𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, August 29, 2022
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Generated Tue 30 Aug 02:41:38 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2022/08/29/
╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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⦿ Your Bank and Other Web Sites Are Running Creepy JavaScript That Records Your Every Action | Techrights
⦿ [Meme] Bringing Cheeks Together | Techrights
⦿ IRC Proceedings: Sunday, August 28, 2022 | Techrights
⦿ The ’Linux’ Foundation is Working Against Linux for People Who Reject Linux | Techrights
⦿ Linux Foundation Drowning in Grift and 7-Figure Salaries (Awarded to People Who Never Created Anything) | Techrights
⦿ EPO Management Trying to Make EPO Staff Miserable and Isolated | Techrights
⦿ The Inquisition of Norbert Preining is a Cautionary Tale About the Clique That’s Killing Debian From the Inside | Techrights
⦿ ZDNet’s Exit Strategy: Ugly/Cheap Redesign, Infinite Scroll for Fake ’Traffic’ (‘Engagement’), and Hardly Any New ‘Content’ | Techrights
⦿ Echoes of Narcissism: How Jim Zemlin Views Himself | Techrights
䷼ Bulletin articles (as HTML) to comment on (requires login):
http://techrights.org/2022/08/29/creepy-javascript/#comments
http://techrights.org/2022/08/29/epo-staff-slapped/#comments
http://techrights.org/2022/08/29/irc-log-280822/#comments
http://techrights.org/2022/08/29/lf-rejects-linux/#comments
http://techrights.org/2022/08/29/lf-still-no-pdf/#comments
http://techrights.org/2022/08/29/making-epo-staff-miserable/#comments
http://techrights.org/2022/08/29/norbert-preining-canary/#comments
http://techrights.org/2022/08/29/zdnet-exit-strategy/#comments
http://techrights.org/2022/08/29/zemlin-narcissism/#comments
䷞ Followed by Daily Links (assorted news picks curated and categorised):
http://techrights.org/2022/08/29/canonical-helping-microsoft/#comments
http://techrights.org/2022/08/29/general-resolution-firmware/#comments
http://techrights.org/2022/08/29/mx-21-2/#comments
䷩ 𝚕𝚒𝚗𝚎 73
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/creepy-javascript/#comments
Gemini version at gemini://gemini.techrights.org/2022/08/29/creepy-javascript/
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Gemini_version_available_♊︎
✐ Your_Bank_and_Other_Web_Sites_Are_Running_Creepy_JavaScript_That_Records_Your
Every_Action⠀✐
Posted in Free/Libre_Software, Protocol, Security, Standard at 2:51 pm by Guest
Editorial Team
Reprinted with permission from Ryan
Your bank and other Web sites are running creepy “Session-Replay” JavaScript
that follows you around the site recording your every movement.
You’re not “supposed to know” about this, but NoScript can block that from
running.
I had a conversation with Matthew Garrett (alleged security person, actual
drama bomb thrower) on IRC the other day about the “security” of JavaScript.
He had previously promoted it as a “great way of running untrusted code”.
Unfortunately, there’s just nothing secure about JavaScript. It’s the most
widely abused platform in all of computing because almost everyone ends up
running it without thinking of the consequences, and browsers which are
instructed to do so, do it without bothering to allow any user control over the
process in their default state.
If you can’t trust code, it’s better to not have it running at all.
Especially if it’s not doing anything to help you, and is proprietary.
Garrett said that “total sandbox escapes” where the program gets out of your
browser sandbox and starts interfering with another tab or running arbitrary
malicious code outside of any sort of confinement is “rare” to the point where
someone would need to be “targeting you” and willing to blow a Zero Day exploit
to do it.
That’s not exactly true as we see time and time again in the real world. But
let us not hang ourselves up too long on what the Dalek of Social Justice has
said.
If you drop a copy of O’Reilly’s book on Sixth Edition JavaScript from the
kitchen counter, you’ll be walking with a limp for a while. Far from something
that adds a little bit of “interactivity” to a Web page, JavaScript is a full
blown computer programming language, Turing-complete, that can be used to write
and run almost anything.
(I laughed the other day when I noted that someone had ported all of the LAME
MP3 Encoder to JavaScript. It’s like, you could. But why? This is even dumber
than online Office suites. People have spent years and lots of effort writing
high performance encoding routines in C. Let’s make things worse and shove it
to a Web server!)
Very little of what I do on the Web calls for something like JavaScript.
Nobody asked me if I wanted applications that run best on my computer, where I
control them, where Big Brother is not looking over my shoulder replaced by
some online version on someone else’s computer that I may or may not be able to
access, and if I can, it’s watching what I do with it.
I don’t use Services_as_a_Software_Substitute where I can avoid it, and the
ones I do use tend to be licensed under the GNU Affero General Public License,
which makes them Free and Open Source Software.
If I don’t like someone’s Searx search engine, I can use someone else’s. If I
don’t like a Matrix (protocol) chat server’s moderation, I can go use another
one. If anyone wants to know what the source code does, or make their instance
work differently, they can!
Web applications don’t have to be malicious. It’s just that many of them are.
In general, every way that Microsoft’s proprietary software could hurt you
before is wrong with their Web applications, and then they’ve invented new ways
of being nasty as well. So thanks, no thanks.
The people who invented the Web and the earliest browsers (such as Marc
Andreeson, who said as much in 1994) wanted to keep it lightweight. The idea of
JavaScript and even Cascading Style Sheets were controversial.
They knew that if these “features” were added, the consequences would be
severe. And they are severe!
The Web has basically become Microsoft Windows. Bloated, fat, slow, and
requiring a new computer every 4-5 years because of how painful things get.
Features that are only useful to advertisers and marketers and spyware and
other parasites being bolted on with no debate by Google and Microsoft, and
tossed in by Mozilla and Apple “for compatibility”. Worse, it’s all impossible
to secure and it’s rather embarrassing how complicated the standards are to get
it to do much at this point. (There are starting to be chat servers implemented
in GeminiSpace. But on the Web, you need to run a 600 MB tab for that!).
Worse, the Web rots. It’s become mostly a spam farm. Things disappear. Domain
squatters come in. All your links go to a scam now. The entire thing has become
so balkanized by megacorporations that come and go that if you use those
“services”, every 10 years you have to figure out where all the people you used
to talk to are.
We have to start backing away from standards that are hacked together by
companies that won’t exist in a few years based on speculative business plans,
many of which ought to be criminal.
Attackers take advantage of whatever they can.
They take advantage of poorly coded applications, gaps in security policy
whether deliberate or accidental (some Windows malware includes the calculator
from Windows 7 to get past User Account Control and evade virus scanners, for
example), or software distributors like Apple which do not ship Web browser
security updates quickly (giving the attackers time to study the fix and start
exploiting a long time before most users are patched), or users who do not
apply fixes.
Recently, Apple had to rush two emergency fixes for the kernel in Mac and iOS
and for Webkit (Safari) for zero day vulnerabilities, and it’s hardly even like
it’s rare for in-the-wild attack code to be targeting these platforms.
A while back, China_attacked_and_targeted_Uyghurs_using_a_Safari_vulnerability
in_the_JavaScript_engine. They’re not the only nation state that hoards
software vulnerabilities. The US FBI and NSA are known to do it.
But aside from the sandbox escapes and arbitrary code execution are privacy
problems that Tracking and Session-Replay scripts cause.
According_to_an_article_from_VICE_from_2017 (compacted with NewsWaffle and
archived), at that time, 482 of the top 50,000 Web sites had JavaScript
programs that followed the user around and recorded things that can even
include keystrokes that aren’t “submitted” yet, and mouse movement patterns,
and some even tie your activity to your real identity.
This is….super creepy and super sketchy!
Richard Stallman’s JavaScript_Trap essay pointed out that many users end up
running non-Free JavaScript programs without thinking much about it. I pointed
out in an earlier post about how much I like the add-on NoScript.
In many cases, JavaScript is bloated, it’s spyware, it’s proprietary, and at
the very least, it does something unwanted and aggravating, such as powering
news site paywalls.
Firefox, some time ago, joined the majority of Web browsers in removing the
user’s ability to turn off JavaScript globally, but NoScript can add this back.
You can do whatever you want to. You can whitelist domains that are “Just
Enough” to make the site work.
Even browsing in the non-default mode of “Temporarily Allow All Top-Level
Domains” would provide a lot of protection from malicious, annoying, and
bloated third-party scripts without forcing you to do too much manual
intervention.
But it isn’t even like JavaScript engines really are that secure. By the time
Mozilla finally does declassify security hole fixes for a Firefox release, you
can go back and easily see that the majority of really nasty ones involved
JavaScript, so the more domains you have it coming in and executing from, the
more likely one is to come in and do something nasty.
Odds approach 100% very quickly that your browser is running some kind of
malware without telling you.
It’s bad enough when programs are “legitimate” in the sense that they are what
they say they are, do something useful, and just won’t tell you how they do it.
That’s what Stallman’s complaints were in The JavaScript Trap.
Unfortunately, there’s never been a more useful language to abuse the user
with, or a better place to run it, than JavaScript in a Web browser.
Admitting defeat and turning it all on out of laziness simply ensures that you
will be encountering serious malware at some point.
Unfortunately, the JavaScipt Problem is bigger yet than proprietary software
and malware running behind-the-scenes. Some site owners set their Web sites to
simply lock out people who are using Tor Browser, a VPN, or just simply have
JavaScript turned off.
CloudFlare, a Web cancer that just keeps growing bigger, now hosts about 1/5th
of major Web sites and about as many smaller ones too, and has convinced site
owners to set “security” settings high to bounce people who fit these
categories. I’m a VPN and Tor user with NoScript, so I run into problems with
those “Checking your browser” pages somewhat frequently.
The other day, I was trying to look at an article on Bleeping Computer, and
CloudFlare blocked me for using my VPN. So I opened up Opera, which I only
occasionally use because CloudFlare blocks their Opera “VPN” (proxy) except in
the EU for some reason, so I had to view the article in Opera and then close
Opera.
JavaScript is a major annoyance on banking Web sites. One of the advantages of
running NoScript and just whitelisting the top domain for the bank is that I
use 6 banks, and they all work with just first party scripting turned on. The
rest is Session-Replay, data analytics, and other crap and garbage.
Why do I want some creepy third-party script looking over my shoulder while I’m
banking or using any Web site for that matter?
When I went to the United States Social Security Administration and the
Internal Revenue Service, I even found Session-Replay scripts that they were
attempting to load from third-party domains!
Once again, with these scripts excised from the site, the functionality I
wanted to use still worked. With your Web browser’s default settings, spyware
companies are recording your actions even on government Web sites that you have
to use!
I counted at least six tracking companies monitoring your usage of the Social
Security Administration’s site. They’ve even outsourced compliance with the
Americans With Disabilities Act to a tracking company that records your
session!
On top of the security and privacy concerns are more practical ones.
Some JavaScript malware is designed to commit theft of utilities. Some sites
resort to “mining” cryptocurrency with JavaScript and WebAssembly (which
NoScript also handles). This runs your CPU hard and causes your power bills to
rise as your battery life falls.
Firefox, indeed most major Web browsers, now have some sort of anti-
cryptomining feature, but nothing’s perfect. The less sites even have the
permission the less chance they’ll get one of these loaded.
Tracking scripts also take resources to run. They slow down page loads and
instruct your computer to do things. That’s not “free”.
The Web site owners don’t want to make a big fuss about all of this crap that
they load, because when you investigate what the companies are telling them,
it’s usually like, “We can help you monetize your site and optimize your search
engine results and tell you all of these things about your visitors and what
they do.”. Stealing your resources to benefit themselves is what they do.
How does this compare with ad blocking, or running add-ons such as
Decentraleyes?
Ad blocking and Decentraleyes (which hosts commonly used Web frameworks locally
to avoid Content Delivery Network requests) compliment NoScript and add to the
privacy you can expect to gain from it.
uBlock-Origin (an ad and tracking blocker) is already a pretty big hammer. It
will block ads and tracker lookups completely if they’re in your blacklists.
Unfortunately, many things are not included for whatever reason. They tend to
give priority to not breaking anything on a site you could conceivably want to
use, and there have been cases where tracking companies used the US DMCA to be
removed from ad blocking lists. So it’s not bulletproof. There are too many
things that slip past them, and that’s where NoScript comes in.
Between these things, you should be able to reduce your browsing data usage by
about half.
There are a few other extensions I really like, such as Google Container. I
don’t use Google very much (preferring the Free and Open Source Searx
instances) and I’d like to stay logged in, but not outside that container (so
Google can’t easily track me in general across the Web).
As I’ve increasingly focused on Gemini (such as Chilly Weather and the
NewsWaffle on Gemi.dev) instead of the Web, I’ve found few cases where I
actually need JavaScript to run to power something I want or need to do on the
Web.
Ironically, writing this blog post about JavaScript requires me to run some
JavaScript.
Even then, not all of the domains that the WordPress.com editor wants to load
are necessary, and when I go to read blogs, I don’t need JavaScript at all. You
don’t even need a graphical Web browser to read this. You can load it in text
browsers that don’t even support JavaScript, with cookies turned off.
You should block most of WordPress’s JavaScript. I think most of it comes from
analytics sites.
As I continue looking into an escape from the Web for most activities, I still
occasionally need to watch a video or refill a prescription or make
appointments with my doctor, or use some dumb banking site, and pay my taxes.
Unfortunately, thanks to JavaScript being as widely abused as it now is, you
need NoScript to make sure that these creepy programs can’t run.
I’m considering moving to a Gemlog instead of WordPress, but I’m going to have
to learn how to do that so it may be a while. Eventually, I would like to leave
an “I’m not here anymore. Use Gemini.” message on WordPress.
We’ll see when I manage to get around to this.
Until then, turn off your JavaScript, mostly. The Web is more pleasant when
there’s less of it.
Although I mostly read news in the NewsWaffle, most of the annoyances and
slowdowns (bloated JavaScripts, annoying videos, tracking) are gone from news
sites with NoScript. Even when I load a CNN article with uBlock-Origin and
NoScript, it comes up instantly. CNN is infamous for its terrible page load
performance.
You can get NoScript here:
Firefox_Add-Ons / Homepage
License: GNU General Public License Version 2
There is also a port of the extension available for Firefox on Android.
Unfortunately, iOS users will just have to live with JavaScript. The version of
Firefox on iOS isn’t the real Firefox with Gecko. It’s a neutered version that
has to use the same engine as Safari by diktat of Apple.
Unfortunately, this means Web browsers on iOS are insecure and impossible to
fix, and issues such as the one Apple rushed an emergency fix for cannot be
user-mitigated by blocking active content. █
䷩ 𝚕𝚒𝚗𝚎 463
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/epo-staff-slapped/#comments
Gemini version at gemini://gemini.techrights.org/2022/08/29/epo-staff-slapped/
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Gemini_version_available_♊︎
✐ [Meme]_Bringing_Cheeks_Together⠀✐
Posted in Europe, Patents at 9:24 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_Staff;_The_'f***ing_president'⦈_
António_Campinos refers to himself as the “f***ing president”
Summary: EPO staff continues to be abused and its patience is being tested
⣿⠀⠀⣾⠀⠀⢠⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀
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⣿⡇⠀⣿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⠿⢛⣳⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧
⣿⢇⠀⢹⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⢿⣿⣿⣛⠿⣻⣴⠞⡚⠉⠊⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣷⡀⢸⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢁⣸⣿⣿⣿⣫⠭⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⢹⡟⣧⠸⡀⢪⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⠠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⢇⠘⣇⡇⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⣿⣿⡿⢿⠟⢀⡤⠤⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣀⠸⡄⠹⡇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⣇⠀⢷⠀⢳⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢻⠀⢸⡀⠘⡇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣿⢿⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣟⠀⠀⡇⠀⢹⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠀⠀⢱⠀⠘⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⢹⣶⢠⢸⡄⠀⡇⢡⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⡸⣿⣿⣄⡇⣶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⣰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⡇⣿⣿⣇⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⣰⣿⣿⣿⣷⠀⢀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⢨⣿⣿⢸⣿⣿⢀⣴⣿⣿⣿⣿⣿⣦⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡘⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⠃⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⡀⢸⣿⣿⠿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣴⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣦⣤⣤
⣿⣾⣿⣷⣿⣶⣶⣯⣟⡛⠛⠛⣿⣿⡿⣿⣿⣏⢉⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⠉⠉⠀⠈⠉⠙⡁⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠛⠛⠉⢉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⠿⠟⠃⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⣀⣒⣢⣤⣤⣤⣤⣤⣶⣶⠶⣶⣖⣛⣻⠃⠀⠀⠀⠀⢠⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠤⣾⣿⣿⣿⣿
⣻⣟⣻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⢶⣶⠆⠀⠀⠂⡛⠛⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣯⣭⣿⣿⣿⣿⣿⣶⣶⣶⣾⠊⠛⠈⢽⣿⣁⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣼⡏⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⠛⠻⠟⠛⠛⠛⠛⠉⠉⠉⠉⠁⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠠⠄⠒⢺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⠀⠀⠀⣾⣿⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⢻⣿⠿⠟⠋⠉⠁⠀⠀⠀⢀⣀⣀⣼⣿⠿⠿⠛
⣤⣄⣤⣤⣤⣶⣿⣤⣴⣴⣤⣤⣤⣤⣤⣵⣥⣵⡶⡦⠀⣿⣿⣾⣿⣿⣆⣀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⣤⣤⣤⠶⠶⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⡿⢿⣿⣿⣷⣶⣶⣞⣛⣛⣿⣿⣿⣿⣿⡟⠛⠻⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠰⢾⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠭⠉⠙⠛⡃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣷⣦⣌⡉⠙⠳⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣯⣟⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠈⠉⠉⢻⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠉⠙⠛⣶⣶⣤⣶⣖⠛
[35A⣿⠀⠀⣿⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀
⣿⠀⠀⡏⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀
⣿⡇⠀⣷⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀
⣿⡇⠀⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⠛⣑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷
⣿⢇⠀⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⢻⣿⣿⢛⠿⣛⡵⠖⠛⠉⠶⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣷⡀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢁⣸⣿⣿⣶⣻⠭⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⢹⡟⣧⠸⠀⢪⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⢇⠘⣇⡇⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⣿⣿⡿⠿⡟⠠⡤⠤⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣀⠸⡄⠹⡆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⣇⠀⣷⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢻⠀⢸⡀⠘⡇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣿⢿⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⠀⠀⡇⠀⢹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠀⠀⢹⠀⠘⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⢹⣶⣠⢸⡀⠀⡇⢡⣤⣶⣶⣶⣶⣶⣶⣶⣶⣖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⡸⣿⣿⡀⡇⣦⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⣰⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⡇⣿⣿⣇⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⣰⣿⣿⣿⣧⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⠐⣿⣿⢸⣿⣿⢀⣴⣿⣿⣿⣿⣿⣆⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠿⠻⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⠃⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⣿⡿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣴⠿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣦⣤⣤
⣿⣾⣿⣷⣿⣶⣦⣭⣛⠛⠛⠛⣿⣿⡟⣿⣿⣟⠩⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠉⠉⠀⠈⠉⠙⠀⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠛⠛⠉⢉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡭⠭⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠻⠟⠛⠃⠀⠀⠀⠸⣾⣿⡄⠀⠀⠀⣀⣒⣠⣤⣤⣤⣤⣤⣶⣶⠶⣶⣖⣛⣻⠃⠀⠀⠀⠀⢠⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⣾⣿⣿⣿⣿
⣻⣟⣻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⣶⠆⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣭⣽⣿⣿⣿⣿⣷⣶⣶⣶⣾⠊⠛⠈⢿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⣼⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡿⠛⠛⠟⠛⠛⠛⠋⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠐⢺⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⣾⣿⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⢻⣿⠟⠟⠋⠉⠁⠀⠀⠀⢀⣀⣀⣼⣿⠿⠿⠛
⣀⣠⣤⣤⣤⣼⣶⣤⣦⣤⣤⣤⣤⣤⣤⣭⣭⣵⡶⡆⠀⣿⣿⣾⣿⣿⣄⣀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⠆⠀⠀⠀⠀⣤⣤⣤⠴⠶⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⠿⢿⣿⣿⣷⣶⣶⣞⣛⣛⣿⣿⣿⣿⣿⡟⠛⠻⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠰⢮⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠭⠉⠙⠛⢃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣷⣦⣌⡉⠙⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣮⣟⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠈⠉⠉⢻⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠉⠙⠛⣶⣶⣤⣶⣖⠛
[35A⣿⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀
⣿⡄⠀⢸⠀⠀⠸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀
⣿⡇⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆
⣿⡇⠀⣼⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠟⢛⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏⢙⢿⠿⣛⠿⣋⡴⠾⠛⠉⠤⠂⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⡀⢸⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠙⣿⣿⣿⣿⣗⣫⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠸⡟⣷⡸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⡏⣀⡤⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⢳⠘⣧⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⠇⢰⣶⣦⠤⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡄⠘⡆⠸⣇⢸⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⢃⠀⢻⠀⢹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣸⠀⠸⡆⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣿⢿⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⡄⠀⣇⠀⢸⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠀⠀⢸⠀⠈⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⢸⣷⣰⠘⡆⠀⡇⢰⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠈⣿⣿⡄⣇⢰⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⣰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⣇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⢠⣿⣿⣿⣷⠀⢀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⠘⣿⣿⢸⣿⣿⠀⣰⣿⣿⣿⣿⣿⣇⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣀⣀⣀⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⣿⣴⠿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣤
⣿⣾⣿⣿⣾⣷⣶⣭⣛⠛⠛⠛⣻⣿⡿⣿⣿⣿⡪⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣦⣹⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠉⠉⠀⠈⠉⠙⡁⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠛⠛⠉⠉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡀⠀⠀⠀⠠⠶⠶⠚⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠛⠟⠿⠃⠀⠀⠀⠰⢿⣿⡆⠀⠀⠀⣀⣒⣲⣤⣤⣤⣤⣤⣶⡶⠶⣶⣶⣻⠂⠀⠀⠀⠀⣾⣯⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⣴⣿⣿⣿⣿
⣛⣿⣻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⣶⡶⠀⠀⠐⠘⠛⠛⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣭⣭⣿⣿⣿⣿⣾⣷⣶⣶⣾⠙⠋⠉⢿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⢠⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠠⠄⠒⠺⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⠀⠀⠀⣾⣿⣷⣶⣶⣶⣶⠆⠀⠀⠀⢻⣿⡿⠿⠟⠋⠉⠁⠀⠀⠀⢀⣀⣀⣴⣿⠿⠿⠛
⣄⣠⣤⣤⣤⣶⣦⣴⣦⣤⣤⣤⣴⣤⣤⣿⣷⣶⣶⡦⡄⢰⣿⣿⣿⣿⣇⣀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣤⣤⣤⡴⠶⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⡿⢿⣿⣿⣷⣶⣶⣞⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠺⢿⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠉⠋⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢘⣷⣶⣬⡉⠙⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣟⡉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⠉⢻⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣄⡀⠉⠙⠛⣶⣶⣤⣴⣖⠚
[35A⣿⠀⠀⢸⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀
⣿⡄⠀⢸⠀⠀⠸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⠀
⣿⡇⠀⣺⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆
⣿⡇⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⣙⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢹⠿⡻⡟⠿⣹⣷⠾⠛⠩⡱⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⡄⢸⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠙⣿⣿⣿⣷⢟⣫⠅⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠸⡟⣷⡸⡆⢸⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⡏⣀⡤⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⢳⠘⣧⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠯⣴⣶⣶⠤⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡅⠘⡇⠸⣇⢸⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⢣⠀⢻⠀⢹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣸⠀⠸⡆⠈⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣿⢿⡟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠄⠀⣇⠀⢸⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠅⠀⢸⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⢸⣿⣠⠘⡆⠀⡇⢰⣶⣶⣶⣶⣶⣶⣶⣷⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠘⣿⣿⡆⡇⢰⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⣰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢸⣿⡇⣸⣿⢀⣿⣿⢻⣿⣿⠀⠀⢠⣿⣿⣿⣧⠀⢀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⢸⣿⣿⢸⣿⣿⠀⣰⣿⣿⣿⣿⣿⣇⣸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⡿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣄⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣴⠿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣤
⣿⣿⣿⣿⣿⣷⣶⣿⣛⡛⠛⠛⣿⣿⡿⣿⣿⣿⢭⣿⣿⡇⠀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣽⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠉⠉⠀⠈⠉⠹⡁⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠟⠛⠉⠉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡀⠀⠀⠀⠠⠶⠶⠚⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠋⠀⠀⠠⠲⣿⣿⡆⠀⠀⠀⣀⣂⣢⣤⣤⣤⣤⣤⣶⣶⠶⣶⣶⣻⠂⠀⠀⠀⠀⣾⣯⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠤⣾⣿⣿⣿⣿
⣛⣿⣻⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⣶⡶⠀⠀⠐⠚⡛⠛⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣭⣭⣿⣿⣿⣿⣿⣶⣶⣶⣾⠛⠛⠩⠽⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠟⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⢠⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿
⣿⡛⠻⡛⠛⠛⠛⠛⠋⠉⠉⠁⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠄⠒⢚⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⠀⠀⣾⣿⣷⣶⣶⣶⣶⠆⠀⠀⠀⢻⣿⡿⠿⠟⠋⠉⠁⠀⠀⠀⢀⣀⣀⣴⣿⠿⠿⠛
⣀⣠⣤⣤⣤⣶⣦⣶⣦⣤⣤⣴⣶⣤⣾⣿⣶⣶⣶⣦⡄⢰⣷⣿⣿⣿⣇⣀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣤⣤⣤⡶⠶⠶⠖⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⠿⣿⣿⣷⣶⣶⣞⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠺⠿⣥⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠿⠿⠿⠟⠛⠭⠉⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢘⣷⣶⣬⣉⠙⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣟⡉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⠉⢻⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣄⡀⠉⠙⠛⣷⣶⣤⣴⣖⡛
[35A⣿⡄⠀⢸⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀
⣿⡇⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀
⣿⡇⠀⢸⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇
⣿⣧⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣑⣂⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⠀⢸⡇⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠙⠻⣿⣛⢿⣫⡵⠶⠛⠉⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⡄⢈⡇⢰⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⣶⣞⣫⡥⠂⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠘⡏⢷⡄⡇⢸⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣧⢸⡛⣠⡤⠄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⢹⡈⢿⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠛⠀⠐⣶⣶⡶⠤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⡇⠘⣧⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢫⠀⢸⠀⢸⣾⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⡾⡃⠈⡇⠀⢿⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⣿⢿⡟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠆⠀⢳⠀⠘⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⢻⣏⠀⢸⡀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⢸⣿⣴⡄⣇⢁⡻⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠁⣿⣿⡇⣿⢸⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣧⢹⣿⣿⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⢀⣿⣿⣿⣿⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⠘⣿⣿⢸⣿⣿⠀⣰⣿⣿⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⣀⣀⣄⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⣿⣤⠿⣿⣿⣿⡟⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦
⣿⣾⣿⣿⣿⣷⣶⣮⣍⣋⠙⠛⢻⣿⡿⣿⣿⣿⣋⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣽⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⢻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠉⠉⠀⠈⠉⠉⡍⠉⠉⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡶⠶⠞⠛⠛⠉⠁⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⠿⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠤⠶⠶⠖⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠻⠃⠀⠀⠐⣾⣿⣗⠀⠀⠀⣀⣦⣤⣤⣤⣤⣤⣶⡶⢶⣶⣾⣛⠂⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⠴⢾⣿⣿⣿⣿
⣹⣿⣽⣿⣿⣿⣿⣧⣤⣤⣤⣴⡶⠶⠶⠶⠶⠶⠶⣶⠂⠀⠀⠀⠛⠛⠛⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣞⢙⢙⡛⣿⣿⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⡿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠔⠒⠚⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⣠⣤⣦⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡀⠀⠀⢠⣿⣿⣷⣶⣶⣶⣷⠀⠀⠀⠻⣿⣿⠿⠿⠟⠋⠉⠀⠀⠀⠀⣀⣀⣀⣤⡿⠿⠿⠛
⣤⣤⣤⣤⣬⣤⣤⣤⣤⣭⣥⣤⣥⣶⣶⣶⣶⣶⣶⣶⣶⠀⣾⣿⣿⣿⣧⣀⡀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⢀⣤⣤⣴⠶⠶⠶⠒⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⡿⠿⠿⢿⣿⣶⣶⣾⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢛⠿⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠟⠛⠋⠙⠋⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⢰⣽⣿⣶⣦⣌⡉⠛⠳⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣿⣉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⠇⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡈⠉⠛⢻⣶⣶⣶⣖⣛
[35A⣿⠄⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀
⣿⡇⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀
⣿⡇⠀⢸⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧
⣿⣷⠀⢸⡄⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣩⣦⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⠀⢸⡇⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣟⣏⡈⠻⡿⣛⠿⣙⡴⠾⠛⠉⠒⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⢿⣿⡆⢀⡆⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡅⠀⢷⣞⣯⠵⠂⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠘⡏⢿⡄⡇⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠸⠑⣀⠤⠔⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⢹⡈⢷⡇⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠍⠁⠀⠶⣶⣶⡶⠄⠀⠈⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣠⠀⣇⠈⣧⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢫⠀⢸⡀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⡞⡁⠈⡇⠀⢿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⢿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠅⠀⢹⠀⠘⡆⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⢻⣖⠀⢸⡆⡀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡸⣿⣴⡀⡇⢀⢛⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡀⣿⣿⣇⣿⢰⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣷⢸⣿⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⡇⣸⣿⢀⣿⣿⢻⣿⣿⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡿⠿⠟⠸⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿
⣀⣀⣤⣀⣰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣷⣿⣿⣿⣿⠿⠃⠠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠿⣿⣿⣿⡟⠈⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶
⣿⣾⣿⣿⣿⣿⣷⣬⣍⡉⠙⠛⣻⣿⡿⣿⣿⣿⣭⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠉⠉⠀⠈⠉⠩⠁⠉⠉⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠶⠶⠟⠛⠋⠉⠁⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠛⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠠⠶⠶⠶⠖⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠻⠇⠀⠀⠰⢿⣿⣇⠀⠀⠀⣠⣤⣤⣤⣤⣤⣴⣶⠶⢶⣶⣟⡓⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠴⠾⣿⣿⣿⣿
⣽⣿⣽⣿⣿⣿⣿⣦⣤⣤⣴⡶⠶⠶⠶⠶⠶⠾⢿⡛⠓⠀⠀⠈⠛⠛⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣏⡉⣉⡉⣿⣿⣄⡀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⣟⠛⢛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠐⠒⠛⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡄⠀⠀⠀⣿⣿⣿⣶⣶⡆⠀⠀⠻⣿⣿⣿⠿⠿⠟⠟⠛⠁⠀⠀⢀⣀⣀⣀⣤⡤⠿⠿⠟⠛
⣤⣤⣤⣤⣴⣬⣤⣤⣭⣿⣯⣴⣷⣶⣶⣶⣶⣶⣶⣶⢶⠄⢾⣿⣿⣿⣧⣄⣀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢉⣥⣤⣤⣶⠶⠶⠶⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⡿⠿⠿⠿⣿⣷⣾⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⢀⣀⣩⣛⡛⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠟⠛⠋⠙⠋⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀⢀⣼⣿⣷⣿⣿⣷⣶⣤⣉⠙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⣿⣉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡿⠁⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠉⠉⢻⣷⣶⣶⣿⣋
[35A⣿⡆⠀⢸⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀
⣿⡇⠀⢸⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀
⣿⡇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧
⣿⣷⠀⢸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣩⡆⢄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⠀⢸⡇⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣟⣏⡉⠛⡿⣟⠿⣻⡴⠞⠛⠉⠂⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⢿⣿⡆⢀⡆⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⢳⣚⣫⡵⠂⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠈⣏⢿⡄⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠸⠁⣠⠤⠔⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⢹⡈⢿⡇⢸⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠍⠁⠀⠶⢶⣶⡶⠔⠀⠈⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣄⠀⣇⠈⣧⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢣⠀⢸⡀⠸⣾⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⡞⡃⠈⡇⠀⢻⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡇⠀⢻⠀⠘⡆⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⢹⣖⠀⢸⡆⠀⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⡸⣿⣶⡀⣇⠁⡹⢰⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡀⣿⣿⣇⣿⢰⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣷⢸⣿⣿⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⡇⣸⣿⢰⣿⣿⢻⣿⣿⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡿⠿⠟⢸⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠈⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠃⠀⠀⠀⠘⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⣀⣀⣤⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣷⣿⣿⣿⣿⠿⠋⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠿⣿⣿⣿⡏⠊⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶
⣿⣾⣿⣿⣿⣿⣶⣬⣍⡉⠙⠛⣻⣿⡿⣿⣿⣿⣭⣿⣿⡇⠀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣺⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⢻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠉⠉⠀⠈⠉⠉⠇⠉⠉⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠶⠶⠛⠛⠋⠉⠁⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⠿⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠠⠶⠶⠶⠖⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠻⠛⠃⠀⠀⠙⢿⣿⣇⠀⠀⠀⣠⣦⣤⣤⣤⣤⣶⡶⠶⢶⣶⣟⡓⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⠴⠾⣿⣿⣿⣿
⣽⣿⣽⣿⣿⣿⣿⣤⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⢿⡛⠃⠀⠀⠂⡛⠛⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣾⣶⣶⣾⣿⣿⣿⣿⣿⣋⢉⣉⢙⣯⣽⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿
⣟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠄⠒⠒⠛⣿⣿⣿⣿
⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡀⠀⠀⠀⣿⣿⣿⣶⣶⡆⠀⠀⠻⣿⣿⣿⠿⠿⠿⠟⠛⠁⠀⠀⢀⣀⣀⣀⣠⡤⠿⠿⠟⠛
⣤⣤⣤⣤⣵⣤⣤⣬⣭⣽⣯⣦⣶⣷⣶⣶⣶⣶⣶⣶⢶⠄⢾⣿⣿⣿⣧⣄⣀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢉⣥⣤⣤⡶⠶⠶⠶⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⡿⠿⠿⠿⣿⣶⣶⣿⣝⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⢀⣀⣉⣛⡛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠋⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀⢀⣼⣿⣷⣿⣿⣷⣶⣄⣉⠙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⢿⣷⣯⣉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠙⢿⡿⠁⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠉⠉⢻⣷⣶⣶⣿⣋
[35A⣿⡆⠀⢸⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀
⣿⡇⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀
⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧
⣿⣷⠀⢸⡄⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⢋⣩⡦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⠀⢸⡇⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣟⡈⠻⡟⣟⢿⣩⡴⠾⠋⠉⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⢿⣿⡆⢀⡆⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡅⠀⢳⢟⣫⠵⠂⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠈⣏⢿⡄⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠄⠸⠁⣠⠤⠔⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⢸⡈⢿⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠉⠁⠀⠶⣶⣶⡦⠤⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣄⠀⣇⠈⣷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢹⠀⢸⡄⠸⣾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠵⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣞⡃⠈⡇⠀⢻⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠅⠀⢹⠀⠈⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⢻⣇⠀⢸⡄⡀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡸⣿⣴⡄⣇⢀⡹⢠⣶⣶⣶⣶⣶⣶⣶⣷⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡀⣿⣿⣇⣿⢰⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣷⢸⣿⣿⣹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡿⠿⠟⢸⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠈⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⣤⣀⣤⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣷⣿⣿⣿⣿⡿⠃⠠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠟⣿⣿⣿⡟⠋⠀⠈⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶
⣿⣾⣿⣿⣿⣿⣷⣶⣍⡉⠙⠛⣻⣿⡿⣿⣿⣿⣭⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣸⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣨⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠉⠉⠀⠈⠉⠉⠁⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠶⠶⠟⠛⠋⠉⠁⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠠⠶⠶⠶⠖⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⡻⠻⠇⠀⠀⠘⢷⣿⣗⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣶⣶⢶⣶⣟⡛⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠤⠤⠾⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⠶⠶⠶⠶⠶⠶⠾⢿⣛⠓⠀⠀⠀⠘⠛⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣷⣶⣷⣶⣿⣿⣿⣿⣿⣿⣋⡉⢋⡉⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿
⣿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠒⠒⠙⣿⣿⣿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡄⠀⠀⠀⣿⣿⣿⣶⣶⡆⠀⠀⠻⣿⣿⣿⡿⠿⠿⠟⠋⠁⠀⠀⢀⣀⣀⣀⣤⡤⠿⠿⠛⠛
⣤⣤⣤⣤⣴⣤⣤⣭⣭⣭⣽⣦⣶⣶⣶⣶⣶⣶⣶⣶⢶⠄⢾⣿⣿⣿⣯⣄⣀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢉⣥⣤⣤⣴⠶⠶⠶⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⡿⠿⠿⠿⣿⣷⣷⣶⣝⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⢀⣀⣍⣛⡛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠋⠉⠋⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀⢀⣼⣿⣷⣿⣿⣷⣶⣤⣉⠙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣾⠿⠿⢿⣷⣿⣉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠙⢿⡿⠁⠙⠛⠛⢿⣿⣿⣿⣾⣿⣿⣿⣶⣤⣄⣀⠈⠉⢻⣿⣶⣶⣿⣋
[35A⣿⡆⠀⢸⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀
⣿⡇⠀⢸⠀⠀⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀
⣿⡇⠀⢸⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷
⣿⣿⠀⢸⡄⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣭⣗⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣿⣿⠀⢸⡇⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣯⡈⠹⡿⡫⣍⣣⠴⠟⠋⠐⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⢿⣿⡆⢠⡇⢸⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⣷⣚⣭⠖⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠈⣏⢻⡆⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢹⣅⡤⠤⠒⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⢸⡄⢻⡇⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠻⠻⠂⠈⡷⣶⣷⠷⠒⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡠⠀⣇⠈⢷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⢸⠀⢸⡀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠵⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡅⠈⣇⠀⢻⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡇⠀⢹⠀⠈⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⢹⣧⡀⠸⡆⡀⣇⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠜⣿⣿⡆⣧⠀⢸⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⣿⣿⣧⣿⢸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⢹⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⡇⣸⣿⢀⣿⣿⢻⣿⣿⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⠿⠟⠰⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢘⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿
⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠂⢀⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⢷⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠟⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣷⣾⣬⡍⠉⠉⣹⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣠⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣧⣿⣿⠇⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠉⠀⠈⠉⠉⣅⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⠶⠶⠞⠛⠛⠉⠁⠀⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠟⠟⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠻⠃⠀⠀⠙⢜⣿⣇⠀⠀⠀⣠⣤⣤⣤⣴⣶⢶⣶⣶⣶⣟⣛⠁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠒⠺⣿⣿⣿⣿
⣭⣽⣭⣽⣿⣿⣿⣷⠶⠶⠶⠶⠶⢶⠶⢿⣿⣛⣛⣛⠋⠀⠀⠀⠍⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿
⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⠘⠿⣿⠦⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⣟⠉⠙⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠔⠀⠒⠈⠙⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠻⠛⠛⠉⠀⠀⠀⣀⣀⣀⣤⣤⠶⠿⠟⠛⠋
⣤⣤⣤⣤⣭⣭⣭⣽⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠷⠆⢸⣿⣿⣿⣧⣤⣀⡀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡏⠀⠀⠘⣛⡋⣉⣭⣤⣤⣴⡶⠶⠞⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢹⠏⠁⠀⠀⠀⣿⣿⣦⣦⣨⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠉⠙⠛⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣤⣔⡐⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡉⠛⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣾⣍⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠉⠛⠿⠲⠀⠀⠉⠉⠙⠻⠿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢹⣿⣷⣾⣯⣍
[35A⣿⡄⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣗⠀
⣿⡇⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀
⣿⡇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷
⣿⣿⠀⢸⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠟⢋⣭⣦⣆⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣿⣿⠀⠘⡇⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣟⣯⡈⠹⡿⠻⣍⣣⠴⠟⠋⠑⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⢿⣿⡆⢀⡇⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆⠀⣷⣚⣭⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠘⣏⢻⡆⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢹⣅⡤⠄⠒⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⢸⡄⢻⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠻⠻⠀⠈⠿⣶⡷⠷⠒⠀⢀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡠⠀⣇⠈⢷⢸⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠈⢀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⢸⠀⢸⡀⠘⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠽⠗⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡃⠈⣇⠀⢻⠠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡇⠀⢹⠀⠈⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿
⢹⣧⠀⠸⡆⡀⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠜⣿⣾⡆⣇⢀⣼⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⣿⣿⣧⣿⢰⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⢹⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⡇⣸⣿⢀⣿⣿⢻⣿⣿⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⠿⠟⢸⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢸⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⢷⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠟⣿⣿⣿⡟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣷⣾⣮⡍⠉⠉⣹⣯⡟⣿⣿⣷⣯⣿⣿⡇⠀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣧⣿⣿⠇⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠉⠀⠈⠉⠉⢅⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⠶⠶⠞⠛⠛⠉⠁⠀⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠃⠀⠀⠁⢸⣿⣇⠀⠀⠀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣛⣛⠃⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠒⠺⣿⣿⣿⣿
⣭⣽⣭⣽⣿⣿⣿⣷⡶⠶⠶⠶⠶⠶⠶⢶⣿⣛⣛⡛⠋⠀⠀⠀⠍⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿
⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣍⢉⢉⡙⢿⣯⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣟⡉⠉⠋⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠀⠒⠈⠉⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠃⠀⠀⠀⣀⣀⣀⣠⡤⠴⠿⠟⠛⠉
⣤⣤⣤⣤⣭⣭⣥⣽⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠷⠆⢸⣿⣿⣿⣧⣤⣀⡀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡏⠀⠀⠘⣛⡋⣉⣭⣥⣤⣤⡶⠶⠖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢹⠏⠑⠀⠀⠀⣿⣿⣦⣦⣨⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠉⠙⠛⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣤⣔⡐⠻⢿⢿⣿⣿⣿⣿⣿⣶⣦⣌⠉⠛⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣾⣍⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠉⠛⠿⠲⠀⠀⠉⠉⠙⠻⠿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢹⣿⣷⣾⣯⣍
[35A⣿⡇⠈⢸⠇⠀⢠⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀
⣿⡧⠀⢸⡀⠀⢸⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇
⣿⣗⠀⣸⡆⠂⡾⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⠀⢿⡇⠀⣧⠤⣞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⡄⢸⡇⢸⡏⢀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡟⢻⣿⣿⣿⣿⡿⣟⣿⠿⡿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣷⣼⡇⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⣿⣛⣽⡿⣟⡋⣈⣤⠴⠒⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠘⣯⢻⣧⣇⢸⡄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⣶⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢻⣿⣾⠿⢞⣛⣁⣠⣴⣿⠿⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡠⢸⡄⢿⣿⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢟⣿⣿⠇⠈⣿⣿⣿⡿⠟⢋⣩⣥⣶⡶⠿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣿⡀⣧⠈⢿⢹⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⢄⠔⡼⠛⠀⠀⡃⢿⣷⠾⠛⠛⣉⣁⣤⡮⢃⣋⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⣿⡧⢹⡆⠸⣿⠇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠡⠈⠠⠀⠁⡠⠀⢀⡅⠂⠀⣹⣿⠿⠿⠛⠋⠉⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣇⠈⣧⠀⢻⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⢿⠿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡐⠔⢶⠀⠀⠀⠀⠀⣀⠠⠀⠂⠒⠀⠀⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⢄⢻⡀⠘⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢐⢂⠀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⢹⣿⣿⣸⡇⡇⣿⣿⣠⣀⣄⣤⣆⣠⣠⣠⣠⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⡾⣿⣿⣏⣷⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣒⡒⠀⠌⠅⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿
⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⣤⣤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠐⡣⣒⣾⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⡀⠀⣀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⠻⠿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠠⠿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⣿⣶⣷⣾⣵⣾⣆⣤⣦⣀⠀⠀⢀⡴⠤⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⠚⠉⠁⠀⠀⠀⠀⣼⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⡿⢏⡋⠛⠛⠛⠛⠿⠛⣿⣿⣗⠀⠀⠀⠁⣀⣀⣬⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⢠⣴⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡎⠭⢟⡿⠔⠄⠀⣀⣀⣀⣤⣤⣷⠶⠶⠟⠛⠛⠉⠉⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⣿⣿⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⠶⠶⠶⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣳⣒⣑⣈⣀⣴⣾⣜⠛⠛⡛⠿⡻⠗⠀⣘⣿⣿⣿⣿⠀⠀⡀⣰⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⡃⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣤⣄⣠⣄⣀⣀⣠⣄⣄⣀⣀⣀⣀⣀⣤⣤⡤⠤⠴⠖⠿⣿⣿⣿⣿
⣭⣿⣽⣿⣿⣿⣿⣿⣷⠶⠶⢶⣶⣶⣶⣿⣿⣟⣛⣛⡛⢰⣿⣿⣿⡋⣿⣠⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠹⢿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠆⠀⠘⣿⣿⠿⠧⠛⢿⡿⠃⠈⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣻⠻⠿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠴⠶⠚⠛⠻⣿⣿⣿⣿
⣿⣿⢯⣅⢐⣀⣠⣄⣀⡠⣀⣀⣀⣄⣀⣀⣀⣠⣤⣤⡀⠀⠀⣶⣾⣷⣀⠀⠀⠀⠀⢠⣠⣠⣐⣀⣶⣶⣶⣾⣭⣽⣭⣤⠀⠀⠀⠀⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠀⠀⢀⣀⣀⣀⣤⣤⠶⠿⠟⠛⠛
⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢷⠆⢸⣿⣿⣿⣯⣤⣄⡀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⡏⠀⠀⠘⣟⣛⣿⣭⣭⣥⣴⡶⠶⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡟⠛⠀⠀⢈⣿⣿⣦⣦⣭⣽⣛⡳⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⠟⢿⣿⣿⣿⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⣦⣤⣴⡘⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡉⠛⠛⠶⢦⣤⣀⣀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣾⣍⡉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡘⢋⣿⠹⣷⠇⣀⣀⣀⡀⠈⠀⠀⠀⠉⠉⠉⠛⢿⠷⢄⠀⠙⠉⠙⠻⢿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢹⣿⣿⣾⣿⣯
[35A⣿⡅⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀
⣿⡇⠀⢸⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆
⣿⡇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷
⣿⣿⠀⢸⡆⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢋⣭⣦⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣿⣿⠀⠘⡇⢰⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣯⠀⠹⡏⠫⣍⣡⠴⠞⡉⠁⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⢿⣿⣇⠀⡇⢸⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⣿⣚⣭⠖⠊⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠈⣏⢻⡆⡇⢸⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣁⡤⠔⠂⠈⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⢸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠻⠻⠀⠀⢿⣶⣿⠷⠖⠀⣀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣀⠀⣇⠈⢷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⢹⠀⢸⡄⠘⣟⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠽⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡁⠀⣇⠀⢻⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠾⠻⠁⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡅⠀⢹⠀⠈⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⢹⣧⢀⠸⡆⠀⢇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡚⣿⣾⡆⣧⢠⣾⢨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⡀⢀⠀⠉⠉⠀⠉⠀⠀⠀⢀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡄⣿⣿⣷⣿⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⡀⣠⣿⣿⣦⡀⢴⡦⢤⣶⢸⣿⣸⣿⣆⣿⡞⣿⡏⣟⡃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣼⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⣿⣿⡟⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣧⢿⡇⠿⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡄⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣧⣤⣄⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⣿⣿⣽⣷⠀⣿⡇⠀⢀⡄⢠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢿⣿⣿⣿⣿⣿⡟⠃⣤⡏⣿⡇⣿⣧⢹⣿⣼⡿⠸⠿⠿⠾⠿⠼⠿⢤⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⠀⠀⢿⣿⠀⠛⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣶⣭⣍⡉⠉⠛⠛⠛⠛⠿⠿⣇⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣠⡄⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠶⠟⠛⠛⠉⠁⠀⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠻⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠃⠀⠀⠐⢞⣿⣗⠀⠀⠀⣠⣤⣤⣤⣤⣶⠶⣶⣶⣶⣛⣛⠃⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠒⠺⣿⣿⣿⣿
⣭⣽⣭⣽⣿⣿⣿⣷⠶⠶⠶⠶⠶⡶⠶⢶⣞⣛⠛⡛⠋⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣁⡉⢉⡐⠾⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⠛⠋⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠐⠒⠉⠉⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠀⠀⠀⣀⣀⣀⣠⡤⠴⠿⠟⠛⠉
⣤⣤⣤⣬⣥⣭⣬⣵⣾⣷⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⠷⠆⢸⣿⣿⣿⣧⣤⣀⡀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⡏⠀⠀⠘⣛⡋⣩⣭⣤⣤⣤⡶⠶⠖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢹⠏⠁⠀⠀⠀⣿⣿⣦⣤⣨⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣤⣔⡘⠛⠿⢿⣿⣿⣿⣿⣿⣷⣤⣈⠉⠙⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⢀
⣿⣿⣷⣿⣿⣷⣿⡿⠿⠿⠿⣿⣾⣅⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠉⠛⠿⠂⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢹⣿⣷⣾⣯⣍
[35A⣿⡇⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀
⣿⡇⠀⢸⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⣿⡇⠀⢸⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⣿⣿⠀⢸⡆⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠛⣋⣡⣶⣐⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⠀⠘⡇⢰⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠙⣿⠫⣙⣧⠾⠛⠉⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⢿⣿⣇⠀⡇⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⢹⣋⡽⠖⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠈⢇⢻⡆⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢸⡇⠤⠔⠂⠁⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠸⡄⢻⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠻⠻⠇⠀⢻⣾⡾⠷⠂⠀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣤⠀⢇⠀⢷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⡀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⢱⠀⢸⡀⠘⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡭⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡇⠀⣇⠀⢻⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠿⠿⠻⠁⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⡇⠀⢹⠀⠈⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢹⣧⢀⠘⡆⠀⠃⠂⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡞⣿⣿⡇⣧⢀⣼⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⡀⡀⠀⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣄⣿⣿⣷⣿⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⡀⣠⣿⣿⣠⡀⢴⡤⢠⣶⢸⣿⣸⣿⣏⣿⡎⣿⡏⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⣿⣏⠈⠁⠈⠈⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡋⢀⣤⠀⠀⠀⠀⠀⣿⣇⢿⡇⠿⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠋⠿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⣿⣿⣽⣷⠀⣿⡇⠀⢀⡤⠶⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣧⣿⣧⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⠃⣤⡏⣿⡇⣿⣧⢻⣿⣼⡿⠸⠿⠿⠾⠿⠸⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠸⠀⠀⢻⣿⠀⠛⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⣸⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣷⣯⣍⠉⠉⠉⠛⠋⠛⠻⠿⣅⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠠⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠋⠉⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⠶⠶⠶⠞⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠃⠀⠀⠀⣛⣛⣃⠀⠀⠀⢠⣤⣤⣶⣶⣶⢶⣶⣞⣛⣻⣏⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠒⠻⢿⣿⣿⣿
⣭⣽⣿⣿⣿⣿⡿⡷⠶⠶⠶⢶⢶⣾⣛⡛⡛⠛⠛⠛⠋⠀⠀⠀⠍⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⢁⠈⠠⠾⠷⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣟⠋⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠤⠀⠒⠂⠈⠉⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣦⠀⠀⠀⠠⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠁⠀⠀⣀⣀⣀⣠⣤⠴⠶⠿⠛⠛⠉
⣤⣤⣴⣤⣽⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠿⠆⢸⣿⣿⣿⣷⣤⣄⣀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡿⠁⠀⠀⢙⣟⡉⢩⣥⣤⣤⣶⠶⠶⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣶⣤⡨⣭⣛⡛⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠋⠛⠛⠛⠉⠑⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣌⠛⠛⠛⢿⣿⣿⣿⣿⣷⣦⣄⡉⠙⠛⠲⠶⣤⣄⣀⡀⠀⠀⠀⣀
⣿⣿⣶⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣅⡈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⠳⠤⡄⠀⠉⠉⠛⠿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠈⢹⣿⣿⣿⣯⣭
[35A⣿⡅⠀⢸⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀
⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⣿⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⠀⢸⡅⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⠀⠈⡇⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠁⠘⠿⠩⣉⣧⠶⠛⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⢿⣿⣇⠀⡇⢰⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣇⠀⢰⣋⡭⠖⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠈⣧⢻⡆⡇⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠸⡇⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠻⢿⡆⠀⠙⠲⡶⠶⠒⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣀⠀⢧⠀⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣤⣤⠐⠉⠀⠀⡀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⣹⠀⠸⡄⠘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠁⣒⣠⡤⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣯⡇⠀⡇⠀⢹⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠟⠿⠻⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣏⠀⠀⠀⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⡆⠀⢸⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢹⣧⣀⠘⡆⠀⠁⠀⠀⠀⢀⡀⡀⠀⢀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡜⣿⣿⡇⣇⠀⠘⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⢀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⢿⣿⣿⣿⣸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⡀⣠⣿⣿⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡆⣿⡏⣿⡇⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⣿⣋⣈⡁⠈⠈⠀⠀⠸⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣇⢿⠇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣿⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠛⠻⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡄⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢿⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣷⢹⣿⣾⡿⢸⡿⠾⠾⠟⠸⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⣿⠀⠙⣿⣿⢿⠷⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣶⣬⣄⠉⠉⠉⠉⠉⠉⠛⠻⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⠁⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠋⠉⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠙⠋⠋⠛⠛⠛⠛⠛⠻⠟⠛⠻⣿⣿⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠶⠶⠶⠞⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿
⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⢘⣛⣃⠀⠀⠀⢠⣤⣤⣴⣶⣶⣶⣖⣛⣛⣛⡏⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿
⣬⣽⣿⣿⣿⣿⠿⠶⠶⠶⠶⠶⠶⡿⢟⢛⡛⠛⠛⠛⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢀⢀⠀⠸⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠀⠐⠂⠉⠉⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣶⣷⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣦⠀⠀⠀⢸⣿⣿⡆⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠁⠀⠀⣀⣀⣀⣠⡤⠤⠶⠿⠛⠛⠉
⣤⣤⣴⣤⣶⣾⣷⣶⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣷⣤⣄⣀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⡿⠁⠀⠀⢙⣟⡋⢩⣭⣤⣤⣶⠶⠶⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣟⣛⣛⣛⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⡨⣭⣛⠓⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⠉⠙⠛⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣴⣦⣌⠙⠛⠛⠻⣿⣿⣿⣿⣷⣦⣄⡉⠙⠛⠲⠶⣤⣄⣀⡀⠀⠀⠀⣀
⣿⣿⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣥⡈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⠳⠤⡄⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠈⢹⣿⣿⣿⣯⣭
[35A⣿⡅⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀
⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⣿⣇⠀⢸⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟
⣿⣿⠀⢸⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣥⣖⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⠀⠘⡇⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣻⣿⠁⠙⡿⢫⣉⣧⠶⢛⠋⠀⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⢻⣿⣇⠀⡇⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣇⠀⢸⣋⡭⠖⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠈⢯⠻⡆⡇⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⢸⡧⠠⠖⠂⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠹⣿⡆⠀⣿⣶⣿⠶⠒⢀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢀⠀⢧⠀⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢿⣿⣿⠷⠒⠉⠀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⣹⡄⢸⡀⠘⣟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠙⠙⣷⣒⣦⡭⠶⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡅⠀⣇⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⠿⠻⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣏⡀⠀⠀⠀⠀⠘⠋⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿
⣿⡇⠀⢸⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⢈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢸⣷⢀⠘⡇⠀⢁⠀⠀⠀⡀⠀⡀⠀⢀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠠⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡏⣿⣿⡆⣧⠐⢔⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⣀⡀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⣿⣿⣷⣿⢰⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⢀⡀⣠⣿⣿⣣⡀⢴⡤⢤⣶⢸⣿⣸⣿⣎⣿⡆⣿⡏⣿⡇⠒⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢿⣿⣿⣿⣾⡅⠈⠈⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⣇⢿⡇⠿⠿⠘⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣭⡍⣿⣷⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠛⠻⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣦⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢟⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⡿⢸⣿⠿⠾⠟⠸⠿⠦⠮⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⢻⣿⠀⠙⣿⣿⢿⠷⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣾⣥⣉⠉⠉⠉⠉⠉⠛⠛⠿⣅⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢈⠄⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠋⠉⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠟⠿⠿⢿⣿⣿⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿
⣿⣿⣿⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢘⣛⣃⠀⠀⠀⢠⣤⣤⣶⣶⣶⣶⣖⣛⣛⣻⡏⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠒⠻⢿⣿⣿⣿
⣭⣽⣿⣿⣿⣿⠿⠶⠶⠶⠶⠶⣶⡿⠛⣛⢛⡛⠛⠛⠃⠀⠀⠀⠉⠉⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⣀⠀⠠⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠀⠒⠂⠉⠉⣿⣿⣿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⡄⠀⠀⠀⣿⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛⠉
⣤⣤⣴⣼⣿⣿⣶⣶⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣷⣤⣄⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡿⠃⠀⠀⠈⣛⡉⠩⣭⣤⣴⣶⠶⠶⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣶⣤⡨⣭⣛⡛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠉⠛⠛⠋⠉⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢰⣷⣶⣦⣶⣶⣌⠙⠛⠙⠻⣿⣿⣿⣿⣷⣦⣄⡉⠙⠛⠲⠶⣤⣄⣀⡀⠀⠀⠀⣀
⣿⣿⣷⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣥⡈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠈⠙⣛⠳⠤⠀⠀⠀⠉⠛⠿⣿⣾⣿⣿⣷⢶⣤⣄⣀⠈⢹⣿⣿⣿⣯⣭
[35A⣿⡅⠀⢸⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀
⣿⡇⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⣿⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟
⢻⣿⠀⢸⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⣥⣶⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⠀⠘⡇⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣻⣿⠁⠘⢟⠫⣉⣭⠶⢛⠉⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⢻⣿⣇⠀⡇⢠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⡇⠀⢸⣋⡭⠖⠉⠁⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠈⢯⠻⡆⡇⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⢸⡧⠤⠖⠂⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠹⣿⡆⠀⣿⣶⡿⠖⠒⢀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡤⠀⢧⠀⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⡗⠚⠉⠀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⣹⡀⢸⡀⠘⣟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠙⠙⢶⣲⣬⡭⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⡅⠀⣇⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⠿⠻⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣏⡀⠀⠀⠀⠀⠘⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⡆⠀⢸⠀⠈⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢸⣧⢀⠘⡆⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡞⣿⣿⡇⣧⠐⣤⢠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⣀⡀⠉⠉⠀⠁⠀⠀⠀⢀⣀⢀⣀⠀⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⢿⣿⣷⣿⢸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⢀⡀⣠⣿⣿⣣⡀⢴⡤⢠⣶⢸⣿⡸⣿⣎⣿⡎⣿⡏⣿⡇⠒⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢿⣿⣿⣿⣾⡅⠈⠈⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣇⢿⠇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣷⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠟⠛⠻⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡄⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣦⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢏⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⡿⢸⣿⠿⠾⠟⠘⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⣿⠀⠘⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠈⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠉⠉⠉⠉⠛⠛⠻⠿⣯⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠋⠉⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢻⣿⣿⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢘⣛⣃⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣖⣟⣛⣻⡋⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄⠒⠻⢿⣿⣿⣿
⣭⣽⣿⣿⣿⣿⢿⠶⠶⠶⠶⠶⣶⡿⢛⡛⠛⡛⠛⠛⠋⠀⠀⠀⠉⠉⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡇⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⢀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠤⠀⠀⠂⠉⠉⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⣶⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⡄⠀⠀⠀⣿⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠁⠀⠀⢀⣀⣀⣠⡤⠤⠶⠟⠛⠛⠉
⣤⣤⣴⣬⣿⣷⣶⣷⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣷⣤⣄⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡿⠃⠀⠀⠈⣟⡉⠩⣭⣤⣴⣶⠶⠾⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣶⣤⡈⣭⣛⡛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣷⣶⣦⣶⣶⣌⠙⠛⠙⠻⣿⣿⣿⣿⣷⣦⣄⡉⠙⠛⠲⠶⣤⣄⣀⡀⠀⠀⠀⣀
⣿⣿⣾⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣥⡈⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠈⠙⣛⠳⠤⠀⠀⠀⠉⠛⠿⣿⣾⣿⣿⣷⣶⣤⣄⣀⠈⢹⣿⣿⣿⣯⣭
[35A⣿⡇⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀
⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆
⣿⣧⠀⢸⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⢸⣿⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠛⣉⣡⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⡀⠀⡇⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡀⠘⡏⠩⣙⣤⠖⠛⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⢻⣿⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢠⣉⠵⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⢿⠹⣆⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠘⡤⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠘⡄⢹⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠈⠻⡇⠀⢰⠶⠦⠑⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣠⠀⢣⠀⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⠈⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣸⡀⠘⡆⠈⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⠋⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡷⢄⣐⣤⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣇⡆⠀⢧⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⡋⠹⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⠀⠀⠀⡀⠀⠛⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⣿⡇⠀⢸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣠⣶⣶⣾⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⢸⣧⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢸⣷⣄⡈⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠻⣿⣿⠟⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠅⣿⣿⡇⣷⠀⡰⢀⣾⣿⣷⣷⣷⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⢸⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣇⢻⣿⣷⣼⢨⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⢀⡀⣀⣴⣷⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡟⣿⡏⣻⡇⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣇⢿⡇⠻⠿⠘⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣷⡾⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠟⠛⠻⠟⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣦⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣼⡿⠸⢿⠿⠾⠟⠸⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⣿⠀⠈⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣬⣀⠉⠉⠉⠉⠉⠉⠛⠿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡴⠶⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠛⠋⠉⠙⠛⠛⠛⠛⠛⠟⠟⠿⣿⣿⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⠀⠲⠖⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣡⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⢀⣛⣃⡀⠀⠀⢠⣤⣤⣶⣶⣶⣶⣚⣛⣛⠁⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠐⠛⢿⣿⣿⣿
⣭⣽⣿⣿⣿⠿⠿⠶⠶⠶⠶⢶⠶⡞⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠰⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⠀⠀⠰⠷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⡟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡶⠶⠦⠄⠂⠒⠀⠈⠉⢹⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁⠀⠀⣀⣀⣀⣠⡤⠤⠶⠛⠛⠋⠉
⣤⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣿⣤⣄⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡈⠉⢥⣤⣶⣶⠶⠾⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣛⣛⣛⣛⣿⣿⣿⣿⣯⣭⣭⣿⠿⠋⠁⠀⢀⡀⢀⣼⣿⣿⣿⡋⠀⠀⠀⠀⠀⣀⣿⣷⣶⣀⢬⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣶⣾⣷⣦⣄⡈⠈⠙⠿⣿⣿⣿⣿⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⢀⣀
⣿⣿⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣷⣧⣀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠉⠛⠛⠛⠤⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣶⣦⣤⣀⡀⢩⣿⣿⣿⣿⣯
[35A⣿⡇⠀⢸⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀
⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆
⣿⣧⠀⢸⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⢸⣿⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠛⣉⣠⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⡀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡀⠈⣍⠯⣋⣤⠖⠛⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⢻⣿⣧⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢸⣩⠵⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⢿⠹⣆⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠘⡅⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠘⡆⢹⡆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠈⠻⡇⠀⢸⠴⠮⠐⠂⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣠⠀⢣⠀⢻⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠉⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣸⡄⠘⡆⠈⣿⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠘⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡷⢀⣐⣦⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣇⡄⠀⢧⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⡋⠹⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⡀⠀⠀⡀⠀⠛⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⣿⡇⠀⢸⡄⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣠⣶⣶⣾⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⢸⣧⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢸⣷⣤⡈⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠹⣿⣿⠟⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠅⣿⣿⡇⢷⢀⡸⠀⣾⣷⣿⣿⣿⣿⣿⣷⣿⣷⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⢸⣿⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡇⢹⣿⣷⣼⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⢀⡀⣀⣶⣷⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡟⣿⡏⣻⡗⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣇⢿⡇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣷⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠟⠛⠻⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣦⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⡿⠸⢿⠿⠾⠟⠸⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⢿⣿⠀⠈⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣁⠉⠉⠉⠉⠉⠉⠛⠻⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣄⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡴⠶⠶⠚⠛⠛⠉⠉⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠛⠉⠋⠛⠛⠛⠛⠛⠻⠿⠟⠿⣿⣿⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⠀⠲⠖⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣛⣃⡀⠀⠀⢠⣤⣴⣶⢶⣶⣶⣚⣛⣛⠁⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠐⠛⢿⣿⣿⣿
⣬⣽⣿⣿⣿⠿⠿⠶⠶⠶⠶⠶⣶⠞⡛⠛⠛⡛⠛⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠠⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠰⠦⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡶⠶⠤⠄⠒⠒⠂⠉⠉⢹⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣶⣶⣀⠀⠀⠀⠀⢀⣠⣀⣀⣤⣤⣤⣤⣄⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⠿⠟⠛⠛⠋⠁⠀⢀⣀⣀⣀⣠⡤⠤⠶⠛⠛⠋⠉
⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣿⣤⣤⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡈⠉⢥⣴⣶⣶⡶⠾⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣟⣛⣛⣛⣻⣿⣿⣿⣯⣭⣭⣿⠿⠋⠁⠀⢀⡀⠀⣼⣿⣿⣿⡋⠀⠀⠀⠀⠀⡀⣿⣶⣶⣄⢬⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣶⣾⣷⣦⣄⡈⠈⠙⠿⣿⣿⣿⣿⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⢀⣀
⣿⣿⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣷⣧⣀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠉⠛⠛⠛⠤⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⢶⣦⣤⣀⡀⢩⣿⣿⣿⣿⣯
[35A⣿⡇⠀⢸⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀
⣿⡇⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆
⢿⣷⠀⢸⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⢸⣿⠀⠘⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⠛⣉⣤⣄⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⡀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⣿⣿⣿⠀⠈⠯⠩⣛⣤⠖⠛⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⢻⣿⣷⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣧⠀⢸⣉⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⢻⠹⣆⢱⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡀⠈⡇⠠⠔⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠘⡆⢹⡾⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠏⠉⠻⠇⠀⢸⣶⠮⠕⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢀⠀⢱⠀⢻⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠈⣷⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣜⡂⠈⡇⠈⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣷⢤⣶⣦⠥⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣷⡇⠀⢳⠀⠸⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣷⠶⢺⣿⢹⣿⢸⣿⣏⡀⠀⠀⡀⠀⠛⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⢿⣆⠀⠸⡄⠀⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠈⠙⠛⢻⣿⡇⢸⣿⣿⣿⡜⣿⡟⠃⠀⢸⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠸⣯⣆⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⢸⣿⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡇⣿⣷⣇⢿⢀⢸⢀⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⢀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⢸⣿⣦⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣇⢹⣿⣿⣾⣸⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢀⡀⣠⣾⣿⣠⡀⢴⡤⢤⣶⢸⣿⡸⣿⣆⣿⡞⣿⡏⣛⡓⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿
⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠁⠈⠈⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣇⢿⡇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣷⡾⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠟⠻⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣦⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣼⡿⠸⣿⡿⠾⠟⠘⠻⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⠿⠿⠿⠟⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⣽⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣥⣉⠉⠉⠉⠉⠋⠉⠛⠻⢍⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡴⠶⠶⠚⠛⠛⠉⠉⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⡗⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⡄⠀⠀⠀⠲⠖⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣛⣃⡀⠀⠀⢠⣤⣤⣶⣶⣶⢶⣖⡂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠐⠛⢻⣿⣿⣿
⣬⣽⣿⣿⣿⠿⠿⠷⠶⠶⠶⡶⣶⠞⠛⡛⡛⡛⠛⠛⠋⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⣻⣿⣋⠀⠀⠀⠀⠀⠨⣿⣿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡶⠶⠦⠄⠒⠒⠂⠉⠉⢹⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣶⣶⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠉⠀⠀⣀⣀⣀⣠⡤⠴⠶⠛⠛⠛⠉
⣥⣤⣤⣶⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣿⣦⣤⣀⡀⠀⠉⣽⣿⣿⣿⡿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠩⢭⣴⣶⣶⡶⠞⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣟⣛⣛⣛⣻⣿⣿⣿⣯⣭⡉⠁⠀⠀⣤⣶⣤⣶⣾⣿⣿⣿⣿⣟⠉⠁⠀⠀⢀⣀⣰⣶⣤⣀⢬⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠉⠉⠙⠋⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣦⣤⡈⠈⠙⠻⢿⣿⣿⣿⣶⣤⣀⠉⠙⠛⠶⢦⣤⣀⣀⠀⠀⢀⣀
⣿⣿⣶⣾⣿⣿⣿⡿⠿⠿⠿⢿⣷⣧⣀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠈⠁⠙⠛⠛⠛⠶⣤⠀⠀⠉⠛⠿⣿⣿⣿⣿⡷⣶⣤⣀⡀⢩⣿⣿⣿⣿⣯
[35A⣿⡇⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀
⢻⡇⠀⢐⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡥⢽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣄
⢹⣿⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⢸⣿⠀⠀⡇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⠿⠛⢉⣡⠄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣾⣟⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣽⣿⣯⡀⠈⣯⠭⣉⣭⠶⢚⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⢹⣿⣧⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢸⣎⡭⠖⠋⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⢻⠹⣇⢱⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠈⣏⠴⠔⠂⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠈⡆⠹⣮⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠹⢻⣿⣿⣿⠿⠃⠀⢸⣶⣾⠗⠒⢀⠀⠠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⢠⠀⢹⠀⢹⡀⠄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⢤⣿⡿⠋⠀⠀⠀⠀⠈⣟⠂⠒⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⡄⡄⠈⡇⠀⢷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠋⡂⢀⣀⣀⠀⠀⠀⠀⠀⢻⠖⣲⣢⡬⠴⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣷⡇⠀⢹⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⣹⣿⣇⠀⠀⠀⠀⢀⡠⠄⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣏⠀⠀⠀⠀⠀⠛⠋⠉⣁⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢻⡄⠀⠘⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣷⣾⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡞⣿⡟⠃⠀⠀⣀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡘⣷⡀⡀⣇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⢰⣿⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡇⣿⣧⡧⢸⠠⣀⠀⣶⣿⣶⣿⣶⣿⣷⣾⣶⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⣀⢀⣀⣿⣿⣦⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡇⢸⣿⣷⢸⡄⣇⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣷⣦⡄⢴⡦⢤⣶⢸⣿⡸⣿⣆⣿⡟⣿⡏⣛⡳⠐⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣼⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣇⠈⠈⠀⠀⠸⣿⡇⣿⣿⣿⡇⣿⣯⢿⣿⠀⠀⠄⠀⠂⠀⠨⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣇⢿⠇⠻⠷⠘⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠿⠟⠸⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣥⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣧⠀⣿⡇⠀⠀⣤⠠⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣤⣀⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠀⠀⠀⠰⣶⡾⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⡿⣿⣿⠿⠾⠟⠸⠿⠦⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⠧⠿⠿⠟⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷
⣶⣶⣿⣿⣿⣿⣿⣷⣤⣌⡈⠉⠉⠙⠉⠻⠻⠟⢄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠴⠶⠖⠛⠛⠋⠉⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⠛⠙⠛⠻⠿⠟⠛⠛⠛⠛⠿⠻⣷⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠰⠶⠶⠖⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢠⣤⣤⣶⠶⠶⠀⠀⠀⠀⠀⠈⣭⣭⣭⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠚⢻⣿⣿⣿
⣭⣭⣭⣭⣽⣽⣿⣷⠶⠶⠶⠶⠶⠶⠶⠶⡛⡛⠛⠛⠛⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣾⣾⣿⡶⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣿⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠀⠒⠂⠈⠉⢹⣿⣿⣿
⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⣶⣆⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄⡀⠀⠀⠀⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛⠉
⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡖⠦⢸⣿⣿⣿⣿⣤⣤⣀⡀⠀⠉⠹⣿⣿⡿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⢭⣥⣤⣶⡶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣟⣛⣛⣻⣿⣿⣶⣮⡉⠻⠀⠀⢠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⢀⡄⣴⣶⣤⣤⣬⣝⣛⠳⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠙⠛⠷⠒⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣠⣈⠈⠙⠻⠿⣿⣿⣿⣶⣤⣀⡉⠙⠛⠶⠦⣤⣄⣀⡀⠀⠀⢀
⣽⣿⣿⣿⣿⣷⣿⣿⠿⠿⠿⢿⣿⣯⣀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠉⠉⠙⠛⠛⠻⠶⡀⠀⠀⠈⠙⠿⣾⣿⣿⣿⣷⣶⣤⣄⡀⠈⣿⣿⣿⣿⣯
[35A⢸⣯⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀
⢸⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧
⢸⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⢸⣿⡄⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠙⢿⣿⣿⣿⣿⠿⠛⢋⣡⡄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣻⣿⣿⡀⠘⣿⠍⣍⣠⡴⢚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠸⣿⣷⠀⢹⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠘⣟⡭⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⢻⠙⣧⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡆⠀⢿⠶⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⣇⠸⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⣿⣿⣿⣿⣿⣧⠀⠸⣷⢶⠿⠖⠀⡈⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⢰⠀⢸⡀⠹⡄⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣰⣿⣿⠟⠋⠁⠀⠀⣟⠕⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⡆⡆⠀⣇⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢟⣋⣀⠀⠀⠀⠀⠀⢹⡖⣖⣲⣬⠭⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣷⠇⠀⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⠀⠀⠀⠀⠀⠚⠋⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢹⡆⠀⠈⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣴⣿⣿⡀⠀⠀⠀⠀⠀⣠⣴⡋⠀⢸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⢸⣯⠉⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⡈⣷⡀⡀⢣⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⣤⣶⣿⣿⣿⡇⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⢠⣿⡆⠈⡿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡆⢻⣷⣷⢸⡀⡀⠀⣴⣾⣿⣷⣿⣷⣶⣶⣶⣶⣾⡆⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠈⠉⠉⠉⠉⢁⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣠⣾⣿⣧⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣧⢸⣿⣿⡞⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⢀⡀⣠⣾⣷⣠⡄⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡿⣿⡏⣟⡗⠒⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⣿⣿⣷⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⡇⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⣷⣿⣯⢿⣿⠀⠀⠀⠀⠂⠠⠬⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣇⢿⠇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣧⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣿⡃⢿⣿⣽⣷⠀⣿⡇⠀⠀⣤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣤⣀⣀⣤⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠐⣶⡾⣶⣸⣿⡿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⡟⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⡟⣿⣿⣿⣟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣿⣿⡿⠾⠿⠘⠿⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⠿⠿⠿⠟⠘⠛⠛⠁⠈⠉⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷
⣿⣶⣾⣿⣿⣿⣿⣶⣮⣭⢉⠉⠙⠛⠻⠿⠻⠟⠋⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠃⢀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⠀⠀⠀⠈⠁⠀⠀⣀⣀⣀⣠⣤⡴⠶⠶⠚⠛⠛⠉⠁⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠻⠿⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠟⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠘⠷⠶⠶⠶⠒⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿
⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣂⠀⠀⠀⣤⣤⣤⠶⠶⠶⠆⠀⠀⠀⠀⠙⣭⣭⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⣿⣿⣿
⣭⣭⣿⣯⣽⣿⣿⣶⣶⡶⠶⠶⠶⠶⠶⣶⣶⣚⢛⡛⡛⠛⠁⠀⠐⠈⠉⠉⠉⠀⠀⠀⢠⣿⣿⣾⣿⡧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠠⢠⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⡟⠛⠛⠋⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠀⠂⠀⠀⠉⢉⣿⣿⣿
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣦⣤⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⢻⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⢀⣀⣀⣀⣠⡤⠴⠾⠛⠛⠋
⣧⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⢶⠀⣿⣿⣿⣿⣧⣤⣄⡀⠀⠉⠙⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢨⣭⣤⣴⡶⠶⠶⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣻⣿⣿⣿⣶⣾⣉⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⢀⣀⣰⣶⣦⣤⣬⣝⣛⠳⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡋⠉⠛⢷⣶⣦⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣷⣶⣿⣷⣄⠀⠈⠉⠙⠿⣿⣿⣿⣶⣤⣈⠉⠙⠛⠶⢶⣤⣄⣀⡀⠀⠀⢀
⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣯⣀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠉⠙⠿⠿⠧⠀⠀⠀⠀⠀⠙⠿⣾⣿⣿⣿⣷⣶⣤⣄⡀⠈⣽⣿⣿⣿⣿
[35A⢸⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀
⢸⣷⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧
⢸⣿⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⢸⣿⡄⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠛⢿⣿⣿⣿⣿⡿⠛⢋⣡⡄⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣻⣿⣿⠀⠘⣿⢭⣍⣠⡵⢚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠸⣿⣧⠀⢹⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠘⣞⡭⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⢻⠙⣧⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡆⠀⢿⠔⠶⠒⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⣇⠸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⢿⣿⣿⣿⣿⣧⠀⢸⣶⣶⠿⠖⠂⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⢰⠀⢸⡀⠸⡄⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣰⣿⣿⠟⠋⠁⠀⠈⣿⡖⠖⠛⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⡆⡆⠀⣇⠀⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢟⣋⣀⠀⠀⠀⠀⠀⢹⡶⣶⣲⣭⠭⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⠇⠀⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⠀⠀⠀⠀⠀⠚⠋⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢹⡆⠀⠘⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣴⣿⣿⡀⠀⠀⠀⠀⠀⣠⣴⡋⠁⢸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠸⣇⠉⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⡈⣷⡀⠀⢧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⣤⣶⣿⣿⣿⡇⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⢠⣿⡆⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡆⢻⣷⣿⢸⡐⠀⠀⣴⣾⣷⣷⣷⣿⣾⣷⣶⣾⣾⡆⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠈⠉⠉⠉⠉⢁⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⣀⢀⣠⣾⣿⣧⣤⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡇⢸⣿⣿⡎⡇⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⢀⡀⣠⣾⣷⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡿⣿⡏⣛⡷⠐⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⡇⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⡇⠈⠀⠀⠀⠸⣿⡇⣿⣿⣿⣷⣿⣯⣿⣿⠀⠀⠀⠀⠒⠠⠬⠥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣇⢿⡇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣧⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣿⡃⢿⣿⣽⣷⠀⣿⡇⠀⠀⣤⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣤⣀⣀⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠐⣶⡾⣶⣸⣿⡿⣿⣿⣿⣿⡿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⡟⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⡟⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣼⣿⣿⣿⡿⠾⠟⠘⠿⠦⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⠿⠿⠿⠟⠘⠛⠛⠁⠈⠉⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣷
⣿⣶⣾⣿⣿⣿⣿⣶⣮⣍⡉⠉⠉⠛⠛⠻⠿⠿⢍⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠁⢀⡀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠈⠁⠀⠀⣀⣀⣀⣠⣤⡴⠶⠶⠛⠛⠛⠉⠁⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠿⠿⠻⠛⠛⠷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠘⠷⠶⠶⠶⠚⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣐⣀⠀⠀⠀⣤⣤⣤⠶⠶⠶⠆⠀⠀⠀⠀⠙⣭⣭⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⣿⣿⣿
⣭⣭⣿⣭⣽⣿⣿⣿⣷⡶⠶⠶⠶⠶⠶⠶⢶⡖⡛⣛⡛⠛⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠰⣾⣷⣶⣾⡧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⡟⠛⠛⠋⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠀⠂⠂⠈⠉⢉⣿⣿⣿
⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⢤⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢻⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⢀⣀⣀⣀⣠⡤⠴⠾⠛⠛⠋
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡗⢶⠀⣿⣿⣿⣿⣧⣤⣄⡀⠀⠉⠙⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢩⣭⣤⣴⡶⠶⠶⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣟⣿⣿⣿⣶⣶⣉⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⢀⣀⣰⣶⣦⣤⣬⣝⣛⠳⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠙⠛⢷⣶⣦⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣷⣶⣿⣷⣄⠀⠉⠉⠛⠿⣿⣿⣿⣶⣤⣈⠉⠙⠛⠶⢶⣤⣄⣀⡀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣯⣀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠉⠙⠿⠿⠷⠀⠀⠀⠀⠀⠙⠿⣾⣯⣿⣿⣷⣶⣤⣄⡀⠈⣽⣿⣿⣿⣿
[35A⢸⣿⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇
⢸⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣏⡘⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⣿⡆⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⡄⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡻⠻⣿⣿⣿⣿⡿⠿⠛⣉⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⢻⣿⣷⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⣭⣿⣿⡅⠀⢿⢭⣭⣁⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠈⣿⣿⡄⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⣗⣫⠽⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠸⡟⢿⡘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣇⠀⢻⡥⠦⠖⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⢣⠘⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⣷⣦⡶⠤⠒⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⡀⠀⠘⡇⠘⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠋⠙⠃⠀⢿⡦⠤⠒⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣇⢁⠀⢻⠀⢹⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡈⢿⣿⣏⠀⠀⠀⠀⠀⠘⠷⢔⣶⣤⡬⠕⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢿⣼⠀⠘⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠾⢺⣿⢻⣿⣼⣿⣏⡀⠀⠀⠀⠀⠐⠛⠋⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠘⣧⡀⠀⢇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡆⢻⣄⢀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠉⠉⠁⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⣿⡇⠘⣿⡏⣿⡟⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⣧⢸⣿⣾⡄⡇⠀⠀⢠⣴⣶⣶⣶⣶⣷⣶⣶⣶⣶⣇⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣬⣧⡄⠀⣩⠉⠀⠁⠀⠀⠀⠀⣉⢛⣃⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡄⣿⣿⣧⣿⢰⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⣸⡋⢴⡤⢠⣶⢸⣿⠘⣿⣆⣿⡆⣿⡏⣛⡃⠀⠀⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣧⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⣿⣿⣿⣿⣏⢈⣁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡏⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢻⣿⠛⣿⣿⣇⠀⠀⠀⠀⣿⣇⢿⡇⠻⠷⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢳⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⡄⣤⡌⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠿⠇⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣿⡏⢿⣿⣽⣷⠀⣿⡇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣤⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠆⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⣿⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⣿⣷⣿⠏⣿⡟⣿⣾⣿⣟⠏⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣿⣿⣿⠞⠿⠘⠿⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷
⣿⣿⣾⣿⣿⣿⣷⣶⣮⣉⡍⠉⠙⠛⠛⠻⠟⠿⢿⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠁⠠⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡠⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠈⠁⢀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠈⠁⠀⠀⢀⣀⣀⣀⣤⣤⠴⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠹⠿⠻⠿⠿⠿⠿⠿⠿⠯⠛⠻⢷⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠘⢷⠶⠶⠶⠖⠒⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⣂⡀⠀⠀⢠⣤⣤⡶⠶⠶⠖⠀⠀⠀⠀⢉⣭⣭⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢿⣿⣿
⣉⣩⣿⣿⣿⣿⣷⣶⣤⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⣖⡛⡛⠛⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢠⣶⣶⣶⣿⣿⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣵⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣁⡈⠁⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⡿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠀⠀⠀⠉⠉⣽⣿⣿
⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣆⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠛⠛⠃⠀⠀⢀⣀⣀⣠⡤⠤⠶⠟⠛⠛
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣷⣶⣶⣶⣶⠰⡄⢺⣿⣿⣿⣿⣧⣤⣀⠀⠈⠙⢻⣿⣿⣿⠟⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣭⣭⣤⣶⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⡿⠿⠿⠿⣿⣿⣿⣷⣞⠿⠛⠁⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⡛⠛⠉⠀⢠⠴⢿⣿⣶⣤⣬⣭⣛⡓⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠷⢶⣿⣿⣦⠀⠀⠈⠉⠻⠾⣽⣿⢷⣦⣄⡉⠙⠛⠳⠶⣤⣄⣀⡀⠀⠀⠀
⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⣯⣍⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣽⣿⢿⣶⣤⣄⣀⠀⢹⣿⣿⣿⣿
[35A⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇
⠀⣿⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣏⡹⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⣿⡇⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⡆⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠟⠛⢉⡄⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⢻⣿⣷⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⣽⣿⣿⡅⠀⢻⡻⣯⣹⡦⠖⠛⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠈⣿⣿⡄⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⣟⣫⠽⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠹⡟⢿⡘⠅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀⢻⣤⠦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⢳⠈⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠐⣷⣶⡿⠤⠂⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⡀⡁⠘⡇⠘⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⠙⠃⠀⢻⡵⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣇⢀⡀⢻⠀⢹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡈⣿⣿⣏⠀⠀⠀⠀⠀⠸⠧⢶⣶⣶⡭⠕⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⢿⣼⠀⠘⡆⠀⢧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠾⢺⣿⢻⣿⣼⣿⣏⡀⠀⠀⠀⠀⠐⠛⠋⠉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠘⣧⡀⠀⢧⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠊⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡄⢻⣄⢀⢸⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠉⠋⠁⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣿⡇⠈⣿⡏⣿⡟⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⡧⠸⣿⣾⡌⡇⠀⠁⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣧⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣬⣧⡄⠀⣩⠉⠀⠁⠀⠀⠀⠀⣉⢛⣃⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡄⣿⣿⣷⣿⢰⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⣸⡋⢴⡤⢠⣶⢸⣿⠘⣿⣆⣿⡆⣿⡏⣛⡃⠀⠀⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣷⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⣿⣿⣿⣿⣯⢈⣁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡏⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠤⠬⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢻⣿⠛⣿⣿⣇⠀⠀⠀⠀⣿⣇⢿⠇⠻⠷⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢳⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⡿⠿⠇⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣿⡏⢿⣿⣽⣷⠀⣿⡇⠀⠀⢠⣤⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣤⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⣿⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣥⡀⠀⠀⠀⠀⠀⣿⣷⣿⠏⣿⡟⣿⣾⣿⣟⠏⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣿⣿⣿⠞⠿⠘⠿⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⢹⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣩⣍⡉⠙⠛⠛⠻⠻⠟⢯⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠁⢨⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠘⠁⢀⡀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠈⠃⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠚⠛⠛⠉⠉⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠿⠿⠿⠿⢿⠟⠿⠟⠻⠷⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠿⠶⠶⠶⠖⠒⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣂⡀⠀⠀⢠⣤⣤⡶⠶⠶⠖⠀⠀⠀⠀⠉⣭⣭⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢿⣿⣿
⣍⣩⣿⣿⣿⣿⣯⣶⣤⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⣖⣛⠛⠓⠀⠀⠀⠈⠙⠉⠉⠁⠀⠀⢠⣾⣶⣿⣿⣿⠀⠀⠀⠀⠀⢐⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣯⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡉⠉⠁⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠐⠀⠈⠉⠉⣹⣿⣿
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣦⣄⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣤⣤⣴⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣿⣿⣿⡿⠿⠛⠛⠃⠀⠀⣀⣀⣀⣠⡤⠤⠶⠟⠛⠛
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣶⣶⣶⣶⣶⠲⡆⢸⣿⣿⣿⣿⣧⣤⣀⠀⠈⠙⢻⣿⣿⣿⠟⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣭⣥⣤⣴⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣿⣿⡿⠿⡿⠿⣿⣿⣿⣷⣾⠿⠋⠁⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⡛⠛⠉⠀⢠⠰⢿⣿⣶⣤⣤⣭⣙⡓⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠷⢶⣿⣿⣦⠀⠀⠉⠉⠛⠾⣽⣿⣷⣦⣄⡈⠉⠛⠳⠶⢤⣄⣀⡀⠀⠀⠀
⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣯⣍⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣻⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⣽⣿⢿⣶⣦⣤⣀⠀⢹⣿⣿⣿⣿
[35A⠀⣿⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷
⠀⣿⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⣿⡇⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⡇⣿⣇⠀⢸⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢿⣿⣿⣿⣿⡿⠿⠛⣉⡤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⢹⣿⣿⠀⢸⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⣻⣿⣿⣷⠀⢹⡿⣭⣙⡾⠖⠋⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⣿⣿⡅⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣹⣿⡆⠀⣿⣫⠽⠖⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠘⡟⢿⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣥⠤⠖⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⢹⠈⢷⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣶⡷⠤⠒⠀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⡄⡄⠈⣇⠈⣇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠙⠃⠀⠹⡶⠶⠒⠁⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣧⢀⠀⢸⡄⠸⣾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡐⢾⣿⣿⠃⠀⠀⠀⠀⠀⠀⢶⣶⣴⡭⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢻⣾⡀⠈⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣶⣶⣶⣤⡄⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⠶⢺⣿⢻⣿⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠈⣿⡅⠀⢹⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢸⣿⡇⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿
⡀⢹⣇⠀⠘⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠻⠛⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣷⡘⣿⣿⡆⡇⠀⠀⢠⣶⣾⣶⣶⣶⣶⣴⣶⣶⣦⣇⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣨⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡃⣿⣿⣿⢻⢸⣾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠿⣿⣧⠀⠀⠀⠀⠀⠀⠘⢿⣞⣡⣤⣄⣠⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡞⣿⣿⣿⣧⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣷⣸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣉⠈⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡉⠀⢀⣀⠀⠀⠀⠀⣿⡇⢻⠇⠻⠷⠘⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠿⣷⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣤⡄⣤⡌⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠿⠟⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣨⣿⣿⣿⣷⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣿⣷⠀⣿⡇⠀⠀⢠⡤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⡿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢿⣿⡟⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⣿⡟⣿⣾⣿⣟⡟⣥⡏⣿⡇⣿⣧⢹⣿⣼⣿⣿⣿⣿⠞⠿⠘⠿⠦⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠘⣿⣿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿
⣿⣿⣶⣿⣿⣿⣷⣶⣦⣍⣉⡉⠙⠛⠛⠛⠿⠻⢿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠘⠃⢀⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠋⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠽⠻⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⡷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠿⠷⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣤⣤⣶⠶⡶⠶⠒⠀⠀⠀⠀⢨⣭⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⢿⣿⣿
⣉⣉⣿⣿⣿⣿⣵⣶⣤⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⣖⣛⠛⠃⠀⠀⠀⠉⠋⠩⠉⠉⠀⠀⠀⣾⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⠚⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣴⣶⣶⣶⣶⣶⣷⣶⣾⣿⣷⡉⠁⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⣿⡿⠛⠛⠛⠛⠙⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠐⠐⠂⠈⠉⣹⣿⣿
⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⢶⣆⣀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⠠⠈⠻⣿⣿⣿⡿⠿⠛⠛⠃⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣶⣶⣶⣶⣶⠶⡆⢰⣿⣿⣿⣿⣿⣿⣧⣀⡀⠉⣿⣿⣿⣿⠟⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⡀⠀⣬⣭⣤⣴⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡟⠋⠉⠀⠠⠜⠿⢿⣷⣦⡤⣭⣙⡛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠀⠐⠠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⠀⠀⠀⠉⠙⠲⣽⣿⣿⣶⣤⣈⠉⠛⠳⠶⢦⣤⣀⣀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣾⣏⡉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠁⠈⠁⠻⣶⡄⠀⠀⠀⠀⠀⠈⠻⢷⣾⣽⣿⣿⣶⣦⣤⣀⡀⢉⣿⣿⣿⣿
[35A⠀⣿⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷
⠀⣿⡇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⡀⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⡇⣿⣇⠀⢸⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠻⣿⣿⣿⣿⡿⠟⠛⣉⡤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⢹⣿⣿⠀⢸⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣿⣿⣿⣷⠀⢻⡯⣭⣉⡤⠶⡊⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⢿⣿⡆⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣹⣿⡆⠈⣿⣫⡽⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠘⡟⢿⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣧⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⢸⠈⢷⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡆⠀⣷⣾⡾⠤⠀⠈⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⡄⡀⠈⣇⠈⣇⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠛⠃⠀⢹⠧⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣷⢀⠀⢸⡀⠸⣾⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢾⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣶⣻⡯⠔⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢹⣿⡄⠈⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣶⣶⣤⡄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣟⡀⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠈⣿⡇⠀⢳⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣿⡇⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⡁⢹⣇⠀⠘⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠻⠏⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠘⣿⣾⡆⣇⢀⠀⢰⣶⣶⣾⣶⣶⣶⣶⣶⣶⣦⣇⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡐⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣨⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡆⣿⣿⣿⣻⢸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠿⣿⣧⠀⠀⠀⠀⠀⠀⠘⢿⣞⣡⣤⣤⣠⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡞⣿⣿⣿⣧⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣸⣿⣿⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣉⠈⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠐⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡉⠀⢀⣀⠀⠀⠀⠀⣿⡇⢿⠇⠻⠷⠘⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠙⠿⣷⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠿⠟⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠀⢀⣨⣿⣿⣿⣷⣤⢰⣶⡔⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⢠⣤⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣠⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⡿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢿⣿⡟⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⡿⣿⣾⣿⣟⡟⣤⡏⣿⡇⣿⣧⢹⣿⣼⣿⣿⣿⣿⠞⠟⠘⠿⠤⠬⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⠿⠿⠿⠿⠘⠛⠛⠁⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿
⣿⣿⣶⣿⣿⣿⣷⣶⣦⣭⣍⣉⠛⠙⠛⠻⠿⠻⠿⢟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠋⠀⡀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡂⠀⠀⠈⠋⠀⠀⢀⣀⣀⣠⣤⣤⠴⠶⠚⠛⠛⠉⠉⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⡿⠿⢿⠿⠛⠛⠿⠿⠿⠿⠿⠟⠟⠙⠿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠿⠷⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣀⠀⠀⠀⣤⣤⣶⡶⠶⠶⠒⠀⠀⠀⠀⢨⣭⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢿⣿⣿
⣍⣹⣿⣿⣿⣿⣿⣦⣴⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⢛⣛⠛⠃⠀⠀⠀⠈⠉⠉⠍⠉⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣽⣿⣽⣶⣶⣶⣶⣶⣿⣿⣿⣿⣯⣉⠁⡀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠐⠂⠀⠉⠉⣹⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣴⣆⣀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⠠⠈⠻⣿⣿⣿⣿⠿⠛⠛⠃⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛
⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣷⣾⣶⣶⣶⣶⣷⠶⡆⢰⣿⣿⣿⣿⣿⣿⣧⣄⣀⠈⣿⣿⣿⣿⠟⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢀⡀⠀⣬⣥⣤⣴⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠁⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡟⠋⠉⠀⠠⠼⠿⢿⣷⣦⡤⣭⣙⡛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠂⠐⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠛⠲⣽⣿⣷⣶⣤⣈⠉⠛⠻⠶⣦⣤⣀⣀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣍⡉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠁⠈⠀⠻⣶⡄⠀⠀⠀⠀⠀⠈⠻⢷⣾⣽⣿⣿⣶⣦⣤⣀⡀⢩⣿⣿⣿⣿
[35A⠀⣿⠅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⣿⡆⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⡀⣿⡇⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⡇⣿⣇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⢟⠛⣉⡤⠐⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⢹⣿⣿⠀⢸⡂⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣛⣿⣿⣷⠀⢹⣿⣭⣉⣿⠶⡚⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⢿⣿⡆⠈⡅⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⡆⠈⣷⣫⡽⠞⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠘⡟⢿⡄⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣧⡶⠖⠂⡀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⢸⡈⢷⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣷⣶⡿⠥⠐⢈⣀⡤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⡄⡀⠀⣇⠈⣇⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠛⠇⠀⢹⠧⠴⠖⠋⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣧⢀⠀⢸⠄⠸⣾⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰⣴⣾⡭⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢹⣿⡄⠘⡇⠀⢻⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣶⣶⣤⡄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⠶⢺⣿⢻⣿⢸⣿⣟⡀⠀⠀⠀⠀⠀⠈⠉⠉⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠈⣿⡆⠀⢳⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⣿⡇⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⣁⢹⣇⢀⠘⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠿⠏⢙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣷⠘⣿⣾⡇⣇⢀⠀⢠⣶⣶⣾⣶⣶⣷⣾⣷⣶⣦⣇⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡄⣿⣿⣿⢻⢸⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⢿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣷⣂⣧⣤⣄⣠⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡆⣿⣿⣟⡻⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣽⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣉⠈⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⠀⣀⣀⠀⠀⠀⠠⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡋⠀⢀⡀⠀⠀⠀⠀⣿⡇⢻⠇⠻⠷⠘⠻⠛⢻⣷⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡜⣽⡿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠿⠟⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⠀⢈⣹⣿⣿⣿⣷⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⢠⣤⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⡿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⣿⡟⣿⣾⣿⣟⡏⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣾⣿⣿⠞⠟⠘⠿⠤⠬⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠉⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣷⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠈⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿
⣿⣿⣶⣿⣿⣿⣷⣷⣦⣭⣍⡉⠉⠛⠛⠻⠿⠻⠻⢭⣅⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⢠⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠈⠁⠄⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠐⠀⠀⠉⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠉⠉⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠿⠷⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣐⣐⣒⣀⠀⠀⠀⣤⣤⣶⠶⠶⠶⠖⠀⠀⠀⠀⠈⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢿⣿⣿
⣍⣉⣿⣿⣿⣿⣿⣿⣤⣤⣤⣶⠶⠶⠶⠶⠶⡶⠶⣚⡛⠛⠃⠀⢀⠀⠙⠛⠉⠍⠉⠀⠀⠠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣽⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡉⡁⡁⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠐⠒⠀⠉⠉⣹⣿⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣶⣦⣀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⠠⠀⠹⣿⣿⣿⣿⠿⠟⠛⠂⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛
⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣶⣶⣶⣶⣷⠶⡆⢸⣿⣿⣿⣿⣿⣿⣧⣄⣀⠈⢿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡀⠀⢨⣭⣤⣶⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣴⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣟⠋⠉⠁⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡟⠋⠉⠀⠠⠼⠿⣿⣷⣦⣤⣭⣝⡛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠃⠒⠂⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠛⠲⣽⣿⡷⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣏⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⠃⠙⠉⠻⣿⣦⠀⠀⠀⠀⠀⠈⠻⢷⣾⣽⣿⡿⣶⣦⣤⣀⡀⢉⣿⣿⣿⣿
[35A⠀⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⣿⡇⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⡀⣿⡇⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⡇⣿⣇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠛⣉⣴⠦⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⢻⣿⣿⠀⢸⡆⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣷⠀⢻⣿⣿⣙⣿⠶⠛⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⢿⣿⡆⠈⡇⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⣦⣾⣿⣿⣿⡆⠈⣿⣫⡿⢞⠋⠀⣀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠘⡟⢿⡄⡇⢸⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣷⣶⢖⢂⡀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⢹⡀⢷⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⣾⣿⠧⠒⢊⣁⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⡄⡄⠀⣇⠈⣇⢸⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡿⠻⠇⠀⢹⡷⠶⠞⠋⣉⣀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣷⢠⠀⢸⡀⠸⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠇⠀⠀⠀⠈⠀⢶⣶⣿⡿⠾⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢹⣿⡄⠈⡇⠀⢻⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⡄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠈⣿⡇⠀⢻⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡞⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿
⡅⢹⣏⢀⠸⡄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠛⠋⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣷⠘⣿⣿⡆⣇⢀⢸⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠀⢠⡼⣇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠇⠀⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⣿⣿⣿⢸⢸⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⢧⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣠⣬⣤⣠⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡎⣿⡏⣟⡛⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣼⣿⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣉⠘⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠩⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⡏⠀⠆⠀⠀⠀⠀⠀⣿⡇⢻⠇⠻⠷⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣿⡿⢾⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⣿⣿⣿⣿⣧⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣿⣷⠀⣿⡇⠀⠹⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠈⣿⡇⣿⣇⣿⣷⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣧⡿⠏⣿⡿⣿⣿⣿⣿⡿⣥⡏⣿⡇⣿⣧⢻⣿⣾⣿⣼⣿⣿⠞⠿⠘⠿⠦⠬⠭⠀⠀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠘⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣶⣦⣭⣍⡉⠛⠛⠛⠿⠿⠿⠿⣿⣉⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⣰⡀⠀⢀⡠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡁⠈⠃⠁⡀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠆⠐⢀⠠⠋⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⠿⠿⣿⣷⡆⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⡿⠷⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣇⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢄⣟⣒⣐⣕⣀⠀⠘⢥⣤⣤⣶⣶⣶⠶⠖⠀⠀⠀⠀⢈⣭⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠒⠚⢿⣿⣿
⣟⣛⣿⣿⣿⣿⣿⣿⣬⣦⣶⣶⡶⠶⠶⠶⠶⢶⡶⡶⣛⡛⠀⠀⣉⠛⠋⠭⠭⠭⠍⠀⠈⢸⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣽⣿⣭⣽⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⣉⣀⠁⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠐⠒⠀⠉⠉⢹⣿⣿
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣶⣶⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⠠⠀⠹⣿⣿⣿⣿⠿⠟⠛⠂⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣷⣿⣶⣶⣶⣶⠷⡆⢰⣿⣿⣿⣿⣿⣿⣿⣅⣀⠈⢿⣿⣿⣿⡿⠁⠀⠀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡀⠀⢨⣭⣤⣶⠶⠶⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣴⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠁⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⣟⠋⠉⠀⢠⠴⠿⢿⣷⣦⣄⣭⣝⣛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⢿⡗⠒⠂⠀⠀⠀⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠙⠲⣽⣿⡿⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣾⣏⡉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠏⠉⠋⠻⣿⣦⠀⠀⠀⠀⠀⠈⠛⢿⣾⣭⣿⣿⣷⣦⣤⣀⡀⠉⣿⣿⣿⣿
[35A⠀⣿⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⣿⡇⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣚⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡆⣿⡇⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⡇⢻⣷⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠛⣉⣤⠖⢂⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠹⣼⣿⠀⢸⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⢻⣿⣯⣉⣭⠶⢛⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⢻⣿⡆⠈⡇⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣶⣿⣿⣿⡆⠈⣿⣯⡽⢞⡋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠈⣟⢻⡄⡇⢸⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣗⣿⣿⠀⢸⣷⠶⠖⠒⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⢸⡀⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡿⠧⠒⢈⣁⠤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⢴⠀⢇⠈⢧⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠷⠀⢸⣷⠶⠚⠋⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣷⢠⠀⢸⡄⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠇⠀⠀⠀⠀⠈⢧⣖⣾⡿⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⡆⠀⣧⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣦⠀⡦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣿⡋⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⡄⣿⡇⠀⢹⠀⠈⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡞⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣇⢸⣏⠀⠈⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡊⣿⣶⣇⢇⠀⠈⢀⣤⣶⣶⣶⣾⣶⣶⣶⣶⣶⣷⠀⣰⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⢻⣿⣿⢸⢀⣧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⣤⣤⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡆⣿⡏⣟⡋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣸⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣉⠈⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣿⠀⠀⢀⠀⠀⠀⠀⠨⠬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡋⠀⢰⡄⠀⠀⠀⠀⣿⡇⢻⠇⠻⠷⠘⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢾⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣶⣶⣶⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⠰⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠈⣿⡇⣿⣇⣿⣧⢿⣿⡛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⡿⠇⣿⣿⣿⣿⣿⣿⡟⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣸⣿⣿⠞⠿⠘⠿⠦⠬⠭⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠈⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿
⣿⣿⣷⣿⣿⣿⣷⣶⣦⣬⣍⠉⠉⠛⠛⠿⠿⠿⠯⣯⣍⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⢀⣀⠀⡀⢀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠸⠉⢀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠐⡀⠠⠛⠀⠀⢀⣀⣀⣀⣤⣤⠴⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡯⡿⠛⢿⣿⣿⡿⣿⠿⠷⠿⡿⠷⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⡿⠿⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⣂⣓⣀⣓⡀⠀⠰⣴⣤⣴⣶⣶⢶⡶⠞⠂⠀⠀⠀⠈⣭⣄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠒⠒⠚⢿⣿⣿
⣭⣉⣿⣿⣿⣿⣿⣦⣥⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⢾⣛⠓⠀⠀⡛⠟⠉⠭⠭⠭⠁⠀⠈⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⠛⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣽⣿⣭⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡍⣉⣉⠈⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠐⠂⠀⠉⠉⢹⣿⣿
⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣴⣶⣶⣄⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⡷⠀⠀⠠⠀⠹⣿⣿⣿⣿⠿⠟⠛⠂⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣶⣶⣶⣶⣶⣾⠶⠂⢸⣿⣿⣿⣿⣿⣿⣿⣅⣀⠈⢻⣿⣿⣿⡿⠁⠀⠀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢀⡀⠀⢨⣭⣤⣴⠶⠶⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠁⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⣟⠋⠉⠀⢠⠶⠿⢿⣷⣦⣤⣭⣝⣛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⢻⡗⠒⠀⠀⠀⠀⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠙⠳⣿⣿⡿⣶⣤⣈⠉⠙⠛⠶⢦⣤⣀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣏⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⠙⠋⠻⢿⡆⠀⠀⠀⠀⠀⠈⠛⢿⣾⣽⣿⣿⣶⣦⣤⣀⡀⠉⣿⣿⣿⣿
[35A⠀⣿⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⡂⣿⡇⠀⢸⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⡄⢿⣧⠀⢸⠇⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣇⢸⣿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡛⣋⣴⠶⢒⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠸⣾⡿⠀⠘⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢹⣿⣿⣝⣿⠷⢚⠋⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⢻⣿⣦⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣼⣿⣿⣿⣇⠈⢻⣻⡽⠿⡛⠁⣀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠈⣿⢻⡆⡇⢰⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠀⠸⣷⣶⠶⢒⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠸⡄⢻⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠧⠒⢉⣁⡠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⠶⠀⢷⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⢿⠀⢸⣿⠶⠖⠋⣁⣀⡀⠤⢆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⢿⣰⡀⢸⡆⠘⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⠅⠀⠀⠀⠉⢱⣶⣿⡿⠿⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠸⣿⡇⠈⣧⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠉⣀⡀⠄⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⡆⢿⣇⠀⢸⡀⠈⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡼⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣇⢸⣿⡀⠐⡇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡎⣿⣿⣇⢷⠀⢘⢠⣴⣾⣾⣷⣿⣶⣶⣿⣾⣶⣦⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿
⣿⣇⢻⣿⣿⣸⡮⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⣤⣤⣡⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡆⣿⡏⣟⡃⡷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣉⠘⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣿⡄⠀⢀⠀⠀⠀⠀⠩⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⡄⠀⠀⠀⠀⣿⡇⢻⠇⠿⠿⠘⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢾⡇⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡿⠿⢽⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣷⣶⣶⣶⣶⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⣿⣿⣿⣷⠀⣿⡇⠀⠀⠰⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠈⣿⡇⣿⣇⣿⣷⢿⣿⣛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡿⠇⣿⣿⣿⣿⣿⣿⡿⣷⡏⣿⡇⣿⣷⢻⣿⣾⡿⢸⣿⣿⡟⠟⠘⠿⠦⠮⠽⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⣷⣭⣍⡉⠙⠛⠛⠻⠿⠿⠿⣿⣍⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⢡⡄⠀⣀⡄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠉⠃⢀⣀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢟⠀⡂⠨⠋⠀⠀⢀⣀⣀⣀⣤⣤⠴⠶⠖⠛⠛⠋⠉⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⡿⠿⠶⠶⠖⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⣖⣒⣓⡀⠀⠸⣤⣤⣶⣶⣶⣶⣶⠞⠂⠀⠀⠀⠀⣭⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠚⢿⣿⣿
⣭⣙⣿⣿⣿⣿⣿⣯⣦⣤⣴⡶⠶⠶⠶⢶⣶⣶⠶⢞⠛⠃⠀⢰⣽⠟⠩⠭⠭⠍⠁⠀⢀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣽⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⢈⡁⡁⠀⣠⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠔⠒⠂⠉⠉⢹⣿⣿
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣴⣶⣆⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⡷⠀⠀⠠⠈⠻⣿⣿⣿⣿⢿⠟⠛⠃⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣷⣷⣶⣶⣶⣶⣿⣾⠷⠂⢸⣿⣿⣿⣿⣿⣿⣿⣅⣀⠈⢻⣿⣿⣿⡿⠁⠀⠀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⡀⠀⢭⣭⣤⣴⠶⠶⠾⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠁⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⠛⠋⠁⠀⢤⠾⠿⢿⣷⣶⡤⣭⣝⣛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⢿⡗⠲⠆⠀⠀⠀⠁⠀⠀⠛⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⠀⠀⠀⠉⠙⠲⣽⣿⡿⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣯⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣭⣿⣿⣷⣶⣤⣀⡀⠉⣿⣿⣿⣿
[35A⠀⣿⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⣿⡇⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡄⣿⣇⠀⢸⡃⠄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣇⢸⣿⠀⠸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡛⢛⣡⡴⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠹⣼⡿⠀⠐⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⢹⣿⣯⣝⣿⠷⡟⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⢻⣿⣆⠀⡇⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡌⢙⣿⣿⠅⠈⢿⣿⡽⠿⡛⠁⣀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠈⣿⢻⡆⡇⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠸⣷⣶⠶⠒⡉⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣿⣿⡇⠀⣿⣾⣾⠧⠖⢊⣉⣠⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⢤⠀⢷⠀⢷⢰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣷⠀⢸⣷⡴⠶⠊⠁⣀⡀⠤⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣿⢰⠀⢸⡆⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⠇⠀⠀⠁⠹⣶⣾⣿⠿⠗⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⡆⠈⣧⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣛⣿⣿⠃⠀⠀⠀⠀⠈⠉⢁⣀⠤⠄⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⡄⣿⣇⠀⢹⠀⠈⡇⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡞⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⡇⢸⣿⠀⠈⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡎⣿⣷⣆⣧⠀⢈⢀⣴⣷⣿⣾⣶⣷⣾⣶⣷⣦⣄⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⢿⣿⣿⣸⣐⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⢿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⣀⣤⣄⣠⣤⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡏⣿⡏⣟⡃⠖⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣁⠘⠉⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣷⠄⠀⢀⠀⠀⠀⠀⠠⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⣿⣇⢻⠇⠿⠿⠘⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡜⣿⣿⡷⢾⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣁⣤⣶⣶⣶⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⢰⣾⣧⣄⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⡇⣿⣧⣿⣧⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⣿⣿⣿⣿⣿⣟⡿⣷⡏⣿⡇⣿⣧⢻⣿⣾⡿⠸⣿⣿⠞⠿⠘⠿⠦⠬⠍⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⣶⣮⣍⡉⠉⠛⠛⠿⠿⠿⠿⢛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⢤⠀⠀⠀⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠉⠁⠀⡁⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠗⠀⡀⠀⠛⠀⠀⢀⣀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠋⠉⠁⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⣿⠷⠶⠶⠶⠒⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣏⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⢲⣞⣳⣜⣐⣖⡀⠠⣯⣥⣤⣴⣶⣶⣶⣶⡶⠓⠀⠀⠀⠀⢨⣥⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠐⠚⢿⣿⣿
⣭⣹⣿⣿⣿⣿⣿⣦⣶⣤⣶⡶⠶⠶⠶⠶⣶⢶⡶⣾⡛⠃⠀⢘⢿⠟⠭⠭⠭⠭⠁⠈⡉⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣧⡀⠀⠀⠀⠀⠈⠨⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣽⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣭⡁⣉⠉⠀⣀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢨⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⣿⣿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠄⠒⠒⠈⠉⢹⣿⣿
⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣶⣶⣤⣴⣶⣄⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠛⣿⣿⣿⣿⣿⡿⡿⠛⠃⠀⠀⠀⣀⣀⣀⣤⡤⠴⠿⠛⠛
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣷⣶⣾⣾⣷⣶⣷⣾⠶⠀⣾⣿⣿⣿⣿⣿⣿⣿⣅⡀⠈⢿⣿⣿⣿⡿⠁⠀⢀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠀⠈⣭⣭⣥⣤⡶⠶⠾⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣙⠉⠉⠁⠀⠀⠀⠈⠉⠀⣿⣿⣿⣿⣟⠋⠋⠁⠀⣤⠶⠆⢶⣶⣤⣬⣭⣙⡛⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⢿⠟⠲⠀⠀⠀⠈⠁⠀⠀⠻⣿⣿⣿⣿⣿⣶⣾⣿⣿⣷⠀⠀⠀⠉⠛⠾⣿⣿⡷⣶⣤⣉⠉⠛⠳⠶⣤⣤⣀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣍⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠋⠙⠛⠿⣿⣶⣤⡀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣶⣦⣄⣀⠀⢉⣿⣿⣿⣿
[35A⠀⣿⡇⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⣿⡇⠀⢸⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡄⣿⣇⠀⢸⠃⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣇⢺⣿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢛⣵⡤⢆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⢹⣼⣿⠀⠘⡇⠀⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⢻⣿⣿⣝⣯⠷⣚⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⢿⣿⣆⠀⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⢉⣻⣿⠄⠈⣿⣿⣽⠿⡛⠉⣀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠈⣿⢿⡆⡇⢸⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢸⣿⣴⠷⡒⡁⠀⠀⢀⡔⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠸⡈⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⠧⠔⢂⣁⣠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡆⣴⠀⢧⠈⣿⢸⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡄⠸⣿⣴⠶⠋⠁⣀⡀⠤⢤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⢠⠀⢸⡆⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⡿⠂⠀⠘⠹⣶⣾⣿⠿⠗⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⡆⠀⣧⠀⢻⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣟⣿⣿⡟⠁⠀⠀⠀⠀⠉⠁⣀⠠⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡌⣿⡇⠀⢹⡀⠈⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡞⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣇⢹⣷⠀⠸⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡜⣿⣷⡦⣧⠀⢸⢰⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⡀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣇⢿⣿⣿⢹⡼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⣤⣄⣰⣤⢴⡦⢠⣶⢸⣿⡸⣿⣆⣿⡆⣿⡏⣟⡃⠰⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣁⠘⠉⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣷⠀⠀⠀⠀⠀⠀⠀⠠⠤⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡉⠀⠀⣀⠀⠀⠀⠀⣿⣇⢻⠇⠿⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡌⣿⣷⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢉⣿⣿⣿⣿⣥⣶⣤⣶⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⢀⣤⣤⣠⣤⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⣿⣧⣿⣧⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠘⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⣿⡿⣷⡏⣿⡧⣿⣧⢻⣿⣾⡿⠸⠿⠿⠞⠿⠸⠿⠤⠬⠭⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠈⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⣷⣯⣍⡉⡛⠛⠛⠻⠿⠿⣿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⡠⠀⠀⠢⣢⣔⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡅⠈⠸⠉⡀⠁⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣵⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⡀⢐⠛⠁⠠⠀⣀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠋⠉⠁⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢿⡿⠾⠶⠶⠖⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⢊⣭⣿⣷⣚⣗⡀⠠⠿⣧⣤⣤⣶⣶⣶⣶⡶⠟⠀⠀⠀⠀⢀⣭⡄⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠄⠒⠺⢿⣿⣿
⣯⣹⣿⣿⣿⣿⣿⣿⣦⣤⣶⣶⠶⠶⠶⠶⠶⣶⠶⠾⡛⠂⠀⣟⣟⡟⠯⡭⠭⠭⠁⢠⡍⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠸⠟⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣽⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⣉⣉⣉⠉⣤⡀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢨⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⣿⣿⡛⠛⢛⠛⠋⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠀⠒⠒⠈⠉⢹⣿⣿
⣿⠟⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣶⣶⣦⣴⣶⣄⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⠀⠀⣀⣀⣀⣤⡤⠴⠿⠟⠛
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣾⣶⣷⣶⣾⣾⠲⠀⢾⣿⣿⣿⣿⣿⣿⣿⣅⣀⠈⢿⣿⣿⣿⠟⠁⠀⢀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⠂⠈⣭⣭⣥⣤⡶⠶⠾⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⣙⠉⠉⠀⠀⠀⠀⠈⠉⠀⣿⣿⣿⣿⡟⠋⠉⠉⠀⢤⡤⠄⢠⣤⣤⣬⣭⣙⡓⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠿⣿⠗⠂⠀⠀⠀⠈⠁⠀⠀⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⠀⠀⠀⠉⠛⠾⣿⣿⣷⣦⣄⣉⠙⠛⠳⠶⣤⣄⣀⡀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣏⡉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⠏⠛⠛⠿⣿⣶⣤⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣷⣶⣦⣄⣀⠈⢉⣿⣿⣶⣿
[35A⠀⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷
⠀⣿⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⡄⣿⡇⠀⢸⡁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣇⢸⣿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣥⡴⠆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⢹⣼⣿⠀⠘⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠂⢿⣿⣿⣏⣻⡵⠞⡋⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⢿⣿⣆⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣿⡶⠀⣿⣟⣿⠿⡟⠉⢀⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠘⣿⢿⡄⡇⢸⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⠄⠸⣿⣶⡷⠖⣀⠀⠀⢀⡀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⢸⡈⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⡄⣯⣶⣿⡯⠔⠂⣉⣡⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⡆⣀⠀⢧⠈⣧⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⢹⣿⣷⠶⠞⠉⠁⣀⠤⢤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣷⢡⠀⢸⡄⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢩⣿⣿⣿⣿⠀⠈⠓⠶⣶⣿⡿⠷⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢹⣿⡆⠈⣇⠀⢻⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣏⠀⢿⣿⡿⠁⠀⠀⠀⠀⠁⠀⡠⠄⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡌⣿⡇⠀⢹⠀⠘⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡼⣿⡟⢃⠘⠻⠅⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿
⡇⢸⣿⠀⠸⡆⠀⢣⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡞⣿⣷⡆⣧⠀⠀⢰⣴⣷⣿⣿⣾⣿⣷⣿⣶⣄⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠇⢿⣿⣿⢹⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠿⣿⣿⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣄⣤⣄⣰⣤⢴⣦⢤⣶⢸⣿⠸⣿⣆⣿⡆⣿⡏⣟⡃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣁⠘⠿⠈⠈⠀⡀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠀⠀⠀⢀⣾⡇⠀⣿⣇⢿⠇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣮⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡄⣶⣶⡶⢾⡇⠈⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣛⡛⣿⣿⣿⣿⣿⣿⣿⢰⣶⡔⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣄⣀⣀⣀⣀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡼⣿⡇⣿⣇⣿⣷⢿⣿⠛⢸⣿⣿⣿⠀⢻⣿⣶⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⣿⡿⣿⡏⣿⣇⣿⣧⢻⣿⣾⡿⠸⠿⠿⠞⠟⠘⠿⠤⢬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣶
⣿⣿⣷⣿⣿⣷⣿⣿⣯⣿⣍⡉⡛⠛⠻⠿⠿⠿⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⢀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⡀⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠟⠂⠄⠀⠀⣀⣀⣀⣤⣤⡴⠶⠞⠛⠛⠉⠉⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣵⠶⠶⠶⠖⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠡⠀⠀⠰⠲⠻⢯⢿⣷⣴⣖⡀⠠⣾⣵⣤⣤⣤⣴⣶⠶⡶⣶⠞⠂⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠾⣿⣿⣿
⣟⣛⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣴⣶⡶⠶⠶⠶⠶⠶⠂⠀⢉⠟⢛⣛⡿⢿⡯⡭⠁⠐⡟⣿⣷⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣧⡀⠀⠀⠀⠀⠹⠻⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣽⣿⣭⣽⣿⣷⣶⣶⣶⣶⣖⠂⠉⠉⠉⣋⣩⣉⠁⠀⠀⠀⠈⠟⠦⠦⠃⠇⠀⠀⠀⠀⠉⠘⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⣿⣿⡟⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠄⠐⠒⠊⠉⣿⣿⣿
⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣤⣤⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⣀⣀⣀⣠⣤⡴⠿⠿⠛
⣿⣦⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⡦⠆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡄⠈⣉⣭⣭⣤⣴⡶⠶⠶⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⡈⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠛⠛⠉⠀⢀⡀⠀⠀⠀⣄⣭⣙⡛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠟⠂⠀⠀⠀⠈⠁⠀⠘⠻⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⣄⠀⠀⠉⠻⠿⣻⣿⣶⣦⣌⠉⠛⠳⠶⢦⣤⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣋⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡋⠛⠻⠿⣿⣿⣷⣤⡀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢙⣿⣷⣶⣿
䷩ 𝚕𝚒𝚗𝚎 1645
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
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Gemini_version_available_♊︎
✐ IRC_Proceedings:_Sunday,_August_28,_2022⠀✐
Posted in IRC_Logs at 2:51 am by Needs Sunlight
Also available via the Gemini protocol at:
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🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇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
Qmc9CFRLenFK2RwWG9geCXFX5mSZaoYnzhcwUzk8sWMUuN #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell
QmdvdufFvS6VcJGSysyPxvUVmgaAMex619fH94FBS6PH1U (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
#boycottnovell-
QmamuW1aeLr8gp7CtGMKiYBy6uErey3NKjAirNYJ5dVfB4 social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell-
QmXgUndwsLst1ZwdrYP6aj1dWwpM71GLpBLvkzp4DA2vGZ social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
(full IRC log
as plain/ASCII
text)
IRC log for
QmbeY1t3e66MQjVZuFm78tAPuoaaScgLJjtthoRE5wCHzg #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techbytes
QmQBd8GcjZiABHWZJ5FDCkSkA32c3vtdsEPLHoWhd22dUu (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
QmcwbaedQvFSEDYMZrUC4KMnEK7xvgoS2FPZUhnXzyuaJV #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techrights
QmXRU9RGGogqni4oiJGin9Qfi5QnFpkaKva2Y5kocauXdP (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈
§ Bulletin for Yesterday⠀➾
Local_copy | CID (IPFS): Qmdj75rdsbiWjm4ms8CTMfcbYno6Pw9hH66AytZ3Hs3qV7
䷩ 𝚕𝚒𝚗𝚎 1772
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/lf-rejects-linux/#comments
Gemini version at gemini://gemini.techrights.org/2022/08/29/lf-rejects-linux/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ The_‘Linux’_Foundation_is_Working_Against_Linux_for_People_Who_Reject_Linux⠀✐
Posted in Deception, Kernel at 8:10 am by Dr. Roy Schestowitz
Video_download_link | md5sum e97cad80e2343157a0717981e1ed2aef
LF is Run by Charlatans and Liars
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/lf-acting-dodgy.webm
Summary: Corporations that reject_Linux_and_the_GPL have managed to position
themselves above Linus Torvalds; due to the name (“Linux Foundation”) a lot of
people cannot realise that this rogue organisation is run by Linux-hostile
people, who don’t even use the “product” named in their payslip (now exceeding
6 figures; some are netting 7-figure salaries despite the revenue shrinking)
LAST night and this morning we posted three articles (about 3 in 12 hours [1,
2, 3]) regarding the so-called ‘Linux’_Foundation. Not only has it gotten
increasingly rogue; it also lost 18 million dollars in revenue (in just one
year!) and its chief’s wife seems to be running a fraud, which was recently
sued — a class action lawsuit — for securities fraud.
“The trademark “Linux” is under attack and Linus (Torvalds) is under the
influence… of frauds.”Not too long ago we mentioned how the so-called ‘Linux’
Foundation is also defrauding_companies with clickfarms. It sells_"tweets"_in
clear_violation_of_Twitter's_rules. It also fails_to_defend_the_founder_of
Linux (which it is called after); instead it is promoting_Microsoft, which
involves a_conflict_of_interest (the chief’s wife). The trademark_"Linux"_is
under_attack and Linus (Torvalds) is under the influence… of_frauds. █
䷩ 𝚕𝚒𝚗𝚎 1823
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/lf-still-no-pdf/#comments
Gemini version at gemini://gemini.techrights.org/2022/08/29/lf-still-no-pdf/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Linux_Foundation_Drowning_in_Grift_and_7-Figure_Salaries_(Awarded_to_People
Who_Never_Created_Anything)⠀✐
Posted in Deception, GNU/Linux at 3:16 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇LF IRS 2020⦈
New screenshot from here, but no further details for now. Regarding the scale
and currency, it is US dollars.
Summary: The cookie jar associated with exploitation (or dilution) of the brand
“Linux” is being opened and emptied by people who don’t use Linux and don’t
contribute anything to it, instead selling control over it to hostile companies
— i.e. opponents — like Microsoft (classic, textbook sellout)
MANAGERS of the Linux_Foundation, i.e. the bosses of the person who actually
made Linux, are parasitic and greedy. As we noted last_night, it’s hard to find
any IRS filing later than 2018. This isn’t normal. For other institutions we
can download the 2020 filings already. It’s hard to tell what’s going on or why
it’s taking so long, but we’ve managed to get the above sneak peek this past
weekend. Now compare it to the prior year. We’ve uploaded a locally-hosted HTML
version, but we’ll carry on pursuing the original PDF. Revenue nosedived.
Salaries, on the other hand, soared. Are they rewarding themselves for failure?
“Revenue nosedived. Salaries, on the other hand, soared.”Compare 2019 to 2020;
27.1% to 35.4% of the money is spent on salaries — an increase of 8.3% in just
one year! A decade ago that was 19%-22%, so clearly something has changed.
Executive compensation leaped from 5% to almost 7%, so that’s like 40%
increase, relatively speaking, in just one year. One year!
But let’s ask the more important question, as it was posed by an associate
yesterday.
Who nets that money? Not people who make Linux (or very few who do):
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇lf-deadweights⦈_
The deadweights
Only about 2 of these people actually code Linux. Only one of them gets paid by
the so-called ‘Linux’ Foundation and he_gets_treated_rather_poorly.
“It is very useful to point out the salaries of the coders versus the dead
wood,” an associate noted. “It might be also useful to point out that the
former are mostly at the bottom of the list.” (Many unpaid, except by
corporations like Oracle)
“Also,” this associate added, “is Brescia the only director representing
Microsoft? I thought there was at leastone other, not to mention all the
partners and license infringers there, too.”
This is from 2019. At least two more have been added since (the Board and the
management team). Some have been identified before (by name), but more have
been recruited. One friend brings another… and another. It’s seen_as_desirable,
not just acceptable.
“Of the fourteen salaried positions listed, only four (29%) are programmers,”
the associate said, “according to your annotations. Except for LT himself, they
are at the bottom of the list and even LT is a distant second to JZ.”
There’s money on top of that. Here’s a screenshot from the HTML_version:
🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇zemlin-totals⦈_
Over a million a year. No tax to pay. █
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⣿⣉⢉⠛⢛⠛⣯⠩⡉⡍⡏⡟⠛⠟⠛⠛⡏⠙⡛⠛⣏⠉⠙⢻⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣼⣤⣤⣤⣯⣤⣧⣤⣥⣥⣤⣀⣠⣤⣷⣤⣇⣼⣿⣤⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡍⢙⠛⡏⠉⠉⡏⡙⠛⠛⢻⠉⠉⠩⣿⠛⡏⣟⡿⠛⡛⠛⠟⠋⡏⣛⡙⢛⠛⠛⠋⠙⠛⢻⠛⠋⠻⢛⣻⡙⡙⠉⢻⣛⠛⠛⣹⠛⣛⠹⢹⡛⠛⠛⠉⠛⠛⢻⡏⠙⠋⠛⠋⡛⠛⡏⠛⠋⠛⡛⠋⡏⠛⢛⣻⣿⣿
⣿⠿⠿⠿⠿⠿⠟⡿⠟⠿⠻⠿⣿⠟⣿⠿⢻⠛⠻⢿⠿⠻⠻⠟⢿⡟⠻⠿⠟⢻⠛⠿⢿⡟⡟⢻⡿⠿⠻⢿⠿⠿⠿⠿⠿⡟⠿⢿⡟⠛⢞⢻⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣶⣷⣦⣶⣷⣶⣶⣶⣶⣿⣿⣷⣶⣾⣾⣶⣾⣼⣶⣶⣿⣶⣷⣶⣶⣶⣾⣾⣶⣾⣿⣶⣾⣿⣶⣶⣷⣶⣶⣶⣾⣶⣿⣶⣿⣷⣶⣷⣾⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⡿⠿⢿⢿⠿⠿⠿⠿⠟⠿⠿⢿⢿⢿⡿⠿⠿⡟⢻⠿⢿⡿⡿⣿⠿⠿⠿⠿⠟⠿⠟⡿⠿⠿⣿⠿⣿⡿⣿⠿⡿⠿⡿⠿⠿⡟⠿⢿⠿⠟⠻⠿⠿⠿⠟⡟⠿⡿⠻⠿⡿⠻⠿⠿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣾⣶⣾⣶⣦⣴⣶⣶⣶⣶⣾⡶⣷⣿⡶⡶⢷⣾⣶⣾⣷⣿⣷⢶⣾⣶⣶⣶⣶⣶⣷⣶⣶⣾⡿⣿⣿⢿⣿⢶⣷⣷⣶⣶⣷⣶⣾⣶⣶⣶⢶⣶⣶⣶⣷⣶⣷⣶⣶⣷⣶⣷⣶⣷⣶⣶⣶⡶⣾⣿⣿⣿⣿⣿⣿
⣿⣯⣮⣄⣼⣤⣤⣦⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣧⣷⣧⣤⣷⣤⣤⣸⣤⣤⣧⣼⣥⣼⣤⣼⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣼⣤⣾⣼⣦⣤⣴⣤⣴⣦⣤⣶⣤⣷⣤⣯⣼⣾⣤⣤⣨⣼⣮⣤⣤⣤⣤⣦⣤⣿⣿⣿⣿
⣿⣉⣩⡉⣏⣝⣹⣏⣉⣭⣻⣭⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢫⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿
⣿⢸⣿⣿⢿⢿⢿⢿⣿⠿⢿⠿⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⠚⠔⠵⠶⠽⡜⠄⢆⣼⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⠶⢶⠶⢷⡶⢷⡶⠶⣾⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⠄⢸⠰⠆⠄⠀⠁⠆⢸⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣷⣶⣾⣶⣾⣶⣶⣷⣶⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⢩⠛⡋⠛⠋⣿⠉⠛⠛⠟⠛⢛⠛⡟⠛⢻⣿⣿⣿⣿⣿⠁⢉⢹⠉⠋⢹⡟⢹⠉⠋⢹⡏⢙⡍⢩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣶⣷⣶⣶⣿⣷⣶⣾⣾⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⣾⣾⣶⣷⣶⣾⣾⣶⣷⣶⣶⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣍⣉⣁⣏⣉⣉⣉⣉⣉⣉⣹⣉⣉⢉⣉⣉⣉⣉⣿⣿⣿⣿⣿⢉⣉⡙⣉⣉⡙⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣏⣉⣉⣏⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣉⡙⣉⣩⡙⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⢠⣀⣀⡠⣄⣇⢅⣀⣀⣀⣅⣇⣴⣠⣀⣄⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣧⣄⣠⣀⣤⣄⣄⣸⣀⣄⣀⣇⣀⣠⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡧⠥⢤⢦⠦⢤⣥⠤⡴⡤⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⡿⠿⠿⡿⡧⡬⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠶⡴⠼⠦⠤⠼⠤⡖⠤⠤⠤⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣮⡆⠥⡆⠆⡝⠇⠖⣿⣧⠠⡄⠠⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣾⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⠻⠖⠖⡶⠶⠶⠳⠷⠗⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⡖⢒⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⠒⠺⠒⢓⠚⢲⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⠙⢓⠙⠋⠛⢛⠛⠛⢛⠛⡏⡛⠛⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣏⣉⠉⣯⢋⣉⢉⢹⡉⣩⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣈⣉⣉⣏⣡⣏⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⢈⣁⣿⣦⣄⣠⣈⣁⣱⣉⣀⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⡔⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣤⣴⣤⣼⣦⣬⣤⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣥⣥⣤⣿⣿⣤⣭⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠿⠿⠿⠻⠿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⡲⠶⠶⡶⠲⠷⡶⠴⠶⠶⠶⠶⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⡟⠛⠟⡟⠟⠟⣿⡗⡶⢲⠒⠚⣶⣶⣾⣶⣶⣶⣷⣶⣴⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⢒⠒⠐⠚⠒⠳⡓⠒⣚⠗⠒⢚⠲⠒⠒⠒⡏⠻⠛⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣶⡆⢓⣿⣧⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⢝⢛⠓⢻⠚⠛⠛⠙⠛⡟⢛⠋⡟⠛⠛⠒⢻⣾⣿⣿⣿⣿⣿⡏⠋⠋⠯⡉⠋⠯⡁⡋⣿⡏⠉⠉⠉⢹⠉⠙⠏⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣏⣈⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡷⣄⣈⣹⣣⣉⣈⡁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡰⣕⣀⣃⣀⣅⣳⣇⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡷⢤⡤⡼⣯⣤⡧⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⡥⡤⡥⡡⡤⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣧⣤⣤⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣥⣵⣧⣤⣥⣤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠛⠛⢛⡟⣿⣟⠛⡛⠟⢻⣿⣿⣿⣿⣿⠛⠻⢿⠿⠿⡟⣿⠛⠿⢿⠿⡿⢿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⠛⡿⢻⣿⠛⠟⠿⠛⣿⠟⠟⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⢻⠓⡓⠚⠒⢻⣗⠚⢒⢾⣿⣿⣿⣿⣿⣇⣇⣠⣌⣀⣄⣿⣠⣁⣠⣄⣄⣠⣀⣇⣠⣀⣼⣿⣿⣿⣿⣿⣧⣀⣿⣘⣀⣥⣸⣡⣄⣄⣌⣀⣫⣄⣄⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠾⠿⡾⠿⣾⠾⡷⠷⢷⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⡿⠿⠿⠿⠟⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠻⠿⠿⢿⠿⠿⠿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠖⠠⡀⠷⢰⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⠿⡶⢶⠶⢷⣶⡶⣶⢶⣶⣶⣶⣿⣶⣦⣶⣶⣶⣶⣶⣿⣿⣿⣷⡼⠾⠾⢦⠶⠶⠶⡶⠶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣶⣶⣷⣶⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣤⣬⣤⣤⣤⣵⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠿⠿⡿⠿⢿⠿⠿⢿⢿⠿⢻⠿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡿⠟⡿⠿⠿⠟⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⢸⣿⣿⠿⠿⠾⠽⠿⠧⠧⠵⠯⠿⠿⢿⣿⣿⣿⢖⠦⠦⢴⠔⠦⡧⠦⠦⠶⢴⣴⣼⣴⣾⣶⣶⣦⣶⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡻⣿⣶⣶⣶⣴⣶⣦⣷⣶⣧⣶⣤⣶⣷⣴⣶⣴⣶⣶⣼⣿⣿⣿⣿⣿
⢸⣿⣿⣿⠿⠿⢿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⠒⠶⠶⠾⠷⠶⢶⠶⠶⠷⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⡟⡟⡿⡟⠛⢻⠻⠰⢲⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⢻⡛⠛⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⠶⠶⠾⡵⠶⡷⠶⠾⢶⣿⣿⣿⣿⣿⠺⠶⠦⠴⠲⠶⠾⠶⢶⠷⠶⠶⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣶⡖⢚⠓⠒⢲⡒⠲⢲⣿⣤⣠⡄⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠛⠒⠒⠒⠓⠒⠓⠒⠒⠊⠛⢿⣿⣿⣿⠒⠶⠷⠖⡶⠶⠶⠷⠺⠺⠲⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⠒⡲⣿⣿⣶⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠒⠒⠖⢲⢓⠞⢲⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⠒⠒⡚⡚⢶⢒⠚⡛⡻⠛⣛⢿⠛⠛⢛⢟⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⠘⠚⢻⢰⠟⠒⠙⠒⠘⠚⠛⢺⣶⣶⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠛⠛⠛⡟⢋⡟⠛⠛⠛⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠹⠝⠜⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⠙⠛⢹⠙⠛⠛⢛⠙⠛⡛⡟⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡟⠻⠛⠛⣟⢻⠛⣿⣿⣿⣿⣿⣿⣿⠩⡉⣙⢛⣻⡛⡛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠩⠹⠉⠩⢙⣿⣿⢽⡫⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠛⠓⠒⠚⠛⠓⠒⠛⠓⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⡉⡉⢙⢉⡉⡏⢉⠍⡋⣉⡋⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⠉⢉⠉⠉⠉⡏⡁⡏⠉⠉⠉⡏⠉⠉⡉⠉⢉⢙⢹⣿⣿⣿⣿
⢸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣠⣉⣉⣉⣉⣈⣉⣏⣉⣉⣉⢉⣉⣉⣉⣉⣈⣉⣹⣿⣿⣿⣿⣿⣿⣿⡃⣁⢃⣈⣉⣙⣈⣨⢘⣿⠸⣇⣟⣪⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣉⣁⣉⣉⣁⣉⣍⣁⣇⣉⣉⣁⣉⣁⣁⣉⠉⣇⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣍⣍⣉⣽⣉⣉⣉⣍⣉⣹⣉⣍⣹⣉⣉⡉⣉⣉⣿⣿⣿⣿⣿⣿⣁⣃⣐⣫⣇⣀⣘⣊⣸⣼⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣄⣈⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣢⣂⣼⣡⣀⣨⡀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣄⣄⣃⣰⣄⣘⣾⣬⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⣦⣤⡼⣼⣤⣷⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⡵⡤⣣⢤⠤⢽⢴⢾⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣡⣤⣤⣬⣤⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⠿⠿⠿⡿⠿⢿⢿⢿⢿⢿⠿⠿⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⢿⣿⢿⢿⠿⢿⠿⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣤⣵⣦⣤⣤⣶⣤⣤⣼⣤⣤⣤⣮⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿
⢸⣿⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣋⣘⣀⣀⣀⣃⣂⣂⣘⣃⣈⣃⣀⣐⣀⣒⣘⣒⣀⣀⣚⣂⣀⣀⣒⣂⣖⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣧⣙⣀⣀⣸⣿⣿⣿⣿
⢸⣿⣿⣿⣇⣻⣐⣕⣸⣀⣷⣂⣿⣿⣿⣿⢸⣿⠹⢉⠉⠉⢹⣭⠍⠉⡙⠋⠹⠉⠉⡏⢉⠩⠿⠏⢝⠛⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⡏⠻⠹⠙⢹⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⢉⠍⠩⢩⢉⣭⠉⡉⠩⠉⢩⡉⡭⡉⢍⢭⠉⣉⠍⢩⢉⡭⠩⠹⣛⠻⡻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣟⠟⢿⠻⠻⢻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⡶⠾⢶⢾⢶⡶⠾⣾⣾⢶⣶⠶⠶⢶⡷⡿⠾⣾⠶⠶⠶⢶⢾⡷⡶⠶⢾⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⡶⡷⣶⠶⢶⢾⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣬⣤⣤⣼⣤⣤⣿⣤⣾⣠⣥⣦⣤⣤⣧⣤⣤⣤⣤⣤⣿⣤⣤⣼⣬⣤⣷⣥⣥⣬⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣧⣬⣽⣴⣼⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣠⣠⣾⣈⣈⣘⣅⣁⣝⣁⣉⣹⢌⣈⣈⣉⣈⣘⣈⣻⣈⣉⣣⣈⣉⣈⣈⡘⣇⣉⣀⣎⣨⣈⣁⣉⣁⡡⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣁⣇⣝⣙⣈⣸⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠛⠟⢛⡟⠻⣿⠛⢛⠛⠛⠟⠛⢻⡙⠛⡛⠻⣙⠛⠛⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⡟⡻⡻⢻⢻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⡷⠷⢷⠿⣿⠿⡿⢷⠿⢿⠷⢷⠿⠷⠿⠿⠷⠷⠿⡿⠾⡾⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠷⠷⡿⢿⢾⠿⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣴⣾⣬⣽⣤⣴⣮⣮⣶⣼⣿⣥⣵⣤⣮⣮⣦⣿⣼⣼⣬⣦⣦⣴⣵⣴⣵⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣦⣿⣴⣬⣼⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣀⣈⣘⣀⣁⣂⣙⣘⣈⣐⣓⣑⣐⣑⣀⣊⣐⣀⣂⣀⣈⣐⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣅⣹⣨⣀⣸⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠉⠉⠉⠋⢻⠉⠉⢙⠹⠉⠉⠩⡫⠉⠉⣽⡍⠍⠍⠩⡹⡉⣭⠫⢹⠩⠙⠉⠉⢽⡉⠝⡹⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣯⡿⠙⠉⢹⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⠍⠉⠉⠩⢩⢩⡍⡉⠉⠍⠉⠍⢩⠉⠉⡉⢉⡉⢍⡉⠉⠉⣍⠉⠉⠉⣉⢉⡉⠉⣩⣭⣭⣭⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⣟⣿⠻⢛⢻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⣶⡶⣶⢶⡶⡶⠶⠶⠶⠶⠶⡶⡶⡶⡶⢶⡶⠶⠶⣶⠶⠶⠶⠶⢶⣶⢶⠶⣶⢶⠶⡶⠶⡶⢶⠶⠶⠶⣶⢸⣿⣿⣿⣿⣿⣿⣿⡷⠶⡶⡿⣷⢶⢶⢾⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣴⣧⣽⣬⣥⣵⣤⣤⣤⣥⣬⣼⣬⣿⣤⣾⣤⣿⣦⣤⣼⣤⣥⣬⣼⣤⣤⣬⣯⣥⣼⣤⣤⣥⣥⣦⣤⣬⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣮⣬⣤⣬⣼⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⣀⣐⣀⣐⣂⣲⣀⣀⣂⣠⣤⣰⢀⣀⣀⣠⣐⣀⣐⣲⣀⣀⣢⣀⣀⣀⣐⡐⣆⣀⣄⣢⣐⣆⣀⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⣐⣁⣅⣙⣈⣨⣸⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠫⠻⠋⠙⠉⠏⠋⠋⠉⠉⠙⠙⠛⠙⠟⠋⠏⠟⠉⠋⠋⠿⠏⠋⠻⠙⠏⠋⠋⠋⠿⠍⠙⠻⠉⠛⠙⠫⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠋⡏⢻⠹⠙⢹⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⠶⠶⠶⡶⡶⢶⡶⠶⠶⣶⢶⠶⡖⡶⠶⠶⠶⣶⠶⠶⢶⢶⠶⡶⠶⢶⡶⠶⠶⠶⠶⠶⠶⢶⠶⠖⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⡿⣿⠿⠿⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠶⠶⠶⠶⠷⠾⠾⠿⠶⠷⠷⠶⠶⠿⠾⠾⠾⠶⠿⠿⠷⠶⠾⠷⠷⠶⠶⠷⠶⠶⠷⠶⠶⠶⠶⠶⠶⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣷⢶⣾⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣘⣤⣨⣧⣢⣋⣤⣴⣼⣀⣠⣠⣀⣔⣶⣔⣤⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣸⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠉⠉⠋⠙⠩⠉⠉⠻⠏⠉⠙⠉⠻⠭⠉⠩⠩⠍⠩⠍⠉⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢉⢽⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠻⡟⣿⠻⣟⠟⠻⡛⠻⡟⡿⢛⠛⠻⠛⡛⠛⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠒⠛⠛⠚⠚⠓⠓⠚⠒⠒⠚⠒⠒⠓⠓⠚⠚⠚⠒⠓⠚⠛⠛⢛⣛⣛⣛⣛⣛⣛⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⢾⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣈⣐⣓⣙⣀⣃⣀⣂⣐⣁⣂⣃⣈⣀⣀⣀⣙⣃⣁⣊⣛⣛⣛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣽⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣩⣇⣻⣈⣇⣋⣚⣘⣁⣊⣀⣃⣑⣂⣐⣁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣺⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⠏⠙⢹⠩⢿⢉⠹⡙⠫⡏⠝⣍⠉⠭⠉⠩⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢽⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡟⠻⠛⢻⠻⠻⠟⠛⢻⠛⠛⠛⠛⠟⣛⢟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⢻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⣶⠶⣾⣶⣶⡶⡶⣾⣵⢶⡶⡶⡶⡿⡶⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢴⢾⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣀⣁⣀⣀⣘⣀⣀⣀⣀⣘⣀⣀⣀⣐⣈⣃⣈⣀⣀⣛⣛⣛⣛⣛⣛⡛⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣼⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣉⣉⣹⢙⡩⣙⣉⣉⢍⢩⢿⢉⠉⢍⢉⡙⢭⣍⣋⣍⢽⣿⣿⣿⡇⣿⣿⣿⡿⣿⣿⢈⢣⢸⡏⠬⢩⡏⠌⡇⢸⠥⢩⢨⠠⣿⣿⣿⣿⣿⣿⣿⣏⢈⢹⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⣭⣭⣥⠟⠋⠁⠀⠛⢻⣾⣿⣾⣿⣶⣿⣿⣾⣷⣾⣷⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠤⠤⢤⢤⠤⠤⠤⠤⠤⢤⢤⠤⢤⠤⠤⠤⠤⠤⡤⢤⡄⠀⠛⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢾⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠈⠀⠀⠈⠀⠈⠀⠈⠀⠁⠀⠀⠈⠉⠈⠀⠉⠁⠀⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣽⣿⣿⣿⣿
⣿⠿⣿⣿⡿⢿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠁⢠⡄⠁⠀⠠⠀⠉⠉⠍⢍⠉⠉⠉⢩⠉⢭⠉⠉⠩⠉⠩⠉⢩⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⢩⠉⢩⠩⠉⠍⠩⠭⠉⠍⡭⠉⠉⠉⡍⠩⠭⢩⠉⠉⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣿⠤⠤⠤⠤⠤⡤⢤⠤⠤⡤⢄⢤⠤⡤⠦⠤⠤⡦⢤⠤⡤⠤⠤⠤⢤⠶⢤⠤⡄⠤⡤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣈⣉⣀⣉⣉⣋⣉⣈⣉⣃⣀⣃⡀⠙⠉⠘⡉⢙⠁⢉⣉⣋⣉⣋⣉⣃⣁⣉⣈⣉⣉⣃⣈⣉⡃⠈⠈⠐⠈⠈⠁⠙⠘⠈⠋⠉⠉⠈⠀⡋⠉⠉⠁⠈⢁⠀⡋⠉⠉⠁⠙⠈⡋⢈⠉⠙⠛⠛⣛⡛⢛⠛⠛⢛⣛⠛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠰⠀⠒⠶⣶⡶⠶⠶⡀⠶⠶⢶⣶⡶⠀⠀⠐⣶⣶⣾⠭⠭⠭⠭⠭⣿⣷⣿⣭⣭⣽⡿⠛⣁⠠⢤⠈⣉⠹⣾⡽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⢷⡄⠄
⣿⣑⣒⣚⣒⣒⣚⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣓⣲⣾⣟⣻⣿⣿⣯⣭⣽⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣭⣭⡅⢸⣿⣿⣭⣭⣭⣿⣿⡇⣸
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠼⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠻⠾⠌⠻⠿⠿⠻⠷⠿⠛⠠⠿
⣿⣠⣀⣁⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣗⣶⣾⣿⣻⣿⣿⣓⣳⣾⣟⣻⣿⣿⣓⣲⣾⣟⣻⣿⣟⣓⣳⣾⣛⣻⣿⣟⣓⣶⣾⣛⣷⣦⣄⣀⣤⣔⣾⣻⣿
⣿⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣾⣿⣿⡿⠽⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣰⣾⣿⣿⣿⣿⣽⣶⣿⣻⣿⣿
䷩ 𝚕𝚒𝚗𝚎 2036
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/making-epo-staff-miserable/#comments
Gemini version at gemini://gemini.techrights.org/2022/08/29/making-epo-staff-miserable/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ EPO_Management_Trying_to_Make_EPO_Staff_Miserable_and_Isolated⠀✐
Posted in Europe, Patents at 9:42 am by Dr. Roy Schestowitz
Video_download_link | md5sum 8bcdadc32da94f7f1f7fa378c73b1402
EPO Breaking Teams Apart
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/epo-teams-apart.webm
Summary: The siege against EPO examiners carries on; the sole goal is to turn
educated, motivated, principled people into demoralised serfs who just grant as
many patents as possible in order to fake_so-called_'production' (in effect,
bypassing the safeguards against fake and invalid patents which beget frivolous
threats and litigation)
THE END of August is imminent. Today is Bank Holiday here in England and
September soon commences. Expect our EPO coverage to be back in “full swing”,
exposing the crimes of António_Campinos, the successor of his_corrupt
compatriot_aand_close_friend. Truth and justice can catch up with them, however
belatedly.
The EPO isn’t saying much at the moment, mostly because people are on vacation
(some physically away from work). We’ve meanwhile spoken to the EFF, trying to
figure out the EFF’s silence on these matters in spite of the EFF’s focus on
patents and on Europe (lots about copyright law in the EU). Don’t they show
interest in European_software_patents? If not, then why not? They ought to
explain and we’ll keep pressing.
“Maybe union-busting consultants suggested this to EPO managers.”The letter
below concerns a meeting that actually took place last month. That’s when the
EPO last issued a statement (regarding Montenegro) — no less than 33 days ago!
The message to staff covers “the project to reshuffle office spaces and
introduce an “office for a day”. [Euphemism]”
Ignore terms like “bringing teams together” as “Breaking Teams Apart” (the
title of the video above) seems to be the real goal, as we_noted_here_back_in
June. It’s a strike-breaking strategy — akin to those which discourage any
other industrial actions, even merely a protest of solidarity. Maybe union-
busting consultants suggested this to EPO managers.
Here’s the message in full:
Bringing teams together – Report on the meeting of the LSCTH with VP1
on 13 July 2022
“The present publication emanates from Local Staff Committee the
Hague which does not have access to mass email. It is re-published
via SUEPO in order to reach a larger number of colleagues.”
Dear colleagues,
your Local Staff Committee The Hague met with VP1, VP4 and a member
of facility management on 13 July 2022 regarding “bringing teams
together”, i.e. the project to reshuffle office spaces and introduce
an “office for a day”.
Main_points:
- The lack of consultation before the decision was taken does not
seem to comply with the requirements of the CODEX and iso 45001
certification;
- LSCTH is concerned about the prominence of managerial discretion in
the attribution of assigned individual offices;
- Decision to assign individual offices to be based on a mature
dialogue with staff;
- Staff can change their minds at any stage;
- Input from colleagues welcome: direct feedback, questions, tips and
ideas relating to the project can be sent by email to Frédéric
Brunelle and Edda Franz, possibly with staff representation (DHSTCOM
for TH, MNSTCOM for MU) in cc.
- Concerns or questions related to managerial discretion should be
addressed to staff representation directly;
- Bona fide consultation on contingency plan was requested.
Conclusions:
The plethora of recent changes will “make the EPO great again”
according to the members of management, while staff representation
pointed to the fact that they are more likely to have far reaching
negative consequences on the wellbeing and social fabric of the EPO,
potentially leading to an increase of psychosocial risks.
See the full report [...] for more details.
Kind regards,
Your Local Staff Committee The Hague (LSCTH)
The video above goes through the original full report, which we’re reproducing
as HTML for Gemini, IPFS, and plain text. It’s a longer version of the above,
bearing the date of last Monday:
Staff Committee The Hague
Comité du personnel de La Haye
Personalausschuss Den Haag
22 August 2022
Bringing teams together
Report on the meeting of the LSCTH with VP1 on 13 July 2022
Dear colleagues,
Members of the LSCTH met Steve Rowan (VP1), Nellie Simon (VP4) and
Frédéric Brunelle (Facility management) on 13th of July 2022.
The administration stated that the purpose of the meeting was to
collect The Hague site specific issues related to the implementation
of the “Bringing Teams Together” project.
While the Staff Representation expressed its appreciation for the
opportunity to exchange on the matter, it noted that the present
meeting could not be considered a consultation. It further noted that
a decision on “Bringing Teams Together” had already been taken
without prior consultation of the Staff Committees and of the Health
& Safety statutory bodies, which goes against the CODEX1 and does not
comply with the requirements for ISO 45001 certification2.
The LSCTH referred to the opinion of the CSC (central staff
committee) members of the GCC on GCC/DOC 13/2022, and added that the
project appears to be rushed, premature and seems to steer staff away
from coming into the buildings.
It also noted that no prior consultation took place for the
contingency plan which determines building temperatures in view of
the energy crisis. The LSCTH indicated its sensitivity to the energy
crisis and pointed out that consultation with the relevant committees
should be carried out to ensure the legality, legitimacy, and
acceptance amongst staff of any contingency measure that may be
taken.
The members of the administration insisted that no consultation would
be required since neither the “Bringing teams together” project nor
the contingency plan would change our working conditions. The LSCTH
expressed its disagreement, insisting that both matters quite
obviously concern aspects of health, safety, and ergonomics, which
are part and parcel of our working conditions.
The LSCTH expressed concerns on the implementation of “Bringing teams
together”, in particular on the prominence of managerial discretion
in the attribution of assigned individual offices and insisted that
staff be treated equitably.
The administration answered that the basis of this concept would be
flexibility and
______
1 Art. 37(1)(a) Service Regulations: the Local Staff Committee “shall
be consulted on any proposal [...] which
concerns the conditions of employment of the whole or part of the
staff at the place of employment concerned”.
2 ISO 45001 certification requires consultation including engaging
health and safety committees and workers’ representatives
=====================================================================
that it would be possible for staff to change their minds at any
stage, even after the planning and implementation phases. There would
be no fixed rules on which staff and line management could rely,
everything will be at the discretion of line management and should be
based on a mature dialogue with staff.
F. Brunelle from facility management stated that all input from
colleagues is welcome, and it was agreed that staff could send direct
feedback, questions, tips and ideas relating to the project by email
to Frédéric Brunelle and Edda Franz, possibly with staff
representation (DHSTCOM for TH, MNSTCOM for MU) in cc.
Concerns or questions related to managerial discretion should be
addressed to staff representation directly.
The LSCTH concluded that the perpetual changes which have been taking
place during and since the heights of the pandemic (for example, the
series of reorganisations, the implementation of the new ways of
working, the “Bringing teams together” initiative and the contingency
plan) may have far reaching negative consequences on the wellbeing
and social fabric of the EPO, potentially leading to disengagement, a
loss of cohesion and sense of belonging as well as to an increase of
psychosocial risks.
The members of management, on the other hand, closed the meeting with
an optimistic outlook, in that all the changes and permanent reforms
would “make the EPO great again” in an energetic, vibrant,
collaborating and connecting environment.
Let’s see what the future brings.
Your Local Staff Committee The Hague (LSCTH)
[...]
Among the references they’ve added to the bottom (redacted) we have “What is
wrong with hot- desking?” and “Appalling lack of consultation are the “New Ways
of Working”?” (Munich)
Workers are clearly unhappy about this. Maybe making them unhappy is a side
goal. █
䷩ 𝚕𝚒𝚗𝚎 2285
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/norbert-preining-canary/#comments
Gemini version at gemini://gemini.techrights.org/2022/08/29/norbert-preining-canary/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ The_Inquisition_of_Norbert_Preining_is_a_Cautionary_Tale_About_the_Clique
That’s_Killing_Debian_From_the_Inside⠀✐
Posted in Debian, GNU/Linux at 7:18 am by Dr. Roy Schestowitz
Video_download_link | md5sum d532ecde5c79535bae77b762cab6a6ee
Passive Bullies Disguised as Victims
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/debian-mob.webm
Summary: This morning Norbert Preining, a veteran GNU/Linux developer
(maintaining key packages including KDE and widely-used LATEX stuff), indicated
that he was still being harassed by the same people who had pushed him out of
Debian, where his volunteering track record is decades long and highly
productive
EARLIER this year we did a video_about_Norbert_Preining and how he had been
(mis)treated by a vocal, abusive minority inside Debian. Dr. Preining isn’t new
to Debian or to GNU/Linux. The thought police probably deemed him a “high-
profile” target and having been put in positions of unjust power (like the so-
called ‘anti-harassment’ team) mischief was likely imminent, firing the first
shot over the word “it”.
To make matters worse, the same incompetent fools are still chasing and mobbing
him. They want nothing short of destruction/end to his career. Maybe they
derive pleasure from causing the downfall of very productive developers. Maybe
this is a mental sickness akin_to_the_Zemlins'. Who knows…
Dr. Preining has already attempted to just go along, sucking up to the mob that
ousted/demoted him from the “DD” status. It didn’t work; nothing would ever
please them, so he just left Debian completely, but they_still_chase_him, just
like FSFE autocrats chased Daniel Pocock after he had exposed to FSFE members
(who elected him!) some of the dirty laundry from inside the FSFE.
I end the video above by commenting on Debian_selling_out_to_a_Microsoft_front
not too long after Microsoft had paid DebConf. There’s a whole bunch of stuff
happening inside Debian that causes my wife and I to reassess our choice of
Debian (for 4 of our computers, which still run Debian for the time being). █
䷩ 𝚕𝚒𝚗𝚎 2348
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/zdnet-exit-strategy/#comments
Gemini version at gemini://gemini.techrights.org/2022/08/29/zdnet-exit-strategy/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ ZDNet’s_Exit_Strategy:_Ugly/Cheap_Redesign,_Infinite_Scroll_for_Fake
‘Traffic’_(‘Engagement’),and_Hardly_Any_New‘Content’⠀✐
Posted in GNU/Linux at 7:54 am by Dr. Roy Schestowitz
10 days ago: ZDNet_Turns_Ugly._Really,_Really_Ugly.
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇ZDNet on Linux⦈
ZDNet has hardly mentioned “Linux” in a long time (nothing in 6 days); then
again, the site in general is barely active
Summary: It’s truly noteworthy that in the past 13 days only three “Linux”
stories were published in ZDNet; the one at the bottom is actually_about
Microsoft promotion, not Linux
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⣿⡇⠀⠀⠀⢿⡇⠀⢸⠀⢀⣀⣀⣀⣀⣸⣀⣀⡀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⡻⡛⠛⠛⢻⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡟⠛⠛⠛⠛⡟⢻⠛⠛⠛⡛⢻⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛
⣿⡇⠀⢸⡀⠈⡇⠀⢸⠀⠈⠉⠉⠉⢹⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾
⣿⡇⠀⢸⣧⠀⠀⠀⢸⠀⠘⠛⠛⠛⠛⢻⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⡏⢰⣿⢸⠀⡟⢋⠻⠛⣿⢻⡛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⣿⣿⣸⣀⣇⣿⣀⣄⣋⣸⣁⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣛⣛⣛⣛⣛⣛⣛⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣼⣏⣰⣃⣁⣇⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⣿⣿⣿⢍⣝⠛⡋⢛⢻⢫⠙⠉⢿⢛⠟⠋⡛⢻⢟⠛⡛⡟⢻⡟⢛⠛⠻⠛⢙⠛⢟⢛⡋⠛⡟⠛⢻⡋⢛⠛⣛⠛⠋⡻⠛⡋⡟⠛⡟⡻⠛⡛⠋⢛⡛⡛⢛⢿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⢷⣾⣾⠶⢾⣶⣿⣴⣷⣶⣶⡾⣷⣶⣷⢷⣾⡷⣾⡶⣶⣶⢶⢶⡿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣿⣾⣶⣷⣶⣷⣷⣶⣷⣾⣶⣷⣶⣶⣶⣾⣴⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣄⣤⣠⣴⣠⣆⣤⣦⣀⣸⣄⣊⣦⣴⣧⣠⣤⣦⣧⣠⣦⣄⣄⣤⣄⣼⣧⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣿⣿⣿⡿⠿⡿⡿⠿⠿⠿⢿⠿⢿⠿⢿⠿⢿⠿⡿⠿⠿⢿⠿⠿⡿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⡿⢿⠿⠿⢿⠿⠿⠿⡿⠿⣿⠿⠿⡿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠛⣿⣿⣿⣿⣿⣿⡶⡶⢶⢷⠶⣖⡶⠿⢶⢲⠲⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣷⣶⣶⣷⣶⣶⣶⣶⣷⣾⣶⣶⣾⣿⣶⣿⣷⣶⣾⣶⣶⣷⣶⣶⣷⣶⣷⣷⣾⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣴⣶⣶⣶⣿⣿⣿⣶⣬⣴⣤⣥⣬⣧⣴⣬⣧⣶⣵⣤⣦⣶⣦⣤⣶⣷⣦⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠩⠝⠝⠋⠋⡏⠍⠉⡏⠙⠍⠋⣿⢋⠋⠋⢹⠋⠛⠙⢉⣟⠉⠋⢻⠉⢋⠉⠉⢹⠩⠉⠋⢹⡿⠏⢩⠋⢻⠋⡟⠍⠋⠋⠉⠫⠙⠙⠩⢻⢹⠉⠏⠋⣽⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⡿⡿⢿⠿⠿⠟⢳⠶⠻⠿⡾⠿⠻⠛⠿⡟⠟⠻⢿⠿⢟⡻⠛⢻⠿⡿⢟⠟⠟⠻⢿⠟⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣠⣬⣤⣥⣧⣥⣤⣼⣼⣼⣬⣤⣥⣧⣦⣼⣤⣧⣧⣴⣤⣤⣬⣮⣵⣤⣼⣬⣦⣿⣴⣼⣤⣴⣥⣮⣤⣤⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⡿⠿⠿⡿⠿⠿⡿⠿⡿⢿⠿⠿⢿⡿⠟⠿⣿⠿⡿⢿⡿⢿⡿⢻⠿⠟⠛⠿⢿⡟⠿⡿⡿⠻⠿⢻⣿⢿⣿⠻⢿⢻⡛⠻⠟⠿⣿⠿⣿⠿⠿⢿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⡞⢚⠛⠓⠛⡛⠛⢛⡟⠺⡗⠓⠛⠓⠛⠛⢳⠛⠺⢾⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣷⣿⣷⣶⣾⣷⣷⣿⣿⣷⣿⣾⣿⣷⣿⣷⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⡿⣿⡿⠿⢿⠿⠿⡿⠿⠿⠿⠿⠿⠿⡿⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣶⣶⣷⣶⠶⠾⠷⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠓⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡰⡊⠉⠉⡉⠉⡍⢈⢍⠉⣹⡏⢉⠁⡩⠀⢸⡿⢈⠀⠤⡆⣾⢈⠍⣇⠇⡇⢉⠏⢩⠁⡙⢹⠂⠔⢸⠇⢊⡁⣻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢶⣭⣭⣽⣭⣯⣼⣭⣯⣭⣽⣍⣭⣽⣵⣬⣝⣧⣼⠝⠛⠉⠉⠒⠙⠁⠀⠐⠈⠀⠒⠩⣭⣿⣧⣤⣦⣧⣤⣤⣼⣭⣼⣥⣬⣧⣥⣭⣽⣧⣿⣭⣉⣿⣿⣿⣿
⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣤⣴⣶⣧⣤⣤⣤⣤⣦⣶⣤⣦⣤⣤⣧⣾⣤⣤⣥⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣍⣉⣉⣉⣏⣹⣫⣛⣋⣏⣹⣉⣉⣉⣉⣍⣉⣉⣉⣩⣏⣉⣉⣉⣉⣏⣉⣋⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 2423
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/zemlin-narcissism/#comments
Gemini version at gemini://gemini.techrights.org/2022/08/29/zemlin-narcissism/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Echoes_of_Narcissism:_How_Jim_Zemlin_Views_Himself⠀✐
Posted in Kernel, Videos at 4:49 am by Dr. Roy Schestowitz
The Elizabeth_Holmes of Linux?
Watch this:
http://techrights.org/wp-content/uploads/2022/08/zemlin-pride.mp4
Compare to this:
http://techrights.org/wp-content/uploads/2020/08/What-the-Tech-Industry-Has-
Learned-from-Linus-Torvalds_-Jim-Zemlin-at-TEDxConcordia-U-Portland.mp4
Summary: This older_talk shows a familiar pattern of megalomania (and an often-
repeated_talking_point), derived by gaining leverage over people who actually
accomplished something, then controlling_them
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Zemlin on humility⦈
Slide he presented only months ago
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⣷⣶⣶⣷⣿⡇⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⢀⡤⣤⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣚⣳⣛⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠍⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠲⠴⠋⠀⠉⠘⠘⠊⠘⠘⠃⠁⠘⠊⠂⠓⠃⠉⠘⠀⠀
䷩ 𝚕𝚒𝚗𝚎 2486
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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_29/08/2022:_Canonical_Helping_Microsoft_Again⠀✐
Posted in News_Roundup at 5:25 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Audiocasts/Shows
o Kernel_Space
o Applications
o Instructionals/Technical
o Games
o Desktop_Environments/WMs
# K_Desktop_Environment/KDE_SC/Qt
# GNOME_Desktop/GTK
* Distributions_and_Operating_Systems
o Reviews
o New_Releases
o Fedora_Family_/_Red_Hat
o Debian_Family
o Canonical/Ubuntu_Family
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o Web_Browsers
# Mozilla
o Productivity_Software/LibreOffice/Calligra
o Programming/Development
# Perl_/_Raku
* Leftovers
o Hardware
o Security
o Internet_Policy/Net_Neutrality
* Gemini*_and_Gopher
o Technical
# Programming
* § GNU/Linux⠀➾
o § Audiocasts/Shows⠀➾
# ⚓ Video ☛ Linux_Wayland_Screen_Lockers_Are_Simply_Better_–
Invidious⠀⇛
While Wayland has a lot of issues in many areas
there’s one thing that Wayland especially wlroots
do objectively better is screenlockers especially
with the way the new screenlocking protocol works
# ⚓ Video ☛ Manjaro_21.3.7_Gnome_Edition_overview_|_OS_FOR
EVERYONE_–_Invidious⠀⇛
In this video, I am going to show an overview of
Manjaro 21.3.7 Gnome Edition and some of the
applications pre-installed.
# ⚓ Episode_3:05:_How_to_Exit_Vim⠀⇛
# ⚓ Jupiter Broadcasting ☛ End_of_the_Road_|_LINUX_Unplugged
473⠀⇛
We’ve reached the end of the road in our immutable
Linux series, and an old friend stops by to give us
the inside scoop on Endless OS.
# ⚓ Video ☛ Steam_Deck_2_—_CONFIRMED._But_also_a_new_Steam
Controller_(plus_other_Steam_Deck_News)_–_Invidious⠀⇛
o § Kernel Space⠀➾
# ⚓ LWN ☛ Linux_5.19.5⠀⇛
I'm announcing the release of the 5.19.5 kernel.
All users of the 5.19 kernel series must upgrade.
The updated 5.19.y git tree can be found at:
git://git.kernel.org/pub/scm/linux/kernel/
git/stable/linux-stable.git linux-5.19.y
and can be browsed at the normal kernel.org git web
browser:
https://git.kernel.org/?p=linux/kernel/git/stable/
linux-s...
thanks,
greg k-h
# ⚓ LWN ☛ Linux_5.10.139⠀⇛
# ⚓ Techgage ☛ SPECviewperf_2020:_GPU_Viewport_Performance_In
Linux_&_Windows_–_Techgage⠀⇛
We’re taking a fresh look at viewport performance
in popular design software with the help of
SPECviewperf 2020. With 21 gaming and workstation
GPUs in-hand, we’re testing not just the
performance in Windows, but also Linux – which has
made for some interesting comparisons.
It’s been nearly a year since we last took an in-
depth look at viewport performance with the help of
SPEC’s SPECviewperf, and with the recent release of
its 2020 v3.1 update, we felt now was a good time
to generate some fresh numbers. As an added bonus,
this article marks the first time we’ve run the
same tests under Linux. That proved to be a good
move, as it gave this article’s results more
flavor.
For those not familiar with SPECviewperf, it’s
important to note the fact that it is not the
benchmark. It’s instead the tool for benchmarking
viewports in individual applications, like 3ds Max,
SolidWorks, and Siemens NX. To make the magic
happen, SPEC captures API traces of the full
versions of said applications, and creates viewsets
that replicate playback – without the native
application needing to be installed.
# ⚓ WCCF Tech ☛ AMD_Zen_4_Last_Branch_Record_Extension_version
2_queued_for_Linux_6.1⠀⇛
The Last Branch Record functionality, or LBR, is
“used for determining and analyzing the control
flow of software by logging branch information to
registers in real-time.” The branch information
will allow the system to decide what paths “hot
code” should be directed to, such as optimizations
to profile-specific compilers or other
optimizations seen active in applications
# ⚓ Neowin ☛ You_can_soon_daisy_chain_three_4K_60Hz_monitors_on
your_Intel_Arc_laptop_running_Linux_–_Neowin⠀⇛
Previously, Intel’s Linux drivers allowed only
connecting two monitors, without daisy chaining,
including Intel’s integrated graphics solutions.
Intel will be pushing this feature out to its open-
source driver stack for Arc GPUs. But whether or
not it will work on the cheaper options like the
Arc A380, which just arrived in the US, remains to
be seen.
# ⚓ PC Perspective ☛ Intel_Arc_A380_On_Linux_–_PC_Perspective⠀⇛
If you need an accelerator on a PC running Linux
that works for a living, this is a decent choice if
you can’t afford a higher end card.
o § Applications⠀➾
# ⚓ DebugPoint ☛ Scrivano:_Fascinating_Whiteboard_App_For
Handwritten_Notes⠀⇛
Scrivano is a new whiteboard application which
recently getting some attention for its unique
features and “ease of use”. It has some seriously
cool feature which I will talk about shortly.
When I write about the top Whiteboard applications
for taking hand written notes using touch devices,
I was not aware of this application since it was
probably under development. In that article, I
mentioned about the major apps which you all know
about.
For example, Xournal++ is probably the most used
and “go to” app for taking quick notes using stylus
in supported devices. Another GTK & Rust based app
which recently became famous is Rnote. It also has
some excellent features.
Now, you can try out another cool app – Scrivano.
It is a Qt based application and comes with a
simple user interface for utmost productivity.
# ⚓ Ubuntu Handbook ☛ Pano_–_Manage_Clipboard_History_in_Ubuntu
22.04_/_Fedora_36_in_New_Style_|_UbuntuHandbook⠀⇛
Need to access your copy & paste history quickly?
Forget about GPaste or CopyQ, try Pano!
It’s a cool new clipboard manager for Ubuntu,
Fedora, and other Linux with GNOME Desktop, such as
Arch and Manjaro.
No system tray indicator or app window, just press
your custom keyboard shortcut will bring up the
bottom bar with all recent clipboard histories.
# ⚓ Linux Shell Tips ☛ Stig_–_A_TUI_and_CLI_Client_for
BitTorrent_Transmission⠀⇛
The BitTorrent client Transmission application is
becoming a must-have for a growing number of Linux
users. The features of this app have more to say
about what it has to offer than the name itself.
For instance, it is resource-friendly since it uses
minimal system resources during its application
runtime. Also, its full support for Magnet Link,
PEX, DHT, µTP, and DHT are some prime features
associated with the BitTorrent client transmission
application. However, to use this app, you will
need to install it from the default repositories.
[...]
The following are some prime features that Stig CLI
and TUI-based client applications have to offer for
your BitTorrent client Transmission endeavors.
o § Instructionals/Technical⠀➾
# ⚓ ID Root ☛ How_To_Install_Chromium_Browser_on_Linux_Mint_21
–_idroot⠀⇛
In this tutorial, we will show you how to install
Chromium Browser on Linux Mint 21. For those of you
who didn’t know, Chromium is an open-source browser
project that aims to build a safer, faster, and
more stable way for all users to experience the
web. Google’s Chromium browser is an open-source
project. The Chromium codebase is also used by many
other browsers, including Microsoft Edge, Opera,
and Vivaldi.
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 a Chromium web browser on Linux
Mint 21 (Vanessa).
# ⚓ OSNote ☛ UUID_in_Linux_–_OSNote⠀⇛
The UUID refers to a Universally Unique Identifier
that consists of 128-bit numbers that have the
probability of having duplicates close enough to
zero but not zero in the local system. It was
originally used in the Networking Computing System
and then, later standardized by the Open Software
Foundation.
The UUID is divided into five groups separated by
hyphens (-) consisting of 8-4-4-4-12 characters in
each group. In total it consists of 36 characters.
You can see the UUID string like the string shown
below.
# ⚓ Investigating_database_replication_in_different
availability_zones_–_formicapunk⠀⇛
In regards to safety of data, it looks similar to
the raft algorithm used by etcd with three members
as a write is only ack’ed if it has been fsynced by
two servers, the difference is that raft has a
leader election, whereas in PostgreSQL the leader
is set at startup and you have to build yourself
the election mechanism.
# ⚓ LinuxTechi ☛ How_to_Setup_EKS_Cluster_along_with_NLB_on
AWS⠀⇛
Are looking for an easy guide for setting up EKS
cluster on AWS?
The step-by-step guide on this page will show you
how to setup EKS cluster along with NLB (Network
Load Balancer) on AWS from the scratch.
# ⚓ HowTo Forge ☛ How_to_Mount_an_NTFS_Drive_on_CentOS_/_RHEL_/
Rocky_Linux⠀⇛
This tutorial will show you how to mount an NTFS
drive ina read/write mode on CentOS and other RHEL
based Linux operating systems with ntfs-3g driver.
NTFS-3G is a stable Open Source NTFS driver that
supports reading and writing to NTFS drives on
Linux and other operating systems.
The ntfs-3g driver is available in the EPEL
repository, it is available for all RHEL-based
systems like AlmaLinux, CentOS, Rocky Linux, and
also RHEL itself from version 6 to 9. The first
step is to install and activate EPEL on your Linux
system.
# ⚓ HowTo Forge ☛ How_to_Enable_HTTP/2_in_Apache_Web_Server_on
Ubuntu_and_Debian⠀⇛
Hypertext Transfer Protocol Version 2 (HTTP/2) is
the latest version of the HTTP protocol, published
as an IETF standard in RFC 7540 in 2015. The focus
of the protocol is on performance; specifically,
end-user perceived latency, network, and server
resource usage. One major goal is to allow the use
of a single connection from browsers to a Web site.
The protocol is backward compatible, so HTTP
methods, status codes, and semantics are the same
as for previous versions of the protocol. Apache
has HTTP/2 support since version 2.4.17. In this
tutorial, I’m going to assume that you already have
a working TLS configuration, and that you have the
required Apache version installed on your Linux
distribution of choice, and that you know how to
use Let’s Encrypt, or you know how to issue a self-
signed certificate.
This tutorial has been tested on Debian 10, Debian
9, Ubuntu 20.04 LTS, and Ubuntu 18.04 LTS.
# ⚓ Vitux ☛ How_to_Install_and_Use_Snapd_on_Debian_11⠀⇛
Snap packages are widely used all across different
Linux distributions. These packages are easier to
create, install, and manage and they are there to
keep all of your applications updated. However, to
use these packages, you need to have an API
installed which is known as Snapd. This API is
responsible for managing snap packages on your
Linux system. It communicates with the Snap Store
to download and install snap packages on your Linux
system.
Most of the flavors of Linux have this API
installed on them by default. However, on some
distributions of Linux like Debian, you have to
install this API manually so that you can
conveniently deal with the snap packages.
Therefore, in this article, we will explain to you
the method of enabling Snapd on Debian 11.
# ⚓ LinuxConfig ☛ Introduction_to_the_dconf_configuration
system⠀⇛
Dconf is the low-level configuration system used by
the GNOME desktop environment. It is basically a
database, where the various configuration are
stored as keys together with their values. The keys
in the database can be inspected, changed, or
dumped with the dconf utility or by using the
dconf-editor graphical tool.
In this tutorial we see how manage dconf keys, how
to backup and restore them and how to keep the
database status in sync with a configuration file.
# ⚓ LinuxConfig ☛ How_to_remove_unnecessary_files_with
BleachBit_on_Linux⠀⇛
BleachBit is a free and open source application
available on Linux and Windows, which can be used,
among the other things, to remove unnecessary files
and directories from a filesystem. BleachBit can be
used to free the caches of many applications,
remove cookies and browsers history, but also to
shred (secure delete) files and directories.
In this tutorial we see how to install and use
BleachBit on the major Linux distributions.
# ⚓ UNIX Cop ☛ How_to_deploy_GLPI_using_Docker⠀⇛
Docker is a software development platform for
virtualization with multiple operating systems
running on the same host. This is made possible by
containers that are distributed as images.
The system is very lightweight because it does not
incorporate an operating system, which also allows
for better use of resources. Docker also allows
applications to be isolated, which is very useful
for testing without bringing down the client’s
production server.
Meanwhile, GLPI is a web application that allows us
to deploy a fleet management system. It has also
evolved and with it, you can also manage hardware,
software, and data centers by linking the asset
inventory to the helpdesk.
# ⚓ Linux.org ☛ LFCS_–_Network_Management⠀⇛
These days, we connect nearly all computers to a
network in some manner. Whether the connection is
Ethernet (hard-wired) or Wi-Fi, there is a method
of sharing data or accessing shared data.
When dealing with TCP/IP for the Internet, these
commands can come in handy when there are
connection issues.
# ⚓ Unix Men ☛ Bash_While_Loop_Examples:_For_Loops,_Until
Loops,_And_More⠀⇛
Bash programming comprises three kinds of loops:
the for loop, the while loop, and the until loop.
The idea of all the loops is to repeatedly execute
some code as long as some specific parameters are
met.
The Bash for loop operates differently from the for
loops in other programming languages you may be
familiar with. With it, you can iterate over a
series of “words” in a string.
On the other hand, the while loop executes the code
under it if the control expression (or simply, the
“condition”) is true. The loop stops executing the
code when the condition becomes false, or there is
an explicit break in the code.
The until loop is comparable to the while loop,
with the only difference being that the code keeps
executing while the control expression is deemed
false.
In this post, we discuss how to use the Bash while
loop with examples.
# ⚓ ZDNet ☛ How_to_kill_a_process_in_Linux_|_ZDNET⠀⇛
Every application and service on your Linux machine
runs as a process. And, for the most part, those
processes run fairly smoothly. Every so often,
however, you might find a process (an application
or a service) that goes astray and either slows
down your system or causes other problems (such as
a locked-up desktop).
# ⚓ TechRepublic ☛ How_to_install_the_Redis_in-memory_database
server_on_Ubuntu_22.04⠀⇛
Redis is an open-source, in-memory key-value store
that can be used as a powerful database server.
Redis supports numerous data structures, such as
strings, hashes, lists, sets, bitmaps, sorted sets
and much more. And given that Redis stores
everything in-memory, it’s blazingly fast. The one
caveat to this is you’ll want to install it on a
server with a fairly large amount of RAM.
What I’m going to do here is walk you through the
process of getting a single node Redis server up
and running. In a later tutorial, we’ll discuss
setting up a Redis cluster, so you can gain high
availability with your server.
Until then, let’s get that single instance server
up and running.
# ⚓ Linux Made Simple ☛ How_to_install_Teamspeak_on_a
Chromebook_in_2022⠀⇛
Today we are looking at how to install Teamspeak on
a Chromebook. Please follow the video/audio guide
as a tutorial where we explain the process step by
step and use the commands below.
o § Games⠀➾
# ⚓ Boiling Steam ☛ Transform_your_Steam_Deck_into_a_Steering
Wheel,_with_Sol_Wheel’s_Clever_New_Model_–_Boiling_Steam⠀⇛
Not long after the first iteration was shared on
Reddit and on Boiling Steam, Ethan from Sol Designs
has made progress with their second iteration of
the Sol Wheel, an accessory that can turn your
Steam Deck into a Steering Wheel. Now there are
massive improvements in usability. The previous
iteration could only make the Steam Deck turn very
slightly left and right, but this new one makes it
possible to do much more drastic wheel turns, along
with rubber bands to give some pull back from the
more extreme positions on the side. Very clever.
# ⚓ Video ☛ How_to_install_Steam_on_Pop!_OS_22.04_–_Invidious⠀⇛
In this video, we are looking at how to install
Steam on Pop!_OS 22.04.
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ Volker Krause ☛ 20_Years_of_KDE_Contributions⠀⇛
On this day twenty years ago I wrote and
submitted by very first patch to a Free
Software project, KDE. What basically started
with changing a single number got slightly
out of control and had consequences my
younger self wasn’t even remotely able to
imagine.
[...]
But in 2000 and 2001 when KDE 2 came out I
was doing my mandatory civil service which
gave me access to “infinite” Internet
(10Mbit/s). So I could download all the
updates and carry them home on floppy disks
and CD-RWs. The step from KDE 1 to 2 was
huge, I wanted more of that.
# § GNOME Desktop/GTK⠀➾
# ⚓ Linux Magazine ☛ GNOME_Project_Releases_a_New
Telemetry_Data_Collection_Tool⠀⇛
Although telemetry (the collection of data
and measurements for the purpose of
monitoring) is a rather touchy subject,
especially for those who value their
privacy), the GNOME foundation has announced
it will be adding a telemetry data collection
tool to the desktop environment.
Before anyone panics, this data will be 100%
anonymous and will be used only to improve
the GNOME desktop environment by informing
various decisions for the future of the
software. Those decisions will help to inform
the GNOME Foundation where resources should
be best used and how to better help users.
* § Distributions and Operating Systems⠀➾
o ⚓ Make Use Of ☛ Is_Linux_Lite_the_Simple,_Fast,_and_Lightweight
Linux_Distro_You_Need?⠀⇛
Linux Lite is one of the many lightweight Linux distros
that run seamlessly on older hardware. But is it the best
operating system for your computer?
Linux is a highly customizable and open-source operating
system kernel. This is why you’ll find tons of Linux
distros out there to choose from, making it pretty hard
to make a choice.
However, if you are looking for a simple, fast, and
lightweight distro, Linux Lite might be the one for you
as it offers a great balance between performance and
functionality. So, let’s look at what Linux Lite is along
with a rundown of its notable features.
[...]
To test it, we used a 2005 Dell laptop. The system
specifications included 2GB of RAM, a 1GHz processor,
250GB HDD storage, and Intel VGA 1280×768.
o ⚓ ZDNet ☛ Want_to_save_your_aging_computer?_Try_these_Linux
distributions_|_ZDNET⠀⇛
On top of this, several modern operating systems aren’t
exactly friendly to older hardware. If you’ve found
yourself in such a situation, there’s hope by way of a
handful of Linux distributions that have been designed
specifically for older hardware. With these operating
systems, you can revive old hardware and make it run as
though it were new.
Let me introduce you to five such Linux distributions,
each of which is perfectly at home on new and older
hardware.
o § Reviews⠀➾
# ⚓ FOSS Post ☛ Linux_Mint_21_Review:_A_Considerable_Upgrade⠀⇛
Linux Mint 21, which is based on Ubuntu 22.04 LTS,
has been released less than a month ago with a
number of considerable changes.
[...]
The Linux Mint 21 distribution contains
considerable improvements, and it should definitely
be recommended over a plain Ubuntu 22.04 LTS
installation. It will remain supported with updates
until 2027, which is a good support period for any
desktop user.
Still, compared to previous releases, not much was
added in this release. Mostly, developers focused
on backend improvements and cleaning old chunks of
code which will enable them to add more features in
the future.
o § New Releases⠀➾
# ⚓ Linuxiac ☛ MX_Linux_21.2_Is_Here_as_a_Bugfix_Release,_Based
on_Debian_11.4⠀⇛
MX Linux 21.2, the second refresh of the MX Linux
21 “Wildflower” release, consists of bug fixes and
application updates.
MX Linux is a desktop-oriented Linux distro based
on Debian’s Stable branch, including the Xfce as a
default desktop. However, the desktop environment
has a slightly modified layout, with the main panel
moved to the left side.
o § Fedora Family / Red Hat⠀➾
# ⚓ Make Use Of ☛ What_Is_Fedora?_Everything_You_Need_to_Know⠀⇛
Alongside Arch and Debian, Fedora is one of “the
big three” Linux distributions. It traces its
lineage back to Red Hat Linux, the original RPM-
based distro.
Fedora is known for its cutting-edge technologies,
the latest software, and frequent updates. It’s
also one of the few major distros to embrace stock
GNOME. Lately, the distribution has become more
user-friendly, with a welcome screen, Flatpak
support, and the ability to enable third-party
repositories in setup.
# ⚓ Fedora Magazine ☛ Fedora_Linux_editions_part_2:_Spins_–
Fedora_Magazine⠀⇛
One of the nice things about using Linux is the
wide choice of desktop environments. Fedora Linux
official Worksation edition comes with GNOME as
default desktop environment, but you can choose
another desktop environment as default via Fedora
Spins. This article will go into a little more
detail about the Fedora Linux Spins. You can find
an overview of all the Fedora Linux variants in my
previous article Introduce the different Fedora
Linux editions.
# ⚓ Red Hat Official ☛ Preview_the_new_system_role_support_for
Microsoft_SQL_Server_Always_On_availability_groups [Ed: Red
Hat is helping its own competition, which ruthlessly blocks
GNU/Linux from even booting!]⠀⇛
# ⚓ Red Hat Official ☛ Red_Hat_Summit:_Connect_2022_lab
sessions_and_topics⠀⇛
Red Hat Summit: Connect 2022 is kicking off in
September. Learn about our self-paced and
instructor-led labs here.
# ⚓ Red Hat ☛ Containers_and_container_images_101_for
developers_|_Red_Hat_Developer⠀⇛
Containers are the backbone of modern development.
Learn the basics of how the components of a
container interact.
# ⚓ Enterprisers Project ☛ Agile:_Starting_at_the_top⠀⇛
Change management can be the hardest part of any
transformation. While you may quickly get people on
board with the idea of change, it can be a long
time before behaviors start to shift. We are all
creatures of habit, after all.
When the IT organization at Thales North America
wanted to transform product and service delivery
from waterfall to agile, they took a radical
approach: Instead of simply talking about what they
wanted to achieve – squads, operating using agile
methods driven by user stories, and ultimately
delivering incremental value – they decided to show
the organization by walking the walk themselves.
“The only way we could truly be effective in
leading the organization through an agile
transformation is if we transformed our leadership
team first,” says Kevin Neifert, CIO of Thales
North America.
o § Debian Family⠀➾
# ⚓ Make Use Of ☛ MX_Linux_21.2_“Wildflower”_Lands,_Keeping
Things_Simple⠀⇛
The Debian-based distribution MX Linux has
announced the release of MX Linux 21 version 21.2,
dubbed “Wildflower.” The update continues MX’s
tradition of simplicity.
The developers stressed that all that existing
users of the distro had to do was run the package
manager to obtain the latest version.
o § Canonical/Ubuntu Family⠀➾
# ⚓ Ubuntu ☛ Ubuntu_Blog:_Canonical_Ubuntu_now_available_on
Ampere®_Altra®_Arm-based_Azure_virtual_machines [Ed:
Microsoft_bought_Canonical. It_does_not_seem_to_bother
Canonical_that_Ubuntu_users_are_being_obstructed_from_booting
because_of_Microsoft.]⠀⇛
# ⚓ Paul Thurrott ☛ Canonical,_Microsoft_Bring_Ubuntu_on_Arm_to
Azure [Ed: Microsofters like Paul Thurrott cannot contain
their excitement; Canonical now works for the company that's
attacking GPL, Linux, Free software...]⠀⇛
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ 9to5Google ☛ Android_14_Developer_Preview_–_9to5Google⠀⇛
# ⚓ Android Headlines ☛ ASUS_ZenFone_9_Gets_Android_13_Beta
Program,_And_You_Are_Invited⠀⇛
# ⚓ Android_12L_is_making_its_way_onto_Samsung_Galaxy_Tab_S8
devices_–_Phandroid⠀⇛
# ⚓ 9to5Google ☛ Samsung_Galaxy_Tab_S8_gets_Android_12L_and_the
taskbar⠀⇛
# ⚓ The Verge ☛ Android_12L-based_update_is_arriving_on_the
Galaxy_Tab_S8_–_The_Verge⠀⇛
# ⚓ How_to_translate_text_on_your_Android_smartphone⠀⇛
# ⚓ Android Central ☛ How_to_add_videos_to_your_Strava_posts_on
Android_|_Android_Central⠀⇛
# ⚓ Giz China ☛ Stolen_or_lost_Android_smartphone:_What_to_do?
–_Gizchina.com⠀⇛
# ⚓ Giz China ☛ 10_tips_to_improve_the_security_of_your_Android
smartphone⠀⇛
# ⚓ 9to5Google ☛ AAWireless_is_soon_to_graduate_from_Indiegogo
–_9to5Google⠀⇛
# ⚓ 9to5Google ☛ Android_Auto_7.8_causing_‘phone_not
compatible’_error_–_9to5Google⠀⇛
* § Free, Libre, and Open Source Software⠀➾
o ⚓ diaspora*'s_10_years_in_community_hands_–_The_diaspora*
Project⠀⇛
This weekend marked the 10th anniversary since the
diaspora* project was handed over by its founders to the
community. Ten years – time really does fly!
During that time we’ve made many fundamental improvements
to the software that this network runs on, from
standardizing the process of making improvements to the
code to completely rewriting the federation protocol on
which communication between pods is based. We’ve also
stabilized performance in many ways, and we’ve added many
improvements to the user interface and new features.
Over the past couple of years things have been a bit
quieter as our team of volunteer developers has been hard
at work on some really huge and complex tasks. The most
fundamental of these have been creating a feature to
allow members to move their account from one pod to
another, and creating an API to allow apps to interact
with diaspora* more easily and in more interesting ways.
o § Web Browsers⠀➾
# § Mozilla⠀➾
# ⚓ SpiderMonkey_Newsletter_(Firefox_104-105)_|
SpiderMonkey_JavaScript/WebAssembly_Engine⠀⇛
SpiderMonkey is the JavaScript engine used in
Mozilla Firefox. This newsletter gives an
overview of the JavaScript and WebAssembly
work we’ve done as part of the Firefox 104
and 105 Nightly release cycles.
o § Productivity Software/LibreOffice/Calligra⠀➾
# ⚓ Document Foundation ☛ Live_town-hall_meetings_with_the
Membership_Committee_candidates_–_The_Document_Foundation
Blog⠀⇛
The Document Foundation is the non-profit home of
LibreOffice, and its Membership Committee (MC)
administers membership applications and renewals
following the criteria defined in the Foundation’s
Statutes.
The election process for a new MC is underway, and
we’ll have live Q&A sessions with the candidates!
o § Programming/Development⠀➾
# ⚓ Barry Kauler ☛ ui_GUI_toolkit_for_Nim⠀⇛
# ⚓ The_Ultimate_List_of_Open_Source_Cloud-Native_Tools_–
Container_Journal⠀⇛
There are so many great open source cloud-native
tools for nearly everything you want to do. And
they’re all in one place—look no further than the
Cloud Native Computing Foundation (CNCF). This
Linux Foundation body has become a locus of some
stellar cloud-native open source projects. The CNCF
now hosts an array of helpful packages, spanning
container scheduling, observability, persistent
storage, container runtime and other areas.
# ⚓ DEV Community ☛ Enable_Gitsign_Today_and_Start_Signing_your
Commits_–_DEV_Community⠀⇛
I have been meaning to write this post for some
time already, but the extra motivation came after
looking at the recent news of PyPI phishing attacks
that have compromised several Python library
maintainers and their packages.
The issue of code provenance is ultimately an
industry-wide threat that needs to be addressed
sooner rather than later. In this post, I will
address something rather simple you can do today if
you are an open source maintainer and/or
contributor, and it can help you attest that the
code pushed to a repository really comes from where
it’s supposed to come: from you.
# ⚓ FOSSLife ☛ Start_Signing_your_Commits_with_Gitsign⠀⇛
The issue of code provenance is an industry-wide
threat that needs to be addressed, says Erika
Heidi. “We need additional layers of security to
prove the provenance of code that is committed to a
repository, especially when it comes to libraries
that are used as dependencies by hundreds or
thousands of other projects.”
# ⚓ LinuxTechLab ☛ A_Complete_Guide_On_Open_Source_Linux
Software_Development_–_LinuxTechLab⠀⇛
There are several important steps, factors, and
elements to know about the world of Linux software
development. Linux can be thought of an operating
system (OS), ecosystem, build environment,
platform, and culture. It supports our tech
infrastructure, stock exchanges, business servers,
and some of the world’s largest supercomputers.
In fact, the entire Android OS is built on Linux
kernels. One of the most interesting facts about
Linux is that the actual OS is open source. Even if
it can be frustrating and time-consuming at first,
learning to develop applications with Linux is
certainly a rewarding process. Learning these
skills, you can take advantage of one of the most
secure, dependable, stable, and scalable operating
systems.
# ⚓ Search_API_Endpoints,_Fully_Documented_–_Open_Build
Service⠀⇛
Here we come again, with another piece of the API
documentation rework. This time we fully documented
the search endpoints.
# § Perl / Raku⠀➾
# ⚓ Rakulang ☛ 2022.35_Reworkout_–_Rakudo_Weekly_News⠀⇛
Mitarashi Dango reports that all of the Raku
exercises at exercism.org have been reworked,
and mentions there are some Raku exercises
that need an example solution. Consider
yourselves invited!
# ⚓ Perl ☛ Perl_Weekly_Challenge_180:_First_Unique
Character_and_Trim_List⠀⇛
* § Leftovers⠀➾
o ⚓ Ruben Schade ☛ Rubenerd:_Cane_toads,_the_“seenzone”_and_message
state⠀⇛
Except, this technocratic solution introduces a new
social issue: the removal of plausible deniability. And
it turns out, humans like having this.
o § Hardware⠀➾
# ⚓ CNX Software ☛ SyncBot_educational_mobile_robot_supports
NVIDIA_Xavier_NX_or_Intel_Tiger_Lake_controller [Ed: Why are
they assuming people still want or need Windows in 2022?]⠀⇛
It runs Windows 10 IoT Enterprise by default, but
Linux is available upon request.
# ⚓ The Next Platform ☛ Details_Emerge_On_Nvidia’s_“Grace”_Arm
CPU⠀⇛
Imagine, if you will, that Nvidia had launched its
forthcoming “Grace” Arm server CPU three years ago
instead of early next year. How much better would
Nvidia be fairing in the gaming and cryptocurrency
downdraft that is impacting its sales today?
o § Security⠀➾
# ⚓ Send_Alert_When_ClamAV_Finds_Infected_Files_on_Linux
Systems_–_kifarunix.com⠀⇛
In this tutorial, you will learn how to send alert
when ClamAV finds infected files on Linux systems.
ClamAV is an opensource antivirus engine for
detecting trojans, viruses, malware & other
malicious threats. It is a good idea to sent alerts
whenever a malicious file is detected on the
system. This enables you to take actions of
analyzing the files and probably removing them from
the system based on the results of the analysis.
# ⚓ LinuxSecurity ☛ BlackHat_USA_2022:_Return_to_Sender_–
Detecting_Kernel_Exploits_with_eBPF⠀⇛
Let’s take a brief look at what Guillaume Fournier
from Datadog presented at Blackhat USA 2022: “One
of the fastest growing subsystems in the Linux
Kernel is, without any doubt, eBPF (extended
Berkeley Packet Filter).”
# ⚓ Michael West Media ☛ Click,_collect_and_regret:_how
scammers_made_a_lazy_$8k_out_of_a_$189_fridge_–_Michael
West⠀⇛
In our embrace of online shopping, we have become
prime targets for scammers. And when bank accounts
are emptied, Australians have to jump through hoops
to get their money back, if at all, writes James
Fitzgerald Sice.
Mike Daws was finally able to visit his mother-in-
law for her 101st birthday in the US in May 2022
after two years of Covid border restrictions, only
for the trip to be ruined by an online scam that
almost cost him $8000.
o § Internet Policy/Net Neutrality⠀➾
# ⚓ The Anarcat ☛ How_to_nationalize_the_internet_in_Canada⠀⇛
Rogers had a catastrophic failure in July 2022. It
affected emergency services (as in: people couldn’t
call 911, but also some 911 services themselves
failed), hospitals (which couldn’t access
prescriptions), banks and payment systems (as
payment terminals stopped working), and regular
users as well. The outage lasted almost a full day,
and Rogers took days to give any technical
explanation on the outage, and even when they did,
details were sparse. So far the only detailed
account is from outside actors like Cloudflare
which seem to point at an internal BGP failure.
Its impact on the economy has yet to be measured,
but it probably cost millions of dollars in wasted
time and possibly lead to life-threatening
situations. Apart from holding Rogers (criminally?)
responsible for this, what should be done in the
future to avoid such problems?
It’s not the first time something like this has
happened: it happened to Bell Canada as well. The
Rogers outage is also strangely similar to the
Facebook outage last year, but, to its credit,
Facebook did post a fairly detailed explanation
only a day later.
The internet is designed to be decentralised, and
having large companies like Rogers hold so much
power is a crucial mistake that should be reverted.
The question is how. Some critics were quick to
point out that we need more ISP diversity and
competition, but I think that’s missing the point.
Others have suggested that the internet should be a
public good or even straight out nationalized.
I believe the solution to the problem of large,
private, centralised telcos and ISPs is to replace
them with smaller, public, decentralised service
providers. The only way to ensure that works is to
make sure that public money ends up creating
infrastructure controlled by the public, which
means treating ISPs as a public utility. This has
been implemented elsewhere: it works, it’s cheaper,
and provides better service.
* § Gemini* and Gopher⠀➾
o § Technical⠀➾
# ⚓ Thoughts_on_sandman_and_my_feelings_on_‘wokeness’⠀⇛
What sparked this log is just how often I see the
term ‘woke’ be used now in general discussion on
the internet. It seems you cant go into a comment
section for a new show, movie, or game without
seeing the term thrown around followed by very
heated rants between random people. Modern
ntertainment seems to be fundimentally changing in
reaction to various social pressures and movements
in real life.
Also Recently I watched ‘the sandman’ on netflix
with my mom and she made the remark after a few
episodes ‘why does every show now have lesbians in
it?’ Its a fair question, and I have never really
thought about it. So here are some of my opinions
on the matter that im sure all of you will
unanimously agree with and there will be no
controversal statements or conflicting feelings
between us.
# ⚓ My_BTRFS_cheatsheet⠀⇛
I recently switched my home “NAS” (single disk!) to
BTRFS, it’s a different ecosystem with many
features and commands, so I had to write a bit
about it to remember the various possibilities…
BTRFS is an advanced file-system supported in
Linux, it’s somehow comparable to ZFS.
# § Programming⠀➾
# ⚓ Do_not_let_MinuzSopht_making_free-software_illegal⠀⇛
I promised myself to not write anything about
“Copilot” but when you are not a developer or
a person involved into coding and licensing,
it easier — or at least I find it easy — to
have a different approach about such topics
and to be concerned about all the possible
incoming scenarios, especially the ones you
think are going to affect your daily
relationship with these technologies.
The point is the following one: end-users,
without coding skills, can just observing the
evolution of the opensource and freesoftware
landscape but anything else; We can only
decide which tools to use but we can’t
influence which tools will be available for
us.
I think this is the main reason why, many of
us, are sincerely concerned when Tech
Corporations use their weight to alter the
balance, and start dragging resources and
development toward them rather than toward
us.
# ⚓ Trying_rust⠀⇛
Rust is not easy to learn for beginner
programmers. I suggest beginner programers
start learning python or javascript then C
and then rust. Learning C helps understanding
the kind of issues that are detected by the
rust compiler. There are tools for C for
detecting the memory issues but they run in
the tests (CI) but they don’t detect all
issues. Rust shows the issues earlier at
compile time when the program is under
development.
=> =============================================================================
World Wide Web but a lot lighter.
䷩ 𝚕𝚒𝚗𝚎 3811
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Gemini_version_available_♊︎
✐ Links_29/08/2022:_Debian’s_General_Resolution_on_Non-free_Blobs⠀✐
Posted in News_Roundup at 12:56 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Applications
o Instructionals/Technical
o Desktop_Environments/WMs
# GNOME_Desktop/GTK
* Distributions_and_Operating_Systems
o New_Releases
o Debian_Family
o Canonical/Ubuntu_Family
o Devices/Embedded
o Open_Hardware/Modding
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o Web_Browsers
# Mozilla
o GNU_Projects
o Programming/Development
o Standards/Consortia
* Leftovers
o Science
o Education
o Hardware
o Health/Nutrition/Agriculture
o Proprietary
o Security
# Integrity/Availability/Authenticity
# Privacy/Surveillance
o Defence/Aggression
o Environment
# Energy
# Overpopulation
o Finance
o AstroTurf/Lobbying/Politics
o Censorship/Free_Speech
o Freedom_of_Information_/_Freedom_of_the_Press
o Civil_Rights/Policing
o Internet_Policy/Net_Neutrality
o Monopolies
# Copyrights
* Gemini*_and_Gopher
o Personal
o Technical
* § GNU/Linux⠀➾
o § Applications⠀➾
# ⚓ Linux Links ☛ ncspot_–_ncurses_Spotify_client⠀⇛
We’ve recently reviewed spotify-qt and Spotify TUI,
third party-clients which let you enjoy Spotify
without needing to use the semi-official bloated
Spotify app.
ncspot is a command-line Spotify client that’s
written in Rust. It’s published under an open
source license. Like the other third-party clients,
you’ll need a Spotify premium subscription to use
it.
o § Instructionals/Technical⠀➾
# ⚓ Dan Langille ☛ Adding_an_SSL_certificate_to_HomeAssistant⠀⇛
In my previous blog post, I got homeassistant up
and running, but without a TLS connection. Let’s
fix that.
# ⚓ TecMint ☛ 3_Ways_to_Install_Skype_in_Fedora_Linux [Ed: This
is malicious spyware, controlled by an anti-Linux company]⠀⇛
Skype is a popular proprietary communication
application well known for its voice calls, chats,
VoIP-based video telephony, and video conferencing
functionalities. It helps people stay connected
regardless of their geographical location; from
colleagues within an organization to family and
friends.
Skype works across a wide range of devices
including smartphones (iOS and Android) PCs, and
tablets. You can also log in to Skype on the
browser to stay in touch with all your contacts.
# ⚓ OpenSource.com ☛ 4_ways_to_use_the_Linux_tar_command⠀⇛
When you have a lot of related files, it’s
sometimes easier to treat them as a single object
rather than 3 or 20 or 100 unique files. There are
fewer clicks involved, for instance, when you email
one file compared to the mouse work required to
email 30 separate files. This quandary was solved
decades ago when programmers invented a way to
create an archive, and so the tar command was born
(the name stands for tape archive because back
then, files were saved to magnetic tape.) Today tar
remains a useful way to bundle files together,
whether it’s to compress them so they take up less
space on your drive, to make it easier to deal with
lots of files, or to logically group files together
as a convenience.
I asked Opensource.com authors how they used tar,
and related tools like zip and gzip, in their daily
work. Here’s what they said.
# ⚓ OpenSource.com ☛ Clean_up_unwanted_files_in_your_music
directory_using_Groovy⠀⇛
In this series, I’m developing several scripts to
help in cleaning up my music collection. In the
last article, we used the framework created for
analyzing the directory and sub-directories of
music files, checking to make sure each album has a
cover.jpg file and recording any other files that
aren’t FLAC, MP3, or OGG.
I uncovered a few files that can obviously be
deleted—I see the odd foo lying around—and a bunch
of PDFs, PNGs, and JPGs that are album art. With
that in mind, and thinking about the cruft removal
task, I offer an improved script that uses a Groovy
map to record file names and counts of their
occurrences and print that in CSV format.
# ⚓ ID Root ☛ How_To_Install_Java_on_Linux_Mint_21_–_idroot⠀⇛
In this tutorial, we will show you how to install
Java on Linux Mint 21. For those of you who didn’t
know, Java is the most popular programming
language, and many applications require Java JRE
(Java Runtime Environments) to execute programs.
Java can be used on different platforms such as
Linux, macOS, Windows, Raspberry Pi, and many
others.
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 Java programming languages on Linux
Mint 21 (Vanessa).
# ⚓ OSTechNix ☛ Manage_Docker_Containers_Using_Portainer_In
Linux_–_OSTechNix⠀⇛
In this tutorial, we will learn what is Portainer,
how to install Portainer and how to manage docker
containers using Portainer in Linux.
# ⚓ Linux Shell Tips ☛ How_to_Block_User-Agents_in_Nginx_Web
Server⠀⇛
Suppose you are after infinite power and control in
web administration. In that case, you have no
choice but to consult Nginx, which is a reputable
web server and is attributed to have almost
infinite configuration footprints, high
performance, and component adaptability in modern
stacks.
That said, if you are dealing with a high-traffic
website and need a web server that is lightweight
and fast, you should consider implementing Nginx.
On the other hand, a user agent is simply a
software package with the responsibility of
retrieving, rendering and interacting with end
users’ web content. Popular examples of user agents
known to the Linux ecosystem include Curl and Wget.
Sometimes the access that these user agents have to
a web server can compromise its integrity. In this
case, you need a way of blocking/restricting their
access. This article will walk us through valid
Nginx configurations for blocking user agents from
having access to your web server data/information.
# ⚓ HowTo Forge ☛ How_to_Install_Focalboard_on_Ubuntu_22.04⠀⇛
Focalboard is an open-source and self-hosted
project management tool. It is multilingual and an
alternative to Asana, Trello, and Notion that can
be used by developers to track and manage work
across teams. It is based on kanban and is
available for desktops and servers. It can be used
as a stand-alone personal server for testing and
development. Focalboard helps developers stay
aligned to complete tasks, reach milestones, and
achieve their goals.
In this post, we will show you how to install
Focalboard with Nginx as a reverse proxy on Ubuntu
22.04.
# ⚓ Linux Handbook ☛ How_to_Ping_an_IPv6_Address_in_Linux
Command_Line⠀⇛
Using the ping command is perhaps the most common
way to check if a remote server is reachable or
not.
By default, the ping command works on the IPv4
address. But what if you need to ping an IPv6
address?
The answer is that you still use the ping command.
Yes, the newer versions of the ping command support
IPv6 addresses.
# ⚓ AddictiveTips ☛ How_to_play_Halo_Infinite_on_Linux⠀⇛
Halo Infinite is the sequel to Halo 5, released in
2021 on PC and Xbox platforms. The games
multiplayer is free, although the campaign costs
money. Unfortunately, the game was never released
on Linux.
Thanks to the hard work of Valve and other Proton
developers in the Linux community, a blockbuster
game like Halo is now available to play on Linux.
If you’re dying to try out the new Halo on Linux,
follow this guide to get it working.
# ⚓ HowTo Forge ☛ How_to_Setup_Kubernetes_Cluster_with_Kubeadm
on_Debian_11⠀⇛
Kubernetes or k8s is an open-source platform for
container orchestration that automates deployments,
management, and scaling of containerized
applications. Kubernetes is a container
orchestration created by Google, and now become an
open-source project and become standard for modern
application deployment and computing platforms.
Kubernetes is the solution for the modern container
deployment era. It provides service discovery and
load-balancing, storage orchestration, automated
rollout and rollback, self-healing service, secret
and configuration management. Kubernetes enables
cost-effective cloud-native development.
# ⚓ Red Hat Official ☛ How_to_use_variables_as_arguments_in
Ansible_|_Enable_Sysadmin⠀⇛
When you write an Ansible playbook, you sometimes
need to pass data into your play at runtime. To do
that, you can use a variable, a sort of placeholder
for data that’s meant to be determined at some
point in the future.
There are lots of places to create variables for
your playbooks, such as an inventory file, included
files, or even dynamically in your playbook itself.
However, you can also pass variables in the
terminal when you launch your playbook.
# ⚓ LinuxOpSys ☛ Rsync_Command_in_Linux_–_Options_+_Examples⠀⇛
As a system administrator or Linux power user, how
do you transfer files from your local system to a
remote?
To synchronize folders or files to another machine
we need a fast and reliable tool. In this tutorial,
we learn about rsync command in Linux with some
useful examples.
o § Desktop Environments/WMs⠀➾
# § GNOME Desktop/GTK⠀➾
# ⚓ Its FOSS ☛ 5_GNOME_43_Features_to_Keep_an_Eye_On⠀⇛
GNOME 43 is due for release on September 21,
2022. As of now, GNOME 43’s beta build is
available to test.
The features/changes that we find with GNOME
43 beta should arrive with the final release.
So, what are the best GNOME 43 features that
you should look forward to?
* § Distributions and Operating Systems⠀➾
o § New Releases⠀➾
# ⚓ 9to5Linux ☛ MX_Linux_21.2_Released_with_Linux_Kernel_5.18,
Based_on_Debian_GNU/Linux_11.4⠀⇛
Coming almost five months after MX Linux 21.1, the
MX Linux 21.2 release is here as an updated
installation medium for those who want to deploy
the lightweight Debian-based distribution on new
computers.
MX Linux 21.2 is based on Debian GNU/Linux 11.4,
which introduced 79 security fixes and 81
miscellaneous bugfixes, and bumps the kernel to
Linux 5.18, despite it reaching end of life earlier
this month, for the AHS (Advanced Hardware Support)
edition. The standard editions stay with Debian’s
Linux 5.10 LTS kernel.
o § Debian Family⠀➾
# ⚓ DebugPoint ☛ Debian_Proposes_Better_Discovery_of_non-free
Firmware_Images⠀⇛
Debian Linux provides two major installer images
based on the firmware type. The “free” images
contain the “open-source” drivers and packages,
whereas the “non-free” images are for proprietary
firmware packages.
If you tried downloading the “non-free” version
from the official website, you might have spent
some time locating the installer images.
Because the “non-free” images are kind of “hidden”
and buried under several directory structures in
the official Debian download server.
# ⚓ Its FOSS ☛ Debian_Finally_Starts_a_General_Resolution_to
Consider_a_Non-Free_Firmware_Image⠀⇛
Debian is one of the most loved Linux distributions
for its approach to stability and a balance between
new features.
But, it does not come with any non-free firmware.
And, that is becoming an issue for users who want
to use Debian on newer hardware.
Most of the latest devices and configurations need
non-free firmware to make things work, which
includes Wi-Fi, graphics, and more.
To address that, Steve McIntyre, a Debian developer
and a former Debian project leader, has been
actively discussing the issue for a while. At the
DebConf 22 conference, Steve recently talked about
fixing the firmware mess to highlight this better
to users and developers, as spotted by Geeker’s
Digest.
As an update to the discussion among the community:
it looks like Debian has started a general
resolution to let its stakeholders vote what to do
with non-free firmware.
o § Canonical/Ubuntu Family⠀➾
# ⚓ IT Pro Today ☛ 3_Ubuntu_Commands_for_Monitoring_System
Resource_Use⠀⇛
Here are three basic Ubuntu commands that will let
you monitor system resource use in Ubuntu and other
Linux distributions.
# ⚓ Ubuntu ☛ Meet_Canonical_at_Hannover_Messe_2022⠀⇛
Hannover Messe USA is almost here! With a 114,000+
net sq. ft exhibition area, 500+ companies, 129400+
registrants and 100+ countries represented,
Hannover Messe USA is the largest gathering of
industrial manufacturing in North America.
Join Canonical, the company behind Ubuntu, at
Hannover Messe USA to discuss open source
innovation in industrial technology. You can meet
with the Canonical team on-site in Chicago and pick
our technical experts’ brains about your industrial
use case.
o § Devices/Embedded⠀➾
# ⚓ CNX Software ☛ Pine64_Star64_SBC_to_feature_StarFive_JH7110
quad-core_RISC-V_processor_with_Imagination_GPU_–_CNX
Software⠀⇛
Pine64 Star64 is an upcoming single board computer
(SBC) powered by StarFive JH7110 quad-core 64-bit
RISC-V processor equipped with an Imagination BXE-
4-32 GPU, and in a form factor similar to the
earlier Pin64 model B boards such as the Quartz64
Model A.
The Star64 SBC will be offered with either 4GB or
8GB of RAM, an HDMI 2.0 video output connector, two
Gigabit Ethernet ports, a WiFi 6 and Bluetooth 5.2
module, USB 3.0 ports, a PCIe slot, and a GPIO
header for expansion.
# ⚓ Linux Gizmos ☛ Pine64_reveals_the_Star64_RISC-V_based
Single_Board_Computer⠀⇛
Yesterday, Pine64 made an announcement about the
Star64 Single Board Computer (SBC) prototype. The
company mentioned this SBC will be powered with the
RISC-V based StarFive JH7110 64-bit processor.
The processor integrated on the Star64 is the same
one found on the recently launched StarFive
VisionFive 2 board.
# ⚓ CNX Software ☛ StarFive_JH7110_RISC-V_processor
specifications_released⠀⇛
Some documentation for the StarFive JH7100
processor has been released and answers some of
those questions. It’s actually an SoC with six
RISC-V cores, of which four 64-bit RISC-V cores run
the main OS, plus a 64-bit RISC-V monitoring core,
and a 32-bit RISC-V real-time core. The AI
accelerators found in the JH7100 (Neural Network
Engine and NVDLA) appear to be gone for good, and
there are two 1-lane PCIe 2.0 interfaces up to 5
Gbps each.
Target applications for the StarFive JH7110
processor include single board computers, home NAS,
routers with software routing, Smart Home
appliances, industrial robots, drones, and video
surveillance applications. Right now, the
documentation website only comes with a product
brief, but the datasheet is coming soon, and a
hardware design reference plus a software developer
guide are also in the works.
# ⚓ Hackaday ☛ A_Pi_Camera_To_Be_Proud_Of⠀⇛
Inside the box is a Waveshare touchscreen that fits
on the GPIO header, and a NanoWave 5000 mAH USB
battery pack. The camera module fits on the front
of the unit, with the C-mount ready to take a lens.
Software is still a work in progress and is
promised to be a Python script controlling the
various camera programs. There are enough Pi camera
projects for software to be a matter of choice and
taste.
We like the form factor and we like the use of the
very compact NanoWave battery, so we think this is
a design with some possibilities. Perhaps a cover
over the Pi ports might be of use though for
general robustness in the face of everyday
photography. The question remains though, whether
it can come close to the performance of even a
budget mirror-less compact camera, and we’re
guessing that will depend as much on the operator
skill, lens quality, and software capabilities as
it does on the Pi HQ module. We look forward to
seeing what comes of this project, but meanwhile
you can see a video with all the details below the
break.
o § Open Hardware/Modding⠀➾
# ⚓ Arduino ☛ Monitoring_the_force_of_a_20-ton_hydraulic_press
|_Arduino_Blog⠀⇛
Material testing often comes down to breaking stuff
and measuring how much force it took to do so. How
a thing breaks is a result of different strength
properties. There are many different types of
strength, but mechanical engineers are most
concerned with tensile, compressive, shear, and
torsional strength. The easiest way to test
compressive strength is to squish something with a
very powerful press. Element14 Presents’ Clem Mayer
purchased a 20-ton hydraulic press for that purpose
and used an Arduino to measure its force.
Even if you don’t have any shop experience, you’ve
probably seen a hydraulic press in action in one of
those YouTube videos where they squeeze household
objects until they explode in an entertaining way.
This particular press can exert up to 20-tons of
force, which is about as heavy as three elephants.
The actual pressure depends on how much area that
force applies to. To calculate the pressure at the
time of failure, Mayer needs the contact area
(which is easy to measure ahead of time) and the
current amount of force that the press is applying.
He collected the pressure data using an Arduino
Leonardo and a load cell.
# ⚓ Raspberry Pi ☛ Remotely_open_your_garage_door_with
Raspberry_Pi_Pico_W⠀⇛
The best part about this creation being
controllable via mobile phone is that you don’t
need a bulky garage door remote on your keychain.
You’ve already got your car key (hence the garage),
your front door key, back door key, gym locker key,
barcode thing you scan at the supermarket to
collect points that never really get you anything.
You get the picture. Also, have you ever tried to
find a replacement battery for an old-fashioned
garage door remote control? Skip the hassle and
keep your keychain slimline with Michael’s Pico W-
based solution.
# ⚓ Hackaday ☛ Share_Screen_To_RGB_Panel_With_Pi_Pico_W⠀⇛
RGB LEDs are great for adding a bit of color to
your life, and it’s even more satisfying to use a
matrix of them as a graphic display. [bitluni]
built an RGB LED display with Pi Pico to which you
can share a pixelated version of your PC’s screen.
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ Google_Pixel_Buds_Pro_review:_Best_Android_AirPod
alternative?_|_NextPit⠀⇛
# ⚓ HowTo Geek ☛ How_to_Split_the_Screen_on_Android⠀⇛
# ⚓ Pixel_7_buyers_in_for_a_treat_if_Android_13_is_as_good_as
on_Pixel_6⠀⇛
# ⚓ Android Police ☛ Some_Pixel_6_users_are_reporting_increased
idle_battery_drain_on_Android_13⠀⇛
# ⚓ SamMobile ☛ Galaxy_Tab_S8_gets_Android_12L_(One_UI_4.1.1)
update_with_better_multitasking_–_SamMobile⠀⇛
# ⚓ 9to5Google ☛ Google_Assistant_tests_Search_this_screen_Lens
button_–_9to5Google⠀⇛
# ⚓ Android Authority ☛ You_told_us:_Over_half_of_you_have
received_storage_alerts_on_Android_TV⠀⇛
# ⚓ 5_Ways_To_Silence_All_Notifications_On_Android_For
Sometime⠀⇛
# ⚓ Make Use Of ☛ How_Many_Phones_Does_Apple_Sell_Compared_to
Android?⠀⇛
* § Free, Libre, and Open Source Software⠀➾
o § Web Browsers⠀➾
# § Mozilla⠀➾
# ⚓ Mozilla ☛ Merging_two_GitHub_repositories_without
losing_commit_history [Ed: Mozilla is outsourced to
proprietary software of Microsoft, betraying both
standards and Free software]⠀⇛
We are in the process of merging smaller
example code repositories into larger parent
repositories on the MDN Web Docs project.
While we thought that copying the files from
one repository into the new one would lose
commit history, we felt that this might be an
OK strategy. After all, we are not deleting
the old repository but archiving it.
# ⚓ Mozilla ☛ The_Truth_is_Out_There [Ed: Mozilla
continues to push for Web censorship under the guise of
battling misinformation]⠀⇛
Murky political groups are exploiting social
media systems to spread disinformation. With
important elections taking place around the
world this year, who is pushing back? We meet
grassroots groups in Africa and beyond who
are using AI to tackle disinformation in
languages and countries underserved by big
tech companies.
o § GNU Projects⠀➾
# ⚓ DebugPoint ☛ GIMP_2.99.12_Released_with_Huge_Updates,_But
No_Date_of_v3.0_Yet⠀⇛
The free and open source drawing program brings the
latest point release (development) in the 2.99
series with a list of new features and updates.
GIMP’s point releases are not minor ones. They
often bring several new features and improvements.
Although, in the official release announcement, the
team did not say specifically when the much-
anticipated GIMP 3.0.0 will be released. As it is a
community project and a complex one, we can guess
it will be released when ready.
o § Programming/Development⠀➾
# ⚓ Everything_markdown_with_pandoc⠀⇛
o § Standards/Consortia⠀➾
# ⚓ Matt Rickard ☛ Timeline_of_Early_Email⠀⇛
The first version of a computer email system that
resembles anything like what we have today showed
up around 1965. Computers had been primitively
networked a few years earlier, and you could
technically send and receive content.
* § Leftovers⠀➾
o ⚓ Counter Punch ☛ Stop_Using_Thermobaric_Flame-Throwers!⠀⇛
o § Science⠀➾
# ⚓ NPR ☛ NASA_is_set_to_return_to_the_moon._Here_are_4_reasons
to_go_back⠀⇛
A 2013 study commissioned by NASA estimates that
commercial products emerging from the space
agency’s research return between $100 million and
$1 billion annually to the U.S. economy. Many of
those “spinoffs” had their origin in the Apollo
program.
# ⚓ Site36 ☛ US_military_test_flight:_Zephyr_solar_glider
crashed⠀⇛
Airbus‘ high-flying drone has crashed in the desert
just hours before setting a record for the longest
flight ever recorded by an aircraft.
o § Education⠀➾
# ⚓ Ruben Schade ☛ Handwritten_HTML_sites⠀⇛
Mine answer is the same, though like him I don’t
run modern Windows. The tool might have changed,
but I still write basic HTML sites by hand. It has
to span dozens of pages, need editing by other
people, or require interactive features for me to
do it any other way.
# ⚓ Data Swamp ☛ My_blog_workflow⠀⇛
I rarely spend more than 40 minutes for a blog
post, the average blog post takes 20 minutes. Most
of them are sharing something I fiddled with in the
day or week, so the topic is still fresh for me.
The content of the short articles often consists of
dumping a few commands / configuration I used, and
write a bit of text around so the reader knows what
to expect from the article, how to use the content
and what’s the point of the topic.
It’s important to keep track of commands/
configuration beforehand, so when I’m trying
something new, and I think I could write about it,
I keep a simple text file somewhere with the few
commands I typed or traps I encountered.
o § Hardware⠀➾
# ⚓ Hackaday ☛ Giant_3D_Printer_Aims_To_Produce_Life-Sized
Boat⠀⇛
As 3D printers become more ubiquitous, the number
of custom designs and styles of printers has
skyrocketed. From different printing materials and
technologies to the movements of the printing head,
we’ve seen all kinds of different takes on these
tools. But one thing that has been largely limited
to commercial and industrial use has been large
print sizes — leaving consumer level prints to be
split into several pieces to fit together later.
Not so with this giant 3D printer from [Ivan],
though.
# ⚓ Hackaday ☛ Automate_Your_Desk_With_The_Upsy_Desky⠀⇛
It might be surprising for some, but humans
actually evolved to be long-distance runners. We
aren’t very fast comparatively, but no other animal
can run for as long or as far as a human can.
Sitting at a desk, on the other hand, is definitely
not something that we’re adapted to do, so it’s
important to take some measures to avoid many of
the problems that arise for those that sit at a
desk or computer most of the day. This build takes
it to the extreme, not only implementing a standing
desk but also a ton of automation for that desk as
well.
# ⚓ Hackaday ☛ Sleep_Posture_Monitor_Warns_You_Away_From
Dangerous_Positions⠀⇛
Age, we’re told, is just a number, but that number
seems to be the ever-increasing count of injuries
of a ridiculous nature. Where once the younger
version of us could jump from a moving car or fall
out of a tree with just a few scrapes to show for
the effort, add a few dozen trips around the sun
and you find that just “sleeping funny” can put you
out of service for a week.
o § Health/Nutrition/Agriculture⠀➾
# ⚓ SUVs_‘eight_times_more_dangerous’_to_kids_walking_or
cycling_than_smaller_cars_are⠀⇛
A recent study from the US has found that children
are eight times more likely to be killed in a
collision involving an SUV or pick-up truck than
they are in a crash in which a standard passenger
car is involved.
# ⚓ Helsinki Times ☛ Instagram_rolls_out_update_to_change
default_content_settings_for_teens⠀⇛
Instagram is also testing prompts for teens that
suggest limiting who can interact with their
content. The test will ask them to review privacy
and security settings related to who can re-share
their content, who can message them, the type of
content they can see, and time management, as per
The Verge.
# ⚓ Is_TikTok_or_Instagram_worse_for_teen_mental_health?:_A
therapist_vs._psychologist_perspective⠀⇛
Although teens think TikTok may be the most harmful
social media platform, therapists and psychologists
disagree. Instagram perpetuates additional issues
due to the fact that users can alter their public
image. Regardless, this is nothing new. Media has
shaped the body standard for decades. Therapists
and psychologists also harp on the benefits of
social media platforms, as they often provide
community to those struggling.
# ⚓ Effects_of_Social_Media_on_Teens:_Understanding_the
Headlines⠀⇛
Social media plays a powerful role in connecting
with others, getting information and expressing
ourselves. But over the past year, the impact of
social media, particularly Instagram, has made
headlines for its negative effects on teens,
especially girls.
Concerns around social media’s impact on self-
esteem adds to national conversations around the
ongoing youth mental health crisis. It’s more
important than ever that parents, caregivers,
educators and youth development professionals guide
young people in having safe experiences online that
support their wellbeing and success.
# ⚓ Counter Punch ☛ The_UN_Proved_Its_Usefulness_in_Crafting
Ukraine_Grain_Deal⠀⇛
Before the war, Ukraine exported more than 45
million metric tons of grain annually to the global
market. The war has caused grain prices to rise
dramatically.
o § Proprietary⠀➾
# ⚓ YLE ☛ Police_solve_4%_of_internet_crime [iophk: Windows
TCO]⠀⇛
A decade ago, police managed to solve more than 30
percent of data breach cases. Police told Yle that
the shrinking percentage of solved cases reflects
the explosion of this type of crime. In 2012, for
example, police said they dealt with fewer than 500
cyber crime cases.
o § Security⠀➾
# ⚓ LWN ☛ Security_updates_for_Monday_[LWN.net]⠀⇛
Security updates have been issued by Debian (curl,
exim4, maven-shared-utils, ndpi, puma, webkit2gtk,
and wpewebkit), Fedora (dotnet3.1, firefox, and
webkit2gtk3), Mageia (clamav, mariadb, net-snmp,
postgresql, python-ldap, and thunderbird), SUSE
(freeciv, gnutls, keepalived, libyang, nim, python-
Django, and varnish), and Ubuntu (schroot).
# § Integrity/Availability/Authenticity⠀➾
# ⚓ SequoiaPGP ☛ sq_User_Testing_Results⠀⇛
I did some user testing of sq with five
volunteers. This blog post is a report of
what I learned. Good news: everyone did get
all the tasks done successfully and within
the one hour I had allocated, with plenty of
time left over. Of course, there were a few
things that could be improved.
# § Privacy/Surveillance⠀➾
# ⚓ Scoop News Group ☛ Most_top_mobile_carriers_retain
geolocation_data_for_two_years_on_average,_FCC_findings
show⠀⇛
Ten of the top 15 mobile carriers collect
geolocation data and provide no way for
consumers to opt-out, according to
information from the telecom companies the
Federal Communications Commission published
Thursday.
The carriers’ answers to questions about data
collection and retention from the FCC come in
response to a July request from the agency
seeking information on geolocation practices
in light of concerns about how law
enforcement could use phone data to arrest
abortion-seekers in states where the
procedure is now illegal or will soon be
outlawed.
# ⚓ Silcon Republic ☛ Norway_reportedly_wants_to_fine
Meta_for_illegal_data_transfers⠀⇛
While Norway is not a member of the EU, it is
part of the European Economic Area which has
incorporated GDPR.
The proposal was a response to a draft ruling
issued by the Irish Data Protection
Commission (DPC) to other EU regulators last
month, following an investigation into
whether Meta’s transatlantic data-sharing
practices comply with EU rules.
A final ruling could force Meta to halt data
transfers between the EU and US.
# ⚓ DaemonFC (Ryan Farmer) ☛ Your_bank_and_other_Web
sites_are_running_creepy_JavaScript_that_records_your
every_action._NoScript_can_block_that_from_running.
Bonus:_“Web_Rot”_|_BaronHK’s_Rants⠀⇛
Your bank and other Web sites are running
creepy “Session-Replay” JavaScript that
follows you around the site recording your
every movement.
You’re not “supposed to know” about this, but
NoScript can block that from running.
I had a conversation with Matthew Garrett
(alleged security person, actual drama bomb
thrower) on IRC the other day about the
“security” of JavaScript.
He had previously promoted it as a “great way
of running untrusted code”.
Unfortunately, there’s just nothing secure
about JavaScript. It’s the most widely abused
platform in all of computing because almost
everyone ends up running it without thinking
of the consequences, and browsers which are
instructed to do so, do it without bothering
to allow any user control over the process in
their default state.
If you can’t trust code, it’s better to not
have it running at all.
Especially if it’s not doing anything to help
you, and is proprietary.
Garrett said that “total sandbox escapes”
where the program gets out of your browser
sandbox and starts interfering with another
tab or running arbitrary malicious code
outside of any sort of confinement is “rare”
to the point where someone would need to be
“targeting you” and willing to blow a Zero
Day exploit to do it.
o § Defence/Aggression⠀➾
# ⚓ ABC ☛ Bali_bombmaker_Umar_Patek_records_on-camera_interview
from_Indonesian_jail⠀⇛
Patek was filmed in recent days walking through the
jail grounds at Porong in East Java, chatting with
the prison governor, both men smiling and laughing
together on camera as he casually discusses his
role in the terror attacks, which killed more than
200 people.
# ⚓ Nature ☛ Global_food_insecurity_and_famine_from_reduced
crop,_marine_fishery_and_livestock_production_due_to_climate
disruption_from_nuclear_war_soot_injection⠀⇛
In conclusion, the reduced light, global cooling
and likely trade restrictions after nuclear wars
would be a global catastrophe for food security.
The negative impact of climate perturbations on the
total crop production can generally not be offset
by livestock and aquatic food (Fig. 5a). More than
2 billion people could die from a nuclear war
between India and Pakistan, and more than 5 billion
could die from a war between the United States and
Russia (Table 1). The results here provide further
support to the 1985 statement by US President
Ronald Reagan and Soviet General Secretary Mikhail
Gorbachev and restated by US President Joe Biden
and Russian President Vladimir Putin in 2021 that
‘a nuclear war cannot be won and must never be
fought’.
# ⚓ New York Times ☛ The_Zaporizhzhia_nuclear_plant_was_cut_off
from_Ukraine’s_grid,_leading_to_outages,_officials_say.⠀⇛
An off-site power supply from the electricity grid
is essential for ensuring nuclear safety, the
director, Rafael Marino Grossi, said in a
statement. The plant has diesel generators and a
separate coal-fired plant to provide backup power
if it loses external power, he noted.
Backup power is required to ensure the continued
operation of cooling systems that remove heat from
the reactors. Without cooling, the nuclear fuel
could overheat and melt down, potentially releasing
radiation.
# ⚓ BBC ☛ How_many_people_cross_the_Channel_in_small_boats?⠀⇛
As at 22 August, 22,557 migrants had made the
crossing in small boats since the start of the
year.
[...]
The government wants to send to Rwanda those who
arrive in the UK through “illegal, dangerous or
unnecessary methods”, such as on small boats or
hidden in lorries, when they could have claimed
asylum in another safe country such as France.
# ⚓ The Telegraph UK ☛ Dozens_more_Channel_migrants_land_in
Kent_as_total_this_year_nears_25,000⠀⇛
It comes as people smugglers are offering “TikTok
Black Friday” cut-price Channel deals to Albanians
to beat a Government crackdown ahead of the bank
holiday.
Gangs are advertising on the social media platform
with offers as low as £3,000 per migrant to cross
the Channel, at least 40 per cent cheaper than the
“standard” rates of around £5,000 to £5,500.
# ⚓ ABC ☛ New_Mexico_man_charged_with_supporting_Islamic_State
group⠀⇛
Federal prosecutors believe Wilson was trying to
establish an “Islamic State Center” in New Mexico
that would teach Islamic State group ideology,
provide martial arts training and serve as a haven
for people preparing to fight for the group in the
U.S. and abroad.
# ⚓ Scheerpost ☛ Why_the_US_and_Israeli_Right_Really_Hate_the
Iran_Nuclear_Deal⠀⇛
Juan Cole explores what right-wingers in both
countries actually want to happen in Iran.
# ⚓ Common Dreams ☛ Opinion_|_Will_Six_Months_of_War_in_Ukraine
Turn_Into_Six_Years?⠀⇛
President Joe Biden announced Wednesday that
Washington will fund an additional $3 billion in
military aid for Ukraine. On the surface, this may
seem like business as usual. After all, the United
States has sent 19 separate tranches of military
support since the war began, and Congress has
already approved funding for at least another $10
billion worth of arms.
# ⚓ Counter Punch ☛ The_Death_of_Daria_Dugina:_Moscow’s
Invocation_of_Terrorism_is_More_Than_Chutzpah⠀⇛
Russian state television called the incident a
“terrorist attack.” That terminology implies an act
in violation of existing rules. A dictionary
definition of terrorism is “The unlawful use of
violence and intimidation, especially against
civilians, in the pursuit of political aims.”
o § Environment⠀➾
# ⚓ BBC ☛ Tyre_Extinguishers:_Activists_deflate_SUV_tyres_in
Leeds_in_climate_protest⠀⇛
The group left leaflets on windscreens telling
owners their “gas guzzler kills” and “SUVs and 4x4s
are a disaster for our climate”.
# ⚓ [Old] Tyre_Extinguishers_target_SUVs_on_home_turf_of_the
‘Chelsea_Tractor’⠀⇛
Tyre Extinguishers, the direct action group calling
for SUVs to be banned from cities, have struck
again, targeting 30 vehicles in London’s upscale
Cheyne Walk area in the district of the capital
that gave 4x4s their ‘Chelsea Tractor’ nickname.
# ⚓ TruthOut ☛ The_Inflation_Reduction_Act_Is_a_Disappointing
Act_of_Federal_Greenwashing⠀⇛
# ⚓ TruthOut ☛ Climate-Fueled_Wildfires_Are_Depleting_the_Ozone
Layer,_New_Study_Shows⠀⇛
# ⚓ TruthOut ☛ Poor_Countries_Are_Suffering_the_Worst_Climate
Woes_But_Getting_the_Least_Help⠀⇛
# ⚓ Counter Punch ☛ America’s_Summer_of_Floods⠀⇛
Floods are complex events, and they are about more
than just heavy rain. Each community has its own
unique geography and climate that can exacerbate
flooding, so preparing to deal with future floods
has to be tailored to the community.
# ⚓ Counter Punch ☛ How_Drought_and_Growth_Threaten_the_Waters
of_the_Northern_Rockies⠀⇛
The government spends millions on studies while
avoiding decisive action. In Utah, ten million to
study why the isolated Great Salt Lake is turning
into a puddle. Hundreds of millions to figure out
how to stop the Lake Mead and Powell reservoirs
from becoming dead pools. The answers are clear.
Forty million people rely on the Colorado system
along with 10 million cows and there isn’t enough
water to go around. Yet states and cities promote
more growth. The water subsidy required would put
other areas of the country at risk of more
impoundments, mega-pipelines and shipments of
water. Action is needed now to protect our water at
its source as part of an interconnected ecological
system.
# § Energy⠀➾
# ⚓ JURIST ☛ California_approves_regulation_phasing_out
gasoline-powered_car_sales_by_2035⠀⇛
The California Air Resources Board (CARB)
approved Advanced Clean Cars II rule on
Thursday making California the first state to
prohibit sales of new gasoline-powered cars.
The rule sets out a roadmap whereby 100% of
new cars and light trucks sold in the state
will be zero emission vehicles (ZEVs),
including plug-in hybrids.
The regulation codifies Governor Gavin
Newsom’s light-duty vehicle goals set forth
in Executive Order N-79-20 and requires
automobile manufacturers to deliver an
increasing number of ZEVs and plug-in hybrid
vehicles (PHEVs) each year beginning in 2026.
Specifically, sales targets of new ZEVs and
PHEVs are set at 35% in 2026, increasing to
68% in 2030 and ultimately 100% in 2035.
# ⚓ Hackaday ☛ Hackaday_Prize_2022:_Compact_Solar
Tracking_System_Doesn’t_Break_The_Bank⠀⇛
If you need to squeeze every available watt
out of a solar panel, you’ll probably want to
look into a solar tracking system.
Unfortunately, they are usually quite large,
heavy, and expensive. As an alternative, [JP
Gleyzes] has put together a DIY solar
tracking system that aims to address these
issues.
# § Overpopulation⠀➾
# ⚓ JURIST ☛ Bangladesh_dispatch:_‘A_silent_famine_is
prevailing_across_Bangladesh_as_food_and_commodity
prices_soar_to_record_highs.’⠀⇛
Many of us may have heard about the so-called
domino effect in which one event causes a
series of like events to happen one after
another. Currently, we hear talk of a domino
effect in South Asian countries. After the
dreadful economic and political crisis in Sri
Lanka, experts fear that other countries in
this region may face a similar situation.
Unfortunately, Bangladesh is on this list of
countries.
Why do experts fear this? The question is
even more interesting because South Asian
country’s $416 billion economy has been one
of the fastest-growing in the world for
years. In fact, in November 2021, the United
Nations decided to strike Bangladesh off its
list of the world’s least developed nations.
# ⚓ The Daily Star ☛ Bringing_population_back_into_the
conversation⠀⇛
At present, the country has more than 167
million people, but strangely, the topic of
“overpopulation” or “population explosion”
receives little attention. Moreover, some
quarters in our country tend to see this
large population as an economic asset. There
is no denying the fact that the population of
a country is the greatest social capital a
nation can have, but unchecked population
growth can be detrimental to economic
development. Some empirical studies have
found that an unchecked rising population
comes with several economic and social
challenges. It diminishes the availability of
capital per head by limiting access to food,
housing, sanitation, healthcare, education
and employment, which in turn reduces the
productivity of its labour force. It often
has devastating effects on the environment as
well.
# ⚓ Climate_Change:_Are_we_heading_towards_extinction?⠀⇛
Dire environmental consequences are happening
in Africa and measures and initiatives are
being attempted in this regard by the United
Nations Environmental Programme (UNEP) within
the theme ‘Only One Earth’. Communities
around the globe have observed World
Environment Day on June 5 by putting
environmental concerns in the spotlight. This
effort is now considered as the UN’s primary
platform to promote action for the protection
of the environment by raising awareness on
issues such as human overpopulation, marine
pollution, global warming, wildlife crime and
sustainable consumption. Celebrated annually
by more than 150 countries worldwide, the day
is a global platform for environmental
outreach, to also showcase initiatives at the
country and global level in the promotion of
environmental health.
# ⚓ Chatham Asset Management ☛ Letter:_Overpopulation_is
cause_of_every_environmental_problem_we_face⠀⇛
As any good doctor can tell you, treating
symptoms can make you feel good for a while,
but if you don’t treat the disease it will
eventually kill you.
o § Finance⠀➾
# ⚓ Common Dreams ☛ Opinion_|_Organizers_Have_Fought_for_Debt
Cancellation_for_Over_a_Decade—and_Their_Work_Is_Far_From
Finished⠀⇛
Following over a decade of activism against the
United States’ massive student debt crisis,
President Biden announced a plan on Wednesday to
cancel a significant amount of student loan debt
for tens of millions of low and middle-income
Americans.
# ⚓ Counter Punch ☛ Biden’s_Student_Debt_Forgiveness_Plan:_Good
Enough_for_Government_Work?⠀⇛
To clarify, the plan gives $10,000 of student loan
forgiveness to people earning less than $125,000 a
year. That probably excludes our Harvard Business
School graduate.
# ⚓ Common Dreams ☛ Sanders_Derides_GOP_for_‘Squawking’_About
Debt_Relief_But_Not_Handouts_to_Billionaires⠀⇛
In response to GOP claims that forgiveness of
$10,000 in student debt for most borrowers would be
“unfair,” the Vermont senator told ABC’s George
Stephanopoulos that “60% of the benefits go to
people who are on Pell Grants” and “87% of the
benefits go to people making $75,000 a year [or
less].”
# ⚓ Counter Punch ☛ Can_a_Deeply_Unequal_Nation_Totally_Reverse
Course?⠀⇛
# ⚓ Telex (Hungary) ☛ The_number_of_Hungarians_working_in
Austria_reaches_historic_high⠀⇛
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ ‘You_are_next’:_Twitter_ignores_sick_death_threat_against
JK_Rowling_from_Islamic_extremist⠀⇛
Afterward, Rowling shared an update from Twitter
expressing that no standards had been broken
corresponding to Aziz’s message after it had
inspected the realities accessible. “[email
protected] These are your principles, right?
Rowling created. Savagery: You are not permitted to
take steps to utilize viciousness against a
particular individual or gathering of people. The
advancement of savagery is additionally taboo.
“Psychological warfare/fierce fanaticism: You may
not compromise or supporter illegal intimidation,”
it peruses.
# ⚓ Consortium News ☛ JOHN_KIRIAKOU:_Don’t_Charge_Trump_With
Espionage⠀⇛
Nobody should be charged with espionage unless they
are working for a foreign power and mean harm to
the United States. The Espionage Act, which was
written 105 years ago to combat German saboteurs,
is rarely used now to target spies and traitors.
Instead, it’s used as a cudgel to silence
whistleblowers, journalists, and occasionally a
stupid former president.
To understand the damage that this deeply flawed
law has done, and will continue to do, we have to
look at its origins. The Espionage Act was written
in 1917, at the height of World War I. The U.S. was
panicked at the thought of German spies working
undercover to steal its secrets and to disrupt its
ability to produce war materiel and support its
allies.
# ⚓ Salon ☛ Truth_Social_is_headed_for_bankruptcy⠀⇛
As the report points out, Truth Social has not been
paying for web-hosting fees to the point where
attorneys are now involved, traffic is collapsing,
the value of stock in the company is plunging and
money is running out.
# ⚓ TruthOut ☛ Dark_Money_Groups_Are_Scheming_to_Bring_Down
Biden’s_Student_Debt_Relief_Plan⠀⇛
# ⚓ Common Dreams ☛ Republican_AGs,_Dark_Money_Groups_Scheme_to
Sue_Over_Student_Debt_Relief⠀⇛
“Conservative jurists, and ultimately the justices
themselves, will be eager to shred the new
program.”
# ⚓ Counter Punch ☛ Will_the_Democrats_Manage_to_Help_Re-Elect
Trump?⠀⇛
I learned about this furious row because I knew a
Canadian paper magnate who had bought a house close
to Mar-a-Lago at about the same time as Trump. My
friend was bitter that the agency that sold him the
property had carefully timed his visit for a moment
in the afternoon when there were no planes flying
directly overhead.
# ⚓ Counter Punch ☛ Weaponizing_Charity_to_Advance_a_Political
Agenda⠀⇛
# ⚓ Counter Punch ☛ Could_Liz_Cheney_Initiate_a_New
Conservative_Party?⠀⇛
Elie Mystal of the Nation points out that
Republicans rejected Cheney because “white
conservative voters trash everything to keep
themselves in power.” In other words, the core
Republican base will not support any candidate who
fails to address their fears of being replaced by
others.
# § Misinformation/Disinformation⠀➾
# ⚓ Gannett ☛ Michigan_students_connected_to_TikTok,
Snapchat_—_and_learning_is_suffering,_teachers_say⠀⇛
Saidi, a teacher at Salina Intermediate in
Dearborn, started to notice students becoming
less engaged in school long before the
pandemic, particularly with the rise of
smartphones and social media.
# ⚓ New York Times ☛ A_Journey_Into_the_Misinformation
Fever_Swamps⠀⇛
Several of my colleagues here at The New York
Times track the trends and shifting tactics
of these fraudsters on their daily beats. So
I exchanged messages this week with Sheera
Frenkel, Tiffany Hsu and Stuart A. Thompson,
all three of whom spend their days swimming
in the muck brewed by fake news purveyors
here and abroad.
Our conversation, lightly edited for length
and clarity: [...]
o § Censorship/Free Speech⠀➾
# ⚓ BBC ☛ Google_‘airbrushes’_out_emissions_from_flying,_BBC
reveals⠀⇛
Flights now appear to have much less impact on the
environment than before.
That’s because the world’s biggest search engine
has taken a key driver of global warming out of its
online carbon flight calculator.
# ⚓ JK_Rowling_compared_to_murderer,_Nazi_collaborator_and
creepy_cult_leader_by_woke_website⠀⇛
Rowling, 57, has been a strong supporter of women’s
rights and has rallied against the use of terms
that excludes ‘female’ or ‘women’. She has also
criticised the Scottish Government’s Gender
Recognition Reform Bill, which has been heavily
criticised by women’s rights groups. The Bill will
make it easier for people to legally change gender.
# ⚓ Modern Ghana ☛ Ordering_Oyerepa_FM/TV_to_shut_down_an_act
of_censorship_–_Sulemana_Braimah⠀⇛
The Executive Director of the Media Foundation for
West Africa (MFWA), Sulemana Braimah does not side
with an order for Kumasi-based Oyerepa FM and TV to
temporarily shut down over comments made by the
founder of the United Progressive Party, Akwasi
Addai Odike on the platform.
Mr. Braimah argued that the order forms part of
attempts to muzzle the independence of the media
house in question.
# ⚓ Gannett ☛ Critics_of_Larry_Arnn_should_oppose_laws
censoring_Tennessee_educators_|_Opinion⠀⇛
Now, Tennesseans should do even more to defend
their educational professionals. Arnn may be the
only person who’s called Tennessee educators
“dumb,” but he’s not the only one insulting them.
As part of my job, I talk to teachers in Tennessee
and across the United States. Right now, many of
them feel hurt, insulted and afraid because of the
avalanche of educational gag orders sweeping the
country.
# ⚓ Gannett ☛ A_Michigan_town_may_lose_its_only_library_after
its_staff_refused_to_remove_an_LGBTQ_book⠀⇛
When a library staff in a west Michigan township
refused to remove its books containing LGBTQ
themes, residents voted to defund their only
library.
# ⚓ Ex-Iran_vice-president_living_in_UK_says_‘I’m_not_to_blame
for_Rushdie_stabbing’⠀⇛
In his 1989 book backing Rushdie’s death sentence
over his “blasphemous” novel, Mohajerani wrote
“whoever insults the prophet deserves to be
killed”.
# ⚓ Facebook_Tells_Moderators_to_Allow_Graphic_Images_of
Russian_Airstrikes_but_Censors_Israeli_Attacks⠀⇛
# ⚓ The Guardian UK ☛ How_to_shut_down_the_internet_–_and_how
to_fight_back [Ed: The Guardian does a lot of censorship for
the British government and rich "sponsors" like Bill Gates,
so that's rich]⠀⇛
# ⚓ The Guardian UK ☛ Flicking_the_kill_switch:_governments
embrace_internet_shutdowns_as_a_form_of_control [Ed: The
Guardian shows its sheer hypocrisy, posting as champion of
free speech whilst attacking it]⠀⇛
# ⚓ The Guardian UK ☛ When_internet_shutdowns_spill_over
borders [Ed: NSA took down the Internet in the whole of
Syria]⠀⇛
o § Freedom of Information / Freedom of the Press⠀➾
# ⚓ Counter Punch ☛ It’s_All_Political:_Julian_Assange_Appeals
his_Extradition⠀⇛
Along this potted judicial road, Assange chalked up
a qualified success before District Court Judge
Vanessa Baraitser on January 4, 2021, who held that
he would be at serious risk of suicide occasioned
by the effects of Special Administrative Measures
and confinement in the ADX Florence supermax
facility in Colorado. This was deemed oppressive
within the meaning of the US-UK Extradition
Treaty. The most obvious aspect of the prosecution
– its self-evidently political nature – was given
little thought.
o § Civil Rights/Policing⠀➾
# ⚓ Six_Months_with_Android:_A_journey_from_a_blind
perspective⠀⇛
During the last six months, I’ve used Android
exclusively as my primary device. I made calls with
it, texted with it, read emails with it, browsed
the web, Reddit, Twitter, and Facebook with it, and
played games on it. Now, I’m going to express my
thoughts on it, its advancements, and its issues.
This will contain mostly opinions, or entirely
opinions, depending on whether you really love
Android or not. But whatever your stance, these are
my experiences with the operating system. My issues
may not be your issues, and so on.
# ⚓ JURIST ☛ Former_Kentucky_police_detective_pleads_guilty_to
falsifying_warrant_affidavit_that_led_to_death_of_Breonna
Taylor⠀⇛
The US Department of Justice announced Tuesday that
a former Louisville, Kentucky detective has pleaded
guilty to two separate federal charges. Detective
Kelly Goodlett admitted that she conspired to
falsify an affidavit to obtain a warrant to search
Breonna Taylor’s home without probable cause and
that, after the search resulted in Taylor’s death,
she also conspired to cover up the illegal warrant
by lying to investigators.
According to her plea agreement, Goodlett
acknowledged that she assisted another LMPD
detective and their unit supervisor in efforts to
obtain a warrant to search Taylor’s home despite
knowing that they lacked any probable cause to do
so. In order to establish probable cause for the
affidavit, the group knowingly created information
that was false, misleading, and stale.
# ⚓ ABC ☛ Fanta_Bility’s_family_reflects_on_grief_1_year_after
8-year-old_was_fatally_shot_by_police⠀⇛
Fanta was shot while exiting a football game with
her family at Academy Park High School on Aug. 27,
2021, when officers Brian Devaney, Devon Smith and
Sean Dolan fired their weapons toward the crowd
after two teens opened fire in a personal dispute
close to the high school, according to Delaware
County District Attorney Jack Stollsteimer.
# ⚓ TruthOut ☛ Disappointed_in_Biden’s_Inaction,_Immigrant
Rights_Advocates_Look_to_the_States⠀⇛
# ⚓ TruthOut ☛ UPS_Workers_Say_Union_Activists_Are_Being
Targeted_Amid_Contract_Negotiations⠀⇛
# ⚓ Counter Punch ☛ To_Democrats:_Make_Labor_Day_A_Workers’
Action_Day⠀⇛
Never mind the dwindling Labor Day parades.
Instead, organize rallies and assemblies in
neighborhoods around real reforms, redirections and
respect that all workers (regardless of their
political labels) want for themselves and their
families.
# ⚓ Common Dreams ☛ Opinion_|_With_Rights_Under_Assault,_We
Must_Create_a_Feminism_That_Promotes_Egalitarian_Values⠀⇛
One of the most liberating moments of my young life
was when, at age 14, the school dress code finally
loosened to the point where it ceased to exist
(this was 1968.) I had always hated the compulsory
skirts and knee socks that allowed the cold wind to
freeze us girls as we walked to and from school. I
definitely felt more comfortable in every way in my
ratty, ripped jeans that I wore to school the
minute I was able.
# ⚓ Counter Punch ☛ Life_Isn’t_Fair._Get_Over_It.⠀⇛
Wolf starts with a cynical view of the American
people: “But the overriding question for a lot of
people who didn’t go to college, those who already
paid off their loans or folks who make more than
$125,000 (or more than $250,000 if they’re married
couples or heads of households) is this: What about
me?” How disgusting. Only Wolf is this selfish. The
American people love one another and we love when
our neighbor is helped. Fuck your fairness.
# ⚓ AccessNow ☛ Saudi_authorities_must_release_women’s_rights
activist_Salma_al-Shehab⠀⇛
We, the undersigned NGOs, call on the international
community to press Saudi Arabian authorities to
immediately and unconditionally release women’s
rights activist and academic Salma al-Shehab, who
was recently sentenced to 34 years in prison based
on tweets in support of women’s rights and for the
respect of basic rights. It is the longest known
prison sentence handed down against a peaceful
activist for their free speech in Saudi Arabia,
signalling an alarming deterioration of the human
rights situation in the country.
Al-Shehab, a 34-year-old mother of two children, is
a dental hygienist and PhD student at Leeds
University in the United Kingdom, where she was
residing before her detention. She was arrested on
15 January 2021 while on holiday in Saudi Arabia,
and subjected to solitary confinement and lengthy
sessions of questioning over a period of nine and a
half months before being brought before the
Specialised Criminal Court (SCC), a court used as
an instrument of repression to silence dissent in
the kingdom. Al-Shehab belongs to the country’s
Shi’a Muslim minority, who have long suffered from
the government’s repression.
# ⚓ AccessNow ☛ Free_Salma_al-Shehab,_Saudi’s_Twitter_activist!
Even_Big_Tech_has_a_role_to_play⠀⇛
Saudi Arabian authorities must immediately and
unconditionally release women’s rights activist and
academic Salma al-Shehab — and all other prisoners
locked up for free expression — and put an end to
their oppressive regime of human rights abuses. Big
Tech must play its part by ensuring human rights
are at the core of any business dealings in the
kingdom.
In a joint statement, Access Now and civil society
organizations from across the globe strongly
condemn the arbitrary arrest and unlawful
sentencing of Salma al-Shehab — “the longest known
prison sentence handed down against a peaceful
activist for their free speech in Saudi Arabia,
signalling an alarming deterioration of the human
rights situation in the country.”
“A woman born into a totalitarian landscape dared
to speak out — via Twitter. Now Saudi authorities
plan on snatching the rest of her life away. Civil
society says, unequivocally, no to this,” said
Marwa Fatafta, MENA Policy and Advocacy Manager at
Access Now. “We demand the Saudi Crown Prince
Mohammed bin Salman immediately release Salma al-
Shehab, and put an end to persecuting all
activists.”
o § Internet Policy/Net Neutrality⠀➾
# ⚓ Moving_blog_from_blogger.com_to_wordpress.com_–
formicapunk⠀⇛
I switched from blogger.com the Google Blog
platform to the hosted wordpress.com of Automaticc,
the WordPress blog engine main authors.
[...]
On the personal side, I also intend to pause
twitter activity, as I notice current microblogging
platforms tend to mostly contain flame wars, self
promotion, or shared links I could find anyway with
a good feed reader.
o § Monopolies⠀➾
# § Copyrights⠀➾
# ⚓ Torrent Freak ☛ YouTube_Holds_Licenses_For_Copyright
Lawsuit_Plaintiff’s_“Entire_Back_Catalog”⠀⇛
YouTube says it will seek summary judgment to
shut down a lawsuit headed by musician Maria
Schneider which alleges mass copyright
infringement. YouTube’s motion reveals that
Schneider’s publisher granted YouTube a
blanket license covering the musician’s
entire back catalog, but that’s just the
beginning.
# ⚓ Torrent Freak ☛ Dash_the_Iranian:_Busted_Pirate_IPTV
Kingpin_Allegedly_Owns_RapidIPTV⠀⇛
In June 2020, a massive international law
enforcement operation targeted an IPTV
provider servicing two million subscribers.
Millions of euros in assets were seized and
authorities arrested the alleged kingpin.
Known to colleagues as “Dash the Iranian” the
businessman faces a legal nightmare. But what
about the fate of the giant piracy service at
the center of his prosecution?
* § Gemini* and Gopher⠀➾
o § Personal⠀➾
# ⚓ The_disease_called_“Perfection”⠀⇛
This post is by Single Dad Laughing. I found it in
2010 (or thereabouts) and it was transformative in
helping me be more at peace with myself and the
world around me. He gives permission to share it,
so I wanted to preserve it here in the smolweb
because it feels important and evergreen.
[...]
We live in communities where people feel
unconquerable amounts of pressure to always appear
perfectly happy, perfectly functional, and
perfectly figured. “Perfection” is much different
than perfectionism. The following examples of
“Perfection” are all real examples that I have
collected from experiences in my own life, from
confidential sources, or from my circle of loved
ones and friends. If you actually stop to think
about some of these, you will probably cry as I
admittedly did while writing it. If you don’t,
maybe you’re infected with a little too much of
this “Perfection” infection.
“Perfection” is a wife who feels trapped in a
marriage to a lazy, angry, small man, but at soccer
practice tells the other wives how wonderful her
husband always is. “Perfection” keeps people from
telling the truth, even to themselves. My husband
is adorable. He called me a whore this week because
I smiled at a stranger. When I started crying, he
said he had a game to go watch. I love him so much.
# ⚓ Verstappen_makes_everyone_look_foolish⠀⇛
Verstappen qualified with a huge advantage, got put
back to 15th with penalties, and still had an easy
win. Everything was working for him this weekend.
He could have won if he’d started last. It was
quite impressive. It doesn’t really matter what
happened to the others.
# ⚓ AUMORTI_Wordo:_BRIDE⠀⇛
# ⚓ Ancom_2022?⠀⇛
This is a follow-up to Ancom 2020? where I argued
that the 2007 IPCC shook my ancom foundations.
There’s another problem that’s come up more and
more these last few years: the tension between
autonomy and human rights.
The federalism component of ancom was that every
workplace, every village, every city block should
be autonomous. The drawback of that view is that
the bar for how humans treat each other can get
placed a li’l too low and things like systematic
racism can thrive. We’ve all seen the old “states
rights” arguments that tramples human dignity in
the name of autonomy.
o § Technical⠀➾
# ⚓ Why_Not_Oberon?⠀⇛
OberonStation was a tiny computer with a VGA output
and ports for keyboard and mouse. It booted into
Oberon in under a second, and featured an SD-card
slot and ton of ports.
It seemed like an ideal computer, the kind I always
blab about. Not a trace of Intel inside – just a
simple (too simple, perhaps) RISC CPU, fully
described in the documentation, designed for the
sole purpose of running compiled Oberon.
But then I tried to write some simple code.
=> =============================================================================
World Wide Web but a lot lighter.
䷩ 𝚕𝚒𝚗𝚎 5869
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_28/08/2022:_Linux_6.0_RC3_and_MX-21.2⠀✐
Posted in News_Roundup at 2:07 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Audiocasts/Shows
o Kernel_Space
o Instructionals/Technical
o WINE_or_Emulation
o Desktop_Environments/WMs
# GNOME_Desktop/GTK
* Distributions_and_Operating_Systems
o Reviews
o New_Releases
o Red_Hat_/_Fedora_/_IBM
o Debian_Family
o Devices/Embedded
o Open_Hardware/Modding
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o Web_Browsers
# Mozilla
o Programming/Development
# Perl_/_Raku
* Leftovers
o Science
o Health/Nutrition/Agriculture
o Security
# Privacy/Surveillance
o Environment
# Energy
o Finance
o AstroTurf/Lobbying/Politics
o Civil_Rights/Policing
o Internet_Policy/Net_Neutrality
* Gemini*_and_Gopher
o Personal
o Politics
o Technical
# Science
# Internet/Gemini
# Programming
* § GNU/Linux⠀➾
o ⚓ 9to5Linux ☛ 9to5Linux_Weekly_Roundup:_August_28th,_2022_–
9to5Linux⠀⇛
The 9to5Linux Weekly Roundup for August 28th, 2022,
brings news about Linux’s 31st birthday, Firefox 104, new
Linux computers, NetworkManager 1.40, KDE Plasma 5.25 in
Kubuntu 22.04 LTS, as well as all the latest distro and
software releases.
o ⚓ Linux Made Simple ☛ Linux_Weekly_Roundup_#197⠀⇛
Welcome to this week’s Linux weekly roundup.
We had a peaceful week in the world of Linux distro and
application releases, with no major release.
I see it as the “calm before the storm”.
May you have a wonderful week and see you in the Autumn.
o ⚓ Linux Links ☛ Linux_Around_The_World:_Finland_–_LinuxLinks⠀⇛
We cover events and user groups that are running in
Finland. This article forms part of our Linux Around The
World series.
o § Audiocasts/Shows⠀➾
# ⚓ Adafruit ☛ Receiving_Weather_Satellites_on_a_Raspberry_Pi
or_Linux_«_Adafruit_Industries_–_Makers,_hackers,_artists,
designers_and_engineers!⠀⇛
This NOAA Weather satellite setup on a Raspberry PI
4 using Raspberry OS either 32 or 64 bit was shared
by TekMaker on Youtube!
# ⚓ Video ☛ Valve_are_cool,_Janet_kills_hard_drives,_Bug
zappers_and_BeReal_app_–_A_Trendy_Talk_–_Invidious⠀⇛
# ⚓ Video ☛ LastPass_Password_Manager_|_Security_Breach_–
Invidious⠀⇛
# ⚓ Video ☛ Neovim_112:_Command-T_–_Invidious⠀⇛
# ⚓ Open Source Security (Audio Show) ☛ Episode_338_–_The
government_didn’t_make_vulnerabilities_illegal._Yet._–_Open
Source_Security⠀⇛
Josh and Kurt talk about the recent National
Defense Authorization Act that requires security
vulnerabilities to be fixed. What does this mean
for us, is it as bad as some people are claiming it
is? It’s actually not a huge deal, for most of us
it’s really just time to deal with product
security.
# ⚓ Linux Made Simple ☛ How_to_install_Shadow_PC_on_a
Chromebook⠀⇛
Today we are looking at how to install Shadow PC on
a Chromebook. Please follow the video/audio guide
as a tutorial where we explain the process step by
step and use the commands below.
# ⚓ Video ☛ How_to_install_FreeOffice_on_Pop!_OS_22.04_–
Invidious⠀⇛
In this video, we are looking at how to install
FreeOffice on Pop!_OS 22.04.
# ⚓ GNU World Order (Audio Show) ☛ GNU_World_Order_475⠀⇛
**kile and LaTeX** , **killbots** ,
**kimageformats** from the Slackware **kde**
package set.
o § Kernel Space⠀➾
# ⚓ Linux_6.0-rc3⠀⇛
So as some people already noticed, last week was an
anniversary week -
31 years since the original Linux development
announcement. How time
flies.
But this is not that kind of historic email - it's
just the regular
weekly RC release announcement, and things look
pretty normal. We've
got various fixes all over the tree, in all the
usual places: drivers
(networking, fbdev, drm), architectures (a bit of
everythinig: x86,
loongarch, arm64, parisc, s390 and RISC-V),
filesystems (mostly btrfs
and cifs, minor things elsewhere), and core kernel
code (networking,
vm, vfs and cgroup).
And some tooling support (perf and selftests).
We've got a few known issues brewing, but nothing
that looks all that
scary. Knock wood.
Please give it a go,
Linus
# ⚓ LWN ☛ Kernel_prepatch_6.0-rc3_[LWN.net]⠀⇛
The 6.0-rc3 kernel prepatch is out for testing.
o § Instructionals/Technical⠀➾
# ⚓ Data Swamp ☛ Solene’%_:_Using_nix_download_bandwidth_limit
feature⠀⇛
I submitted a change to the nix package manager
last week, and it got merged! It’s now possible to
define a bandwidth speed limit in the nix.conf
configuration file.
# ⚓ 15+_RPM_Commands_with_Examples_in_Linux_–_LinuxWizardry⠀⇛
The RPM Package Manager (RPM) is an open packaging
system used in Red Hat Linux and its distributions
such as CentOS and Fedora. An RPM Package contains
archive files and metadata including dependencies
and installs location.
An RPM package has a .rpm file format. rpm command
is used to install, update, remove, verify, query,
and manage RPM packages.
This tutorial will demonstrate different examples
of rpm commands in RHEL-based Linux systems.
# ⚓ How_to_Install_Chrome_on_Ubuntu_–_Linux_Stans⠀⇛
In this tutorial, we’re going to show you how to
install Chrome on Ubuntu. This tutorial was tested
on Ubuntu 22.04, but it will work on other Ubuntu
releases and Ubuntu derivatives.
Google Chrome is one of the most popular browsers
for all OSes, including Linux. Firefox is pre-
installed by default on Ubuntu. If you want to
install Chrome, you’ll have to do it manually, it’s
not available in the Ubuntu Software center. If you
need other recommendations for browsers on Linux,
check out The 4 Best Linux Browsers I’ve Used in
2022 and Top 5 Most Secure Browsers for Linux
# ⚓ ID Root ☛ How_To_Install_Telegram_on_Linux_Mint_21_–
idroot⠀⇛
In this tutorial, we will show you how to install
Telegram on Linux Mint 21. For those of you who
didn’t know, Telegram is the free instant messaging
application that can be used to connect to friends,
family, and relatives. With Telegram you can send
and receive text & voice messages, multimedia files
like images and videos, as well as make and receive
video calls. Telegram is available for Linux,
Android, Windows Phone, iOS, and macOS.
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 Telegram messenger on Linux
Mint 21 (Vanessa).
# ⚓ XDA ☛ How_to_install_Python_on_Windows,_Linux,_and_macOS⠀⇛
If you want to get into development, one of my
favorite programming languages that I’ve learned is
Python. It’s a multi-paradigm language, supporting
imperative, functional, procedural, and object-
oriented programming. It’s wide open and can be
used for practically anything, and is a go-to
language for many when working in artificial
intelligence or machine learning. I use it for a
lot of automation, and it’s even the language that
some of the testing tools that we’ve used are
written in.
Python is a powerful language, and if you want to
get started with it, this guide will teach you the
basics. Not only will you need to install the
Python binaries and ensure that it’s in your PATH,
but you’ll also need something to actually write
code in. You could use a full-fledged IDE
(Integrated Development Environment) like PyCharm,
or you could lean towards a text editor such as the
pre-installed IDLE or Sublime Text 3. There are a
lot of options, but this guide should kick-start
you on the basics.
# ⚓ 10+_Seq_Commands_with_Examples_in_Linux_–_LinuxWizardry⠀⇛
seq command prints a sequence of numbers in Linux.
It is super-fast in generating a list of sequential
numbers.
The output of seq command can be piped to various
other commands for additional functionality. The
seq command is also useful in for loops and bash
scripts.
This article will discuss different examples of the
seq command to print a sequence of numbers in the
Linux system.
o § WINE or Emulation⠀➾
# ⚓ Neowin ☛ Wine_7.16_arrives_two_days_late,_brings_game
enhancements_–_Neowin⠀⇛
In a world where Valve’s Proton dominates gaming
headlines, it’s hard to remember that it would be
nothing without the forward progress of Wine. Wine
7.16 was released this morning, breaking with its
tradition of releasing every other Friday. It’s the
latest on the march toward 8.0 which is due out
later this year. Thankfully, we don’t have to wait
for version 8.0 to benefit from lots of meaningful
fixes.
o § Desktop Environments/WMs⠀➾
# § GNOME Desktop/GTK⠀➾
# ⚓ OMG Ubuntu ☛ ‘Nephrite’ is_a_Classy_New_GTK_Theme_for
Linux_Desktops_–_OMG!_Ubuntu!⠀⇛
One of Linux desktop’s most prolific — not to
mention best, imo — theme makers has released
a brand new GTK theme for us all to go gaga
over.
Designer Vince Liuice’s latest creation is
called Nephrite, and it was made available to
download from Pling and from GitHub this
weekend.
Nephrite maintains the high quality this
theme maker is famed for, and the theme looks
pixel perfect on my high resolution display,
i.e. no blurry corners or pixelated edges
some themes inadvertently offer.
Always one for options, Vince has made the
Nephrite theme available in light, dark, and
mixed versions. All come paired with a
calming teal accent colour by default, making
it the ideal compliment to Vince’s Colloid
icon theme.
* § Distributions and Operating Systems⠀➾
o § Reviews⠀➾
# ⚓ Distro Watch ☛ Review:_Qubes_OS_4.1.1_and_Alchg_Linux⠀⇛
Qubes OS is an unusual project which strives to
perform two difficult tasks in parallel. First, it
attempts to isolate various tasks and elements of
the operating system to prevent the compromising of
one component from affecting other components.
Second, it attempts to make this experience
virtually seamless for desktop users.
The idea here is that the user should be able to
use their applications in a way which allows each
application (or a group of applications) to be
isolated from the rest of the system. If our web
browser is hijacked it shouldn’t give access to our
office documents, for example.
I downloaded the latest version of Qubes OS, which
is provided as a 5.4GB ISO for 64-bit (x86_64)
computers. Booting from this ISO displays a boot
menu where we can immediately launch the system
installer or run a self-check on the media and then
start the install process. There is no option to
launch a live desktop environment.
By default, Qubes runs Fedora software. This
includes getting up and running using the Anaconda
system installer. The installing experience is
virtually identical to setting up Fedora 36
Workstation with the exception the default software
selection uses the Xfce desktop instead of GNOME.
The Anaconda installer presents the steps we take
to set up the operating system as a series of
modules we can access in the order of our choosing
from a hub screen. After going through the modules
and (mostly) taking the defaults, the installer
refused to continue. At the bottom of the page a
message informed me that I’d need to complete all
the steps currently marked with an alert icon. The
problem was none of the modules was marked with an
icon.
I went through the modules again and ran into the
same warning without the ability to continue. I
restarted the computer and tried again. This time I
took all the defaults. This caused the partitioning
module to complain, saying the automated partition
layout wouldn’t work. I set up partitions for
booting, swap, and root. Then returned to the hub
screen where I was shown the same warning about
completing all marked modules before continuing,
despite no modules being marked.
o § New Releases⠀➾
# ⚓ MX Linux ☛ MX-21.2_“Wildflower”_released!_–_MX_Linux⠀⇛
We are pleased to offer MX-21.2 for your use.
MX-21.2 is the second refresh of our MX-21 release,
consisting of bugfixes, kernels, and application
updates since our original release of MX-21. If you
are already running MX-21, there is no need to
reinstall. Packages are all available thru the
regular update channel.
o § Red Hat / Fedora / IBM⠀➾
# ⚓ Kubernetes Blog ☛ Red_Hat_on_Kubernetes_1.25:_CSI_Inline
Volumes_have_graduated_to_GA_|_Kubernetes⠀⇛
CSI Inline Volumes were introduced as an alpha
feature in Kubernetes 1.15 and have been beta since
1.16. We are happy to announce that this feature
has graduated to General Availability (GA) status
in Kubernetes 1.25.
CSI Inline Volumes are similar to other ephemeral
volume types, such as configMap, downwardAPI and
secret. The important difference is that the
storage is provided by a CSI driver, which allows
the use of ephemeral storage provided by third-
party vendors. The volume is defined as part of the
pod spec and follows the lifecycle of the pod,
meaning the volume is created once the pod is
scheduled and destroyed when the pod is destroyed.
# ⚓ Video ☛ Flathub_Is_Introducing_Paid_Apps!?!?_–_Invidious⠀⇛
Flathub is the main place that you acquire Flatpaks
on Linux and soon a big change is coming to the
service, allowing developers to to have paid apps
if they choose to do so.
# ⚓ IBM’s_Competitive_Analysis_For_The_Power10_Midrange_Machine
[Ed: This publisher fails to properly disclosure that it is
funded by IBM to publish such puff pieces. Same for the ones
below.]⠀⇛
# ⚓ Moving_To_The_Cloud_Should_Be_Easier_Than_Switching_Homes⠀⇛
# ⚓ Kisco_Makes_Moves_In_the_IBM_i_Security_Business⠀⇛
# ⚓ Two_Weeks_Of_Webinars_On_IBM_i_Security⠀⇛
# ⚓ IBM_i_PTF_Guide,_Volume_24,_Number_35⠀⇛
o § Debian Family⠀➾
# ⚓ Slashdot ☛ Debian_Replaces_Google_with_DuckDuckGo_as
Chromium’s_Default_Search_Engine [Ed: There’s this discussion
now in Slashdot. DuckDuckGo_is_a_Microsoft_front
basically.]⠀⇛
# ⚓ Norbert Preining ☛ Debian_complaining_to_KDE_…_|_There_and
back_again⠀⇛
So now some Debian boohoos are complaining about my
blog which is aggregated at Planet KDE, directly to
KDE, how nice.
[...]
Funny that those few ….. over at Debian cannot get
a grip on reality and continue to witch hunt me.
# ⚓ Andrew_Cater:_Debian_Barbeque,_Cambridge_2022⠀⇛
And here we are: second day of the barbeque in
Cambridge. Lots of food – as always – some alcohol,
some soft drinks, coffee.
Lots of good friends, and banter and good natured
argument. For a couple of folk, it’s their first
time here – but most people have known each other
for years. Lots of reminiscing, some crochet from
two of us. Multiple technical discussions weaving
and overlapping
o § Devices/Embedded⠀➾
# ⚓ MakeTech Easier ☛ Battle_of_Android_Desktops:_Android_x86_v
Bliss_v_Phoenix_OS_v_PrimeOS⠀⇛
The Android desktop scene is relatively new, with a
handful of distributions like in the early days of
Linux. In theory, Android desktops should provide a
new way of using your PC, with a conventional
desktop harnessing the enormous Android ecosystem.
That’s the idea at least. But how do they stack up
really? We put the four main players to the test to
decide which Android desktop is the best.
o § Open Hardware/Modding⠀➾
# ⚓ Andrew Hutchings ☛ Australian_Commodore_64:_Keyboard_Repair
–_LinuxJedi’s_/dev/null⠀⇛
In my previous post about the repair of my
Australian C64 I got as far as diagnosing that I
needed a new CIA chip. The CIA chip has arrived so
I thought I would try it out and see how far I get.
The CIA chip arrived and I popped it straight into
the socket where the dead one originally was (the
U2 socket).
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ GSM Arena ☛ Weekly_poll_results:_Most_of_you_are_excited
about_Android_13_as_long_as_your_phone_gets_it_–_GSMArena.com
news⠀⇛
# ⚓ XDA ☛ How_to_check_Android_13_bootloader_version_on_the
Google_Pixel_6_series⠀⇛
# ⚓ Android Police ☛ How_to_take_better_photos_with_your
Android_phone⠀⇛
# ⚓ CNET ☛ Take_Control_of_Your_Data:_How_to_Manage_Android_App
Permissions_–_CNET⠀⇛
# ⚓ Hectic Geek ☛ Best_10_Tech_News_Top_Apps_for_Android_in
2022⠀⇛
Time changes, and with it, technology is evolving
with swift changes with every passing day. If you
are in the tech industry, you must stay in touch
with all these rapid changes and the coming trends
to stay up to date.
* § Free, Libre, and Open Source Software⠀➾
o § Web Browsers⠀➾
# § Mozilla⠀➾
# ⚓ James G ☛ Is_Firefox_a_search_engine?⠀⇛
After sharing this with others, I was
informed this is not the first time Firefox
has been referred to as a search engine.
o § Programming/Development⠀➾
# ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_littler_0.3.16_on
CRAN:_Package_Updates⠀⇛
The seventeenth release of littler as a CRAN
package just landed, following in the now sixteen
year history (!!) as a package started by Jeff in
2006, and joined by me a few weeks later.
littler is the first command-line interface for R
as it predates Rscript. It allows for piping as
well for shebang scripting via #!, uses command-
line arguments more consistently and still starts
faster. It also always loaded the methods package
which Rscript only started to do in recent years.
littler lives on Linux and Unix, has its
difficulties on macOS due to yet-another-
braindeadedness there (who ever thought case-
insensitive filesystems as a default were a good
idea?) and simply does not exist on Windows (yet –
the build system could be extended – see RInside
for an existence proof, and volunteers are
welcome!). See the FAQ vignette on how to add it to
your PATH. A few examples are highlighted at the
Github repo, as well as in the examples vignette.
# ⚓ Barry Kauler ☛ Commandline_and_file_IO_in_Nim⠀⇛
This post explains some more code fragments;
concerning reading parameters from the commandline
and file reading and writing. Also, some notes on
string manipulation.
# ⚓ Jim Nielsen ☛ Re:_“The_web_is_a_harsh_manager”,_Pt._II_–
Jim_Nielsen’s_Blog⠀⇛
It would be easy to conclude that, since you’re not
sure what a “front-end engineer” is — The person
who styles the page or queries the data layer? The
person who animates things on screen or keeps the
bundler and tooling humming along? — you can’t
consider yourself a “real” front-end engineer.
# ⚓ Matt Rickard ☛ Webhooks_Aren’t_So_Bad⠀⇛
Webhooks are the ultimate escape hatch to systems
integration. Event publishing that doesn’t require
you to know much about who is listening on the
other end. It’s trivial to create a publisher or
consumer (bring your own HTTP server/client).
On the surface, Webhooks seem antithetical to the
rise of the cloud native – it’s easier than ever to
set up servers that long-poll, managed pub/sub
infrastructure, or simple event queues. But the
opposite might be happening.
# ⚓ Matt Rickard ☛ The_Issues_with_Buildpacks⠀⇛
Buildpacks promise source-to-image generation. No
need to write a Dockerfile or maintain
dependencies. Get started with golden
configurations for languages, frameworks, and more.
[...]
The trade-off between Dockerfiles and buildpacks is
challenging for many developers to assess. We’re
usually much better at identifying upfront costs
rather than future costs. And Dockerfiles have an
initial learning curve.
# ⚓ Bozhidar Batsov ☛ OCaml_Tips:_Multiple_Let_Bindings_–_
(think)⠀⇛
One thing that was a bit weird for me in OCaml
early on was how to introduce multiple let bindings
(e.g. in the body of a function definition).
# ⚓ Rlang ☛ the_Kelly_criterion_and_then_some_|_R-bloggers⠀⇛
The Kelly criterion is a way to optimise an
unlimited sequence of bets under the following
circumstances: a probability p of winning each bet,
a loss of a fraction a of the sum bet, a gain of a
fraction b of the sum bet, and a fraction f of the
current fortune as the sum bet.
# ⚓ Rlang ☛ Surprising_Things_You_Can_Do_With_R_|_R-bloggers⠀⇛
If you are interested to learn more about data
science, you can find more articles here finnstats.
Surprising Things You Can Do With R, R has changed
the way we think about data. R has had a
significant impact on a wide range of data science
fields, from machine learning and artificial
intelligence to data visualization and analysis.
As a result, a large number of academic experts,
data scientists, and analysts employ the incredibly
flexible R programming language.
R, a long-standing participant in the TIOBE index
that gauges the popularity of several programming
languages, is utilized by individuals from all
occupational fields.
# ⚓ Barry Kauler ☛ debdb2pupdb.nim_cross-compiled_in_OE⠀⇛
# § Perl / Raku⠀➾
# ⚓ @data».sparkle_|_Playing_Perl_6␛b6xA_Raku⠀⇛
While reading solutions to the PWC, I spotted
a pattern. There where plenty of .map-calls
that contained only simple maths. It must not
be so! Task 179-2 leans itself to use vector
operations.
* § Leftovers⠀➾
o § Science⠀➾
# ⚓ Matt Rickard ☛ r/K_Startup_Theory⠀⇛
In ecology, r/K selection theory relates to the
tradeoff organisms make between quantity and
quality of offspring. Some organisms choose K-
selection, i.e., to have few offspring but offer
them substantial parental investment (e.g., humans,
whales, elephants). Others choose r-selection,
having many offspring with low probabilities of
reaching adulthood (dandelions, rodents, bacteria).
o § Health/Nutrition/Agriculture⠀➾
# ⚓ High_incarceration_rates_fuel_COVID-19_spread_and_undermine
U.S._public_safety_–_Northwestern_Now⠀⇛
Extremely high rates of incarceration in the U.S.
undercut national public health and safety. The
overcrowded, tight quarters in jails fuel constant
risks of outbreaks. Add to that the daily movement
of 420,000 guards in and out of the facilities and
30,000 newly released people who are likely to
inadvertently carry the virus back to communities.
o § Security⠀➾
# § Privacy/Surveillance⠀➾
# ⚓ No_Days_Off_|_Matt_Murphy⠀⇛
Workplace surveillance goes mobile
[...]
Time off task is a perverse little metric; a
product of run-amok capitalism’s
fetishization of productivity, efficiency,
and other quantifications. It’s the kind of
policy that was only a dream for burgeoning
companies of the industrial revolution, as
they clawed for more time and yield from
laborers. Now though, calculating time off
task can be fully realized by using the right
technologies to scrupulously track workers.
For Amazon, those handheld scanners are the
perfect gadgets to facilitate workplace
surveillance because they are essential tools
that are built into the infrastructure of the
work itself: the workers must use them to
scan packages. The scanners are also,
conveniently, extensions of workers’ physical
bodies, making the data they collect a
reliable depiction of physical locations and
movements—or inactivity.
o § Environment⠀➾
# § Energy⠀➾
# ⚓ Price Of Oil ☛ Calls_grow_for_a_U.S_windfall_tax
after_Exxon_makes_USD_$2,245.62_every_second⠀⇛
The amounts are obscene. They are mind-
boggling. This is profit-making like you have
never seen it before. It is also profiteering
from war and price gouging at our expense.
Big Oil is making billions of the misery of
millions.
On Friday, oil giants Exxon and Chevron
reported record second quarter profits, a day
after Shell’s results.
First, let’s look at Exxon. The company made
USD 17.9 billion in net profit in the 2nd
quarter of 2022.
We should call it out for what it is. This is
blood money. This is crude capitalism at its
worse.
o § Finance⠀➾
# ⚓ WSWS ☛ Poverty_in_Germany:_Food_banks_count_2_million
people_seeking_help_–_World_Socialist_Web_Site⠀⇛
Social inequality in Germany continues to rise at
an alarming rate. As a result of the pandemic, war
and high inflation, the official poverty rate
climbed to 16.6 percent last year, which
corresponds to 13.8 million people living in
poverty. This means that for ever more people—the
unemployed, single parents, low-wage workers, poor
pensioners—they no longer have the resources to
live on.
[...]
“The food banks are at their limit and report to us
that many people are coming to them who have
previously managed to make ends meet and need help
for the first time,” Brühl said. Since the food
banks can barely, or no longer can, meet the
demand, every third food bank has had to stop
accepting entrants, according to his data. There is
a shortage of food and volunteers to help everyone
who asks for support.
Tafel Deutschland surveyed 962 of its member food
banks in June and July, 603 of which responded.
According to the results, 60 percent of the food
banks have seen their customer load increase by up
to 50 percent since the beginning of the year. Just
under a quarter (22.6 percent) of respondents said
they were now supporting 50 to 100 percent more
people than before. At 16 percent of the food
banks, the number of people seeking help had
doubled or more than doubled.
# ⚓ The_Future_of_Work_Is_No_Work_–_YES!_Magazine⠀⇛
Activists have long suggested that oppressive
institutions should be abolished rather than
reformed. The same could be said about labor.
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ Mark Curtis ☛ ‘CIA_sidekick’_gives_£2.6m_to_UK_media_groups
–_Mark_Curtis⠀⇛
A US government-funded agency that claims to
promote democracy but which helps undermine
governments independent of Washington has moved
decisively into Britain’s media space since 2016.
# ⚓ How_the_American_Legislative_Exchange_Council_Turns
Disinformation_Into_Law⠀⇛
In June 2021, Texas Governor Greg Abbott signed
into law a bill banning the state from contracting
with or investing in businesses that divest from
coal, oil or natural gas companies. For Texas
Railroad Commissioner Wayne Christian—one of the
state’s top energy regulators—the message was
clear: “Boycott Texas, and we’ll boycott you.”
Since the beginning of this year, lawmakers in
Indiana, Oklahoma and West Virginia have introduced
bills that read a lot like the Texas anti-
divestment law, and legislators in a dozen other
states have also expressed support for the
legislation’s objective.
o § Civil Rights/Policing⠀➾
# ⚓ New York Times ☛ Pope_Francis_Will_Travel_to_Canada_to
Apologize_to_Indigenous_Community_–_The_New_York_Times⠀⇛
Pope Francis is traveling to Canada this week to
apologize to Indigenous communities for the Roman
Catholic Church’s role in the country’s notorious
residential school system, where thousands of
Indigenous children died, and countless others were
sexually and physically abused.
The visit comes after years of pleas from
Indigenous leaders and leading politicians for a
Vatican apology about the schools, which were
designed to erase Indigenous culture and language
by forcibly separating children from their families
to assimilate them into Western ways.
And some Indigenous leaders say it will fill in one
of the biggest remaining pieces in Canada’s efforts
at reconciliation over a brutal education system
that a national commission declared to be a form of
“cultural genocide.”
# ⚓ The Toronto Star ☛ Another_pope’s_apology_isn’t_enough_when
Church’s_shameful_acts_continue_|_The_Star⠀⇛
The truth is, there have been many apologies issued
by many popes.
[...]
The Catholic Church and its officials have
directed, authorized, counselled and/or were
complicit in the horrific physical and sexual abuse
of children; subjugation, vilification and violence
against women; and the deaths of millions of
Indigenous peoples in Canada, the United States,
Australia, New Zealand, South America and the
African continent. According to recent inquiries,
that abuse has continued into the present.
For some First Nation, Inuit and Métis survivors,
this papal visit to Canada that begins this weekend
in Alberta is an important part of their healing
journey. For others, the Pope is the last person
they want on their territories, as he represents a
religious organization that has caused much misery
around the world.
o § Internet Policy/Net Neutrality⠀➾
# ⚓ Patrick Louis ☛ Ten_Years⠀⇛
Writing.
Ten years ago I had an inner urge to lay my ideas
on the web, on a place I owned.
The page was initially hosted on 1.ai, a now-
defunct free platform that existed way before any
similar service surfaced (resurfaced). I was
immensely thrilled to design everything from
scratch and to add Easter eggs. Hence, the blog
became my medium of expression, my badge, an
integral part of my journey and progress as I
joined different online communities, looking to
bond over shared interests.
A blog is a persona, a blog is a canvas, a blog is
a series of sketches that are often seen only by
the author. As the brainstorming gets less rigid
and conventional, the more enthralled and absorbed
by the sentences we are.
These days blogs have changed but I try to keep
mine unaltered: each piece is uniquely me, not a
pastiche or the echo of someone else.
# ⚓ Data Swamp ☛ My_blog_workflow⠀⇛
I rarely spend more than 40 minutes for a blog
post, the average blog post takes 20 minutes. Most
of them are sharing something I fiddled with in the
day or week, so the topic is still fresh for me.
The content of the short articles often consists of
dumping a few commands / configuration I used, and
write a bit of text around so the reader knows what
to expect from the article, how to use the content
and what’s the point of the topic.
* § Gemini* and Gopher⠀➾
o § Personal⠀➾
# ⚓ Reactionaries⠀⇛
I still think that intersectional feminism has a
bigger kernel of truth than its enemies: anti-PC,
gamergaters, anti-SJW, anti-woke… an old movement
with many names that’s founded on
misrepresentations and second-hand accounts.
# ⚓ There’s_a_Monster_in_Your_Room⠀⇛
There’s a monster in your room. It stays awake
while you sleep; it can feel you when you move; it
listens to you while you dream. The monster speaks
in a language you cannot see, nor hear, nor sense.
Indeed, the monster speaks faster than you can
comprehend. It can make strange noises and sound
exactly like your friend. This creature can and
will interrupt your deep slumber. During the day it
will surely make you dumber. You cannot stop
checking to see if it is there. When it disappears
then you might be given a scare.
Though ’tis small in scale it will perform endless
deeds. At half past nine you find your mind inside
its hold. Your attention is its desired feast upon
which it feeds. It does not matter if it can or
cannot fold.
# ⚓ We’re_Going_the_Wrong_Way:_Childhood_Exploration_in_Video
Games⠀⇛
If you aren’t able to read it right now, the
(overly) short summary is that she discusses
playing video games as a child, ignoring the rules
and intended gameplay in favour of exploring and
observing the worlds they portrayed.
Reading this essay resonated strongly with my own
childhood computer experiences. I’ll talk about
this more generally later on, but the first thing
it brought to mind was the 1999 PC game “Mobil 1
Rally Championship”, so I want to focus on that.
# ⚓ Catacombs_of_the_Crazy_Cat_Conjurers⠀⇛
I ran the 39th installment of my quarterly old
school tabletop rpg convention yesterday. It was
absolutely lovely. Without question the most fun
I’ve had on the con this year.
For this one I had taken the time to properly
prepare a dungeon of the type I typically like. A
mix of puzzles, a lot of danger which is avoidable,
a fun magic item or two, and some gonzo elements.
As you may guess from the title there’s also a fair
bit of humour involved.
I’m hoping to do a little write-up about the
dungeon and the process of writing it, but for now
I just want to share my joy over how well the two
sessions played out.
o § Politics⠀➾
# ⚓ Three_stories_about_appeal_to_authority
⠀⇛
Who do you like?
Earlier this summer, I was having dinner with some
friends and to my surprise, they started speaking
positively about some fairly well-known reactionary
public voices. I didn’t wanna start a whole thing
but I didn’t wanna say nothing either so I tried
clearing out what I thought were misconceptions.
They listened but then they asked me a question I
couldn’t answer. “Sandra, who do you like? Which
public figure do you approve of?”
I’m right because he says so
There’s another friend of mine who always has had a
kind of “appeal to authority”–based reasoning. He’d
latch on to such-and-such book or writer. We were
in an argument about a project and a lot of his
arguments were based around his judgments of the
people involved. He’d be like: this is good because
these guys are the only one in the field who can
think about this stuff, that other project is bad
because the people working on it are futzes who
don’t know what they’re doing.
o § Technical⠀➾
# ⚓ Make_HAM_video_on_Ubuntu_22.04_from_MP4_files⠀⇛
There is a script to convert mp4 files to .hv. It
ran on 32-bit linux and won’t work by default on
64-bit linux. Below are the steps I took to get it
working.
# ⚓ Preliminary_Job_Reflections⠀⇛
My position is full-time remote–the company is
located in a different part of the country from
where I live. That is going to be a challenge for
me. I worked remote for several months during the
height of the COVID-19 pandemic, but I found that I
was more susceptible to distractions and less
productive at home. This is the first time I’ve
ever accepted a position knowing ahead of time that
I would not have an office to work at.
The company is located in the America/New York time
zone, while I’m located in the America/Chicago time
zone. That means I’ll have to log into my work PC
an hour earlier than I would at my previous job.
Working from home is a benefit there–I don’t have
to factor in travel time when considering what time
to wake up.
# ⚓ Reinstalling_from_backups⠀⇛
Now that we have a working backup setup, the only
thing left to try is to test a restore (and more
dangerously, a reinstallation). I planned on doing
a reinstall anyway, so this is a good exercise to
make sure my backups work as expected.
# ⚓ Farewell_to_Arm⠀⇛
It’s been a good three years at least since I gave
up my last desktop PC in favor of a cluster of
Raspberry Pi’s running various small services. I
still have some x86_64 machines in the form of two
laptops, but they run when needed rather than 24/
7 like the Pi’s. In that time I’ve discovered that
provided you keep the expectations reasonable a Pi
makes for a great little home server.
My little cluster until today consisted of Frodo,
Samwise, Gimli and Legolas. Frodo a Caldav and
Carddav service as well as serving my ebook library
via Calibre. Samwise is a torrent box and sometime
DNS cache. Gimli runs this capsule over both Gemini
and Spartan, a Finger service and a Gitea instance.
Finally, Legolas runs a web server which also
proxies a few of the other services on the network.
Since yesterday after an upgrade and reboot Legolas
has been offline, and today I tracked the problem
down to a failed ethernet connection.
# § Science⠀➾
# ⚓ Scientific American ☛ Eating_Too_Much_Protein_Makes
Pee_a_Problem_Pollutant_in_the_U.S._–_Scientific
American⠀⇛
Protein-packed diets add excess nitrogen to
the environment through urine, rivaling
pollution from agricultural fertilizers
# § Internet/Gemini⠀➾
# ⚓ The_most_popular_Gemini_hosting⠀⇛
# ⚓ Create_a_Custom_Filter_for_Antenna⠀⇛
I remembered how I had to do some digging and
experimentation before I got a working filter
for antenna.
My personal reason for filtering or excluding
content was because there are frequent posts
in languages that I do not know and wanted a
way to view the list of recent posts of only
the languages that I do know.
# § Programming⠀➾
# ⚓ In_“Why_Not_Oberon?”,_I_mentioned_I_had_a_project_in
mind._This_is_it.⠀⇛
The board is 15×15, represented in simple
ascii originally. It’s now using unicode
characters for special squares.
The board is still way too busy, and
something will need to be done about that
(more/better use of unicode might be the
answer to that issue).
Next major “game play” step is adding turn-
taking and the handling of the bag of tiles
and user racks. And then I might have to hook
it up to gemini. Still need a better board
display, imho, for that, though.
# ⚓ Enjoying_Lisp⠀⇛
About a year and a halve ago I decided to
look for a way to explore coding in Forth and
Lisp. This was the main incentive to make a
serious start to learn to use Emacs. Also the
fact that support for things like the GNU
recutils and ledger in Emacs is much better
than in Vim, helped.
Now, one and a halve year later, I am using
Emacs on a daily basis.
Still I am not as efficient with Emacs as I
am with Vim, but having a few decades of Vim
under my belt, this is to be expected.
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World Wide Web but a lot lighter.
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