⡷⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣽⡯⣥⣭⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⡇⣷⡇⡿⢹⢹⡟⡾⡾⣾⡇⡇⣹⢳⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⣷⣶⠐⣶⢰⢶⡖⡴⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⢛⢃⣑⣛⢓⣚⣛⣺⢃⣓⣛⣂⣑⡚⣒⣒⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣰⢽⡝⣇⡿⣼⢫⢣⡻⡵⣕⢥⢟⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⠸⠿⢯⠾⡼⠏⠸⢹⢸⠤⠿⠯⡟⠇⠧⠌⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠭⠭⠸⢘⡘⠣⠙⣃⣛⡚⠜⣃⣇⡛⠞⣎⣃⣁⠀⠀⠀⠀
⠀⠀⠀⡄⡗⣆⡮⣶⢰⡵⣏⣿⡆⡖⣖⢲⡔⠆⣾⢹⣽⢹⠒⣖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⢿⣼⣼⢳⣗⠂⣾⠐⣮⢖⣧⣹⢻⢓⢲⡻⢹⡻⣀⠀⠀⠀
⠀⠀⣼⣯⠇⠫⣯⣾⣼⡝⣚⡧⣧⣧⣧⣽⢵⣓⢩⣞⣹⣼⢾⢷⣦⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⡇⠿⣸⣯⣼⢛⠇⠟⢮⡏⠿⣸⣥⠷⡽⡳⠽⠋⠁⠀⠀
⠀⢰⣿⣻⠗⣖⢺⣴⣶⣖⢣⢖⣖⡖⣶⣮⠖⣆⣶⣰⢠⡤⠀⠀⠀⠉⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣔⣒⢕⣨⣫⣫⡡⣼⣿⢻⣛⣭⣹⢭⣍⣍⡣⡁⠀
⠀⠘⣿⣸⣦⢯⣖⡼⠻⠧⠞⠦⠎⣷⣾⣟⣮⣏⡿⣻⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣏⡯⢾⣹⡥⣧⣇⢇⣇⣏⡯⣼⡻⣼⣵⣽⣯⠇⠀
⠀⠀⢻⣻⡣⣶⢲⢩⣩⡍⡭⢬⢭⢩⡝⡭⢿⢥⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⢷⡲⣬⢲⣶⡆⣀⣖⣶⣶⣦⢰⣲⣶⡆⠒⠀⠀
⠀⠀⠀⠘⠛⢿⣞⣸⢢⣋⣯⢿⡹⠼⣱⣣⣾⣵⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢱⢢⣤⣤⣴⠮⢨⢤⣄⠤⡡⡶⣒⠲⠈⠀⠀⠀
⠀⠀⠀⠠⣄⠀⠒⠒⢷⣾⣺⣿⡟⡪⣻⣿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣭⣭⣧⣭⣯⣼⠉⠉⠊⠙⠉⠁⠠⠄⠀⠀⠀
⠀⠀⠀⠀⠈⠵⠴⠤⢄⡀⢀⡉⣉⣉⣉⣉⠁⣀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⢅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣴⣬⡭⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠊⣏⣻⡽⡏⣟⢏⡟⠇⡖⢮⢻⣵⡟⣇⡟⢿⢷⣰⠺⣟⣟⣿⣸⠻⡝⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⡏⣻⣎⣭⢩⢿⠭⡭⣭⢭⠥⢦⡿⡍⡭⢭⣭⡵⢢⠽⡬⣭⢯⣻⡾⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢧⣯⠽⡭⢷⠬⢟⢧⢆⢯⡾⢸⠻⠇⣟⠟⣾⣥⠻⡴⣂⡿⠿⠹⣵⡇⣟⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠗⣇⣣⣏⣿⢨⣽⡆⡗⣏⢸⣋⣬⣹⡆⡗⣯⣿⣋⣼⣀⡄⢸⠰⠾⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠾⠿⢿⣿⣿⣛⣃⣗⠖⠶⠰⡿⣷⣎⡛⢝⣫⣛⢻⢇⡷⠿⡿⠿⢷⡾⠻⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⢽⢫⢻⣣⠨⣿⣖⣽⢾⠧⠮⢯⣭⢦⢯⣖⣣⣽⣿⣿⣶⣿⣆⣭⡶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠽⢹⢲⢻⡾⣟⣋⣿⣻⢻⢰⢟⣗⣿⢹⣟⢏⣿⣼⣁⡞⣻⣹⣶⢯⠀⠀⠀⠀⠀⠀⠀⠰⣏⣙⢓⡑⣛⠚⣛⡏⢩⣻⡫⣚⣻⢗⡪⣟⢳⡛⡛⣛⣛⡆⣘⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⣬⢿⣴⣯⣴⣿⢰⢾⢸⣧⡷⢿⣸⣿⡜⡟⢻⢋⢧⡵⣩⣿⢘⠀⠀⠀⠀⠀⠀⠼⢿⡇⣿⣾⢘⣿⡆⣿⢹⣾⣧⣢⡧⢾⣾⡧⣿⣹⣷⢼⢙⣅⣳⠣⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⣧⣿⣽⢯⡻⣉⢷⣿⣿⣖⡾⢷⡶⡟⢣⣼⡿⡿⡷⣟⣿⣿⣻⠀⠀⠀⠀⠀⠀⠈⠿⣧⣷⡽⢜⡃⣿⣟⣯⣚⣿⡣⠽⡿⡠⠿⠧⡋⣜⡮⣛⣅⠛⠜⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣚⣛⡫⡇⣶⣰⡆⢰⣆⣴⡖⣯⣷⢰⣖⣛⡶⣶⣞⣷⣠⢖⠀⠀⠀⠀⠀⠀⠀⠀⢩⣍⣦⢳⢰⢺⣵⣽⢺⡓⣞⡌⣯⢻⡏⡟⣇⢻⢻⣻⡹⣱⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⢚⡇⣿⢻⡏⡾⣻⣸⣏⡷⣿⢸⣧⡩⡇⣻⡿⠾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣼⠾⠾⠾⢹⣘⣒⣋⠳⢹⣾⣪⢃⠷⠿⠘⠭⠧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⡟⣖⣘⣵⡖⢫⣿⣴⣶⡎⡟⠳⠆⣞⣰⣗⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡮⣾⡬⣎⣾⡅⣷⡱⡷⣱⡯⣹⠽⠿⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠀⠉⠉⠉⠉⠁⠈⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢮⣭⠄⠈⠈⠈⠀⠁⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣶⣤⣶⣤⡀⠀⠀⠀⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣤⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣶⣷⣿⡅⠀⢀⣴⣅⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⡆⠀⢀⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠭⣽⣿⣿⣿⣍⣿⣿⣿⣿⣧⣼⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⡿⢿⣿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠉⣻⣿⣿⠿⠿⢿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⠿⠿⠟⠛⠛⢿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣧⠀⠀⠀⢰⡞⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⢰
⠀⠀⠈⣿⣶⣤⣤⣄⣾⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⡈⠀⠸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣸
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠁⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⠇⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⡿⠋⠀⠐⢲⣿⣿⣿⣿
⠀⢀⠀⠿⠿⠋⠉⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣟⠍⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣰⣿⣿⣿⣿⣿
⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠀⢀⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼
⣿⣿⣦⣀⠀⠀⠀⣠⣴⣿⣿⡋⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣾
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣄⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣶⣤⣶⣤⡀⠀⠀⠀⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣶⣷⣿⡅⠀⢀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡂⠀⠀⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠭⣽⣿⣿⣿⣍⣿⣿⣿⣿⣧⣼⣿⣿⣿⡿⣶⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡿⢿⣿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⡿⠇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠉⣛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⠿⠿⠟⠛⠛⢿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⢠⡞⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣤⡀⠀⠀⠀⠀⢰
⠀⠀⠈⣿⣦⣤⣤⣄⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣸
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠃⠈⠛⠿⣶⣄⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⡿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⡿⠋⠁⠐⢺⣿⣿⣿⣿
⠀⢀⠀⠿⠟⠋⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠀⠘⠛⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢸⣟⡍⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣰⣾⣿⣿⣿⣿
⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⢀⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼
⣿⣿⣦⣀⠀⠀⠀⢀⣠⣾⣿⠿⠃⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣾
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣦⣀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣷⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣿⣶⣴⣶⣤⡀⠀⠀⠀⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣾⣷⣿⣇⠀⠀⣠⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠭⣽⣿⣿⣿⣍⣿⣿⣿⣿⣧⣼⣾⣿⣿⡿⣶⣿⣿⣿⣿⣿⣿⣶⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⡿⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠉⢛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⠿⠿⠟⠛⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⢀⡎⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⣾⣿⣿⣷⣽⣿⣿⣿⣿⣧⣤⣤⡀⠀⠀⠀⠀⣼
⠀⠀⠈⣿⣦⣤⣤⣄⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠙⠻⠿⣶⣄⣹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⡿⠛⠁⠐⢺⣿⣿⣿⣿
⠀⢀⠠⠿⠟⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠘⠛⠿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣟⠉⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰⣾⣿⣿⣿⣿
⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴
⣿⣿⣦⣀⠀⠀⠀⠀⢀⣠⣶⣶⠖⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣷⣦⡀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣿⣧⣴⣶⣤⡀⠀⠀⠀⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣾⣷⣿⣧⠀⠀⣠⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠭⣽⣿⣿⣿⣍⣿⣿⣿⣿⣧⣼⣾⣿⣿⡿⣶⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣟⠋⢛⣿⣿⡿⠿⢿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⠿⠿⠟⠛⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⣼
⠀⠀⠘⣿⣦⣤⣤⣄⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣽
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠙⠻⠿⣆⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⠟⠁⠀⠺⣿⣿⣿⣿
⠀⢀⠠⠿⠟⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢸⣟⡍⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⢠⣾⣿⣿⣿⣿
⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠀⢀⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠂⠀⣴⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼
⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣴⣦⡴⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⣿
⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣦⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⡚⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣍⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠈⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢀⣾⣿⣿⣿⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣠⣴⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⣽⣿⣿⣿⣭⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠟⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⡋⢙⣿⣿⡿⠿⢿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀
⠀⠙⠿⠿⢿⠟⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⣛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⢿⣷⣿⣿⣿⣮⣷⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⣼
⠀⠀⠘⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣿
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠻⢿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⠟⠁⠀⠚⣿⣿⣿⣿
⠀⢀⠠⠿⠟⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⢠⣾⣿⣿⣿⣿
⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⢀⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⣶⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴
⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣾
⣿⣿⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣭⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡘⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣅⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠘⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣿⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣆⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⠙⣻⣿⡿⠿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀
⠀⠙⢿⠿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣷⣿⣿⣿⣦⣶⣾⣿⣿⣿⢠⣤⣀⠀⠀⠀⠀⣸
⠀⠀⢘⣿⣦⣤⣄⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣀⠀⠸⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣽
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠛⠻⠿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠟⠋⠀⠚⣿⣿⣿⣿
⠀⢀⠰⠿⠟⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⠉⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⢠⣾⣿⣿⣿⣿
⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠁⠀⢀⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴
⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢯⣶
⣿⣿⣿⣿⣿⣷⣦⣤⣠⣴⣾⣿⣟⡁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⡜⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣅⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠘⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣿⡄⠀⢀⣤⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣠⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⣽⣿⣿⣿⣭⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⢧⣾⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⣛⠛⢻⣿⣿⠿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀
⠀⠻⢿⡿⢿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣾⣷⣿⣿⣿⣦⣴⣾⣿⣿⣿⢠⣤⣀⠀⠀⠀⠀⢸
⠀⠀⢘⣷⣦⣤⣄⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣀⣀⠀⠸⣷⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸
⠀⠀⠈⣿⣿⣿⣽⣿⠿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠻⠿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⠿⠋⠀⠚⣿⣿⣿⣾
⠀⢀⠰⠿⠟⠋⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣟⠉⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⢀⣾⣿⣿⣿⣿
⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⣀⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴
⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢯⣿
⣿⣿⣿⣿⣿⣶⣦⣄⣀⣠⣴⣾⡿⠟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢳⡜⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣍⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣄⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣬⣽⣿⣿⣿⣿⣦⣦⣶⣤⡀⠀⠀⠘⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣤⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣿⡄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⢧⣶⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⢿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢣⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠯⠛⠛⠻⣿⣿⡿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀
⠀⠻⢿⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⡟⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣷⣾⣿⣿⣦⣴⣶⣿⣿⣿⠁⢀⣀⠀⠀⠀⠀⢰
⠀⠀⢘⣷⣤⣤⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⣀⣀⠀⠸⣾⣿⣿⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠃⠀⠀⠀⢸
⠀⠀⠈⣿⣿⠻⣭⣾⠿⠋⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⡇⠈⠛⠿⢿⣆⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⠛⠁⠒⢷⣷⣿⣾
⠀⢀⠰⠿⠟⠃⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠉⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⣶⣿⣿⣿⣿
⣔⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⣈⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⣿⡿⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣾⣿⣧⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠯⣧
⣿⣿⣿⣿⣿⣾⣭⣌⣉⠙⣛⣿⣿⡿⣿⣿⣿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⡜⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣅⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣄⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣬⣿⣿⣿⣿⣿⣤⣴⣶⣦⡀⠀⠀⠘⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣿⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⣠⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣼⣾⣿⣿⣿⢧⣶⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡾⢿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠇⠀⠀⠀⠀⢷⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠻⠉⠛⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀
⠀⠻⢿⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣿⣾⣿⣿⣶⣴⣶⣿⣿⣿⠁⣀⣀⠀⠀⠀⠀⢰
⠀⠀⢘⣷⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠇⠀⠀⠀⠸
⠀⠀⠈⣿⣿⣯⣭⣿⠿⠋⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠇⠈⠛⠿⢿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⠟⠁⠐⢶⣷⣶⡾
⠀⢀⠰⠿⠟⠋⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠉⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⠀⠀⣴⣿⣿⣿⣧
⣔⡿⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⣈⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⢠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢸⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣿⣿⣧⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠿⣧
⣿⣿⣿⣿⣿⣾⣭⣌⣉⠙⢛⣻⣿⣯⣿⣿⣿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⣠⣦⣄⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣄⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣼⣿⣿⣿⣿⣿⣦⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣀⣴⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡠⢿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠻⢯⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀
⠀⠹⣿⠿⠿⠿⠟⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠸⠉⠟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣿⣶⣿⣿⣷⣤⣦⣼⣿⣿⡏⢀⣀⠀⠀⠀⠀⢰
⠀⠀⢐⣶⣄⣠⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⣀⣀⠀⠸⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠏⠀⠀⠀⢸
⠀⠀⠀⣿⣿⣋⣵⣿⠿⠃⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠃⠈⠛⠿⢿⣤⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⠟⠋⠐⢺⣿⣿⡿
⠀⠀⣐⠿⠛⠋⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⠀⠀⣰⣾⣿⣿⣧
⣀⡿⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⣀⣨⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠀⠀⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢹⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣿⣿⣥⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣣
⣿⣿⣿⣿⣿⣾⣭⣌⣉⠙⠛⢛⣛⡯⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⡅⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣟⣁⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣼⣿⣿⣿⣿⣷⣤⣶⣶⣦⡀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣇⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢀⣴⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⠭⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣴⣦⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀
⠀⠙⣿⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⠉⠟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣿⣶⣿⣿⣷⣤⣶⣼⣿⣿⡟⠀⣀⡀⠀⠀⠀⢰
⠀⠀⠐⣶⣄⣠⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣀⡉⠀⠸⣷⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠀⠀⠀⢸
⠀⠀⠀⣿⣿⣩⣵⣿⠿⠃⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠁⠈⠛⠿⠷⣤⣤⡹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⠿⠋⠀⢺⣿⣿⡿
⠀⠀⣐⠻⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠐⠚⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⠀⢰⣾⣿⣿⣧
⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣆⣀⣨⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢻⣿⣿⣿⡋⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⡟⠛⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠿⣣
⣿⣿⣿⣿⣿⣾⣯⣌⣉⠙⠛⣛⣿⠋⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣽⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⡁⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠤⣿⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣿⣿⣿⣧⢀⢲⣿⣿⣿⣿⣾⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀
⠿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣻⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⢟⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣿⠈⠟⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⣧⣷⣾⣿⣿⣦⣐⣬⣿⣿⣿⠃⢀⡀⠀⠀⠀⢰
⠀⠀⠀⣤⣀⣀⣀⢠⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⡠⢿⠀⠸⣶⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠁⠀⠀⠸
⠀⠀⠀⢻⣍⠉⣥⣾⠿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠿⠆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⡿⠟⠁⠒⣿⣿⡿
⠀⠀⠠⠿⠛⠀⠉⠀⠀⠀⣿⣿⣿⠿⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠀⠀⢠⣾⣿⣿⣷
⣆⣼⠉⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣆⣀⣴⣿⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢹⣿⣿⣿⡉⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣾⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠿⣫
⣿⣿⣿⣿⣿⣾⣯⣌⣉⠙⢛⣿⣟⣫⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣦⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⡁⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣢⣾⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠬⣽⣿⣿⣯⣭⣿⣿⣿⣿⣧⣾⣿⣿⣿⣷⢀⡶⣷⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⢻⣿⣿⣟⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⢯⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠈⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⢰⣶⠀⠟⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⣧⣼⣾⣿⣿⣦⣐⣬⣿⣿⣿⠏⢀⡀⠀⠀⠀⠀
⠀⠀⠀⢈⠁⣀⣀⢀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡄⣀⣀⡈⡃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠓⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠇⠀⠀⠠
⠀⠀⠀⢻⡛⠋⣹⣮⠻⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠛⠷⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠘⠿⠿⣿⣿⣿⣿⣿⠟⠃⠰⢿⣿⡿
⡄⠀⠀⠾⠟⠀⠉⠀⠀⠀⣿⣿⡿⠿⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠻⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠂⠀⠀⣴⣿⣿⣿
⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣆⣀⣴⣿⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿
⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⢈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿
⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢹⣿⣿⣿⡉⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣿⣿⣦⣀⣿⢹⣿⣿⣟⣺⣿⣾⣶⣿⣾⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠿⣿
⣿⣿⣿⣿⣿⣾⣯⣌⣩⣽⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣶⣤⣈⡁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠉⠛⢻⡷⠟⠋⠉⠉⠿⡿⢿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣦⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⡃⠀⠀⡀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⠤⣿⣿⣿⣯⣽⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⢀⣾⣷⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀
⠻⣟⣛⣿⣿⣿⣭⣭⣿⣿⣿⡿⣿⡿⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠟⢟⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⡄⠀⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⡧⢸⣶⣿⣿⣷⣄⣠⣭⣿⣿⡟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢩⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⣈⡃⠀⠸⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠃⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡟⠀⠀⠀
⠀⠀⠀⢸⡟⠛⢛⣵⠹⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠛⠷⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⡿⠋⠠⢾⣾⣶
⡆⠀⠀⠼⠟⠁⠉⠀⠀⠀⣿⣿⡿⠿⠟⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⢠⣾⣿⣿
⡧⢠⠆⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣆⣀⣴⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⢰⣾⣿⡟⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿
⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿
⡿⠇⠀⠀⠀⢀⣾⣦⠀⠀⣼⠃⠀⠀⢸⣿⣿⣿⣿⣭⣭⣭⡛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣧⠀⢀⣤⣴⣾⣿⠟⠀⠀⠈⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣿⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣺⣿⣶⡶⣿⣶⣿⣿⣤⣶⣭⣿⢛⣛⣟⣛⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡿⣿
⣿⣿⣿⣿⣿⣿⣯⣌⡉⠙⠛⠛⠛⠋⣿⣿⠿⠿⢿⢿⡿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢧⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⣿⣿⣿⣿⣿⡿⠛⠻⠃⠀⠀⠀⠀⠈⣽⣿⣿⣿⣦⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠋⠁⣤⢰⠃⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣍⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣦⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡀⢠⣾⣿⣿⡇⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⠤⣽⣿⣿⣮⣽⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⢀⣾⢷⣶⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀
⠻⢟⣛⣿⣿⣿⣭⣭⣿⣿⣿⡟⣻⣿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⢟⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⡄⠀⢟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣧⢠⣷⣿⣿⣿⣆⣀⣍⣿⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣈⡃⠀⠘⣷⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡿⠀⠀⠀
⠀⠀⠀⠸⣟⠛⢋⣥⠹⠃⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⠷⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠑⠻⠿⣿⣿⣿⣿⣿⡿⠛⠠⢶⣿⡶
⡆⠀⠀⠸⠟⠀⠉⠀⠀⠀⢿⣿⡿⠟⠛⠻⣿⣿⣿⡿⢀⣤⡄⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡯⠉⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡏⠀⠀⢠⣾⣿⣿
⣷⢀⡎⣼⣦⠀⠀⠀⠀⠀⢸⣯⣶⡆⣠⣶⣿⣿⣿⣇⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿
⣿⣿⣠⣿⣿⠁⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡆⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⢈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠃⠀⠀⠸⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣟⡟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣥⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠻⠇⠀⠉⠛⠉⢻⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⣿⣿⣿⣇⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⢘⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡿⢿
⣿⣿⣿⣿⣿⣾⣭⣌⡉⠙⠛⠛⠛⠋⣿⣿⠿⠿⢿⢿⡿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢧⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠻⣿⠟⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣍⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣳⣦⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣼⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⢠⣿⣷⣿⣷⠀⠀⢀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣾⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣠⣿⣿⣿⣧⣼⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣆⣼⠿⣶⣾⣿⣿⣷⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⢿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀
⠻⢿⣛⣻⣿⣿⣯⣭⣿⣿⣿⣿⢟⣛⢿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⠛⡀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣷⠀⣷⣾⣿⣿⣦⣀⣤⣹⣿⣿⠃⢀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣈⣃⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠁⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⠂⠀⠀
⠀⠀⠀⠀⣟⠙⠛⣥⠙⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠁⠒⠿⢿⣿⣿⣿⣿⡿⠟⠁⠶⣿⣿
⡧⠀⠀⠰⠛⠀⠁⠀⠀⠀⢹⣿⠟⠛⠛⠛⣿⣿⣿⡿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢯⠉⠉⠛⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠀⠀⢀⣴⣿⣿
⣿⠀⡬⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡆⣠⣾⣿⣿⣿⣇⣀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣄⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡟⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣾⣿⣿⣿
⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣾⡏⢻⣿⣿⣦⡀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿
⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⠀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⣿⣿⣷⣄⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡾⢏
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⣾⣿⣷⣦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣆⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢟⣻⣿⣿⣿⣿⡄⢠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⣿⣿⣿⣷⣼⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣇⣼⡿⣶⣾⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⡿⠿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠛⢿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠛⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢶⣷⠀⣾⣾⣿⣿⣦⣄⣤⣹⣿⣿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡉⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠁⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠆⠀⠀
⠀⠀⠀⠀⣟⠛⠛⣡⠘⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⠿⢅⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⠒⠿⠿⣿⣿⣿⣿⣿⠟⠃⠴⣾⣿
⣷⠀⠀⠠⠛⠀⠀⠀⠀⠀⢹⣿⠟⠛⠛⠙⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠉⠉⠙⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠀⣴⣿⣿
⣿⠀⡴⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣆⣠⣾⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣾⣿⣿⣿
⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⡀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣷⣄⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣿⣿⣤⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡾⢟
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⠳⡸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣦⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⢶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⡆⠠⣾⣷⣿⣿⡀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣿⣇⣾⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⣽⣿⣿⣧⣼⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣇⣴⡿⣶⣶⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠛⡀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢤⣷⠀⣸⣮⣿⣿⣧⣀⣬⣹⣿⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠋⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⣀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⡆⠀⠀
⠀⠀⠀⠀⢲⠲⠲⢃⡜⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⠿⣿⡅⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠽⠿⠛⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣿⣿⣿⡿⠋⢰⣶⣶
⣷⠀⠀⠀⠞⠃⠈⠉⠀⠀⢹⣿⡿⠛⠛⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠍⠉⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠇⠀⠀⣠⣾⣿
⣿⡆⣠⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣆⣀⣴⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⣶⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⣶⣿⣿⣿
⣿⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣗⣶⡆⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠸⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣄⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣾⣿⣥⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣯⣿⢿
⣿⣿⣿⣿⣿⣾⣯⣌⡉⠙⠛⠛⠛⠋⣿⣿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣤⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠀⢶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⡆⠀⣾⣷⣿⣿⡄⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣿⡇⣴⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣽⣿⣿⣧⣼⣿⣿⣿⣿⣧⣾⣿⣿⢿⣿⣇⣴⣿⢲⣶⣿⣿⣷⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⠟⡇⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⡃⠀⠀⠀⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢤⣿⠀⢸⣮⣿⣿⣧⣄⣬⣹⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠋⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣀⣀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⡖⠀⠀
⡀⠀⠀⠀⢸⠶⠶⢛⣜⠋⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣅⠀⠀⠈⠿⣿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣿⣿⡿⠟⢡⣶⣶
⣷⠀⠀⠀⠼⠓⠈⠉⠁⠀⢻⣿⡿⠛⠛⠛⢿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠷⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡍⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡇⠀⠀⢀⣼⣿
⣿⡆⢠⠂⠀⠀⠀⠀⠀⠀⠘⣿⣶⣆⣀⣴⣿⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⣴⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠠⣴⣿⣿⣿
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⢹⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢿⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣄⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣥⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣯⣌⡉⠙⠛⠛⠛⠋⣿⡿⡿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣷⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣶⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠀⢰⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡇⠀⣶⣿⣿⣿⡄⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⢂⣼⣿⣿⣷⣾⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣇⣰⣿⢢⣶⣾⣿⣿⣾⣶⣤⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣸⣿⣿⣿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀
⠻⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠿⡇⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⡆⢠⣷⣿⣿⣷⣄⣠⣽⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢉⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣷⠀⠀
⡄⠀⠀⠀⢸⡟⠛⢛⣥⠛⣿⣿⣍⡛⢿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣧⠀⠀⠀⠻⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠶⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠳⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁⣴⣶
⣿⡄⠀⠀⠸⠿⠶⠛⠋⠀⢿⣿⡿⠟⠛⠛⢿⣿⣿⡟⠀⠀⠉⠙⠛⠀⠀⠀⠠⠿⣯⣀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡏⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡟⠀⠀⢀⣴⣿
⣾⡇⢀⡂⠀⠀⠀⠀⠀⠀⠈⣿⣶⣆⣀⣴⣿⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢴⣾⣿⣿
⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⡟⠛⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣆⣿⢹⣿⣿⣟⣺⣿⣾⡶⣿⣶⣶⣿⣧⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣯⣌⡉⠙⠛⠛⠛⠋⣿⡿⣿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⢀⣠⣀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣤⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⣶⣾⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡇⠀⣶⣿⣾⣿⡄⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣿⡇⣠⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢓⣂⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⡇⣰⣿⢇⣶⣾⣿⣿⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀
⠻⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⠿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠿⠇⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⢿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⣾⡆⢀⣷⣿⣿⣿⣤⣢⣬⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢡⣈⡀⢀⠀⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣷⠀⠀
⣄⠀⠀⠀⠘⡏⠉⢉⣵⠉⣿⣿⣭⡉⢿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣧⣴⣶⣦⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠴⠞⢋⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠓⠾⠿⣿⣿⣿⣿⣿⣿⠟⠁⣴⣶
⣿⡆⠀⠀⠸⠿⠓⠙⠉⠀⢿⣿⣿⠿⠛⠛⢿⣿⣿⡿⠀⠈⠉⠛⠛⠛⠻⠿⠿⢿⣯⣁⣐⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡍⠉⠛⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠀⠀⢀⣤⣿
⣾⣷⢀⡆⠀⠀⠀⠀⠀⠀⠈⢿⣷⣆⣀⣴⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⣴⣿⣿⠃⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢤⣾⣿⣿
⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿
⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣧⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⡿⢿⠿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⢉⣻⣿⣿⣦⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣴⣶⣾⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⡛⠻⣿⣿⣿⣿⣧⠀⣾⣿⣾⣿⡅⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣾⣿⣿⣷⣷⣿⣿⣿⣿⣿⣼⣿⣿⣏⣿⣧⣠⣾⠇⣴⣾⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀
⠻⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣛⡻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⠿⣧⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⠿⣿⣿⣿⣤⣶⣦⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣾⡇⠀⣷⣾⣿⣿⣦⣰⣬⣿⣿⣿⠃⢀⠀⠀⠀
⠁⠀⠀⠀⠠⣌⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠆⠀
⣦⠀⠀⠀⠀⣿⡋⢉⣡⡎⢿⣿⣿⣛⢻⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣀⣀⢠⣼⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠡⠖⠊⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠑⠺⠿⢿⣿⣿⣿⣿⣿⠿⠋⢠⣶
⢿⣧⠀⠀⠀⠿⠓⠘⠛⠀⢸⣿⣿⡿⠿⠿⢿⣿⣿⣿⠇⠈⠛⠛⠻⠿⠿⠿⣿⣿⣿⠋⠉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⡏⠉⠙⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠀⠀⠀⣠⣾
⣼⣿⠀⡔⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⣀⣀⣴⣿⣿⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣴⣿⣿⠇⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠠⣶⣿⣿
⣿⣟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿
⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⣿⣿⠉⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣿⣶⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⡿⢿⡿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⢀⣴⣶⣤⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣧⠀⣾⣿⣾⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢳⣂⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣼⣿⣿⣟⣿⣧⢀⣾⡇⣴⣶⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀
⠻⠿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⢿⠀⠀⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣇⠀⣴⣼⣿⣿⣦⣐⣬⣿⣿⣿⠋⠀⡀⠀⠀
⡁⠀⠀⠀⠈⣌⡁⠀⠀⢹⣿⣿⣿⣯⣽⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠃⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⡆⠀
⣧⡀⠀⠀⠀⣿⠉⠉⣩⡌⢹⣿⣿⣛⢛⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠛⠉⠉⠡⠴⠊⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠑⠺⠿⢿⣿⣿⣿⣿⣿⡿⠋⢠⣶
⣾⣷⠀⠀⠀⠿⠓⠚⠛⠁⠸⣿⣿⣿⠿⠿⢿⣿⣿⣿⡇⠈⠛⠻⠿⠷⠀⠀⠀⣿⣿⠟⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡫⠉⠙⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠀⠀⠀⣠⣼
⣼⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⣀⣀⣴⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⣶⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣴⣿⣿⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⣴⣿⣿
⣿⣟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿
⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⠏⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⡟⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣿⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣿⣷⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣌⣉⠙⠛⠛⠛⠋⣿⡿⠿⣿⢿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣤⣄⣠⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣡⣄⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣷⠀⣴⣿⣿⣿⡅⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⣂⣰⣿⣿⣷⣶⣿⣿⣿⣿⣿⣼⣿⣿⡟⣿⣿⢀⣾⡇⣠⣶⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀
⠻⠿⣿⣿⣛⣿⣿⣿⣻⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⠯⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣭⣨⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣧⠀⢸⣾⣿⣿⣦⣔⣦⣽⣿⣿⡏⠀⡀⠀⠀
⡄⠀⠀⠀⠘⡉⠋⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡆⠀
⣷⡄⠀⠀⠀⣿⠶⠖⢲⡌⠻⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠛⠉⠉⡡⠤⠎⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠙⠾⠿⢿⣿⣿⣿⣿⣿⡿⠋⢠⣴
⠿⣿⠀⠀⠀⣿⠷⠔⠟⠃⠀⣿⣿⣿⡷⠿⠿⣿⣿⣿⡿⠀⠙⠻⠿⠿⠀⠀⠀⣹⣿⣿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡫⠉⠙⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡅⠀⠀⢀⣼
⣾⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣠⣾⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⣤⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⣴⣾⣿⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠠⣤⣾⣿
⣿⣟⣶⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠿
⡿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣿⣿⡏⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣿⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣔⣶
⣿⣿⣿⣿⣿⣿⣯⣬⣉⠙⠛⠛⠛⠋⣿⡿⠿⣿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣣⣆⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣷⠀⣴⣿⣿⣿⣇⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣂⣸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣼⣿⣿⡟⣿⣿⢀⣾⡇⢠⣶⣿⣿⣷⣷⣶⣄⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀
⠻⠿⣿⡿⢿⣿⣿⣟⣛⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⢿⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣭⣬⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣧⠀⢸⣾⣿⣿⣶⣔⣶⣽⣿⣿⡏⠀⡀⠀⠀
⡄⠀⠀⠀⠘⡛⠋⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡗⠀
⢿⣄⠀⠀⠀⢾⢶⠶⠶⣘⠻⣿⣿⡻⠿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠛⠋⢉⣥⠴⠎⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠙⠾⠿⢿⣿⣿⣿⣿⣿⡿⠋⢠⣴
⠿⣿⠄⠀⠀⣼⠧⠀⠟⠋⠀⣿⣿⣿⡷⠾⠿⣿⣿⣿⣿⠀⠙⠛⠿⠿⠀⠀⠀⣹⣿⣿⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣿⡫⠉⠙⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡟⡁⠀⠀⢀⣼
⣶⣿⡇⣠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣠⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢤⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⣴⣾⣿⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢤⣾⣿
⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣼⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣿⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣬⣿
⣿⣿⣿⣿⣿⣿⣯⣬⣉⠙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣎
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣴⣶⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⡏⠽⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣧⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠱⣀⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⡟⣿⣿⣀⣾⡟⢰⣶⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⢀⣟⣻⣿⣿⣿⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⢿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠛⠿⣿⣿⣛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⢟⠀⠀⠘⠛⢿⣿⡿⠿⣿⣿⣿⣿⣿⠟⠃⠀⠀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣭⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣧⠀⢸⣶⣿⣿⣷⣤⣶⣾⣿⣿⡏⠀⣀⠀⠀
⣦⠀⠀⠀⠈⣉⠉⠀⠁⠈⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡟⠀
⣻⣦⠀⠀⠀⢾⡷⠶⠞⣜⠛⣿⣿⣟⡛⣻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠋⠉⣩⠵⠖⠋⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠑⠺⠿⢿⣿⣿⣿⣿⣿⠿⠋⠠⣶
⠋⣿⡇⠀⠀⠼⠗⠀⠚⠋⠀⢿⣿⣿⠿⠿⠟⢿⣿⣿⣿⠀⠈⠛⠛⠛⠻⠿⢿⣿⣿⡿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⣿⡯⠉⠙⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠁⠀⠀⢀⣴
⣿⣿⡇⣰⠀⠀⠀⠀⠀⠀⠀⢨⣿⣇⣀⣀⣠⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣴⣿⣿⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⢴⣾⣿
⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠻
⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣬⣉⡙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⡀⠀⠀⠀⠻⢿⣿⣷⣆⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠐⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣀⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⡍⠽⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣧⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⣿⣿⣤⣾⡟⢰⣶⣿⣿⣷⣾⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣟⣛⣿⣿⣿⡿⠿⢿⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⠿⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠻⠿⣿⣟⣛⣿⣿⣿⣭⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⠛⡀⠀⠘⠛⢿⣿⡿⠿⣿⣿⣿⣿⣿⠟⠃⠀⠀
⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣤⣤⣦⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣷⠀⢸⣾⣿⣿⣷⣤⣶⣾⣿⣿⡏⠀⣀⠀⠀
⣦⠀⠀⠀⠈⡈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡏⠀
⣻⣧⠀⠀⠀⢾⡷⠶⠟⣬⠋⣿⣿⣿⡛⣻⣿⣿⣿⣿⣿⡏⢿⣿⣿⣆⠀⣶⣼⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠋⢉⡭⠷⠒⠃⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠑⠺⠿⢿⣿⣿⣿⣿⣿⠿⠋⠠⢶
⠈⣿⡇⠀⠀⠼⠃⠀⠉⠉⠀⢻⣿⣿⠿⠛⠛⢿⣿⣿⣿⠀⠈⠉⠛⠛⠛⠻⠿⠿⣿⡿⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⡏⠉⠙⢛⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⠁⠀⠀⢠⣴
⣿⣿⠇⣰⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣀⣀⣠⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣴⣿⣿⡏⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⢴⣾⣿
⣿⣟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠻
⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣼⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣬⣍⡙⠛⠛⠛⠋⣷⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣴⣶⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⢠⣶⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⡿⠿⢿⣿⣿⡍⠿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣷⠀⠀⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢫⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣦⣾⡟⣰⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣟⣛⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠿⠟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠻⠿⣿⣟⣻⣿⣿⣿⣭⣿⣿⣿⣿⢿⣻⡻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⢻⠀⠀⠘⠛⣿⣿⡿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣤⣶⣦⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠠⣾⣧⠀⣸⣾⣿⣿⣶⣤⣶⣿⣿⣿⡇⢀⣀⠀⠀
⣆⠀⠀⠀⠈⡉⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀
⣻⣦⠀⠀⠀⣿⡷⠶⢿⣌⠋⣿⣿⣿⡏⢽⣿⣿⣿⣿⣿⡏⢿⣿⣿⣷⣦⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢋⣭⡿⠿⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠑⠻⠿⢿⣿⣿⣿⣿⣿⠟⠋⠠⢶
⠉⣿⡄⠀⠀⠟⠋⠁⠉⠁⠀⢻⣿⣿⠟⠛⠛⢿⣿⣿⣿⠀⠀⠉⠉⠉⠛⠀⠈⠻⣿⠛⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡿⡍⠉⠙⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢛⡁⠀⠀⢠⣾
⣿⣿⠇⣴⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣀⣀⣴⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣶⣿⣿⠇⠀⠀⠀⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢶⣿⣿
⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠻
⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣟
⣿⣿⣿⣿⣿⣿⣿⣬⣉⡙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠣⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⢀⣾⣿⣶⣄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣯⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⡀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸⡿⠿⣿⣿⣿⡭⢿⣿⣿⣿⣿⡇⢐⣿⣿⣿⣿⣧⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢋⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢷⣿⣿⣄⣾⡇⣴⣶⣿⣿⣷⣷⣶⣤⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣞⣛⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣸⣿⣿⢿⠟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠻⠿⣿⣟⣻⣿⣿⣯⣭⣿⣿⣿⣿⢿⣛⡻⢿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠿⠀⠀⠘⠛⣿⣿⡿⠿⢿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣴⣶⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⡇⠀⣸⣾⣿⣿⣶⣤⣶⣿⣿⣿⡇⢀⣀⠀⠀
⡆⠀⠀⠀⠉⡉⠁⠈⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⠀
⣿⣆⠀⠀⠀⣷⡶⠶⣧⣜⠋⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⠇⢻⣿⣿⣆⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⣻⣿⡿⠛⠊⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⡿⠟⠋⠰⢶
⠉⣿⠀⠀⠀⠛⠀⠈⠉⠀⠀⢻⣿⡿⠛⠛⠛⢻⣿⣿⣿⠀⠀⠀⠉⠉⠁⠀⠈⠻⠿⠛⠹⣿⣿⣿⣿⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡿⡍⠉⠙⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⣏⠀⠀⠀⢠⣾
⣿⣿⠀⣴⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣀⣀⣴⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣴⣿⣿⠇⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢴⣿⣿
⣿⣯⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⠀⢰⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠻
⡿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⠀⢿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣬⣉⠙⠛⠛⠛⠋⣷⡿⠿⢿⣿⢿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠣⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⠀⠀⣠⣾⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡏⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣶⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⣿⡭⢿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣧⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢠⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢃⣀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⢳⣿⣿⣄⣾⡟⣴⣾⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⣿⣿⠿⠿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⢿⠟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀
⠻⠿⣿⢿⣿⣿⣿⣛⣿⣿⣿⣿⣿⠿⠿⠿⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⠀⠀⠙⢛⣿⣿⠿⠿⢿⣿⣿⣿⣿⠛⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠠⣾⡇⠀⣾⣾⣿⣿⣶⣤⣶⣽⣿⣿⠃⢀⡀⠀⠀
⡄⠀⠀⠀⠙⠋⠉⠁⠈⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡄⣀⣀⣀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠃⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠇⠀
⢷⡄⠀⠀⠀⡤⠴⠶⣆⠛⠃⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡇⠙⠿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⡿⠟⠁⠰⣶
⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠋⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠜⠁⠋⠁⠀⠀⠀⢸⣿⡍⠉⠛⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣋⠀⠀⠀⣠⣾
⣾⣿⢀⡴⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⡀⣴⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣴⣿⣿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠠⢶⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⢠⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠙⠻
⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠀⠀⢻⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⢫
⣿⣿⣿⣿⣿⣿⣿⣬⣉⡙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣾⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠄⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⢻⠛⣛⠻⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⠀⠀⠀⢀⣠⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣶⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣿⠭⢿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⢇⣀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⢳⣿⣿⣆⣼⡗⣶⣾⣿⣿⣿⣶⣶⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⢿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀
⠻⢿⣿⢿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣋⣿⣿⣛⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⢿⠀⠀⠙⢛⣿⣿⠿⠿⢿⣿⣿⣿⣿⠛⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⣼⡇⠀⣿⣾⣿⣿⣷⣤⣶⣿⣿⣿⠁⢀⡀⠀⠀
⡀⠀⠀⠀⠛⠋⠉⠁⠉⣿⣿⢿⣿⣟⢛⣛⣿⣿⣿⣿⣿⡇⢀⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠃⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠃⠀
⢷⡀⠀⠀⠀⢤⢶⠶⠾⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢀⣴⣿⣯⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠰⣶
⠻⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣿⡿⠛⠉⠉⢙⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠫⠞⠋⠁⠀⠀⠀⢸⣿⠉⠉⠛⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠋⠀⠀⠀⣠⣾
⣾⣿⢀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣀⣀⣴⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣧⡘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⣴⣿⣿⠇⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⢶⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣶⡆⠀⣿⣿⣿⣿⣿⣎⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠙⠻
⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⣿⣿⠉⠉⠛⠙⠛⠛⠛⠿⠃⠘⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣧⣾⢹⣿⣿⣟⣺⣿⣶⡶⣿⣶⣶⣿⣼⣿⣤⣄⢀⣀⣀⡀⡀⠀⠀⠀⣀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⢋
⣿⣿⣿⣿⣿⣿⣿⣬⣉⠙⠛⠛⠛⠋⣿⡿⠿⢿⣿⣿⡿⢸⡏⣿⣿⣿⣿⣿⣧⣿⣷⣶⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠄⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠛⢛⣟⣻⠿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⢠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⠭⢿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⢇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢳⣾⣿⣇⣰⣿⣶⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣼⣛⣻⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀
⠻⢿⡿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⠿⠀⠀⠙⢛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠛⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⡄⠀⠀⣿⡿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⣼⣧⠀⣷⣾⣿⣿⣶⣬⣶⣿⣿⣿⠁⣀⡀⠀⠀
⠀⠀⠀⠀⢛⠉⠉⠀⢸⣿⣿⡟⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣠⣤⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠃⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣧⡀⠀⠀⠐⡶⠞⠛⠚⠋⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣠⣾⣿⣽⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠴⣶
⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠛⠛⠛⢿⣿⣿⡏⢻⣿⣿⣿⣿⣿⠀⠈⠉⠙⠻⢿⣿⣿⣿⠀⠀⠀⠜⠴⠛⠋⠁⠀⠀⢁⢸⣟⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⣋⠀⠀⠀⣤⣿
⣾⣿⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢠⣾⣿⣿⣿⠀⠈⠉⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⣶⣿⣿⠃⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠠⣶⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠸⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠙⠻
⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣗⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣋
⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠛⣿⣿⣿⣿⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣇⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢳⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢱⣾⣿⣇⣰⣿⣶⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⣼⣛⣻⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀
⠻⠿⠟⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡟⠁⠀⠛⢛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠛⠀⠀⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣼⣧⠀⣷⣾⣿⣿⣷⣼⣶⣿⣿⣿⠁⣤⡀⠀⠀
⠀⠀⠀⠀⢿⡁⠈⠀⢸⣿⣿⡟⣻⣿⣿⣿⣯⣽⣿⣿⣿⣿⣆⣄⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠃⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⣦⠀⠀⠀⢸⣿⡟⠻⠘⠋⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⠤⠄⠀⢨⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⢀⣴⣾⣿⣝⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠁⢴⣶
⢻⣧⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⠀⠀⢀⢎⠴⠛⠋⠁⠀⠀⢁⢸⣟⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠁⠀⠀⠀⣤⣿
⣼⣿⢀⣴⣿⣿⣯⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⢀⣶⣿⣿⠃⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠠⣶⣿⣿
⣿⣯⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣿⣿⣿⣿⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠛⠻
⡿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⢻⣿⣿⡇⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣗⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠙⢻⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣹⡟⣃
⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣶⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣏⠩⢿⣿⣿⣿⣿⠀⢰⣿⣷⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣆⣠⣾⣿⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣱⣶⣿⡇⣠⡞⣤⣶⣿⣷⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⣸⣛⣻⣿⣿⣿⡿⢿⣯⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡿⣿⣿⣷⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀
⠿⠿⢟⣻⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⠟⠛⠀⠀⠛⠛⣿⣿⠿⠿⢿⣿⣿⣿⡿⠛⠀⠀⠀
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⡿⣿⣿⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣠⣦⠀⣷⣾⣿⣿⣦⣴⣶⣿⣿⣟⠁⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠀⣹⣿⣿⡛⠋⢸⣿⢿⣿⣿⣿⣿⣿⠿⢋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀
⡄⠀⠀⠀⠘⠛⢟⣣⡝⠿⠋⠋⠀⢸⣿⣦⣀⢈⣤⣤⣶⣿⣿⡇⠻⢧⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣋⠀⠀⠀⣠⡴⡲⡉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠙⠳⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣤⣶
⢝⠆⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⣡⠴⠛⠉⠀⠀⠀⠀⢸⢟⠉⠙⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠀⠀⠀⠀⣠⣿
⣠⣧⠀⡀⠀⠀⠀⠀⢠⣄⡀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡾⠀⢠⣶⣿⣿⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠠⣴⣿⣿
⣿⣏⡾⠁⠀⠀⢀⣀⣼⣿⣧⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢉⣃⠀⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠹⠀⠀⠈⠛⢿
⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠰⡿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣃⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠠⢾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣇⠀⠀⠀⠘⣿⣿⣿⣿⠿⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣦⡀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣹⣿⣁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⡇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠻⠃⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⢰⠁⢿⣿⣿⣧⣿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢰⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⡿⠿⣿⣿⣏⠩⢿⣿⣿⣿⣿⠀⢰⣿⣷⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣂⣰⣿⣿⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣰⣾⣿⣇⣠⣞⣤⣴⣾⣷⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣛⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡿⣿⣿⣿⡯⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀
⠿⠿⢿⣻⣿⣿⣯⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⠿⠛⠁⠀⠛⠛⢿⣿⠿⠿⣿⣿⣿⣿⡿⠛⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠟⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⠁⣠⣦⠀⣷⣾⣿⣿⣦⣴⣦⣿⣿⡿⠁⢀⠀⠀⠀
⠀⠀⠀⠈⠋⠁⠁⠈⣿⣿⣿⡛⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠻⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀
⡀⠀⠀⠀⠐⢞⡛⣧⠟⣿⣿⠿⠇⠀⣼⣏⡛⠿⠿⠿⠟⠛⢉⣴⠹⣧⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⣏⡀⠀⢀⣠⠔⢚⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣤⣶
⢽⣆⠀⠀⠀⠈⠟⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⣶⣶⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⢚⣤⠾⠛⠁⠀⠀⠀⠀⢸⢟⠙⠙⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡿⠏⠁⠀⠀⠀⣠⣿
⣠⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣾⣾⡾⠀⢠⣾⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠄⠠⣴⣿⣿
⣿⠏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⣠⣽⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣉⢉⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠟⠀⠀⠈⠻⢿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⠀⢾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣇⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣸⡛⣁
⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⣿⣿⣿⡟⠻⣿⣿⣿⣿⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣦⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠻⠃⢸⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠙⢿⣿⣿⣷⣦⣤⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢠⣶⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠈⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣏⠩⢿⣿⣿⣿⣿⠀⢰⣿⣷⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣴⣾⣿⡇⣰⢞⣤⣴⣾⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣛⣻⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⡿⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀
⠿⡿⠿⣿⣿⣛⣛⣻⣿⣿⣿⣶⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⠻⠛⠀⠀⠛⠻⢿⣿⡿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡤⠀⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠀⣠⣆⠀⣦⣽⣿⣿⣦⣲⣦⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠈⠋⠉⠀⠙⣿⣿⣿⠛⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢿⣿⣿⣿⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⣀⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣷⠀⠀
⡀⠀⠀⠀⠰⠶⡶⣜⢻⣿⣳⣾⠆⠀⠀⠘⣿⣿⣿⣿⣿⣷⣾⣿⣿⠎⠁⠀⠀⢈⣿⣿⣿⣿⣿⡿⣋⠀⠀⢀⡤⣒⠛⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⢶⣾⡿⣿⣿⣿⣿⣿⡿⠟⠁⣴⣶
⣛⠄⠀⠀⠀⠸⠿⠋⠊⠙⠙⠋⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠟⢋⣵⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠐⢡⣴⠾⠛⠀⠀⠀⠀⠀⢸⡟⠙⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⠋⠁⠀⠀⠀⣠⣿
⣨⣧⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⣠⣴⣾⣿⡟⠀⠀⠀⠀⠙⠻⣿⣿⡿⣿⣿⡏⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⣾⡗⠀⢠⣾⣿⡿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣦⠀⢠⣾⣿⣿
⣿⢏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠛⠻⣿⣿⣿⡿⠁⠀⠀⠀⣀⣀⣀⣀⣉⠀⣈⢙⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣘⣿⣿⢃⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠟⠀⠀⠙⠻⢿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⣠⣴⣿⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣿⣇⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢪⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣿⣦⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⠛⣐
⣿⣿⣿⣿⣿⣶⣦⣄⡀⣽⣿⣿⣿⣿⣿⣿⣿⡀⣾⡏⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠿⠂⢾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢠⣶⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡿⣭⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⣡⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠈⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣏⠩⢿⣿⣿⣿⣷⠀⢰⣿⣿⢿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣂⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣴⣾⣿⡇⣠⢎⣤⣴⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢈⡛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⡻⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀
⠿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣴⡂⠀⠀⢰⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⠿⠛⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠇⣠⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⣠⣆⠀⣶⣯⣾⣿⣤⣶⣤⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠙⠉⢻⣿⣿⡟⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁⢿⣿⣿⣿⣿⣶⣾⣿⠇⠀⠀⠀⠀⠀⢀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡷⠀⢠
⡀⠀⠀⠀⠠⠴⢶⡸⢿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣷⣿⣿⣿⣟⣻⣯⣍⢻⣧⢶⣌⣿⣿⡿⢿⣿⡿⣋⠀⠀⢀⣤⣒⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⢴⣾⡿⣿⣿⣿⣿⣿⡿⠟⠁⣤⡶
⣻⠄⠀⠀⠀⢰⡿⠓⠉⠙⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣱⠄⠙⢿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠐⢡⣴⠿⠛⠀⠀⠀⠀⠀⣸⡟⠙⠛⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠁⠀⠀⢀⣼⣿
⣨⣧⠀⡴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⣋⣥⣶⣿⡏⠀⠀⠀⠈⠻⠿⠿⠿⣿⣿⡏⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⠀⢠⣾⣿⡿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣦⠀⢤⣾⣿⣿
⣿⣏⡾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠻⠖⣿⣿⣿⣿⡏⠀⠀⠀⣀⣀⣀⣀⣁⠀⣈⢙⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⢣⣀⣘⢿⣿⢃⡀⠀⣀⣉⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠟⠀⠀⠙⠻⢿
⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⣼⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢪⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣤⡀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⢋⣠
⣿⣿⣿⣿⣿⣶⣦⣄⡀⢺⣿⣿⣿⣿⣿⣿⣿⠀⣸⡟⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣀⢮⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡿⠁⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢸⣿⣨⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠴⠀⠀⠀⢰⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣯⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣂⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣶⣾⣿⡇⠰⢮⣤⣶⣾⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣧⣶⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣯⣼⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡿⡿⠋⠀⠘⠛⠻⣿⣿⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣽⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⢀⣤⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠁⣠⣆⢀⣦⣽⣿⣷⣦⣶⣤⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠛⠙⢻⣿⣿⡟⠋⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡟⠀⢸
⠀⠀⠀⠀⠠⠶⣖⡸⣿⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣟⣛⣿⣯⣼⠉⠀⣼⣿⣿⡿⢿⣿⡿⢋⠀⠀⢀⣤⣒⡻⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠛⢴⣾⡿⣿⣿⣿⣿⣿⡿⠛⠠⣴⡮
⡳⡄⠀⠀⡀⣿⡿⠃⠋⠛⠛⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⢋⣼⠁⠐⠿⣿⣿⣿⣿⣿⣿⣿⠀⡐⣡⣶⠾⠛⠀⠀⠀⠀⠀⣿⡟⠛⠛⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠁⠀⠀⢀⣼⣷
⣨⣦⢀⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⣛⣉⣴⣾⣿⠋⠀⠀⠀⠈⠙⢿⢿⣿⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣶⣿⡗⠀⢠⣾⣿⡿⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠀⢤⣾⣿⣿
⣿⢏⣞⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠙⠛⢻⣿⣿⣿⣿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣉⢛⣀⡀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣡⣀⣸⣿⣿⢁⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠏⠀⠀⠙⠻⢿
⣿⣿⠏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣠⣴⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢃⣧⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡄⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣦⣄⡀⣶⣾⣿⣿⣿⣿⣿⡆⠀⢸⡿⠁⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣴⣢⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠿⠀⠏⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⠁⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣧⣸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣠⣖⣸⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠘⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣏⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣂⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡟⣶⣾⣿⡇⣠⢮⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡸⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡂⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣯⣴⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⠿⠛⠀⠘⠛⠻⣿⣿⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣶⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⣠⣆⢀⣦⣥⣿⣷⣦⣒⣤⣿⣿⡟⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠛⠙⠉⢻⣿⣿⡟⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⢸
⠀⠀⠀⠀⢰⠶⣶⣸⢿⣿⣿⣷⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣽⣿⣷⠆⡍⠀⢈⣿⣿⣿⣿⣿⡿⢋⠀⠀⢀⣤⣶⣋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠛⢶⣾⡿⣿⣿⣿⣿⣿⠿⠋⠠⣴⡮
⡳⡄⠀⠀⢀⢾⡿⠏⠉⠛⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠟⣡⣾⠃⠀⠸⢿⣿⣿⣿⣿⣿⣿⠀⡐⣩⡴⠾⠓⠀⠀⠀⠀⠀⣿⡟⠛⠛⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠋⠀⠀⠀⢀⣼⣷
⣸⣦⢀⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⣉⣭⣤⣾⣿⣿⠋⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣶⣿⡇⠀⢠⣾⣿⡟⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠀⢤⣾⣿⣿
⣿⢏⣞⠨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠹⣿⣿⣿⡿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣉⢛⣁⡀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣠⣀⣸⣿⣿⢁⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠏⠀⠀⠙⠻⢿
⣿⣿⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⣶⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣽⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⡀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⡛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣦⣄⣠⣶⣿⣿⣿⣿⣿⣿⡄⠀⢸⡿⠁⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣩⣿⣶⡦⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠿⠀⠏⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⠁⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣧⣸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡧⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣠⣖⣸⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣽⣡⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠘⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⢿⡿⢿⣿⣿⣏⠩⢿⣿⣿⣿⣷⠀⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡟⣶⣾⣿⡇⡠⢮⣤⣶⣷⣶⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣟⣻⣿⣿⣿⣟⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢈⡿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⠿⡿⢿⣟⣿⣿⣛⣛⣻⣿⣿⣧⣖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣼⣿⣿⣿⣿⣿⣯⣭⣽⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⡟⠟⠀⠘⠛⠻⣿⣿⠿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⣠⣦⢰⣦⣥⣿⣷⣦⣖⣮⣿⣿⡏⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠙⠉⠉⠀⢹⣿⣿⠛⠁⠀⠀⠈⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⡟⠁⢿⣿⣿⣿⣷⣮⣽⣿⡇⠀⠀⠀⠀⠀⠀⢀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⢸
⠀⠀⠀⠀⢲⠞⠛⣣⡟⣿⢿⣾⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⡗⠀⢨⣿⣿⠿⢿⣿⣿⣏⠀⠀⢀⣠⠴⠊⠉⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠙⠑⣶⣿⡿⣿⣿⣿⣿⣿⠿⠋⠠⣴⡮
⡳⡄⠀⠀⠼⠓⠛⠛⠀⠁⠘⠁⠀⠀⠀⠀⠀⢈⣿⠛⠛⢛⣉⣤⣶⣿⣿⠃⠀⠈⠙⠿⣿⣿⣿⣿⣿⠀⡰⢋⡵⠞⠓⠀⠀⠀⠀⠀⣿⡛⠛⠛⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠟⠃⠀⠀⠀⢀⣼⣷
⣸⡄⢀⢺⣷⡤⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣶⣷⡇⠀⣠⣾⣿⡟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠀⢴⣾⣿⣿
⣿⢏⡞⢸⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠘⣿⣿⣿⠟⠀⠀⠀⣀⣀⣀⣀⣀⠀⣈⢉⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣠⣀⣸⣿⡿⢁⡀⠀⣀⣉⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠏⠀⠀⠙⠻⣿
⣿⣿⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣻⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠈⠉⣿⠉⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣿⣾⠇⠀⠀⠀⠀⣀⣴⣿⣿⣿⣄⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣻⠟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣉⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⣼⠏⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡈⣿⣤⣏⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠏⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣡⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⢿⠿⢿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡟⣶⣾⣿⡇⡠⢮⣤⣶⣶⣶⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣟⣛⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢈⡿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡄⠀⠀⠀
⠿⣿⣿⣛⣻⣿⣯⣿⣛⣿⣿⣿⣴⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣶⣿⣿⣿⣿⣿⣿⣿⣭⣽⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⡻⠛⠀⠘⠛⠻⣿⣿⠿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⣠⣦⢰⣦⣥⣿⣷⣦⣶⣦⣿⣿⡏⠀⡀⠀⠀⢠
⠀⠀⠀⠘⢉⠉⠁⠈⠀⣹⣿⡟⠋⠀⠀⠸⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣉⣥⠀⢿⣿⣿⣿⣷⣦⣽⣿⡇⠀⠀⠀⠀⠀⠀⣀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⢸
⠀⠀⠀⠀⢻⣟⠛⢚⣢⠛⣿⣷⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠛⠋⢰⣿⡿⠀⠈⣿⣿⡿⠿⣿⣿⣟⠀⠀⢀⣠⠴⠺⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠲⣶⣿⠿⣿⣿⣿⣿⣿⠿⠋⠠⣶⡮
⡳⡄⠀⠀⣼⠗⠐⠛⠋⠀⠀⠁⠀⠀⠀⠀⠀⠉⣯⣉⢉⣠⣴⣶⣿⣿⡿⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⠀⠠⢋⡡⠟⠋⠀⠀⠀⠀⠀⣿⡛⠛⠛⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠟⠃⠀⠀⠀⢀⣼⣷
⣸⡆⢀⢺⣷⡤⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣶⣷⡇⠀⣠⣾⣿⡟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⠀⢴⣾⣿⣿
⣿⢇⡏⠀⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢉⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣠⣀⣸⣿⣿⢁⡀⠀⣀⣉⢀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠏⠀⠀⠙⠻⣿
⣷⣿⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⢻⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣿⠉⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣿⣼⠁⠀⠀⠀⢀⣤⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⠟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣍⣿⣋⣸
⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⠃⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⠟⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⠃⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣲⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣣⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠘⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⢿⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣂⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣶⣶⣿⡇⡀⢮⣴⣶⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣤⡄⠀⣾⡻⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⣷⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣭⣽⣿⣯⣭⣝⣻⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣍⣹⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⠟⠛⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀
⠀⠈⠙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⣠⣦⢰⣤⣥⣿⣷⣤⣒⣬⣿⣿⡏⠀⠀⠀⠀⢠
⠀⠀⠀⠸⣿⣯⣄⠉⠀⠀⢀⣧⣿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⡆⢻⣿⣾⣿⣿⣯⣽⣿⡟⠀⠀⠀⠀⠀⠀⢀⣈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠘⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⢸
⠀⠀⠀⠀⣿⣿⣿⠉⠉⢁⡌⣻⠟⠀⠀⠸⢿⢿⡿⠿⠿⣿⣿⣷⣿⣿⣿⣿⠃⠀⢿⣿⣿⡿⣿⣿⠟⠀⠀⠀⣠⡴⠞⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠙⠙⣶⣾⠿⣿⣿⣿⣿⣿⠿⠋⢠⣴⣮
⡳⡀⠀⠀⣼⠿⠟⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠙⢻⣿⣿⣿⣿⠀⢀⠞⡩⠞⠊⠀⠀⠀⠈⠀⣿⡛⠛⠛⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠛⠉⠀⠀⠀⢠⣾⣷
⣹⡄⢀⠀⣿⣷⠤⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⡇⠀⣠⣾⣿⡟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠀⢴⣿⣿⣿
⣿⢳⡏⠀⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢈⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣠⣀⣸⣿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠇⠀⠀⠙⠿⣿
⣿⣿⠆⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣰⣇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠈⠉⣽⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⡀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣿⣄⣦⠀⠀⣤⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣻⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡟⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⠟⠄⢮⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣦⡀⠘⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣲⣆⣼⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣣⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠐⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀⠀⠀⠀⢿⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣶⣾⣿⡇⡠⢮⣤⣶⣷⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢨⣿⣿⣿⣿⣿⣿⣿⣿⡷⣐⣤⣤⣤⠀⠀⣾⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⣷⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣯⣭⣽⣿⣏⣍⣛⣻⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣛⣛⣇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⠟⠛⠃⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⣠⣦⢰⣤⣥⣿⣷⣦⣒⣬⣿⣿⡏⠀⠀⠀⠀⢠
⠀⠀⠀⠹⣿⣿⣯⡄⠉⠀⠀⢈⣥⡾⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⢹⣿⣾⣿⣿⣯⣽⣿⡟⠀⠀⠀⠀⠀⠀⢀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠇⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣏⠉⠉⣡⢘⡿⠂⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⣀⣤⡶⠯⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠙⠫⣶⣾⠿⣿⣿⣿⣿⣿⠿⠋⠠⣴⣯
⡳⠀⠀⠀⢸⡿⠿⠟⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢠⣝⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠼⡋⠖⠛⠉⠀⠀⠀⠀⣿⡟⠛⠛⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠟⠉⠀⠀⠀⢠⣾⣷
⣽⡄⢀⠀⢸⣿⡦⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⡇⠀⣠⣾⣿⡟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠀⢴⣿⣿⣿
⣿⢳⠇⠀⣼⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢈⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣠⣀⣸⣿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠇⠀⠀⠙⠿⣿
⣿⡿⠄⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣰⣇⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣽⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣄⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣿⣄⣶⡆⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣻⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣿⢋⣸
⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⠏⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⠟⠀⠯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣦⡀⠈⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣲⣎⣨⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣹⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡆⠀⠀⢠⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣵⣣⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠐⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⡀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢀⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣶⡄⠀⠀⠀⢿⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣿⠀⢰⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣶⣶⣿⣇⠀⣤⣤⣾⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣦⠀⠀⠀⣰⡿⢿⣿⣿⣿⡿⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣛⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡿⠛⠛⠃⠚⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠁⣀⣦⢰⣤⣴⣿⣧⣄⣒⣌⣿⣿⠏⠀⠀⠀⠀⢀
⠀⠀⠀⠹⣿⣿⣿⣿⣤⠈⠁⠀⠀⣍⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⣿⣿⣿⣿⣯⣩⣿⣿⠀⠀⠀⠀⠀⠀⠀⣈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠘⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠇⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠁⠁⡈⣻⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣠⡴⡪⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠙⠫⣵⣾⠿⣿⣿⣿⣿⣿⠟⠋⠠⣶⣯
⡷⠀⠀⠀⠉⣽⡙⠿⠟⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⢠⠋⠓⠊⠉⠀⠀⠀⠀⣿⡟⠛⠛⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠟⠁⠀⠀⠀⣤⣿⣷
⣼⡄⢀⠀⠀⣿⣿⠦⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡇⠀⢠⣾⣿⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠀⢶⣿⣿⣿
⣿⢳⡇⠀⢀⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣁⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣡⣀⣸⣿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠃⠀⠀⠙⠻⣿
⣷⡿⠁⠀⣸⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣸⡇⠀⠀⠟⠀⠀⢀⣤⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⣹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣷⣄⢀⡾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣿⢋⣠
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⠀⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣼⣢⣤⣴⡆⢠⣿⣴⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⡿⣂⢾⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣧⣸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣤⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠺⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣧⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⣄⠀⠀⠀⢻⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣿⡀⢰⣿⣿⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣶⣾⣿⣇⢀⣤⣤⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠀⠀⠀⣰⣟⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⡿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣟⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣛⣻⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡾⠻⠛⠃⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⠁⣀⣦⢠⣤⣴⣿⣧⣄⣠⣈⣿⣿⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠨⣿⣿⣿⣿⣿⣤⠉⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣯⣭⣿⣿⠂⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⠃⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠉⠀⢀⠘⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣠⡴⡺⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠙⠫⢵⣿⢿⣿⣿⣿⣿⣿⠟⠁⠰⣶⣞
⡧⠀⠀⠀⠉⢸⣿⠛⠿⠏⠀⠐⠉⠀⠀⠀⠀⠀⠈⡽⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⠆⠀⠠⠊⠓⠂⠁⠀⠀⠀⠀⣿⡟⠛⠛⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠟⠀⠀⠀⠀⣴⣿⣷
⣽⡄⢐⠀⠀⢸⣿⡷⢤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡇⠀⢠⣾⣿⡿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⢾⣿⣿⣿
⡿⣱⠇⡀⠀⣾⣏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣡⣀⣸⣿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠃⠀⠀⠙⠻⢿
⢷⡿⠉⠁⢀⡟⠁⠀⣀⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣸⡄⠀⠀⠸⢀⣴⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣧⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣿⣿⣷⣄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⡛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣉⣿⠋⣀
⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣄⡀⠈⠀⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣻⣦⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⡿⠂⢼⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣧⣸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣦⣶⣠⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣏⣤⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣦⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⡀⠀⢀⣾⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣄⠀⠀⠀⢹⡿⠿⣿⣿⣯⠭⠿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡠⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣆⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣾⣿⡇⠀⣤⣤⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣿⡻⢿⣿⣿⡿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣛⣛⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡿⠛⠛⠁⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠁⢀⣶⣦⣤⣶⣿⣧⣀⣠⣙⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠡⣽⣿⣿⣿⣿⣿⣤⠈⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣍⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⠀⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠐⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⡴⠒⠉⠁⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠙⠻⢽⣿⣿⣿⣿⣿⣿⣿⠟⠁⠴⣶⣾
⢧⠀⠀⠀⠉⠉⣹⣿⠛⠿⠛⠀⠀⠈⠀⠁⠀⠀⠀⠹⠟⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣇⠀⠠⠚⠑⠊⠀⠀⠀⠀⠀⣿⡟⠛⠛⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠛⠁⠀⠀⠀⣴⣿⣷
⣿⡀⣐⠀⠀⠀⣿⣿⠗⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡗⠀⢠⣾⣿⡿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠰⢾⣿⣿⣿
⡿⣰⡷⠀⠀⢰⣿⣇⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⢣⣀⣘⢿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠃⠀⠈⠛⠻⣿
⢿⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣸⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣷⣄⢸⡿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣦⡀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣿⡛⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠈⠙⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⡿⠂⢸⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣦⣶⣠⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣇⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣀⣀⡀⠀⢀⣾⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣄⠀⠀⠀⢹⡿⠿⣿⣿⣿⠭⠿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣆⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣾⣿⡇⠀⣤⣤⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣿⡻⢿⣿⣿⡿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣛⣻⡃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡿⠛⠛⠁⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠁⢀⣶⣦⣤⣦⣿⣧⣀⣠⣙⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠨⣥⣿⣿⣿⣿⣿⣤⠈⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣍⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⠀⠀⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠐⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⣠⠴⠒⠉⠁⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠉⠹⢭⣿⣿⣿⣿⣿⣿⣿⠟⠁⠴⣶⣾
⢧⠀⠀⠀⠉⠉⣹⣿⠙⠻⠛⠀⠀⠈⠀⠀⠀⠀⠀⠹⠟⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣇⠀⠠⠛⠑⠂⠁⠀⠀⠀⠀⣿⡟⠛⠛⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠁⠀⠀⠀⣴⣿⣷
⣵⡀⣐⠀⠀⠀⣿⣿⠗⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡗⠀⢠⣾⣿⡿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠰⣾⣿⣿⣿
⡟⣰⡷⠀⠀⢰⣿⣇⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣘⢿⣿⢁⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠃⠀⠈⠛⠻⣿
⢿⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣸⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠈⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣷⣄⢸⡿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣦⡀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣿⡋⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠈⠙⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⡿⠂⢸⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢿⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣦⣶⣠⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣎⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⣀⠀⠀⣴⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⣴⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⢹⣿⠿⣿⣿⣿⡉⠽⣿⣿⣿⣿⡆⢠⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣌⠄⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢗⣂⣬⣿⣿⣿⣷⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⡇⠀⣤⣤⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆⠀⠀⠀⢀⣾⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣛⣻⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡿⠛⠛⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⣠⣦⣦⣐⣮⣿⣍⡈⣍⣹⣿⡿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠡⣿⣿⣿⣿⣿⣟⣷⣤⠈⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣍⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⡿⠀⠀⢸
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡍⠉⠀⡀⢺⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⠴⠖⠉⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠛⠛⣭⣿⣿⣿⣿⣿⣿⣿⠟⠁⢶⣶⣞
⠆⠀⠀⠀⠉⠉⢉⣿⣟⣻⠟⠃⠀⠀⠁⠈⠀⠀⠈⢻⠿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠰⠋⠁⠋⠁⠀⠀⠀⠀⣾⡟⠛⠛⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⠟⠁⠀⠀⠀⣶⣿⣷
⣷⠀⡐⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⠀⢠⣶⣿⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠰⣾⣿⣿⣿
⡟⣾⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣘⢿⣿⢃⡀⠀⣀⣉⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠁⠀⠈⠛⠿⣿
⢿⡿⠀⠀⢀⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣾⡄⠀⠀⣼⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣧⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠈⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣧⠀⠀⢸⣿⣿⣷⣶⠾⠄⠘⣿⣿⣿⣿⣧⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⣿⣿⣷⣀⠸⣻⣿⣿⣶⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⢺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣿⡛⣀
⣿⣿⣿⣿⣿⣿⣯⣅⣀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⣿⣁⢸⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣧⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣞⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣾⣿⣿⣿⣿⣶⣾⣷⣶⡄⠀⠀⠀⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣀⠀⠀⣠⣶⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠸⣿⠿⣿⣿⣿⡋⡽⣿⣿⣿⣿⡆⢠⣾⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢗⣂⣨⣿⣿⣷⣷⣿⣿⣿⣿⣧⣾⣾⣿⢷⣿⣿⠀⠀⣠⣤⣶⣤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⢀⣾⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⣛⣻⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠿⠛⠛⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⣠⣦⣄⣐⣽⣿⣉⠉⢉⣻⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠩⣻⣿⣿⣿⣿⣟⣻⣤⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⣷⣿⣿⣯⣝⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣔⣷⠀⠀⢸
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡏⠉⠑⠂⠸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢻⣿⣿⣿⣿⣿⠟⠀⠀⢀⣠⠴⠖⠈⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠉⠛⠛⣫⣿⣿⣿⣿⣿⣿⣿⠟⠁⢴⣶⣞
⠆⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⣶⣶⡁⠈⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢶⣾⣿⣿⡇⠀⡰⠋⠅⠚⠁⠀⠀⠀⠀⢸⡟⠛⠛⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⠟⠉⠀⠀⢠⣴⣿⣿
⣶⠀⣐⠀⠀⠀⢰⣿⡿⠛⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠰⣾⣿⣿⣿
⡟⣼⠋⠀⠀⣀⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⡀⠀⠀⠀⢰⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣘⢿⣿⢃⡀⠀⣀⣉⢃⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠘⠁⠀⠈⠻⠿⣿
⢿⡿⠀⣠⣿⣿⣿⣿⡃⠀⠀⠀⠰⣿⣿⣿⣇⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣾⡀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣇⠈⢿⣿⣿⣾⣿⠗⠀⠀⠀⠀⠻⣿⣿⣿⣷⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⢪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣷⡈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣹⡛⣀
⣿⣿⣿⣿⣿⣿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠋⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⣷⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠸⣿⡿⠋⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣞⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣶⣷⣶⣶⣦⡀⠀⠀⠀⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣀⠀⠀⣠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡛⣽⣿⣿⣿⣿⡆⠀⣶⣷⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢓⢂⣨⣿⣿⣷⣷⣿⣿⣿⣿⣧⣼⣿⣿⢿⣿⣿⠀⢀⣄⣠⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣆⠀⠀⠀⢀⡾⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣾⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⣛⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⡿⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⣴⣆⣄⣠⣽⣿⣋⠉⠛⢻⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣦⠈⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣿⣿⣯⣛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⢿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⡷⠀⠀⢰
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣉⣐⣂⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣠⠴⡖⠈⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠛⠻⢛⣿⣿⣿⣿⣿⣿⣿⠟⠁⠰⣴⣾
⡄⠀⠀⠈⠉⠉⠉⣿⣟⠛⠿⠛⢿⣿⣿⣿⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠻⣶⣿⣿⣿⡇⠀⠐⡋⠥⠚⠁⠀⠀⠀⠀⢸⣟⠛⠛⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠟⠉⠀⠀⢠⣾⣿⣿
⣤⠀⡀⠀⠀⠀⢰⣿⡿⠳⣶⠖⠂⠹⣿⣿⣦⠀⠀⠈⠀⠀⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣾⠀⢀⣴⣿⣿⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡆⠰⣿⣿⣿⣿
⡏⣾⠁⣿⡇⠀⣸⣟⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣈⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣈⢿⣿⢇⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠈⠁⠀⠈⠻⠿⣿
⣿⣿⣿⣿⣷⠀⡟⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣾⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⣹⡟⣁
⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠟⠁⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠇⠰⣙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢐⣴⣃⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣶⣶⣶⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣜⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣾⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⡀⠀⣠⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣷⣠⣴⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⣽⣿⣿⣿⣿⡆⠀⣶⣷⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⡀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢓⢂⣨⣿⣿⣷⣷⣿⣿⣿⣿⣷⣼⣿⣿⢿⣿⣷⠀⢀⡄⣤⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣦⠀⠀⠀⢀⡾⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣾⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⡀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣛⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠿⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣴⣆⣄⣀⣹⣿⣉⠉⡙⢻⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣻⣦⠈⠁⠈⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣭⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠿⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡷⠀⠀⢠
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠂⠸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢿⣿⣿⣿⣿⣿⢋⠀⠀⣀⡤⠴⠀⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠙⠻⢛⣿⣿⣿⣿⣿⣿⣿⠟⠁⠰⣶⣾
⠄⠀⠀⠈⠉⠉⠉⣿⣿⣿⣿⣿⣷⡄⠉⠀⠀⠀⠈⢛⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠻⢿⣿⣿⣿⡇⢀⠞⡉⠔⠛⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠉⠀⠀⢠⣾⣿⣿
⣧⢀⡄⠀⠀⣀⣰⣿⡿⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣾⠀⢀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⢏⣾⣀⣤⣾⣿⣿⣿⡄⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢘⣿⣿⣣⣀⣈⢿⣿⢇⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠉⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣦⡀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣾⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣧⡀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⣹⡟⣁
⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⠇⠰⣝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢒⣴⣇⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣜⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣿⣷⣶⡄⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣀⣀⡀⠀⣴⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣧⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣦⠀⠀⠀⠀⠘⣿⠿⣿⣿⣿⡏⠽⢿⣿⣿⣿⡇⠀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢓⣂⣠⣿⣿⣷⣷⣿⣿⣿⣿⣷⣼⣿⣿⢿⣿⡇⠀⢠⣤⣤⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣷⠀⠀⢠⡻⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣺⣿⣷⠀⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣯⣍⣻⣇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡻⠟⠃⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣴⡆⣄⣐⣽⣿⣉⠉⣉⣻⣿⡟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣻⣷⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣭⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⡟⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⢀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠘⢿⣿⣿⣿⣿⢿⡃⠀⢀⣠⠤⢲⠈⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠉⠉⠛⠯⣿⣿⣿⣿⣿⣿⡿⠛⠀⢰⣶⣶
⠆⠀⠀⠈⠁⠀⠀⣾⣿⣙⣛⠛⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⡠⢋⡡⠞⠃⠀⠀⠀⠀⠀⢸⢟⠙⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠋⠉⠀⠀⢠⣾⣿⣿
⣦⢀⡄⠀⠀⢶⣤⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠰⣿⣿⣿⣿
⢇⣟⡀⠀⠛⣿⢿⣿⣿⣿⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠇⠉⠂⣨⠁⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣶⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⣿⣿⣤⡀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣧⣀⢀⣤⣾⣿⣿⠁⠈⠿⣿⣿⣿⣿⣦⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⡿⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠏⡀⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣹⣿⡿⠁⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢶⣴⣆⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣀⠀⣴⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣧⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⠿⢿⣿⣿⡏⠽⢿⣿⣿⣿⣇⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣠⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢳⣂⣰⣿⣿⣷⣷⣿⣿⣿⣿⣿⣼⣿⣿⢿⣿⡇⠀⣠⣤⣴⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆⠀⣰⡻⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣸⣿⣷⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣯⣍⣻⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠿⠛⠃⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠹⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣼⡆⣄⣒⣽⣿⣍⡉⣉⣻⣿⡟⠁⢀⠀⠀⠀⠀
⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣻⣷⣂⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⡟⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢁⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢿⣿⣿⣿⣿⣟⣃⠀⢀⣠⡴⠒⠈⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠛⢫⣿⣿⣿⣿⣿⣿⡿⠛⠀⢰⣶⣶
⡆⠀⠀⠈⠀⠀⠀⣾⣿⣛⡛⠛⠀⠀⠉⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⡴⢙⡵⠟⠓⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠉⠀⠀⢠⣾⣿⣿
⣧⢀⡆⠀⢤⣶⣶⣿⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠁⠀⢀⣻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠰⣿⣿⣿⣿
⣇⡟⠀⠀⢠⡿⢽⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠇⠀⠀⣌⢀⡾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣧⠀⠀⠀⠈⠛⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⠇⢿⣿⣿⣿⣷⣄⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣦⡀⣀⣴⣿⣿⣿⠉⠀⠀⠙⢿⣿⣿⣿⣷⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢩⣵⣿⢃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠹⣿⣿⣿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠟⡀⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠐⣿⡟⠁⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢰⣶⣆⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⣣⣄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣀⡰⢯⣤⣴⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⣘⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣿⣿⣿⣿⣿⣭⣭⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⠛⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣤⣿⡄⣤⣐⣼⣿⣥⣀⣈⣹⣿⡿⠀⢀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣯⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⡟⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣠⢀⡠⢈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠹⣿⣿⣿⣿⣿⢿⡁⠀⣀⡤⡶⠌⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠻⢽⣿⣿⣿⣿⣿⣿⡿⠟⠀⢰⣶⣶
⡆⠀⠀⠈⠁⠀⠀⣾⣿⣿⠿⢿⣿⣏⠀⠀⠀⠀⢠⡷⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠙⠻⣿⣿⣿⣧⣞⣩⡾⠟⠒⠀⠀⠀⠀⠀⢸⣟⠛⠛⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⢠⣾⣿⣿
⡧⢀⣤⡀⢀⣴⣿⣿⣿⣟⡁⠀⢹⣿⣶⡄⠀⠀⡜⠀⠀⢀⣽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡁⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣣⣿⠋⠀⢸⣿⣿⣿⣿⠛⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⡁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠇⠀⠀⢸⣿⣿⣿⣡⣴⠇⠀⠈⣿⣿⣿⣇⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠈⣿⣿⣿⡿⠃⠀⠀⠀⢻⣿⣿⣿⣆⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⠉⣿⣿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣇⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣦⣀⣸⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡿⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⣵⡿⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣹⠿⠀⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣾⣶⣾⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⣀⣀⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣴⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠹⣂⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⣿⢀⡴⢏⣤⣴⣶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⠀⣘⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣽⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣭⣭⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⠻⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣄⡀⢸⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣤⣾⡄⣤⣤⣾⣿⣥⣀⣈⣹⣿⡟⠁⢀⠀⠀⠀⠀
⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⡿⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⡄⠉⠛⠙⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠻⣿⣿⣿⣿⣿⣟⡀⠀⣠⠤⡶⠈⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉⠛⢽⣿⣿⣿⣿⣿⣿⡿⠟⠀⢶⣶⣶
⡆⠀⠀⠈⠁⠈⠀⣾⣿⡛⠛⠉⠙⣿⣧⠀⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⢚⣡⡾⠟⠒⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠯⠁⠀⠀⢠⣾⣿⣿
⡇⢠⣤⣠⣴⣦⣴⣿⠟⠋⠀⠀⠀⣿⣿⣷⡀⠀⠏⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡁⠊⠁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⠂⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣣⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⣾⣿⣿⠟⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⡁⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⣿⠇⠙⣿⣿⣿⡏⢀⡤⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⣿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣆⠀⠀⢿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣦⣀⣸⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡿⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣭⡾⢋
⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⢼⣿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣽⡿⠀⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣾⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠰⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢀⣀⣀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢿⡿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣷⠀⢴⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣂⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣴⣿⣿⡿⣇⣀⡾⢯⣤⣴⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡿⢀⣛⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣧⣽⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣬⣽⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⠃⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⢿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣾⣿⡄⣦⣄⣾⣿⣥⣀⣈⣙⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣻⣷⣆⣀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠛⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡿⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣡⠈⠽⠉⠉⣍⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢿⣿⣿⣿⣿⣿⣫⡀⢀⣠⠴⠦⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⢭⣿⣿⣿⣿⣿⣿⡿⠟⠀⢶⣶⣶
⠆⠀⠀⠋⠉⠈⠁⣿⣟⣛⡛⠀⠀⠁⠀⠀⠀⠀⣿⠿⠿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⢋⣥⡿⠟⠒⠀⠀⠀⠀⠀⢸⣿⠋⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠉⠀⠀⢠⣾⣿⣿
⡇⢠⠀⠀⠀⣠⣤⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⠸⠁⠀⢀⣬⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⠃⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣱⡇⢠⡖⠀⠸⣿⣿⣿⣿⣿⣿⣽⣿⠆⠀⠀⠀⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⡃⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⡿⠂⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣋⡀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⠀⠀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⣿⠉⠉⠉⢉⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⠀⠀⠀⠄⢀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣦⡀⢀⣠⣾⣿⣿⡟⠁⠈⠻⣿⣿⣿⣷⣦⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡿⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⣩⣾⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⠀⠀⠘⢿⣿⣿⣿⠋⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣸⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⢲⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣯⠩⢿⣿⣿⣿⣷⠀⣴⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣀⣰⣽⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⡿⡇⣠⡾⢇⣠⣴⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡿⢀⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾⣿⣿⣿⣿⣿⣭⣽⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⠃⡀⠰⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣾⣿⠀⣦⣔⣾⣿⣥⣀⣈⣹⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣷⣀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣷⣿⣿⣶⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡟⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣡⠈⡟⠁⠉⣍⣹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣋⡀⢀⣠⠴⠶⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠭⣿⣿⣿⣿⣿⣿⡿⠛⠀⢶⣶⣶
⠇⠀⠀⠋⠉⠉⠁⣿⣝⣻⣟⣥⠑⠉⠀⠀⠀⢸⡿⠿⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⡷⢋⣵⡿⠗⠒⠀⠀⠀⠀⠀⢸⣿⠋⠛⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠉⠀⠀⢠⣾⣿⣿
⡧⣠⠀⠀⠀⠠⢴⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠸⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⠃⠀⣴⣿⣿⠇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣱⡇⠀⣠⣴⣶⡟⢻⣿⣿⣿⣿⣷⣶⠶⠀⠀⠀⠀⠰⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣈⡃⣀⣀⢀⣀⠀⣀⢀⣀⢐⣻⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⣿
⡿⠂⠀⠁⠀⠀⠃⢸⣿⣿⣿⣿⣿⣤⡦⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⠀⠀⠀⢠⡀⠀⢸⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⣿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣷⣄⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣦⡀⠀⣠⣾⣿⣿⣟⠁⠀⠙⠻⣿⣿⣿⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡿⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢮⣻⣴⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣨⠿⠃⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢾⣿⠏⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⣿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⢲⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⣀⣤⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⣯⠭⢿⣿⣿⣿⣧⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣀⡄⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢹⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣀⣰⡾⢣⣤⣴⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⢐⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣯⣬⣽⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣯⣭⣽⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠟⢁⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣼⣷⠀⣦⣤⣾⣿⣥⣀⣈⣹⣿⣿⠁⢀⠀⠀⠀⠀
⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⢠⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣷⣿⣿⣶⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡟⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⡡⠈⠭⠀⢰⣦⣼⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠿⣿⣿⣿⣿⣿⣯⡄⢀⣤⢶⠆⠉⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠽⣿⣿⣿⣿⣿⣿⡿⠟⠀⢶⣶⣶
⡂⠀⠀⠋⠉⠉⠁⣿⣟⣻⣿⣦⣉⡀⠀⠀⠀⣼⠟⠿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡗⣋⣶⡿⠗⠂⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⠀⠀⢠⣾⣿⣿
⡇⡰⠀⠀⠀⠰⠚⢻⣿⣿⣿⣿⣿⣋⠀⠀⠀⠏⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡴⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣽⠃⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⢰⠀⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣘⡁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⡿⠀⠀⠀⠘⠃⠀⣿⣿⣿⣯⣴⣿⣿⣿⡀⠈⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠦⠀⠀⣿⣿⣿⣿⡏⢹⣿⣿⣿⣄⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⣸⣿⣿⣿⡿⠀⠀⠻⣿⣿⣿⣷⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⣆⡀⢀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣝⣦⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣠⡽⠋⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⢳⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣀⣀⣤⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⣿⡿⢿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⡄⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢱⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡟⣀⣴⡿⢡⣤⣴⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⢰⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣾⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⡟⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣯⣭⣽⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢀⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣿⣷⠀⣦⣤⣾⣿⣥⣄⣀⣙⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣶⣀⡀⠀⢠⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢿⣷⣿⣿⣶⣽⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⡟⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣏⣀⣉⣡⠈⠯⠀⢹⣦⣠⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠿⣿⣿⣿⣿⣿⣏⡀⢀⡤⠴⡆⠉⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠽⣾⣿⣿⣿⣿⣿⡿⠛⠠⢶⣶⣶
⡀⠀⠐⠋⠉⠉⠁⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⠟⠛⠛⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡟⣫⣼⡿⠗⠂⠀⠀⠀⠀⠀⢸⣟⠋⠋⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠀⠀⠀⢠⣾⣿⣿
⡇⡴⠀⠀⠀⢠⣾⣿⣿⣿⡿⣋⣹⣿⣶⡄⢀⡇⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣴⣿⣿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠲⣿⣿⣿⣿
⣼⠃⠀⠀⢀⣼⣿⣿⣿⣿⡿⠛⢛⣿⣿⣧⢸⠃⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣘⠁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⡿⠀⠀⠀⠸⣿⣿⣿⣿⣋⣴⡾⠋⣿⣿⣿⣏⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠈⠆⢸⣿⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⣧⡀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣦⣀⣀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣝⣦⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢴⣿⡿⠋⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣠⡽⠟⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⡿⣵⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣠⣤⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⡿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⠀⣀⠄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠹⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡏⣠⣾⡿⢀⣤⣴⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠇⢸⠿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢰⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣮⣽⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠏⠀⣿⣿⣿⣿⣿⣿⣭⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⢀⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣧⠀⣦⣤⣾⣿⣥⣄⣀⣙⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⡀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡟⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⡎⠝⠁⣸⣭⣀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠻⣿⣿⣿⣿⣿⣿⣫⡀⢀⣠⠴⠂⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠋⠽⣿⣿⣿⣿⣿⣿⡿⠛⠠⢶⣶⣶
⠀⠀⠘⠋⠉⠉⠁⣿⣏⡛⠋⠉⢿⣿⣧⠀⠀⣿⠿⠻⠛⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⡶⣫⣵⡿⠗⠂⠀⠀⠀⠀⠀⢸⣟⠉⠋⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⢠⣾⣿⣿
⡇⡄⢀⠀⢠⣤⣀⠛⠁⠀⠀⠀⢸⣿⣿⡆⠀⡏⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠲⣿⣿⣿⣿
⣼⢵⠟⢡⣾⣿⣿⣿⠿⠀⠀⠀⠀⢻⣿⣿⣰⠇⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣘⡁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⠟⠀⠀⢌⢻⣿⣿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠈⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⢿⣿⣿⣷⣄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⣄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⣆⡀⣉⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⣯⣶⡼
⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠟⠁⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⢻⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣾⣿⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣀⣠⣤⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣴⣿⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⡄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠸⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡏⣠⣾⡿⢠⣤⣴⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠇⢸⠿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⣄⠀⠐⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣄⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣧⠀⣦⣤⣾⣿⣧⣄⣀⣩⣿⣿⠁⢀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣿⣿⣿⣿⣾⣽⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡟⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⠈⠟⠁⣸⣍⣉⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣯⡀⢀⣠⠴⠖⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠛⠷⣿⢿⣿⣿⣿⣿⡿⠛⠠⣶⣶⣶
⠀⠀⠘⠋⠉⠉⠁⣿⣿⣿⣿⣀⡈⠀⠀⠀⠀⣿⡿⠿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡶⢫⣵⡿⠗⠂⠀⠀⠀⠀⠀⢸⣟⠉⠋⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⢠⣾⣿⣿
⡇⣴⠆⠀⠀⠀⠐⠿⣿⣿⣿⣿⣷⣶⠶⠀⠀⡏⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡔⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠲⣿⣿⣿⣿
⣼⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⠖⠀⡇⠀⢸⣿⣿⡟⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣈⠁⣀⣀⢀⣀⠀⣀⢀⣀⢰⣿⣿⣯⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⠟⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡶⠘⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠐⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⣤⠀⠀⢠⣿⣿⣿⣿⡟⢻⣿⣿⣿⣦⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠒⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⣆⡀⠁⢀⣴⣿⣿⣿⡟⠉⠀⠀⠹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢯⣲⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠙⣿⣿⣿⡿⠀⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⠿⣯⠟⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠘⢿⣿⠋⠁⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣶⣟⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣀⣠⣄⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⠄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠹⣨⣱⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣏⣾⣿⡇⢠⣴⣴⣾⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠇⢸⠿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣾⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣣⡄⠀⠐⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⣦⣤⣴⣿⣧⣄⣀⣨⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣶⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡟⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠠⠌⠋⠁⢹⣭⣉⣹⣿⣿⣿⣿⣿⡿⠁⠀⠘⣿⣿⣿⣿⣿⣿⣯⠀⠀⣠⡤⡶⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠛⠶⣿⢿⣿⣿⣿⣿⡿⠟⠠⣶⣶⣶
⠀⠀⠜⠛⠋⠉⠁⣿⡟⠛⠛⣇⣀⡀⠀⠀⠀⣸⡿⠿⠿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⢀⠞⣑⠼⠛⠂⠀⠀⠀⠀⠀⢸⣟⠉⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⠋⠀⠀⢠⣾⣿⣿
⢄⡄⠀⠀⠀⢀⣰⣿⣶⣾⣷⣿⣿⣿⣶⡶⠀⣟⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡁⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣶⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠲⣿⣿⣿⣿
⣾⢸⠏⠀⠀⠙⠛⠋⠉⣽⣿⣿⣿⣿⣷⡾⠗⡏⠀⠐⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⠟⠀⠀⡄⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣤⡶⠁⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⠁⠸⣿⣿⣿⣦⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣷⣄⡀⠀⢀⣤⣾⣿⣿⣿⠋⠁⠀⠀⠘⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣳⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀⠀⢘⣿⣿⣿⡏⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣦⣬⠟⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⢿⠟⠋⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡂⠀⢀⣀⣤⣄⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⡄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠸⣩⣱⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣏⣾⣿⠇⢠⣄⣴⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠏⢸⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⡿⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣽⣿⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣳⣆⠀⠐⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⣶⣤⣵⣿⣧⣤⣀⣬⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⢍⣿⣾⣿⣿⣿⣿⣿⣶⣄⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣷⣿⣿⣶⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡟⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠠⠌⠉⠁⢰⣯⣄⣺⣿⣿⣿⣿⣿⣿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿⡀⠀⣀⡤⠖⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠛⠷⣿⢿⣿⣿⣿⣿⡿⠟⠠⣶⣶⣶
⠀⠀⠞⠛⠋⠉⠁⣿⠟⠛⠋⢱⣄⠀⠀⠀⠀⢸⣿⠿⠿⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⢆⠞⣩⠾⠛⠀⠀⠀⠀⠀⠠⢸⢿⠉⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠋⠀⠀⢠⣾⣿⣿
⢀⡆⠀⠀⠀⠀⢼⣿⣿⣿⣿⣾⣿⣧⣤⡦⠀⢸⠁⠀⢀⣤⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠲⣿⣿⣿⣿
⡿⠀⡾⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⠆⡾⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⠗⠀⠀⣀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠟⣿⣿⣄⠃⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠘⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⠿⣿⣿⣦⡀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠁⠀⠻⣿⣿⣿⣦⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⡀⠀⢀⣤⣿⣿⣿⡿⠛⠁⠀⠀⠀⠘⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣳⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣦⣬⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣡⣄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣾⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣤⣤⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢹⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠀⢠⣤⣴⣾⣷⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠸⠟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣭⣭⣯⡿⣾⣿⣿⠿⣿⣿⣿⣿⣿⠿⠏⠀⣿⣿⣿⣿⣿⣷⣬⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣷⡆⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣯⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⣶⣦⣵⣿⣷⣤⣀⣌⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⣷⣯⣿⣿⣿⣿⣿⢿⣷⣄⡀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣷⣿⣿⣷⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠡⢬⡉⠁⠀⣤⣄⣼⣿⣿⣿⣿⣿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⣟⡀⠀⣀⡤⠴⠊⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠙⠲⢾⡿⣿⣿⣿⣿⡿⠟⠡⢶⣶⣶
⠀⠀⠞⠛⠋⠉⠁⠿⠉⢋⣿⣿⣿⢿⣿⣿⡄⠀⣿⡿⠿⠿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠚⠿⣿⣿⣿⣯⠞⡩⠜⠛⠀⠀⠀⠀⠀⠀⢸⢿⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠀⠀⢠⣾⣿⣿
⢀⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣶⣯⠀⠀⣀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠰⣿⣿⣿⣿
⡟⠀⠀⠀⡶⠀⣿⣷⣶⣧⣤⡤⠀⠈⢿⣿⣿⣿⡇⠀⠸⣿⣿⣿⠃⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠙⠻⢿
⠇⠀⠀⣀⠀⢰⣿⣿⣿⣿⣫⣴⡖⠀⠈⣿⣿⣿⣷⡀⠀⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠘⠀⢸⣿⣿⣿⣿⠟⢁⣠⠄⠀⠙⢿⣿⣿⣷⣄⣿⠃⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⡀⠀⠀⠀⠘⣿⣿⣿⣷⣶⠿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣀⠀⢀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣳⡾
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡿⠋⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣶⣼⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⣤⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣿⠿⢿⣿⣿⣯⠽⢿⣿⣿⣿⣧⠀⣾⣿⣆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣤⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢹⣩⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⠀⠀⣤⣴⣾⣿⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢹⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠼⠟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣭⣭⣯⡿⣾⣿⣿⢿⣿⣿⣿⣿⣿⠿⠟⠁⣿⣿⣿⣿⣿⣷⣤⣽⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣵⡆⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠙⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡆⠀⣷⣦⣽⣿⣷⣦⣀⣠⣽⣿⠃⠀⠀⠀⠀⠀
⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⢿⣷⣿⣿⣷⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣁⠆⢩⡉⠁⢠⣄⣻⣿⣿⣿⣿⣿⣿⣿⠃⠈⢻⣿⣿⣿⣿⣿⣯⡀⠀⣀⡤⠴⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢾⡿⣿⣿⣿⣿⡿⠟⠡⢶⣶⣶
⠀⠀⠞⠛⠋⠉⠁⠿⠉⠉⠻⠿⠿⠿⣿⣿⣷⡀⣸⡿⠿⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠚⠿⣿⣿⣿⣿⡞⠹⠞⠋⠀⠀⠀⠀⠀⠠⢸⢿⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠟⠀⠀⢠⣾⣿⣿
⢠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⠀⠀⢀⣤⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠰⣿⣿⣿⣿
⡟⠀⠀⠀⢠⠴⣿⣆⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⣿⣿⢃⡀⠀⣀⣀⢀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠙⠻⢿
⠃⠀⠀⣀⠀⣠⣿⣿⣿⣿⢏⡀⠀⠀⠀⣿⣿⣿⣷⡀⠀⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠈⠀⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⠿⣿⣿⣷⣀⣿⠏⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠘⣿⣿⣿⣯⣴⡿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⡀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣳⣾
⣿⣿⣿⣿⣿⣶⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣶⣬⠟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⡿⢭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣵⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡂⠀⣀⣀⣤⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠽⢿⣿⣿⣿⣷⠀⣾⣿⣆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣤⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢹⣨⣱⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⠇⠀⠀⣤⣦⣾⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⢓⠻⢿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠸⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣯⣭⣭⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣷⣤⣽⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡀⠀⠀⠛⠛⠻⣿⣿⠿⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⣿⡽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⢹⣶⣾⣿⣿⣦⣄⣤⣽⣿⡏⠀⠀⠀⠀⠀
⠀⠀⣰⣽⣿⣿⣿⣿⣿⣿⣷⣆⣀⡀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠄⠙⠁⠈⢡⣌⣻⣿⣿⣿⣿⣿⣿⣿⡟⠈⢻⣿⣿⣿⣿⣿⣿⡀⠀⣀⡤⠴⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢾⡿⣿⣿⣿⣿⡿⠟⠁⢶⣶⣶
⠀⠀⠛⠛⠉⠉⠁⠾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠉⠻⢿⣿⣿⣿⡇⡴⠋⠘⠉⠀⠀⠀⠀⠀⢠⢸⢿⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠀⠀⢠⣾⣿⣿
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣦⣦⠀⣀⠀⢸⡁⠀⠀⣠⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⢿⣿⣿⣿
⡏⠀⠀⠐⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⣼⠁⠀⣾⣿⣿⡿⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⢣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠙⠻⢿
⠃⠀⠐⣦⡄⠀⠀⠻⠿⠏⣿⣿⣿⣿⣿⣷⡾⠿⠃⠀⠀⢸⣿⡟⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⡖⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠿⢻⣿⣷⣄⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠛⠀⠙⣿⣿⣿⣷⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣱⡼
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣏⣤⠀⠀⠀⠘⣿⣿⣿⣿⣿⠁⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣽⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣶⣬⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣼⣿⣿⣿⠟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣵⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡁⠀⣀⣠⣤⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠭⢿⣿⣿⣿⣷⠀⣴⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣠⣤⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⣨⣡⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⠃⠀⠀⣴⣶⣾⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢃⡛⢿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣾⣭⣍⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣷⣤⣽⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡀⠀⠀⠛⠛⠻⣿⣿⠿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⡀⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⢸⣶⣾⣿⣿⣦⣄⣤⣽⣿⡏⠀⠀⠀⠀⠀
⠀⠀⣐⣿⣿⣿⣿⣿⣿⡿⣷⣦⣀⣀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣿⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣏⠀⠀⠔⠉⠁⠈⢉⣉⣹⣿⣿⣿⣿⣿⣿⣿⡿⠈⢻⣿⣿⣿⣿⣿⣿⡀⠀⢀⡤⠴⠀⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢾⡿⣿⣿⣿⣿⡿⠟⠁⢶⣶⣶
⠀⠠⠟⠛⠋⠉⠁⠾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠚⢿⣿⣿⣿⡇⡰⠋⠐⠉⠁⠀⠀⠀⠀⢀⢸⢿⠉⠉⠛⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠀⠀⠀⣾⣿⣿
⢠⠀⣠⡄⠀⠀⠀⠀⢀⣀⣀⣿⣼⣷⣾⣆⣤⡄⢸⡇⠀⠀⣠⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⣿⣿⣿⣿
⡏⢠⣏⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⡿⣋⣡⣼⠁⠀⢾⣿⣿⡿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠻⢿
⠃⠀⠹⣷⠀⠀⠀⠙⠛⠉⣿⣿⣿⣿⣿⣿⡟⢋⣃⠀⠀⢸⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢸⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⢫⣾⣿⣷⣄⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣸⠀⠀⢀⣴⣾⣿⣿⣿⠿⠋⠁⠈⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣱⡼
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡗⢛⣟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠸⣿⣿⣿⠟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣵⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣠⣤⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠩⢿⣿⣿⣿⣷⠀⣴⣿⣦⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢀⣠⣤⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣨⣡⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⡿⠀⠀⠀⣤⣶⣾⣿⣷⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⢂⡛⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡘⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⠄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣼⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣷⣤⣽⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣷⡀⠀⠀⠛⠛⠻⢿⣿⠿⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⡀⣿⡽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠀⢸⣶⣾⣿⣿⣶⣤⣤⣽⣿⡏⠀⠀⠀⠀⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⠀⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠉⠉⠄⠉⠁⠉⢉⣉⢿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢿⣿⣿⣿⣿⣿⣿⡀⠀⢀⡠⠴⠆⠁⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢿⣿⣿⣿⣿⣿⡿⠟⠁⢶⣶⣶
⠀⠰⠟⠛⠋⠉⠁⠿⠋⢉⣉⣀⣀⡀⢰⣆⠀⠀⢸⣿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠘⠿⣿⣿⣿⡇⡰⠏⠚⠋⠁⠀⠀⠀⠀⢀⣸⢿⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠀⠀⠀⣼⣿⣿
⣠⣴⡆⠀⠀⠀⠀⠀⠀⢿⣟⣻⣿⣿⣿⣿⣦⠀⢸⡇⠀⠀⣠⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⣾⣿⣿⣿
⠇⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⣸⠁⠀⢾⣿⣿⡿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠛⠿⢿
⠃⠀⠹⣆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢟⣿⣷⡋⠀⠀⢸⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣿⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡿⢿⣿⣷⡀⠀⢸⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠋⠀⠸⣿⣿⣿⣦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣸⠀⠀⢀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠘⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣯⣲⡼
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡞⢻⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣠⣤⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠩⠿⣿⣿⣿⣷⠀⣴⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣠⣤⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⣨⣡⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⡿⠀⠀⠀⣤⣶⣶⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢂⠛⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡘⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣭⣭⣩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣦⣽⣷⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣷⡀⠀⠀⠘⠛⠛⢿⣿⡿⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⡀⣿⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡷⠀⠀⢸⣶⣾⣿⣿⣶⣤⣤⣽⣿⡟⠀⡀⠀⠀⠀
⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⠃⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠉⠉⠄⠙⡉⠉⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⡟⠈⢻⣿⣿⣿⣿⣿⣿⡅⠀⢀⣠⠴⠆⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠛⠷⢿⡿⣿⣿⣿⣿⡿⠟⠁⢶⣶⣶
⠀⠰⠟⠛⠋⠉⠁⠿⠋⠉⢩⣷⣶⣶⣤⣼⣷⠀⢸⣿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠛⠿⣿⣿⣿⡇⡰⠋⠙⠉⠁⠀⠀⠀⠀⢀⣸⢯⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠀⠀⠀⣼⣿⣿
⣠⠀⣀⠀⠀⠀⠀⠀⣶⡀⣀⣴⣦⣠⣬⣿⣿⣇⣸⡅⠀⠀⣠⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠁⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠰⢾⣿⣿⣿
⠇⢸⣏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠁⠀⢾⣿⣿⡿⠃⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢀⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠁⠀⠈⠙⠻⢿
⠃⠀⠹⣆⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⢉⣽⣿⣿⣿⡀⠀⢸⣿⡿⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⠁⠀⠀⠀⣿⣿⣿⣿⣧⣴⡿⠛⢿⣿⣿⣷⡀⢸⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠃⠀⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠹⣿⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣷⣄⣀⠀⠀⢀⣼⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣯⣲⡼
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣥⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣭⢟⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠈⠻⡿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣽⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣠⣄⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣏⠩⠿⣿⣿⣿⣷⠀⣾⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⣄⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣨⣱⣽⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⠟⠀⠀⠀⣠⣴⣶⣿⣶⣶⣦⣤⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢀⠻⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡊⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣭⣝⣛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣦⣽⣷⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣧⡀⠀⠀⠘⠛⠛⢿⣿⡿⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣄⡀⣿⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠀⠀⢸⣶⣦⣿⣿⣶⣤⣠⣼⣿⡏⠀⠀⠀⠀⠀
⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣧⡈⠁⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣷⣿⣿⣷⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣾⣿⠛⠈⠀⠌⠋⠉⠉⢉⣉⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⣿⣿⣿⣿⣄⠀⢀⣠⡴⠆⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠛⠷⢾⣿⣿⣿⣿⣿⡿⠿⠋⢴⣶⣶
⠀⠰⠟⠛⠋⠉⠁⣾⠉⢛⣋⣁⠀⠀⢀⠀⠀⠀⢸⣿⠿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⡷⠛⠑⠉⠀⠀⠀⠀⠀⢀⣸⢯⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠟⠁⠀⠀⣴⣿⣿
⡠⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡆⠀⠀⢼⡁⠀⠀⣠⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠐⢾⣿⣿⣿
⠇⠀⠀⠰⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⠀⠀⣾⣿⣿⡿⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠂⠈⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⠀⠃⠀⠀⢸⣿⡟⠁⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⢿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠈⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠋⠉⣿⣿⣷⣄⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣷⣄⣀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃⠀⠀⠹⣿⣿⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣟⣦⠾
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣦⣽⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣽⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡂⠀⣀⣠⣄⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣏⠭⢿⣿⣿⣿⣧⠀⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⢄⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣩⣱⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⢿⠏⠀⠀⠀⣠⣴⣶⣿⣷⣶⣶⣤⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢀⡻⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡊⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣯⣭⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣦⣽⣷⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣇⡀⠀⠀⠘⠛⠛⢿⣿⡿⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣀⠀⣿⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⢸⣶⣶⣿⣿⣶⣤⣠⣼⣿⡟⠀⠀⠀⠀⠀
⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⢠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣿⣿⣷⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣾⣿⠋⠉⠁⠄⠙⠛⠉⢉⡉⣩⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣿⡁⠀⢀⣠⢴⠆⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠛⠷⢾⡿⣿⣿⣿⣿⣿⠿⠋⢴⣶⣶
⠀⠰⠟⠛⠋⠉⠁⣾⠝⠛⠋⠁⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠚⢿⣿⣿⣿⣷⡿⠟⠙⠋⠁⠀⠀⠀⠀⢀⣼⢯⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠋⠁⠀⠀⣴⣿⣿
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣀⣶⣴⣶⠀⠀⣿⠁⠀⢀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⡿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠐⢾⣿⣿⣿
⠇⠀⠀⠀⣴⠆⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡿⠃⡿⠀⠀⣿⣿⣿⡟⠁⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣡⣀⣈⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠂⠀⠀⣀⠀⠀⠀⠀⢰⡿⣹⣿⣿⣿⣿⣿⣶⠶⠃⠀⠀⢿⣿⡟⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣿⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡏⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⣦⡀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣶⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁⢿⣿⣿⣿⣦⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⣺⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣝⣦⢿
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡆⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣴⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣦⡽⠟⢼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢈⣿⣿⣿⣿⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⠿⣵⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣵⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠂⠀⣀⣠⣤⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⣿⣯⠩⠿⢿⣿⣿⣷⠀⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣨⣁⣽⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⠃⠀⠀⠀⣠⣴⣶⣿⣷⣶⣶⣤⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⡿⢀⣛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⣷⣤⣭⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣆⠀⠀⠀⠘⠛⠛⢿⣿⡿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⡀⠀⣿⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⢸⣶⣾⣿⣿⣦⣤⣦⣼⣿⡟⠀⠀⠀⠀⠀
⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣟⣥⣿⣿⣿⠀⢸⣷⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠋⠉⠡⠌⠛⠁⠉⣍⡉⢙⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⢀⣠⢴⠖⠉⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠷⣿⡿⣿⣿⣿⣿⣿⠟⠋⠴⣶⣶
⠀⠰⠛⠛⠉⠉⠀⣾⠟⠛⠋⠁⠀⡀⠀⠀⠀⠀⣿⡿⠿⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠉⠛⠻⣿⣿⣿⡇⡰⠋⠓⠉⠀⠀⠀⠀⠀⠀⣸⢯⠉⠉⠛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠉⠀⠀⠀⣴⣿⣿
⣠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣤⣴⣿⣿⣧⣶⣴⣟⠀⠀⢀⣬⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢠⣾⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠐⢾⣿⣿⣿
⡇⠀⠀⠀⢠⠆⠀⠘⠛⢉⣽⣿⣿⣿⣿⣿⣷⣾⡏⠀⠰⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠃⠀⠀⣀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣧⣼⡅⠀⠀⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⢸⣿⣿⣷⣤⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠉⠀⠀⠙⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣕⣤⠿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣡⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣽⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣤⡿⠋⢆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⠿⣽⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣠⣤⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠈⣿⡿⢿⣿⣿⣿⣫⠿⣿⣿⣿⣿⠀⣴⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣒⣄⣽⣿⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⡿⠃⠀⠀⠀⣠⣴⣶⣿⣷⣶⣶⣤⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⢀⡛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⣷⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠘⠛⠻⢿⣿⡿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠙⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⡀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⢸⣶⣼⣿⣿⣦⣤⣦⣼⣿⡏⠀⠀⠀⠀⠀
⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣧⠀⢸⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠋⠉⠡⠌⠛⠁⢨⣭⡉⢙⣿⣿⣿⣿⣿⣿⡟⠀⠀⢻⣿⡿⣿⣿⣿⣿⡄⠀⢀⣠⣴⠖⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⠷⣾⡿⣿⣿⣿⣿⡿⠟⠋⠴⣶⣶
⠀⠠⠛⠛⠉⠉⠁⣾⠝⠛⠛⠁⠀⢠⣦⠀⠀⢠⣿⡿⠿⠿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡇⢰⠟⠟⠋⠁⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠉⠁⠀⠀⣴⣿⣿
⣠⠁⠀⠀⠀⠀⠀⠀⣴⡟⣻⣿⣿⣿⣿⣷⠀⢸⡏⠀⠀⣀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⢠⣾⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠐⢾⣿⣿⣿
⡇⠀⠀⠺⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣸⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠃⠀⠠⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⢋⣽⣿⣿⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣶⡿⠛⣿⣿⣧⡀⠀⣿⠇⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠏⠀⠀⠹⣿⣿⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⢀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣱⣼⠯
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⡿⠋⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⢿⡿⠃⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣯⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⣡⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡅⢀⣀⣠⣄⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣛⣽⣿⣿⣿⣿⠀⢰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣒⣄⣼⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⠁⠀⠀⠀⣠⣶⣶⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⢀⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣷⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣆⠀⠀⠀⠘⠛⠻⣿⣿⡿⢿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣆⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⢸⣶⣽⣿⣿⣦⣴⣦⣽⣿⡏⠀⠀⠀⠀⠀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣋⣷⣿⣿⡇⠀⢹⣿⣿⣿⣷⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀
⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠋⠉⠠⠌⣻⠀⢸⣭⡉⢙⣿⣿⣿⣿⣿⣿⠃⠀⠤⣿⣿⠿⢿⣿⣿⣿⡀⠀⠀⣀⡤⠖⠈⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠷⣾⡿⣿⣿⣿⣿⡿⠟⠋⠰⣶⣶
⠀⠠⠛⠛⠋⠉⠁⣾⡟⠿⠿⠿⠛⠿⣶⣿⣇⢸⣿⠿⠿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⡇⢠⠞⠛⠋⠁⠀⠀⠀⠀⠀⢸⢿⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⠋⠁⠀⠀⣴⣿⣿
⢠⣷⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⡃⠀⠀⣠⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠠⣶⣿⣿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠐⢾⣿⣿⣿
⣿⣿⡄⠀⠀⠀⢻⣷⣤⣄⣤⡄⠀⠀⣿⣿⣿⣿⠃⠀⢸⣿⣿⡿⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠃⠈⠻⣆⠀⠀⣾⣿⣿⣿⣟⣥⡄⠀⠘⣿⣿⣿⣧⠀⠸⣿⡿⠁⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠁⠀⠀⢻⣿⣿⣿⡿⠋⣠⡀⠀⠿⣿⣿⣿⣧⣀⣿⠃⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⢀⡄⠀⠘⣿⣿⣿⣴⡾⠋⠀⠀⠀⠈⠛⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣈⠁⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣼⢏
⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣥⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣡⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠆⢀⣀⣠⣄⣀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣛⣿⣿⣿⣿⣿⠀⢰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣒⣄⣨⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⠁⠀⠀⠀⢠⣶⣶⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡇⢀⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣦⣭⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣭⣽⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣿⣁⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣽⣿⣿⣦⣐⣤⣽⣿⡟⠀⠀⠀⠀⠀
⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣾⡄⠀⢹⣿⣿⣿⣷⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⡇⠀⠀
⠀⠀⢻⣿⣿⣿⡿⣿⣿⣿⣿⠋⠁⣠⠝⠛⠀⣼⣍⡉⣙⣿⣿⣿⣿⣿⣿⠁⠀⠀⣻⣿⣿⢿⣿⣿⣿⡄⠀⠀⣀⣤⡶⠊⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠛⢷⣾⡿⣿⣿⣿⣿⡿⠟⠋⠰⣶⣶
⠀⠀⠟⠛⠋⠉⠁⣾⣟⣿⣿⣀⣀⣀⠀⠀⠀⣹⣿⡿⠿⢿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⡇⢠⠞⠙⠊⠀⠀⠀⠀⠀⠀⣸⢟⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠋⠀⠀⠀⣴⣿⣿
⢀⣤⡤⠀⠀⠀⠀⠉⣿⣿⠿⣿⣿⣿⣷⡀⠀⣿⡁⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠠⣾⣿⣿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠐⢾⣿⣿⣿
⡟⣹⡁⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣧⡀⣿⠁⠀⣾⣿⣿⡟⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢏⡀⠀⣀⣀⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠃⠀⠀⠙⠻⢿
⠃⠈⢻⣆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣿⣧⠏⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠁⠘⣿⣿⣿⣦⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠀⠀⠀⠘⢿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣢⣾⣏
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣡⢄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⣿⣿⣿⣿⣿⣶⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣠⣀⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣛⣽⣿⣿⣿⣿⠀⢰⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣒⣄⣬⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⡿⠁⠀⠀⠀⢠⣦⣶⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣷⠀⢀⡿⠿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣤⣭⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⣿⣿⣿⣿⣿⣭⣭⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀
⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣷⣾⣿⣿⣶⣶⣿⣿⣿⣏⡁⠀⠀⣻⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣦⣽⣾⣿⣤⣀⣄⣹⣿⡟⠀⠀⠀⠀⠀
⠀⠀⢡⣻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣟⣩⣿⣧⠀⠀⢸⣿⣾⣿⣷⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠉⠁⣤⠻⠋⠀⣮⡉⠉⣙⣿⣿⣿⣿⣿⡟⠀⠀⠀⣻⣿⠿⢿⣿⣿⣿⡅⠀⠀⣀⣤⡔⠊⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⠿⣶⡿⢿⣿⣿⣿⣿⠿⠋⠰⢶⣶
⠀⠀⠞⠛⠋⠉⠁⣿⡻⠿⠟⠀⠉⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⡇⢠⠞⠛⠂⠀⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠀⠀⢠⣾⣿
⢀⠄⠀⠀⠀⠀⠀⠉⠀⢀⣶⣤⣿⣾⣿⣴⣶⡟⠀⠀⢀⣬⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⢶⣿⣿⣿
⣾⠀⠰⠏⠀⠀⢀⣤⠾⠿⣹⣿⣿⣿⣿⣯⣴⡿⠀⠰⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠏⠀⠀⠙⠻⢿
⠟⠀⢪⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣷⠆⠀⢿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⣾⣿⣿⣦⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣷⣄⣀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠉⠀⠈⢻⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣦⣿⢏
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⢿⣿⣿⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⠈⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣡⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⣿⣿⣿⣿⣿⣷⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⣤⣄⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣛⣽⣿⣿⣿⣿⠀⢰⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣖⣄⣨⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⡿⠁⠀⠀⠀⢠⣴⣶⣾⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣷⠀⢀⡾⠿⣿⣿⣿⣻⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣦⣭⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣯⣭⣿⡄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣯⡁⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣶⣽⣿⣿⣤⣀⣄⣹⣿⡟⠁⠀⠀⠀⠀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣷⣇⠀⠀⢸⣿⣾⣿⣷⣶⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⡇⠀⠀
⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣟⠉⠉⣤⠻⠃⠂⣮⡉⠉⣉⣿⣿⣿⣿⣿⠏⠀⠀⠀⣻⣿⡿⠿⣿⣿⣿⡅⠀⠀⣀⣤⡔⠊⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠿⣶⡿⢿⣿⣿⣿⣿⠿⠋⠰⢶⣶
⠀⠀⠘⠛⠋⠉⠁⣿⡻⠿⠟⠀⢁⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣧⠞⠛⠊⠁⠀⠀⠀⠀⠀⣸⢿⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠉⠀⠀⠀⢠⣾⣿
⠀⡌⠀⠀⠀⠀⠀⠉⢀⣰⣤⣤⣾⣿⣿⣶⣶⡟⠀⠀⢀⣬⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⢠⣾⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⢶⣿⣿⣿
⣼⡆⠀⢴⠇⠀⠀⠛⠋⢩⣽⣿⣿⣿⣿⣷⣾⡟⠀⠰⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠏⠀⠀⠙⠻⢿
⠟⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣼⡷⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⢿⣿⣦⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡟⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⣿⣿⣦⣀⠀⠀⠀⣠⣿⣿⣿⡿⠛⠁⠀⠀⠉⢿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⣲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣕⣤⡿⣏
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣿⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡽⠉⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠻⣿⡟⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣶⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣶⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣄⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡄⢰⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣗⣖⣨⣿⣿⣿⣷⣾⣿⣿⣿⣧⣾⣿⡿⠀⠀⠀⠀⠀⣴⣴⣾⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⠂⠀⣜⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣭⣽⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠟⠿⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⠁⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣦⣴⣾⣿⣥⣀⣤⣙⣿⣿⠃⠀⠀⠀⠀
⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⠀⠀⢸⣿⣾⣿⣿⣶⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣷⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣟⠉⢩⣤⣹⠏⢸⣿⣍⠉⣉⣿⣿⣿⣿⣿⠇⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣴⠚⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠛⢿⣵⡿⣿⣿⣿⣿⣿⡿⠛⠁⢶⣶
⠀⠀⠐⠋⠉⠉⠁⣿⡻⣿⣿⣷⣭⣤⣽⣧⢸⣿⣿⡿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⡇⢠⠾⠛⠊⠁⠀⠀⠀⠀⠀⢸⢟⠉⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡟⠉⠁⠀⠀⢠⣾⣿
⡄⡰⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⢺⣿⣿⣿⣟⠀⠀⢀⣬⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠲⣿⣿⣿
⣽⠇⠀⢀⠄⠀⣿⣦⣶⣿⣷⡿⣃⣼⣿⣿⣿⣿⠀⠐⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⡟⠀⠀⠈⠻⠿
⡿⠂⢀⣌⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣆⠀⢿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⠀⠀⠁⠀⠀⣿⣿⣿⣿⡟⢁⣴⠟⠙⢿⣿⣿⣿⣦⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠢⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣿⣦⣀⠀⠀⢸⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣴⡽⢃
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⠋⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣽⠟⢡⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⢀⣀⣤⣄⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⡗⣒⣨⣿⣿⣿⣷⣶⣿⣿⣿⣧⣾⣿⡿⠀⠀⠀⠀⠀⣴⣤⣾⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⠃⠀⣼⡻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠋⠀⢰⣿⣿⣿⣿⣿⣿⣭⣽⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀
⠈⠹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⢿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣿⠁⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⣤⣾⣿⣧⣀⣬⣙⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠐⣽⣿⣿⣿⣿⣿⣿⣆⡀⠀⢰⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⣯⣷⡇⠀⠀⠸⣿⣿⣿⣿⣶⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣷⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣉⢩⣤⡹⡏⢸⣿⣍⡉⣉⣿⣿⣿⣿⣿⠇⠀⠀⠀⣹⣿⣿⢿⣿⣿⣿⣇⠀⠀⢀⣠⣴⠚⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠛⢯⣽⣿⣿⣿⣿⣿⣿⣿⠟⠁⢴⣶
⡀⠀⠐⠋⠉⠉⢁⣿⡻⠿⣿⠿⠿⢶⣶⣿⣼⣿⣿⡿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⡇⢀⠾⠛⠊⠁⠀⠀⠀⠀⠀⢸⣟⠉⠋⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⡿⠏⠁⠀⠀⢀⣴⣿
⡆⣠⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣟⠀⠀⢀⣬⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠂⠀⣴⣿⣿⠇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄⠰⣾⣿⣿
⣵⠇⠀⠟⠁⢴⣤⢀⠀⢀⡀⠀⠀⠐⣿⣿⣿⣿⠀⠰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⠿⠀⠀⠈⠻⠿
⡿⠃⢰⣤⠀⢸⣿⣿⣷⣿⢇⡀⠀⠀⢹⣿⣿⣿⣆⠀⢿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠁⠀⢸⣿⣿⣿⣿⡿⢋⠀⠀⠘⣿⣿⣿⣿⣦⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⣿⠉⠉⠉⢉⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣆⠀⠀⠀⠈⣿⣿⣿⣏⣴⡿⠁⠀⠀⠀⠉⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⣿⣿⣦⣀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣴⡽⣣
⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣥⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠟⢤⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣶⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣶⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣄⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣗⣒⢀⣿⣿⣿⣷⣴⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⣠⣤⣶⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⠁⠀⣸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣿⣿⣿⣿⣿⣿⣭⣭⣯⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣟⠁⠀⠀⢸⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣤⣶⣿⣯⣀⣩⣉⣿⣿⡏⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣗⠀⠀⠀⢰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣼⡆⠀⠀⠸⣿⣿⣿⣿⣷⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⠆⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡋⠙⣩⣴⠹⠋⢸⣶⣍⡉⣉⣿⣿⣿⣿⣿⠃⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⡧⠀⠀⢀⣠⣴⠚⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠙⠻⢿⣭⣿⣿⣿⣿⣿⡿⣿⠿⠋⠰⣶
⠄⠀⠀⠚⠉⠉⢩⣟⠻⠿⠟⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉⠚⠻⢿⣿⣿⡇⢀⠴⠋⠓⠈⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⠛⠁⠀⠀⠀⣴⣿
⣦⢠⠅⠀⠀⠀⠘⠋⠁⠀⣤⣄⣤⣤⠀⣀⣸⠏⠀⠀⢀⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠰⣾⣿⣿
⣧⣿⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⠟⣹⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢿⠃⠀⠈⠛⠿
⣿⠏⢳⡄⠀⠀⠀⠰⡿⢹⣿⣿⣿⣿⣿⡿⢻⠁⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢉⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣇⠀⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢻⣿⣿⣦⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣾⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⣿⣿⣧⣛⠀⠀⠀⢀⣼⣿⣿⣿⣿⠗⠸⢿⣿⣿⣿⣾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣱⣼⡿⣣
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣟⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠟⢄⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢈⣿⣿⣿⣿⠃⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡧⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣶⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⣶⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣤⣄⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣗⣒⣀⣿⣿⣿⣷⣴⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⢠⣤⣶⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⠇⠀⣸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣭⣭⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⠁⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣤⣶⣿⣯⣉⢩⣉⣻⣿⡟⠁⠀⠀⠀
⠀⠀⠀⣞⣿⣿⣿⣿⣿⡛⠀⠀⠀⢰⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣯⣼⡆⠀⠀⠈⣿⣷⣿⣿⣷⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣺⡆⢀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠛⢋⣼⠹⠋⢸⣶⣍⡉⣉⣿⣿⣿⣿⣿⠇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⡴⠒⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⠻⠿⣯⣽⣿⣿⣿⣿⣯⢼⡿⠋⠰⢾
⠄⠀⠀⠚⠉⠉⢹⣟⠻⠿⠏⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⡇⢀⠴⠛⠓⠁⠀⠀⠀⠀⠀⢸⣟⠉⠛⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢿⣿⠟⠁⠀⠀⠀⢠⣾
⣦⢀⠆⠀⠀⠀⠘⠉⠀⠀⢰⣄⣶⣶⣄⣠⣼⡏⠀⠀⢀⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠀⢶⣿⣿
⣯⣿⡀⠀⠀⠀⢀⣠⣼⡿⣿⣿⣿⣿⣿⣟⣽⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢻⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢿⠏⠀⠀⠛⠿
⣿⠟⢳⡄⠀⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣹⡅⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⣷⡀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⣿⣿⣿⣦⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣾⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠
⣿⣿⣷⣌⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⠀⠙⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣵⣼⡿⣡
⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⠟⠄⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⣷⣿⣿⣿⣷⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⣀⣀⣤⣄⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⣗⣒⣠⣿⣿⣿⣶⣴⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⠆⠀⣰⡿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣯⣭⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡉⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣦⣴⣿⣿⣉⢉⣉⣻⣿⡿⠁⠀⠀⠀
⠀⠀⠀⢘⣿⣿⣿⣿⣿⡖⠀⠀⠀⢠⣿⣟⢙⣿⣿⣿⣿⣿⣿⣿⣫⣴⣇⠀⠀⠀⣿⣿⣿⣿⣿⣯⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣰⡶⢠
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡋⠋⢡⡌⠽⠃⠀⣷⣮⡉⣉⣹⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣤⠒⠛⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠛⠿⣯⣽⣿⣿⣿⣿⣿⡼⡿⠛⠁⢾
⠀⠀⠀⠘⠉⠉⢹⣟⠻⠿⠃⠀⠁⢠⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⡿⠀⡴⠛⠃⠉⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢾⣿⡟⠉⠀⠀⠀⢠⣼
⣶⠀⣄⠀⠀⠀⠘⠉⢰⣾⠛⣻⣿⣿⣿⣧⢰⡟⠁⠀⢀⣨⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⣠⠀⢴⣾⣿
⣏⣿⠿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⢯⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢿⡿⠀⠀⠙⠿
⢿⠿⢨⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀
⣾⡄⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣠⣿⣿⣿⣿⣧⡀⣻⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠁⠀⠙⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠
⣿⣿⣷⣄⠀⠀⠀⣰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣼⡿⣡
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣿⣿⣦⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠙⢿⡿⠉⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⢠⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣴⣶⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡆⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⣗⣒⣲⣿⣿⣿⣷⣼⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⡆⠀⢰⣟⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣾⣿⣿⣿⡿⢿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣯⣭⣽⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀
⠀⠈⢻⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡋⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣦⣴⣾⣿⣍⡉⣍⣻⣿⣿⠋⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡀⠀⠀⢠⣿⡟⢙⣿⣿⣿⣿⣿⣿⡿⣋⣵⣧⠀⠀⠀⢿⣿⣿⣿⣿⣮⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣐⣶⢠
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡯⢏⣥⡎⠽⢁⠀⣿⣦⣉⣉⣹⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⡿⠀⠀⢀⣠⣤⠒⠛⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⠿⣿⣭⣿⣿⣿⣿⣿⣡⣿⠟⠁⢼
⠆⠀⠀⠘⠉⠉⢹⣛⠻⠿⣷⡾⠷⣶⣶⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⢀⡴⠟⠃⠉⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢾⣿⡿⠁⠀⠀⠀⠀⣼
⣾⠀⡤⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠁⠀⢀⣨⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣤⣠⡄⠰⣾⣿
⡿⣾⠃⡾⠀⠀⠈⣿⣧⣶⣿⣷⡿⣓⣿⣿⣿⣿⡄⠠⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣿⡿⠁⠀⠙⠿
⢿⡿⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠹⣿⣿⣿⣷⠀⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀
⣺⡆⠀⠁⠀⠀⠀⣿⣿⣿⣿⠟⢁⣴⠞⠻⣿⣿⣿⣷⣽⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣾⠟⠁⠀⠀⠈⠙⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠢⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⣀⣀⣠
⣿⣿⣷⣄⠀⠀⢀⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣼⡿⣡
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⣿⣿⠛⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣠⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣦⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⡆⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⣗⣒⣠⣿⣿⣿⣾⣴⣿⣿⣿⣧⣼⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡆⠀⢠⣿⣛⣿⣿⣿⣟⣿⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣭⣭⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠿⡿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡋⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣴⣶⣿⣯⣁⢉⢙⣿⣿⡟⠁⠀⠀
⠀⠀⠀⢰⣻⣿⣿⣿⣿⣶⣀⣀⣀⢀⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⢛⣠⣧⠀⠀⠀⢹⣿⣿⣿⣿⣷⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣲⣶
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢡⣴⡖⠿⠁⠀⣿⣦⣍⢉⣡⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⠁⠀⠀⣠⣤⡖⠋⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⠿⣿⣭⣽⣿⣿⣿⣿⡅⢼⡿⠋⢸
⠦⠀⠀⠀⠉⠉⢹⣏⢛⣿⣷⣦⣄⣠⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠀⡴⠛⠃⠉⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⡿⠋⠀⠀⠀⠀⢸
⣶⡄⡴⠀⠀⠀⠈⢁⡈⠉⠉⢻⣿⣿⣿⡆⠀⣟⠁⠀⠀⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣀⡄⠠⣴⣿
⣟⣼⠇⢠⠖⠀⠀⢸⣿⣦⣶⣿⣿⣿⣿⣿⣴⡿⠀⠠⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣯⣀⣀⢿⣿⢃⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣿⣿⠇⠀⠈⢻
⣿⡿⢂⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣺⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⠋⠀⠀⠀⠈
⣸⣦⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⢟⣩⣿⢿⣿⣷⣄⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢉⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠁⠈⠻⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⣀⣀⣤
⣿⣿⣿⣦⠀⠀⠀⣸⣿⣿⣿⣿⡅⠀⠀⠀⠀⠹⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣢⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡈⠛⠻⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠺⣿⣿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣤⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣶⣿⣿⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡗⢀⣀⣤⣄⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⡆⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣗⣒⣠⣿⣿⣿⣶⣴⣿⣿⣿⣧⣼⣿⡿⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡆⠀⢀⣾⣛⣻⣿⣿⣿⣻⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣯⣭⡧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡋⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣤⣶⣿⣯⣅⢉⣉⣿⣿⡟⠁⠀⠀
⠀⠀⠀⢠⣸⣿⣿⣿⣻⣶⣄⣀⣀⠀⣿⡟⢉⣿⣿⣿⣿⣿⣿⣿⢋⣡⣇⠀⠀⠀⢸⣿⣿⣿⣿⣷⣭⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⣶
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡗⠁⣴⡶⠽⠁⠀⣿⣦⣉⢉⣡⣾⣿⣿⣿⡟⠀⠰⡄⢠⣿⣿⣿⡿⣿⣿⣿⠅⠀⠀⣀⣤⡒⠋⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⠿⢿⣯⣽⣿⣿⣿⣿⡏⢸⡿⠋⢸
⠂⠀⠀⠀⠉⠉⢹⣍⠙⠛⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⠀⡰⠟⠃⠈⠀⠀⠀⠀⠀⢸⣟⠋⠛⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣿⣿⠋⠀⠀⠀⠀⢸
⣶⡄⣰⢀⠀⠀⠈⠁⠀⣀⣰⣆⣰⣶⡶⢆⣠⡟⠁⠀⢀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣠⣄⣠⠀⢴⣿
⣿⣽⡿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢻⣏⠀⢰⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⢯⣀⣀⢿⣿⢋⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣽⣿⠏⠀⠈⢻
⡿⡿⢧⣄⠀⠀⠀⠀⠿⢡⣿⣿⣿⣿⣿⣿⢿⠟⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⠏⠀⠀⠀⠘
⣰⣦⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⣆⡀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠂⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣀⡤
⣿⣿⣿⣦⡀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠀⣿⣿⣿⣿⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠆⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣄⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠋⢄⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢘⣿⣿⣿⡿⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣷⣶⣯⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠈⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣶⣿⣿⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣄⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⡄⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⡗⣒⣈⣿⣿⣷⣧⣼⣿⣿⣿⣧⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣦⣄⣠⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⡆⠀⠀⣼⣟⣛⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀
⢿⣿⣿⣿⣻⣿⣿⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⢿⣿⣷⣾⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣭⣽⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⡟⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣦⣰⣾⣿⣉⠉⡉⢻⣿⣿⠃⠀⠀
⠀⠀⠀⠠⣿⣿⣿⣿⣻⣿⣤⣄⣀⠀⣾⣿⢉⣿⣿⣿⣿⣿⣿⣿⣛⣡⣇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⢀⣶
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣗⠂⣤⡶⠽⠃⠀⣿⣦⣉⢉⣡⣾⣿⣿⣿⡟⠀⠀⢠⣤⣿⣿⣿⠿⢿⣿⣿⠃⠀⠀⢀⣠⣴⡚⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⢿⠿⣿⣭⣿⣿⣿⣿⡏⠀⣺⠟⢻
⡷⠀⠀⠀⠉⠉⢹⣇⠉⠛⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⠀⠀⠞⠋⠀⠁⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣾⣿⠏⠀⠀⠀⠀⢸
⣶⡄⣠⠀⠀⠀⠈⠁⠀⣀⣰⣧⣀⣿⣶⣿⣷⣿⡅⠀⢀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⡀⢀⠀⢠⣾
⣿⣱⡏⠀⠀⠀⠀⠰⠾⠿⣟⣿⣿⣿⣿⣿⣿⣿⡶⢰⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢏⡀⠀⣀⣈⢉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢹
⡿⡿⢧⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣁⣤⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⡟⠀⠀⠀⠘
⣁⣷⡀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⢻⣿⣿⣦⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⣀⣀⡤
⣿⣿⣿⣧⡀⠀⢀⣤⣾⣿⣿⣿⠿⠛⠁⠘⢻⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣢⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠋⠄⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣗⣶⣯⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢇⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣾⣿⣿⣿⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣤⣄⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⣛⣿⣿⣿⣿⡀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⡗⡒⣸⣿⣿⣿⣧⣾⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⡆⠀⠀⣼⣟⣛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀
⢿⣿⣿⣿⣻⣿⣿⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⢿⣿⣷⣾⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣯⣭⣽⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡟⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣤⣰⣾⣿⣉⠉⣉⢻⣿⣿⠋⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣧⣄⣀⠀⣾⣿⢋⣿⣿⣿⣿⣿⣿⡿⣛⣤⣇⠀⠀⠀⠈⣿⣿⣿⣿⣷⣮⣽⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠀⣶
⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠂⢤⡶⠽⠃⠀⣿⣦⡉⣉⣡⣶⣿⣿⣿⡟⠀⠀⠀⢀⣿⣿⣿⡿⢿⣿⣿⡏⠀⠀⢀⣠⣴⡚⠛⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⠿⣿⣭⣿⣿⣿⣿⡏⠀⢻⠟⢻
⡗⠀⠀⠀⠉⠉⢹⣏⠉⠛⠛⠉⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⠀⠀⠴⠛⠁⠁⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣿⠟⠀⠀⠀⠀⢸
⣿⡆⣠⠀⠀⠀⠈⠁⢠⣶⣶⣦⣤⣾⣿⣷⣴⡿⠁⠀⢀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⡀⢀⡀⢠⣾
⣿⣱⡟⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⡷⠀⢰⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢏⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣾⣿⡿⠁⠀⢹
⡿⡿⢧⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣿⣅⡀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣿⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⡿⠁⠀⠀⠘
⣃⣷⡀⠇⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣷⣾⣿⣿⡀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣧⣡⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⣿⣿⣿⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⡤
⣿⣿⣿⣧⡀⠀⢀⣤⣿⣿⣿⣿⠿⠋⠀⠀⠙⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣲⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣽⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡿⠛⢄⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢾⣿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⣇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣟⣷⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣴⣼⣿⣿⣿⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣠⣤⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⡀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡧⡀⣝⣿⣿⣯⣧⣿⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣦⣤⣤⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⡆⠀⠀⢠⣿⣛⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⠀
⢿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣿⣿⣧⣭⣭⣿⣿⡿⢿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣍⣙⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣽⠁⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣀⣮⣿⣏⠉⢉⠛⣿⣿⠏⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⣴⣿⢛⣿⣿⣿⣿⣿⣿⡿⣋⣵⣇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣭⣽⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢰
⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠈⢥⡴⠹⠃⠀⣿⣦⣉⣉⣥⣾⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣤⣶⠛⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠐⢿⠿⣿⣫⣽⣿⣿⣿⣿⠁⢘⠿⢻
⣿⠀⠀⠀⠉⠉⢹⣇⠙⠛⠋⣀⣀⣀⣀⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡇⠀⠀⠊⠁⠀⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣿⡿⠁⠀⠀⠀⢸
⣿⡧⢠⠇⠀⠀⢈⣉⠀⠀⠘⠛⠛⠛⢻⣿⣿⡟⠁⠀⠀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⢀⠀⡀⠀⣼
⣿⣣⡟⠀⠀⠀⠘⣿⣧⣾⣿⣶⡿⢀⣾⣿⣿⣷⡀⢰⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣈⣉⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣶⣿⣿⠃⠀⢸
⡿⣿⢷⠀⠀⠀⢰⣿⣿⣿⣿⣿⡾⠋⠹⣿⣿⣿⡇⠘⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⣸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⡿⠃⠀⠀⠘
⣇⣷⡌⠃⠀⠀⢸⣿⣿⣿⡿⠋⢀⣴⠾⣿⣿⣿⣿⡄⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⣿⣿⣷⠀⠀⠀⠈⣿⣿⣿⣿⣾⠟⠁⠀⠉⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣀⣠⣤
⣿⣿⣿⣷⡀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣰⣼⠿⣡
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣥⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣽⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡈⡿⠛⢧⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣼⣿⣿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣠⣤⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡀⠀⠈⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡇⡀⣘⣿⣿⣯⣧⣿⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣄⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⡄⠀⠀⢀⣿⣛⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣬⣭⣿⣿⡿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣍⣙⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡟⣻⠃⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣄⣾⣿⣏⡉⢉⠙⣿⣿⡟⠁⠀
⠀⠀⠀⠐⣾⣿⣿⣿⣟⣷⣖⣀⣀⠀⢸⣾⠛⣿⣿⣿⣿⣿⣿⣿⣃⣽⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣏⣽⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢰
⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠍⢉⡴⠨⠋⢠⣷⣄⣉⣉⣠⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣀⣤⣶⠛⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠐⢻⡿⢿⣫⣽⣿⣿⣿⣿⠁⠐⠿⢻
⢿⡂⠀⠀⠉⠉⢹⣏⠙⠛⠛⣀⣀⣀⢀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⠀⠀⠊⠉⠀⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣿⡿⠁⠀⠀⠀⢸
⣿⡧⢠⠇⠀⠀⠚⠉⠀⠀⠿⠛⠛⢻⣿⣿⣾⡟⠁⠀⢀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⡀⠀⣼
⣿⣣⣿⠁⠀⠀⣿⣦⣀⠀⣀⠀⠀⠠⣿⣿⣿⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣶⣿⣿⠇⠀⢸
⣿⢿⢿⡀⠀⠀⣿⣿⣿⣿⢟⣡⡀⠀⢿⣿⣿⣇⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⠋⠀⠀⠀
⣇⣲⡄⠃⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⡆⠀⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀
⣿⣿⣿⡀⠀⠀⢹⣿⣿⣿⣡⣾⠟⠀⠈⠿⣿⣿⣿⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⢀⣠⡤
⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣴⣾⠿⢁
⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣦⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⣿⣿⡻⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢼⣿⣿⠟⠁⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣾⣿⣿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀⣠⣤⣀⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣶⡄⠀⠈⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⡀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⡇⡀⣜⣿⣿⣯⣧⣿⣿⣿⣿⣧⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣤⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣶⠀⠀⠀⠀⣼⣟⣛⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⣭⣿⣿⡿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣯⣙⣛⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣹⠏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠸⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣄⣲⣿⣿⡉⠉⡙⢿⣿⡿⠃⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣻⣶⣂⣀⠀⢀⣾⣻⣿⣿⣿⣿⣿⣿⢟⣡⣼⡝⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣩⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠
⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡗⠉⣡⠌⠟⢸⣷⣤⣀⣠⣼⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⢀⣠⣴⠟⠋⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠐⢺⡿⠿⣟⣭⣿⣿⣿⡿⠁⠀⠻⢿
⢿⡇⠀⠀⠈⠁⢰⣧⣈⠛⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⡇⠀⠀⠐⠉⠀⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣿⠇⠀⠀⠀⢠
⣿⣿⢠⡇⠀⠀⠘⠋⠁⠀⣠⡀⠀⠀⠀⠀⣸⠏⠀⠀⢈⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⢀⠀⣼
⣿⣇⣿⠗⠀⠀⠀⠀⣤⣤⣿⣷⣶⣶⣠⣤⣿⠁⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢃⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣴⣯⣾⡟⠀⠘
⣿⠿⢿⣀⠀⠀⠀⢾⡟⣻⣿⣿⣿⣿⣟⣁⣟⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀
⣇⣻⡄⠋⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣋⡉⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣤⢀⣠⡤
⣿⣿⣿⣷⡄⠀⠀⢀⣾⣿⣿⣿⣿⢫⣿⣿⣿⣤⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣰⣾⠿⢁
⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⠁⠀⠛⢿⣿⣿⣿⣷⣦⣄⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡘⣽⠟⠳⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣾⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣴⣼⣿⣿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⣤⣄⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣶⣄⠀⠈⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⠀⢰⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡓⡀⣹⣿⣿⣿⣧⣿⣿⣿⣿⣦⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣤⣤⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣦⠀⠀⠀⠀⣼⣟⣛⣿⣿⣿⡿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣧⣼⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣙⣻⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣋⣿⡏⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣽⣿⣉⠉⡙⠻⣿⣿⠋⠀
⠀⠀⠀⠀⣬⣿⣿⣿⣿⣻⣷⣆⣀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢟⣠⣾⡹⠃⠀⠀⠀⢸⣿⣿⣿⣿⣯⣭⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠈⣉⡆⠍⢹⣷⣄⣀⣠⣾⣿⣿⣿⡿⠁⠐⠶⣶⣶⣸⣿⣿⣿⡿⢿⣿⣿⠃⠀⠀⠀⣠⣴⠞⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠐⢺⡿⠿⣟⣭⣿⣿⣿⣿⠉⠀⠠⢿
⢻⡂⠀⠀⠈⠀⢸⣿⣄⠙⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠋⠁⠀⠀⠀⠀⣸⢟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣿⣷⣿⣿⠏⠀⠀⠀⢸
⣿⣿⢠⡇⠀⠀⠘⠋⠁⠀⣄⠀⠀⠀⠀⠀⣾⠋⠀⠀⣈⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢀⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⢀⠀⢼
⣿⣧⣿⠃⠀⠀⠀⣀⣤⣤⣿⣿⣿⣷⣴⣶⣿⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣤⣮⣾⡿⠀⠘
⣿⠿⢿⡀⠀⠀⠙⠉⠉⣽⣿⣿⣿⣿⣯⣶⡿⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀
⣇⣺⡄⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣭⡤⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢿⣿⣦⡀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⢀⣠⡤
⣿⣿⣿⣷⡄⠀⠀⢀⣾⣿⣿⣿⣿⠃⢸⣿⣿⣷⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⣾⠿⢁
⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠛⠁⠀⠈⠛⣿⣿⣿⣿⣾⣦⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣽⣿⣄⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣴⣾⣿⣿⣷⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⣤⣤⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣷⠀⣰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡁⡂⣹⣿⣿⣿⣤⣿⣿⣿⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣀⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡆⠀⠀⠀⠀⢰⣿⣛⣿⣿⣿⣿⣿⣿⡏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣾⣿⣿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣥⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣛⣻⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣏⣿⡟⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣮⣿⣏⡉⢉⠛⣿⣿⠟⠀
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⣿⣦⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣋⣴⣿⠹⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣭⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠊⢀⠤⠉⣿⣦⣄⣀⣤⣴⣿⣿⣿⡿⠀⠀⠀⣰⣦⣤⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣤⠶⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠲⣿⠿⣿⣫⣿⣿⣿⣿⠋⠀⠘⠽
⢻⡅⠀⠀⠈⠉⢰⣿⣦⡉⠛⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⢟⠙⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢿⣿⣾⣿⡟⠀⠀⠀⢠
⣾⣿⢀⠇⠀⠀⠘⠋⣡⣤⣶⣦⣴⣿⡄⠀⡿⠋⠀⠀⣙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢀⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠁⠀⠀⠀⢸
⣿⣏⣿⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣤⣿⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⣠⣾⣵⡿⠁⠈
⣿⢻⠟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⡿⠁⠀⠀
⣇⣺⡆⠃⠀⠀⠀⢸⣿⣿⣿⡟⢁⣴⣿⣿⣿⡄⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀
⣿⣿⣿⣄⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠁⢿⣿⣿⣆⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⣠⡤
⣿⣿⣿⣿⣄⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠘⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣢⣾⡿⣁
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⡽⠟⢤⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⣿⣷⣿⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣴⣿⣿⣿⣷⣶⣴⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣠⣄⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣿⣧⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣆⠀⢹⠡⠀⣽⣿⣿⣽⣭⣿⣿⣿⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣤⣀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⡄⠀⠀⠀⠀⢰⣿⣛⣿⣿⣿⣿⣿⣿⡿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣵⡶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣛⣻⡃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣿⡿⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣾⣿⣏⡉⢉⠛⢿⣿⠟⠁
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⣿⣶⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣉⣴⣿⠙⠃⠀⠀⠀⠘⣿⣿⣿⣿⣯⣍⣿⣿⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠱⠘⣿⣤⣄⣠⣴⣾⣿⣿⣿⡟⠀⠐⠲⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣠⠴⠞⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠒⣿⠿⢿⣫⣽⣿⣿⣿⠏⠀⠐⢼
⢿⡁⠀⠀⠈⠉⢁⣿⣯⡙⠛⣋⣁⠀⣠⡀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⢟⠛⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢿⣿⣾⣿⡿⠀⠀⠀⢀
⣾⣿⢠⡇⠀⠀⠘⠋⠉⠀⠛⠋⠛⢻⣿⣷⡿⠉⠀⠀⣙⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢠⣴⣿⣿⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠁⠀⠀⡀⢸
⣿⣏⣿⠀⠀⠰⣿⣦⣤⣤⣤⠄⠀⠀⣿⣿⣿⡄⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣾⣵⣾⠁⠀
⣿⢻⠟⠀⠀⢰⣿⣿⣿⣿⣿⡶⠂⠀⢿⣿⣿⣇⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀
⣇⣸⡆⠂⠀⢸⣿⣿⣿⣿⠋⢀⣤⠀⢾⣿⣿⣿⡄⢹⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀
⣿⣿⣿⡀⠀⠘⣿⣿⣿⣧⣶⡟⠁⠀⠘⠻⣿⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⣠⣤
⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣾⡿⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣽⠟⢤⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⢧⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⣿⣿⣿⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣧⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⠡⠀⣻⣿⣿⣽⣭⣿⣿⣿⣿⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣤⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⡄⠀⠀⠀⠀⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⡿⠂⠀⠀⣾⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣩⣿⡿⠁⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣶⣿⣿⡉⠉⡙⢻⣿⡿⠁
⠀⠀⠀⠀⣴⣼⣿⣿⣿⣿⣿⣦⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣛⣴⣯⠋⠁⠀⠀⠀⠘⣿⣿⣿⣿⣯⣙⣿⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠉⡠⠛⣿⣦⣈⣁⣴⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠⠴⠶⠊⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⡿⢿⣿⣭⣿⣿⣿⡟⠀⠀⠲
⢿⠆⠀⠀⠈⠉⢉⣿⣏⠙⠿⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⠛⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣿⡿⠀⠀⠀⠀
⣾⣿⢀⡆⠀⠀⠸⣟⣿⣷⣶⣤⣤⡄⠀⠀⡿⠁⠀⠀⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠀⢠⣴⣿⡿⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⡀⢠
⣿⣏⣾⠀⠀⠀⠘⣿⣄⣉⣿⣿⣿⣿⡀⢠⡇⠀⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣔⣷⣾⠃⠀
⣿⢿⢿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢸⠇⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀
⣟⣺⣎⠋⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⣿⣏⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢹⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿⣿⣷⣾⠿⣿⣿⣧⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠺⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡄⣀⣤
⣿⣿⣿⣿⣄⠀⠀⣾⣿⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣰⣾⡿⢏
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣵⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣭⠟⢠⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⢧⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣴⣿⣿⣿⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣄⠀⠘⣿⣿⣿⣿⣿⡿⢟⣻⣿⣿⣿⣧⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⢡⠀⣹⣿⣿⣽⣭⣿⣿⣿⣿⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣄⣀⡀⠀⠀⠀
⣿⣟⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣦⠀⢀⣀⠀⠀⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⡛⠻⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠿⣹⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣶⣿⣿⣉⠉⡙⢻⣿⡿⠃
⠀⠀⠀⠀⣦⣾⣿⣿⣿⡿⣿⣶⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣣⣼⡏⢁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣻⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠉⣠⠛⣷⣄⣈⣠⣤⣿⣿⣿⣿⠇⠀⠓⠂⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠⠴⠶⠚⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⡿⢿⣯⣭⣿⣿⣿⡟⠀⠀⠳
⢿⡆⠀⠀⠈⠉⠉⣿⣏⡛⠿⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠛⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣶⣿⣿⠁⠀⠀⠀
⣾⣿⢀⡆⠀⠀⠸⠟⠋⢀⡀⢀⠀⠀⠀⢀⡟⠁⠀⢀⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⠀⢠⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⡀⢠
⣿⣏⣾⠁⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣀⣬⡇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣈⢿⣿⢃⡀⠀⣀⣈⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣖⣷⣾⠃⠀
⣿⢻⢿⣆⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣟⣹⡁⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀
⣿⣸⣆⠋⠀⠀⠀⠘⢣⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠋⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡃⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣦⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⡄⣀⣤
⣿⣿⣿⣿⣄⠀⠀⢠⣿⣿⣿⣿⣿⢋⣿⣿⣷⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢲⡟⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣔⣾⡿⢏
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠛⠁⠀⠙⣿⣿⣿⣿⣿⣶⠀⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⠟⢠⡘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣯⣾⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣷⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣀⣀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣇⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢫⢥⠬⢿⣿⣿⣽⣭⣿⣿⣿⣿⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣦⣤⣄⣀⠀⠀⠀
⣿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣿⠇⠀⢀⣾⡟⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⣿⣷⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⡛⠻⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠻⢿⠁⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣅⠬⡍⣻⣿⡿⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⣿⡇⢠⣾⡀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣻⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠉⣀⠘⣷⣤⣀⣤⣾⣿⣿⣿⣿⠃⠀⠙⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢠⠴⠶⠚⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⡿⢿⣯⣽⣿⣿⣿⡟⠀⠀⠵
⢿⣆⠀⠀⠈⠁⠀⣿⣿⡛⠿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣿⡿⠀⠀⠀⠀
⣾⣿⢀⡬⠀⠀⠠⠟⠛⢡⣀⢰⣦⣤⡄⣠⡟⠁⠀⢈⣻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠁⠀⠀⡀⢠
⣿⣏⣾⡿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢃⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣾⣷⣿⠃⠀
⣿⢻⢿⣇⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠉⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⡿⠃⠀⠀
⣿⣸⣆⠙⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠈⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀
⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⢫⣿⣿⣦⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡄⣀⣤
⣿⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⣿⠿⠀⠘⢻⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠀⠛⢂⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣮⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⢾⣿⣧⣜
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⣿⠟⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣴⣿⣿⣿⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⢿⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣇⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⣀⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢫⢥⠬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣦⣤⣄⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣾⣿⣿⠏⠀⢀⣾⡻⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⡛⠻⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣷⣿⣿⣿⣷⣿⣿⡿⢏⠀⠈⠉⠁⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣶⣾⣿⣄⣤⣍⣹⣿⡿⠁
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡆⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣥⣿⡇⢤⡾⠀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣻⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀
⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠘⣧⣄⣀⣴⣴⣿⣿⣿⣿⠃⠀⠁⠰⣿⣾⣦⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⡤⠶⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠒⠲⣿⡟⢻⣭⣿⢿⣿⣿⡏⠀⠀⠿
⢯⣇⠀⠀⠀⠁⠀⣿⣿⡛⠿⠟⢃⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣿⡿⠀⠀⠀⠀
⣼⣿⢀⡬⠀⠀⠀⢿⣿⣿⣶⣶⣾⣿⣆⢠⡟⠁⠀⢈⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⡀⢠
⣿⡟⣾⠟⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣾⡆⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣧⣀⣀⢿⣿⢃⡀⠀⣀⣈⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢠⣾⣷⣿⠁⠀
⣿⢿⢿⣧⡀⠀⠀⢠⣿⣿⣿⣿⣿⠿⣿⣿⣇⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀
⣿⣸⣆⠙⠁⠀⠀⢸⣿⣿⣿⣿⣁⣴⣿⣿⣿⣆⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢩⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀
⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠊⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⣀⣠
⣿⣿⣿⣿⣄⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠻⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠀⠛⢂⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢕⣦⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡏⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⣿⣧⡔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠺⣿⡿⠋⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢸⣿⣷⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣬⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣤⡀⠸⣿⣿⣿⣿⣿⡿⣛⣿⣿⣿⣿⡆⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡇⠀⠀⣀⣠⣤⣤⠄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢯⠴⢮⣿⣿⣿⣭⣿⣿⣿⣿⣷⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⡿⠀⢀⣾⣛⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡿⠛⠿⢿⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣏⠀⠀⢀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⣮⣽⣿⣿⣤⣐⣄⣹⣿⡟⠁
⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣖⡀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣵⣿⡆⢾⡿⠀⠀⠀⠀⣿⣿⣿⣿⣯⣙⣿⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡀
⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠒⢂⣸⣦⣉⣉⣠⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡤⠶⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⡟⣿⣷⣾⠿⣿⣿⠏⠀⢘⠟
⠽⣣⠀⠀⠀⠀⠀⣸⣿⣛⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡟⠀⠀⠀⠀
⣴⣿⠀⡼⠀⠀⠀⠿⠟⠋⠁⠀⠀⠹⣿⣿⣏⠁⠀⢈⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠀⡀⢀⠀⢠
⣿⣟⣾⠃⠰⣶⣀⡀⢀⡀⠀⠀⠀⠀⣿⣿⣿⡆⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢰⣿⣾⡿⠀⠀
⣿⢿⣿⠀⢀⣿⣿⣿⡿⣃⣄⠀⠀⠀⢹⣿⣿⣧⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀
⣿⣸⣦⠇⢸⣿⣿⣿⣿⠟⢁⠀⠀⠀⢺⣿⣿⣿⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀
⣿⣿⣿⡇⠘⣿⣿⣿⣏⣴⠟⠀⠀⠀⠀⠙⢻⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣤
⣿⣿⣿⣿⣄⣸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠛⢂⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢕⣦⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡿⠁⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣼⡿⢣⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢨⣠⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣰⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣿⣿⣿⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣄⠀⠸⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⡆⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⢀⣀⣤⣤⣤⠄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⢯⠄⣬⣿⣿⣿⣭⣿⣿⣿⣿⣧⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣤⣤⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⡟⠀⢀⣾⡛⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣉⠀⠀⣀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣽⣿⣿⣤⣀⣄⣹⣿⠟⠀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⠿⠀⠀⠀⠀⣿⣿⣿⣿⣯⣙⣿⣿⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⢰⣌⣉⣉⣭⣿⣿⣿⣿⡿⠀⠀⠀⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣤⠶⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠲⣿⣛⣻⣷⣾⠿⣿⣿⠏⠀⠘⠟
⠽⣷⠀⠀⠀⠁⠉⢸⣿⣿⣿⣿⣋⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡟⠀⠀⠀⠀
⣴⣿⠄⡼⠀⠀⠀⡿⠿⠛⠿⣿⣿⣿⡄⢸⠏⠉⠀⢈⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⢀⠀⢠
⣿⡟⣼⠃⠀⠀⣿⣧⣀⣠⣀⣹⣿⣿⣷⣼⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⢁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢰⣯⣾⡟⠀⠈
⣿⢿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⢾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⡟⠁⠀⠀
⣿⣸⣮⡤⠀⠀⢻⣿⣿⣿⣿⠟⢉⣿⣿⣿⣷⡄⢈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣷⡿⠋⠁⠙⢿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣠
⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢢⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣦⣿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣄⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⠿⠣⡐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠰⣿⣿⠟⠁⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢸⣷⣾⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣄⠀⠸⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡆⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣠⣤⣴⣶⠄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠿⠖⣾⣿⣿⣷⣶⣿⣿⣿⣿⣧⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣶⣤⣤⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡾⣿⣿⣿⣿⡟⠀⢀⣾⡿⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠉⠙⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣛⢻⡇⠀⠈⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⣿⣿⣿⣶⣿⣿⣿⣿⡁⠀⢀⣀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣽⣿⣿⣤⣒⣄⣹⣿⠟⠀
⠀⠀⠀⠀⠠⣮⣿⣿⣿⣿⡿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣿⣿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀
⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠓⠂⢤⣍⡉⣩⣽⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⡤⠴⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠺⣿⡛⣿⣷⣾⢿⣿⣿⠋⠀⠸⠟
⠭⣗⠀⠀⠀⠁⠉⢸⣿⣛⠿⠿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣶⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠏⠀⠀⠀⠀
⣤⣿⡆⣰⠀⠀⠀⣿⠿⢫⣤⣀⢀⣀⠀⢸⠋⠈⠀⣙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⠀⢀⣴⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⣀⠀⣤
⣿⡿⣹⠇⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⡀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⢀⣀⠀⣀⢀⣀⢸⣿⣿⣣⣀⣀⢿⣿⢃⡀⠀⣀⣀⣁⡀⣀⡀⡀⣀⣀⡀⣀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠈
⣿⣿⣿⠂⠀⠀⢴⣿⠿⣾⣿⣿⣿⣿⣿⡿⠛⠀⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⠀⣿⢿⣿⣻⣿⣿⢸⣿⣯⣿⣻⣻⣯⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀
⣿⣰⣶⡇⠀⠀⠈⠁⢠⣿⣿⣿⣿⣿⣿⣶⠇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠉⠈⠉⠁⠉⠉⠈⠉⠀⠉⠈⢩⣿⡿⠉⠉⠉⢹⠏⠉⠈⠉⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣻⣿⣦⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣴⣶⣴⣶⢶⣶⠛⣿⠪⣿⣷⢶⣶⣶⣮⣶⡆⢴⣶⣿⢲⣾⣧⡶⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⣤
⣿⣿⣿⣿⣦⡀⠀⣠⣿⣿⣿⣿⡿⠁⢿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠂⠛⢂⡟⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠚⠛⠋⠓⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢕⣦⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⣤⣄⣤⣤⣶⣠⣄⣤⣄⣤⣠⣤⣠⣤⣤⣠⣤⣠⣤⣴⡆⢠⣼⣷⡆⣠⣤⣠⣤⣤⣤⣶⢤⣤⣤⣴⡆⣆⣤⣄⣤⣄⣴⡆⢰⣶⣤⣶⣠⣤⡀⣬⠿⠫⡔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣹⣿⣿⡿⠃⠀⢿⡿⣿⣿⣿⢿⡿⣿⠸⣷⠾⣿⢿⣿⢿⡿⣿⢿⣿⣿⡇⢸⣿⢻⡇⢿⡶⢿⡿⣿⣿⢿⣼⠷⣿⡿⡇⡇⣿⡿⣿⠿⣿⡇⠸⣷⢾⣿⡿⣿⠆⢻⣿⣾⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠏⠧⠄⠷⠻⠆⠨⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣶⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⡿⡟⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⢿⣿⢛⣿⣿⢻⢻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣼⣇⣇⣇⣆⣆⣿⣷⣠⣸⣸⣀⣨⣺⣈⣾⣇⣷⣺⣸⣸⣸⠠⢾⣰⣰⣸⣷⣸⣸⣸⣸⣨⣸⣰⣠⣈⣇⣇⣆⡇⡧⣾⣗⣜⣿⣗⣸⣰⣎⣲⣇⣇⣇⣇⣇⣆⣇⣾⡆⣆⣇⣇⣫⣸⣰⣸⣀⣆⢸⠴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⠿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿
⣿⡱⢈⢸⠸⠸⡄⣳⡿⢧⡁⠕⠸⠄⠾⢸⡏⠮⡱⢎⠹⠈⠰⡡⢬⢸⠸⠰⣿⠰⠹⢰⢉⠰⢸⡯⠒⡱⢎⠰⡇⢯⣏⠦⡋⢎⠇⣌⠤⣿⡇⠎⡡⢎⠁⡼⢰⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣯⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣤⣀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⣿⣿⣿⣿⣿⣿⠋⠁⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⢀⡀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⢸⣿⡿⣿⣿⣿⣦⡀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠈⢻⣿⣿⣿⣆⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠘⠀⠀⠀⠂⠀⠀⠃⠀⠀⠒⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠀⠙⠀⠀⠘⠀⠀⠘⠃⠀⠈⠁⠀⠀⠋⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠷⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠋⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢾⢿⢶⣶⣶⣷⣾⣿⣾⡷⣾⢿⣾⣶⡷⢿⣿⣾⣾⣾⣾⢶⢾⣷⣿⡷⣶⡷⣿⡾⣿⣾⣾⣷⢶⣿⡷⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⡿⣿⢿⢿⡿⣿⢿⣿⣻⣿⡟⣿⣿⡾⡿⢿⢿⣻⣿⣿⡿⢿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡗⣿⣿⣿⣿⣿⣿⣿⣷⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣼⣿⣷⣷⣿⣷⣿⣿⣽⣼⣾⣿⣷⣷⣵⣽⣾⣾⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⠟⠿⡟⣿⢿⢿⡿⡿⣻⣿⢿⣿⢿⡟⠻⢿⠿⢿⠟⢿⡿⡿⣿⠻⣟⢿⣿⣿⢿⡿⣿⡿⢿⡿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⣿⠿⣿⢿⡿⡿⣿⠿⣿⠿⢿⢿⠿⠿⡿⢿⠿⢿⡿⠿⡿⢿⡿⢿⡿⢿⡿⠿⢿⡿⠾⣿⣿⠿⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣾⣷⣾⣷⣾⣿⣾⣷⣾⡶⣿⣿⣿⣷⣾⣾⣶⣿⣿⣶⢿⣿⡷⣾⣶⣶⣿⣶⣿⣷⣿⣷⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣷⣷⣿⣷⣶⣶⣿⣾⣾⣿⣷⣾⣷⣶⣿⣷⣷⣾⣶⣶⣿⣷⣾⣿⣴⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⡿⠿⡿⣿⡿⠿⢿⣿⢿⢿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⡿⢿⡿⢿⠿⠿⢿⣿⢿⢿⢿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣾⣷⣶⡿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣾⣾⣿⢷⣾⣾⡷⣶⡷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣷⣾⣷⣶⣷⣾⣿⣷⣷⣿⣶⣿⣾⣿⣿⣿⣿⣿⣷⣿⣷⣷⣿⣷⣶⣿⣾⣶⣶⣾⣾⣶⣾⣶⣿⣷⣶⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣽⣷⣭⣿⣯⣭⣿⣧⣭⣯⣯⣿⣿⣿⣿⣮⣬⣯⣼⣩⣽⣿⣯⣯⣽⣟⣿⣿⣿⣯⣥⣽⣿⣽⣽⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣝⣛⣏⣉⣙⣝⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⡇⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡰⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⣿⠀⣿⡇⣿⠀⠀
⢸⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣠⣤⣶⣶⣶⣶⣶⣄⠈⢻⣿⣿⣿⣿⣿⡿⠛⣩⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣭⣭⣙⣛⠻⠿⡖⠁⢸⡇⣿⠀⣿⡇⣿⠀⠀
⢸⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⡿⢿⢻⢟⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣈⠃⢿⠀⣿⡇⣿⠀⢀
⢸⡇⣿⠀⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⡆⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⡿⣿⣳⣺⣿⣾⣵⣥⣥⣟⣆⣟⣿⣆⠫⠋⠿⢹⡿⢿⡟⡟⣿⣿⣦⣀⠻⡇⣿⢰⡟
⢸⡇⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⢒⢙⣿⡀⠭⣭⣿⣷⣽⣿⣿⣿⣿⣷⣌⠻⣿⣶⣷⣿⢿⢽⣦⣯⣜⣫⣿⣿⡘⣿⡟⠋⡟⡽⡟⢻⡓⢾⣿⡿⡿⣿⣿⣿⣧⠀⢿⠸⠀
⢸⡇⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠆⢙⣿⣿⣤⣿⣘⣿⣴⣽⠩⢭⢍⠛⣿⢻⣿⣲⣷⣾⣿⣧⣼⣥⣿⣸⣽⣿⣿⠃⣸⢸⡀
⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣥⣾⣿⣿⣿⠿⣿⣿⣿⣿⡿⠏⠠⠾⠿⠟⠛⣛⣋⣉⣛⡻⠿⠿⣿⣿⣷⣿⣶⣿⣥⣤⣧⣿⣍⣫⣿⣿⣿⠿⠛⣁⡄⣿⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠉⠉⠙⢿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⣭⣕⣒⣲⣶⣿⡏⠀⠀⠉⠉⠉⠁⠀⠀⠒⠻⠛⠉⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣭⣭⣭⣭⣍⣭⣉⠭⠉⠀⠀⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⢸⣿⣋⡿⠿⠟⠁⠀⠀⠀⠈⢿⣻⠿⠿⠿⠟⢛⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣀⣀⣀⣼⣿⢻⣿⠿⣿⠏
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢠⠀⠀⠀⠰⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣤⡀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠸⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⡀⠀⢀⣙⣿⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣉⣉⣿⣿⣿⣿⠟⠛⠛⠛⠛⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠹⣿⣇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⣿⣿⣿⣿⣿⡟⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⢻⣿⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠤⠤⣦⣭⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⣿⣿⣿⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣇⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣌⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⡿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠛⠿⡷⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠈⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⢰⣿⣯⣎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣦⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠴⣪⠿⣉⠽⢿⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠡⠚⠉⢠⣿⣿⣷⣦⣄⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣇⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⡄
⠀⠀⢀⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠁
⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 4064

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 21/02/2025: Web Browsers,
Mechanical Shortcuts, and Internet Hygiene⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ The_Sentinel⠀⇛


                       We dance to the algorithm
                       as it learns all our moves;
                       the two step authentication,
                       swipe to electric slide.
                       ~
                       The beat, hauntingly familiar,
                       sounds like your own heartbeat;
                       the cadence quickens as you move,
                       the music matching with your groove.
                       ~
                       You know you’ve heard this song before,
                       but once more cannot hurt;
                       the DJ spins a tempting web,
                       please switch on your alerts.
                       ~
                       The playlist is repeating now,
                       the songs all sound the same;
                       there are no exit signs in sight
                       and so, we must remain.
                # ⚓ 🔤SpellBinding:_ACDETVX_Wordo:_GRAMS⠀⇛


          o § Technology and Free Software⠀➾


                # ⚓ An_in_depth_review_of_all_the_old_style_Firefox_browsers_
                  (Palemoon_vs_Basilisk_vs_Seamonkey)⠀⇛


                       There is a sea of Firefox browsers, all with
                       varying degrees of quality and usability, I will
                       attempt to review the three most popular "old" ones
                       against modern Firefox.


                       [...]


                       I am a simple man, so is the test, a wikipedia page
                       open and a Youtube video running in the background,
                       with Ublock installed. Ublock tends to bong out on
                       Youtube, trying to stop all the spyware.


                       Firefox, Palemoon and Basilisk all use about 10%
                       cpu and around 850MB of ram to accomplish this
                       task, but Seamonkey accomplished it with 10% cpu
                       and only 580MB of ram.


                       The biggest surprise though, came in that all
                       browsers except Firefox, seemed to immediately
                       garbage collect when I paused the video, shrinking
                       their ram use by about 30-60MB.


                       A disclaimer here is that Firefox resource use is a
                       guesstimate, as it insists on polluting the entire
                       process tree with webworkers and other weird
                       processes.


                # ⚓ Mechanical_Shortcuts⠀⇛


                       Last year I bought a Japanese abacus, called a
                       soroban (そろばん). I had played with slide rules
                       extensively at that point, and I wanted to learn
                       about other forms of mechanical calculation. The
                       model I purchased was a simple 17-rod educational
                       tool, analogous to a a basic four-function pocket
                       calculator one might find at a convenience store.
                       But the beauty of mechanical calculators abacus is
                       that the cheapest and the most expensive models
                       work just as efficiently as each other.


                       The standard soroban contains rods held inside a
                       frame. The rods are divided into top and bottom
                       sections, with one bead in the top and four beads
                       in the bottom. This creates a "bi-quinary" system:
                       the four beads on the bottom represent units, and
                       the top bead represents fives, allowing any number
                       from 0 to 9 to be encoded onto one rod.


                       To learn mathematics on a soroban, I have been
                       using the book "The Japanese Abacus: Its Use and
                       Theory" by Takashi Kojima. A product of the 1950s,
                       the book is very dense but extremely informative,
                       and is still considered one of the definitive
                       beginner's English texts on using a soroban.


                # ⚓ Overhauling_my_internet_hygiene⠀⇛


                       Current coffee: Maude Cafe Delas (V60)


                       I'm not going to lie - the future is scary. Even
                       though I don't live in the US, having the most
                       powerful nation in the world nose dive into fascism
                       is a concern for us all.


                       One way I'm preparing is overhauling my internet
                       hygiene and I just wanted this post to show what
                       I'm doing, much of it likely being old hat for
                       Geminauts.


                       First off: browsing. Aside from using Gemini much
                       more for general surfing and checking the news,
                       I've switched to Vivaldi as my browser of choice
                       across devices. After trying a bunch, including
                       Pale Moon, Libre wolf, and Brave, I settled on
                       Vivaldi as my private browser of choice, using
                       Ecosia by default for search.


                       I've been systematically changing my passwords to
                       unique and highly secure versions with the help of
                       KeePassDX, which lets me generate random passwords
                       and keep them safe in a vault.


                # ⚓ The_foreseeable_future⠀⇛


                       Me: I don't know. Maybe I'm just meant to be a sort
                       of starving FOSS community volunteer who lives with
                       his parents for the foreseeable future.


                       Rubber duck: Perhaps. You also have aspirations to
                       become a Debian developer, which could open doors
                       for future job opportunities, including sysadmin.


                       Me: Yeah. But I'd be middle-aged by then, and
                       companies tend to want younger folks.


                # ⚓ Designing_the_perfect_lock_screen_and_notifications
                  system⠀⇛


                       No scheduling, no easy toggling, no time outs (like
                       “don’t disturb for the next N minutes”), no
                       allowlist for specific numbers to punch through, no
                       “if they call twice let them through”.


                       The two options for “new activity icon” are a
                       bigger problem. You see, the problem for us caught
                       in the “check-check-check” mentality is that the
                       activity icon is like a slot machine, crack-a-pack,
                       treasure chest, gambling, choosing a scratch ticket
                       over bread, dopamine injection! “Ooh do I have a
                       li’l hug waiting for me if I unlock?”, that’s what
                       the asterisk says. That damage would be minimized
                       if the lock screen gave just a little bit mit more
                       info about what’s going on instead of all
                       activities (no matter how trivial or disappointing)
                       showing the same li’l light-up Christmas star.


                       And turning off that alluring lootboxy li’l
                       asterisk is a thousand times worse because then the
                       entire phone becomes a constant, never-ending slot
                       machine. I can’t know whether or not I have
                       anything without going through that li’l addictive
                       “unlocking” ritual. Unrapping the pack, flipping
                       the ante, scratching the ticket, pulling the slot
                       machine lever... and unlocking the phone. Those
                       extra hoops ironically is what makes it more
                       addictive.


                # § Internet/Gemini⠀➾


                      # ⚓ Revisiting_Gopher-Commerce:_FRST_Gopher_Store
                        Launches!⠀⇛


                             I'm still working on it, but I've hacked a
                             bit of PHP to create a functional mechanism
                             for placing orders for my FRST Computer stuff
                             via Gopher. I've been sticking with Motsognir
                             (because I resolved my earlier dilemma by
                             patching Motsognir to produce Apache-style
                             access logs) so I decided to try the built-in
                             PHP support and you know what? It's great.
                             It's great to be writing PHP code again,
                             actually. It's been a damn long time, and
                             it's been a fun trip down coding memory lane.
                             While I had cut my teeth on BASIC and C, PHP
                             was really the first language I felt truly
                             proficient in, building actual, functional
                             things with it.


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





                    ䷩ 𝚕𝚒𝚗𝚎 4309

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 21/02/2025: Doomscrolling and
European Ham Radio Show⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇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⠀➾


                # ⚓ the_mystery_that_is_a_social_life⠀⇛


                       i was washing some berries for breakfast in the
                       morning and remembering all the time spent at my
                       grandparents' allotment when i was younger. how
                       often my sister (well, cousin) would fail to join
                       us, because she was just so busy. i remember at
                       first it baffled me, what could she be busy with?
                       we're kids. we have homework and that's basically
                       it. i was almost in total control of my time
                       outside of school. granted, i was burnt out as an
                       autistic and greatly avoided most activities, even
                       just going out of the house. i spent hours and
                       hours stimming/regulating by playing what's now
                       called single person card games (insert blood
                       orange meme - it's fuckin' solitaire), wore out
                       many a deck by playing on floors and carpets all
                       over. it hadn't occurred to me that you could be so
                       tied up time-wise that you couldn't come over hang
                       out in nature and help your grandma?


                # ⚓ Casino_Royale_by_Ian_Fleming⠀⇛


                       This is the first work of fiction featuring James
                       Bond and I'm sure a lot has been said of it since,
                       so I'll try to take a different approach with this
                       review. 


          o § Politics and World Events⠀➾


                # ⚓ Gendery_thoughts⠀⇛


                       Over the last year I've been questioning my gender.
                       Until last year I've always gone along with the
                       "default" for someone AMAB: cis man. Like many
                       cisgender people I never thought about it. But back
                       in February I read a story where someone
                       transitioned (magically and instantly) and the joy
                       I felt at reading that made me re-evaluate. I kinda
                       thought "there's no way a cis man would feel like
                       that, right?"


          o § Technology and Free Software⠀➾


                # ⚓ A_functional_analysis_of_doomscrolling⠀⇛


                       First of all, doomscrolling is likely to be
                       reinforced through encountering novel or
                       significant information once in a while. In this
                       respect, the Doomscroller is on a variable-ratio
                       reinforcement schedule. This is one of the most
                       effective and treacherous amplification plans,
                       which also underlies slot machines, for example.


                       Although it is, theoretically, possible using any
                       website that regularly updates its content and
                       includes the latest news, doomscrolling is mainly
                       done on social media apps. Likes, shares and
                       interactions or discussions with others engaging in
                       similar behavior constitute social reinforcement.


                # ⚓ I_Guested_The_European_Ham_Radio_Show⠀⇛


                       The European Ham Radio Show is a weekly YouTube
                       live-show about everything amateur radio. I
                       discovered it late 2023 (when they were guests at
                       the Ham Radio Workbench podcast) and quickly found
                       my way into the friendly community on their Discord
                       server. The Discord is a great active place where
                       people share their adventures in portable
                       operation, DIY projects, and so much more.


                       I was very happy (and a bit starstruck) when they
                       invited me into the show to talk about my DIY
                       projects! The show went great, despite me being a
                       bit nervous at first. I had a really fun time
                       hanging out with them and in the end the hour just
                       swooshed by. I admire the amount of work they put
                       into sharing their hobby – it certainly has
                       inspired me to try many new things – and I relish
                       that I was given the opportunity to join one of
                       their shows.


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





                    ䷩ 𝚕𝚒𝚗𝚎 4445

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 21/02/2025: Linux Foundation
Openwashing, Microsoft Copilot Goes Down⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Career/Education
          o Health/Nutrition/Agriculture
          o Proprietary
          o Linux_Foundation
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
                # Open_Data
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Patents
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Ruben Schade ☛ Rubenerd_Show_430:_The_two_mugs_episode⠀⇛


                 Bit of a weirder one today; talking about the time last
                 week when the trolls won! But I got some amazing feedback
                 and some help, so maybe there are lessons here I can pass
                 on. Have you heard of this thing called the block button?
                 I should do that! Thanks again, will be a more normal
                 episode next time.


          o ⚓ Ruben Schade ☛ Ey,_fuhgeddaboudit⠀⇛


                 Yesterday I made this_throwaway_comment:


                 Forget about it, as my beloved New York friends would say
                 in an accent I can’t muster, but it doesn’t stop me
                 trying.


                 That public troll earlier this week must be infuriated
                 that once again I’m quoting someone, only this time it’s…
                 myself! On my own blog, no less! The absolute hide of
                 some people. Hyde? Is Hyde Park where you go not to be
                 seen? Wait, Hyde Park is London. Also, every Australian
                 city for some reason.


          o § Career/Education⠀➾


                # ⚓ ACLU ☛ What_Students_Lose_When_School_Becomes_a_Political
                  Battleground⠀⇛


                       At the ACLU, we know that students’ First Amendment
                       rights don’t disappear at the schoolhouse gates.
                       However, the Convicted Felon administration is
                       attempting to challenge this and other
                       constitutional rights by forcing schools to teach a
                       curriculum that aligns with its political agenda.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ Dairy_Workers_May_Have_Passed_Bird_Flu_to
                  Pet_Cats,_CDC_Study_Suggests⠀⇛


                       But the study, whose publication was delayed by a
                       pause in public communications by the agency,
                       leaves key questions unanswered.


                # ⚓ New York Times ☛ Emergency_Food,_TB_Tests_and_H.I.V._Drugs:
                  Vital_Health_Aid_Remains_Frozen_Despite_Court_Ruling⠀⇛


                       The Convicted Felon administration appears to be
                       flouting a judge’s order pausing the dismantling of
                       U.S.A.I.D.


          o § Proprietary⠀➾


                # ⚓ Microsoft_Copilot_Down:_Company_Investigates_and_Resolves
                  Copilot_Features_and_Service_Disruption⠀⇛


                       Microsoft Copilot services were down today.
                       Microsoft acknowledged that it had identified an
                       issue affecting its Copilot features and services
                       on February 21, 2025. Users may have experienced
                       disruptions in Microsoft Copilot services. In
                       response, Microsoft initiated an investigation and
                       reviewed service telemetry and available data to
                       determine the cause of the issue. The team
                       discovered that a recent code change was the
                       potential cause of the issue. To address it, they
                       began rolling back the change. Microsoft confirmed
                       that the rollback successfully mitigated the impact
                       on Copilot features and services. Mark Zuckerberg-
                       Run Meta Approves Executive Bonuses of up to 200%
                       Following Layoffs.


                # ⚓ Bryan Lunduke ☛ Leaked_Recording_Confirms_Apple's
                  Discriminatory_DEI_Hiring_Policies⠀⇛


                       Apple VP of Engineering, Jon Andrews, on refusing
                       to hire for a management role "until we find a
                       diverse slate": [...]


                # ⚓ Bryan Lunduke ☛ Microsoft_Creates_New_Form_of_Quantum
                  Matter_to_Avoid_Fixing_Windows⠀⇛


                       Microsoft's new quantum processor, Majorana 1,
                       currently can do nothing.


                # ⚓ Tom's Hardware ☛ Microsoft_trims_File_Explorer's_Recent,
                  Favorites,_and_Recommended_content_in_Europe⠀⇛


                       Microsoft is removing a couple of features from a
                       backdoored Windows 11 24H2 Preview Build in Europe
                       to comply with the GDPR.


                # ⚓ WhichUK ☛ Microsoft_365_prices_have_risen_by_up_to_£30_a
                  year_–_here's_how_to_beat_them [Ed: Avoid Microsoft
                  altogether]⠀⇛


                       Microsoft 365 prices are going up, but there’s a
                       simple way to avoid paying more


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ The Straits Times ☛ China_faces_talent_shortage_amid
                        DeepSeek-fuelled_Hey_Hi_(AI)_jobs_surge⠀⇛


                             Some firms are dangling large sums of money
                             to entice the existing talent or expanding
                             their search abroad.


          o § Linux Foundation⠀➾


                # ⚓ The Fast Mode ☛ VyOS_Networks_Joins_Linux_Foundation_and
                  OPI_Project_to_Advance_Open_Networking⠀⇛


                       VyOS Networks proudly joins the Linux Foundation as
                       a Silver member and becomes a General member of the
                       Open Programmable Infrastructure (OPI) Project, an
                       initiative focused on open, interoperable DPU/IPU
                       architectures for high-performance networking,
                       security, and storage acceleration.


                       This marks a significant step towards advancing
                       open networking innovation. These strategic
                       collaborations reinforce VyOS Networks' commitment
                       to open-source development, interoperability, and
                       next-generation networking architectures.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ China_repatriates_200_citizens_from_Myanmar_scam
                        centers_amid_crackdown⠀⇛


                             Many thousands more people are believed to be
                             working in fraud centers in Myanmar and
                             beyond.


                      # ⚓ The Straits Times ☛ Philippine_police_arrest_over_450
                        in_‘Chinese-run’_scam_centre_raid⠀⇛


                             Scammers have been targeting victims in China
                             and India with sports betting and investment
                             schemes.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Meduza ☛ Officials_in_St._Petersburg_are_about_to
                        equip_surveillance_cameras_with_‘ethnic_recognition’
                        technology_—_Meduza⠀⇛


                      # ⚓ China’s_homegrown_tech_boosts_global_surveillance,
                        social_controls:_report⠀⇛


                             The ruling Chinese Communist Party is using
                             Hey Hi (AI) and big data to monitor citizens
                             at home and abroad, and is exportin


                      # ⚓ EDRI ☛ Protect_Not_Surveil_position_paper:_Stop
                        Europol’s_expanding_digital_surveillance_against
                        migrants!⠀⇛


                             EDRi and the Protect Not Surveil coalition
                             published position paper today to call for
                             the rejection of the Europol reform. The
                             proposed legislation would expand Europol’s
                             surveillance powers, put lives at risk, and
                             criminalise migrants and solidarity
                             organisers.


                      # ⚓ AccessNow ☛ How_a_new_Europol_reform_threatens
                        digital_war_on_migrants⠀⇛


                             The #ProtectNotSurveil coalition analyses a
                             proposed reform of the Europol agency which
                             will increase unlawful surveillance against
                             migrants.


          o § Defence/Aggression⠀➾


                # ⚓ JURIST ☛ Dictator_media_companies_sue_Brazil_justice
                  involved_in_Bolsonaro_coup_investigation⠀⇛


                       Media companies tied to US President The
                       Insurrectionist filed a lawsuit Thursday against
                       Brazillian Federal Supreme Court Justice Alexandre
                       de Moraes, accusing him of violating a US-based
                       far-right commentator’s right to free speech when
                       issuing orders suspending social control media
                       accounts for spreading disinformation.


                # ⚓ New Yorker ☛ The_Convicted_Felon_Administration_Trashes
                  Europe_and_NATO⠀⇛


                       Speeches delivered by J. D. Vance and Pete Hegseth
                       were not just verbal lashings of America’s allies
                       but a wholesale rejection of eighty years of U.S.
                       foreign policy.


                # ⚓ Federal News Network ☛ Unions_sue_over_federal_worker
                  firings,_alleging_Convicted_Felon_administration_misused
                  probationary_periods⠀⇛


                       Unions for federal workers have filed a lawsuit to
                       block the mass firings of probationary federal
                       employees by President The Insurrectionist’s
                       administration, alleging that officials are
                       exploiting and misusing the probationary period to
                       eliminate staff across government agencies. The
                       unions allege in the federal lawsuit filed late
                       Wednesday that the administration’s Office of
                       Personnel Management acted unlawfully by directing
                       federal agencies to use a standardized termination
                       notice, falsely claiming performance issues.


                # ⚓ JURIST ☛ Mexico_president_threatens_to_take_legal_action
                  against_Surveillance_Giant_Google_over_Gulf_name_change⠀⇛


                       Mexico’s President Claudia Sheinbaum threatened
                       Monday to take Surveillance Giant Google to court
                       if its map continues to show US-based users the
                       label “Gulf of America” instead of “Gulf of
                       Mexico.”


                # ⚓ Defence Web ☛ Gunners_show_their_mettle_in_border
                  protection⠀⇛


                       Kimberley-based 10 Anti-Aircraft Regiment is a non-
                       infantry unit currently doing border protection as
                       per the standing Operation Corona with three solid
                       “scores” to its name over the weekend. The first
                       saw the gunners turned border guards on foot patrol
                       from the Pontdrift operational base close to the
                       Botswana/South Africa boundary encounter would-be
                       cigarette smugglers.


                # ⚓ The Straits Times ☛ ST_Picks:_Does_the_Philippines_need_a
                  China_rethink_in_the_Convicted_Felon_era?⠀⇛


                # ⚓ The Straits Times ☛ Asian_Insider:_Panama’s_out,_who’s
                  next?_|_Saving_Kolkata’s_big_yellow_taxis⠀⇛


                       Asian Insider brings you insights into a fast-
                       changing region from our network of correspondents
                       and commentators.


                # ⚓ The Straits Times ☛ Australia,_Papua_New_Guinea_eye_defence
                  treaty_as_China_woos_region’s_island_nations⠀⇛


                       They seek to deepen integration of their forces and
                       make it easier to offer security support.


                # ⚓ The Straits Times ☛ Director_Bong_Joon_Ho_'proud'_of_South
                  Koreans_overcoming_martial_law_bid⠀⇛


                       SEOUL - Oscar-winning director Bong Joon Ho said on
                       Thursday he was proud of how his fellow South
                       Koreans had overcome the fallout from impeached
                       President Yoon Suk Yeol's short-lived imposition of
                       martial law on December 3.


                # ⚓ The Straits Times ☛ South_Korean_drivers_cleared_in_death
                  of_woman_who_leapt_from_taxi,_fearing_kidnapping⠀⇛


                       This situation led to a fatal misunderstanding of
                       the driver’s intent.


                # ⚓ The Straits Times ☛ South_Korean_teacher_who_fatally
                  stabbed_8-year-old_girl_‘laughed_in_ER’⠀⇛


                       Eight-year-old Kim Ha-neul was stabbed to death by
                       her teacher on Feb 10.


                # ⚓ The Straits Times ☛ South_Korea’s_ousted_PM_says_he_tried
                  to_stop_martial_law_decree⠀⇛


                       Han Duck-soo was testifying for the first time at
                       President Yoon Suk Yeol's impeachment trial.


                # ⚓ North_Korea’s_‘Day_of_the_Shining_Star’_festivities_muted
                  amid_travel_restrictions⠀⇛


                       Kim Jong Il’s birthday touted as the country’s
                       greatest holiday, but no ‘presents’ from late Dear
                       Leader in 2025.


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


                      # ⚓ France24 ☛ Zelensky_calls_for_strong_ties_with_US,
                        MElon_slams_Ukraine's_leader_as_'despised'⠀⇛


                             The United States is urging Ukrainian
                             President Volodymyr Zelensky to sign deal on
                             US access to Ukraine's critical minerals,
                             White House national security adviser Mike
                             Waltz has said. Zelensky has refused the
                             offer, saying: "I can't sell our state." The
                             comments in the White House news briefing
                             came shortly after Zelensky wrapped up a
                             meeting with Convicted Felon's Ukraine envoy
                             in Kyiv, saying he was ready to make an
                             "investment and security agreement" with the
                             US to end the war.


                      # ⚓ France24 ☛ Dictator_upends_decades_of_foreign_policy
                        in_pivot_towards_Putin⠀⇛


                             FRANCE 24's Fraser Jackson in Washington
                             takes a look at the fallout of an
                             extraordinary week in geopolitics as US
                             President Convicted Felon upends decades of
                             foreign policy doctrine with a pivot towards
                             Vladimir Putin's Russia.


                      # ⚓ France24 ☛ Macron_says_France_won't_send_troops_to
                        Ukraine_'tomorrow'_but_may_give_security_guarantees⠀⇛


                             President Emmanuel Macron said Thursday that
                             France would not be sending troops to Ukraine
                             "tomorrow" but reiterated that France could
                             provide security guarantees to the war-torn
                             nation after a ceasefire. Macron will be
                             meeting US President The Insurrectionist at
                             the White House on Monday.


                      # ⚓ France24 ☛ Zelensky_meets_US_envoy_after_Convicted
                        Felon_brands_him_a_'dictator'⠀⇛


                             Tensions between Zelensky and Convicted Felon
                             over the US President's outreach to Moscow
                             have exploded this week in a series of
                             escalating barbs traded in press conferences
                             and on social control media. Amid the war of
                             words, Zelensky said Thursday he had held a
                             "productive meeting" with US envoy Keith
                             Kellogg. In the US, some of Convicted Felon's
                             team doubled down on their attacks on
                             Zelensky, and VP Vance on Thursday defended
                             Convicted Felon's negotiations with his
                             Russian counterpart Vladimir Putin.


                      # ⚓ France24 ☛ Putin_using_Convicted_Felon_ties_as
                        'legitimisation'_in_Russia,_exiled_opponent
                        Khodorkovsky_says⠀⇛


                             FRANCE 24 spoke to exiled Russian opponent
                             Mikhail Khodorkovsky, who was jailed for a
                             decade until he was pardoned by President
                             Vladimir Putin in 2013. Over the past few
                             weeks, Putin and his US counterpart The
                             Insurrectionist have spoke to each other and
                             agreed to work toward ending the war in
                             Ukraine – a huge diplomatic shift after years
                             of tensions. Putin "has presented this in the
                             country as his legitimisation; a breakthrough
                             in Russia's international isolation",
                             Khodorkovsky said.


                      # ⚓ RFERL ☛ Zelenskyy_Stresses_Need_For_Strong_Agreements
                        With_U.S._After_Meeting_Envoy⠀⇛


                             Ukrainian President Volodymyr Zelenskyy cast
                             his talks with U.S. envoy Keith Kellogg in a
                             positive light on February 20 despite a
                             further sign of tension when a planned joint
                             news conference was canceled.


                      # ⚓ New Yorker ☛ The_Insurrectionist’s_Putinization_of
                        America⠀⇛


                             It’s not just in foreign policy that the
                             President is turning Russia’s way.


                      # ⚓ CS Monitor ☛ Trump-Putin_summit_prospect_brings
                        Moscow_in_from_the_cold⠀⇛


                             Proposing talks with Vladimir Putin to end
                             his war in Ukraine, The Insurrectionist has
                             freed the Russian president from his
                             diplomatic isolation and confounded U.S.
                             allies.


                      # ⚓ New York Times ☛ Thomas_Friedman_on_Convicted_Felon’s
                        Desire_to_Be_President_for_Life⠀⇛


                             The president wants to create a revolution
                             abroad. This Opinion columnist would love to
                             see a plan.


                      # ⚓ New York Times ☛ Dictator_Elevates_Kremlin_Talking
                        Points,_a_Familiar_Pattern_From_His_First_Term⠀⇛


                             President Convicted Felon’s description of
                             President Volodymyr Zelensky of Ukraine as a
                             “Dictator without Elections” echoes the
                             Kremlin’s messaging.


                      # ⚓ Meduza ☛ Moscow’s_media_shares_photos_of_rocket
                        launchers_in_Kursk_region_as_Ukraine_denies_Putin’s
                        claim_about_border_breach_—_Meduza⠀⇛


                      # ⚓ Latvia ☛ Latvian_president_cautious_on_peacekeeper
                        possibility⠀⇛


                             President Edgars Rinkēvičs said in an
                             interview on the Latvian Television program
                             "Today's Question" February 19 that sending
                             Latvian troops to Ukraine as part of a
                             possible peacekeeping force had been
                             discussed but that such a move would require
                             several conditions to be met first.


                      # ⚓ Latvia ☛ Latvia's_defense_has_developed_rapidly_since
                        beginning_of_war⠀⇛


                             Next week marks three years since Russia's
                             full-scale invasion of Ukraine. Latvia has
                             not only provided support to Ukraine but has
                             also developed its defense. Latvian Radio on
                             February 20 asked what has been done and
                             whether these activities have made Latvia
                             safer.


                      # ⚓ Atlantic Council ☛ Ukrainians_are_proudly_democratic
                        but_resoundingly_reject_wartime_elections⠀⇛


                             Ukraine's fight for democracy has been at the
                             heart of the country's struggle against the
                             past two decades of escalating Russian
                             aggression, but Ukrainians overwhelmingly
                             reject the idea of staging dangerous wartime
                             elections before peace is secured, writes
                             Peter Dickinson.


                      # ⚓ Atlantic Council ☛ Issue_brief:_A_NATO_strategy_for
                        countering_Russia⠀⇛


                             Russia poses the most direct and growing
                             threat to NATO member states' security. This
                             threat now includes the war in Ukraine,
                             Arctic militarization, hybrid warfare, and
                             arms control violations. Despite NATO's
                             military and economic superiority, a unified
                             and effective strategy is essential to
                             counter Russia's aggression. Key priorities
                             include defeating Russia in Ukraine,
                             deterring threats to NATO allies, containing
                             Russian influence, and undermining its
                             revisionist ambitions.


                      # ⚓ Atlantic Council ☛ What_Europeans_think_of_Convicted
                        Felon’s_approach_to_Ukraine_(and_what_they_might_do
                        next)⠀⇛


                             European leaders are waking up to calls from
                             the Convicted Felon administration to take
                             the lead on security for Ukraine. Atlantic
                             Council experts share what that might look
                             like from Berlin to Vilnius.


                      # ⚓ Atlantic Council ☛ Ukraine_can_unleash_energy
                        investment_even_amid_war⠀⇛


                             To bolster energy security in Ukraine, its
                             leaders must foster stability for investors
                             to finance new, decentralized power
                             generation. Achieving this will require
                             overcoming three key challenges.


                      # ⚓ France24 ☛ NATO_US_security_guarantee,_credibility_of
                        Article_5_already_weakened,_former_NATO_official_says⠀⇛


                             Trump’s national security adviser, Mike
                             Waltz, said the US president is “obviously
                             very frustrated” with Ukrainian President
                             Zelensky. “Some of the rhetoric coming out of
                             Kyiv, frankly, and insults to President
                             Convicted Felon were unacceptable,” Waltz
                             said. FRANCE 24's Mark Owen speaks to former
                             NATO Assistant Secretary-General Antonio
                             Missiroli. He says that there has already
                             been a degree of weakening of the US security
                             guarantee within the NATO framework and the
                             credibility of Art.5.


                      # ⚓ France24 ☛ Zelensky,_Convicted_Felon_envoy_give_no
                        statement_after_Kyiv_meeting⠀⇛


                             Ukrainian President Volodymyr Zelensky and US
                             President The Insurrectionist's special envoy
                             for Ukraine did not give public statements
                             following their meeting in Kyiv Thursday, "at
                             the request of the American side" Zelensky's
                             spokesman said. FRANCE 24's Gulliver Cragg
                             reports from Kyiv


                      # ⚓ France24 ☛ Germany's_crunch_elections:_Can_mainstream
                        parties_blunt_surging_far_right?⠀⇛


                             Crunch elections for Germany at perhaps the
                             most pivotal moment since the fall of the
                             Berlin Wall. Back then, it was about making a
                             success of reunification. Now comes a
                             reckoning over the German model that ensued.
                             Under threat, the kind of global free trade
                             that powers Germany’s export-driven economy.
                             Instead it’s Convicted Felon’s tariffs, a
                             Russian aggression that’s inching closer in
                             not-so-far off Ukraine and an aging
                             population that needs to replenish its
                             workforce, but doesn’t want more migrants.


                      # ⚓ France24 ☛ Ukrainian_filmmaker,_and_soldier,_Vadym
                        Adamov_warns_“Russia_won’t_stop”⠀⇛


                             He enlisted the month of his 18th birthday.
                             Three years on, film director and
                             videographer Vadym Adamov shares with France
                             24's François Picard his harrowing plight as
                             a veteran of the brutal battle of Bakhmut:
                             “Europe has a God-given chance to learn from
                             Ukraine’s mistakes,” insists Adamov, now 21.
                             On a whirlwind trip to Berlin and Paris
                             before returning to the frontline, he fears
                             that Europeans haven’t taken the full measure
                             of the danger at hand.


                      # ⚓ France24 ☛ Zelensky_meets_US_envoy_after_Convicted
                        Felon_brands_him_a_'dictator'⠀⇛


                             Volodymyr Zelensky was meeting Thursday with
                             US envoy Keith Kellogg after The
                             Insurrectionist branded the Ukrainian leader
                             a "dictator" and said the Russians "have the
                             cards" in any talks to end the war. Analysis
                             by FRANCE 24 International Affairs Editor,
                             Kethevane Gorjestani.


                      # ⚓ France24 ☛ Twenty-four_hours_in_Ukraine’s_Kharkiv,
                        where_life_goes_on_despite_the_war⠀⇛


                             Kharkiv, eastern Ukraine’s largest city, is
                             resolutely entering its fourth year of war,
                             with residents stoically coping with
                             emergency laws, night curfews and incessant
                             air alerts. Underground schools have been
                             built, and the city still offers a few
                             leisure activities to ward off fear and help
                             overcome personal tragedies. FRANCE 24 shares
                             the daily lives of the city’s residents over
                             24 hours.


                      # ⚓ France24 ☛ Press_conference_between_Zelensky_and_The
                        Insurrectionist’s_Ukraine_envoy_is_canceled_by_US⠀⇛


                             A news conference after talks between
                             Ukrainian President Volodymyr Zelenskyy and
                             President The Insurrectionist’s Ukraine envoy
                             was canceled at the request of U.S.
                             officials, a Kyiv official said. More
                             information with FRANCE 24 correspondent in
                             Kyiv, Gulliver Cragg.


                      # ⚓ LRT ☛ Lithuania_strips_former_Ukrainian_PM_of_state
                        award⠀⇛


                             Lithuanian President Gitanas Nausėda has
                             stripped former Ukrainian Prime Minister
                             Mykola Azarov of a Lithuanian state award.


                      # ⚓ LRT ☛ Lithuanian_FM_says_Convicted_Felon’s_statements
                        false,_but_not_‘Russian_narrative’⠀⇛


                             Lithuanian Foreign Minister Kęstutis Budrys
                             says that US President The Insurrectionist’s
                             statements about Ukraine are not “Russian
                             narrative”, even though they are false and
                             should be corrected.


                      # ⚓ LRT ☛ Lithuanian_president_proposes_2030_as
                        ‘reference’_for_Ukraine’s_EU_membership⠀⇛


                             Lithuanian President Gitanas Nausėda has
                             proposed to EU leaders to set January 1,
                             2030, as a “reference date” for Ukraine’s
                             accession to the EU.


                      # ⚓ RFERL ☛ Dictator_'Very_Frustrated'_With_Zelenskyy,
                        U.S._National_Security_Adviser_Says⠀⇛


                             Senior U.S. Republican Party figures have
                             been pushing back against President The
                             Insurrectionist's latest statements attacking
                             his Ukrainian counterpart, Volodymyr
                             Zelenskyy.


                      # ⚓ RFERL ☛ How_Norway_Fed_Russia's_War_Machine_Despite
                        EU_Sanctions⠀⇛


                             A leading Norwegian automotive supplier has
                             exported millions of dollars in sanctioned
                             truck parts that ended up feeding Russia’s
                             war machine via Turkey, an RFE/RL
                             investigation has found.


                      # ⚓ The Straits Times ☛ China_backs_Convicted_Felon's
                        Ukraine_peace_bid_at_G20_as_US_allies_rally_behind
                        Zelenskiy⠀⇛


                             China came out in support of U.S. President
                             The Insurrectionist's bid to strike a deal
                             with Russia to end the war in Ukraine, at a
                             G20 meeting in South Africa on Thursday,
                             while U.S. allies rallied around Ukrainian
                             President Volodymyr Zelenskiy.


                      # ⚓ New York Times ☛ U.S._Objects_to_Calling_Russia
                        ‘Aggressor’_in_G7_Statement_on_Ukraine_Invasion⠀⇛


                             The American opposition to a draft of a Group
                             of 7 statement marking the third anniversary
                             of Russia’s attack on Ukraine comes after
                             President Convicted Felon blamed Kyiv for
                             starting the war.


                      # ⚓ New York Times ☛ With_Explosive_Goggles,_Ukraine
                        Sought_to_Blast_Russian_Drone_Operators⠀⇛


                             A senior Ukrainian intelligence official
                             confirmed the plot to blow up drone goggles.
                             But it was unclear how much effect the scheme
                             had on Russian forces.


                      # ⚓ New York Times ☛ Thanks_to_Convicted_Felon,_Saudi
                        Arabia_Gets_a_Big_Week_in_Diplomacy⠀⇛


                             Riyadh is hosting U.S., Russian and Arab
                             officials for high-stakes talks on Ukraine
                             and Gaza, more proof of its regional clout
                             and warm relations with President Convicted
                             Felon.


                      # ⚓ New York Times ☛ Bucha,_Site_of_Massacre,_Feels_Sting
                        of_Convicted_Felon_Shift_on_Ukraine⠀⇛


                             Residents of a Ukrainian suburb that was the
                             site of notorious attacks on civilians after
                             Russia invaded are alarmed by President
                             Convicted Felon’s warm words for Moscow.


                      # ⚓ New York Times ☛ Zelensky_Meets_Kellogg,_U.S._Envoy
                        to_Ukraine,_Amid_Public_Spat_With_Convicted_Felon⠀⇛


                             Keith Kellogg and President Volodymyr
                             Zelensky were expected to discuss possible
                             paths to ending the war and ways to defuse
                             tensions between Washington and Kyiv.


                      # ⚓ New York Times ☛ What_to_Know_About_the_Saudi_Crown
                        Prince’s_Role_in_Global_Diplomacy⠀⇛


                             The kingdom’s de facto leader, Crown Prince
                             Mohammed bin Salman, was once shunned in
                             diplomatic circles. Now he is playing an
                             important role in negotiations over Gaza and
                             Ukraine.


                      # ⚓ The Straits Times ☛ China_backs_Convicted_Felon’s
                        Ukraine_peace_bid_at_G-20_as_US_allies_rally_behind
                        Zelensky⠀⇛


                             Foreign Minister Wang Yi said China is
                             willing to continue playing a constructive
                             role in the political resolution of the
                             crisis.


                      # ⚓ Meduza ☛ 25_Russian_conscripts_were_killed_last
                        summer_in_Ukraine’s_surprise_incursion_into_the_Kursk
                        region_—_Vertska_Media_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Ukrainian_military_intelligence_head_says_he
                        expects_a_ceasefire_deal_before_the_end_of_the_year_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_guided_aerial_bomb_hits_apartment
                        building_in_Ukraine’s_Kherson_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Trump_says_the_Russians_‘have_the_cards’_in
                        negotiations_to_end_war_in_Ukraine_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Trump_may_keep_pursuing_Ukrainian_minerals
                        deal,_seeking_‘simplified’_agreement_first_and_details
                        later_—_Reuters_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia_pummels_Ukraine’s_Odesa_with_drones
                        for_second_day,_causing_more_power_outages_—_Meduza⠀⇛


                      # ⚓ Latvia ☛ Russian_property_purchase_ban_moves_forward
                        in_Latvia⠀⇛


                             Latvia's parliament, the Saeima, gave support
                             to a bill Thursday, February 20 that would
                             ban real estate purchases in Latvia by
                             Russian and Belarusian citizens.


                      # ⚓ Latvia ☛ Contract_signed_to_put_surveillance_systems
                        on_Latvian-Russian_border⠀⇛


                             The design and construction company Citrus
                             Solutions has signed five cooperation
                             agreements with the Latvian State Radio and
                             Television Centre (LVRTC) for the design,
                             construction, and supervision of automated
                             technological border surveillance
                             infrastructure at the external land border
                             between Latvia and Russia, the company said
                             on February 20.


                      # ⚓ North_Korea’s_‘largest’_warship_under_construction
                        with_Russian_aid:_report⠀⇛


                             Construction of the vessel started in May
                             2024 at the Chongjin Shipyard on the
                             northeast coast.


                      # ⚓ RFERL ☛ 3_Tajik_Migrants_'Killed_In_Russian_Security
                        Forces_Raid'⠀⇛


                             Three Tajik migrants have been killed in a
                             Russian security forces raid, relatives and
                             friends said, after local authorities claimed
                             they had uncovered a terrorist plot in
                             Russia's western Pskov region.


                      # ⚓ New York Times ☛ In_Private_Remarks_on_Russia,_Rubio
                        Tries_to_Reassure_Europeans⠀⇛


                             European officials were not sure what to make
                             of the secretary of state’s measured
                             assessment of Washington’s apparent pivot
                             toward Moscow.


                      # ⚓ New York Times ☛ Next_Likely_Chancellor_Promises_a
                        Tougher_Germany⠀⇛


                             Friedrich Merz, whose conservative party is
                             ahead in polls before Sunday’s election, sees
                             an “epochal rupture” with a United States
                             that is more aligned with Russia.


                      # ⚓ Meduza ☛ Three_tankers_damaged_by_explosions_in_the
                        Mediterranean_after_recent_visits_to_Russian_ports_—
                        Reuters_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Latvia_expels_Russian_human_rights_activist
                        recently_exposed_for_lying_about_her_past_—_Meduza⠀⇛


                      # ⚓ JURIST ☛ Rights_group_urges_Poland_to_reject_bill
                        suspending_asylum_rights_at_border_with_Belarus⠀⇛


                             Human Rights Watch (HRW) on Wednesday issued
                             a statement urging Poland to scrap a bill
                             that would temporarily suspend asylum rights
                             at its border with Belarus.


                      # ⚓ Atlantic Council ☛ Dictator_and_Putin_seek_economic
                        reset_but_businesses_may_not_rush_back_to_Russia⠀⇛


                             As the Convicted Felon administration seeks
                             to reset relations with Russia as part of a
                             peace process to end the war in Ukraine,
                             Moscow is pushing the idea of increased
                             economic cooperation, writes Edward Verona.


                      # ⚓ NYPost ☛ Mr._President:_Putin_is_THE_dictator_and_9
                        other_Ukraine-Russia_war_truths_we_ignore_at_our
                        peril⠀⇛


                             This has been a dizzying and disorienting
                             week in international diplomacy. One with
                             wild implications for Ukraine, the future of
                             America’s standing in the world and President
                             Convicted Felon’s legacy. President Convicted
                             Felon is absolutely right in wanting to end
                             the bloodshed in Ukraine. The suffering has
                             been appalling and the stalemate brutal.


                      # ⚓ Meduza ☛ Trump’s_sudden_turn_against_Zelensky_came_as
                        a_shock_to_many_Americans._It_shouldn’t_have._—
                        Meduza⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # § Open Data⠀➾


                      # ⚓ Le Monde ☛ Digital_archivists_on_the_offensive
                        against_Trump's_'unprecedented'_purge_of_government
                        websites⠀⇛


                             Since Donald Trump's return to power, Lynda
                             Kellam has been sleeping less. Outside of her
                             working hours and her activities as secretary
                             of IASSIST, an organization of public data
                             professionals, she is part of a group of a
                             dozen volunteers who are busy, in their spare
                             time, day and night, running and coordinating
                             the "Data Rescue Project."


                             They first coordinated a large part of the
                             needs and actions for safeguarding American
                             public data in a Google Doc, before switching
                             to a dedicated site. These efforts rely on
                             the goodwill of citizens and, above all, on
                             dozens of organizations dedicated to
                             archiving the web and public resources, made
                             up in particular of archivists working in
                             American universities.


          o § Environment⠀➾


                # § Energy/Transportation⠀➾


                      # ⚓ Ruben Schade ☛ Electrarc240_explains_switch_mode
                        power_supplies⠀⇛


                             This was such a fun video! Teachers that can
                             explain abstract or difficult concepts using
                             relatable analogies are worth their weight in
                             linear power supplies.


                # § Wildlife/Nature⠀➾


                      # ⚓ Barrons ☛ US_National_Park_Workers_Reckon_With_Fear,
                        Anger_After_Layoffs⠀⇛


                             Erikka Olson spent five years building her
                             resume with a seasonal job at California's
                             Yosemite National Park before she finally
                             landed a permanent position with the US
                             Forest Service in Nevada.


                             This past weekend, the Trump administration
                             laid her off, along with thousands of other
                             federal employees.


                             The cuts were part of the work of the newly-
                             created Department of Government Efficiency
                             (DOGE), led by billionaire Elon Musk, as part
                             of a declared effort to reduce public
                             spending by dismantling the federal
                             bureaucracy.


                             The National Parks Conservation Association
                             (NPCA) estimates 1,000 US National Park
                             Service employees who were on one-year
                             probationary periods were laid off. About
                             3,400 employees of the US Forest Service were
                             among the cuts too, according to multiple US
                             media reports.


                      # ⚓ The Straits Times ☛ ‘Upgrade_from_the_usual_monitor
                        lizard_sighting’:_Visuals_of_crocodile_in_KL_river_go
                        viral_online⠀⇛


                             Photos of the reptile were shared by a user
                             on X.


          o § Finance⠀➾


                # ⚓ Tech_layoffs_continue_into_2025_as_industry_cuts_another
                  26,000_jobs_|_Capacity_Media⠀⇛


                       The wave of job cuts in the tech and telecoms
                       sector shows no signs of slowing, with new data
                       revealing that 26,215 employees have already been
                       laid off in 2025.


                       This follows 2024, which saw 280,991 jobs lost
                       globally as companies struggled with economic
                       uncertainty, declining revenues, and shifting
                       market conditions.


                # ⚓ Hong Kong Free Press ☛ Beijing_says_China,_US_should_show
                  ‘mutual_respect’_on_trade_tensions⠀⇛


                       China called on Thursday for the United States to
                       show “mutual respect” in managing commercial
                       tensions after President The Insurrectionist said a
                       trade deal with Beijing was “possible”. Convicted
                       Felon has threatened sweeping tariffs on allies and
                       adversaries alike, including China, in the month
                       since he took office.


                # ⚓ The Straits Times ☛ Malaysia_set_to_grab_bigger_share_of_US
                  glove_market_with_new_Convicted_Felon_tariffs_on_China
                  goods⠀⇛


                       Its glove makers could gain an additional 10 per
                       cent slice of the US medical glove pie, analysts
                       say.


                # ⚓ The Straits Times ☛ China_says_'doing_its_best'_to_push_for
                  tariff_negotiations_with_EU⠀⇛


                       China has been "doing its best" to push for
                       negotiations with the European Union over its
                       tariffs on Chinese-made electric vehicles, a
                       commerce ministry spokesperson said on Thursday,
                       almost four months after the punitive import curbs
                       took effect.


                # ⚓ The Straits Times ☛ More_ryokan_inns_in_Japan_encouraging
                  guests_to_eat_out_due_to_staff_shortage⠀⇛


                       It is crucial for ryokan, restaurants and other
                       facilities to collaborate to attract tourists.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ France24 ☛ A_model_in_crisis:_Germans_head_to_polls_amid
                  economic_downturn⠀⇛


                       The economy is a top concern for voters in Germany
                       as they go to the polls on Sunday to elect a new
                       government. The country has seen two consecutive
                       years of economic contraction and this stagnation
                       could very well continue for a third year. Its
                       post-Covid recovery was completely stunted by
                       Russia's full-scale invasion of Ukraine and the
                       energy crisis that followed, laying bare Berlin's
                       deep dependence on Moscow's oil and gas. Now the
                       return of The Insurrectionist as US president is
                       further muddying the prospects for growth. To
                       better understand how Germany got here and how it
                       can dig itself out of this hole, Charles Pellegrin
                       talks to Shahin Vallée, senior research fellow at
                       the German Council on Foreign Relations.


                # ⚓ New York Times ☛ China_Defends_South_Africa’s_G20_Ambitions
                  as_Rubio_Snubs_Meeting⠀⇛


                       The absence of Secretary of State Marco Rubio hung
                       over the year’s first high-level meeting of the
                       world’s largest economies, with diplomats fretting
                       over turbulent times.


                # ⚓ New York Times ☛ Chinese_Embassy_Plan_in_London_Sets_Off
                  Opposition⠀⇛


                       Britain appears ready to approve what would be the
                       largest diplomatic outpost in Europe, but neighbors
                       and activists fear tapped phone lines and
                       suppressed protests.


                # ⚓ CS Monitor ☛ Gawkin’_in_a_winter_wonderland:_The_festival
                  in_Harbin,_China,_is_as_cool_as_it_looks⠀⇛


                       The Harbin International Ice and Snow Sculpture
                       Festival features ephemeral artworks built from ice
                       blocks pulled from the Songhua River.


          o § Censorship/Free Speech⠀➾


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_university_student_union
                  axes_Burmese_film_screening,_citing_last-minute_gov’t
                  warning⠀⇛


                       A student union at a Hong Kong university has
                       cancelled the screening of a Burmese film set in
                       Myanmar’s ongoing civil war, citing a last-minute
                       government warning that hosting the event may break
                       the law.


                # ⚓ Silicon Angle ☛ FCC_launches_probe_into_censorship_on_Big
                  Tech_platforms⠀⇛


                       The Federal Trade Commission today announced that
                       it will investigate alleged censorship on tech
                       platforms, explaining that any wrongdoing would
                       “have violated the law.” “Tech firms should not be
                       bullying their users,” said FTC Chairman Andrew
                       Ferguson, recently chosen by President Convicted
                       Felon to lead the commission.


          o § Civil Rights/Policing⠀➾


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_police_intercept_8_cars
                  over_suspected_illegal_hire_after_cab_union_chief_apologises
                  for_strike_threat⠀⇛


                       Hong Kong police have intercepted eight drivers on
                       suspicion of using their private vehicles for
                       illegal hire. Six men and two women, aged between
                       36 and 63, were intercepted on Wednesday by police
                       officers who posed as passengers, the police said.


                # ⚓ Uyghur_freed_from_captivity_in_Morocco_arrives_in_United
                  States⠀⇛


                       Human rights activist Idris Hasan had been detained
                       since July 2021, awaiting possible extradition to
                       China.


                # ⚓ Hong_Kong’s_Democratic_Party_to_discuss_disbanding:
                  leader⠀⇛


                       Party leaders will talk about disbanding amid an
                       ongoing crackdown on political opposition.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ Join_the_Cooperation_SIG_to_help_shape_the_WSIS+20
                  Review_process⠀⇛


                       Learn how you can take action in the WSIS+20 Review
                       process during APRICOT 2025 / APNIC 59.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Dennis Crouch/Patently-O ☛ Reimagining_Patent_Examination:
                  A_(Half-Baked)_Proposal_for_Pre-Filing_Certification⠀⇛


                       Amid this dramatic reshaping of federal operations,
                       I wanted to explore a potential structural reform:
                       allowing patent monopoly applicants to obtain pre-
                       filing certification of their applications through
                       rigorous outside examination equivalent to USPTO
                       standards. This certification could then facilitate
                       expedited examination at the USPTO, similar to how
                       the Patent Prosecution Highway (PPH) program
                       operates for international applications, but with
                       important distinctions that could make it more
                       effective.  The U.S. patent monopoly examination
                       system faces persistent challenges of long pendency
                       times, substantial unpredictability, variable
                       quality despite the USPTO’s continued efforts at
                       improvement, and high costs. Although not without
                       potential serious concerns, the proposal could
                       address many of these elements.


                # ⚓ Unified Patents ☛ IPVal_entity,_5G_IP_Holdings,_5G_patent
                  monopoly_found_invalid⠀⇛


                       On February 18, 2025, the Central Reexamination
                       Unit (CRU) entered a notice of intent to issue a
                       reexamination certificate canceling all claims
                       (claims 1-12) of U.S._Patent_10,813,163, owned and
                       asserted by 5G IP Holdings LLC, an NPE and IP
                       Valuation_Partners,_LLC entity. The '163 patent
                       monopoly generally relates to discontinuous
                       reception (DRX) and utilizing slots within
                       subframes to adapt DRX to function within the 5G
                       frame structure.


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ How_transparent_is_the_Unified_Patent_Court?
                        [Ed: Unified Patent Court is illegal, so this Team UPC-
                        funded rag is asking the qrong question. It's just EPO
                        corruption crossing over to the EU.]⠀⇛


                             The Unified Patent Court cannot be accused of
                             not striving for transparency. Last week, it
                             not only published the budget for 2025, which
                             provides insights into the key economic
                             figures and reveals that the court is
                             planning to greatly expand the judiciary.


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Korean_Music_Groups_Call_for_Anti-
                  Tampering_Law_Amid_Ugly_NewJeans_v._Hybe_Contract_Battle⠀⇛


                       What’s stopping K-pop sensations from nixing agency
                       contracts, rebranding, and setting out on their
                       own? Not too much, according to Korean music
                       groups, which are warning that the ongoing
                       NewJeans/NJZ controversy “threatens the entire
                       industry.”





                    ䷩ 𝚕𝚒𝚗𝚎 5813

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 21/02/2025: Myanmar Scam Centre and
Disruptions at USPTO⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025,
updated Feb 21, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Integrity/Availability/Authenticity
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Ruben Schade ☛ Reconciling…_my_brain!⠀⇛


                 I was reconciling my accounts over lunch—like a
                 gentleman—when I went to my budget view and none of the
                 resulting numbers made sense. All these accounts,
                 transactions, and budget envelope amounts that had been
                 zero’d out suddenly had wildly incorrect numbers going
                 back to last year.


                 I scoured all the transactions I’d added since the
                 beginning of the year. Everything looked correct! Why
                 were some envelopes suddenly stuffed with extra money,
                 and others were in the red, over the period of twelve
                 months!? I’d literally entered these before, and they’d
                 never been a problem before.


          o § Science⠀➾


                # ⚓ France24 ☛ How_Earth_can_defend_itself_against_the_'city
                  killer'_asteroid⠀⇛


                       NASA said on Tuesday that the recently
                       discovered 2024 YR4 asteroid has a 3.1 percent
                       chance of hitting Earth in December, 2032 -- the
                       highest probability for an impact by such a large
                       space rock in modern forecasting. But there's no
                       need to worry, as experts say that humanity is 'not
                       defenseless'.


                # ⚓ Science Alert ☛ Hundreds_of_Black_Hole_'Missing_Links'_May
                  Have_Been_Discovered_in_New_Survey⠀⇛


                       Guess they're not so missing.


                # ⚓ Science Alert ☛ 3,500-Year-Old_Pharaoh's_Tomb_Found_in
                  Egypt_Is_First_Since_Tutankhamun's⠀⇛


                       The search for his treasures continues.


                # ⚓ Science Alert ☛ Here_Are_Our_Defense_Options_Against
                  Potential_'City_Killer'_Asteroid_Impact⠀⇛


                       "Don't panic."


                # ⚓ Science Alert ☛ 'Shocking':_Global_Glacier_Ice_Loss
                  Accelerates_by_36%_in_Last_Decade⠀⇛


                       Faster than ever recorded.


          o § Career/Education⠀➾


                # ⚓ Latvia ☛ Suspicions_of_Hey_Hi_(AI)_use_in_pupil_education
                  competitions_in_Latvia [Ed: Hey Hi (AI) and LLMs aren't the
                  same; this is about plagiarism tools, not intelligence]⠀⇛


                       This week, dozens of pupils and their schools
                       received news that their results in a regional-
                       level Olympiad (a competition in a certain subject
                       among the most talented) have been annulled. The
                       State Agency for Educational Development (VIAA)
                       believes that the students may have used artificial
                       intelligence to complete the work remotely, Latvian
                       Television reported on February 18.


          o § Hardware⠀➾


                # ⚓ Ruben Schade ☛ Unobtainium_PC_building_in_early_2025⠀⇛


                       This is a bit of a thinking out loud post that
                       normally I’d push to drafts, but Wouter has
                       convinced me that it should go out into the world
                       anyway :).


                       I don’t know how else to say it, but it’s a weird
                       time to be building PCs. After a brief reprieve
                       when blockchain guff fizzled out, graphics cards
                       have become unobtainium again in either
                       availability or price. We all hold out hope for AMD
                       and/or defective chip maker Intel to deliver the
                       goods, and at a price that will make them
                       reasonable against the entrenched market leader,
                       but we also know how this has worked out the last
                       couple of times.


                # ⚓ The Straits Times ☛ Taiwan_seeks_to_persuade_US_that_it
                  offers_chip_cooperation_–_not_competition⠀⇛


                       For Taiwan, maintaining a positive relationship
                       with the US is not just for economic, but also
                       security reasons. 


                # ⚓ Hackaday ☛ Be_Careful_What_You_Ask_For:_Voice_Control⠀⇛


                       We get it. We also watched Star Trek and thought
                       how cool it would be to talk to our computer. From
                       Kirk setting a self-destruct sequence, to Scotty
                       talking into a mouse, or Picard ordering Earl Grey,
                       we intuitively know that talking to a computer is
                       better than typing, right? Well, computers talking
                       back and forth to us is no longer science fiction,
                       and maybe we aren’t as happy about it as we thought
                       we’d be.


                # ⚓ Hackaday ☛ Retrotechtacular:_Yamming_CRT_Yokes⠀⇛


                       Those of us who worked in TV repair shops, back
                       when there was such a thing, will likely remember
                       the cardinal rule of TV repair: Never touch the
                       yoke if you can help it. The complex arrangement of
                       copper wire coils and ferrite beads wrapped around
                       a plastic cone attached to the neck of the CRT was
                       critical to picture quality, and it took very
                       little effort to completely screw things up. Fixing
                       it would be a time-consuming and frustrating battle
                       with the cams, screws, and spacers that kept the
                       coils in the right orientation, both between
                       themselves and relative to the picture tube. It was
                       best to leave it the way the factory set it and to
                       look elsewhere for solutions to picture problems.


                # ⚓ Hackaday ☛ Homebrew_CPU_Gets_A_Beautiful_Rotating_Cube
                  Demo⠀⇛


                       [James Sharman] designed and built his own 8-bit
                       computer from scratch using TTL logic chips,
                       including a VGA adapter, and you can watch it run a
                       glorious rotating cube demo in the video below.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Latvia ☛ Health_Ministry_considers_taking_over_regional
                  hospitals_in_Latvia⠀⇛


                       The Ministry of Health (VM) will soon start
                       negotiations on the takeover of several large
                       regional hospitals or the formation of joint
                       capital companies with local governments, but the
                       hospital association does not support such a move,
                       Latvian Television reported on February 19.


                # ⚓ New York Times ☛ Dictator_Administration_Has_Fired_Health
                  Inspectors_at_Some_Border_Stations⠀⇛


                       Scientists worry that the losses may open the door
                       to human, plant and animal diseases that would
                       otherwise have been caught.


                # ⚓ New York Times ☛ DOGE_Cuts_9/11_Survivors’_Fund,_and
                  Republicans_Join_Democrats_in_Rebuke⠀⇛


                       After 20 percent of the World Trade Center Health
                       Program staff was terminated last week, Democratic
                       lawmakers were outraged. On Wednesday, Republican
                       lawmakers joined them.


                # ⚓ New York Times ☛ RFK_Jr._Announces_New_HHS_Guidance
                  Recognizing_Only_Two_Sexes⠀⇛


                       The new guidance follows President Convicted
                       Felon’s demand that the Health and Human Services
                       Department align with his executive order barring
                       transgender athletes from women’s sports.


                # ⚓ Parents_weigh_in_on_teens’_non-surgical_cosmetic
                  procedures⠀⇛


                       The U-M Health C.S. Mott Children's Hospital
                       National Poll on Children's Health showed that one-
                       sixth of parents would support their teens
                       receiving non-surgical cosmetic procedures.


                # ⚓ Science Alert ☛ Common_Mushroom_Fiber_May_Protect_Against
                  Flu,_Study_Finds⠀⇛


                       A promising new approach.


                # ⚓ New York Times ☛ Updates_on_Pope_Francis’_Health_Leave_Room
                  for_Speculation⠀⇛


                       Updates on Francis’ condition, which was said to be
                       stable on Wednesday, have typically been spare,
                       leaving plenty of room for suspicion and
                       speculation.


                # ⚓ Study_examines_how_to_cut_wasteful_pre-surgery_testing⠀⇛


                       A study by a team from U-M and Brigham and Women's
                       Hospital tested a program designed to reduce
                       unneeded preoperative tests at U-M Health.


                # ⚓ Rohingya_in_limbo_as_some_aid_groups_suspend_health
                  services_at_Bangladesh_camps⠀⇛


                       Facilities set up by foreign aid groups provide
                       medical treatment for thousands of Rohingya
                       refugees.


                # ⚓ LRT ☛ Lithuania_is_a_unique_case_in_cutting_alcohol
                  consumption_–_experts⠀⇛


                       Lithuania has managed to cut alcohol consumption
                       significantly in record time after implementing
                       the World Health Organization’s (WHO)
                       recommendations, foreign and local experts have
                       said.


                # ⚓ The Straits Times ☛ China_woos_Bangladesh_with_healthcare
                  as_India_ties_sour⠀⇛


                       Three hospitals had been designated for Bangladeshi
                       patients to improve medical services.


                # ⚓ Science Alert ☛ Study_Reveals_How_This_Artificial_Sweetener
                  May_Cause_Heart_Damage⠀⇛


                       "We have to know the long-term health impact."


                # ⚓ Science Alert ☛ Going_Gluten_Free_Could_Come_at_a_Cost_to
                  Your_Nutrition_And_Your_Pocket⠀⇛


                       It's a medical necessity for some.


                # ⚓ Science Alert ☛ Scientists_Put_a_Human_Language_Gene_Into
                  Mice_And_Changed_Their_Voice⠀⇛


                       Squeak squeakin' squeak squeakity.


                # ⚓ Science Alert ☛ Ozempic_Reduces_Desire_to_Binge_Alcohol,
                  Suggests_Amazing_New_Study⠀⇛


                       What else can this drug do?


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ The Straits Times ☛ Chinese_workers_from_Myanmar_scam
                        centres_heading_home_via_Thailand⠀⇛


                             China has put on 16 flights over the next
                             three days to ferry 600 of its nationals
                             home.


                      # ⚓ The Straits Times ☛ Myanmar_returns_first_batch_of
                        Chinese_scam_workers_to_Thailand⠀⇛


                             China has put on 16 flights over the next
                             three days to ferry 600 of its nationals
                             home.


                      # ⚓ OPINION:_China_pushes_Thailand_to_act_on_cross-border
                        scam_centers⠀⇛


                             Bangkok is finally offering an unprecedented
                             degree of cooperation in combating scam
                             centers along the Myanmar bord


                      # ⚓ The Straits Times ☛ Myanmar_scam_centre_survivors
                        recall_torture_and_coercion⠀⇛


                             260 people, mostly victims, were sent from
                             Myanmar to Thailand as a multinational
                             crackdown on scam centres.


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ South_Korean_Officials_Convicted_Over
                  Forcibly_Sending_North_Koreans_Home⠀⇛


                       The case of two North Korean fishermen, who
                       murdered 16 compatriots before they sought asylum,
                       has become a political minefield in the South.


                # ⚓ The Straits Times ☛ Top_South_Korean_judge_faces
                  disinformation_deluge_as_Yoon_Suk_Yeol’s_impeachment_looms⠀⇛


                       The allegations include bogus child pornography
                       claims and fabricated support for communism.


                # ⚓ The Straits Times ☛ South_Korea_court_finds_former
                  officials_guilty_of_forcible_return_of_North_Korean
                  fishermen⠀⇛


                       The government of former president Moon Jae-in
                       called the fishermen “dangerous criminals”.


                # ⚓ The Straits Times ☛ North_Korea_reopens_to_tourists,
                  including_Singapore_visitors⠀⇛


                       The reopening is restricted to tours of the Rason
                       Special Economic Zone.


                # ⚓ The Straits Times ☛ North_Korea_criticises_US_over_Aukus
                  nuclear_submarine_deal⠀⇛


                       A KCNA commentary said Washington should be wary of
                       consequences for what it said were nuclear
                       alliances.


                # ⚓ The Straits Times ☛ South_Korean_president’s_lawyer_says
                  martial_law_bid_sought_to_stop_‘dictatorship’⠀⇛


                       He has been behind bars since he was arrested in
                       January on charges of insurrection.


                # ⚓ The Straits Times ☛ Seoul_says_it_supports_North_Korean
                  POWs’_right_to_asylum_in_South⠀⇛


                       A South Korean official said North Korean soldiers
                       are "constitutionally considered our nationals".


                # ⚓ North_Korea’s_‘Day_of_the_Shining_Star’_dimmer_this_year⠀⇛


                       Kim Jong Il’s birthday touted as the country’s
                       greatest holiday, but no ‘presents’ from late Dear
                       Leader in 2025.


                # ⚓ JURIST ☛ UN_publishes_report_detailing_human_rights
                  violations_in_North_Korea⠀⇛


                       The UN Office of the High Commissioner published a
                       report on Friday detailing North Korea’s ongoing
                       and worsening human rights crisis.


                # ⚓ France24 ☛ South_Korea's_Yoon_becomes_first_sitting
                  president_to_stand_trial_in_criminal_case⠀⇛


                       Impeached South Korean president Yoon Suk Yeol went
                       on trial on Thursday. The former prosecutor has
                       been behind bars since January on charges of
                       insurrection, for which he could be sentenced to
                       life in prison or face the death penalty.


                # ⚓ New York Times ☛ An_Opening_for_China,_Made_in_America⠀⇛


                       Trump’s long and growing list of shortsighted
                       actions in Latin America has created an opening
                       there for America’s adversaries, most notably
                       China.


                # ⚓ The Straits Times ☛ China_promises_to_always_be_Latin
                  America’s_‘trustworthy’_friend_as_Convicted_Felon_lays_out
                  demands⠀⇛


                       China is looking to improve its foothold in a
                       region historically under the US sphere of
                       influence.


                # ⚓ The Straits Times ☛ China_opposes_Vietnam’s_building_work
                  on_disputed_reef_in_South_China_Sea⠀⇛


                       Vietnam’s land reclamation has expanded the reef by
                       10 times since 2022, according to a Chinese study.


                # ⚓ China_denounces_Vietnam’s_island_building_in_South_China
                  Sea⠀⇛


                       In a rare protest Beijing said Hanoi has been
                       constructing on ‘illegally-occupied’ Spratly
                       islands and reefs.


                # ⚓ The Strategist ☛ Still_not_confident_enough:_China_isn’t
                  likely_to_move_on_Taiwan_in_2025⠀⇛


                       Despite China’s rapid military improvements, it’s
                       unlikely to use large-scale force against Taiwan in
                       2025.


                # ⚓ The Straits Times ☛ Foreign_spies_seeking_AUKUS_secrets,
                  Australia_intelligence_chief_says⠀⇛


                       Canberra - Australia's military is being targeted
                       by foreign intelligence over its AUKUS nuclear
                       submarine partnership with the United States and
                       Britain, and faces growing espionage and sabotage
                       threats, Australia's spy chief said on Wednesday.


                # ⚓ The Straits Times ☛ New_Zealand_must_‘reset’_Cook_Islands
                  ties_after_China_pact:_Foreign_Minister⠀⇛


                       The deals raise concerns over China’s growing
                       presence in the region and potential threats to
                       national security.


                # ⚓ The Straits Times ☛ Gunmen_kill_seven_bus_passengers_in
                  southwest_Pakistan⠀⇛


                       Separatist gunmen shot dead seven passengers on a
                       Lahore-bound bus in southwestern Pakistan's
                       Balochistan province on Tuesday after forcing them
                       off the vehicle and checking their identity
                       documents, officials said.


                # ⚓ Myanmar_adopts_law_for_foreign_firms_to_provide_armed
                  security⠀⇛


                       Former Chinese soldiers could guard energy
                       pipelines in the event of war.


                # ⚓ LRT ☛ Reeling_after_Munich,_Lithuanian_leaders_consider_new
                  approaches_to_security⠀⇛


                       With the new US administration indicating in no
                       uncertain terms that Washington is moving away from
                       Europe, Lithuania, having long been staking its
                       security on NATO and the US, is grappling with the
                       new possible scenarios.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_seeks_to_tighten_labour
                  union_laws_on_national_security_grounds⠀⇛


                       The Hong Kong government has proposed legislative
                       amendments to permanently bar those convicted of
                       national security offences from serving in labour
                       unions and to require all foreign funding to be
                       vetted by the authorities.


                # ⚓ Defence Web ☛ Hensoldt_launches_new_data_link_at_Idex
                  2025⠀⇛


                       Hensoldt has launched the sixth generation of its
                       data link solution, the DL-6000, at the Idex 2025
                       exhibition underway this week in Abu Dhabi.
                       “Engineered to deliver exceptional security and
                       reliability, the DL-6000 enables seamless, long-
                       range, line-of-sight HD video and telemetry data
                       exchange across multiple platforms,” the company
                       said.


                # ⚓ Scoop News Group ☛ Energy_CISO:_Agencies_can’t_implement
                  zero_trust_alone⠀⇛


                       Federal IT and cybersecurity officials said
                       companies who sell zero trust technologies to the
                       government must do more to make them interoperable.


                # ⚓ Defence Web ☛ AU_adds_its_voice_to_calls_for_DRC
                  ceasefire⠀⇛


                       The voice of the Peace and Security Council (PSC)
                       of the African Union (AU) has been added to those
                       worldwide calling for an immediate and
                       unconditional ceasefire in the eastern Democratic
                       Republic of Congo (DRC).


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


                      # ⚓ Meduza ☛ Trump_calls_Zelensky_a_‘dictator’_and
                        accuses_him_of_profiting_from_war_—_Meduza⠀⇛


                      # ⚓ France24 ☛ Baltic_region_prepares_for_war_as_Russia
                        and_US_debate_Ukraine's_fate⠀⇛


                             As Russia and the US debate Ukraine’s future,
                             countries on the Baltic Sea are ramping up
                             preparations for a military conflict amid
                             fears that Russia is preparing for a future
                             war with NATO.


                      # ⚓ France24 ☛ Andrey_Kurkov:_'You_can't_write_fiction
                        when_your_houses,_cities_are_shelled_with_missiles,
                        drones'⠀⇛


                             As we approach the third anniversary of
                             Russia's full-scale invasion of Ukraine,
                             FRANCE 24's Erin Ogunkeye welcomes celebrated
                             Ukrainian novelist and author Andrey Kurkov
                             to share his very powerful and personal
                             accounts of a veritable proxy war, an
                             unprovoked war of attrition as seen from his
                             war diaries 'Our Daily War'. "Every small
                             detail of life is now very different from
                             pre-war Ukraine, he explains. "We're all now
                             different people: I've lost my feeling of
                             value for material, my feeling that my house
                             and my apartment don't belong to me anymore,
                             they belong to the war."


                      # ⚓ LRT ☛ Lithuania_suspends_transit_of_Belarusian
                        rapeseed_oil_from_occupied_parts_of_Ukraine⠀⇛


                             Thousands of tons of rapeseed oil made by
                             Belarusian company Agroprodukt have been
                             passing through Lithuania by rail, the
                             15min.lt news website reported on Wednesday,
                             having carried out an investigation with
                             several foreign partners.


                      # ⚓ France24 ☛ Dictator_calls_Ukranian_president
                        "dictator",_Zelensky_says_Convicted_Felon_living_in
                        "disinformation_space"⠀⇛


                             Relations between Ukrainian President
                             Volodymyr Zelenskyy and U.S. President The
                             Insurrectionist deteriorated rapidly
                             Wednesday as Zelenskyy said Convicted Felon
                             was living in a Russian-made “disinformation
                             space" and Convicted Felon called Zelenskyy
                             “a dictator without elections” in comments
                             that were sure to complicate efforts to end
                             the war. FRANCE 24's Gulliver Cragg reports
                             from Kyiv.


                      # ⚓ LRT ☛ Lithuanian_president_to_join_2nd_European
                        summit_on_Ukraine_remotely⠀⇛


                             Lithuanian President Gitanas Nausėda will
                             take part in a second summit on Ukraine and
                             European security, hosted by France on
                             Wednesday, via video link, his office
                             confirmed to BNS.


                      # ⚓ RFERL ☛ Dictator_Appears_To_Blame_Ukraine_For_War_But
                        'Confident'_Of_Reaching_Peace_Deal⠀⇛


                             U.S. President The Insurrectionist seems to
                             have blamed Volodymyr Zelenskyy for Moscow's
                             invasion of Ukraine, saying he was
                             “disappointed” that the Ukrainian president
                             complained about being frozen out of U.S.-
                             Russia talks in Saudi Arabia on ending the
                             war.


                      # ⚓ RFERL ☛ Dictator_Praises_MElon_For_Work_Cutting
                        Government_Waste⠀⇛


                             U.S. President The Insurrectionist defended
                             his decision to give billionaire businessman
                             MElon a major role in his administration as
                             head of the Department of Government
                             Efficiency (DOGE) amid backlash over the
                             freezing of funding for USAID, which affected
                             foreign assistance programs around the world.


                      # ⚓ RFERL ☛ France_Prepares_To_Host_Second_Ukraine_War
                        Summit⠀⇛


                             Following an emergency summit in Paris,
                             European leaders expressed willingness to
                             offer security guarantees to Ukraine, but
                             they warned that the level of such assurances
                             would be based on Washington’s participation
                             in the event of a comprehensive peace
                             agreement.


                      # ⚓ The Straits Times ☛ US_ally_Australia_says_Ukraine
                        conflict_must_be_resolved_on_Ukraine's_terms⠀⇛


                             U.S. security ally Australia, which has
                             provided A$1.5 billion in support to Ukraine
                             in its war with Russia, said on Thursday that
                             Moscow was the aggressor in the conflict and
                             it must be resolved on Kyiv's terms.


                      # ⚓ The Straits Times ☛ Kazakhstan_to_contact_Ukraine
                        over_drone_attack_on_Caspian_pipeline,_official_says⠀⇛


                             Kazakhstan will seek contact with Ukraine in
                             order to avoid any repeat of this week's
                             Ukrainian drone strike in southern Russia
                             that hit a pumping station of the main Kazakh
                             oil export pipeline, an official was quoted
                             as saying on Wednesday.


                      # ⚓ Latvia ☛ Event_series_at_Latvian_National_Art_Museum
                        for_Ukraine's_support⠀⇛


                             As the third anniversary of Russia's war in
                             Ukraine approaches, the Latvian National
                             Museum of Art has launched a series of events
                             in support of Ukraine. On Wednesday, February
                             19, the first event took place, inviting
                             everyone to print a piece of clothing with a
                             design by artist Elīna Brasliņa.


                      # ⚓ Hackaday ☛ The_US_Military’s_Unsecured_UFO_Satellites
                        And_Their_Use_By_Russia⠀⇛


                             Something that you generally don’t expect as
                             a North-America-based enthusiast, is to
                             listen in on Russian military communications
                             during their war in Ukraine via WebSDR, or
                             that these communications would be passing
                             through US military satellites that are happy
                             to just broadcast anything. Yet that’s the
                             situation that the Saveitforparts YouTube
                             channel recently described. As it turns out,
                             there is a gaggle of UFOs up there, as the US
                             DoD lovingly calls them.


                      # ⚓ Meduza ☛ Russian_attack_on_Ukraine’s_Odesa_knocks_out
                        power_and_heating_in_hundreds_of_apartment_buildings_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ U.S._suspends_immigration_applications_from
                        certain_Ukrainian_and_Latin_American_migrants_—_CBS_—
                        Meduza⠀⇛


                      # ⚓ Latvia ☛ Association:_Basic_hygiene_items_always
                        needed_for_Ukrainian_soldiers⠀⇛


                             Socks, wet wipes, fast food, shaving
                             accessories – invariably the things that
                             Ukrainian soldiers in the trenches are most
                             excited about. There are many needs at the
                             front, but self-care is not a daily routine
                             for soldiers, Latvian Television reported on
                             February 18.


                      # ⚓ Latvia ☛ Name_change_trend_observed_in_Latvia_after
                        Russian_invasion_of_Ukraine⠀⇛


                             Since Russia's full-scale invasion of Ukraine
                             almost three years ago, Latvia has seen a
                             trend of more and more people choosing to
                             change their Slavic name, according to data
                             from the Ministry of Justice, Latvian Radio
                             reports on February 19.


                      # ⚓ North_Korea_building_possibly_its_‘largest’_warship
                        with_Russian_help:_report⠀⇛


                             Construction of the vessel started in May
                             2024 at the Chongjin Shipyard on the
                             northeast coast.


                      # ⚓ Latvia ☛ Prison_drone_delivery_caught_by_Latvian
                        police⠀⇛


                             While law enforcement was monitoring critical
                             infrastructure at the time of Latvia
                             disconnecting from Russian electricity grid,
                             police near the Rīga Central Prison got a
                             catch – a drone that was carrying goods for
                             inmates, Latvian Television reported on
                             February 19.


                      # ⚓ Meduza ☛ ‘Who_else_would_they_glorify?’:_In_occupied
                        Mariupol,_Russia_just_opened_a_museum_to_a_key_enforcer
                        of_Stalinist_repressions_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Rubio_told_European_allies_that_U.S._won’t
                        lift_sanctions_against_Russia_until_war_is_over_—
                        Bloomberg_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ U.S._Ukraine_special_envoy_Keith_Kellogg
                        arrives_in_Kyiv_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ E.U._preparing_to_send_six_billion_euros_in
                        military_aid_to_Ukraine_—_Politico_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ The_‘strong’_versus_the_‘weak’_Former
                        Russian_diplomat_Boris_Bondarev_explains_the
                        shortcomings_and_risks_of_Trump’s_‘Ukraine_peace’_and
                        the_perils_of_European_indecision_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ U.K._considering_deploying_Typhoon_fighter
                        jets_to_Ukraine_as_part_of_peacekeeping_mission_—_The
                        Times_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘Weakness_leads_to_war’:_The_U.K._says_it’s
                        ready_to_send_troops_to_Ukraine_as_part_of_a_ceasefire
                        deal._What_would_this_actually_entail?_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘We’ll_have_to_win_it_militarily’:_Following
                        U.S.-Russia_talks,_many_pro-invasion_Russian_bloggers
                        see_an_end_to_Ukraine_—_but_not_to_the_war_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ U.S._Vice_President_Vance_says_Zelensky
                        endangers_Ukraine’s_‘existence’_by_criticizing_Trump
                        publicly_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘Why_would_Russia_concede_anything_when_it’s
                        already_winning?’_Carnegie_Russia_Eurasia_Center_fellow
                        Maksim_Samorukov_explains_Donald_Trump’s_negotiating
                        disadvantages_and_likely_cynical_plans_in_Ukraine_—
                        Meduza⠀⇛


                      # ⚓ France24 ☛ Dictator_"is_very_interested_in_doing
                        business_with_Russia":_analyst⠀⇛


                             President Zelensky said he will meet US envoy
                             Kellogg on Thursday and that he hopes for
                             "constructive" work with the US. The meeting
                             comes as Convicted Felon used an extended
                             social control media post on his Truth Social
                             platform to lash out at Zelensky and call the
                             Ukrainian a “dictator without elections."
                             Michael Benhamou, director of OPEWI, Europe's
                             War Institute, says that Convicted Felon is
                             aiming to open the Russian market to American
                             companies, rather than support Ukraine and
                             its allies.


                      # ⚓ France24 ☛ Fact-checking_The_Insurrectionist’s
                        statements_on_Ukraine⠀⇛


                             President The Insurrectionist has launched a
                             flurry of controversial claims about the war
                             in Ukraine and President Volodymyr Zelensky,
                             while addressing reporters at his Mar-a-Lago
                             resort. Many of these claims were made
                             without providing any evidence.


                      # ⚓ France24 ☛ Ukrainians_dismiss_Convicted_Felon's
                        broadside_against_Zelensky⠀⇛


                             US President, The Insurrectionist, has
                             branded Volodymyr Zelensky a 'dictator' who
                             'refused to have elections'. Defiant
                             Ukrainians are dismissing the extraordinary
                             broadside, saying they have to fight on, even
                             as their key ally engages in talks with the
                             enemy. They're also rejecting the idea of
                             holding elections during the war. Mayors,
                             officials and MPs from across the political
                             spectrum in Ukraine have been taking to
                             social control media to urge people to unite
                             behind their president. James Vasina reports.


                      # ⚓ France24 ☛ Dictator_blames_Ukraine_war_on_'dictator'
                        Zelensky⠀⇛


                             After the US held bilateral talks with
                             Russian delegates in Saudi Arabia on Tuesday,
                             breaking from US policy on the Ukraine war,
                             US President The Insurrectionist chided
                             Ukrainian President Volodymyr Zelensky in a
                             social control media post on Wednesday,
                             calling him a "dictator" and baselessly
                             faulting him for causing the war. Zelensky
                             responded by qualifying Convicted Felon's
                             comments as "disinformation" from Russia, and
                             called for pragmatism during his meeting with
                             Convicted Felon's Ukraine envoy, Keith
                             Kellogg, which is set for Thursday.


          o § Environment⠀➾


                # § Energy/Transportation⠀➾


                      # ⚓ The Straits Times ☛ Vietnam_Parliament_approves
                        $10.7b_rail_link_to_China⠀⇛


                             China will provide some funding through loans
                             for the project, which is expected to cost
                             more than US$8 billion.


                      # ⚓ Atlantic Council ☛ Make_Europe_more_energy_secure_by
                        reforming_EU_regulations⠀⇛


                             Streamlining the European Union’s regulatory
                             environment could help ensure energy security
                             throughout the bloc.


                # § Wildlife/Nature⠀➾


                      # ⚓ Science Alert ☛ 90_Dolphins_Stranded_in_Australia_Are
                        Being_Euthanised._Here's_Why_They_Can't_Be_Saved.⠀⇛


                             Tragic.


          o § Finance⠀➾


                # ⚓ Federal News Network ☛ That_alarm_bell_about_the_nation’s
                  fiscal_health_is_growing_louder_and_louder⠀⇛


                       The government will once again spend a trillion
                       dollars more than it takes in this year, according
                       to the Government Accountability Office.


                # ⚓ New York Times ☛ Nepal_Took_a_Risk_on_a_$500_Million_U.S.
                  Grant._It_May_Now_Regret_It.⠀⇛


                       President Convicted Felon’s freezing of foreign aid
                       provides an opening for China to portray America as
                       an unreliable partner.


                # ⚓ Chinese_state_firms_win_billions_as_Hong_Kong_splurges_on
                  cross-border_development⠀⇛


                       Beijing-backed companies get 80% of cash spent on
                       two key projects, sparking questions over value for
                       Hong Kongers.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Federal News Network ☛ Governmentwide_firings_‘devastating’
                  to_probationary_federal_employees⠀⇛


                       The National Science Foundation fired 168 federal
                       employees, marking one of many agencies who fired
                       probationary feds at the Convicted Felon
                       administration's directions.


                # ⚓ The Straits Times ☛ ‘Drain_the_swamp’:_Australian
                  billionaire_Clive_Palmer_launches_Convicted_Felon-inspired
                  political_party⠀⇛


                       Mr Palmer said his Convicted Felonet of Patriots
                       party would “drain the swamp” in Canberra.


                # ⚓ New York Times ☛ Dictator_Media_Group_Sues_Brazilian_Judge
                  Weighing_Arrest_of_Jair_Bolsonaro⠀⇛


                       The lawsuit came hours after the justice received
                       an indictment of Brazil’s former president, who is
                       an ally of President Convicted Felon.


                # ⚓ New York Times ☛ MElon’s_DOGE_Seeks_Access_to_Americans’
                  Data,_Alarming_Government_Employees⠀⇛


                       Employees from MElon’s so-called Department of
                       Government Efficiency are gaining access to vast
                       amounts of information held by federal agencies,
                       even as lawsuits try to stop them.


                # ⚓ New York Times ☛ Dictator_Administration_Moves_to_End_New
                  York’s_Congestion_Pricing_Tolls⠀⇛


                       The transportation secretary said he would revoke
                       federal approval for the program, citing the cost
                       to motorists; the Metropolitan Transportation
                       Authority quickly filed a lawsuit to stop the move.


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


                # ⚓ ‘Time_is_running_out’_for_jailed_pro-democracy_media_mogul
                  Jimmy_Lai⠀⇛


                       Lai’s son Sebastien calls on Britain and the United
                       States to push for his father’s release.


          o § Civil Rights/Policing⠀➾


                # ⚓ CS Monitor ☛ Appeals_to_conscience_in_Damascus⠀⇛


                       A newly liberated Syria brings back activists who
                       long relied on nonviolent tactics in hopes of
                       building a democracy.


                # ⚓ New York Times ☛ China_Uses_Public_Shaming_to_Motivate
                  State_Workers⠀⇛


                       Local governments are handing out “snail awards” to
                       underperforming employees. But, for many, doing as
                       little as possible seems like the safest bet.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Dennis Crouch/Patently-O ☛ New_USPTO_Leadership_on_the
                  Horizon:_Lutnick_Confirmed_as_Commerce_Secretary,_Squires
                  Expected_as_Director⠀⇛


                       Yesterday, the Senate voted to confirm Howard
                       Lutnick as Secretary of Commerce. Lutnick, has been
                       CEO of Cantor Fitzgerald and a prolific inventor
                       named on over 400 U.S. patents. Commerce has a wide
                       coverage, including housing the USPTO.


                       Meanwhile, Dani Kass at Law360 is reporting that
                       John A. Squires, currently a partner at Dilworth
                       Paxson and former chief IP counsel at Goldman
                       Sachs, is expected to be nominated as the next
                       USPTO Director.  Like Lutnick, Squires has
                       extensive fintech experience.


                       The Director position requires presidential
                       nomination and Senate confirmation under 35 U.S.C.
                       § 3(a)(1). The statute specifically requires that
                       the Director be a U.S. citizen with a professional
                       background and proven ability in patent monopoly or
                       trademark law.  I expect that Sec. Lutnick will
                       play a key role in advancing Squires’ potential
                       nomination through the process.


          o § Trademarks⠀➾


                # ⚓ Federal News Network ☛ Trump-era_mandates_threaten_USPTO
                  stability,_trademark_filings⠀⇛


                       With the new administration's push toward a leaner
                       federal government, it could lead to unintended
                       consequences for the U.S. Patent and Trademark
                       Office.


                # ⚓ TTAB Blog ☛ TTAB_Grants_Petition_to_Cancel_VIVACE
                  Registration_for_Microneedling_Device:_Manufacturer_Owns_the
                  Mark,_Not_Distributor⠀⇛


                       In a 55-page decision, the Board granted a petition
                       for cancellation of registrations for the mark
                       VIVACE for a "radio frequency microneedling device"
                       on the ground of non-ownership. and the mark THE
                       VIVACE EXPERIENCE for "providing personalized
                       beauty spa services, namely, cosmetic body care and
                       microneedle services" on the ground of likelihood
                       of confusion with Petitioner's common law mark
                       VIVACE for microneedling devices. This blog post
                       will attempt to hit the high points. Sung_Hwan_E&B
                       Co._Ltd._d/b/a_SHEnB_Co._Ltd._v._Aesthetics
                       Biomedical,_Inc., Cancellation No. 92074719
                       (February 14, 2025) [not precedential] (Opinion by
                       Judge Cheryl S. Goodman). (Oral Argument held on
                       June 12, 2024).


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Altice_USA_Ordered_to_Disclose
                  Subscriber_Names,_Addresses,_and_More_in_Warner_Music
                  Copyright_Battle⠀⇛


                       A federal court has ordered Altice USA to turn over
                       the identities of up to 100 subscribers accused of
                       copyright monopoly infringement by Warner Music
                       Group (WMG) and Sony Music Entertainment (SME).





                    ䷩ 𝚕𝚒𝚗𝚎 7000

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 21/02/2025: TikTok Layoffs, WebOS
Software Patents in Bad Hands⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 21, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Wild_Garlic⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Ness Labs ☛ What_Type_of_Experimentalist_Are_You?⠀⇛


                 How do you respond to uncertainty? Do you jump straight
                 into action, carefully analyze the situation first, or
                 perhaps spend time imagining all the potential outcomes?


          o ⚓ At This Link ☛ Blog_Question_Challenge_2025⠀⇛


                 That post really solidified to me that there might be
                 something to this blogging rather than it just being a
                 way to shout into the void.


          o ⚓ Lucas da Silva ☛ About_30h_or_so_sleeping_until_arriving_in
            Japan⠀⇛


                 Sleeping while traveling has been my favorite pastime
                 lately, when I travel, that is, almost never.


          o ⚓ Idiomdrottning ☛ Designing_the_perfect_lock_screen_and
            notifications_system⠀⇛


                 No scheduling, no easy toggling, no time outs (like
                 “don’t disturb for the next N minutes”), no allowlist for
                 specific numbers to punch through, no “if they call twice
                 let them through”.


          o § Standards/Consortia⠀➾


                # ⚓ Wired ☛ The_National_Institute_of_Standards_and_Technology
                  Braces_for_Mass_Firings⠀⇛


                       Approximately 500 NIST staffers, including at least
                       three lab directors, are expected to lose their
                       jobs at the standards agency as part of the ongoing
                       DOGE purge, sources tell WIRED.


                # ⚓ The Korea Times ☛ Korea_to_invest_$29.5_million_in
                  developing_international_standards_for_advanced
                  technologies⠀⇛


                       The Korea Agency for Technology and Standards
                       (KATS), a standards agency under the ministry, will
                       spend most of the budget on developing technology
                       standards in 12 advanced industries that include
                       semiconductors, future mobility, robotics, quantum
                       energy and nuclear power.


          o § Science⠀➾


                # ⚓ Futurism ☛ Elon_Musk_Just_Caused_a_Huge_Headache_for_the
                  New_Head_of_NASA⠀⇛


                       In a tweet today, the mercurial entrepreneur
                       asserted that it's "time to begin preparations for
                       deorbiting the space station," arguing that "it has
                       served its purpose," with "very little incremental
                       utility."


                       Instead, Musk argued, the station should be
                       destroyed within two years — but left the final
                       decision "up to the President."


                # ⚓ Omicron Limited ☛ 60_years_ago:_Ranger_8_moon_photos_aid_in
                  Apollo_site_selection⠀⇛


                       Before Apollo astronauts set foot upon the moon,
                       much remained unknown about the lunar surface.
                       While most scientists believed the moon had a solid
                       surface that would support astronauts and their
                       landing craft, a few believed a deep layer of dust
                       covered it that would swallow any visitors. Until
                       1964, no closeup photographs of the lunar surface
                       existed, only those obtained by Earth-based
                       telescopes.


                # ⚓ The Register UK ☛ NSF_decimation_puts_future_US_science
                  leadership_in_doubt⠀⇛


                       The NSF confirmed the cuts to us in an email,
                       saying that it had dismissed 86 employees
                       classified as probationary, and 84 part-time expert
                       appointees. The agency says it has "approximately
                       1,500 federal employees and 200 scientists from
                       research institutions in temporary positions."


                # ⚓ Omicron Limited ☛ Plasma_arc_cutting:_Scientists_decode_gas
                  flow_dynamics⠀⇛


                       Plasma arc cutting (PAC) is a thermal cutting
                       technique widely used in manufacturing applications
                       such as shipbuilding, aerospace, fabrication,
                       nuclear plants decommissioning, construction
                       industry, and the automotive industry. In this
                       process, a jet of plasma or ionized gas is ejected
                       at high speeds, which melts and subsequently
                       removes unwanted parts of materials from
                       electrically conductive workpieces such as metals.


                # ⚓ The Register UK ☛ NASA_and_the_on-again,_off-again_job
                  cuts⠀⇛


                       On Tuesday February 18, NASA staffers on
                       probationary status who were warned by managers
                       they might be gone by the end of the day, leaked
                       their concerns to the press. Upwards of 1,000
                       employees at the space agency were facing the axe.


          o § Career/Education⠀➾


                # ⚓ Jeff Triplett ☛ Office_Hours_at_a_Glance⠀⇛


                       I have been hosting a weekly(ish) office for a few
                       years now. Most Fridays start around 2:30 PM
                       Central because that works well for me. These
                       started as an excuse for me to work on open source
                       and side projects and became a banter for many
                       remote people.


                       I also plan to host a monthly morning edition so
                       friends in other time zones can join.


                # ⚓ Brandon ☛ Too_Many_Hobbies,_and_Not_Enough_Time⠀⇛


                       He’s not wrong, but his initial question about how
                       we make time is one that haunts me often.


                # ⚓ Giovanni Collazo ☛ Demo_Days:_A_Simpler_Approach_to
                  Engineering_Leadership⠀⇛


                       While most demos focused on current work projects,
                       the format was open to anything that might interest
                       the team - a cool new technology, a competitor's
                       product, a side project, or a game someone built
                       over the weekend.


                       This freedom to share whatever they found exciting
                       kept the sessions fun, engaging and low pressure.
                       Despite how good it worked and felt, demo days
                       gradually faded from our routine as we defaulted
                       back to standard "agile" ceremonies.


                # ⚓ Tim Kellogg ☛ Target_Practice:_Resumes,_But_Better⠀⇛


                       So you have to spoon feed the hiring manager.
                       Sounds easy.


                       Except it’s not. One single resume won’t work,
                       because it’s basically impossible to satisfy all
                       potential job postings and also have it be succinct
                       enough to properly spoon feed.


          o § Hardware⠀➾


                # ⚓ Quanta Magazine ☛ Catalytic_Computing_Taps_the_Full_Power
                  of_a_Full_Hard_Drive⠀⇛


                       Wrong. In 2014, Loff and four other researchers
                       discovered that adding full storage space can in
                       principle make computers more powerful. Their
                       theoretical framework, called catalytic computing,
                       has become an object of study in its own right. And
                       recently, it also helped researchers prove a
                       startling result in a related area of computer
                       science: The standard approach to resolving a major
                       open question about the role of memory in
                       computation is most likely a dead end.


                # ⚓ Omicron Limited ☛ Topological_quantum_processor_uses
                  Majorana_zero_modes_for_fault-tolerant_computing⠀⇛


                       "We have created a new state of matter called a
                       topological superconductor," Nayak explained. This
                       phase of matter hosts exotic boundaries called
                       Majorana zero modes (MZM) that are useful for
                       quantum computing, he explained. Results of
                       rigorous simulation and testing of their
                       heterostructure devices are consistent with the
                       observation of such states. "It shows that we can
                       do it, do it fast and do it accurately," he said.


                       The researchers also followed up their Nature
                       result with a paper currently in preprint on arXiv,
                       outlining a roadmap for scaling up their technology
                       into a fully functional topological quantum
                       computer.


                # ⚓ David Mead ☛ Setting_up_CEC_on_Sceptre_4K_TV⠀⇛


                       For a few years I've had my eye on getting a "dumb"
                       TV from Sceptre.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ NYPost ☛ 11-year-old_Texas_girl_dies_by_suicide_after_being
                  bullied_over_family’s_immigration_status:_report⠀⇛


                       Little Jocelyn was remembered as a sweet and joyful
                       girl who played the French horn, was an avid
                       swimmer, and loved getting manicures with her
                       beloved grandmother.


                # ⚓ US News And World Report ☛ USDA_Says_It_Will_Release_$20
                  Million_of_Frozen_Farmer_Funds⠀⇛


                       The sum represents a tiny sliver of program funding
                       the USDA suspended after the White House's broad
                       freeze of federal loans and grants last month.
                       Although the administration rescinded the memo
                       ordering the freeze and it has been blocked in
                       court, a U.S. judge has said the government was
                       still withholding funds.


                # ⚓ [Old] Jason Heppler ☛ Becoming_News-Resilient⠀⇛


                       While there remains a lot of uncertainty and
                       questions in the wake of the 2024 elections, one
                       thing that seems clear to me is about myself: I’m
                       more terminally online than I realized, and I don’t
                       love that. As I’ve written before, the urge for up-
                       to-the-moment news doesn’t actually make me a more
                       informed person but only works to drive emotions
                       that aren’t particularly healthy. Plus, I feel as
                       though I really misjudged this election. I’m a
                       historian, not someone who predicts the future; but
                       I really feel as though social media skewed the way
                       I was thinking about things.


                # ⚓ Annie Mueller ☛ If_you_don’t,_somebody_else_will:_-_annie's
                  blog⠀⇛


                       Run your life


                       It’s true. If you don’t, somebody else will.


                # ⚓ Vox ☛ Red_states_are_testing_their_power_to_restrict
                  abortion_nationwide⠀⇛


                       Last week, a Texas judge ordered Dr. Margaret
                       Carpenter — a New York abortion doctor — to pay at
                       least $100,000 in penalties for failing to appear
                       in court. Carpenter has found herself at the center
                       of two major abortion lawsuits: In December, she
                       became the target of the first-ever civil suit
                       against an out-of-state abortion provider, and
                       officials in Louisiana are now also seeking her
                       extradition, with newly appointed US Attorney
                       General Pam Bondi signaling that she’d “love” to
                       get involved.


                # ⚓ Wired ☛ USDA_Layoffs_Derail_Projects_Benefiting_American
                  Farmers⠀⇛


                       One laid-off employee described the weeks preceding
                       the firing as “chaos,” as the USDA paused (in
                       response to orders from the Trump administration)
                       and then unpaused (in response to a court order)
                       work connected to the Inflation Reduction Act
                       (IRA)—the landmark 2022 law passed under President
                       Joe Biden that set aside large amounts of federal
                       money for climate policies. “It was just pause,
                       unpause, pause, unpause. After four or five
                       business days of that, I’m thinking, I literally
                       can’t get anything done,” says the former employee,
                       who worked on IRA-linked projects and asked to
                       remain anonymous to protect them from retribution.


                # ⚓ Jeroen Sangers ☛ Although_time_pressure_makes_us_work
                  faster,_it_does_not_automatically_mean_we_work_better⠀⇛


                       Under pressure, we can indeed accomplish more work
                       in less time, but this often comes at the expense
                       of accuracy and depth. Researchers like Don Moore
                       and Elizabeth Tenney have shown that while
                       deadlines can help us complete tasks that might
                       otherwise be left unfinished, the quality of the
                       work often suffers due to the rush. This is
                       because, under pressure, we tend to make quicker
                       decisions and spend less time checking our work,
                       increasing the likelihood of errors.


          o § Proprietary⠀➾


                # ⚓ India Times ☛ TikTok_layoffs:_Job_cuts_to_affect_employees
                  in_this_unit⠀⇛


                # ⚓ Microsoft_backtracks_controversial_account_sign-in_change⠀⇛


                       Less than a month ago, Abusive Monopolist Microsoft
                       announced that it would keep users logged in to
                       their Abusive Monopolist Microsoft account from
                       February 2025.


                # ⚓ New York Times ☛ Apple_Unveils_Lower-Priced_iPhone_16e_With
                  Hey_Hi_(AI)_Features⠀⇛


                       The iPhone 16e is the first update to the company’s
                       most affordable model since 2022, but carries a
                       higher price tag of $599.


                # ⚓ Scoop News Group ☛ Salt_Typhoon_gained_initial_access_to
                  telecoms_through_Cisco_devices⠀⇛


                       Cisco Talos said it hasn’t identified any evidence
                       to confirm Salt Typhoon’s exploitation of other
                       known Cisco vulnerabilities. The company declined
                       to answer questions.


                # ⚓ The Verge ☛ Fitbit’s_got_a_battery_problem⠀⇛


                       Technically, fixing this kind of problem is a good
                       thing. You don’t want batteries to overheat and
                       burn a customer — and the official notice also
                       notes that this issue doesn’t impact all Versa 3 or
                       Sense devices. However, affected users have
                       reported on Fitbit’s forums and subreddit that the
                       update dramatically reduced their devices’ battery
                       life.


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ The Register UK ☛ GitLab_thrice_sued_for_'misleading'
                        investors_with_AI_hype⠀⇛


                             The initial complaint [PDF], a federal
                             securities investor lawsuit, was filed on
                             September 9, 2024, and subsequently amended
                             [PDF] with more detail on February 5, 2025.


                             Soon after, two derivative lawsuits were
                             filed: one [PDF] on February 14, 2025, and
                             the other [PDF] on February 19, 2025. In a
                             derivative suit, shareholders sue executives
                             or board members on behalf of the company
                             itself, usually over alleged mismanagement or
                             breaches of fiduciary duty.


                      # ⚓ Vox ☛ The_rapid_development_of_AI_has_benefits_—_and
                        poses_serious_risks⠀⇛


                             But there’s another way the field of
                             artificial intelligence has been transformed
                             in the past 10 years: Concerns about the
                             societal effects of artificial intelligence
                             are now being taken much more seriously.


                      # ⚓ 404 Media ☛ Public_Library_Ebook_Service_to_Cull_AI
                        Slop_After_404_Media_Investigation⠀⇛


                             Hoopla, a service that provides public
                             libraries around the country with ebooks,
                             announced that it will do more to prevent the
                             spread of low quality AI-generated books
                             after a 404 Media investigation showed that
                             they were common on its platform.


                      # ⚓ Louie Mantia ☛ Humane⠀⇛


                             Even prior to posting this, in response to
                             any skepticism I had about Humane, people
                             told me—publicly and privately—to “wait and
                             see.” Some of these people knew Imran
                             Chaudhri, Humane’s founder. Others had no
                             idea who he was. Either way, a lot of people
                             were giving him and Humane the benefit of the
                             doubt from the start. I think we have to stop
                             doing that in this industry.


                             Next time, let’s not “wait and see.” Instead,
                             let’s spot the red flags more easily and have
                             them be addressed.


                      # ⚓ Pivot to AI ☛ Businesses_still_don’t_know_what_an_‘AI
                        agent’_is_and_they_don’t_really_want_one⠀⇛


                             But that doesn’t describe the things sold as
                             agents. In practice, they’re any old AI
                             rubbish that promises it might do something
                             in the future. Because it certainly doesn’t
                             do it in the present.


                      # ⚓ India Times ☛ DeepSeek's_outside_funding_draws
                        interest_from_Alibaba,_Chinese_state_funds⠀⇛


                             The Chinese company stunned the tech industry
                             in January with low-cost AI models that can
                             match or even outperform Western rivals at a
                             fraction of the cost, stirring doubts about
                             the lead US has in the race to dominate the
                             technology.


                      # ⚓ Futurism ☛ Researchers_Find_Elon_Musk's_New_Grok_AI
                        Is_Extremely_Vulnerable_to_Hacking⠀⇛


                             The team found that the model is extremely
                             vulnerable to "simple jailbreaks," which
                             could be used by bad actors to "reveal how to
                             seduce kids, dispose of bodies, extract DMT,
                             and, of course, build a bomb," according to
                             Adversa CEO and cofounder Alex Polyakov.


                             And it only gets worse from there.


                      # ⚓ CBC ☛ Does_ELIZA,_the_first_chatbot_created_60_years
                        ago,_hold_lessons_for_modern_AI?⠀⇛


                             ELIZA was a simple program created in the
                             1960s by Joseph Weizenbaum, a professor at
                             the Massachusetts Institute of Technology who
                             was interested in human-computer interfaces.


                             He designed ELIZA to be a generalized
                             conversation program to make a natural
                             language conversation with a computer
                             possible. The program could run scripts with
                             different language rules to represent
                             individual conversational personas.


                # § Social Control Media⠀➾


                      # ⚓ Futurism ☛ Elon_Searching_for_Investors_Gullible
                        Enough_to_Pour_More_Money_Into_Twitter⠀⇛


                             Flash forward to the present day, and X-
                             formerly-Twitter has lost upward of 79
                             percent of its original value after neo-Nazis
                             flocked to the platform and big-name
                             advertisers fled in droves.


                             Now, in a somewhat rare move for the richest
                             man on Earth, Musk has taken to beg investors
                             for more funds at a valuation of at least $44
                             billion, according to reporting by Bloomberg.
                             That's the same price Musk acquired it for
                             nearly two years ago — a pretty bold move, to
                             say the least.


                      # ⚓ LabX Media Group ☛ A_State_of_Flux_Leaves_Teen_Brains
                        Sensitive_to_Experiences⠀⇛


                             Session moderator Beatriz Luna, a
                             developmental neuroscientist at the
                             University of Pittsburgh, opened with a stark
                             warning: “Right now, there is a crisis in
                             adolescent mental health.”


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ WhichUK ☛ How_scammers_use_fake_sales_posts_on
                        Facebook⠀⇛


                             Which? finds scammers posting the same item
                             for sale across multiple Facebook (Farcebook)
                             community groups


                # § Privacy/Surveillance⠀➾


                      # ⚓ EDRI ☛ GDPR_Procedural_Regulation:_A_critical
                        opportunity_to_strengthen_cross-border_enforcement⠀⇛


                             As EU negotiators continue trilogue
                             discussions on the GDPR Procedural
                             Regulation, civil society organisations
                             across Europe are raising the alarm: the
                             proposed reforms risk failing to address the
                             long-standing enforcement challenges that
                             have undermined the GDPR’s effectiveness. In
                             a joint letter, EDRi, Access Now and 34
                             fellow organisations call on policymakers to
                             prioritise robust, rights-centred enforcement
                             mechanisms that ensure individuals can
                             meaningfully exercise their rights.


                      # ⚓ EDRI ☛ 12_civil_society_organisations_tell_delivery
                        platforms_it’s_time_to_deliver_answers_on_how_they_use
                        algorithms_to_manage_their_workers⠀⇛


                             EDRi member Privacy International and more
                             digital rights groups, together with trade
                             unions, call out food delivery platforms for
                             their algorithmic management of workers.


                      # ⚓ EDRI ☛ The_ePrivacy_Regulation_proposal_has_been
                        withdrawn,_but_the_fight_for_your_privacy_is_far_from
                        over⠀⇛


                             The European Commission's withdrawal of the
                             ePrivacy Regulation proposal is a major
                             setback for privacy rights in Europe, driven
                             by pressure from industry interests and
                             national security concerns. However, EDRi
                             remains committed to advocating for stronger
                             privacy protections, challenging commercial
                             and state surveillance in future legislative
                             efforts.


                      # ⚓ EDRI ☛ The_EDPB’s_Rorschach_Test:_What_the_data
                        protection_body’s_Opinion_on_Hey_Hi_(AI)_training_Means
                        for_GDPR_Enforcement⠀⇛


                             In December 2024, the European Data
                             Protection Board (EDPB) released a much-
                             awaited Opinion on Hey Hi (AI) model
                             training. While the Opinion reaffirmed GDPR
                             principles and underscored the need for
                             robust safeguards, its ambiguities may leave
                             room for regulatory evasion, reinforcing the
                             ongoing struggle between data protection
                             rules and commercial Hey Hi (AI) development
                             wishes.


                      # ⚓ EDRI ☛ EDRi-gram,_19_February_2025⠀⇛


                             What has the EDRis network been up to over
                             the past two weeks? Find out the latest
                             digital rights news in our bi-weekly
                             newsletter. In this edition: Commission
                             withdraws ePrivacy proposal, new database to
                             track investigations into Big Tech, & more!


                      # ⚓ Unicorn Media ☛ How_to_Tell_a_Really_Smart_Home_From
                        a_Not-So-Smart_Home_That_Only_Thinks_It’s_Smart⠀⇛


                             To get Nixon, "Deep Throat" advised Woodward
                             and Bernstein to "follow the money." To "get"
                             this article, written by the latest addition
                             to the FOSS Force team, we suggest that you
                             follow the links. You'll be glad you did.


                      # ⚓ EPIC ☛ EPIC_Testifies_in_Support_of_Vermont_Age
                        Appropriate_Design_Code⠀⇛


                             EPIC Counsel Suzanne Bernstein testified
                             before the Vermont Senate Committee on
                             Institutions on February 18 in support of S.
                             69, the Vermont Age Appropriate Design Code
                             (AADC). In her testimony, Suzanne illustrated
                             how the Vermont AADC would protect kids’
                             privacy, enhance kids’ autonomy, and ensure
                             their online safety by prohibiting abusive
                             data and design practices. It does not ban
                             minors from social media, nor does it not
                             block minors from accessing any type of
                             content.


                             The Vermont AADC provides covered minors with
                             autonomy and choice over their online
                             activity by requiring covered businesses to
                             configure all default privacy settings to the
                             highest level of privacy for covered minors,
                             including settings to limit unwanted adult
                             contact and push notifications. The bill
                             would also require transparency around
                             automated recommendation features and service
                             features that use personal data of covered
                             minors.


                      # ⚓ BBC ☛ Fingerprinting:_Critics_say_Google_rules_put
                        profits_over_privacy⠀⇛


                             But opponents to the change say
                             fingerprinting and IP address collection are
                             a blow to privacy because it is harder for
                             users to control what data is collected about
                             them.


                             "By allowing fingerprinting, Google has given
                             itself - and the advertising industry it
                             dominates - permission to use a form of
                             tracking that people can't do much to stop,"
                             said Martin Thomson, distinguished engineer
                             at Mozilla, a rival to Google.


                      # ⚓ Forbes ☛ Clearview_AI’s_CEO_Resigns_As_Facial
                        Recognition_Company_Focuses_On_Trump_'Opportunities'⠀⇛


                             Ton-That has long been the public face of
                             Clearview and its facial recognition tool.
                             Built on a database of billions of photos
                             scraped from Facebook, Instagram, LinkedIn,
                             and other websites, the tool could be used to
                             reveal just about anyone's true identity from
                             a surveillance image in a matter of seconds.
                             The tool was widely tested — often without
                             oversight or public disclosure — by the
                             Department of Justice, retailers like Best
                             Buy and Macy’s, and law enforcement and
                             government-affiliated agencies in dozens of
                             countries, raising concerns that facial
                             recognition could be deployed at a mass
                             scale.


                      # ⚓ The Register UK ☛ Dutch_medical_data_breach_uncovered
                        at_airport_flea_market⠀⇛


                             And where exactly was this cybercriminal
                             goldmine? At a flea market next to Weelde
                             airbase, obviously.


                      # ⚓ Scoop News Group ☛ Federal_judge_denies_request_to
                        block_DOGE_[sic],_Musk_from_seven_agencies’_data
                        systems⠀⇛


                             Judge Tanya Chutkan of the U.S. District
                             Court for the District of Columbia ruled that
                             the states did not show that they would
                             “suffer imminent, irreparable harm absent a
                             temporary restraining order.” The state AGs
                             had argued that Musk’s actions in deploying
                             DOGE [sic] surrogates to root around in
                             federal computer systems violated the
                             Constitution’s appointments clause due to the
                             fact that he has not been nominated by the
                             president and confirmed by the Senate.


                      # ⚓ The Record ☛ DOGE_[sic]_access_to_Social_Security,
                        IRS_data_could_create_privacy_and_security_risks,
                        experts_say⠀⇛


                             The Department [sic] of Government Efficiency
                             (DOGE) may already have access to sensitive
                             tax and medical data stored at the IRS and
                             Social Security Administration (SSA), which
                             jointly retain disability diagnoses, child
                             adoption information, exceptionally detailed
                             financial data and individuals’ immigration
                             status, experts say.


                             The data could easily be leaked in a breach,
                             experts and civil liberties advocates say,
                             and public perceptions that tax return
                             information is no longer private could lead
                             to fewer people filing taxes. There is also a
                             possibility that the data will be weaponized
                             against perceived political enemies,
                             advocates say, pointing to public comments
                             from the Trump administration.


                      # ⚓ The Record ☛ New_Google_ad_tracking_policy_a
                        ‘Pandora’s_box’_for_privacy,_experts_warn⠀⇛


                             Digital fingerprints allow advertisers and
                             data brokers to collect consumer data based
                             on internet users’ activities across web
                             browsers, online sessions and often multiple
                             devices. Google’s new policy enabling them
                             will make it difficult for people online,
                             including those using VPNs, Tor and privacy
                             browsers, to stay anonymous, experts say.


                             Google had previously allowed advertisers to
                             shadow users with cookies, which only track
                             people across websites and sometimes across
                             sessions.


                      # ⚓ Techdirt ☛ ICE_Wants_To_Set_Up_A_Social_Media_Dragnet
                        So_It_Can_Figure_Out_Who’s_Criticizing_The_Agency⠀⇛


                             In fact, what the actual wording says
                             suggests something different: ICE is
                             experiencing an uptick in visible criticism
                             from publicly-accessible social media
                             accounts, which is definitely not the same
                             thing as evidence it’s more dangerous to be
                             employed by ICE now than it has been in the
                             past.


                      # ⚓ EFF ☛ Saving_the_Internet_in_Europe:_Defending
                        Privacy_and_Fighting_Surveillance⠀⇛


                             EFF’s mission is to ensure that technology
                             supports freedom, justice, and innovation for
                             all people of the world. While our work has
                             taken us to far corners of the globe, in
                             recent years we have worked to expand our
                             efforts in Europe, building up a policy team
                             with key expertise in the region, and
                             bringing our experience in advocacy and
                             technology to the European fight for digital
                             rights.


                             In this blog post series, we will introduce
                             you to the various players involved in that
                             fight, share how we work in Europe, and
                             discuss how what happens in Europe can affect
                             digital rights across the globe.


                      # ⚓ The Atlantic ☛ DOGE_[sic]_Has_'God_Mode'_Access_to
                        Government_Data⠀⇛


                             The employee’s account, along with the
                             accounts of several others across federal
                             agencies, offers the clearest portrait yet of
                             just how deep DOGE [sic] has burrowed into
                             the systems of the federal government—and the
                             sensitive information of countless Americans.


                      # ⚓ Michigan Advance ☛ Social_Security_head_leaves_as
                        Musk-led_DOGE_[sic]_seeks_Americans’_data_•_Michigan
                        Advance⠀⇛


                             King, who was with the agency for more than
                             30 years before becoming its acting director
                             last month, left over the holiday weekend.
                             She declined to give the Musk-led effort to
                             cut federal spending and the workforce, known
                             as the Department of Government Efficiency
                             (DOGE [sic]), access to a centralized
                             database that includes information about
                             income, addresses, retirement benefits and
                             sometimes even medical records for any
                             American with a Social Security number,
                             people familiar with the situation told The
                             19th. They spoke on condition of anonymity as
                             they were not authorized to speak on behalf
                             of the agency or the individuals involved.


                      # ⚓ EDRI ☛ ePrivacy_Regulation,_but_the_fight_for_your
                        privacy_is_far_from_over⠀⇛


                             It’s official – the ePrivacy Regulation
                             proposal has been withdrawn (yes, cue the
                             collective groan from digital rights
                             advocates in the EU). After years of hard
                             work, hope, and tireless campaigning, it
                             seems that powerful industry interests and
                             some EU member states have successfully
                             blocked this critical reform. But don’t reach
                             for the tissues just yet – while this marks a
                             setback in the fight for stronger privacy
                             protections, it also reinforces the urgency
                             of continuing the struggle for digital
                             rights.


          o § Defence/Aggression⠀➾


                # ⚓ Michigan Advance ☛ Election_officials_blast_Trump’s
                  ‘retreat’_from_protecting_voting_against_foreign_threats_•
                  Michigan_Advance⠀⇛


                       The administration is shuttering the FBI’s Foreign
                       Influence Task Force and last week cut more than
                       100 positions at the U.S. Cybersecurity and
                       Infrastructure Security Agency. President Donald
                       Trump signed the law creating the agency in 2018.
                       Among its goals is including helping state and
                       local officials protect voting systems.


                       Secretaries of state and municipal clerks fear
                       those moves could expose voter registration
                       databases and other critical election systems to
                       hacking — and put the lives of election officials
                       at risk.


                # ⚓ Deseret Media ☛ IRS_fires_6,000_employees_as_Trump_slashes
                  US_government⠀⇛


                       The cuts are part of President Donald Trump's
                       sweeping downsizing effort that has targeted bank
                       regulators, forest workers, rocket scientists and
                       tens of thousands of other government employees.
                       The effort is being led by tech billionaire Elon
                       Musk, Trump's biggest campaign donor.


                       Labor unions have sued to try to stop the mass
                       firings, but a federal judge in Washington ruled
                       that they can continue for now.


                # ⚓ Wired ☛ DOGE_[sic]_Puts_$1_Spending_Limit_on_Government
                  Employee_Credit_Cards⠀⇛


                       “Effective immediately, all GSA SmartPay Travel and
                       Purchase Cards issued to GSA employees and
                       contractors are being paused and will not be
                       available for use except in very limited
                       circumstances,” GSA wrote in a memo to staff
                       Thursday morning viewed by WIRED. The memo later
                       stated that for “up to 0.1% of the GSA workforce,
                       requests may be made for certain individual
                       purchase charge card spend thresholds be set above
                       $1. Please provide the rationale for all such
                       deviations on an employee-by-employee basis along
                       with the proposed increased threshold.”


                # ⚓ Parker Molloy ☛ Stop_Analyzing_Trump's_Unhinged_Ideas_Like
                  They're_Normal_Policy_Proposals⠀⇛


                       Sometimes a piece of journalism is so wildly off-
                       base that it perfectly encapsulates everything
                       wrong with political coverage. Today's example
                       comes from the New York Times's Peter Baker, who
                       decided to treat Donald Trump's delusional
                       ramblings about annexing Canada as a serious policy
                       proposal worthy of electoral analysis.


                # ⚓ Chris O'Donnnell ☛ We_Are_The_Bad_Guys⠀⇛


                       So we can't count on Congress or the Courts. We
                       probably shouldn't wish for a military coup. What
                       does that leave us?


                       It leaves us. Us. We the people.


                # ⚓ BBC ☛ The_'3.5%_rule':_How_a_small_minority_can_change_the
                  world⠀⇛


                       Nonviolent protests are twice as likely to succeed
                       as armed conflicts – and those engaging a threshold
                       of 3.5% of the population have never failed to
                       bring about change.


                # ⚓ The Nation ☛ Elon_Musk_Wants_to_Decide_Who_Sits_on_the
                  Wisconsin_Supreme_Court⠀⇛


                       Not satisfied with controlling the federal
                       government, the shadow president’s political action
                       committee is suddenly spending big on a crucial
                       Wisconsin Supreme Court election.


                # ⚓ [Repeat] PHR ☛ 1762_Attacks_on_Health_Care_Over_Three_Years
                  as_Russia_Escalates_its_War_on_Ukraine’s_Doctors_and
                  Hospitals:_PHR⠀⇛


                       PHR calls on the global community to hold
                       perpetrators of attacks on health to account and
                       support Ukraine; U.S. government must restore
                       humanitarian and health aid to Ukraine


                # ⚓ Mike Brock ☛ The_Nobody_Saw_This_Coming_Brigade⠀⇛


                       This isn't just cowardice—it's a revelation of how
                       thoroughly our democratic institutions have been
                       captured by technological intimidation. When United
                       States senators cannot state truths they've
                       witnessed with their own eyes because they fear a
                       billionaire's social media platform, we're not just
                       watching individual moral failure—we're seeing the
                       complete collapse of institutional independence.


                       Two plus two equals four. Russia invaded Ukraine.
                       Mass graves don’t tweet.


                # ⚓ Mike Brock ☛ The_Perilous_Incoherence_of_Democratic
                  Minimalism⠀⇛


                       This is, after all, a philosophy blog. And as I've
                       warned readers, in between my polemics, I do intend
                       to try and maintain some connection back to my
                       roots, here. So let me close this preamble with a
                       fundamental philosophical truth: Democracy is not
                       just a system of governance; it's an
                       epistemological project. It's how we, as societies,
                       grapple with reality and make collective decisions
                       based on our best understanding of that reality.


                # ⚓ CoryDoctorow ☛ Pluralistic:_Ad-tech_targeting_is_an
                  existential_threat⠀⇛


                       The other witnesses were fascinating – and
                       chilling, There was a lawyer from the AARP who
                       explained how data-brokers would let you target ads
                       to categories like "seniors with dementia." Then
                       there was someone from the Pentagon, discussing how
                       anyone could do an ad-buy targeting "people
                       enlisted in the armed forces who have gambling
                       problems." Sure, I thought, and you don't even need
                       these explicit categories: if you served an ad to
                       "people 25-40 with Ivy League/Big Ten law or
                       political science degrees within 5 miles of
                       Congress," you could serve an ad with a malicious
                       payload to every Congressional staffer.


                       Now, that's just the data brokers. The real action
                       is in ad-tech, a sector dominated by two giant
                       companies, Meta and Google. These companies claim
                       that they are better than the unregulated data-
                       broker cowboys at the bottom of the food-chain.
                       They say they're responsible wielders of
                       unregulated monopoly surveillance power. Reader,
                       they are not.


                # ⚓ The Atlantic ☛ DOGE_[sic]’s_Reign_of_Ineptitude⠀⇛


                       In theory, DOGE [sic] exists to promote efficiency.
                       And the need for efficiency is real. The federal
                       government is deeply in debt. Its interest payments
                       now exceed what it spends on defense. Even if the
                       United States had no issue with its debt, it would
                       still be a mitzvah to find ways to make government
                       work better—to take the same tax dollar further, to
                       do one more unit of good. But judging by DOGE
                       [sic]’s early returns, the only objective
                       conclusion one can reach about the agency seems to
                       be that it’s out of control. What we’re witnessing
                       in government right now—across the Departments of
                       Energy, Veterans Affairs, Education, and beyond—is
                       not only a bonfire of cruelty but a reign of
                       ineptitude.


                # ⚓ Federal News Network ☛ Federal_judge_won’t_immediately
                  block_Elon_Musk_or_DOGE_[sic]_from_federal_data_or_worker
                  layoffs⠀⇛


                       The decision came in a lawsuit filed by 14
                       Democratic states challenging DOGE [sic]’s
                       authority to access sensitive government data. The
                       attorneys general argued that Musk is wielding the
                       kind of power that the Constitution says can be
                       held only by those elected or confirmed by the
                       Senate.


                # ⚓ C4ISRNET ☛ Ukrainian_defense_planners_envision_a_drones-
                  only_front_line⠀⇛


                       The project, dubbed the Drone Line, was announced
                       by the Ukrainian Ministry of Defense on Feb 9.
                       According to statements made by Ukrainian Defense
                       Minister Rustem Umerov, it has two core objectives:
                       building a continuous drone reconnaissance
                       capability along the line of defense, and boosting
                       support for and coordination with infantry units to
                       create a kind buffer strip where no troops can move
                       undetected.


                # ⚓ Techdirt ☛ Lithuanian_Adtech_Firm_And_Florida_Data_Broker
                  Trafficked_In_Sensitive_U.S._Military_And_Intelligence_Worker
                  Location_Data⠀⇛


                       The original story documented how Wired was able to
                       buy 3.6 billion location coordinates, some logged
                       at millisecond intervals with meter precision, from
                       up to 11 million mobile advertising IDs in Germany
                       over a one-month period. The data detailed
                       intelligence and military employees as they
                       wandered not just around European towns and cities,
                       but their movement at sensitive military locations.


                       At the time, Wired didn’t have a solid bead on the
                       origins of the data, outside of the fact they were
                       able to buy the data in question from a Florida
                       data broker named Datastream. But in an also
                       excellent follow up report they say they’ve figured
                       out where it originated: a Lithuanian adtech firm.


                # ⚓ Techdirt ☛ State_Plaintiffs_Lose_A_Disappointing_Battle,
                  While_Musk_And_DOGE_[sic]_Get_Closer_To_Losing_The_War⠀⇛


                       With this case the plaintiff states are swinging
                       for the fences, asking for one big injunction to
                       knock Musk and DOGE [sic] out of every agency. It’s
                       a strategy we haven’t really seen before, to aim
                       for Musk and DOGE [sic] directly and with respect
                       to all of their activities; most of the other
                       litigation brewing seeks to take on their
                       destructive meddling an agency at a time, if not
                       also an activity at a time. Those cases also,
                       although with some exceptions, sue the agency and
                       its heads directly, to challenge the lawfulness of
                       them having effectively handed over the keys to
                       their agencies (and their computer systems) to
                       these shmucks. Whereas this case, notably, was
                       against the shmucks themselves, challenging their
                       presence in government and how much false authority
                       they’ve wielded over its operations (and computer
                       systems). In this case, New Mexico v. Musk, the
                       basic contention is that nothing in the
                       Constitution allows Musk and DOGE [sic] to have had
                       the power they’ve wielded, and they need to be made
                       to stop wielding it. And by asking for a temporary
                       restraining order (TRO) as a first step the states
                       were also asking that they be made to stop yielding
                       it asap.


                # ⚓ Futurism ☛ Top_Trump_Ally_Says_Elon_Musk_Is_a_"Parasitic
                  Illegal_Immigrant"⠀⇛


                       "Musk is a parasitic illegal immigrant," a wound-up
                       Bannon told UnHerd, a right-wing British
                       publication. "He wants to impose his freak
                       experiments and play-act as God without any respect
                       for the country’s history, values, or traditions."


                       It's true that Musk's immigration status during his
                       early in the United States was dubious, with his
                       brother recalling that "we were illegal
                       immigrants." But like many people fortunate enough
                       to be able to access sound legal aid, he was able
                       to fix his status and eventually gained US
                       citizenship in 2002.


                # ⚓ VOA News ☛ Vietnam_parliament_approves_$8_billion_railway
                  with_loan_from_China⠀⇛


                       The country's rubber-stamp parliament gave the go-
                       ahead to the project, with 455 of the 459 members
                       voting for the project.


                       The approval marks a significant step forward in
                       Vietnam’s infrastructure modernization efforts, as
                       the country seeks to boost connectivity and
                       economic growth, local media reported.


                # ⚓ CBC ☛ Subsea_fibre_optic_cable_deliberately_cut_for_the_2nd
                  time_between_N.S._and_N.L.⠀⇛


                       Telecommunications giant Bell is exploring
                       surveillance options in the Gulf of St. Lawrence
                       after one of its subsea fibre optic cables between
                       Cape Breton Island and Newfoundland's west coast
                       was recently severed for the second time.


                       David Joice, the company's director of networks,
                       said it's suspected that an anchor or a piece of
                       gear, such as a trawling net, snagged the cable
                       last Dec. 24. He said the cable was then brought to
                       the surface along with the gear, and deliberately
                       cut by someone.


                # ⚓ Federal News Network ☛ Lead_CMMC_architect_returns_to
                  Pentagon_as_DoD_CISO⠀⇛


                       Katie Arrington's return to DoD comes as her
                       lawyers work out a settlement with the government
                       related to the suspension of her security clearance
                       in 2021.


                # ⚓ The Straits Times ☛ Australia,_Papua_New_Guinea_vow_to
                  strike_defence_treaty⠀⇛


                       They are committed to deepen integration of their
                       forces and make it easier to offer security
                       support.


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


                      # ⚓ ‘I_want_to_defect_to_South’:_North_Korean_soldier
                        captured_in_Kursk_breaks_silence⠀⇛


                             The soldier confirmed earlier intelligence
                             reports of heavy casualties in drone attacks,
                             language barrier.


                      # ⚓ Meduza ☛ ‘They_brought_results’:_Putin_comments_on
                        U.S.-Russia_negotiations_in_Saudi_Arabia_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘They_have_only_themselves_to_blame’:_Putin
                        comments_on_U.S.-Russia_talks,_a_potential_meeting_with
                        Trump,_and_worsening_transatlantic_relations_—_Meduza⠀⇛


                      # ⚓ New York Times ☛ European_Leaders_Try_to_Recalibrate
                        After_Convicted_Felon_Sides_With_Russia_on_Ukraine⠀⇛


                             The American president’s latest remarks
                             embracing Vladimir Putin’s narrative that
                             Ukraine is to blame for the war have
                             compounded the sense of alarm among
                             traditional allies.


                      # ⚓ New York Times ☛ Kremlin_Message_to_Convicted_Felon:
                        There’s_Money_to_Be_Made_in_Russia⠀⇛


                             Russian officials are arguing that American
                             companies stand to make billions of dollars
                             by re-entering Russia. The White House is
                             listening.


                      # ⚓ New York Times ☛ With_Convicted_Felon’s_Prostration
                        to_Putin,_Expect_a_More_Dangerous_World⠀⇛


                             This is a humiliating month to be an
                             American.


                      # ⚓ New York Times ☛ Dictator_Flips_the_Script_on_the
                        Ukraine_War,_Blaming_Zelensky_Not_Putin⠀⇛


                             As he seeks to negotiate a peace deal with
                             Moscow, President Convicted Felon is
                             rewriting the history of Russia’s invasion of
                             its neighbor.


                      # ⚓ RFERL ☛ Dictator_Calls_Zelenskyy_'Dictator_Without
                        Elections,'_Urges_Him_To_'Move_Fast'⠀⇛


                             Ukrainian President Volodymyr Zelenskyy has
                             reiterated concerns over U.S.-Russian talks
                             held in Saudi Arabia on ending Moscow's
                             ongoing invasion of Ukraine launched almost
                             three years ago.


                      # ⚓ RFERL ☛ Dictator_Repeats_Harsh_Criticism_Of
                        Zelenskyy,_Says_He_Could_Have_Attended_Riyadh_Talks⠀⇛


                             U.S. President The Insurrectionist doubled
                             down on his criticism of Ukrainian President
                             Volodymyr Zelenskyy in a speech, saying
                             Zelenskyy has done a terrible job and could
                             have attended talks with Russia this week in
                             Saudi Arabia if he had wanted to.


                      # ⚓ France24 ☛ 🔴_Follow_live:_Convicted_Felon_brands
                        Zelensky_'a_dictator'⠀⇛


                      # ⚓ France24 ☛ Why_Europe’s_leadership_is_skeptical_of
                        negotiating_with_Putin⠀⇛


                             The idea that US President The
                             Insurrectionist’s negotiations with Russian
                             President Vladimir Putin will bring about
                             lasting peace in Ukraine has been met with
                             scepticism across Europe. FRANCE 24 spoke to
                             political scientist Anton Shekhovtsov about
                             what the US can learn from earlier attempts
                             to end Russian occupation across the former
                             Soviet Union.


                      # ⚓ The Strategist ☛ How_Europe_can_pay_for_rearmament⠀⇛


                             Europe urgently needs to rearm. Russia’s
                             invasion of Ukraine, and the broader threat
                             that President Vladimir Putin’s regime poses
                             to Europe, requires nothing less.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Advance Local Media LLC ☛ Elon_Musk_caught_following_X
                  account_posting_only_Nazi_content_and_soft-core_porn_-
                  lonestarlive.com⠀⇛


                       Elon Musk, richest man in the world and federal
                       government up-ender, has been discovered to follow
                       an account on X that exclusively posts Nazi content
                       and soft-core porn.


                # ⚓ [Old] Rachel Kroll ☛ The_Bozo_Loop_(epub_format)⠀⇛


                       Take a trip into the world of systems
                       administration, programming, networking, tech
                       support, and living in Silicon Valley. The Bozo
                       Loop is a collection of stories from 2011 which
                       expose the inner workings of things some people
                       would rather keep quiet.


          o § Environment⠀➾


                # ⚓ Science Alert ☛ Places_on_Earth_Too_Hot_For_Humans_Will
                  Triple_This_Century,_Scientists_Warn⠀⇛


                       The average global temperature has already risen by
                       1.5 °C above preindustrial levels. We reached this
                       grim milestone just last year.


                       Now scientists report that adding 0.5 °C of extra
                       heat to the global average will triple the area of
                       land on our planet too hot for even a healthy adult
                       human to inhabit. That's equivalent to writing off
                       a landmass about the size of the United States.


                       For people over 60, whose bodies are even more
                       vulnerable to extreme heat, that danger zone will
                       span about 35 percent of Earth's landmass, a steep
                       incline from the 21 percent that's off-limits to
                       them today.


                # ⚓ Omicron Limited ☛ Bird_study_finds_much_larger_volumes_of
                  toxic_PFAS_chemicals_than_previously_reported⠀⇛


                       He is the lead author of an article published in
                       the Journal of Hazardous Materials that addresses
                       new findings regarding the toxins. PFAS contain
                       fluorine, and have received particular attention in
                       Norway because they are used in ski wax, Teflon and
                       fire retardants.


                # ⚓ Jacobin Magazine ☛ Trump_Is_Moving_to_Kill_a_Key_Federal
                  Environmental_Law⠀⇛


                       Over the weekend, the Trump administration appeared
                       to begin the process of rolling back enforcement of
                       the National Environmental Policy Act (NEPA), the
                       “Magna Carta” of federal environmental law. In a
                       filing submitted February 16, administration
                       officials announced an interim rule titled “Removal
                       of National Environmental Policy Act Implementing
                       Regulations.”


                # ⚓ The Korea Times ☛ Sweden's_top_court_rejects_Greta_Thunberg
                  lawsuit_on_climate_action⠀⇛


                       Activists filed a lawsuit in 2022 arguing that the
                       state violates the European Convention on Human
                       Rights by not doing enough to limit climate change,
                       or mitigate its effects, and the case has since
                       been subject to review on procedural grounds.


                       The group of 300 plaintiffs in the case, who call
                       themselves the Aurora group, wanted the courts to
                       order Sweden to do more to limit global warming to
                       1.5 degrees Celsius.


                # § Energy/Transportation⠀➾


                      # ⚓ Hong Kong Free Press ☛ Vietnam_parliament_approves
                        US$8_billion_rail_link_to_China,_boosting_links_between
                        2_communist-ruled_countries⠀⇛


                             Vietnam‘s parliament approved plans on
                             Wednesday for an US$8 billion rail link from
                             its largest northern port city to the border
                             with China, boosting links between the two
                             communist-ruled countries and making trade
                             easier.


                      # ⚓ DeSmog ☛ Elon_Musk’s_Embrace_of_Far-Right_Energizes
                        Transatlantic_Climate_Denial⠀⇛


                      # ⚓ DeSmog ☛ Canadian_Fossil_Fuel_Advocate_Stewart_Muir
                        on_ARC_Attendees_List⠀⇛


                      # ⚓ Futurism ☛ Man_Wakes_Up,_Finds_That_Large_Chunk_of
                        SpaceX_Rocket_Has_Crashed_Into_His_Garden⠀⇛


                             It seems likely that the object once belonged
                             to a Falcon 9 rocket that made an
                             "uncontrolled reentry" over Poland early
                             Wednesday morning, according to the Polish
                             Space Agency.


                             The incident serves as yet another reminder
                             of the very real risks involved in having
                             rockets uncontrollably drop back down to
                             Earth. We've already seen several instances
                             of SpaceX debris raining down over populated
                             areas, from two separate Australian farms to
                             the British islands of Turks and Caicos,
                             which were recently littered with the
                             exploded remains of SpaceX's prototype
                             Starship rocket.


                      # ⚓ The Register UK ☛ Using_dark_mode_to_save_energy?_You
                        might_want_to_rethink⠀⇛


                             "Dark mode is a popular dark-theme colour
                             content scheme and research has found that,
                             for some devices, switching to dark mode can
                             reduce device power consumption. Energy
                             conscious internet users are therefore
                             encouraged to browse in dark mode," say the
                             authors of a BBC R&D blog post.


                             "The catch is that the advertised energy
                             savings haven't been tested in the wild,
                             where user behavior can cause unexpected
                             consequences."


                      # ⚓ APNIC ☛ So_you_want_to_build_your_own_data_centre⠀⇛


                             So in response, we kicked off a ‘Railway
                             Metal’ project last year. Nine months later
                             we were live with the first site in
                             California, having designed, spec-ed, and
                             installed everything from the fibre optic
                             cables in the cage to the various contracts
                             with ISPs. We’re lighting up three more data
                             centre regions as we speak.


                             To deliver an ‘infra-less’ cloud experience
                             to our customers, we’ve needed to get good at
                             building out our own physical infrastructure
                             fast. That’s the topic of our blog post
                             today.


                      # ⚓ The Register UK ☛ France_tops_China’s_tokamak_record
                        in_22-minute_plasma_trap⠀⇛


                             The Commissariat (French Alternative Energies
                             and Atomic Energy Commission, or CEA)
                             announced that its CEA WEST Tokamak
                             maintained plasma for more than 22 minutes
                             last week.


                      # ⚓ MIT Technology Review ☛ What's_driving_electricity
                        demand?_It_isn't_just_AI_and_data_centers.⠀⇛


                             If that sounds familiar, it may be because
                             there’s been a constant stream of headlines
                             about energy demand recently, largely because
                             of the influx of data centers—especially
                             those needed to power the AI that’s spreading
                             seemingly everywhere. These technologies are
                             sucking up more power from the grid, but
                             they’re just a small part of a much larger
                             story.


                             What’s actually behind this demand growth is
                             complicated. Much of the increase comes from
                             China, India, and Southeast Asia. Air-
                             conditioning, electric vehicles, and
                             factories all play a role. And of course, we
                             can’t entirely discount the data centers.
                             Here are a few key things to know about
                             global electricity in 2025, and where things
                             are going next.


                      # ⚓ Michael Burkhardt ☛ Old_Motors_-_Michael_Burkhardt's
                        Whirled_Wide_Web⠀⇛


                             Inspired by Dave’s “Cars and Motorcycles”
                             page, these are the cars I’ve driven over the
                             years.


                # § Overpopulation⠀➾


                      # ⚓ Kevin Kelly ☛ The_Technium:_The_Handoff_to_Bots⠀⇛


                             It has been nearly a thousand years since we
                             last saw the total number of humans on this
                             planet decrease year by year. For nearly a
                             millennium we have lived with growing
                             populations, and faster rates of growth. But
                             in the coming decades, for the first time in
                             a thousand years, the number of deaths on the
                             planet each year will exceed the number of
                             births. This seems hard to believe at first
                             because superficially there is no evidence
                             for that change in direction. As this chart
                             shows, the line wants to go up.


          o § Finance⠀➾


                # ⚓ Unicorn Media ☛ Cybersecurity_Chief_Says_MElon_Can_Use
                  Purloined_IRS_Data_Against_Taxpayers⠀⇛


                       "Musk needs to be arrested with no bail until he
                       accounts for the information that he has stolen and
                       tells where it has been stored and located," Perez
                       said. "Unfortunately, that is very unlikely to
                       happen."


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ VOA News ☛ China's_sprawling_rail_projects_around_Asia⠀⇛


                       Vietnam approved plans on Wednesday for a
                       multibillion-dollar railway with China, boosting
                       links between the two communist countries.


                       Around the region, China has been financing
                       railways under its Belt and Road Initiative, which
                       funds infrastructure projects globally but has come
                       under fire with a number of plans stalled or mired
                       in controversy.


                       Here are some of the key installments in Asia's
                       China-backed railway network: [...]


                # ⚓ VOA News ☛ EU_approves_$960_million_in_German_aid_for
                  Infineon_chips_plant⠀⇛


                       The measure will allow Infineon to complete the
                       MEGAFAB-DD project, which will be able to produce a
                       wide range of different types of computer chips,
                       the Commission said.


                       Chipmakers across the globe are pouring billions of
                       dollars into new plants, as they take advantage of
                       generous subsidies from the United States and the
                       EU to keep the West ahead of China in developing
                       cutting-edge semiconductor technology.


                # ⚓ Techdirt ☛ Donald_Trump_Is_Turning_CISA_Into_The_Embodiment
                  Of_His_Election_Conspiracy_Theories⠀⇛


                       CISA (Cyber security and Infrastructure Security
                       Agency) has been doing its best to thwart security
                       threats and deter the spread of misinformation
                       about government security. Trump apparently doesn’t
                       like that. He’d rather turn the agency on itself to
                       serve his own egotistical ends while turning CISA
                       into just another distribution option for his
                       “stolen election” conspiracy theories. Here’s Eric
                       Geller, reporting for Wired.


                # ⚓ Wired ☛ The_Showdown_Between_Elon_Musk_and_Sam_Altman⠀⇛


                       The relationship between Scam Altman and Elon Musk
                       goes back to the early days of OpenAI—then a
                       nonprofit research lab. But now the two men find
                       themselves in a very public feud over the billion-
                       dollar AI company. Today on the show, we catalog
                       their friendship turned feud and how the company
                       that started it all still remains core to their
                       beef.


                # ⚓ Federal Trade Commission ☛ Federal_Trade_Commission
                  Launches_Inquiry_on_Tech_Censorship_|_Federal_Trade
                  Commission⠀⇛


                       The FTC issued a Request for Information (RFI)
                       requesting public comment on how consumers may have
                       been harmed by technology platforms that limited
                       their ability to share ideas or affiliations freely
                       and openly.


                       “Tech firms should not be bullying their users,”
                       said FTC Chairman Andrew N. Ferguson. “This inquiry
                       will help the FTC better understand how these firms
                       may have violated the law by silencing and
                       intimidating Americans for speaking their minds.”


                # ⚓ Nick Heer ☛ U.S._Federal_Trade_Commission_Launches_Inquiry
                  Into_Tech_‘Censorship’⠀⇛


                       This whole thing is written in neutral language,
                       but almost certainly motivated by a longstanding
                       belief that technology companies are biased against
                       U.S. conservatives. This administration also wants
                       to curtail the protections of Section 230 (PDF) of
                       the Communications Decency Act; the questions in
                       this RFI are directly tied to that goal.


                # ⚓ Manton Reece ☛ Humane_pin_wrap-up⠀⇛


                       The lesson for me is not that anything resembling
                       this product was doomed to fail. There were
                       interesting ideas in it. There were talented people
                       working on it. The lesson is trying to do too much
                       and not leaving room (and money) to ramp up. Wait
                       for AI voice models to get to where you need to be.
                       Only ship the features you can absolutely nail.


                # ⚓ Logikal Solutions ☛ Is_Microsoft_Going_Out_of_Business?⠀⇛


                       Given recent pricing decisions, one has to ask if
                       Microsoft is going out of business. Wall Street has
                       been worried about the massive financial abyss that
                       is AI and Cloud Computing. Despite what you might
                       see in the chart, smart money has been getting out
                       while fools rush in.


                # ⚓ Digital Music News ☛ TikTok's_Head_of_Music_Ole_Obermann
                  Exiting_for_Apple_Music⠀⇛


                       While Obermann oversaw TikTok’s music strategy
                       during a period of meteoric growth, there are mixed
                       sentiments about his strategy in the industry. He
                       is regarded as hard-negotiating against IP owners
                       and generally being creator-unfriendly. The UMG
                       licensing dispute last year was a result of low
                       royalty payments from the platform. Obermann also
                       oversaw TikTok’s strategy of divide and conquer
                       among independent Merlin members by refusing to
                       collectively bargain with the collective.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ VOA News ☛ China_falsely_accuses_Philippines_of
                        illegal_intrusion_after_midair_standoff_over_South
                        China_Sea⠀⇛


                             Journalists from The Associated Press and
                             other media outlets were on the Philippine
                             aircraft and witnessed the incident.


                             The Philippine pilot at one point warned the
                             Chinese navy helicopter by radio that he was
                             violating the safety standards managing
                             distance between aircraft set by the U.S.
                             Federal Aviation Administration and the
                             International Civil Aviation Organization.


                             Yet China said it was the Philippines that
                             violated the law by flying over the
                             Scarborough Shoal.


                      # ⚓ Los Angeles Times ☛ Trump_makes_false_claims_on
                        Russia's_war_on_Ukraine._Here_are_the_facts⠀⇛


                             President Trump this week falsely blamed
                             Ukraine for starting the war that has cost
                             tens of thousands of Ukrainian lives, causing
                             outrage and alarm in a country that has spent
                             nearly three years fighting back the invasion
                             of a much larger Russian military.


                      # ⚓ VOA News ☛ Philippines_reports_intrusions_targeting
                        intelligence_data⠀⇛


                             The Philippines has detected foreign attempts
                             to access intelligence data, but its cyber
                             minister said on Tuesday no breaches have
                             been recorded so far.


                             Attempts to steal data are wide-ranging, said
                             minister for information and communications
                             Ivan Uy. Advanced Persistent Threats or APTs
                             have repeatedly attempted but failed to
                             infiltrate government systems, suggesting the
                             country's cyber-defenses have held firm.


                      # ⚓ The Korea Times ☛ Activist_warns_of_false,_anti-
                        Korean_content_spreading_on_Chinese_social_media_app
                        RedNote⠀⇛


                             Chinese social media app, Xiaohongshu — known
                             as RedNote in English — has been flooded with
                             unfounded anti-Korean claims, warned
                             professor Seo Kyoung-duk, a longtime advocate
                             of Korean culture.


                      # ⚓ RFA ☛ Does_a_video_show_France’s_Macron_snubbing_the
                        Indian_leader_at_Paris_AI_summit?_–_Radio_Free_Asia⠀⇛


                             But the claim is misleading. The video, taken
                             out of context, ignores interactions between
                             the two leaders earlier in the event.


                             The 22-second video was shared on X on Feb.
                             11.


          o § Censorship/Free Speech⠀➾


                # ⚓ Hong Kong Free Press ☛ Hong_Kong’s_Democratic_Party_will
                  not_rule_out_discussion_of_potential_disbandment,_says_party
                  head⠀⇛


                       Hong Kong’s Democratic Party will not rule out
                       discussion on potentially disbanding during an
                       upcoming meeting this week, its chairperson has
                       said following reports that the party may shut
                       down. Chair Lo Kin-hei told reporters on Wednesday
                       that the executive committee of the Democratic
                       Party will convene on Thursday.


                # ⚓ The Straits Times ☛ Ex-Karabakh_official_held_by_Azerbaijan
                  declares_second_hunger_strike_amid_terrorism_trial⠀⇛


                       Ruben Vardanyan, a former top official in the
                       ethnic Armenian administration of Nagorno-Karabakh
                       which Azerbaijan retook in 2023, announced a second
                       hunger strike on Wednesday in protest against his
                       criminal trial in Baku.


                # ⚓ VOA News ☛ Azerbaijan_suspends_BBC⠀⇛


                       The suspension comes after Azerbaijani state-run
                       media last week reported that the Azerbaijani
                       government wanted to reduce the number of BBC staff
                       working in the country to one.


                       The BBC said it has received nothing in writing
                       about the suspension from the Azerbaijani
                       government. While the news agency seeks
                       clarification, its team of journalists in the
                       country have stopped their journalistic activities,
                       according to the BBC.


                # ⚓ Common Dreams ☛ No_Nazis:_Be_Like_Chris_Kluwe,_And_All_Who
                  Came_Before_|_Opinion⠀⇛


                       So Chris Kluwe, 43-year-old Huntington resident and
                       decent guy, showed up at Tuesday's City Council
                       meeting to tell them what he thought of their
                       “propaganda” and offer a calm but robust indictment
                       of what MAGA really means. And it was great.


                # ⚓ Nick Heer ☛ Clearview_A.I.’s_CEO_Resigns,_New_Leadership
                  Likes_Its_Chances_Under_Trump⠀⇛


                       Near-universal facial recognition in the hands of
                       this administration — what a frightening prospect.
                       Keep an eye on that terrible settlement.


                # ⚓ Techdirt ☛ ExTwitter_Pays_Trump_$10M_to_Settle_Case_It_Had
                  Already_Won⠀⇛


                       The plot twist was telegraphed back in November,
                       when ExTwitter filed something with the Ninth
                       Circuit that basically said “hey, don’t bother
                       ruling on this appeal, we’re working on a
                       settlement.” The appeal in question? Oh, just
                       Trump’s absolutely batshit lawsuit claiming that
                       Twitter (this was back in the pre-Ex days) violated
                       his First Amendment rights by shutting down his
                       account while he was president.


                       Let’s do a quick First Amendment refresher: The
                       First Amendment stops the government from silencing
                       speech. That’s it. That’s the whole thing. Private
                       companies can moderate their platforms however they
                       want. (This is not exactly a controversial
                       interpretation — it’s First Amendment 101.) But in
                       this case, Trump (who was the head of the
                       government at the time of the events in the case)
                       was suing the private company arguing that it
                       somehow violated his First Amendment rights to ban
                       his account, even if he had violated the company’s
                       rules.


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


                # ⚓ Hong Kong Free Press ☛ Jimmy_Lai_denies_condoning_violence
                  despite_urging_solidarity_between_protesters,_as_nat._sec
                  trial_continues⠀⇛


                       Jailed media tycoon Jimmy Lai has denied condoning
                       violent protest despite urging solidarity between
                       demonstrates in 2019. He also told the court that
                       his calls for amnesty were not at odds with his
                       stance against violence.


                # ⚓ Truthdig ☛ Letting_Trump_Have_His_Way_With_Words_Erodes_the
                  First_Amendment⠀⇛


                       The capitulation of Apple and Google validates a
                       widespread fear that it isn’t just Elon Musk who is
                       doing Trump’s dirty work to undo democracy, but
                       that the Big Tech community generally has lined up
                       to stay in the good graces of executive power.
                       Apple CEO Tim Cook and Google each donated $1
                       million to this year’s presidential inauguration.


                # ⚓ Scheerpost ☛ Burying_the_CIA’s_Assange_Secrets⠀⇛


                       A United States judge dismissed a lawsuit pursued
                       by four American attorneys and journalists, who
                       alleged that the CIA and former CIA Director Mike
                       Pompeo spied on them while they were visiting
                       WikiLeaks founder Julian Assange in Ecuador’s
                       London embassy.


                       “The subject matter of this litigation,” Judge John
                       Koeltl determined [PDF], “is subject to the state
                       secrets privilege in its entirety.” Any answer to
                       the allegations against the CIA would “reveal
                       privileged information.”


                       Few publications followed this case as closely as
                       The Dissenter. It unfolded at the same time that
                       the U.S. government pursued the extradition of
                       Assange, making any outcome potentially
                       significant.


                # ⚓ The Walrus ☛ Local_News_Is_Dying._The_Consequences_Are
                  Worse_than_You_Think⠀⇛


                       The misfortunes that have ravaged local
                       journalism—some self-inflicted, some not—have been
                       unfolding for more than a decade. Spending cuts by
                       owners have hollowed out local newsrooms, tech
                       platforms have hoovered up advertising revenue, and
                       cellphones and the internet have eliminated the
                       control traditional media once had over when and
                       where people get news. More recently, Meta’s move
                       to banish journalism from Facebook and Instagram
                       has made it much more difficult for news
                       organizations, especially small local outlets, to
                       get their stories to readers.


          o § Civil Rights/Policing⠀➾


                # ⚓ AccessNow ☛ Oral_statement_at_the_Informal_Meeting_of_the
                  UNGA_Third_Committee⠀⇛


                       Access Now's oral statement at the Informal Meeting
                       of the UN General Assembly Third Committee on
                       February 6, 2025.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_taxi_group_halts_strike
                  plan_after_city’s_leader_warned_against_‘drastic_action’⠀⇛


                       A Hong Kong taxi union has called off a planned
                       strike demanding a government crackdown on
                       unlicensed ride-hailing services – a day after
                       Chief Executive John Lee warned that “drastic
                       action” would not receive public support.


                # ⚓ Common Dreams ☛ Public_Service_Unions_and_State_Democracy
                  Defenders_Fund_Challenge_Unlawful,_Mass_Federal_Firings⠀⇛


                       The complaint says that OPM’s egregious firings
                       were made on false pretenses and violate federal
                       law, including the Administrative Procedure Act and
                       other statutes defining federal employment and
                       OPM's role. These firings were executed across
                       federal agencies, based on directives from OPM.
                       OPM, the complaint asserts, acted unlawfully by
                       directing federal agencies to use a standardized
                       termination notice falsely claiming performance
                       issues. Congress, not OPM, controls and authorizes
                       federal employment and related spending by the
                       federal administrative agencies, and Congress has
                       determined that each agency is responsible for
                       managing its own employees.


                # ⚓ The Register UK ☛ IBM_co-location_program_described_as
                  worker_attrition_plan⠀⇛


                       The mainframe giant's recent return-to-office (RTO)
                       push is already arguably achieving that, namely
                       forcing out those kinds of workers, but we're told
                       that Big Blue is taking a broader approach, echoing
                       a 2016 initiative from then marketing chief
                       Michelle Peluso.


                # ⚓ The Register UK ☛ Thousands_of_trafficked_scammers_await
                  return_to_Thailand⠀⇛


                       Prime Minister Paetongtarn Shinawatra said around
                       7,000 individuals are awaiting transfer to Thailand
                       and confirmed the government was working as quickly
                       as possible to remedy the issue.


                # ⚓ The Washington Post ☛ Office_work_is_on_the_rise_with_new
                  record_highs⠀⇛


                       As of the first week of February, office occupancy
                       remained stable at 54.1 percent on average in those
                       10 cities, according to Kastle. Houston led at 65.1
                       percent, while San Francisco brought up the rear at
                       43.2 percent.


                # ⚓ Omicron Limited ☛ Struggling_men_may_hurt_noncollege
                  women's_marriage_prospects⠀⇛


                       But that concern is misplaced, finds new research
                       co-authored by a Cornell economist. In fact, the
                       researchers found, college women have married at a
                       steady rate for decades, while the rate for women
                       without degrees has dropped precipitously—their
                       prospects undermined by the declining fortunes of
                       noncollege men.


                # ⚓ Wired ☛ Microsoft_Hosted_Explicit_Videos_of_This_Startup
                  Founder_for_Years._Here's_How_She_Got_Them_Taken_Down⠀⇛


                       More than a month later, a few dozen additional
                       pieces of content had been removed. Of the 202 that
                       remained online, 142 were hosted on Microsoft’s
                       Azure services. A Point de Contact investigator
                       emailed Liu and alleged, “Microsoft's abuse team
                       did not answer our notification emails” and said
                       the team was trying some of its individual contacts
                       at the company. Around that time, a frustrated Liu
                       mentioned Microsoft’s slow response in an interview
                       with The Street. An unnamed Microsoft spokesperson
                       told the news outlet that the company was
                       investigating and noted that any potential
                       violations of its acceptable use policy are taken
                       seriously. Yet again, no action followed.


                       “The main issue we had was the lack of response
                       from Microsoft,” Dirani says. He alleges that
                       Microsoft’s abuse team believed that it needed more
                       information, but he says the company never
                       communicated what that information was. Even a
                       higher-up contact wouldn’t give a straight answer
                       on what additional details could trigger a
                       takedown. Point de Contact tried to “push”
                       Microsoft more, including opening a new case,
                       according to Dirani. “We were sending reminders of
                       all the URLs that were still online,” he says. “But
                       unfortunately, even the new reports we sent were
                       not responded to.”


                # ⚓ VOA News ☛ Taliban_withdraw_Afghanistan_from_International
                  Criminal_Court⠀⇛


                       The decision follows the ICC chief prosecutor’s
                       announcement last month, seeking arrest warrants
                       for the reclusive Taliban supreme leader,
                       Hibatullah Akhundzada, and a close associate,
                       accusing them both of being “criminally responsible
                       for persecuting Afghan girls and women.”


                # ⚓ The Nation ☛ If_Trump_Crushes_Federal_Workers,_We’re_All
                  Next⠀⇛


                       “I’m a federal worker, and I feel like a canary in
                       the coal mine right now—because what they’re doing
                       to us is going to happen to the entire American
                       public.” That’s how Chris Dols, who works for the
                       US Army Corps of Engineers and is the president of
                       a local chapter of the International Federation of
                       Professional and Technical Engineers, began his
                       video response to Elon Musk’s instantly infamous
                       Oval Office press conference last week.


                       Dols is right: Musk’s attacks on federal employees
                       and their unions aren’t just a threat to the
                       specific workers in his current line of fire. They
                       pose an unparalleled danger to every single
                       American.


                # ⚓ Michigan Advance ☛ Here’s_the_latest_on_how_states_are
                  cooperating_with_Trump’s_deportation_plans⠀⇛


                       Conservative cities and states across the country
                       have taken to President Donald Trump’s deportation
                       plans and are increasing cooperation with federal
                       authorities — even seeking new laws against illegal
                       immigration that would be enforced by local and
                       state police.


                # ⚓ California State University Northridge ☛ “We_will_not_be
                  erased!”_Students_rise_against_ICE_–_Daily_Sundial⠀⇛


                       Students rallied to walk out onto the University
                       Lawn with the Students Organizing Against
                       Repression Coalition (SOAR), Anakbayan Northridge,
                       M.E.Ch.A de CSUN, Students for Justice in Palestine
                       and others to voice their frustrations with CSUN’s
                       compliance with ICE.


                       Chicano Studies Department Chair Rosa Rivera
                       Furumoto and organization representatives gave
                       speeches before the marchers began their march from
                       the University Lawn to Jacaranda Walk and back
                       around.


                # ⚓ Techdirt ☛ Court_Grants_Immunity_To_DA_Who_Shared_Nude
                  Photos_From_A_Searched_Phone_With_Local_Law_Enforcement⠀⇛


                       The phrase “no harm, no foul” doesn’t apply to law
                       enforcement personnel, whether they’re patrol
                       officers or the chief local prosecutor. Instead —
                       thanks to the qualified immunity doctrine — the
                       phrase is: “whatever amount of harm, no foul.”


                       As long as the harm isn’t something specifically
                       covered by precedent, the general feeling of courts
                       is that law enforcement shouldn’t be punished for
                       rights violations they can plausibly (at least
                       under precedent) claim they had no idea were rights
                       violations, no matter how immediately egregious
                       those rights violations were.


                # ⚓ EDRI ☛ How_do_delivery_platforms_use_algorithms_to_manage
                  workers?⠀⇛


                       Algorithmic management of workers has become the
                       norm for gig-economy platforms. Decisions made by
                       algorithms can determine how much people get paid,
                       what work they receive, and even if their account
                       (and employment) is suspended. But workers are too
                       often left in the dark about how those algorithms
                       work and how those decisions get made, leaving them
                       playing a game they don’t know the rules to.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Public Knowledge ☛ New_Orders_are_Scrubbing_the_Internet_of
                  Equity,_Dismantling_Transparency,_and_Making_it_Harder_To
                  Implement_Bipartisan_Law⠀⇛


                       The continued attacks on DEI are making the Digital
                       Equity Act harder to follow.


                # ⚓ APNIC ☛ [Podcast]_RPKIViews:_The_archive_of_RPKI_states⠀⇛


                       Job Snijders discusses his global RPKI validation
                       archive, and the annual 'state of RPKI' report he
                       produces.


                # ⚓ RIPE ☛ Introducing_the_New_RIPEstat_UI⠀⇛


                       After working toward this goal for some months,
                       we're pleased to present a first look at the new
                       RIPEstat: [...]


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ MWL ☛ Now_available:_combined_print/ebook_bundles_direct
                  from_my_bookstore⠀⇛


                       The question I get asked most often is “Can I get a
                       print and ebook combo of your books?” No, hang on,
                       that’s not quite true. Technically, the most common
                       questions are “Are you mad?” followed by “Are you
                       serious?” but the print/ebook combo thing is a
                       solid third place.


                # ⚓ Digital Music News ☛ TikTok’s_Head_of_Music_Ole_Obermann
                  Reportedly_Exiting_for_Fashion_Company_Apple_Music⠀⇛


                       After a mixed legacy, TikTok’s Head of Music
                       Business Development Ole Obermann is reportedly
                       leaving for Fashion Company Apple Music.


                # ⚓ Rachel ☛ My_books_have_moved_to_Gumroad⠀⇛


                       As of earlier this week, they are no longer on
                       Amazon at my direction. Instead, I put them on
                       Gumroad as .epub files. They are still DRM-free, so
                       once you have a copy, you can shove them onto all
                       of your devices without having something "phone
                       home" to approve it first.


                # ⚓ Press Gazette ☛ Digital_magazine_ABCs_2024:_Half_of_titles
                  down_in_past_year⠀⇛


                       ABC-audited magazines had a combined average
                       digital circulation of three million per edition
                       (excluding any copies distributed in bulk for free)
                       – up 14% compared to 2023.


                       Some 1.6 million, or 55%, of the combined 2024
                       digital magazine circulation came from services
                       like Apple News+, Cafeyn, Kindle Unlimited and
                       Readly.


                # ⚓ Ethan Zuckerman ☛ Liz_Pelly_at_UMass:_Spotify,_the_Mood
                  Machine⠀⇛


                       In particular, Pelly is interested in the myth of
                       Spotify as a neutral meritocracy, a space in which
                       the best work rises algorithmically to the top. The
                       reality is more about arrogant billionaires
                       overconfidently celebrating their machines and
                       ignoring the social problems they leave behind. To
                       tell this sometimes hidden history of Spotify,
                       Pelly interviewed over 100 people, many of them
                       artists affected by the rise of the platform. She
                       offers this as a “pro-artist” work, noting that
                       it’s strange to have to put yourself in the “pro-
                       artist” camp. Swedish journalists, who covered the
                       platform during its emergence, were also an
                       important source.


      § Monopolies/Monopsonies⠀➾


          o ⚓ KOL453_|_Objections_to_Argumentation_Ethics,_Libertarian_Property
            Rights,_Scarcity,_Intellectual_Property:_Discussion_with_a
            Student⠀⇛


                 I was approached recently by my old friend, legal scholar
                 and philosopher David Koepsell (a fellow opponent of IP
                 who appeared on the John Stossel show with me a few years
                 back), (( KOL308 | Stossel: It’s My Idea (2015). )) as
                 one of his students at Texas A&M, Eliot Kalinov, was
                 interested in my and Hoppe's work on argumentation ethics
                 and related issues. I offered to have a discussion with
                 Eliot about these issues for his research and publication
                 plans, which we did yesterday (Feb. 18, 2025).


          o § Patents⠀➾


                # ⚓ Kluwer Patent Blog ☛ Patent_case:_Huang_v._Amazon.com,_Inc,
                  USA⠀⇛


                       It was within the discretion of the trial court to
                       deny leave to amend a complaint because the
                       proposed amendment, like the complaint it was
                       intended to cure, failed to specifically identify
                       the accused products.


                # ⚓ Tom's Hardware ☛ AMD_could_block_the_sale_of_defective_chip
                  maker_Intel_due_to_a_cross-licensing_agreement⠀⇛


                       Want to get Intel's product business? You will have
                       to deal with AMD due to a wide patent monopoly
                       cross-licensing agreement.


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ UPC_to_hire_multiple_new_judges_in_2025 [Ed:
                        UPC is illegal. JUVE knows it is illegal. But JUVE got
                        paid by Team UPC to prop up and try to legitimise these
                        constitutional violations and a kangaroo court.]⠀⇛


                             The UPC has published its budget for 2025 and
                             it clearly states the number of judges at the
                             UPC will grow significantly this year.
                             Officials will make funds available for 6.9
                             full-time equivalent judges (FTEs) for the
                             Court of Appeal alone.


                # § Software Patents⠀➾


                      # ⚓ Unified Patents ☛ $4,000_for_STT_WebOS_web-based
                        communication_patents_prior_art⠀⇛


                             Unified Patents added two new PATROLL
                             contests, each with a $2,000 cash prize,
                             seeking prior art on the list below. The
                             patents are owned and asserted by STT WebOS,
                             Inc. The patents relate to web based control
                             management systems and communications.They
                             have been asserted against ByteDance.


                             The contests will expire on March 22, 2025.


          o § Trademarks⠀➾


                # § Right of Publicity⠀➾


                      # ⚓ Futurism ☛ Fury_Erupts_After_Netflix_Used_AI_to_Clone
                        the_Voice_of_a_Murdered_Influencer_for_a_True_Crime_Doc
                        About_Her_Death⠀⇛


                             It's an eerie artistic choice, even for the
                             fraught true crime genre, that had audiences
                             startled, with one user calling it "deeply
                             unsettling use of AI."


                             "Watching the Gabby Petito doc, absolutely
                             invested... until the part it started using
                             AI to make HER read out her texts and journal
                             entries," another user wrote. "That is
                             absolutely NOT okay. She’s a murder victim.
                             You are violating her again."


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ Meta_Says_it_Made_Sure_Not_to_Seed_Any
                  Pirated_Books⠀⇛


                       In one of the AI lawsuits faced by Meta, the
                       company stands accused of distributing pirated
                       books. The authors who filed the class-action
                       lawsuit allege that Meta shared books from the
                       shadow library LibGen with third parties via
                       BitTorrent. Meta, however, says that it took
                       precautions to prevent 'seeding' content. In
                       addition, the company clarifies that there is
                       nothing 'independently illegal' about torrenting.


                # ⚓ Tom's Hardware ☛ Microsoft_Xbox_showcases_an_incredibly
                  impractical_AI_model_for_'gameplay_ideation'⠀⇛


                       Yesterday, Microsoft Xbox debuted Muse, "a
                       generative AI model designed for gameplay
                       ideation," alongside an open-access Nature.com
                       article and corresponding blog post with a YouTube
                       video. Not sure what "gameplay ideation" means?
                       While Microsoft defines it as generating "game
                       visuals, controller actions, or both," its actual
                       functional purposes are pretty limited and
                       certainly don't do anything like skipping an actual
                       game development pipeline.


                # ⚓ Torrent Freak ☛ Cloudflare_Asks_Court_to_End_LaLiga's
                  "Illegal"_Blocking_Response_to_Encrypted_Client_Hello⠀⇛


                       After the gloves came off earlier this week,
                       Cloudflare has asked a Spanish court to declare
                       LaLiga's “disproportionate” piracy blocking
                       measures illegal. Details are currently scarce, but
                       Cloudflare looks set to challenge the legitimacy of
                       the court's original order. LaLiga and Telefonica
                       sought enhanced blocking measures to counter
                       internet users' adoption of Encrypted Client Hello.


                # ⚓ Digital Camera World ☛ Using_copyrighted_material_to_train
                  AI_isn’t_always_fair_use,_judge_rules._But_what_are_the
                  implications_for_photographers?⠀⇛


                       In Thompson Reuters Vs Ross Intelligence, US
                       Circuit Judge Stephanos Bibas ruled that Ross
                       Intelligence's use of editorial content owned by
                       Thompson Reuters did not fall under fair use.


                       The legal battle arose after Thompson Reuters
                       claimed that Ross Intelligence used its copyrighted
                       material published on Westlaw to build an AI-
                       powered legal research platform called LegalEase.
                       Bibas issued a summary judgment for part of the
                       case, reversing a previous decision that denied
                       summary judgment. It sided with Thompson Reuters,
                       saying that LegalEase’s use did not have a
                       sufficiently different purpose and directly
                       competed with the original.


                # ⚓ EFF ☛ AI_and_Copyright:_Expanding_Copyright_Hurts
                  Everyone—Here’s_What_to_Do_Instead⠀⇛


                       The stakes are high, because ML is critical to
                       helping us interpret the world around us. It's
                       being used by researchers to understand everything
                       from space nebulae to the proteins in our bodies.
                       When the task requires crunching a huge amount of
                       data, such as the data generated by the world’s
                       telescopes, ML helps rapidly sift through the
                       information to identify features of potential
                       interest to researchers. For example, scientists
                       are using AlphaFold, a deep learning tool, to
                       understand biological processes and develop drugs
                       that target disease-causing malfunctions in those
                       processes. The developers released an open-source
                       version of AlphaFold, making it available to
                       researchers around the world. Other developers have
                       already iterated upon AlphaFold to build
                       transformative new tools.


                # ⚓ Digital Music News ☛ RHCP_Not_Giving_It_Away_Now—Looking_to
                  Sell_Music_Catalog⠀⇛


                       Sources tell Billboard that Eric Greenspan of Myman
                       Greenspan Fox Rosenberg Mobster Younger & Light has
                       been spearheading a recorded music catalog deal, as
                       he did for their publishing rights in 2021. Back
                       then, the Red Hot Chili Peppers sold their music
                       publishing assets to Hipgnosis for between $140
                       million and $150 million.


                # ⚓ EFF ☛ Copyright_and_AI:_the_Cases_and_the_Consequences⠀⇛


                       These cases can end one of three ways:
                       rightsholders win, everybody settles, or developers
                       win. As we’ve noted before, we think the developers
                       have the better argument. But that’s not the only
                       reason they should win these cases: while creators
                       have a legitimate gripe, expanding copyright won’t
                       protect jobs from automation. A win for
                       rightsholders or even a settlement could also lead
                       to significant harm, especially if it undermines
                       fair use protections for research uses or artistic
                       protections for creators. In this post and a
                       follow-up, we’ll explain why.




╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 9587
    ➮ Generation completed at 02:49, i.e. 21 seconds to (re)generate ⟲