𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, October 16, 2021
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Gemini index for the day: gemini://gemini.techrights.org/2021/10/16/


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

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QmScBUgZwyXW8e6VTQ7hn4TPr2dPrqRq4mBq4A6SJD33QU
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QmRVquEDfjUxjZohz6NpGuYae1hJY5sYhcGTzygC15t1qe
QmS8QHtXh2RotXbWpZsvGPyWGq3WgJPQrsFc5JaTmqKcxD
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QmZ9XrCCvCG4m4kD1sxmesDGxEpk9EjEVk5vNUFHZ87Ryw


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

⦿ EFF Pushes for Users to Install DuckDuckGo Software After Being Paid to Kill HTTPS Everywhere | Techrights

⦿ The EPO’s Overseer/Overseen Collusion — Part XIV: Battistelli’s Iberian Facilitators  -  Portugal | Techrights

⦿ In Picture: After Billions Spent on Marketing, With Vista 11 Hype and Vapourware, No Real Gains for Windows | Techrights

⦿ “Facebook Whistleblowers” Aside, It Has Been a Dying Platform for Years, and It’s Mentally Perverting the Older Generation | Techrights

⦿ IRC Proceedings: Friday, October 15, 2021 | Techrights

⦿ [Meme] [Teaser] Double-Dipping Friedrich Rödler | Techrights

⦿ [Meme] Microsoft Has Always Been About Control Over Others | Techrights

⦿ [Meme] Spanish Inquisition | Techrights

⦿ Why You Shouldn’t Use SteamOS, a Really Incompetent GNU/Linux Distribution With Security Pitfalls (Lutris is a Great Alternative) | Techrights

⦿ The Reign in Spain | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/10/16/duckduckgo-and-eff/#comments
		http://techrights.org/2021/10/16/epo-portugal-role/#comments
		http://techrights.org/2021/10/16/failure-of-vista-11-hype/#comments
		http://techrights.org/2021/10/16/fb-dying-platform/#comments
		http://techrights.org/2021/10/16/irc-log-151021/#comments
		http://techrights.org/2021/10/16/meme-friedrich-rodler/#comments
		http://techrights.org/2021/10/16/microsoft-linkedin-github/#comments
		http://techrights.org/2021/10/16/spanish-gov-epo/#comments
		http://techrights.org/2021/10/16/steamos-and-lutris/#comments
		http://techrights.org/2021/10/16/the-reign-in-spain/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/10/16/sculpt-os-21-10/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 74

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/16/duckduckgo-and-eff/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/16/duckduckgo-and-eff/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.16.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EFF_Pushes_for_Users_to_Install_DuckDuckGo_Software_After_Being_Paid_to_Kill
HTTPS_Everywhere⠀✐


Posted in Deception, Microsoft, Search at 7:50 am by Guest Editorial Team


Guest post by Ryan, reprinted with permission from the_original


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇DDG_meme⦈_


I’ve been writing lately about how DuckDuckGo is shady and their business is
questionable.


It seems that some donations went the EFF’s way and now they plan on killing
off_HTTP_Everywhere_permanently.


$25,000 a year buys them the Tor Project and $150,000 keeps the EFF in their
back pocket. But where does the money for this come from, and what does
DuckDuckGo get from it?


No company gives out millions of dollars a year and expects to get back
nothing.


Is it just DuckDuckGo’s own advertising paying for this?


DuckDuckGo pretends they’re a startup, but that’s not true. They admit that
they have been profitable since 2014, have over 105 million searches a day
sometimes, and are growing rapidly.


They’re not small. They have very close ties with Microsoft, which also dumps
money into these sorts of organizations in order to corrupt them and shield
itself from criticism.


(Relatively speaking, the chump change that Microsoft pays off the “Linux
Foundation” with corrupted and silenced that organization too.)


In fact, the number one factor in DuckDuckGo’s search results is what Microsoft
Bing returns to DuckDuckGo.


So I think it can fairly be said that DuckDuckGo is a way for Microsoft to gain
market share with people for whom the Microsoft brand itself is toxic, due to
their many decades of law breaking, bad software, spyware, advertising network,
and corrupt business practices.


Microsoft itself tries to get away from its own brands too, but even though
Edge is named differently than Internet Explorer, and uses a different
rendering engine now, they haven’t had much luck in getting people, on Windows,
to use it.


This despite malware tactics to steal back default settings and scream at the
user that Firefox and Chrome and the others “aren’t safe” (Oh, but Edge is?
Well, pardon the hell out of me!). Not that this has stopped their shills from
recommending it to people on GNU/Linux, who actually have a choice about what’s
on their computers. (Hey, and it ain’t gonna be Edge!)


Anyway, it seems the corruption (the intended effect of DuckDuckGo’s money,
which is potentially gleaned from *cough* some other source), is convincing the
EFF to shut down its own security applications and pitch DuckDuckGo’s products
instead.


DuckDuckGo used to have an application for Android that merely let you search
it from your Home screen.


Now, the only app they make for Android is an entire web browser, where
DuckDuckGo is in a position to monitor everything you do in it. It’s also not
particularly convenient because there’s no desktop version of it to sync with.


But just last year, it_was_caught_tracking_its_users, and they had an
explanation for the tracking when they got caught, like they always seem to.
“Just a bug.” Was it?


DuckDuckGo also has a Chrome and Firefox extension called “Privacy Essentials”,
and the EFF is also recommending users move from HTTPS Everywhere to
DuckDuckGo’s extension.


     As HTTPS Everywhere goes into “maintenance mode”, users will have the
     opportunity to move to DuckDuckGo’s Privacy Essentials or use a
     browser that has HTTPS by default.


     Electronic Frontier Foundation


But DuckDuckGo certainly isn’t a charity.They want all of this software on your
computers for a reason, and if that reason was only to bolster their search
engine, they’re already in every major web browser, and you can already use
them for search that way.


They have other things to be gained from having more of a presence on your
computer, or they wouldn’t be writing this stuff in the first place.


It would be better to have nothing of the sort installed on your computer than
to replace HTTPS Everywhere with a DuckDuckGo application.


As the corrupt EFF itself points out, Chromium is moving in the direction of
HTTPS by default, and Firefox today has an HTTPS-Only Mode (you can make
exceptions), without stuffing this ducking nonsense into your computer and
letting their “Whoops it’s another bug that lets us track you, but pay_no
attention_to_the_man_behind_the_curtain!” position keep coming up.


(Note: I had to pull that Reddit post about Gabriel Weinberg out of the
Internet Archive because Reddit, a platform for censorship from “Conde Nasty”,
removed it. Reddit operates with bans and shadowbans and removes posts all the
time.)


It’s unlikely that DuckDuckGo keeps getting caught violating their own privacy
policy (and these are just the times they get caught) and that it’s “just
bugs”. At this point, it is more likely that their privacy policy is bullshit
and a lie.


The EFF has gone from being a good cause to not being worth a bag of beans in
the span of a few short years. █


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⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⣠⡄⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢐⣠⣷⣄⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⠀⠀⠀⣰⡇⠀⠀⠀⠙⢷⣄⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀
⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠙⠳⣦⣬⣿⣿⣿⣿⣿⣿⣏⣉⣧⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣛⣛⡛⣋⣉⡁⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡶⡾⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠡⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿
⠀⠀⠀⢿⣧⢿⣇⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢹⣿⣿
⠀⠀⠀⠈⢿⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⢻⡏⡿⠿⠛⠉⠀⠀⠀⣀⣤⣾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠈⠛⠞⠿⡿⠿⠿⠿⠟⠛⠋⠈⠁⠀⠀⣀⣠⣤⣶⣟⣿⢯⠿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠶⠶⠿⠿⠿⠿⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢶⣤⣀⣀⣀⢀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⡷⢶⣿⡦⣿⠥⠥⡮⡧⠀⢺⣵⢰⣿⣦⣮⣷⣿⡸⣼⣶⢻⡇⣷⢴⢱⡆⠀⢧⡞⣶⢱⢼⣆⡇⠀⢸⠊⣶⢵⢤⣽⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠟⠉⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣾⣿⣿⣿⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣫⣿⣿⣿⣿⠃⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣾⠏⣹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡴⢁⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣶⣿⣭⣥⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⣿⣿⠀⣷⣰⣷⣧⣤⣤⣤⢤⣤⢤⠤⣼⢵⠄⢸⣵⡁⡤⣄⡤⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⠀⠀⠀⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⠀⠏⠟⠿⠟⠿⣿⡻⡾⠿⠟⢶⠿⠘⠆⠸⠞⠀⠇⠋⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢞⣣⣣⣭⣛⠉⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠚⠏⠁⠑⣤⣥⣬⣤⣆⣀⣄⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣟⣥⣶⣿⢏⣽⣵⣆⠀⠀⠴⢀⣄⠖⣴⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣆⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 283

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

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✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian
Facilitators_–_Portugal⠀✐


Posted in Europe, Patents at 3:56 pm by Dr. Roy Schestowitz


Series parts:


   1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In!
   2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous”
      Endorsement?
   3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes
   4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States
   5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja”
   6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch
      Courage
   7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity
   8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and
      Pusillanimous_Hibernia
   9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss
      Cheese
  10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the
      Controversial_Christian_Bock
  11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_–
      Battistelli’s_Swiss_Apprentice?
  12. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection
  13. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian
      Facilitators_–_Spain
  14. YOU ARE HERE ☞ Battistelli’s Iberian Facilitators – Portugal
      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Campinos_with_Maria_Leonor_Mendes_da_Trindade⦈_

Campinos with Maria Leonor Mendes da Trindade, his deputy and successor at the
                               Portuguese INPI.


Summary: How illegal “Strike Regulations” and regressive ‘reforms’ at the EPO,
empowering Benoît_Battistelli to the detriment of the Rule of Law, were ushered
in by António_Campinos and by Portugal 5 years before Campinos took
Battistelli’s seat (and power he had given himself)


In this part we will take a look at the Portuguese delegation on the EPO’s
Administrative Council which helped to rubber-stamp Battistelli’s “Strike
Regulations” in 2013.


At the time in question, the delegation was headed by Maria Leonor Mendes da
Trindade, Director of the Portuguese INPI. Trindade was assisted by her deputy
Marco Dinis, who was head of the INPI’s “Department of Information and
Promotion of Innovation”.


Trindade had been Campinos’ deputy when he was in charge of the Portuguese INPI
between 2005 and 2010. She “inherited” his position when he moved to Alicante
in October 2010 to take up his new job at the head of the EU trademark agency
OHIM/EUIPO.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Maria_Leonor_Mendes_da_Trindade_and_her_deputy_Marco_Dinis⦈_
  The Portuguese delegation in 2013: Maria Leonor Mendes da Trindade and her
                              deputy Marco Dinis.


In the context of the EPO’s Administrative Council, Trindade was very much a
“captured delegate” like her Spanish counterpart García-Escudero. She gave
unquestioning support to Battistelli and was regarded as one of his loyal “pet
chinchillas” on the organisation’s governing body.


“In the context of the EPO’s Administrative Council, Trindade was very much a
“captured delegate” like her Spanish counterpart García-Escudero. She gave
unquestioning support to Battistelli and was regarded as one of his loyal “pet
chinchillas” on the organisation’s governing body.”Trindade’s career as head of
the Portuguese INPI proceeded in a relatively uneventful manner until August
2018 when she suddenly came to grief due to a catastrophic_breakdown of the
INPI’s IT systems.


The IT system collapse was caused_by_a_heatwave in Lisbon. Not only was this a
PR disaster for the national “IP” office. It also created a great deal of legal
uncertainty because between 13 August and 4 September 2018 the publication of
the “Industrial_Property_Bulletin” was disrupted. [PDF]


The “Industrial Property Bulletin” is the official gazette listing newly
registered patents and trademarks and other such information relating to “IP
rights” and it is an essential source of information for patent and trademark
applicants and their legal representatives.


“Even after the IT systems were restored to operation, there were ongoing
problems and another serious breakdown is reported to have occurred a few
months later in December 2018.”The malfunctioning_of_the_INPI’s_IT_systems
[PDF] also prevented B2B communications, payments through current accounts,
online_file_inspection, as well as the_transmission [PDF] of email_messages
confirming_receipt_of_electronic_filings.


Even after the IT systems were restored to operation, there were ongoing
problems and another serious breakdown is reported to have occurred a few
months later in December 2018.


Shortly afterwards it was reported in the Portuguese media that Trindade and
her deputy Dinis had accepted responsibility for the INPI’s “IT meltdown” and
had already submitted their resignations to the Ministry of Justice in November
2018. The resignations were accepted by the Ministry in January 2019.


“Following her resignation from the INPI, Trindade managed to obtain a position
as a “technical specialist” at the Portuguese Ministry of Economy and Digital
Transition.”The IT problems at the INPI didn’t disappear with the departure of
Trindade and Dinis. As a matter of fact, in March_2019, the Portuguese “IP”
office was still reporting serious disruptions_to_its_IT_services. [PDF]


Following her resignation from the INPI, Trindade managed to obtain a position
as a “technical specialist” at the Portuguese Ministry_of_Economy_and_Digital
Transition. [PDF]


She later moved to a similar position at the Ministry_of_Planning_and
Infrastructure and in 2020 she was appointed as an “assistant” or “deputy” in
the Office of the Minister of Planning and Infrastructure.


“…after her fall from grace due to the IT disaster at the national “IP” office,
Trindade is probably grateful to have any kind of job in the Portuguese public
sector.”According to official_Portuguese_records, Trindade’s latest post comes
with a_monthly_after-tax_salary_of_€2,201.89. [PDF]


It’s a far cry from the mouth-watering five-digit monthly remuneration that her
erstwhile boss Campinos gets as head of the EPO. And it’s probably less than
what she would have earned as head of the INPI. But after her fall from grace
due to the IT disaster at the national “IP” office, Trindade is probably
grateful to have any kind of job in the Portuguese public sector.


“With connections like that, it can’t have been too difficult for Dinis to
bounce back from the little setback that derailed his career at the INPI in
2018.”Trindade’s deputy Marco_Dinis seems to have done better for himself. From
June 2019 to October 2020 he held a position as a “Seconded National Expert” at
the EUIPO in Alicante. After that he was appointed as a “Principal Technical
Attaché” with the Portuguese Permanent Representation to the EU in Brussels.


That’s quite impressive for someone who had to resign from his previous
position for failing to ensure that the national “IP” office had a fault-
tolerant IT system with adequate temperature regulation.


However, it’s not entirely surprising because Dinis is known to be well-
connected to António Campinos and his "faithful_acolyte", João Negrão. Those
connections go back to the days when Campinos was the boss at the Portuguese
INPI between 2005 and 2010 and Negrão was in charge of the INPI’s Department of
International Relations.


“In a later part of the series we will return to the Mediterranean region to
consider the Italian delegation.”For example, it is known that Dinis
participated with Campinos and Negrão in a_meeting_which_took_place between the
INPI, the WIPO Academy and the Lisbon Institute of Economics and Management
(ISEG) in June 2008. The purpose of this meeting was to establish a cooperation
agreement between the three institutions for the creation of a postgraduate
course in “Innovation Management and Industrial Property”.


With connections like that, it can’t have been too difficult for Dinis to
bounce back from the little setback that derailed his career at the INPI in
2018.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Marco_Dinis_together_with_António_Campinos_and_João_Negrão⦈_
Marco Dinis together with António Campinos and João Negrão a meeting which took
  place between the INPI, the WIPO Academy and the Lisbon ISEG in June 2008.


That concludes our look at Battistelli’s Iberian facilitators who helped to
rubber-stamp his “Strike Regulations” in June 2013.


“[Italy] was the only one of France’s traditional allies from that part of
Europe to withhold its support from Battistelli’s efforts to crush the
fundamental rights of EPO staff.”In a later part of the series we will return
to the Mediterranean region to consider the Italian delegation. This was the
only one of France’s traditional allies from that part of Europe to withhold
its support from Battistelli’s efforts to crush the fundamental rights of EPO
staff.


“…we plan to take an in-depth look at the controversial head of the Austrian
delegation, the notorious “double-dipper” Friedrich Rödler.”In the next part,
our attention will shift to Central_Europe and we will examine the role played
by the EPO’s third host state, the Federal Republic of Austria.


More specifically, we plan to take an in-depth look at the controversial head
of the Austrian delegation, the notorious “double-dipper” Friedrich Rödler. █


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⢀⣰⡇⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠒⠀⠲⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠸⣿⣿⣿⣿⣿⣿⣿⢃⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⠃⠄⠀⢰⡄⠚⠂⠝⠽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡧⠾⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⢀⢴⠀⠀⣶⠀⠀⣄⠰⡄⠄⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠻⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⠀⢠⡄⠉⡀⢠⡄⣅⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢠⠀⢁⡀⠻⠀⢀⠀⡈⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⢡⠀⣄⠘⠃⠀⣦⠘⠃⠉⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣄⠀⡤⢽⣤⣾⠀⠈⡀⠘⠈⠙⣿⣿
⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠛⢀⠀⢲⠀⠀⠀⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢁⠀⣰⠶⣿⣷⡦⣰⠄⠸⠆⠑⢻⣿
⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠛⢀⡘⠃⣀⠁⠀⠠⠄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠁⠉⢱⣿⠠⡁⡘⣷⠈⢄⣀⠴⢤⠆⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣄⠀⠀⠈⠃⢀⡈⠠⠤⠄⡀⡁⠀⢀⠀⠀⠀⠀⠠⡄⢤⠠⡦⠀⠗⠀⢹⣿⠀⡗⠷⣿⡀⠀⣑⡀⠀⠒⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⠈⠈⢁⣴⣶⣤⣤⣄⠀⢀⠁⣙⠈⠀⠀⠀⠀⣿⡉⢉⣙⠉⣉⣙⡆⢀⣿⣯⣯⣽⣿⠏⠀⢀⢙⠁⠉⡇
⣿⣶⣶⣶⣶⣶⣶⣶⡀⠀⢀⣴⣿⣧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠘⠀⠖⢠⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣶⣤⣤⣤⢟⠉⠉⢩⠝⠉⢹⣷⣿⣿⣿⣿⣿⣿⡀⢶⠔⠻⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠟⠃⠀⠀⠀⠂⠀⠀⠀⠀⠒⣒⣒⢒⣦⡄⣀⣠⣤⣤⣤⣤⣿⣿⣿⣿⣟⣻⣻⣿⣿⣿⣟⢿⣿⠟⣿⡻⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⢀⡦⢺⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣗⣤⡆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣶⣶⣶⣎⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⣭⣤⣥⣴⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢋⣩⣠⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠚⠛⠝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣳⣿⣿⣿⣿⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣻⣿⣿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⢤⣤⣀⣀⣀⣴⣾⣿⠀⠀⠀⣶⢿⡁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⡏⢹⣿⣿⣿⣿⣿⣿⣈⣛⡿⠿⣿⡿⠿⡿⠀⠀⠀⢻⢿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⠋⠁⠀⠤⠤⠌⢙⣻⣿⣿⡿⣿⡗⠴⣦⣼⠓⠶⠁⠀⠀⠀⠘⠊⠻⠇⠀⠀⠀⠀⠀⠀⢿⣷⣦⡀⠀⠀⠀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⣶⣶⣒⣺⣭⣾⣿⣿⣿⣿⣯⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣤⣀⠀⢀⣄⣀⣀⡀⠈⠉⢳⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⡙⠿⣿⣿⠆⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣿⣿⡿⣿⡤⠀⢁⡾⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣥⣬⡿⠀⢾⠗⠁⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⠟⠛⢋⣿⣿⣿⣿⣿
⠻⠿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⢩⠀⡌⢠⢰⣿⣿⣿⣿⣿⣿⣿⣶⣤⣌⣉⣉⣡⣽⣴⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠅⠀⠀⡊⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠒⠀⢸⣿⣿⣿⣿⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠌⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠁⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣹⠦⣄⡀⣀⣤⣄⣀⠀⠀⠉⠙⠀⠚⠋⠁⠀⠀⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣦⣭⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠽⡛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⠉⠉⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⢀⣠⣠⡄⣷⣿⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢺⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠃⠈⠺⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦
⣿⣿⠁⠉⠉⠉⠛⠻⢿⣿⣿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⣤⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠿⣷⣴⠠⠙⠛⠛⠋⢿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠅⠀⠈⠙⠃⣀⣀⣤⣴⣶⣾⣿⣶⣦⣤⣈⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠉⠀⠂⠐⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠟⠷⠂⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠙⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣐⣯⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⠁⠀⠃⣿⣿⠀⠀⠙⣵⣶⡢⢶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠉⠛⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⢹⣿⣿⣿⡿⠟⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢊⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢁⣴⣶⣶⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣱⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡇⢛⣿⣻⣆⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⣿⣿⣧⣸⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠈⣿⣿⣰⡾⣷⣷⡿⣻⣿⣿⣿⣿⡟⣠⣤⣤⠸⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡸⣿⣿⣽⣿⣿⣿⢿⣿⣿⣿⡟⠀⣠⣤⡌⢻⣿⣿⣿⣿⠀⠀⠃⠀⠀⢻⣿⠿⠛⣿⣿⣿⣧⠛⢛⢿⢌⡵⡽⠿⢣⣝⣿⡟⠚⠏⣿⣿⢻⣿⣷⢶⣻⣾⣿⣿⣿⣿⣿⣿⠿⢛⡬⣿⠏⠈⠉⠛⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣧⠛⠛⠹⣿⣿⣿⠃⠿⠿⠿⠀⢸⣿⣿⣷⠀⠛⠛⠛⠛⡀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⡞⠀⠀⠀⠀⠘⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⡟⠀⠀⡼⠀⠏⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠐⠒⠀⠀⠀⠀⠙⣿⣟⡄⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⢀⣀⣤⣿⣦⣤⣾⣦⣤⣀⡀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢼⣿⠠⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⠀⠀⠀⠀⠀⠀⢻⣿⠐⠀⠀⠨⣿⣿⡏⡟⣿⣿⣿⣿⣿⣿⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢸⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⢸⣿⣿⣿⣿⣿⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠸⡼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠟⢿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⣀⠀⣻⣿⢸⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠂⠠⠟⣲⠂⡼⢹⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠉⠁
⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⣀⣴⡾⠃⠐⣿⣿⣸⣿⣿⣿⠇⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢽⣄⣩⣿⣿⣿⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠙⠖⠀⠀⠀⡿⠿⠟⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⢸⡇⣺⣿⣿⠻⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢸⢸⡆⠸⠧⠞⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡛⢀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠐⠀⠀⡀⣿⡇⣀⡘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣷⣶⠀⠀⣀
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢡⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢘⣁⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⠾⠇⠀⠀⠛
⠀⠀⠿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠨⡿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠘⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⣅⡟⠀⠀⠀⠀⠀
⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⣀⣀⣀⡀⢀⣄⡀⠀⠀⢰⣶⡷⣾⠣⠼⠷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⣻⡿⠉⣽⣿⣿⡆⠈⠛⠻⠩⠘⠸⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 583

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/16/failure-of-vista-11-hype/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/16/failure-of-vista-11-hype/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.16.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ In_Picture:_After_Billions_Spent_on_Marketing,_With_Vista_11_Hype_and
Vapourware,_No_Real_Gains_for_Windows⠀✐


Posted in Deception, Marketing, Microsoft, Windows at 5:52 pm by Dr. Roy
Schestowitz


The hype started this past summer


                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Windows share⦈
   Windows market share as a function of time from 2009 until October 16th
                      (today). Raw_data [ODS] available.


Summary: The very latest figures from Web_usage show that it’s hardly even a
blip on the radar; Windows continues bleeding to death, not only in servers


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠉⠉⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠘⠛⠛⠛⠋⠙⠋⠁⠸⠿⠿⠿⠿⠛⠛⠉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠻⠿⠛⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 646

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/16/fb-dying-platform/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/16/fb-dying-platform/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.16.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ “Facebook_Whistleblowers”_Aside,_It_Has_Been_a_Dying_Platform_for_Years,_and
It’s_Mentally_Perverting_the_Older_Generation⠀✐


Posted in Deception at 9:33 am by Guest Editorial Team


Guest post by Ryan, reprinted with permission from the_original


The Facebook Whistleblowers, as they are called, didn’t tell us much that we
didn’t know already.


The platform is pure evil. It spies on people, and ignores extremists and
political terrorists (like Trump’s January 6th “supporters”) in order to drive
“engagement”.


Over time, it’s been getting worse. It’s certainly no wonder why young people
are abandoning it.


They may not be primarily concerned with the spying or the manipulation.


If it’s true that they are just going to other Facebook platforms like
Instagram, WhatApp, as well as the non-FB Snapchat, which is actually worse in
some ways, then they aren’t learning the important lessons.


But, all things being aside for the moment, since Facebook was invaded by “Your
Parents” and they started posting a bunch of racist crap, “We hate Biden!”, and
“Gee, don’t you miss Trump even though he nearly destroyed our entire country
and did the majority of that in just his last 9 months!”, their userbase on
Facebook itself has been plummeting.


The remaining users are left going down a rabbit hole of increasing insanity as
increasingly the only thing left are a bunch of self-important, entitled baby
boomers, who are obviously going through their second childhood (I mean, when
the police have to come out because you knocked someone’s teeth out over a
“mask dispute”….), and don’t understand shit about science. (Vaccine
“hesistancy”. AKA, I don’t know how this works, so instead of learning about
how it works, I’ll decide to be ignorant and afraid instead!”)


All other things aside, and_there_are_plenty_of_other_things, do we really want
to share a platform with right-wing terrorists and trolls who support Trump and
are dumb enough to not only break the law, but take pictures of themselves
doing it, admit everything on CNN, and then upload the evidence to Facebook?


Both of my parents voted for Trump and they were very “Hah! In your face!”
about it, but they’re very weak now and don’t want to discuss the fact that he
lost to Joe Biden, of all people. Even though Biden spent a lot of his Senate
career doing things that they would have approved of had they actually paid any
attention to it. He was behind the 1994 Crime Bill and he’s still fighting in
court to deport asylum seekers under Trump’s made up “Title 42” nonsense.


CBP and ICE are as bad as they ever were under Trump. Why, just a few weeks
ago, they were photographed on horseback whipping black people from Haiti at
the border.


So not much has changed. To hear mom and dad, you’d think that Biden will turn
us into a Communist country, even though the facts don’t support this either.
It was Trump that signed the biggest corporate welfare bill ever (the CARES
Act) and mollified the anger of those whom he caused to become unemployed with
rent moratoriums, the illegal CDC eviction ban, and “extended unemployment
checks”. Biden let the unemployment program expire, the eviction ban is gone,
and the CARES Act and “American Rescue Plan” money turned into state slush
funds for bread and circuses and new prisons.


But they won’t pay attention. Facebook has radicalized and mentally perverted
and corrupted them both to the point of no return. We should feel sorry for
both of them, and those like them.


Of course some, like my parents, were already sort of like this, but Facebook
made them worse. It put them in a bubble and let them speak with people who
were even more fit for a lunatic asylum than either of them were, and they
started getting crazier and crazier ideas in their heads.


In an episode of Babylon 5, when the Narn (who have been oppressed by the
Centauri) wanted revenge, G’Kar has to shout “No! They are a DYING PEOPLE! We
should just let them pass.”


I suppose the same can be said of our parents, the boomers, at this point. They
can’t be reasoned with. They live in an alternate reality with “alternative
facts”, and they are very much on the way out. It’s up to us to salvage what we
can when they’re no longer as much of a force. █



                    ䷩ 𝚕𝚒𝚗𝚎 758

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/16/irc-log-151021/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/16/irc-log-151021/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.16.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_October_15,_2021⠀✐


Posted in IRC_Logs at 2:07 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      151021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-151021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-151021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      151021.txt
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmZMbTCinKEJbtmjK73pNkkf5xPd31EBdfQ9aArsPkzoit #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmWb5o1X1VUnrBJCfAvGLeJhuYfN7P8ZU6DYuuNWKtuahp (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
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                                                 IRC log for
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                                                 IRC log for
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 QmcsG72vjKbJ1Cre7tZDcY8L6ps8rFcgSxX2FyttCjHBhd social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
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 QmYjDVPDef6vTbkbSE4DbWyEzh4n7eBzMRv5jR2sRiPrfH #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
                                                 #techbytes
 QmPcVrboJYBdrnf27D2bJ48hTKnnQkLtffiw6ygkG1Jv9R (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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                                                 IRC log for
 QmcKedwf7cQg9T6sQnq9eZDkiyj5tXrnSYAZuswXJjy4oG #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
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                                                 as plain/ASCII
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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmZ9XrCCvCG4m4kD1sxmesDGxEpk9EjEVk5vNUFHZ87Ryw



                    ䷩ 𝚕𝚒𝚗𝚎 887

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/16/meme-friedrich-rodler/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/16/meme-friedrich-rodler/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.16.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_[Teaser]_Double-Dipping_Friedrich_Rödler⠀✐


Posted in Deception, Europe, Patents at 4:08 pm by Dr. Roy Schestowitz


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


Summary: As we shall see tomorrow night, the EPO regime was supported by a fair
share of corrupt officials inside the Administrative Council


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⣀⣄⣀⢀⣀⣀⣀⠀⠀⣀⣀⣀⠀⣀⡀⣀⣀⢀⣀⣀⡀⢀⣀⣀⡀⠀⣀⣀⢀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠾⠿⢸⣿⢸⣿⡇⣿⡿⣿⡅⣿⣿⠀⣿⣿⢸⣿⢈⣉⣱⣿⣜⣿⣿⣮⢸⣿⠿⢸⣿⡇⣉⡁⡇⣿⡇⢸⣿⡇⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⣼⣿⠃⣿⣧⣿⡇⣿⣿⣶⣿⣿⠸⣿⣼⣿⢷⣿⢻⣿⣼⡿⢸⣿⣾⡞⣿⣧⣿⢇⡇⣿⡇⠈⢿⣧⣿⠇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⣾⣿⣿⣿⣾⣷⣾⣷⣶⣶⣾⣶⣿⣶⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠛⡃⠈⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁⠀⠀⢀⣴⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣉⣿⣿⣿⣿⠋⣠⣴⡶⠶⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠀⠚⢁⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠛⢛⣃⠀⠉⣻⣿⣿⣿⠁⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣆⠘⠻⣿⠁⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⣤⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠠⣾⣶⣶⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⢠⣄⣀⣌⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣿⡇⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⡿⠀⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣃⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢀⣼⡃⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢠⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⣿⠃⠀⣸⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⠇⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠋⠀⠀⣸⣷⣾⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣙⠛⠿⠿⠿⠿⠿⠟⠛⠉⢀⣶⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢄⣤⠀⠀⠀⠐⠉⢿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢂⢿⣷⣾⣿⣿⣦⡰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⠛⣉⣿⣿⣿⣷⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣝⡆⢹⣿⣿⣿⣿⣄⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⢹⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣻⣼⠁⠊⠓⡿⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⠀⠀⢀⣘⣛⣛⢟⣛⣛⣛⠿⣛⣛⣛⣛⢛⣛⡛⣛⣛⡛⢛⣛⣛⣛⣛⣛⣛⢻⡿⢛⣛⣛⠿⣛⣛⣛⠿⣛⣛⡉⢈⣘⣛⣛⠁⣀⣀⡀⠁⣘⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⡇⣿⣿⣿⣷⢰⡾⣿⡟⣿⣿⣿⡟⣿⡇⣿⣿⢿⣿⢸⣿⢣⣿⣿⣧⢘⢻⣿⠛⣿⣿⠛⢸⡇⣿⣏⠿⠇⣿⣿⠛⢸⣿⢹⣿⡞⢻⣿⠛⢸⣿⢻⣿⡆⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⡇⣿⣿⣿⣯⢺⡗⣿⡿⠿⢻⣿⡟⣿⡅⣿⣿⢸⣿⣾⣿⢸⣿⣹⣿⠈⢸⣿⠀⣿⣿⠿⣸⡇⣙⡿⣷⡆⣿⣿⠿⢸⣿⢈⣉⡁⢸⣿⠀⢸⣿⢸⣿⡇⣿⡟⣿⡅⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣿⠇⣿⣿⣿⣿⢸⣁⣿⡇⣿⢸⣿⡇⣿⡇⣿⣿⠘⣿⣿⡏⣼⣿⢻⣿⡆⣸⣿⠀⣿⣿⣶⣞⡇⢿⣧⣿⠇⣿⣿⣶⠸⣿⣼⡿⠃⢸⣿⠀⠸⣿⣾⡿⢃⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣿⣶⣶⣶⣾⣿⣶⣶⣶⣾⣶⣶⣶⣿⣶⣶⣾⡶⠶⠄⠀⣀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 955

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/16/microsoft-linkedin-github/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/16/microsoft-linkedin-github/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.16.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Microsoft_Has_Always_Been_About_Control_Over_Others⠀✐


Posted in Microsoft at 8:14 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_censors_LinkedIn_for_China;_Microsoft_censors_Free
software_community_for_Microsoft⦈_


Summary: Hosting by Microsoft means subjugation or a slavery-like relationship;
contrary to the current media narrative, Microsoft has long been censoring
LinkedIn for China’s autocratic regime; and over at GitHub, as we shall show
for months to come, there’s a war on information, a war on women, and gross
violations of the law


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⡀⣀⡀⠀⢀⣠⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢐⠂⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢀⠀⠰⠟⠛⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉
⢸⣿⣾⡇⣿⢸⡿⠇⣿⣿⢸⣿⣷⢿⣟⢸⡏⣷⣿⡉⢹⡏⠀⣿⠿⢾⣏⢹⣧⣿⢿⣟⢸⣿⣷⣿⣽⠾⣿⡃⢀⣀⣀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀
⠸⢿⠏⠇⠿⠸⠿⢇⠿⠿⠸⠿⠟⠿⠽⡺⠧⠟⠿⠀⠸⠇⠀⠿⠾⠻⠧⠼⠿⠿⠿⠽⠸⠿⠟⠿⠸⠿⠯⠟⢸⣿⣿⣿⣷⣦⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⠀⠀⠀⠘⢷⡄
⠀⠛⣥⢠⡄⣤⢠⣬⣍⡭⣤⠤⣬⢭⣭⣭⣭⢩⡅⢠⡤⢠⣦⡄⣤⣤⠀⣠⢶⡄⣤⣤⢠⡄⣤⣤⢠⣤⠀⠀⢸⣿⠿⣿⣿⣿⣿⣿⣦⣤⣀⣸⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⡀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⠟
⠀⠀⣿⢻⡇⣿⣿⣿⣿⣇⣿⠓⣿⢸⣿⣿⣿⣿⡇⢸⡟⢸⣿⡇⣿⣿⠀⣿⢨⡅⣿⣿⢸⡇⡿⣿⢸⣿⡇⠀⠸⠁⠀⠀⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡏⠐⠋⠈⠉⠉⠙⠋⠉⠀⠀⢠⡾⠃⠀
⠀⠀⠉⠉⠁⠉⠈⢩⣥⣭⣭⣭⣭⣭⣭⣭⣭⣬⣵⡬⠵⠎⠉⠁⠉⠉⠀⠈⠉⠁⠉⢉⣨⣅⡁⠉⠉⠉⠁⠀⢸⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠋⠀⠀⠀
⠀⠀⠀⢶⣶⣶⣶⣾⣿⡿⢋⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣷⣮⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⢶⣶⣶⣶⣶
⠀⠰⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⡄⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣿⡿⠟⠛⠻⡿⠛⣿⠿⢿⣿⠉⢹⣿⡆⠀⣿⣿⣿⠿⢿⠀⠘⠛⠻⣿⣿
⠀⠀⠀⠀⠀⢀⠀⢹⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢻⣆⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣀⣀⣀⣀⣤⡆⠈⢻⣿⡏⠀⣴⣶⣾⣷⠀⠚⠂⠈⠉⡄⠈⠉⠁⠀⡇⠀⣿⡀⢸⠀⢰⣷⠀⢸⣿
⠀⠀⢀⡀⠀⣾⣷⣿⣿⣿⣿⣿⣿⣆⡀⡀⠀⠀⠀⠚⣿⣿⣷⣦⠀⠀⠀⣂⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣷⠀⠀⣿⡇⠀⣿⣀⠀⢸⠀⢸⡇⠀⣿⡇⠀⣿⣷⠀⢧⠀⠛⠃⠈⡇⢈⡉⣀⣼⣿
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⣿⣿⣿⡿⠟⠀⠀⠿⠷⠀⠈⠉⠀⣘⣀⣈⣷⣄⣀⣥⣤⣿⣿⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣄⠐⠤⢼⣿⡇⠀⣀⣆⣀⣀⣠⣀⣀⣀⡉⠻⣿⣿⠿⢿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣿⣿⣶⣼⣿⣷⣾⣿⣿⣿⣿⣿⡿⢿⣟⣟⢣⣶⡴⣟⡉⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢹⣿⣿⣿⣿⣿⠿⢿⢟⣿⣫⡿⣏⣿⢿⡻⣾⡜⣯⣷⠻⢼⣙⡺⠿⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣏⣷⣴⣷⢿⣹⡞⣭⣿⢻⡹⠾⣫⡿⠷⣾⣳⡍⣿⣦⢻⣥⢿⡎⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣈⣙⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣹⡿⡿⠞⠇⠛⢉⠈⣠⣍⣿⣾⢺⣽⡘⢸⡗⢻⣽⡞⠷⢞⠛⠼⣛⢻⢩⡵⣶⠛⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⢿⣷⢲⡭⢷⣰⡼⣿⣏⣷⢿⣹⡿⡗⠧⠟⠀⠋⣈⡀⣬⣱⣆⣷⢿⣹⣿⡏⣷⢸⡏⡜⢇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢸⣿⣿⢻⣝⡛⣷⡺⣟⡷⠻⠟⠈⢋⠀⣠⢤⣰⡶⣎⣿⣾⣷⢿⣿⣻⡹⠾⢏⡃⢯⣭⣶⣾⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣞⣳⣫⠭⣝⢲⣭⢱⣶⡞⣯⣼⣹⡎⣭⢷⣿⠹⢟⠚⠊⢍⣲⡊⣵⠖⣿⢻⣿⣿⣿⣿⣿⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣀⣀⣀⣀⡉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡻⣻⡯⢿⡖⣧⣿⣿⣼⣿⣞⣿⢷⠻⠖⠡⢭⢕⣳⣞⣵⢶⡼⣿⣛⣷⣿⢹⡇⣸⠇⣿⠿⠿⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⢰⣞⡆⣿⢿⣽⡟⡼⣧⡽⠿⣛⣫⠧⣿⣲⣯⣵⢲⣼⡏⢗⢿⣿⡼⣟⡧⠶⠟⣙⣫⣼⣶⣿⣿⣅⠀⠀⠀⠀⠀⠀
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣉⡀⠀⠀⠉⠙⣿⣿⣿⣿⠿⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⠜⢿⣧⣯⣿⣳⡟⣽⣾⢻⣽⡾⣼⣿⡿⡟⣷⠻⠟⣘⣫⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⣼⡗⢻⣾⡏⠷⣟⠁⠋⠁⠀⠀⠈⠁⠈⠉⠙⠛⠿⠿⢿⠿⠟⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠻⠿⣿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1013

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/16/spanish-gov-epo/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/16/spanish-gov-epo/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.16.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Spanish_Inquisition⠀✐


Posted in Europe, Patents at 6:00 am by Dr. Roy Schestowitz


“The repressive labour and social policies of Pétain’s État Français were
closely modelled on those of Fascist Italy.” July_2021


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


Summary: Let it be widely known that Spain played a role in crushing the basic
rights of all EPO workers, including hundreds of Spaniards


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⢺⡄⢝⡻⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢁⣬⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣤⣤⣶⣶⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣼⣦⡧⠩⢛⡿⡃⠃⣿⡿⡿⠇⠀⠀⢀⢀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⢂⡄⠀⠀⠀⠀⣰⣿⢿⣿⣿⣿⣿⣿⣿⣶⣾⢳⣶⢢⢽⣿⣾⣾⣿⣭⣭⣭⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣴⣾⣷⡆⠀⠀⠀⣴⣶⣿⣿⠿⠿⢟⣿⣿⣷⣶⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⢀⣨⣦⣤⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠯⢻⣿⣿⣿⡷⠅⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠐⠁⢨⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⠀⠀⠀⣀⣻⣍⣍⢉⣙⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣅⣽⣿⣿⣿⣿⢧⣍⣄⣹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⡿⢹⣿⣦⣯⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠋⠉⠙⠋⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣍⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡿⣧⣨⢙⡻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢉⣬⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣤⣤⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣴⣾⣇⡏⢹⡿⠓⠃⣿⡿⠿⠇⠀⠀⠀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡦⢀⡄⠀⠀⠀⠀⣴⣿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣝⢨⣹⣿⣾⣾⣽⣭⣭⣭⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣴⣾⣷⡆⠀⠀⠀⣴⣶⣿⡿⠿⠿⣟⣿⣿⣷⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣏⠀⠀⠀⢀⣨⣤⣤⣄⣰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⢻⣿⣿⣿⣏⠅⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⠀⢸⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡷⠀⠀⠀⢨⣿⣯⡍⡍⣹⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡻⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠈⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⡟⢘⣿⣮⣯⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⠟⠋⠉⠙⠋⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣍⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⡟⡀⣟⣛⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣁⠀⣤⣿⣿⣿⣿⡿⣿⣿⣿⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣇⣿⣿⣿⠛⠻⣿⣿⡿⠇⠀⠀⢀⣠⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠋⣆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⣿⣿⣿⣿⣿⣽⣭⣽⣿⣶⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⠀⠙⠙⢛⠉⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣀⣀⣀⣤⣶⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣾⣉⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠝⣿⣿⣿⣿⢧⠄⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠁⠈⠁⣾⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⢀⠀⠀⢈⣱⣿⣍⡙⣛⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣦⣤⣭⣭⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡟⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡄⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠉⠉⠙⡀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣈⣉⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⡍⢙⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣆⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣯⣡⣴⣿⣿⣿⣿⡿⣿⣿⣿⡟⠛⠛⢟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣾⣟⣿⣛⢹⣿⣿⡿⡟⠀⠀⣀⣀⣄⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣟⣬⣿⣦⡀⠀⠀⠠⠴⣶⠿⠿⠿⠛⣿⣿⣿⣿⣷⣬⣿⣿⣽⣾⣿⣿⣿⣿⣭⣽⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣨⣤⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡿⠿⢿⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣦⡾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡧⢿⣿⣿⣿⣿⣷⣇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⢸⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⡇⠀⢀⣁⢻⡿⣛⡛⣻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠉⠛⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⡻⠟⣻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣤⣄⣀⣁⣄⣴⣾⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⢻⣿⣤⣽⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣵⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠻⠋⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠉⠙⣃⠀⠀⠀⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠉⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⢿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣧⣣⣼⣿⣿⣿⣿⡿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢦⡄⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⣛⣍⣁⣹⣿⣿⡟⢀⢀⣀⣠⣄⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣶⣿⣿⣶⠀⠀⠀⠚⠛⠛⠛⠉⠉⢉⣭⣿⣿⣿⣿⣮⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣶⣾⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢀⣴⣶⣾⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⠛⠛⣿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣾⡿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢟⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⢻⣿⣿⣿⣷⣖⠺⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠠⣾⣿⣿⣿⣿⡯⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠋⠀⣸⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣘⣟⡟⠛⢛⣟⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠉⠛⠿⡿⠿⠿⠿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣛⣺⡻⠿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⣦⣄⣀⣀⣀⣀⣸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⢧⣿⣩⣽⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠉⠛⢿⣿⣯⠙⢿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣴⣴⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⢀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⣉⣺⣇⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⡿⢿⣿⣿⣿⣯⢩⣿⣟⣯⡙⣿⣿⣟⡃⣈⣄⣀⣤⣤⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠈⠉⠉⠉⡁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣷⣷⣷⣾⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣿⣿⣿⣷⣀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣡⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡟⣿⣿⣿⣿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢩⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⣿⣒⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢸⣿⣿⣿⣿⣿⣭⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⣿⣿⡟⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⢞⣻⡙⠛⢛⣻⣟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠙⠛⠛⠛⣛⣻⠿⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠉⣃⡿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣀⣀⣀⣀⡀⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⣿⡾⢼⣭⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣬⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢀⡅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠱⣑⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⢿⡿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠾⠥⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣩⠈⠀⠙⠏⠉⠉⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣥⣶⣾⣷⡦⠀⠠⡤⣴⠾⠿⠿⠛⠛⣉⣿⣿⣿⣿⣿⣶⣲⣿⣯⣤⣿⣿⣿⣿⣧⣤⣴⣶⣶⣶⣶⣒⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡟⠀⠀⠀⢀⣀⣤⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡟⠛⢻⣿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣷⡾⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣿⡟⢻⣿⣿⣿⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢽⣿⣿⡷⢴⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠟⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠃⠀⢻⣿⡷⢞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠻⠿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠈⠒⠛⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣴⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⠉⠉⢉⣭⣿⣯⣿⢯⣇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣦⡂⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣀⣀⣀⣀⣀⣤⣄⣿⣿⣷⢠⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣗⣴⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡖⠺⠀⢀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠍⠀⣾⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠓⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⢲⣾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⠀⠁⠀⠀⠀⢀⣨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣴⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠵⡂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⢿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣿⣖⠀⠤⠴⠶⠿⠟⠛⠛⠋⣉⣿⣿⣿⣿⣿⣿⣷⣻⣿⣽⣿⣿⣿⣿⣿⣶⠤⡶⣶⣶⣶⣂⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⣀⣤⣤⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠋⣹⣿⢷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣿⣿⣿⡿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡿⠁⣾⣿⣿⣟⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠁⠈⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠨⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠈⣋⣋⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⣰⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣮⣬⡄⠃⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣠⣤⣤⣤⣶⣶⣿⣾⣿⣿⣧⠉⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣇⣱⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡾⠇⢰⠏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠘⠀⣹⡧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⢪⣇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠁⠀⠀⠈⠟⠏⠯⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣒⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡿⠛⣛⡃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⠉⠘⠉⢀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣷⢠⣤⡶⠾⠿⠛⠛⠋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣞⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣏⠁⠀⢀⣀⣤⣀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⣶⣾⣿⣏⠉⣽⠛⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣿⣿⣿⣿⣿⣿⢿⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢻⠹⣿⡟⢹⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣢⠚⠉⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡓⠀⠀⢸⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣾⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠉⠙⠙⠋⢉⢹⣿⣿⣷⣼⣿⣷⣶⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡖⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠉⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢸⣧⠀⠄⠀⠀⠈⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⢀⣤⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠿⠟⢹⣿⡅⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⢶⣶⡀⠀⠀⠀⠿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠈⠩⠭⠱⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⢀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣏⣻⡿⠟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡿⢛⣛⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣝⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠈⠁⠀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⣦⣾⣿⣿⣿⣆⣤⣴⡶⠿⠟⠛⠛⢩⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡴⢛⣻⣟⣻⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⣀⣠⣄⡀⢠⣾⣿⡯⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤⣤⣶⣾⣾⣙⠛⠛⢻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⠟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⣿⣿⠧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⠛⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⠙⠛⠃⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⢠⣿⣿⡟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠘⠛⠋⠀⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⢋⢸⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⣉⣀⣲⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⣟⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣶⠖⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⡀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣟⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣟⢾⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢩⡠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⢉⣁⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠔⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠁⠀⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⣿⣦⠀⠀⠀⠀⠙⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠼⠿⠿⣿⣯⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣟⣗⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⢶⣶⣤⠀⠀⠀⢻⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠀⠀⠀⠩⠝⠫⢭⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣶⣿⣟⣽⡟⡻⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⣿⡿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠻⢿⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠖⣍⣁⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣌⣵⣾⣿⣷⣦⣤⣶⡾⠿⠟⠛⠛⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣟⣚⣿⣿⣭⣥⣦⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢉⣿⣿⣿⣿⡟⠂⠀⣀⣠⣀⡀⠠⣾⣿⣿⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⣀⣤⣴⣮⠟⠛⠛⢳⣤⣾⣿⣿⣿⣿⣯⣮⣿⣯⣮⡛⣹⣿⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⡿⢿⣿⡿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⣭⡿⠿⠃⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⠇⠀⣸⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠙⠀⠀⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡴⡀⠰⠿⠟⠀⢠⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠁⠀⠀⠀⠀⠀⠻⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⠛⣹⣶⣾⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⡀⠉⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⠀⣾⣶⣄⠀⠀⠀⠀⠀⠀⣈⣤⣴⣿⣿⣿⣿⣿⣿⣿⣟⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢛⡁⡉⠉⠀⠀⠀⠀⠀⢿⣿⣿⡀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠋⠉⢁⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢏⠚⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡃⢀⡺⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠝⠃⠀⠉⠀⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣽⣧⣾⣿⣿⠇⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢰⠤⠄⠀⣿⡆⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡗⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⠈⢀⠀⢰⣿⣷⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣷⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣾⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠁⠀⠈⣿⣝⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⣶⣄⣀⠀⠀⠀⠿⠓⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠐⠀⠀⠹⠽⠭⢽⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣷⣾⣟⣯⣿⢟⠟⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⣿⠟⠛⠛⢻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠰⠆⢩⢁⣄⣀⡀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣌⣩⣶⣾⣿⣶⣤⣴⡶⠿⠿⠛⠛⠛⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣓⣛⣛⣻⣭⣭⣾⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠉⣻⣿⣿⣿⣿⠓⠀⢀⣀⣄⡀⠀⣾⣿⣿⣉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠀⡀⠀⠀⠀⣀⣤⣮⡿⠿⠛⠻⣦⣴⣿⣿⣿⣿⣿⣷⣽⣿⣷⡽⠛⣿⣿⣿⢾⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣿⣿⡿⢿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣆⠀⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡛⠏⠁⢰⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣃⡤⠀⠸⠿⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⢏⠓⠀⠀⠀⠀⠸⢿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠟⢫⣭⣥⣿⣿⣿⣿⣿⣿⣛⣩⣭⣉⡉⠁⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢠⣄⡀⠀⠀⠀⠀⢰⣦⣌⠉⠀⠀⠀⠀⠉⠉⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣧⠆⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣯⢉⠉⠀⠀⠀⠀⠀⢸⣿⣿⡀⢀⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠿⠒⠓⠒⠊⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠃⠙⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣽⣿⣿⠂⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⢶⠄⠐⠀⠀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣧⣼⣿⣿⣿⡃⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⣀⠄⠀⣰⡇⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡧⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⢙⠀⠀⣿⣿⠄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣄⣤⣤⣀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠀⣠⣾⣿⣿⡅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⡿⡽⡃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⣷⣀⡀⠀⠀⠀⢘⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠐⠀⠉⠛⠡⣽⢝⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣦⣼⣿⣽⡿⣿⢟⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⠛⣻⣛⠛⠛⠻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢾⣷⠄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⠌⢁⣀⣀⡀⢀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣣⣴⣿⣦⣄⣤⣴⣾⣿⠿⠟⠛⢫⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣷⡞⣛⣛⣫⣯⣭⣧⣯⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠍⠀⣀⣀⡀⠀⣀⣾⣿⡏⡉⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣀⣈⣻⢿⡿⠿⣧⣠⣼⣿⣿⣿⣿⣷⣭⣿⣿⣧⣿⠙⣿⣿⣿⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⣠⣾⣿⣿⣿⡆⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⣿⣿⣫⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⠇⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⣤⣭⡍⠙⠀⢸⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⣿⣿⡕⠃⠀⠀⠙⠁⢸⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠿⣟⣿⣿⣿⣿⣿⣿⡿⠿⡛⣛⠛⠋⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠁⠀⠀⠀⠀⠈⠉⣿⡘⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡟⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡄⠠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡷⠀⠀⠻⠁⠀⠈⠀⠀⣿⣿⡆⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⡭⡍⠉⠥⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡐⣷⡷⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠀⠀⣤⣤⣤⣤⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⣱⣤⠀⣧⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠏⢱⣿⣄⣼⣿⣿⣿⣧⠀⠠⠮⢧⣄⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡑⠉⢻⢀⠀⠀⣰⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠃⠘⠏⠀⠀⣿⡄⠀⠀⠀⠈⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⡉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⡦⠀⠚⣄⣴⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⠻⣿⣟⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢷⡀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠃⠁⠁⠉⠀⠁⠴⠛⢟⠻⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣠⣴⣿⣿⣻⠿⡟⣛⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣛⠛⠛⠛⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣧⣒⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠐⠁⡉⢉⢀⣀⣀⠀⣠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⢟⣠⣼⣧⡀⣀⣤⣴⣿⣿⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⡴⢾⣾⣚⣻⣿⣿⣅⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠚⠃⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⢀⣰⣿⣿⠋⢋⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡀⣠⣾⣿⣿⣷⣾⣟⣻⣿⡷⢐⣷⡟⢻⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠐⢊⠈⢀⣤⣾⣿⣿⡅⠁⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⢻⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⡿⣳⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⠛⢿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣶⡶⢤⠈⠀⣽⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⣿⣧⠀⠀⠀⠀⠈⠘⠛⢻⣇⢿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣿⣿⠛⠛⠛⠛⣫⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣶⣶⣾⣦⡀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣴⣾⡿⠀⠰⡖⠀⠸⠃⠀⢸⣿⣦⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⡿⠟⠃⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢸⣦⡏⢀⠀⠀⠀⠀⠰⠀⠀⢸⣿⣿⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣻⣿⣿⣿⡛⠋⠉⠉⠀⠀⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⠛⡄⡈⠳⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠋⢀⣴⣧⣤⣠⣿⣿⣿⣿⠃⠀⣸⣏⡻⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠘⠿⠃⠀⠋⠀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢿⣃⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠙⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠲⠀⢦⠂⠀⣶⣇⠀⠀⠀⠈⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡷⠦⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣇⡀⠈⠇⠀⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣤⣀⣤⣤⣤⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠛⡋⠀⢪⣾⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠷⡀⠀⠁⠈⠀⠀⢹⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠉⠓⠉⠁⠀⠶⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⠿⢛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⠛⢛⣛⡛⠛⠛⢻⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡖⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠀⠈⠋⠉⢁⣀⡀⠠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠻⠿⣒⣽⣧⡀⢀⣠⣤⣿⣿⡿⠿⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⡷⣶⣟⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠸⠧⣾⣿⣿⣿⣿⣟⠛⠉⠉⠀⠀⠀⣨⣿⣿⡿⠻⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡀⣀⣾⣷⣷⣷⣾⡟⣿⣿⣿⢯⣳⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⠉⠁⠘⠃⠁⣨⣶⣿⣿⡌⠉⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣰⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⢀⣽⣿⣿⣿⡿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣦⣬⡉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠔⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠘⢻⣿⠃⠀⠀⠈⠛⠻⠿⢿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⣶⣦⣄⡨⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⣼⣿⠀⢰⡶⠀⠠⡇⠀⢸⣷⣦⡀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠂⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⠄⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢙⣏⣟⠋⠀⠀⠑⠀⢠⠀⠀⢸⣿⣿⣇⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣶⣾⣿⣿⣿⠿⠛⠋⠛⣿⣿⣿⣿⣿⠛⠛⠛⠋⠈⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢺⡿⡟⠀⠲⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⣿⣿⣿⣿⣿⠋⠁⢠⣶⣦⣌⣽⣿⣿⣿⣿⠀⠀⣶⡾⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠐⣿⠷⠀⠳⠇⠤⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡨⣿⣿⣿⣿⡅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠙⠛⠳⠾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⠀⣧⣴⠀⢰⣶⠀⠀⡀⠘⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣇⢀⠈⣇⠀⢺⣿⡄⠀⠀⠀⠀⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣧⣀⣀⣀⣀⢀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠿⡟⠀⢙⣷⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⡘⠀⠁⠐⠊⠉⢹⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠛⠑⠄⠹⠻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣀⣤⣴⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⠛⢻⣿⡿⠟⠛⡛⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⢄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢗⢶⠊⠉⠀⣀⡀⠀⠼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⡿⠿⢧⣿⣧⡀⢀⣠⣤⣼⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣻⣻⣿⣿⣤⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠺⠧⣴⣿⣿⣿⣿⣿⠻⠛⠉⠁⠀⠀⢠⣿⣿⣿⣿⡛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠁⠁⠀⢿⣿⣿⣿⣿⡋⢀⣴⣷⣶⣷⣾⣿⣿⣿⣿⣲⣧⣽⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠉⠋⠶⢃⠺⣀⣽⣷⣷⡍⠙⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠀⢈⣼⣿⣿⣿⣿⢧⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣯⡉⠛⠻⠟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⢿⣿⡷⠀⠀⠺⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡛⣯⣭⣭⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣸⣿⠅⣠⣤⡄⡀⣤⠈⢸⣧⣝⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠙⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⣟⣻⣿⠀⠘⠛⠀⡀⡇⠀⢸⣿⣿⣇⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠻⣥⣤⣽⣿⠛⠋⢺⣿⣿⣿⣿⣿⣿⣿⣷⡶⠾⠧⠘⠃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣼⣿⡿⢉⡀⠀⠀⢰⢀⠀⠀⠸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢡⣿⣿⣿⡟⠋⠉⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⡅⢀⢤⣤⢦⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠡⣷⣼⢀⣧⡤⡠⠔⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣙⣻⣿⣵⣦⣴⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠸⠮⣧⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢡⢠⡎⢫⣠⠏⣑⣿⠂⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢟⠄⠿⣿⠆⢹⣿⡇⠀⣨⠃⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⣏⠉⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢾⡼⠐⢹⣶⣼⣿⡇⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⣿⢠⠈⠡⢠⡴⠿⠿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠋⠙⠚⠛⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣆⣠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣟⣿⡿⢿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡒⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣩⣤⣥⣖⣒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠿⠿⢿⣭⣧⣀⢀⣠⣤⣾⣿⣿⠿⠛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢻⠅⣾⣿⣿⣿⣿⣟⠛⠏⠉⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⡉⢀⣴⣷⣾⣷⣾⣿⣟⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡏⠛⠷⢃⠊⣨⣽⣿⣷⡉⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢉⣿⣿⣿⣿⣿⢧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡛⠛⠿⠿⡗⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣷⣦⣤⠀⠀⠏⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣟⣿⣯⣿⡟⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣸⣿⠇⢀⣀⣀⡀⣩⡙⢹⣧⡻⠿⠿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⣿⠿⢿⣿⢟⢛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡿⢻⣿⠀⠸⢻⡡⡁⡿⠀⢸⣿⣿⣇⠀⣠⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⣀⢠⣤⡿⠋⠹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣼⣿⣿⠍⠥⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣰⣷⣿⣿⠄⠀⠐⣇⠇⡃⠀⢸⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡽⠟⠉⠉⠀⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣀⣀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣹⢍⣧⣹⡀⣄⣰⢜⡨⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣀⠀⣤⣶⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢏⢐⡟⣟⢣⡟⢳⣼⠊⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢺⡾⠒⣾⣿⣶⢺⣿⡍⠀⠀⡼⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⣼⣰⠃⣽⣬⣸⣿⣏⠀⢸⡋⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⣿⢠⠘⡏⢁⣭⣿⡿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⢍⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⣉⣛⣿⡟⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣆⣤⣶⣾⣿⣿⣟⡻⠿⠟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣍⠉⣻⠍⠋⠋⢝⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣔⣒⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣯⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠩⠧⠀⢀⣠⣀⣥⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⢀⡿⠿⠿⣿⣿⣧⡀⣀⣤⣴⣾⣿⡿⠟⠻⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⡻⢦⣾⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀⣤⣿⣿⣿⣟⣟⢫⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡁⢀⣶⣷⣾⣿⣾⣿⣟⣿⣿⡦⣽⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡏⠋⠾⢋⢙⣨⣿⣿⣷⡉⠋⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣹⣿⣿⣿⣿⡿⢧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠻⠿⠿⣿⡆⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⢻⣶⣤⡀⠀⠀⠿⣹⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣿⡿⢛⣛⣻⣟⠙⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⣿⠃⠀⣀⣀⡈⢹⡛⢻⣇⡸⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠻⣿⠿⠿⢿⣿⣟⣛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢿⡻⢿⡟⠀⠸⢿⣑⡇⡝⠁⢸⣿⣿⡆⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠎⠏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣽⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣸⣷⣷⣷⠀⠀⠀⣲⠃⠀⠀⢸⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⣁⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣹⠉⣏⣹⠀⣀⣀⢸⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⣴⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣛⣽⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡟⠀⠿⡏⢂⠟⠣⣽⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣾⣶⣼⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⠈⠉⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠠⣿⣾⠦⢾⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠷⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣥⢠⠈⣯⢤⢸⣿⣿⠀⠀⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣆⣄⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⠀⠞⡏⠀⢈⣷⣿⣿⡧⠀⢀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠁⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣉⣿⣭⡋⠻⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣦⣴⣶⣿⣿⣿⣿⣙⠿⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣫⢠⢙⠿⠏⠛⠵⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣖⣲⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣙⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡎⢀⣄⣠⣤⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢠⡟⠿⢿⣾⣿⣦⣀⣠⣤⣶⣿⣿⣿⠟⢛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣿⣿⣿⣽⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠿⢰⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⢀⣰⣿⣿⣿⠿⠟⣟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⣠⣾⣷⣿⣿⣾⡿⣽⣿⣷⡒⢽⡗⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠋⠛⣅⣉⣤⣶⣿⣦⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⣽⣿⣿⣿⣿⡿⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⢐⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠿⠿⢿⣿⡀⢰⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢶⣦⣀⠈⠀⢸⠋⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣸⣿⠟⣛⣛⣛⡛⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⣀⡀⡉⣩⠛⣿⣇⡻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠿⢿⡿⠿⣿⣿⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡿⣿⡏⠀⢸⢿⣹⡅⠯⠅⣿⣿⣿⡀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣽⣽⣋⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣧⣯⣷⠀⠀⠘⢷⠅⠀⠀⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠒⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣽⠙⡏⣹⠀⠀⢠⣽⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣛⢟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠘⠿⡟⢀⠿⢦⣿⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣤⣤⣸⡿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡮⢤⣷⣾⣠⣺⣿⣲⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡷⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⡆⡡⠉⣇⠠⢸⣿⣿⠀⠀⠌⠁⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⢿⣿⠿⠿⣿⣿⣷⣶⣿⣗⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⢨⠿⡙⠈⢘⣷⣿⢿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣍⠁⠛⠉⢙⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣟⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠞⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡷⡾⣍⣵⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣙⣱⣤⣴⣦⣾⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⢾⡛⠒⣻⣿⣿⡆⣠⣤⣶⣿⡿⠿⢟⠛⢛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣽⣿⣾⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⣾⣿⣿⣿⣿⣿⠉⠉⠂⠀⣀⠀⣠⣾⣿⣿⣿⣛⢛⣿⡫⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢀⠀⠀⠀⠀⡸⢿⣿⣿⣿⣏⢀⣴⣿⣷⣿⣿⣿⡟⣽⣿⣿⣈⢤⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡎⠉⠑⢫⣅⣤⣶⣿⣿⡆⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⢿⣿⣿⠇⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⣦⡀⠁⠀⠀⠙⠉⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣾⣿⠿⣟⣛⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣷⠀⠀⠀⠀⡉⢙⢿⣿⡀⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⡁⠀⡸⣟⢱⠀⠍⠘⣿⣿⣷⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠀⠀⠀⠀⠙⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣏⣋⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⣼⡍⣁⠀⠀⢸⣿⠀⠀⠐⣿⣿⣿⣷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠶⠶⠀⠀⠀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡟⢻⠉⡏⠀⠀⢀⣹⠄⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢘⠟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⢺⣿⠇⢐⢶⠩⣿⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣤⣀⣠⠰⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡎⢸⣦⣯⠤⣾⠅⢀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣤⣠⠈⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢹⠀⡐⠛⣋⡁⣿⡃⣾⡇⠀⢸⡝⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣁⠀⠀⣸⣿⣿⣷⣦⣬⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠷⢸⢷⠇⠘⢱⣽⣿⠄⢻⡂⠀⠈⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣆⠀⠀⢀⣉⣽⣿⣿⡿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠛⠛⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⣫⢿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡞⢔⡤⠘⠉⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⡿⢻⡯⢤⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣟⣄⣨⣶⣴⣼⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣿⠓⢊⣵⣿⣷⣢⣤⣶⣿⠿⠿⠛⠿⠉⢻⣿⣿⣧⢰⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠀⣿⣿⣿⣿⣿⡯⠀⠀⣀⠀⣀⡀⢰⣿⣿⣿⡷⠋⣈⣝⢧⣼⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⡀⣀⢀⡀⢀⢀⡛⣿⣿⣿⣿⣄⣠⣾⣿⣿⣿⣿⣿⣫⣼⣿⣿⣄⡈⣷⣴⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡏⠉⠘⣱⣴⣶⣾⣿⣷⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣻⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⣌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⣿⣿⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⠀⣿⡟⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⣿⠆⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣀⣀⠙⠉⠀⠀⠻⠀⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡀⣿⡿⢿⡛⢛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠙⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⡟⠁⠀⡼⡛⣽⠄⠁⣿⣿⣿⡆⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠈⠁⠉⠁⠙⢻⣦⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣼⢋⡀⠀⠀⢹⣾⠀⠀⢹⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⠶⢶⠎⠀⠀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠟⣟⢺⡇⠀⠀⢀⠻⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⢲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣂⢿⡾⡂⢀⡔⢠⠗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣠⡀⣶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣠⠋⣳⣤⡎⢀⡖⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠏⠀⠹⢿⠁⠀⣫⠀⠀⣀⠀⠸⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⣨⣿⣿⣿⣿⣯⣍⣛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⢾⣾⡗⢜⢶⣧⣿⠀⠰⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣇⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⡿⢟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠟⠛⠻⣿⣛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣎⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠤⠀⠉⢀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢻⢷⢤⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣇⣶⣧⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⠁⣉⣴⣿⣷⣠⣴⣾⣿⠿⠟⠛⠋⠉⢹⣿⣿⡧⢴⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⣿⣿⣿⣿⣿⢿⠀⠈⣀⢀⣀⡀⢴⣾⣿⣿⡟⠋⣩⣟⣧⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠤⠀⣀⠀⡀⢀⣀⠻⣿⣿⣿⣿⣠⣠⣾⣿⣿⣿⣿⣿⣟⣭⣿⣿⣤⣘⣽⣦⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⠉⠁⠉⣰⣴⣶⣿⣿⣧⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡛⢄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⢸⣿⣿⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⢸⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⢸⣽⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⡉⠛⠉⠀⠸⠗⠀⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⠿⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣆⡀⠀⠀⠀⠈⠛⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡾⠻⠃⠀⣶⣛⣶⠀⠀⣿⣿⣿⡄⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠽⠉⠋⠉⢛⣷⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⣞⡟⠀⠈⠀⣽⣿⠀⠀⣿⣿⣿⣿⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠒⠶⡾⠁⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠿⡟⢻⡆⠀⠀⠈⡋⠀⠀⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠠⢧⡾⠂⢀⣔⢎⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣀⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠚⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⠃⣥⣠⡃⢐⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡟⠀⠹⢿⠁⠈⡕⠀⠀⢰⠀⠙⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣿⣍⡛⢿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢶⣷⣼⣆⠼⡞⣡⣿⠀⠀⡗⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡄⢄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣦⠀⢀⣀⣤⣶⣿⣿⣿⡿⣟⣿⠟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠉⠉⢙⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⣄⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⡻⣷⣿⣛⣫⣷⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣮⠈⠴⠀⠀⠁⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⢹⠒⣸⠂⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠵⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣫⣭⣮⣃⠠⠖⠾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡅⠉⣠⢴⣿⣧⣠⣶⣾⣿⠟⠛⠛⠋⠁⢹⣿⣷⡧⠀⣼⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣷⣾⣿⣿⡿⠒⠀⢀⣀⢀⣀⡀⢢⣿⣿⣿⡟⠉⣛⠨⡾⣮⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣶⡦⠀⠄⠀⠀⠀⡀⠻⣿⣿⣿⣇⣀⣠⣿⣿⣿⣿⣿⣿⣗⣬⣿⣿⣄⡈⣼⣟⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠈⣰⣶⣶⣿⣿⡆⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⣀⣜⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⢸⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⢸⣿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠨⡿⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠛⠋⠁⠀⢰⠃⠀⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⡀⣽⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡄⠀⠀⠀⠀⠀⠻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡯⣥⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⠟⠀⠀⣶⢒⣦⠀⠍⣿⣷⣿⠉⠉⠉⠀⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠉⠉⠙⠛⠛⠉⠙⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⡤⠄⠀⠘⠀⢻⡿⠀⠀⣿⣿⣿⣷⡆⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠒⠿⠿⠃⢀⣐⣛⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⠋⣦⠀⠀⠀⠙⢽⠀⠀⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⢧⡿⠀⠀⠀⣽⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣤⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠋⡇⢀⠎⢡⡅⠀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠛⠀⡹⡿⠂⠀⠅⠀⠀⢸⠈⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢶⣷⣼⡁⡼⣆⢄⠇⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣧⠀⢀⣀⣤⣶⣾⣿⣏⣿⢿⢙⠟⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠋⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⡛⢷⣿⢟⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠠⠃⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⢻⠒⢜⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠴⠋⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣴⣾⠿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣿⠅⠁⣠⣴⣿⣆⣤⣶⣾⣿⠟⠛⠛⠋⠁⢹⣿⣿⡧⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣷⣾⣿⣿⡿⠰⠀⢀⣀⢀⣀⡠⢲⣿⣿⣿⡗⠋⠛⡭⢽⣃⣬⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⠀⢀⢀⠀⠀⡀⢻⣿⣿⣿⣇⣀⣠⣿⣿⣾⣿⣿⣿⣋⣌⣿⣿⣄⡐⢩⣏⣽⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣬⠀⠁⠉⣵⣶⣷⣿⣿⡆⠀⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣠⣘⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣠⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠀⣿⣿⡿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⣿⡿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢻⣟⠀⢰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠟⠃⠀⣺⡁⠀⣸⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⠙⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠉⠀⠀⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣅⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠖⠀⠠⣤⢤⡆⠀⢻⣿⣦⣝⠛⠛⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⠛⠻⢿⠻⠿⠏⠙⢿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⣤⠀⠀⡰⠉⠹⣿⠀⠈⣿⣿⣿⣥⡄⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠲⠿⡿⠂⢀⡖⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⣄⠀⠀⠀⡄⠫⠀⠠⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⢰⣾⣗⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣆⣏⠀⠀⠀⠦⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠞⡄⠀⠞⠃⡅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠦⠐⢲⡾⠆⠀⢧⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢿⣄⣠⠉⣧⣀⢀⣯⠀⠀⢠⡃⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣦⠀⢀⣀⣤⣶⣾⣿⣟⣻⢿⢟⠿⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡉⠉⠙⢉⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢽⣝⢿⣻⣿⣽⣷⣷⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⢤⢄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⢻⠂⢜⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣟⠡⠃⣰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣽⣠⣾⠾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣿⡉⠁⣁⣴⣿⣔⣤⣶⣾⣿⠿⠛⠛⠋⠉⢙⣿⣿⡧⠀⣼⣿⣏⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⢸⣷⣴⣿⣿⡿⠀⠀⢀⡀⢀⣀⡀⢠⣿⣿⣿⡗⠚⠙⣯⣵⢏⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⠀⢀⣀⠀⡠⠀⢻⣿⣿⣿⣇⡀⣠⣿⣿⣾⣿⣿⣿⢋⣌⣿⣿⣄⠀⢀⣯⣽⡿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠁⠊⣳⣴⣶⣿⣿⡄⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠉⠡⣰⣿⣿⣿⣿⣿⡿⡿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣟⠇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣠⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⣿⣿⣇⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡯⠀⣿⣿⡯⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⣿⡿⠃⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢻⣿⠀⢰⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡿⠟⠁⠀⢹⠇⠀⣸⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣉⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠁⠀⠀⢾⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣏⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠖⠀⢀⠤⢀⡄⠈⢻⣿⣤⣻⠛⠛⠛⠋⠙⡛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠛⠿⢟⠻⢿⡿⠛⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⣁⠀⠀⡰⠁⢸⡏⠀⢸⣿⣿⣿⣤⡀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠴⢾⣿⠂⠀⡀⢪⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢧⡄⠀⠉⠀⠀⢿⠀⠐⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⣼⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢈⣞⡋⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⠿⡁⠀⡔⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡮⠀⢧⡼⠀⠀⠄⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⡄⣠⠋⣷⣀⣀⡆⠀⠀⢀⠇⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣆⠀⠀⣀⣠⣤⣼⣿⣿⣟⡿⣟⡽⠛⣡⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠉⠉⢉⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣟⣛⢭⣿⢿⣟⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣧⡠⡄⡀⣁⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⠟⢛⠤⠼⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠟⢌⣴⣾⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣽⣷⢀⣰⡿⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⣿⡉⠐⢈⣼⣿⡄⣠⣴⣶⣿⠿⠿⠛⠛⠉⢛⣿⣿⡏⠀⣰⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⢰⣧⣴⣿⣿⣯⠉⠁⢀⡀⠀⣀⠀⢤⣾⣿⣿⣦⠚⠙⡉⠰⡯⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⠀⡀⠀⡀⠀⠈⢿⣟⣱⣿⡇⢀⣠⣿⣿⣼⣿⣿⣷⠻⣙⣿⣗⡁⠈⠁⣇⡱⣿⠟⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈⠁⠚⣠⣤⣶⣶⣷⠀⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡏⠩⡁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⣿⣿⣿⣿⣿⡟⠇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣿⣿⣿⡿⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⣿⣿⣉⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠀⣿⣿⠟⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⣿⡯⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠄⠀⢿⡇⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠂⠀⡗⠀⠀⢸⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣛⣛⣛⠋⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠁⠀⣽⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣛⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣧⡆⠀⠀⣀⠀⡀⠘⢿⣿⣄⡿⠿⠿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⡉⠀⠀⢠⠂⢰⡇⠀⢸⣿⣿⣿⣀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣼⡇⠀⠈⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣇⡀⠀⠛⠀⠀⢣⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠈⢀⣿⣾⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢙⣾⠃⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡿⡇⠀⡠⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡌⠀⣧⣴⡅⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⡝⢈⠚⢧⠀⠀⣇⠀⠀⠀⡇⠙⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣄⠀⠀⣀⣠⣤⣼⣿⣿⣟⣻⣿⣿⠿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢋⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣟⡛⣿⣽⣿⣯⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠑⢀⡄⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⢿⠥⠵⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠟⢵⣦⣿⣶⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿⣻⣿⠏⣨⣿⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠃⢊⣨⣷⡀⣠⣤⣶⣿⡿⠿⠿⠛⠉⢹⣿⣾⡇⠀⣴⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠋⠀⢰⣯⣡⣿⣿⣯⢉⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣥⠴⠻⡿⣠⣏⣨⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⡀⠀⠂⠀⠈⢿⣟⣡⣿⡆⠀⣠⣾⣷⣼⣿⣿⣾⠏⣹⣿⣗⡉⠀⠉⣏⣽⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠋⠘⣣⣬⣵⣶⣷⡌⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠏⠡⠋⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣾⣿⣿⣿⣿⡷⠂⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣎⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⣿⡿⢀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣿⣿⡃⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⣿⣿⣻⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⣿⣿⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⢻⣇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠄⠄⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⠉⠀⠀⠀⠁⠀⠀⣾⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢽⡟⠋⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣆⡀⠀⠀⢀⠀⠀⠘⢿⣯⣀⢿⡿⠿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠋⠀⠀⢂⠀⠰⡇⠀⢸⣿⣿⣿⡀⠀⢀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣸⠆⠉⠉⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣇⡀⠀⠿⡀⠀⢷⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠉⢰⣿⣾⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣼⠇⠀⠀⠀⠀⠀⠂⠈⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⣿⡆⠀⡠⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣼⠀⣷⣰⡇⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⡅⢀⠘⣯⠁⢨⡧⠀⠀⠀⡏⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣙⣻⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⡄⠀⠀⢀⣠⣤⣴⣿⣿⣿⣻⡟⣿⠿⢋⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡋⣹⣯⣽⣿⡿⣛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠤⢀⠀⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡷⢾⢍⣱⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠾⢵⣦⣽⣷⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡷⣠⣾⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢸⣿⡛⠂⠚⣰⣦⠀⣀⣤⣴⣾⣿⠿⠿⠛⠉⣹⣿⣽⡄⠀⣠⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠁⢰⣯⣩⣿⣿⡏⠉⡉⠁⠀⠀⠀⠠⣠⣾⣿⣿⣥⠴⠛⢛⣰⡗⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠂⠀⠈⢿⣯⢃⣿⡅⠀⣠⣾⣷⣸⣿⣶⣾⢿⣻⣿⣗⠀⠀⠉⡛⣶⣿⠗⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠙⠸⣊⣨⣧⣤⣶⠈⠙⠋⢹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⠋⠀⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢨⣾⣿⣿⣿⣿⡗⠄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣶⣿⣿⣿⣿⣯⡻⢻⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡗⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⣿⣿⠃⣇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⣿⣿⠿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⠫⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⡕⠄⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠛⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⡿⠋⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣗⡀⠀⠀⠀⠀⠀⠘⢿⣯⡀⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣧⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠛⠋⠀⠀⢀⠀⢠⡧⠀⢸⣿⣿⣧⡀⠀⠀⢀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣹⡉⠛⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠁⠀⠀⠾⠀⠀⣇⠀⢸⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠉⠰⣷⣾⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠙⣼⠇⠀⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⣦⣹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⣿⡀⠀⢠⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⠀⣷⣰⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⡕⢒⠞⢯⠁⠀⡿⠀⠀⠀⡟⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣙⢿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⡀⠀⠀⠀⣀⣀⣤⣿⣿⣿⢿⣿⣿⡿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣴⣾⡿⣿⢿⡻⣿⣹⣿⡽⡻⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡰⠆⡔⠀⣫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⡶⢶⣁⣢⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⣴⡁⣠⣼⣮⣿⣿⣷⣿⣿⣿⣿⣟⢿⣿⣿⣿⣻⣿⣾⣿⣿⣿⣿⣻⠥⣀⣨⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⢸⣿⠻⠢⠜⣰⣦⢀⢀⣠⣤⣶⣿⣿⢿⠟⠛⣻⣿⣿⡅⠀⢡⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠅⢠⣞⣉⣿⣯⣟⠛⠋⠉⠀⠀⠀⠀⣠⣾⣿⣿⣁⠤⠟⠛⢏⡇⣀⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠄⠀⠘⣿⣿⠫⣿⠁⠀⢢⣿⣦⣸⣷⣶⣿⢿⠻⣿⡿⠂⠈⠩⢿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢹⠱⢽⣀⣧⣥⣦⡈⠛⠛⢻⣧⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣦⣰⡇⣉⠛⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢰⣶⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢦⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⣿⣿⣚⠃⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠀⣿⣯⣩⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⣿⣿⠌⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⣯⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⣟⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⠙⠀⠀⠀⠇⠀⠀⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢘⣿⡟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⡀⠸⢿⣇⠘⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠛⠀⠀⠀⠉⠀⢇⠀⢸⣿⣿⣯⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠻⡟⠻⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠀⠀⠀⢸⠀⠀⠃⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠛⠀⣼⣤⣶⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠛⣷⡆⠀⠀⠉⠀⠀⠀⠐⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣤⣶⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠲⣿⡄⠀⢀⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⣱⣠⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⡍⠔⡵⢯⠓⠒⡧⠀⠀⠀⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡛⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣦⠀⠀⠀⠀⢀⣈⣁⣿⣿⣿⢿⡿⣿⣿⠟⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⡿⠿⠿⣿⣻⣿⡽⠟⣿⣶⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⠐⠀⠀⡠⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣶⣖⣒⣂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡰⡋⣦⣵⣮⣽⣿⣿⣾⣿⣿⣿⣟⣻⣿⣿⣿⢟⣿⣾⣿⣿⡟⢛⣿⡃⣀⣰⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⠟⠧⠼⢰⣯⠀⢀⣀⣤⣶⣿⣿⣿⠟⠛⢿⣿⣻⣅⠂⢁⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣵⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢟⡂⢠⣖⣋⣿⣶⡟⠛⠟⠋⠁⠀⠀⠀⣠⣿⣿⣿⣃⠠⠾⠟⢛⣯⠁⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠄⠀⠸⣿⣿⣫⣿⠁⠀⢀⣴⣆⣰⣶⣮⣿⡿⢻⣿⡷⠠⠐⠐⢐⡩⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠠⢜⣐⣂⣄⣤⠘⠻⠛⢻⣧⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣤⣰⡏⠁⠻⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢀⣶⣿⣿⣿⣿⡇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡷⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠛⣿⣿⣂⡇⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⣿⣿⢡⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⣿⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣋⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆⠀⠟⠂⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠛⠛⠁⠀⠀⠀⡀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⠟⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠹⢿⣇⠰⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡻⠿⠁⠀⠀⠈⠀⣀⠀⢸⣿⣷⣾⠉⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢸⡄⠀⣷⠀⢸⣿⣿⣿⣷⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠛⠀⣄⢀⣴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠞⣶⡄⠀⠀⠁⠀⠀⠀⠈⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣠⣄⠘⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠠⢿⡅⠀⢀⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠋⢱⣀⡎⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⡟⠍⡿⢿⠓⠂⡵⠀⠀⠀⢹⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⠀⠀⠀⠀⢉⣉⢩⣿⣿⡿⢿⡿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠻⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⡿⠿⣟⣻⣿⢝⡛⣿⢠⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣧⢘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣶⣶⢖⣒⣦⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣠⣛⣉⣨⣯⣽⣿⣷⣶⣿⣿⣟⡛⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣛⣻⣗⠀⣐⣤⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⢸⣿⡟⠧⠼⢸⣏⠀⠀⣀⣤⣴⣿⣿⣿⠟⠛⣻⣿⣻⡡⠂⢁⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⢀⠨⣟⠂⢠⣖⣛⣿⣶⡟⠛⠛⠋⠁⠀⠀⢀⣠⣾⣿⣿⢁⣠⠾⠿⠊⣿⠉⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠄⠀⠸⣿⣿⣯⣿⠃⠀⢀⣼⣆⢰⣶⣬⣽⣿⢿⣿⡯⠀⠀⠠⢼⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⠡⠜⣀⣂⣀⣤⠘⠻⠟⢻⣥⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣄⣠⡞⠑⠺⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢐⣴⣿⣿⣿⣿⡏⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢛⣿⣿⣿⣿⣿⣿⣿⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠉⣿⣿⠛⠇⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⣿⣿⢣⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⣿⣿⡆⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠻⡗⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠄⠀⠘⠃⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣿⠟⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠺⢿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣶⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⠟⠀⠀⠀⠈⠀⣦⠀⢸⣿⣷⡎⠁⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠂⠀⠀⢸⡄⠀⣿⠀⢸⣿⣿⣿⣷⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠋⠀⡀⢉⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠞⣮⣄⠀⠀⠉⠀⠘⠇⠘⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠⡀⠘⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⢿⡄⠀⢀⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣝⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠋⢱⣀⡌⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⡝⠥⡻⢿⠹⠂⣞⠀⠀⠀⢻⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣄⠀⠁⠀⠉⢈⣉⣉⣿⣿⣿⣿⡿⣟⣿⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⡿⡿⣿⣻⣿⢿⠿⣯⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣶⣤⣶⣒⣤⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⡟⣍⣱⣮⣽⣿⣵⣶⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢿⠅⠀⣐⣾⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⣸⣿⠟⠧⠼⢨⣅⠀⠀⣀⣤⣴⣿⣿⣿⠿⠻⣿⣿⣻⡡⠆⠉⣼⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣦⣍⣭⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀⠨⣿⡂⢠⣖⢛⣿⣶⡿⠛⠛⠋⠉⠁⠀⠀⣀⣾⣿⣿⢋⣀⠼⠛⠏⣻⡉⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⠀⠸⣿⣿⣟⣿⠁⠀⢀⣴⣄⢰⣶⣭⣽⢿⢿⣿⡿⠀⠀⠀⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠻⢠⡞⣀⣲⣁⣤⠘⠻⠟⢻⣥⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣦⣄⣠⡎⠙⠸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⢀⣴⣿⣿⣿⣿⡇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿⣿⣾⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⣿⣿⠛⠏⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⣿⣿⣙⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⣿⣿⠜⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢹⡃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⢸⡀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠛⠛⠁⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣦⡀⣿⠟⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠺⢿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠿⠀⠀⠀⠀⠀⡐⠀⢸⣿⣷⣏⠉⠉⠁⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢰⡄⠀⢶⠀⢸⣿⣿⣿⣷⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⠋⠀⠉⠉⣕⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠟⣷⡄⠀⠀⠁⠀⠈⠃⠈⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣀⠀⠸⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢾⡇⠀⠀⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠎⢹⢀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣧⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⡟⠭⢻⣿⠓⠂⣧⡀⠀⠀⢹⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣄⠀⠉⠀⠈⢉⣉⡉⣽⣿⢿⣿⣿⣿⣿⡿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⠻⠿⢿⣻⣿⢿⡛⣿⣆⣾⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠁⢢⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣤⣔⣒⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢀⣞⣉⣈⣯⣽⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣧⠀⣳⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠠⣸⣿⠟⠧⠼⢨⣍⠀⡀⣀⣤⣴⣿⣿⡿⠟⠛⣿⣯⣿⣡⠐⠉⣼⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣭⣭⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⢀⡨⣟⡊⢠⣖⣛⣿⣶⡿⠛⠛⠉⠁⠀⠀⢀⣰⣿⣿⣿⠁⢀⠼⠟⠳⣸⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⢠⣴⣄⢲⣶⣬⣽⠟⢿⣿⡟⠀⠀⠀⢾⡏⢲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠿⠠⡾⣀⣲⣀⣤⡙⠛⠟⢻⣥⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣤⡀⢀⡞⠋⠸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢀⣴⣿⣿⣿⣿⡏⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡅⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠛⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⣿⣿⠋⠇⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⣿⣿⣧⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⣿⣿⠈⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢺⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆⠀⠠⠃⠀⢰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠃⠀⠀⠈⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣦⡀⣿⠟⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠿⠀⠀⠀⠀⠀⡀⠀⢸⣿⣶⣍⠉⠉⠉⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠄⠀⠀⢰⡄⠀⢷⡀⢸⣿⣿⣿⣶⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⠋⠉⠉⠋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠞⣾⣔⠀⠀⠁⠀⠈⢣⠘⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠄⠘⢂⣸⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢾⡇⠀⠀⣠⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⠊⢹⣀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⡏⠥⢻⢷⡓⠀⣶⡀⠀⠀⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢨⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣄⠀⠈⠈⠉⣀⡉⢉⣽⣿⣿⢿⣿⣿⣿⠿⢛⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⡿⡿⠾⢿⣿⣿⢞⠿⣟⣣⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠂⠀⣀⠀⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣦⣔⡒⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣞⣍⣉⣮⣽⣿⣽⣾⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⡻⣟⣷⡀⣾⣽⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠀⠠⣸⣿⡿⠦⠼⢨⣅⠀⠀⣀⣤⣴⣿⣿⠿⠛⢛⣿⣯⣿⠠⠄⠉⣴⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⡨⣟⡊⣠⣖⣛⣿⣶⡟⠛⠛⠉⠀⠀⠀⢀⣼⣿⣿⣿⠁⣠⠼⠟⢿⣺⡟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⣀⣴⣄⣾⣶⣬⣿⡿⢿⣿⡕⠀⠀⠈⢜⣋⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⡠⣜⣀⣢⣀⣤⡘⠻⠛⢻⣥⣼⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣦⣄⠀⢀⡶⠛⠸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⢀⣴⣿⣿⣿⣿⡇⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣽⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠅⣿⣿⡃⠃⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣝⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⣿⣿⣥⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⣿⣿⠘⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢹⡋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠁⠀⠀⠈⠀⠀⢸⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣦⡀⣿⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢸⣿⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣝⠉⠉⠉⠁⢈⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠤⠀⠀⢰⡄⠀⢬⡄⢸⣿⣿⣿⣦⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠹⠋⠉⠉⠋⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠟⣶⣴⠀⠀⠉⠀⠈⢄⠈⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠰⢐⣴⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⢾⡇⠀⠀⣠⠀⠀⠈⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⡄⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡎⢹⣀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⡟⠭⢫⢷⡛⠆⣶⡀⠀⠀⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢈⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣄⠀⠈⠀⢀⣈⡉⡉⣽⣿⡿⢿⣿⣟⣿⠟⢛⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⠟⠛⠾⠿⡛⣵⢌⠻⣟⣁⣶⠿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⡀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣔⡒⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⡞⣉⣁⣢⣭⣭⣽⣿⣿⣿⣾⡟⡫⠭⣿⣿⡫⡍⣁⣿⣿⡿⡛⢛⠅⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⢸⣿⠛⠯⠼⢠⣅⠀⠀⣀⣤⣴⡿⠿⠟⠋⠙⣯⣬⣿⠀⠀⠈⣴⣿⢿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣿⣿⣿⣿⣷⣿⣿⣧⣠⣬⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠨⡟⡂⣠⣞⣛⣿⣶⡟⠛⠋⠉⠀⠀⠀⠀⣸⣿⣿⡿⠀⢀⡴⠛⠟⣹⡋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣹⣿⠁⠀⢀⣴⡄⣶⣶⣤⣽⡛⢿⣿⡄⠀⠀⠀⢀⠉⢵⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⡜⣀⣲⣀⣤⠘⠛⠛⢻⣥⣴⣿⣿⣿⣿⣿⣿⣯⣼⣾⣷⣦⣀⠀⢀⡔⠑⠸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⢀⣴⣿⣿⣿⣿⡇⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⢹⣷⣷⣴⣿⡝⢫⣭⣉⣛⣛⣻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⡙⠛⠿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠂⣿⣿⠁⠇⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣯⣻⣿⡿⣞⣈⠁⢹⣿⣿⣿⣿⣿⡻⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⣯⣷⣤⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣧⣵⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⠃⠀⢻⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⠿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣝⣿⣟⣂⣲⣿⡿⣿⣿⣟⠻⠟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠠⠀⠀⢠⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣬⢩⣤⣀⣀⡈⠁⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠁⠀⠀⠈⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣧⣝⢻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⡋⢛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠀⠀⠀⠀⠀⢀⠀⢸⣿⣶⣝⠋⠉⠉⠁⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠻⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢠⡄⠀⢾⠄⠈⣿⣿⣿⣦⡀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⠉⠉⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣽⣽⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠞⢦⣤⠀⠀⠁⠀⠀⢀⠀⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠐⢀⠴⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠼⡅⠀⠀⡠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣝⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠌⢸⡀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⡏⠥⠩⢶⡓⠀⣶⠀⠀⠀⢹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⢿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣄⠀⠈⢁⣠⡤⠉⢉⣽⣿⣿⠿⣿⠏⣾⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣾⢿⠟⠛⠋⠒⢟⠛⡶⢮⠝⢶⡃⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡦⢶⣂⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠚⣉⣉⣦⣽⣮⣽⣷⣿⣿⣿⡹⡶⢈⣿⣿⣟⣛⢸⣿⣿⡿⡻⠫⠃⠀⢀⣐⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠄⠠⣼⣿⠟⠶⠞⣠⣅⠀⠀⠀⣠⣴⣿⡿⠛⠉⢉⣿⣿⣿⠀⠀⠈⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣼⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣗⣇⣩⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠨⡟⡁⣠⣞⣙⣿⣶⡶⠛⠛⠉⠀⠀⠀⠀⣾⣿⣿⣿⠀⣀⡰⡟⠿⡻⠏⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣿⠁⠀⢀⣤⣀⣶⣶⣤⣝⡟⢻⣿⡜⠀⠀⠀⠉⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠆⠶⣀⣐⣀⣤⠈⠛⠛⢻⣥⣴⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣤⡀⠀⠀⡜⠁⠸⠛⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⢀⣶⣿⣿⣿⣿⣇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢹⣷⣷⣴⣿⡝⢫⣭⣉⣛⣛⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⡭⠙⠛⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠗⣿⡿⠁⠁⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣯⣻⣿⡿⣞⣈⠁⢹⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⡯⣿⠠⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⠇⠀⢸⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⢹⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣝⣿⣟⣒⣲⣿⡿⣿⣿⣟⠻⠟⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣺⣬⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⢻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⣋⢛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠀⠀⠀⠀⠀⢀⡀⠉⣿⣦⣝⠋⠉⠉⠉⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠠⡄⠀⢶⠀⠀⣿⣿⣿⣤⡀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠑⠉⠛⠙⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠞⢷⣄⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠐⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠾⣇⠀⠀⡠⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠎⢹⡀⡔⠁⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⠟⠧⢨⢿⡑⠐⢦⡀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⣳⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⠛⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡀⠀⠈⣀⣥⡧⠉⢉⣽⣿⣿⠿⣿⠿⣶⠟⢓⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣿⡿⠏⠙⠛⠳⠿⠻⢾⢎⠟⣀⡀⢶⣯⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡶⢶⣒⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠞⣉⣁⣤⣽⣮⣽⣷⣼⣿⣮⣩⡶⣻⣿⣿⣿⣿⣾⣿⣿⣿⡛⢫⡅⠀⢀⣒⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠄⠠⣼⣿⠛⠢⠜⣠⣆⠀⠀⠀⣀⣬⣿⠿⠟⠉⢡⣷⣿⣿⠀⠒⠈⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣩⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠨⠟⠁⣰⣞⣉⣿⣦⡶⠞⠛⠉⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⡴⠛⠟⣸⠋⢘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⠀⠸⣿⣿⣿⣿⠉⠀⢀⣤⣀⣾⣶⣥⣯⣟⣿⣿⡄⠄⠀⠀⠀⣁⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠆⠾⣀⣸⣀⣦⡘⠛⠛⢻⣥⣴⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣤⡀⠀⢀⡶⠂⠸⠙⣿⣿⣿⣿⣟⣿⣿⣿⣿⣏⣿⡿⢿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢀⣶⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡸⠆⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜⢹⣷⣷⣴⣿⡝⢫⣭⣉⣛⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⣿⡽⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⡍⠛⠛⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠉⣿⣿⠉⡉⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⣿⣿⣿⣯⣻⣿⡿⣞⣈⠁⢹⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⣿⣿⠀⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⡇⠀⢸⣝⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣝⣿⣟⣆⣲⣿⡿⢿⣿⣿⠻⠟⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠈⠀⠀⢀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣷⡶⣺⣬⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠃⠀⠀⠀⠀⠀⢰⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⣋⢛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠿⠀⠀⠀⠀⠀⠀⠀⠉⣿⣦⣝⠛⠉⠉⠉⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠙⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡄⠀⠀⢠⡄⠀⠘⠂⠀⣿⣿⣿⣦⡄⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠏⠙⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢧⣤⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠠⢔⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠼⡇⠀⠀⡠⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⣶⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠌⢸⡀⡔⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⠟⠥⢪⢾⡑⠀⣠⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⢀⣨⣾⣿⠉⠉⢉⣽⣿⠿⠿⣿⢿⣾⠟⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠫⠁⠀⠒⠓⢿⡛⡧⡼⠽⢀⡀⣶⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡶⢶⣂⣂⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠞⠉⣙⣶⣽⣯⣥⣷⣾⣿⣿⣿⣛⢜⣿⣿⡯⣯⣁⣿⣿⣿⠛⢛⢇⠀⢀⣀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠄⠀⣼⣿⠛⠢⠚⣰⣆⠀⠀⠀⠀⣨⣿⣿⠟⠋⢡⣿⣿⣿⠇⠖⠈⣰⣾⢟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣓⣩⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠰⡿⠁⢰⣞⣉⣿⣶⣆⣴⡾⠟⠉⠀⠀⢀⣿⣿⣿⣿⠀⡀⡰⠿⠟⢩⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⠀⠘⣿⣿⣯⣿⡉⠀⢀⣀⢀⣴⣿⣿⣿⣟⣿⣿⡴⠃⠀⠀⡈⢕⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠆⠄⣂⣸⣁⣦⡈⠛⠛⢹⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⡀⠀⢀⡼⠙⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⢠⣶⣿⣿⣿⣿⡇⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⠁⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢹⣷⣷⣴⣿⡝⢫⣭⣉⣛⣛⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⡩⠛⠻⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⣿⣿⠟⠁⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣯⣻⣿⡿⣞⣈⠁⢹⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⣿⣿⣄⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣿⣿⡇⠀⢳⡧⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡁⠀⠸⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣝⣿⣟⣖⣲⣿⡿⢿⣿⣿⠻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡆⠀⠈⠀⠀⠀⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣺⣬⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣝⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⢋⡛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⠀⠀⠄⠀⠀⠀⡀⠉⣿⣶⣌⠛⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⠀⢠⡄⠀⠘⠃⠀⣿⣿⣿⣧⡄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠃⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣽⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢧⣖⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠠⠠⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠺⡇⠀⠀⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣦⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡎⢘⡄⣜⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⡿⠏⠡⠨⠿⡁⠀⣥⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⠛⠻⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⢀⣨⣾⣿⠉⠉⢉⣽⣿⠿⡿⣿⡟⣾⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠒⠒⢿⡋⡧⢨⠙⢠⡁⣴⣿⡿⣻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⠶⣁⣂⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠞⡙⣉⣆⣽⣿⣽⣶⣹⣿⣼⣛⣉⠽⣿⣿⡏⡫⣮⣽⣿⣿⡛⢿⠥⠀⢀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠄⠀⣼⣿⠛⠂⠚⣰⡆⠀⠀⠀⠀⢘⣿⣿⣿⠟⠋⣽⣿⣿⡷⠔⠈⣰⣾⠿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣏⣩⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⡸⡿⠅⣰⣯⣩⣿⣶⣆⣴⣾⠿⠟⠉⠀⣀⣸⣿⣿⣿⡅⢀⡴⠿⠿⣨⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣸⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⠀⠘⣿⣿⣙⣿⡉⠉⢀⡀⠀⢰⣾⣿⣿⣿⣻⣿⣶⠁⠀⠀⠈⢩⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠛⠇⠮⣀⣨⣠⣶⠈⠛⠛⢻⣥⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⣼⠑⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢠⣷⣿⣿⣿⣿⡇⠀⠀⢀⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⠁⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢹⣷⣷⣴⣿⡜⢫⣭⣉⣛⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣟⠋⠛⠻⠿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⠿⠁⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣰⣿⣿⣿⣿⣻⣿⡿⣚⣈⠁⢩⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⠀⣿⡿⠀⠓⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⡏⠀⣻⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⡿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃⠀⢸⠇⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣝⣿⣟⣖⣲⣿⡿⣿⣿⣿⠻⠟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣷⡶⣺⣤⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠉⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⡋⡛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠿⠀⠀⠄⠀⠀⠀⠀⠉⣿⣷⣬⠛⠙⠉⠉⠉⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠠⡆⠀⠛⠃⠀⣿⣿⣿⣷⡄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠃⠛⠛⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢷⣄⠀⠀⠈⠀⠈⢂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠼⡇⠀⠀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣦⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡌⢘⡄⡴⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⢟⠡⢈⠿⡑⠐⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢈⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣟⠛⠻⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠈⣨⣽⣿⠋⠉⠈⣽⣿⣿⡿⣿⡟⣾⠿⢟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠰⠲⠑⠿⣛⣯⡬⠛⢧⡁⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠶⠾⢅⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢀⡚⡉⣉⣂⣽⣿⣽⣿⣻⣿⣿⡏⢛⠜⣿⣿⡏⢋⣭⣿⣿⡿⠟⠟⡅⠀⢀⣐⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠄⠠⣼⣿⠛⠒⠛⣰⡆⠀⠀⠀⠀⣸⣿⣿⣿⡿⠛⢹⣿⣿⡷⠀⠈⣠⣾⢟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⢼⣿⡿⣿⣿⣿⣿⣿⣿⣇⣩⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⡯⠅⣴⣏⣹⣿⣶⣆⣴⣾⡿⠟⠋⠉⢀⣴⣿⣿⣿⡅⣀⡠⠛⠟⢱⠋⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣻⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⠀⠘⣿⣿⣉⣿⡉⠁⢀⡀⠀⢠⣶⣿⣿⣿⣿⠿⡿⠇⠀⠀⠀⢻⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠇⠤⣀⣺⣤⡦⠈⠋⠉⢹⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⢀⡴⠋⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢠⣷⣿⣿⣿⣿⡇⠀⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⠃⣀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢹⣷⣷⣴⣿⡝⢫⣭⣉⣛⣛⣻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣟⠉⠛⠻⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠈⣿⣿⡟⠋⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣰⣿⣿⣿⣿⣻⣿⡿⣚⣈⠁⢩⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⣿⣿⠄⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⣿⣿⡇⠀⢹⡧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⡿⣿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣝⣿⣟⣆⣲⣿⡿⢿⣿⣿⠻⠟⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠇⠀⠈⠀⠀⠀⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠃⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣝⣻⠻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⣋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠿⠂⠀⠄⠀⠀⠀⠀⠈⣿⣷⣬⠙⠉⠋⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⢿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠐⠠⡄⠀⠲⠃⠀⣿⣿⣿⣷⣄⢰⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠓⠛⠛⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣭⣽⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢷⣄⠀⠀⠉⠀⠀⢀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠐⠼⡇⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣴⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡌⢸⡄⣴⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢿⢏⠡⢨⠿⡟⠐⣢⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢨⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣟⠛⠿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⣄⠀⣨⣽⣿⡟⠉⠉⣹⣿⣿⡿⣿⢿⣾⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠰⠖⠿⠿⣛⣦⣾⡝⢇⡅⣴⣿⡿⣿⣿⣿⣿⡿⢿⣻⣿⣿⣿⣿⡀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠖⡿⢅⡆⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⢀⡞⠁⣑⣂⣽⣯⣽⣿⣿⣿⣿⡻⣫⣭⣿⣿⡯⣯⣤⣿⣿⡿⠟⡋⡁⠀⢀⣰⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠄⠀⣼⣿⠋⠀⢋⣴⣆⠀⠀⠀⢀⣨⣿⣿⣿⣿⠟⠛⣻⣿⡿⠆⠈⣰⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢷⣿⢿⣿⣿⣷⣾⣿⣿⣅⣩⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠰⠏⠀⣼⣥⣸⣿⣶⣖⣴⣿⡿⠿⠛⠉⢁⣰⣾⣿⣿⡇⢀⡰⠟⠟⢺⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠀⠘⣿⣿⣱⣿⠉⠁⢀⡀⠀⠐⣶⣾⣿⣿⢿⠿⠿⠇⠀⠀⠈⢍⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⠇⠴⣂⣺⣤⡶⠈⠉⠉⢹⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⣴⠓⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⣠⣷⣿⣿⣿⣿⣇⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠐⠇⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢹⣷⣷⣴⣿⡍⢫⣭⣉⣛⣛⡻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣿⣿⣿⡝⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣟⠉⠙⠻⢿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⠿⠃⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣰⣿⣿⣿⣯⣻⣿⡿⣚⣈⠁⢙⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣿⡿⠀⣿⡟⠁⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⡇⠀⢹⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⡿⣿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⢰⠆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣝⣿⣟⣆⣲⣿⡿⢿⣿⣿⠻⠟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠅⠀⠈⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⣋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠿⠂⠀⠄⠀⠀⠀⠀⠈⣿⣷⣤⠛⠋⠋⠉⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡄⠀⠐⠠⡄⠀⠦⠃⠀⣿⣿⣿⣷⣤⢠⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠃⠛⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⣄⠀⠀⠉⠀⠀⢀⠀⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠸⣅⠀⠀⣠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣦⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡌⠘⣄⣴⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⢯⠣⠍⣿⡝⠀⢀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⣩⣽⣿⡟⠉⠉⣹⣟⢿⡿⣿⢿⣾⣿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠡⠓⠶⠿⠏⣾⡖⢉⢃⡃⣴⣿⣿⢛⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠒⡿⢿⠆⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⡞⠂⣁⣦⣽⣭⣯⣶⣼⣿⣿⣫⢋⠔⣿⣿⡟⠛⣭⣿⣿⣿⠛⠯⢍⡀⢀⣐⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠄⠀⣽⣿⠋⠁⣁⣴⣆⠀⠀⠀⢀⣨⣿⣿⣿⣿⡿⠛⣿⣿⣿⠖⠈⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢿⣿⢳⣿⣫⣿⣿⣧⣶⣿⣷⢀⣩⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⢼⣥⣼⣿⣶⣶⣴⣿⡿⠿⠛⠋⢉⣠⣶⣿⣿⡇⢀⡴⠟⠟⣚⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠄⠀⠘⣿⣿⣸⣿⠉⠁⢀⡀⠀⠀⣶⣾⣿⣿⢿⠻⠿⠇⠀⠀⠠⣅⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠇⣤⣀⣠⣠⡶⠈⠉⠉⢹⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⣴⠋⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⣠⣶⣿⣿⣿⣿⣇⠀⠀⠀⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠐⠇⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣸⢹⣷⣷⣴⣿⡍⢫⣭⣉⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⣿⣿⣿⡿⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣟⠉⠙⠛⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⣿⣿⠟⠇⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣯⣻⣿⡿⣚⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣻⣿⣧⠀⣿⡟⠀⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⡇⠀⢻⡂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⢸⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣝⣿⣟⣂⣲⣿⡿⢿⣿⣿⠻⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣬⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⠋⠛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠀⠀⠄⠀⠀⠀⠀⠈⣿⣷⣤⡙⠛⠛⠋⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠐⠀⡄⠀⠀⠁⠀⣿⣿⣿⣷⣤⢠⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣽⣿⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡝⢣⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠸⡁⠀⠀⡠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣓⣛⣳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡌⠈⡀⣰⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠿⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣏⠣⢌⢿⡝⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣶⣄⠀⣨⣽⣿⣿⠙⠉⣹⣿⢿⡿⣿⢿⣿⡿⢟⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠿⠷⠿⠟⣷⠦⠙⢃⡁⣴⣿⣿⢻⣿⣿⣿⡿⣏⣿⣿⣿⣿⣿⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠛⡟⠿⠆⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⡖⢃⣛⣠⣽⣯⣯⣶⣼⣿⣿⣛⣭⠩⣿⣿⡟⡛⣨⣿⣿⣿⡛⢻⡛⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⣽⣟⠉⠉⣡⣾⣆⠀⠀⠀⢀⣨⣿⣿⣿⣿⡿⠿⣻⣿⣿⠖⠈⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣧⣸⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⣾⣽⣼⣿⣿⣷⣴⣿⣿⠿⠟⠋⠉⢀⣴⣿⣿⡅⠀⡴⠟⠟⢺⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠘⣿⣿⣾⣿⠈⠉⠀⣀⠀⠀⢶⣾⣿⣿⢿⠻⠿⠆⠀⠀⠠⣄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠛⠇⡤⣀⣴⣐⡶⡌⠉⠁⢰⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⣴⠛⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣠⣶⣿⣿⣿⣿⣧⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠸⠇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢸⣷⣷⣴⣿⡝⢫⣭⣉⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⣿⣿⣿⡯⠂⠠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠁⠙⠛⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⠟⠇⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣻⣿⡿⣚⣈⠁⠙⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⣿⡯⠀⣿⡏⠂⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⢹⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣝⣿⣟⣂⣐⣿⣿⢿⣿⣿⠻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠅⠀⠨⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣬⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⠋⠛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡿⠀⠀⠆⠀⠀⠀⠀⠈⣿⣿⣤⡙⠛⠛⠛⠉⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠐⢀⡄⠀⠀⠀⠀⣿⣿⣿⣷⣤⢀⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠘⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡽⢣⡄⠀⠀⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠸⡃⠀⠀⣠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡜⠘⡄⣰⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠀⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣶⠫⢼⣿⡟⠂⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠐⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣶⣄⠈⣩⣽⣿⣿⠛⠉⣹⣿⣿⡿⣿⠿⣿⡿⢓⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⠾⠾⠿⠟⣦⡦⠙⢂⡁⣴⣿⣿⢻⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠛⡟⠿⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⡴⡃⣚⣤⣽⣽⣤⣶⣼⣿⣿⣛⢾⠍⣿⣿⡟⢛⣕⣿⣿⡿⠛⠛⡛⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⣿⣿⠉⢉⣡⢶⣦⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⠿⢛⣿⡿⡦⠊⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣷⢃⣸⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⣾⣾⣾⣿⣿⣷⣴⣿⣿⡿⠟⠛⠉⢁⣴⣿⣿⡍⠀⡴⠿⠿⢸⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣿⣿⣼⣿⠉⠉⠁⣀⠀⠀⣶⣶⣿⣿⢟⡿⢿⠆⠀⠀⠀⣍⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠇⣤⣀⣰⣀⡾⡌⠉⠁⢲⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⣼⠛⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠟⣠⣾⣿⣿⣿⣿⣷⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠸⠅⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢸⣷⣷⣴⣿⡍⢫⣽⣙⣛⣛⡻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣿⣿⣿⡻⠂⠠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣯⡇⠙⠛⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⠟⠇⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣯⣻⣿⡿⣚⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣿⣯⠀⣿⠏⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠸⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣝⣿⣟⣂⣐⣿⡿⢿⣿⣿⠻⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡁⠀⠸⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣭⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠫⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⠋⠛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡿⠀⠀⠆⠀⠀⠀⠀⠈⣿⣿⣤⡙⠛⠛⠛⠉⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢾⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠐⢀⡄⠀⠀⠀⠀⣿⣿⣿⣷⣤⠀⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠰⠘⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡽⢢⡄⠀⠀⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠸⡁⠀⠀⢠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣛⣛⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡌⠘⡄⡰⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠟⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣾⠫⠼⡿⡟⠀⠀⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣄⠀⣩⣿⣿⣿⠙⡉⣹⣿⣿⡿⣿⡟⣾⡿⢓⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠷⠵⠿⠟⡿⣤⠩⢂⡅⣴⣿⣿⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⢛⡗⠳⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡴⠃⣐⣤⣽⣯⣦⣶⣾⣿⣿⠟⢏⠊⣿⣿⡟⠿⣹⣿⣿⣿⠛⠻⡉⡀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⣿⣯⠁⢀⣴⢿⣦⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⡿⢻⣿⡿⡦⠈⣱⣾⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡔⣻⣿⢷⣿⣿⣿⣿⣿⣶⣿⣿⣇⣘⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠗⠀⣿⣾⣾⢿⣿⣷⣴⣿⣿⡿⠿⠛⠉⠁⣴⣿⣿⣯⠀⣰⠿⠟⢸⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠘⢿⣿⣼⣿⡉⠉⠙⣀⠀⠠⢶⣶⣿⣿⣟⡿⢿⠎⠀⠀⠀⣄⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠛⠇⣴⣂⣤⣀⡗⠌⠁⠀⢲⣤⣄⣾⣿⣿⣶⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⡼⠘⠸⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠛⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⡸⠇⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢸⣷⣷⣴⣿⡍⢫⣽⣉⣛⣛⡻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⣿⣿⣿⡿⠂⠠⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣯⡁⠉⠛⣻⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⣿⣿⠟⠁⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣯⣻⣿⡿⣚⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⢿⡏⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡟⠀⢹⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⠇⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣝⣿⣟⣂⣒⣿⣿⢿⣿⣿⡻⠟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡁⠀⠸⡀⠀⠀⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣬⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣻⠻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⢋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡿⠀⠐⠆⠀⠀⠀⠀⠀⣿⣿⣤⡙⠛⠛⠛⠋⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠐⢀⡄⠀⠀⠀⠀⢻⣿⣿⣷⣤⠀⣴⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⠘⠛⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡱⢶⡀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠅⠸⠃⠀⠀⣠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡜⠙⡄⣰⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠀⢐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣖⠣⠜⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⢰⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣄⠈⣨⣿⣿⣿⠉⠋⣹⣿⡿⡿⣿⡿⣶⣿⢿⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠶⠴⠾⠟⣧⣦⡙⢇⡃⣴⣾⣿⢻⣿⣿⣿⡿⣛⣿⣿⣿⣿⣿⡀⠀⢀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⢛⡗⠷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡴⣂⣐⣆⣹⣼⣯⣴⣾⣿⣯⡿⢽⠀⣿⣿⡟⠿⣰⣿⣿⣿⠛⠿⠋⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⢠⣴⢿⣆⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⡿⢿⣿⡿⠦⠚⣡⣾⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣮⣦⢿⣿⢷⣿⣯⣿⣿⣧⣶⣿⣷⢆⣈⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣿⣶⣾⢿⣾⣶⣴⣿⣿⣿⠿⠛⠋⠁⣴⣾⣿⣧⠀⣠⠿⡟⢿⡋⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢈⢿⣿⣼⣿⠉⠉⠙⣀⠀⠀⢤⣤⣿⣿⣟⡙⠿⠇⠀⠈⠀⢴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⠟⠃⣖⣂⣠⣐⡗⡀⠀⠐⣺⣤⣀⣾⣿⣿⣶⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⡼⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠓⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠸⠇⣠⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣸⢸⣷⣷⣴⣿⡝⢫⣿⣋⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⣿⣿⣿⡿⠂⠠⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣯⣄⠉⠙⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⠟⠀⢨⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣻⣿⡿⣚⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠀⢻⡟⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢯⣿⣝⣿⣟⣂⣒⣿⣿⢿⣿⣿⠻⠟⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⠸⡀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢨⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠟⠙⠁⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⢋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡿⠀⠐⠆⠀⠀⠀⠀⠀⣿⣿⣤⡘⠛⠛⠛⠛⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠋⠿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢶⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠰⢀⡄⠀⠀⠀⠀⢹⣿⣿⣿⣄⡀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠘⠛⠻⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡱⢒⣀⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠅⠸⡃⠀⠀⢠⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡃⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡜⠙⡄⣰⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡟⠟⠿⠀⢐⣻⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣾⣿⣿⣷⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣮⠇⠌⣽⡟⠠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⠛⢿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣄⠀⣩⣿⣿⣿⠉⠛⣹⣿⢿⡿⣿⡿⣷⣿⠿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡷⡞⠾⠟⣧⡆⠹⢯⡉⣴⣾⣿⣻⣿⣿⡿⣿⣿⣿⣿⣷⣿⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣻⢒⠷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⡰⢂⣒⣀⣹⣿⣯⣷⣼⣿⣿⠟⢻⠄⣿⣿⡟⠟⢫⣿⣿⣿⡟⠿⠳⠀⠀⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⣠⡴⣿⣄⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⢿⣿⣿⠦⠀⣡⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡐⣿⣿⣷⣿⣭⣿⣿⣿⣶⣿⣷⣗⢚⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠘⣿⣷⣿⣿⣿⣮⣴⣿⣿⣿⠿⠟⠛⠉⣠⣾⣿⣷⣀⣰⠿⡟⢺⡋⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⣿⣿⣿⠉⠉⠉⡁⠀⠀⣤⣤⣾⣿⣟⡋⠻⠏⠁⠀⢨⣇⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣺⠿⠗⣐⣂⣤⣐⡟⠄⠔⠒⣳⣤⣀⣾⣿⣷⣶⣾⣿⣿⣿⣿⣧⣄⠀⠀⠀⡴⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠇⣠⣿⣿⣿⣿⣿⣷⠀⠀⢀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⢗⣤⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣷⣷⣴⣿⡝⢻⣿⣋⣛⣛⣻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣿⣿⣿⡯⠂⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⠈⢉⣽⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⠟⠇⢀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣻⣿⡿⣚⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢻⡇⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⡿⠀⠸⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢰⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣝⣿⣟⣒⣒⣿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠅⠀⢸⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢨⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠏⠁⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡌⢛⢛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠆⠐⠆⠀⠀⠀⠀⠀⣿⣿⣇⡘⠿⠿⠟⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠉⢿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡀⠀⠰⢀⡄⠀⠀⠀⠀⢸⣿⣿⣷⣀⠀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠷⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣟⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡹⢣⣀⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠥⠸⠇⠀⠀⢀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡐⠉⡄⣠⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣾⠣⠜⣽⡟⠤⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣮⣉⠉⣩⣿⣿⣿⠋⠙⣹⣿⢿⡿⣿⡿⣾⣿⢻⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠮⠷⠻⠟⢯⠕⠙⢇⠉⣵⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣻⢒⠗⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡴⠀⢂⣀⣹⣿⣧⣴⣼⣷⣾⣟⢯⣀⣹⣿⣷⣿⣇⣽⣿⣿⠿⠿⣛⠀⢀⣂⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⣠⣶⣿⡄⢀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⢿⣿⣿⡤⠐⢡⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣫⣾⣿⣿⣿⣿⣱⣾⣧⣺⢻⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠸⣿⣷⣿⣿⣿⢤⣤⣾⣿⣿⡿⠟⠛⠋⣠⣾⣿⡇⠀⣠⠿⡟⢚⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢙⣿⣿⣿⣿⠙⠛⠙⡉⠀⠀⣤⣴⣶⣿⢿⠿⣷⡖⠀⠀⢀⣮⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⣺⠿⠇⣀⣂⣠⣐⡟⢦⡤⠖⢿⣤⣀⣼⣿⣶⣶⣾⣿⣿⣿⣿⣦⣀⠀⠀⠀⣠⠚⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠟⣠⣶⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠰⢏⣤⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢹⣷⣷⣴⣿⡝⢻⣿⣛⣛⣛⡻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⣿⣿⣿⡏⠆⢀⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣥⣀⣽⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⠂⣿⣿⠟⠁⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⡿⣚⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠀⢻⡏⠀⠐⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣷⣿⣿⡧⠀⢸⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣝⣿⣟⣂⣒⣿⣿⣿⣿⣿⡻⠟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠅⠀⠸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢡⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠌⠊⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⠋⠛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⠀⠀⡄⠀⠀⠀⠀⠀⢻⣿⣇⡸⠿⠿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠛⠿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠁⠀⠰⠀⡄⠀⠀⠀⠀⢸⣿⣿⣿⣀⠀⣠⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠣⠉⠛⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣛⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡹⢧⡀⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡅⢸⠋⠀⠀⢀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣦⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡐⠙⡄⢠⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⡿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣶⢃⠤⣿⡝⠥⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢨⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣮⣀⠉⣉⣽⣿⣿⠛⠛⣻⣿⣿⡿⣿⡿⣶⡿⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠽⢿⠟⠧⠄⠙⢆⠉⣥⣾⡿⡿⣿⣿⡿⡿⣿⣿⣿⣷⣿⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣟⣻⠒⠗⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡠⠃⠂⣄⣙⣽⣧⣤⣼⣷⣿⣏⢿⣀⣿⣿⣇⢯⣯⣿⣿⣿⠿⠿⣛⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣏⠀⣠⣶⣿⡄⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⢿⣿⣷⡤⠐⢩⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣳⣾⣿⣿⣿⣿⣹⣾⣷⣸⣛⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠰⣿⣿⣿⣿⣿⢤⣴⣾⣿⣿⡿⠿⠛⠋⣠⣾⣿⡃⠀⣠⡿⠿⢚⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠉⠉⠉⡉⠀⠀⣤⣴⣶⣿⢿⠿⣷⡖⠀⠀⠀⣎⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣺⠿⠇⣐⣂⣠⣐⡟⢦⡵⠖⣧⣤⣀⣼⣿⣷⣶⣾⣿⣿⣿⣿⣤⡀⠀⠀⠀⣬⠋⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠟⣠⣾⣿⣿⣿⣿⣷⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠰⢏⣤⣾⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⣿⢸⢸⣷⣷⣴⣿⡝⢻⣿⣋⣛⣛⡻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⣿⣿⣿⡍⠆⢀⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣵⣤⣴⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⠂⣿⣿⡟⠁⢀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⡿⣘⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⢻⡇⠀⠐⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⢘⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣝⣿⣟⣂⣐⣿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠂⠀⢘⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢡⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠝⠓⠂⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣙⣻⠻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⠋⠛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⠄⠀⡄⠀⠀⠀⠀⠀⢻⣿⣇⡸⠿⠿⠿⠛⠋⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠍⠻⢿⡿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠁⠀⠠⠀⡄⠀⠀⠀⠀⢸⣿⣿⣷⣀⠀⣠⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠣⠉⠋⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡹⠧⡀⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡅⢸⠋⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡰⠉⡄⢠⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣶⢃⢰⣿⡽⠤⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢘⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣦⡄⠈⢙⣩⣷⣶⡟⠛⢻⣿⢿⣿⣿⣿⣶⡿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⠷⠷⣿⢟⣦⡅⠻⠖⠋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣞⢻⠢⠖⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡠⠂⠀⣈⣙⣭⣷⣤⣼⣷⣿⡟⠏⠏⣿⣿⡷⢷⣟⣿⣿⣿⠟⠿⡓⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣋⠈⣡⣶⣷⡄⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠐⢡⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⣿⣿⣯⣾⣿⣿⣿⣿⣽⣾⣿⢰⢘⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠅⢰⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⠿⠟⠛⠋⣀⣾⣿⡇⠁⢠⣿⠞⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⢹⣿⣿⣿⣿⠉⠉⢉⡁⠀⠀⣤⣴⣶⣿⣻⠻⢷⡆⠁⠀⢀⡼⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣺⠯⡇⣀⣂⣄⣀⡟⢮⡭⠖⢮⣤⣀⣼⣿⣷⣶⣾⣿⣿⣿⣿⣄⡀⠀⠀⠀⣠⠟⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⣠⣶⣿⣿⣿⢿⣧⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢏⣤⣾⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⢸⢹⣷⣷⣴⣿⡍⢻⣿⣋⣛⣛⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣿⣿⣿⡏⢆⢀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⠟⠂⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡿⣘⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⢹⡇⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠸⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠘⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣝⣿⣟⣀⣐⣿⣿⣿⣿⣿⡻⠟⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣙⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡎⢋⡛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⠀⠀⣀⠀⠀⠀⠀⠀⢻⣿⣇⡸⠿⠿⠿⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠍⠙⢿⡿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣉⠁⠀⠠⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣀⠀⣠⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠣⠍⠛⠻⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢧⠀⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠐⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠅⢰⠟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡐⠉⡀⢠⠊⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣶⢇⡐⣿⡿⠤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣯⣍⠉⠁⢋⣩⣶⡏⠚⣻⣿⣿⣿⣿⡿⣾⡿⠿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣧⣾⣿⣿⢿⣷⠾⣿⡿⣯⡃⠻⠎⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡶⢻⠥⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡠⠂⠂⣠⣹⣯⣿⣥⣼⣷⣿⠟⠟⠎⣿⣿⣷⢷⣧⣿⣿⣿⠿⠿⣓⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢘⣿⡟⠉⢩⣾⣶⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠿⣿⣿⣷⣤⠔⢃⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡦⣿⣿⣯⣾⣾⣿⣿⣿⣾⣾⣧⣰⢘⣟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠡⢰⣿⣿⣿⣿⣿⣠⣴⣿⣿⠿⠟⠛⠋⠁⣠⣿⣿⡏⠁⢠⢿⡾⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⢀⠀⠀⠙⣿⣿⣿⣿⡉⠁⠀⣀⠀⠀⣤⣴⣾⣿⠿⠻⣿⡶⠁⠀⢀⡬⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠿⠇⣄⣂⣀⡠⣿⣬⣭⠵⢬⣄⣀⣼⣿⣷⣶⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢠⠛⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⢀⣴⣿⣿⣿⣿⣯⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢿⣤⣴⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢸⢹⣷⣷⣴⣾⡍⢻⣿⣛⣛⣛⡻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⣿⣿⣿⡟⠆⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⣿⣿⠟⠁⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⡿⣘⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢸⡇⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⡟⠀⠰⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢻⣿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡇⠀⠀⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣝⣿⣟⣐⣒⣿⣿⣿⣿⣿⡻⠟⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡷⠂⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡎⠋⠛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣷⠀⠀⣄⠀⠀⠀⠈⠀⢻⣿⣇⠸⠿⠿⠿⠟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⠋⢿⣿⢿⣿⣯⣍⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁⠀⠠⠀⡀⠀⠀⠀⠀⢸⣿⣿⣷⣀⠀⣠⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠺⠍⠙⠛⠿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢧⠀⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠐⢶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡅⢸⠿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁⡰⠙⡄⢠⠂⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣴⢗⡰⣿⡟⠤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⣤⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣬⣮⡌⠈⠑⠈⣉⣭⡝⠛⢻⣿⣿⣿⣿⣿⣶⣿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣦⣴⣿⡿⢿⠴⠯⠿⡿⣯⣣⡻⢎⠍⣡⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⢻⠥⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⡠⠂⠐⣤⣹⣎⣫⣭⣼⣷⣿⠏⠿⠏⣻⣿⣏⠿⣯⣙⣿⣿⠿⠿⡷⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⡀⢐⣿⡏⠉⢈⣼⣶⡀⠀⠀⠀⠀⣀⣿⣿⣿⣿⡿⠿⣿⣿⣧⣀⠐⢃⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣤⣿⣿⣫⣾⣿⣿⣿⣿⣱⣶⣧⣀⢘⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⠧⢠⣿⣿⣿⣿⣿⣠⣴⣾⠿⠟⠛⠋⠁⢀⣰⣿⣿⡏⠁⢀⢿⠾⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠻⣿⣿⣿⣿⠀⠀⠀⣀⠀⠠⣤⣶⣿⡟⠟⠿⣷⡆⠁⠀⠀⣞⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠿⡇⣀⢂⣄⠠⡶⣬⡍⠽⢯⣄⣀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⣰⠛⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢀⣴⣾⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢏⣠⣴⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢸⢹⣷⣷⣴⣾⡍⢻⣿⣋⣛⣛⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣿⣿⣿⡏⠆⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⣿⣿⠏⠁⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⡿⣘⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢸⡇⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⠀⠘⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⠀⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣝⣿⣟⣀⣒⣿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣷⡶⣲⣤⢨⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⡋⡛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣶⠀⠀⣀⠀⠀⠀⠀⠁⢻⣿⣃⠸⠿⠿⠿⠿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠝⠛⢿⣿⢿⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠋⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⣿⣷⣀⠀⣀⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠺⠭⠙⠻⠟⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢫⢧⠀⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠰⢦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⢸⡷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡰⠙⡄⢀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣄⠇⠐⣿⡟⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣭⣤⣄⠉⠀⠘⢉⣪⡟⠛⢻⣿⢿⣿⣿⣿⣷⣷⢿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣧⣴⣾⣿⢟⠶⠶⣿⡟⣧⡉⠿⢋⠉⣡⣾⣿⡟⣿⣿⣿⣿⣟⣻⣿⣯⣿⣿⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢺⠿⠦⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡠⠀⠐⢄⣱⣾⣾⣤⢼⣷⣯⡿⠛⠋⣻⣿⡟⢿⣏⣹⣿⡿⠿⠿⠓⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢐⣿⠛⠙⢚⣴⣶⡀⠀⠀⠀⠀⣀⣿⣿⣿⣿⠿⠿⣿⣿⣧⣀⠰⢓⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⣿⣿⣧⡾⢚⣿⣿⣷⣹⣾⣦⣤⢘⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠫⠠⣿⣿⣿⣷⣿⣠⣷⣿⡿⠟⠋⠉⠀⢀⣰⣿⣿⡏⠁⢀⣾⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⢀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⣀⠀⢠⣤⣶⣾⡛⠿⣿⣷⡔⢁⠀⠖⣚⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠿⡇⣀⢆⣀⠀⡶⣌⣛⠩⣭⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⣠⠟⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢀⣤⣾⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢏⣠⣴⣿⣿⣿⣟⠿⠿⣿⣿⣿⣿⣿⢸⢹⣷⣷⣴⣾⡝⢻⣿⣛⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⣿⡿⠆⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⣿⣿⠑⠁⠀⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⡿⣘⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢸⡇⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠈⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡏⠀⠀⡧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣝⣿⣟⣀⣂⣿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠂⠀⠀⠀⠀⢀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⢋⠛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣀⠻⠿⠿⠿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠜⠙⢿⣿⢿⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⡀⠀⠀⠀⠀⢺⣿⣿⣇⣀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠘⠭⠙⠛⠟⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⠾⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣻⢧⠀⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠐⢦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅⢸⠿⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡰⠁⡄⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣔⢇⡰⣿⡟⠀⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠀⣤⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⣤⣌⠉⠙⠒⠋⠙⡙⠛⢻⣿⣿⡿⣿⣿⣷⣿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣀⣴⣶⣿⣿⢤⣽⡟⢟⡎⠻⠁⠋⣡⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⢶⠿⠦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⠆⠀⢄⣉⣶⣗⣥⣼⣷⣿⡿⠿⠋⣻⣿⡯⠿⣿⣻⣿⡿⠿⢿⠳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢐⣻⡟⠑⠒⣣⣶⡀⠀⠀⠀⠀⣀⣽⣿⣿⣿⠿⠛⢿⣿⣏⢀⠠⢓⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣿⣿⣯⣾⢴⣿⣿⣿⣵⣶⣷⣄⢘⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠀⣾⣿⣿⣿⣶⣤⡶⠿⠿⠛⠋⠉⠀⠀⣤⣿⣿⡟⠁⢀⣾⣾⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣿⣿⣿⡀⠀⠀⣀⡀⢀⣤⣴⣾⡾⢿⣿⣧⡐⠈⠀⠀⣚⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠿⡇⣀⠆⣀⠀⡶⣌⣛⡻⣯⣂⣀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣀⡉⠀⠀⠀⢠⠿⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢀⣠⣾⣿⣿⣿⣷⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠏⣠⣴⣿⣿⣿⣛⡿⠿⣿⣿⣿⣿⣿⢸⢹⣷⣷⣴⣾⡍⢻⣿⣛⣛⣛⣻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⡯⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡅⢹⡿⠛⠁⠀⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⡿⣚⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⠘⡇⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⠀⠀⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⣿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠾⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣝⣿⣟⣂⣀⣿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⠛⠛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣴⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠻⠿⠿⠿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠹⠿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠬⠉⠛⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⡿⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢫⢦⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠐⠂⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⢷⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠠⠛⡄⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠿⠀⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣄⢇⡐⣳⡝⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣠⣌⠉⠃⠒⠊⠉⠛⠙⢻⣿⣿⣿⣷⣿⣷⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣀⣠⣴⣾⡿⠷⣿⡿⡇⣗⠿⢣⠛⣡⣴⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⠿⣶⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢠⠆⡀⢄⣙⣟⣗⣶⣾⣷⣯⡿⣿⠟⣻⣿⠿⠿⣮⣿⣿⣿⠿⠿⠳⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⡀⠀⣿⡿⠓⠒⣧⣦⡀⠀⠀⠀⠀⣀⣼⣿⣿⣿⠿⠟⢫⣝⣟⢀⠤⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣇⣿⣿⡋⣿⣿⣿⣿⣿⣦⣶⣶⣀⢘⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣟⠀⣴⣿⣿⣿⣶⡤⡶⠿⠟⠛⠉⠉⠀⠀⣠⣾⣿⡟⠋⢀⣾⢿⠷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣿⣿⣿⡀⠀⠐⢀⣄⢠⣤⣤⣶⣾⣿⣿⣧⡔⠉⠀⡲⣞⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠿⡇⣀⠄⢄⠀⡰⡌⣛⡛⢯⣁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣀⡈⠀⠀⠀⣰⠿⠵⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠿⠀⣠⣼⣿⣿⣿⣷⠈⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠏⣠⣴⣿⣿⣿⣟⠿⠿⣿⣿⣿⣿⣿⡘⢹⣷⣷⣴⣾⡝⢻⣿⣛⣛⣛⡻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⣿⣿⡟⠆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢹⣿⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⡿⣞⣈⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡂⠘⡇⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⣧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⣿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⡿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣝⣿⣟⣒⣂⣿⣿⣿⣿⣿⡻⠟⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⠋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣶⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⠿⠿⠿⠿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠙⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠟⠃⠀⠀⡀⠀⠀⠀⠀⢿⣿⣿⣇⣀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠤⠉⠙⠛⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡷⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢫⢦⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢂⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇⢸⢶⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢠⠛⡄⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠻⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣄⠗⠐⣷⡻⠄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⣠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣉⡁⠀⠘⠁⠈⠈⠛⢻⡿⢿⣿⣿⡿⢧⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣆⣀⣠⣴⡾⠯⢾⡿⢅⣕⠛⠃⠙⣡⣴⣿⣟⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡴⣾⣶⠄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢩⠄⠀⢠⣘⣟⣃⣤⣴⣷⣏⢳⠏⡋⣿⣿⡣⣿⣉⣿⣿⣿⠿⠿⠳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⣞⡿⠛⠢⢇⣲⡄⠀⠀⠀⠀⢀⣠⣿⣿⣿⡿⠟⠛⣛⣽⡃⠠⢓⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⣾⣿⠡⡵⢆⣾⣿⣷⣴⣶⣶⣀⢐⣓⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠂⣰⣿⣿⣿⣶⣦⠶⠾⠟⠛⠋⠉⠀⠀⢀⣴⣿⣿⠋⢀⣾⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣲⣿⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡅⠀⠀⠁⣀⣠⣤⣤⣤⣼⣿⣿⣿⣴⠉⠀⠠⢚⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠆⢀⠀⢀⡀⢠⣌⢛⠛⢻⣃⣀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠁⠀⠀⢠⠞⠬⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠿⠀⣠⣼⣾⣿⣿⣿⡈⠉⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠏⢀⣤⣾⣿⣿⣿⣻⠟⢿⣿⣿⣿⣿⣾⢹⣷⣷⣴⣾⡝⢻⣿⣛⣛⣛⡻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡝⠣⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⢸⣿⠗⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⡿⣾⣈⠁⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⡇⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⢱⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⠿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⠀⢸⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣝⣿⣟⣓⣀⣿⣿⣿⣿⣿⡻⠟⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⠋⢛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⣶⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣀⠿⠿⠿⠿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠙⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡴⡮⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠟⠃⠀⠀⡄⠀⠀⠀⠀⢹⣿⣿⣧⣀⠀⣀⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠤⠈⠙⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣿⠷⠶⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢩⢦⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⢶⡦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢠⠛⡆⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣟⣻⠝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣄⠇⠠⡳⡝⠄⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣁⣉⠁⠐⠛⠋⠛⠛⢻⣿⣿⣿⣷⣿⣷⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣷⡀⣀⣠⣴⣶⣾⡿⣯⣔⡻⠏⠛⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⡦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠍⠄⠤⢹⣿⣳⣧⣴⣷⣎⡿⠿⡋⣿⣿⣷⣿⣏⣿⣿⣿⠿⠿⠓⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⢼⣿⠟⠦⢼⣰⣄⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡿⠟⢛⣹⣟⠠⢓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣢⣻⣿⡎⣍⣿⣿⣿⣿⣮⣶⣧⣄⠚⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⡂⢀⣾⣿⣿⣶⣶⠤⠶⠿⠿⠛⠋⠉⠁⠀⣠⣾⣿⡿⢀⡾⢻⠃⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣏⠀⠀⠀⢀⣀⣠⣄⣀⣦⣿⣿⣿⣕⠈⠠⡠⠾⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠦⢀⠄⠡⡀⢀⣌⠛⢿⢛⣏⣀⣀⣼⣿⣿⣿⣿⣿⣿⣯⢻⣿⠅⠀⠀⣠⠝⠼⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠿⠀⢀⣬⣾⣿⣿⣿⡎⠉⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠏⠀⣠⣶⣿⣿⣿⣟⠛⠻⣿⣿⣿⣿⣾⢹⣷⣷⣴⣾⡝⢻⣿⣛⣛⣛⡻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣟⠳⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠈⣿⠿⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⡿⣾⣎⠁⠙⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⢿⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⢸⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⠿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⢸⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣝⣿⣟⣛⣂⣿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⠛⡛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡦⣶⣄⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠻⠿⠿⠿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣭⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢱⠸⠋⠀⠀⡜⠀⠀⠀⠀⢸⣿⣿⣷⣤⡀⣀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠐⠈⠉⠉⠉⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠷⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢩⢧⠂⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣦⣶⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡄⠰⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⢠⠛⡅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣄⢗⠰⣳⡻⠀⠊⢀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣰⡤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⢀⣉⡑⠘⠛⠃⠚⠛⢿⣿⣿⣿⣿⣿⢿⣿⣿⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣄⠀⣀⣤⣴⣾⡿⢿⠁⡻⠯⡛⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⠗⠨⢻⣿⣃⣤⣤⣷⣏⡿⠻⠋⣻⣿⡿⣿⣛⣿⣿⣿⠿⠿⠳⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⣿⠻⠧⠼⣠⣆⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⠿⠻⡛⢿⠢⠓⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣻⣿⡿⣾⣽⣿⣿⣿⣥⣾⣦⣄⠞⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡆⢀⣾⣿⣿⣧⣶⡠⠴⠾⠟⠛⠋⠉⠁⠀⢀⣴⣿⡿⢆⢾⢿⢧⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣏⠀⠀⠀⢀⣀⣀⣄⣀⣤⣿⣿⣿⡯⠊⠠⠠⠜⢓⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠦⢠⠄⠁⡀⢀⣌⠛⠿⢟⣛⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⠀⠀⢠⡿⠈⡟⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡿⠀⢀⣬⣶⣿⣿⣿⡎⡛⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠏⠀⣠⣷⣿⣿⣿⡽⠛⠻⢿⣿⣿⣿⣾⢹⣷⣷⣴⣾⡝⢻⣿⣛⣛⣛⡻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠓⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠈⣿⣿⠟⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣻⣿⡿⣞⣮⠁⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢻⡃⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣯⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⢸⣇⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⡿⠿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡯⠀⢸⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣍⣿⣟⣛⣒⣿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠛⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⣴⣄⠀⠀⠀⠀⠀⠀⠈⢹⣿⣦⡛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⣿⣿⣿⣿⣾⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣧⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⠘⠛⠀⠀⡘⠀⠀⠀⠀⢸⣿⣿⣿⣶⡄⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠐⠀⠉⠉⠁⠉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢩⢧⠂⠀⠀⠉⠄⠀⠀⠀⢸⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣦⣶⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⢠⠛⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣤⢇⠠⣷⡿⠀⠈⢀⠀⠀⠀⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠁⠙⠋⠁⠑⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣄⠀⢠⣔⣼⡿⢧⡙⡻⠯⠜⢡⣴⣶⣟⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣖⢢⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⡏⠹⣟⣟⣠⣤⣶⣿⣿⠿⠏⣿⣿⣿⢿⣋⣽⣿⣿⠿⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠄⣇⣽⡀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⡿⠿⠛⢻⠟⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⡯⣽⣿⣿⣿⣿⣠⣴⣧⣀⠘⢛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠀⣠⣾⣿⣷⣴⡄⠀⠴⠶⠿⠛⠛⠉⠉⠀⠀⣰⣿⣾⣿⢿⡅⡟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣇⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠻⣿⣿⣿⣿⠁⠀⠁⠀⠀⣀⣀⣀⣀⣐⣼⣿⣿⡿⠈⢀⡹⠃⣦⡸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣖⡆⢀⠤⠈⣄⠀⣀⡙⠿⠿⣟⣃⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⠀⢀⡼⠘⡟⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⡿⠀⠀⣨⣵⣾⣿⣿⣧⢓⣿⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⠀⢀⣠⣾⣿⣿⣯⡛⠛⢿⣿⣿⣿⣿⢹⣷⣷⣴⣾⡜⢻⣿⣛⣛⣛⡻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣛⠀⠛⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⢿⣿⣿⠇⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⡿⣾⣺⠧⠉⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⢸⣿⡃⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠂⠘⣿⣥⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⣿⠿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⣿⠟⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣭⣟⣟⣳⣿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠁⠀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣾⣿⣿⣿⣿⢿⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠈⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣮⠋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣧⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠈⠿⠁⠀⡸⠁⠀⠀⠀⠀⢽⣿⣿⣿⣿⡀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠆⠀⠈⠀⠀⠉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⡿⡾⣽⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⠖⠀⠀⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢘⣤⣴⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⢠⠚⡄⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⣠⠇⠠⣳⡺⣀⠘⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠃⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⡀⣴⣶⣘⣿⣥⣝⠿⡯⠜⢡⣴⣶⣟⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣖⢂⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣟⠿⣾⣖⣠⣼⣶⣿⣿⠯⠋⢿⣿⣯⣿⣙⣽⣿⣿⡿⢿⠗⠀⠀⠀⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠿⠄⡴⢬⡀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⠟⠛⣿⣵⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⢄⢿⣟⠓⣴⢢⣿⣿⣿⢠⣶⣦⠠⠐⠛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠂⢠⣾⣿⣷⣤⡆⠀⠠⠶⠾⠿⠛⠛⠉⠁⠀⠀⣲⣶⣿⣿⠳⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣄⣯⣬⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⣿⣿⣿⡇⡁⠸⠂⣤⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡆⢀⠄⠀⢥⠀⣀⡙⠿⠿⣿⣃⡠⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣹⣿⠇⢠⠸⢺⡟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡿⠀⠠⣨⣵⣾⣿⣿⣧⠁⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡀⠀⣠⣶⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⢻⣷⣷⣴⣿⡝⢻⣿⣛⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⠀⠛⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢿⣿⣿⠟⠀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⡿⣾⣾⠷⠙⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⢸⣿⣟⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠘⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⣿⠟⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣍⣭⣟⣛⣳⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠁⠀⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣾⣿⣿⣿⣿⢯⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠈⠈⠉⠁⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣎⠋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠛⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣿⡿⣿⣿⣷⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣰⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠉⠿⠃⠀⠰⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⠾⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⢦⠂⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣆⣴⡆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⢩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⢀⠚⡌⠀⠀⢀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣠⠇⠀⣷⡾⣂⠘⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠁⠀⠀⠐⠚⠚⠙⠈⠙⠛⠿⣿⣿⣿⣿⣿⣻⣿⣿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣄⢤⠤⢼⣿⣦⠑⠟⡅⠻⣉⣴⣶⡿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣔⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠿⣟⣟⣀⣐⣶⣭⣿⡾⠁⢻⣿⣿⠿⠩⢻⣿⣿⡿⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢅⡴⢨⡅⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⡇⣤⢲⢦⣿⣯⣀⣴⣤⢰⠐⡛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡵⠂⢀⣴⣟⣷⣤⡆⠀⠀⢴⡶⠿⠿⠛⠛⠋⠁⠀⢀⣶⣾⣿⡇⡟⠻⣼⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡁⣿⣴⣽⣿⣿⣿⣿⣿⣷⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢰⣿⣿⡿⠐⡶⢀⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢤⣶⡆⠀⠄⠠⣄⡀⢠⡈⠿⠿⣿⣃⡀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣷⡏⣻⡿⢀⡕⠼⡿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⠀⠀⣈⣵⣾⣿⣿⣯⠁⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣀⣴⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⢻⣷⣷⣴⣾⡍⢻⣿⣛⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣼⣿⣿⣿⣿⣯⣝⠀⠹⠟⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡗⢹⣿⣿⣿⠀⢀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⡿⣾⣾⠷⠍⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⢸⣿⣿⡏⣀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡃⠈⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⣿⡿⣿⢿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣿⠟⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣍⣭⣟⣛⣳⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁⠀⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣾⣿⣿⣿⣿⢧⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣾⣿⣿⣷⣿⣿⣿⣎⢋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⠉⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢹⠉⠿⠛⠀⡐⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣾⣿⣿⣿⠀⠀⠀⠉⢰⣾⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⠾⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢙⢮⠣⠀⠀⠉⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣇⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢈⣄⣴⡦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⢈⠚⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⣾⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⣠⠗⠀⣷⡺⠂⠘⢠⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠈⠒⠘⠋⠀⠁⠛⠿⣿⣿⣿⣿⣿⢻⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣷⣤⡤⠸⣿⣢⣄⠞⠅⠸⢉⣴⢶⡿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⡒⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⣿⣇⣠⣐⣶⣮⣿⡮⠎⢻⣿⣧⢟⠉⢕⣿⣿⡿⢿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡿⢧⡰⢨⣁⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣗⣬⠲⢦⣿⣯⣀⣴⣤⠠⠐⠒⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡵⠆⢀⣴⣛⣿⣦⣆⠀⠀⢠⣴⡾⠿⠿⠛⠛⠉⠉⠀⢰⣦⣿⡕⡟⠳⣼⣿⣿⣿⣿⣿⣿⣿⣷⣮⣯⠐⣿⣵⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⣾⣿⣿⡃⠴⠀⣤⡰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢤⣖⡆⠀⠄⠀⡥⡀⢀⡈⠿⠿⣿⣃⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣯⢽⣿⣇⠙⠤⡿⠉⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⠀⠀⢈⣵⣶⣿⣿⣿⠁⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀⣴⣿⣿⣟⠟⢻⣿⣿⣿⣿⣿⢻⣷⣷⣴⣿⡍⢻⣿⣛⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣟⠀⠻⣿⠟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⢹⣿⣿⣿⡄⢠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣻⣿⡿⣾⣾⠷⠍⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡃⢸⣿⣿⣿⣧⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⣿⣿⣿⡯⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⣿⡿⣿⢿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣿⡿⠗⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣍⣭⣝⣛⣳⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁⠀⠿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣾⣿⣿⣿⣿⢇⢸⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠁⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣷⣿⣿⣿⣎⠋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣥⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢹⠉⠿⠟⠀⠐⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⣿⣿⣿⣿⡀⠀⠉⢰⣾⣿⣿⣿⣿⣿⣿⣿⣟⡻⡿⠾⢧⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢙⢮⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣹⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢀⣆⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⠿⢛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⢀⠚⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣝⣛⣷⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠶⣠⠗⠀⣷⡜⠂⠘⢀⠀⠀⠀⠀⠸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠈⠀⠈⠁⠉⠊⠐⠛⠿⡿⣿⣿⣿⣿⢿⣿⢿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣷⣦⣼⣿⢮⣑⣾⡅⠻⢉⣴⣶⡿⣿⣿⣿⣿⡿⢿⣿⣟⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣓⣨⣷⣬⣿⣽⡇⣿⣿⡫⢿⠍⠓⣿⣿⡿⣿⠗⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠯⣉⠆⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡟⣔⠸⣶⣿⣯⣀⣤⣤⠠⠐⠒⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠖⠀⣠⢞⢻⣧⣤⠀⠀⠀⢀⣤⣶⠿⠿⠿⠛⠋⠉⠀⢠⣶⣽⡿⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⡀⣿⣠⣿⣿⣿⣿⣿⣿⣷⣺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢴⣿⣿⣿⠁⣠⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣤⣶⡆⠀⠄⠀⠄⡀⢀⣀⠻⠿⢿⣟⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠄⡿⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⠀⢀⢈⣵⣶⣿⣿⣿⡘⣰⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⢹⣷⣷⣴⣿⡌⢻⣿⣛⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠹⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢸⣿⣿⣿⣦⣠⡏⢑⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣯⣻⣿⡿⣾⣾⠷⢭⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣧⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⣿⣿⣿⣿⣽⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⣿⣿⣿⠉⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣍⣭⣝⣚⣳⢿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃⠀⢹⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣾⣿⣿⣿⣿⢇⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠧⠀⠀⢸⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣷⣿⣿⣿⣎⢋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⣶⣶⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢹⣿⣿⣿⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣥⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢹⠉⠟⠻⢋⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢻⣿⣿⣿⣿⡅⢠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠦⢷⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⢮⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⢀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢀⣄⣴⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⢀⠚⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⣳⣾⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣢⠗⠀⣷⡾⠂⠘⢀⡀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠈⠋⠀⠁⠒⠐⠛⠿⣿⣿⣿⣯⣿⢯⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣷⣾⣿⡆⢁⣚⣅⡺⢉⣴⢶⡿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣔⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣦⣼⣯⡤⡱⣿⣯⣯⠟⠉⣱⣿⣿⡿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠾⢅⡴⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡟⣄⠀⢠⣿⣧⣀⣴⣦⠀⠐⠖⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡷⠀⢠⣖⢛⣷⣤⡄⠀⠀⠀⠀⣤⣴⡾⠿⠿⠟⠛⠉⠉⠉⣦⣽⡗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⢀⣗⢾⣼⣿⣿⣿⣿⣿⣶⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢠⣾⣿⣿⣥⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣤⡶⡆⠀⠄⠀⠄⢀⠀⣀⠹⠿⠿⣿⡀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣶⣿⣛⣿⣿⡿⠃⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⠀⠀⢈⣠⣶⣿⣿⣿⡏⢀⣦⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢻⣷⣷⣴⣿⡌⢻⣿⣛⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣯⢡⠘⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠙⣿⣿⣿⣷⣠⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⡿⣞⣾⠷⢭⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣥⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⣿⣿⣿⣿⣽⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣹⣿⣿⣇⠀⢿⣿⣿⣿⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣭⣝⣛⣳⢿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⠇⠀⢸⣿⠿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣾⣿⣿⣿⣿⢇⢸⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⢟⠾⠄⠀⠀⢸⡿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠉⠀⠀⠸⠁⠀⠀⠠⠾⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣷⣿⣷⣿⣿⣿⣎⢋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⣶⣶⣼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⠆⠈⠘⢿⣿⣿⣿⣿⡇⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣨⣥⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢱⠉⠙⠛⠋⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠃⠈⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⠶⢦⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⢮⠣⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⢈⣄⣼⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠏⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⢀⠚⡈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⣳⣶⣯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⣤⠇⠀⣷⡸⡂⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠛⠿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⡆⣁⠚⣅⡺⢉⣴⢶⣿⣿⣿⣿⣿⡿⠿⣿⣟⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣧⣯⣯⣭⠓⣿⣿⣧⠯⠍⠙⣿⣿⡿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢇⡰⢨⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⡆⣄⠄⢀⣿⣷⣀⣤⣤⠀⠀⠒⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠂⢀⡴⠛⣿⣤⡄⠀⠀⠀⠀⠀⣤⣶⡿⠿⠿⠟⠛⠋⠉⢳⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡃⣟⢱⣜⣿⣿⣿⣿⣿⣷⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⣴⣿⣿⣿⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠄⠀⡄⢀⠀⣀⠙⠿⠿⣿⣃⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣿⣻⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⠀⠀⠈⣤⣶⣿⣿⣿⣇⢉⣶⣴⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢹⣷⣷⣴⣿⡌⢻⣿⣛⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⠱⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⣿⣿⣿⣦⣠⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⡿⣞⣾⠷⢭⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⡯⠀⢸⣿⣿⣿⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣭⣝⣚⣳⢿⣿⣿⣿⣿⡻⠛⠿⠿⢿⣿⡟⣾⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣿⣿⣿⠃⠀⢸⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⢇⢸⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠹⣿⡿⠤⠀⠀⢸⣿⡋⠀⠀⢀⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠉⠀⠀⠸⠏⠁⠀⢠⢾⠟⠛⠛⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣷⣿⣷⣿⣿⣿⣎⠋⣛⠛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⣶⣶⣶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡀⠈⠘⠛⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢰⣥⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⠉⠙⠛⢏⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⠶⢤⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢮⠣⠀⢀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⢈⣄⣴⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⢀⠚⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣟⣓⢾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣶⡇⠀⣷⡘⠂⠈⢠⡀⠀⠀⠀⣈⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠀⠀⠁⠈⠉⠁⠀⠼⠻⠿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣇⢛⡍⡿⢉⡴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣽⣿⣿⡿⢿⠫⢵⣿⣿⡿⣿⣶⠀⠀⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡷⠯⣀⠎⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣿⡗⣟⢲⣾⣿⣿⣀⣴⣤⡠⠐⠖⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⣽⠗⠀⣠⠞⢻⣦⣄⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠿⠿⠛⠋⢻⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣇⢠⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣀⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣶⣦⠀⠄⢀⡄⢤⡂⢀⡈⠿⢿⣿⣗⠀⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣶⣾⣻⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⠀⠀⠉⣰⣶⣾⣿⣿⣿⢉⣷⣶⣾⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⢻⣷⣷⣴⣾⡜⢻⣿⣛⣛⣛⡻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣟⡸⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⡿⣾⣾⠷⢽⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣯⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡟⠛⢁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣭⣝⣛⣳⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠛⠀⢸⣿⣿⣿⣿⠁⠀⡾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣾⣿⣿⣿⣿⢇⢸⣿⠷⣶⡶⣲⣤⢡⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢏⡂⠀⢸⣿⣿⣟⠁⢠⣼⡇⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣻⣻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠁⠀⠸⢿⠿⠂⣰⣿⠿⠁⠀⠛⠛⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣷⣿⣿⣿⣎⢋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⣴⣷⣿⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠸⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⠉⠙⠛⡫⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢙⣮⠫⠉⣅⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⢈⣄⣴⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⢠⠞⡎⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⣻⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⣶⣿⣲⣷⡸⠂⠈⢠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠈⠙⠋⠐⠁⠒⠖⠛⠿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣷⣷⣿⡏⠚⢋⣴⢶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣴⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣬⣶⣾⣿⣿⢯⣻⣿⡟⣿⣝⣿⣿⣿⡿⣿⠷⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⡿⢩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢿⣿⣗⣅⣿⣿⣿⣿⢧⣶⣧⡀⠰⠚⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢩⠿⠂⢠⡴⠿⣷⣠⡀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⠿⠿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣹⣫⣿⣿⣿⣿⣿⣷⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠒⣂⠀⠀⢹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⣐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢴⣶⣦⡀⠄⠀⡄⢠⣔⢀⠈⠻⣿⣿⣿⠀⡀⢀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⠀⠀⠉⣱⣴⣾⣿⣿⣿⡝⣰⣦⣿⣿⣿⣷⣶⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣫⡉⣻⣿⣿⣿⢻⣷⣷⣴⣾⡍⢻⣿⣛⣛⣛⡻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⢻⣿⣿⣿⣧⣬⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⡿⣾⣾⠷⣍⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣝⣟⣳⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⠿⠀⢸⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣾⣿⣿⣿⣿⢧⢸⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⢘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⡷⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣟⣿⣻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠈⠁⠀⠀⠀⠿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠛⠋⠀⠀⠈⠉⠉⠙⠿⣿⣿⣿⣷⣼⣿⣿⣿⡿⠟⢁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⢋⢛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣼⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣾⣿⣿⣿⡗⢾⣿⣿⣧⡀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⠉⡜⠛⢻⠉⠁⠀⠀⣸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⠿⣧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢜⢮⠧⢌⣠⣭⣄⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⢘⣆⣜⠿⠿⠁⠀⠀⠹⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠀⣸⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⣨⠞⡜⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣶⣿⣲⣷⡾⡂⠘⢠⣤⡀⠀⠀⣻⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠊⠃⠁⠛⠐⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣷⣿⣿⠺⣫⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣟⣻⣯⡯⣿⢟⢻⣿⣿⡿⣿⠷⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡾⢏⣺⢭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣷⣝⣷⣿⣿⣿⣶⣦⣦⡀⠴⠟⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡿⠂⢀⡤⠚⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⠿⠿⠿⠛⠛⢽⣿⣽⣿⣿⣿⣿⣿⣿⣽⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠂⠀⠒⢂⠁⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣶⣦⠀⠄⢀⡀⢠⣐⢂⡀⠹⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⠁⠀⠈⣡⣴⣿⣿⣿⣿⡽⣳⣦⣾⣿⣿⣷⣶⣤⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣛⣻⣿⣿⣿⢻⣷⣷⣴⣿⡍⢻⣿⣛⣛⣛⣻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⡅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢻⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⡿⣾⣾⠷⠍⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠅⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣯⣝⣟⣳⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡯⠁⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣾⣿⣿⣿⣿⢧⢹⣿⠷⣶⡶⣲⣤⢨⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣜⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⠇⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣟⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠈⠉⡁⠀⠀⠿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⣿⣿⣿⠟⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⢛⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣼⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣶⣶⣦⠀⠀⢀⣶⣶⣄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⠉⡞⠛⢻⡉⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⠻⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢞⢮⢧⢌⣠⣥⣄⠁⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⣦⡀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣈⣆⣜⠿⠟⠁⠀⠐⣿⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣿⣧⣀⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⣪⢞⡝⢀⡀⠀⠀⠀⣝⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣶⣿⣶⣷⡾⣂⠚⢠⣤⣇⢀⣀⣼⡇⠀⠀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠘⠓⠐⠛⠒⠗⠛⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⣾⣿⣾⣷⣿⣿⡻⢉⣴⣾⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣠⣤⣤⣠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⢿⣿⡿⣟⣝⣿⣿⣿⣿⣿⡷⠀⠐⠆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⢷⢿⣽⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢼⣿⡕⣽⣾⣿⣿⣿⣄⣤⣦⡐⠰⠗⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⣉⡽⠇⠀⣠⠼⣿⣄⡄⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⠿⠿⠿⠟⠛⠋⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠀⠀⠀⠂⠀⠒⢲⡀⠀⠸⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⠀⡠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣶⣦⠀⠄⢀⡄⢠⣐⢂⡀⠹⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢠⠉⣑⣤⣶⣿⣿⣿⣟⣲⣦⣼⣿⣿⣷⣶⣦⡄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⢹⣷⣷⣴⣿⡝⢻⣿⣛⣛⣛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡯⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢹⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⡿⣾⣾⠷⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣯⣝⣟⣳⣿⣿⣿⣿⣿⣿⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡿⠂⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⣾⣿⣿⣿⣿⣷⢹⣿⠷⣶⡶⣲⣤⢠⣤⣀⣀⡈⠁⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣿⣿⠇⠀⠙⠻⠿⠻⠿⠻⠟⠟⠛⠏⠀⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠈⣁⠀⠀⠿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠋⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣎⢛⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⣼⣿⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣶⣤⣶⣶⣦⣶⣶⣷⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⠉⡞⠛⢛⣝⠀⠀⠀⣼⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠉⠉⠀⣽⣿⣿⣿⣿⣿⣿⣿⣛⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢞⣾⢧⠌⣠⣭⣦⠁⠀⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢱⣆⠀⢀⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣘⣆⣜⡿⠿⠁⠀⠀⣿⣿⡇⢼⠂⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢻⣿⡄⣺⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠑⢪⠾⣔⢂⡀⠀⠀⢠⣿⣿⡉⣼⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣷⣿⣷⣷⡾⡂⠚⢰⣴⣿⣇⣀⣸⡿⣿⣤⣼⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠀⠉⠀⠀⠘⠋⠈⠚⠒⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣭⣿⣿⣿⡾⢻⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⣤⣄⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⢛⣿⣿⣿⡿⣿⠷⠀⠠⡆⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣼⣏⣻⣗⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣿⣿⣃⣜⢾⡻⣿⣯⣰⣴⣦⡠⠰⠟⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠉⢉⣭⠿⠀⢈⣥⣾⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⠿⠿⠿⠟⠛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠂⠀⠒⠲⡀⠀⠀⣿⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣀⠄⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢴⣶⣦⠀⠄⢀⡀⠠⢀⣒⣀⡸⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⢀⣠⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⠁⢀⠉⣑⣤⣷⣿⣿⣿⣯⣑⣮⣤⣿⣿⣷⣶⣤⣀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⢹⣷⣷⣴⣾⡝⢻⣿⣛⣛⣛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢳⢹⣿⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠘⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣾⣾⠅⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣝⣧⣟⣟⣳⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣯⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣾⣿⣿⣿⣿⣿⢹⣿⠿⣶⡶⣲⣤⢩⣤⣀⣀⡈⠁⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡟⠉⠈⠙⠙⠙⠉⠉⠀⠁⢸⣿⣿⣿⣿⣿⣿⡯⣟⣃⣙⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⣀⣤⣤⣄⣄⣀⣀⡀⠠⣤⣸⣿⡏⠉⢋⣉⣩⣥⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣎⢛⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣿⣿⣿⣄⠀⠀⠀⣀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣇⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⠉⡞⠛⢻⣯⠁⠀⠀⣼⣿⣧⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠙⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢞⣾⢧⠜⣡⣤⣤⣅⠀⣿⣿⣯⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡆⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣘⣆⣼⡿⠿⡧⠐⠀⣿⣿⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠑⣪⢾⣝⢂⡄⠀⠀⠀⣿⣿⣿⣾⣷⢀⡀⣠⣤⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣲⣿⣿⣷⣾⣂⠚⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠁⠀⠈⠛⠃⠙⠓⠒⠖⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣾⣿⣯⣽⣿⣿⣾⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡉⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣤⣤⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⣿⣏⣿⣿⣿⡿⣿⡧⠀⠐⢡⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣿⣨⣟⢽⣗⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣃⣞⣽⣿⣿⣯⣷⣴⣧⢱⠤⠟⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠁⠈⠉⣉⣭⠿⠂⢈⣩⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⡿⠿⠿⠿⠛⢛⣿⣿⣿⣿⣿⣿⣷⣼⣿⣟⣯⣼⣽⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠀⠀⠀⠂⠀⠒⠲⡆⠀⠀⢿⣷⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣠⣤⣤⣀⡀⡠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣶⡦⠀⠄⢀⡀⠠⢀⣖⣂⠘⢿⣿⣿⡇⠀⢀⡀⠀⠀⠀⠀⢀⣨⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠁⠀⠉⢱⣤⣷⣾⣿⣿⣯⣛⣦⣬⣿⣿⣿⣾⣦⣀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢹⣷⣷⣴⣾⡍⢻⣿⣛⣛⣛⡻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠉⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣾⠁⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣤⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣯⣟⣟⣳⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢩⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣯⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⡟⠃⠈⠙⠉⠉⠁⠀⠀⠈⠉⠛⠙⠛⠛⠋⠁⠛⠃⣙⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⡀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⢩⣤⣤⣤⣤⣤⣤⣤⣶⠦⠀⢂⡀⠀⠀⣀⣀⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣥⣿⣿⣿⣦⠀⠀⠀⣀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣷⠀⠙⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢳⠉⡝⠛⠻⣯⠉⡀⠀⣸⣿⣧⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠏⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢟⢿⢿⠜⣁⣤⣴⡥⠀⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣘⣆⣜⠺⠿⡯⠀⠀⣿⣿⣿⣸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠑⢪⢾⣟⢂⡄⠁⠀⠀⣿⣿⣿⣶⣿⣷⣀⣠⣶⡦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣲⣿⣿⣿⣿⣂⠚⠀⣶⣿⣿⣿⣫⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠃⠀⠛⠋⠐⠒⠒⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣰⣾⣷⣞⣯⣿⣿⣿⣯⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠉⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⣤⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢵⣖⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡧⠀⠂⠥⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡯⣬⡿⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣽⣿⣿⣿⣿⣵⣼⣧⣠⠠⠿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠁⠀⠁⠀⢉⣉⣩⣭⠿⠀⢉⣩⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠿⠿⠟⠿⣿⣿⣿⣿⣽⣷⣽⣿⣽⣿⣽⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠂⠀⠒⠐⠤⠀⠀⢰⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠈⣠⣦⣤⣀⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣦⠀⠄⢀⡀⢀⢀⣐⣒⡀⢻⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⢀⣨⣼⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⠘⢹⣠⣷⣾⣿⣿⣿⣹⣠⣩⣽⣿⣿⣶⣦⣄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢹⣷⣷⣴⣾⡜⢻⣿⣛⣛⣛⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⡙⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢻⣿⣿⣧⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣊⠁⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⢿⣿⣍⣽⣟⣗⣂⣿⣿⣿⣿⣿⡿⠟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⡟⠋⠁⠐⠀⠀⠀⠈⠀⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣷⡶⣲⣤⢡⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠉⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠙⢣⣝⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⡀⠁⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣹⣷⣶⣶⣶⣶⣤⣤⡄⠄⣠⣽⣿⣄⢀⣀⣤⣴⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⢋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣥⣾⣿⣿⡧⠀⠀⠀⢀⠀⠀⣤⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⠉⡝⠛⠛⣿⡇⠀⠀⢤⣿⣿⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢞⣾⢷⠜⣩⣴⣶⣥⠄⣼⣿⣿⡀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣘⣆⣜⠸⠿⠯⠁⠀⢽⣿⣿⣇⣿⣿⣿⣥⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠃⢨⣿⣟⢀⡄⢀⠀⠀⢹⣿⣿⣷⣿⣿⣿⣿⣿⣿⡦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣶⣾⣿⣿⣿⡆⠚⠀⣶⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠅⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠙⠉⠉⠊⠛⠋⠛⠓⠊⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣏⣫⣿⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠉⠌⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢀⣤⣤⣄⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠹⣻⣿⣿⣿⣿⣦⠀⠀⡴⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣿⢨⡿⣿⣻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣺⣻⣿⣿⣴⣾⣦⣠⠠⠿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⢉⣉⣈⣭⠿⠀⠉⣋⣽⡆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠿⠿⠻⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠂⠀⠒⠲⠰⠀⠁⠰⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢈⣀⣷⣠⣀⣀⡤⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠄⢀⡀⠀⠀⣐⣂⡀⢻⣿⣿⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢁⠙⢱⣤⣵⣾⣿⣿⣿⣿⣤⣭⣽⣿⣿⣶⣦⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢹⣷⣷⣴⣿⡜⢻⣿⣛⣛⣛⡻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣿⣏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢻⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⡿⣥⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣊⠁⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠁⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡉⠻⢿⣿⢻⣿⣍⣽⣟⣗⣂⣿⣿⣿⣿⣿⡿⠟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠀⠀⠀⠀⠀⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠿⣶⡶⣲⣤⢩⣤⣀⣀⡈⠁⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡋⠀⠉⠉⠉⠉⠁⠀⠀⢠⣄⠀⠀⠀⠀⠙⢣⣝⣿⣻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠁⠀⠀⣀⠀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢹⣿⣶⣶⣶⣾⣾⣿⣷⢶⣶⣾⣿⣦⠀⣀⣤⣤⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⢋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣥⣼⣿⣿⣧⠀⠀⠀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢳⠉⡝⠛⢛⢿⡏⡀⠀⣴⣿⣿⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢞⣶⢗⡘⣉⣤⣦⣥⡄⢾⣿⣿⡇⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⢸⣆⣜⠸⡿⠫⠀⠀⢹⣿⣿⣏⣿⣿⣿⣷⣀⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⢪⣿⣟⢀⡄⢀⠀⠀⢺⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⢦⣾⣿⣿⣿⣖⡚⠀⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⠈⠈⠉⠀⠙⠋⠝⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣟⣛⣿⣯⣽⣯⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢉⠁⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡦⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⣿⣿⣿⣿⣿⡦⠀⠀⠅⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣿⢪⡽⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡗⣶⣟⣿⣿⣿⣬⣤⣧⢤⠤⠿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠁⠀⠁⠈⣉⣉⣈⣭⡽⠄⠈⣚⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣽⣷⣾⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠀⠀⠀⠂⠰⠰⠀⠀⠀⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⢀⣤⣄⣄⣀⣀⣀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣶⣆⠀⡄⢀⡀⢀⠀⣘⣓⣂⡹⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠈⣉⣥⣶⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⠀⢁⠉⢠⣤⣴⣾⣿⣿⣿⣿⣦⣉⣹⣿⣿⣶⣦⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢹⣷⣿⣴⣿⡝⢻⣿⣛⣛⣛⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⣷⣿⣿⣿⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢹⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣊⠁⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣿⡗⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠙⠿⣿⢻⣿⣍⣽⣟⣗⣀⣿⣿⣿⣿⣿⡿⠛⠿⠿⢿⣿⡏⣿⡇⣽⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠑⠀⠀⠀⠀⠀⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢩⣤⣀⣀⡈⠁⠙⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⢿⣿⣿⣿⣼⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⡟⠀⠙⠋⠉⠉⣉⣀⣆⢰⣦⡀⠀⠀⠀⠙⢣⣝⣿⡻⠿⢿⣿⣾⣿⡇⣿⢣⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠂⡀⡀⡀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢩⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣀⣤⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢋⣛⡛⠃⠿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣼⣿⣿⣿⠀⠀⠀⣀⡀⠀⣤⣤⣤⣤⡅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⠉⡽⠛⣛⣿⡅⠀⠀⢤⣿⣿⡄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢞⣾⢇⡜⣯⣵⣴⣧⡄⢻⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⢘⣆⣜⠀⠿⢿⠉⠀⣸⣿⣿⣗⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠁⢈⣾⣽⢐⡄⠈⠁⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣷⣶⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣦⣯⣾⣿⣾⣂⠚⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠙⠓⠈⠀⠛⠋⠙⠟⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣾⣿⣟⣏⣻⣯⣽⣯⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠉⠈⠀⠄⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⣤⣄⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⡧⠀⠀⠀⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⢇⣽⠿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⣜⣮⣿⣿⣿⣯⣤⣭⠠⠤⠾⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠁⠀⣉⣉⣀⣯⡽⠆⠈⣓⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠒⠰⠠⠆⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡂⣰⣄⣄⡀⢀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢴⣶⣆⠀⡄⢀⡀⣀⠀⣀⣓⡂⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⢁⠚⢠⣄⣴⣶⣿⣿⣿⣏⣅⣍⣯⣿⣿⣶⣦⣄⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢹⣷⣷⣴⣿⡝⢻⣿⣛⣛⣛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣿⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢹⣿⣿⣿⣇⣨⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣊⠁⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡯⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡻⢻⣽⣛⣛⣻⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠈⠉⠻⢫⣿⣍⣽⣟⣗⣀⣿⣿⣿⣿⣿⣿⠟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣼⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢨⣤⣀⣀⡈⠁⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⢿⣿⣿⣿⣿⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡟⠀⠙⠉⠙⠉⢉⣁⣲⣲⣶⣅⠀⠀⠀⠙⢃⣝⣻⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠂⣀⢀⡀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠉⣽⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⡤⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⠋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣥⣤⣼⣿⣿⣿⡀⠀⠀⢀⣀⠀⣠⣤⣤⣤⡅⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⠉⡝⠛⡛⢻⡝⠀⠀⢠⣼⣿⡇⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢞⣾⢧⠘⣽⣥⣾⣧⡄⢸⣿⣿⣇⢽⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⢸⣆⣜⠀⡿⠟⠃⠁⢸⣿⣿⣟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⢊⣾⣿⠀⡅⠀⠀⠀⢸⣿⣿⣷⣽⣿⣿⣿⣿⣿⣶⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢷⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣦⣮⣿⣿⣿⣂⠚⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠃⠀⠛⠉⠝⠛⠟⠾⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣸⣿⣏⣟⣻⣯⣽⣭⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠉⡍⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⢄⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣧⠀⠀⡠⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⡇⣭⢿⣟⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣷⣿⣿⣿⣟⣬⣯⠆⠴⠷⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠁⠀⠀⠀⣉⣉⣀⣯⡽⠶⠈⢑⣫⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣽⣿⢗⣿⣶⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠒⠰⠀⠆⠀⠀⢴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⣠⣆⣀⣀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⡄⢀⡀⢀⠀⣀⣳⣂⡸⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠈⣠⣤⣾⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢈⠘⣡⣄⣥⣶⣿⣿⣿⣿⣷⣍⣙⣿⣿⣿⣮⣤⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢹⣷⣷⣴⣿⡜⢻⣿⣛⣛⣛⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠻⣿⣿⣿⣇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣊⠁⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⣿⣿⣿⢿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠛⢿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣾⡿⢻⣼⣛⣛⣻⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡉⠉⠻⢻⣿⣍⣽⣟⣗⣀⣿⣿⣿⣿⣿⣿⢟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣼⣿⣿⣿⣿⢿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢨⣤⣀⣀⡈⠀⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⢿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⡟⠁⠈⠉⠉⠉⠉⣁⣲⣰⣶⣭⡄⠀⠀⠙⠃⢙⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠐⣀⣀⣀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣹⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡀⢠⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⢋⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣤⣼⣿⣿⣿⠀⠀⠀⠀⣀⠀⣠⣤⣤⣤⡌⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⠉⡝⠛⢛⠻⠭⡀⠀⢠⣾⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢚⣾⢇⠘⣿⣽⣶⣧⡄⢸⣿⣿⡇⢺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⢘⣆⣜⠀⣿⠿⠋⠀⢘⣿⣿⣿⢾⣿⣿⣿⣷⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠃⢈⠾⣿⢂⡅⢀⠁⠀⢨⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⡆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⣤⣮⣾⣿⣿⣂⡺⠈⢷⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠈⠈⠛⠀⠀⠛⠋⠽⠛⠫⠽⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣼⣿⡟⣟⣛⣿⣽⣭⣽⣷⡿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠉⡈⠁⠄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣤⣄⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⣄⣱⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⡦⠈⠀⡦⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⡏⣨⡿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣵⣿⣿⣿⣽⣤⣬⠠⠴⠿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠉⣈⣀⣫⣽⠧⠄⢑⣫⣿⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⡿⠿⠿⣿⣯⣿⣿⣷⣽⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣵⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠰⠈⠖⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣘⢰⣤⣀⣀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⡄⢀⡀⣀⢀⣀⣱⣂⡘⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢈⠘⢣⣄⣥⣶⣿⣿⣿⣟⣽⣭⣙⣿⣿⣶⣦⣤⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢹⣷⣷⣴⣷⡝⢻⣿⣛⣛⣛⡻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣧⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣎⠁⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⢿⣿⣿⣽⣿⡗⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣼⣟⣟⣻⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠙⠿⢫⣿⣍⣭⣟⣟⣂⣿⣿⣿⣿⣿⣿⠛⠿⠿⢿⣿⡏⣿⡇⣽⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣼⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠿⣶⡶⣲⣤⢨⣤⣀⣀⡈⠁⠙⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⣿⣿⣿⣾⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡏⠁⠈⠉⠉⠉⠉⣉⣠⣠⣦⣯⡌⠀⠀⠙⠃⢙⣿⡻⠿⢿⣿⣾⣿⡇⣿⢣⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠉⠀⠐⣀⣀⣰⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢹⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢠⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⢛⣛⡛⠃⠿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣥⣬⣴⣿⣿⣿⠄⠀⠀⢀⣀⠀⣠⣤⣤⣤⡍⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⠉⡝⢻⡛⣻⣭⠁⠀⠀⣾⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢹⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢚⣞⢧⠘⣽⣵⣶⣷⠄⢘⣿⣿⣧⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⢘⣆⣜⠀⡿⠻⡇⠀⢐⣿⣿⣿⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠃⢊⢾⣷⡀⡕⠀⠀⠁⢈⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣦⣮⣿⣿⣿⣒⡺⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠀⠋⠀⠀⠛⠋⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⡞⢽⣛⣭⣿⣭⣭⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠉⠈⠁⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⣄⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢈⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⡀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣟⣨⡿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣴⣿⣿⣿⣮⣤⣮⠠⠤⠷⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⣉⣁⣀⣨⣭⠷⠀⢑⣪⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⠿⠿⢻⣯⣿⣿⣿⣽⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣵⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠂⠰⠠⠶⠀⠀⢰⣿⣿⣿⣿⠔⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⣑⢸⣦⣀⣀⠀⢀⢀⣿⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⠀⡄⢀⡀⢀⠀⣀⣹⣂⡈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢈⠘⢡⣄⣧⣶⣿⣿⣿⣿⣧⣍⣙⣽⣿⣷⣶⣤⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢹⣷⣷⣴⣷⡜⢻⣿⣛⣛⣛⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣿⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡛⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣎⠅⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⢿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣚⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⡿⣿⣼⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⢿⢫⣿⣍⣭⣟⣟⣂⣿⣿⣿⣿⣿⣿⠛⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣴⣿⣿⣿⣿⣿⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢨⣤⣀⣀⡈⠁⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠿⡿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠉⠉⠉⠉⢁⣉⣠⣦⣯⣍⠀⠀⠙⠃⠙⣻⠻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠐⣀⣀⣠⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢩⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⢠⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣎⠛⣛⡛⠃⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣭⣤⣤⣿⣿⣿⡄⠀⠀⠀⣀⡀⢠⣤⣤⣤⡌⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⠉⡝⢻⠛⡻⣿⠀⠀⠀⣼⣿⡇⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢞⣖⢧⡸⣿⣵⣶⣷⡆⢈⣿⣿⣿⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⢘⣄⣜⠀⡿⠛⡁⠀⢀⣿⣿⣿⢺⣿⣿⣿⣷⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠃⢊⢾⣿⠂⡔⠀⠀⠀⢀⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⢾⣤⣦⣿⣿⣿⣒⡚⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠙⠛⠉⠛⠛⠛⠿⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⡏⣝⣛⣿⣾⣭⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠉⠈⠁⠅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣤⣄⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢧⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢈⡽⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡴⠴⠾⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⣉⣉⣀⣨⣭⠿⠆⠙⣺⣽⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠰⠈⠶⠀⠀⢰⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⢄⠊⠉⣈⢭⣥⣀⣀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠀⡄⠀⡀⢀⠀⣀⣹⣒⡈⣿⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣵⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢈⠘⢡⣀⣤⣶⣿⣿⣿⣿⣿⣍⣙⣽⣿⣷⣶⣤⣀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢹⣷⣷⣴⣷⡝⢻⣿⣛⣛⣛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣷⣿⣿⣾⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣞⣾⠅⠝⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⢿⣿⣿⣽⣿⡿⣿⣟⣾⣷⣿⣿⣿⣿⣿⣿⣴⣛⣒⢈⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣾⣿⣟⣻⣿⡿⣿⣿⣿⢿⣷⣾⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⢻⡿⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⢿⣿⣍⣭⣟⣟⣷⣿⣿⣿⣿⣿⣿⢟⠿⠿⢿⣿⡟⣿⡇⣽⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣴⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣿⣿⠏⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⢸⡿⣾⣿⣿⣿⣿⣿⢹⣿⠷⣶⡶⣲⣤⢨⣤⣀⣀⡈⠁⠙⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠿⠿⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠉⢀⠀⠀⣶⣯⣅⠀⠀⠙⠃⠙⣿⡻⠿⢿⣿⣾⣿⡇⣿⢧⣿⣿⣼⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 2804

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

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✐ Why_You_Shouldn’t_Use_SteamOS,_a_Really_Incompetent_GNU/Linux_Distribution
With_Security_Pitfalls_(Lutris_is_a_Great_Alternative)⠀✐


Posted in GNU/Linux at 4:20 am by Guest Editorial Team


Guest post by Ryan, reprinted with permission from the_original


It was bowling night on Wednesday, and between frames, I was reading about
SteamOS.


Michael Larabel on Phoronix and plenty of others have blogged about it over the
years, and Richard_Stallman_gave_some_vague_opinions_about_relativistic_harms
vs._good_that_it_may_do_for_the_Free_Software_community.


While I don’t think there’s anything wrong with proprietary games, in
particular, one of the issues I do have with them is DRM, or Digital “Rights”
Management. A better name for this is Digital Restrictions Management, or just
“digital handcuffs”.


The industry has tried it on everything from movies, music, video games, and
books, but it never stops people from attacking it and eventually winning. On a
good day, DRM flakes out and causes problems for people who went and paid for a
licensed copy of the program, on a bad day, it makes what they’ve “purchased”
completely unusable and worthless.


It also causes perfectly good TVs to malfunction because you tried to plug them
into your computer to watch Amazon Prime Video or something, and instead it
tells you the screen doesn’t support the latest HDCP DRM version.


In another example, when Borderlands 3 released with that horrible DRM that ran
in a virtual machine and caused the game to chug along and crash, and finally
(after it was pirated), the publisher removed that form of DRM. Or when
Microsoft’s Activation servers occasionally glitch and start telling the user
they’re running “counterfeit Windows”.


When a person pays for something, and then gets this, it’s not just an insult,
it’s an outrage.


But there are some people, like the fools who used iTunes, and then spent years
having Apple telling them how and when and where they could use their music
files, then finally could PAY THEM AGAIN for a clean copy, and THEN had Apple
delete all of their files without asking and tell them to subscribe for $12.99
a month to Apple music.


These fools may or may never learn that DRM is, at a fundamental level, just a
way to cheat them out of their money over and over again.


It sucks to be them, but we shouldn’t join them just because a computer seems
“easy to use” or “pretty to look at”. I mentioned earlier, we can make Free
Software easy to use and pretty to look at too.


All of these issues aside, Valve, the company that makes Steam, also made
“SteamOS”, which is a GNU/Linux distribution pitched as “really optimized for
gaming”.


However, when you look at what Reddit users say about it, you quickly find
complaints that Valve has committed the horrendous security practice of logging
in everyone as the same “user”, meaning even if you have different passwords,
it’s really the same Linux account, and none of your files or browsing history
or anything is off limits.


You’re all using this same account, which is bad for privacy, and you end up
stepping on each other’s toes due to the organizational mess.


They’ve essentially re-invented Windows 98’s concept of “users” for some
godforsaken reason.


Moving right along, we see that Valve also sometimes goes more than a year and
a half without even patching it for security issues. Nothing wrong with using
an OS that hasn’t gotten a security patch in 18 months, right?


Then they complain that while it includes the proprietary Nvidia drivers,
they’re usually much older than the ones you could install yourself if you have
an Nvidia card and some other GNU/Linux distribution, and due to the
unpredictable releases and long periods without any patching, the open source
AMD and Intel drivers which are bundled with the OS in every GNU/Linux distro
have fallen far behind and may not be up to the task of running current
software or hardware.


Then what really made me go “OMGWTF” was when Valve switched the underlying
system away from Debian (because $@%@ stability, I guess?) and towards Arch
Linux. I still don’t know if they release security updates or not, but it was
at this point where I just became completely disinterested in SteamOS. Even for
amusement.


But the list of reasons why you shouldn’t use Steam OS isn’t just that Valve
designs shitty software that doesn’t give a damn about your Freedom or your
security, it’s that there’s a million ways to get things done and this is a
classic example of “If you want something done right, do it yourself!”.


These days, it’s not particularly hard to install and configure a GNU/Linux
system like Debian or Mageia or the others.


Even if you want to install Steam, it’s not like it’s a “SteamOS” exclusive.
There is a Debian package, and a Flatpak.


But what I’ve recently taken a liking to is Lutris, it has concepts like
“Runners” and makes installing video games from all kinds of sources (and
classic consoles) a breeze.


It’s not _just_ Wine that Lutris makes dead simple to use, either, but my
favorite feature is definitely that it can configure and manage games and other
programs in Wine for you, without you having to worry about mucking up settings
and trying to figure out DLL overrides to make things like DXVK or VKD3D work.


In my Debian 11, I’ve been having a lot of fun playing games when before it was
more of a pain in the ass trying to set up Wine in order to do something the
right way. In fact, the biggest trouble I’ve had out of a game lately, and I
blogged about it, was Fallout New Vegas crashing all of the time, and the NVSE/
New Vegas Anti Crash mods are something you’d need to screw around with on
Windows as well.


While Steam is proprietary software under a proprietary license which brings in
tons of crap and garbage and still often doesn’t work right, Lutris is licensed
under the GNU GPLv3.


I’ve installed the latest version for Debian according to the Lutris
instructionsand paired_it_with_the_Wine_Development_Branch_for_my_“System
Wine”, which is currently sitting at 6.19 as of the time I’m writing this.


Every two weeks, WineHQ pushes the latest version into my copy of Debian and I
get all of their latest improvements.


But how did SteamOS go so wrong?


Well, it’s not hard to imagine why, for me at least. Gabe Newell is a former
Microsoft employee, and everyone there had nothing but Windows development
experience when they ported Steam over, and that almost never ends well because
they take an attitude of “Whatever gets it working now, just toss it in there.”
that they learned from Windows, and well, gross.


Then they decided to do an entire GNU/Linux distribution.


Luckily, their Wine fork, Proton, ends up seeing most of the genuine
improvements code reviewed and then merged back into Wine itself.


Years ago, we had a different problem. Wine had been licensed under the MIT X11
license, which is basically one of those “Do whatever the hell you want with
it.” ones. A company called “Transgaming” came along and forked it and made
“Cedega” for GNU/Linux, and “Cider” for the Apple Mac.


When the Wine project realized that they had made a huge mistake and that this
hostile closed fork was competing with them, Wine changed its license to the
LGPL v2.1 going forward. Then, Transgaming’s days were numbered. They no longer
had any Wine code to swipe, so they did a “go it alone” version of Direct3D and
some other things.


For a short while, it worked better than upstream Wine did, but eventually they
couldn’t keep up and went out of business.


If Wine was still under the MIT license, Proton would have been another Cedega/
Cider. But since it’s copyleft, we get to benefit from any improvements Valve
makes. And like I’ve pointed out before, we don’t particularly need any Valve
software on our computers.


There are other companies that have treated their customers better over the
years, such as Gog.com, and they’re supported in Lutris.


In closing, if you like gaming on GNU/Linux and don’t want to tear your hair
out, avoid Valve entirely if you can, or at least ignore “Steam(ing Pile)OS”
and install a real GNU/Linux distribution, for crying out loud.


The security mess alone reminds me of Linspire, years ago (original company,
under Michael Robertson) saying it logged everyone in as root because security
would confuse Windows users, and Hans Reiser’s new file system would have ACLs
that made UNIX permissions obsolete soon anyway.


I tried to reach out to Mr. Reiser to see how that’s coming along, but he’s
still really really in prison in California for murdering his wife with a
knife. █



                    ䷩ 𝚕𝚒𝚗𝚎 3030

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/16/the-reign-in-spain/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/16/the-reign-in-spain/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.16.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Reign_in_Spain⠀✐


Posted in Europe, Patents at 7:38 am by Dr. Roy Schestowitz


Video_download_link | md5sum d45db422598047eafa235edcbc2acdf9


http://techrights.org/videos/spain-epo-role.webm


Summary: Discussion about the role of Spain in the EPO‘s autocratic regime
which violates the rights of EPO staff, including Spanish workers


LAST night we published this thirteenth_part of the series, this time dealing
with Spain, a close neighbour of Benoît_Battistelli‘s home country. António
Campinos is Spain’s neighbour on both sides, as he’s both French and
Portuguese.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Patricia García-Escudero and Benoît Battistelli⦈ Spain may
not be so (in)famous for corruption, but what we find in its patent system is a
pattern of nepotism and inappropriate political appointments, placing focus on
party loyalty rather than suitable qualifications.


Tonight at around midnight (i.e. the usual) we shall publish the next part in
the series, this time dealing with Portugal. █


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


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⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢣⡛⠿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣛⣒⣨⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣿⠿⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⢀⣀⣀⡀⣀⣀⢀⣀⢀⡀⣀⢀⣠⣄⢀⣠⣁⡅⠀⣄⣂⣀⢠⡕⣶⣤⣠⡄⢤⣿⣷⡟⣿⣛⣪⡚⣿⢟⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⠿
⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣷⡆⠀⠀⠀⠀⠸⣿⣟⢻⣿⣽⣧⣿⣿⢸⣿⣾⡇⣿⠸⣿⣟⢻⣿⣿⡇⠃⣿⣿⣿⣾⡇⣿⣯⣿⡇⢸⣿⣿⡇⣿⣭⣿⣷⣿⢸⣿⠿⢿⣿⣽⣿⣿⣿⣿⣿⡿⣿⠿⣓⡝⠳⣾⠄⡈⡉⠀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⣾⣿⢿⣿⠡⢸⣿⣿⣿⣿⣿⡇⣿⢰⣾⣿⢿⣿⣿⡇⠀⣿⣿⣿⣿⡇⣿⣟⣿⣧⡼⣿⣿⢇⣿⣤⣿⡿⣿⢸⣿⣿⢿⣿⣼⢿⣿⣿⣯⣾⣯⣴⣿⣥⣘⠁⠈⠻⡇⠐⠉
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢁⠀⢀⣀⡀⠀⠀⣀⡀⠤⠤⠤⠤⠬⢵⠶⢶⠶⢶⡿⣶⣶⠶⡶⣶⣶⣾⣲⣶⣲⣾⣷⣷⣶⢖⠖⣲⣶⢶⣾⣷⣷⣶⣲⡟⡛⠟⡙⢉⡋⠫⣏⠉⠉⠉⠉⠉⠉⠳⠁
⡀⠀⠀⠀⠀⠀⠹⠟⡯⢿⠏⠄⠀⠀⠀⠀⠀⠰⠺⠢⠷⠋⠁⠡⠞⠀⠠⠀⠀⠀⠀⠐⢁⣎⣁⣞⣋⣿⣷⣵⣯⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣦⣵⣾⣽⣿⣿⣿⣷⠶⡄⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⢀⣈⠈⠊⠐⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣔⣖⣀⣲⣸⣧⣋⣡⣉⣛⣉⣝⣯⣫⣙⣿⣙⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣷⣾⣽⣍⠈⠁⣀⢀⠀⡈⢀⠈⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⣀⣤
⡇⠀⠀⠀⠀⠀⠋⠁⠀⠼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠉⢽⣭⣭⣭⡿⣽⣿⡿⣽⣿⢍⡙⡋⡋⢽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⠷⠄⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣤⣔⣦⣰⣿⣿
⣷⣆⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡂⠀⠀⠆⠀⢉⠃⠹⠿⢽⣿⣟⡋⣻⠿⣩⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣷⣦⣴⣥⣾⣗⣷⣾⣦⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠀⠀⡠⠀⠀⢒⣶⡦⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⠛⠟⠟⠛⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠄⠐⠀⠰⣲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⣿⣿⣿⡄⠁⣷⠀⢿⣿⣿⡟⠁⠀⢄⣀⡦⠄⠀⠤⠄⣀⠀⢸⣿⣿⣿⣿⡏⠀⠈⢽⣿⣿⣿⣿⡇⠀⠀⡄⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢟⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⣍⣹⠛⠃⠄⢉⣶⣬⣏⡾⣧⢔⡤⢸⡉⢧⢴⡂⣶⣶⢻⣴⣾⣿⣿⣿⣿⢴⣂⣰⣼⣿⣿⡿⢻⣥⠀⣆⡔⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿
⣯⣤⠄⠀⠀⠀⣀⠀⣤⠀⠀⢃⠀⠌⠀⠁⠂⡤⠀⠑⠘⠁⠀⢡⡐⠋⢿⡜⣀⡿⣮⣿⣿⣿⣿⣿⣿⣿⢟⣫⣿⣮⣿⣿⣿⣿⠟⠆⠀⢻⣟⡌⣁⣈⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣉⠁⠀⣂⣻⣿⣿
⢛⠀⠀⠋⠒⠂⠆⠒⣁⠀⠀⠀⣁⠐⢶⣷⡆⡀⠀⠀⠀⠀⢣⣼⣶⠘⣼⣷⣦⣾⣿⣿⡿⠟⣿⡍⠈⠉⠈⠚⣽⢿⢿⣿⣿⠁⠀⡇⠀⢹⡛⢁⠻⠶⣤⡦⡀⠘⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⣴⡀⣀⡀⠀⠁⠠⠊⠁⠃⠠⡀⠻⣵⣬⣿⣶⣦⣬⣉⠀⠱⣾⡿⢿⣷⢺⡿⠟⣿⢿⠉⠁⢠⣽⠀⠠⢠⣠⣐⠃⠀⠻⠿⢽⡀⠀⠃⠀⠂⠾⠟⣹⡂⢉⣝⣃⣦⣐⠠⠍⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠛⠃⠘⠃⠀⠀⣤⠀⠘⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡿⢿⡷⣿⡯⣴⣶⣧⠀⠀⢦⣿⣿⣟⠿⠿⣥⣄⣀⣠⣤⣼⣉⣱⠈⠀⠀⠀⠶⠟⠌⠇⣻⣟⡟⣻⡟⠀⡀⣀⠤⣀⣟⣿⣿⣿⣿⣿⣿⣿⢟⣗⣾⣿⣿⣿
⣘⣁⣤⡤⣴⣜⠓⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠛⢃⣽⡞⣀⠀⠈⠻⡯⠀⠀⣼⣍⣉⠞⣧⠴⣲⠶⠾⠋⢻⣿⠷⠛⠇⠀⠀⠐⠱⣼⢢⣤⣈⣊⠀⡀⠁⣽⣿⣿⣾⢭⡏⢆⡩⠙⠿⡛⠻⣾⣿⣿⣿⣿⣿⣿
⠉⠁⠀⣀⣘⢣⣀⣀⠠⠜⣶⣖⣲⣶⣻⡿⠿⢿⠟⠁⠙⠀⠙⠛⠛⠋⠀⠀⠀⠳⠀⠐⣿⣿⣿⣿⣿⣿⣿⣷⣶⢷⢀⣽⡉⠻⢆⠀⠀⠠⢠⣴⣾⣿⢿⡿⠑⠫⠭⣭⡍⠝⢷⣿⣿⣿⣿⣆⣠⣿⣿⣿⣽⣿⣿⣿⣿⣿
⣶⣿⣿⡿⠇⢤⡏⠀⠁⣠⣭⣭⡤⠯⡿⣇⣦⣶⡎⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣴⣄⣃⣀⣀⣀⣾⣿⣿⣿⣿⠊⣤⣥⣭⠀⠀⠀⠀⠀⠘⠟⠋⠙⡃⠤⠙⠛⢚⠜⠦⠠⠈⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿
⣷⣿⣿⣿⣷⣿⣷⢤⣰⣿⡏⠁⠀⠀⠁⠏⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡈⠁⠀⠨⣿⣿⣿⣿⣿⡏⢽⠝⢫⣿⣿⣿⡇⠀⠀⠀⢀⠀⠱⡄⠀⠈⢿⣷⣶⣿⣿⣖⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠂⢙⢻⣁⣀⢻⣿
⣿⣿⣿⣿⣿⡿⠧⠀⠛⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⠏⣴⣼⣿⣷⣶⡶⠀⣿⣿⣿⣿⣿⣷⣆⠀⠉⢉⡀⠈⠀⠀⠀⠀⠀⠀⠀⢳⠉⣍⣉⡉⡉⠋⠛⠛⠛⠛⠉⠙⢿⡿⠿⠿⣿⣿⣋⣈⡈⠉⠛⠘⠉
⡿⠏⢹⠘⠁⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣿⣟⣿⣿⣿⣿⠏⠀⠀⢛⣻⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣽⣿⣿⣿⣖⡖⠀⠀⠀⠀⠀⣼⠫⠛⢽⠿⢿⣿⣿⣷⠄⠈⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠳⠿⠿⠿⠿⠟⠶⠤⠄⠀⠃⢫⣾⣿⣾⡷⣶⠤⠄⠄⠘⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⢠⣿⣿⣦⢳⠀⠑⠈⠙⠻⠿⠗⠒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢈⡹⣿⢿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢸⡿⣿⣿⣯⡿⠧⠸⠇⠠⠤⢩⣭⣿⣟⣛⣛⣛⣿⣟⠛⠛⠛⠛⠓⠀⠀⠀⠿⠆⠀⠀⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢻⠷⣾⣷⣮⣴⡟⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⠀⢀⠀⡃⢉⠉⠠⠀⠀⠀⠀⠀⠀⡒⣿⣿⣿⣿⣟⠟⠙⢃⣩⢾⣿⣿⣿⣿⣿⣿⣦⣶⣦⡀⢠⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡸⣽⣿⣶⣦⣼⣿⣿⢟⠋⠈⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠇⡘⣾⣴⣿⣴⣸⣷⠆⠀⠀⠀⠀⡮⠋⢨⠿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣟⣟⢻⣿⣿⣿⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣀⣀⣈⣛⣃⣈⣁⣀⣀⢤⣂⣵⣿⣧⣷⢹⡀⠏⠽⡿⣿⢿⠸⠻⠟⣂⠪⢿⠀⠃⠀⣈⢪⣿⣿⣿⣿⣿⣯⣛⠛⢿⢛⠚⠛⠛⠻⠛⠛⣗⣮⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠙⠛⠙⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣻⣟⣛⣉⣁⣿⣿⢿⢸⡇⣴⣿⣯⣿⠀⠀⠈⠀⠀⠀⠀⠀⠘⠘⠚⣾⠈⢛⣿⣿⣿⣿⣿⣧⣀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢀⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⣿⣿⡿⠟⠟⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3135

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

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Gemini_version_available_♊︎


✐ Links_16/10/2021:_SparkyLinux_Turns_10_and_Sculpt_OS_21.10⠀✐


Posted in News_Roundup at 3:41 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Is_Linux_a_Waste_of_Time_and_Should_You_Stick_to_Windows?⠀⇛


                       But Linux is not bad just because it’s different.
                       Far from being a waste of time, Linux can be one of
                       the most rewarding operating systems to learn,
                       because once you gain knowledge about how it works,
                       that knowledge lasts for a long time.


                       No one company has the authority to substantially
                       change how all of Linux works from one release to
                       the next. So if you want a computer you can learn
                       and stick with for a long time to come, Linux can
                       be more than worth the investment of your time.


          o § Server⠀➾


                # ⚓ Announcing_Istio_1.11.4⠀⇛


                       This release contains bug fixes to improve
                       robustness. This release note describes what’s
                       different between Istio 1.11.3 and Istio 1.11.4


          o § Audiocasts/Shows⠀➾


                # ⚓ Video_Editing_with_Linux:_How_to_Get_the_Most_Out_of
                  Kdenlive⠀⇛


                       Next in our video editing series for the Librem 14,
                       Gardiner Bryant digs into tuning Kdenlive’s
                       performance and editing high-resolution video.
                       Kdenlive is a multiplatform freedom-respecting and
                       open source video editing solution. This video will
                       also help those who use Kdenlive on any other
                       hardware.


                # ⚓ Linux_From_Scratch_–_You’re_Gonna_Make_Me_COOMPILE!!_–
                  Invidious⠀⇛


                       Last time we made a good amount of progress through
                       LFS and this week we’re going to have some very
                       exciting content get ready for 3 hours of compiling
                       code


                # ⚓ Ubuntu_Budgie_21.10_Quick_overview_#Shorts_–_Invidious⠀⇛


                       A Quick overview of Ubuntu Budgie 21.10.


                # ⚓ The_Worst_Ubuntu_Release_In_Years_(21.10)_–_Invidious⠀⇛


                       Ubuntu 21.10 was just released so I thought I would
                       take it for a quick spin. I’ve always been a big
                       fan of Ubuntu. It was the first desktop Linux
                       distribution that I used when I switched away from
                       Windows, so it has a special place in my heart.


          o § Kernel Space⠀➾


                # ⚓ Developers_finally_get_Linux_running_on_an_Apple_M1-powered
                  Mac [Ed: Another older one]⠀⇛


                       This is a big deal because Apple uses a bunch of
                       proprietary tech that doesn’t play nice with you if
                       you’re trying to run an operating system that isn’t
                       macOS on one of its computers. Some adventurous
                       developers have been trying ways to open up Apple’s
                       closed M1 ecosystem for a while now, and Asahi
                       Linux might have just cracked the code.


                       The M1 is Apple’s custom Arm-based SoC (system on
                       chips) started showing on Macs in 2020 after
                       ditching Intel’s x86 silicon chip. The M1 is the
                       most powerful chip Apple’s ever made, so you can
                       imagine why some folks might want to run Linux and,
                       let’s say, install Proton, which would turn their
                       Mac into a killer gaming PC.


                # ⚓ Realtek_802.11ax_WiFi_Driver_“rtw89″_Queued_Ahead_Of_Linux
                  5.16_–_Phoronix⠀⇛


                       Arriving in the wireless-drivers-next branch this
                       week is the “rtw89″ driver as a Realtek-contributed
                       open-source 802.11ax WiFi driver.


                       This new rtw89 Linux Wifi driver is initially for
                       supporting the Realtek 8852AE 802.11ax ASIC. A new
                       driver was developed rather than extending the
                       existing Realtek wireless kernel drivers since the
                       register address ranges have been totally refined,
                       new formats, and other fundamental changes over
                       existing Realtek wireless chipsets.


                # ⚓ SALSA_Back_In_Development_As_A_Small_ALSA_Library_For_Linux
                  Systems_–_Phoronix⠀⇛


                       Linux sound subsystem maintainer Takashi Iwai of
                       SUSE is back to hacking on SALSA, the “small ALSA”
                       library that he started a decade ago but hadn’t
                       seen a new release in six years or any code
                       activity for the past four years… until this week.


          o § Applications⠀➾


                # ⚓ 7_Best_Free_Linux_Desktop_Search_Engines⠀⇛


                       Desktop search is a software application which
                       searches the contents of computer files, rather
                       than searching the internet. The purpose of this
                       software is to enable the user to locate
                       information on their computer. Typically, this data
                       includes emails, chat logs, documents, contact
                       lists, graphics files, as well as multimedia files
                       including video and audio.


                       Searching a hard disk can be painfully slow,
                       especially bearing in mind the large storage
                       capacities of modern hard disks. To ensure
                       considerably better performance, desktop search
                       engines build and maintain an index database.
                       Populating this database is a system intensive
                       activity. Consequently, desktop search engines will
                       carry out indexing when the computer is not being
                       used.


                       


                # ⚓ The_5_Best_Remote_Desktop_Clients_for_Linux⠀⇛


                       Do you want to control a computer you don’t have
                       physical access to? Perhaps you’re assisting a non-
                       technical friend with their computer over voice
                       call and want better control over their system.


                       The solution to all these problems is a remote
                       desktop client. On Linux, you can find a plethora
                       of free and open-source remote desktop apps that
                       allow you to establish connections and access a
                       remote computer efficiently. But which one works
                       the best and has superior functionalities to the
                       rest? Let’s find out.


          o § Instructionals/Technical⠀➾


                # ⚓ Steps_To_Install_Rocky_Linux-8.4_With_Screenshots_|
                  LinuxTeck⠀⇛


                       Rocky Linux is a Community-based Enterprise
                       Operating System, officially released by Rocky
                       Enterprise Software Foundation (RESF) which is a
                       free support platform with a complete binary-
                       compatible release using the Red Hat Enterprise
                       Linux (RHEL) operating system source code. The
                       advantage of Rocky Linux is that it is completely
                       free to install on any 64-bit x86 and ARM64
                       (aarch64) system.


                # ⚓ Tips_to_be_more_efficient_in_a_Linux_Terminal_–_ByteXD⠀⇛


                       The life of Linux users became a lot easier with
                       the advent of X Environments (Graphical User
                       Interfaces). Many tasks can now be performed very
                       quickly in these environments using simple clicks.


                       Does this mean that there is no need for a command-
                       line interface anymore or to remember text commands
                       and their parameters?


                       No, the terminal is the bread & butter of any Linux
                       user worth his salt.


                       In this tutorial, you will learn a few tips and
                       tricks to work efficiently with Linux commands.


                # ⚓ Hardware_profiling_for_kernel_module_loading⠀⇛


                       EasyOS, when on a portable media such as a USB-
                       stick, can be booted on different computers. For
                       this to work, Easy needs to remember any settings
                       for the particular hardware being booted on,
                       especially for video and audio.


                # ⚓ Install_and_Set-up_ELK_Code_Physics_Software_on_Ubuntu [Ed:
                  New update]⠀⇛


                # ⚓ Vulnerable_docker_environment_for_learning_to_hack
                  ⠀⇛


                # ⚓ ThinkPad_P15v_Gen1,_Xorg_and_a_Samsung_QHD_Display⠀⇛


                       Wasted quite some hours until I found a working
                       Modeline in this stack exchange post so the
                       ThinkPad works with a HDMI attached Samsung QHD
                       display.


                # ⚓ Data_center_admins:_Learn_how_to_run_a_basic_vulnerability
                  scan_on_your_Linux_servers_with_Nessus⠀⇛


                       Make sure the Linux servers in your data center are
                       free from vulnerabilities by scanning them
                       immediately using Nessus.


                # ⚓ Case_files_of_a_TSE:_Would_you_have_the_time?⠀⇛


                       This is the first part of a series that attempts to
                       showcase the kind of work that SUSE Support does
                       and how we help customers resolve issues when
                       running SUSE Products. The cases that are selected
                       will be based on real cases. However, all details
                       will be fully anonymized and stripped of
                       identifying marks.


                       This is a case where the time from when I took it
                       to when it was resolved happened to be about half
                       an hour. Being half an hour late might not mean a
                       lot to some people, but computer systems are much
                       more sensitive to time and need it to be accurate
                       and synchronized. That’s why it’s crucial to have a
                       solid NTP (Network Time Protocol) infrastructure.
                       This case shows how important attention to detail
                       can be when troubleshooting a system.


                # ⚓ Looking_at_the_outlying_data_points⠀⇛


                       The solution was great: they came up with something
                       that looked like a server for airflow purposes, but
                       which didn’t actually do anything. It was basically
                       two very big paperboard pizza boxes side by side.
                       They would then slip that into the rack right below
                       the last server, or any time they pulled one from
                       somewhere higher in the stack. This would keep the
                       airflow doing its thing happily for whatever was
                       right above it.


                       This rolled out and my hot spots disappeared.
                       Fantastic!


                # ⚓ How_To_Install_OpenBoard_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       OpenBoard on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, OpenBoard is an open-source cross-
                       platform teaching software for interactive
                       whiteboards designed primarily for use in schools
                       and universities. It is so rich in terms of
                       features that it even allows you to record live
                       sessions with audio while making use of the
                       whiteboard. Other than that, you are even allowed
                       to import files to be displayed on your whiteboard
                       while it is shared with different viewers.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the OpenBoard open source cross-
                       platform teaching software on Ubuntu 20.04 (Focal
                       Fossa). You can follow the same instructions for
                       Ubuntu 18.04, 16.04, and any other Debian-based
                       distribution like Linux Mint.


                # ⚓ How_to_configure_SSH_to_use_a_non-standard_port_with
                  SELinux_set_to_enforcing_–_TechRepublic⠀⇛


                       Switching the SSH listening port is an easy way to
                       help secure remote login on your Linux servers. But
                       when SELinux is involved, you have to take a few
                       extra steps. Jack Wallen shows you how.


                       [...]


                       On Linux distributions that don’t use SELinux, this
                       process is quite easy. However, if SELinux is
                       involved, you can’t simply change the port, without
                       letting the security system in on your little
                       secret.


                       And that’s exactly what I’m going to do here,
                       configure Fedora 35 to use port 33000 for incoming
                       SSH traffic. This same process will work on any
                       Linux distribution that uses SELinux (such as RHEL,
                       Alma Linux and Rocky Linux).


                # ⚓ How_to_Extract_(Unzip)_Tar_Gz_File_in_Linux_–_ByteXD⠀⇛


                       In this article, we will explain how to extract a
                       tar.gz file using the tar command.


                       Tar is an abbreviation for tape archive, and it is
                       one of the most commonly used commands for dealing
                       with compressed archive files.


                       Gz is an abbreviation for gunzip. It is a
                       particular compression algorithm. Most Linux
                       distributions have the tar command pre-installed.
                       The tar program compresses and extracts files using
                       various methods.


                       Tar supports a broad range of compression methods,
                       including gzip, bzip2, xz, lzip, and others.


                # ⚓ How_to_Install_KDE_Plasma_Desktop_on_Fedora_35_–
                  LinuxCapable⠀⇛


                       The name KDE comes from “K Desktop Environment”.
                       For those not familiar with KDE Desktop, it is a
                       free, open-source desktop environment. It provides
                       Linux users on various distributions an alternative
                       graphical interface to customize their desktop
                       environment and applications for everyday use
                       enhancement.


                       In Fedora’s case, this is Gnome. Besides the
                       graphical enhancements and changes, it is also a
                       lightweight, fast, smooth environment with superior
                       performance compared to native shipped desktops
                       with some Linux Distributions. However, with Fedora
                       35 having the latest Gnome 41, the choice will come
                       down to personal preference overall.


                       At the end of the tutorial, you will have learned
                       how to install KDE Desktop Environment on your
                       Fedora 35 system.


                # ⚓ How_to_Install_MATE_Desktop_1.26_on_Ubuntu_21.10_Impish
                  Indri_–_LinuxCapable⠀⇛


                       For those not familiar with MATE Desktop
                       Environment, it is the continuation of GNOME 2. It
                       is famous for being lightweight, fast, and stable
                       that runs on Linux and most BSD operating systems.
                       MATE is also an excellent choice for a lower-end
                       system or those looking to remain efficient on
                       system resources. Also, a dedicated Ubuntu MATE
                       edition exists for this desktop environment,
                       enticing users to switch from Ubuntu altogether.


                       In Ubuntu 21.10 Impish Indri, MATE desktop 1.26 is
                       the default version that brings Wayland support
                       extension, which reaches applications in the
                       environment such as ATRIL, System Monitor, Pluma
                       Text Editor, and Terminal Emulator amongst the top
                       changes. For a complete list of changes, visit the
                       changelog wiki.


                       In the following tutorial, you will have learned
                       how to install MATE Desktop 1.26 on your Ubuntu
                       21.10 operating system.


                # ⚓ Export_Logs_to_a_File_with_Journalctl_–_Putorius⠀⇛


                       For old hats like me journalctl seems unnecessarily
                       complicated. Back in the olden days (just a few
                       years ago) system and service logs were all kept in
                       files. It was quite easy to grep through these
                       files for information you wanted. Of course
                       journalctl has similar functionality built in, but
                       old habits die hard. So let’s take a look at how to
                       export logs to a file with journalctl.


                       There are many reasons why someone might wants to
                       export logs. Maybe you are an old hat like me and
                       just prefer to manipulate logs from a simple text
                       file. Or maybe you want import the logs into a
                       different program, or use a custom Python log
                       aggregator?


                       If you are new to journalctl I recommend first
                       reading Viewing Logs with Journalctl. It contains a
                       bunch of great information that can also be used
                       when exporting logs to a file.


                # ⚓ How_to_Install_or_Enable_Cockpit_on_AlmaLinux_8_–
                  LinuxCapable⠀⇛


                       Cockpit is a free remote server manager that is
                       lightweight and easy to use for GNU/Linux servers.
                       Cockpit is a web-based graphical interface for
                       servers intended for people new to Linux to the
                       experts such as sysadmins. Cockpit makes Linux
                       discoverable, allowing anyone using the software to
                       perform tasks such as start containers, administer
                       storage, configure networks, and inspect logs.


                       In the following tutorial, you will learn how to
                       install Cockpit on your AlmaLinux 8 system.


                # ⚓ How_to_install_Snap_on_your_Raspberry_Pi_–_Anto_./_Online⠀⇛


                       Follow this guide if you want all the benefits
                       Snaps has to offer. This guide will show you how to
                       install Snap on your Raspberry Pi.


                # ⚓ How_to_install_WPS_Office_2019_on_a_Chromebook_in_2021⠀⇛


                       Today we are looking at how to install WPS Office
                       2019 on a Chromebook and some core fonts like Arial
                       and New Times Roman. Please follow the video/audio
                       guide as a tutorial where we explain the process
                       step by step and use the commands below.


                # ⚓ How_to_install_and_set_up_Gitlab_CE_Server_on_Centos_8⠀⇛


                       GitLab allows you to host an on-premise Git
                       repository that can be accessed from either your
                       local LAN or (if you have an available public IP
                       address) from outside your company. GitLab is an
                       open-source repository manager based on Rails
                       developed by GitLab Inc. It is a web-based git
                       repository manager that allows your team to
                       collaborate on coding, testing, and deploying
                       applications. GitLab provides several features,
                       including wikis, issue tracking, code reviews, and
                       activity feeds.


                       In this guide, we will install the GitLab CE on the
                       CentOS 8 server. We will install the GitLab CE
                       using the ‘omnibus’ package provided by GitLab.


                # ⚓ Integrate_Gitlab_with_OpenLDAP_for_Authentication⠀⇛


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ KDE_Plasma_23_Overview_and_Where_To_Download⠀⇛


                             Congratulations to KDE community, KDE Plasma
                             5.23 has been released at Wednesday, 14
                             October 2021 celebrating the 25th KDE
                             Anniversary! This overview highlights several
                             of its new features and informs you where to
                             download and how to try Plasma quickly on
                             your own computer. Let’s try it together!


                      # ⚓ This_week_in_KDE:_Plasma_25th_anniversary_edition_is
                        released!⠀⇛


                             But after you read this post, I bet you’ll
                             want to jump straight to Plasma 5.24 already!
                             A lot of good keyboard navigation and
                             Discover-related work was done this week, as
                             well as loads of bugfixes.


                             Keep in mind that this blog only covers the
                             tip of the iceberg! Tons of KDE apps whose
                             development I don’t have time to follow
                             aren’t represented here, and I also don’t
                             mention backend refactoring, improved test
                             coverage, and other changes that are
                             generally not user-facing. If you’re hungry
                             for more, check out https://planet.kde.org/,
                             where you can find blog posts by other KDE
                             contributors detailing the work they’re
                             doing.


                      # ⚓ KDE’s_Plasma_Wayland_Session_Continues_Seeing_More
                        Crash_Fixes⠀⇛


                             This week marked the release of Plasma 5.23
                             in celebrating 25 years of the KDE desktop
                             project while celebrations didn’t last long
                             with developers already hard at work on the
                             Plasma 5.23.1 point release, feature work for
                             Plasma 5.24, and also improvements to the KDE
                             Applications and KDE Frameworks.


                             KDE developer Nate Graham is out this morning
                             with his usual weekly development summary.
                             This week continued seeing a lot of crash
                             fixes and other fixes landing, particularly
                             around the Plasma Wayland experience that has
                             been seeing plenty of work almost weekly.


                      # ⚓ Blasting_bugs_and_passing_reviews_—_Kalendar_devlog
                        19⠀⇛


                             Last Sunday, we received our first round of
                             feedback for KDE Review (thanks Albert!) and
                             have spent this week addressing the issues
                             brought up there. These were mainly
                             technical, but we also had some useful UI
                             feedback which we have taken on board and
                             addressed (and are included in this update
                             post).


                             You can follow the KDE Review process for
                             Kalendar on the mailing list, or keep tuning
                             in to the weekly updates, where we will let
                             you know how things are going.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ How_to_disable_Gtk-Message_warnings_in_your_app⠀⇛


          o § Distributions⠀➾


                # ⚓ Best_Linux_distros_for_Windows_users_in_2021⠀⇛


                       It can be an inundating experience, especially for
                       people coming from proprietary operating systems
                       like Windows. Linux distributions, thanks to their
                       open source nature, offer a lot more access than
                       their closed source cousins, which makes the
                       transition particularly difficult for many users.


                       This is where these specialized distros, designed
                       for Windows users, come into the picture. Their
                       objective is to allow users to experience the
                       goodness of Linux while minimizing the learning
                       curve that’s associated when switching to a
                       different operating system. They all take various
                       steps to ensure that the transition is as
                       effortless as possible.


                # ⚓ How_to_Stop_Distro-Hopping_and_Find_the_Perfect_Linux
                  Distro_for_Yourself⠀⇛


                       Do you ever find yourself stuck in the never-ending
                       loop of switching between multiple Linux distros
                       for months? Maybe you want to explore all the
                       available options in search of the best, but with
                       so many distros to try, that seems like an
                       impossible task.


                       Although as fun it is to install and test new
                       operating systems, settling with a feature-rich
                       Linux distro that fits your needs is far better
                       than going on a wild goose chase.


                       Let’s dive deep into distro-hopping, and learn how
                       to put an end to it by finding a perfect Linux
                       distro for yourself.


                # § BSD⠀➾


                      # ⚓ helloSystem,_the_Mac-like_FreeBSD_OS,_Takes_Another
                        Step_Towards_Full_Release⠀⇛


                             Most of you have probably never heard of
                             helloSystem before. The project was started
                             by the creator of AppImage, Simon Peter,
                             early last year. Simon’s goal is to create a
                             “friendly Libre Desktop operating system with
                             focus on simplicity, minimalist elegance, and
                             usability”.


                             Simon takes inspiration from the simpler
                             operating system of the 80s and 90s,
                             specifically early MacOS, specifically System
                             1. If you just look at screenshots of the
                             system in action, you may be tempted to say,
                             “I don’t see what the fuss is all about.
                             There are a bunch of Linux distros or themes
                             that look just like MacOS.”


                             The project goes beyond merely looking like
                             MacOS, it wants to return to a simpler,
                             easier to use design. According to the
                             website, “helloSystem is a desktop system for
                             creators with a focus on simplicity,
                             elegance, and usability. Its design follows
                             the “Less, but better” philosophy. It is
                             intended as a system for “mere mortals”,
                             welcoming to switchers from the Mac.” You can
                             find out more about Simon’s thoughts on what
                             he plans for helloSystem by watching his
                             presentation at FOSDEM 21.


                      # ⚓ [Old] 64-bit_Time_on_OpenBSD⠀⇛


                             Switch time_t, ino_t, clock_t, and struct
                             kevent’s ident and data members to 64bit
                             types. Assign new syscall numbers for (almost
                             all) the syscalls that involve the affected
                             types, including anything with time_t,
                             timeval, itimerval, timespec, rusage, dirent,
                             stat, or kevent arguments. Add a d_off member
                             to struct dirent and replace getdirentries()
                             with getdents(), thus immensely simplifying
                             and accelerating telldir/seekdir. Build perl
                             with -DBIG_TIME.


                             Bump the major on every single base library:
                             the compat bits included here are only good
                             enough to make the transition; the T32 compat
                             option will be burned as soon as we’ve
                             reached the new world are are happy with the
                             snapshots for all architectures.


                # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾


                      # ⚓ MPV_»_PCLinuxOS⠀⇛


                             The MPV video player has been updated to
                             0.33.1 and shipped to the PCLinuxOS Software
                             Repository.


                      # ⚓ Waterfox_classic_browser_»_PCLinuxOS⠀⇛


                             Waterfox classic browser has been updated to
                             2021.10 and shipped to the software
                             repository.


                      # ⚓ Pidgin_»_PCLinuxOS⠀⇛


                             The Pidgin chat client has been updated to
                             2.14.8 and shipped to the software
                             repository.


                # § Debian Family⠀➾


                      # ⚓ 10_years_of_SparkyLinux!⠀⇛


                             Exactly 10 years ago, in October 2011, we
                             started a work with a new Linux distribution,
                             and on November 4, 2011 the first beta of our
                             system released.


                             A bit of history:


                             Initially, our project began to live under
                             the name ue17r as Ubuntu Enlightenment17
                             Remix and was a modification of Xubuntu
                             Linux, from which the standard desktop was
                             removed and replaced by Enlightenment 17.


                      # ⚓ Puppy_and_EasyOS_used_in_physics_lab⠀⇛


                             Stuart is a professor at Lyon College,
                             Arkansas, USA (lyon.edu). He has been using
                             Puppy Linux, Precise Puppy, until recently,
                             and is now using EasyOS 3.0.


                             Stuart is ‘phdzaps’ in the old Puppy Forum,
                             posts back around 2011 – 2013. He has kept me
                             updated via emails since 2018, about progress
                             with using Puppy in a laboratory.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Ubuntu_22.04_LTS_Codename_Is_“Jammy_Jellyfish”⠀⇛


                             The codename for Ubuntu 22.04 LTS has been
                             finalized and the codename for the Ubuntu
                             22.04 LTS is ‘Jammy Jellyfish’. Ubuntu 22.04
                             LTS is due for release in April 2022 and it
                             is the next long-term support release of
                             Ubuntu.


                      # ⚓ Ubuntu_Web_Remix_20.04.3_Released_with_/e/_on
                        WayDroid_and_Linux_Kernel_5.11⠀⇛


                             Remember Ubuntu Web? It was first announced
                             last year in November as an alternative to
                             Chrome OS or Chromium OS. It’s an unofficial
                             Ubuntu flavor created by Rudra Saraswat, the
                             maintainer of Ubuntu Unity, offering Web
                             Apps, Android apps, and support for apps from
                             the de-Googled /e/ Foundation.


                             While it has an emphasis on Web Apps, Ubuntu
                             Web Remix looks and feel like a real GNU/
                             Linux distribution that you can easily put on
                             your desktop or laptop computer. It features
                             the GNOME desktop environment by default, but
                             with a minimal set of native Linux apps pre-
                             installed.


                      # ⚓ Ubuntu_21.10_Released_–_gHacks_Tech_News⠀⇛


                             The next version of Ubuntu, 21.10 “Impish
                             Indri” has been released, with nine months of
                             support since it is not an LTS release.


                             This version of Ubuntu comes with some new
                             features, and some great performance, at
                             least on my system.


                             [...]


                             Ubuntu 21.20 brings new multitouch gestures,
                             available when using Wayland, by default. As
                             well, 21.10 now has a persistent trahs can
                             icon in its dock, rather than a desktop icon,
                             which makes for a nicer workflow option.
                             Also, speaking of Wayland, NVIDIA users can
                             now use Wayland when using the proprietary
                             drivers.


                             The latest version of Pipewire is included
                             with this Ubuntu install, making a variety of
                             tools and applications such as screensharing
                             applications function better with Wayland.
                             Wayland is finally starting to really shine,
                             compared to the buggy mess it had been over
                             the past years.


                      # ⚓ Ubuntu_21.10_“Impish_Indri”_Available_To_Download⠀⇛


                             After 6 months of development, Ubuntu 21.10
                             codenamed “Impish Indri” is now available for
                             download. Ubuntu 21.10, a short-term support
                             release, improves on its predecessor Ubuntu
                             21.04 by including an updated desktop
                             environment, applications, and several bug
                             fixes.


                             Ubuntu 21.10 “Impish Indri” Released – What’s
                             New in Ubuntu 21.10?


                             Six months after the release of Ubuntu 21.04,
                             Ubuntu has released another short-term
                             version, Ubuntu 21.10. This is a short-time
                             release that will only be supported for 9
                             months, until July 2022, and is recommended
                             for desktop users who want to stay ahead of
                             the competition. The majority of the packages
                             in this version have been updated to their
                             most recent versions, including Gnome, the
                             default desktop environment.


                      # ⚓ Linux_distribution_Ubuntu_21.10_with_Gnome_40_and
                        Firefox_as_snap_package⠀⇛


                             Ubuntu 10/21 “Impish Indri” is generally
                             available as of Thursday, Thursday. The new
                             edition of the popular Linux distribution
                             provides the Linux kernel 5.13 to support the
                             next Intel and AMD CPUs, raises LibreOffice
                             to version 7.2.1 and presents Gnome 40 with
                             the ported, Ubuntu-typical extensions in the
                             main edition. For LUKS2-encrypted
                             installations, the Ubiquity installer now
                             offers to create and save a recovery key
                             during installation. A notable but
                             controversial change is the packaging of the
                             Firefox browser, which is preinstalled in all
                             official Ubuntu variants: Firefox is now
                             available as a snap package in the main Gnome
                             edition.


                             Ubuntu 21.10 follows the solid, semi-annual
                             release cycle of the distribution. It is the
                             last edition with nine months of support
                             until the next Ubuntu version with long-term
                             support in April next year. As in the
                             previous editions, Ubuntu 21.10 delivers the
                             last major changes before the consolidation
                             of the features for the upcoming LTS version
                             begins. Ubuntu 22.04 LTS is planned for April
                             2022.


                      # ⚓ Ubuntu_21.10_in_server_practice:_all_important_new
                        features_explained⠀⇛


                             Several rituals have established themselves
                             with great regularity in the past IT decade.
                             Only recently, version 24 of the free cloud
                             environment OpenStack, which Canonical patron
                             Mark Shuttleworth once made the standard
                             cloud in Ubuntu and thus gave the project a
                             powerful boost, was released on schedule. And
                             because OpenStack and Ubuntu are still very
                             closely linked, experienced system
                             administrators know: Where a new OpenStack
                             version appears, a new Ubuntu release cannot
                             be far away. Canonical released Ubuntu 21.10
                             recently, as planned, in mid-October.


                             Even if you prefer the LTS version, you
                             should already look into the new features of
                             the server: Most of them will also be found
                             in Ubuntu 22.04, the upcoming LTS version.


                      # ⚓ OpenStack_Xena_for_Ubuntu_21.10_and_Ubuntu_20.04
                        LTS⠀⇛


                             The Ubuntu OpenStack team at Canonical is
                             pleased to announce the general
                             availability of OpenStack Xena on Ubuntu
                             21.10 (Impish Indri) and Ubuntu
                             20.04 LTS (Focal Fossa) via the Ubuntu Cloud
                             Archive. Details of the Xena
                             release can be found at: https://
                             www.openstack.org/software/xena


          o § Devices/Embedded⠀➾


                # ⚓ You_Can_Use_Raspberry_Pi_400_As_a_PC_Keyboard_and_Mouse
                  Combo⠀⇛


                       If you’re a fan of Pimoroni, you’re probably
                       familiar with its software lead Phil Howard (aka
                       Gadgetoid) and his developments in the Raspberry Pi
                       community. Today we’re sharing an awesome project
                       he put together using our favorite keyboard PC, the
                       Raspberry Pi 400.


                       Using the right cable and a bit of code, the
                       Raspberry Pi 400 can function as a regular, USB HID
                       keyboard. The best Raspberry Pi projects are easy
                       to recreate and the only accessory you need to pull
                       this project off is a USB Type-C to USB Type-
                       A cable.


                # ⚓ Alibaba_T-head_RVB-ICE_dual-core_RISC-V_SBC_supports
                  Android_10,_Debian_11_–_CNX_Software⠀⇛


                       The very first RISC-V single board computer with a
                       3D GPU reveals itself with “Alibaba T-head RVB-ICE”
                       SBC available for pre-order for $399 together with
                       a 7-inch display. The board is based on Alibaba T-
                       Head “ICE” dual-core XuanTie C910 RISC-V processor
                       with a Vivante GC8000UL GPU, and follows the
                       announcement of Android 10 being ported to a RISC-
                       V board earlier this year.


                       Besides the dual-core RISC-V processor clocked at
                       1.2 GHz, the board is equipped with 4GB LPDDR4,
                       16GB eMMC flash, and offers Gigabit Ethernet, WiFi
                       and Bluetooth connectivity, as well as a 48-pin
                       GPIO header. But it lacks HDMI output, relying on
                       an LCD interface instead, as well as full-size
                       (Type-A) USB ports with only one micro USB 3.0 OTG
                       port, and a USB-C port for serial console.


                # ⚓ PCIe_adapter_adds_four_USB_3.2_ports_to_Raspberry_Pi_CM4_IO
                  board⠀⇛


                       Waveshare has introduced a non-standard PCIe
                       adapter that adds four USB 3.2 ports to the
                       Raspberry Pi Compute Module 4 IO carrier board in a
                       way that does not take too much height.


                       It’s non-standard as it can not be inserted
                       directly into a typical computer PCIe slot, and
                       Waveshare recommends a PCIe extension cable to
                       connect it to a motherboard. Having said that It
                       looks much better on the IO board.


                # ⚓ Raspberry_Pi_4,_Rockchip_RK3399_SBC’s_get_Arm_SystemReady
                  IR_certification⠀⇛


                       The first hardware platforms getting Arm
                       SystemReady IR certification for IoT Edge
                       applications were announced a few months ago with
                       namely NXP i.MX 8 Mini evaluation kit and Compulab
                       IOT-GATE-IMX8 gateway being able to run off-the-
                       shelf operating system images such as Fedora IoT,
                       OpenSuSE Leap 15.3, and Debian 11 thanks to UEFI
                       firmware.


                # ⚓ OAK-D_Depth_Sensing_AI_Camera_Gets_Smaller_and_Lighter⠀⇛


                       The OAK-D is an open-source, full-color depth
                       sensing camera with embedded AI capabilities, and
                       there is now a crowdfunding campaign for a newer,
                       lighter version called the OAK-D Lite. The new
                       model does everything the previous one could do,
                       combining machine vision with stereo depth sensing
                       and an ability to run highly complex image
                       processing tasks all on-board, freeing the host
                       from any of the overhead involved.


                       [...]


                       Since the vision processing is all done on-board,
                       even a Raspberry Pi Zero can be used effectively as
                       a host.


                # ⚓ Single_board_computer_features_AMD_processors_and
                  graphics⠀⇛


                       The IB952 offers hardware-based security and high-
                       speed peripheral support.


                # ⚓ The_Pi_400_As_A_PC_Peripheral_|_Hackaday⠀⇛


                       The Raspberry Pi 400 all-in-one computer is a neat
                       little unit that is powerful enough to take on most
                       humdrum computing tasks while doing an excellent
                       job of freeing up valuable desktop space. But what
                       about those moments when both the Pi and a PC are
                       needed on the same desktop? How can the Pi and the
                       bulky PC keyboard share the same space?


                       [Gadgetoid] may have the answer, with a clever bit
                       of software that presents the Pi’s mouse and
                       keyboard as peripherals on its USB-C power port. If
                       your PC has a high-power USB socket that can run
                       the Pi then it can use the small computer’s input
                       devices just as well as the Pi itself can. It’s
                       fair to say that the Pi 400’s keyboard is not it’s
                       strongest point, but we can see some utility in the
                       idea.


                # ⚓ Simply_NUC®_Launches_Cypress_Long-Life_Mini_PC_Powered_by
                  Latest_AMD®_Ryzen™_Embedded_Processors⠀⇛


                       Offering a variety of operating systems, Cypress
                       can support custom needs on Windows 10, Ubuntu, and
                       Fedora.


                # ⚓ Simply_NUC®_Launches_Cypress_Long-Life_Mini_PC_Powered_by
                  Latest_AMD®_Ryzen™_Embedded_Processors⠀⇛


                # § Open Hardware/Modding⠀➾


                      # ⚓ This_wizard-themed_book_nook_diorama_features_a_face
                        detection_system,_LEDs,_and_an_ePaper_display_|_Arduino
                        Blog⠀⇛


                             The fantastical world of wizards and magic is
                             one that can be explored by reading a book,
                             and what better way to represent this than
                             building your very own interactive diorama
                             within a reading corner? Well, that is
                             exactly what Andy of element14 Presents
                             created when he combined a small display,
                             computer vision, and LED lights into a fun
                             bookshelf adornment, which would accompany
                             readers on their journeys.


                             To begin, Andy had to figure out how to get a
                             computer vision system into a space that is
                             no larger than a shoebox, and for this task,
                             he settled on using the Portenta H7 board
                             plus its Vision Shield to gather images and
                             classify them. His attempts to integrate a
                             string of NeoPixels and an ePaper display
                             module with MicroPython were unsuccessful, so
                             this required a switch to only using C with
                             TensorFlow Lite and some custom functions to
                             take the framebuffers from the camera and
                             determine if a face is present.


                      # ⚓ PocketView_is_an_LED_display_that_shows_info_through
                        clothes_and_other_fabrics_|_Arduino_Blog⠀⇛


                             hen receiving a notification on your phone,
                             it can be a tedious process to take the
                             device out of a pocket, unlock the screen,
                             and then read the message. In order to make
                             viewing simple information much faster,
                             University of Waterloo researchers developed
                             a small pocketable display that can shine
                             images and text through fabric. This means
                             seeing the current time or directions can be
                             done far more quickly since all the user has
                             to do is look down.


                             The technology driving this system consists
                             of an Arduino Pro Mini board, an HC-05
                             Bluetooth module for receiving data from a
                             host phone, an 8×8 RGBW NeoPixel matrix, and
                             a single 420mAh LiPo battery cell for power.
                             All of these components were assembled into a
                             single unit and placed within a 3D-printed
                             enclosure that can easily fit into the user’s
                             pocket.


                      # ⚓ Ecodesign_Directive:_FSFE_calls_for_Device_Neutrality
                        and_Upcycling_of_Software⠀⇛


                             As contribution to the revisal of the EU
                             ecodesign directive and to help understand
                             the impact of software obsolescence, the FSFE
                             publishes a study on the sustainability of
                             software. The findings of the study culminate
                             in five core demands for a more sustainable
                             digitisation, covering the interplay of
                             devices, software, and infrastructure.


                             In the European Union we currently see a
                             strong desire to make digitisation more
                             sustainable with the European Commission
                             aiming at making products more resource-
                             efficient as well as circular economy methods
                             applicable. The ecodesign directive from 2009
                             shall be updated in this regard with the
                             “Sustainable Products Initiative” (SPI) that
                             aims “to make products placed on the EU
                             market more sustainable”. The SPI will then
                             serve as the main European product policy
                             instrument, in the electronic sector
                             additionally complemented by the “Circular
                             Electronics Initiative” (CEI).


                      # ⚓ Sousaphone_sound-reactive_lights⠀⇛


                             It is just a Teensy 4.0 I had lying around,
                             together with an audio board, a basic lav
                             mic, and a spare 74XX245 from my grab bag
                             held together with hot glue and proto wire.
                             It drives a cheapo 300 LED RGB strip that is
                             VHB’d to the bell. I think the LEDs will only
                             last a few more transport sessions, but with
                             any luck I’ll make a slightly more polished
                             revision with better longevity in the not too
                             distant future.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ The_Best_New_Android_Games_This_Week_–_Botworld
                        Adventure,_Tesla_Force,_Kitty_Q_and_More_–_Droid
                        Gamers⠀⇛


                      # ⚓ Oxygen_OS_12:_Hands-on_the_new_features_in_OnePlus’
                        Android_12_update⠀⇛


                      # ⚓ Sony_China_collaborates_with_Meizu_to_provide_a_new
                        version_of_Android_to_its_customers_–_NotebookCheck.net
                        News⠀⇛


                      # ⚓ Weekly_poll_results:_Android_12_loved_for_its_looks
                        more_than_its_features_–_GSMArena.com_news⠀⇛


                      # ⚓ Oxford_Study:_iPhone_App_Privacy_Not_Superior_to
                        Android,_Equal_Amounts_of_User_Tracking_Seen_on_Both
                        Platforms_–_CPO_Magazine⠀⇛


                      # ⚓ Best_contact_widgets_for_Android_–_Phandroid⠀⇛


                      # ⚓ Best_Android_app_deals_of_the_day:_Botanicula,
                        CHUCHEL,_more_–_9to5Toys⠀⇛


                      # ⚓ Best_Bookmark_Manager_Apps_For_Android_2021_|
                        Organize_Your_Links_Using_Them_|_Tech_Times⠀⇛


                      # ⚓ How_to_enable_the_iOS-style_Google_Photos_memory
                        widget_on_Android_|_Android_Central⠀⇛


                      # ⚓ Study_Warns_Android_Phones_From_Samsung,_Xiaomi_And
                        Others_Are_Spying_On_Users_|_HotHardware⠀⇛


                      # ⚓ OnePlus_Co-Founder_Might_Release_A_New_Android_Phone
                        In_2022⠀⇛


                      # ⚓ This_is_the_Android_12_Widget_I_Really_Want_Google_to
                        Make⠀⇛


                      # ⚓ Realme_3_Pro_receives_Android_11-based_Realme_UI_2.0
                        update⠀⇛


                      # ⚓ Android_Circuit:_Galaxy_S22_Ultra_First_Look,
                        Mysterious_Pixel_Pass_Details,_OnePlus_9RT_Launched⠀⇛


                      # ⚓ Google_Maps_widget_for_Android_launched,_will_be
                        available_to_all_users_gradually:_Report⠀⇛


                      # ⚓ Introduced_PinePhone_Pro_Linux_Smartphone,_shipped
                        with_KDE_Plasma_Mobile⠀⇛


                             Community Pine64, engaged in the creation of
                             open devices, presented smartphone PinePhone
                             Pro , the preparation of which was taken into
                             account the experience of the production of
                             the first model PinePhone and customer
                             feedback. The main goal of the project has
                             not changed, and the PinePhone Pro continues
                             to be positioned as a device for enthusiasts
                             who are tired of Android and iOS and want a
                             completely controlled and secure environment
                             based on alternative open Linux platforms.


                      # ⚓ PINEPHONE_PRO_ANNOUNCED!_Specs_and_Features!_–
                        Kockatoo_Tube⠀⇛


                      # ⚓ Pine64_Announces_Updated_PinePhone_Pro_Linux_Powered
                        Cellphone_–_Slashdot⠀⇛


                             Pine64 today announced its latest Linux-
                             powered device, the PinePhone Pro, an update
                             to the original PinePhone which sees a more
                             powerful device running mainline Linux
                             (Manjaro in this case) on a mobile device
                             that works as a cellphone and a desktop
                             computer.


                      # ⚓ PinePhone_Pro_|_PINE64⠀⇛


                      # ⚓ PinePhone_Pro_Linux_Smartphone_is_Now_Available_for
                        Pre-order⠀⇛


                             The PinePhone Pro costs $399 and is designed
                             to be user repairable. The spare parts will
                             be sold through the Pine Store.


                             The PINE64, the hardcore nerds behind Linux-
                             powered hardware, has just announced the
                             PinePhone Pro. It seems that the PINE64 has
                             decided to offer a more premium device this
                             time around.


                             On the other hand, Pine64 is making it very
                             clear this smartphone is not for everyone.


                      # ⚓ The_5_Best_Linux_Smartphones_of_2021_–_Linux_on_the
                        Go⠀⇛


                             Today our data is becoming vulnerable each
                             day. This is attributed to how some operating
                             systems are not giving enough attention to
                             privacy or malware, phishing, and viruses
                             which with time are becoming powerful.


                             We need to opt for OS which provides the most
                             privacy features and you know that all of the
                             base, backend, and source code is open
                             source. This is why we have recommended some
                             of the best Linux smartphones that you can
                             choose.


          o § Free, Libre, and Open Source Software⠀➾


                # ⚓ Sculpt_OS_release_21.10⠀⇛


                       At the first glance, the just released Sculpt 21.10
                       looks and feels nearly identical to the time-tested
                       previous version 21.03. However, a look at the
                       installable packages reveals a firework of exciting
                       new features.


                       First and technically most exciting, the new
                       version enables the use of hardware-accelerated
                       graphics on Intel GPUs, paving the ground for
                       graphics-intensive applications and games. The GPU
                       support is based on the combination of the Mesa
                       library stack with our custom GPU multiplexer as
                       featured in Genode 21.08. Note that this fresh new
                       feature should best be regarded as experimental and
                       be used with caution.


                # ⚓ Genode-Based_Sculpt_OS_21.10_Adds_Intel_GPU_Acceleration,
                  USB_Web_Camera_Support_–_Phoronix⠀⇛


                       On Thursday in addition to the releases of Ubuntu
                       21.10 (plus its derivatives) and OpenBSD 7.0, the
                       Genode OS Framework based Sculpt OS saw its 21.10
                       release.


                       Sculpt OS continues to serve as a general purpose
                       operating system built off the Genode OS Framework
                       as an original, open-source operating system
                       platform.


                # § Events⠀➾


                      # ⚓ It’s_Safety_First_as_‘All_Things_Open’_Returns_In-
                        Person_on_Sunday_–_FOSS_Force⠀⇛


                             On Sunday when All Thing’s Open kicks off at
                             the Raleigh Convention Center it will mark a
                             return to in-person events for the open
                             source conference. Like most in-person
                             events, last year ATO was forced to go
                             digital in the midst of the global COVID-19
                             pandemic.


                             To use a term that tech usually reserves for
                             cloud deployments, this year’s All Things
                             Open will be a hybrid event — meaning it’ll
                             take place as an in-person event at the
                             Raleigh Convention Center in downtown
                             Raleigh, North Carolina, and online for folks
                             at home. Even the presentations will be
                             hybrid, with some being live streamed as they
                             take place before an in-person audience, and
                             others being prerecorded and available only
                             online.


                             We asked Todd Lewis, the creator and chair of
                             the event that in 2019 drew over 5,000
                             attendees, how it felt to be launching the
                             in-person part of this years conference now
                             that vaccinations have made that possible,
                             despite the continuing spread of the COVID
                             virus.


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ Google_clarifies_Spanner/PostgreSQL_interface_•_The
                        Register⠀⇛


                             Google has clarified details of the interface
                             between its popular distributed SQL database-
                             management-cum-storage-service Spanner and
                             the open-source RDBMS PostgreSQL.


                             According to a blog published this week,
                             Spanner’s PostgreSQL interface uses “the
                             familiarity and portability of PostgreSQL” to
                             make developers’ lives easier.


                             “Teams can be assured that the schemas and
                             queries they build against the Spanner
                             PostgreSQL interface can be easily ported to
                             another PostgreSQL environment, giving them
                             flexibility and peace of mind,” said Justin
                             Makeig, product manager for Cloud Spanner.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ Week_numbers_in_LibreOffic_Calc⠀⇛


                             I use week numbers for all sorts of things.
                             It gives me more granularity than a month,
                             and they’re more accurate for certain use
                             cases. For example, people assume a month has
                             four weeks, but 48 leaves us four weeks short
                             of the 52 weeks in a year. Renters and
                             mortgage payers know all to well the fun of
                             realising a specific month has three
                             payments, not two.


                # § SFC⠀➾


                      # ⚓ How_We_Hired_Our_Last_Employee:_Equitable_Hiring
                        Processes_for_Small_(and_Large)_Organizations⠀⇛


                             It’s really hard for Conservancy to hire new
                             employees. Like many small organization that
                             are overloaded with work, it’s hard to make
                             the time to conduct a proper hiring process,
                             and no one on staff is dedicated to making
                             sure the process goes smoothly. Because it is
                             very important to our organizational values
                             to make sure that our hiring is fair and also
                             that we wind up with the best person for the
                             job, we were very careful in how we designed
                             our search.


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ Legacy_Social_Media:_Free_as_in_Beer,_Not_as_in
                              Speech⠀⇛


                            # ⚓ A_first_for_search_and_rescue_from_space⠀⇛


                                   “Once it was confirmed that we could
                                   detect the faint transmissions on-board
                                   I used ‘GNU Radio’ to build the signal
                                   processing system that would run on the
                                   satellite. GNU Radio is a free and
                                   open-source library that breaks down
                                   complex signal processing systems into
                                   simple blocks. The ability to reprogram
                                   the SDR payload for any type of signal
                                   demonstrates the versatility when open-
                                   source software is combined with a
                                   powerful space platform such as OPS-
                                   SAT.”


                      # § Licensing/Legal⠀➾


                            # ⚓ The_Ministry_of_Finance_of_the_Russian
                              Federation_has_developed_an_open_license_–
                              itsfoss.net⠀⇛


                                   In the git repository of the software
                                   complex “Data showcases of the NSUD”,
                                   developed by order of the Ministry of
                                   Digital Development, Communications and
                                   Mass Media of the Russian Federation,
                                   the text of the license entitled “State
                                   open license, version 1.1” was found.
                                   According to the explanatory text, the
                                   rights to the text of the license
                                   belong to the Ministry of Finance. The
                                   license is dated June 25, 2021.


                                   In fact, the license is permissive and
                                   close to the MIT license , but it was
                                   created with an eye on Russian
                                   legislation and is much more verbose.
                                   The terms of the license contain many
                                   clarifications, already following from
                                   the legislation of the Russian
                                   Federation. At the same time, the
                                   license contains controversial points
                                   in terms of definitions. Thus, the
                                   source code is defined as “a computer
                                   program in the form of text in a
                                   programming language that can be read
                                   by a person”, which does not
                                   necessarily imply the possibility of
                                   obtaining executable code from it, and
                                   also that this code is not generated
                                   from the real source code (that is,
                                   code in the preferred form for making
                                   changes).


                            # ⚓ Article_from_Krzysztof_Żok,_Faculty_of_Law_–
                              University_of_Poznań⠀⇛


                                   Krzysztof Żok, Assistant Professor at
                                   the Faculty of Law and Administration
                                   of the Adam Mickiewicz University in
                                   Poznań (Poland), publishes in the
                                   Masaryk University Journal of Law and
                                   Technology (volume 15, winter 2021) a
                                   well-documented article on the EUPL and
                                   in particular on the reference to “a
                                   work or software” as the factor
                                   determining the scope of the licence.


                                   Here are the summary notes that the
                                   author provides in conclusion: [...]


                # § Programming/Development⠀➾


                      # ⚓ How_the_Integrated_Gradients_method_works?_–_Vincent
                        Lequertier’s_blog⠀⇛


                             For artificial intelligence (AI) transparency
                             and to better shape upcoming policies, we
                             need to better understand the AI’s output. In
                             particular, one may want to understand the
                             role attributed to each input. This is hard,
                             because in neural networks input variables
                             don’t have a single weight that could serve
                             as a proxy for determining their importance
                             with regard to the output. Therefore, one
                             have to consider all the neural network’s
                             weights, which may be all interconnected.
                             Here is how Integrated Gradients does this.


                      # ⚓ Want_a_piece_of_GitLab?_It’s_going_to_cost_you:_IPO
                        price_per_share_settles_at_$77⠀⇛


                             The one-stop shop approach by DevOps darling
                             GitLab appears to have attracted an Initial
                             Public Offering price of $77, giving the
                             loss-making biz a potential valuation of
                             $11bn


                             GitLab finally filed for an IPO in September
                             and this week upped the estimated price per
                             share to between $66 and $69. The eventual
                             price has turned out to be $77, well above
                             the initial $55 to $60 first estimated.


                             8.42 million shares of Class A common stock
                             are being sold. Founder and CEO Sytse
                             Sijbrandij is selling another 1.98 million
                             shares, according to the filing. Should that
                             $77 price survive the start of trading today,
                             GitLab’s market value will nudge past $11bn.


                      # ⚓ Functional_vs._object-oriented_programming:_The
                        basics⠀⇛


                             Committing to a programming paradigm is an
                             important step in any application development
                             effort. While they are hardly the only two
                             options when it comes to overarching
                             development models, the choice between
                             functional programming and object-oriented
                             programming is one that an increasing number
                             of developers face today.


                      # ⚓ There_is_no_‘printf’.⠀⇛


                             Pop quiz! What will the following program
                             return?


                      # § Perl/Raku⠀➾


                            # ⚓ Perl_Weekly_Challenge_134:_Pandigital_Numbers
                              and_Distinct_Term_Count⠀⇛


                      # § Python⠀➾


                            # ⚓ Malicious_packages_mitmproxy2_and_mitmproxy-
                              iframe_removed_from_PyPI_directory_–
                              itsfoss.net⠀⇛


                                   The author of mitmproxy , a tool for
                                   analyzing HTTP / HTTPS traffic, drew
                                   attention to the appearance of a fork
                                   of his project in the Python Package
                                   Index (PyPI) directory. The fork was
                                   distributed under the similar name
                                   mitmproxy2 and the non-existent version
                                   8.0.1 (current release of mitmproxy
                                   7.0.4) with the expectation that
                                   inattentive users will perceive the
                                   package as a new version of the main
                                   project ( typesquatting ) and wish to
                                   try the new version.


                                   In terms of its composition, mitmproxy2
                                   was similar to mitmproxy, with the
                                   exception of changes in the
                                   implementation of malicious
                                   functionality. The changes were reduced
                                   to the termination of setting the HTTP
                                   header ” X-Frame-Options: DENY “, which
                                   prohibits the processing of content
                                   inside the iframe, disabling protection
                                   against XSRF attacks and setting the
                                   headers ” Access-Control-Allow-Origin:
                                   * “, ” Access-Control- Allow-Headers: *
                                   “and” Access-Control-Allow-Methods:
                                   POST, GET, DELETE, OPTIONS “.


                      # § Shell/Bash/Zsh/Ksh⠀➾


                            # ⚓ Sourcing_vs_executing_in_Bash⠀⇛


                                   What if, from the shell prompt, I could
                                   source the script, to bring the
                                   function definitions into my current
                                   environment, and then manually invoke
                                   the check function on a single pull
                                   request?


                                   Sourcing the script as it is would have
                                   the unwanted effect of running checks
                                   on all the pull requests, because the
                                   last line in the script actually
                                   invokes main, as it’s supposed to.


                      # § Rust⠀➾


                            # ⚓ Rust-Based_Cloud-Hypervisor_19.0_Released_With
                              Improved_Live_Migration,_Faster_Boot_Time_–
                              Phoronix⠀⇛


                                   Cloud-Hypervisor 19.0 debuted this week
                                   as the Intel-led open-source VMM
                                   focused on supporting modern cloud
                                   workloads and written in the Rust
                                   programming language while leveraging
                                   the Linux’s KVM virtualization code or
                                   the Microsoft MSHV hypervisor on
                                   Windows.


                                   Cloud-Hypervisor 19.0 continues to
                                   focus on only supporting 64-bit
                                   software, providing a minimal attack
                                   surface and other security improvements
                                   in part by leveraging Rust, and other
                                   modern-focused design principals.


                            # ⚓ Dyn_async_traits,_part_6⠀⇛


                                   A quick update to my last post: first,
                                   a better way to do what I was trying to
                                   do, and second, a sketch of the crate
                                   I’d like to see for experimental
                                   purposes.


    * § Leftovers⠀➾


          o ⚓ An_Entangled_History:_Christianity_Faces_Off_With_The
            Enlightenment⠀⇛


                 As the doyen of historians of the Enlightenment, Peter
                 Gay (The Party of Humanity: essays in the French
                 revolution [1964]), reminds us: “The stakes in the attack
                 on Christian theology were higher than the fate of
                 theology itself: to discredit Christianity was to take a
                 decisive step in the direction of a secular, modern
                 civilization” (p. 46). But during the time of this great
                 shaking—from the scientific revolution of the sixteenth
                 and seventeenth centuries to the Enlightenment era of the
                 eighteenth—Christian churches, both Catholic and
                 Protestant, did not simply wake up one morning and crown
                 Reason as their new Lord and Redeemer. Nor did Christian
                 thinkers simply reject the Enlightenment teachings and
                 new rational sensibilities.


                 In France, for instance, a virulent anti-philosophe
                 movement—a kind of counter-enlightenment—was spearheaded
                 by the Roman Catholic Church (McMahon, Enemies of the
                 Enlightenment: the French Counter-Enlightenment and the
                 Making of Modernity [2001]). McMahon tells us a story
                 seldom told by Enlightenment scholars. “There is no more
                 religion in France. All is lost!” cried out Joseph-
                 Laurent Gilbert at one of Voltaire’s plays. This cry of
                 fear from the anguished heart captures something of the
                 rage militant clergy, enlightened aristocrats, Sorbonne
                 censors and ordinary others watched in horror during the
                 Reign of Terror of 1793-1794 when blood-soaked
                 revolutionaries sought to sweep away all traces of
                 royalist, Christian France. They destroyed churches and
                 desecrated sanctuaries, plundered altars, forced priests
                 and nuns to marry.


          o ⚓ Another_Shit_Storm_in_Berkeley⠀⇛


                 “I don’t think the toilet was meant intentionally to be
                 malicious, though it amounts to that,” Neumann told me.
                 He added, “If I hadn’t heard about it I think it would
                 have gone through. The city is focused on toilets, not on
                 murals.”


                 Lord knows, the city desperately needs places for people
                 to pee and poop. Signs everywhere and especially in  the
                 front windows of cafes and restaurants say, “restrooms
                 for customers only.” It’s not just a problem in Berkeley.
                 It’s a problem all over post-pandemic America.


          o ⚓ Discontent_by_Design:_The_Lost_World_of_the_West⠀⇛


                 The greatest crisis of all, however, is humanity, and the
                 culture that we, specifically ‘The West’, have built and
                 are wedded to. The Culture of Pleasure sits tightly
                 within and feeds the pervasive Ideology of Consumerism, a
                 socio-economic model that has poisoned the environment
                 and led to the commodification of everything, and
                 everyone.


                 While there are counter trends with people living
                 simpler, more responsible lives, broadly speaking
                 humanity is immersed in the world of pleasure, and has
                 lost its way. Our ancient connection to and respect for
                 the planet has gone, as has relationship with others and
                 with ourselves – with who and what we essentially are;
                 the mystery and wonder of life has been trampled on in
                 the race to consume, to achieve, to ‘succeed’.


          o ⚓ The_Moon_and_Six-Pence⠀⇛


          o ⚓ Why_Activists_Are_Calling_on_Kathy_Hochul_to_“Free_Them_All”⠀⇛


                 “Get them from behind the wall! Governor Hochul, free
                 them all!” On Friday, more than five dozen people
                 gathered in midtown Manhattan. They were repeating their
                 demand that New York’s new governor do what her
                 predecessor failed to do: release abuse survivors
                 imprisoned throughout New York, particularly given the
                 state’s widespread failure to provide protection and
                 resources, such as housing, medical and mental health
                 care, and other supports that would enable them to escape
                 or survive violence.


          o ⚓ The_LA_Olympics_Are_Being_Planned_Behind_Closed_Doors⠀⇛


                 The 2028 Los Angeles Olympics are still nearly seven
                 years away. But the city council has set a self-imposed
                 deadline of November 1 to come up with an agreement with
                 the United States Olympic and Paralympic Committee and 
                 LA 28, the private nonprofit consortium responsible for
                 running the games as to how the city will host the event.
                 The city, whose outgoing mayor, Eric Garcetti, has been
                 an outspoken supporter of the Olympic bid, has also
                 determined that by that date it will make a decision on
                 whether to expand LAX airport to accommodate the
                 anticipated Olympic crowds. The council is also slated to
                 decide whether to expand a loophole in the City’s housing
                 codes to allow up to 14,000 more short-term rentals in a
                 city that already has a vast number of unhoused
                 residents. Why would the City do this? One answer is that
                 AirBnb is one of the corporate sponsors of the 2028
                 Olympics.


          o ⚓ How_Latin_America_became_tech’s_next_big_frontier⠀⇛


                 Start-ups created to tackle problems like these are
                 propelling the region to the forefront of the emerging
                 market tech boom. Last year US $4.1 billion of venture
                 capital investment flowed into Latin America, exceeding
                 southeast Asia’s $3.3 billion and beating Africa, the
                 Middle East and central and eastern Europe combined,
                 according to the Global Private Capital Association.


                 In the first half of this year, Latin America pulled in
                 $6.5 billion of venture capital, not far short of India’s
                 $8.3 billion.


          o § Education⠀➾


                # ⚓ Texas_School_Administrator_to_Teachers:_Teach_“Opposing”
                  Sides_of_the_Holocaust⠀⇛


                # ⚓ ‘Holocaust_Denial_Has_No_Place_in_Our_Society’:_AOC
                  Reprimands_Texas_School_Official⠀⇛


                       A top school administrator from Southlake,
                       Texas—and the state GOP’s reactionary curriculum
                       policies—came under fire after NBC News revealed
                       Thursday that she recently told teachers that books
                       about the Holocaust should be accompanied by books
                       with “opposing” views.


                       “We find it reprehensible for an educator to
                       require a Holocaust denier to get equal treatment
                       with the facts of history… It’s worse than absurd.”


                # ⚓ Texas_school_chief_calls_for_‘opposing’_views_on
                  Holocaust⠀⇛


                       A Texas school administrator came under fire in the
                       US after a viral audio recording revealed she
                       instructed teachers to have books with “opposing”
                       views on the Holocaust available for students in
                       classrooms.


                       Gina Peddy told teachers during a training session
                       on what books they are permitted in their classroom
                       libraries that if they offered a book on the
                       Holocaust they needed to offer students access to a
                       book with an “opposing” perspective.


                # ⚓ A_Blackface_‘Othello’_Shocks,_and_a_Professor_Steps_Back
                  From_Class⠀⇛


                       The incident might have remained just the latest
                       flash point at a music program that has been roiled
                       in recent years by a series of charges of
                       misconduct by star professors. But a day before
                       Professor Sheng stepped down, a long, scathing
                       Medium post by a student in the class rippled
                       across Twitter before getting picked up in
                       Newsweek, Fox News, The Daily Mail and beyond,
                       entangling one of the nation’s leading music
                       schools in the supercharged national debate over
                       race, academic freedom and free speech.


                       [...]


                       Professor Sheng, in his emailed response to
                       questions from The Times, said that the purpose of
                       the class had been to show how Verdi had adapted
                       Shakespeare’s play into an opera, and that he had
                       chosen the Olivier film simply because it was “one
                       of the most faithful to Shakespeare.” He also said
                       that he had not seen the makeup as an attempt to
                       mock Black people, but as part of a long tradition
                       — one that has persisted in opera — which he said
                       valued the “music quality of the singers” over
                       physical resemblance.


          o § Hardware⠀➾


                # ⚓ PSA:_Publishing_supply_chain_shortages⠀⇛


                       The publishing industry is being sandbagged by
                       horrible supply chain problems. This is a global
                       problem: shipping costs are through the roof,
                       there’s a shortage of paper, a shortage of workers
                       (COVID19 is still happening, after all) and
                       publishers are affected everywhere. If you
                       regularly buy comics, especially ones in four
                       colour print, you’ll already have noticed multi-
                       month delays stacking up. Now the printing and
                       logistics backlogs are hitting novels, just in time
                       for the festive season.


          o § Health/Nutrition⠀➾


                # ⚓ Mondaire_Jones,_Katie_Porter_Urge_Fellow_Democrats_to
                  Reject_Means-Testing_Folly⠀⇛


                       Democratic Reps. Mondaire Jones and Katie Porter
                       are again pushing back against any effort to
                       implement means-testing to water down potentially
                       historic social investments proposed in their
                       party’s Build Back Better plan.


                       Making the proposed investments in the social
                       safety net—including child care and Medicare
                       expansion—universal is both “good policy and good
                       politics,” they wrote in a Washington Post op-ed
                       published Thursday.


                # ⚓ Toothless:_the_Build_Back_Better_Bill’s_Dental_Coverage⠀⇛


                       So that’s why, for months, Senator Bernie Sanders
                       has told us Medicare must cover dental work. The
                       notion is wildly popular with seniors,
                       understandably, as many cannot afford to keep their
                       teeth and would like to continue chewing with them.
                       Medicare coverage would be a way to hang onto their
                       molars and incisors. Now those voters’ hopes will
                       likely be dashed, as the House bill that deals with
                       this matter would postpone its implementation till
                       2028. In short, the House is kicking seniors in the
                       teeth.


                       Federal officials, according to the Washington
                       Post, cite as their excuse for this delay vetting
                       new dentists for Medicare and instituting a pricing
                       system to reimburse them. This is hogwash. When
                       president Lyndon Baines Johnson signed the law
                       establishing Medicare, on July 30, 1965, at the
                       ceremony former president Harry Truman was
                       instantly enrolled as Medicare’s first beneficiary
                       and received the first Medicare card. Nineteen
                       million people enrolled when Medicare officially
                       geared up some MONTHS later. So now the Dems would
                       have us believe that they can’t do in the 2020s
                       what they did in the ‘60s? Who’s going to buy that
                       nonsense? Something here just doesn’t wash.


                # ⚓ The_Great_Barrington_Declaration_strikes_back⠀⇛


                       About a year ago, three scientists wrote and issued
                       the Great Barrington Declaration. When I wrote
                       about it at the time, I characterized the
                       Declaration as “magnified minority” and eugenics,
                       the former because it followed a common crank
                       playbook of issuing a declaration about a fringe
                       science position and getting lots of doctors and
                       scientists, the vast majority of whom have no
                       expertise in the area, to sign it, and the latter
                       for reasons I will describe. Named after the town
                       in Massachusetts where the right wing “free market”
                       think tank, the American Institute for Economic
                       Research is located, the Great Barrington
                       Declaration proposed, in essence, letting COVID-19
                       rip through the “healthy” younger population in
                       order to build up “natural herd immunity,” all
                       while using “focused protection” to protect those
                       at high risk for severe disease and death from
                       coronavirus, such as the elderly and those with
                       chronic health conditions like type 2 diabetes.


          o § Integrity/Availability⠀➾


                # ⚓ Short_URLs_come_in_handy_for_cybercrooks⠀⇛


                       However, there are downsides too. URL shorteners
                       are often used by online fraudsters to trick users
                       into following a link to compromise their systems,
                       swindle money from their bank accounts or even
                       trick them into mine cryptocurrency without the
                       intervention of the user. Recipients could be
                       clicking a malware link (short links) or be
                       directed to a spoofing page where the victim’s
                       sensitive information could be recorded and later
                       used for stealing sensitive data or money.


                # § Proprietary⠀➾


                      # ⚓ Citrix_has_built_a_browser,_and_lost_a_CEO⠀⇛


                             According to a regulatory filing, in early
                             October, the company’s board appointed Robert
                             M. Calderoni as interim CEO, after David
                             Henshall stepped down from the role.


                      # ⚓ User_locked_out_of_Microsoft_account_by_MFA_bug,
                        complains_of_customer-hostile_support_•_The_Register
                        [Ed: By Microsoft Tim]⠀⇛


                             Konstantin Gizdov, an IT professional, was
                             locked out of his Microsoft account by a bug
                             in the company’s Multi-Factor Authentication
                             (MFA), but says support refused to
                             acknowledge the bug or recover his account.


                             Gizdov is founder of KGE Consultancy Ltd in
                             Edinburgh and an Arch Linux Trusted User.


                             His problems began when he received an email
                             informing him that his Microsoft account had
                             been renamed. “I immediately clicked on the
                             ‘That was not me’ button,” he said in a post,
                             after which he managed to contact support.


                      # ⚓ Apple_patches_‘actively_exploited’_iPhone_zero-day
                        with_iOS_15.0.2_update⠀⇛


                             If you’re using an iPhone, install the iOS
                             15.0.2 update immediately: Apple has warned
                             that the latest OS upgrade patches an
                             “actively exploited” zero-day.


                             Described as a “memory corruption issue” by
                             Apple, the vuln is present within the
                             IOMobileFrameBuffer kernel extension, used
                             for managing display memory. Malicious
                             applications are said to be capable of
                             triggering an integer overflow in the
                             framebuffer, permitting execution of
                             arbitrary code with kernel privileges.


                             The bug, publicly tracked as CVE-2021-30883,
                             has not yet been published in full although
                             technical descriptions and proofs of concept
                             are already circulating on security-focused
                             areas of the web.


                      # ⚓ Podcast:_67%_of_Orgs_Have_Been_Hit_by_Ransomware_at
                        Least_Once [iophk: Windows TCO]⠀⇛


                             According to Fortinet’s Global State of
                             Ransomware Report 2021 (PDF), released last
                             week, most organizations report that
                             ransomware is their top most concerning
                             cyber-threat. That’s particularly true for
                             respondents in Latin America, Asia-Pacific
                             and Europe-Middle East-Africa, who report
                             that they’re more likely to be victims than
                             their peers in the U.S. or Canada.


                      # ⚓ Treasury:_$590M_paid_out_by_victims_of_ransomware
                        attacks_in_first_half_of_2021 [iophk: Windows TCO]⠀⇛


                             Just over 450 ransomware payments were
                             reported to FinCEN from the beginning of
                             January through end of June, with the amount
                             of suspicious activity reports increasing by
                             30 percent from last year. The amount paid by
                             victims also massively increased compared to
                             2020, when $416 million was paid out over the
                             entire year.


                      # ⚓ Ransomware?_No_fear,_Scott_Morrison_has_a_plan._An
                        action_plan⠀⇛


                             Hence the Ransomware Action Plan. It’s just
                             like the numerous other plans which Morrison
                             and his ministers have put forth, meaningless
                             jumbles of words, all aimed at that one
                             Saturday before next May when the election
                             will have to be held.


                             When something that should necessarily have
                             some gravitas starts out like this: “The
                             world has never been more interconnected and
                             our reliance on the internet to fuel
                             Australia’s prosperity and maintain our way
                             of life has never been greater”, you just
                             know that it’s weapons-grade BS.


                      # ⚓ Apple_to_make_10_million_fewer_iPhones_due_to
                        microchip_shortage⠀⇛


                             Chip suppliers such as Broadcom and Texas
                             Instruments have reportedly told the
                             smartphone maker that they won’t be able to
                             deliver as many units as they said they
                             could.


                      # ⚓ New_Windows_10_KB5006670_update_breaks_network
                        printing⠀⇛


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ A_class_of_its_own,_CNCF_&_Linux
                                          Foundation_Kubernetes_exam [Ed:
                                          Adrian Bridgwater publishing spam for
                                          Zemlin now over in ComputerWeekly…
                                          real journalism is dead. It’s all
                                          sponsored.]⠀⇛


                                        # ⚓ KubeCon_2021:_New_Kubernetes
                                          Certificate_and_the_future_of
                                          Kubernetes_–_Market_Research
                                          Telecast⠀⇛


                                               The CNCF, the foundation
                                               under the umbrella of the
                                               Linux Foundation, which is
                                               responsible for the
                                               administration of the
                                               Kubernetes source code, has
                                               the KubeCon North America
                                               opened and welcomed
                                               visitors again after two
                                               years. In autumn 2019,
                                               users and developers of
                                               Kubernetes and cloud native
                                               technologies from their
                                               environment met for the
                                               last time on site at
                                               KubeCon & CloudNativeCon in
                                               the USA. The following
                                               European edition 2020 at
                                               the end of March took place
                                               via live streams from
                                               living rooms.


                      # § Security⠀➾


                            # ⚓ Running_a_recent_Apache_web_server_version?_You
                              probably_need_to_patch_it._Now⠀⇛


                                   The Apache Software Foundation has
                                   hurried out a patch to address a pair
                                   of HTTP Web Server vulnerabilities, at
                                   least one of which is already being
                                   actively exploited.


                                   Apache’s HTTP Server is widely used,
                                   and the vulnerabilities, CVE-2021-41524
                                   and CVE-2021-41773, aren’t great. The
                                   latter, a path traversal and file
                                   disclosure flaw, is particularly
                                   problematic.


                                   The former was reported to Apache’s
                                   security team on 17 September and can
                                   be exploited by an external source to
                                   DoS a server with a specially crafted
                                   request. It turned up in version
                                   2.4.49, which was released on September
                                   15, and the Apache crew is not aware of
                                   any exploit.


                            # ⚓ VoIP_Unlimited_hit_by_outage_in_wake_of_DDoS
                              claims_•_The_Register⠀⇛


                                   A British VoIP firm has staggered back
                                   to its feet after being smacked with a
                                   series of apparent DDoSes a month after
                                   suffering a series of sustained attacks
                                   it said were delivered by the REvil
                                   ransomware gang.


                                   In an update at 11:56 UK time, it said
                                   it was “continuing to suffer from large
                                   scale DDoS attacks. VoIP Unlimited
                                   engineers are continuing to mitigate
                                   the impact on services.”


                            # ⚓ Source_Tags_&_Codes⠀⇛


                                   The saga of the Missouri governor
                                   reflects a failure by the powerful to
                                   embrace curiosity—curiosity encouraged
                                   by the HTML language he fails to
                                   understand.


                            # ⚓ blog.ipfire.org_–_Feature_Spotlight:
                              Weaponising_IPFire_Location_to_proactively_detect
                              Fast_Flux_setups⠀⇛


                                   Thanks to libloc, the free & open
                                   source location database, IPFire comes
                                   with an accurate, trustworthy database
                                   for mapping IP addresses to countries
                                   and Autonomous Systems, and vice versa.
                                   This allows us to introduce a new
                                   feature: Proactive detection of Fast
                                   Flux setups, which are commonly used by
                                   ne’er-do-wells for hosting questionable
                                   and malicious content on compromised
                                   machines around the world, switching
                                   from one infected PC, IoT device, or
                                   router to another within minutes.


                                   To the best of our knowledge, this is a
                                   unique feature. Contrary to other
                                   security mechanisms such as AV
                                   scanners, which are often lagging
                                   behind, it detects malware, phishing,
                                   C&C servers and other nefarious things
                                   proactively – before any threat
                                   intelligence source in the world even
                                   knows about them. Even better,
                                   measurements done so far indicate it
                                   comes with a near-zero false positive
                                   rate in productive environments.1


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ The_Surveillance_And_Privacy_Concerns_Of
                                    The_Infrastructure_Bill’s_Impaired_Driving
                                    Sensors⠀⇛


                                         There is no doubt that many folks
                                         trying to come up with ways to
                                         reduce impaired driving and
                                         making the roads safer have the
                                         best of intentions. And yet,
                                         hidden within those intentions
                                         can linger some pretty dangerous
                                         consequences. For reasons that
                                         are not entirely clear to me, the
                                         giant infrastructure bill (that
                                         will apparently be negotiated
                                         forever) includes a mandate that
                                         automakers would eventually need
                                         to build in technology that
                                         monitors whether or not drivers
                                         are impaired. It’s buried deep in
                                         the bill (see page 1066), but the
                                         key bit is:


                                  # ⚓ Entering_the_Matrix⠀⇛


                                         For a long time, the Tor
                                         community has been running many
                                         day-to-day activities using the
                                         IRC network known as OFTC. IRC
                                         has worked out well for us, and
                                         our community on IRC has been
                                         evolving over the years with new
                                         people joining in and new
                                         channels appearing for specific
                                         needs in the organization.


⚓ Clearview_Celebrates_10_Billion_Scraped_Images_Collected,_Claims_It_Can_Now
Recognize_Blurred,_Masked_Faces⠀⇛


     Clearview’s not going to let several months of bad press derail its
     plans to generate even more negative press. The facial recognition
     tech company that relies on billions of scraped images from the web
     to create its product is currently being sued in multiple states, has
     had its claims about investigative effectiveness repeatedly debunked
     and, most recently, served (then rescinded) a subpoena to
     transparency advocacy group Open the Government demanding information
     on all its Clearview-related FOIA requests as well as its
     communications with journalists.


⚓ Flight_of_the_Concord_Drones⠀⇛


     The City Council of Concord, California, is tone deaf to community
     concerns regarding a proposed police Unmanned Aerial Surveillance
     (UAS) system – commonly referred to as drones. In a city where the
     police department is responsible for nearly 60% of the city budget,
     this should come as no surprise. The UAS program, however, will
     strangely be funded by Marathon Petroleum, which has no offices or
     facilities in Concord. EFF, ACLU, and 15 other Contra Costa community
     organizations opposed this action. We also demanded police oversight
     and ample safeguards to protect civil liberties and civil rights if
     the program were to be adopted.


     Privacy and police accountability are a massive issue with UAS
     systems, and are both high priority issues for California voters, as
     evidenced by the passage of California Consumer Privacy Act and
     police accountability legislation.


     Drones are unmanned aerial vehicles that can be equipped with high
     definition, live-feed video cameras, thermal infrared video cameras,
     heat sensors, and radar—all of which allow for sophisticated and
     persistent surveillance. Drones can record video or still images in
     daylight or at night (with infrared lenses). They can also be
     equipped with software tools like license plate readers, face
     recognition, and GPS trackers that extend the dangers they pose to
     privacy. There have even been proposals for law enforcement to attach
     lethal and non-lethal weapons to drones. Additionally, newly
     developed drone automation allows for automatic tracking of vehicles
     and individuals.


⚓ Human_rights_activist_suing_Twitter_for_allegedly_giving_Saudi_spies_access
to_his_info⠀⇛


     Al-Ahmed also claims in the lawsuit that his Twitter account was
     suspended in 2018 without explanation and has yet to be reinstated
     despite repeated appeals. The lawsuit alleges that the company has
     kept Al-Ahmed’s Arabic-language account inaccessible so as not to
     displease the Saudi government.


⚓ Bugs_in_our_pockets?⠀⇛


     Now, in Bugs in our Pockets: The Risks of Client-Side Scanning,
     colleagues and I take a long hard look at the options for mass
     surveillance via software embedded in people’s devices, as opposed to
     the current practice of monitoring our communications. Client-side
     scanning, as the agencies’ new wet dream is called, has a range of
     possible missions. While Apple and the FBI talked about finding still
     images of sex abuse, the EU was talking last year about videos and
     text too, and of targeting terrorism once the argument had been won
     on child protection. It can also use a number of possible
     technologies; in addition to the perceptual hash functions in the
     Apple proposal, there’s talk of machine-learning models. And, as a
     leaked EU internal report made clear, the preferred outcome for
     governments may be a mix of client-side and server-side scanning.


⚓ Apple’s_Child-Porn_Tracking_System_Is_Flawed,_Report_Says⠀⇛


     The 46-page report counts among its 14 authors pioneers in encryption
     software. It outlines, in detail, what the authors deem the numerous
     risks of a technique called “client-side scanning,” which was at the
     heart of a controversy that erupted when Cupertino, California-based
     Apple announced a plan in August to scan users’ iCloud Photos
     accounts for sexually explicit images of children and then report
     instances to relevant authorities. Apple later postponed those plans
     amid the backlash. The New York Times previously reported on the
     experts’ concerns.


§ Confidentiality⠀➾


    * ⚓ Missouri_governor_calls_for_prosecution_of_journalist_who_flagged
      website_flaw⠀⇛


           “It’s incredibly wrong to characterize what occurred here as
           anything less than fully responsible and ethical,” said Aaron
           Mackey, an attorney at the Electronic Frontier Foundation, a
           nonprofit that advocates for digital rights.


           “It’s news. It’s important that the public and the folks who
           live in Missouri know that the state was failing to secure
           hundreds of thousands of people’s personal information and
           leaving them vulnerable,” he said.


    * ⚓ Netflix_Fires_Employee_for_Sharing_Confidential_Data_About_Dave
      Chappelle_Stand-Up_Special_Outside_the_Company⠀⇛


           Netflix famously operates a corporate culture in which it
           openly shares information with employees. However, according to
           its employment policies, Netflix staff members are not allowed
           to share private info outside the company with the
           understanding that they may be fired for doing so.


§ Defence/Aggression⠀➾


    * ⚓ Tory_Lawmaker_Stabbed_to_Death_During_Meeting_With_Constituents_in_UK⠀⇛


           This is a breaking story… Check back for possible updates…


           Conservative Party MP David Amess was fatally stabbed in the
           United Kingdom on Friday during a meeting with local
           constituents in Leigh-on-Sea, a coastal town in eastern
           England.


    * ⚓ ‘It_Was_Torture’:_African_Asylum-Seekers_Describe_Restraint_Agony_on
      ICE_‘Death_Flights’⠀⇛


           With images of U.S. Border Patrol agents using horses and whip-
           like reins to round up Haitian asylum-seekers fresh in their
           minds, Black immigrants’ rights advocates this week filed a
           human and civil rights complaint condemning what they called
           the torture of African deportees last year by Immigration and
           Customs Enforcement personnel.


           “I truly felt I was meeting my death in that moment… When I
           complained, they just pulled the WRAP tighter.”


    * ⚓ Abandoning_Yemen?⠀⇛


           “This is a major setback for all victims who have suffered
           serious violations during the armed conflict,” the GEE wrote in
           a statement the day after the U.N. Human Rights Council refused
           to extend a mandate for continuation of the group’s work.  “The
           Council appears to be abandoning the people of Yemen,” the
           statement says, adding that “Victims of this tragic armed
           conflict should not be silenced by the decision of a few
           States.”


           Prior to the vote, there were indications that Saudi Arabia and
           its allies, such as Bahrain (which sits on the U.N. Human
           Rights Council), had increased lobbying efforts worldwide in a
           bid to do away with the Group of Experts. Actions of the Saudi-
           led coalition waging war against Yemen had been examined and
           reported on by the Group of Experts. Last year, the Saudi bid
           for a seat on the Human Rights Council was rejected, but
           Bahrain serves as its proxy.


    * ⚓ Jan_6_Committee_Will_Hold_Steve_Bannon_in_Contempt_for_Violating
      Subpoena_Order⠀⇛


    * ⚓ The_Modern_History_of_Africa_is_the_Natural_Extension_of_the_Struggle
      of_the_Palestinian_People⠀⇛


           Built of largely self-serving excuse, as a starting point,
           these arguments fail to consider the entirety of the historical
           context of the relationship between the African continent and
           Israel. A plain read of Israeli-African relations clearly
           indicates that they were affected, if not determined, by
           parallel Arab-Israeli interactions. Thus, as statements of
           principle and solidarity, many African countries severed extant
           relations with Israel following the Israeli aggressions against
           Arab countries in 1967 and, then again, in1973.


           Though, to some degree, these countries eventually
           reconstructed their relations with Israel once Egypt did so in
           1978, and following the Madrid Conference of 1991 and the Oslo
           Agreements, it proved to be but a fleeting gesture as Israel
           was unable to exploit this temporary détente beyond the period
           when the Organization of African Unity morphed into the African
           Union.  .


    * ⚓ Leaked_Video_Helped_Lead_to_the_Conviction_of_a_Far_Right_“Proud_Boy”⠀⇛


    * ⚓ Ascendant_Democratic_Warhawk_Wants_to_Pre-Authorize_War_With_China⠀⇛


    * ⚓ Study_Says_Official_Count_Of_Police_Killings_Is_More_Than_50%_Lower
      Than_The_Actual_Number⠀⇛


           In 2019, the FBI claimed to be compiling the first-ever
           database of police use of force, including killings of citizens
           by officers. It was, of course, not the first-ever database of
           police killings. Multiple databases have been created (some
           abandoned) prior to this self-congratulatory announcement to
           track killings by police officers.


    * ⚓ Endless_Enemies_and_the_Permanent_War_Economy⠀⇛


           Ross Douthat contends that this failure has been known for some
           time, its irredeemable nature especially evident during the
           early Obama years when a decent political settlement couldn’t
           be reached despite the troop surge; when our forces “blunted
           but did not reverse the Taliban’s recovery.” And subsequent
           efforts were devoted to merely managing stalemate versus
           pursuing victory (“Joe Biden’s Critics Lost Afghanistan,”
           NYTimes, 8/31/21).


           The targeting of the Obama years is telling not only because of
           the surge. Mr. Obama received the Nobel Peace Prize as he
           entered office, giving him the defaulted moniker as the “Peace
           President.” His acceptance speech mimicked the reasons the
           committee gave for granting him the prize. It voted to affirm
           his desire to achieve peace, likely swayed by the impact of his
           pre-election speeches, masterful pieces of rhetoric against war
           (and against neoliberalism as well, though effectively
           nullified after the election). The speech itself then was an
           embarrassing justification for the potential of war to produce
           peace. If the committee had voted after his decision to boot up
           the Afghan War, he would probably have gotten the prize anyway
           since the war’s material subsidies indentured a host of players
           and interests and bolstered support for it. So, the rhetoric of
           the speech and the decision soon after to expand the war, mesh
           efficiently into a saleable message that nicely smooths over an
           embarrassing contradiction.


    * ⚓ The_Haitian_Migration_Crisis:_Made_in_the_U.S.A.⠀⇛


           Biden recently ordered the breakup of a camp of 15,000 mainly
           Black Haitian migrants under a border bridge in Del Rio, Texas.
           The migrants—many of whom had traveled thousands of miles—had
           fled to the U.S. in the hopes of being granted asylum from the
           horrific oppression and exploitation they face in Haiti, Chile,
           Brazil, and other states in the region.


           In scenes that evoked the history of U.S. slave catchers,
           Border Patrol agents on horseback used their reins as whips to
           beat the refugees they chased down and captured. Eager to join
           the racist frenzy, Texas Governor Greg Abbott ordered the
           National Guard and Texas police to form a miles-long “steel
           wall” of patrol cars and military vehicles to block migrants
           from escaping Biden’s dragnet.


    * ⚓ How_Feminists_Can_Support_Afghan_Women_Living_Under_the_Taliban⠀⇛


           There’s little question that gains made by Afghan women over
           the past 20 years, particularly urban women, have been rolled
           back—at least temporarily. Since coming to power, the Taliban
           have said girls would be allowed to go to school, but in some
           parts of the country, girls are being kept out of grades 7-12.
           And while female students have continued to attend private
           universities, most women enrolled in public universities have
           not been attending classes due to fear, canceled classes or
           Taliban restrictions. Even though Taliban spokesmen insist that
           women can continue to work, there are also frequent reports of
           Taliban militants ordering women to leave their workplaces.


           While we should all be outraged about the abuses and
           deterioration of rights that Afghan women are experiencing, the
           Taliban aren’t the only cause of women’s distress right now.
           The economy and public services are screeching to a halt
           because the international community has pulled the plug on
           funding. Afghanistan is a country that has relied on outside
           donors to fund its vital services for most of its modern
           existence. When the U.S. pulled out of Afghanistan, it froze
           $9.5 billion of the Afghan Central Bank’s assets and pushed the
           International Monetary Fund to block Afghanistan’s access to
           over $450 million earmarked for COVID-19 relief. Adding fuel to
           the fire, the World Bank suspended financing to the Afghan
           healthcare system through its Afghanistan Reconstruction Trust
           Fund. Given that foreign aid to Afghanistan had previously been
           about $8.5 billion a year — nearly half of the country’s gross
           domestic product — the impact of freezing these funds is
           catastrophic for women and their families.


    * ⚓ Afghanistan_Tackles_the_Islamic_State⠀⇛


           The name of the attacker raised red flags across the region. It
           indicated that he belonged to the Uyghur community and had a
           relationship with the Xinjiang region of western China, which
           is home to most of the world’s Uyghur population. That a
           Chinese extremist attacked a Shia mosque raised eyebrows in
           Beijing and in Tehran.


           Foreign Terrorists


    * ⚓ America’s_Instinctive_Fascism_Creeps_On⠀⇛


           ‘The United States is heading into its greatest political and
           constitutional crisis since the Civil War, with a reasonable
           chance over the next three to four years of incidents of mass
           violence, a breakdown of federal authority, and the division of
           the country into warring red and blue enclaves…We are already
           in a constitutional crisis. The destruction of democracy might
           not come until November 2024, but critical steps in that
           direction are happening now. In a little more than a year, it
           may become impossible to pass legislation to protect the
           electoral process in 2024. Now it is impossible only because
           anti-Trump Republicans, and even some Democrats, refuse to
           tinker with the filibuster. It is impossible because, despite
           all that has happened, some people still wish to be good
           Republicans even as they oppose Trump. These decisions will not
           wear well as the nation tumbles into full-blown crisis.’”


           Millions of racist, sexist, and nativist white Americans, many
           if not most of them armed, are angrily panting for the
           Amerikaner Party of Trump’s (APoT’s) return to full national
           power and revenge. The storming of the US Capitol last January
           6th is for them just a test run for further and more serious
           efforts to “take our country back.” The second American civil
           war they want is already being waged in numerous ways,
           including the right’s interrelated assaults on minority voting
           rights, gun control, election integrity, women’s reproductive
           rights, racially honest school curriculum, and basic public
           health measures to defeat COVID-19.


    * ⚓ ‘Dozens’_of_Oregon_Cops_Have_Paid_Dues_to_the_Oath_Keepers_Militia
      Group:_Report⠀⇛


           According to the leaked data obtained by Distributed Denial of
           Secrets, a non-profit whistleblower organization that shares
           leaked information with journalists and researchers, Oregon
           police signed up to join the group as early as 2009. The data
           includes members’ names, the date they joined Oath Keepers and
           contact information for anyone who paid dues to the group,
           which is comprised of nearly 40,000 individuals across the
           country. But, according to OPB, it is difficult to discern from
           the available data whether people on the list were current
           members of Oath Keepers, unless they had paid the group’s
           $1,000 lifetime membership fee.


    * ⚓ Capitol_Police_Officer_Charged_With_Helping_a_Guy_in_His_Facebook
      Fishing_Groups_Hide_Insurrection_Evidence⠀⇛


           Riley, who has served on the Capitol Police force for over 25
           years, was on duty the day of the attack not in the Capitol,
           but he allegedly sent dozens of messages to the rioter, whose
           name has not been revealed, recommending he get rid of any
           incriminating selfies or videos that would place him in the
           Capitol that day. Prosecutors said Riley also gave the person
           information about how the FBI was going to track down the
           identities of the rioters, and he later deleted all the
           messages he sent to him. What Riley didn’t know is that
           prosecutors can obtain deleted copies of photos and messages
           from social media companies, which is exactly what they did.


    * ⚓ Apple_removed_a_popular_Quran_app_in_China⠀⇛


           While it’s logical for business, that framing has placed the
           company in questionable positions before. Apple has removed VPN
           apps that allowed Chinese users to avoid censorship and
           proactively filtered out apps that mentioned Tiananmen Square,
           the Dalai Lama, or Taiwanese and Tibetan independence. Apple’s
           suppliers in the region have also been connected to the
           oppression of China’s predominantly Muslim Uyghur minority.


    * ⚓ It’s_Not_Q._It’s_You⠀⇛


           As Uscinski explains it, conspiracy theories don’t affect
           people so much as people affect them. And those people aren’t
           unwittingly sucked by powerful algorithms down a rabbit hole of
           dis- and misinformation but rather are drawn there by what they
           already believe — or want to believe — is true. “This
           discussion is often framed backwards,” Uscinski tells me. “It
           suggests that internet content, or the algorithms, have magical
           powers of persuasion. But [a QAnon adherent] wasn’t looking at
           recipes on YouTube then slipped on a banana peel and got
           inadvertently pulled down the QAnon rabbit hole. Maybe they
           were on YouTube looking for fringe conspiracy theories or
           extremist religious stuff; maybe they were already into all
           sorts of Bible conspiracy nonsense. The internet didn’t
           persuade them of some foreign idea. It gave them exactly what
           they already believed.”


    * ⚓ Why_Isn’t_Steve_Bannon_in_Jail?_Ask_the_Democrats.⠀⇛


           Bannon missed the deadline to submit documents last week, but
           Democrats did not act because the deadline to sit for a
           deposition was this week. I’m not sure why the Select Committee
           thought an extra week would change Bannon’s mind, but it
           didn’t. Now that he’s missed the deposition deadline as well as
           the document deadline, Committee Chairman Benny Thompson says
           that they will start the process of referring Bannon for
           criminal contempt proceedings… next week. There’s a three-day
           “notice” period before a Congress member can call a vote on a
           criminal contempt referral, and instead of starting that
           process last week when Bannon missed a deadline to turn over
           documents, the Select Committee waited until this week when he
           missed the documents and deposition deadlines. Cool system
           we’ve got here, bro.


    * ⚓ [Old] We_must_confront_the_Taliban_apologists_in_the_west⠀⇛


           The collapse of the government, the withdrawal of western
           forces and attacks on Kabul airport – claimed by the terrorist
           group ISIS-K – have made Afghanistan a hellhole for the
           citizens of the country, who have been left at the mercy of the
           Taliban’s barbaric regime.


           No doubt this will be a victory for the Taliban apologists, who
           have longed for the establishment of an Islamic state to
           enforce Sharia law – while overlooking human rights violations.


    * ⚓ Islamic_council_forum_with_Taliban_‘not_a_free_speech_issue’⠀⇛


           “This is a little bit like if a Christian organisation decided
           to get three members of the KKK to speak at an event.”


    * ⚓ Sermons_in_a_mosque_in_France_advocate_armed_jihad,_martyrdom_and_the
      committing_of_terrorist_attacks⠀⇛


           The Sarthe prefecture announced on Wednesday that it had
           initiated proceedings to close the mosque in Allonnes, a small
           town of about 11,000 inhabitants southwest of Le Mans. The
           mosque has about 300 worshippers and its sermons legitimise
           “armed jihad”.


§ Transparency/Investigative Reporting⠀➾


    * ⚓ Russ_Kick,_‘Rogue_Transparency_Activist,’_Is_Dead_at_52⠀⇛


           He was among the first to post documents in full, including all
           16,000 pages of the F.B.I.’s file on the Rev. Dr. Martin Luther
           King Jr. (The agency had released only a fraction of them.)


           “The work he was doing was phenomenal,” David Cuillier, a
           University of Arizona professor who studies government
           transparency and public-records access, said in an interview.
           “He showed that anybody in this country could get public
           records out of the government, even when the government didn’t
           want to give them out.”


    * ⚓ Sanders_blames_media_for_Americans_not_knowing_details_of_Biden
      spending_plan⠀⇛


           While many of the ideas behind the spending bill are popular
           with voters, a CBS News poll released this week found that only
           10 percent of Americans knew a lot about the specifics and 57
           percent indicated they didn’t know any details about the
           multitrillion-dollar proposal.


§ Environment⠀➾


    * ⚓ Rings⠀⇛


    * ⚓ In_Colorado_Just_Another_Environmental_Whitewash_for_the_Polis
      Administration⠀⇛


           Up till now, the Polis administration, allied with the oil
           industry as a silent partner, has been somewhat successful in
           confounding the true causes of our air quality problems. They
           initiated a fairly successful trope claiming the source of our
           miserable air quality was the massive fires on the west coast.
           It was California’s fault. But the actions of these courageous
           three, who incidentally comprise the entire air-quality
           modeling branch for the APCD, may have turned the tables on
           this flimsy political contrivance.


           First of all Polis’s repeated claim that California is
           responsible is a laugher. Colorado’s front range has had air
           quality problems for decades. They didn’t start with the
           wildfires on the west coast, though those certainly haven’t
           helped. Neither, with a radically heating planet, are these
           fires likely to diminish. Hidden in the soot from the west
           coast fires is the fact that the state and the oil industry
           admitted in 2013 that most of the volatile organic compounds,
           VOCs, come from oil activities centered in Weld County.
           Colorado’s fracking activity and oil production is centered in
           that county. Ozone, formed through the chemistry of VOCs
           reacting with sunlight, which in Colorado is also abundant, is
           recognized as a primary cause of asthma in children and a
           dangerous health threat to all people with lung and heart
           disease. Ozone pollution is the primary reason Colorado is
           under threat of going from serious to severe noncompliance with
           the federal Clean Air Act. Severe is exceeded only by extreme
           in the CAA’s hierarchy of risks. Soot from forest fires near
           and far is simply icing.


    * ⚓ After_Hurricane_Ida,_Louisianians_Offer_Bold_Visions_for_Climate
      Resilience⠀⇛


    * ⚓ How_to_Save_the_World_(From_a_Climate_Armageddon)⠀⇛


           Of course, politicians, scientific groups, and environmental
           organizations will offer plans of every sort in Glasgow to
           reduce global carbon emissions and slow the process of
           planetary incineration. President Biden’s representatives will
           tout his promise to promote renewable energy and install
           electric-car-charging stations nationwide, while President
           Macron of France will offer his own ambitious proposals, as
           will many other leaders. However, no combination of these, even
           if carried out, would prove sufficient to prevent global
           disaster — not as long as China and the U.S. continue to
           prioritize trade competition and war preparations over
           planetary survival.


           In the end, it’s not complicated. If the planet’s two “great”
           powers refuse to cooperate in a meaningful way in tackling the
           climate threat, we’re done for.


    * ⚓ Waking_up_to_Climate_Change_Dinosaurs⠀⇛


           The first interview, with Nationals Senator Bridget McKenzie,
           is filled with the sort of rejigged reality that is less mind
           expansion than contraction.   It is easy to forget that she is
           a member of the government.  She tells listeners that her
           constituents and the electorate she represented were not
           interested in climate change or its effects.  A bold, quixotic
           reading.  They were also the “most marginalised” and vulnerable
           in Australia.  This would be a fascinating take for those in
           the employ of Rio Tinto and other mining giants.


           McKenzie (“Fran, Fran, Fran,” she implored with adolescent
           petulance) was all for those in rural areas, claiming that, “We
           have been able to avoid very bad outcomes for our country.” 
           Environmental catastrophe, imminent impoverishment of the
           farming sector due to climate change, are evidently palatable
           and digestible outcomes.  Interest, suggested McKenzie, should
           instead be shown for those workers who, in erecting solar
           panels, ended up mowing the grass underneath them.


    * ⚓ Over_530_Arrested_in_Historic_Indigenous-Led_Climate_Protests_in_DC⠀⇛


    * ⚓ ‘We’re_Not_Stopping’:_Weeklong_D.C._Climate_Protests_End_With_650+
      Arrests,_Vows_to_Fight_On⠀⇛


           Earth protectors and climate campaigners from across the
           continent Indigenous peoples call Turtle Island vowed to keep
           up the fight as they marched on Friday, the final day of action
           in the “People vs. Fossil Fuels Mobilization,” a weeklong
           series of protests in Washington, D.C. in which over 600
           demonstrators were arrested as they demanded that President Joe
           Biden and Congress act in the face of a planetary emergency.


           “We need climate action now. We are out of time to address this
           issue.”


    * ⚓ Opinion_|_There’s_Only_One_Way_to_Save_the_World_From_Climate
      Armageddon⠀⇛


           This summer we witnessed, with brutal clarity, the Beginning of
           the End: the end of Earth as we know it—a world of lush
           forests, bountiful croplands, livable cities, and survivable
           coastlines. In its place, we saw the early manifestations of a
           climate-damaged planet, with scorched forests, parched fields,
           scalding cities, and storm-wracked coastlines. In a desperate
           bid to prevent far worse, leaders from around the world will
           soon gather in Glasgow, Scotland, for a U.N. Climate Summit.
           You can count on one thing, though: all their plans will fall
           far short of what’s needed unless backed by the only strategy
           that can save the planet: a U.S.-China Climate Survival
           Alliance.


    * § Energy⠀➾


          o ⚓ To_Find_Out_If_ExxonMobil_Really_Supports_a_Carbon_Tax,_Just
            Follow_the_Money⠀⇛


                 Wood’s reaction was reminiscent of Captain Louis Renault
                 feigning surprise to discover gambling at Rick’s Café in
                 the 1942 film “Casablanca.” After quietly pocketing his
                 winnings, Renault justifies closing down the nightclub
                 by exclaiming, “I’m shocked, shocked to find that
                 gambling is going on in here!”


                 Woods was shocked? Really? Just one look at his company’s
                 financial records would show that despite claiming to
                 endorse a carbon tax—initially in a cynical attempt to
                 derail a cap-and-trade bill that was under consideration
                 in 2009—ExxonMobil has funneled millions of dollars over
                 the last decade to lawmakers who staunchly oppose the
                 idea.


          o ⚓ Tory_Climate_Policies_are_‘Socialist’_Says_New_Head_of_Policy_at
            Influential_Westminster_Think_Tank⠀⇛


                 An influential think tank with close ties to MPs has
                 hired a head of policy who called the government’s
                 climate policies “socialist” and likened proposed green
                 legislation to a “Soviet Five Year Plan”. 


                 Matthew Lesh, who was head of research at the Adam Smith
                 Institute, this week confirmed he would be taking up a
                 new role at the Institute of Economic Affairs (IEA), a
                 free market think tank with a history of criticising
                 green government policies. 


          o ⚓ Bobby_Lewis_on_One_America_News,_Jean_Su_on_People_vs._Fossil
            Fuels⠀⇛


                 This week on CounterSpin: “If you have 12 Americans being
                 fed a diet of untruth, that’s 12 too many.” So says John
                 Watson, an American University journalism professor
                 specializing in ethics and media law. He’s talking about
                 OAN, or One America News Network, and its audience, which
                 has been told, among other things, that Donald Trump
                 really won the 2020 election and that chemical cocktails
                 are a better response to Covid-19 than government-
                 authorized vaccines. We’ll talk about how we got here
                 with Bobby Lewis, researcher and editorial writer from
                 Media Matters.


          o ⚓ Jack_Dorsey’s_Square_Considers_Building_a_Bitcoin_Mining_System⠀⇛


                 Dorsey said in a thread on Twitter that the company would
                 follow a hardware wallet model and “build in the open in
                 collaboration with the community.”


          o ⚓ Jack_Dorsey_says_Square_may_build_a_bitcoin_mining_system,_adding
            to_bitcoin_price_surge⠀⇛


                 Dorsey’s goal would be to make [cryptocurrency] mining —
                 the process of creating new bitcoins by solving
                 increasingly complex computational problems — more
                 accessible, much as Square’s original vision was to make
                 it easier for small businesses and independent
                 proprietors to take credit card payments. He wrote that
                 bitcoin mining should be “as easy as plugging a rig into
                 a power source.” Today, the bitcoin mining industry is
                 dominated by large-scale players who can afford to buy
                 tens of thousands of ASICs, the type of specialty gear
                 used to mint new coin.


          o ⚓ The_Great_Mining_Migration⠀⇛


                 China’s Cryptocurrency Crackdown has been dramatically
                 effective. The total hashrate dropped by over a half from
                 its peak before recovering. As I write it is still down
                 about 15% from the peak.


                 The latest figures from the Cambridge Bitcoin Energy
                 Consumption Index provide more detail on what happened.
                 In May China was producing 70.9 Exahash/sec and 44% of
                 the total, as against 75% in 2019. In July, it produced
                 none, triggering the collapse in the hash rate.


          o ⚓ Raido_Saar:_Cryptocurrency_companies_facing_another_gauntlet⠀⇛


                 Almost four years ago, RAB (still part of the Police and
                 Border Guard Board at the time) started issuing
                 cryptocurrency licenses in Estonia. Corresponding
                 regulation was drawn up carelessly and hastily and led to
                 a situation where over 1,500 crypto firms had been
                 registered a few years later. Many were made to be sold
                 as corporate shells, with considerable demand from
                 foreign customers.


                 It needs to be said in hindsight that while registering
                 cryptocurrency companies was the right call for an
                 innovative e-state, the hack regulation was a mistake.
                 The poisonous fruits of that mistake is what the head of
                 RAB is trying to combat with what little resources he
                 has, and we find that he has been successful.


          o ⚓ Epic_says_it’s_‘open’_to_blockchain_games_after_Steam_bans_them⠀⇛


                 Epic’s CEO Tim Sweeney has said that the company isn’t
                 interested in touching NFTs, but that statement now
                 appears to only apply to its own games. Epic tells The
                 Verge that it will clarify the rules as it works with
                 developers to understand how they plan to use blockchain
                 tech in their games. Sweeney also tweeted some additional
                 thoughts after we published this story: he says Epic
                 welcomes “innovation in the areas of technology and
                 finance,” and suggests that blockchain isn’t inherently
                 good or bad.


    * § Wildlife/Nature⠀➾


          o ⚓ Opinion_|_Kunming_Declaration’s_30×30_Biodiversity_Target_Is_a
            Good_Start,_But_Not_Nearly_Enough⠀⇛


                 The recently issued Kunming Declaration from the High-
                 Level Segment of the United Nations Biodiversity
                 Conference lays the foundation for the post-2020 Global
                 Biodiversity Framework (GBF) to be negotiated next year.
                 Its stated goal is to reverse the extinction crisis and
                 build an “ecological civilization,” and it includes an
                 important reference to a new proposed area-based target:


          o ⚓ ‘Embarrassing’:_US_Absent_as_World_Joins_Together_to_Protect
            Biodiversity⠀⇛


                 As the United Nations Biodiversity Conference wrapped up
                 Friday, critics are once again pointing to the glaring
                 absence of the United States from negotiations to
                 strengthen an international treaty to restore and protect
                 the variety of life on Earth that has been ratified by
                 every country except the U.S.


                 “The world cannot afford for China and the U.S. to not
                 find ways to work together to address climate change and
                 nature loss.”


          o ⚓ The_United_States_Must_Rejoin_the_Global_Biodiversity
            Conservation_Community⠀⇛


                 The Convention on Biological Diversity (CBD) is moving
                 full speed ahead on the creation of a post-2020 Global
                 Biodiversity Framework that is expected to be finalized
                 and adopted at the UN Biodiversity Conference COP15,
                 scheduled to take place, in-person, in Kunming, China,
                 next year. The first part of the negotiations started on
                 Monday, with meetings to take place virtually through
                 Friday of this week. The United States, however, is not
                 at the table helping to shape that Framework as an
                 official member. Why?


                 Check the “List of Parties” page on the CBD website, and
                 you’ll find a long, numbered list of nation states, 196
                 in total. But there are also two unnumbered entries at
                 the very bottom: the “Holy See” and then, dead last,
                 “United States of America.” The U.S. did sign the
                 agreement in 1993, a year after the CBD was established
                 at the historic 1992 UN Earth Summit in Rio de Janeiro,
                 but never ratified it. Hence the ignominious bottom-of-
                 the-pile spot it occupies today. And not only is the U.S.
                 not a party to the Convention on Biological Diversity, it
                 hasn’t joined the Convention on the Conservation of
                 Migratory Species of Wild Animals (CMS) either.


          o ⚓ Opinion_|_The_Common_Sense_Case_for_More_Urban_Parks⠀⇛


                 We all have our own coping mechanisms to get us through
                 the pandemic. For many of us, a visit to a park offers
                 respite in times of stress. But it’s increasingly clear
                 that there aren’t enough parks to meet that crucial
                 need—especially in urban neighborhoods.


          o ⚓ Brazil,_Amazon,_World:_Crimes_Against_Humanity⠀⇛


                 Take Article 10 of the Bill of Rights of the New
                 Hampshire Constitution (1784) for starters: “The doctrine
                 of nonresistance against arbitrary power, and oppression,
                 is absurd, slavish, and destructive of the good happiness
                 of mankind”. Then, the Grundgesetz, the constitutional
                 law of Germany (1949), recognises in Article 20 (4) the
                 “right to resist any person seeking to abolish this
                 constitutional order, if no other remedy is available.”
                 We have come to this. We’re in an almost full-blown form
                 of fascism that has taken the whole planet to the brink
                 of extinction. There is no “other remedy” or notable
                 institutional effort to counter the erosion of
                 constitutional rights. Surely unity based on upholding
                 principles of justice has to be stronger than the veneer
                 of unity derived from submission to authority. Article 1
                 of the Universal Declaration of Human Rights stresses
                 that human beings are endowed with “reason and
                 conscience”. If we don’t uphold human rights, “reason and
                 conscience” are empty words. But they can also be our
                 strength because, as Thomas Paine knew a long time ago,
                 “We have it in our power to begin the world over again”.


                 We can claim our rights, and the rights of all those who
                 haven’t got voices to claim them. And also start to deal
                 with the evildoers. Some of today’s worst crimes are
                 happening in Brazil, perpetrated by the world’s worst
                 (genocidal and ecocidal) criminals. With impunity. Some
                 progress to protect the Amazon and its peoples was made
                 in Brazil after the dictatorships when the new
                 Constitution (1988) codified Indigenous rights, including
                 the right to tribal homelands. Since so much of the
                 Amazon is Indigenous territory and, owing to the people’s
                 understanding of the inseparable relations of human and
                 natural existence, Indigenous sovereignty became an
                 essential part of Brazilian environmental policy.
                 Indigenous people represent about 5% of the world’s
                 population. Fighting for their ancestral lands, they are
                 also trying to protect some 85% of the planet’s
                 biodiversity. Hence, the crimes of ethnocide and ecocide
                 are closely linked. And the rise of fascistoid forms of
                 power should tell us—if only we are able to look
                 carefully enough—that the rights and wellbeing of any one
                 person critically depend on the rights and wellbeing of
                 others.


          o ⚓ Why_Ecology_Is_the_Infrastructure_of_the_Future⠀⇛


                 When Hurricane Ida hit the Gulf Coast 16 years after
                 Hurricane Katrina, all eyes were on New Orleans’s new
                 levee system. The levees that had failed so disastrously
                 in 2005 had been rebuilt—and this time they held. You
                 could almost hear a collective sigh of relief, but
                 MacArthur award–winning landscape designer Kate Orff
                 believes that “gray infrastructure” (levees, flood gates,
                 and sea walls) can only take us so far. The
                 infrastructure we really need, she says, is green. Orff,
                 recently profiled in The New Yorker, insists that ecology
                 is the infrastructure of the future. Her work with SCAPE
                 Studio restores and harnesses—rather than resists—natural
                 systems to ensure the livability of our rapidly changing
                 world.


          o ⚓ Species_Spotlight:_The_Greater_Hog_Badger,_Cornered_by_a_Hunting-
            Driven_Extinction_Crisis⠀⇛


§ Finance⠀➾


    * ⚓ Opinion_|_The_High-Paid_Media_Types_Are_Unhappy_Workers_Are_Demanding
      Fair_Wages⠀⇛


    * ⚓ Why_Americans_Don’t_Know_What’s_in_the_Build_Back_Better_Act⠀⇛


           Yet, polling also shows that despite President Biden having
           introduced this proposal five months ago, a majority of
           Americans have very little knowledge as to what is in this bill
           – one of the most consequential pieces of legislation for
           working people in the modern history of our country. Americans
           can be for the bill. They can be opposed to the bill. But it is
           absurd that so many of them don’t know what is in the bill.


           Why is that? There are a number of reasons but, at the top of
           the list, is the reality that the mainstream media has done an
           exceptionally poor job in covering what actually is in the
           legislation. There have been endless stories about the politics
           of passing Build Back Better, the role of the president, the
           conflicts in the House and the Senate, the opposition of two
           senators, the size of the bill, etc. – but very limited
           coverage as to what the provisions of the bill are and the
           crises for working people that they address.


    * ⚓ Corporations_Shouldn’t_be_Masters_of_Our_Fate⠀⇛


    * ⚓ The_Future_of_Social_Security:_What_If_We_Make_It_Bigger?⠀⇛


           According to their report, if nothing changes, the trust fund
           is fully funded through 2033. After that, the benefits are 74
           percent payable (down from 79 percent in last year’s report).
           The fund has a projected shortfall of 3.54 percent of payroll
           over the next 75 years. This shortfall is a fairly large
           increase compared to last year’s projection of 3.21 percent of
           payroll. The report attributes virtually all this increase to
           advancements in the economic models used to forecast the fund’s
           future (things like birth rates, labor force demographics,
           etc.)


           A shortfall of 3.54 percent of payroll means that payroll taxes
           would need to be increased by 3.54 percentage points to fully
           fund the program. While this would constitute a relatively
           modest increase, no tax increase is unimpactful, particularly
           for low-income workers. However, the Trustees project
           substantial increases in wages over the next 75 years. That
           growth overwhelms the impact of the tax increase.


    * ⚓ French_Finance_Minister_Issues_Declaration_of_Independence_–_From_the
      U.S.⠀⇛


           It is not surprising that the differences relate to China after
           the brouhaha over the sale of U.S. nuclear submarines to
           Australia and the surprising (to the French) cancellation of
           contracts with France for submarines.  Mr. LeMaire, sounding
           very much like a reproving parent, characterized this as
           “misbehavior from the U.S. administration.”


           Mr. LeMaire made it crystal clear that the disagreement over
           submarines is symptomatic of deeper differences in world view
           that have emerged not only in France but in the EU as a
           consequence of China’s rise.  The article states:


    * ⚓ Ousted_by_AOC,_Joe_Crowley_Now_Lobbying_Against_Tax_Hikes_on_Corporate
      Giants⠀⇛


           Soon after losing his 2018 primary against progressive newcomer
           Rep. Alexandria Ocasio-Cortez (D-N.Y.) in a major political
           upset, 10-term Congressman Joe Crowley joined one of K Street’s
           largest lobbying outfits, and fresh reporting reveals that the
           former chair of the House Democratic Caucus is now working to
           torpedo his party’s proposed tax hikes on corporations and the
           wealthy.


           A recently filed document on the Senate’s disclosure website
           shows that Crowley and other lobbyists at Squire Patton Boggs—a
           massive corporate law firm whose clients include Amazon, Royal
           Dutch Shell, UnitedHealth, and the Saudi monarchy—were hired in
           July by the Securities Industry and Financial Markets
           Association (SIFMA), “one of Wall Street’s most powerful
           advocacy groups,” The Intercept reported Friday.


    * ⚓ Ignore_the_Naysayers._A_Full-Employment_Recovery_Is_Possible.⠀⇛


           It feels like eons ago, but as recently as March the Democrats
           took major action to address the ongoing Covid-19 recession
           with the American Rescue Plan. Yet ever since Congress passed
           the legislation, there have been critics, both conservative and
           centrist, who have attacked the plan for being too big and
           doing too much. Over the spring and summer, these naysayers
           made two dire predictions. Both proved wrong, but instead of
           pausing to reevaluate the policies they’d attacked, the critics
           continued at the same volume, moving the goalposts with brand-
           new claims.


    * ⚓ Squid_Game,_Capitalist_Game⠀⇛


           I believe that Squid Game is one of the best aesthetic
           depictions of the essential situation of capitalism: it reveals
           the destructive social fabric that capitalism generates,
           especially the profound barbarism that exists in our society
           behind the thinnest of veneers. It is hardly surprising that
           the series comes from South Korea, a country that has undergone
           capitalist development in one of its purest, most savage
           versions recently.


           The “updated” children’s games that appear in the series have
           much in common with modern team sports, almost all of
           which – soccer, American football, basketball, and baseball
           among others – were born in the nineteenth-century epoch of
           industrial capitalism in the US and the UK. What is remarkable
           about these games is not play, which even animals do,
           but rules. The concepts of fair play and an equal playing
           field both belong to this new world of rule-based interactions,
           reflecting the novel social situation typical of capitalism in
           which birth status, station, and caste do not, in principle,
           affect one’s position in the society. This differs sharply from
           the feudal, tributary, and slave-based societies that preceded
           capitalism.


    * ⚓ The_American_Way—2021⠀⇛


           Refugees from wars and nature’s revenge populate places while
           they await a future based on the whim of those who fear and
           even hate them. Other refugees, victims of capitalist upheaval
           and the neuroses even psychoses such an economy spawns live out
           their lives under bridges, in aqueducts bled dry, on city
           streets and in jails. Much of the world truly believes it is
           the unhoused poor’s fault they have no home except a tent and
           no medicine except a drink. The wealthy and their media
           encourage this perception while they squirrel away the cash
           they haven’t spent, their own psychosis portrayed as a virtue;
           to have more wealth than anyone can ever spend in a hundred
           lifetimes. Politicians of almost every stripe wager with our
           children’s futures for another few years of their benefactors’
           profits, unwilling to acknowledge the Faustian nature of their
           dealing or in many cases not caring.


           Parallel universes exist side by side as if they are in
           different dimensions. Capitalism’s casualties eat breakfasts
           scrounged from unfinished meals of the citizens—some who are
           but a few thousand dollars away from a similar, shared fate. In
           the belly of the beast, the whores of capitalism posturing as
           politicians contemplate destroying the shell game they call the
           economy for reasons composed of spite, hatred, and greed. Their
           blindness and stupidity doesn’t seem to provide them with the
           obvious: the destruction of the economy will not leave them
           untouched. Perhaps their goal is to create a Pinochet-style
           economy and regime. Or maybe an echo of the Russian debacle
           under Yeltsin; the one the capitalist press called a miracle.
           Potential profits made on the destruction of lives too numerous
           to count. It’s a great system when you’re near the soulless top
           of it.


    * ⚓ Ocasio-Cortez_Slams_GOP_for_Lying_About_Effects_of_Unemployment
      Insurance⠀⇛


    * ⚓ Perpetuating_Poverty: Tech_and Temp Workers⠀⇛


           “The issues of temp work aren’t just about an extra few dollars
           an hour,” DeSario told me, “it’s the larger system of
           “temporary” staffing. Temp jobs promise a path to permanent
           work, but the industry profits by perpetuating poverty for
           working people, keeping us stuck in low-wage permatemp
           positions for years, working hard but falling behind. It’s
           about being denied a fair chance at ever getting ahead.”


           Such denial is the business model of tech firms where temp
           workers labor. Employer promises to temp workers of becoming
           permanent workers are hollow. Just ask Gina DePelsMaeker, who
           blogged about her eight years as a temp worker for Dow Inc.
           Kelly IT Services was the staffing agency that contracted with
           Dow for her labor. During that time, Gina lacked employer-
           provided health care insurance. She did not receive employer-
           matching contributions to her 401K, either.  https://
           www.tempworkerjustice.org/blog


    * ⚓ Cherry-Picking_Polls_to_Hide_Public_Support_for_Biden’s_Spending_Plan⠀⇛


           Washington Post columnist Henry Olsen (9/30/21) lauded Sen. Joe
           Manchin’s opposition to the $3.5 trillion reconciliation
           package being considered by Congress, because Manchin
           “correctly reads public opinion.”


    * ⚓ Roaming_Charges:_Supply_Chain_of_Fools⠀⇛


           The attempt of the elites to restrict voting rights to their
           own propertied class has been one the of the defining features
           of American “democracy”. From 1789 to 1835, free black men were
           able to vote in Tennessee, Virginia & North Carolina, (as well
           as many northern states). Even slave owners like Andrew Jackson
           and Sam Houston campaigned for their votes. But after Nat
           Turner’s rebellion in 1831, when human “property” rose up
           against the ownership class, most of the southern states,
           freaked out at the revelation of just how tenuous their grip on
           power really was, enacted new constitutions outlawing black
           suffrage, while the northern states, even the ones which
           mouthed the rhetoric of abolition, enacted Black Codes, deny
           black suffrage, prohibiting blacks on juries and even
           restricting black residence (In Ohio, blacks had to pay bonds
           when they entered to the state). Illinois enacted its Black
           Codes in 1858, and despite repeated pleas from abolitions and
           black activists in Chicago, Lincoln, two years from being
           elected president, refused to speak out against it.


           Less than six months after Lee’s surrender at Appomattox, the
           southern states began enacting their own Black Codes which were
           nearly has onerous as the old peculiar institution itself.
           South Carolina passed a law ordering blacks confined to their
           former plantations, restricted the right to travel, and
           compelled them to work off their freedom in the fields for 12
           hours a day. Mississippi made it a crime punishable by flogging
           and forced labor in work camps for blacks to hunt or fish,
           thereby making them even more dependent on white businesses for
           food. Florida enacted a vaguely worded statute that made it a
           felony for blacks to ride in public transport or to display
           “disrespect” for their white employers or business owners. The
           punishment was to be publicly whipped and locked in a pillory.


    * ⚓ There_Are_No_Borders_for_the_Rich⠀⇛


           You’d think it a reasonable assumption that the people most
           invested in the idea of the nation-state would be the same
           people who lead them; that the men (and regrettably, it is
           mostly men) who go out of their way to run for president,
           weasel their way into a parliamentary post, or seize power by
           other means would want to maintain the facade that their
           borders, their anthems, and their founding myths mean
           something. You’d think that a figure whose rhetoric leans on
           national pride would put faith in his country and its people
           and that an individual charged with shaping policy would at
           least feign confidence in the bylaws of his own making.


    * ⚓ Billionaires_Barely_Pay_Taxes_—_Here’s_How_They_Get_Away_With_It⠀⇛


           The report, copublished by the Institute for Policy Studies and
           Americans for Tax Fairness, examines pandemic-era wealth
           accumulation by U.S. billionaires. Since it was last updated in
           August, the estimated wealth of all of these astoundingly rich
           individuals has only exploded further. But despite their
           individual economic growth, the country’s richest people often
           manage to pay exactly $0 in federal income taxes. ProPublica’s
           widely read, ongoing, in-depth reporting on “a vast trove” of
           recently leaked Internal Revenue Service (IRS) documents
           revealed that billionaires like Bezos and Musk have all avoided
           paying any federal income taxes in previous years — some for
           multiple years, in fact.


§ AstroTurf/Lobbying/Politics⠀➾


    * ⚓ Corrupt_politicians_in_Gurnee,_Illinois_hand_half_a_million_dollars_in
      taxpayer_money_to_the_Hobby_Lobby_Crime_Syndicate_for_35_jobs._–
      BaronHK’s_Rants⠀⇛


           Corrupt politicians in Gurnee, Illinois hand half a million in
           taxpayer money to the Hobby Lobby Crime Syndicate for 35 jobs.


           Just from punching that into my little calculator app, that’s
           precisely half a million dollars too much for 35 minimum wage
           jobs from a criminal outfit.


           Illinois, having a long history of corruption, and the Green
           Family having a history of using Hobby Lobby as a front to
           steal historical artifacts from the Middle East and then
           negotiate with the feds for a slap on the wrist, how much does
           anyone want to bet that there was some bribery involved?


    * ⚓ New_Study_Reveals_Poor,_Low-Income_Voters_Were_Crucial_in_Toppling
      Trump_in_2020⠀⇛


           “Rather than writing white low-income voters off, it is
           possible to build coalitions of low-income voters across race
           around a political agenda that centers the issues they have in
           common.”


           “While mechanisms to increase registration are important for
           low-income voters, there is an even greater need for policies
           and legislation that increase their ability to cast a ballot
           and actually vote.”


    * ⚓ Macedonian_Ramble:_the_Ghost_Train_to_Tirana⠀⇛


           When not reading my fireside books, I was plotting my train
           journey for the next day by consulting an old Cook’s
           Continental Timetable (if the trains are thirty years old, then
           why not have a schedule of the same vintage?) and several rail
           maps that I had copied from the internet.


           I also had from the website The Man in Seat 61 (devoted to rail
           passenger service around the world) an updated schedule, which
           showed an 8:15 a.m. train to Elbasan and Pogradec, the town on
           the border with North Macedonia to which I was headed (although
           there was some uncertainty in the posts about when the line ran
           between Elbasan and Pogradec).


    * ⚓ ‘Disgusting’:_Rahm_Emanuel_Confirmation_Vote_to_Be_Held_on_7th
      Anniversary_of_Laquan_McDonald’s_Murder⠀⇛


           Despite outspoke opposition to his nomination, a confirmation
           vote for Rahm Emanuel to become U.S. Ambassador to Japan has
           reportedly been scheduled for next week, October 20—a date that
           critics of the disgraced former Chicago mayor immediately
           pointed out is the seventh anniversary of the police killing of
           Laquan McDonald.


           “It’s disgusting that Rahm Emanuel’s confirmation hearing is
           being held on the 7 year anniversary of Laquan McDonald’s
           murder,” tweeted RootsAction, a progressive advocacy group that
           has campaigned against Emanuel’s appointment specifically for
           withholding police video of McDonald’s killing—which took place
           on Oct. 20, 2014—from the public while running for reelection
           in 2015.


    * ⚓ Imagine_a_World_with_U.S.-China_Cooperation⠀⇛


           At the moment, however, the governments of the two nations seem
           far from a cooperative relationship. Indeed, intensely
           suspicious of one another, the United States and China are
           increasing their military spending, developing new nuclear
           weapons, engaging in heated quarrels over territorial issues,
           and sharpening their economic competition. Disputes over the
           status of Taiwan and the South China Sea are particularly
           likely flashpoints for war.


           But imagine the possibilities if the United States and China
           did cooperate. After all, these countries possess the world’s
           two largest military budgets and the two biggest economies, are
           the two leading consumers of energy, and have a combined
           population of nearly 1.8 billion people. Working together, they
           could exercise enormous influence in world affairs.


    * ⚓ What_Kind_of_a_Threat_is_Russia?⠀⇛


           No matter how much the U.S. may disagree with one or another of
           Russia and China’s domestic policies, Mueller believes that
           both countries are more interested in getting rich and
           receiving the recognition they believe is their due as world
           powers than in military conquest. Mueller writes that “neither
           state seems to harbor Hitler-like dreams of extensive expansion
           by military means, and to a considerable degree it seems
           sensible for other countries, including the United States, to
           accept, and even service, such vaporous, cosmetic, and
           substantially meaningless goals.”


           Yet among the legacies of the first Cold War was the creation
           of a self-anointed caste of foreign policy alarmists in
           Washington who, according to Mueller, specialize in inferring
           “desperate intent from apparent capacity.” Well, plus ça
           change… U.S. policy toward Putin’s Russia remains driven by
           threat inflation, emotion and the duplicitous lobbying of
           various foreign interest groups on Capitol Hill, rather than a
           level-headed assessment of American national security
           interests.


    * ⚓ AT&T_and_OAN:_Not-So-Strange_Bedfellows⠀⇛


           A report linking AT&T, one of the US’s most powerful
           telecommunications corporations, to the far-right One American
           News Network has been presented as a “bombshell” revelation
           (Daily Beast, 10/6/21; Poynter, 10/7/21; Guardian, 10/7/21)
           about the connection between big capital and Trumpian populism.
           The question is: Should it be so surprising?


    * ⚓ 75_Percent_of_Democrats_Want_Party_to_Go_Big_on_Social_Spending,
      Climate_Action⠀⇛


    * ⚓ Why_Won’t_New_York’s_Top_Democrats_Back_the_Democratic_Nominee_for
      Mayor_of_Buffalo?⠀⇛


           The race for governor of New York won’t be decided for more
           than a year, but potential contenders for the Democratic
           nomination are lining up on different sides of the question of
           whether their party’s leaders should back the Democratic
           nominee for mayor of the second-largest city in the state. New
           York City Public Advocate Jumaane Williams is all in for India
           Walton, the choice of Democratic primary voters for mayor of
           Buffalo. But another prospective contender, US Representative
           Tom Suozzi, swooped into Buffalo last weekend to endorse the
           candidate Walton beat in the primary, incumbent Mayor Bryon
           Brown, who is mounting a sore-loser write-in campaign with
           substantial support from Republicans. Meanwhile, Governor Kathy
           Hochul, who hails from the Buffalo region, is taking hits for
           refusing to endorse Walton. What gives?


    * ⚓ Head_of_Koch-Tied_Group_Urges_Sinema_to_‘Stay_Strong’_as_She_Opposes
      Tax_Hikes_on_Rich⠀⇛


           The head of a right-wing organization with ties to the Koch
           network offered words of encouragement to Democratic Sen.
           Kyrsten Sinema on Thursday amid reports that she’s holding up
           her party’s budget reconciliation package over its proposed tax
           hikes on the rich and big businesses.


           “It’s wrong that she is helping profitable big corporations
           avoid taxes.”


    * ⚓ New_Filing_Reveals_Sinema_Pads_Campaign_Coffers_With_More_Pharma_and
      Finance_Funds⠀⇛


           U.S. Sen. Kyrsten Sinema, the right-wing Arizona Democrat
           obstructing her party’s $3.5 trillion Build Back Better bill,
           is the recent beneficiary of six-figure largesse from pharma-
           and finance-linked donors apparently rewarding her opposition
           to the flagship social and climate investment legislation,
           according to campaign finance disclosures filed Friday.


           Politico and The Daily Poster report that Sinema raised over
           $1.1 million between July and September, with 90% of the
           campaign donations coming from outside Arizona. At least
           $100,000 of those contributions came from individuals or
           entities linked to the pharmaceutical and financial services
           industries.


    * ⚓ LinkedIn_Loses_Its_China_Connection⠀⇛


           LinkedIn’s troubles in China came to the fore in March, when it
           paused new Chinese sign-ups and was given 30 days by China’s
           internet regulator to further police content on its platform.
           The pressure led LinkedIn to block the profiles of several
           activists and academics from being viewed in China, regardless
           of whether they were residents or not.


           It’s not the end for Microsoft in China. It still makes
           software that is widely used, and its search engine Bing is
           still available in a country where Google is not. Even LinkedIn
           in China won’t go fully dark, as the company plans on retooling
           as a pure jobs board, removing any features that could run
           afoul of Chinese regulators.


    * ⚓ Microsoft_shuts_down_LinkedIn_in_China⠀⇛


           LinkedIn will replace its localized platform in China with a
           new app called InJobs that has some of LinkedIn’s career-
           networking features but “will not include a social feed or the
           ability to share posts or articles.”


    * ⚓ LinkedIn_to_Shut_Down_Service_in_China,_Citing_‘Challenging’
      Environment⠀⇛


           LinkedIn’s action ends what had been one of the most far-
           reaching experiments by a foreign social network in China,
           where the internet is closely controlled by the government.
           Twitter and Facebook have been blocked in the country for
           years, and Google left more than a decade ago. China’s
           internet, which operates behind a system of filters known as
           the Great Firewall, is heavily censored and has gone in its own
           direction.


    * ⚓ Microsoft_to_Shut_Down_LinkedIn_in_China_Over_Censorship_Concerns⠀⇛


           LinkedIn is not completely leaving the Chinese market. It will
           now offer something called InJobs, which will not have a social
           feed and will not allow users to share content, Reuters
           reported.


           LinkedIn was the only U.S.-based social networking site still
           available to Chinese users.


§ Censorship/Free Speech⠀➾


    * ⚓ Billy_Mitchell_Survives_Anti-SLAPP_Motion_From_Twin_Galaxies_A_Second
      Time⠀⇛


           The Billy Mitchell and Twin Galaxies saga rolls on, it seems.
           Mitchell has made it onto our pages several times in the past,
           most recently over a lawsuit filed against gaming record
           keepers Twin Galaxies over its decision to un-award his high
           score record for Donkey Kong on allegations he achieved it on
           an emulator instead of an official cabinet. The suit is for
           defamation and Twin Galaxies initially tried to get the case
           tossed on anti-SLAPP grounds, but the court denied that request
           under the notion that Mitchell only has to show “minimal merit”
           in the overall case to defeat the anti-SLAPP motion.


    * ⚓ Fed_up_of_Facebook’s_censorship,_Vienna_sends_nudes_to_OnlyFans⠀⇛


           Vienna Tourist Board is on OnlyFans. Yes you read that right,
           the Austrian capital has taken to the subscriber-only site
           better known for pornography, to showcase its nude art.


           In a bid to attract more real life visitors – and make a bold
           statement about the place of nude art in Western culture – the
           tourist board has uploaded photos of naked muses painted by the
           likes of Modigliani.


    * ⚓ France_honours_‘quiet_hero’_teacher_killed_for_showing_Prophet_Mohammed
      cartoons⠀⇛


           His killer, 18-year-old Chechen refugee Abdullakh Anzorov, who
           had been living in France for years, claimed the attack as
           revenge for Paty showing his class the Mohammed cartoons in a
           lesson on free speech.


           On Saturday, several ceremonies will be held in memory of the
           popular teacher hailed by President Emmanuel Macron as a “quiet
           hero” of the French republic.


    * ⚓ Congress_vs._“the_algorithm”⠀⇛


           How it works: The bill would modify Section 230 of the
           Communications Decency Act, which protects websites from
           liability over content posted by their users.


    * ⚓ House_Democrats_target_algorithms_in_liability_shield_bill⠀⇛


           Driving the news: House Energy & Commerce Committee Chairman
           Frank Pallone’s (D-NJ) Justice Against Malicious Algorithms Act
           would remove Section 230 protections for online platforms if:
           [...]


    * ⚓ Pastor_Killed_for_Proclaiming_Christ_to_Muslims,_Sources_Say⠀⇛


           Pastor Simon Okot of Life of God Ministry in Namwenda village
           said Pastor Musana drew the ire of area Muslims while holding
           evangelistic events and public debates about Christianity and
           Islam.


    * ⚓ One_year_after_the_killing_of_Samuel_Paty_–_the_opinion_of_French_18-30
      year_olds_on_this_Islamist_attack:_23%_“not_totally”_condemn_the_Islamist
      perpetrator⠀⇛


           One year after the beheading of Samuel Paty, our Ifop survey
           shows that the opinion of 18-30 year olds on this Islamist
           attack remains ambiguous. While they say they are “shocked”,
           one in five refuse to appreciate the teacher’s educational
           efforts.


    * ⚓ France:_Muslims_threaten_to_kill_pupils_for_imitating_Muslim_prayer⠀⇛


           It all started with a video shot in a private setting in
           January that was not intended for broadcast. According to the
           newspaper, the 17-second film, shot during a birthday party,
           shows the youths, who were in ninth grade at the time, laughing
           as they imitate Muslims praying. Nevertheless, the footage was
           posted on Twitter and Instagram in early October, triggering a
           stream of abuse and death threats. Unlike the case of Mila, who
           was accused by her harassers of publicly insulting Islam, “this
           is more of a very silly goings-on,” a source familiar with the
           case told Ouest France. “But we can see that it is already
           getting out of control.The pseudonyms and sometimes even the
           real names of the youths were published on social networks. The
           investigators therefore claim that they are taking the matter
           seriously. A few days after the first broadcast of the video
           and the filing of the first complaints, on Wednesday October
           13, they were still in the consultation phase.But then they
           began to identify the anonymous user accounts behind which the
           abusers were hiding. They face up to five years in prison. At
           the same time, their school headmasters and parents’
           associations say they are careful not to stigmatise them and
           warn students not to misuse social networks.


§ Freedom of Information/Freedom of the Press⠀➾


    * ⚓ Turkish_Media_Face_18_Trials_in_One_Week⠀⇛


           Lawyers and media rights groups say the trials show how
           Turkey’s laws on terrorism and protests can be used to detain
           or harass journalists.


           Nearly all those in court this week face accusations of
           belonging to or creating propaganda for a terrorist
           organization—often a reference to the militant group, the
           Kurdistan Workers’ Party (PKK). Others face charges of defying
           Law 2911, which regulates public meetings and demonstrations,
           according to the Media and Law Studies Association (MLSA), a
           Turkey-based group that offers legal support to journalists.


           Media who cover protests can sometimes be accused of organizing
           an illegal gathering. And in April, Turkey’s Interior Ministry
           issued an order requiring journalists to have permits for
           covering approved protests.


           Some rights lawyers have said the ruling appears designed to
           silence journalists.


§ Civil Rights/Policing⠀➾


    * ⚓ Opinion_|_A_Zen_Koan_on_Columbus_Day⠀⇛


           It’s too easy, right? Too simple—shoving Christopher Columbus
           off the historical honor roll, pulling down his statues,
           yanking his “day” away from him and renaming it in honor of the
           people he murdered, kidnapped, turned into property?


    * ⚓ Progressives_to_Biden:_Ignore_Panel_Advice_and_Embrace_Supreme_Court
      Expansion⠀⇛


           Progressive lawmakers and advocacy groups on Friday urged
           President Joe Biden to disregard the advice of a bipartisan
           panel he convened earlier this year and embrace Democratic
           legislation that would add four justices to the U.S. Supreme
           Court, an effort aimed at combating the right-wing takeover of
           the nation’s judicial system.


           “Democrats must move swiftly to pass the Judiciary Act to add
           four seats to the court before it’s too late.”


    * ⚓ We_Reported_on_a_County_That_Has_Jailed_Kids_for_a_Crime_That_Doesn’t
      Exist._Readers_Reacted.⠀⇛


           In 2016, in Rutherford County, Tennessee, 11 kids were
           arrested, the youngest just 8 years old. The arrested kids were
           accused of not stopping a scuffle involving two 5- and 6-year-
           old boys who were throwing punches at a larger boy. At least
           one of the kids arrested did try to step in. Some of the others
           hadn’t even been there. More importantly, the formal charge
           approved by judicial commissioners — “criminal responsibility
           for conduct of another” — is not even a crime.


           The police arrested four of the kids directly from school.
           Their principal, Tammy Garrett, collected three of them from
           their classrooms at an officer’s insistence.


    * ⚓ “People_vs._Fossil_Fuels”:_Over_530_Arrested_in_Historic_Indigenous-Led
      Climate_Protests_in_D.C.⠀⇛


           This week over 530 climate activists were arrested during
           Indigenous-led civil disobedience actions in Washington, D.C.,
           calling on President Joe Biden to declare a climate emergency
           and stop approving fossil fuel projects. Indigenous leaders
           have issued a series of demands, including the abolition of the
           Bureau of Indian Affairs, whose offices they occupied on
           Thursday for the first time since the 1970s. The protests come
           just weeks before the start of the critical U.N. climate summit
           in Glasgow, Scotland, which President Biden and senior Cabinet
           members are expected to attend. “We’re not going anywhere,”
           says Siqiñiq Maupin, with Sovereign Iñupiat for a Living
           Arctic, who traveled from Alaska to D.C. and was among those
           arrested during the BIA occupation. “We do not have time for
           negotiations, for compromises. We need to take this serious and
           take action now.” We also speak with Joye Braun, with the
           Cheyenne River Sioux Tribe and the Indigenous Environmental
           Network, who was deeply involved in the Standing Rock protests
           to stop the Dakota Access pipeline. “The United States
           government brought the frontlines to us, to the Indigenous
           people, to our doorsteps,” says Braun. “And we wanted to bring
           the frontlines to his doorstep to let him see that we are very
           serious about climate change and declaring a climate
           emergency.”


    * ⚓ Cori_Bush_Slams_GOP_Governor_for_Threat_to_Prosecute_Reporter:_“Shame
      on_You”⠀⇛


    * ⚓ A_Death_Trap?_As_12th_Prisoner_Dies_at_NYC’s_Rikers_Island,_Calls_Grow
      to_Close_World’s_Largest_Jail⠀⇛


           We take an in-depth look at the growing humanitarian crisis at
           the world’s largest jail complex, Rikers Island in New York
           City. After touring the jail, New York City Public Advocate
           Jumaane Williams describes it as “a disaster.” In response to
           mounting public pressure, most of the women and transgender
           people at Rikers are being transferred to two prisons,
           including a maximum-security facility, even as most are still
           awaiting trial. “It’s like putting a Band-Aid on a gunshot
           wound,” says Anisah Sabur, who was formerly incarcerated at
           Rikers and one of the prisons and is now a leader with the HALT
           Solitary Campaign. Prosecutors and judges “hold the keys to
           Rikers,” notes Jullian Harris-Calvin, director of the Greater
           Justice New York program at the Vera Institute of Justice, who
           says they must be pressured to continue bail reform and not
           fall prey to misconceptions about crime rates, and instead
           adopt measures to adequately address public safety. “We need to
           make bail affordable or just release them,” Harris-Calvin says.


    * ⚓ Here_Come_the_Abortion_Bounty_Hunters⠀⇛


           Texas’s cruel new anti-abortion law is more than just an
           unconstitutional restriction on reproductive choice. It’s also
           an egregious new frontier in late capitalism.


           In addition to banning abortion beyond six weeks into
           pregnancy, the Texas law allows private citizens to sue anyone
           who helps a person abort a pregnancy, promising $10,000
           payments for the bounty hunters.


    * ⚓ Resisting_Fascism:_A_Review_of_Shane_Burley’s_Why_We_Fight⠀⇛


           Wisely, journalist Shane Burley bypasses this debate in his new
           collection of essays Why We Fight: Essays on Fascism,
           Resistance, and Surviving the Apocalypse. It’s clear there are
           both similarities and differences between classical fascism, on
           the one hand, and Trumpism and the modern far-right on the
           other. (For this reason, one might call the latter neofascism
           or proto-fascism, as an acknowledgement of the valid points
           made on both sides of the debate.) Instead, Burley takes it for
           granted, and illustrates throughout his book, that a vast
           constellation of groups and individuals on the right today have
           salient fascist characteristics and would happily tear down
           democracy if they could. Why We Fight consists mostly of
           articles Burley has published in recent years shedding light on
           these shadowy groups, this underworld of the Alt-Right and its
           relatives.


           In seventeen chapters, Burley illuminates the methods and
           varieties of both fascist and anti-fascist organizing. Among
           the topics he covers are the rise and fall of the Alt-Right,
           from 2008 to the aftermath of the Charlottesville “Unite the
           Right” rally in 2017; the nature of the “Alt-Light,” a less
           extreme version of the far-right that coalesced around figures
           like Milo Yiannopoulos, Alex Jones, and online “manosphere”
           leader Mike Cernovich; the toxic cult of masculinity that
           unites a wide range of far-right groups; the world of fascist
           publishing in Europe and the U.S., led by companies like Arktos
           Media and Counter-Currents that are dedicated to “creating the
           intellectual foundation for a new fascism” (p. 151); attempts
           by anti-fascists to colonize cultural spaces that have often
           attracted fascists, such as soccer, gun clubs, mixed martial
           arts, the paganism and heathenry subculture, and, in music,
           black metal and neofolk; the deep-rooted and continuing appeal
           of antisemitism to the far-right; and even the remarkable
           Kurdish experiment in an anarchist, anti-fascist society at
           Rojava. Altogether, the book gives a nuanced and compelling
           picture of the highly fragmented, internally divided, typically
           amateurish, but very frightening world of the contemporary far-
           right—from the Proud Boys to militia organizations, from
           journalist provocateurs like Andy Ngô to the neo-Confederate
           Council of Conservative Citizens (founded in 1985), from “lone
           wolf” mass shooters to student groups like Turning Point USA
           that seek to intimidate and silence left-wing voices at college
           campuses.


    * ⚓ “Long_March_for_Justice”_Underway_Across_New_Jersey_to_Demand_Police
      Reform,_Reparations⠀⇛


           We get an update from New Jersey, where the People’s
           Organization for Progress is leading a 67-mile march to demand
           the state Legislature pass legislation to hold police
           accountable. The nine-day march wraps up Saturday, and
           activists are demanding passage of a state policy that would
           give police review boards subpoena power, ban and criminalize
           chokeholds, establish requirements for use of deadly force and
           end qualified immunity in New Jersey. At the national level,
           they are calling for the passage of the George Floyd Justice in
           Policing Act and the John Lewis Voting Rights Act. “We know
           that electoral politics alone is not enough,” says Larry Hamm,
           chair of the People’s Organization for Progress, when asked
           about his activism following his run for the U.S. Senate this
           past year. “The primary antidote to police brutality is the
           organized and mobilized people.”


    * ⚓ “Striketober”_Roars_as_Nearly_100,000_Workers_Authorize_Work
      Stoppages⠀⇛


    * ⚓ Opinion_|_Strike_Wave_Exemplifies_Why_We_Need_More_Unions⠀⇛


           Ten thousand John Deere workers went on strike Thursday. Sixty
           thousand IATSE members may be on strike by Monday. They will
           join the thousands of nurses, miners, hospital workers, factory
           workers, and others already on strike across America. Here we
           are, in our long-awaited strike wave. What does this thrilling
           development tell the labor movement about what its future
           direction should be? 


    * ⚓ Journalists_In_St._Louis_Discover_State_Agency_Is_Revealing_Teacher
      Social_Security_Numbers;_Governors_Vows_To_Prosecute_Journalists_As
      Hackers⠀⇛


           Last Friday, Missouri’s Chief Information Security Officer
           Stephen Meyer stepped down after 21 years working for the state
           to go into the private sector. His timing is noteworthy because
           it seems like Missouri really could use someone in their
           government who understands basic cybersecurity right now.


    * ⚓ Comparing_France_to_Afghanistan_is_an_insult_to_the_women_oppressed_by
      the_Taliban⠀⇛


           France is trying to defend Enlightenment values – which is more
           that can be said for most Western countries. The ridiculous
           comparisons of France to the Taliban reflects poorly on Muslims
           who proliferate this argument. Instead of demonising France and
           spreading nonsense accusations, they should focus on Muslim
           countries that are actually violating even basic human rights.


§ Internet Policy/Net Neutrality⠀➾


    * ⚓ GOP_Very_Excited_To_Be_Handed_An_FCC_Voting_Majority_By_Joe_Biden⠀⇛


           Consumer groups have grown all-too-politely annoyed at the
           Biden administration’s failure to pick a third Democratic
           Commissioner and permanent FCC boss nearly eight months into
           his term. After the rushed Trump appointment of unqualified
           Trump ally Nathan Simington to the agency (as part of that dumb
           and now deceased plan to have the FCC regulate social media),
           the agency now sits gridlocked at 2-2 commissioners under
           interim FCC head Jessica Rosenworcel.


§ Monopolies⠀➾


    * § Patents⠀➾


          o ⚓ ‘How_Many_More_People_Must_Die?’_EU,_UK_Under_Fire_for_Tanking
            Patent_Waiver_Talks⠀⇛


                 The latest meeting of the World Trade Organization’s
                 intellectual property council ended Thursday without a
                 deal to suspend coronavirus vaccine patents as the United
                 Kingdom, Germany, and other rich European nations
                 continued to stand in the way, shielding the
                 pharmaceutical industry’s stranglehold on production of
                 the lifesaving shots.


                 “Our current inequality in access to Covid-19 vaccines is
                 morally unacceptable.”


    * § Trademarks⠀➾


          o ⚓ Trader_Joe’s_Threatens_Man_Over_Parody_‘Traitor_Joe’_Political_T-
            Shirt⠀⇛


                 The last time we found niche grocery chain Trader Joe’s
                 playing intellectual property bully, it was over one
                 enterprising Canadian man who drove across the border,
                 bought a bunch of good stuff from Trader Joe’s, and then
                 resold it at his Canadian store called “Pirate Joe’s”.
                 While that whole setup is entertaining, Trader Joe’s sued
                 for trademark infringement in the United States, which
                 made zero sense. The store was in Canada, not the States,
                 reselling purchased items is not trademark infringement,
                 and Trader Joe’s was free to open up Canadian stores if
                 it chose.


    * § Copyrights⠀➾


          o ⚓ Suing_Infrastructure_Companies_for_Copyright_Violations⠀⇛


                 I was an expert witness for Cloudflare in this case,
                 basically explaining to the court how the service works.


          o ⚓ ‘Copyright_Troll’_Boss_Faces_Arrest_Over_Failed_Payments_in
            Piracy_Case⠀⇛


                 Malibu Media, an adult entertainment company that has
                 collected settlements from thousands of pirates over the
                 years, is now facing legal issues of its own. An Illinois
                 federal court has ordered the arrest of Malibu’s CEO
                 after the company failed to pay compensation to a falsely
                 accused Internet subscriber. The order is conditioned for
                 now but will be executed if there’s no progress in the
                 weeks to come.


          o ⚓ Police_Hit_‘Criminal_Network’_Behind_Pirate_IPTV_Service_&
            Investigate_Customers⠀⇛


                 Following raids across Germany carried out in the past
                 several weeks, police say they have successfully shut
                 down a pirate IPTV provider and identified 10 individuals
                 connected to the service. Among the suspects is a 34-
                 year-old that police believe to be the head of the
                 operation. The service allegedly caused significant
                 financial damages to broadcasters including Sky.


          o ⚓ Join_us_at_‘The_Future_of_Open’_Webinar_on_9_November!⠀⇛


                 In May this year, we announced that four working groups
                 of the Creative Commons Copyright Platform would examine
                 policy issues affecting the open ecosystem. For the past
                 five months, they have worked vigorously to provide
                 clearer articulation of the issues and consider possible
                 solutions in four areas: 


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