𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, December 24, 2024
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Generated Wed 25 Dec 02:49:19 GMT 2024
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2024/12/24/


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

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QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu


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

⦿ Techrights  -  Advertisers and Their Covert Impact on Publications' Output (or Writers' Topics of Choice, as Assigned or Approved by Editors)

⦿ Techrights  -  Brittany Day Connects Windows Ransomware to "Linux" Using Microsoft LLMs (FUD Galore, Zero Effort, No Accountability)

⦿ Techrights  -  IRC Proceedings: Monday, December 23, 2024

⦿ Techrights  -  [Meme] Coin-Operated Publishers (Gaming the Message, Buying the Narrative)

⦿ Techrights  -  [Meme] How to Kill Unions (Staff on Shoestring Budget Cannot Afford Lawyers)

⦿ Techrights  -  Microsoft Windows Slides to New Lows in Colombia

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Terrible Year for Microsoft Windows in Cyprus

⦿ Techrights  -  The EPO's Staff Union (SUEPO) Takes Legal Action to Rectify the Decrease in Wages (Lessening of Purchasing Power)

⦿ Techrights  -  Where the Population is Controlled by Skinnerboxes Inside People's Pockets (or Purses)

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/12/24/Advertisers_and_Their_Covert_Impact_on_Publications_Output_or_W.shtml
https://techrights.org/n/2024/12/24/Brittany_Day_Connects_Windows_Ransomware_to_Linux_Using_Microso.shtml
https://techrights.org/n/2024/12/24/IRC_Proceedings_Monday_December_23_2024.shtml
https://techrights.org/n/2024/12/24/Meme_Coin_Operated_Publishers_Gaming_the_Message_Buying_the_Nar.shtml
https://techrights.org/n/2024/12/24/Meme_How_to_Kill_Unions_Staff_on_Shoestring_Budget_Cannot_Affor.shtml
https://techrights.org/n/2024/12/24/Microsoft_Windows_Slides_to_New_Lows_in_Colombia.shtml
https://techrights.org/n/2024/12/24/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/12/24/Terrible_Year_for_Microsoft_Windows_in_Cyprus.shtml
https://techrights.org/n/2024/12/24/The_EPO_s_Staff_Union_SUEPO_Takes_Legal_Action_to_Rectify_the_D.shtml
https://techrights.org/n/2024/12/24/Where_the_Population_is_Controlled_by_Skinnerboxes_Inside_Peopl.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/12/24/Gemini_Links_24_12_2024_Deedum_Gemini_Client_Gets_Colour_Suppor.shtml
https://techrights.org/n/2024/12/24/Links_24_12_2024_Labour_Strikes_and_TikTok_Scrambling_to_Prop_U.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 75

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/24/Advertisers_and_Their_Covert_Impact_on_Publications_Output_or_W.shtml
    Gemini version at https://techrights.org/n/2024/12/24/Advertisers_and_Their_Covert_Impact_on_Publications_Output_or_W.gmi

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Publications' Output (or Writers' Topics of Choice, as Assigned or Approved by
Editors)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024,
updated Dec 24, 2024


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


It cannot be trivially denied that sponsorship in the form of "advertising"
impacts where publishers go (or don't go, won't go)


This post is based on a private conversation, so a lot of small details will be
left out. Instead, the general message will be relied upon.


Knowing that IBM is criticised a_lot (and strongly) by its_very_own_employees,
that is still_attacks_high-profile_Free_software_people, and that it_buys
favourable_coverage_about_itself, we recently criticised The Register for
taking money from IBM. The Register sought to contest this criticism. It
perceived or interpreted that as an accusation that was barely credible or
baseless, but we stood our ground and explained why. I want to just quickly
give an outline of this, without having to repeat what we said about IBM, Red
Hat, and The Register (we have not changed our minds or our position on this).


"I have my share of criticism," I told them, "and not as opinionated as you
might assume [...] am still frustrated that El Reg [The Register] does many
shallow pieces and sponsored pieces [...] good publishers need not rely on
those [...] wealthy? maybe [...] but history shows money related not to
quality..."


I asked them to "bite the hand", quoting the original motto of the site. And
"do not swim with the sharks"...


The Register's position was that the advertisers or partners had no impact; To
quote, "well I'm happy to tell you that the sponsored content is handled by a
completely separate team from editorial, the journalists. that's not to say the
sponsored product is bad, we put a lot of effort into it to make it worthwhile
for our clients. but none of journalists are involved nor are they aware of
what's being advertised / run until it's live" (whereupon everyone can see it).


But "it is Utopian," I told them, as "they are part of the same "organism"
[...] the lipstick does not change the pig [...] I worked in media ages ago"...


They didn't exactly deny this, "but we have a clear separation, and crossing
that line internally is a no-no," they said (also said yes, acknowledging the
above).


"I saw how the ads led to censorship and then self-censorship," I told them, "I
think you can sleep over it [...] and think how your writers feel [...] in
terms of 6th sense [...] and job security..."


I took SJVN as an example because "sjvn writes for El Reg [...] he also did LF
[Linux_Foundation] gigs [...] in another site [...] that's a conflict [...] he
cannot write some things without risking gigs elsewhere..."


Imagine SJVN writing a critical Linux Foundation piece in The Register. He
would risk losing his other gigs, in Linux Foundation-sponsored (bribed) sites.
So he just won't go there; instead he's likely to just parrot OIN, LF and other
corporate front groups, including IBM's.


Can journalism and honest reporting be done under these conditions? The capital
flows from the companies one is meant to criticise. They're buying silence. Or
silence at the very least (compulsory puff piece tend to follow).


By The Register I was told, "we're not a publisher beholden to public
shareholders; we're still owned by the same 3 guys and they give us free rein
to say what we want. we like working here because we know that other places
aren't as independent..."


The "same 3 guys," I said, "but_not_the_founder [...] he did not agree with
your direction [...] you did_not_cover_his_death, AFAIK [...] we checked
everywhere [...] only nick [Nick Farrell] mentioned his death..."


They did not deny that they had ignored the death of their own founder. Instead
the conversation went on to covering SJVN some more.


To quote: "SJVN is a freelancer who we pay to write things for us and we edit
and run them if they are good enough. what he does in his other time is up to
him. if there's a conflict of interest we take it on a case by case basis..."


But they cannot ignore that he's tied to some other businesses and publishers.
They said, "we have rules on what people can and can't write about if they have
a commercial interest in something. if you think anyone's crossed that, let me
know. eg on SJVN's about page we disclose he advises a firm that has a client
connected to Rocky Linux" (there's lots more).


I explained to them that "he has his own blog [...] but barely uses it [...] so
he is beholden to sponsors (the publishers') [...] days_ago [an] obligatory
puff piece right there with his name on it [...] they made sam varghese do the
same [and] he_is_gone_now" (no articles for half a year; that's over 6 months
now).


About SJVN and companies he is connected to (through publishers), I said "he
covers them [..] without disclosing that" (conflict). And "days ago he did this
puff_piece [...] "in partnership with..."" (see screenshots at the bottom).


But the "thing is," they told me, "if ZD Net wants to run that kind of thing,
it can. you don't see us doing it. I suppose it's no surprise I'm not a massive
fan of ZDNet, we've always been rivals..."


But "do not become zdnet," I advised them, as "you are close to it [...] but
they are Red Ventures [1, 2] [...] literally a marketing company..."


Their response to this was fair: "I don't think we're anything close to
becoming ZDnet, which runs stories like top 10 washing machines for 2025 [...]
we got no need to, we're not into affiliate marketing and B2C, that's
scrambling around in the pennies left over by Facebook..."


Well, "not yet," I responded, but "look at the trajectory of WWW [...] it's
really saddening [...] it's getting so bad govt. pass laws against access to it
[...] for kids, for now [and] there are still many stories you miss".


We can agree that ZDNet is miles worse, but they've failed to convince me that
corporate money (for their writers, who are tied to ZDNet sometimes) has no
impact on their coverage. There's always room for improvement and independent
journalism demands that we reject GAFAM money. Otherwise the coverage is deeply
tainted. The screenshots below show that SJVN is paid by snakeoil pushers in
"hey hi" (AI) clothing. █


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


               🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Learn_AI_in_5_Minutes_a_Day⦈_


Whatever this "AI" is, it won't save time, it'll waste other people's time
(reading slop 'articles', fake E-mails and code/commit messages that don't make
sense and cannot be properly reviewed/audited). So SJVN promotes corporate
gaslighting_of_people. How disappointing.




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⠿⣿⣿⣦⣄⣀⣀⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠈⠛⠻⠟⠿⠿⡿⠿⠿⠿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣯⠄⢻⣦⣄⣠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢫⡛⠛⠋⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠀⠀⢠⣤⣤⣤⣄⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⣿⣿⣿⣶⡶⠂⠀⠀⠀⠀⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣵⠗⡀⡀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣴⣿⣿⣭⣿⣯⣥⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣁⣀⣀⣀⣀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣦⢴⣿⣆⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣛⡋⠿⣻⡿⠻⠇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠗⠂⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⣿⡭⠁⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⣿
⢮⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠅⠂⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠑⠀⠀⠌
⣷⣾⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣫⠓⠁⠀⠰⠾⢱⠈⠨⠚⢀⡀⠀⠀⠀⠀⠀⠀
⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣬⢻⣒⠳⠀⠁⢤⣀⠁⢀⠄⠀⠂⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣸⣝⣯⡁⣁⠂⠐⠀⠁⠈⣀⠨⠁⠀⠄⠀⠀⠠
⢟⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠼⠁⠀⠈⡰⠲⡀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣹⡏⢊⡦⡗⢻⣇⡔⠐⡂⠀⠀⠂⠀⠀⠀⠐⠀⠀
⣿⣿⡟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡙⢏⡏⡻⡿⡻⡟⡻⣿⡏⡟⡟⣟⢹⢻⣟⡻⡟⣻⣛⡟⣿⢻⢻⢟⣻⢛⡟⡟⡟⣻⢟⢿⣿⣛⢿⢛⣿⡟⣫⣿⢟⢿⢻⢹⢟⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣼⣷⣧⣷⣽⣧⣧⣿⣧⣧⣷⣿⣾⣼⣷⣧⣿⣷⣯⣧⣿⣾⣾⣾⣿⣮⣷⣧⣧⣿⣮⣿⣿⣾⣼⣿⣿⣿⣮⣿⣾⣾⣾⣼⣮⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⢩⢹⠉⢹⠨⣿⡇⠶⣹⠉⢹⡹⣹⠰⢎⡏⠍⡏⠫⡯⣿⡧⠖⡏⠭⡻⠋⣟⠭⡏⡉⡇⡏⡇⣭⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣽⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣛⣭⣭⣭⣭⣤⣤⣤⣭⣭⣭⣭⣙⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣻⣿⣟⣿⣟⣻⣹⣻⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣝⣛⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢛⣛⣋⣭⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣴⣤⣾⣤⣤⣭⣼⣭⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⣋⣻⣡⣍⣉⣹⣉⣉⣩⣏⣋⣩⣹⣙⣉⡉⣉⣯⣍⣉⣍⣹⣍⣩⣉⣹⣏⣋⣉⣹⣉⣉⣉⣯⣉⣝⣉⣿⢉⣭⣹⣁⣉⣉⣉⣏⣼⣉⣏⣍⣿⣉⣙⣏⣇⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⢛⣻⣿⣫⣛⣯⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠛⠛⠻⣻⡻⠛⠛⠟⠛⡛⠛⢿⠻⢛⠿⠛⡟⠛⠛⡟⠟⠟⠛⡟⠟⠛⠛⠛⡟⠛⠻⡻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠽⠛⠿⠏⠽⠹⠽⠋⠿⠿⠟⠹⠿⠋⠿⠻⠫⠯⠯⠿⠿⡟⠝⠽⠟⠋⠝⠫⢏⡻⠋⠿⠩⠽⢿⠿⠩⠿⠟⠟⠟⠩⠽⠛⠟⠽⠽⠹⠝⢟⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣿⠟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣧⣿⣿⣮⣽⣵⣽⣿⣿⣯⣯⣽⣬⣧⣭⣼⣿⣽⣾⣽⣟⣿⣮⣽⣭⣴⣧⣾⣷⣭⣿⣼⣵⣯⣼⣷⣵⣿⣦⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢛⣿⢿⣿⣟⣿⣻⢿⣿⢿⣿⣿⢛⠿⣿⣟⣻⡿⣟⡿⢿⣿⡿⡿⢿⢿⢿⣻⣿⣿⣿⣿⣿⠿⣿⢿⣻⣿⣿⠿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣾⣷⣿⣾⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣷⣿⣾⣿⣿⣷⣶⣿⣶⣿⣾⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢏⢙⢽⣍⣽⣏⣋⣏⣩⣿⢜⣏⣉⣿⣽⠏⣹⢙⢹⡏⣹⡹⣉⣩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⢠⠲⢀⢲⢰⠔⡆⢢⠀⢰⣹⡀⡇⠀⡇⡖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣄⣀⣀⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⢈⣉⠀⠉⠈⠉⠈⡀⠁⠈⠀⠁⢀⠁⠁⠀⠁⠁⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣑⠆⢰⠚⡎⡆⡆⡆⡆⣆⣰⢸⢰⣑⢐⣥⠀⢠⣱⠀⢴⣹⢰⣵⠐⣴⢀⡀⠀⠀⠀⠀⢀⣾⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⠛⢻⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⣼⡭⠭⠭⣟⣛⣻⡿⠿⠿⡿⣿⣿⣶⣶⣶⣤⣤⣾⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣛⣯⣭⣷⣖⣚⣽⡿⠿⣿⣷⣾⣾⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠭⠭⣳⣚⣒⠾⢭⣯⣝⣛⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢖⣒⣶⠯⢭⣭⣻⣛⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⡀⡌⠈⠏⠊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⣷⣾⣿⣯⣽⣿⣻⣿⣿⣿⣿⣷⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⠃⠻⠁⠸⠂⠧⠘⠀⠍⠐⠅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣯⣭⣽⣛⣛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⣯⣽⣿⣟⣻⣿⢿⣷⣶⣾⣾⣭⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠛⡟⠿⡛⣟⠛⢟⠿⣛⡟⠿⠛⠟⡿⢟⡛⠟⡟⠻⠛⠻⠛⢟⠿⠻⠿⡻⢻⠻⠛⣿⡛⡻⠛⣟⠻⢟⠿⡛⠿⣻⠛⠻⢛⠛⠛⠛⢿⢻⣟⡟⡻⢻⠿⡻⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠿⡿⠿⠿⣿⠿⣿⡿⢿⠿⡿⢿⠿⠿⠿⢿⠿⠿⢿⠿⠿⠷⠿⠿⠿⠷⡞⠻⢿⢟⠿⠿⢿⣻⣿⠛⠿⠟⠿⣿⠟⠿⡿⣿⠟⠻⠿⠿⠿⠻⡿⠿⡿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣶⣿⣶⣶⣶⣶⣷⣿⣶⣶⣶⣶⣾⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣷⣷⣶⣷⣷⣾⣷⣾⣶⣶⣾⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣷⣾⣷⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣵⣴⣿⣤⣦⣦⣦⣶⣧⣤⣴⣿⣼⣵⣴⣦⣼⣦⣵⣷⣴⣴⣤⣷⣤⣿⣦⣽⣧⣧⣷⣴⣤⣶⣧⣦⣾⣦⣤⣼⣥⣤⣽⣴⣤⣧⣴⣴⣤⣿⣦⣤⣼⣧⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣴⣤⣤⣸⣦⣤⣽⣴⣤⣧⣥⣤⣧⣤⣠⣤⣶⣥⣤⣤⣥⣧⣼⣬⣤⣤⣧⣤⣤⣧⣴⣥⣧⣥⣤⣼⣦⣤⣦⣯⣤⣴⣄⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣟⢿⣽⡿⣽⣛⣯⣽⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⣩⣫⣹⣊⣙⣈⣉⣍⣝⣹⣹⣉⣉⣑⣿⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 340

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/24/Brittany_Day_Connects_Windows_Ransomware_to_Linux_Using_Microso.shtml
    Gemini version at https://techrights.org/n/2024/12/24/Brittany_Day_Connects_Windows_Ransomware_to_Linux_Using_Microso.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Brittany Day Connects Windows Ransomware to
"Linux" Using Microsoft LLMs (FUD Galore, Zero Effort, No
Accountability)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


FUD and misinformation made by Microsoft LLMs again?


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LockBit_4.0_Warning:_Enhancing_Linux_Defenses_Against
                             Evolving_Ransomware⦈_


Definitely LLM slop:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇In_this_article,_I'll_examine_this_threat_in_detail,_explain
 how_it_differs_from_previous_LockBit_variants,_and_offer_practical_advice_for
      securing_your_systems_against_evolving_Linux_ransomware_variants.⦈_


On the same day, framing a Microsoft proprietary GitHub issue as "Linux", using
the 'creative' thinking [sic] of LLMs.


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GitHub_Exploits:_Navigating_The_Latest_Linux_Security
                                 Challenges_⦈_


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇To_help_you_prepare_for_these_trends_and_future-proof_your
  systems,_I'll_discuss_Dr._Web's_recent_findings_and_their_implications_for
                  Linux_security_heading_into_the_new_year.⦈_


This lazy FUD agent needs to be called out. This has gone on for many months
already. █




⣿⢿⡿⡽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⡘⣿⣷⣷⣶⣴⣾⣽⣷⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⣿⢟⡻⢟⢿⠹⣻⢹⢹⢹⢛⣿⡏⣿⣿⢹⢻⣯⢻⢹⣿⡻⡟⣻⢛⢿⢹⢻⢻⢛⣻⢿⣿⢹⣽⢛⢿⣛⢿⡛⡟⡟⡿⡻⡏⡟⡻⢟⢛⣿⢹⣿⢹⢻⢻⢻⢻⡛⣻⣿⢹⡝⢟⢻⢙⢟⢿⢻⢻⢛⡿⡻⠟⣻⣿⣿
⣿⣥⣭⣮⣽⣮⣿⣴⣽⣬⣾⣼⣾⣿⣧⣽⣿⣮⣾⣿⣼⣷⣧⣧⣧⣿⣼⣼⣼⣼⣼⣩⣽⣽⣯⣬⣭⣬⣬⣭⣼⣵⣧⣧⣵⣽⣥⣥⣧⣯⣽⣿⣬⣽⣼⣼⣬⣮⣬⣽⣼⣿⣬⣷⣮⣿⣬⣮⣿⣼⣼⣵⣷⣽⣭⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⡿⡛⣿⣻⣿⡟⡻⠟⣛⢻⣿⢹⣝⢻⡿⡻⡏⡛⣟⢹⢿⢻⢟⢿⣿⠹⣹⢟⢿⢛⢿⢛⡿⡻⡟⡻⡻⡛⡿⣻⡟⣿⣟⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⣇⣭⣧⣯⣭⣥⣧⣯⣾⣼⣯⣬⣽⣾⣷⣵⣥⣷⣿⣼⣬⣬⣩⣹⣿⣼⣼⣼⣬⣼⣼⣵⣯⣵⣥⣥⣧⣷⣷⣿⣴⣭⣽⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠇⠱⠹⠛⣿⣿⣿⢟⢛⢛⣟⡿⡟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣿⣦⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⢛⢛⠛⡛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣭⠶⠀⡀⣬⣿⣤⣧⡤⣤⠤⣤⠤⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠶⠀⠀⠘⣿⢿⣸⣿⣿⣤⠤⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣌⣿⣿⣿⣀⣀⣘⣀⣛⣈⣀⣘⣛⣋⣀⣀⣈⣉⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿
⣿⣿⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⢠⡇⣿⠇⠓⢛⠙⠂⠃⢉⣃⡃⠃⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣴⣿⣦⣴⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⡾⠫⠍⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⣾⡏⠀⡀⣼⡿⡟⡟⣿⣿⡿⣿⡿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⡇⠀⠁⠃⠁⠀⠁⣿⣿⢷⡍⣿⠁⠋⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠻⣧⡀⠀⠀⢀⣀⣐⡻⠷⠟⢁⣿⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⠶⠶⠟⢛⣛⠻⣦⡀⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠶⢶⣿⠉⣷⠈⢿⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠙⢷⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⢷⣄⠀⠀⠀⣴⣿⠟⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⢷⣤⡾⠋⣁⣴⣿⠟⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠉⢠⣞⠉⠈⠁⣴⣿⠟⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⢷⣄⠀⣸⠁⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⠟⠁⠠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿
⣿⣿⠿⠿⠿⠿⡿⠿⠿⠿⢿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠠⠆⠀⡇⠀⢢⠀⢸⠀⢰⣲⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⣀⣀⣀⣇⣀⣀⣀⣸⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⢻⢿⣿⣿⢿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⡿⣿⢿⣿⣿⡿⣿⣿⡿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣻⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣽⣯⣿⣿⣯⣿⣿⣿⣿⣯⣯⣿⣿⣿⣽⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣽⣯⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡇⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠿⠿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣿⣿⣿⡇⢸⣿⣿⠟⢿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⠿⠿⢿
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣯⣤⣬⣿⠒⠒⡗⠒⠚⠒⠒⢷⣶⣿⣶⣾⣶⣶⣶⣾⣶⣶⣶⣾⣷⣶⣶⣾⣶⣶⣷⣶⣶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⡇⠈⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⡇⠀⣿⣿⣿⠿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣾⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⡿⠛⠋⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡿⠋⢀⣴⣾⣿⣷⣦⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡇⠀⣿⣿⡿⠻⢻⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣇⠀⢻⣿⣷⣷⣿⣿⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣦⡀⠉⠛⠛⠛⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣧⣤⣼⣬⣤⣇⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣧⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡟⠛⠛⠛⠟⠿⠻⠟⠟⠛⢿⠻⡿⠿⠿⠿⠟⠿⢻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣏⣉⣫⣛⣟⣛⣛⢛⣛⣛⣉⣙⣛⣙⣛⣉⣛⣛⣉⣛⣟⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡏⣉⣙⣉⣉⣙⣹⣉⣉⣉⣉⣉⣉⣹⣉⣉⣋⣉⣉⣉⣏⣹⣉⣉⣉⣉⣙⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣏⣉⣉⣉⣏⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣇⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⢟⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡟⠻⢿⠻⠿⠻⠛⠛⠿⡟⠿⠿⠿⠻⡟⡿⠿⠿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣷⣷⣷⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡟⡛⠻⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡟⠛⠛⠛⠻⠟⠛⠛⡟⡟⠛⢻⠛⡛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⡿⠋⢁⣀⣤⣀⡈⠙⢿⣿⣿⣿⡟⢛⠛⡟⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡟⠀⣴⣿⣿⣿⣿⣿⣆⠀⢻⣿⣿⣷⣾⣶⣷⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣇⣠⣀⣇⣁⣈⣉⣉⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣷⡀⠙⢿⣿⣿⣿⡿⠃⢀⣾⣿⣿⡟⢟⠟⠟⢿⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣦⣀⡀⠉⢀⣀⣴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣧⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⢟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣙⡛⡛⣯⣿⣿⠿⠛⠛⢿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⢻⡟⣿⢻⢻⣟⣿⣟⢿⡟⣿⡿⢿⡏⡿⣿⣿⣿⡿⣿⢿⢿⠿⣿⣿⢻⢿⣿⣿⢟⣿⣻⠿⡿⣿⢻⣿⢻⡿⡿⣿⢹⢿⣿⡟⣿⣻⢿⢿⡿⡿⣿⢹⡿⢿⡏⡿⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⣷⣿⣸⣈⣇⣿⣾⣰⣿⣿⣿⣌⣇⣿⣸⣸⣇⣧⣳⣸⣗⣅⣿⣸⣧⣻⣾⣿⣱⣝⣿⣿⣜⣿⣹⣀⣇⣿⣰⣿⣸⣇⣇⣿⣸⣣⣿⣇⣷⣻⣦⣻⡇⣗⣼⣸⣸⣧⣇⣿⣸⣮⣹⣺⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⡹⣿⡫⢹⡍⣯⡟⢹⢫⢫⣟⡝⡏⣽⢺⡏⣯⢻⢫⣫⣿⣾⢸⣿⢸⡝⡟⣝⣿⣿⢸⣿⡫⢹⡅⡝⣯⣻⠫⢯⢨⣿⡇⣿⣿⢸⡟⡝⣿⢹⢹⣍⢯⣿⣧⡛⠿⢫⣻⢫⣻⢻⡏⣿⢩⡗⣯⢨⡍⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣾⣾⣿⣾⣷⣾⣼⣽⣷⣷⣷⣿⣾⣷⣿⣾⣾⣹⣿⣿⣾⣿⣾⣷⣷⣿⣿⣿⣾⣿⣾⣾⣷⣿⣾⣿⣿⣾⣾⣿⣷⣿⣿⣾⣷⣷⣿⣾⣾⣿⣶⣿⣿⣿⣿⣾⣿⣾⣿⣶⣷⣿⣾⣷⣿⣾⣻⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣻⢻⣿⣿⣿⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⠸⡇⣗⣅⣿⢸⠇⣇⢷⡿⢸⢸⡸⠼⣇⢷⡧⢍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⣨⡅⢁⣂⣿⣿⣿⣣⣼⣷⣼⣼⣾⣱⣇⣿⣼⣵⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⠀⢀⢅⡀⡸⣿⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⣀⣰⡈⠉⠈⠁⠁⣿⣟⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⣿⣿⡤⠤⠥⠠⢽⣿⡿⠟⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣽⣃⣀⣠⣯⣭⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⣰⢷⣦⢰⣠⣤⣄⡠⢂⣤⣄⣀⡠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠉⠘⠃⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⢆⠀⠄⢰⠔⠴⠆⠶⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠐⡄⡤⢠⠀⠠⠄⣤⠀⠤⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡄⣠⡀⠀⠠⠀⡄⢠⣤⡀⢤⢤⣤⡀⢤⢐⢠⢀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⢀⢀⠀⠀⢀⣠⣴⣶⣦⣤⣀⡀⡄⡀⢀⡀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⡬⠠⡀⠀⣀⣠⣿⢟⡁⢁⠈⠙⣿⣇⢁⢀⡀⠀⡀⡁⠈⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⡀⡀⡀⣀⠈⣈⣿⣏⣀⣀⣀⣀⣉⣸⣿⣈⠉⠁⡀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡀⠈⠀⣁⠁⠀⣹⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠊⠀⠑⠘⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⢉⠀⠁⠀⠀⠂⢸⣿⣿⣿⡅⠀⢀⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠀⠀⠐⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⡀⡀⠄⢄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠂⠛⠈⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠐⠀⡀⠄⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⠀⠗⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠰⠆⣂⢰⠀⡀⢠⠀⠤⠀⠤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⡀⡀⡄⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⣿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⢸⠃⠀⣿⡇⠀⣷⡁⠀⣿⠀⢸⣻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣿⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿⣟⣿⣿⣿⢿⣻⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣟⣿⣿⣻⣟⣟⣯⣿⣹⣿⣿⣟⣿⣻⣻⣹⣿⣭⣿⣿⣻⣿⣿⣿⣿⣻⣛⣿⣹⣟⣿⣻⣻⣿⣿⣿⣿⣏⣿⣟⣫⣿⣿⣻⣿⣿⣿⣻⣻⣻⣿⣟⣿⣻⣿⣟⣿⣹⣿⣿⣿⣽⣻⣻⣿⣿⣿⣿
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⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⣉⡉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣷⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣟⣜⣿⣿⡷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣍⡟⠉⠉⠩⠉⠉⣏⣙⣉⣹⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣬⣬⣼⣤⣯⣤⣬⣬⣤⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣋⣏⣍⣹⣋⣋⣙⣍⣋⣏⣙⣹⣉⣻⣙⣏⣹⣙⣉⣍⣙⣏⣋⣝⣛⣟⣻⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣝⣭⣯⣽⣽⣭⣿⣭⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 591

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

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    Gemini version at https://techrights.org/n/2024/12/24/IRC_Proceedings_Monday_December_23_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Monday, December 23,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now




⠀⠈⠀⠀⠀⠀⠀⣐⢚⣛⣛⣉⠉⢉⣉⠁⠀⠀⡀⡉⢹⣉⣉⣉⣫⣶⣜⢛⣿⠏⣐⣶⠶⠉⠀⠀⡈⠈⠉⣨⠯⠁⣐⠲⠶⠶⣂⡀⠀⢈⠉⢉⣁⣀⣉⠉⠉⠉⠐⠂⠤⠭⠥⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣐⣂⣽⣤⣰⡄⢀⠀⠒⠚⠛⠚⠒⠞⠋⠛⠉⠩⠤⠤⣬⡭⠍⢿⠀⣼⣋⣭⣰⡀⠀⠀⡴⠛⡙⠃⠀⣤⣿⡯⠷⠶⠛⠋⢛⣊⣭⣽⡏⠙⠛⠳⠖⢀⣈⣁⣀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀
⠀⠁⠤⠀⠠⠬⠭⠭⠭⠁⠴⡇⠀⣀⣀⣀⡀⢐⣀⢀⣀⠀⠄⠨⢒⣒⢹⡏⡘⠛⠋⣉⣉⣤⡾⢛⠻⢦⣤⣄⡀⠙⣿⣶⢶⣦⡠⠰⢿⠾⡷⠚⠓⠓⠊⢀⣀⢀⠀⠒⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣤
⣰⠀⠤⠄⡴⠤⠄⠿⡖⢶⣾⣿⣿⣟⣻⣿⣼⣶⣾⣷⠟⢶⣶⣿⣯⠖⠜⠐⠒⣠⡾⢋⣭⣥⣶⣿⣿⣦⣬⣭⠻⣦⣈⠙⠂⠿⣶⣦⣖⡷⠛⠛⣿⣿⣷⣿⣋⣋⠀⢀⡀⠤⠤⠀⠄⡀⠀⡀⠀⠀⠀⣰⣷⠏⠉⣡⡶⠀
⠁⠀⠈⢉⠛⠛⠀⠒⡒⠒⠛⣛⣻⣿⡛⣛⣻⣿⡷⢃⣤⣤⣤⣤⣤⣤⡤⠶⠛⢉⠠⣾⣿⣿⣿⣿⣿⣿⣿⠿⣷⣄⡙⠛⠶⠶⢶⣶⡶⠶⠶⣄⠘⠿⣿⣿⣿⣷⣤⣴⡬⠤⠶⠲⠂⠀⠀⠀⠀⠀⢿⣿⡆⠠⠚⠛⠁⠀
⢀⢀⠉⠁⢁⣐⡒⣤⣬⣬⣴⣿⣿⣿⡶⣻⠟⢉⣴⠟⣡⣶⣶⣤⣤⣴⣶⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣶⣶⣶⣶⡉⠻⣦⣀⠲⣿⣿⣷⣭⣁⠈⠉⠊⠀⣄⡀⠀⠀⢀⠄⠈⠁⠀⠀⠀⠀⠀
⠗⠖⣟⣒⣒⡂⠞⠞⠛⠛⠻⠟⢛⠿⡿⢁⣶⢛⣵⣾⣿⣿⣿⣿⣿⣏⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣼⣿⣿⣿⣿⣿⣿⣶⣬⠻⣧⠈⢿⣵⣿⣷⡆⣷⣶⣦⠬⠄⠀⢀⠀⠀⠈⠀⠀⣀⣀⣀⣀
⠶⠛⡓⠲⣦⣶⣟⠓⠂⠀⠀⠀⠀⡟⢠⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣧⠀⣶⣷⣒⣳⣿⡿⠦⠀⠀⠀⠀⠀⣀⣀⣀⡀⡭⣯⣔⠛
⠿⠿⠿⢶⣿⣿⣯⣝⣻⣧⣠⣤⣾⠃⣼⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣾⣿⣿⣧⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣯⡆⣿⠀⢹⣿⣿⣿⡿⠿⠿⢿⠸⣶⣴⣶⣤⣍⠃⠀⢴⡤⠤⠄
⢿⣶⣶⣶⣶⣶⣮⣭⣭⡟⠳⣶⣿⠀⣿⡄⣿⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣧⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣽⣴⣭⠛⠻⠿⠑⠦⠤⠄⠈
⠃⠻⠿⢿⣿⣿⣿⣿⣿⣿⣶⣮⣽⡆⠸⣷⢻⣿⣿⣿⢟⣿⣟⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣭⡯⠭⣿⠿⣿⣿⣟⣻⠿⣿⣿⣿⡷⠐⠀⢙⠻⣷⣶
⣭⣐⣒⣲⣶⣦⣦⣴⣽⣿⣿⣿⣾⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣥⣭⣽⣾⣽⣽⣿⣿⣿⣿⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⣰⣟⠷⢉⣵⣫⣉⡭⡉⠛⢶⣊⠻⣿⣿⣦⣀⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣰⣿⣧⡀⣽⣿⣿⣿⡷⠃⠀⠀⡟⠀⣼⣿⣦⠤⠀⠀⣠⡂
⣉⣉⣩⣭⣭⣭⣭⣭⣯⣏⣟⣷⣾⣿⣿⣿⣦⣀⠀⠙⣿⣿⣯⣻⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣾⣿⣿⣿⣿⡶⠶⠶⠂⠀⠀⠀⠘⠁⣰⣻⡟⠿⣟⣰⣾⣿⣿
⠛⣛⣛⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⢠⡿⡉⠷⡅⠈⠀⠘⣿⣿⣿⡿⠛⢋⠁⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡀⢶⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣋⣴⣾⣷⣖⣏⣽⣿⣷⣦⣐⠾⡝⣿⣿
⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⠂⠘⠋⠀⠀⠈⠀⠘⡆⢿⢻⣿⡇⠀⠀⢴⣤⡆⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⠻⠗⣘⢻⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠀⢿⣦⠀⠀⠀⠀⠀⠘⢔⠛⡯⠀⠀⠀⣿⣿⣿⣿⣛⣰⡄⠁⠈⠙⠙⠋⢝⢍⣿⣿⡿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣽⣿⣶⣿⡿⠱⡶⠦⠑
⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠛⠀⠀⠀⠀⠄⠀⡀⡀⠐⠤⣑⠹⣇⠀⠀⠑⠙⠛⠟⠋⠁⠀⢀⣶⣆⣠⣤⣤⣽⣯⡿⠖⠶⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣶⣶⣶⣿⢿⣿⣿⣿⣿⣶⣿⣷⡶
⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⠐⠦⠀⠀⣰⡆⠒⡛⠠⠄⠒⠉⠀⠐⠛⠒⠶⠤⠤⢀⣀⠤⢴⠞⠛⠋⠛⠛⠟⠃⠀⠀⠠⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠽⠫⠶⠶⣉
⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢙⠁⠀⠀⠁⠀⢀⣀⠊⠀⣀⣀⡀⠀⠀⠀⠶⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣯⣥⣞⠿⣻⢿⣿
⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⢀⢔⠟⠁⠀⢰⣿⣿⣿⣷⣦⡀⠻⠛⢀⣤⣦⣄⠀⠀⠀⠀⣀⠐⠀⠀⠀⠰⠿⠽⣿⣿⣿⣟⢻⡿⠿⠿⠿⠿⠿⠿⠏⠩⠿⠿⠯⢿⣿⣿⣿⣲⣶⣥⡶⠛
⣿⡭⠠⣻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠎⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢂⣠⣿⣿⣿⣿⡄⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⢤⡬⠉⠍⣛⣚
⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣴⣤⣀⣤⣸⣿⣿⣿⣿⣿⡿⠃⢀⣀⠁⠀⠙⣿⣧⠀⣀⠀⠀⠃⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣾⣭⣹⣿⣿⣿⣟⡃⠀⠈⠉⠉
⣿⣿⣿⣛⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣯⣭⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠟⠀⠀⠀⠀⣿⣿⣿⣿⣧⡂⠈⠀⠐⣦⣄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⡧⠤⠠⠂⠀
⣙⣛⣙⠋⠘⢻⣟⣍⣹⣟⣻⣿⣿⣿⣿⣿⡟⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢰⣧⣤⣴⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣯⣭⣿⣿⣿⣿⣿⣿⣽⣆⡄
⣿⣻⣯⣾⡆⢶⣿⣿⣭⣯⣭⣭⣽⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⣿⣿⣿⣿⠿⠯⠉⠉⠉⠩⠝⠛⠨⠛⢛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 817

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

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    Gemini version at https://techrights.org/n/2024/12/24/Meme_Coin_Operated_Publishers_Gaming_the_Message_Buying_the_Nar.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Coin-Operated Publishers (Gaming the
Message, Buying the Narrative)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


              🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Advertise_(sponsor)_to_'play'⦈_


Context. There's no lack of examples.




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⢛⠉⠻⣿⠿⠆⠸⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢰⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣽⣭⣴⣿⣾⣿⣿⡇
⠟⢛⡛⣫⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡧⠤⠤⠤⠀⠉⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢛⣿⣽⣿⣿⣿⠿⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣯⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣮⣭⡍⣴⢈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢍⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠈⣫⣭⣦⣬⡁⠉⣤⣀⣉⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣋⣀⣈⣡⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⢟⣛⣛⣛⣛⣛⡿⢿⣿⣿⣟⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣴⣿⢟⣛⡻⢿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠁⠀⠘⢟⣿⣿⣿⣷⣿⣷⣶⣮⣭⢻⣷⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠊⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡗⠟⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠰⣿⣿⣛⣿⠇⢰⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠳⠾⠿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠜⠀⡔⢠⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⠈⠠⠊⡴⡇⠀⣠⠤⠒⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣏⣽⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡼⠃⢊⠄⢊⡼⠓⠉⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⠀⠀⠀⣧⣿⣏⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠊⢀⠔⣡⠖⠁⠀⢀⠤⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣿⠀⠀⡠⠊⠀⠁⢀⠔⠁⣠⡒⠉⠁⢀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠫⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠠⠊⠀⠀⠀⢐⣡⣶⣿⣿⣿⣶⣄⠻⣿⣿⣿⣷⣀⣀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠺⠲⠶⢤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡀⠀⢀⣔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⢿⣿⡇⠀⠁⠁⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣶⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿⣿⣿⣿⣇⣿⣿⣽⣿⠋⠇⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣋⣵⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠄⠠⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢸⡇⣿⣿⣿⣿⣿⣿⣯⣿⡛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⠈⠛⠿⠿⣿⣿⣿⣿⣧⠛⣼⣿⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠄⠑⠒⠆⠀⢍⣉⠉⡀⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡇⠀⢠⠀⠀⠀⠀⠀⠀⢰⣿⠀⠲⠠⢌⠉⠛⠻⠿⢿⠿⠟⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⢶⣾⣿⣿⣤⡄⢸⣿⠀⠀⠀⠀⠀⠀⠐⠒⠐⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠈⠉⠛⠻⠝⠄⠛⢠⣶⣶⣾⣄⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣾⣷⣿⡄⠀⠀⠀⣽⠀⣠⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠈⠐⠀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⢠⣿⣧⢙⢿⣿⣿⣿⣿⣿⣿⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣼⣿⣿⢀⠄⡀⣙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠿⠋⣿⣿⠀⠀⠠⣙⠚⡠⢀⠄⠍⡉⠛⠿⠿⢿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠦⠀⡀⠀⡀⡘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠀⢀⣿⣿⠀⡀⡀⠠⡀⠀⠄⠀⠀⠀⠑⠀⢤⣄⣉⣉⡙⠛⣯⣿⣯⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠁⠉⠉⠠⠐⠦⠠⠄⡀⠀⠀⠀⠀⠭⡀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠈⠻⠁⠀⠀⠓⠇⠠⡀⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠲⢢⣧⡧⣏⢽⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢜⠛⣉⠃⢢⣰⣴⣤⣄⣀⡀⠀⠐⠰⡦⡀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢄⠀⡀⣀⡀⠀⠀⠀⠀⠈⠀⠈⠠⠁⠂⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠈⠁⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⣁⣨⢟⣟⣿⣿⣿⣲⣦⣄⡈⠀⠀⠀⠄⢀⢀⡄⠀⠀⠀⠀⢸⡆⡀⠀⡀⡀⣀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⣭⣿⠝⠉⠛⠛⠛⠛⠷⠦⠀⠀⠈⠺⠛⠂⠐⠀⠀⠸⠇⠀⠀⠛⠚⠚⠀⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠻⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢰⣦⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⡈⠈⠀⠀⠈⠉⠻⠽⣿⣿⣷⣴⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠐⠚⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠊⡄⠀⠀⣠⠀⠀⡈⠙⠿⣿⣿⣿⣷⣶⣤⡄⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠈⠐⣄⠐⠀⠀⠤⢤⡄⠈⠙⢿⣿⣿⣿⣿⣷⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⠒⢲⢲⣤⣀⡀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠉⠃⠓⣛⡛⠟⢒⡤⣄⡈⠉⠻⢿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠓⠀⠽⣷⣦⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠁⠻⣿⠿⠆⠸⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢰⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣭⣶⣿⣿⣿⣿⡇
⠟⢛⡛⣋⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠤⠀⠉⠀⠉⡉⠉⠉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢛⣿⣽⣷⣿⣿⠿⠟⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣮⣭⡍⣴⢈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢡⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠈⣫⣭⣦⣬⡁⠉⣤⣀⣉⣉⠙⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣾⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⣀⣈⣡⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣟⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⣟⣛⣛⣛⣛⣛⡿⢿⣿⣿⣟⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣶⣿⠟⣛⡻⢿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠁⠀⠘⢟⣿⣿⣿⣷⣿⣷⣶⣮⣭⢻⣷⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡋⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡗⠟⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠰⣿⣿⣛⣿⠇⢰⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠻⠾⠿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠜⠀⡔⢠⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠊⠠⠊⡴⡇⠀⣠⠤⠒⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣏⣹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡼⠃⢊⠤⢊⡼⠓⠉⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⠀⠀⠀⣧⣿⡟⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠊⢀⠔⣡⠐⠁⠀⢀⠤⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢼⣿⠀⠀⡠⠊⠀⠁⢀⠔⠁⣠⡐⠉⠁⢀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠉⠶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠠⠊⠀⠀⢀⢐⣡⣶⣿⣿⣿⣶⣄⠻⣿⣿⣿⣷⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠶⣶⠤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣞⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⢿⣿⡇⠈⠀⠈⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣷⣶⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣇⣿⣿⣽⣿⠋⠃⠀⠂⠀⠀⠀⠀⠉⠙⠓⠲⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣋⣵⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⠄⠀⠀⠀⠀⠠⠠⠀⠀⠉⠙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠉⠛⠿⠿⣿⣿⣿⣿⣧⠛⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⠒⠦⠀⢍⢉⠉⡀⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣮⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡇⠀⢠⠀⠀⠀⠀⠀⠀⢰⣿⠀⠒⠠⢌⠉⠛⠻⠿⢿⠿⠟⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⣷⠀⠀⢶⣾⣿⣷⣤⡄⢸⣿⠂⠀⠀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠈⠉⠛⠻⠝⠀⠛⢠⣶⣶⣾⣀⢀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣾⣷⣿⡀⠀⠀⠀⣹⠀⡐⣶⣲⣲⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠇⠀⠀⢠⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣧⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣼⣿⣿⠠⡄⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠿⠋⣿⣿⠀⠀⠈⠈⠛⢂⡄⠀⡍⡉⠛⠿⠿⢿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠄⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠀⡄⢀⠀⡕⠅⠄⠀⠀⠀⠀⠂⠢⢄⣉⣉⠛⠻⣿⣿⣿⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠈⠀⠈⠁⠀⢡⠥⠔⠀⠀⠀⠀⠀⠀⡀⠂⡀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠂⠀⠀⠈⠻⠁⠀⠐⠐⠘⢀⠃⠁⠄⡂⠐⠀⠀⠀⠀⠀⠀⠉⠂⠒⣬⣬⠯⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠩⢅⢂⣿⡝⣿⢠⢠⣄⣄⣀⠀⠀⠀⠂⡀⠀⠀⠠⠄⠀⠀⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠠⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠨⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠵⡀⢸⢿⣟⣿⣻⣿⢳⣤⣄⡈⠁⠀⠀⠐⠢⢀⡀⠄⠀⠀⠀⢸⡇⡁⣤⣤⢀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⣽⣿⡍⠛⠙⠛⠛⠛⠷⠦⠀⠀⠀⠺⠫⠈⠐⠀⠀⠸⠇⠀⠋⠈⠋⠙⠐⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠙⠿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢰⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣾⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠂⠀⠀
⠀⠀⡀⢀⠀⠀⠹⠿⣿⣷⣵⣦⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠰⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠄⣤⠀⠀⣀⠀⠀⠈⠛⠿⣿⣿⣿⣷⣦⣤⡄⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣁⡹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⠀⠐⣀⡐⠀⠀⠤⠄⠀⠀⠙⢿⣿⣿⣿⣿⣯⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠒⠖⠶⢲⣤⣀⡀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣄⠈⠃⠓⡛⢟⠁⣀⣦⣀⡘⠉⠹⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢖⣾⣷⣤⣌⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠉⠻⣿⠿⠆⠸⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢰⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣭⣶⣷⣿⣿⣿⡇
⠟⢛⣛⣋⣭⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠤⠀⠉⠀⢉⠉⠉⠉⣡⣤⡘⠛⠛⠛⢀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢠⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢛⣯⣽⣿⣿⣿⠿⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣽⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣮⣭⡍⣴⠈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢁⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠈⣫⣭⣦⣬⡁⠉⣤⣀⣉⣉⠙⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣋⣀⣈⣁⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣦⣶⣶⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣍⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣻⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⢟⣛⣛⣛⣛⣛⡿⢿⣿⣿⣟⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣴⣿⢟⣛⡻⢿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠁⠀⠘⢟⣿⣿⣿⣷⣿⣿⣶⣮⣽⢻⣷⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠊⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡗⠟⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠰⣿⣿⣛⣿⠇⢰⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠻⠾⠿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠜⠀⡔⢠⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠊⠠⠊⡴⡇⠀⣠⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡼⠃⢈⠄⢊⡽⠓⠉⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⠀⠀⠀⣧⣿⣿⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠊⢀⠔⣡⠖⠁⠀⢀⠤⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣿⠀⠀⡠⠊⠀⠃⢀⠔⠁⣠⡐⠉⠁⢀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠲⠫⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⠠⠊⠀⠀⢀⢐⣡⣶⣿⣿⣿⣶⣄⠻⣿⣿⣿⣷⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠲⠶⠶⠤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⢿⣿⡇⠈⠈⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣷⣶⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣇⣿⣿⣽⣯⠋⠃⠀⠂⠀⠀⠀⠀⠈⠙⠓⠒⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣋⣵⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⡀⠥⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠈⠙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⣿⣿⣿⣿⣿⣿⣯⣿⡛⡛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⠉⠛⠿⠿⣿⣿⣿⣿⣧⠛⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⠒⠦⠀⢍⢉⠉⡀⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⠀⠀⠀⠀⠀⢰⣿⠀⠒⠤⠌⠉⠛⠻⠿⢿⠿⠟⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⢼⣿⣿⣷⣤⡄⢸⣿⠀⠀⠀⠑⠀⠀⠐⠒⠰⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠈⠉⠛⠿⠝⠀⠛⢠⣶⣶⣾⣄⣀⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣷⣿⡀⠀⠀⠀⣻⠀⡐⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⢠⣿⣧⠸⢻⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⢠⣦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣼⣿⣿⠀⡄⣀⢉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠿⠋⣿⣿⠀⠀⠨⠚⠹⠢⠠⢄⠌⡉⠛⠿⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⢆⡁⠀⠂⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠀⡢⢠⣦⠄⠈⡀⠀⠂⠈⠁⠀⢤⢄⣉⣉⠛⠻⣿⣿⢯⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠈⠻⠁⠀⠀⠁⠘⡛⠃⠃⠤⠀⠂⠀⠀⠀⠀⠀⠈⠁⠒⠰⣽⣽⣏⣟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠏⣂⡐⢯⢀⣤⣤⣄⣀⡀⠈⠐⠰⡄⣀⠀⠠⠀⠀⠀⠀⠁⠉⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠭⡑⡱⠟⣟⡟⡻⣿⢶⣦⣄⡀⠀⠄⠄⠀⠀⢀⠀⢠⠀⠀⠀⢸⡇⠀⠤⣤⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⣿⣽⡟⠛⠙⠛⠛⠛⠷⠦⠀⠀⠈⠰⠋⠀⠐⠀⠀⠸⠇⠀⠉⠛⠀⠁⠀⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠻⢶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠫⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢰⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠈⠉⠉⠿⢿⣷⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠐⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⣀⠀⢀⡀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣴⣄⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠈⠀⣆⡀⠀⠀⠀⠂⠀⠈⠙⠿⣿⣿⣿⣿⣿⣤⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣦⣤⣀⡀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠙⠃⠃⢛⡟⠂⠤⢦⣀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣧⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠈⠙⣲⡟⣷⣦⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣭⣬⣀⢙⣛⣁⣁⣛⡛⠛⠛⠿⠿⠿⠻⠿⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢡⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣶⣾⣿⣿⣿⡇
⠟⠛⠛⠋⡉⡉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⡧⠤⠄⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⢿⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣫⣽⣿⣿⡿⠿⠟⠃
⣤⡎⠀⠘⠋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⣩⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡑⠂⠀⠀⠀⠀⠘⠛⢶⣾⠣⠆⠀⣀⣠⣌⠉⣉⣄⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⢓⣾⡐⢟⢗⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣾⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣥⣀⣈⣉⠙⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣫⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣸⣿⣿⣿⡯⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⢰⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣭⡄⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢖⣽⣺⣿⣿⡿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⡧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢁⣀⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣦⣾⣿⣷⣶⣾⣿⣷⣶⣶⣬⣩⣭⣴⣶⣭⣭⠤⠛⠛⣤⣙⠻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣟⣿⣟⣩⣬⡹⣿⣿⣿⣿⣿⣵⠿⠿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⣋⠩⠼⠞⠛⠉⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⡏⠈⣿⣾⣿⣿⣿⣿⣳⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⡻⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣮⡉⣿⣿⣿⣿⣷⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣏⠔⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣶⣽⣿⣿⣿⣧⣝⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⡿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣁⣾⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠋⢱⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⣾⣿⣿⣿⠀⢠⣿⣿⣿⡇⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠠⠈⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣼⣇⠀⠀⡠⠂⠠⠊⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⣿⡇⠀⠘⠆⠋⣤⠊⣀⣀⣀⣀⠀⢀⣾⣿⣿⣆⡀⡀⠀⠀⢸⣿⣿⣿⣿⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠦⠢⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠀⠀⣿⣷⣤⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⣬⣛⢿⣿⣿⣿⡄⠀⣸⣿⣿⣿⡿⣁⣿⣿⠀⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠘⠃⠀⠀⠸⣿⣿⣿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣼⣷⠄⠀⠀⠀⠀⠀⠈⠙⠓⠒⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣩⣼⣿⢿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠈⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣶⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⢸⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠀⠘⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠉⠙⠛⠿⠿⣿⣿⣿⡜⢠⣿⣿⣿⣿⣿⣽⣿⡿⢿⣿⣿⡙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠂⠠⠬⠉⢡⡘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠂⠀⠈⠉⠙⠛⠛⠻⠛⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⢐⠬⡶⣄⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠐⠄⠀⠈⠀⣨⢴⣾⡄⠀⠀⠀⠀⠄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠁⠵⢨⣤⣤⣄⠀⠀⠀⢸⡇⢀⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⢀⣿⣿⠀⠛⣽⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡀⡀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣦⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠻⠋⣿⣿⠃⠀⠠⠐⢛⠂⠀⠀⠄⠉⠛⠻⠿⢿⣿⣿⣿⣷⣆⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠄⢉⡉⠙⠉⢟⣿⣎⣶⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠂⠃⠀⠘⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢉⠧⠉⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⡀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⠤⡭⢿⠉⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⠘⠐⠐⠙⠛⠛⠓⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⠇⠀⠀⠀⠐⠀⠂⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠹⣙⣖⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢰⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣦⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠛⢻⣶⣂⣠⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⡿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣥⣤⣀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣀⡹⣷⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⣤⣀⡀⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⢈⣻⣷⣤⣀⠀⠃⠑⠛⠊⠀⠀⣀⠀⠀⠉⠋⠻⣿⣿⣿⣿⣷⣦⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠿⢶⣦⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⠛⣋⣉⣛⣛⡛⠛⠛⠻⠿⠿⠻⠿⠿⡿⠿⠛⠫⠭⢙⣿⣻⣯⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣻⣿⣟⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣾⣾⣿⣿⡇
⠟⠛⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣡⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⢿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣽⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡙⠛⢋⣉⣀⡀⠀⠀⠀⠈⠛⠛⠀⠠⠀⠀⠀⠀⣀⣠⣌⠉⠉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠸⠛⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⠀⣿⣿⠀⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡃⠘⣠⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠤⠱⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⡽⠈⢠⣿⣿⣿⣿⠇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠲⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢰⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⡸⣷⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⢀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣦⣶⣿⣿⣷⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣝⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣺⡯⠿⠿⠿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣋⣭⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⡆⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠉⠉⠀⠔⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⡿⣛⣋⡵⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢟⣛⡻⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠿⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣥⣍⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢽⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣌⡛⣻⣿⣿⣿⣿⣿⣿⢺⣄⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣻⣿⣿⡿⣿⣿⣿⣿⣿⣎⡛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢻⣭⣭⡍⠉⠙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⣼⣿⣿⡇⠀⠀⣿⣿⣷⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠛⠿⠿⠇⠀⢸⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣾⡷⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣄⣀⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⢊⡱⣿⣿⣄⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣬⡛⢿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣛⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⠋⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⢿⣿⡯⣼⣿⣿⣿⣿⣿⣿⡇⣿⠁⠀⠀⠀⠀⠀⠈⠉⠒⠒⠢⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠻⠂⠀⡴⠇⠠⣲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣴⣿⣿⣿⣿⣿⣿⣿⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠠⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠀⠀⠀⠀⠣⢃⠜⠁⠀⣿⣿⣿⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠁⣞⡇⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠉⢰⡄⠉⠁⠀⣿⠀⠉⠛⠻⠿⢿⣿⣿⡆⠀⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣏⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠠⠉⢁⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠈⠉⠛⠛⠿⠿⠿⠿⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⢄⣰⣄⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠪⢿⣿⣿⣿⣿⣦⣂⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠂⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠻⠿⢿⣷⣿⣷⣢⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠛⠛⠛⣷⠀⢦⠢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣶⣆⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⡿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠙⡺⢶⣀⠀⢀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⡄⠡⢸⣿⣿⣿⣿⣿⣿⣿⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡘⠆⢠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠪⣽⣿⣶⣮⣾⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀
⠣⢉⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⣿⣿⣾⣥⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠤⡀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⢛⣉⣉⣙⣛⡛⢛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠍⢝⣟⣿⣽⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⢶⣾⣿⣽⡇
⠟⠛⠛⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⣁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⢿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣭⣵⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠅⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡙⠛⢋⣉⣀⡀⠀⠀⠀⠈⠛⠛⠀⠠⠀⠀⠀⠀⣀⣠⡌⠉⢉⣄⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣸⣿⣿⣿⠀⣿⣿⠀⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣄⣀⣈⣉⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣠⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⡔⡢⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢰⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢘⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⢕⣯⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⢀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣦⣶⣿⣿⣶⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡾⡣⠿⠿⢿⣿⣿⣋⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣭⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠔⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⠿⡿⣛⡉⠵⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣋⡻⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠯⠂⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣌⠛⣻⣿⣿⣿⣿⣿⣿⢺⣀⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣻⣿⣿⡿⣿⣿⣿⣿⣿⣎⡛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢛⣭⣭⡍⠉⠙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⣼⣿⣿⡇⠀⠀⣿⣿⣷⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠛⠿⠿⠇⠀⢸⣿⣿⡿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣾⡷⠂⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣄⣀⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⢊⡱⣿⣿⣄⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣬⣛⢿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣛⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⢿⣿⡿⣼⣿⣿⣿⣿⣷⣿⡇⣿⠃⠀⠀⠀⠀⠀⠀⠉⠒⠒⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠻⠂⠀⡴⠇⠠⣲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⣭⣴⣿⣿⣿⣿⣿⣿⣿⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠣⢃⠜⠁⠀⣿⣿⣷⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠃⣞⡇⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠉⢠⡄⠉⠀⠀⣿⠀⠉⠛⠻⠿⢿⣿⣿⡆⠀⣾⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣏⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠂⠀⠤⠉⢁⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠌⠉⠛⠛⠿⠿⢿⠿⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠄⡠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⢓⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠻⠿⠿⣧⣻⣶⡄⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠘⠿⣷⠀⠄⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣠⡀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣽⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠬⢀⠄⠄⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡄⠈⢹⣻⣿⣿⣿⣟⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠞⣿⣷⣮⣼⣿⣳⣳⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⢀⠀⠀⠀⠀⠀⠀
⢀⠑⣶⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣴⢤⣴⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠉⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣾⣷⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⢸⣷⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣤⣭⣭⣙⢛⣉⣉⣙⣛⡛⠛⠛⠿⠿⠿⠻⠿⠿⡿⠿⠛⠫⠍⢙⣛⣿⣽⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⡿⢿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣽⡇
⠟⠛⠛⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢠⣿⣿⣿⠧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠰⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢛⣫⣵⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠓⠀⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣈⡉⠀⢀⣀⣀⡈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡌⠉⣉⢀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣸⣿⣿⣿⠀⣿⣿⠀⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣀⣉⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⠀⠘⣀⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⠇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⠀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢠⣼⣄⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣰⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⢀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣾⣿⣷⣿⣿⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⠙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠈⠻⠿⠿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣭⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠁⠀⠐⠛⠁⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⡿⡿⣟⡋⠵⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠫⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣯⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢟⡻⣿⣿⣿⣿⣿⣿⣿⣫⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣫⢙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣻⣿⣿⣿⣿⣿⣯⢇⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣭⣯⣿⣿⣿⣿⣿⣮⣽⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣾⣛⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⠿⠿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣼⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⣠⣄⡀⢻⣿⣽⣿⣿⣿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣀⢀⣄⣠⣤⣦⣶⣶⣶⣦⣤⣉⡻⠿⢿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣋⡀⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠹⣿⣿⠿⣿⣿⣉⣩⣭⣽⣿⣿⣿⣿⣿⣿⣶⣤⣙⠛⠿⣣⣿⣿⣿⣿⣿⣿⣷⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡀⠀⠀⠀⣠⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠁⠀⢀⡼⠉⠀⠀⢹⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⢀⠀⢴⠄⠀⠀⢠⢶⣀⣴⠟⠀⣄⠀⠀⢸⠺⣿⣿⣿⣿⣿⣿⣿⡛⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠁⠀⠀⢸⠀⠄⠉⠙⠻⠿⣿⣿⣇⠀⣾⣿⣿⣿⣿⣿⣛⡿⣿⣿⣿⢏⡻⠿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠈⠁⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡷⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣿⣷⠐⠪⢿⣿⣿⣿⣾⣖⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣷⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣷⣏⡯⡄⠠⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢀⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠊⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣭⣛⣿⣿⣿⣿⣦⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⡀⠈⠸⠻⢿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣿⣷⣦⣮⣻⡿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣦⢠⢀⠀⠀⠀⠀⠀⠀
⠀⠘⠴⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣽⣽⣿⣛⣿⣷⣿⣽⣟⣿⣷⣥⢃⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣉⣉⣋⣛⡛⢟⠃⠹⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣿⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣥⣴⣶⣿⣿⣿⡇
⠟⠛⡛⢋⠍⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠄⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣯⣽⣿⣿⣿⠿⠟⠃
⣶⣷⣯⣽⢽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣍⣩⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡁⠲⠒⠀⠀⠀⠀⠀⠀⠚⠿⣷⣶⡆⡮⢈⣉⣉⣄⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣷⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣽⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠈⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠈⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⣀⣈⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣃⢈⣉⣩⣰⣆⣍⣩⡄⣛⠛⣀⡙⡻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣩⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣻⣿⡿⣿⣿⣿⣼⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡏⠀⢺⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⢟⣛⣛⣛⠻⠿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⢱⣾⢯⣶⣶⣏⣿⡿⣛⣒⠯⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠙⣾⣿⣿⡟⣿⣷⣿⣿⣿⡾⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡇⠛⢻⣿⣿⣿⡇⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠸⢿⣿⣿⠇⠀⣿⣟⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣰⠀⠀⠀⠠⠀⣴⡄⠙⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠀⠀⠂⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⡀⠔⠋⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠊⠀⠀⠠⠂⠈⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢃⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⡰⣿⣿⣷⡀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⢦⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣧⠀⣸⣿⣿⣿⠿⣿⣇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⡄⣿⣿⣿⣿⣿⡜⠂⠀⠀⠀⡀⠀⠀⠉⠙⠳⠶⢦⡄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⠟⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⢈⠈⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢦⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠙⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⣿⣿⣿⣿⣿⣟⢉⠿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠷⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠛⠛⠿⠿⣿⣿⣿⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠀⠓⠂⡠⢤⡍⢀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠴⠲⠀⢈⠉⠉⠛⠋⠛⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠹⠦⢪⣺⣦⣀⠸⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⣟⣿⠀⠀⠀⠈⠉⠉⠊⠀⠉⠀⣿⣾⢿⣃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣯⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠫⠙⠬⣱⢻⢶⠃⠀⠀⠀⢸⡆⣤⣛⣴⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⢠⣿⣿⠘⢹⢿⣿⣿⣿⣿⣷⣦⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡄⠀⡀⡉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⠋⣿⣿⠇⠁⡀⠴⠛⢂⠂⠀⠨⡉⠛⠻⠿⢿⣿⣿⣿⣳⢦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⣿⣿⠀⠄⠐⠢⠠⠳⠄⠄⠀⠀⠁⠀⠀⠄⡉⠉⠛⠹⠯⣿⣯⣷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠈⡛⡝⠓⠐⠄⡀⢀⠀⢀⠀⠀⠀⠉⠓⢢⢄⣝⡭⢔⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡠⠀⢀⡄⣄⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠤⠈⢌⠈⠀⠀⠁⢂⠀⠀⠀⠀⠀⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠂⢀⢱⠬⣝⢻⣿⢲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⡇⠂⢀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⣌⠁⠓⠘⠙⠛⠛⠓⠆⠀⠀⠀⠀⠁⠀⠀⠂⠀⠸⠇⠀⠀⠘⠀⠂⠀⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⢦⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠑⠫⣢⣖⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⢤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠈⠛⢿⣿⣖⣠⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠂⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣯⣿⣿⣿⣿⣿⣷⣦⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣅⠹⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠙⠻⣿⣿⣿⣷⣶⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢦⣤⣄⠀⠒⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀
⣬⣿⣿⣤⣀⠘⠃⠙⠛⠋⠀⠀⣄⢀⠈⠉⠙⠿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⡙⣶⣦⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣭⣭⣙⢛⣉⣉⣋⣛⡛⢟⠃⠹⠿⠿⠿⠿⢿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣥⣴⣶⣿⣿⣿⡇
⠟⠛⡛⠋⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡧⠤⠄⠄⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⢀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣯⣿⣾⣿⣿⠿⠟⠃
⣴⡾⡟⣚⡯⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⡡⣼⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡑⠲⠒⠀⠀⠀⠀⠀⠀⠚⠿⣷⣶⡆⡖⢈⣉⣉⣤⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣧⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢁⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠘⣡⣤⣤⣤⡈⠉⣥⣀⣈⣉⠙⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢷⣾⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠈⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢉⣀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣴⣾⣿⣶⣶⣿⣿⣿⣃⢨⣉⣩⣰⣆⣍⣩⡄⣛⠛⣀⡙⡻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣹⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⡇⢀⣺⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⣟⣛⣛⣛⠻⠿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠂⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⢱⣾⢯⣶⣶⣏⣿⣿⣛⣒⠯⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠙⣾⣿⣿⡿⣿⣿⣿⣿⣿⡾⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⢰⣿⣿⣿⡇⠛⢻⣿⣿⣿⡇⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠸⢿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣰⠀⡀⠀⠠⠀⣴⡄⠙⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠊⠉⠀⠀⠂⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⡀⠔⠉⠴⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠊⠀⠀⠠⠂⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢃⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣡⣴⣶⣶⣶⣦⣄⡰⢿⣿⣷⡀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠢⡤⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣦⠀⣸⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⡄⣿⣿⣿⣿⣿⡜⠂⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⠟⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⣟⠉⠿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡷⢂⡀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠛⠛⠿⠿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡹⠿⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠉⠁⠑⠂⡄⢤⡍⢀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡁⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⠶⠢⠀⠈⠉⠉⠛⠋⠛⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠹⠾⣰⣾⣦⣀⠸⣿⡇⠀⠀⢀⡄⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣿⠀⠀⠀⠈⠁⠙⠉⠁⠉⠀⢿⢾⣾⡇⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣯⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠻⠤⢥⣞⣷⡇⠀⠀⠀⢸⡆⣤⢿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⢠⣿⣿⠘⢿⢿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡀⣀⡀⡈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣦⡤⣄⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⠋⣿⣿⠇⠀⢀⠌⡋⠀⠢⠠⠠⠉⠛⠻⠿⢿⣿⣿⣿⣻⣂⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⢀⣿⣿⠀⠀⡄⠂⠢⠖⠈⠀⠀⠀⠁⠀⠀⠄⠉⡉⠛⠉⢿⣿⣿⣶⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠙⠁⠀⠀⠘⠀⠘⢄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢴⡞⢤⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡠⡀⠠⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠨⠀⠀⠀⠀⠉⠀⠄⢀⠀⠀⠀⠀⠈⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢈⡺⠉⣟⣛⡉⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠽⣢⠂⠂⠀⠙⠛⠛⠳⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⠇⠀⠐⠈⠀⠀⠐⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠣⣾⣳⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢰⢄⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣴⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠈⠙⢿⣧⣶⣠⣄⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠐⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⡿⢾⣿⣿⣿⣿⣿⣧⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣤⣤⣄⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡄⡑⡺⢿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠉⠻⣿⣿⣿⣿⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⣤⣄⡀⠒⠾⣿⣿⣷⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣲⣀⡀⠀⠀⠀⠀⠀
⡬⣿⣿⣦⣀⠉⠂⠂⠉⠉⠀⠀⡄⣀⠀⠉⠙⠻⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡻⡿⣶⣦⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠁⠻⣿⠿⠇⠸⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣴⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣿⣿⣿⢡⣿⣿⠋⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢁⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣭⣷⣿⣿⣿⣿⡇
⠟⢛⡛⣫⣭⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠄⠀⠉⠁⠉⡉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢠⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣿⣽⣾⣿⣿⠿⠿⠃
⣷⣽⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢛⣉⣉⡛⠲⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣾⣭⡍⣴⠈⠛⠛⠋⣁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢁⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠈⣫⣭⣦⣬⡉⠉⣥⣈⣉⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡟⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢋⣀⣈⣡⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⣟⣛⣛⣛⣛⣻⡿⢿⣿⣿⣝⣻⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣵⣿⢟⣛⣻⢿⣿⣿⣿⣿⣶⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣷⣿⣧⣶⣾⣝⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⡇⠿⣿⣿⣿⣿⣿⣿⠿⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠿⠶⠿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢀⠜⠀⡔⢀⠆⠀⠀⠸⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⠎⡠⢊⡴⡇⠀⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡼⠣⢂⠱⢋⠼⠓⠉⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠊⡀⠔⣡⠖⠁⠀⢀⠤⠂⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣿⠀⠀⡠⠊⠀⠀⢀⠐⠁⣠⡂⠉⠁⢀⣤⣤⣄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠉⠹⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠀⠊⠀⠀⢀⢊⣥⣶⣿⣿⣿⣶⣄⠻⣿⣿⣿⣇⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠳⢷⠦⡀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢀⣔⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣴⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣇⣿⣿⣽⣯⢻⠁⠀⠀⠠⡀⠀⠀⠉⠙⠓⠶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠂⣈⡒⡄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣛⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠥⠠⠀⠤⠄⠀⠀⠀⠀⠠⠤⠄⢁⠉⠙⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡐⢀⠀⠀⠀⠀⠀⠱⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠿⠿⣿⣿⣿⣿⣧⠁⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢒⡂⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⠈⠁⠒⠦⠄⣍⣉⠋⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠅⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡇⠀⠀⡀⠀⠀⠈⠀⠈⢠⣿⠀⠲⠤⣍⣉⡛⠻⠿⢿⠿⠟⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⢿⣿⣶⣿⣦⡄⢸⣿⠀⠀⠀⠉⠋⠉⠓⠂⠦⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠉⠛⠿⢿⡌⠛⢠⣶⣶⣾⣄⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢤⠄⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠿⣟⣻⣿⡿⣿⣞⡅⠀⠀⠀⣼⠀⣠⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠉⠉⠛⠛⠃⠀⠀⢠⣿⣧⠸⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⢰⣶⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢠⠢⣠⣉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⢀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠿⠋⣿⣿⣌⣈⣾⢿⠿⠶⡢⡄⠭⡉⠛⠻⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠲⠆⡀⢀⡂⠁⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠀⢀⣿⣿⠀⢃⠟⢽⢫⠉⣅⠙⠀⠁⠉⠂⠢⣄⣉⣉⠛⠻⢿⣿⣿⣷⣦⠀
⠁⠀⠀⠀⠀⠁⠐⠀⢀⡀⢀⢀⠀⠀⠀⠉⠀⠊⢁⠐⠸⠀⠀⠀⠀⠀⠀⠀⠶⢀⡀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⢀⠀⠀⠀⠘⠟⠈⡀⠀⠀⠘⠻⠁⠀⠛⠻⣚⡁⡻⠰⡂⡤⡠⡀⠀⢀⠀⠀⠀⠀⠒⡂⣵⡽⣊⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣘⢾⢖⣶⠯⣀⣤⣤⣄⣀⠀⠀⠐⢴⣄⠠⠁⢀⢀⠀⠀⠀⠠⠀⠄⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠿⠈⡁⢀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠐⠄⠗⢈⡳⠒⠤⠛⠈⠲⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢛⠛⣯⣿⣛⣿⣻⣿⣳⣦⣄⡀⠀⠄⠰⠲⢒⡡⢂⠤⠀⠀⠀⢸⡇⠂⢢⣄⠀⡀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠄⠀⠓⠃⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢⠈⠈⢤⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠛⣯⣿⠍⠙⠛⠙⠛⠛⠻⠦⠀⠀⠈⠱⠂⠘⠀⠂⠀⠸⠇⠀⠀⠛⠉⠋⠐⠦⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠐⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀
⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠄⠰⠄⢈⠀⠀
⡀⠈⠙⠻⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢰⣤⠄⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣦⣿⣦⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠠⠀⠀⠀
⡐⠈⠂⢀⠈⠉⠩⠿⢿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠋⡀⢸⣿⣿⠀⠠⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠀⣁⠀⠀⠀
⠁⠂⠁⠀⢀⣀⠀⠅⠈⠛⠻⣿⣿⣿⣶⣶⣢⡄⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⣀⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀
⣤⣄⠉⠐⣐⠃⠐⠀⣂⡀⡀⠀⠛⢿⣿⣿⣿⣿⣿⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠠⠀⠒⠒⣒⣒⢶⣤⣄⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣷⣦⣄⠉⠓⠛⠝⡛⠵⣺⣦⣄⡈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠐⣻⢿⣿⣿⣤⣌⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠁⠻⣿⠿⠆⠸⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⠇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⢡⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣨⣭⣭⣴⣶⣾⣿⣿⡇
⠿⠛⣛⣫⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠤⠀⠉⠀⠉⡉⠉⠉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢠⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣿⣿⣿⣿⣿⠿⠟⠃
⣿⣿⣿⣻⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣽⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣮⣭⠍⣴⠈⠛⠛⠋⣁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠈⣫⣭⣦⣬⡁⠉⣥⣀⣉⣉⠙⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡟⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢋⣀⣈⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣟⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⣟⣛⣛⣛⣛⣛⡿⢿⣿⣿⣽⣿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣵⣿⢟⣛⣻⠿⣿⣿⣿⣿⣶⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡿⠁⠀⠘⢟⣿⣿⣿⣷⣿⣧⣶⣾⣍⣻⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⡇⠿⣿⣿⣿⣿⣿⡿⠿⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢰⣿⣻⣿⣿⠇⢰⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠿⠾⠿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠜⠀⡔⢀⠄⠀⠀⠸⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⠆⡠⠊⡴⡇⢀⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡼⠣⢀⠠⢃⠼⠓⠉⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠊⡀⠔⣡⠖⠁⠀⢀⠤⠂⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣿⠀⠀⡠⠊⠀⠀⠀⠐⠁⣠⡒⠉⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠁⠙⠒⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠀⠈⠀⠀⠀⢊⣥⣶⣿⣿⣿⣶⣄⠻⣿⣿⣿⣇⢀⣀⡀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠶⢦⡀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢀⣔⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⣯⠀⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣴⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣇⣿⣿⣽⣿⢻⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠲⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠉⠀⡀⡈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⢤⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⣽⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠂⠄⡀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠛⠿⠿⣿⣿⣿⣿⣧⠀⣸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠃⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠁⠒⠦⠨⣍⣉⠋⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠀⠲⠤⢉⣉⠛⠻⠿⢿⠿⠟⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠀⢷⣷⣶⣷⣤⡄⢸⣿⠆⠀⠀⠉⠁⠀⠑⠂⠲⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠙⠛⠿⡿⠄⠋⠀⣶⣲⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⢿⣿⣿⣾⡂⠀⠀⠀⣸⠀⣀⣷⣷⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⢠⣿⣧⠘⢿⣿⣿⣿⣿⣿⣷⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⢰⣦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢠⣤⣠⡉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠿⠋⣿⣿⡌⡪⡋⢟⠺⠃⠆⣤⠍⡉⠛⠻⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡀⠀⢐⠠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠀⣿⣞⡽⣂⣍⡃⠀⠀⠐⠓⠠⠤⢄⡉⣉⠙⠻⠿⣿⣻⣷⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠈⣄⠢⠄⠀⠀⠀⠀⠀⠀⠀⣨⠠⣄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠐⠀⠀⠀⠈⠻⠁⠀⠙⠱⠼⡝⣿⠀⡂⢦⡆⠆⠀⢀⡀⠀⠀⠐⠒⠤⣤⡭⡾⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢭⠆⣧⣄⠀⡀⡤⣄⣀⠀⠀⠁⠤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠠⠀⠀⠀⣀⡀⠀⠀⠀⠀⠁⠉⠡⠷⠈⠅⠁⠈⠁⠡⠁⡀⡀⢀⠀⠀⠀⠉⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠯⣊⢿⣿⡿⣻⣻⣶⣤⣄⡀⠀⠀⠀⠀⢐⠀⣀⠄⠀⠀⠀⢸⡆⠄⢀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠳⢯⣾⡟⠋⠛⠛⠛⠛⠳⠦⠀⠀⠀⠒⠺⠂⠐⠀⠀⠸⠇⠀⠈⠋⠃⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣧⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠙⠻⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢰⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣾⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠛⠿⣿⣿⣶⣤⣄⡀⡀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠚⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣷⣶⣦⣄⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢠⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠈⠀⣂⠁⠀⠀⠀⠠⠀⠈⠉⠻⣿⣿⣿⣿⣾⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡶⣶⣤⣄⡀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⢿⣿⣿⣤⣄⠉⠂⠚⢋⠟⠳⡄⡄⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡥⣿⢶⣦⣌⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣥⣬⣀⢚⣛⣁⣉⣛⡛⢛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢡⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣶⣿⣿⣿⡇
⠟⠛⠛⠋⡉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡧⠤⠤⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠃⠿⢿⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣯⣿⣿⣿⡿⠿⠟⠃
⣶⣦⢚⡹⣽⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠂⠀⠀⠀⠀⠘⠛⠶⣾⠣⠆⠀⣀⣠⣌⢉⣉⣄⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣟⣮⣕⠗⠯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⣽⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠉⣡⣤⣤⣤⡈⠉⣥⣀⣈⣉⠙⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣸⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣭⡄⣿⣿⡇⣿⣿⡇⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣥⣽⣿⣿⠿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⡧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢁⣀⣀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣶⣶⣾⣿⣶⣶⣶⣿⣵⣶⣶⣬⣩⣭⣴⣶⣭⣭⠤⠛⠛⣤⣙⠻⠿⢟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢟⣭⣭⡝⣿⣿⣿⣿⣿⣿⠿⠿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠋⠭⠾⠞⠛⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣏⠈⣿⣾⣿⣿⣿⣿⣳⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⡻⣿⣿⢿⣿⣿⣿⡏⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⡟⣿⣿⣮⡩⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⠄⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣻⣿⣿⣿⣶⣽⣿⣿⣿⣧⣝⣋⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣽⡿⠿⡿⣿⣿⣿⡽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⢱⣿⣿⣿⠀⠀⣾⣽⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⣾⣿⣿⣿⠀⢀⣿⣿⣿⡇⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠿⣿⣿⡏⠀⢸⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠄⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣼⣇⠀⠀⡀⠊⡠⠈⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⣿⡇⠀⠸⠖⠁⣠⠂⣠⣀⣀⣀⡀⢠⣾⣿⣿⡄⢀⡀⠀⠀⢸⣿⣿⣿⣿⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡠⠔⠁⢿⣷⣄⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣮⡛⢿⣿⣿⣿⡄⠀⣸⣿⣿⣿⣿⣑⣿⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠘⠃⠀⠀⠘⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣽⡟⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⠤⢤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣼⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠈⢸⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠘⢹⢸⣿⣿⣿⣿⣿⣿⣿⣭⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⡙⠛⠿⠿⣿⣿⣿⡄⢠⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⡙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠈⠑⠐⠀⣬⡉⢡⡘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⢀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠠⠂⠄⠌⠉⡙⠛⠟⠻⠋⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠈⠓⢨⣵⣦⣤⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠁⠛⠻⠅⠈⠀⣵⢦⢆⣋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠥⣿⣿⡷⢶⢤⠀⠀⠀⢸⡇⢠⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⣷⠐⠻⢿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡄⠄⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⠋⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠈⠉⠛⠿⠿⠿⣿⣿⣿⡷⢦⢄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠛⠛⢿⣿⡃⣶⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠬⡍⣒⠎⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⢠⡘⠣⠋⠩⠩⢶⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠢⢜⠈⠀⠈⠛⠓⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠂⣔⡄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠐⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣖⣶⣆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠶⣢⡴⢄⠄⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣀⡹⣿⣿⣿⣿⣟⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢇⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⢬⣿⣿⣤⡀⠀⠁⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣶⣤⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣋⣛⣛⠿⣟⡛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⢛⣉⣉⣙⣛⡛⢛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢝⣿⣿⣽⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢸⣿⣿⣿⣿⡿⢿⢿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣽⡇
⠟⠛⠛⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣫⣵⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡉⠛⢋⣉⣀⡀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⣀⣠⣈⠉⢉⣀⡈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⠀⣿⣿⠀⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠈⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡁⠘⣠⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢱⢱⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⠥⠁⢀⣿⣿⣿⣿⠇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⢤⣣⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⢘⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠵⣫⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⢀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⡿⣖⣾⣿⣿⣶⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢮⡟⠿⠿⢿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢻⣩⣴⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⣿⣶⠄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠀⠐⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⣿⠿⣟⣋⠵⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⢟⣙⡻⣷⣿⣿⣿⣿⣿⣵⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠯⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣀⣿⣿⣿⣿⣿⣿⣿⣏⡭⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣞⣛⣫⣿⣿⣿⣿⣿⣿⢸⣀⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⡿⣿⡿⣿⣿⣿⣿⣿⣮⡛⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⢛⣭⣭⡍⠉⠙⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⣼⣿⣿⡇⠀⠀⣿⣿⣷⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠛⠿⠿⠇⠀⢸⣿⣿⡟⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣾⣧⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⡄⣀⣤⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⢊⡡⣿⣿⣌⡠⣠⣤⣶⣶⣶⣾⣿⣿⣶⣶⣭⣙⠿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠉⠀⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⣿⡷⣼⣿⣿⣿⣿⣿⣿⡇⣿⠁⠀⠀⠀⠀⠀⠈⠁⠒⠐⠢⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠻⠀⠀⣴⡏⠠⣺⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣦⣭⣴⣿⣿⣿⣿⣿⣿⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠡⢋⠔⠁⠈⣿⣿⣾⣮⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣟⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠁⣾⡆⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⡻⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠁⢠⠄⠉⠁⠀⣿⠀⠉⠙⠛⠿⣿⣿⣿⡇⢀⣾⣿⣾⣝⢿⣟⣟⢿⣿⣿⣿⣏⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⡈⠿⢿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣷⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠨⠉⠛⠛⠿⠿⠿⠿⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠈⠈⠐⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⢖⣲⣆⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠈⠺⢿⣿⣿⣷⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠙⠻⠿⢷⣿⣿⣿⣿⣿⣦⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⣿⣯⡫⡀⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠊⣧⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⡿⣿⣿⣿⣾⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠶⣳⣷⣤⣶⡿⢯⣿⣿⣿⣿⣯⣿⣿⢿⣿⣖⣤⢀⠀⠀⠀⠀⠀⠀
⠀⢙⢷⡄⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀⠠⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠛⣿⣿⣿⣿⣞⣏⣿⣿⣿⢿⣽⣽⡿⣿⣧⢿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⢛⣉⣉⣙⣛⡛⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠛⠫⠝⢍⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⡿⢿⢟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⣻⣿⣟⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣆⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣿⡇
⠟⠛⠛⠉⠉⠉⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣩⣵⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣈⡙⠛⢋⣉⣀⡀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⣀⣠⡈⠉⠉⣀⡈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⠀⣿⣿⠀⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⢠⣶⣶⣶⣦⠉⣠⣤⣤⣤⡀⠉⣤⣀⣀⣉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠀⢄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠘⣀⣿⣿⣿⡇⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⢠⢀⡔⣼⣿⣿⣿⣿⣿⣿⣿⢿⣝⠈⢀⣿⣿⣿⣿⠇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡱⢣⠪⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⣀⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⢰⣤⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⢀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣖⣶⣿⣾⣶⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣓⡅⠿⠿⠿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣯⣼⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠁⠀⠐⠛⠁⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣻⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⢿⠿⣟⣫⠽⠒⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣙⡻⣷⣿⣿⣿⣿⣿⣵⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⣯⣀⣿⣿⣿⣿⣿⣿⣿⣏⣭⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣞⡛⣋⣿⣿⣿⣿⣿⣿⢸⣀⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⡿⣿⡿⣿⣿⣿⣿⣿⣎⡛⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⢛⣭⣭⡍⠉⠙⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⣼⣿⣿⡇⠀⠀⣿⣿⣷⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠛⠿⠿⠇⠀⢸⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣾⡧⠈⡀⠀⠠⠈⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⣀⣤⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⢊⡥⣿⣿⣌⡀⣠⣤⣾⣶⣶⣾⣿⣿⣶⣶⣭⣙⠿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠉⠀⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣿⡧⣼⣿⣿⣿⣿⣿⣿⡇⣿⠃⠀⠀⠀⠀⠀⠈⠉⠐⠀⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠀⠺⠀⠀⣴⡏⠠⣪⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣦⣭⣴⣿⣿⣿⣿⣿⣿⣿⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠁⢋⠔⠁⠀⣿⣿⣾⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣛⣻⣿⣿⣿⣟⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠁⣾⡆⠀⣟⣿⣿⣿⣿⣿⣿⣷⣿⠻⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠁⢰⠄⠉⠁⠀⣿⠀⠉⠙⠛⠿⢿⣿⣿⡇⢀⣾⣿⣾⣝⠿⣿⣟⣿⣿⣿⣿⣏⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠿⢿⣿⣿⣿⣿⣿⣷⣯⢻⣿⣿⣷⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠈⠉⠛⠛⠿⠿⠿⠿⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣦⣄⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠺⢿⣿⣿⣿⣾⣷⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣷⣦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣻⠤⣠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠺⠴⠂⠰⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣆⣄⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⢿⣾⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣀⠘⠮⢿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⣾⣧⣴⣸⢟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢀⠀⠀⠀⠀⠀⠀
⠀⢰⡦⣤⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡻⣿⣾⣷⣿⣾⡿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣛⣛⠿⣟⡛⠛⠻⠿⠿⠿⠿⣿⣿⢻⣷⢼⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣭⣭⣭⣙⠛⣉⣉⣙⣛⡛⢛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠛⠫⠍⢙⣿⣿⣽⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢸⣿⣿⣿⣿⠿⢿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣩⣤⣴⣶⣾⣿⣽⡇
⠟⠛⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢠⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⣁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣵⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠀⢀⣀⣀⡈⠙⠛⠋⠀⠀⠀⠀⠤⠀⠀⠀⠀⣀⣠⡌⠉⢉⡀⡈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⢠⣶⣶⣶⣤⠈⣠⣤⣤⣤⡈⠉⣤⣀⣈⣉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⡄⠘⣀⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⣿⣿⣿⣿⠃⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⠀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⢐⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢠⣽⣄⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣠⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⢀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⠙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠱⠌⠿⠿⠿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣯⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠀⠐⠊⠁⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⡿⠿⣟⣋⠵⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠯⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣭⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢟⡛⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣫⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⢇⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣮⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣞⣿⣭⣭⣷⣿⣿⣿⣿⣮⢿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣿⣿⠿⠿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⣀⣀⡀⢻⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣀⢀⣀⣀⣤⣤⣶⣶⣶⣦⣤⣌⣛⠿⢿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠹⣿⣿⠿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣶⣮⣉⠻⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⡀⠀⠔⠁⣠⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡄⠀⠀⠀⠁⠀⢀⡴⠋⠀⠀⢡⣴⣾⣾⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⠀⣶⠀⠀⠀⢠⢶⣀⣶⠏⠀⣄⠀⠀⢸⠽⣿⣿⣿⣿⣿⣿⣿⡙⠛⢿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠁⠀⠀⢸⠀⠀⠉⠙⠻⠿⣿⣿⣇⠀⣾⣿⣿⣮⣛⣛⣛⡿⣿⣿⣿⢏⡻⠿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡷⡗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⣿⠂⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠙⠻⠿⣿⣿⡿⣿⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⢂⣄⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠈⠙⡾⣧⣿⣵⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠉⠋⠹⢿⣿⣿⣿⣷⣶⢤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠻⣿⠞⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢂⠀⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⢀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⢨⠥⢿⣾⣿⣶⣤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⠀⠀⠈⠿⣿⣿⣫⣻⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢄⠤⢄⠀⠘⣻⢿⣿⣿⣿⣿⣿⣿⢿⣧⣆⡠⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠲⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠠⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠘⣦⡿⠠⣸⢿⠼⣉⠟⢟⡟⢳⢷⣟⣿⣷⣼⡗⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣭⣭⣙⢛⣉⣉⣋⣛⡛⢛⠁⠹⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣥⣴⣶⣾⣿⣿⡇
⠟⠛⠛⣋⣩⣍⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠀⠄⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢻⣽⣿⣿⣿⣿⠿⠟⠃
⣤⣦⣭⢿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡁⠲⠒⠀⠀⠀⠀⠀⠀⠚⠿⣷⣶⣆⡎⣌⣉⣉⣤⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢁⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠘⣡⣤⣤⣤⡈⠉⣥⣀⣈⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠀⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢃⣀⣀⣁⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣇⢬⣉⣩⣰⣆⣍⣩⣄⡛⠛⣀⡙⡻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣷⢀⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣴⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⠿⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡿⠿⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⣿⣟⣛⣛⠻⠿⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⢱⣿⣯⣶⣶⣽⣿⣿⣛⣒⠯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡇⠛⣸⣿⣿⣿⡇⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠸⢿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣰⠁⡰⠀⡠⠀⣴⡌⠉⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠎⠉⠈⠰⠈⣀⠤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⡀⠔⠈⠴⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠊⠀⢀⡤⠒⠁⣀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢋⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣤⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠐⣡⣴⣶⣶⣶⣦⣄⠰⣾⣿⣷⠀⢀⡀⠀⠀⢸⣷⣿⣿⣿⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠢⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣆⠀⢸⣿⣿⣿⡿⣿⡿⠀⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⣄⣿⣿⣿⣿⣿⡽⠁⠀⡀⠀⠀⠀⠀⠈⠙⠓⠒⠦⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⠟⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⡏⠉⠻⢿⣿⣿⣿⣿⣿⣽⣟⣫⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣴⠂⡀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢉⡛⠛⠿⠿⣿⣿⣿⠀⢰⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠉⠀⠀⠀⠤⠌⢠⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⡄⠑⠒⠶⡤⢠⢉⣙⠛⠋⠛⠉⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠚⠆⢯⣶⣶⣀⠸⣿⡇⠀⠀⠀⠀⠀⠈⠒⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢀⠄⠀⠈⠉⠋⠛⠆⠉⢀⣉⣽⣻⣂⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣯⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⡫⠮⡽⡿⡆⠀⠀⠀⢸⡄⣤⣗⣴⣦⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣿⣿⠘⠽⢿⣿⣿⣿⣿⣷⣶⣢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⡀⣄⣉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣦⡤⣄⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⠋⣿⣿⡆⠀⡈⢑⠀⠂⡄⠀⠄⠉⠛⠿⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣿⡿⠀⠄⠀⠂⠀⠀⡀⠀⠀⠀⠀⠂⠠⠀⣉⠉⠛⠛⢻⣿⡿⣶⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠈⠙⠁⠀⠀⠘⠀⠄⣶⢂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠑⡛⡟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢄⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠘⠐⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠄⢀⢆⠒⢛⠛⣓⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠈⠙⠙⠛⠛⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣲⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠃⢆⣶⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢀⠄⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠈⠛⢷⣦⣴⣤⡄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣷⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣄⡹⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣾⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢠⣤⣄⡀⠒⠾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀
⡨⣽⣿⣤⣀⠈⠀⠀⠉⠉⠀⠄⡄⣀⠀⠉⠙⠻⣿⣿⣿⣾⣶⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢛⢶⣦⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣉⣙⣋⣛⡛⢟⠃⠹⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣥⣴⣾⣿⣿⣿⡇
⠟⠛⠛⢋⣩⣩⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠀⠄⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⢀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢠⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣿⣿⣿⣿⠿⠟⠃
⣦⢖⢿⣽⢻⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡑⠲⠒⠀⠀⠀⠀⠀⠐⠚⠿⣷⣶⣆⡎⣌⢉⣉⣤⡈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⢯⡿⣱⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⢀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠘⣠⣤⣤⣤⡈⠉⣥⣀⣈⣉⠙⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣸⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣾⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠀⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢃⣀⣀⣡⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣾⣿⣿⣿⣇⢨⣉⣩⣰⣆⣍⣹⡄⡛⠛⣀⡙⡻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣣⣿⣿⣿⣿⣿⣷⢀⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠟⠛⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⢿⣿⣿⡿⢿⣽⣿⣿⣿⣿⣿⡷⠀⢼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⢟⣛⣛⣛⠻⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠟⢱⣿⢯⣶⣶⣝⣿⡿⣛⣒⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠙⣿⣿⣿⣿⣿⣷⣿⣿⣷⡌⣷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡇⠙⢹⣿⣿⣿⡇⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠸⢿⣯⣽⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣔⠁⡠⢀⡠⠀⣴⡌⠉⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠎⠉⠈⠰⠊⣀⠤⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⡀⠔⠊⠴⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠊⠀⢀⡠⠒⠁⣀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢏⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠐⣡⣴⣶⣶⣶⣦⣄⠰⣿⣿⣷⠀⣀⡀⠀⠀⢸⣷⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠤⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣆⠀⢸⣿⣿⣿⡿⣿⣟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⡀⣿⣿⣿⣿⣿⡽⠃⠀⠂⠀⠀⠀⠀⠈⠙⠓⠒⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⠟⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠾⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⡏⠉⠻⢿⣿⣿⣿⣿⣿⣽⣟⣫⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣵⠂⣀⠀⠀⠀⠀⠀⠀⠀⡗⠈⢉⠛⠛⠿⠿⣿⣿⣿⠐⢰⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⠀⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠉⠁⠀⠀⠤⡍⢠⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠲⠲⡄⢄⢉⣙⠛⠋⠛⠉⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠒⠐⠔⣢⣂⣠⠸⣿⡇⠀⠀⢐⠁⠀⠈⠚⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢀⠀⠀⠈⠉⠛⠛⠆⠉⠀⢰⣿⣿⣄⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠿⠪⠥⡬⣻⣇⠀⠀⠀⢸⡀⢤⢗⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⠈⢿⣿⣿⣿⣿⣿⣶⣦⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⣀⠀⡈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⠋⣿⣿⠎⠀⠀⠁⢀⠂⠠⠀⠄⠉⠛⠻⢿⣿⣿⣿⣿⣷⣢⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠄⠉⠉⠛⠛⠻⣿⢫⣷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠈⠙⠁⠀⠀⠁⠁⠀⣹⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢀⠀⠫⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣀⠀⠀⠄⣄⢀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠈⠀⠁⠄⠠⠀⢀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠈⠄⠼⢙⠓⣆⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢑⢖⠃⠈⠛⠋⠛⠛⠲⠆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸⠇⠀⠐⠀⠀⠀⠐⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣤⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠳⡟⣰⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠠⣠⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠈⠛⢳⣧⣥⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣽⢿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣧⣤⡀⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣅⣹⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣾⡶⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠦⢄⣀⡀⠒⠾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⣣⢿⣷⣤⣀⠈⠀⠙⠚⠛⠁⢐⣠⣀⠀⠉⠁⣚⣾⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡃⢿⣲⣤⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⢿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠉⠹⣿⠿⠇⠸⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢁⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣥⣶⣾⣿⣿⣿⡇
⠿⢛⠛⣋⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠠⠀⠉⠀⠉⠉⠉⢉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣿⣿⣿⣿⣿⠿⠟⠃
⣿⣾⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣮⣭⡍⣴⢈⡛⠛⠋⣁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢤⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠈⣫⣭⣦⣬⡁⠉⣥⣉⣈⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡟⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣽⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣋⣀⣈⣁⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⣟⣛⣛⣛⣛⣛⠿⢿⣿⣿⣝⣻⢿⣿⣟⣯⣾⣿⣿⣿⣿⡿⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣵⣿⢿⣟⡻⢿⣿⣿⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠘⢯⣿⣿⣿⣷⣿⢣⣶⣾⣝⢻⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠰⣟⣟⣻⣿⠃⢰⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠿⠶⠿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠜⠀⡐⢠⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠊⡀⠊⡴⡇⢀⣀⠤⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡴⠃⢈⡴⢋⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣧⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠠⠊⢀⠔⡡⠒⠁⠠⢀⠤⠊⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢼⣿⠀⠀⡠⠊⠀⠀⢀⠐⠁⣠⡐⠉⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠈⠉⠓⠂⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠀⠂⠀⠀⠀⢊⣡⣾⣿⣿⣿⣶⣄⠻⣿⣿⣿⡇⢀⣀⡀⠀⢸⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⡶⢤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣷⡄⣸⣿⣿⢿⣿⡏⠀⠀⠁⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⣶⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣇⣿⣿⣽⣿⠏⠐⠨⠂⠀⡀⠀⠀⠉⠙⠛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡴⠤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣤⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣛⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠠⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠙⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠿⠿⣿⣿⣿⣿⣇⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠁⠒⠠⠀⢉⣉⠋⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢤⡀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⢸⡇⠀⠀⡀⠀⠀⢐⠀⠀⢠⣿⠐⠦⢤⣍⢉⠛⠻⠿⣿⠿⠿⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣾⣷⠀⠀⠷⢭⣶⣦⣤⡄⢸⣿⠀⠀⠀⠈⠊⠁⠁⠒⠢⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⡂⠀⠀⠙⠛⠿⠿⡄⠏⢀⢶⣶⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣤⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣼⣷⡂⠀⠀⠀⢸⠀⣰⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠉⠋⠛⠃⠀⠀⢰⣿⣧⠛⢛⣿⣿⣿⣿⣿⣿⣾⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠑⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠈⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⣼⣿⣿⠀⡠⣠⡀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠀⠁⢀⢀⠀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⠿⠟⣿⣿⠄⠲⡛⣮⡆⣓⠦⣄⠥⠉⠛⠿⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠩⠝⠠⢖⠁⢀⠘⣁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠠⣷⣶⣷⡩⢹⡝⠀⠀⠁⠐⠖⠠⢤⣉⣉⡛⠿⣿⣿⣻⣷⣦⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⢀⠀⠀⠀⠈⠀⠀⢁⠉⡁⢀⠄⠀⠈⠀⠀⠂⢽⡰⢄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠠⠀⠀⠀⠈⠻⠃⠀⠙⠿⣿⢾⣿⣷⣶⡦⣄⠢⡀⢀⠀⠀⠀⠈⠓⢒⣿⠮⠭⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⣿⣼⣵⣿⣐⢰⣤⣤⣀⠀⠈⠁⢵⡄⣐⠢⠀⠀⠀⠀⠈⠉⠋⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠔⠀⠠⠄⠀⠀⠀⠀⠀⠈⠿⠿⠷⠿⠿⠀⠄⠗⠖⠖⠄⡀⡀⠀⠀⠈⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣋⣿⣿⣿⣿⣿⣶⣦⣄⡈⠀⠀⠀⠀⠓⢠⡆⠄⡀⠀⠀⢸⡇⠀⣤⣦⡀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠰⠒⢽⢍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⠟⠛⠛⠛⠛⠛⠳⠦⠀⠀⠈⠺⠳⠄⠀⠂⠀⠸⠇⠀⠛⠛⠊⠛⠓⠢⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀
⠀⠈⠙⠿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣦⣴⣦⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀
⠩⠈⠂⢀⠈⠙⠻⢿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠟⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀
⠈⠂⡀⢀⢀⠄⠀⠀⠈⠛⢿⣿⣿⣿⣷⣴⣤⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢠⣅⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣢⣀⠈⠰⣕⡃⠀⠀⠄⡀⡀⠀⠛⢿⣿⣿⣿⣿⣿⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣤⣄⡀⠚⠿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣄⠉⠃⠛⢿⣻⣥⣴⣦⣤⡉⠛⠻⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣌⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⢛⠉⠻⡿⠿⠇⠸⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢁⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣥⣴⣾⣿⣿⣿⡇
⠟⠛⣛⢋⣍⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠀⠀⠉⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣿⣿⣿⣿⣿⠿⠟⠃
⣾⣾⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣽⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣯⣭⡍⣴⠈⡛⠛⠋⡁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢁⣽⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠈⣫⣭⣦⣬⡁⠉⣥⣀⣉⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡟⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣂⣀⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⢿⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⣟⣛⣛⣛⣛⣛⠿⢿⣿⣿⣝⣻⠿⣿⣟⣿⣾⣿⣿⣿⣿⡿⠌⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣵⣿⢿⣿⡿⢿⣿⣿⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠘⢯⣿⣿⣿⣷⣿⢧⣶⣾⣍⢻⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢄⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠰⣟⣛⣻⣿⠃⢰⡿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠻⠾⠿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠜⠀⡐⢠⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠂⡀⠊⡴⡇⢀⣀⠤⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡼⠃⢈⡴⢋⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣧⣿⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠊⣀⠔⣁⠖⠁⠠⢀⠤⠊⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣿⠀⠀⡠⠊⠀⠀⢀⠐⠁⣠⡐⠉⠀⢈⣤⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠁⠉⠀⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠀⠊⠀⠀⠀⢊⣡⣾⣿⣿⣿⣶⣄⡻⣿⣿⣿⣇⢀⣀⡀⠀⢸⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠲⠶⡶⢤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⢿⣿⡯⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⣶⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣇⣿⣿⣿⣿⠇⠐⠉⠄⣀⡀⠀⠀⠉⠙⠓⠲⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠄⢍⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡶⣤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣛⣽⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸⡇⣿⣿⣿⣿⣿⣿⣯⣿⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣻⣿⣿⣿⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠈⠀⠓⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠙⡛⠿⠿⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠈⠁⠀⠐⠆⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠁⠒⠠⠀⢉⢉⠋⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⢤⣠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠰⠀⠉⢀⣷⠀⠢⠤⣍⡉⠛⠻⠿⣿⢿⠿⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠹⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⢿⠴⣤⣦⣤⡄⢸⣿⠆⠀⠀⠈⠁⠀⠂⠒⠶⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⡂⢀⠈⠈⠛⠿⢿⡄⠋⢀⣶⢶⣮⣄⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣭⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢿⣿⣿⣾⣷⣿⡆⠀⠀⠀⢸⠀⣠⣿⣾⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠃⠀⠀⢰⣿⣧⠛⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⡧⣄⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⢀⡀⠀⠠⢐⣀⢀⠀⠀⠀⢀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⡄⠀⠀⠀⠿⠟⣿⣿⠀⣗⣯⡚⡯⣥⢆⣠⠀⡉⠛⠿⠿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⢈⢲⠍⠆⠀⢀⡷⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⢀⣶⣿⣛⣸⣤⡀⠐⠈⠁⠓⠰⠤⢄⣉⣉⡻⠻⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠈⠀⠘⣛⡃⠤⠀⡄⠀⠀⠀⠠⠀⠀⡠⢄⡀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⡀⣀⠀⠈⠻⠃⠀⠉⠻⠿⣿⣿⣿⣀⢀⡄⢂⡀⡀⡀⠀⠀⠘⠃⢶⡄⡸⣯⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢸⢬⣟⣷⢀⣴⣤⡤⣀⠀⠈⠙⠥⡄⠀⠄⠀⠀⠀⠀⠀⠋⠹⠆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠛⠙⠹⠞⠷⠈⠦⠍⢛⠅⠀⠀⠀⠀⠀⠀⠈⠈⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⣹⣞⡮⡿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠐⠢⣤⣦⣄⠀⠀⠀⢸⡇⠰⣦⣒⣀⡀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠰⣀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠽⣿⡟⠛⠛⠛⠛⠛⠳⠦⠀⠀⠀⠺⢿⠟⠙⠂⠀⠸⠇⠀⠛⠛⠛⠛⠂⠦⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠻⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣽⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⢀⠀⠢⢀⠈⠙⠻⢿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠛⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡄⢀⢀⢀⠄⢀⠈⠛⢿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⣠⣅⡹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⣦⣀⠈⠰⣄⡀⠀⠀⢤⠀⠄⠉⠛⢿⣿⣿⣿⣿⣿⣶⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠶⣶⣤⣄⡀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⣯⣿⣿⣦⣄⠉⠂⠛⢻⠋⡑⢲⣦⣄⡉⠛⢿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠻⣿⣿⣷⣦⣌⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣥⣬⣀⢘⣛⣁⣉⣛⡛⢛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠝⢟⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⠇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢡⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢸⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣥⣴⣾⣾⣿⣿⡇
⠟⠛⠛⠉⡉⡉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⡧⠤⠄⠄⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠃⠿⢿⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢻⣯⣿⣿⣿⡿⠿⠟⠃
⣼⣆⡀⢛⣟⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣯⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠂⠀⠀⠀⠀⠘⠛⠶⣾⠣⠆⢀⣀⣤⣌⢉⣉⣀⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣯⣗⣶⣟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣭⡄⣿⣿⡇⣿⣿⡇⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣣⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⡇⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢂⣀⣈⣁⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣶⣾⣿⣷⣶⣶⣬⣩⣭⣶⣦⣭⣭⠤⠛⠛⣤⣙⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣟⣭⣥⡙⣿⣿⣿⣿⣿⣷⠿⠿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣦⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠛⡯⠿⠟⠛⠋⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⠈⣿⣼⣿⣿⣿⣿⣣⣾⣿⣶⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣫⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢛⡻⣿⣿⢿⣿⣿⣿⡏⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣮⡉⣿⣹⣿⣿⣿⢿⣷⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣶⣭⣿⡾⣿⣧⣝⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣝⡿⠿⡿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠋⢱⣿⣿⣿⠀⠀⣾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⣼⣿⣿⣿⠀⢀⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠿⣿⣿⡏⠀⢸⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠊⡔⠁⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣼⣇⠀⠈⡠⠊⠁⠊⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠊⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢋⣿⡇⠀⠸⠆⠂⣠⢊⣠⣆⣀⣀⠀⢠⣾⣿⣿⡄⣀⡀⠀⠀⢸⣿⣿⣿⣿⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠢⡤⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠖⠁⢿⣷⣄⣁⣠⣤⣾⣿⣿⣿⣿⣿⣿⣷⣮⡛⢿⣿⣿⣿⡄⠀⢸⣿⣿⣿⡿⣀⣿⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠝⠀⠘⠃⠀⠀⠸⣿⣿⣿⡿⣫⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣽⣷⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠰⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣼⣿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⢤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠊⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⢻⢸⣿⣿⣿⣿⣿⣾⣯⣯⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⢉⠙⠛⠿⠿⣿⣿⣿⡄⢠⣷⣶⣾⣿⣮⣿⣿⡿⢿⣿⣿⡛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠁⠃⠒⠀⠬⡉⢁⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⡀⠀⠀⣾⡄⠀⠶⢲⢄⠈⠉⡙⠛⠟⠻⠛⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠺⠷⠮⣤⣧⣤⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠁⠁⠛⠿⢡⠈⠀⢰⣶⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣿⣩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠿⣢⣵⣶⣶⡶⠀⠀⠀⢸⡇⣠⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⣿⣷⠘⢿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠁⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⡠⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠻⠏⣿⣿⠃⠈⠈⠈⠈⠑⠀⠀⡠⠉⠛⠿⠿⣿⣿⣿⣿⣷⣖⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢉⡉⠛⠛⠿⣿⣿⣶⡤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⣚⣀⢞⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠗⠹⠙⠛⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠁⠙⠙⠛⠓⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⢠⡴⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣆⣐⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣔⣂⣤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠾⣷⣟⢥⣤⡀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡅⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⣯⡍⠐⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⢀⡀⠐⠾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀
⠼⢿⣷⣦⡀⠀⠁⠉⠛⠙⠁⠀⡀⡀⠀⠀⠀⠀⠲⣶⣷⣴⣆⣀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠂⢤⡄⠙⠻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣛⣛⣛⠿⣟⡛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⢽⣿⣿⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⢛⣉⣉⣙⣛⡛⠛⠛⠻⠿⠿⠻⠿⠿⡿⠿⠛⠫⠽⢙⣟⣿⣭⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣿⡇
⠟⠛⠛⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⣁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠰⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣵⣶⣿⡿⠿⠟⠃
⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠋⡀⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠛⢋⣉⣀⡀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⢀⣀⣠⡈⠉⢉⡀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣸⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣀⣉⠙⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣀⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢿⡋⠀⢠⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡊⠌⡤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡞⠂⠀⢸⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⡳⣡⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣷⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡭⠿⠿⢿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣭⣷⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠀⠐⠊⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⠿⠿⣟⡫⠵⠖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢟⣉⡻⣷⣿⣿⣿⣿⣿⣿⣾⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡻⠿⠆⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⢀⣷⣽⣿⣿⣿⣿⣿⢏⣭⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣞⣛⣋⣿⣿⣿⣿⣿⣿⢾⣀⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⡻⣿⡿⣿⣿⣿⡟⣿⣎⡛⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⢛⣭⣭⡍⠉⠛⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⣸⣿⣿⡇⠀⠀⣿⣿⣷⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠛⠿⠿⠇⠀⢸⣿⣿⡿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣾⣷⠊⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡄⣀⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⢊⡡⣿⣿⣄⡐⣀⣠⣶⣶⣶⣾⣶⣷⣶⣶⣭⣙⠿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿⡟⣸⣿⣿⣿⣿⣿⣿⡇⣿⠂⠀⠀⠀⠀⠀⠈⠉⠐⠂⠂⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠻⠀⠀⣴⡇⡠⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⢿⣦⣭⣴⣿⣿⣿⣿⣿⣿⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⢄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠡⢃⠜⠁⠈⣿⣿⣶⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣛⣛⣽⣿⣿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⣞⡆⠀⡟⣿⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠃⠠⡆⠉⠁⠀⣷⠀⠉⠙⠛⠿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣏⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⠉⠁⠈⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠐⠂⠀⠌⠉⠛⠛⠿⢿⢿⠿⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⢧⣐⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠈⠻⢿⣿⣿⣿⣷⣶⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣽⣥⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠗⠱⠂⠄⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣾⡿⢿⣿⣿⣿⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡀⠀⠪⠿⣿⣿⣿⣿⣿⣿⣷⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠩⢻⣧⣠⣠⣾⣻⢿⡿⣿⣿⣿⣿⣿⣿⣷⣦⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠪⢷⡤⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⣾⣿⣿⣿⣯⣿⣽⣿⡽⣻⡼⣿⣿⣾⣟⣖⠐⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣉⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⢸⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⢛⣉⣉⣙⣛⡛⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠛⠫⠝⢙⣟⣿⣭⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⠿⢿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣥⣴⣶⣾⣿⣽⡇
⠟⠛⠛⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣢⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⢿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣭⣵⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠛⢋⣉⣀⡀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⢀⣀⣠⡈⠉⢉⡀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⣸⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣀⣉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢠⣿⣿⣿⡇⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡠⢄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢏⠁⢠⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡣⢬⡬⣰⣿⣿⣿⣿⣿⣿⣿⣿⡗⠄⠀⢸⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡊⣷⣡⣿⣿⣿⣿⣿⣿⠿⠿⠟⠑⠀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣷⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⡥⠿⠿⢿⣿⣿⣫⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣿⣼⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠀⠄⠘⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⠿⠿⢛⡫⠷⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢟⣉⡻⣷⣿⣿⣿⣿⣿⣿⣾⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠏⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣟⢿⢀⣿⣽⣿⣿⣿⣿⣿⢏⣭⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣞⣛⣋⣿⣿⣿⣿⣿⣿⢾⣀⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⡻⣿⡿⣿⣿⣿⡟⣿⣎⡛⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣝⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⢛⣭⣭⡍⠉⠛⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⣸⣿⣿⡇⠀⠀⣿⣿⣷⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠛⠿⠿⠇⠀⢸⣿⣿⡿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡠⣾⣷⠊⠠⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠄⣀⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⢊⡡⢿⣿⣌⡐⣀⣠⣶⣶⣶⣷⣶⣿⣶⣶⣭⣙⠿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿⡟⣸⣿⣿⣿⣿⣷⣿⡇⣿⠃⠀⠀⠀⠀⠀⠀⠉⠒⠂⠂⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠻⠀⠀⣴⡇⡠⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⣭⣴⣿⣿⣿⣿⣿⣿⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠡⢃⠜⠁⠈⣿⣿⣷⣾⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣛⣛⣽⣿⣿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⣜⡇⠀⡟⣿⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠃⠠⡆⠉⠁⠀⣷⠀⠉⠙⠻⠿⣿⣿⣿⡇⠀⣾⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣏⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⠉⠁⠈⠿⢿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣷⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠐⠂⠠⠈⠉⠛⠛⠿⢿⢿⠿⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣷⣴⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣿⣷⠈⠹⠿⣿⣾⣾⣷⣶⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠯⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠳⠳⠢⠀⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣖⢄⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⡿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣄⠈⠱⠿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⣿⣷⣗⢽⣿⣻⡽⣿⣿⣿⣿⣿⣿⣿⣷⣦⡤⢀⠀⠀⠀⠀⠀⠀
⠊⢼⡲⡤⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠹⣾⣿⣿⣿⣿⣎⡟⢻⠅⢓⣿⣿⣿⣷⡷⣛⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣛⣛⠿⣟⡛⠛⠻⠿⠿⠿⠿⣿⣿⢸⣷⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣭⣭⣭⣙⠛⣋⣉⣙⣛⡛⠛⠛⠿⠿⠿⠻⠿⠿⡿⠿⠛⠫⠝⢙⣿⣿⣭⣯⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⠿⢿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣆⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣽⡇
⠟⠛⠛⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢋⣯⣥⣾⣿⡿⠿⠟⠃
⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣈⡉⠀⢀⣀⣀⡈⠛⠛⠋⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣠⡌⠉⢉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣀⣉⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠘⣠⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡔⠀⠀⢂⣼⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⠇⠀⣿⣿⠀⣿⣿⡎⣿⣿⠀⣿⣿⠉⣩⠀⣿⣿⡇⣿⣿⡇⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡃⢨⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢠⣿⣆⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣁⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⢀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⡙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠴⠾⠿⢿⣿⣿⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣭⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠁⠀⠐⠒⠉⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⡿⠿⢟⣩⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠋⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣭⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⡛⣿⣿⣿⣿⣿⣿⣿⣫⣶⣶⣮⣻⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⡹⣿⣿⣿⣿⣿⣿⣿⡿⣫⣝⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣯⣭⣿⣿⣿⣿⣿⣮⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⠿⠟⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣀⣀⣀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣠⣤⣤⣶⣶⣶⣦⣤⣍⣛⠿⢿⣾⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣫⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠘⣿⣿⠿⣿⣿⣋⣭⣭⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠛⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠈⡀⠀⠔⠀⣠⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠈⠀⢀⠁⠀⢀⡼⠋⠀⠀⢡⣼⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢀⠀⢴⠀⠀⠀⢠⢶⣀⣴⠟⠀⣄⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⣯⡛⠛⢛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠁⠀⠀⢸⠀⠀⠉⠙⠻⠿⣿⣿⣇⠀⣾⣿⣿⣯⣛⣛⣻⣿⣿⣿⣿⣏⡻⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣷⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣿⠀⠈⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠐⠂⠀⠈⡙⠛⠿⣿⣿⡿⣿⠟⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠐⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠂⠢⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡇⢠⡤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠺⠗⢿⣿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢿⣿⣷⣷⡣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢠⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠊⠗⢆⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⢰⣦⡠⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣶⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⣀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⡀⠀⠠⢻⢿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣬⢯⣦⣤⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⢀⡀⠀⠀⠀⠀⠀
⠀⠈⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢊⢿⣿⣿⣷⣷⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣉⣛⣛⠿⣟⡛⠛⠻⠿⠿⠿⠿⣿⣿⢻⣷⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣬⣭⣭⣙⠛⣉⣉⣙⣛⡛⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠝⢙⣟⣿⣭⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠈⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⠿⢿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣆⢸⣿⣿⠿⠇⣈⣭⣤⣴⣶⣾⣿⣽⡇
⠟⠛⠛⠉⠉⠉⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣭⣥⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠀⢀⣀⣀⡈⠛⠛⠋⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣠⡌⠉⠉⣀⡈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⢠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡃⠸⢠⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠔⣆⣼⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⢠⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⠀⣿⣿⠉⣩⠀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢚⠊⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢠⣿⣄⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠩⠕⣳⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⢀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⠙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠍⠿⠿⢿⣿⣟⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣯⣧⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠀⠚⠒⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⠿⠿⣛⣫⠵⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠯⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣭⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⡻⣿⣿⣿⣿⣿⣿⣿⣫⣶⣶⣯⣻⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⡽⣿⣿⣿⣿⣿⣿⣿⡿⣫⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⢇⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣿⣻⣽⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣯⣭⣿⣿⣿⣿⣿⣮⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⠀⣀⣄⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣀⣀⣀⣠⣤⣤⣶⣶⣶⣦⣤⣝⣛⠿⢿⣾⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣋⡀⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠙⣿⣿⠿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠛⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠈⡀⠀⠖⠁⣠⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠠⠀⠀⢀⠁⠀⢀⡼⠋⠀⠀⢡⣼⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢀⠀⢴⠀⠀⠀⢠⢶⣀⣴⠟⠀⣄⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⣮⡛⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠁⠀⠀⢸⠀⠀⠉⠙⠻⠿⣿⣿⣇⠀⣾⣿⣿⣯⣛⣛⣻⣿⣿⣿⣿⣏⡻⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠈⠁⡀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣿⠀⠈⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠐⠂⠀⠈⠙⠛⠿⣿⣿⣿⣿⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠐⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⣢⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠻⠟⣿⣷⣿⣶⣶⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣿⣿⣿⣽⣇⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢠⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠛⢦⠄⣦⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⢰⣶⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⡀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡄⠈⢉⠻⣿⣿⣿⣿⣿⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠹⣿⣾⡥⠸⣞⣶⣿⣿⣿⣿⣿⡿⣿⣿⣷⣦⠤⢀⠀⠀⠀⠀⠀⠀
⠠⠠⡷⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣴⡆⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⣷⣷⣷⣿⡾⣯⢿⡿⣿⡿⣿⣿⣿⣿⣷⠿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣉⣉⣋⣛⡛⢛⠁⠹⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣾⣾⣿⣿⡇
⠟⢛⠛⣋⣭⣍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠤⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢠⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢻⣿⣿⣷⣿⣿⠿⠟⠃
⣶⣶⡷⣞⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠂⠀⠀⠀⠀⠀⠀⠚⠿⣷⣶⣆⡎⣈⢉⣉⣀⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠘⠛⠋⠉⠁⠀⠀⠀⠀
⡟⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⣽⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠘⣠⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣺⣿⣿⣿⡯⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣼⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠀⣾⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢋⣀⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣾⣿⣶⣶⣿⣿⣿⣃⢨⣉⣩⣰⣆⣍⣹⡄⣛⠛⣀⡙⡻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣫⣿⣿⣿⣿⣿⣯⣀⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣴⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⣟⡻⠵⠿⠛⠋⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣾⣿⣿⣟⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢟⣵⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⢛⣛⣛⣛⠻⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⢤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⢱⣾⢯⣶⣶⣍⣿⡿⣛⣒⠭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠙⣾⣿⣿⣿⣿⣧⣿⣿⣷⡌⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡇⠙⢹⣿⣿⣿⡇⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠸⢿⣯⣽⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⣰⠁⡠⠀⡠⠀⣴⠌⠉⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠈⠉⠀⠀⠊⣀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣠⠔⠊⠤⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠊⠀⢀⠠⠒⠁⣀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠝⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠀⠀⠃⣀⡀⠀⠀⠀⠀⠀⢸⡟⣿⣿⡃⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠐⣡⣴⣶⣶⣶⣦⣄⠰⣿⣿⣷⡀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠶⠤⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣆⠀⣸⣿⣿⡿⡿⣿⡃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⡄⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⠟⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⣤⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠴⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⡏⢉⠛⢿⣿⣿⣿⣿⣿⣿⣛⣻⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠃⡀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⡛⠛⠿⠿⣿⣿⣿⠘⢰⣿⣶⣾⣿⣯⣿⣻⢿⣿⣿⣿⡻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠂⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠀⠒⠀⠠⠉⣠⠘⠻⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢺⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠓⠒⢲⡄⠈⠉⠉⠛⠛⠛⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠲⠶⠾⠶⡂⡄⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠘⠑⠀⠈⢀⢱⣿⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢫⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠛⠫⠀⡄⠆⢦⣃⠀⠀⠀⢸⡀⢤⣿⣷⣴⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢠⣿⣿⠸⢿⢿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣼⣿⣿⠀⢀⡠⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⠋⣿⣿⠇⡨⠀⠺⠂⠂⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣿⡿⠀⠐⠀⠀⡂⠀⡁⠀⠀⠀⠁⠀⠄⠀⣉⣉⠛⠛⢿⣿⢷⣷⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡄⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠐⢺⠃⡹⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢀⢤⣄⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠌⠨⠒⠗⠟⡯⠑⣆⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡌⠤⠑⠀⠈⠙⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠑⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠢⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠈⠙⠋⢮⡴⣤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⢄⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠁⠳⢷⣝⣴⣀⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠈⠂⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣧⣤⣀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣅⢙⣟⣻⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⣀⣀⠀⠚⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠟⣿⣷⣤⣄⠀⠀⠀⠂⠛⠁⢀⣀⡀⠈⠉⠙⢿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⣶⣦⣀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⢿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⢛⠁⠻⡿⠿⠇⠸⠿⣿⠿⠛⠻⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣨⣭⣥⣶⣾⣾⣿⣿⡇
⠿⢛⣛⣋⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠤⠀⠉⠀⠉⠉⠉⠉⣡⣦⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣯⣽⣿⣿⣿⠿⠟⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣾⣭⠍⣴⠈⠛⠛⠋⣁⠘⠛⠻⠿⠃⠘⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠈⣫⣭⣦⣬⡁⠈⣥⣀⣉⣉⠙⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡟⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣹⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢊⣁⣀⣁⣤⣴⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⢿⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⠛⠛⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⡿⠷⠿⠛⠋⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣻⣿⣾⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⢟⣛⣛⣛⣛⣛⡿⢿⣿⣿⣝⡻⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣶⣿⢟⣛⡻⢿⣿⣿⣿⣿⣶⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠘⢏⣿⣿⣿⣷⣿⢣⣶⣮⣝⢻⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡇⠿⣿⣿⣿⣿⣿⣿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠰⣿⣟⣛⣿⠇⢰⡿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠻⠿⠿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠜⠀⠐⢀⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⠂⡠⠊⡴⡇⢀⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡼⠣⢊⡴⢊⡼⠓⠁⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣏⣿⣟⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠠⠊⣠⠔⡩⠖⠁⠠⢀⡤⠊⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢼⣿⠀⠀⠠⠊⠀⠁⣠⠐⠁⣠⡐⠉⠁⢀⣤⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠳⠖⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⠠⠊⠀⠀⠠⢈⣥⣾⣿⣿⣿⣶⣤⡻⣿⣿⣿⣇⠀⡀⡀⠀⢸⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠒⠶⠶⡀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣔⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⡟⠀⠀⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⣶⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣇⣿⣿⣽⣿⠏⠀⠀⠀⠄⠀⠀⠀⠈⠛⠓⠖⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⡿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢶⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣛⣵⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡛⡻⠻⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠛⠿⠿⣿⣿⣿⣿⣧⠃⣼⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⠉⠑⠒⠤⠄⠉⣉⠉⡀⠻⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣮⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠐⠦⠤⢭⣉⠛⠻⠿⢿⠿⠿⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣿⣷⠀⠀⢦⣵⣶⣼⣤⡄⢸⣿⠀⠀⠀⠀⠀⠉⠛⠲⠲⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠠⠀⠈⠙⠛⠿⠺⠄⠋⢠⣳⣶⣾⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣭⡇⠈⠇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣷⣾⡄⠀⠀⠀⢺⠀⣰⣿⣲⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠋⠛⠃⠀⠀⢠⣿⣧⠻⠿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⣼⣿⣿⠀⣤⡄⡉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠿⠟⣿⣿⡆⢨⠻⢁⠛⡒⡠⡀⠀⡙⠛⠿⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡰⠰⠐⢀⡀⠀⢀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠀⠠⣘⠠⠠⡒⡮⠙⠉⠉⠉⠂⠄⢄⣉⡉⡛⠻⢿⣿⢿⣷⣶⡀
⠁⠀⠀⠀⠀⠂⠀⡀⢀⠀⢀⢀⠀⠀⠈⠀⠀⠀⡤⠀⠀⠀⠀⠀⠐⠀⠀⠐⠄⠄⢀⡀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠄⠀⠀⠈⠻⠃⠀⠙⠃⠃⡁⣷⢔⠄⣄⠄⡄⠂⡀⠀⠀⠀⠈⠍⢦⣤⣾⢟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣔⣮⠩⢶⣤⣤⣄⣀⠀⠀⠁⠤⣄⡀⠀⠀⠀⠀⠀⠈⠋⠐⠆⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠅⠛⠊⠥⠈⠀⣀⠀⡀⠀⠀⠀⠀⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠸⠿⢚⣿⣿⣿⠿⣿⣖⣤⣄⡈⠀⠀⠀⠀⠐⢖⣀⣀⠀⠀⠀⢸⡇⠌⣀⣒⡀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⡿⡿⠎⠉⠛⠛⠛⠛⠳⠆⠀⠀⠀⠻⠟⠆⠘⠃⠀⠸⠇⠀⠒⠛⠓⠋⠒⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣧⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠈⠙⠻⣾⣿⣶⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠰⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣾⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠢⢀⠈⠉⠁⠿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⢚⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠇⢄⠀⠀⠀⠀⡀⠈⠙⢿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣄⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠈⠀⣀⠀⠀⠀⢒⡀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠒⠲⣦⣤⣀⡀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣄⠙⠂⠛⢛⡛⢃⣤⢤⣀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠿⡿⣶⣦⣌⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠁⠻⣿⠿⠆⠸⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣻⣿⣿⢡⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢰⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣨⣭⣥⣶⣾⣿⣿⣿⡇
⢿⣛⡛⣫⢩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡧⠤⠤⠠⠀⠉⠀⠉⡉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢠⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣿⣿⣾⣿⣿⠿⠿⠃
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣻⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢛⣉⣉⡙⠳⠖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣾⣭⠍⣴⠈⠛⠛⠋⣁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠈⣫⣭⣦⣬⡁⠉⣤⣀⣉⣉⠙⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡟⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣊⣀⣉⣡⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣶⣶⣿⣿⣿⣷⣮⣭⣭⣦⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⡿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣞⣻⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢟⣛⣛⣛⣛⣛⡿⢿⣿⣿⣝⡻⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣶⣿⢟⣛⡛⢿⣿⣿⣿⣿⣶⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠘⢏⣿⣿⣿⣷⣿⢧⣶⣮⣝⢻⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⡇⠿⣿⣿⣿⣿⣿⣿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠰⣿⣟⣛⣿⠇⢰⡿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠻⠿⠿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠌⠀⠐⢀⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠂⡠⠊⡴⡇⢀⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡸⠣⢊⡴⢈⡽⠓⠉⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠠⠊⣠⠔⣡⠞⠁⠠⢀⡤⠊⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣿⠀⠀⠠⠊⠀⠁⢠⠔⠁⣠⡒⠉⠁⢀⣤⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠋⠑⠰⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠠⠊⠀⠀⢠⢊⣤⣾⣿⣿⣿⣶⣤⡻⣿⣿⣿⣇⠀⠀⡀⠀⢸⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠒⠷⠦⡄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣔⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢿⣷⣶⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣇⣿⣿⣽⣿⠏⠈⠘⠁⢠⠀⠀⠀⠉⠙⠻⠶⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⡿⣽⣿⣿⣿⣿⠀⠀⠁⠁⠘⠛⢠⣀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠻⢦⣤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣛⣼⣿⣿⣻⣿⣿⠆⠀⠀⠀⠀⠀⠸⠶⠀⠇⠠⠀⠀⠀⠁⠀⠀⠁⠐⢀⡈⠻⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡛⡻⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠤⠄⠀⠀⠁⠀⠐⠀⢐⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠿⠿⣿⣿⣿⣿⣧⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠐⠄⡀⠀⠀⡀⠀⠀⠀⠮⡭⣘⢀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⣄⠀⢸⡇⠀⠈⠁⠒⠦⠄⢍⢉⠋⡀⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠩⠳⣁⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⢬⣌⣈⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠐⠶⠤⠍⣉⡛⠻⠿⢿⢿⠿⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⢀⣾⣷⠀⠀⢵⣵⣶⣶⣤⡄⢸⣿⠀⠀⠀⢹⠈⠉⠙⠂⢶⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⣿⡇⠀⡀⠈⠙⠛⠿⢿⡀⠋⢠⡲⣶⢾⣀⣀⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠄⣐⡄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣭⡇⠘⠅⠀⠀⠀⠀⠀⠈⠀⠙⠛⠟⢿⢿⢿⣿⣿⣿⡂⠀⠀⠀⢸⠀⣰⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠀⠀⠴⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠅⣢⠀⠀⠀⠀⠉⠐⠉⠛⠃⠀⠀⢠⣿⣧⠻⢿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡕⣄⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠠⣦⠀⢈⡙⠁⢃⣠⠀⠀⠀⠀⠀⠀⣐⡒⢑⣼⣿⣿⢠⣦⡄⡈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⠀⠀⠄⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠠⠀⠀⢠⡄⠀⠉⠁⠿⠟⣿⣿⡄⠲⡿⡿⠺⢶⡖⠠⠌⣉⠛⠿⢿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀
⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠯⣄⠺⣦⣑⡄⡐⡤⠂⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠰⣴⢀⣱⣦⣶⣸⠋⠀⠈⠋⠲⠠⢌⣉⣉⣛⠻⢿⣿⣿⣿⣶⡀
⠁⠀⠀⠀⠀⠀⠀⠀⢀⡐⣀⠀⠀⠀⠀⠀⠈⠈⣠⠲⠆⢆⡇⡰⠀⠀⢀⠀⡠⣀⢀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠐⠀⠈⠻⠃⠀⠘⠸⢾⠷⢯⡧⣴⣲⢶⣷⣄⣀⠀⠀⠀⠹⠋⣳⣯⣼⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢓⣒⢾⣶⡄⢠⢤⣤⣀⠀⠈⠙⢝⡓⢀⠁⠠⠀⠀⠀⠀⠚⠒⣴⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⠀⢀⠀⠀⠀⠄⠀⠀⠀⠈⠉⠙⠋⠼⠿⠥⠝⢟⢲⡠⠤⢄⣀⠀⡀⠀⠉⠉⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⠹⢟⡁⢞⡟⣻⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠄⣰⡂⣄⠀⠀⠀⢸⡇⠲⡦⣔⣀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠟⢽⡢⡄⠁⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠸⣷⣾⠟⠋⠛⠛⠛⠛⠷⠦⠀⠀⠀⠚⢄⠟⠐⠂⠀⠸⠇⠀⠀⠂⠙⠓⠀⢠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀
⠿⣷⣢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⡀⠀
⡀⠈⠙⠻⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣾⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣐⢀⣀⢀⠀⠁⠙⠻⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠓⠃⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣽⣿⣿⣿⣿⣿⣧⣦⣀⡀⠀⠀⠀⠀⠀⠈⠃⠘⠀⠀⠀⠀⠀
⠀⢌⢅⣨⣐⠀⠠⡄⠈⠙⢿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠀⠩⣀⠀⠀⠀⡂⠠⡀⠈⠙⢿⣿⣿⣿⣿⣷⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠂⠒⠒⠶⣤⣤⣀⡀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣄⠈⠂⠙⣟⡙⣳⢴⣢⣀⣈⠙⢛⢿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠻⢿⣷⣦⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣥⣬⣀⢛⣛⣁⣃⣛⡛⢛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢟⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢡⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢸⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣾⣿⣿⣿⡇
⠿⠛⠛⠋⠉⡉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡧⠤⠄⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⢿⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣽⣿⣿⣿⠿⠟⠃
⣴⠯⡧⡯⠣⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡭⣻⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡉⠂⠀⠀⠀⠀⠘⠛⠶⣾⠧⠆⠀⣀⣤⡌⢉⣉⣀⣈⠛⠛⠋⡁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⢯⣙⢣⣕⠩⣺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠉⣡⣤⣤⣤⡈⠉⣤⣀⣉⣉⠙⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣟⣟⣍⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠼⣲⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⢾⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣭⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢷⣼⣿⣿⠿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⡧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠓⢂⣀⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣦⣼⣿⣷⣶⣶⣿⣷⣿⣶⣬⣩⣭⣶⣶⣭⣽⠄⠛⠛⣤⣝⡻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣿⠿⢻⣿⣿⣿⣿⣟⣿⣟⣭⣭⡹⣿⣿⣿⣿⣿⣷⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⢿⠏⢯⠷⠿⠛⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⡏⠈⣿⣼⣿⣿⣿⣿⣣⣾⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⡻⣿⣿⢿⣿⣿⣿⡟⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⣿⣿⣿⣮⡫⣿⣿⣿⣿⣿⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣶⣽⣿⡿⣿⣷⣝⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣇⣂⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣝⡿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⢱⣿⣿⣿⠀⠀⣾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⣾⣿⣿⣿⠀⢠⣿⣿⣿⡇⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢿⣿⣿⡏⠀⢸⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠠⠊⠄⠁⡀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣾⡏⠄⠀⡠⠊⡁⠊⣀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⣿⡇⠀⠘⠖⠂⣠⠊⣠⣐⣀⣀⠀⢠⣾⣿⣿⣄⣀⠀⠀⠀⢸⣿⣿⣿⣿⡅⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠒⡀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠖⠀⢿⣷⣄⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣬⡛⢿⣿⣿⣿⡄⠀⣸⣿⣿⣿⣿⣀⣿⣿⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠘⠃⠀⠀⡼⣿⣿⣿⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠦⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣼⣿⢻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠊⢹⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠘⢻⢸⣿⣿⣿⣿⣿⣿⣿⣭⢉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⣙⠛⠿⠿⣿⣿⣿⡜⢠⣷⣶⣿⣿⣿⣽⣿⡿⡿⣿⣟⡛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠒⠀⢤⠍⢡⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⡀⠀⠀⠀⠀⠀⣾⡇⠁⠒⢢⠠⠌⣉⡙⠛⠿⠻⠛⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠠⠄⣾⣿⣧⣤⠀⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠈⠉⠛⠣⣃⠉⢀⣨⣴⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠡⠽⡿⣯⣶⣶⣶⠀⠀⠀⢸⡇⢴⣿⣦⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠁⠛⠀⠀⠀⣿⣿⠘⢿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣸⣿⣿⠀⠀⣀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠻⠋⣿⣿⡆⠀⠀⠁⠁⠂⠀⠀⠈⡉⠛⠻⠿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⣉⠉⠛⠛⢛⠿⣿⣷⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠁⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⣈⡁⣏⡹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⣀⣀⡴⠠⠄⣤⡄⡀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠃⠂⠔⢖⠘⣻⢹⢳⢴⣤⣄⡀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠲⡳⠚⠐⠉⠋⠙⠛⠳⠦⠀⠀⠀⠀⠄⠂⠚⠀⠀⠸⠇⠀⠐⠈⠈⠐⠐⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠑⣶⣂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠻⢶⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⢤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠈⠛⠛⢻⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠐⠋⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣤⣿⣿⣿⣿⣿⣿⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣧⣤⣠⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⡄⢹⣛⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣷⣦⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠖⣦⡄⣀⠀⠐⠶⣭⣿⣿⣾⣍⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⡻⣿⣷⣤⣀⠀⠀⠐⠣⠉⠃⠀⢄⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢹⢶⣦⣌⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣥⣬⣀⢛⣛⣁⣁⣛⡛⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢛⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢡⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢴⣿⣿⣿⣿⠿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣶⣿⣿⣿⡇
⠟⠛⠛⠋⠉⡉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣗⣭⣿⣿⣿⡧⠤⠄⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⢿⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢻⣯⣽⣾⣿⣿⠿⠟⠃
⠔⢫⠟⠷⢼⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡭⣻⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡉⠂⠀⠀⠀⠀⠘⠛⠶⣾⠧⠆⠀⣀⣤⣌⢉⣉⣀⣈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⢸⣷⣄⡚⡿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⢠⣶⣶⣶⣦⠉⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣮⣷⣻⣍⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠸⣸⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢴⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣭⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢓⢿⣽⣿⣿⠿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⡧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠓⢂⣀⣈⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⢶⣦⣾⣿⣷⣶⣾⣿⣷⣷⣶⣬⣩⣭⣶⣶⣭⣽⡄⠛⠛⣤⣝⡻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣵⣿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣭⣭⡹⣿⣿⣿⣿⣿⣷⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠛⡭⠾⠿⠛⠋⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⡏⠈⣿⣼⣿⣿⣿⣿⣳⣾⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠿⠿⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⠻⣿⣿⢿⣿⣿⣿⡏⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⣿⣿⣿⣮⡫⣿⣽⣿⣿⣿⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣶⣽⣿⣿⣿⣷⣝⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣺⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣝⡿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⢱⣿⣿⣿⠀⠀⣾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⣾⣿⣿⣿⠀⢠⣿⣿⣿⡇⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠿⣿⣿⡏⠀⢸⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠠⠊⠤⠁⡀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣾⡏⠄⠀⡠⢂⡡⠊⡡⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣫⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠪⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⣿⡇⠀⠸⠖⠊⣠⠊⣠⣐⣀⣀⠀⠠⣾⣿⣿⣄⣀⠀⠀⠀⢸⣿⣿⣿⣿⡀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠈⠂⠤⠤⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⠖⠁⢿⣷⣄⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣬⡛⢿⣿⣿⣷⡄⠀⣸⣿⣿⣿⣿⣀⣿⣿⠅⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠘⠃⠀⠀⡼⣿⣿⣿⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣼⣿⢻⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠊⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠘⢹⢸⣿⣿⣿⣿⣿⣿⣯⣯⢉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⡙⠛⠿⠿⣿⣿⣿⡌⢠⣷⣶⣿⣿⣿⣽⣿⡿⡿⣿⣟⡙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠈⠑⠒⠀⠠⠍⢡⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠁⠰⢢⢤⠌⣉⡙⠛⠿⠻⠋⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠠⠠⣿⣿⣦⡠⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠈⠉⠛⠃⢀⠉⢀⡀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠙⠾⡿⣯⣶⣶⣶⠀⠀⠀⢸⡇⢤⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⠁⠛⠀⠀⠀⣾⣿⠈⢿⢿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣸⣿⣿⡀⠄⢀⡈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠻⠋⣿⣿⡆⠀⠀⡐⠈⠀⠀⠀⢈⠉⠛⠻⢿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠄⢀⡉⠉⠛⠛⠿⣿⣿⣶⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠛⠁⠀⠀⠂⠉⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣐⣞⣉⠙⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⣅⣠⠄⠤⢤⢄⡀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠴⠁⠊⡈⡇⢉⡟⡽⣶⣤⣀⡀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢸⡇⠀⠀⠤⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡷⠛⠘⠂⠛⠊⠛⠳⠆⠀⠀⠀⠂⠄⠒⠀⠂⠀⠸⠇⠀⠁⠀⠉⠁⠐⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠱⡴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠻⣷⣷⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢀⢤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣶⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠈⠙⠻⢿⣵⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠑⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⢄⠹⡻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠖⣦⡄⢀⡀⠒⠦⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣷⣤⣀⠀⠀⠂⠖⢒⠈⠀⣄⡀⠀⠛⠙⢿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣲⣦⣀⠙⠻⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣋⣛⣛⠿⣟⡛⠛⠛⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣿⣿⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⠛⣋⣉⣙⣛⡛⠛⠛⠿⠿⠿⠟⠿⠿⠿⠿⠛⠫⠭⢙⣟⣿⣽⣯⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⠿⢿⣟⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣆⢸⣿⣿⠿⠇⢈⣭⣤⣴⠶⣾⣿⣽⡇
⠟⠛⠛⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣫⣵⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠑⡁⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡉⠛⢋⣉⣀⡀⠀⠀⠀⠈⠛⠛⠀⠠⠀⠀⠀⠀⣀⣠⠈⠉⢉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣽⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣀⣉⠁⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠘⢠⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠢⢀⡂⣼⣿⣿⣿⣿⣿⣿⣿⣟⡆⠀⢀⣿⣿⣿⣿⡃⠀⣿⣿⠀⣿⣿⠎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠞⢙⢼⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁⠀⢸⣿⡿⠿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣃⢣⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⢀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⠶⣶⣿⣾⣷⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠴⠿⠿⠿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣽⣵⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⠄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉⠠⠐⠚⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣻⣛⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⣿⣿⣿⣿⣿⡿⠿⣛⣩⠵⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⢟⣛⡻⣷⣿⣿⣿⣿⣿⣵⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠿⠗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⢏⣭⣭⢻⣿⣽⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣜⣛⣫⣿⣿⣿⣿⣿⣿⢼⣀⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⡻⣿⡿⣿⣿⣿⣿⣿⣮⡛⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⢛⣭⣭⡍⠉⠉⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⣼⣿⣿⡇⠀⠀⣿⣿⣷⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠙⠿⠿⠃⠀⢸⣿⣿⡿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡄⣺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣾⡷⠊⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣄⣀⣤⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⢊⡡⢿⣿⣎⡐⣁⣤⣶⣶⣶⣾⣿⣶⣶⣶⣭⡙⠿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣟⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠋⠀⢞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠻⢿⣿⡟⣼⣿⣿⣿⣿⣷⣿⡇⣿⠁⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠻⠀⠀⣴⡏⢠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⡇⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠀⠀⠀⠀⠧⢃⠞⠁⠀⣿⣷⣷⣮⡻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠁⣜⡆⠀⡟⣿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢠⡄⠉⠁⠀⣷⠀⠉⠙⠻⠿⣿⣿⣿⡇⠀⣾⣿⣿⣟⣿⣟⣟⢿⣿⣿⣿⣏⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠉⢁⠀⠿⢿⣿⣿⣿⣿⣿⣷⣯⣩⣽⣿⣷⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠬⠉⠛⠻⠿⢿⠿⠟⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣧⣤⣄⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠘⠿⠟⣿⣿⣿⣷⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠀⠀⢀⠈⠉⠛⠻⢟⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣻⣧⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠑⠚⠷⢦⣄⣠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣦⣀⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣬⣿⣿⣿⣿⣷⣧⣄⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⣀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠦⣟⣷⣦⣀⡋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⢀⠀⠀⠀⠀⠀⠀
⠓⠱⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠛⢫⣿⣿⣯⣦⣌⣘⣿⣿⣿⢿⣿⣿⡿⣿⣏⢏⡐⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣋⣛⣛⠿⣟⡛⠛⠛⠿⠿⠿⠿⣿⣿⢿⣷⢼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡄⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣭⣭⣭⣙⢛⣉⣉⣙⣛⡛⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠛⠫⠭⢙⣛⣿⣽⣯⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⠰⣿⣿⣿⣿⡿⠿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣩⣤⣴⡶⣾⣿⣭⡄
⠟⠛⠋⠉⠉⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⢡⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠰⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⠛⣩⣵⣶⣿⡿⠿⠟⠃
⠄⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠉⡁⢈⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠀⢀⣀⣀⡈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡈⠉⠉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⣸⣿⣿⣿⠀⣿⣿⠀⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠁⣤⣀⣀⣉⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣏⠀⠘⢠⣿⣿⣿⡇⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠅⠐⠀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⢀⣿⣿⣿⣿⠇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⠀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢅⠠⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⡿⠟⠁⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢠⣾⣄⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠨⢳⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⣀⣀⣀⣤⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⠙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠠⠾⠿⢿⣿⣟⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣭⣶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⣿⣿⣿⣿⠿⣿⢟⡋⠥⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠟⠯⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣭⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⡻⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣮⣻⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠆⡹⣿⣿⣿⣿⣿⣿⣿⣿⡫⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣇⣇⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣭⣭⣭⣷⣿⣿⣿⣿⣮⢿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⣀⣄⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣄⣡⣤⣴⣶⣶⣶⣤⣤⣍⡛⠿⢿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣋⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⣿⣿⡿⢿⣿⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⡛⠿⢡⣿⣿⣿⣿⣿⣿⣷⣿⣷⡏⠁⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠈⠉⡀⠀⠔⠀⢠⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠁⠀⢀⡔⠋⠀⠀⢡⣼⣿⣾⣟⣛⣛⡻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⠀⢶⠀⠀⠀⢠⢶⣀⣴⠟⠀⣄⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣮⡛⠻⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠁⠀⠀⢸⠀⠀⠉⠛⠻⠿⣿⣿⣇⠀⣾⣿⣿⣯⣛⣛⣛⣿⣿⣿⣿⣏⡻⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣷⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠠⠈⠙⠛⠿⣿⣿⡟⣿⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⣤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠻⢿⢿⣿⣾⣧⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢀⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠲⠕⢠⣠⡤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣤⣿⣿⣿⣿⣷⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⡀⠀⠙⠻⣿⣿⣿⣿⣷⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣕⣮⣤⡄⢉⣻⡟⢿⣿⣿⣿⣿⣿⣿⣷⡶⠠⠀⠀⠀⠀⠀⠀⠀
⠋⠺⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⢖⢢⣾⣾⡾⣿⣿⣿⣿⣿⣿⣯⣖⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣙⣛⣛⠿⣟⡛⠛⠛⠿⠿⠿⠿⣿⣿⢻⣷⢼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣬⣭⣭⣙⠛⣉⣉⣙⣛⡛⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠍⢙⣻⣿⣽⣯⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢠⣿⣿⣿⣿⡿⢿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣆⢸⣿⣿⠿⠇⢈⣭⣤⣴⢶⣾⣿⣭⡅
⠟⠛⠛⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠰⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣉⣵⣶⣿⡿⠿⠟⠃
⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠉⡁⢨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠀⢀⣀⣀⡈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠈⠉⠉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣸⣿⣿⣿⠀⣿⣿⠀⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⢠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠁⣤⣀⣀⣉⠑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢠⣿⣿⣿⡇⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡒⠀⠂⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣓⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⠀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡂⠨⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⢸⣿⣿⠿⠟⠂⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢠⣿⣄⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⢄⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣬⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⠙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣖⠠⠾⠿⢿⣿⣿⣋⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣭⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠉⠀⠐⠀⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⣿⣿⣿⣿⡿⡿⢟⡋⠴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠟⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣭⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⡻⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣮⣻⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠆⣹⣿⣿⣿⣿⣿⣿⣿⡿⣫⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣧⣇⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣭⣭⣭⣿⣿⣿⣿⣿⣮⢿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⣀⣄⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣔⣡⣤⣴⣶⣶⣶⣤⣤⣝⡛⠿⢿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣋⡀⣿⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⣿⣿⡿⢿⣯⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⡛⠿⢣⣿⣿⣿⣿⣿⣿⣷⣿⣷⡟⠁⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠈⠉⡀⠀⠔⠀⢠⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠀⠀⠁⠀⢀⡴⠋⠀⠀⢡⣼⣿⣾⣟⣟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⠀⢶⠀⠀⠀⢠⢶⣀⣴⠟⠀⣄⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣮⡛⠿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠁⠀⠀⢸⠀⠀⠉⠛⠻⠿⣿⣿⣇⠀⣾⣿⣿⣯⣛⣛⣛⣿⣿⣿⣿⣏⡻⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠌⠁⠀⠻⠿⣿⣿⣿⣿⣿⣿⣮⣍⣿⣿⡷⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠨⠙⠛⠿⣿⣿⣟⣿⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⡧⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠐⠻⢿⢿⣷⣷⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠉⠛⠹⢿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠾⢾⣿⣿⣽⡆⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢀⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠻⠆⢠⣄⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣦⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣬⣿⣿⣿⣿⣿⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⠀⠈⠁⠹⣿⣽⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⣦⣤⣄⠈⣻⠿⣿⣿⣿⣿⣿⣿⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠋⢘⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣷⣶⡯⡢⢲⣟⣿⣿⣿⣿⣿⣾⣯⡷⡆⢂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣉⣙⣋⣛⡛⢟⠁⠻⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣬⣴⣿⣾⣿⣿⡇
⠿⡛⢛⣋⣉⡭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠤⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢠⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣯⣿⣿⣿⣿⠿⠟⠃
⣾⣿⣟⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡑⠲⠒⠀⠀⠀⠀⠀⠀⠚⠿⣷⣶⡆⣮⣌⣉⣉⣀⣈⠛⠛⠛⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠘⣡⣤⣤⣤⡈⠉⣥⣀⣉⣉⠛⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢀⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢊⣀⣈⣁⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣇⣨⣉⣩⣰⣆⣍⣽⣄⡛⠛⣀⡙⡻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣯⣀⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣴⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡿⠿⠿⠛⠋⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⢿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣛⣛⣛⣻⠿⢿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠎⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⢱⣾⣿⣶⣶⣿⣿⣿⣛⣒⢭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡏⠙⣹⣿⣿⣿⡇⠋⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⡸⢿⣿⣽⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⣔⠁⡠⠀⡠⠂⣴⡎⠉⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠎⠉⠈⠰⠊⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠠⠔⠋⠥⠀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠠⠊⠀⠀⡠⠒⠁⢀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⡉⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠐⣡⣴⣶⣶⣶⣦⣄⡐⢿⣿⣷⡀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠙⠖⠀⡄⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣆⠀⣸⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⡄⣿⣿⣿⣽⣿⡝⠀⠐⠐⠀⠀⠀⠀⠈⠙⠓⠶⠦⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠿⢟⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⢤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⡏⠉⠿⢿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡰⠂⡀⠀⠀⠀⠀⠀⠀⠀⣷⠈⣉⠛⠛⠿⠿⣿⣿⣿⠀⢰⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠠⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠁⠑⠒⠀⢤⠉⣀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡅⠀⠞⠁⠀⠀⠀⠀⠄⠀⠀⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⡄⠑⠐⠲⢦⠤⠉⢙⡛⠛⠛⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⣒⡵⡗⣶⡤⠘⣿⡇⠀⠀⢠⠀⠈⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠉⠑⠉⠆⠉⠀⠙⣿⣷⠇⠀⡀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠑⢝⣿⣶⢧⡆⠀⠀⠀⢸⡀⣴⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠀⠀⢠⣿⣿⠘⢿⣿⣿⣿⣿⣿⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡒⢐⣼⣿⣿⡄⣀⣀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⠻⠋⣿⣿⡇⠝⠩⠏⠊⠐⢀⠀⠄⡙⠛⠻⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢀⣿⡿⠀⠀⠐⠀⢀⢂⠄⠂⠀⠉⠉⠠⠤⢀⣉⡉⠛⠛⠿⣿⣿⣷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠈⠛⠁⠀⠀⠐⠶⢂⣙⢥⢴⠖⡐⣀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡭⣿⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣄⢄⢀⣠⢤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠋⠁⡉⠛⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠈⠰⠹⡛⢻⢲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠐⠋⠙⠛⠓⠆⠀⠀⠀⠲⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠡⣔⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠻⢿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⣀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣤⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠈⠘⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣴⣄⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡄⢙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣯⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⢤⠄⢀⡀⠘⠶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⣻⣿⣷⣦⣀⠉⠀⠀⠚⠛⠑⠐⡄⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⣶⣦⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣉⣙⣋⣛⡛⠛⠁⠻⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢴⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⣿⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣾⣿⣿⣿⡇
⠟⡛⡛⢋⢍⣭⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠄⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢠⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢻⣯⣿⣿⣿⣿⠿⠟⠃
⣾⣟⣾⢷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠒⠀⠀⠀⠀⠀⠀⠒⠿⣷⣶⣆⣮⣈⣉⣉⣀⣈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⡿⣿⣟⣷⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠘⣡⣤⣤⣤⡈⠉⣥⣀⣈⣉⠙⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣸⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠀⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢊⣀⣈⣡⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣇⢨⣉⣭⣰⣦⣍⣹⡄⡛⠛⣀⡙⡻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣱⣿⣿⣿⣿⣿⣯⣀⣿⣷⣿⣿⣿⣿⣿⣿⣶⣶⣴⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⢿⣿⡭⠿⠿⠛⠛⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠿⠓⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⢿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⢟⣛⣛⣛⡿⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⢱⣾⢯⣶⣶⣭⣿⡿⣛⣒⢭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡇⠙⢹⣿⣿⣿⡇⠋⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⡸⢿⣯⣽⡇⠀⣿⣟⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⣔⠁⡠⠀⡠⠀⣔⠌⠉⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠎⠉⠈⠠⠊⢀⠠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣠⠔⠊⠥⠀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠊⠀⠀⡠⠒⠁⢀⡠⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⡀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠈⠩⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠔⣠⣴⣶⣶⣶⣦⣄⡰⢿⣿⣷⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠖⠠⡄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⢿⣿⣿⣿⣆⠀⣸⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⣿⣿⣿⣽⣿⡜⠀⠐⠑⠀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠿⢟⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡶⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⡏⠈⠟⢿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡴⠂⡀⠀⠀⠀⠀⠀⠀⠀⣷⠈⢉⠛⠛⠿⠿⣿⣿⣿⠀⢰⣿⣷⣾⣿⣿⣿⡿⣿⣿⣿⣿⣹⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠑⠒⠀⢤⠉⢀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⡄⠑⠐⠂⠤⠀⢉⠙⡛⠛⠛⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⢒⠿⠇⣠⡄⠘⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠁⠉⠐⢄⠉⢀⠹⢟⡿⠁⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠍⢙⣾⣶⡐⣄⠀⠀⠀⢸⡀⣤⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠐⠀⠀⢠⣿⣿⠐⢿⣿⣿⣿⣿⣿⣿⣦⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡂⢐⣼⣿⣿⡄⢀⣀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⠻⠋⣿⣿⡇⠈⠫⠈⠉⠄⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⠀⠀⠀⠀⢀⣿⡿⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠉⠐⠀⠀⢉⡉⠛⠛⠻⣿⢿⣷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠈⠙⠁⠀⠀⠐⢑⡁⠑⢃⡲⢄⡐⢔⠂⠀⠀⠀⠀⠀⠑⠰⢜⡨⠛⠫⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠄⠀⠠⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠍⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⠊⢹⢿⣳⣖⣤⣄⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠛⠘⠋⠛⠛⠓⠂⠀⠀⠀⠂⠄⠀⠀⠐⠀⠸⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠡⡄⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠻⣷⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⢄⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠈⠒⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣷⣤⣀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⢠⠄⣀⡀⠒⠶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⢻⣿⣷⣤⣀⠈⠁⠙⠓⠓⠀⠐⣀⠀⠈⠙⠙⢻⣿⣿⣿⣿⣷⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢲⣦⣈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠉⠻⣿⠿⠇⠸⠿⣿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⠇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣨⣭⣥⣴⣷⣿⣿⣿⡇
⠿⡛⣛⣋⣭⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠤⠀⠉⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢠⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢻⣯⣿⣿⣿⣿⠿⠟⠃
⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣮⣭⡍⣤⠈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢩⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠈⣫⣭⣦⣬⡁⠉⣥⣀⣉⣉⠙⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡟⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⢹⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢉⣁⣈⣁⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣶⣶⣿⣾⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⠛⠛⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡽⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⣟⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⣟⣛⣛⣛⣛⣛⡿⢿⣿⣿⣿⣻⠿⢿⣛⣯⣿⣿⣿⣿⣿⣿⠋⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⣴⣿⢟⣛⡻⢿⣿⣿⣿⣿⣮⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣷⣿⣧⣶⣮⣝⢿⣷⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡴⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠠⣿⣿⣛⣿⠃⢸⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠛⠻⠿⠿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠜⠀⡔⢀⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⠂⡠⢊⡴⡇⠀⣠⠤⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⡿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡴⠣⢊⠔⢉⡽⠓⠉⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⠀⠀⠀⣇⣿⡟⢹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠠⠊⣠⠔⣡⠔⠁⠠⢀⠠⠊⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢺⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣿⠀⠀⡠⠊⠀⠀⢀⠐⠁⣠⡒⠉⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠠⠊⠀⠀⣀⢂⣡⣾⣿⣿⣿⣶⣄⡻⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠒⠗⠂⢄⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣜⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⢿⣿⣿⠀⠈⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣿⣷⣴⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣇⣿⣿⣵⣿⠟⠘⠉⠻⠀⠀⠀⠀⠈⠉⠓⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⡿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣋⣵⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠈⠟⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠈⠈⠊⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠿⠿⣿⣿⣿⣿⣧⠃⣼⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠪⠡⡡⢄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠑⠒⠦⠤⠉⡉⠋⡄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣮⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠢⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠨⠀⠈⢠⣿⠈⠂⢤⣍⣙⠛⠻⠿⢿⠿⠟⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣿⣷⠀⠀⠿⣿⢾⡼⣢⡄⢸⣿⠀⠀⠀⠰⠉⠈⠉⠒⠢⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠄⠀⠉⠙⠒⠿⢷⡄⠛⠠⣲⢶⢾⡀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠿⣯⣛⣻⣿⣿⣖⡇⠀⠀⠀⢸⠀⣸⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠉⠉⠙⠛⠂⠀⠀⢠⣿⣧⠹⢿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠉⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢲⡒⢀⣼⣿⣿⢀⢤⣄⡉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠃⠿⠟⣿⣿⠄⢙⠻⣿⠗⡖⠂⢠⢈⠙⠛⠻⢿⣿⣿⣿⣿⣿⢶⣄⠀⠀⠀⠀
⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⢆⣘⢔⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠡⠺⠆⣆⣵⣯⣯⠀⠁⠊⠛⠰⠤⡤⣉⡉⡛⠻⠿⡿⣿⣶⣦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠌⠀⡀⠁⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠸⠀⠀⠈⠻⠁⠀⠈⠺⣯⣿⣿⣿⣴⣶⣴⣴⣄⡀⠀⠀⠀⠀⠙⠶⢤⣽⡟⠹⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣐⣨⡶⡄⣤⣤⣤⣀⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠜⠿⠿⠧⠑⠭⣀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠴⠼⢓⢍⡖⢙⣻⢿⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇⠀⠠⢤⣀⢀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⠙⢾⡰⡂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡻⠟⠉⠛⠛⠙⠛⠳⠆⠀⠀⠀⠢⠴⠀⠀⠀⠀⠸⠇⠀⠀⠛⠁⠐⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠻⣽⣧⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢀⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣦⣦⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠀⠀⠀⠛⠻⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠈⠺⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣾⣿⣿⣿⣿⣿⣯⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠂⠀⠀⠀⠀⠀⠈⠙⠻⡿⣿⣿⣷⣶⣄⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡄⣙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠉⠁⣀⠀⠀⠀⠀⠠⠀⠀⠀⠙⣿⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣤⣤⣀⡀⠛⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⢿⣿⣷⣦⣀⠈⠃⠘⠛⠛⠁⡐⣄⡀⠈⠙⠳⣽⣿⣿⣿⣿⣿⣿⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠍⠺⢶⣤⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣭⣭⣀⢘⣛⣁⣋⣛⡛⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⠇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢡⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢸⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣶⣾⣿⣿⡅
⠟⣛⠛⣋⣍⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠤⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⢿⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣽⣾⣿⣿⠿⠟⠃
⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣩⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡑⠂⠀⠀⠀⠀⠘⠻⠶⣾⠣⠆⢀⣀⣠⣌⢉⣉⣄⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠀⠀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠉⣡⣤⣤⣤⡈⠉⣥⣀⣈⣉⠙⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣭⡄⣿⣿⡇⣿⣿⡇⣿⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣽⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⡇⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⢊⣀⣈⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣦⣼⣿⣷⣶⣶⣿⣵⣶⣶⣬⣩⣭⣴⣦⣍⣭⠄⠛⠛⣤⣙⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣻⣿⣿⡿⠿⢃⣿⣿⣿⣿⣿⣿⣟⣭⣬⡙⣿⣿⣿⣿⣿⣷⠿⠿⢷⣮⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣛⠹⠿⠿⠛⠋⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠈⣿⣼⣿⣿⣿⣿⣣⣾⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠽⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢛⡻⣾⣿⣿⣿⣿⣿⣯⣿⡇⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣮⡋⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢺⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣶⣭⣿⣿⣿⣧⣍⣉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣝⡻⢿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠋⢱⣾⣿⣿⠀⠀⣬⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⣾⣿⣿⣿⠀⢠⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠿⣿⣿⡏⠀⢸⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠊⡔⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣼⣇⠀⠀⡠⠊⠀⠈⠀⠄⠈⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣿⡇⠀⢘⠆⠀⣠⠀⣠⣆⣀⣀⡀⢠⣾⣿⣿⣄⣀⠀⠀⠀⢸⣿⣿⣿⣿⠇⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠹⠅⠠⢀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡠⠖⠁⢿⣷⣄⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣮⡛⢿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣁⣿⡿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠝⠀⠘⠃⠀⠀⡸⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣭⣭⣼⣿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠻⢦⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠟⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢻⢸⣿⣿⣿⣿⣿⣿⣿⣭⢉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⠀⠉⠙⠛⠿⠿⣿⣿⣿⡌⢠⣿⣿⣿⣿⣿⣽⣟⣿⡿⢿⣿⡛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠈⠈⠒⠀⠨⡉⢱⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⣀⡀⠀⠀⠀⠀⣾⡇⠈⠀⠂⡤⠬⠉⠙⠛⠟⠿⠛⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⢝⢷⢻⠀⠰⠀⣿⡇⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠈⠐⠀⢡⠈⠀⢀⠖⡴⡆⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠈⠝⠋⠿⣷⣷⡆⡀⠀⠀⠀⢸⡇⢀⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣿⣿⠨⢿⢿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⢀⣀⢀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠋⣿⣿⡂⠘⠟⠡⠉⠄⠀⠄⠈⠉⠛⠻⢿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⣿⣿⠀⠢⠀⠀⠂⠀⡈⠀⠀⠀⠁⠖⠀⠄⢉⣉⡛⠛⠿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠀⠀⠀⠓⠒⠂⠘⠕⣣⠔⠠⠀⠀⠀⠀⠀⠀⠀⠈⠲⠢⢙⣙⡋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣅⠀⢀⠠⠠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⠅⠺⡟⠓⡲⣤⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠂⠒⠋⠙⠛⠓⠆⠀⠀⠀⠀⠐⠈⠀⠀⠀⠸⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠡⣤⢆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠻⠾⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⢄⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣔⣠⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠈⠘⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣯⣾⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣥⣴⣤⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⢄⡉⠻⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⡄⢀⡀⠐⠾⣿⣿⣿⣽⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⡻⣿⣷⣤⣀⠀⠀⠘⠋⠛⠀⠀⣄⠀⠈⠙⠛⣿⣿⣿⣿⣿⣷⣲⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⣦⡈⠙⠻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣬⣀⢘⣛⣁⣁⣛⡛⢛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢟⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢡⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢴⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣻⣿⣿⢡⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣾⣾⣿⣿⡇
⠿⠛⠛⠋⢉⡉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣪⣿⣿⣿⡧⠤⠄⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⢿⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢻⣻⣿⣿⣿⣿⠿⠟⠃
⢶⣏⠦⠍⣸⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣩⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡙⠛⢋⣉⣉⡑⠂⠀⠀⠀⠀⠘⠻⠶⣾⠣⠆⢀⣀⣠⣌⠉⣉⣄⡈⠛⠛⠋⠁⠘⠛⠻⠿⠃⠘⠛⠋⠉⠁⠀⠀⠀⠀
⢣⣥⣳⡍⠖⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠉⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣮⣿⢯⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠽⣸⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⢼⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣭⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⢿⣸⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⡧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢈⣀⣀⣁⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣶⣾⣿⣵⣶⣶⣬⣩⣭⣴⣦⣭⣭⠄⠛⠛⣤⣝⠻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⢿⣿⣿⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣭⣬⡙⣿⣿⣿⣿⣟⣷⠿⠿⢷⣮⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣤⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⠽⠿⠿⠛⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⡏⠈⣿⣼⣿⣿⣿⣿⣣⣾⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠿⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⡻⣾⣿⣿⣿⣿⣿⡏⣿⡇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣮⡋⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣶⣽⣿⣿⣿⣧⣍⣉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣝⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠋⢱⣾⣿⣿⠀⠀⣾⣭⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⣾⣿⣿⣿⠀⢠⣿⣿⣿⡇⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠿⣿⣿⡏⠀⢸⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢊⠔⠁⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣼⣇⠀⠀⡠⠊⠡⠊⢀⠄⠈⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣿⡇⠀⢘⠆⠀⣠⠀⣠⣆⣀⣀⠀⢠⣾⣿⣿⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⡅⣺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠚⠥⠄⣀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠔⠁⢿⣷⣄⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣮⡛⢿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣃⣿⣿⠁⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠝⠀⠘⠃⠀⠀⡸⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣭⣭⣼⣿⢿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠋⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⢹⢸⣿⣿⣿⣿⣿⣿⣿⣯⢉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⠀⠉⠙⠛⠿⠿⣿⣿⣿⡌⢠⣿⣾⣿⣿⣿⣭⣿⣿⡿⠿⣿⡛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠒⠂⠨⡉⢱⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⣀⠀⠀⠀⠀⠀⣾⡇⠘⠐⢠⠠⠌⠉⠙⠛⠛⠿⠛⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠈⢟⣿⣿⣄⡠⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⡇⠀⠀⠀⠉⠉⠙⠁⠈⢀⢂⣴⡺⣄⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠳⠟⠯⣻⣿⣵⢢⠤⠀⠀⠀⢸⡇⢠⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠁⠀⠀⠀⣿⣿⠈⢻⣿⣿⣿⣿⣿⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠻⠋⣿⣿⡆⠀⠀⠐⠁⠠⠀⢄⠈⠉⠛⠻⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⢀⠉⠉⠛⠛⠿⣿⣿⣷⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠈⠀⠀⠀⠀⠐⡀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠖⠢⠘⣉⢙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢄⣄⣠⣀⠠⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢢⠠⡐⡝⠨⢻⡷⣶⣤⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠠⠄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠍⠠⠉⠛⠛⠚⠙⠛⠓⠆⠀⠀⠀⠠⠄⠀⠀⠀⠀⠸⠇⠀⠀⠀⠉⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠩⣴⢦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠻⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠠⢤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠀⠀⠀⢀⠀⠁⠉⢿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠙⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣴⣤⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡀⡙⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣾⣢⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢦⡄⣀⡀⠐⠾⣿⣿⣿⣶⣷⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀
⡻⢻⣷⣦⣀⠀⠀⠑⠋⠋⠃⡀⡠⢄⠈⠙⠙⣿⣿⣿⣿⣿⣷⣆⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢹⢶⣤⡈⠙⠻⣿⣿⣿⣿⣷⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣋⣛⣛⠿⣟⡛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⢛⣉⣉⣙⣛⡛⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠝⢛⣿⣿⣯⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢸⣿⣿⣿⣿⠿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣽⡅
⠟⠛⠛⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣥⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣽⣶⣿⡿⠿⠟⠃
⠀⠁⠀⠀⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⡍⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡙⠛⢋⣉⣀⡀⠀⠀⠀⠈⠛⠛⠀⠠⠀⠀⠀⢀⣀⣠⡈⠉⢉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠉⣡⣤⣤⣤⡈⠉⣤⣀⣀⣉⠙⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⡀⢀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠘⢰⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡒⢃⣒⢓⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢀⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⣸⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣲⣾⣵⣿⣿⣿⣿⣿⣿⡿⠿⠟⠓⠀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣃⡌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡷⠿⠿⢿⣿⣿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣋⣭⣷⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠋⠉⠂⠓⠒⠊⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⡿⠿⣟⣉⠭⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣟⣙⡻⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡛⠯⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⢀⣿⣿⣿⣿⣿⣿⣿⢏⡭⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣝⡛⣻⣿⣿⣿⣿⣿⣿⢾⣀⣼⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⡻⣿⡿⣿⣿⣿⣿⣿⣎⡛⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⢛⣭⣭⡍⠉⠙⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠋⠀⠀⣼⣿⣿⡇⠀⠀⣿⣿⣷⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠛⠿⠿⠇⠀⢸⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡄⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣾⣧⠂⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡄⣀⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⢊⡥⢿⣿⣄⡀⣀⣠⣶⣶⣶⣾⣿⣿⣶⣶⣭⣛⠿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣛⢻⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡰⠋⠀⢞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣿⡇⣼⣿⣿⣿⣿⣷⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⠀⠻⠂⠀⣴⡏⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠢⠄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠥⢋⠔⠁⠈⣾⣿⣿⣾⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠁⣜⡆⠀⣟⣿⣿⣿⣿⣿⣿⣷⣽⠻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠃⢰⡆⠉⠁⠀⣿⠀⠉⠙⠛⠿⣿⣿⣿⡇⠀⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⢇⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠂⠀⠀⠉⢁⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠠⠈⠉⠛⠛⠿⠿⠿⠿⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠛⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠂⠈⢠⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⣤⣠⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠈⢻⠿⣿⣿⣿⣿⣶⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠀⢀⠀⡈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣡⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠿⠗⣰⣶⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣆⢤⡤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣯⣼⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⢀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣷⣦⣼⣊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣀⡀⠀⠀⠀⠀⠀
⡋⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣾⣯⣯⣧⣵⡩⣟⢻⣿⣿⣿⣿⣿⣶⣯⠐⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⢿⣿⣿⣿⡟⣿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⢛⣋⣉⣙⣛⡛⢛⠛⠿⠿⠿⠻⠿⠿⡿⠿⠛⠫⠍⢙⣟⣿⣽⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢸⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣽⡅
⠟⠛⠛⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⢠⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣏⣽⣾⣿⡿⠿⠟⠃
⢄⠁⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠛⡅⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡙⠛⢋⣉⣀⡀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⢀⣀⣠⣈⠉⢉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⢀⢀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢰⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⡽⢤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡫⠁⢀⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠞⠋⠄⢸⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⢀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣃⡌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡯⠿⠿⢿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣋⣽⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠀⠗⠒⠋⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⢟⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⡿⣿⢛⣫⠭⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⢟⣙⡻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠏⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⢀⣿⣿⣿⣿⣿⣿⣿⢏⡭⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠝⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣿⣝⡛⣋⣿⣿⣿⣿⣿⣿⢾⣀⣼⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣛⡻⣿⡿⣿⣿⣿⣿⣿⣎⡛⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⢻⣭⣭⡍⠉⠙⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠋⠀⠀⣼⣿⣿⡇⠀⠀⣿⣿⣷⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠛⠿⠿⠇⠀⢸⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡄⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣾⡧⠂⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣄⣀⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⢞⡥⢿⣿⣄⡀⣀⣠⣶⣶⣶⣾⣿⣿⣶⣶⣬⣛⠿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣛⢻⣿⡇⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡰⠋⠀⢞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿⡿⣼⣿⣿⣿⣿⢷⣿⡇⣿⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠻⠂⠀⣴⡏⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⢤⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠥⢋⠔⠁⠈⣾⣿⣿⣾⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠁⣜⡆⠀⣟⣿⣿⣿⣿⣿⣿⣷⣽⡻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠃⢠⡆⠉⠁⠀⣿⠀⠉⠙⠛⠿⣿⣿⣿⡇⠀⣾⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⢇⡻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠠⠌⠉⠛⠛⠿⠿⠿⠿⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠂⠀⠀⠀⠐⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⢸⡇⠠⢧⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣾⣷⠘⠿⢿⣿⣿⣿⣷⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣼⣿⣿⠀⠀⡀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣽⡵⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠺⢽⣶⣶⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣶⣠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠂⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⡀⠉⠑⠿⣿⣟⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⣮⣷⣷⣦⣶⣞⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀
⠛⡻⣷⣦⡀⠀⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠛⢿⣿⣾⣽⢚⣲⡿⣿⢿⠮⣷⣿⣿⣿⣿⣦⣗⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣛⣛⠿⣟⡛⠛⠛⠿⡿⠿⠿⣿⣿⢻⣷⣴⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣭⣭⣭⣙⠛⣉⣉⣙⣛⡛⠛⠛⠻⠿⠿⠻⠿⠿⡿⠿⠛⠫⠭⢙⣟⣿⣽⣽⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠈⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⠰⣿⣿⣿⣿⡿⢿⣟⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⢶⣾⣿⣭⡅
⠟⠛⠛⠉⠉⠉⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⢠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⢁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⠛⣯⣵⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠋⡁⣈⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠀⢀⣀⣀⡈⠛⠛⠋⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣀⡈⠉⠉⡀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣸⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡀⠉⣤⣀⣀⣉⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢀⣿⣿⣿⡇⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⠙⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⠀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⢭⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⢐⣿⣿⠿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢠⣾⣄⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠠⣶⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⠙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⡢⠾⠿⢿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣩⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠀⠀⠒⠋⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⡿⠿⢛⡉⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠿⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣭⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⡛⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣮⣻⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⣻⣿⣿⣿⣿⣿⣿⢿⣿⣋⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣷⣿⣿⣿⣿⣿⣿⣿⣗⣇⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢨⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣯⣿⣽⣾⣿⣿⣿⣿⣮⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣿⣿⠿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⠀⣠⣤⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣀⢀⣀⣠⣤⣴⣶⣶⣶⣦⣤⣍⣙⠿⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣻⡁⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠙⣿⣿⠿⢿⣿⣍⣭⣭⣿⣿⣿⣿⣿⣿⣿⣶⣬⣍⠛⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡈⠋⡀⠀⠔⠁⣠⡴⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⠄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡔⠁⠀⠀⠁⠀⢀⡴⠋⠀⠀⢡⣴⣿⣾⣟⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢀⠀⣶⠀⠀⠀⢠⢶⣀⣴⠟⠀⣄⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣮⡙⠿⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠉⠀⠀⢸⠀⠀⠉⠙⠻⠿⣿⣿⣇⠀⣾⣿⣿⣯⣛⣛⣛⡿⣿⣿⣿⢏⡻⠿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⢀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⢿⣿⣿⣿⣿⣿⣿⣮⣝⣿⣿⡷⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⣿⠄⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠛⠿⢿⣿⡯⣿⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠐⠀⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠠⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡇⠀⢦⣴⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣿⣿⠐⠻⢟⣿⣿⣿⣷⣶⣤⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⢀⠀⠉⠋⠻⢿⣿⣿⣿⣿⣷⡦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣟⣿⣿⣥⣡⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢠⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠉⠾⠴⢤⣶⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣢⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣮⣻⣿⣾⣿⣿⣵⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⠀⠈⠈⢹⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣽⣧⣴⢠⣍⡻⣿⣿⣿⣿⣿⣿⣟⣷⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀
⠘⠩⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣞⡘⣎⣟⠿⡟⣿⣽⣿⣿⣿⣯⡆⢃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣋⣛⡛⢟⠃⠹⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣽⣤⣴⣿⣿⣿⣿⡇
⠿⡛⡛⢋⣩⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠄⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢠⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣽⣿⣿⣿⠿⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠒⠒⠀⠀⠀⠀⠀⠀⠚⠿⣷⣶⣆⡆⣈⢉⢉⣤⣈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠘⣠⣤⣤⣤⡈⠉⣥⣀⣈⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣸⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠀⣾⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠓⢊⣀⣈⣁⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣾⣿⣿⣿⣃⢨⣉⣩⣰⣆⣍⣹⡄⣛⠛⣠⡙⡻⠿⠟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢛⣫⣿⣿⣿⣿⣿⣇⢀⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡭⠿⠿⠛⠋⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣾⣿⣿⣟⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠿⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⢿⣛⣛⣛⠻⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⢱⣿⢯⣶⣶⣍⣿⣿⣛⣒⢯⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠙⣾⣿⣿⣿⣿⣧⣿⣿⣿⡞⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡇⠙⣸⣿⣿⣿⡇⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠸⢿⣯⣽⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣰⠀⡠⠀⡠⠀⣴⡌⠉⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠄⠉⠀⠀⠊⢀⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣠⠔⠈⠤⢀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠊⠀⢀⡠⠞⠁⣀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡋⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣥⣺⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠣⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⣡⣴⣶⣶⣶⣦⣄⡐⣾⣿⣷⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠻⠲⠠⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⣆⠀⢸⣿⣿⡿⡿⣿⡯⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⡄⣿⣿⣿⣿⣿⡝⠀⠀⡱⠀⠀⠀⠀⠈⠉⠓⠶⠶⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⠟⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠻⠶⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠿⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡴⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⡏⢉⠻⣿⣿⣿⣿⣿⣿⣿⣛⣫⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠐⡵⠃⡀⠀⠀⠀⠀⠀⠀⠀⣟⠈⢉⡛⠻⠿⠿⣿⣿⣿⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣠⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠂⠒⠂⠤⠍⣠⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⢄⠀⠀⠀⠀⠀⢀⣿⡆⠉⠀⢠⡤⡤⢉⠙⠛⠋⠛⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠻⢶⢿⣶⣶⣦⠸⣿⡇⠀⠀⢈⡀⠁⠀⠂⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠈⠉⠙⠻⢇⠉⠠⣷⣾⣿⣇⣀⠀⠀⠀⡁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣯⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣶⡇⠀⠀⠀⢸⡄⢤⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⢠⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠂⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⢐⣼⣿⣿⡀⣤⣀⡉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⠻⠋⣿⣿⠇⠘⠏⣰⣯⠀⢠⢄⠈⡉⠛⠛⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢠⣿⣿⠀⠲⡾⡲⣇⡢⠆⠁⠈⠀⠉⠐⠀⠤⣉⡉⠛⠛⣿⣿⣿⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠈⠛⠁⠀⠀⠒⠉⢠⠏⣺⣶⢴⡔⢠⠂⠀⠀⠀⠀⠈⠊⠶⢢⡼⣍⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣀⣱⣤⠠⢄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠐⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠈⠄⠦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣆⡔⠒⡙⣻⣿⡗⣶⣤⣄⡀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⢸⡇⠀⡀⠠⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⠌⠨⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠾⠛⠓⠛⠉⠛⠛⠳⠆⠀⠀⠀⠙⠌⠒⠈⠐⠂⠸⠇⠀⠈⠓⠀⠊⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠡⡲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠻⣿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣦⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠷⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⣴⣤⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⡄⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠐⠁⣀⠀⠀⠀⠀⠀⠄⠀⠉⠿⣿⣿⣿⣷⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢦⠄⢀⡀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣷⣦⣀⠉⠁⠙⢿⡛⠃⠰⡂⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢛⢶⣦⣈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣭⣭⣙⢛⣋⣉⣋⣛⡛⢟⠃⠹⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣾⣿⣿⣿⡇
⠟⣛⡛⣋⣩⣍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠄⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⣀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢠⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣿⣿⣿⣿⣿⠿⠟⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠒⠒⠀⠀⠀⠀⠀⠀⠚⠿⣷⣶⣆⡦⡈⠉⣉⣤⡈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢁⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠈⣠⣤⣤⣤⡈⠉⣥⣁⣈⣉⠙⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣸⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠈⣾⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢋⣀⣈⣡⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣾⣿⣿⣿⣃⢨⣉⣩⣰⣆⣍⣹⡄⣛⠛⣀⡙⡻⠿⠟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢛⣫⣿⣿⣿⣿⣿⣧⢀⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⡭⠿⠿⠛⠋⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣾⣿⣿⣟⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⡇⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⢿⣛⣛⣛⠻⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢱⣿⢯⣶⣶⣍⣿⣿⣛⣒⢯⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠙⣾⣿⣿⣿⣿⣯⣿⣿⣿⡞⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡇⠙⣸⣿⣿⣿⡇⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠸⢿⣯⣽⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣰⠀⡠⠀⡠⠀⣴⠌⠉⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠄⠉⠀⠀⠊⢀⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣠⠔⠉⠤⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠊⠀⢀⡠⠒⠁⣀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣏⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠉⠗⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⣡⣴⣶⣶⣶⣦⣄⡀⣾⣿⣷⠀⢀⡀⠀⠀⢸⣷⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠲⠒⠤⠄⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⣆⠀⢸⣿⣿⡿⡿⣿⣯⠀⠀⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⡄⣿⣿⣿⣿⣿⡽⠑⠀⠐⠀⠀⠀⠀⠈⠙⠓⠶⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠿⠟⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡴⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣿⣿⣿⣿⣿⣿⣿⡏⢉⠻⣿⣿⣿⣿⣿⣿⣿⣛⣫⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡵⠃⡀⠀⠀⠀⠀⠀⠀⠀⣟⠈⢉⠛⠛⠿⠿⣿⣿⣿⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠂⠒⠀⠤⡍⢠⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⢀⠀⠀⢀⠀⠀⢀⣿⡆⠈⠀⠄⣤⡤⣉⡙⠛⠋⠛⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠻⠾⢿⣷⣷⣦⠸⣿⡇⠀⠀⢀⡀⠀⠀⠒⠀⠅⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠈⠉⠙⠛⠇⠉⠀⣤⣿⣿⣇⣀⡀⠀⠀⡁⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣾⡆⠀⠀⠀⢸⡆⢤⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢠⣿⣿⠸⢿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠊⠀⠠⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⢐⣼⣿⣿⡀⣤⡤⣉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⠻⠋⣿⣿⡇⠙⡯⠸⣿⠇⠠⡄⠈⡉⠛⠻⢿⣿⣿⣿⣿⣿⣖⣄⡀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢀⣿⣿⠀⢖⣶⢗⣆⣳⢅⠀⠈⠁⠙⠒⠤⢀⡉⠉⠛⠛⠿⣿⣿⣷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠈⠛⠁⠀⠁⠛⠉⡀⢱⣹⢗⣄⡒⣤⢀⡀⠀⠀⠀⠉⠋⠰⢦⡼⠫⣙⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡣⣤⠠⣴⣤⣄⣀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⠨⠃⠽⠈⠈⡀⠀⠀⢀⠀⠀⠀⠈⠈⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⢓⢹⠖⡱⣿⣟⡛⣶⣤⣄⡀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⢸⡇⠀⡄⣠⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠩⠕⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠯⠛⠘⠋⠊⠛⠛⠳⠆⠀⠀⠀⠘⠆⠀⠀⠒⠂⠸⠇⠀⠀⠑⠀⠀⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠭⣢⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠈⠙⠻⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠁⠙⠿⣿⣷⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠲⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠉⠿⣿⣿⣿⣷⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠦⢦⡄⢀⡀⠚⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⡿⣿⣷⣦⣀⠈⠀⠉⠛⡛⠂⢖⣠⣄⠈⠙⠛⢻⣿⣿⣿⣿⣿⣭⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠘⢫⢶⣦⣈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠉⠻⣿⠿⠇⠸⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⣿⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣨⣭⣥⣴⣿⣿⣿⣿⡇
⠿⡛⣛⣫⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠤⠤⠠⠀⠉⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣿⣿⣿⣿⣿⠿⠟⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⡏⣰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠳⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣭⠍⣴⠈⠛⠛⠋⣁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣦⠈⣫⣭⣦⣬⡁⠈⣭⣀⣉⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡟⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⣉⣉⣡⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠠⠙⠻⠿⢟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⠛⠛⢻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡯⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣟⣛⣛⣛⣛⣛⡻⢿⣿⣾⣝⡻⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⣵⣿⢿⣛⣻⢿⣿⣿⣿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠘⢏⣿⣿⣿⣷⣿⣷⣶⣾⣝⢻⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡇⠟⣿⣿⣿⣿⣿⣿⠿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⢰⣿⣟⣻⣿⠇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠋⠀⠈⠛⠻⠶⠿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠌⠀⡔⢠⠂⠀⠀⠘⠏⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠊⢠⠊⡴⡇⠀⡠⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡰⠣⢒⠴⢁⡼⠓⠉⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣇⣿⠷⢻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠊⣠⠔⣡⠔⠁⠠⢀⠄⠚⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣿⠀⠀⡠⠊⠀⠀⢠⠔⠁⣠⡒⠉⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠈⠻⠗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠠⠊⠀⠀⣠⢘⣤⣶⣿⣿⣿⣶⣄⡻⣿⣿⣿⣇⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠻⠷⠢⣤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣔⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⡆⣸⣿⣿⢿⣿⠿⡄⠀⠑⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⣶⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣇⣿⣿⣽⣧⠃⠟⠀⣞⡤⡀⠀⠀⠉⠉⠓⠶⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⡿⣽⣿⣿⣿⣿⠀⠀⠈⠀⡠⠈⢐⠀⡀⠀⠀⠀⠀⠀⠀⠉⠙⡻⢦⣤⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣛⣵⣿⣿⣿⣿⣿⡀⠠⡄⠀⠀⠀⠰⢶⠹⠅⠀⠀⠀⠀⠈⠀⠡⠀⡌⣀⣈⠻⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⢀⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠿⠿⣿⣿⣿⣿⣧⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢤⠀⠠⠄⠀⡀⠀⠀⠙⢂⣸⡀⡄⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠂⠙⠒⠒⠤⢍⣉⠉⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠉⠰⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⢸⡇⠀⠀⡀⠀⠀⠈⠀⠀⢠⣿⠐⠒⠤⠍⣉⠛⠻⠿⢿⠿⠿⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⢠⣾⣷⡀⠀⢷⣾⣶⣿⣤⣄⢸⣿⠀⠀⠀⢸⠈⠁⠙⠒⠢⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠈⠙⠛⠿⣿⡌⠋⠀⣶⣶⣾⣀⢀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣿⣭⡇⠐⠦⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣦⡆⠀⠀⠀⢸⠀⣸⣿⣷⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠰⠀⠀⠀⠀⠀⠀⢢⣀⠀⠀⠀⠀⠉⠉⠛⠛⠁⠀⠀⢠⣿⣧⠹⢿⣿⣿⣿⣿⣿⣿⣾⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠂⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠉⠀⠀⠀⠀⢠⣦⠀⢀⠀⠘⡉⡀⠀⠀⠀⠀⠀⠀⣠⡊⢑⣼⣿⣿⠰⣦⣤⣉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⡀⢀⣂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⠀⠿⠛⣿⣿⠖⠸⠿⢿⣯⡇⠤⠤⡈⡙⠛⠿⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠆⣐⢎⠒⢢⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠀⢆⣫⣓⣷⣲⣭⠔⠈⠁⠋⠲⠀⠀⣉⣉⡛⠻⠿⣿⣿⣿⣶⡀
⠊⠀⠂⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠋⠑⢼⠀⣨⠤⣐⠾⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⢀⠀⠀⠘⠻⠁⠀⠙⠳⣋⣿⠿⠿⢵⢲⢲⣕⢀⡀⠀⠀⠀⠈⠘⠷⢶⣬⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⣶⣿⢿⣦⣴⣤⣄⣀⠀⠉⠂⠀⣬⠀⢄⣀⠀⠀⠈⠀⠉⠂⠒⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⢐⣀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠉⠡⠌⠸⠿⣷⡂⠫⡆⡨⣀⠀⠀⠀⠀⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⠙⢘⢻⣟⣟⡿⣿⣶⣦⣄⡉⠀⠀⠈⠀⠉⠀⠆⠀⠀⠀⠀⢸⡇⠠⠖⣀⠄⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠘⠂⠀⠭⠄⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠹⣿⣿⠟⠉⠛⠙⠛⠛⠷⠦⠀⠀⠀⠺⠓⠚⠙⠂⠀⠸⠇⠀⠒⠙⠋⠀⠁⢐⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⣖⢢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠈⠛⠻⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢀⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠃⠀⡀⢀⠀⠁⠛⢿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠑⠿⠀⢸⣿⣿⠀⠠⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢀⠀⠀
⠄⢀⠠⠀⠀⠀⠀⠄⠈⠛⢿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⣀⣍⣙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠐⠐⣀⠀⠀⠂⡀⠠⠠⠉⠙⢿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⣶⣦⣄⣀⡀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣷⣦⣄⠈⠃⠚⣛⡛⢳⢼⣦⢀⠈⠙⠛⢻⣿⣿⣿⣿⣷⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⢙⠃⠉⢽⣷⣦⣈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⢿⣟⡛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣋⣉⣛⣛⡛⠛⠁⠻⡿⠿⠇⠸⠿⡿⠿⠛⠫⠽⣟⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠏⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣽⣤⣴⣾⣾⣿⣿⡇
⠿⡛⠛⣋⣩⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠠⠀⠉⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⠀⢸⣿⣿⢠⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢻⣿⣽⣿⣿⣿⠿⠟⠃
⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣍⣯⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠲⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣾⣭⠍⣴⠈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠈⣫⣭⣦⣬⡁⠈⣥⣀⣈⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡯⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠿⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢊⣀⣈⣁⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣶⣶⣿⣿⣿⣷⣮⣭⣭⣤⣶⣭⣹⣤⣛⡛⠀⠙⠻⠿⢟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣾⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣻⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣟⣛⣛⣛⣛⣛⡻⢿⣿⣿⣽⣻⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⣵⣿⢟⣛⣛⢿⣿⣿⣿⣿⣶⣝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠘⢏⣿⣿⣿⣷⣿⢧⣶⣶⣝⢻⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⡇⠟⣿⣿⣿⣿⣿⣿⠿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠰⣿⣟⣻⣿⠇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠉⠉⠉⠋⠀⠈⠛⠻⠾⠿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠌⠀⡔⢀⠂⠀⠀⠘⠋⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⠊⢠⠈⡴⡇⠀⡠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡰⠣⢒⠔⢁⡼⠓⠉⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⠀⠀⠀⣇⣿⠗⢹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠊⣠⠔⣡⠖⠁⠠⢀⠤⠚⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡌⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣿⠀⠀⡠⠊⠀⠀⢠⠔⠁⣠⡒⠉⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠉⠰⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⠠⠂⠀⠀⡠⢘⣤⣶⣿⣿⣿⣶⣄⡻⣿⣿⣿⣇⢀⢀⡀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠻⠶⡢⠄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⠀⢀⣔⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⡄⣸⣿⣿⢿⣿⠯⡄⠈⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⣶⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣇⣿⣿⣽⣧⠋⠈⠂⠸⡄⡀⠀⠀⠉⠉⠓⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⡿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠁⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣛⣵⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡻⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀⠄⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡇⠙⠛⠿⠿⣿⣿⣿⣿⣧⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠤⠄⠀⡀⠀⠈⠐⠘⠅⠑⠀⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠆⠑⠒⠒⠠⠍⣉⠉⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⢰⣷⠀⠖⠤⠉⣉⠛⠻⠿⢿⠿⠿⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢀⣾⣷⡀⠀⠷⣾⣦⣷⣤⡄⢸⣿⠀⠀⠀⢈⠀⠀⠁⠂⠢⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠈⠙⠛⠿⢿⡄⠋⢠⣶⣶⣾⣄⢀⢀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⢿⣿⣿⣷⣦⡆⠀⠀⠀⢸⠀⣸⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠃⠀⠀⢠⣿⣧⠻⢿⣿⣿⣿⣿⣿⣷⣮⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠃⠂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠉⠀⠀⠀⠀⢠⣦⠀⠀⠄⠀⠁⠥⠀⠀⠀⠀⠀⠀⢐⡂⢈⣼⣿⣿⠰⣦⣀⡉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠿⠛⣿⣿⡴⠸⣿⡿⡿⡦⡄⠀⠈⡙⠛⠿⢿⣿⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀
⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⢂⠈⢀⡢⣀⢂⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⠀⠀⣾⣞⣒⣵⡠⠀⠈⠉⢉⠴⠀⢀⣉⣉⠛⠛⠿⣿⣿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡟⠄⠐⠈⡀⠚⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠘⠻⠁⠀⠘⠻⠑⣻⡿⣾⣧⣖⡰⡁⠄⠀⠀⠀⠀⠙⠚⠳⢖⣨⣟⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣬⡷⣴⢦⢠⣤⣄⣀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠈⠀⠑⠂⠂⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠞⠉⠿⠴⠡⠙⡠⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠏⢻⡁⢻⣯⣟⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠁⡂⠄⠀⠀⠀⠀⢸⡇⠀⣀⢀⡄⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠤⠟⠈⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⢵⡿⠛⠙⠛⠋⠛⠛⠳⠦⠀⠀⠈⠠⠃⠉⠀⠂⠀⠸⠇⠀⠈⠀⠈⠚⠁⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⡶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠻⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠁⠛⢿⣿⣷⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠱⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣄⣙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠐⠀⡀⠀⠀⠀⠐⠀⠀⠀⠙⢿⣿⣿⣿⣿⣾⣰⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢲⣦⣄⣀⡀⠚⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠉⠀⠙⠛⢛⡵⠔⡦⢀⠈⠙⠛⢻⣿⣿⣿⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠫⢟⣶⣦⣈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣬⣀⢘⣛⣁⣁⣛⡛⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠛⠫⠭⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢡⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢸⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠈⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣾⣿⣿⣿⡇
⠟⡛⡛⣋⣉⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡧⠤⠄⠀⠀⠈⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⢀⠸⠿⠿⠿⠃⠿⢿⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣯⣿⣿⣿⣿⠿⠟⠃
⣾⣿⣻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣫⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠂⠀⠀⠀⠀⠘⠛⠶⣾⠣⠆⢀⣀⣠⣌⣉⣉⣀⣈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⡿⣿⣽⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢈⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠛⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢹⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣭⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⡧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢊⣀⣈⣡⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣶⣾⣿⣷⣶⣶⣬⣩⣭⣶⣶⣭⣭⡄⠛⠛⣤⣙⠻⠿⠟⣃⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣭⣭⡻⣿⣿⣿⣿⣿⣷⠿⠿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⡽⠿⠟⠛⠋⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⡏⠈⣿⣼⣿⣿⣿⣿⣣⣾⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠛⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⡻⣿⣿⢿⣿⣿⣿⣟⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣿⣿⣮⡫⣿⣽⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⣻⣿⣿⣿⣶⣽⣿⣿⣿⣧⣝⣋⣵⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣐⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠋⢱⣿⣿⣿⠀⠀⣾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⣼⣿⣿⣿⠀⢠⣿⣿⣿⡇⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡠⢊⠄⠁⠀⠀⢀⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣾⡇⠐⠀⠀⠊⡀⠊⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⣿⡇⠀⠘⠆⢈⣠⠊⣠⣌⣀⣀⡀⠀⣾⣿⣿⣀⣀⡀⠀⠀⢸⣿⣿⣿⣿⠤⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠐⠳⡠⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠞⠁⢿⣷⣄⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣮⡛⢿⣿⣿⣿⡄⠀⢸⣿⣿⣿⡿⣃⣿⣿⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠘⠃⠀⠀⠸⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣼⡿⠂⠊⠀⠀⠀⠀⠈⠉⠓⠶⠦⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣼⣿⢯⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⠻⢦⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠊⢹⢻⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠛⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⢻⢸⣿⣿⣿⣿⣿⣿⣿⣧⢙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⠙⠛⠿⠿⣿⣿⣿⡈⢠⣷⣿⣿⣿⣿⣽⣿⡿⡿⣿⣿⡛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠁⠐⠀⠠⠉⢁⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣸⣄⠀⢀⠀⠀⠀⠀⠀⠀⣾⡇⠈⠰⢆⠠⠀⠉⠙⠛⠟⠻⠛⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠸⠏⠯⣸⠄⣤⠀⣿⡇⠀⠀⠀⠂⠀⠀⠈⠈⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠈⠉⠒⠼⠧⠉⠀⡀⠴⢶⡂⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣿⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠟⡓⡊⢼⣤⣦⡄⠀⠀⠀⢸⡇⢠⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⣿⣿⠐⠿⣿⣿⣿⣿⣿⣷⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣼⣿⣿⠀⢀⣄⡉⠉⠛⠿⠿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠂⠻⠋⣿⣿⡃⠈⠻⠷⠅⡀⠀⢀⠀⡉⠛⠻⢿⣿⣿⣿⣿⣳⣆⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⡿⠀⠢⢂⢠⢆⣠⡀⠀⠀⠈⠁⠢⠠⠀⣈⠉⠛⠛⠻⣿⣿⣷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠁⠀⠀⠒⠘⢛⠎⠲⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠀⡘⣉⡛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⡀⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠁⠀⠃⠀⠁⢀⠀⠀⠀⠀⠀⠈⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⠢⠳⠷⢋⣳⡶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⠄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠟⠂⠀⠊⠚⠛⠛⠳⠆⠀⠀⠀⠂⠀⠀⠂⠀⠀⠸⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠤⢂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠻⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢠⢄⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣴⣶⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠈⠈⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣥⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣄⠙⣟⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣯⣶⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⣤⡄⢀⡀⠐⠶⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠿⣿⣷⣦⣀⠈⠀⠈⠓⠋⠀⠒⣀⡀⠈⠙⠛⢻⣿⣿⣿⣿⣷⣢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣦⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣙⣛⣛⠿⣟⡛⠛⠛⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⠛⣋⣉⣙⣛⡛⢛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠛⠫⠍⢙⣿⣿⣽⣯⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⠰⣿⣿⣿⣿⠿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣭⡄
⠟⠛⠛⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢈⣠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣫⣵⣶⣿⡿⠿⠟⠃
⠀⠁⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣟⡋⡁⣨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡙⠛⢋⣉⣀⡀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⣀⣠⡈⠉⠉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⣼⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠉⣡⣤⣤⣤⡈⠉⣤⣀⣈⣉⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢀⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠰⢠⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣙⠁⠀⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⡈⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣸⣿⣿⠿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢰⣿⣇⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢱⠅⣡⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⢀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⡿⠖⣶⣿⣿⣶⣶⣶⣿⣿⣿⣷⣬⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣙⠻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⡭⠿⠿⢿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣋⣭⣶⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠀⠀⠒⠋⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣛⣟⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⣿⣿⣿⣿⡿⢿⣛⣉⠭⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⢟⣛⡻⣷⣿⣿⣿⣿⣿⣵⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠿⠑⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣷⣿⣿⣿⣿⢏⣭⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢾⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠍⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣜⣛⣻⣿⣿⣿⣿⣿⣿⣼⣀⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⡿⣿⡿⣿⣿⣿⣿⣿⣎⡛⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣻⣿⣿⣿⣷⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⢛⣭⣽⡍⠉⠙⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠋⠀⠀⣸⣿⣿⡇⠀⠀⣿⣿⣷⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠛⠿⠿⠃⠀⢰⣿⣿⡟⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⣺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣾⡷⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠆⣠⣤⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⡥⣿⣿⣄⡐⣈⣠⣶⣶⣶⣶⣿⣿⣶⣶⣬⣛⠿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠋⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⢿⣿⡗⣼⣿⣿⣿⣿⣷⣿⡇⣿⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠺⠂⠀⣴⡏⢠⣮⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣴⣿⣿⣿⣿⣿⣾⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⢄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠧⢋⠜⠁⠀⣿⣿⣿⣾⣻⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣻⣛⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠁⣜⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⠻⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠃⢰⠄⠉⠁⠀⣿⠀⠉⠙⠛⠿⣿⣿⣿⡇⢀⣿⣿⣷⣿⣿⣟⣻⢿⣿⣿⣿⣏⡻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⢿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣷⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠐⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣦⣐⣄⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠻⢿⣿⣿⣿⣿⣦⣢⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣽⡔⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠺⠷⢶⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣮⣻⣿⣿⣿⣷⣴⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣰⢷⣤⡴⣄⣟⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣶⡢⣀⠀⠀⠀⠀⠀⠀
⠩⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣞⣳⣿⣿⣿⠗⣿⣿⣽⣯⣽⣧⣷⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣋⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣦⡍⢨⣭⣭⣬⣘⢛⣋⣉⣙⣛⡛⢛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠫⠍⢟⣻⣿⣽⣭⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⠰⣿⣿⣿⣿⠿⢿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⠀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣿⣭⡅
⠟⠛⠛⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣁⣤⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣫⣵⣶⣿⡿⠿⠟⠃
⠐⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡋⡅⢨⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣈⡙⠛⢋⣉⣀⡀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⢀⣀⣤⡈⠉⢉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠋⠋⠉⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⣽⣿⣿⣿⠀⣿⣿⠀⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣤⠈⣠⣤⣤⣤⡈⠉⣤⣀⣀⣉⠙⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠈⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⢰⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣹⡄⠡⠌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣝⠀⢀⣿⣿⣿⣿⡃⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣉⡀⣿⣿⡇⣿⣿⡇⣾⣿⢿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠼⢳⣲⣹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⣸⣿⣿⠿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢸⣿⣇⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⠀⣶⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⡿⠆⣶⣿⣿⣶⣶⣶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣭⣭⣤⣛⣛⣤⣝⠻⠿⠟⣣⣌⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣖⡴⠾⠿⢿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣩⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⣿⣶⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠉⠀⠀⠚⠋⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⢿⣛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⣿⣿⣿⣿⡿⠿⣟⡉⠬⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⢟⣛⡻⣷⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠿⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢀⣷⢻⣿⣿⣿⣿⣿⢏⣭⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣜⣛⣫⣿⣿⣿⣿⣿⣿⣼⣀⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣛⡻⣿⡿⣿⣿⣿⣿⣿⣎⡛⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣯⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⢛⣭⣭⡍⠉⠙⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠋⠀⠀⣸⣿⣿⡇⠀⠀⣿⣿⣷⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠛⠿⠿⠃⠀⢰⣿⣿⡟⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣾⡷⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⡆⣠⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⢊⡥⣿⣿⣄⡐⣨⣠⣶⣶⣶⣾⣿⣿⣶⣶⣬⣙⠿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠋⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⢿⣿⡟⣼⣿⣿⣿⣿⣷⣿⡇⣿⠅⠀⠀⠀⠀⠀⠈⠉⠒⠒⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠻⠀⠀⣴⡏⢠⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣾⣿⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠧⢃⠜⠁⠀⣿⣿⣿⣾⣻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣛⣛⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠁⣞⡆⠀⣟⣿⣿⣿⣿⣿⣿⣿⣽⡻⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠃⢰⠆⠉⠁⠀⣿⠀⠉⠙⠻⠿⣿⣿⣿⡇⢀⣿⣿⣷⣿⣿⣟⣛⣿⣿⣿⣿⣏⡻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠿⢿⣿⣿⣿⣿⣿⣷⣯⣹⣿⣿⣷⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠐⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣧⣴⣄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⣾⣷⠐⠻⢿⣿⡿⣿⣿⣶⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠉⠛⠽⢿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣭⡡⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠺⠶⢶⡆⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⡲⢀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣦⣹⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⡀⠈⠃⢻⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢮⣽⣧⣶⣔⣞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡤⣀⠀⠀⠀⠀⠀⠀
⠛⢯⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠛⣯⢿⣿⡾⣟⣮⣯⣿⡿⣿⣿⣿⣿⣿⣯⣯⡞⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣛⣛⠿⣟⡛⠛⠛⠿⠿⠿⠿⣿⣿⢻⣷⣴⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡄⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣬⣭⣭⣙⠛⣉⣉⣙⣛⡛⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠛⠫⠍⢝⣿⣿⣭⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⠿⢿⣟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣆⢸⣿⣿⠿⠇⢈⣭⣤⣴⡶⣾⣿⣭⡅
⠟⠛⠙⠉⠉⠉⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢠⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⢁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠰⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⢛⣋⣥⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⠋⡁⢈⣿⣿⣿⠏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠀⢀⣀⣀⡈⠙⠛⠛⠀⠀⠀⠀⠤⠀⠀⠀⢀⣀⣤⡌⠉⠉⣀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⢠⣶⣶⣶⣤⠈⣠⣤⣤⣤⡈⠉⣄⣀⣀⣉⠑⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠘⢀⣿⣿⣿⡏⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠆⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⡃⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⠀⣿⣿⡇⣿⣿⡇⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⢘⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⣿⡿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⢟⠸⢿⣿⢠⣴⣄⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⢥⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣬⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⠙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⡤⠿⠿⢿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢋⣩⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠀⠐⠘⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⣿⣿⣿⣿⡿⡿⣟⡉⠤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣭⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣯⣿⢟⡛⣿⣿⣿⣿⣿⣿⣿⣯⣷⣶⣯⣻⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⡽⣿⣿⣿⣿⣿⣿⣿⡿⣫⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣗⢇⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⢲⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣭⣭⣭⣷⣿⣿⣿⣿⣮⣽⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣿⣿⠿⠿⠟⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⣀⣄⡀⢻⣿⣽⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣀⣀⣀⣠⣤⣤⣶⣶⣶⣦⣤⣍⣛⠻⢿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣻⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⣿⣿⡿⢿⣿⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣶⣮⣙⠻⠿⢣⣿⣿⣿⣿⣿⣿⣷⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⡀⠀⠐⠀⣠⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠅⠋⠀⠀⠁⠀⢀⡴⠋⠀⠀⢱⣼⣿⣿⣟⣛⣛⡻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⢀⠀⣶⠀⠀⠀⢠⢶⣀⣴⠟⠀⣄⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⣿⡙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠁⠀⠀⢸⠀⠀⠉⠛⠻⠿⣿⣿⣇⠀⣾⣿⣿⣾⣛⣛⣛⡿⣿⣿⣿⢏⡻⠿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠻⢿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⡇⡗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⣿⠄⠉⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠛⠿⣿⣿⡿⣿⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠠⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⡇⠀⣗⡠⡄⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠐⠿⣿⣿⠿⣿⣿⣦⣤⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠉⠛⠹⢿⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣭⡥⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢠⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠺⠷⢶⣆⡦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⢐⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣬⣼⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⠀⡈⠑⢻⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⣽⣮⣤⣠⠉⠟⣻⡿⣿⣿⣿⣿⣿⣿⣾⣶⠄⠀⠀⠀⠀⠀⠀⠀
⠈⢛⣷⣄⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣯⣿⣄⣣⣝⡙⣿⣿⣿⣿⣿⣿⣯⣦⣇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣛⣛⠿⣟⡛⠛⠛⠿⠿⠿⠿⣿⣿⢻⣷⣴⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡄⣿⣿⡆⣶⣶⡆⣶⣶⣦⡄⢨⣬⣭⣭⣙⢛⣉⣉⣙⣛⡛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠫⠍⢙⣟⣿⣽⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣸⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⠘⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⠁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⢰⣿⣿⣿⣿⠿⠿⡟⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣄⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠃⢸⣿⣟⣀⡀⣿⣿⠇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⢈⣭⣤⣴⣶⣾⣻⣭⡅
⠟⠛⠉⠉⠉⠉⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡅⢀⢠⣿⣿⣿⡧⠄⠀⠀⠀⠈⠀⠉⠉⠉⠉⣁⣄⡘⠛⠛⠛⠀⠸⠿⠿⠿⠁⠿⠿⠰⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡀⠋⣉⣥⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⢈⣾⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣤⣉⡉⠀⢀⣀⣀⡈⠙⠛⠛⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣤⡈⠉⠉⢀⠈⠛⠛⠋⠁⠘⠛⠛⠿⠃⠘⠛⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣸⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⢠⣶⣶⣶⣤⠈⣠⣤⣤⣤⡈⠁⣤⣀⣀⣉⠁⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣣⠀⠘⢀⣿⣿⣿⡇⠀⣿⣿⠀⠈⠻⣿⣷⣄⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢉⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠂⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⢀⣿⣿⣿⣿⠇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣩⠀⣿⣿⡇⣿⣿⡇⣾⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠘⢇⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⠿⠟⠃⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⢠⣵⣄⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⠄⣦⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⣿⣿⣿⣷⣮⣭⣭⣴⣦⣍⣉⣀⣛⣛⣀⠙⠻⠿⠟⢃⣈⠻⢿⣿⠿⠃⢸⣿⡏⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣘⡢⠿⠿⠿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣩⣵⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠀⠐⠐⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⣿⣿⣿⣿⣿⡿⠿⢛⡉⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠏⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣭⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣯⣿⢟⡛⣿⣿⣿⣿⣿⣿⣿⣯⣷⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⡹⣿⣿⣿⣿⣿⣿⣿⡿⣫⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣗⢇⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣭⣭⣭⣷⣿⣿⣿⣿⣮⢽⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⣿⠿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⣀⣤⣀⢻⣿⣼⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣀⣀⣄⣠⣤⣤⣶⣶⣶⣦⣤⣍⡛⠻⢿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣻⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠙⣿⣿⡿⢿⣿⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣶⣮⣙⠻⠿⢣⣿⣿⣿⣿⣿⣿⣷⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⡀⠀⠐⠀⢠⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠃⠀⠀⠁⠀⢀⡴⠋⠀⠀⢱⣼⣿⣿⣟⣛⣛⡻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⢀⠀⢾⠀⠀⠀⢠⢶⣀⡴⠟⠀⣄⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⣿⡟⠟⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠈⠀⠀⠀⠀⠀⠸⣾⠟⠁⠀⠀⠁⠀⠀⢸⠀⠀⠉⠛⠻⠿⣿⣿⣇⠀⣾⣿⣿⣮⣛⣛⣛⡿⣿⣿⣿⢏⡻⠿⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⢿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⡇⡗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⣿⠄⠉⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠙⠛⠿⣿⣿⡿⣿⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⣤⢀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠐⠻⣿⣿⢿⣿⣷⣦⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠉⠛⠹⢿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢾⣿⣿⣥⡠⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢠⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠑⠲⠍⢰⡤⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣰⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣄⣿⣿⡿⣿⣿⡆⢸⣿⡇⠀⣤⣽⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⠀⠀⠈⠈⠻⢿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣵⣦⣤⣠⣞⡿⣻⢿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⣻⣿⣿⣁⣤⣌⠿⣿⡿⣿⣿⣿⣿⣯⣞⢃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⠿⣟⡛⠛⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⡿⣿⣷⡌⣿⣿⡆⣶⣶⡆⣶⣶⣶⡌⢩⣭⣭⣭⣙⢛⣉⣉⣋⣛⡛⢟⠃⠹⠿⠿⠿⠿⠿⡿⠿⠛⠫⠽⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡟⣿⣿⠀⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢱⣿⣿⠉⠁⣼⣿⡏⣿⣿⡞⠛⣿⣿⡿⠇⣿⣿⡇⣴⣿⡿⣿⣦⠀⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠁⣿⣿⠁⣿⣿⣿⣿⡟⢸⣿⣿⣿⠇⣿⣿⣷⣿⣟⢁⠀⣿⣿⠁⠀⣿⣿⡇⣿⣿⣦⡛⠛⢠⣿⣿⠉⠁⣼⣿⣿⣿⣿⡿⢿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⣻⣿⣿⢠⣿⣿⠉⣿⣿⣤⣿⣿⣼⣿⣿⠀⢹⣿⣿⣿⠇⢸⣿⣟⣀⡀⣿⣿⡇⣿⣿⠀⢠⣿⣿⠀⢠⣿⣿⢀⣈⣛⢿⣿⣦⢸⣿⣿⠿⠇⣈⣭⣤⣴⣾⣿⣿⣿⡇
⠟⡛⢛⣋⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠄⠀⠀⠉⠀⠉⠉⠉⠉⣡⣤⡘⠛⠛⠛⡀⠸⠿⠿⠿⠃⠿⠿⠸⣿⣿⢠⢸⣿⣿⠀⢸⣿⣿⠘⣿⣿⣸⣿⡿⢸⣿⣿⣀⡐⢻⣯⣿⣿⣿⣿⠿⠟⠃
⣾⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣩⣿⣿⣿⡏⢰⣶⣶⢀⣤⣶⣦⣤⠀⣤⣤⣬⣉⡙⠛⢋⣉⣉⡙⠒⠒⠀⠀⠀⠀⠀⠀⠚⠿⣷⣶⡆⣮⣈⣉⣉⣀⣈⠛⠛⠋⢁⠘⠛⠻⠿⠃⠸⠛⠋⠉⠁⠀⠀⠀⠀
⢿⣟⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢀⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣏⠿⠿⠇⣿⣿⡟⣿⣿⢰⣿⣿⢻⣿⡆⢸⣿⣧⢸⣷⡆⣠⣶⣶⣶⣮⠘⣠⣤⣤⣤⡈⠉⣤⣀⣉⣉⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡟⠀⣿⣿⠀⠈⠻⣿⣷⣆⠀⣿⣿⣧⣿⡿⢸⣿⡏⣼⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⣇⠿⠿⢀⣿⣿⢩⣿⣿⠀⣿⣿⢻⣿⣷⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⡎⣿⣿⢀⣿⣿⠉⣍⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣆⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⠟⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣿⣿⣿⡿⠟⠓⠀⠛⠛⠃⠙⠿⠿⠿⠟⠸⢿⣿⠈⣿⣧⠻⣿⣧⣿⡿⠃⣿⣿⢸⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⢸⣿⣿⢹⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠓⢊⣀⣈⣡⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣇⢨⣉⣩⣰⣦⣍⣭⡄⡛⠛⣀⡙⡻⠿⠟⣫⣌⠻⢿⣿⠿⠃⢸⣿⡟⣼⣿⡇⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣻⣿⣿⣿⣿⣿⣷⣀⣿⣇⣿⣿⣿⣿⣿⣷⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡽⠿⠿⠛⠛⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡿⠿⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⣛⣛⣛⣛⠻⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⢱⣾⣯⣶⣶⣍⣿⡿⣛⣒⢬⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠙⣾⣿⣿⣿⣿⣷⣿⣿⣿⣼⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⡏⠛⣸⣿⣿⣿⡏⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠸⢿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠀⠀⣰⠁⡰⠀⡠⠀⣶⠌⠙⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠎⠉⠈⠰⠊⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠁⠀⠀⠀⠐⠋⠵⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠊⠀⢀⡠⠒⠁⢀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⣹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣆⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠈⠁⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠔⣡⣴⣶⣶⣶⣦⣄⠠⣿⣿⣷⢀⢀⡀⠀⠀⢸⣷⣿⣿⣿⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠳⠠⠄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⣇⠀⣸⣿⣿⣿⡿⣿⡷⠀⠀⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⡆⣿⣿⣿⣽⣿⡽⠑⠰⠧⠤⠀⠀⠀⠈⠉⠓⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠻⢟⣽⣿⣿⣿⣿⣿⡇⠈⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠹⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⢿⣿⣿⣿⣿⣿⣿⣻⣫⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⡵⠂⡀⠀⠀⠀⠀⠀⠀⠀⡧⠈⣉⡛⠛⠿⠿⣿⣿⣿⠀⢰⣿⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⣻⠿⠿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠋⠀⠀⣠⠈⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠐⠀⠠⡍⣠⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡁⠰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠀⠀⠀⠀⠀⠀⢀⣿⡆⠉⠂⢂⣤⠀⣉⡙⠛⠋⠛⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠉⣻⣿⢧⣲⣄⠸⣿⡇⠀⠀⢨⡄⠀⠈⠘⠈⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠈⠈⠙⠳⠂⠉⠀⠵⣿⣿⣄⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢫⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢯⣻⣿⣷⡆⠀⠀⠀⢸⡀⣰⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢠⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢂⣼⣿⣿⠀⣠⣀⣉⠋⠻⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⠋⣿⣿⡇⠼⢿⠛⣧⢆⡤⢀⠈⡙⠛⠻⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠪⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢀⣿⡿⠀⢰⡰⠲⣦⣴⣐⠀⠀⠈⠋⠆⠠⠀⣉⣉⠛⠻⣿⣿⣿⣿⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⡑⠿⠫⡿⠴⣦⣂⠀⠀⠀⠀⠀⠀⠀⠉⠲⢆⣙⣭⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣆⢤⢠⣤⣤⣄⣀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠣⠌⢽⠘⠅⠈⠀⡀⠀⠀⠀⠀⠀⠀⠁⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠩⠙⠱⠉⣻⢯⡿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⢸⡇⠀⢀⠄⠄⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠪⡹⠋⠋⠛⠚⠛⠛⠳⠆⠀⠀⠈⠒⠀⠀⠀⠀⠀⠸⠇⠀⠘⠀⠁⠐⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⣴⣾⢿⣶⣄⠀⠀⢰⣶⢰⣶⣶⣶⣶⡄⣶⣶⡆⠀⠀⣶⣶⣶⡆⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⡶⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⠀⠘⠛⢸⣿⣿⢸⣿⡇⣿⣿⡇⠀⢰⣿⡿⣿⣷⠸⣿⣿⣿⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠻⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⠀⢀⣤⠀⢸⣿⣿⠿⠿⠃⣿⣿⡇⡀⢸⣿⡇⣿⣿⠀⢿⣿⡟⠀⣶⣶⣰⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣸⣿⡿⠀⠘⠓⠀⢸⣿⣿⠀⠀⠀⣿⣿⣧⣅⣿⣿⡿⣿⣿⡇⢸⣿⡇⠀⣾⣿⣿⣿⣿⣿⣷⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣧⣴⣀⡀⠀⠀⠘⠛⠛⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠛⠛⠃⠘⠛⠃⢀⣄⣙⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⢻⢿⣿⣿⣿⣾⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⣤⡄⢀⡀⠚⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⣿⣿⣷⣦⣀⠈⠂⠁⠊⡙⠃⡀⢠⠀⠈⠙⠛⢻⣿⣿⣿⣿⣿⣦⣂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠈⠙⡶⣦⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3540

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] How to Kill Unions (Staff on
Shoestring Budget Cannot Afford Lawyers)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


Some new_"young_professionals" at the EPO are paid ridiculously low salaries
and aren't expected to have qualifications and/or experience as required by the
EPC (upon which the very EPO as we know it today must exist).


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


What next for the EPO? "Gig economy"? Book a table, come in for a day, wait for
the next time the rubber-stamping line managers call in?


Context: The_EPO's_Staff_Union_(SUEPO)_Takes_Legal_Action_to_Rectify_the
Decrease_in_Wages_(Lessening_of_Purchasing_Power)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Quit_complaining._Your_salary_is_up_0.1%_while_inflation_is
       10%._If_we_lower_salaries,_we'll_defund_the_union..._Brilliant!⦈_




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

                    ䷩ 𝚕𝚒𝚗𝚎 3637

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/24/Microsoft_Windows_Slides_to_New_Lows_in_Colombia.shtml
    Gemini version at https://techrights.org/n/2024/12/24/Microsoft_Windows_Slides_to_New_Lows_in_Colombia.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Windows Slides to New Lows in
Colombia⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇500_Pesos_Tail⦈_


No_longer a 'cash cow'


JUDGING by the numbers we see on the_last_week_of_the_year, Windows_slid_to
about_a_quarter_of_the_market ("OS" "market share") in Colombia. Notice how
high a percentile (in the high 90s) Windows used to occupy in Colombia:


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


Narrowing down to laptops and desktops, it is even higher than that for GNU/
Linux:


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


We saw something similar this_past_summer when GNU/Linux_had_climbed_a_lot and
reached new_peaks. Evidently it was not_some_temporary_thing because over the
coming_months_this_would_carry_on. Now Windows is at an all-time low. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠄⣄⠀⠄⠑⠀⠨⡔⡆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⠀⠀⠀⠀⠠⣿⣋⠁⠀⠀⠀⠀⠌⢁⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠁⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⣩⠗⠀⠀⠀⡀⠀⢀⠐⠀⠀⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠢⠄⠀⠑⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢖⣒⣒⣒⣒⣒⣒⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣿
⣇⣖⢹⣯⣿⣋⣾⣿⣙⢹⣀⣭⣙⣋⣽⣿⣹⣘⣾⣹⣇⣉⣁⣿⣜⣏⣋⣹⡁⣖⣾⣯⣟⣉⣿⣿⣹⣍⣿⣷⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣯⣉⣹⣫⣋⣉⣿⣟⣉⣹⣋⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣝⣛⣛⣛⣛⣛⣫⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⡟⣛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿
⣿⣿⡇⣿⣿⣶⣶⣶⣶⣶⣶⣭⣭⣭⣭⣬⣭⣭⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿
⣿⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣀⡙⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠊⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣤⣤⠀⠀⠀⢠⣶⠃⠙⢉⡙⠛⡋⣛⠟⢛⠛⠻⠋⡙⠟⠛⠛⠙⠟⠛⠟⠛⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠿⠟⠀⠀⢀⣸⣿⣀⣼⣈⣅⣀⡄⢡⣄⣡⣄⣀⣄⣁⣇⡆⠀⣈⣄⣀⣄⣄⢠⣴⡇⣿⣿⣿⣿⣿⠋⠿⣿⡟⣠⠹⡏⠻⡿⠉⢿⠟⣿⡇⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⢛⠻⠿⣃⣾⣷⣆⣣⣿⣧⣴⣧⣴⣿⣦⣼⡌⡁⣿⣿
⣿⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀⣬⣤⣤⡌⣭⡭⡍⡉⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣷⣤⣶⡒⣃⣙⣉⠛⠋⢛⣛⣛⠛⢛⣃⢻⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠛⠿⠏⣉⣴⣦⣤⣦⡌⢡⠙⡟⢻⡿⠉⣿⠿⠿⢡⠉⣈⡙⠃⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣈⣁⡀⢀⣨⡍⣼⣿
⣿⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢡⣥⣥⣤⣥⣬⣤⣬⣭⣭⣭⣭⣭⣭⣭⣥⣬⣤⣄⣥⣬⣤⣬⣭⡭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⢭⣭⠭⠍⡅⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣡⣾⣿⣿⣿⣿⣿⢿⣿⠿⡿⠟⠛⠛⢋⡙⡙⡙⣋⡌⢃⣴⣤⣶⣦⣶⣬⣭⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⣰⣤⣤⣶⣿⡇⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⢀⣒⢋⢉⠉⠉⠉⠉⠐⣀⠒⢒⠒⠂⠚⠛⠛⠿⠛⠿⠿⠿⠠⠂⠻⠛⠻⠟⠟⡛⠛⠇⣉⡉⠉⠙⠉⠉⠉⠀⠁⠾⠇⠌⠟⠻⠿⠿⠿⠿⠇⣿⣿
⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣴⣶⣶⣶⣶⣴⣶⣶⣴⣶⣶⣤⣦⣤⣤⣶⣤⣤⣴⣤⣶⣴⣦⣶⣴⣦⣶⣶⣶⣴⣦⣶⣴⣦⣦⣴⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣾⣷⣿⣶⣶⣶⣿⣾⣿⣾⣿⣾⣶⣶⣿⣶⣷⣶⣶⣶⣿⣾⣿⣶⣾⣷⣾⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⡅⠤⠀⢣⠀⣤⡼⠁⣠⣤⡏⢀⣤⡀⢹⠀⣿⠀⢸⠀⣠⡄⢸⡄⢠⣤⠃⠠⠄⢹⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⢙⠀⠀⡀⢸⡀⠘⢱⡀⠙⠋⣃⠈⠛⢀⣼⠀⠉⡀⢸⠀⢸⡇⢸⣇⠈⠉⣄⠐⠛⢹⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⣉⣉⠹⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⠛⠟⠋⠛⠛⠻⠛⠻⠟⢁⣄⠈⠉⢠⣶⣶⣴⣶⣾⣿⣿⣿⣿⣶⣦⣴⣤⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠿⠿⠟⠛⠟⢉⠁⣴⣶⣾⣶⣶⣶⣿⣿⣿⣤⣾⣤⣴⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡿⢿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣤⣦⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣈⣉⣉⣉⡉⠛⠀⠈⠛⠻⠛⠛⠛⠋⣉⢉⣉⣁⣈⢀⣉⣉⣉⣉⡉⣉⣉⢉⠉⣉⣉⣉⣁⡉⢻⣿
⠿⠛⢉⣉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣴⠀⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠏⢰⣤⣁⣤⣈⣠⣄⠁⠯⠴⠤⠼⠿⠬⠥⠼⠦⠿⠬⠤⠼⠵⠭⠤⠿⠿⠿⠇⢸⣿
⠶⠾⠿⠿⠷⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠀⠚⠛⠃⠈⠀⠴⠦⠈⠛⠛⠻⠿⠛⠛⠛⠛⠟⠉⠁⠈⠁⠀⠐⠀⠀⠒⠛⠛⠛⠛⠛⠛⠛⠂⠀⡀⠐⠒⠐⠀⢀⢀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠄⣶⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿
⣿⣿⢟⡛⡟⡟⡛⣟⢻⣿⡟⣛⢿⠛⢛⢻⣿⡟⣿⢿⠻⠛⡛⡛⠛⣻⣿⡿⠿⢿⢛⠛⠛⠛⢻⢛⢛⢛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣷⣶⣷⣶⣾⣿⣿⣶⣿⣶⣶⣾⣿⣿⣶⣿⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3742

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/24/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2024/12/24/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Dec 24, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Serpent_OS_Enters_Alpha_with_GNOME_and_COSMIC_Spins,_Powered_by_Linux
      6.12_LTS⠀⇛


           Ikey Doherty released today the long-anticipated alpha version
           of his new independent Linux distro, Serpent OS, which features
           some of the latest and greatest technologies and applications.


   2. ⚓ Want_a_Really_Lightweight_Desktop_Linux_Experience?_Try_a_Window
      Manager⠀⇛


           Window managers manage only windows in the X Window System,
           providing you an alternative to Linux desktop environments


   3. ⚓ Linux_6.13-rc4⠀⇛


           So this definitely is looking a bit smaller than most rc4s


      ⚓  New⠀⇛


   4. ⚓ siduction_Linux_2024.1.0_Released_with_Xfce_4.20,_KDE_Plasma_6.2,_and
      LXQt_2.1⠀⇛


           siduction 2024.1.0 has been released today as a major update to
           this Debian-based GNU/Linux distribution featuring some of the
           latest and greatest technologies and desktop environments.


   5. ⚓ postmarketOS_24.12_Released_with_KDE_Plasma_Mobile_6.2.4,_GNOME_Shell
      46⠀⇛


           postmarketOS 24.12 was released today as the latest version of
           this Linux-based operating system for mobile devices that
           brings new features, support for new devices, and updated
           components.


   6. ⚓ GNU/Linux_and_Free_Software_Stories⠀⇛


           today's leftovers


   7. ⚓ Only_166_Voters_in_Fedora_Elections_Under_IBM⠀⇛


           very low


   8. ⚓ Programming_Leftovers⠀⇛


           Development news


   9. ⚓ Distributions_and_Operating_Systems:_NixOS_Hates_Precompiled_Programs,
      EasyOS_File_Information_App⠀⇛


           2 OS related picks


  10. ⚓ Applications:_Popcorn_Time,_Flatpak,_ScummVM,_Calibre⠀⇛


           Software and news about "apps" (Applications)


  11. ⚓ BSD_Leftovers⠀⇛


           BSD people and their reasonably technical posts


  12. ⚓ Audiocasts/Shows:_LINUX_Unplugged_and_Open_Source_Security_Podcast⠀⇛


           a pair of episodes


  13. ⚓ Kernel:_Unleashing_the_kernel_with_eBPF_Steinar_H._Gunderson's_Kernel
      adventures⠀⇛


           some Linux pieces


  14. ⚓ Open_Hardware/Modding/Retro:_Raspberry_Pi,_ESP32,_and_More⠀⇛


           Hardware picks for today


  15. ⚓ today's_howtos⠀⇛


           many for today


  16. ⚓ Security_Leftovers⠀⇛


           Security related picks, Windows too


  17. ⚓ Android_Leftovers⠀⇛


           Google proposes Android, browser contract changes to address
           Search antitrust ruling


  18. ⚓ OpenShot_3.3_Pre-Release_Introduces_Fresh_UI_and_Performance_Boosts⠀⇛


           The pre-release OpenShot 3.3 open-source video editor debuts
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  19. ⚓ 9to5Linux_Weekly_Roundup:_December_22nd,_2024⠀⇛


           The 219th installment of the 9to5Linux Weekly Roundup is here
           for the week ending on December 22nd, 2024.


  20. ⚓ Free_and_Open_Source_Software⠀⇛


           This is free and open source software


  21. ⚓ Review:_The_best_of_2024⠀⇛


           Another calendar year is drawing to a close


  22. ⚓ Archman_XFCE_Edition_2024-12_Stable_Release⠀⇛


           Archman XFCE Edition 2024-12, the final stable release of the
           year


  23. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


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


                         Span from 2024-12-17 to 2024-12-23
      890 /n/2024/12/17/
          Kali_Linux_2024_4_Released_with_Linux_Kernel_6_11_GNOME_47_and_.shtml


      725 /n/2024/12/15/
          Xfce_4_20_Desktop_Environment_Released_with_Experimental_Waylan.shtml


      691 /n/2024/12/17/
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      643 /index.shtml


      594 /n/2024/12/17/
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      522 /n/2024/12/22/Wine_10_0_rc3.shtml


      519 /n/2024/12/21/
          Darktable_5_0_Open_Source_RAW_Image_Editor_Officially_Released_.shtml


      502 /n/2024/12/21/today_s_howtos.shtml


      499 /n/2024/12/20/today_s_howtos.shtml


      497 /n/2024/12/19/
          _Kdenlive_24_12_Added_Multiple_Subtitle_Tracks_Removed_Qt5_Supp.shtml


      494 /n/2024/12/20/
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      481 /n/2024/12/20/
          DXVK_2_5_2_Improves_Support_for_Alpha_Protocol_Borderlands_2_an.shtml


      480 /n/2024/12/19/today_s_howtos.shtml


      472 /n/2024/12/17/Security_Leftovers.shtml


      471 /n/2024/12/19/today_s_howtos.2.shtml


      464 /n/2024/12/20/today_s_leftovers.shtml


      459 /n/2024/12/17/today_s_howtos.shtml


      459 /n/2024/12/20/today_s_howtos.1.shtml


      454 /n/2024/12/18/today_s_howtos.shtml


      444 /n/2024/12/21/today_s_leftovers.shtml


      443 /n/2024/12/20/Programming_Leftovers.shtml


      442 /n/2024/12/21/Programming_Leftovers.shtml


      441 /n/2024/12/19/
          LibreOffice_24_8_4_Office_Suite_Is_Now_Available_for_Download_w.shtml




⣿⠀⠸⢻⢣⢸⣧⢘⠈⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠹⢿⣭⡼⣿⣧⠁⡇⠀⢾⢠⣽⡇⠇⠀
⣟⢘⠇⢈⣀⣾⡟⢘⠠⠨⢟⣹⣿⣿⠏⠟⢞⡫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣧⣇⠹⣿⡇⠸⡿⠂⠑⠰⢀⡗⢸⡇⠈⠀
⠦⡛⢐⠂⠀⠖⠀⠘⡄⠈⢂⣇⡋⠁⠁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡧⠛⠀⠂⠹⣿⢇⢻⡄⠿⠀⡇⡇⠂⠀⢠⠎⢧⠘⠇⠀⠀
⣌⠁⠄⣀⢰⣷⡄⠈⠃⠂⡜⠃⠀⠀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡁⡻⠂⠀⠀⠄⢩⢨⡍⣛⡀⠀⡈⠑⠀⠀⠘⠘⢨⠀⠼⠀⠀
⠀⣀⡴⠀⢘⠙⣃⠠⠔⡐⢀⠠⠁⣾⣿⡿⣡⢃⣿⡽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣯⠃⠁⠀⠀⠀⠀⢸⠠⡅⠙⠂⠀⠃⠆⠀⠀⠂⠀⠊⠀⠘⢸⠀
⡠⠖⠚⢀⠈⠄⠠⠄⠀⠰⠆⠉⠈⣉⡍⠀⠸⠀⡞⣲⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡀⠀⠇⣆⢈⠂⠤⠤⠠⡈⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀
⠀⠀⢀⠈⠀⠈⠀⡤⠈⠠⢂⠠⠓⠛⠂⠁⠄⠀⠀⢃⢼⢻⢿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢹⢙⠃⠢⠅⠒⠀⢩⠀⠀⠀⠀⠀⠀⠈⠐⢠⡢⠄⡠⠤⠤⠠⠀⠢⠬⠉⠀⠤⠐
⠁⠐⠀⢀⠀⠀⠀⡙⠚⣋⠁⠀⠐⠁⢀⠐⠃⡀⠀⠀⠈⢘⠙⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⢿⢛⠀⠁⠀⠈⠀⠀⢀⠀⢀⠈⣀⢀⠀⠀⠀⠀⠀⣀⠠⠃⠡⠄⠀⢤⡀⠄⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠐⠂⠀⠐⠂⠈⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢉⠀⠉⠂⠦⠀⡘⠡⠀⠀⠀⡀⠀⢊⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠄⠀⡀⠀⠀⠉⡹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠀⠈⠀⠀⠀⠀⠈⠑⠒⠀⠐⠶⠂⠀⠀⡘⠤⠀⠀⠐⠠⡃⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⡠⠔⠃
⠐⠀⠀⠀⠀⠀⣀⡀⠀⠐⠀⠀⠀⢀⡀⠁⡀⣀⣀⢐⣲⣂⢀⡀⢀⠀⠀⠀⠈⠁⠉⠛⠛⠛⠛⠛⠋⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⢀⠁⠀⠈⠉⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠤⠠⠴⠄⠒⠀⠀⠒⡒⠃⢘⠁⠠⠒⠈⠀⠀⠂⠀⠀⡀⠀⣀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠐⠀⠁⠀⣀⡀⢀⠠⠀⠀⠀⠀⠠⠈⢀⣢⡔⠈⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠠⠈⠀⢄⡀⠤⢄⠀⠀⣈⣔⠲⠴⠚⠋⠅⣘⢋⠉⢁⠠⠀⠄⠀⢰⣶⣶⡶⠂⠀⠀⠀⡠⠀⡀⠠⠀⠉⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠉⠀⠁⠀⠈⠉⠁⢀⡀⠀⠁⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣩⡁⠠⠈⣩⣥⡂⣀⠌⢀⡰⠞⠫⠁⠐⠍⠋⠂⠁⠀⢸⣿⣿⡧⠀⢁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢉⡩⢅⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢢⠢⠆⠀⠀⡀⠁⠀⠁⠀⢀⣀⡂⠀⢀⠀⠴⠀⢀⠉⠠⣄⣬⣵⣖⣶⣶⣤⣦⣴⣤⣼⣯⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⡀⢀⣄⡀⠀⠀⠠⠄⠀⢀⣀⣀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⣄⡀⠀⠄⠀⠀⠀⠰⢿⡮⠁⠀⠀⢤⢄⣲⣦⣶⣄⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣛⣻⡖⡲⠃⠁⠀⢲⠶⡄⠂⠀⠀⠀⢠⠆⠄⣠⠄⢠⡀⠀⠀⠀⡀⢀⡀⠐⠀⠀
⢽⡐⣞⠞⢷⣦⠀⠀⠃⣛⣓⣠⣌⣩⠿⣾⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣀⣈⣋⣛⠀⡀⠀⠒⠛⠂⡛⣭⡾⣿⡇⠀⢀⠆⣡⣴⣆⣼⣷⣾
⣿⣿⣾⣾⣾⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⢟⣿⣿⣿⠛⡿⠁⠀⠰⠧⠟⡿⠙⣾⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⡀⢀⣠⣴⣤⣶⣤⣿⣧⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 4030

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/24/Terrible_Year_for_Microsoft_Windows_in_Cyprus.shtml
    Gemini version at https://techrights.org/n/2024/12/24/Terrible_Year_for_Microsoft_Windows_in_Cyprus.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Terrible Year for Microsoft Windows in
Cyprus⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024,
updated Dec 24, 2024


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


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


In Cyprus, Windows has_been_steadily_falling_as_a_platform_for_desktops/laptops
(down from 86% to 72% since January) and that matters a lot because desktops/
laptops_usage_there_is_still_about_50% - a lot higher than the global average.
Vista 11's adoption there has been rather poor (over_70%_of_Windows_users_still
believed_to_be_using_Vista_10) and this past summer we_saw_GNU/Linux_measured
at_over_5%_there.


What will 2025 bring? █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⢛⠽⣋⢫⢿⣟⣟⠛⠛⠅⠈⣀⡈⠁⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣀⣔⡷⠭⣛⢟⣄⣭⠽⣛⡛⢀⣂⣛⣋⡁⠐⠀⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡾⠷⣽⣨⣷⢫⣺⣿⣿⣿⠛⠿⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⡽⣿⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣟⣩⣿⣛⣛⢣⡀⠂⠀⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣎⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⠿⢹⡾⣷⣿⠈⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠐⡀⣹⣿⡏⢀⢘⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣼⠟⠡⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⢁⣿⣿⣷⠈⠂⠘⡻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣲⣏⣿⣁⠤⣠⣄⢤⡤⠤⠴⠤⠥⠬⠀⡤⠀⡀⠀⠠
⣿⣿⣿⣿⡻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⣿⣿⣇⠀⣄⣼⣿⠿⢿⡿⠿⠻⠋⠽⠉⠩⣉⠭⠟⣛⡓⠊⠒⠋⠐⠁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⢿⣷⠂⡄⢀⣿⣿⣿⣿⣿⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠒⠀⠀⠀⠀⠐⠤⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⡭⣽⣟⣯⡍⢹⠿⢿⢟⠷⢻⣷⣳⠝⠉⡤⠕⠉⡈⣀⡆⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠐⡴⠂
⢟⣿⣿⣻⣿⣿⣿⡿⢛⣫⡬⣭⣷⢭⢷⣟⠟⠫⡿⣟⣗⣹⣛⣻⣯⣡⣝⣝⠻⣀⡾⣿⣣⠝⢱⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣤⡂⠈⠥⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⣀⡈⠀⠀⠘⠁⠀
⣿⣿⣿⣿⣟⣛⣼⣭⢷⣉⣭⣷⣾⣿⢮⣽⡾⢚⣷⡶⣟⡿⡦⣾⡏⣙⢝⣟⢦⣶⣴⡥⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⠯⠾⠯⣻⣿⣿⢿⢿⢟⡿⣟⡟⢿⣂⠴⢿⢿⠇⠊⢾⣈⢖⣿⡟⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⠁⠅⠄⠁⠐⠢⢐⣤⣼⣿⣿⠟⠑⠗⢉⠘⢐⣽⣷⣶⡶⣨⠄⡆⣴⣵⡟⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣋⡃⣠⡯⣷⣿⣿⣻⣿⣿⣛⣟⣿⢾⠄⠈⠀⣺⣿⡿⡿⢺⡿⣿⠿⢡⠉⠴⠉⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀
⢷⣾⡿⣿⡿⣻⣭⣿⣿⣿⡿⣿⣿⣶⣦⡴⠿⣟⢭⣮⡏⠉⣋⠡⠐⠘⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠙⠽⢿⣿⣿⢽⣏⣋⣯⡥⡹⠋⠂⠘⠂⠉⠤⠄⠀⠂⠌⠀⠀⠀⠀⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⠀⠀⠀⠀⢠⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡷⠶⠶⢶⠤⠀⠈⠩⠭⢉⣉⣉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠡⠔⠀⠂⢀⠤⣤⡀⡤⠉⠉⠉⠙⠛⢛⠻⠿⠿⢿⣿⣿⣷⣸⣗⣲⡶⠦⠰⠖⠀⢸⠀⠂⠀⠦⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⣬⢠⠀⡀⠀
⠐⠀⠀⠀⠈⠀⠀⢤⡸⣿⣭⣍⣋⡛⠙⠭⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠐⢶⠾⣿⣿⡟⡟⠛⢻⠻⣿⡉⢩⣀⣠⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
⠒⠒⠒⠒⠓⠛⠚⠚⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⣶⣦⣤⣄⣙⡫⠶⣿⣿⣦⣿⣿⣾⣶⣿⣀⣿⠿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠤⠄⠀⠀⠀⠀⠀⠀⠂⠀⠐⣲⠂⠀⠻⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⣠⣤⣭⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠠⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡗⣶⣾⣿⣿⣿⣿⣿⣻⣿⣟⣾⣿⣯⣽⠿⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠞⠚⠿⠿⠯⢭⣿⡤⠶⠶⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⣤⣤⣤⣤⣤⣶⣦⣶⣶⣴⣾⠟⠚⠓⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣛⡻⢿⣿⣿⣿⣿⣿⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⢸⢑⣂⣧⣒⢾⠘⢱⡆⣶⢱⣶⢹⢰⣶⢹⣿⠰⣿⣿⢸⢰⣶⢹⢐⣂⡇⣴⡗⣒⢸⢰⣾⣿⢰⡆⣏⠶⢰⣿⣧⣍⡻⡜⡏⣆⡒⢶⢰⡇⣒⣸⣧⣶⢰⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣭⣵⣾⣦⣭⣧⣭⣼⣼⣧⣵⣭⣦⣥⣾⢠⣥⣾⣿⣷⣬⣵⣿⢠⣥⣾⣦⣭⣧⣿⣧⣥⣼⣮⣽⣿⣼⣧⡏⠤⢌⣿⣧⣭⣴⠗⣼⣧⣭⣾⣬⣷⣭⣽⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⠹⣿⠏⢹⠿⢿⡿⠿⡏⣿⢿⠿⢿⠟⢿⣿⢋⣭⣹⠹⠿⣿⠿⠿⡿⠿⡿⠿⢿⣿⡟⣩⣍⢿⣿⠿⠿⠿⡿⠿⡿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣧⠋⡄⠘⣩⠅⡇⣿⡇⡑⢇⢬⡥⡇⣿⣿⢷⡮⢹⢸⣿⢸⢩⠅⡇⣿⡁⣭⢼⣿⡟⢿⣿⣆⢋⡆⢾⠇⡇⣿⡇⣿⠇⢧⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣾⣷⣾⣶⣷⣷⣿⣷⣿⣾⣶⣶⣷⣶⣿⣶⣶⣿⣾⣿⣾⣶⣶⣷⣿⣿⣶⣾⣿⣿⣶⣶⣛⣼⣇⣶⣾⣷⣿⣿⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⡏⡿⠿⡿⠿⢿⣿⣿⣿⣯⣭⢻⠿⠿⠿⠿⣿⣩⡝⣏⣍⢟⣭⢻⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⡇⣏⣂⣇⣿⣸⣿⣿⣿⣟⣛⣹⣐⣒⣜⣛⣿⣋⣚⣟⣛⣞⣑⣫⣬⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣟⠻⠻⠻⣻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣧⣴⣴⣴⣼⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡐⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣷⣦⣀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣦⣁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠻⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⡿⠿⠿⠿⠟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣤⣤⣤⣤⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣉⣠⣤⣤⣤⣤⣦⣤⣄⣀⣀⠱⠉⠉⠉⠉⠁⠎⠉⠙⠛⠛⢛⠻⠿⠿⠿⠿⡻⠿⠿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣗⣔⣠⣀⣸⡇⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣀⡐⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⣀⠀⠀⠀⢀⣿⠿⠿⠛⠿⠿⠟⠻⡿⠿⡿⠿⡿⠿⠿⠿⠿⠛⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⢿⣿⠂⠀⠀⢀⣿⠀⢐⠀⠂⠀⠀⠐⡀⠒⡀⠂⡀⠀⠀⢰⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⡟⠛⢛⠛⢻⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣶⣶⣶⣶⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⠿⠿⢿⢿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣗⣀⣠⣠⣹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⡏⠉⢩⠉⢹⡇⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡻⠟⠛⠋⠉⠐⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣛⠿⠿⠛⠛⢛⠛⠛⠋⠉⠁⠒⠉⠉⠉⠉⠉⠍⠉⠁⣀⣀⣬⣤⣤⣤⣤⣤⣅⣀⣀⣀⣀⠐⢀⣀⣀⣠⣤⣥⣤⣶⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠿⡿⠿⠟⠋⢠⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⠉⠛⡍⠛⠛⠛⠛⠟⡛⠿⠿⠿⠿⢛⠻⠛⠛⠛⠋⡝⠉⠉⠉⢀⣘⣀⣀⣀⣀⠀⠂⠉⠉⠙⠛⢃⠻⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⠱⠉⠉⠀⠀⠀⠃⢀⣠⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⠱⠁⠀⠠⠀⠂⠭⠉⠉⠉⠉⠐⠈⠉⠛⠛⠻⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⡿⠿⠿⢿⠘⠀⠤⠤⠴⠶⡲⠿⠿⠿⠿⠛⠻⠷⠶⠶⠤⠡⠤⠤⠤⠤⠌⠡⠤⠤⠤⠄⡉⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠉⠤⠤⠤⠤⠤⠡⠤⠤⠤⠤⠈⠠⠤⠤⠤⠤⡡⠤⠤⠤⠤⠈⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣧⣴⣴⣼⣦⣤⣤⣤⣤⡤⠤⢤⣤⣤⣶⠦⢴⣦⣤⣤⡤⠤⢤⣤⣤⣶⠤⠶⣦⣴⣦⡴⠦⢤⣶⣤⣶⠤⠶⣤⣦⣤⡤⠤⢤⣤⣤⣤⡤⠤⣤⣤⣤⣴⠦⢴⣦⣤⣤⡤⠤⣤⣤⣤⣶⠤⢼⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡅⠄⣾⣿⣿⣫⠁⣰⣿⣿⣟⡉⠄⣾⣿⣿⣫⡡⢰⣿⣿⣟⡉⠀⣾⣿⣿⣏⡁⢰⣿⣿⣟⣉⠀⣾⣿⣿⣏⡑⢰⣿⣿⣿⣉⠀⣶⣿⣿⣏⡕⢰⣿⣿⣿⣩⠀⣲⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢂⣾⣿⣿⡃⠑⣰⣿⣿⠟⠀⢂⣾⣿⣿⢃⠑⣰⣿⣿⡟⠀⢂⣾⣿⣿⢃⠑⣰⣿⣿⡟⡀⠂⣼⣿⣿⢓⠐⣰⣿⣿⡟⡀⠂⣴⣿⣿⢛⠐⢢⣿⣿⡟⡂⠂⣰⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢣⣾⣿⣿⠏⠿⣴⣿⣿⡿⠹⢧⣾⣿⣿⠯⠻⣴⣿⣿⣿⠛⢧⣾⣿⡿⠯⠹⣴⣿⣿⣿⠉⠧⣼⣿⣿⠏⠹⣴⣿⣿⡿⠉⠇⣼⣿⣿⡿⠙⢦⣿⣿⣿⠫⠗⣼⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠋⢀⣠⣿⣿⡿⠁⢀⣼⣿⣿⡛⢀⣀⣿⣿⣿⡁⠀⣴⣿⣿⣟⠀⢠⣾⣿⣟⠛⠀⣸⣾⣿⡟⠅⢀⣶⣿⡿⡟⠈⣀⣿⣿⡏⢥⢠⣾⣿⡿⠍⠀⣸⣿⣿⠟⡃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣦⣿⣿⣿⣶⣤⣼⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣤⣿⣿⣿⣷⣬⣿⣿⣿⣧⣔⣸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣽⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⣿⡟⠟⠟⠻⠿⠿⠻⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠻⣿⠛⡟⠿⠟⡿⠿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣣⣾⣧⣠⣰⣀⣇⣘⣀⣣⣠⣐⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣡⣾⣄⣃⣸⣀⣌⣸⣇⣣⣀⣀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⣿⡿⡛⠟⣛⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠻⣿⠛⡟⠿⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣣⣾⣧⣋⣔⣂⣏⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣡⣾⣀⣃⣰⣀⣃⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡛⣿⡿⢛⠻⠿⠿⠿⠿⠿⡿⢿⡟⡛⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⠿⠻⠿⢿⠿⡿⡻⠛⠿⠿⠿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣾⣧⣭⣼⣤⣤⣥⣼⣼⣤⣴⣧⣭⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣤⣥⣤⣼⣤⣦⣼⣇⣠⣤⣤⣤⣤⣤⣤⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 4151

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/24/The_EPO_s_Staff_Union_SUEPO_Takes_Legal_Action_to_Rectify_the_D.shtml
    Gemini version at https://techrights.org/n/2024/12/24/The_EPO_s_Staff_Union_SUEPO_Takes_Legal_Action_to_Rectify_the_D.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The EPO's Staff Union (SUEPO) Takes Legal
Action to Rectify the Decrease in Wages (Lessening of Purchasing
Power)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Litigation_on_the_2021_Salary_Adjustments:_Streamlined
Process⦈_


Aside from labour abuses or violations of the rights of workers and serious
violations_of_patent_laws_(in_pursuit_of_more_money) there have been actual
crimes at the EPO; nobody is ever held accountable for those because of
diplomatic immunity (legal vacuum)


SUEPO Central Bureau (staff union of the EPO "Central Bureau", i.e. all
branches) circulated a call to join the union yesterday. In the Benoît
Battistelli days most EPO staff was in the union; under António_Campinos staff
gets paid a lot less (new recruits are on terrible contracts), so joining the
union in order to support the union is probably a lot harder, at the very least
due to prohibitive costs. Either way, here is what the union published:


     23 December 2024
     su24019cp 0.2.1 – 5.1 – 5.2


     § Litigation on the 2021 Salary Adjustments:
     Streamlined Process⠀➾


     Dear SUEPO members,
     Dear colleagues,

     The new salary adjustment method has resulted in a significant
     reduction in our annual salary adjustments from 2021 to 2025. A fair
     salary adjustment method is fundamentally a statistical tool
     reflecting the average salary adjustments in real terms for civil
     servants in selected reference Contracting States of the EPC to our
     adjustments. After decades of salary adjustment methods without major
     social unrest, this balanced approach was disrupted by the
     Administrative Council’s decision CA/D 4/20, adversely affecting both
     employees and pensioners. If national salary indexations exceed
     inflation on average, our adjustments are cut; conversely if they
     fall below inflation, we bear the full impact. Furthermore, the
     current adjustment method contains numerous legal inaccuracies and
     mathematical inconsistencies.


     When this inequitable method was first applied to the calculations
     for 2021 salaries and pensions, it resulted in an immense reduction
     of the statistically correct adjustment amounts by more than –86%. As
     a reaction to this, SUEPO has supported its members in challenging
     this salary adjustment method and its implementation through
     managerial review requests and internal appeals (reference numbers:
     RI/2021/054 for active employees, RI/2021/055 for pensioners). Many
     members participated in these procedures, leading to a largely
     positive opinion from the Appeals Committee. However, the appellants
     ultimately received a negative decision from the Office, which
     diverged from the Appeals Committee’s unanimous opinion without
     providing convincing justifications.


     SUEPO's lawyers have therefore prepared a complaint regarding the
     salary adjustment method and its implementation for 2021 before the
     Administrative Tribunal of the ILO. It has been crucial for SUEPO to
     pursue a well-organised lawsuit to minimise unnecessary
     administrative burdens for the Tribunal while ensuring legal
     certainty for our members. The approach consisted of two key
     strategies:


        1. Negotiations with the Office: SUEPO has initiated discussions
           (see our publication of 31 October 2024) to ensure that the
           President issues a declaration confirming that any Tribunal
           judgment on the validity of the method will be given global
           effect. We are pleased to report that on 17 December 2024, the
           President issued such an erga omnes declaration, creating
           individual rights for all concerned. This erga omnes
           declaration holds significant importance for all SUEPO members
           and for all EPO staff.


        2. Simplified Complaint Procedure: Our law firm has successfully
           coordinated with the Registrar of the Tribunal to establish a
           streamlined complaint procedure. A restricted group of
           representative complainants (active employees and pensioners
           residing in various places of employment and Contracting
           States) will be represented by the lawyers in a joint reference
           complaint against the new salary adjustment method and its
           implementation in 2021. SUEPO will therefore refrain from
           distributing complaint templates to the members so that the
           litigation can be conducted as efficiently as possible before
           the Tribunal and we can contribute to a hopefully timely
           judgment.


     These developments mark a significant milestone in our efforts to
     streamline the litigation on the 2021 salary adjustments. The law
     firm engaged by SUEPO and the individual complainants will submit the
     joint reference complaint in close consultation with us by the
     deadline of 8 January 2025. If you have any further questions, please
     reach out to your Local Bureau. SUEPO is committed to efficient
     proceedings before the Tribunal.


     SUEPO will further work to ensure that we establish a fair, balanced
     and legally sound salary adjustment method again in the coming years.
     It is worth noting that consensus on salary adjustment methods is
     common among other international organisations. SUEPO is eager to
     achieve a similar outcome with the Office in the future.


     Thank you for your engagement and your continued support.


     Your SUEPO Central Bureau


     PS: SUEPO legal cases are prepared by lawyers specialised in
     international labour law, and the associated costs which are not
     reimbursed by the opponent are covered by the yearly contributions of
     union members. A warm thank you to our faithful members!


There is also a shorter and more concise version of the above: (hyperlinks
included)


     Dear SUEPO members, Dear colleagues,

     The new salary adjustment method has resulted in a significant
     reduction in our annual salary adjustments from 2021 to 2025. SUEPO
     has supported its members in challenging it via internal appeals RI/
     2021/054 for active employees and RI/2021/055 for pensioners.
     However, the appellants ultimately received a negative decision from
     the Office, which diverged from the Appeals Committee’s unanimous
     opinion.

     SUEPO's lawyers have therefore prepared a complaint regarding the
     salary adjustment method and its implementation for 2021 before the
     Administrative Tribunal of the ILO. We followed two steps:


        1. Negotiations with the Office: SUEPO initiated discussions (see
           our publication_of_31 October_2024) to ensure that any Tribunal
           judgment on the validity of the method will be given global
           effect. We are pleased to report that on 17 December 2024, the
           President issued an erga_omnes_declaration, creating individual
           rights_for_all_those_concerned_by_the_salary_adjustment,
           regardless of whether they file the complaint.
        2. Simplified Complaint Procedure: Our law firm has coordinated
           with the Registrar of the Tribunal to establish a streamlined
           complaint procedure. A restricted group of complainants will be
           represented by the lawyers in a joint reference complaint.
           SUEPO will therefore refrain from distributing complaint
           templates to the members so that the litigation can be
           conducted as efficiently as possible before the Tribunal.
     The law firm will submit the joint reference complaint by the
     deadline of 8 January 2025. If you have any further questions, please
     reach out to your Local Bureau. SUEPO is committed to efficient
     proceedings before the Tribunal.

     SUEPO will further work with the Office to ensure a fair, balanced
     and legally sound salary adjustment method again in the coming years.
     It is worth noting that consensus on salary adjustment methods is
     common among other international organisations.

     [...]
     Your SUEPO Central Bureau

     PS: SUEPO legal cases are prepared by lawyers specialised in
     international labour law, and the associated costs which are not
     reimbursed by the opponent are covered by the yearly contributions of
     union members. A warm thank you to our faithful members!

     The bargaining power of staff increases with every new SUEPO member –
     please consider joining your local SUEPO section if you have not done
     so yet!

     Membership form Munich, The_Hague, Berlin, Vienna


What they keep referring to as "the Tribunal" has its own issues. The tribunal
itself has openly (publicly) complained that it was unable to cope with the
volume of complaints emanating from the corrupt EPO. The corruption at the EPO
has rapidly become a problem for the European Union (EU) and the EU's
reputation. In a sense, the EPO_is_highly_damaging_to_the_European_Project (or
Union and beyond). One wonders if the EU can survive such scandals, among other
problems. It must do something about the EPO. Covering up EPO corruption is not
a viable, long-term option. Complicity_and_participation_in_the_corruption
worsens_matters. █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣶⣾⣿⠿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠓⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣼⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣙⣿⠯⠭⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⣛⣛⣛⣿⣟⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠁⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠠⠤⣄⣒⣂⣀⣀⣀⣀⣀⣀⣤⣤⣤⡄⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⢸⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠋⢸⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⡟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣐⣒⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⡏⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿

                    ䷩ 𝚕𝚒𝚗𝚎 4397

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/24/Where_the_Population_is_Controlled_by_Skinnerboxes_Inside_Peopl.shtml
    Gemini version at https://techrights.org/n/2024/12/24/Where_the_Population_is_Controlled_by_Skinnerboxes_Inside_Peopl.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Where the Population is Controlled by
Skinnerboxes Inside People's Pockets (or
Purses)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


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


Let us say that a skinnerbox nation is a nation where the large majority of
people are attached to a_skinnerbox, controlling or manipulating them through
"apps". Judging by data_from_here, here are the top nations by mobile usage
(skinnerbox nations):


Country                            Mobile usage (percent of Web-connected
                                   devices)


Sudan                                                               94.48


Chad                                                                90.78


Iraq                                                                90.21


Syrian Arab Republic                                                89.41


Philippines                                                         88.55


Palestinian Territory                                               88.47


Gambia                                                              87.94


Mali                                                                 87.5


Mayotte                                                             87.38


Congo (Democratic Republic of the)                                  86.54


Cameroon                                                            86.54


Niger                                                               86.49


Comoros                                                             86.35


Mauritania                                                          86.34


Haiti                                                               86.23


Djibouti                                                             86.2


Guinea                                                              86.13


Wallis and Futuna                                                   85.84


Christmas Island                                                    85.71


Afghanistan                                                          85.6


Nigeria                                                             84.75


Central African Republic                                            83.77


Sierra Leone                                                        83.51


Vietnam                                                              83.5


Liberia                                                             82.21


Senegal                                                             81.63


Benin                                                               81.45


Libya                                                               81.31


French Polynesia                                                     81.2


Swaziland                                                           81.07


Saudi Arabia                                                        80.76


Cote dIvoire                                                        80.65


Zambia                                                              80.61


Mexico                                                              80.52


Tanzania                                                            80.41


Guinea-Bissau                                                       80.31


Mozambique                                                          79.64


Albania                                                             79.64


Gabon                                                                79.6


India                                                               79.55


Somalia                                                             79.55


United Arab Emirates                                                79.52


Turkmenistan                                                        79.47


Norfolk Island                                                      79.43


Nauru                                                               78.95


Burkina Faso                                                         78.8


Yemen                                                               78.75


New Caledonia                                                       78.35


Jordan                                                              78.26


Kiribati                                                            78.24


Vanuatu                                                             78.16


Oman                                                                78.04


Kuwait                                                              77.21


Ethiopia                                                            77.03


Myanmar                                                             76.62


Malawi                                                              76.58


Maldives                                                            76.54


Lao Peoples Democratic Republic                                     75.34


Ghana                                                               75.31


Nepal                                                               75.18


Cuba                                                                74.93


Uganda                                                              74.84


Qatar                                                               74.52


Burundi                                                             73.91


Turkey                                                              73.74


Pakistan                                                            73.49


Iran                                                                73.48


Tonga                                                               73.42


Fiji                                                                73.41


French Guiana                                                        73.2


Aruba                                                                73.1


Papua New Guinea                                                     72.2


Mauritius                                                           72.13


Guadeloupe                                                          71.88


Bahrain                                                             71.86


Bangladesh                                                          71.74


South Africa                                                        71.73


Indonesia                                                           71.57


Kenya                                                               71.39


Azerbaijan                                                          70.85


Cape Verde                                                          70.52


Zimbabwe                                                            70.51


Jamaica                                                             70.39


Congo (Republic of the)                                             70.35


Tajikistan                                                          70.25


Macedonia                                                            70.1


Angola                                                              70.06


Montenegro                                                          69.91


Bahamas                                                             69.84


Bermuda                                                             69.63


Algeria                                                             69.51


Bhutan                                                              69.22


Guatemala                                                           69.13


Suriname                                                            68.98


Namibia                                                             68.71


Reunion                                                              68.7


Solomon Islands                                                     68.55


Lebanon                                                             68.36


Dominican Republic                                                  68.02


Colombia                                                            67.46


Bulgaria                                                            67.44


Brazil                                                              67.29


Lesotho                                                             67.12


Guyana                                                              66.37


China                                                               66.26


Egypt                                                               65.94


Samoa                                                               65.77


Israel                                                              65.42


Honduras                                                            65.18


Madagascar                                                          65.14


Micronesia                                                          64.55


Puerto Rico                                                         64.39


Gibraltar                                                           64.31


Timor-Leste                                                         64.29


Kyrgyz Republic                                                     64.22


Botswana                                                            63.94


Singapore                                                            63.9


Saint Martin                                                        63.69


Hungary                                                             63.57


Tunisia                                                             63.55


British Virgin Islands                                              63.51


Saint Helena                                                        63.45


Nicaragua                                                           63.41


Bosnia and Herzegovina                                              63.27


France                                                              63.12


American Samoa                                                      62.74


Serbia                                                              62.41


Palau                                                               62.24


Venezuela                                                            61.9


Morocco                                                             61.28


Belize                                                              61.16


Cook Islands                                                        60.91


Poland                                                              60.71


Uzbekistan                                                          60.17


Argentina                                                            60.1


Panama                                                              59.91


Ireland                                                             59.82


Martinique                                                          59.45


South Korea                                                         59.36


Togo                                                                59.07


Spain                                                               58.95


El Salvador                                                         58.17


Georgia                                                             57.88


Paraguay                                                            57.86


Saint Lucia                                                         57.82


Cambodia                                                            57.78


Bolivia                                                             57.62


Niue                                                                57.25


Thailand                                                             57.2


Moldova                                                              57.2


Falkland Islands (Malvinas)                                         57.01


Trinidad and Tobago                                                 56.92


Cayman Islands                                                      56.91


Costa Rica                                                           56.7


Antigua and Barbuda                                                 56.52


Brunei Darussalam                                                   56.37


Marshall Islands                                                     55.8


Kazakhstan                                                          55.62


Andorra                                                             55.16


Macao                                                               55.01


Faroe Islands                                                       54.41


Croatia                                                             54.36


Norway                                                              54.16


New Zealand                                                         53.98


United Kingdom                                                      53.97


Greenland                                                           53.93


Guernsey                                                            53.81


Tokelau                                                              53.7


Ecuador                                                             53.38


Turks and Caicos Islands                                            53.37


Malta                                                               53.36


Guam                                                                53.03


Romania                                                             52.99


Malaysia                                                            52.83


Grenada                                                             52.44


Saint Kitts and Nevis                                                52.4


Cyprus                                                              51.74


Anguilla                                                            51.69


Northern Mariana Islands                                            51.67


Mongolia                                                            51.65


Rwanda                                                              51.23


Uruguay                                                             51.05


Jersey                                                              51.02


Belgium                                                             50.84


Hong Kong                                                           50.58


Lithuania                                                           50.44


Taiwan                                                              50.23


Pitcairn Islands                                                       50


Luxembourg                                                           49.9


Isle of Man                                                         49.85


Seychelles                                                          49.84


Saint Vincent and the Grenadines                                    49.48


Italy                                                                49.3


United States of America                                            49.06


Barbados                                                               49


Germany                                                             48.93


Chile                                                               47.77


Slovenia                                                            47.47


Peru                                                                46.49


Czech Republic                                                       46.3


Dominica                                                            46.28


Belarus                                                             46.26


Australia                                                           45.65


Sweden                                                              45.55


Equatorial Guinea                                                   45.32


Austria                                                             45.14


Japan                                                               45.07


Slovakia (Slovak Republic)                                          44.94


Canada                                                              44.85


Iceland                                                             44.46


North Korea                                                         43.86


Eritrea                                                             43.41


Switzerland                                                         43.21


Sao Tome and Principe                                               42.96


Netherlands                                                            42


Saint Barthelemy                                                    39.08


Sri Lanka                                                           38.98


Greece                                                              38.71


Saint Pierre and Miquelon                                            38.6


Monaco                                                               37.1


Russian Federation                                                  35.94


Ukraine                                                             34.08


Portugal                                                            33.81


Finland                                                             33.53


Armenia                                                             33.36


Liechtenstein                                                        33.1


Denmark                                                             31.84


Svalbard & Jan Mayen Islands                                        30.36


San Marino                                                          30.08


Montserrat                                                          29.88


Latvia                                                              27.06


Estonia                                                              19.5


Tuvalu                                                              14.71


Holy See (Vatican City State)                                        8.29


It should be noted that most of today's mobile devices are very freedom-
hostile. A very small fraction of mobile users practise or exercise freedom/
control over the skinnerbox. █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣶⢶⡨⠻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣄⠀⠀⢀⠀⠀⠀⣀⣔⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢺⠛⠒⠛⠛⣿⢸⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5152

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 24/12/2024: Deedum Gemini
Client Gets Colour Support, Advent of Code
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Technology and Free Software⠀➾


                # ⚓ Counterpoint_Parsing_Problems⠀⇛


                       Counterpoint assumes distinct voices that may not
                       be present in the input material; for example the
                       voices may be presented as simultaneous events in
                       MIDI, and if the number of events vary vertically,
                       into what voice do the various events belong, if
                       any? Here one may guess based on the range of
                       previously identified voices and give priority to
                       the typically more important bass and soprano
                       lines, but that still leaves problems. And now for
                       a very contrived example.


                # ⚓ Adding_Blender_(publ._2024-12-23)⠀⇛


                       Silas drew up the initial sketches for another
                       adding machine. The basic concept is presented in
                       three steps: [...]


                # ⚓ pinephone_postmarketos_vs_termux⠀⇛


                       As I've written before, I bought a Pinephone
                       earlier this year. It was not a good experience,
                       although the crashes have been less frequent. Now
                       I'm only getting crashes whenever I try to rotate
                       the screen on VLC or go fullscreen. Still a big
                       bug, but I can do other things as well. I should
                       mention I barely ever try any new apps because they
                       all run like shit.


                       I use PostmarketOS (PMOS; excuse me for any
                       capitalization differences). It's been the best OS
                       I've used with it, but it's far from perfect. I'm
                       pretty sure my Pinephone only has 2GB RAM, which
                       would be decent 10 years ago, but really struggles
                       with anything that is mildly complex, like Firefox.
                       I believe the app store in PMOS is using mainly GTK
                       stuff, but I don't know: they're all pretty slow,
                       which is a bit disheartening. I'm able to get links
                       -g working, which is great. Lynx also predictably
                       works. I can even run a PHP server if I wish, but
                       the main feature I was looking for: a mobile Linux
                       PC, is just underwhelming thanks to the low-spec
                       hardware. I've rarely used it as such and the last
                       time I did, I plugged it directly into a monitor
                       which evidently had a higher power output than the
                       Pinephone was prepared to handle. Nothing like
                       smelling burning circuitry when you're done with a
                       session. To be fair, that is definitely user error
                       as the instructions clearly stated not to go over
                       10W with charging. Nothing seems to have been
                       damaged, but I know better for next time.


                # ⚓ update:_Bad_hypens_break_documentation?⠀⇛


                       The kind folks of my local Linux User Group
                       suggested, that the value of the well known
                       environment Variable LANG might be responsible for
                       this. In my alplinelinux instance LANG ist set to
                       'C.UTF-8'. And resetting that to just 'C' makes the
                       funny characters go away. So an alias might help:
                       [...]


                # ⚓ Fed_up_with_the_industry⠀⇛


                       Seriously, I'm sick and tired. The mainstream IT
                       industry is a total mess now.


                       Yes, I say that. It stopped solving real problems
                       long ago, it stopped making the world a better
                       place long ago, it started being "a thing in
                       itself" with all the "innovations" made up to
                       merely justify its own further existence. And it's
                       not just because a new fad appears every 3 to 5
                       years, which in turn just adds to an already long
                       list of totally useless and, in the long run, even
                       harmful things that simply must die. No, the main
                       issue with that is being able to produce at least
                       some value for the company (or even the entire
                       industry) no longer equals to being able to produce
                       any value for the world's people. In fact, in some
                       cases, NOT producing that value for the companies
                       (especially big corporations) ends up being more
                       useful for the society.


                # ⚓ Come_wander_the_aisles_of_my_digital_doomsday_library⠀⇛


                       The attentive amongst you may have intuited that
                       like to read. In the tradition of my forebears, I
                       have amassed quite the treeware collection.
                       Likewise, as an early participant in the
                       information age, I have also amassed quite the
                       digital archive. Call it my digital Svarlsbard if
                       you will; my Library Galactica at the end of the
                       Universe. Here is a subsection that I choose to
                       share; if you would like access to a sealed
                       section, please send me a misfin mail and let me
                       know who you are (maybe provide some Gemini links),
                       what you want access to, and the SHA-256
                       fingerprint of your client certificate.


                # ⚓ December_(with_no)_computing⠀⇛


                       December at work was a bit busy. A much more
                       travelling than I have been used to and also other
                       things. So I had little time for anything else.
                       Even my cycling (I normally commute daily on a
                       bicycle) was somewhat limited. Also I had some flu
                       in November and as a result I was cautious when it
                       came to outdoor and social activities.


                # § Internet/Gemini⠀➾


                      # ⚓ First_"release"_with_color_support⠀⇛


                             Hi everyone who might be interested!


                             since a couple of weeks ago, I've been
                             tinkering with the idea of adding ANSI color
                             support to the Deedum Gemini client.


                             This has been relatively easy (in hindsight,
                             a lot of things are), due to the nature of
                             open source software, and the availability of
                             libraries that made it easier. My lack of
                             knowledge made it a bit harder.


                             [...]


                             To get this to work, I had to fork and modify
                             a bit not only Deedum itself, but also the
                             library I found that already interpreted the
                             ANSI color codes ( but only had support for
                             some of the available formats).


                # § Programming⠀➾


                      # ⚓ Advent_of_Code_2024,_Day_7⠀⇛


                             If you check the operands from the right, you
                             can prune recursion branches, because you
                             know that * a concatenation with the last
                             operand can only have happened if the result
                             ends in the same digits as the operand, * a
                             multiplication with the last operand can only
                             have happened if the result is divisible by
                             the operand, and * an addition with the last
                             operand can only have happened if the result
                             is not less than the operand. I only found
                             this tip later.


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





                    ䷩ 𝚕𝚒𝚗𝚎 5368

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 24/12/2024: Labour Strikes and TikTok
Scrambling to Prop Up Radical Politicians That Would Protect
TikTok⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 24, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Pseudo-Open_Source
                # Openwashing
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # 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
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Jacobin Magazine ☛ Finnish_Right-Wingers_Are_Defunding_Culture⠀⇛


                 Connecting the anti-cuts movement to Finland’s
                 existential struggle in the tsarist period is a move
                 aimed at drawing cross-sectional support. While it
                 opposes government cuts, Sakset seis is keen to point out
                 that it is nonpartisan, a point that Hanna Kosonen —
                 cofounding member of Sakset seis and secretary general of
                 Forum Artis, a cooperative of arts organizations —
                 emphasized to me in our telephone interview. The campaign
                 insists that an “Independent Finland cannot exist without
                 a culture of its own,” positing the cuts as a threat to
                 the Finnish way of life, which has long included strong
                 welfare and public spending provisions. The statement
                 continues, stating that it is “determined to prove the
                 burning desire of a small nation for independence and a
                 culture of its own.”


          o ⚓ PC World ☛ Gordon_Mah_Ung,_PCWorld_editor_and_renowned_hardware
            journalist,_dies_at_58⠀⇛


                 Gordon studied journalism at San Francisco State
                 University and then worked as a police reporter for the
                 Contra Costa Times in the late 1990s. In 1997, he joined
                 Computerworld (a PCWorld sister publication) before I
                 recruited him to join boot magazine (later re-launched as
                 Maximum PC), where he would ultimately lead hardware
                 coverage for 16 years.


          o ⚓ Simon Willison ☛ My_approach_to_running_a_link_blog⠀⇛


                 I started running a basic link blog on this domain back
                 in November 2003—publishing links (which I called
                 “blogmarks”) with a title, URL, short snippet of
                 commentary and a “via” links where appropriate.


                 So far I’ve published 7,607 link blog posts and counting.


          o ⚓ Matan Abudy ☛ Dividing_cost_by_times_of_use⠀⇛


                 This isn’t a justification for buying expensive
                 things—it’s just how I try to evaluate buying things that
                 I want and believe will serve me well. Whether they’re
                 practical (apps I use or services I’m subscribed to) or
                 simply add joy to my life every time I use them (I’m
                 looking at you, my sneakers collection.)


          o § Science⠀➾


                # ⚓ Deutsche Welle ☛ 2024-12-11_[Older]_Einstein:_Letters
                  reveal_legendary_scientist's_love_of_women⠀⇛


                # ⚓ Science Alert ☛ Cracked_Piece_of_Metal_Self-Healed_in
                  Experiment_That_Stunned_Scientists⠀⇛


                       They then observed the self-healing at ultra-small
                       scales in a 40-nanometer-thick piece of platinum
                       suspended in a vacuum.


                       Cracks caused by the kind of strain described above
                       are known as fatigue damage: repeated stress and
                       motion that causes microscopic breaks, eventually
                       causing machines or structures to break.


          o § Career/Education⠀➾


                # ⚓ Nicholas Tietz-Sokolsky ☛ Feel,_don't_think⠀⇛


                       I found a teacher through a piano teacher in town.
                       I asked if she knew any saxophone teachers, since
                       my instrument uses sax fingerings, especially
                       someone who also plays jazz. She connected me with
                       Charles, a local musician who's served as principal
                       clarinet in some esteemed ensembles. So I reached
                       out, asking him if he'd teach me on this unusual
                       instrument.


                       Charles teaches clarinet and saxophone, not wind
                       synth. I'm the first student he's had who uses an
                       amplifier. But the instrument uses sax fingerings,
                       and it responds to breath the way an acoustic
                       woodwind does, so he figured he can probably help
                       me. We decided to try it.


                # ⚓ [Old] Westenberg ☛ Why_Elite_Education_is_the_Next_Ponzi
                  Scheme_to_Collapse⠀⇛


                       Last week I recorded a podcast with a friend who
                       works in private equity. More on that later. He
                       mentioned that his firm looks at education the same
                       way they looked at housing in 2007 - a market
                       propped up by cheap debt, artificial scarcity, and
                       mass delusion about underlying value. But the more
                       we talked, the more I realized we're not looking at
                       one bubble - it’s a triple threat. A wealth bubble,
                       a debt bubble, and a cultural bubble all
                       reinforcing each other.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_It’s_rarely_lethal,_but
                  genital_herpes_costs_the_world_$35_billion_a_year_and_20%_of
                  people_have_it⠀⇛


                # ⚓ US News And World Report ☛ 2024-12-12_[Older]_Hardest-Hit
                  Nigeria_Is_Latest_African_Country_to_Provide_Malaria_Vaccine
                  to_Young_Children⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_More_aging_Japanese
                  need_to_cope_with_living_alone⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_These_healthy_foods_can
                  reduce_your_chronic_pain⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_FOMO_is_real,_so_can_it
                  be_overcome?⠀⇛


                # ⚓ The Conversation ☛ 2024-12-17_[Older]_Children_of_parents
                  not_in_a_romantic_relationship_are_just_as_happy_as_those_in
                  nuclear_families_–_new_research⠀⇛


                # ⚓ Why_do_RFK_Jr._apologists_think_eliminating_NIH_study
                  sections_is_a_good_idea?⠀⇛


                       [Orac note: Regular readers will have noticed that
                       it’s been two weeks since my last post, which was a
                       repurposed version of a post from my not-so-super-
                       secret other blog. The reason for that is simple.
                       Since the beginning of November, I’ve been dealing
                       with the prolonged hospitalization of my father,
                       which has taken up the “free time” that I used to
                       dedicate to this blog—and then some. Unfortunately,
                       a week and a half ago, Dad passed away, and I’ve
                       been dealing with funeral arrangements and the
                       aftermath. I hope to get back to a more regular
                       schedule after the holidays, but in the meantime I
                       thought that this post about what a certain
                       contrarian oncologist thinks that the NIH should
                       use instead of study sections to decide which grant
                       applications are funded would be of interest here.]


                # ⚓ Yury Molodtsov ☛ How_I_Stopped_Hating_Running⠀⇛


                       Running slower to build endurance and finding a
                       scenic, convenient route helped me fall in love
                       with running. By forming a habit, I’ve discovered
                       running’s benefits: reduced anxiety, improved
                       fitness, and a meditative escape.


                # ⚓ Rlang ☛ Depression_incidence_by_county_and_vote_for_Trump
                  by_@ellis2013nz⠀⇛


                       A skeet floated across my Bluesky feed that looked
                       at the cross-sectional relationship between
                       incidence of depression in 2020 and voting for
                       Trump in the 2024 Presidential election. The data
                       in the skeet and immediate blog post was at state
                       level, but the hypothesis of interest in an article
                       that sparked all this was an individual one (are
                       depressed people voting for Trump). I don’t have
                       the individual level microdata that might help
                       explore the actual hypothesis, but I was surprised
                       to see that the state-level regression had a
                       significant evidence of an effect, and wondered if
                       this would continue at the county level, which
                       still has relatively accessible data.


                       This also led me down an interesting but familiar
                       rabbit hole of multilevel modelling in the presence
                       of a spatial correlation nuisance.


                # ⚓ BoingBoing ☛ Tea_found_in_delicious_microplastic_infusion
                  bags⠀⇛


                       Good news for loose tea fans: so-called "tea bags"
                       release millions of nanoplastic and microplastic
                       particles when infused, according to mutagenesis
                       researchers at the University of Alabama in
                       Birmingham. Oh, you thought they were made of
                       paper? Most commercially available ones are made of
                       "nylon-6, polypropylene and cellulose."


                # ⚓ Sightline Media Group ☛ Soldiers_will_soon_get_more
                  financial_help_for_emergency_travel⠀⇛


                       This applies only to airfare. Qualifying expenses
                       for other emergency travel, such as gas for
                       personal vehicles, food and lodging are still
                       eligible for the 50% grant and 50% interest-free
                       loan. But depending on the soldier’s financial
                       circumstances, the interest-free loan portion could
                       be converted to a grant.


                # ⚓ The Codist ☛ How_Many_Hours_Can_You_Code?⠀⇛


                       Someone requested a massive expansion of the mostly
                       completed product that would also affect the entire
                       business unit's operations. Suddenly, many new
                       teams had to be added, and everyone would have to
                       make massive changes, but there was no more budget,
                       so I would have to do all the iOS work by myself.
                       In addition, a new team was required to build a
                       crucial piece with which I would interact. They
                       only had two contractors and a lead who did
                       nothing. They had no idea what to do or start, so I
                       told them I would help and became their virtual
                       lead, reviewing the code and guiding the
                       development. I even had to do QA, as that team had
                       no QA.


                       Of course, I also had to work on my changes,
                       support that team every day, and work on that
                       customer service app simultaneously. This turned
                       into three months of working seven days a week,
                       around 70 hours each week.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ The Conversation ☛ 2024-12-20_[Older]_‘Yes,_I_am_a_human’:
                  bot_detection_is_no_longer_working_–_and_just_wait_until_AI
                  agents_come_along [Ed: More HEY HI hype, as if those things
                  did not exist before!]⠀⇛


                # ⚓ Scoop News Group ☛ Feds_lay_blame_while_Chinese_telecom
                  attack_continues⠀⇛


                       The United States’ telecommunications
                       infrastructure has been infiltrated by actors
                       affiliated with China. Some of our nation’s most
                       powerful leaders have been targeted — including
                       President-elect Donald Trump and Vice President-
                       elect JD Vance. This is one of the most severe
                       cybersecurity incidents against telecom the United
                       States has ever been subject to, and — worse yet —
                       it is ongoing.


                       Commonly called Salt Typhoon, actors affiliated
                       with China have successfully gained access to at
                       least eight of our nation’s largest communications
                       companies. In fact, federal officials say that no
                       networks have fully removed the threat and that
                       individuals should rely on encrypted messaging
                       platforms in the meantime.


                # ⚓ Security Week ☛ Beware_Of_Shadow_AI_–_Shadow_IT's_Less
                  Well-Known_Brother⠀⇛


                       Research shows that from 50 to 75% of employees are
                       using non-company issued AI tools and the number of
                       these apps is growing substantially. A visibility
                       problem emerges. Do companies know what is
                       happening on their own networks? According to our
                       research, beyond the popular use of general AI
                       tools like ChatGPT, Copilot and Gemini, another set
                       of more niche AI applications being used at
                       organizations include: [...]


                # ⚓ Michał Sapka ☛ LLMs_are_everything_that_it_wrong_in_the
                  world_of_computing⠀⇛


                       I am often accused of romanticizing past, but I am
                       far from that. Software of the golden age had lots
                       of problems, it was far from perfect. I am critical
                       of the path we took - as it was aimed not at better
                       software, but at better return of investment. We
                       could have had much better working computers, but
                       here we are. Everything is barely working but
                       dollar pours. Some call it enshittification, others
                       distribution. All I know is this is not going to
                       stop. It is never enough.


                # ⚓ Society for Scholarly Publishing ☛ Our_Algorithmically-
                  driven_Homogenized_Future⠀⇛


                       It’s worth considering as we rapidly seem to be
                       shifting much of our research and information
                       discovery practices over to the AI systems driven
                       by the algorithms from these very same companies.
                       What happens to innovation when everyone is using
                       the same tool with the same biases that is
                       essentially built to offer us more of the same
                       stuff that we already like/know? Is this a recipe
                       for a similar homogenization and stagnation of
                       science and knowledge building in general?


                # ⚓ US News And World Report ☛ The_Internet_Is_Rife_With_Fake
                  Reviews._Will_AI_Make_It_Worse?⠀⇛


                       The deceptive practice, which is illegal in the
                       U.S., is carried out year-round but becomes a
                       bigger problem for consumers during the holiday
                       shopping season, when many people rely on reviews
                       to help them purchase gifts.


                       Where are AI-generated reviews showing up?


                       Fake reviews are found across a wide range of
                       industries, from e-commerce, lodging and
                       restaurants, to services such as home repairs,
                       medical care and piano lessons.


                # ⚓ Lionel Dricot ☛ My_colleague_Julius⠀⇛


                       But Julius excelled in formatting, presentation,
                       and meeting management. Regularly, my boss would
                       come up to me and say, “We’re really lucky to have
                       this Julius! What talent! What a contribution to
                       the team!”


                       I tried, without success, to explain that Julius
                       understood nothing of what we were doing. That we
                       had reached the point where we sent him to useless
                       meetings to get rid of him for a few hours. But
                       even that strategy had its limits.


          o § Pseudo-Open Source⠀➾


                # § Openwashing⠀➾


                      # ⚓ Silicon Angle ☛ Microsoft_reportedly_integrating_non-
                        OpenAI_models_into_Microsoft_365_Copilot⠀⇛


                             Today’s report didn’t specify which open-
                             source models could find their way into
                             Copilot. However, it’s probable that Meta
                             Platforms Inc.’s Llama LLMs are among the
                             algorithms under consideration. The LLM
                             series is one of the most advanced in the
                             open-source ecosystem and outperforms some
                             proprietary frontier models across certain
                             tasks.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ The Age AU ☛ 2024-12-12_[Older]_Australia_news_LIVE:
                        Labor_to_force_big_tech_to_pay_for_Australian
                        journalism;_Meta_outage_impacting_Facebook,_Instagram
                        and_WhatsApp⠀⇛


                      # ⚓ The Age AU ☛ 2024-12-12_[Older]_Users_worldwide
                        unable_to_access_Facebook_and_Instagram_amid_outage⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-11_[Older]
                        Facebook,_Instagram_Down_for_Thousands_of_Users,
                        Downdetector_Shows⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ EFF ☛ Defending_Encryption_in_the_U.S._and_Abroad:
                        2024_in_Review [Ed: EFF_became_part_of_the_problem]⠀⇛


                             That’s why we’ve always got an eye out for
                             attacks on encryption. This year, we pushed
                             back—successfully—against anti-encryption
                             laws proposed in the U.S., the U.K. and the
                             E.U. And we had a stark reminder of just how
                             dangerous backdoor access to our
                             communications can be. 


                             The U.S. Senate’s EARN IT Bill is a
                             wrongheaded proposal that would push
                             companies away from using encryption and
                             towards scanning our messages and photos.
                             There’s no reason to enact such a proposal,
                             which technical experts agree would turn our
                             phones into bugs in our pockets. 


                             We were disappointed when EARN IT was voted
                             out of committee last year, even though
                             several senators did make clear they wanted
                             to see additional changes before they support
                             the bill. Since then, however, the bill has
                             gone nowhere. That’s because so many people,
                             including more than 100,000 EFF supporters,
                             have voiced their opposition. 


                      # ⚓ AntiWar ☛ You'd_Better_Watch_Out:_The_Surveillance
                        State_Is_Making_a_List,_and_You're_on_It⠀⇛


                             Geofencing dragnets. Fusion centers. Smart
                             devices. Behavioral threat assessments.
                             Terror watch lists. Facial recognition.
                             Snitch tip lines. Biometric scanners. Pre-
                             crime. DNA databases. Data mining.
                             Precognitive technology. Drones. Contact
                             tracing apps. License plate readers. Social
                             media vetting. Surveillance towers.


                             What these add up to is a world in which, on
                             any given day, the average person is now
                             monitored, surveilled, spied on and tracked
                             in more than 20 different ways by both
                             government and corporate eyes and ears.


                             Big Tech wedded to Big Government has become
                             Big Brother.


                      # ⚓ Scoop News Group ☛ Judge_grants_ruling_in_favor_of
                        WhatsApp_against_spyware_firm_NSO_Group⠀⇛


                             A federal judge has dealt the first major
                             legal blow against spyware maker NSO Group,
                             ruling in favor of WhatsApp in a five-year-
                             old lawsuit against the Israeli firm over
                             allegations that it hacked the chat service.


                      # ⚓ Axios ☛ Pornhub_to_block_Florida_users,_citing_age
                        verification_law_-_Axios_Tampa_Bay⠀⇛


                             Why it matters: That's one less freedom for
                             those who live in the free state of Florida.
                             The restriction comes as a protest from
                             Pornhub against states that enact age
                             verification laws.


                             Driving the news: "You will lose access to
                             Pornhub in 13 days," says a popup that greets
                             users in Florida, adding that "your
                             government wants you to give your driver's
                             license before you can access" the site.


                      # ⚓ The Local SE ☛ Swedish_government_wants_to_allow
                        police_to_secretly_monitor_children's_communications⠀⇛


                             Sweden's government said on Wednesday it
                             wanted to give police the power to secretly
                             monitor phone calls and electronic
                             communications of those under 15 years of
                             age, in response to a surge in gang [sic]
                             violence in the Nordic country.


                      # ⚓ Defence Web ☛ Cattle_rustling:_a_lifeline_for_Boko
                        Haram_in_the_Lake_Chad_Basin⠀⇛


                             Rustling has grown in both scale and
                             violence. And when perpetrated across
                             national boundaries by actors such as Boko
                             Haram, it demonstrates the terror-crime nexus
                             in the Lake Chad Basin.


                             A recent assessment carried out by ENACT and
                             the Central African Police Chiefs Committee
                             (CAPCCO) identified cattle rustling as a
                             priority crime affecting the region.


                      # ⚓ New York Times ☛ Under_Pressure,_Telegram_Turns_a
                        Profit_for_the_First_Time⠀⇛


                             In the conversations, Telegram told investors
                             that it was tackling its legal troubles head-
                             on by policing more user-generated content.
                             The company also said it had paid down a
                             “meaningful amount” of its debt, according to
                             an investor in the talks who was not
                             authorized to discuss confidential
                             information.


          o § Defence/Aggression⠀➾


                # ⚓ CBC ☛ 2024-12-12_[Older]_Ottawa_quietly_expands_gun_buyback
                  program_to_include_parts⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_Hamburg_places_blanket
                  ban_on_weapons_in_buses_and_trams⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-14_[Older]_Brazil:_Ex-defense
                  minister_held_for_meddling_in_coup_probe⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_Libya:_Armed_clashes
                  close_key_oil_refinery_as_fires_erupt⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_South_Korea's_acting
                  president_reaffirms_alliance_with_US⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_Dutch_court_rules
                  against_ban_on_weapon_sales_to_Israel⠀⇛


                # ⚓ YLE ☛ Finland_plans_info_package_for_Finns_joining_Ukraine
                  forces⠀⇛


                       More Finnish soldiers have died on the battlefield
                       in Ukraine than has been reported in the news
                       media, according to Finnish news agency STT, citing
                       a story in Turun Sanomat.


                # ⚓ LRT ☛ Lithuania_to_spend_€15m_to_upgrade_Russia_border
                  surveillance_systems⠀⇛


                       Lithuania plans to use 15 million euros provided by
                       the European Commission to upgrade electronic
                       border surveillance systems at four frontier
                       stations on the country’s border with Russia.


                # ⚓ VOA News ☛ Mozambique_council_to_rule_on_election_results
                  Monday⠀⇛


                       Mozambique's constitutional council will announce
                       Monday whether it will validate the results of
                       elections that have plunged the country into deadly
                       turmoil, the body said.


                # ⚓ Digital Music News ☛ Can_Trump_Save_TikTok?_Ban_'D-Day'_Is
                  Under_A_Month_Away⠀⇛


                       Trump has also met with TikTok CEO Shou Zi Chew,
                       after having said at a news conference that he had
                       a “warm spot” for TikTok after learning of his
                       campaign’s success on the platform.


                       The U.S. Department of Justice has argued that
                       ByteDance’s control of TikTok poses a continuing
                       threat to national security, as companies within
                       Beijing’s jurisdiction are subject to CCP requests
                       for data. Most U.S. lawmakers agree with this
                       position.


                # ⚓ India Times ☛ Trump's_TikTok_love_raises_stakes_in_battle
                  over_app's_fate⠀⇛


                       On Sunday, Trump had displayed his support for the
                       app just days after meeting with TikTok chief
                       executive officer Shou Zi Chew in Florida. He
                       partly opposes the banning of the social media
                       platform, because he believes that it would benefit
                       Meta, the Mark Zuckerberg-led company behind
                       Instagram and Facebook.


                # ⚓ India Times ☛ As_TikTok_bill_steams_forward,_online
                  influencers_put_on_their_lobbying_hats_to_visit_Washington⠀⇛


                       The platform is once again bringing influencers to
                       Washington, this time to lobby members of Congress
                       to reject a fast-moving bill that would force
                       TikTok's Beijing-based parent company to sell or be
                       banned in the United States. On Tuesday, some
                       influencers began a two-day advocacy event in
                       support of TikTok, which arranged their trip ahead
                       of a House floor vote on the legislation on
                       Wednesday.


                # ⚓ RTL ☛ Trump's_TikTok_love_raises_stakes_in_battle_over
                  app's_fate⠀⇛


                       "We got to keep this sucker around for a little
                       while," Trump told supporters on Sunday, just days
                       after meeting with TikTok CEO Shou Zi Chew in
                       Florida.


                       Trump, who credits the wildly popular platform with
                       delivering him a large young user base, opposes
                       banning TikTok partly because he believes it would
                       primarily benefit Meta, the Mark Zuckerberg-led
                       company behind Instagram and Facebook.


                # ⚓ Wired ☛ The_Invisible_Russia-Ukraine_Battlefield⠀⇛


                       In Russia’s war against Ukraine, electronic
                       warfare, including signal-jamming, anti-drone
                       weapons, and innovative protections for critical
                       military systems, has become a key piece of the
                       conflict.


                # ⚓ USMC ☛ Marine_gunner_has_AWOL_charges_tossed,_gets
                  reprimand_for_statements⠀⇛


                       Some of the allegations stemmed from the fact that
                       he’d accepted a role at the defense contractor
                       ManTech and completed a few tasks for the company,
                       including sending emails, while still in uniform.
                       LaRose said he was on terminal leave at the time.


                # ⚓ JURIST ☛ Saudi_Arabia_to_reopen_embassy_in_Taliban
                  Afghanistan⠀⇛


                       Saudi Arabia announced on Sunday that it has
                       resumed diplomatic operations in Kabul, the capital
                       of Afghanistan. This marks the reopening of its
                       embassy, which had been closed since February 2023
                       due to security concerns.


                # ⚓ Sightline Media Group ☛ Following_controversy,_Maryland
                  governor_receives_Bronze_Star⠀⇛


                       Maryland Gov. Wes Moore received a Bronze Star for
                       his deployment to Afghanistan 18 years ago, several
                       months after a controversy arose when a newspaper
                       reported he had claimed to have received it on a
                       2006 White House fellowship application when the
                       paperwork had not been fully processed.


                # ⚓ Modern Diplomacy ☛ Piracy_as_Non-Traditional_Security
                  Threat_in_Indian_Ocean:_Countermeasures_by_Pakistan⠀⇛


                       Piracy in the Indian Ocean, particularly near Horn
                       of Africa, has been a non-traditional security
                       threat to regional maritime trade. Pirates,
                       operating from the Somali coastline, often target
                       commercial vessels, using small, fast boats to
                       board and hijack larger ships and take crew as
                       hostage for ransom. Frequent pirates attack
                       compromise the safety of shipping, crew members,
                       and cargo transportation, compelling shipping
                       companies to undertake security measures or even
                       shift to longer routes which results in higher
                       expenditure. This badly affects the regulated flow
                       of maritime transit from Indian Ocean to
                       Mediterranean Sea via Red Sea.


                # ⚓ The Local DK ☛ China_vows_'cooperation'_as_ship_linked_to
                  Baltic_Sea_cables_sets_sail_from_Denmark⠀⇛


                       Early on November 17th, the Arelion cable running
                       from the Swedish island of Gotland to Lithuania was
                       damaged.


                       The next day, the C-Lion 1 submarine cable
                       connecting Helsinki and the German port of Rostock
                       was cut south of Sweden's Öland island, around 700
                       kilometres from Helsinki.


                # ⚓ LRT ☛ We_need_to_be_ready_to_attack_inside_Russia_–
                  interview_with_Lithuanian_general⠀⇛


                       Geography determines a lot, you do not choose your
                       neighbours – we have what we have. Over the
                       centuries, we have been at a crossroads between
                       South and North, East and West. But when we joined
                       the NATO alliance, everything changed.


                # ⚓ Axios ☛ Trump_suggests_keeping_TikTok_around_for_"a_little
                  while"⠀⇛


                       Why it matters: The popular short-form video app
                       could be banned in the U.S. in less than a month —
                       but Trump, who threatened to boot the app during
                       his first term, has suggested he'd offer TikTok a
                       lifeline.


                       TikTok is staring down a Jan. 19 ban. But before
                       then, the Supreme Court will hear arguments over
                       whether the bipartisan law that forced the app's
                       sale by its parent company is constitutional.


                # ⚓ India Times ☛ Taiwan_faces_almost_1_million_monthly_cyber
                  attacks_from_China⠀⇛


                       Cheng Hui-pin, the head of the IT department,
                       revealed this information in response to questions
                       from Democratic Progressive Party (DPP) Legislator
                       Chung Chia-pin. Chung asked questions about the
                       security and quality of the legislature's wifi
                       during a review of the LY's budget by the Judiciary
                       and Organic Laws and Statutes Committee last
                       Thursday, as per Taipei Times.


                # ⚓ NPR ☛ Albanian_prime_minister_says_TikTok_ban_was_not_a
                  rushed_reaction⠀⇛


                       Prime Minister Edi Rama said Saturday the
                       government will shut down TikTok for one year,
                       accusing the popular video service of inciting
                       violence and bullying, especially among children.


                       Authorities have held 1,300 meetings with teachers
                       and parents since the November stabbing death of a
                       teenager by another teen after a quarrel that
                       started on social media apps. Ninety percent of
                       them approve of the ban on TikTok.


                # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_Nigerian_cyber_fraud
                  suspect_extradited_to_US_from_Ghana⠀⇛


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


                      # ⚓ Deutsche Welle ☛ 2024-12-14_[Older]_Georgia:_Far-
                        right_loyalist_elected_president_amid_unrest⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_Georgia:_Violence
                        escalates_ahead_of_presidential_election⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_US_bans_visas_for
                        Georgians_accused_of_undermining_democracy⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-19_[Older]_As
                        Russia's_Threat_Looms,_Guns_and_Defense_Training_Surge
                        in_Finland⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-20_[Older]_Russian
                        Central_Bank_Holds_Rates_Steady_at_21%_Amid_Criticism
                        From_Key_Business_Figures⠀⇛


                      # ⚓ US News And World Report ☛ 2024-12-20_[Older]_A
                        Russian_Official_Says_a_Ukrainian_Strike_With_US-
                        Supplied_Missiles_Kills_6⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Techdirt ☛ Federal_Officials_Resorting_To_In-Person
                  Meetings_With_Trump_Transition_Team,_Since_They_Insist_On
                  Using_Easily_Hacked_Private_Email⠀⇛


                       There’s usually only one reason government
                       officials use personal email accounts: to dodge
                       FOIA requests. The excuses offered by those caught
                       doing it are never credible. And those who do opt
                       for personal email — especially at the federal
                       level — are putting themselves in peril. There are
                       also practical security reasons for using
                       government email addresses.


                       A lot of Donald Trump’s first presidential campaign
                       focused on his opponent’s use of a personal email
                       server to handle official State Department
                       business. The FBI even looked into this before
                       deciding (twice!) Hillary Clinton’s personal email
                       server was careless and stupid, but probably not
                       criminal.


                # ⚓ Wouter Groeneveld ☛ How_Bad_Is_Link_Rot_At_Brain_Baking?⠀⇛


                       There’s no denying that online content disappears.
                       Depending on the type and thoroughness of the
                       study, reports claim that 38% to 66.5% of webpages
                       that existed a decade ago are dead. Sometimes we’re
                       treated with a 3xx redirect code but more often
                       than not they’re simply gone forever if it wasn’t
                       for the Internet Archive.


                       That got me wondering how bad link rot actually is
                       on this site as lately I’ve been looking for
                       specific things in my own archive and failed to
                       successfully click through some references that
                       would have come in handy.


                       In order to investigate that, I used the following
                       methodology: [...]


          o § Environment⠀➾


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_Can_the_UN_COP16_summit
                  help_stop_Earth's_land_drying_out?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-14_[Older]_Severe_cyclone_batters
                  French_overseas_territory_Mayotte⠀⇛


                # ⚓ CBC ☛ 2024-12-10_[Older]_No_coast_was_spared_from_2024's
                  extreme_weather_impacts⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_Cyclone_Chido_kills
                  multiple_in_Mayotte,_batters_Mozambique⠀⇛


                # ⚓ Renewable Energy World ☛ Vistra_connects_two_new_solar
                  projects,_delays_coal_plant_closure_in_Illinois⠀⇛


                       Vistra announced that two new utility-scale solar
                       projects in Illinois have connected to the grid and
                       that, amid what it called “widespread concern over
                       reliability” in the MISO market, it is pushing back
                       the retirement of its 1,185-megawatt (MW) Baldwin
                       Power Plant in Baldwin, Illinois.


                       The company said it now intends to run the Baldwin
                       plant through 2027 instead of retiring in 2025, as
                       previously announced, while still meeting federal
                       Environmental Protection Agency retirement and pond
                       closure obligations.


                # ⚓ The Washington Post ☛ Space_Station_keeps_dodging_debris
                  from_China’s_2007_weapon_test⠀⇛


                       The evasive maneuver was the second in just six
                       days for the space station, which has four NASA
                       astronauts and three Russian cosmonauts aboard.
                       That is the shortest interval ever between such
                       actions, illustrating the slowly worsening problem
                       of space junk in orbit. Debris is an increasingly
                       vexing issue not only for NASA, but also for
                       companies such as SpaceX and OneWeb seeking to
                       protect the thousands of small satellites they send
                       into space to provide high-speed internet.


                       Analysts say the most worrisome debris cloud stems
                       from Fengyun 1C, a weather satellite that the
                       Chinese government intentionally destroyed with a
                       missile in 2007. The high-altitude explosion
                       created an estimated 3,500 pieces of debris,
                       according to records maintained by the U.S. Space
                       Force; most of them are still in orbit. They get
                       slightly closer to the atmosphere with each pass,
                       but an analysis shortly after the event predicted
                       it would take more than 100 years for the debris to
                       hit the atmosphere and largely burn up.


                # ⚓ Rolling Stone ☛ Donald_Trump_EPA’s_Pick,_Lee_Zeldin,_Is
                  Fossil_Fuel’s_Inside_Man⠀⇛


                       While the country is focused on President-elect
                       Donald Trump’s most controversial cabinet picks,
                       such as Kash Patel for FBI director or Tulsi
                       Gabbard for director of national intelligence, the
                       fossil fuel industry is surely celebrating a pick
                       that has mostly flown under the radar. Trump has
                       chosen Lee Zeldin to lead the EPA, and the former
                       New York Republican lawmaker is poised to reverse
                       the clock on climate progress and hand America’s
                       environment over to its most notorious polluters.


                # § Energy/Transportation⠀➾


                      # ⚓ Deutsche Welle ☛ 2024-12-14_[Older]_Spain:_Founder_of
                        Mango_fashion_chain_dies_in_accident⠀⇛


                      # ⚓ CBC ☛ 2024-12-12_[Older]_Canadian_oil_majors_to_boost
                        production_in_2025⠀⇛


                      # ⚓ CBC ☛ 2024-12-12_[Older]_Why_Quebec_struck_a_new
                        hydro_deal_with_Newfoundland_and_Labrador⠀⇛


                      # ⚓ CBC ☛ 2024-12-12_[Older]_Quebec,_N.L._prepare_to_end
                        bitter,_decades-long_dispute_with_new_Churchill_Falls
                        hydro_power_deal⠀⇛


                      # ⚓ CBC ☛ 2024-12-09_[Older]_Vancouver_mayor's_idea_to
                        create_bitcoin_reserve_for_city_'extremely_risky':_law
                        professor⠀⇛


                      # ⚓ CBC ☛ 2024-12-11_[Older]_Vancouver_council_passes
                        mayor's_motion_to_make_city_'bitcoin-friendly'⠀⇛


                      # ⚓ The Independent UK ☛ A_FedEx_driver_running_late_on
                        his_routes_so_he_ditched_dozens_of_parcels_in_woods,
                        Florida_cops_say⠀⇛


                             Officers made the arrest after residents
                             reported several dumped packages in the woods
                             or on the side of the road in the city of
                             Bonifay. The sheriff’s office then contacted
                             FedEx to help identify the driver.


                      # ⚓ Dan Langille ☛ Eaton_5PX_UPS_–_clear_the_‘Replace
                        Battery’_warning⠀⇛


                             Still this did not fix the warning for me.
                             I’m going to consult the NUT mailing list.


                      # ⚓ Omicron Limited ☛ Getting_people_out_of_their_cars_is
                        possible_with_the_right_plans_and_policies—case_study⠀⇛


                             One recent example of how this can succeed is
                             documented in a four-yearly survey conducted
                             by the University of Canterbury to identify
                             travel trends among staff and students.


                             The survey also asks about the main barriers
                             to switching from driving, which helps inform
                             policies to encourage more sustainable travel
                             options. This year's results show particular
                             promise.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Sloths,_Salmon,_and_Autocrats:_Our
                        Most-Read_Articles_of_the_Year⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_Cambodia:
                        Fishermen_find_six_rare_Mekong_giant_catfish⠀⇛


                      # ⚓ EcoWatch ☛ Right_Whales_Can_Live_130_Years_or_Longer,
                        Research_Finds⠀⇛


                             Scientists have estimated that bowhead whales
                             — the longest-living whale species — can live
                             more than 200 years.


                             It was once thought that the bowhead’s
                             cousin, the right whale, had an average
                             lifespan of about 70 to 80 years, but new
                             research has revised that estimate to more
                             than 130 years — nearly twice as long!


                      # ⚓ Michigan Advance ☛ Iconic_monarch_butterfly
                        recommended_for_‘threatened’_list_as_population_shrinks
                        •_Michigan_Advance⠀⇛


                             The once common sightings of the brightly
                             colored monarch butterfly have become a rarer
                             experience in recent years across Georgia and
                             other travel paths during the pollinator’s
                             annual migration across North America.


                      # ⚓ Omicron Limited ☛ New_study_documents_evolution_of
                        fast-growing,_fish-eating_herring_in_Baltic_Sea⠀⇛


                             "When I learned that the locals are aware of
                             a specific population of very large Baltic
                             herring that always spawns in the same area
                             year after year, I decided to sample and
                             explore their genetic constitution. Now we
                             know that this is a genetically unique
                             population that must have evolved over
                             hundreds, if not thousands, of years in the
                             Baltic Sea," says Leif Andersson, Professor
                             at the Department of Medical Biochemistry and
                             Microbiology at Uppsala University, who led
                             the study.


                # § Overpopulation⠀➾


                      # ⚓ Los Angeles Times ☛ California_water_plan_touted_as
                        'durable'_solution,_but_disputes_loom⠀⇛


                             The rules took effect last week as the
                             federal Bureau of Reclamation approved the
                             plan and the supporting biological opinions,
                             which determine how much water can be pumped
                             and how river flows are managed in the
                             Sacramento-San Joaquin River Delta. The rules
                             govern the operations of dams, aqueducts and
                             pumping plants in the Central Valley Project
                             and the State Water Project, two of the
                             world’s largest water systems, which deliver
                             supplies to Central Valley farmlands and
                             about 30 million people.


                             Withdrawals of water by the massive pumps
                             that feed the systems have contributed to the
                             ecological degradation of the Delta and San
                             Francisco Bay, where threatened and
                             endangered fish species include steelhead
                             trout, two types of Chinook salmon, longfin
                             smelt, Delta smelt and green sturgeon.


          o § Finance⠀➾


                # ⚓ Silicon Angle ☛ PayPal_Honey_browser_extension_accused_of
                  misleading_consumers_and_creators⠀⇛


                       The accusations come from YouTube creator MegaLag,
                       who claims in a recent 23-minute long YouTube video
                       that the popular extension engages in unethical
                       practices such as intercepting affiliate
                       commissions intended for influencers and
                       selectively promoting discount codes from its
                       business partners over potentially better deals.


                       MegaLag’s investigation also alleges that the
                       manipulation not only deprives content creators of
                       fair earnings but also misleads consumers,
                       undermining the platform’s promise of delivering
                       the best discounts.


                # ⚓ CBC ☛ 2024-12-11_[Older]_AquaBounty_cutting_'substantially
                  all'_staff,_plans_to_shut_down_P.E.I._salmon_hatchery⠀⇛


                # ⚓ CBC ☛ 2024-12-10_[Older]_Proposed_class-action_lawsuit
                  accuses_companies_of_price-fixing_rents_in_Canada⠀⇛


                # ⚓ US News And World Report ☛ 2024-12-11_[Older]_Bank_of
                  Canada_Cuts_Interest_Rate_by_Half_a_Percentage_Point,
                  Highlights_Risk_of_Trump's_Tariffs⠀⇛


                # ⚓ CBC ☛ 2024-12-11_[Older]_Bank_of_Canada_cuts_key_interest
                  rate_to_3.25%_with_slower_pace_of_cuts_going_forward⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_Can_China_climb_out_of
                  economic_stagnation_in_2025?⠀⇛


                # ⚓ CBC ☛ 2024-12-10_[Older]_Judge_approves_$2.6M_Dollarama
                  class-action_settlement⠀⇛


                # ⚓ CBC ☛ 2024-12-13_[Older]_The_Body_Shop_Canada_sells
                  majority_of_its_business,_100_workers_to_lose_jobs⠀⇛


                # ⚓ CBC ☛ 2024-12-13_[Older]_Liard_First_Nation_fires_employees
                  who_criticized_governance,_deputy_chief_told_to_'go_back_to
                  the_rez'⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-14_[Older]_Moody's_lowers_France's
                  credit_rating_over_sliding_finances⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_German_central_bank
                  slashes_growth_outlook_for_2025,_2026⠀⇛


                # ⚓ Sunday Times ☛ Europe's_embattled_car_sector_plans_plant
                  closures_and_layoffs⠀⇛


                       Automotive companies across Europe have announced
                       plant closures and big layoffs as they struggle
                       with weak demand, high costs, competition from
                       China and a slower-than-expected transition to
                       electric vehicles.


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_ECB_trims_interest_rate
                  with_eye_on_political_unease⠀⇛


                # ⚓ US News And World Report ☛ 2024-12-13_[Older]_Musk_Says_US
                  Is_Demanding_He_Pay_Penalty_Over_Disclosures_of_His_Twitter
                  Stock_Purchases⠀⇛


                # ⚓ CBC ☛ 2024-12-09_[Older]_Union_says_it_met_with_Canada_Post
                  for_first_time_since_mediator_suspended_talks⠀⇛


                # ⚓ CBC ☛ 2024-12-11_[Older]_Tensions_rising_between_Canada
                  Post,_union_as_strike_nears_4-week_mark⠀⇛


                # ⚓ CBC ☛ 2024-12-11_[Older]_Unfair_labour_practice_complaint
                  over_Canada_Post_layoffs_resolved⠀⇛


                # ⚓ CBC ☛ 2024-12-11_[Older]_Assembly_of_First_Nations,_Inuit
                  Tapiriit_Kanatami_call_for_resolution_to_Canada_Post_strike⠀⇛


                # ⚓ CBC ☛ 2024-12-13_[Older]_Labour_minister_asks_Canada
                  Industrial_Relations_Board_to_step_into_Canada_Post_contract
                  dispute⠀⇛


                # ⚓ CBC ☛ 2024-12-11_[Older]_Air_Canada_ordered_to_pay_$10K
                  after_couple_endures_'horrendous_experience'⠀⇛


                # ⚓ CBC ☛ 2024-12-14_[Older]_B.C._developer_accused_of
                  misappropriating_funds,_as_2_more_condo_projects_placed_into
                  receivership⠀⇛


                # ⚓ TruthOut ☛ 2024-12-15_[Older]_Amazon_Workers_Threaten
                  Holiday_Strike_If_Company_Keeps_Refusing_to_Bargain⠀⇛


                # ⚓ TruthOut ☛ 2024-12-17_[Older]_Amazon_Hit_With_Potential
                  Strike_and_Damning_Senate_Report_Ahead_of_Holiday_Rush⠀⇛


                # ⚓ US News And World Report ☛ 2024-12-19_[Older]_Amazon
                  Workers_Strike_at_Multiple_Facilities_as_Teamsters_Seek_Labor
                  Contract⠀⇛


                # ⚓ International Business Times ☛ 2024-12-19_[Older]_Amazon
                  Workers_in_New_York,_San_Francisco,_Atlanta,_and_Other_Cities
                  Plan_Walkout_on_Thursday⠀⇛


                # ⚓ CBC ☛ 2024-12-19_[Older]_Amazon_workers_strike_at_seven
                  U.S._locations,_alleging_unfair_treatment⠀⇛


                # ⚓ TruthOut ☛ 2024-12-19_[Older]_Teamsters_Launch_Historic
                  Nationwide_Strike_Against_Amazon⠀⇛


                # ⚓ CBC ☛ 2024-12-20_[Older]_Will_the_Amazon_strike_be_the
                  grinch_to_consumers'_holiday_shopping?_Probably_not.⠀⇛


                # ⚓ Yahoo News ☛ Amazon_and_AT&T_want_an_end_to_remote_work:
                  will_2025_finally_be_the_death_of_WFH? [Ed: Mass_layoffs_in
                  disguise,_with_newer_and_more_novel_excuses]⠀⇛


                       Amazon and AT&T may appear to be winning high-
                       profile battles to bring staff back to the office,
                       but flexible workers are quietly prevailing in the
                       remote-work war.


                       With the pandemic behind us, some executives argue
                       that remote work has outlived its usefulness. Yet
                       the data tells a different story. The economy has
                       outperformed expectations, hybrid-friendly
                       companies are seeing better stock performance, and
                       productivity is up.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_UK_joins_Indo-Pacific
                  trade_bloc_as_first_European_member⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-14_[Older]_Italy_grants
                  citizenship_to_Argentine_President_Javier_Milei⠀⇛


                # ⚓ Overpopulation ☛ 2024-12-15_[Older]_Which_international_aid
                  to_Africa_do_Swedish_voters_prefer?_A_new_survey_provides
                  answers⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_How_Africa's_young
                  urbanites_are_changing_political_culture⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_X:_Holocaust
                  remembrance_organizations_quit_platform⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_Australia_seals_PNG
                  rugby_deal_to_counter_Chinese_influence⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_Romania,_Bulgaria
                  become_full_members_of_Schengen_zone⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_Most_young_Germans_see
                  no_point_in_politics,_survey_says⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_Passing_through:
                  Croatia's_'invisible_migrants'⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_Is_the_rise_in_internal
                  border_controls_ending_the_EU_dream?⠀⇛


                # ⚓ The Conversation ☛ China_has_banned_US_exports_of_key
                  minerals_for_computer_chips_–_leaving_Washington_with_limited
                  options⠀⇛


                       China has overwhelming market power over supply,
                       because it is the source of 98% of primary gallium
                       and 91% of primary germanium. Primary refers to
                       “raw” sources such as mineral ore. In several
                       sectors where the minerals are used, there are no
                       substitutes for them.


                       Gallium and germanium are present in very low
                       concentration as byproducts of major minerals –
                       they’re known as trace minerals. Germanium’s
                       primary source is the residue from zinc refineries
                       and coal fly ash (a powdered residue produced when
                       coal is burnt in power plants).


                # ⚓ The Record ☛ FCC_‘rip_and_replace’_provision_for_Chinese
                  tech_tops_cyber_provisions_in_defense_bill_|_The_Record_from
                  Recorded_Future_News⠀⇛


                       The annual defense policy bill signed by President
                       Joe Biden Monday evening allocates $3 billion to
                       help telecom firms remove and replace insecure
                       equipment in response to recent incursions by
                       Chinese-linked hackers.


                       The fiscal 2025 National Defense Authorization Act
                       outlines Pentagon policy and military budget
                       priorities for the year and also includes non-
                       defense measures added as Congress wrapped up its
                       work in December. The $895 billion spending
                       blueprint passed the Senate and House with broad
                       bipartisan support.


                # ⚓ The Register UK ☛ The_global_firmware_threat_nobody's
                  tracking⠀⇛


                       This sounds like a conspiracy theory because the
                       evidence is ambiguous. Line up the circumstantial
                       evidence and it's at least plausible. If TP-Link
                       does have a corporate fondness for crap coders, how
                       come the features visible to owners in everyday use
                       work well, while invisible vulnerabilities are so
                       common? Chinese law compels all domestic companies
                       to cooperate with state security in secret. There
                       is already evidence of widespread Chinese
                       infiltration of communication infrastructure with
                       Salt Typhoon. Motive, opportunity, ability, and
                       history: where does the balance of probabilities
                       lie?


                # ⚓ Techdirt ☛ Ohio_Steps_Up_To_Defend_Free_Speech_As_Congress
                  Dithers_On_Anti-SLAPP_Law⠀⇛


                       The bill itself, SB 237, looks decent enough. It
                       appears to be modeled on the Uniform Law
                       Commission’s anti-SLAPP model law, which is very
                       strong. Other anti-SLAPP laws based on that model
                       law have been passed in a handful of states and
                       it’s becoming more of a standard for these types of
                       laws. Just this year alone, Pennsylvania, Maine,
                       and Minnesota have enacted similar anti-SLAPP laws
                       based on the ULC model.


                       But still, without a federal anti-SLAPP law, there
                       is always the risk that the law won’t apply in
                       federal court. Federal Circuits have been all over
                       the map in deciding if state anti-SLAPP laws can
                       apply. The First and Ninth Circuits have said that
                       you can use state anti-SLAPP laws in federal court,
                       while at last check, I believe the Second, Fifth,
                       Tenth, Eleventh, and DC Circuits have all said you
                       cannot (though this has changed over time, as I
                       believe the Second and Fifth Circuits flipped
                       positions from “allow” to “don’t allow” at some
                       point).


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Scoop News Group ☛ State_Department’s_disinformation
                        office_to_close_after_funding_nixed_in_NDAA⠀⇛


                             The Global Engagement Center, which tracks
                             foreign disinformation, will lose its
                             authority on Dec. 24. Despite a concerted
                             push by State officials to lobby Congress for
                             an extension, a measure to extend the
                             center’s authority into 2031 was stripped out
                             of the final version of defense authorization
                             legislation that passed through the Senate.


                             “The Global Engagement Center will terminate
                             by operation of law [by the end of the day]
                             on December 23, 2024,” a State Department
                             spokesperson told CyberScoop in an email.
                             “The Department of State has consulted with
                             Congress regarding next steps.”


                      # ⚓ New York Times ☛ A_Canceled_Vote_in_Romania_Hands
                        Russia_a_Propaganda_Coup⠀⇛


                             Elon Musk, who has echoed Russian talking
                             points on the Ukraine war, also weighed in,
                             misconstruing the unanimous decision by a 10-
                             member Romanian tribunal as the diktat of a
                             single judge: “How can a judge cancel an
                             election and not be considered a dictator?”
                             he said on social media last week.


                      # ⚓ Wired ☛ AI_Agents_Will_Be_Manipulation_Engines⠀⇛


                             People are far more likely to give complete
                             access to a helpful AI agent that feels like
                             a friend. This makes humans vulnerable to
                             being manipulated by machines that prey on
                             the human need for social connection in a
                             time of chronic loneliness and isolation.
                             Every screen becomes a private algorithmic
                             theater, projecting a reality crafted to be
                             maximally compelling to an audience of one.


                             This is a moment that philosophers have
                             warned us about for years. Before his death,
                             philosopher and neuroscientist Daniel Dennett
                             wrote that we face a grave peril from AI
                             systems that emulate people: “These
                             counterfeit people are the most dangerous
                             artifacts in human history … distracting and
                             confusing us and by exploiting our most
                             irresistible fears and anxieties, will lead
                             us into temptation and, from there, into
                             acquiescing to our own subjugation.”


          o § Censorship/Free Speech⠀➾


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_Why_Polish_author_Jacek
                  Dehnel_feels_he_can_return_home⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-12-15_[Older]_Iran:_Singer_arrested
                  for_performing_without_hijab⠀⇛


                # ⚓ Modern Diplomacy ☛ Weaponized_Justice:_Patterns_of
                  Repression_in_Russia⠀⇛


                       The Kremlin’s manipulation of Russia’s criminal
                       justice system stands as a cornerstone of its
                       strategy to suppress dissent, consolidate power,
                       and maintain authoritarian control. Over time, this
                       system has evolved into a finely tuned instrument
                       of repression, employing a variety of methods to
                       eliminate opposition, silence independent voices,
                       and enforce state narratives. Three distinct
                       patterns—selective prosecution, legal ambiguity,
                       and performative repression—underline this
                       weaponization of justice. Together, these methods
                       institutionalize authoritarianism, ensuring dissent
                       is not only punished but systematically deterred.


                # ⚓ Torrent Freak ☛ 'Destroyed'_Usenet_Provider_Sues_Anti-
                  Piracy_Group_for_Millions_in_Damages⠀⇛


                       Once-thriving Usenet provider NSE was targeted by
                       Dutch anti-piracy group BREIN many years ago. Under
                       legal pressure, the provider felt forced to shut
                       down its successful business. Though NSE ultimately
                       triumphed in court, that victory came years later.
                       NSE is now demanding millions of euros to
                       compensate for the alleged damage to its business.
                       BREIN, however, sees things differently.


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


                # ⚓ BIA Net ☛ 7_journalists_among_arrested_following_Istanbul
                  protests⠀⇛


                       The journalists placed under arrest sent the
                       following message via their lawyers: [...]


                # ⚓ VOA News ☛ Azerbaijani_journalist_says_he_was_jailed_over
                  his_work⠀⇛


                       Farid Mehralizada, an economist and journalist with
                       VOA’s sister outlet Radio Free Europe/Radio
                       Liberty, has been jailed since May on charges
                       including conspiring to smuggle foreign currency.
                       The journalist, his employer and press freedom
                       groups believe the case is retaliatory and part of
                       a wider crackdown in Azerbaijan.


                       In messages relayed to VOA through his wife,
                       Mehralizada spoke about his passion for journalism
                       and said he believed he was targeted for his work.


                # ⚓ CPJ ☛ Turkey_jails_7_journalists_and_media_workers,_places
                  one_under_house_arrest⠀⇛


                       “The Turkish government is attempting to control
                       the flow of news about Syria by intimidating the
                       press, as evidenced by the arrest of journalists at
                       a protest, the house arrest of Özlem Gürses, and
                       other legal actions,” said Özgür Öğret, CPJ’s
                       Turkey representative. “Turkish authorities must
                       immediately release the imprisoned journalists and
                       media workers, free Gürses, and allow members of
                       the media to do their jobs without fear of
                       retaliation.”


                # ⚓ Marcy Wheeler ☛ The_BezosPost_Struggles_with_the_Boundaries
                  of_Press_Freedom⠀⇛


                       It’s not the details of this that I find curious.


                       It’s that a media reporter and a democracy reporter
                       working for Jeff Bezos did not distinguish the
                       things that are journalism (at a stretch, the ABC
                       licenses) from what is not (the action hero movies
                       and other corporate acquisitions).


                # ⚓ The Guardian UK ☛ Journalists_who_were_unlawfully_spied_on
                  have_‘no_doubt’_UK_reporters_are_still_targeted⠀⇛


                       In a landmark judgment, the investigatory powers
                       tribunal (IPT) found last week that the Police
                       Service of Northern Ireland (PSNI) and the
                       Metropolitan police unlawfully carried out covert
                       surveillance on Belfast-based journalists Trevor
                       Birney and Barry McCaffrey.


                       The case stemmed from the pair’s 2018 wrongful
                       arrest, condemned by Northern Ireland’s top judge,
                       after they produced No Stone Unturned, an award-
                       winning documentary alleging collusion between
                       police and loyalist paramilitaries in a notorious
                       Troubles massacre.


                # ⚓ Axios ☛ Media's_suck-up_moment⠀⇛


                       State of play: Amid a record media trust deficit,
                       outlets once critical of Trump are now making
                       overtures to the former and future president, and
                       the majority of American voters who voted for him.


                # ⚓ Nebraska Examiner ☛ Changes_at_rural_Nebraska_newspaper
                  raise_subscribers_—_and_hope_for_the_future⠀⇛


                       Finneman, along with colleagues at universities in
                       Colorado and Missouri, are on a crusade to save
                       rural, weekly newspapers in a period when the
                       United States has seen 3,300 papers close in the
                       past 20 years. “News deserts” — areas without
                       newspapers — are expanding, raising the risk of an
                       uniformed electorate and one that is more polarized
                       by social media and talking heads.


                       That crusade brought the professor to this central
                       Nebraska ranching community last summer in an
                       effort to revive the financial fortunes of the
                       Chief, which has chronicled life in this corner of
                       Nebraska since 1892.


          o § Civil Rights/Policing⠀➾


                # ⚓ CBC ☛ 2024-12-15_[Older]_Federal_public_servants_vie_for
                  prized_co-working_spaces_to_avoid_downtown_commute⠀⇛


                # ⚓ Greece ☛ Syria’s_Christians_fearful_of_new_Islamist_leaders
                  as_Christmas_approaches⠀⇛


                       Although himself a former leader of the Sunni
                       Muslim Islamist group, which sees Christians as
                       infidels, Sharaa has quickly shed his jihadist
                       uniform for business suits.


                       And he has told the Western officials visiting him
                       that HTS will neither seek revenge against the
                       former regime of Bashar al-Assad, drawn mostly from
                       the Alawite sect, nor repress any other religious
                       minority.


                       But many Christians have yet to be convinced.


                # ⚓ ANF News ☛ Investigation_against_female_journalist_who
                  reacted_against_sexist_harassment_by_a_police_officer⠀⇛


                       The reason for the action against Değer is her
                       reaction to sexist remarks made by a Turkish police
                       officer. The case occurred on Sunday in the
                       district of Midyat, which is located in the east of
                       Mardin. Değer was accompanying a condolence visit
                       by activists from the Free Women's Movement (TJA)
                       to the family of journalist Cihan Bilgin, who was
                       killed along with her colleague Nazım Daştan in a
                       Turkish drone attack in northern Syria last week,
                       when a police officer made offensive and
                       intimidating verbal sexual harassment.


                # ⚓ RFA ☛ Tibetan_champion_of_language_preservation_dies_after
                  release⠀⇛


                       A Tibetan village chief who was detained in May for
                       championing Tibetan language preservation, died
                       three days after his release on Dec. 15, with
                       electrical burn and torture marks found on his body
                       during the cremation service, suggesting he was
                       abused in police custody, two sources said.


                # ⚓ Jacobin Magazine ☛ How_Capitalism_Undermines_Freedom⠀⇛


                       In his refutation of the famous libertarian
                       arguments of Robert Nozick’s Anarchy, State, and
                       Utopia, socialist thinker G. A. Cohen showed the
                       absurdity of thinking that we had to accept an
                       unequal society in order to preserve liberty.


                # ⚓ The Hill ☛ Former_DC_police_officer_convicted_over_leaks_to
                  Proud_Boys_leader⠀⇛


                       U.S. District Court Judge Amy Berman Jackson found
                       Lamond guilty on one count of obstructing justice
                       and three counts of making false statements to
                       federal law enforcement officials, including when
                       Lamond lied and said that he did not tip off Tarrio
                       to the fact that law enforcement had a warrant out
                       for his arrest. Tarrio was a prime suspect at the
                       time in an investigation into the burning of a
                       Black Lives Matter banner.


                # ⚓ Los Angeles Times ☛ Hand-written_signatures_were_a_sticking
                  point_for_young_California_voters⠀⇛


                       For young Americans, a written signature doesn’t
                       mean much anymore — except when voting by mail,
                       when a signature is critical to determining whether
                       a ballot is counted. In California, voters younger
                       than 25 made up 10% of the November electorate, but
                       had nearly 3 in 10 of the ballots set aside for
                       signature issues, according to a new survey.


                # ⚓ Los Angeles Times ☛ Cops_lie_to_suspects_during
                  interrogations._Should_detectives_stick_to_the_truth?⠀⇛


                       They were. The tale of his father on a gurney in
                       the morgue was a deception used to push Perez to
                       confess to killing him.


                       Over several more hours, interview transcripts
                       show, detectives shut Perez down when, again and
                       again, he told them he hadn’t harmed anyone.
                       Instead, they hammered him with accusations.
                       Exhausted, in despair and desperate to stop the
                       “pounding,” Perez said later, he finally agreed
                       with police that he had killed his father.


                       Then, he tried to hang himself using a shoelace —
                       hours before his father was located, alive and
                       well.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Deutsche Welle ☛ 2024-12-13_[Older]_Vietnam's_new_data_law
                  a_test_for_its_big_tech_ambitions⠀⇛


                # ⚓ Inside Towers ☛ NTCA_Members_Receive_$142.7_Million_in_USDA
                  Broadband_Deployment_Funding⠀⇛


                       Members of NTCA–The Rural Broadband Association,
                       received over $140 million in loans and grants for
                       broadband deployment through the U.S. Department of
                       Agriculture’s (USDA) latest distribution of loan
                       and grant funding under the ReConnect Program. Most
                       of the projects will support the delivery of 100
                       Mbps symmetrical or better broadband service.


                # ⚓ The Guardian UK ☛ ‘Security_through_obscurity’:_the_Swedish
                  cabin_on_the_frontline_of_a_possible_hybrid_war⠀⇛


                       Since Russia’s invasion of Ukraine in 2022, Sweden
                       has experienced a rise in hybrid warfare – attacks
                       on an adversary using methods other than
                       traditional military action – blamed on pro-Russia
                       groups. With governments in northern Europe on high
                       alert over hybrid Russian activity, the Guardian
                       was given exclusive access to the Stockholm
                       datacentre site.


                       Daniel Aldstam, the chief security officer at
                       GlobalConnect, which transports 50% of the
                       [Internet] capacity of the Nordics and runs the
                       centre, described the approach to its location and
                       ordinary outward appearance as “security through
                       obscurity”.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Silicon Angle ☛ Report:_Apple’s_M5_chips_will_use_TSMC's
                  N3P_process_and_2.5D_packaging_technologies⠀⇛


                       Apple’s M-series Mac chips each include a central
                       processing unit, a graphics processing unit and an
                       artificial intelligence accelerator. The latest M4
                       is available in standard, Pro and Max versions with
                       10, 14 and 16 CPU cores, respectively. Apple
                       earlier launched a chip called the M2 Ultra that
                       combines two 2022 M-series processors into a single
                       product.


                       The company is expected to take a similar approach
                       with the upcoming M5 chip by offering it in
                       standard, Pro, Max and Ultra editions. It’s unclear
                       how many CPU cores the different versions will
                       offer. However, Kuo detailed that all four
                       processors are set to be made using a new version
                       of TSMC’s three-nanometer node.


                # ⚓ The Scotsman ☛ Netflix:_do_you_need_a_TV_licence_to_watch
                  NFL_games?⠀⇛


                       And if you are caught watching live TV - including
                       live events on Netflix - you could find yourself
                       facing a big fine. Which would really put a damper
                       on your Christmas.


                # ⚓ New Yorker ☛ What_Spotify_Is_Really_Costing_Us⠀⇛


                       Just as we train Spotify’s algorithm with our likes
                       and dislikes, the platform seems to be training us
                       to become round-the-clock listeners. Most people
                       don’t take issue with this—in fact, a major Spotify
                       selling point is that it can offer you more of what
                       you like. Liz Pelly’s new book, “Mood Machine: The
                       Rise of Spotify and the Costs of the Perfect
                       Playlist,” is a comprehensive look at how the
                       company’s dominance has profoundly changed the way
                       we listen and what we listen to. A contributing
                       editor to The Baffler, Pelly has covered the ascent
                       of Spotify for years, and she was an early critic
                       of how the streaming economy relies less on
                       delivering hit tunes than on keeping us within a
                       narrow gradient of chill vibes. Her approach is
                       aggressively moralistic: she is strongly
                       influenced, she explains, by D.I.Y. spaces that
                       attempt to bring about alternate forms of
                       “collective culture,” rather than accept the
                       world’s inequities as a given. She sympathizes with
                       the plight of artists who feel adrift in the
                       winner-take-all world of the Internet, contending
                       with superstars like Adele or Coldplay for
                       placement on career-making playlists and,
                       consequently, a share of streaming revenue. But her
                       greatest concerns are for listeners, with our
                       expectations for newness and convenience. Pelly is
                       a romantic, but her book isn’t an exercise in
                       nostalgia. It’s about how we have come to view art
                       and creativity, what it means to be an individual,
                       and what we learn when we first hum along to a
                       beloved pop song.


      § Monopolies/Monopsonies⠀➾


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ Rojadirecta_&_Site_Operator_Hit_With_$33m
                  Piracy_Damages_Judgment⠀⇛


                       Around 2016, sports streaming site Rojadirecta
                       closed its doors to visitors from Spain after
                       losing its legal battle with Mediapro. Despite the
                       win, the broadcaster was disappointed that the
                       court had found the company behind Rojadirecta
                       liable, but not company owner Igor Seoane. After
                       the Supreme Court held that Seoane could be held
                       liable, last Friday a court confirmed total damages
                       of $33 million, with Seoane and the company jointly
                       liable for half of that amount.


                # ⚓ Deutsche Welle ☛ 2024-12-12_[Older]_Australia_to_force_tech
                  giants_to_pay_for_news_media⠀⇛


                # ⚓ Variety ☛ The_Temptations_Celebrate_60th_Anniversary_of_'My
                  Girl'⠀⇛


                       The Temptations already had a 60th anniversary
                       celebration, but not as often do people celebrate
                       the anniversary of a song, which you’re doing now
                       with the 60th for “My Girl.”


                # ⚓ Techdirt ☛ Copyright_Doesn’t_Provide_A_‘Living’_For_A
                  Successful_Author⠀⇛


                       She says that she earns about $43,200 from such
                       direct patronage – a decent sum, but one that
                       requires a lot of work in terms of encouraging fans
                       to contribute, an activity that takes away time
                       from her creative writing. For what it’s worth, it
                       precisely the model that I advocate in Walled
                       Culture, and it’s interesting to see it working
                       here. But the fact that a successful author like
                       Byrne depends on patronage underlines the point
                       that copyright simply does not do what most people
                       think it does: provide a decent income for a good
                       writer. Commenting on the reasons why today’s
                       copyright model is not working for her or others,
                       Byrne writes: [...]




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