𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, December 31, 2021

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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔

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Gemini index for the day: gemini://gemini.techrights.org/2021/12/31/

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Previous bulletins in IPFS (past 21 days, in chronological order):

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⦿ My Year as a Digital Vegan — Part VII — Staying the Course and Fake It Till You Make It? | Techrights

⦿ 2018, 2019, 2020, 2021: 4 Years of António Campinos Failing and EPO Granting Loads of Invalid Patents | Techrights

⦿ IRC Proceedings: Thursday, December 30, 2021 | Techrights

⦿ [Meme] EPO ’Social Dialogue’: Blah Blah Blah Blah (But Nothing Gets Changed for the Better) | Techrights

⦿ Why the Open Source Initiative Cannot be Saved (It’s Too Heavily Controlled by Monopolies) | Techrights

⦿ 2022, Our Sixteenth Year | Techrights

䷼ Bulletin articles (as HTML) to comment on (requires login):

	http://techrights.org/2021/12/31/article-on-digital-rights-in-2021-part-7/#comments

	http://techrights.org/2021/12/31/campinos-far-below-expectations/#comments

	http://techrights.org/2021/12/31/irc-log-301221/#comments

	http://techrights.org/2021/12/31/meme-epo-social-dialogue-blah-blah-blah-blah-but-nothing-gets-changed-for-the-better/#comments

	http://techrights.org/2021/12/31/open-source-initiative-floundering/#comments

	http://techrights.org/2021/12/31/welcome-2022/#comments

䷞ Followed by Daily Links (assorted news picks curated and categorised):

	http://techrights.org/2021/12/31/goodbye-to-centos-8/#comments

	http://techrights.org/2021/12/31/libadwaita-1-0/#comments

                ䷩ 𝚕𝚒𝚗𝚎 63

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/31/article-on-digital-rights-in-2021-part-7/#comments

Gemini version at gemini://gemini.techrights.org/2021/12/31/article-on-digital-rights-in-2021-part-7/

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Gemini_version_available_♊︎

✐ My_Year_as_a_Digital_Vegan_—Part_VII—_Staying_the_Course_and_Fake_It_Till

You_Make_It?⠀✐

Posted in Free/Libre_Software at 1:31 pm by Guest Editorial Team

By Dr. Andy Farnell

Series parts:

My_Year_as_a_Digital_Vegan_—Part_I—_2021_in_Review

My_Year_as_a_Digital_Vegan_—Part_II—Impact_of_a‘COVID_Year’

My_Year_as_a_Digital_Vegan_—Part_III—_Lost_and_Found;_Losing_the_Mobile

  Phone_(Cellphone)

My_Year_as_a_Digital_Vegan_—Part_IV—_Science_or_Scientism?

My_Year_as_a_Digital_Vegan_—Part_V—_Change_in_Societal_Norms_and

  Attitudes

My_Year_as_a_Digital_Vegan_—Part_VI—_The_Right_Words

YOU ARE HERE ☞ Staying the Course and Fake It Till You Make It?

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Fake Tech Vegan⦈ Summary: Dr. Andy Farnell continues sharing

his ‘Tech Vegan’ experiences from this past year; this series will carry on

well into the new year (2022)

§ Staying the course⠀➾

Another theme I have dealt with this year is “tenacity versus resignation”.

People have different coping mechanisms to technological

stressors, some get mad, some get even, some get the hell out of there. I began

the year helping a student edit an inspiring_story of how he graduated without

non-free software. I was very impressed with this individual’s ability to

unerringly act with firm politeness and perseverance against the kind of

institutional steamroller that crushes other students.

“I began the year helping a student edit an inspiring story of how he graduated

without non-free software. I was very impressed with this individual’s ability

to unerringly act with firm politeness and perseverance against the kind of

institutional steamroller that crushes other students.”Elsewhere I have

encountered learned_helplessness (see Seligman et al. Hiroto75). Defeatism is

one of the greatest enemies we face in seeking digital rights, as people seldom

feel able to confront what they do not understand. A disappointing number of

people (wrongly) said to me “What’s the point boycotting your supermarket Andy?

They’re all just doing the same”. Despite there being absolutely no evidence

that other British supermarkets were violating privacy rights there’s a

pervading sense around tech that a possibility_once_is_a_necessity_forever,

which feeds into a nihilistic refusal to resist even the most tepid incursions

by technological abusers.

What I’ve learned is that small, polite but resolute gestures make big changes.

Standing up for principles as a single voice does make a difference. Sometimes

you need to start as an army of one and remember that all progress “depends

upon_the_unreasonable_man“. Despite every armchair theorist’s wisdom on the

intractability of ‘network effects’ we successfully flipped our whole family

communication circle from Whatsapp to Signal in a few weeks.

But this raises a troubling question. By what right am I an evangelist? What

prophet made me an influencer and missionary charged with saving the souls of

technological sinners? None whatsoever. And wouldn’t it be grandiose and

egotistical to take on such a role?

How the world has changed since the ’90s when I had a T-shirt that said, “No. I

will not fix your computer”, because like every other geek I was inundated with

requests for help. “Help me install a new hard drive”. “Help me connect to the

Internet”. “Help me build this web page”… I have yet to hear an honest

request – “Please, help me get off social media”.

“Like many of the most insidious harms, technological harms are invisible,

delayed, accumulative and tolerance building. All you can do is stand back and

hope others see the harm and abuse they are bringing upon themselves.”I wrote

several chapters in Digital Vegan, about addiction, cults, entrenched behaviour

and the impossibility of proselytising others to a crazy cause. I advise

against it – and indeed the book title is an ironic take on that problem.

Anyone who has dealt with alcohol or drug problems knows the pain of seeing

those you love harm themselves and knowing that, generally, any interventions

only make things worse. Like many of the most insidious harms, technological

harms are invisible, delayed, accumulative and tolerance building. All you can

do is stand back and hope others see the harm and abuse they are bringing upon

themselves.

§ Fake it till you make it?⠀➾

Being a Vegan “impostor” myself I’ve developed a sharp nose for “Fake Digital

Vegans” – those who say “Oh yes, how ghastly it all is”, while messaging on

Facebook. They care deeply about everything, so long as changing would not

inconvenience them. I’ve also noticed a slew of click-bait stories in the

popular press that tease us with “I quit my smartphone for a month and you’ll

never guess what happened to me next!”. Actually, I can guess… you got

paid a big bag of money for lying about it. Celebrities making grand public

theatre of their few weeks without Alexa (the horror) actually subtract from

responsible, moderate use.

“All platforms encourage token dissenters, because that legitimises them as

“democratic”.”Only this week another latecomer joined the party. Comedian_David

Baddiel made his own apologies on the BBC for correctly naming everything wrong

with social media, including his own daughter’s distress, before admitting his

hopeless addiction and crawling back to it. The point is that Baddiel is a

courageous_intellectual, but ultimately seemed defeated in his bid to

extricate. What does that bode for us lesser beings?

All platforms encourage token dissenters, because that legitimises them as

“democratic”. One cannot wholly burn-down ones own platform in protest. How did

this public spectacle of failure help? And if he had been successful, who would

have ever heard of David Baddiel again? So, here lies the paradox of

celebrities attempting to set an example regarding social media.

I’ve come to think that fetishism of “tech-fasting” only cements addict-like

behaviour. It’s flip-side is Cyber Monday bingeing on IoT junk to “reward

yourself”. Do or do not, there is no try. Like Baddiel’s, these accounts are

generally pessimistic in their conclusion that it’s “impossible” to stand up

against Big-Tech. They are coded messages from the establishment saying, “Don’t

be so silly, nobody can really live without a smartphone and social media”. Of

course that’s not true. But you won’t ever hear that on social media.

“When I made video lectures criticising Google, it felt awful that the most

likely outlet would be YouTube.”Thus I am ambivalent towards those conflicted

pragmatists “changing the system from the inside”. I decline joining their

“Overthrow The Empire” Facebook groups. Yet I have respect for their courage.

It takes something to fully embrace hypocrisy, or dualism. When I made video

lectures criticising Google, it felt awful that the most likely outlet would be

YouTube.

Successful projects I have encountered seem advocate modest_and_gradual_change

and are not too Puritan to use the platforms they denounce to spread their

message. However, many projects that attempt to address subjects like social

media_dependency_disorder and have been active since around 2015 have not found

traction. They’ve achieved only modest success despite the growing prevalence

and visibility of the problem. Why is this?

“If token dissent is no longer being tolerated and disaffection swept under the

rug, it means the big platforms are scared.”Amidst mounting scientific_evidence

and whistleblower reports, widespread sentiment on the need for society to back

away from collective smartphone and social media delirium is booming. However,

critical discussion now encounters suppression across all corporate mass

communications systems like Twitter, Facebook, TikTok, etc.

Active censorship of social technology critique is a good thing (and quite

inevitable). It marks a vital advance in the sequence “first they ignore you,

then they ridicule you, then they fight you, then you win.” If token dissent is

no longer being tolerated and disaffection swept under the rug, it means the

big platforms are scared. █

✐ Bibliography⠀✐

* [Hiroto75] “Hiroto & Seligman, Generality of learned helplessness in man,

  “Journal of Personality and Social Psychology”, 31, 311-327 (1975).

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣷⠎⢙⢿⣿⣶⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⢿⣿⣮⣉⠰⣿⣶⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣋⣠⣉⠿⣿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣷⠟⠻⣿⣿⣯⣀⣬⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣾⣿⣿⣶⣄⡈⠙⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠁⠘⠻⣿⣿⣦⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣷⣠⢠⢀⡄⢠⢀⣄⢠⡀⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡘⢙⡘⠇⠻⠘⠛⠸⠇⢿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠙⠃⠃⠸⠘⠃⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⠓⠂⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣀⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣰⣿⡟⠁⣰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣈⠙⢿⣿⣟⡻⠿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⣾⡿⠏⢀⡺⢿⣿⣦⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⣷⣶⣍⡻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⡿⠁⣰⣶⣦⣈⡙⢿⣿⣿⣙⠿⠋⠀⠀⣠⣾⡶⠉⠿⣿⣷⣍⣹⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣀⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣶⣽⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⣙⠿⣿⣶⣄⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣈⠻⣿⣷⣿⡿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣷⠎⢙⢿⣿⣶⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠛⠃⠃⠸⠘⠃⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣴⣿⡟⠁⣰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣈⠙⢿⣿⣟⡻⠿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⣾⡿⠋⢀⡺⢿⣿⣦⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⣷⣶⣍⡻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣀⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣾⣝⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣷⠎⢙⢿⣿⣶⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣋⣠⣙⠿⣿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡜⢙⡘⠇⠻⠘⠛⠸⠇⢿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢰⣾⡟⠁⣐⢿⣷⣌⠙⠿⣿⣶⣴⣷⠆⠀⠀⣀⣶⣶⣤⠉⠿⣿⣾⣿⠿⡿⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⡿⠁⣰⣶⣦⣈⡹⢿⣿⣿⣙⠿⠋⠀⠀⣠⣾⡶⠉⠿⣿⣷⣍⣹⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣄⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣾⣽⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⡿⠏⠀⠾⣿⣿⣿⣿⣶⣦⣌⣻⠿⠁⠀⠀⠀⣿⣯⣙⢋⣶⣶⣍⡿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣄⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣶⣽⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⣙⠿⣿⣶⣄⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⣙⠿⣿⣶⣄⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⠾⠁⣰⣶⣦⣈⡹⢿⣿⣿⣙⠿⠋⠀⠀⣠⣾⡶⠉⠿⣿⣷⣍⣹⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⡀⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣶⣽⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣀⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣾⣽⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣄⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣶⣝⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⡀⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣾⣽⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⡘⢙⡘⠇⠻⠘⠛⠸⠇⢿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⡀⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣾⣝⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⡀⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣾⣝⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣷⠎⢙⢿⣿⣶⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢠⣾⠟⠁⣐⢿⣷⣌⠙⠿⣿⣶⣴⣷⠆⠀⠀⣀⣶⣶⣤⠉⠿⣿⣾⣿⠿⡿⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⡀⠉⠻⢿⣿⣿⣁⠙⢿⠿⠀⠀⠀⠰⢿⣿⣾⣽⣿⣿⣦⡉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⠟⠁⣰⣶⣦⣈⡙⢿⣿⣿⣙⠿⠋⠀⠀⣠⣾⡶⠉⠿⣿⣷⣍⣹⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⢀⣴⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡐⠀⠵⠊⠁⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⣀⠆⣪⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢡⠾⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⡀⠀⣲⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣫⠪⢡⠸⠋⠀⠀⠀⠀⠀⠀⠄⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡒⡇⣧⣿⣿⣿⣿⠿⣻⢻⡛⢻⢛⢛⠛⠟⣛⠿⡻⢸⠆⢋⢺⣣⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢨⣋⢏⣿⣿⡿⣻⣣⢿⢸⠿⡸⡼⡰⢐⠒⠘⡰⢐⠨⠚⠘⠚⡈⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⢎⢟⡾⣿⣿⡗⠕⢉⠓⢙⢜⣬⠚⡊⠑⢚⡕⢨⠚⠘⠚⣪⠡⢀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠂⡋⢴⣿⡯⡁⡀⠁⠀⢈⣠⠤⠚⢻⣬⢠⡜⠠⡛⠈⠁⢀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠀⠀⢸⣿⡇⠐⠐⠈⠂⠤⠠⠻⠬⠠⠤⠠⠔⠨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠈⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠢⠨⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⡑⠁⡈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠐⠀⠀⠀⠤⡐⠄⠀⠁⡄⡂⠆⠃⠀⢘⠉⠡⠠⣀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠈⠀⠄⡁⠁⢄⡀⠡⠀⠈⡀⢁⠀⢀⠢⠅⠢⠔⠠⢈⡑⠀⡠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠀⠀⠀⠂⠐⠈⠈⠁⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⡀⣀⢀⠀⠀⢀⠀⠀⡀⢀⠀⢀⢀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠃⠃⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⡀⣀⢰⡶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡀⣐⠐⠝⠊⠈⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⠆⣪⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠄⣩⠿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠐⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⢁⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⢠⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢩⡭⣌⢹⠏⠀⠀⠀⠀⠀⠀⠄⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡈⣯⣷⣿⣿⣿⢛⣛⡟⣻⢛⢻⣻⣿⠛⡻⣛⢻⡻⡻⡰⢸⢸⣵⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢈⣀⢛⣿⣿⡿⣛⣙⠤⣻⡺⢯⢥⡤⣸⢠⡕⢜⢜⣔⠬⢜⢤⠘⠃⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠎⣝⠿⣿⣿⣷⠻⢭⠛⢸⢺⢜⢨⡔⡌⡚⡜⠜⢼⠠⠞⡥⠣⢴⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠨⢴⣿⡏⣥⣤⠃⡈⠈⡸⢜⡬⡪⢮⣸⢜⠜⢣⠀⠠⠂⠠⠨⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⢠⣸⣿⡗⢫⣤⡯⠚⠕⡼⠱⠭⡸⢤⣘⠔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠉⠉⠁⡐⠐⠀⠀⠠⡂⠠⡀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣁⢪⡰⡑⠃⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠎⠂⠅⢊⠐⠈⢈⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠊⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⢀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠀⢀⣀⠀⣀⢀⠀⠀⣀⠀⠀⣀⢀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠃⠃⣀⠀⠀⠀⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⡀⢔⠂⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⡀⣀⠀⠐⠊⠁⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠖⣓⠞⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢁⡴⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡜⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⡻⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢐⢅⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢋⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠢⠘⢸⣿⡿⡛⠛⣿⢛⠛⠛⠛⠛⢛⠛⠛⢋⠉⠉⢊⢤⠀⠇⠆⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣩⠆⡠⣿⣿⢯⢀⠿⣸⢿⠑⠠⢄⠠⠀⠚⡤⢀⡄⠘⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠅⡁⢿⣿⡟⡈⠍⠀⠉⠘⠀⠀⠀⠚⠨⢀⡤⢀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠠⣽⣿⡇⠀⠄⠄⠀⠀⠀⠐⠀⡀⢠⡠⡰⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣓⠟⠉⠁⠈⡑⠁⠐⠐⠀⠀⠀⠀⠈⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠁⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠀⢀⣀⠀⣀⢀⠀⠀⣀⠀⠀⣀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠃⠃⣀⠀⠀⠀⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⡠⣰⠆⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⡠⣀⠐⠑⠊⠁⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠖⣑⠖⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢉⡶⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡜⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⣟⡯⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢐⠡⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠃⠨⠑⠁⠀⠀⠀⠀⠀⠀⠀⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢐⡢⠀⢹⣿⡿⣛⠛⢛⢛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠈⠀⠀⠀⠇⠆⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠨⠀⡠⣿⣿⢿⠍⠤⠑⠔⣅⠀⠂⠀⠀⠄⠀⠀⠁⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠄⠁⢻⣿⡟⡈⠂⠠⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢀⠠⣽⣿⡇⡈⢤⢀⠂⠀⠀⠄⠀⠀⠁⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢚⠏⠉⠁⠨⡁⠀⠀⠀⠀⠀⠀⠐⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣄⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠔⠎⠎⠠⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠅⡄⠁⠊⠈⠈⢐⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠂⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠀⡤⠤⠤⠀⠀⠀⡤⠤⠀⠀⡤⠤⣄⠀⣤⠤⠤⠀⠤⢤⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠟⡛⠉⠁⠀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣤⡀⡕⠀⠀⠀⠀⠀⠓⠤⡀⡎⠀⠀⢸⠀⣿⠀⠀⠀⠀⢸⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠛⠉⠁⠃⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣖⠒⠀⠀⠀⠂⠒⠁⠈⠒⠒⠋⠀⠛⠀⠀⠀⠀⠘⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠀⢀⣀⠀⣃⢀⠀⠀⣀⠀⠀⣀⢄⡁⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⡄⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠃⠃⣀⠀⠈⠈⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠃⠀⠀⠀⠃⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⡠⢒⠖⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠠⢀⠀⠰⠊⠁⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣐⠖⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡟⣯⡜⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢐⠡⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡁⠁⠑⡈⠋⠁⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⠢⢈⢸⣿⡿⡛⠛⠛⡛⠛⠛⠟⠛⠛⠛⠛⠉⠉⠀⠀⠂⠀⢄⠆⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠱⢀⠠⣿⣿⣿⠄⠬⠀⠂⠀⠀⠀⠀⡀⠀⠁⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠠⠈⢻⣿⡟⠀⠃⠀⠁⠀⠀⠀⠂⠀⡀⠀⠃⠀⠂⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠠⣽⣿⡗⡂⠄⣢⠀⠀⠄⠀⠀⠀⠀⡀⠂⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣒⠟⠉⠁⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠟⡟⠉⠁⠈⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣤⡀⡕⠀⠀⠀⠀⠀⠓⠤⡀⡎⠀⠀⢸⠀⣿⠀⠀⠀⠀⢸⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠛⠋⠉⠇⠑⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣷⣖⠒⠀⠀⠀⠂⠒⠁⠈⠒⠒⠋⠀⠛⠀⠀⠀⠀⠘⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠀⢀⣀⠀⣅⢀⠀⠀⣀⠀⠀⣀⢀⡉⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⡄⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠃⠃⣀⠀⠀⠀⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠃⠀⠀⠀⠃⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⣾⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣴⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢾⣿⠟⠀⠀⢀⢀⠀⠀⢀⠀⠀⡀⢀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿

⠟⠃⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠿⠿⠟⠿⠿⢿⡿⣿⠿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⡛⣟⣻⡿⢿⡿⠛⣛⣿⣿⣿⣿⣿⣿⣿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢟⣿⢿⢿⣻⢿⣟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿

⢸⣿⣿⠿⠇⡯⠭⠭⢍⣻⣾⠛⠶⣓⣛⠿⢿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢊⣟⢝⢬⡟⡝⢾⢹⣿⣟⢷⢷⣯⣯⣭⣿⣿⣿

⢸⣿⣿⣿⡟⣿⣿⣿⣿⣮⣉⣿⣿⣿⡷⣹⢻⡻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣽⣾⣶⣶⣵⣿⣻⣿⣯⣯⣻⣿⣿⣿⣿

⢸⠾⠹⠻⠇⠟⠝⠻⡿⠟⢟⣛⠿⠽⠛⡥⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠻⢿⡋⡉⣿⣿⡿⠋⠋⠉⠛⢛

⢸⢦⢱⠥⣰⠠⣠⠥⡦⠦⡰⠹⢪⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡯⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣃⣁⠟⠊⢓⡀⡀⣠⠪⠂

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠙⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⢈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠠⣔⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣻⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⡾⣿⣯⣯⣿⢻⡻⡻⣯⢿⢟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣿⢿⢿⢻⣿⣟⢻⣿⣿⣿⡿⣟⣿⢿⣿⣿⣻⣿

⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠿⠿⣿⣿⣿⣨⣭⣿⣩⠈⡽⢼⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢨⢌⢬⡿⡝⢾⢹⢗⣟⢣⢽⣟⣎⢭⣽⣿⢾

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠛⠛⠛⠑⠱⠙⢘⠧⣏⠘⢈⠜⠊⠺⠺⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢑⠜⡶⡆⡅⠛⠿⠰⠪⢊⠓⠞⠋⠛⠺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢂⠁⢀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⢘⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣻⣻⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⢿⣿⣿⣿⣭⣭⣿⣺⡨⣽⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢝⢤⡿⡕⢮⢹⣿⣟⢣⢽⣿⡮⣭⣿⣿⣿

⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠛⠛⢻⣿⣿⣽⣿⣿⣾⣼⣾⣾⣿⣺⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣶⣵⣿⣿⣷⣮⣿⣷⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠟⣟⠟⣟⡿⣛⡻⠛⣏⠫⣺⢿⡛⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⣻⡛⣾⣿⣿⠛⠚⢹⢺⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣏⠛⠑⠀⠀⠀⠀⠀⠀⠉⠐⠉⠈⠁⠃⠃⣐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢡⡈⣽⢹⣀⢆⣸⢵⣺

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠫⣭⣽⢫⣫⣽⣽⣯⣯⣿⣿⣿⣿⣶⣟⣛⠛⣾⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⢂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠕⠝⠏⠙⠊⠟⠻⠙⠏⠟⠛⠏⠷⠫⠩⠏⠀⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⢟⣏⠿⡯⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠻⠿⡿⡿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⢻⢿⣿⣿⣿⡿⡿⢿⢿⢿⣿⣿⣿⣿⣽⣿⠿⣟⣿

⠀⠀⠻⠓⠛⠗⠓⠃⡋⠚⠙⠃⠐⠂⠐⠀⠈⠀⠘⠘⠰⠐⠀⠈⢀⠈⠀⠀⠈⠀⠉⠀⠩⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢚⠰⠀⠉⠉⠙⠀⠈⠐⠠⠐⠤⠢⠁⠅⠈⠀⠆⠀⠋⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[38A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡿⢿⢿⣿⡿⢿⣿⣿⢿⠿⢿⠻⠛⢟⠿⣿⣿⣿⡟⣿⣻⣿⣿⣿⣿⣿⣿⠿⢟⣿⡇⢸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠊⠀⠀⠐⠀⠀⠀⠘⠈⠈⠰⢀⠸⡑⠀⣿⠋⠛⠙⠠⡳⠃⠂⢊⡿⠟⠇⢥⡷⢻⡇⢸⣂⣷⡹⠏⠗⡘⢓⠗⠙⠛⠪⠐⢰⠹⠉⠁⢘⠒⠎⠰⠖⠲⢟⠒⠉⠛⠑⠃⠁⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠆⠁⠄⠃⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⢿⣻⣛⠻⠻⢻⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠟⣻⣿⡇⢸⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⠄⠐⠀⠐⠀⠐⠐⠑⠀⠒⢨⠐⢨⠿⠒⢗⢉⡯⢓⡎⢉⠏⠩⡟⠿⠃⣵⠿⢿⡇⢸⣗⣒⡞⠹⢏⡘⢃⡺⠻⠛⠚⠙⠩⠐⠀⢐⠲⠲⠲⠠⠴⠾⠖⠟⠐⠛⠒⠃⠀⠃⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠂⠉⠀⠀⠁⠀⠀⠀⠀⠅⠀⠀⠃⠀⠇⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⠻⠻⢿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⡟⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠡⠀⠐⠀⠐⠐⠀⠘⠉⠊⠐⢠⢑⢘⠶⠛⠷⢖⡦⢛⡔⢉⠟⢍⠟⠟⠋⢬⠟⢾⡇⢸⠭⡯⡽⡫⠝⢗⡒⠊⢹⠻⢻⠶⠹⠨⠂⠐⠲⠲⠲⢀⢔⠲⡛⠖⠙⠊⠓⠃⠀⠃⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈⠐⠐⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠂⠀⠂⠀⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠈⠀⠸⠀⠩⠙⠹⠁⢘⠨⠒⠲⡲⠒⠶⠟⠿⠙⠀⡃⠐⠖⠒⠖⠶⠗⣾⡇⢸⢦⠤⣯⣝⢿⠷⠾⠷⠾⠶⢊⠈⢉⠛⠹⠱⠾⠶⠒⠲⠚⠽⠿⠿⠀⣒⠐⠒⠖⠇⠀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠀⠠⠘⠠⠘⠐⠩⠿⠶⠾⠶⢺⠐⠒⠒⠶⠺⠒⡷⠂⠷⠶⠷⡶⡷⡾⡯⢷⣾⡇⢘⠶⣖⣸⣷⣷⣿⣿⣿⠿⢿⠋⠹⢉⠙⠹⠶⠾⠾⢂⠊⢈⠙⣉⠛⠤⠶⠒⠒⡀⡓⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠁⠀⠀⠂⠂⠁⠀⠁⠁⠁⠀⠁⠀⠁⠀⠀⠁⠉⠙⠋⠐⠂⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠿⢿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠒⠒⠐⠾⢲⠨⠒⢺⠺⢉⠹⠉⠹⢀⠘⠐⠟⠾⠮⠛⡎⠉⠷⠩⡏⢽⠗⡏⠵⢺⡇⢈⣂⣅⣺⣿⣷⣿⣿⣿⠿⠿⠿⠻⠙⠙⢉⠚⠒⠒⠒⢘⠈⢉⠻⠂⠛⠐⠆⡒⡂⠗⡊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠁⠁⠂⠀⠀⠃⠀⠀⠁⠚⠋⠉⠁⠈⠑⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⠿⢿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠚⠰⠒⠶⠂⠖⠲⢞⠱⢙⠩⠙⠙⠀⠘⣀⠛⣀⠛⠴⡃⠄⠷⡎⠩⢫⡿⠶⠧⣾⡇⠸⣆⡠⢾⣷⣷⣾⣿⣿⢽⠱⠷⠃⠙⢙⠑⠺⢒⠙⠂⠒⢀⠙⣉⠳⠒⠶⠂⠒⠖⡒⠓⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠂⠂⠀⠀⠂⠃⠀⠁⠀⠉⠙⠋⠐⠂⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣯⣭⣭⣙⣛⣛⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠼⣼⠹⢐⠢⠋⡙⠙⠒⠰⢄⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠃⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⢀⣤⣼⣿⣿⣿⣻⡟⠀⠀⠀⠀⠀⠀⠈⠛⠛⠚⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⢿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⣻⢿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢵⡿⣺⣿⠉⡻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⢪⡋⢟⠾⠹⡽⡿⡹⣿⢏⡳⡱⢑⠿⡱⠱⠈⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡪⢏⠠⢫⡩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⠘⠐⠈⠈⠛⠈⠐⠐⠈⠦⠂⠑⠀⠆⠀⠄⠂⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⠹⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠙⠙⠛⠛⠛⠛⠛⠉⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢿⣿⣿⣟⣻⠿⣟⣛⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣟⣿⣟⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⣿⣿⣿⣿⣭⣭⣿⣿⡻⣽⣼⣿⢨⣽⣿⡅⣭⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠝⢬⡿⡛⡶⢿⡿⣟⣫⢽⣿⣯⣭⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣽⣷⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣵⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢠⣿⣽⣿⣿⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠿⣻⡻⣿⣿⣿⠻⣿⢻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣯⣛⣼⣿⣿⣿⣟⣻⣿⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣷⣛⣳⣿⣿⣿⣰⣦⣸⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠛⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿

⣟⢽⢾⢾⣿⢹⣿⣹⢿⢝⡫⢽⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣻⢽⣽⣻⣿⣿⢺⣾⣽⡹⢞⢺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿

⣽⣹⢿⢿⢼⢾⢽⢽⢿⢮⠽⠳⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣾⣿⣿⣿⢻⣼⢺⢽⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠀⠙⠸⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⢀⠀⣀⢀⠀⠀⢀⠀⠀⡀⠀⠀⢀⢀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⢈⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⡿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⡿⣿⣫⣿⢿⣟⣿⣹⡣⡫⢼⡵⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿

⡾⣞⡧⣻⣏⡫⡪⡢⠵⡽⣟⣾⣻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿

⢯⢕⡏⡺⡙⣾⢗⡱⠵⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⣓⡯⡳⠥⡚⡕⡘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⠀⡀⢀⠀⠀⢀⠀⠀⡀⠀⠀⢀⢀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠃⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⢈⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠷⣞⠽⡻⠷⣽⢿⠖⣕⢽⣗⢾⢾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿

⡎⣮⡹⣳⢖⡟⡖⡍⡆⣿⢷⣽⢾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿

⡫⡞⡵⡇⢇⢿⠖⣑⠵⡍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⡫⠑⠊⠊⢮⠗⠉⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠑⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⠀⣀⢀⠀⠀⢀⠀⠀⡀⠀⠀⢀⢀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢈⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠈⠉⠉⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⡿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣹⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⣿⢾⣿⣾⣻⣿⣿⣻⢽⢝⡳⣫⢺⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿

⣹⣻⢺⢿⢿⣹⢽⢼⣿⡮⢕⣝⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿

⢿⢿⣼⣿⣽⢽⢙⢹⠹⡳⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠻⠺⢙⠛⢿⠞⡙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿

⠀⠀⢀⢀⠀⡀⢀⠀⠀⢀⠀⠀⡀⠀⠀⢀⢀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣹⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿

⡯⢞⠖⣗⣚⠷⡩⣓⢕⣝⡎⣺⢾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿

⡽⣱⠯⣰⢩⠆⡡⠇⡆⣇⡠⡙⣺⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿

⣞⡦⢐⣍⢒⢸⢔⢩⠣⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻

⠓⠂⠈⠉⠌⡆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⢀⠀⡀⢀⠀⠀⢀⠀⠀⡀⠀⠀⢀⢀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠈⠉⠉⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠋⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣹⣻⣽⣽⣹⣿⣿⣿⣿⡟⣻⣸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠿⠁⠀⠀⠉⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⢿⡷⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿

⣿⣻⣿⣿⣿⣽⣻⣾⣽⣷⡯⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿

⣿⣿⢿⣿⣿⣿⣿⣾⣽⣿⣟⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⣛⠙⣚⢙⢛⠹⢻⣻⡿⠋⠚⢺⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢐⠅⡢⠠⠀⠀⠀⠠⠀⢀⡰⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠐⠑⢑⠔⠀⡀⠀⠀⠀⢊⠑⡄⢸⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠂⠂⠂⠀⠠⠀⠠⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⢀⠀⡀⢀⠀⠀⢀⠀⠀⡀⠀⠀⢀⢀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣭⣭⣽⣛⣻⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢿⣿⣿⣿⣿⣿⣿⣿⡝⢽⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣝⠛⢙⢬⠙⡻⢻⠻⠻⢣⠣⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠼⠸⠽⠬⡿⣸⠐⠘⢻⢠⡃⢮⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠒⠒⠒⠘⠚⠉⠬⠹⠚⠚⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠉⠉⠉⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⢟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢿⢿⢿⣿⣿⣿⡿⣿⣟⣿⣿⡿⣿⣿⣟⣟⣟⡿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⠾⣺⠿⣿⠋⢗⣵⠪⢍⡿⡺⠿⣿⢻⠙⠇⢸⠼⡸⠌⡸⡣⠬⡘⠍⡮⡏⣷⡗⡯⡇⠯⡧⡑⡭⡻⣏⡏⣯⢏⣖⠕⣈⢽⢹⢹⠵⣫⢺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡫⣷⠯⡳⠉⢶⠉⢊⢘⠹⠪⢔⠫⠺⢒⢙⣚⢀⠂⠀⠈⠈⠁⠐⠉⠌⠀⠈⠁⠅⠎⠮⠏⠏⠍⠜⠰⠁⠁⡑⣁⡈⠅⠙⠀⠀⠁⠉⠈⠁⠮⠩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣝⣪⢬⡙⢘⠝⠝⢻⠝⠋⡝⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠜⠺⠻⠨⠼⠺⢡⠣⣘⢅⣄⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠐⠒⠒⠙⠛⠥⠩⠨⠺⠓⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠉⠉⠉⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠋⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣿⣿⡻⢿⢿⢿⢿⢿⡿⡿⡿⡿⡿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣗⣟⡍⡿⡿⣏⢏⣿⢸⡲⣹⢹⣸⣻⢿⠻⠟⠅⠸⣻⢩⡪⡪⡌⡐⢘⢇⡏⡆⡵⡫⣎⢎⠍⡲⡕⡇⣟⡯⣗⡷⡗⡭⡻⣟⣿⢿⣻⢿⢿⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⠯⠞⠤⢻⠂⠑⠸⠫⠞⠸⢘⣚⢊⣚⠹⠠⠀⠀⠉⠁⠁⠁⠈⠁⠈⠔⠆⠁⠉⠈⠈⠚⠦⠂⠷⠑⠷⡁⠥⣉⠀⠐⠄⠊⠘⠈⠚⠴⠲⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣭⣭⣽⣛⣛⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢻⠻⠺⢛⣟⢙⡝⢻⠞⡱⠆⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢧⠫⠮⠥⠠⢔⣊⠋⣊⢘⣃⡝⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠒⠒⠐⠘⠒⠔⠍⠪⠋⠙⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠉⠉⠉⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣽⣿⣿⣿⠿⣻⢿⢻⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣷⣯⣟⣿⣟⡯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⣗⠈⣦⠉⡺⡠⣻⢸⢺⠨⣪⡹⣼⣿⢺⠽⡃⢸⠹⣹⣸⣫⡏⢻⣟⣟⣋⠍⡧⣻⡫⣱⠏⣯⢕⡍⣷⣿⣿⣟⡿⣻⠻⣟⢽⢿⣿⣿⢹⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠇⠯⠂⠑⠀⠊⠎⠾⠾⢙⠷⠯⠲⠾⠾⠽⠈⠆⠈⠀⠉⠀⠀⠀⠀⠁⠈⠀⠉⠈⠁⠉⠐⠁⠉⠁⠉⠊⠁⠉⡑⡙⡐⠀⠊⠊⠘⠈⠑⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣭⣭⣽⣛⣛⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢿⢿⢿⢿⣿⣻⢿⣹⣏⡹⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢻⢩⣝⢘⣝⢸⡝⡹⠺⡪⠘⣳⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠡⠪⠢⠬⢬⢗⢠⢈⣟⡢⣎⠣⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠒⠒⠀⠐⠋⠠⠅⠒⠐⠊⠑⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡯⣽⣿⣿⣿⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡿⣟⡿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣕⡍⠔⡬⡪⣲⠨⣪⢺⡰⢜⠪⠾⠿⠼⣹⠯⠃⢩⢪⢸⣫⢟⣟⣟⣻⢟⡯⡱⡕⡵⢇⡍⡯⡍⡷⡵⣿⡿⣿⣿⢟⣿⢿⢻⣹⣻⢿⣿⣻⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⡳⠢⠛⡀⠊⠐⠠⠳⠱⠣⢑⡒⡻⣐⢊⡊⠩⡂⠀⠈⠉⠀⠀⠀⠁⠀⠀⠁⠙⠮⠎⠎⠀⠉⠂⠉⠁⠋⠁⠁⡋⡈⠍⠾⠚⠞⠉⠮⠓⠈⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 1993

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/31/campinos-far-below-expectations/#comments

Gemini version at gemini://gemini.techrights.org/2021/12/31/campinos-far-below-expectations/

Gemini_version_available_♊︎

✐ 2018,_2019,_2020,_2021:_4_Years_of_António_Campinos_Failing_and_EPO_Granting

Loads_of_Invalid_Patents⠀✐

Posted in Europe, Patents at 9:19 am by Dr. Roy Schestowitz

Video_download_link | md5sum 640866be4f6461a68485cdf7ca904c88

http://techrights.org/videos/suepo-2021-report.webm

Summary: According to an internal (February 2021) publication from elected

leaders of EPO examiners, António Campinos has failed to enchant the staff and

has performed “far below expectations”

THE report below was published in February 2021 by people who had suffered the

wrath of Team Battistelli. The EPO has been largely the same under António

Campinos, who just needed to obey ILO rulings and could therefore not engage in

some of the same witch-hunts (though he continued to try to find some dirt on

Elizabeth Hardon, based on the text below).

“Well, the rule of law was abandoned a long time ago and we have a couple more

installments about mis-governance and mismanagement of the EPO.”The growing

issue of European_software_patents (disguised as “Hey Hi” and other buzzwords)

is made apparent by the part which speaks of patent “quality issues with 1 out

of 4 grants not being compliant”. The law/litigation firms profit from these

and these patent maximalists want to impose this non-compliance on courts too,

using the UPC. Incidentally, Miquel Montañá (Clifford Chance) pretends

everything_will_be_OK as “EPO will be responsible for granting the forthcoming

European patents with unitary effect,” (not really, this makes the false

assumption that UPC is inevitable and impending) and that “it is only natural

to wonder whether, in view of this responsibility and the fact that these

patents will be scrutinized by the Unified Patent Court, the organs of the

European Patent Organisation will go the extra mile to ensure the utmost

respect for the rule of law.”

Well, the rule of law was abandoned a long time ago and we have a couple more

installments about mis-governance and mismanagement of the EPO. There’s lots

more (in terms of examples) in the publication below, which I’ve commented on

in the video above.

 01 February 2021

 su21002mp – 0.2.1

 § SUEPO Chairman’s report 2019 – 2020⠀➾

 The SUEPO Munich committee election for the period 2019-2020 took

 place in November/December 2018. The Election results were announced

 on 19 December 2018, and the committee constituted on 14 January

 2019. Presently the committee is composed of seven members and two

 deputy members. A much needed and welcomed improvement for the SUEPO

 committee, since the previous committee was only composed of three

 members (Malika Weaver, Tom De Backer and Ion Brumme).

 Operational

 In January 2019 the office mandated Willis Towers Watson to perform

 an office-wide “Staff Engagement Survey” (the first since 2011). In a

 publication to staff on 30 January 2019, the Munich SUEPO committee

 encouraged EPO staff members to take part in the survey and to voice

 their opinion “unhindered and without fear of reprisals”.

 Indeed, the survey showed, as expected, a particularly deep mistrust

 in higher management of the Office. Over 85% of staff members

 answered the survey and thousands of free-text comments were added.

 Despite the fact that the President wants everyone to know that he

 considers transparency to be of paramount importance, he never

 allowed these comments to be published (not even in anonymized form).

 In February 2019 an audit of IT infrastructure at the EPO, performed

 by the Boston Consulting Group, painted a very negative picture. This

 was in stark contrast to the IT Roadmap Final Report, made under the

 Battistelli administration just 6 months previously. This latter

 report mentioned that the EPO had “state of the art” IT

 infrastructure and that after 8 years of work 90% of the IT programs

 were almost finished. The new audit, however, criticized that the

 lauded IT programs were in fact 90% not future-ready, meaning that

 the 223 million euro invested in the EPO IT infrastructure under

 Battistelli had been completely wasted.

 A few months later, and without questioning the loss of 223 million

 euro, the Administrative Council (AC) decided that an even greater

 budget of 300 million euro would bring the IT infrastructure back on

 track. This new investment and the introduction of new staff in the

 IT area, now known as BIT and led by the new VP4, Nellie Simon,

 showed its value during the 2020 Covid-19 pandemic. More on this

 later.

 Nine months after Mr. Campinos’ inauguration, SUEPO published a paper

 revealing all the urgent issues which Mr. Campinos failed to deal

 with in this time (unchanged production pressure, quality issues with

 1 out of 4 grants not being compliant, no improvement in social

 dialogue, 26 million euro wasted for renting a building in Haar for

 the Boards of Appeal when half of BT8 has been kept empty for years,

 etc.).

 In June 2019, following a very disappointing meeting on 16 May 2019

 when it became abundantly clear that the President had no intention

 in making any progress with union issues, SUEPO informed the

 President that it would call for a strike.

 For his first year in office SUEPO reviewed the President’s

 performance as “far below expectations”.

 In October 2019 EPO General Assemblies (GA) were held in all places

 of employment to inform staff of the bias in the freshly-published

 Financial Study which had been mandated by the President and carried

 out by Mercer and Oliver Wyman.

 SUEPO published a four-part publication entitled “Financial Study –

 Yet Another Hoax”. The Financial Study was indeed so severely flawed

 that it became obvious to all EPO staff that it was merely a pretext

 for further cuts in the employment package, including pay.

 A demonstration, the first to be held during Mr. Campinos’

 presidency, took place on 23 October 2019 in front of the Isar

 building and at the same time as an Administrative Council meeting.

 In November 2019, EPO management presented staff with 17 measures,

 aimed at covering an alleged financial gap of 3.8 billion euro. The

 President, of his own volition and without providing any evidence,

 demanded another 2 billion euro from staff as a so-called financial

 buffer. It is obvious that this Financial Study cannot be taken

 seriously. Not even the Administration trusted the outcome, which is

 why a more than 50% (2 billion euro) buffer was added to take any

 error into account. It is quite interesting that for other EPO-

 financed projects within the Office the financial margin of error is

 always assumed to be in lower single digits. However, when staff must

 pay, the outcome is so detached from reality that the President finds

 a 50% error buffer necessary.

 It was abundantly clear that EPO staff was going to be the only

 stakeholder paying for the alleged financial gap. SUEPO therefore

 informed the President that it would organize a strike ballot to see

 how high the support for a strike would be. Participation was high,

 with thousands of staff members voting across all places of

 employment and with a massive 84% of votes in favour of a strike.

 2019 ended in turmoil, with a General Assembly on 11 December 2019

 and a resolution demanding that the President conduct a new

 independent assessment of the EPO financial situation.

 2020 started in the same way that 2019 ended – with the EPO in total

 disarray.

 Despite numerous interventions, suggestions, proposals, and

 explanations by Staff Representatives in the Working Group concerned

 with the new Salary Adjustment Procedure (SAP), Elodie Bergot (PD4.3)

 forced a new and faulty SAP through the AC without the support of

 either Staff Representation or staff members.

 Meanwhile, SUEPO Munich developed an online salary simulator where

 every staff member could calculate the detrimental effect this new

 SAP would have on his/her salary for the years to come. The salary

 simulator provided an exceptionally good visual aid to clearly see

 the loss of purchasing power which every one of us will have to

 endure in the coming years and for the rest of our active and retired

 lives.

 Since the Office was not inclined to carry out a real independent

 financial study, SUEPO took over this task.

 In May 2020, SUEPO subsequently published the analysis of Ernst &

 Young, in the form of a new independent Financial Study. The Office

 was stunned to see that one of the big four consultant companies had

 confirmed the position expressed by SUEPO and by the Pensioners

 Association. During the next Administrative Council meeting the

 President threatened to open an investigation into the ethical policy

 of Ernst & Young, wondering how the authors of a Financial Study

 could have possibly complied with it. Of course, nothing happened

 because the President has no jurisdiction over other companies.

 Furthermore, all ethical and conflict-of-interest aspects had been

 properly assessed and considered at the time the Financial Study had

 been carried out.

 In their report, Ernst & Young identified a series of ‘conservative’

 (read totally wrong) assumptions made by Mercer and Oliver Wyman.

 Ernst & Young identified further technical mistakes, such as non-

 compliance with the general principles of discounting financial

 positions, as stipulated by the IDW (Institute der

 Wirtschaftsprüfer).

 The 2019 Financial study by Mercer and Oliver Wyman can only be

 viewed as excessively overcautious. It also reflects the clearly

 malicious intention of the EPO Administration to find an artificial

 financial gap for the sole purpose of degrading the conditions of

 staff. SUEPO will support its members in their legal battle against

 this unjust and unilateral cut in EPO staff’s purchasing power. The

 ILOAT will not be happy to see the number of EPO complaints rise

 again, but the Administration has left the staff with no other

 choice.

 A link to the entire Ernst & Young Financial Study with more

 explanations can be found on the SUEPO Munich and SUEPO Central

 webpages.

 In April 2020 SUEPO helped coordinate the filling of a Request for

 Management Review against the reduced possibility of contributing

 towards the Salary Savings Plan (SSP). This possibility had been

 promised to young colleagues when they entered the EPO. It should be

 noted that the injection of cash into the SSP has been 16 times

 higher for Senior Management than for staff members in lower grades.

 Following the disastrous implementation of the SAP, SUEPO and Staff

 Representation called an online General Assembly (GA) to discuss next

 steps. The GA was attended by over 1300 staff in Munich, the highest

 ever GA attendance. The outcome was that staff mandated SUEPO to

 draft a petition demanding renegotiation of the SAP and also mandated

 SUEPO to call for a strike. A strike took place on 15 December 2020

 to coincide with the last Administrative Council meeting of 2020.

 Thousands of staff have also signed the petition – the closing date

 was 31 January 2021.

 During December 2020, staff representation in cooperation with SUEPO

 initiated a so-called floor meeting action. Seven virtual meetings

 were held in Munich, with hundreds of staff attending every meeting.

 This information campaign had the additional effect that staff

 rallied in great numbers in support of striking. 1448 staff members

 went on strike. It was the highest number of staff members that had

 taken part in industrial action since 2016 and a clear signal to the

 President that there cannot be social peace in the EPO if staff is

 not heard.

 As such, the year 2020 ended as it started – in total disarray. Not a

 pretty picture for a President who likes to boost about his

 negotiation skills, his transparency and his fairness to all (“nobody

 should be left behind”).

 Political_cases

 In July 2018 the EPO was found guilty by the ILOAT in interfering in

 SUEPO affairs and for unlawfully dismissing its Chair, Elizabeth

 Hardon. Not only was the decision to dismiss her set aside but the

 EPO was also ordered to pay her moral damages. One would think that a

 new President would be keen to distance himself from the managers

 responsible for this abuse, and to close the worst chapter in the 40

 years’ history of the EPO. We were thus surprised when instead of

 swiftly complying with the judgement (Judgement 4047) the office

 thought it would be better to only partly follow it and instead

 initiate yet another disciplinary action against Ms. Hardon (the

 third one) trying to still somehow find her guilty of something.

 It took the Office more than a year to finally come to its senses and

 settle the case. In November 2019, more than 4 years after she had

 been unlawfully dismissed because of her job in Staff Representation

 and as SUEPO Chair, the EPO finally found a way to settle with Ms.

 Hardon, fearing, of course, another embarrassment in front of the

 Tribunal.

 In July 2020, the Office also reached a settlement with yet another

 high ranking SUEPO official, Laurent Prunier from The Hague. His

 ordeal, being unlawfully dismissed for being a Staff Representative

 and Vice Chair of SUEPO The Hague, also lasted more than four years.

 We are very happy for both of them that they can finally put this

 nightmare behind them.

 Nevertheless, there are still two unresolved cases: Aurelien Petiaud

 (MU) and Michael Lund (TH). Both have been unfairly prosecuted and

 downgraded just for having done their jobs as Staff Representatives

 nominated in the Appeals Committee. The President has no interest in

 settling these cases. We will continue to support them in the pursuit

 of justice because they have been unfairly punished and unjustly

 downgraded.

 All of the above are not ‘one off cases’ but have resulted from a

 coordinated campaign of Union bashing, championed by Ms. Bergot as

 head of the Human Resources (HR) department (P.D. 4.3) and with the

 full support and knowledge of both the previous and present

 Presidents. The Employment Law department, working directly under the

 supervision of Ms. Bergot, prides itself as being bold in pushing the

 interpretation of the law to the extreme, irrespective of the damage

 done to staff. For instance, Mr. Laurent Germond, head of the

 Employment Law department, wrote in the report on ILOAT judgements

 published in the EPO intranet on 09.07.2018 that ‘the EPO was aware

 that it is highly sensitive to impose such disciplinary measures’

 against staff representatives and Union representatives or against

 persons appointed by these bodies. Nevertheless, the Office decided

 to try it anyway just to see how far it can go. It is appalling that

 the Employment Law department is more focused on trying to push

 extreme legal interpretations to favor the wish of a manager rather

 than protecting its staff from harm. The mantra in the Employment Law

 department seems to be that as long as the ILOAT does not impose a

 judgement one way or another, every interpretation of the Service

 Regulations favouring the Office is fair play. Arguing in favour of

 common sense and applying the law as it was meant to be is pointless

 when confronted with EPO lawyers supporting this vision.

 Throughout all this ordeal and at an immense cost to the Office, not

 only financially but also reputationally, the person responsible for

 attacking SUEPO officials remains in office and unsanctioned. This

 shows that incompetence and nepotism thrives at the EPO, at least at

 higher levels. As long as you are the President’s friend you can

 abuse anyone in the Office with impunity. We still hope that when

 leaving his post this President won’t leave behind a similar legacy

 to that of his predecessor.

 Final_words

 To make matters worse, the Covid-19 pandemic has caused unforeseen

 additional problems to add to our already-brimming basket of EPO

 political and social problems. However, following their initial shock

 at working mostly from home using different methods, staff members

 have shown tremendous flexibility in quickly adjusting to their new

 environment. Presently, they appear to be able to do their jobs

 relatively well with no notable production drop and the 300 million

 euro investment in the new IT infrastructure seems to have been money

 well spent. For this, praise should be given to the hard-working BIT

 staff in DG4 as well as to Nellie Simon, the present VP4. We thank

 her for her leading role in the IT area. That said, we wish she would

 pay just as much attention to the HR area, which she is also

 responsible for.

 SUEPO had great hopes that with a new President social dialogue at

 the EPO would improve. However, after two-and-a-half years “Social

 Dialogue” is still an empty phrase. This is not surprising, since the

 same managers are in charge of social dialogue now as were during the

 Battistelli era. As such, a quote usually attributed to Albert

 Einstein comes to mind: “Insanity is doing the same thing over and

 over again and expecting different results.” So, it is not surprising

 that until these managers are removed no substantial advance in

 social dialogue nor an improvement in trust of management will be

 seen.

 Nellie Simon once wondered aloud what it would take for staff members

 to change their views, become more optimistic, and start to trust

 senior management again. Well, Ms. Simon, if the thousands of free-

 text comments left in the Staff Survey did not spell out the problem

 clearly enough then the previous paragraph surely will.

 Malika Weaver

 Chairman SUEPO Munich (2019)

 Ion Brumme

 Chairman SUEPO Munich (2020)

Happy new year, EPO staff. █

                ䷩ 𝚕𝚒𝚗𝚎 2395

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Posted in Europe, Patents at 9:43 am by Dr. Roy Schestowitz

A deep_gap in understanding

             🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Antonio-Campinos-cartoon⦈_

Summary: “I appreciate that for some of you, things may not be changing as

quickly as you would like,” António_Campinos_said, but 2022 will_be_his_fifth

year_in_the_Office (he was parachuted into the Office as President despite a

lack of experience or an understanding of this institution) and like Biden

relies on being “not Trump” (while dragging his heels) Campinos still relies on

being “not Battistelli” and the Administrative Council hopes to buy time while

many valuable workers leave the Office, causing a talent crisis — the subject

of an impending Techrights post

⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠿⢿⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣴⣾⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⡟⠈⠀⠁⠀⠀⠀⠀⡀⣠⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡦⠀⠀⠀⠠⠀⠀⠀⣸⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣉⠀⠀⠒⠐⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠛⣿⣿⠁⠀⠀⠀⠀⠀⣰⠿⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠛⠿⢿⢷⢶⠲⠛⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣛⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢰⣆⣶⢠⡄⣶⢫⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⣰⢠⢀⡀⢌⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[18A⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣦⣤⣤⣦⢄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣮⡴⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣴⣾⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠠⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠁⢹⡏⠀⠀⠁⠀⠀⠀⡀⠠⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣉⠀⠀⠒⠐⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⡐⠛⠉⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠉⠛⠿⠿⣷⠶⠶⠛⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣛⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢰⣆⣶⢠⡤⣶⢫⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣿⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⣀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣷⣠⠀⠀⠀⠁⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠉⢹⡟⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡦⠀⠀⠀⠀⠄⠀⠀⣸⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡏⠁⠀⠒⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠙⣿⣿⠁⠀⠀⠀⠀⠀⣐⠟⠃⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⣀⣠⡴⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠉⠿⠿⠿⣿⠶⠚⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣙⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⣰⢠⢀⡀⢌⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣿⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⠄⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣧⡠⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣤⣴⣾⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠠⠩⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠟⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠁⢹⡟⠈⠀⠐⠀⠀⠀⠀⡀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⢹⣿⣿⡁⠀⠀⠀⠀⠀⣰⠛⠉⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣟⠷⢶⡶⡶⠆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠁⠛⠿⠿⢷⠶⠾⠛⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢰⣆⣶⢠⡄⣶⢫⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⡰⢠⢀⡀⢌⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢿⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⢄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⣴⠀⠀⠀⠀⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠈⢹⡟⠀⠀⠁⠀⠀⠀⠀⡀⣠⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢹⣿⣿⠉⠀⠀⠀⠀⠀⠰⠿⠃⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣍⠛⠶⠲⠞⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠻⠿⠿⣷⠶⠞⠟⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣟⣛⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[18A⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣿⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢿⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠿⣿⣿⣿⠿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠁⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣏⣉⡀⠀⠀⠀⠀⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠹⢿⣿⠁⠀⠀⠀⠀⠀⣠⠛⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠛⠛⠛⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠉⠹⠿⠿⣷⠶⠞⠛⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣟⡙⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢰⣆⣶⢠⡄⣶⢪⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⣄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⣴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⡟⠈⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⣸⣾⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣏⣉⡀⠀⠀⠀⣀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⣠⠛⠉⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠛⠛⠛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠁⠛⠿⠿⣷⠶⠾⠛⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣙⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡶⢰⣆⣶⢠⡤⣶⢪⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣿⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⣤⣤⣄⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠉⠀⢹⣟⠈⠀⠐⠀⠀⠀⠀⠀⣠⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣍⣉⡀⢀⣀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠙⠿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠛⠿⠿⢷⠶⠞⠛⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠑⢆⠚⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣙⠛⠇⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢰⣆⣶⢠⡤⣶⢪⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣤⣦⣤⣤⣦⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⡟⠀⠀⠁⠀⠀⠀⠀⡀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣭⣉⡁⣀⣀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠛⢿⣿⡁⠀⠀⠀⠀⠀⢐⡿⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠙⠿⢿⢷⠶⠶⠟⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢿⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣙⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢰⣆⣶⢠⣄⣶⢫⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[18A⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣆⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⡾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠉⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣭⣉⡁⣀⣀⡀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠹⢿⣿⡁⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠻⠿⠿⠿⢶⠾⠛⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢿⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣙⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣦⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⣿⣿⣿⠿⠿⢿⣿⣦⣴⠀⠀⠀⠈⠉⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠉⠉⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣾⠇⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣤⣉⡁⣀⣀⡀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠻⢿⣿⠁⠀⠀⠀⠀⠀⠐⠟⠁⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠛⠿⠿⣷⢶⠞⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢿⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣟⡛⠛⠧⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣆⢄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡠⠀⠀⠀⠈⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠉⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣤⣉⡁⣀⣀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠛⢿⣿⡁⠀⠀⠀⠀⠀⣐⠛⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠻⠿⢿⢿⠶⠞⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢿⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣛⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[18A⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠝⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣿⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣦⣤⣤⣦⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠈⠁⢹⣟⠀⠀⠅⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡤⠀⠀⠀⠀⠄⠀⠀⣺⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣤⣀⠀⣂⣐⣂⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠛⣿⡿⠁⠀⠀⠀⠀⠀⠐⠟⠍⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠛⠿⢿⢿⠶⠾⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢷⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⢄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⢿⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠈⠉⠀⢹⣟⠈⠀⠐⠀⠀⠀⢀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣰⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣦⣀⡀⡒⠐⢂⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠹⢿⡿⠀⠀⠀⠀⠀⠀⡠⠟⠉⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠉⠻⠿⢿⣿⢶⠞⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⡰⢠⢀⡀⢌⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠝⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⣴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⠛⠋⠉⠉⠀⠀⠉⠉⠀⢹⣟⠀⠀⠅⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⡾⠿⡧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⢠⣴⣿⣿⣿⣿⣷⣦⠐⠀⠓⠒⠂⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢙⢿⡿⠁⠀⠀⠀⠀⠀⣰⡟⠅⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠙⠿⠿⣿⠶⠖⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢿⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣤⣦⣤⣤⣦⢀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣧⡴⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣴⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠟⠛⠋⠉⠉⠀⠀⠉⠁⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣶⣆⠀⠀⠀⠠⠀⠀⠀⣸⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣄⠙⠉⠛⠛⠋⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠻⣿⣿⠁⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠉⠻⠿⠿⣿⠶⠾⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡙⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣇⣤⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣤⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠉⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣄⠙⠉⠛⠛⠋⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠻⣿⣿⡁⠀⠀⠀⠀⠀⠰⠛⠟⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣤⣤⣤⣆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠹⠿⠿⠿⠶⠾⠟⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡙⠛⠧⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣾⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡰⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠋⠉⠉⠀⠀⠈⠉⠀⢹⣿⠀⠀⠀⠀⠀⠀⢀⠀⣠⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣰⣾⠃⠀⠀⠀⢠⣴⣿⣿⣿⣿⣷⣦⡘⢉⣛⣛⣋⠈⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⢛⢿⡿⠀⠀⠀⠀⠀⠀⡐⠿⠉⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠙⠿⠿⠿⠖⠿⠟⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣟⡙⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢰⣆⣶⢠⡄⣶⢪⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣧⡰⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣤⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠋⠉⠉⠀⠀⠉⠁⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣷⣤⣴⣿⣶⣶⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠛⢿⡿⠀⠀⠀⠀⠀⠀⢐⠛⠉⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠙⠿⢿⣿⢖⠶⠟⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡙⠛⠇⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⠿⠿⢿⣿⣆⡤⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠈⠉⠁⢹⣟⠀⠀⠐⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣾⠃⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣷⣶⣴⣷⣶⣶⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠉⠿⣿⠁⠀⠀⠀⠀⢀⢐⠛⠃⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠙⠿⢿⢷⠒⠾⠟⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⡿⠀⠀⠄⠀⠀⠀⠀⠀⢠⣀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣶⣄⣈⣛⣛⣋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠛⠿⣿⠁⠀⠀⠀⠀⠀⢐⠛⠏⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠙⠿⠿⡿⠶⠾⠟⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⠿⠿⢿⣿⣦⣴⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣤⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣷⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠛⠋⠉⠉⠁⠀⠉⠀⠀⢹⡟⠀⠀⠁⠀⠀⠀⠀⠀⣠⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣸⣾⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣦⡀⠈⠛⠛⠋⠈⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠐⠻⠁⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠙⠿⠿⣿⠶⠾⠛⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡛⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⣰⢠⢀⡀⢌⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣾⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢿⣶⠄⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡴⠀⠀⠀⠉⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣤⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣦⡀⠈⠛⠛⠋⠈⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠻⣿⣿⡂⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠈⠛⠿⠿⣿⠶⠾⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣶⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣤⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣞⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠁⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣸⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣦⡐⠈⠛⠛⠋⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢻⢿⣿⠀⠀⠀⠀⠀⠀⣐⡛⠏⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠉⠙⠿⢿⢿⠶⠾⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣶⣰⠀⠀⠀⠉⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣤⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⡀⣠⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⢹⣿⣿⡁⠀⠀⠀⠀⠀⣠⠟⠃⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠙⠿⠿⣷⠶⠞⠛⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢋⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⡰⢠⢀⡀⢌⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣿⣼⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⣤⣤⣤⣦⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡰⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣄⣠⣮⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠁⢹⡟⠀⠀⠁⠀⠀⠀⠀⡠⣠⣀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣥⡀⣀⣛⣛⣂⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⡀⠛⠃⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠐⠹⠿⠿⢿⠶⠾⠟⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡛⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠹⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡤⠀⠀⠀⠉⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠈⠁⠀⢹⣟⠀⠀⠐⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣯⣤⡀⣾⣿⣂⣀⠤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⢻⡿⣿⣇⠀⠀⠀⠀⢀⢰⡟⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣌⠛⠛⠛⠉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠈⠙⠿⢿⡷⠶⠾⠛⠉⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠐⢶⠚⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⣰⢠⢀⡀⢌⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣾⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⢀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣧⡰⡀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣤⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⠀⠀⠀⠚⠛⠃⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⠀⠀⠀⠔⠀⠀⠀⣼⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣯⢤⡄⠐⠴⣀⡤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⢹⣿⣿⢏⠀⠀⠀⠀⢀⣰⢿⠅⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠛⠛⠋⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠉⠹⠿⢿⣿⠶⠾⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢆⠊⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡴⡀⠀⠀⠈⠉⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣟⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⠀⠀⠀⠚⠛⠃⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣯⢤⣄⠐⠔⣀⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠻⣿⣿⠏⠀⠀⠀⠀⠀⡐⠻⠁⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠛⠟⠋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠈⠹⠿⢿⣷⠶⠾⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢤⠂⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⣰⢠⢀⡀⢌⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣿⣼⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣦⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡰⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⣟⠀⠀⠁⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠚⠛⠃⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣯⣠⡀⢰⣴⢀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠛⣿⣿⢏⠀⠀⠀⠀⠀⣴⠟⠃⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡌⠛⠿⠿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠁⠿⠿⠿⣿⠶⠞⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣟⣙⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡰⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣄⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠀⠀⢹⣟⠀⠀⠐⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣏⣀⠀⣐⣐⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⢹⢿⣿⢇⠀⠀⠀⠀⠀⢘⡟⠁⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡻⢷⣿⣿⣽⠿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠹⠿⠿⢿⠶⠞⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣧⣴⠀⠀⠀⠉⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣺⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣍⡁⠀⠀⠀⢂⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠻⣿⣿⣏⠀⠀⠀⠀⢀⣨⠟⠁⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠁⠸⠿⠿⣿⠶⠞⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⢀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣙⠛⠧⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⣰⢠⢀⡀⢌⣡⣠⣔⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣿⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⣤⣦⡄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣤⣠⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣟⠀⠀⠐⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣍⠁⠀⠀⠀⢀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⢹⣿⣿⣋⠀⠀⠀⠀⠀⣨⡛⠉⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠻⠿⠿⢿⠶⠿⠟⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⢀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡛⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⣦⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣧⡤⡀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣤⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣟⠀⠀⠀⠀⠀⠀⠀⡠⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣦⠀⠀⠀⠄⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡉⠁⠀⠒⠐⠂⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠻⢿⣿⣏⠀⠀⠀⠀⢀⣘⠛⠁⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⣶⣤⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠻⠿⠿⠿⠶⠾⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡤⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣟⠀⠀⠀⠀⠀⠀⢀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡉⠀⠀⠂⠐⠂⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠻⣿⣿⣏⡁⠀⠀⠀⢀⣘⠟⠉⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣴⣶⣤⢄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠻⠿⠿⣿⠶⠿⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣷⣶⠆⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡴⡀⠀⠀⠁⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣤⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠈⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣺⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣉⠀⠀⠒⠐⠂⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠻⣿⣿⡏⠀⠀⠀⠀⢀⣼⢟⠉⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠻⠿⠿⠿⠶⠾⠟⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢉⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣛⠛⠇⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢰⣆⣶⢠⡤⣶⢪⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣦⣰⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣄⣠⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠈⠉⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⣠⠾⣿⢧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠙⣿⣿⣏⠀⠀⠀⠀⢀⣈⡻⠇⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠹⠿⠿⠿⢶⠞⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢛⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣟⡛⠛⠇⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣾⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣦⣤⣤⣦⠄⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡤⡀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣄⣤⣦⣀⣼⣿⣤⣴⣇⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⡠⣤⣀⠀⠀⠠⠾⠿⠧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣺⣿⡏⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣯⡤⢤⣄⣀⣤⡤⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⢻⣿⣿⡇⠀⠀⠀⠀⢀⣌⠟⠋⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣈⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠻⠿⠿⢿⠶⠿⠟⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢛⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣛⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣍⣀⣀⣀⣸⣿⣅⣉⣀⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣷⢿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠈⠁⠀⢹⣟⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⢠⠾⠿⢧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣯⣁⡀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢛⢿⣿⣏⡁⠀⠀⠀⢀⣸⠟⠋⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠷⠶⠟⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠻⠿⠿⣿⠶⠿⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡤⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⣈⣉⣀⣹⣿⣅⣉⣉⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⣠⡾⠿⢧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣍⡀⠀⠒⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⢙⣿⣿⣏⠀⠀⠀⠀⢀⣨⠟⠁⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣶⣶⣶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠛⠿⠿⣿⠶⠿⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣟⣙⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⢀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣅⣈⣉⣀⣸⣿⣄⣈⣁⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⣟⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⢠⠾⠿⠧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣤⡀⠀⣒⣐⣂⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⢻⣿⣿⣏⡀⠀⠀⠀⢀⡼⠟⠉⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠺⠿⠿⢷⠶⠿⠛⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⢀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡙⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⣤⣤⣦⢄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⣿⣿⣿⣿⡿⢿⣿⣦⣴⠀⠀⠀⠈⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣄⣀⣄⣀⣼⣿⣤⣤⣄⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣰⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣤⡀⢀⣒⣒⣂⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⢻⣿⣿⣏⠀⠀⠀⠀⢀⣸⡿⠃⠁⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠉⠹⠿⠿⢿⠶⠿⠟⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠐⢒⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣿⢿⣿⣿⣿⣿⡿⢿⣿⣦⡤⠀⠀⠀⠉⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣄⣀⣤⣀⣸⣿⣤⣤⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣷⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣤⡀⢀⣒⣒⣂⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢹⣿⣿⣏⠀⠀⠀⠀⢀⡸⠟⠁⠁⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠹⠿⠿⢿⠶⠾⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠐⢀⠂⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡤⠀⠀⠀⠈⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣄⣠⣦⣀⣼⣿⣤⣤⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⣠⠾⠿⢧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡉⠀⠀⠒⠐⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⢹⣿⣿⠏⠀⠀⠀⠀⢀⣸⠟⠑⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠉⠹⠿⢿⣿⠶⠾⠟⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣟⣛⠛⠇⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠹⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢿⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣦⢀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣆⡴⠀⠀⠀⠈⠉⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣤⣠⣦⣀⣼⣿⣤⣤⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠠⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣿⠀⠀⠑⠀⠀⠀⠀⡠⣤⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣰⣾⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡋⠁⠀⠒⠐⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠹⣿⣿⢉⠀⠀⠀⠀⢀⡰⠻⡉⠁⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣦⣤⣤⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠻⠿⠿⣿⠶⠿⠟⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣛⠛⠇⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡄⠀⠀⠀⠈⠉⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣠⣦⣀⣼⣿⣤⣤⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠈⠁⠀⢹⡿⠀⠀⠀⠀⠀⠀⢀⡀⣤⣀⠀⢀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣲⣿⠇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠻⣿⣿⣋⠀⠀⠀⠀⠀⣠⡛⠉⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠘⠙⠿⠿⢿⠶⠾⠟⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣙⠛⠧⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⡰⢠⢀⡀⢈⣡⣠⣔⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣬⣥⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⣦⣤⣤⣦⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣆⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣤⣠⣦⣀⣼⣿⣤⣴⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣋⢉⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⢛⣿⢿⡅⠀⠀⠀⠀⠀⣰⡿⠉⠁⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⡹⠿⠿⠏⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠘⠸⠿⠿⣿⣶⠾⠟⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢿⣶⠆⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣄⣠⣦⣀⣸⣿⣤⣴⣆⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣿⠈⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠛⣿⣿⡅⠀⠀⠀⠀⠀⣰⡟⠏⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠐⠹⠿⠿⢷⠶⠾⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⢉⠁⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢿⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡰⠀⠀⠀⠉⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣄⣠⣦⣀⣼⣿⣤⣴⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣿⠀⠀⠐⠀⠀⠀⠀⠀⣠⣀⠀⢀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣸⣾⡇⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠙⣿⣿⡁⠀⠀⠀⠀⠀⡰⡻⠛⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠀⠹⠿⠿⣷⢖⠾⠛⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⢉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡙⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢿⣶⠄⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⣤⣦⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣠⣦⣀⣼⣿⣤⣴⣆⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠉⠉⠉⠁⠀⠉⠉⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⢀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣲⣿⡇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠹⢿⣿⠁⠀⠀⠀⠀⠀⡰⡟⠋⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣶⡶⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠸⠿⠿⢷⠶⠾⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡠⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⣠⣦⣀⣼⣿⣤⣴⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣟⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠁⠀⢹⣿⠀⠀⠁⠀⠀⠀⠀⡀⣠⣀⠀⢀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣺⣿⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣏⣉⡀⠀⣈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠹⣿⢿⡁⠀⠀⠀⠀⠀⣐⠟⠋⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠛⠟⠋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠁⠹⠿⠿⢿⡖⠾⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[18A⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣦⢀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡰⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣀⣦⣀⣸⣿⣤⣴⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡾⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠁⠀⢹⡟⠀⠐⠐⠀⠀⠀⠀⠀⣤⣀⠀⢀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣋⣉⠁⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⢛⣿⣿⠀⠀⠀⠀⠀⠀⠰⡟⠃⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⠿⠿⠋⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡄⠈⠹⠿⠿⢷⠶⠞⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡙⠛⠇⠀⣴⣶⣦⣤⣸⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[18A⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣿⡷⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢷⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⣤⣤⣦⢀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣧⡴⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣤⣠⣦⣀⣼⣿⣤⣴⣆⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣷⣞⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⣟⠀⠀⠐⠀⠀⠀⠀⠀⣤⣀⠀⢀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠹⣿⣿⡁⠀⠀⠀⠀⠀⢰⠟⠃⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣄⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠈⠛⠿⠿⣿⠶⠾⠻⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢙⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⡛⠛⠇⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠹⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣦⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣇⡰⠀⠀⠀⠈⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣠⣦⣀⣼⣿⣤⣴⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠭⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠁⠀⠉⠉⠀⢹⣿⠀⠐⠖⠀⠀⠀⠀⠀⣠⣀⠀⠀⣠⣾⣿⣧⡀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣅⠀⠀⠒⠐⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠻⣿⣿⣁⠀⠀⠀⠀⠀⢠⡟⠋⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣿⣿⣿⣷⡄⠙⠹⠿⠿⢿⠶⠾⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢛⠉⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢯⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣦⣄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢽⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣶⡰⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⣄⣦⣀⣼⣿⣤⣴⣆⣠⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢿⣿⣿⡾⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠁⠀⢹⡟⠀⠰⠐⠀⠀⠀⠀⠀⢠⣀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⢴⣿⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣄⠀⠀⣒⣐⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠛⠿⣿⡀⠀⠀⠀⠀⠀⡐⠛⠃⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠉⠙⠿⠿⢷⠶⠾⠞⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢉⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣛⠛⠇⠀⣴⣶⣦⣄⣸⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⣦⣤⣤⣆⢄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⡴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣄⣠⣦⣀⣸⣿⣤⣴⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠋⠉⠉⠀⠀⠉⠁⠀⢹⡟⠀⠐⠀⠀⠀⠀⢀⠀⣤⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡦⠀⠀⠀⠀⠄⠀⠀⣼⣿⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣦⡘⠽⣿⣿⠿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠛⣿⣿⠁⠀⠀⠀⠀⠀⡠⡟⠁⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠹⠿⠿⣿⠶⠞⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢧⣶⠄⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⠄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣦⣴⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣄⣄⣦⣀⣼⣿⣤⣴⣆⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠟⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠉⠉⠀⠀⠉⠁⠀⢹⡟⠀⠐⠂⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⠾⠿⠧⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣦⠉⠉⠛⠛⠋⠈⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠙⠿⣿⡀⠀⠀⠀⠀⠀⠐⡟⠓⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣷⡀⠀⠚⠿⠿⣿⠶⠖⠟⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 3585

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/31/open-source-initiative-floundering/#comments

Gemini version at gemini://gemini.techrights.org/2021/12/31/open-source-initiative-floundering/

Gemini_version_available_♊︎

✐ Why_the_Open_Source_Initiative_Cannot_be_Saved_(It’s_Too_Heavily_Controlled

by_Monopolies)⠀✐

Posted in Deception, Free/Libre_Software, Microsoft, OSI at 2:55 pm by Dr. Roy

Schestowitz

Video_download_link | md5sum 1491d3d203261f185fc762fac719b488

http://techrights.org/videos/osi-captured-by-monopolies.webm

Summary: The Open Source Initiative (OSI) is a floundering institution whose

real budget is decreasing (Microsoft is just ‘laundering’ money through the

OSI) and it doesn’t want people — especially paying members — to understand

what’s really going on

COMMUNITIES can see that the Open Source Initiative (OSI) does not represent

them. The OSI cannot be salvaged. Throwing money at “membership” won’t help

either because members'_contributions_are_only_4%_of_the_budget. Most of the

OSI’s spending is a redirection of Microsoft to Microsoft and the OSI’s_Board

of_Directors is basically a bunch of “tech giants”, with the odd pair that is

not (still a minority/small part of the whole).

“OSI isn’t pressured to rename itself; but we need to recognise that today’s

OSI isn’t the same OSI we knew over a decade ago.”Techrights used to be an ally

and a friend of OSI; heck, management figures from the OSI used to speak to us,

send us material, and read us regularly. But today’s OSI is an entirely

different institution, mostly riding the reputation of its past self (as the

Southern_Poverty_Law_Center_does). We need to move on and focus on more

legitimate institutions, not misleadingly named. Incidentally, the FSFE, which

also tries to censor Techrights (but_fails) is_in_violation_of_its_agreement

with_the_FSF_and_it_needs_to_rename. OSI isn’t pressured to rename itself; but

we need to recognise that today’s OSI isn’t the same OSI we knew over a decade

ago. █

                ䷩ 𝚕𝚒𝚗𝚎 3640

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/31/welcome-2022/#comments

Gemini version at gemini://gemini.techrights.org/2021/12/31/welcome-2022/

Gemini_version_available_♊︎

✐ 2022,_Our_Sixteenth_Year⠀✐

Posted in Site_News at 4:17 am by Dr. Roy Schestowitz

                 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Happy new year!⦈

Summary: Greetings in advance, as in some parts of the world 2022 is only_6

hours_away (Japan) or 3_hours_away (New Zealand)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⣆⣰⣿⣯⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣾⡄⣿⢰⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⣰⣶⣦⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢻⣷⡀⢰⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⡀⠀⣦⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⣠⣴⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣿⣿⡏⠁⣾⣷⣾⣷⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⡀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⡿⣿⡇⢰⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⢸⣿⣿⣿⠈⢹⣿⣿⡛⢿⣿⡇⢸⣿⡟⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⢛⣛⣫⡭⢿⡟⢀⡇⠀⠈⠛⠛⠉⠈⠀

⠰⢶⣶⣶⣤⣄⣀⣀⠀⠀⣿⣿⣿⣷⣿⠃⠈⣿⣿⣿⡿⠀⣀⣀⠄⠀⠺⣿⣿⣿⣿⣾⣿⠀⣿⣿⣿⠀⢨⣿⣿⡇⢸⣿⣷⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣑⢸⣷⣿⢻⣤⣤⣤⣶⣶⡔⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣻⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣧⡤⢸⢻⣿⣿⣿⣿⢹⣿⠀⢺⣿⣿⠀⣼⣿⣿⣷⣼⣿⣿⡄⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭⣽⣷⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣆

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣠⣾⣿⣿⣿⠋⠸⢿⢲⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣼⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠋

⠀⠀⠀⠘⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⢷⣶⣿⣿⣿⡷⢬⣿⣿⣿⣿⣠⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠸⣿⣿⣿⣿⣦⠀⠀⢸⣿⣿⣿⣧⣸⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣾⠳⣤⣾⣿⣊⠈⢻⢹⣿⡏⠏⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣏⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣟⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⡝⣧⣟⠻⣿⣯⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣶⣾⣿⣿⣿⣿⣿⣿⣿⠾⠷⠶⠷⠶⢦⡶⢾⣰⣾⠶⡶⠷⠰⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⢿⣿⡄⠀⠀⠀⠀⠀⠸⡇⠀⠿⡿⣯⡏⠀⣼⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠂⠰⣶⠀⠲⠄⠠⠠⠖⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⡿⠻⣿⠂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣼⣿⣿⣿⠃⣻⣿⣿⣆⠘⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣾⡇⣿⢰⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⣰⣶⣦⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣷⡀⢰⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⣀⠀⣦⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⣠⣶⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡏⠁⣾⣷⣾⣷⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⡀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⡿⣿⡇⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⢸⣿⣿⣿⠈⢹⣿⣿⡛⢿⣿⡇⢸⣿⡗⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⣛⣛⣯⡭⢿⡟⢀⡇⠀⠘⠛⠛⠉⠈⠀

⠰⢶⣶⣶⣤⣤⣀⣀⠀⠀⣿⣿⣿⣷⣿⠇⠈⣿⣿⣿⡿⠀⣀⡀⠄⠀⠺⣿⣿⣿⣿⣾⣿⠀⢿⣿⣿⠀⢀⣿⣿⡇⢸⣿⣷⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣷⣿⢷⣤⣤⣤⣶⣶⡔⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣦⡤⢸⢻⣿⣟⣿⣿⢹⣿⠀⢹⣿⣿⠀⣼⣿⣿⣷⣼⣿⣿⡄⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭⣽⣶⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣦

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣠⣾⣿⣿⣿⠋⠸⢿⢲⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣾⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣵⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠘⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⢶⣶⣿⣿⣿⡷⢬⣿⣿⣿⣿⣠⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢰⣿⣿⣿⠸⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣧⢸⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣾⠳⣤⣾⣿⣊⠈⢻⢹⣿⡟⠻⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣏⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣟⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⡝⣧⣟⠻⣿⣧⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡶⣾⣿⣿⣿⣿⣿⣿⣿⠾⠷⠶⠷⠶⡦⡶⢾⣰⣾⠶⡶⠷⠰⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⣿⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠿⡟⣯⡇⠀⣼⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠲⣶⠀⠰⠄⠠⠰⠶⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⣿⠻⣿⠂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣼⣿⣿⣿⠋⣹⣿⣿⣆⠘⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⢂⣰⣿⣯⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣴⡆⣿⢰⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⣰⣶⣢⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣷⡀⢰⡅⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⡀⠀⣦⡄⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⣠⣶⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣽⡏⠁⣾⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⡀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡿⣿⡇⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣿⢻⣿⣿⣿⠈⢹⣿⣿⡛⢿⣿⡇⢸⣿⡿⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⣛⣛⣯⢭⢿⡟⢀⡇⠀⠈⠛⠛⠉⠈⠀

⠰⢶⣶⣶⣤⣤⣀⣀⠀⠀⣿⣿⣿⣷⣿⠃⠈⣿⣿⣿⡯⠀⢀⠠⠄⠀⠺⣿⣿⣿⣿⣾⣿⠀⢻⣿⣿⠀⢨⣿⣿⡇⢸⣿⣿⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⢸⣷⣿⢿⣤⣤⣤⣶⣶⡐⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣿⣿⣿⣠⣼⣿⣿⣿⣿⣿⣿⣧⡀⢸⣻⣿⣿⣿⣿⢹⣿⠀⢸⣿⣿⠀⣼⣿⣿⣷⣼⣿⣿⡀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭⣼⣶⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣆

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣿⣿⣿⣿⠃⢸⢻⢲⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣵⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠘⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⢴⣶⣿⣿⣿⡟⠻⠿⣿⣿⡟⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠸⣿⣿⣿⣿⣦⠀⠀⢸⣽⣿⢿⣧⣸⣿⣯⡟⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣾⠒⣤⣾⣿⡀⠈⢻⢹⣿⡇⠥⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣇⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣟⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣟⡝⣧⣟⠻⣿⣯⡿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡶⣾⣿⣿⣿⣿⣿⣿⣿⠾⠷⠶⠷⠲⠦⣶⢾⣰⣾⠶⡶⠷⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠨⡇⠀⠿⡿⡿⡯⣼⣿⣿⣿⣿⣿⣧⡘⢻⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠰⠶⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⡿⠛⣿⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⢸⣿⣿⣷⠀⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣾⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⢆⣰⣿⣯⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣶⡄⣿⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⣿⣿⣿⡀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⣰⣶⣦⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣷⡀⢸⡅⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⡀⠀⣤⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⣠⣶⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡏⠁⣾⣗⣾⣷⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⡿⣿⡇⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⢸⣿⢸⣿⣿⣿⠈⢹⣿⣿⡋⢿⡿⡏⢸⣿⡿⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⢛⣛⣫⡭⢿⡟⢀⡇⠀⠈⠛⠟⠋⠈⠀

⠀⢶⣶⣶⣤⣤⣀⣀⠀⠀⣿⣿⣾⣷⣿⠃⠈⣿⣿⣿⡯⠀⢀⡠⠄⠀⢻⣿⣿⣿⣿⣾⣿⠀⢻⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣷⣿⢳⣤⣤⣤⣶⣶⡔⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣤⡄⢸⣻⣿⣿⣿⣯⢸⣿⠀⢸⣿⣿⠀⣼⣿⣿⣷⣸⣿⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣯⣭⣽⣷⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣆

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣠⣿⣯⣿⡿⠁⢸⠻⢲⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣵⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠘⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⣷⣶⣿⣿⣿⠏⠀⠿⣿⣿⡟⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠘⣿⣿⣿⣿⣦⠀⠀⢸⣿⣿⢿⣧⣸⣿⣏⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣾⠒⣤⣾⣿⡀⠈⢻⢹⣿⡇⠠⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣏⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣛⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣟⡝⣧⣟⠻⣿⣯⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣟⣿⣭⣿⣧⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡶⣾⣿⣿⣿⣿⣿⣿⣿⠾⠷⠶⠷⠶⢦⣶⢾⣰⣾⢶⡶⢷⣿⣿⣿⣿⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⢿⣿⡄⠀⠀⠀⠀⠀⠸⠇⠀⠿⡿⢿⣅⣾⣿⣿⣿⣿⣿⣎⠙⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⡿⠛⣿⠂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠏⣿⣿⣿⣆⠘⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⢂⣰⣿⣯⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣾⡆⣿⢰⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⣰⣶⣦⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣷⡀⢠⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⣦⣼⣧⡀⠀⣦⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⣠⣶⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡏⠁⣾⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠼⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⡀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⡿⣿⡇⢰⣾⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⣄⡀⡀⢸⣿⣿⣿⣿⣿⠈⠹⣿⣿⠋⢿⣿⡇⢸⣿⡟⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⢛⣛⣫⢭⣿⡟⢀⡇⠀⠈⠛⠛⠉⠈⠀

⠰⠶⣶⣶⣤⣄⣀⣀⠀⠀⣿⣿⣿⣷⣿⠇⠈⣿⣿⣿⡿⠀⢀⠀⠄⠐⢿⣿⣿⣿⣗⢸⣿⠀⢿⣿⣿⠀⢠⣿⣿⡇⢸⣿⣿⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣷⣿⢳⣤⣤⣤⣶⣶⡔⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣿⣿⣿⣠⣼⣿⣿⣿⣿⣿⢏⣀⠀⠀⣿⣿⣿⣿⣷⢼⣿⠀⢺⣿⣿⠀⣼⣿⣿⣷⣼⣿⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣯⣭⣽⣶⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣦

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣸⣿⣿⣯⡟⠈⠸⠛⢲⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣼⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠙⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⢿⣶⣿⣿⣿⠟⠁⠼⣿⣿⡇⢀⠀⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠸⣿⣿⣿⣿⣦⠀⠀⢸⣽⣿⢿⣧⣸⣿⣇⢌⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣷⠐⣠⣾⣿⡀⠈⢻⣽⣿⡇⠦⡠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣏⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⡝⣧⣟⠻⣿⣯⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣭⣿⣧⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣶⣾⣿⣿⣿⣿⣿⣿⣿⠾⠷⠶⠷⠶⠦⡶⢾⣰⣶⠶⡶⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⢿⣿⡁⠀⠀⠀⠀⠀⠨⡇⠀⠿⡿⢿⣧⣿⣿⣿⣿⣿⣎⠙⣿⣿⣿⣿⣟⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠂⠲⣶⠀⠲⠄⠠⠠⠖⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⡿⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⡏⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⢆⣰⣿⣯⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣶⡆⣿⢰⣷⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣦⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢳⣷⡀⢰⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⡀⠀⣤⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣾⡏⠁⣾⡗⣾⣷⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⡟⣿⡇⢰⣾⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⢸⣿⣾⣿⣿⣿⠈⢹⣿⣿⡋⢿⣿⡇⢸⣿⡟⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⣛⣛⣫⡭⢿⡟⢀⡇⠀⠈⠛⠟⠉⠈⠀

⠰⢶⣶⣶⣤⣤⣀⣀⠀⠀⣿⣿⣿⣷⣿⠃⠈⣿⣿⣿⡯⠀⢀⡀⠀⠘⣿⣿⣿⣷⡇⢸⣿⠀⣿⣿⣿⠀⢸⣿⣿⡇⢹⣿⣿⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡈⢸⣷⣿⢿⣤⣤⣤⣶⣶⡔⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣿⣿⣿⣠⣼⣿⣿⣿⣷⣿⢏⣀⠀⠀⣿⣿⣿⣿⣷⣼⣿⠀⢸⣿⣿⠀⣼⣿⣿⣷⣸⣿⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭⣼⣶⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣆

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠃⢀⣸⣿⣫⣿⡹⠛⡜⠛⢲⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣵⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠘⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⢷⣶⣿⣿⣿⠟⠁⣼⣿⣿⡇⢀⠀⢸⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢰⣿⣿⣿⠸⣿⣿⣿⣿⣦⠀⠀⢹⣿⣿⢿⣧⢸⣿⡇⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⣠⣾⣿⠀⠈⢻⣽⣿⡯⢦⡠⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣏⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣛⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⡝⣧⣟⠻⣿⣯⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣭⣿⣧⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣶⣾⣿⣿⣿⣿⣿⡿⢿⠾⠷⠶⠷⠶⠦⡶⢾⣰⣾⢶⡶⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠈⡇⠀⠿⠿⡿⣇⣿⣿⣿⣿⣧⡉⢻⣿⣿⣿⣿⡟⠻⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⣿⠳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣷⠈⣿⣿⢻⣿⣧⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⢆⣰⣿⣯⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣴⡆⣿⠰⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣦⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣷⡀⢰⡅⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣧⣤⣼⣧⣀⠀⣤⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣶⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡏⠁⣾⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⡿⣿⡇⢠⣾⣾⣿⣿⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⢸⣿⣾⣿⣿⣿⠈⢹⣿⣿⡋⢿⣿⡇⢸⣿⡟⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⣛⣛⣫⡍⢿⡟⢀⡇⠀⠘⠛⠟⠉⠈⠀

⠠⠶⣶⣶⣤⣄⣀⣀⠀⠀⣿⣿⣿⣷⣿⠃⠈⣿⣿⣿⡯⠀⢀⠠⠀⠘⣿⣿⣿⣷⡇⢸⣿⠁⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣷⠸⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣀⢸⣷⣿⢿⣤⣤⣤⣶⣶⡔⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣿⣿⣿⣠⣼⣿⣿⣿⣿⣿⢏⣀⡄⠀⣿⣿⣿⣿⣷⣼⣿⠀⢸⣿⣿⠀⣼⣿⣿⣷⣸⣿⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣯⣭⣽⣷⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⡆

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢀⣸⣿⣁⣿⡹⠛⡌⠛⢲⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠘⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⣳⣶⣿⣿⣿⠟⠁⣼⣿⣿⡇⢀⠀⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠘⣿⣿⣿⣿⣦⠀⠀⢹⣿⣿⢿⣧⢸⣿⡇⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⣠⣾⣿⡀⠈⢻⢽⣿⡯⠮⣠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣇⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⡝⣧⣟⠻⣿⣯⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠠⠇⠀⠿⡿⠿⣇⣿⣿⣿⣿⣧⠉⢻⣿⣿⣿⣿⡟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠠⠶⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⣿⠳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣷⠈⣿⣟⢻⣿⣧⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⣆⣰⣿⣯⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣴⡄⣿⢰⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⡟⡄⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣦⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢻⣷⡀⢰⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣷⣷⣶⣿⣷⣤⣼⣧⡀⠀⣶⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣽⡏⠁⣾⣇⣾⣿⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⡀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⡿⣿⡇⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⡟⢿⣿⡇⢸⣿⡿⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⣛⣛⣫⠭⢿⡟⢁⡇⠀⠈⠛⠛⠉⠈⠀

⠠⢶⣶⣶⣤⣄⣀⣀⠀⠀⣿⣿⣿⣷⣿⠇⠈⣽⣿⣿⡯⠀⢀⣠⠀⠀⢲⣿⣿⣷⣴⣿⣿⠉⣿⣿⡇⠀⢸⣿⣿⡇⢸⣿⣷⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣁⢸⣷⣿⢳⣤⣤⣤⣶⣶⡐⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣿⣿⣿⣠⣼⣿⣿⣿⣿⣿⣿⣤⣤⠀⢸⣿⣿⣿⣿⣿⣯⠀⢹⣿⣧⠀⣼⣿⣿⣷⣼⣿⣿⡌⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣯⣭⣴⣶⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣦

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣠⣾⣟⣟⣻⠛⣿⣟⢲⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣷⣴⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣵⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠈⠃⠀⠀⠀⠀⡌⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⣳⣶⣾⣿⣿⡿⠋⢸⣿⣿⡇⣘⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠘⣿⣿⣿⣿⣧⠀⠛⢿⣿⣿⢿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⠦⣠⣾⣳⡂⠘⢻⢸⣿⡿⡿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⡝⣧⣟⠻⣿⣯⡿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣶⣾⡿⣿⣿⣿⣿⣿⣿⠾⠷⠶⠷⠲⠦⡶⢾⣰⣾⢶⣶⠷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠠⠇⠀⠿⠿⣿⣿⢰⣿⣿⣿⡟⠻⣿⣿⢻⣿⣿⣿⣿⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⣿⣿⣿⣿⡆⢻⣿⡜⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⢂⣰⣿⣿⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣴⡄⣿⢰⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡗⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⣰⣶⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢷⣷⡀⢰⡅⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⡀⠀⣶⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⣠⣶⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣿⣾⡏⠁⣾⣇⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢻⡿⣿⡇⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⠋⢿⡿⡇⢸⣿⡿⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣛⣛⣯⣭⢿⡟⢀⡇⠀⠈⠛⠟⠉⠈⠀

⠰⢶⣶⣶⣤⣤⣀⣀⠀⠀⣿⣿⣿⣷⣿⠃⠈⣿⣿⣿⡿⠀⣀⠀⠀⠀⢺⣿⣿⣷⣴⣿⡏⠉⣿⣿⡇⠀⢸⣿⣿⡇⢸⣿⣷⠘⣿⣷⠀⠘⢻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢿⣤⣤⣤⣶⣶⡔⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣿⣿⣿⣠⣼⣿⣿⣿⣿⣿⠏⡀⡄⠀⣾⣿⣿⣿⣯⣿⡇⠀⢹⣿⡇⠀⣼⣿⣿⣷⣸⣿⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭⣽⣿⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣦

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣿⣿⣟⡿⠛⣿⡗⣢⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣷⣴⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠘⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⢷⣶⣿⣿⣿⡟⠁⣼⣿⣿⡇⡉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠘⣿⣿⣿⣿⣄⠀⠛⣿⣿⡿⣿⣆⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣼⠦⣠⣿⡇⡀⠙⢿⢰⣿⣟⢿⣶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡏⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⡝⣧⣟⢻⣿⣧⡿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡶⣾⡿⣿⣿⣿⣿⣿⣷⠾⠷⠶⠷⠲⠦⡶⢾⣰⣶⣶⣶⠷⢽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠨⠇⠀⠿⠿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠍⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣿⣿⣿⣿⣿⣿⠙⣿⠀⢸⣿⣿⣧⣄⠀⠀⠀⠀⢀⠀⠀⠙⢿⣿⠁⠰⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣣⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⢂⣰⣿⣯⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣶⡄⣿⠰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡗⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣷⡀⢰⡅⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⣀⠀⣦⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⣠⣴⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣾⡏⠁⣾⣷⣾⣷⠀⠀⠀⠀⠀⠀⠀⠸⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⡿⣿⡇⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⡇⠉⠹⣿⣿⡋⢿⣿⡇⢸⣿⡗⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣛⣛⣯⣭⢿⡟⢀⡇⠀⠈⠛⠛⠉⠈⠀

⠠⢶⣶⣶⣤⣄⣀⣀⠀⠀⣿⣿⣿⣷⣿⠃⠈⣿⣿⣿⡯⠀⢀⠀⠄⠀⢺⣿⣿⣷⣴⣿⡟⠉⣿⣿⡇⠀⢸⣿⣿⡇⢸⣿⣷⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢳⣤⣤⣤⣴⣶⡐⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠗⢸⣿⣿⣻⣿⣿⣤⣼⣿⣿⣿⣿⣿⢏⣠⡄⠀⣾⣿⣿⣿⣯⣿⡇⠀⢻⣿⡇⠀⣼⣿⣿⣷⣸⣿⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭⣽⣿⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣦

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣠⣿⣿⣟⡿⠛⣿⡟⣲⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣢⣿⣿⣿⣷⣴⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠘⠁⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⣶⣶⣿⣿⣿⡟⠁⣼⣿⣿⡇⡉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠘⣿⣿⣿⣿⣄⠀⠛⣿⣿⣿⣿⣆⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣼⠦⣠⣿⡇⡈⠙⣿⢰⣿⡯⢿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣏⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⡝⣧⣟⠻⣿⣯⡿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣶⣾⣿⣿⣿⣿⣿⣿⣷⠾⠷⠶⠷⠲⢦⡶⢾⣰⣾⣶⣶⠿⣽⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⢿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠨⡇⠀⠿⠟⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡭⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣿⣿⣿⣿⣿⣿⠙⣿⠀⢈⣿⣿⣧⣄⠀⠀⠀⠀⢀⠀⠀⠙⢿⣿⠉⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣳⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⢆⣠⣿⣿⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣼⡆⣿⢰⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣢⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢻⣷⡀⢀⡅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⡀⠀⣦⡄⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣿⣽⡏⠁⣾⡷⣾⣷⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⡷⣿⡇⢠⣾⣾⣿⣿⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⠋⢿⣿⡇⢸⣿⡗⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣛⣛⣯⣍⢿⡟⢀⡇⠀⠈⠛⠛⠉⠈⠀

⠀⢶⣶⣶⣤⣤⣀⣀⠀⠀⣿⣿⣿⣷⣿⠃⠈⣿⣿⣿⡿⠀⢀⡀⠀⠀⢺⣿⣿⣿⣼⣿⡿⠙⣿⣿⡇⠀⢸⣿⣿⡇⢸⣿⣿⠸⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢷⣤⣤⣤⣶⣶⡐⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠟⢸⢿⣿⣿⣿⣿⣠⣼⣿⣿⣿⣿⣿⠏⣀⡀⠀⣾⣿⣿⣿⣯⣿⡇⠀⢻⣿⡇⠀⣼⣿⣿⣷⣼⣿⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭⣽⣿⣷⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣦

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠋⠀⣠⣿⣿⣟⡻⠛⡟⠗⣢⠀⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣷⣴⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣭⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠈⠃⠀⠀⠀⠀⡜⠀⢼⣿⣿⣿⣿⣿⠙⣿⣿⣿⢶⣶⣿⣿⣿⡟⠉⣹⣿⣿⡇⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠘⣿⣿⣿⣿⣄⠀⠛⣿⣿⣿⣿⣆⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣼⠠⣠⣿⣳⡊⠙⣿⢰⣿⡯⡿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣇⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡝⣧⣟⠻⣿⣏⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣶⣾⣿⣿⣿⣿⣿⣿⣷⠾⠷⠶⠷⠶⢦⡶⢾⣰⣶⣶⣶⣷⣵⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⠿⠿⠿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠸⠇⠀⠿⠟⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⡟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠌⢽⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠲⢶⠀⠰⠄⠠⠠⠖⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⣿⡟⢿⣿⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⣿⣿⣿⣿⣿⡟⢿⡇⢀⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠈⠻⣿⣿⠉⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣾⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⣆⣰⣿⣿⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣦⡆⣿⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣦⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣷⡀⢀⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⣀⠀⣴⡆⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⣠⣴⣶⡦

⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣽⡏⠁⣾⡧⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣼⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⡿⣿⡇⢰⣾⣽⣿⣿⠀⠀⠀⠀⠀⣀⣤⣦⣄⢀⢸⣿⣾⣿⣿⡏⠀⢹⣿⣿⠋⢿⣿⡇⢸⣿⡟⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣛⣛⣯⣭⢿⡟⢀⡇⠀⠈⠛⠛⠉⠈⠀

⠀⢶⣶⣶⣤⣤⣀⣀⠀⠀⣿⣿⣿⣷⣿⠃⠈⣿⣿⣿⡿⠀⢀⡀⠀⠀⣹⣿⣿⣿⣿⢾⣿⠉⣿⣿⣗⠀⢸⣿⣿⡇⢸⣿⣿⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢷⣤⣤⣤⣶⣶⡔⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠟⢸⢿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⠏⣀⡀⠸⣿⣿⣿⣿⢷⢾⣿⠀⠸⣿⣿⠀⣼⣿⣿⣷⣼⣿⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣭⣽⣿⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣥⣦

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠋⠀⣰⣿⣿⣿⡟⠁⡌⠙⢰⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣷⣼⡿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣭⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠘⠃⠀⠀⠀⠀⡌⠈⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⣳⣶⣿⣿⣿⠋⠉⠿⣿⣿⣇⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡿⢰⣿⣿⣿⠘⣿⣿⣿⡿⡄⠀⠀⢹⣾⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣗⠢⣠⣿⣿⣊⠈⢿⢸⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣼⣟⣿⣺⣿⣿⣿⣿⣿⣿⢻⣿⣿⣟⣿⣟⡝⣧⣟⠻⣿⣯⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠶⠿⠷⠶⠷⠶⣦⡶⢾⣰⣶⣶⣶⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢸⡇⢠⠿⠟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠰⠄⠠⠰⠖⠆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠻⡇⠢⠀⠀⠀⠀⡀⣾⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣾⠿⣿⡇⠀⢻⣿⣾⣦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣺⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⢆⣰⣿⣯⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣲⡄⣿⢰⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⢳⣷⡀⢈⡅⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⣼⣧⡀⠀⣤⡄⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣶⣶⡦

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣼⡏⠁⣾⡇⣾⣷⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣴⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣻⡟⣿⡇⢰⣾⣾⣿⣿⠀⠀⠀⠀⠀⣀⣤⣦⣄⣀⢸⣿⣾⣿⣿⣿⠀⢹⣿⣿⠋⢿⡯⡇⢸⣿⡟⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣛⣛⣯⣍⢿⡟⢀⡇⠀⠈⠛⠛⠉⠈⠀

⠠⠶⣶⣶⣤⣄⣀⣀⠀⠀⡿⣷⣻⣷⣿⠇⠈⣿⣿⣿⡯⠀⢀⣀⠀⢈⣹⣿⣿⣿⣿⢾⣿⠀⢿⣿⣿⠀⢸⣿⣿⠃⢸⣿⣷⠘⣿⣷⠀⠘⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢳⣤⣤⣤⣶⣶⡐⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠓⢸⢟⣿⣻⣿⣿⣤⣴⣿⣿⣿⣿⣿⠋⣀⠀⠸⣿⣿⣿⣿⣷⢸⣿⠀⠸⣿⣿⠀⣬⣿⣿⣷⣼⣿⣿⠀⣿⣿⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣯⣭⣽⣿⣶⣾⠿⠁⣸⡉⠁⠀⢠⣤⣤⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠋⠀⣰⣿⣿⣾⡟⠁⠜⠘⢰⠄⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣷⣼⡿⣿⣿⣟⣻⣿⣋⣽⣿⣋⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠈⠃⠀⠀⠀⠀⡜⠀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⣲⣶⣾⣿⣿⠋⠨⣿⣿⣿⣇⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠈⣿⣿⣿⡿⡆⠀⠀⢻⣿⣿⣿⣧⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣗⠢⣠⣿⣿⣞⢽⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⢀⣀⣀⡀⣀⣤⣴⣶⣶⣶⣾⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⢻⣟⣿⣛⣿⣛⡝⣯⣟⠻⣿⣏⡿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⠋⠉⠙⠛⠛⠛⠛⠛⠛⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠶⠷⠶⣶⠷⠶⣦⣷⣾⣰⣶⣶⣶⣷⣵⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⢠⣄⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⠿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠶⠄⠰⠶⠶⠆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡇⣠⠄⠀⠀⣼⣷⣿⣿⡀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣏⠀⣿⣿⣿⣮⠈⠀⠈⠻⣿⡿⠻⠉⠉⠉⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⢂⣠⣿⣯⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣤⡆⣿⠰⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⢳⣷⡀⠈⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⢟⣿⣿⣿⣷⣶⣿⣧⣤⣼⣧⡀⠀⣤⡄⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡦

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣿⣼⡏⠁⣾⡗⣾⣧⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⠀⣴⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣻⡟⣿⡇⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣀⢀⢸⣿⣾⣿⣿⣿⠀⢹⣿⣿⠉⢿⣯⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣛⣛⣯⣍⢿⡟⢀⡇⠀⠈⠛⠛⠉⠈⠀

⠠⠶⣶⣶⣤⣤⣀⣀⠀⠀⡿⣿⣺⣷⣿⡇⠘⣿⣿⣿⡧⠀⢀⠀⠀⠀⣙⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⠀⢸⣿⣿⠇⢸⣿⣷⠘⣿⣷⠀⠐⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢳⣤⣤⣤⣴⣶⡀⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠓⢸⠟⣿⣻⣿⣿⣥⣼⣿⣿⣿⣿⡿⠏⣀⡀⠐⣿⣿⣿⣽⣿⢾⣿⠀⢸⣿⣿⠀⣼⣿⣿⣷⣼⣯⣿⠀⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣯⣭⣽⣿⣶⣾⠿⠁⡸⡉⠁⠀⢠⣤⣤⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠉⠀⣠⣿⡿⣿⡿⠉⠈⠙⢲⡄⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣴⡿⣿⣿⣟⣻⣿⣋⣽⣿⣋⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠃⠀⠂⠈⠛⠛⠃

⠀⠀⠀⠈⠃⠀⠀⠀⠀⡜⠀⢼⣿⣿⣿⣿⣿⠙⣿⣿⣿⢠⣶⣿⣿⣿⠏⠀⣿⣿⣿⣇⢀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢰⣿⣿⣿⠀⣿⣿⣿⣿⣆⠀⠀⢻⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠉⠉⠉⢉⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣏⠀⣠⣿⣿⣞⣽⢿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣠⣤⣤⣤⣄⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⢻⣟⣿⣛⣿⣟⣝⣧⣟⠻⣿⣏⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣭⣿⣧⣿⣿⣱⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠛⠋⠙⠛⠻⠿⣿⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠽⠷⠶⣶⠷⠶⣦⣷⣾⣰⣶⣶⣶⣿⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⡇⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠠⢀⣠⣢⣿⣿⣹⡿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠻⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢢⠀⢶⠄⢸⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡇⢀⠀⢠⣿⣿⣿⣿⣿⣃⣤⣸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠸⣿⣟⠈⣿⣿⣿⣎⠈⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣰⠀⣼⠃⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⠂⣰⣿⣯⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⡿⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣰⣶⣤⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣿⣞⣿⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠉⣿⣿⣷⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⡀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡦

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⡇⣾⣷⠀⠀⠀⠀⠀⠀⠀⠰⣇⣤⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠁

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⣿⣿⣿⣿⣴⣿⣿⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⢸⣿⣾⣿⣿⡇⠀⢹⣿⣿⠂⢻⣿⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣟⣛⣛⣭⣍⢿⡏⢀⡇⠀⠀⠛⠉⠉⠀⠀

⠀⠤⣶⣤⣤⣄⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⢀⠀⠀⠺⣿⣿⣿⣶⠇⣾⡏⠀⢿⣿⡇⠀⢨⣿⣿⡁⢸⣿⣧⠘⣿⣷⠀⠀⢻⣿⣿⣿⣯⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢳⣀⣤⣤⢄⢲⡀⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢰⣿⣿⣿⣿⣦⣿⡇⠀⢸⣿⡇⢀⣼⣿⣿⣷⣸⣿⣿⣠⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣯⣭⣭⣿⣶⣾⠿⠁⡸⠉⠀⠀⢠⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠀⠀⣼⡿⣿⣿⡟⠋⡏⡟⣷⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣾⣿⣿⣿⣟⣻⣿⣋⣽⣿⣫⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠁⠀⠂⠀⠛⠛⠀

⠀⠀⠀⠈⠀⠀⠀⠀⠀⡜⢾⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣦⣶⣶⣿⣿⠟⢿⣿⣿⣿⡇⢈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠉⢉⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣁⠀⢀⢾⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣤⣶⣶⣶⣶⣦⣦⣶⣾⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣻⣟⣿⣟⣽⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣭⣿⣧⣾⣿⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠛⠟⠛⠛⣻⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣶⡷⣶⠶⠶⣾⣿⣾⣰⣾⣿⣿⣿⣿⣿⣿⡿⠾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢠⢀⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣿⣦⠀⢸⣿⡿⣻⣿⣿⣿⣿⣿⣿⠿⢿⠿⡿⣿⡿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣴⠀⣼⠏⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣃⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⢂⣠⣿⣧⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⡗⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣤⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣏⢉⣿⣿⣷⣷⣶⣿⣧⣤⣼⣇⡀⠀⣤⡀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡦

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⣿⣿⣿⡇⣼⣿⠀⠀⠀⠀⠀⠀⠀⠰⣇⣤⣾⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⣿⣿⣿⣿⣅⣿⣿⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⣿⡇⣾⣿⣿⡇⠀⢹⣿⣿⠀⢻⣿⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣟⣛⣛⣭⣍⢿⡏⢀⡆⠀⠀⠋⠉⠉⠀⠀

⠀⠴⣦⣤⣤⣄⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⣾⡇⣿⡇⠀⣿⣿⡇⠀⢨⣿⣿⠀⢸⣿⣧⠸⣿⣷⠀⠀⢻⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢣⣠⡤⣤⢀⡲⠀⠀

⠀⠀⠀⠀⠀⠉⠉⠉⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⢼⣿⣿⣿⣿⣧⣿⡇⠀⣿⣿⡇⢀⣼⣿⣿⣧⣸⣿⣿⣤⣿⣿⣄⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣛⣻⣿⣯⣭⣭⣶⣶⣾⠿⠁⡸⡉⠀⠀⢠⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠟⠁⠀⣿⣿⣿⣿⠋⠁⡟⡗⣷⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣾⣿⣿⣿⣟⣻⣿⣋⣹⣿⣫⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠁⠀⠂⠀⠛⠋⠀

⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣦⣶⣶⣿⡿⠿⢿⣿⣿⣿⡇⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠹⢻⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣉⢉⢉⡉⠁⢹⣿⣿⣿⣿⣿⣿⣷⣂⠀⢠⢿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣇⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣴⣶⣶⣶⣶⣦⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢻⣏⣿⣋⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣟⣿⣭⣿⣧⣿⣿⢉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠛⠟⠛⠛⢻⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣴⡶⠶⣾⣿⣾⣽⣿⣿⣿⣿⣿⡿⢷⡿⠶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣷⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢿⣿⣿⣿⣧⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣶⠀⣸⠏⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣴⢂⣰⣿⣯⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⠇⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣤⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣿⣿⣷⣷⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡦

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⣿⣿⣿⡇⣼⣷⠀⠀⠀⠀⠀⠀⠀⠰⡇⢤⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⣿⣿⣿⣿⣄⣿⣿⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⣿⡇⣿⣿⣿⠇⠀⢸⣿⣿⠀⢻⣯⡇⢸⣿⡇⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣛⣛⣛⣯⣍⢿⡏⢀⡄⠀⠀⠉⠉⠉⠀⠀

⠀⠴⢤⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣾⣿⡇⢨⣿⣿⡀⠀⢸⣿⣿⡀⢸⣿⣧⠘⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⢣⡀⠤⡄⠀⠰⠀⠀

⠀⠀⠀⠀⠀⠈⠉⠉⠓⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⡇⢀⣼⣿⣿⣧⣸⣿⣿⠀⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣭⣭⣭⣶⣶⣾⠿⠁⡸⠉⠀⠀⢀⣠⣄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⠞⠁⠀⣸⡿⣿⣿⡏⠉⠀⡗⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣿⣿⣿⣟⣻⣿⣋⣹⣿⣋⣤⣿⣯⣤⣼⣟⠁⠀⠈⠁⠁⠀⠀⠀⠛⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣷⣴⣶⣾⣿⠿⢿⣿⣿⣿⡀⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠙⢻⣿⢿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⡿⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣉⠁⢹⣿⣿⣿⣿⣿⣿⣷⡇⠀⣠⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢠⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣏⣽⣋⣿⣟⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣭⣿⣧⣿⣿⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠹⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣴⠶⢲⣾⣿⣾⣿⣿⣿⣿⣿⣿⠿⠷⠶⢶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢟⣿⣿⣿⣯⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣴⠀⣸⠏⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠂⣠⣿⣧⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡇⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣽⣿⣿⠃⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣰⣶⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⢸⣿⣿⣶⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡦

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⡇⣼⣷⠀⠀⠀⠀⠀⠀⠀⠠⠇⣤⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣄⣿⣿⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⣿⠀⣿⣿⣿⠁⠀⢸⣿⣿⠀⢻⣏⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⡟⣛⣛⣏⡍⢿⡏⢀⡄⠀⠀⠉⠉⠉⠀⠀

⠀⠤⢤⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⣿⣿⣿⣷⣿⣿⠀⢘⣿⣿⠀⠀⢸⣿⣿⠀⢸⣿⣇⢸⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⢸⣷⣿⢡⠀⠤⠄⠀⠐⠀⠀

⠀⠀⠀⠀⠀⠈⠉⠉⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠁⠀⠀⢸⣿⣿⣿⣿⣷⣿⠀⠀⣿⣿⡀⢀⣼⣿⣿⣧⣸⣿⣿⠀⣿⣿⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣭⣭⣭⡶⣶⣾⠿⠁⡘⠁⠀⠀⢀⣠⣄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡶⠖⠀⠀⣼⣿⣿⣽⠃⠁⠈⣓⣷⣾⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣋⣹⣿⣋⣤⣿⣯⣤⣼⣟⠁⠀⠈⠁⠁⠀⠀⠀⠙⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣶⣶⣶⣾⣿⠿⢷⣿⣿⣿⠀⣈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠹⢻⣿⢿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⡿⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣠⢿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣏⣽⣋⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣭⣿⣧⣿⣿⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⡶⠲⣾⣿⣾⣿⣿⣿⣿⣿⣿⠿⠶⠾⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢯⠚⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣴⠀⣸⠏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠂⢠⣿⣧⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡇⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣽⣿⣿⠂⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣠⣶⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⢸⣿⣿⣶⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡤

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⡇⣼⣷⠀⠀⠀⠀⠀⠀⠀⠠⠇⣤⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣄⣿⣿⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⣿⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⢻⣿⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡛⣛⣛⣋⡍⢿⡏⢀⡄⠀⠀⠉⠉⠉⠀⠀

⠀⠠⢤⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣷⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⣿⠀⢸⣿⣇⢸⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣷⣿⢡⠀⠠⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⠉⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠊⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢺⣿⠀⢀⣼⣿⣿⣧⣸⣿⣿⠀⣿⣿⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣭⣭⣥⡶⣶⣾⠿⠁⡘⠁⠀⠀⢀⣠⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡶⠆⠀⠀⣼⣿⢿⣷⢏⣉⠀⣛⣷⣾⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣋⣹⣿⣋⣤⣿⣯⣤⣼⣟⠁⠀⠈⠁⠁⠀⠀⠀⠙⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣦⣴⣶⣾⡿⠿⢿⣿⣿⣿⡀⣠⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣶⣦⣾⣾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠹⢻⣿⢿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⡿⢱⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣠⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣏⣽⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣭⣿⣧⣾⣿⢀⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⠶⠶⢶⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣷⣾⣿⣿⣿⡟⣸⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠚⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣴⠀⣸⠏⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠂⢠⣿⣧⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⣿⣿⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣠⣾⣿⣶⣿⣿⣷⣿⣿⣽⣷⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⣿⣷⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡤

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⡇⣼⣷⠀⠀⠀⠀⠀⠀⠀⠠⠇⠤⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣄⣿⣿⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⣿⠃⠾⣿⣿⡇⠀⢹⣿⣿⠀⢻⣯⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢛⣛⣉⡉⢿⡏⢀⡄⠀⠀⠉⠉⠉⠀⠀

⠀⠠⢤⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣾⣿⡀⠀⢹⣿⡅⠀⢨⣿⣿⠀⢸⣿⣇⠸⣿⣶⢀⣤⣻⣿⣿⣿⣯⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⣿⠄⢸⣷⣿⢠⠀⠤⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⠉⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠊⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢈⣿⡇⢀⣼⣿⣿⣷⣼⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣯⣭⣭⣥⠶⣶⣾⠿⠁⡘⠁⠀⠀⢀⣠⣀⠀

⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣆⠀⣸⡿⠟⢷⣯⣌⠀⡓⣷⣼⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣋⣠⣿⣯⣤⣼⣟⠁⠀⠈⠁⠀⠀⠀⠀⠙⠀⠀

⠀⠀⣴⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠿⢿⣿⣿⣿⡀⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠙⢻⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⡿⢱⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⡇⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣯⣭⣿⣧⣾⣿⠀⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⡶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣟⣼⣿⣟⣩⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠥⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠒⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣴⠀⣸⠋⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠂⢠⣿⣧⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣠⣾⣿⣶⣿⣿⣷⣿⣿⣽⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⣷⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡤

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⡃⣼⣷⠀⠀⠀⠀⠀⠀⠀⠠⠇⠠⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣄⣿⣿⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⣿⡇⢼⣿⣿⡇⠀⢸⣿⣿⠀⢻⣯⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢛⣛⣉⠉⢿⡏⠀⡄⠀⠀⠉⠉⠉⠀⠀

⠀⠠⠤⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣙⣿⣿⣿⣦⣿⡇⠀⢸⣿⡇⠀⢠⣿⣿⠀⢸⣿⡇⢘⣿⣂⣠⣤⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⣿⢡⠀⠠⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⠉⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣀⣀⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⡇⢀⣼⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣯⣭⣥⣤⠶⣶⣾⠿⠁⡘⠁⠀⠀⢀⣠⡀⠀

⠀⢀⣤⣦⣶⣶⣶⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⡿⠟⢣⣿⢿⣿⣿⣭⠀⠗⣷⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣠⣿⣯⣤⣼⣟⠁⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀

⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠿⣾⣿⣿⡀⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣩⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣩⣿⡇⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠀⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣟⣉⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢁⣯⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡥⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠅⠀⢊⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣤⠀⣸⠏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢤⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠂⠠⣿⣧⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠞⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣠⣾⣿⣶⣿⣿⣷⣿⣿⣽⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣿⣿⣷⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡤

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠇⣼⣷⠀⠀⠀⠀⠀⠀⠀⠠⠇⠠⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣄⣿⣿⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⣿⡇⠛⢻⣿⡇⠀⢸⣿⣿⠀⢻⣏⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡛⢛⣛⣉⠉⢿⡏⠀⡄⠀⠀⠉⠉⠉⠀⠀

⠀⠀⢤⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣷⡇⣿⡇⠀⢸⣿⡇⠀⢠⣿⣿⠀⢸⣿⡇⠘⣿⣠⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⢸⣷⡿⢠⠀⠠⠄⠀⠀⠀⠀

⠀⢀⣠⣤⣿⡯⡭⡉⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣷⣦⣤⣴⣿⣿⣿⣿⢷⣿⣀⣀⢸⣿⡇⢀⣼⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⠶⣶⣾⠿⠁⡘⠁⠀⠀⢀⣠⡀⠀

⢠⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⡟⠿⢿⡏⢉⠀⠣⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣼⣟⠁⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀

⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣾⣿⣿⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡇⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⠀⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣛⣋⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡤⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠂⠄⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠄⠀⢊⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣰⠀⣸⠏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠂⢠⣿⣧⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣠⣾⣿⣶⣿⣿⣿⣿⣿⣽⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣽⣿⣿⣶⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡤

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠇⣼⣷⠀⠀⠀⢰⣶⣾⣷⣤⣧⢸⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣄⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣯⣸⠋⣿⣿⣿⣿⠀⠀⢸⣿⣿⠀⢻⣿⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⠉⢿⡏⠀⡄⠀⠀⠉⠉⠉⠀⠀

⢀⣶⣶⣦⣤⣄⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⡿⣿⡟⠛⢻⢀⣤⣿⣿⣿⣧⣄⢰⣿⣿⡀⢸⣿⡇⢘⣿⣤⢀⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢸⣷⡿⢠⠀⠠⠄⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣉⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣼⣿⣿⣾⣿⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠿⠁⡘⠀⠀⠀⢀⣀⡀⠀

⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀

⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⣋⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢊⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⡆⠈⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣴⠀⣸⠋⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠂⣠⣿⣧⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣶⣿⡏⠀⠀⠀⠀⣶⣿⣿⣧⣴⠂⠀⣿⢀⣴⣿⣿⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣠⣶⣠⣾⣿⣶⣿⣿⣿⣿⣿⣽⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⠀⢸⣿⣿⣿⣿⣶⡄⡏⠈⠿⣿⣿⣿⣶⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣶⡤

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢸⣿⣿⣿⠇⣼⣧⠀⠀⢸⣿⠛⣹⣯⠙⣧⡇⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣴⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣄⣿⣿⠀⠀⣼⣿⡾⠟⠡⠞⠁⢀⣾⣿⣿⣿⣿⣿⣷⢸⣿⣿⠀⢹⣿⡇⢸⣿⡇⠀⠈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡄⠀⠀⠉⠉⠉⠀⠀

⠠⣶⣶⣦⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⢀⣿⣿⣧⡄⠀⠀⠀⣸⣧⢹⡟⣿⣿⣿⣿⣞⣿⣿⡀⢸⣿⡇⠘⣿⣷⣢⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢡⠀⠠⠄⠀⠀⠀⠀

⠀⢪⣯⣭⣿⣯⣍⣉⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⣸⣤⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣷⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⡸⠀⠀⠀⢀⣠⡀⠀

⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀

⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⣠⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⣰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⣿⡆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣀⠀⠀⠀⠘⣿⣿⣿⣧⣆⠀⢻⠂⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣴⠀⣸⠋⢸⣿⠀⠀⠀⠀⣿⣿⠿⠟⣿⠸⢸⠀⠀⠉⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣤⠂⢠⣿⣧⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣶⣿⡏⠀⠀⠀⠀⣿⡏⢰⣶⠇⠀⢸⡇⣀⣀⣿⣿⣿⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⢰⣿⣷⡉⠀⠀⠀⠀⣇⣿⡇⣿⢿⣿⣷⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡄⠀⠀⠀⠀⣠⣴⣶⡤

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠇⣼⣧⠀⣾⣿⣿⣿⣧⣶⣦⣀⣹⣿⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⣴⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣀⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⢸⣿⣿⠀⢹⣿⡇⢸⣿⡇⡀⠈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠉⠉⠀⠀

⠠⣶⣦⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⣿⣿⣿⣿⣷⣿⣿⡀⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣔⠂⠀⠀

⠀⢬⣯⡏⠁⠉⣩⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣧⣸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠁⠀⣀⠀⠀

⠀⣻⣿⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢸⡄⠀⠀⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣦⠀⢸⡆⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⢻⠇⠀⡇⠀⠙⠛⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣏⣴⡟⠀⠀⣷⠀⢀⡄⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⣿⣿⢻⣿⠆⠀⠀⢿⢀⣾⡟⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣀⠀⠀⢸⣿⣿⣦⣀⣴⣿⣶⣤⣾⣿⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣰⠀⣸⠋⢸⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣤⣂⣠⣿⣧⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣾⣿⡏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⢸⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣥⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣷⣶⣶⣿⣦⣤⣼⣆⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣠⣴⣶⡤

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠃⣼⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡆⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⣴⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣾⣿⣿⣿⣀⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⠀⢸⣏⡇⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⠎⠉⠉⠁⠀⠀

⠀⢴⣤⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠉⠈⠛⠛⢀⣿⣿⡀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣶⣶⣶

⠀⠀⠀⠀⠀⠉⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⢀⣼⣿⣿⣧⣸⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⢀⣶⣷⡖⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀

⠀⢘⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀

⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣧⠀⠀⠀⠀⠀⠀

⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢉⡉⠀⢰⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣥⣾⠃⠀⢸⡀⠀⢠⡀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠀⠀⠈⠁⢠⣿⣇⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⣾⣿⣶⣶⣿⣿⣿⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣰⠀⣸⠏⣸⣿⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣇⢀⣠⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⡂⣠⣿⣧⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣶⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣥⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣅⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣧⣤⣼⣇⡀⠀⣤⡀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣠⣴⣦⡤

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠃⣼⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡇⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⣴⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠸⣿⣿⠀⢸⣿⡇⢹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠀

⠀⠀⣤⣤⣤⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣿⣿⡀⢸⣿⡧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠉⠉⠉⠷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠙⠿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢀⣼⣿⣿⣧⢸⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣤⣶⣶⣂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⣿⣿⠋

⠀⠈⢛⣻⣿⣿⣿⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡟⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⠇⠀

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀

⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⡀⠀⠀⠀

⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠁⠀⠀⠀

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀

⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⣀⣬⣿⣿⣿⣥⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢻⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⡿⠋⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣰⣷⣿⣿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢰⠀⣸⠋⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣤⡂⣠⣿⣧⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣾⣿⡟⠻⣿⣧⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣧⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢱⣿⣿⣿⡇⢀⡿⠿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣠⣴⣶⣶⣾⣶⣶⣶⣾⣦⣤⣼⣇⡀⠀⣤⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣴⣦⡄

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠃⣼⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⣤⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣴⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣾⣿⣿⣿⣄⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠸⣿⣿⠀⢸⣯⡇⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢈⠉⠉⡉⠀⠀

⠀⠠⢠⣤⣄⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⠀⠀⠀⠀⢀⣿⣿⡀⢸⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦

⠀⠀⠀⠀⠀⠀⠉⠉⠓⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⢀⣼⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠁

⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⡟⠀⢠⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣆

⠀⠀⠀⠀⣀⣀⣄⢀⣀⣠⣰⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠁

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠉⠉⠁⠀

⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠀⠀

⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠸⠟⢣⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⠟⠀⠀⠀⣠⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠑⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡿⣿⣦⡸⣿⣿⣿⣿⣿⣿⣿⣏⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣀⣴⣿⣿⣧⡙⣿⣿⣿⣿⣿⣿⣿⠂⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢰⠀⣸⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⣂⣠⣿⣇⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡄⣿⣾⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣴⣶⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣅⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢱⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⠀⣴⣶⣶⣾⣶⣶⣶⣿⣦⣤⣼⣆⡀⠀⣤⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⣠⣴⣦⡄

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢸⣧⡇⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠉⠉⠁⠀⠀

⠀⠀⠤⣤⣄⣀⣀⣀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⠀⠀⠀⠀⠀⢀⣿⣿⡀⢸⣿⣇⠸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠉⠉⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⢀⣼⣿⣿⣧⢸⣿⣿⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣿⠁⠀⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠈⢻⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⣰⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⢡⢳⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠙⢻⡿⠣

⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⠃⠀

⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡶⡶⣶⣶⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣳⣿⣿⣿⠃⠙⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀

⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⡿⠀⠀⠻⠛⢣⣽⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⡿⢻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⠂⣰⣿⣿⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣧⣾⣿⣶⣿⣿⣿⣿⣿⣽⣿⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢴⣶⣶⣾⣶⣶⣶⣾⣦⣤⣼⣆⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣴⣦⡄

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣶⣿⡄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢸⡧⡇⢸⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣍⣭⣿⡏⣹⡆⠀⠀⠉⠉⠁⠀⠀

⠀⠀⠠⣤⣄⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⠀⠀⠀⠀⢀⣿⣿⡀⢸⣿⣇⠸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣄⣤⣤⣶⣶⣶⡖

⠀⠀⠀⠀⠀⠀⠉⠉⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣼⣿⣿⣧⢸⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⢋⣿⣏⠀⠀⢹⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⣾⣿⠋⠀⠛⠛⠻⠃⠀⠀⠻⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡏⣿⣿⣿⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀

⠀⠀⢀⣤⣴⣶⣶⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣧⣻⢹⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣯⣿⣿⣀⣿⣿⣿⣷⣶⣤⣿⣿⣿⣦⡄⠀⠀

⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢳⢴⢶⠦⢦⣶⠾⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⢎⣾⣿⣿⡇⠀⠛⣿⡞⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣾⣿⣿⠉⠉⣥⣬⣿⠇⠀⠀⠛⠟⢠⣼⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣴⠂⢠⣿⣇⡰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣶⣧⣾⣿⣶⣯⣿⣷⣿⣿⣽⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢴⣶⣶⣿⣶⣶⣶⣾⣦⣤⣼⣆⡀⠀⣤⠀⠀⢸⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣦⡄

⣄⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣧⣤⣴⣾⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡯⣿⣶⣿⡄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣰⣿⣿⢿⠀

⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣧⡇⢸⣿⡇⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣍⡉⢿⡏⢀⡀⠀⠀⠉⠉⠁⠀⠀

⠀⠀⠤⣤⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⢠⠀⠀⠀⠀⢠⣿⣿⡀⢸⣿⡇⠸⣿⣷⣷⣾⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⡿⠁⠀⠀⠄⠀⠐⠀⠀

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⢀⣼⣿⣿⣧⣸⣿⣯⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣭⣭⠶⣶⣾⠿⠁⡘⠀⠀⠀⢀⣄⡀⠀

⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡟⠋⠹⣿⣷⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣟⣽⣿⣯⣥⣿⣯⣤⣾⣿⠁⠀⠈⠁⠀⠀⠀⠀⠛⠁⠀

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠇⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡟⣿⣿⣿⠀⠀⠀⠀⣠⣆⣀⠀⠀⠀

⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣻⣥⣻⢻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣀⣿⣿⣿⣆⢀⠀⠈⣿⣿⣿⣷⡄⠀

⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⡶⠴⠶⢦⠦⠶⠶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣶⣿⣿⣿⣿⡁⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣷⣟⡴⠿⠿⡇⠀⠘⣹⣷⡉⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣾⣿⣿⣿⣿⣿⣿⡆

⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢱⣿⠿⠃⠀⠰⣶⠀⠁⠀⠀⠉⠠⠁⣀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⢿⣿⣿⣿⣿⣿⡇

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣤⠂⢠⣿⣇⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣦⣾⣿⣶⣿⣿⣷⣿⣿⣿⣷⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠇⠀⠀⠀⠀⢴⣶⣶⣾⣶⣶⣶⣾⣤⣤⣼⣆⡀⠀⣤⠀⠀⢸⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣦⡄

⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⢰⣇⣤⣴⣾⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣶⣿⡄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣰⣿⣿⢿⠀

⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣧⡇⢸⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⣛⣛⣭⠉⢿⡏⢀⡀⠀⠀⠉⠉⠁⠀⠀

⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⠄⠀⠀⡀⠀⠀⠀⠀⢠⣿⣿⡀⢸⣿⡇⠸⣿⣦⣶⣾⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢸⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣶⣆⡀⢀⣼⣿⣿⣧⣸⣿⣯⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣭⣭⣭⠶⣶⣾⠿⠁⡈⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⠟⠋⠻⣿⣷⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣟⣽⣿⣯⣤⣿⣯⣤⣾⣟⠁⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢠⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣭⣿⡏⣿⣿⣿⠀⠀⠀⠀⣠⡄⣀⣀⡀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣻⣥⣻⢻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣁⣿⡿⢿⡆⠀⠀⠀⠘⢛⣟⣿⡇⠀

⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡖⡶⠴⠶⣦⠦⠶⠶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣀⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⡧⢏⠴⠃⠻⡇⠀⠘⣼⣷⠉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⡄⠀⠀⣸⣿⣿⣿⣷⡀

⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠈⢁⡀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⢊⡇⠀⠀⢽⣿⣿⣿⣿⠁

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣽⣿⢩⣿⣿⣿⣯⣿⣿⣿⣿⣿⢫⣷⣾⠽⠀⢸⡇⠀⠀⣎⠀⠀⡖⠀⠀⠀⠀⠀⡆⠀⠀⠔⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⢸⣿⣿⣿⣟⣛⣻⢹⣿⡧⣿⣿⣿⣇⡀⢸⡗⠒⠒⡷⠀⠀⡇⠀⠒⠁⠀⠀⡇⠀⢸⠀⠀⠀⠐⠒⠒⠀⡇⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣻⣸⡇⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠇⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠘⣿⣿⣿⣶⣶⣿⣿⣷⣶⣶⣶⣶⣿⣿⣷⣾⣷⣾⠉⡀⠀⢀⣀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠸⠈⠀⠀⠇⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠂⢠⣿⣇⡰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣶⣦⣾⣿⣶⣿⣿⣷⣿⣿⣿⡷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢴⣶⣶⣾⣶⣶⣶⣾⣦⣤⣼⡆⡀⠀⡄⠀⠀⢸⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣦⡄

⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠇⠠⠤⠾⠿⠿⣿⣿⠿⢿⣿⣿⡿⣿⡯⡿⣶⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⣰⣿⣿⢿⠀

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢸⡇⡇⢸⣿⡇⠀⠈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⣛⣛⣍⠉⢿⡏⠀⡀⠀⠀⠉⠉⠁⠀⠀

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣿⣿⠀⢸⣿⡇⠸⣿⣄⠀⣼⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣦⣀⣀⡄⠈⢳⣦⣀⢀⣼⣿⣿⣧⢸⣿⣯⡀⣿⣿⣿⣿⡾⣷⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣭⣭⣭⠶⣶⣾⠿⠁⡐⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣥⣠⣿⣿⣿⣿⣿⣿⡿⠛⠉⠻⣿⣷⣿⣿⣿⣿⣶⡿⢻⣿⣿⣿⣿⣟⣽⣿⣯⣵⣿⣯⣤⣼⣟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠂⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡏⣿⣿⣏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣅⣙⢹⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣿⣧⣿⣿⣀⣿⡿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡖⡶⠰⠦⢦⠦⠶⠶⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⡿⠃⡀⢹⠀⠀⠀⠀⠀⠀⢾⡇⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⡇⠅⠴⠃⠛⡇⠀⠘⣸⣷⡉⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⡄⠀⠀⠀⠀⢠⣼⣇⠀

⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢹⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠈⣇⣀⠀⠀⠀⣿⣿⣿⠀

[22A⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⢀⣀⢀⢀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣼⣿⣿⣿⣿⣿⣶⣶⣶⣾⣾⣿⣿⣦⣶⣶⣄⡀⣀⣄⣞⣹⣿⣏⣃⣥⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣿⡏⣉⡇⣽⣯⣿⣿⣿⣿⣿⣯⣭⣭⣻⢀⣹⡏⣥⣬⣿⠋⣼⣿⢩⣽⣿⣿⣿⣿⣯⣿⣿⢫⣽⣿⣿⢸⣷⣿⢡⣾⣾⣿⢰⢏⣭⣿⠠⢴⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣾⣿⡗⣛⣛⣿⠈⣿⣿⢼⣿⣛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣿⢚⣛⣛⣿⢸⣻⣤⣿⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠾⠷⠿⠿⠿⢿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣴⢿⣿⣇⣿⣿⣿⣀⣿⣿⣸⣿⣿⣿⣿⣿⣇⢿⡿⣽⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣿⡏⠀⠀⠈⠅⣀⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠐⢖⣸⠯⣴⣶⣶⣶⣶⣿⣿⣷⣿⣵⣶⢿⣶⠶⢾⣿⡶⣖⣒⢲⣶⣿⣷⣶⣾⣖⣄⣘⣿⣷⣾⣷⣶⣿⣿⣶⣾⣿⣷⣶⣶⣿⣷⣀⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⣈⡫⡼⣨⣸⣹⣾⣿⣧⣧⣻⣟⢿⣸⣷⣾⡬⣪⣾⣸⣤⣾⣪⣾⣷⢇⣾⣿⣿⣿⣿⣿⣻⣿⣿⣬⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣧⣿⣷⣸⣶⣷⣣⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⡯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣟⡃⠀⣀⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠈⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⣄⠀⠀⠀⠐⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣦⣄⡞⠉⠹⣿⠀⠀⣿⢷⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⠀⠀⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠛⠛⢿⢿⣿⣿⣿⣿⣿⣿⣟⣯⣖⠈⣿⢿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⡿⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⡀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⠀⠀⠀⠀⠀⣠⣠⣿⡆⠙⠛⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⠋⠻⡄⢠⡙⠿⠿⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⢀⣀⣤⣀⠀⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠓⠄⡀⠀⠀⢀⡀⠀⠀⣴⣿⣿⣿⣷⣾⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣟⣿⣽⢻⣿⣿⣏⢻⣿⣿⣛⣽⣟⣽⣿⣿⣿⣿⣯⡿⣟⣻⣿⣧⣻⢻⡻⣿⣿⣻⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣧⣋⣟⣇⡀⢀⡌⣷⣾⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣷⣾⣿⣷⣷⣶⣷⣾⣾⣦⣿⣿⣾⣿⠷⠶⠶⢾⣿⣿⣿⣿⣿⣾⣷⡿⣵⠶⢷⢷⢶⠶⠶⠶⣝⡍⠹⣿⣿⣿⣿⣿⣶⡄⣀⠀⠀⠈⣿⣷⣾⣏⣸⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⣾⣶⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣯⣭⣭⣿⣿⣧⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⡿⠗⠛⠀⢄⡒⠀⢙⡟⢈⣽⣳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⢸⣿⣿⢟⣿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⠆⢲⣾⣿⣿⡿⠿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⡿⠟⡿⣾⣶⣦⣶⡶⣿⣯⣿⣽⣗⡟⣹⠻⣿⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢻⡿⠶⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣧⣄⣀⢀⢀⢀⢀⠀⢀⣀⣀⢀⣀⣼⣿⣿⣿⣿⣿⣦⣶⣶⣶⣾⣿⣿⣦⣶⣿⣆⣠⣠⣀⣨⣉⣿⣯⣒⣥⡠⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡉⣿⡏⣩⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢠⣹⡏⣠⣬⣿⠋⣬⣿⢩⣽⣿⣿⣿⣿⣯⣾⣿⢫⣽⣿⣿⢸⣿⣿⢱⣾⣾⣿⢰⠏⣭⣷⠀⢴⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣾⢿⡗⣛⣛⣿⠘⣿⣿⢼⣟⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣿⢚⣛⣛⣿⢸⣯⣵⣿⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣇⣿⣿⣿⣀⣿⣿⣸⣿⣿⣿⣿⣿⣇⢿⡿⣽⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣿⡇⡀⠀⠀⠄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢀⣰⣟⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣒⢒⣺⣟⠒⢲⣖⣶⣶⣿⣷⣶⣾⣖⣄⣨⣿⣷⣾⣵⣶⣿⣿⣶⣶⣿⣷⣶⣶⣿⣷⣤⣤⣄⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠀⣯⡬⣐⣹⣹⣿⣿⣿⣿⣿⣟⢿⣸⣿⣿⡾⣲⣿⣸⣲⣿⣪⣾⣷⢗⣾⣿⣻⣿⣿⣿⣻⣿⣿⣬⣿⣯⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣷⣸⣾⣶⣣⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣋⡀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠉⠁⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠞⠉⠹⣿⠀⠀⣿⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⠀⠀⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠛⠛⢿⢿⣿⣿⣿⣿⣿⡿⣛⣭⡖⠈⣿⢿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⠿⠿⠛⠛⠛⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⢿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠇⠀⠀⠀⠀⠀⣴⣾⣿⡈⠛⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠋⢻⡄⢤⡻⠿⠿⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠁⣀⣠⣠⣄⠀⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⢾⣿⣿⠿⡿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠓⠄⡀⠀⠀⢀⡀⠀⠀⣴⣿⣿⣿⣿⣾⡿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣟⣿⣽⢻⣿⣿⣏⢻⣿⣿⣛⣽⣟⣽⣿⣿⣿⣿⣯⣿⣟⣋⣿⣧⣻⢻⡻⣿⣿⣛⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣧⣋⣛⣇⡀⢀⡜⣷⣶⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣷⣾⣿⣷⣷⣶⣷⣾⣾⣇⣿⣿⣶⣿⠷⠶⠶⢾⣿⣿⣿⣿⣿⣾⣷⡿⡵⠶⢷⢷⢶⠶⠶⠾⣝⣅⢹⣿⣿⣿⣿⣵⣧⡄⣀⠀⠀⠈⣿⣷⣾⣏⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣰⣾⣶⣮⣻⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣿⣯⣭⣭⣿⣿⣧⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⡿⠗⠛⠀⢄⡲⠀⢋⡏⣉⣽⣳⣼⣿⣿⣿⣿⣿⣿⣷⣿⣷⣄⣸⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⠆⢲⣾⣿⣿⡿⠿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⣿⡿⢟⡿⣺⣴⣤⣶⢖⣿⣿⣿⣿⢳⡏⣽⠿⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠻⠿⠶⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣿⣿⣿⣿⣧⣄⣀⢀⢀⢀⢀⠀⢀⣀⣀⢀⣀⣨⣿⣿⣿⣿⣿⣦⣶⣶⣶⣾⣿⣿⣦⣶⣷⣢⣤⣠⣀⣘⣭⣭⣯⣒⣥⡠⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣿⡏⢩⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣹⡏⣥⣌⣿⠋⣬⣿⢩⣽⣿⣿⣿⣿⣯⣿⣿⢫⣽⣿⣿⢸⣿⣿⢡⣾⣾⣿⢸⠏⣭⣿⠀⠴⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣠⣴⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣾⣿⡗⣛⣛⣿⠘⣿⣿⢼⣿⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣻⣿⢚⣛⣛⣿⢸⣻⣶⡯⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠐⠐⠿⠿⠿⠿⠿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣽⣇⣿⣿⣿⣀⣿⣿⣸⣿⣿⣿⣿⣿⣇⣿⡿⣼⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣿⡗⠀⠀⠀⠅⣀⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢀⣘⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣵⣶⣟⣶⡶⢾⣿⠒⢒⣲⣶⣶⣿⣷⣶⣾⣶⣄⣨⣿⣷⣾⣵⣶⣿⣿⣶⣶⣿⣷⣶⣶⣿⣷⣤⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⣠⣯⡮⣠⣿⣹⣿⣿⣿⣿⣿⣟⣿⣸⣿⣾⡬⣲⣽⣸⣰⣿⣪⣾⣷⢇⣾⣿⣻⣿⣿⣿⣻⣿⣿⣬⣿⣏⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣷⣸⣶⣾⣣⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣈⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠈⠁⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⠀⠀⠀⠔⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡖⠉⠹⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣛⣭⡖⠈⣿⢿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⡿⠿⠛⠛⠛⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⣿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠆⠀⠀⠀⠀⠀⣴⣾⣿⡈⠛⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠋⢻⡄⢤⠻⠿⠿⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠁⢀⣀⣤⡄⠀⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢶⣿⣿⠿⡿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠗⠄⡀⠀⠀⢀⡀⠀⠀⣴⣿⣿⣿⣿⣾⡿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣟⣿⣽⢻⣿⣿⣏⢻⣿⣿⣛⣽⣟⣽⣿⣿⣿⣿⣿⣿⣟⣛⣿⣧⣻⢻⡛⣿⣿⣛⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣧⣉⣛⣇⡀⢀⡜⣷⣶⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣷⣾⣿⣷⣷⣶⣷⣾⣾⣦⣿⣿⣾⣿⠷⠶⠶⢾⣿⣿⣿⣿⣷⣾⣷⡿⣵⠶⢶⢷⢶⠶⠶⠾⣝⣍⢹⣿⣿⣿⣿⣽⣷⡄⣀⠀⠀⠈⣿⣷⣾⣟⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣰⣾⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣯⣯⣭⣭⣿⣿⣧⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⡿⠗⠛⠀⢄⡲⠀⢋⡏⣈⣽⣳⣼⣿⣿⣿⣿⣿⣿⣷⣿⣷⣄⣸⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀

⠀⠆⢲⣾⣿⣿⡿⠿⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⣿⡿⠟⡿⣺⣴⣤⣶⢖⣿⣿⣿⣿⣲⡏⣽⠿⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢻⡿⠶⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣸⣿⣿⣿⣿⣿⣦⣶⣶⣶⣾⣿⣿⣷⣶⣷⣦⣀⣀⣀⣈⣥⣭⣯⣐⣁⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣿⡏⣩⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢹⡏⣥⣬⣿⠋⣬⣿⢩⣽⣿⣿⣿⣿⣯⣿⣿⢫⣽⣿⣿⢸⣿⣿⢡⣾⣾⣿⢰⠏⣭⣿⠉⠴⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⣤⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣽⡗⣛⣛⣿⠘⣿⣿⢼⣟⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣿⢚⣛⣛⣿⢸⣋⣥⡗⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣇⣿⣿⣿⣀⣿⣿⣸⣿⣿⣿⣿⣿⣇⢿⡿⣼⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣿⡏⠀⠀⠀⠄⣀⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢀⣺⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣿⣶⢒⣒⢲⣶⣾⣷⣶⣾⣖⣄⣘⣿⣷⣾⣷⣶⣿⣿⣶⣶⣿⣷⣶⣶⣿⣗⣀⣄⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠯⢁⣫⡼⣘⣻⣹⣿⣿⣿⣿⢿⣟⢿⣸⣿⣿⢼⣶⣸⣸⣰⣿⣪⣾⣷⢇⣾⣿⣻⣿⣿⣿⣻⣿⣿⣬⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣧⣧⣿⣷⣸⣾⣶⣣⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣎⡀⠀⢀⢀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠁⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠞⠉⠹⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣿⠀⠀⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠛⠛⠿⢿⣿⣿⣿⣿⣿⡿⣛⣭⡖⠈⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⠿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⠿⢿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠂⠀⠀⠀⠀⠀⣴⣼⣿⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠋⢻⡄⢤⠻⠿⠿⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⣀⣀⣠⣀⡀⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢾⣿⣿⠿⠿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠳⢄⡀⠀⠀⢀⡀⠀⠀⣴⣿⣿⣿⣷⣾⡿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡟⣿⣟⣿⣿⢻⣿⣿⣇⢻⣿⣿⣛⣽⣟⣽⣿⣿⣿⣿⣯⣿⣟⣛⣿⣧⣻⢻⡻⣿⣿⣛⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣧⣉⣛⣇⡀⢀⡜⣷⣶⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣶⣿⣿⣷⣷⣶⣷⣾⣾⣆⣿⣿⣶⣿⠷⠶⠶⢾⣿⣿⣿⣿⣷⣾⣷⡿⣵⠶⢶⢷⢶⠶⠶⢾⣽⣍⢹⣿⣿⣿⡿⣯⣧⡄⣀⠀⠀⠈⣿⣷⣾⣗⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣰⣾⣶⣮⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣭⣭⣽⣿⣿⣧⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⠿⠗⠛⠠⢄⡲⠀⢫⡏⣩⣽⣳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀

⠀⠆⢲⣾⣿⣿⡿⠿⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⣿⡿⢿⡿⣺⣴⣤⣶⢶⣿⣏⡿⣿⢰⡏⣽⠿⣿⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠻⠿⠶⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⢀⠀⢀⣀⣀⢀⣀⣸⣿⣿⣿⣿⣿⣶⣤⣴⣤⣿⣿⣿⣶⣶⣥⣄⣤⣀⣀⣈⣍⣽⣅⣠⣁⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣹⡏⣁⣈⣿⠋⣨⣿⢩⣯⣿⣿⣿⣿⣯⣿⣿⢫⣽⣿⣿⢸⣿⣿⢡⣾⣾⣿⢸⠏⣬⡆⠠⠰⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⣛⣿⠘⣿⣿⢼⣟⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣿⢚⣛⣛⣿⢸⣿⣄⡇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣇⣿⣿⣿⣀⣿⣿⣸⣿⣷⣿⣿⣿⣇⢿⡿⣼⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣿⡇⡀⠀⠀⠅⣀⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢀⣸⣿⣿⣾⣾⣿⣶⣿⣿⣿⣿⣿⣾⣿⣶⠶⢖⣛⣴⣆⣂⢲⣶⣾⣷⣶⣾⣶⣄⣀⣿⣶⣾⣷⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣧⣤⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⣀⣫⡼⣘⣿⣻⣿⣿⣿⣿⣿⣿⢿⢹⣿⣿⢾⣶⣼⣸⣤⣾⣪⣾⣷⠇⣾⣿⣻⣿⣿⣿⣻⣿⣿⣬⣿⣯⣿⣸⣿⣿⣿⣿⣿⣿⣿⣧⣷⣿⣷⣸⣶⣶⣣⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣋⡀⠀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠈⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣿⠀⠀⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⣟⣯⡶⠈⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⠿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⠿⣿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣐⣼⣷⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠋⢻⡄⢄⠻⠿⠿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠃⣀⣤⣀⡀⡀⣀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢾⣿⣿⠿⡿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠳⢄⡀⠀⠀⢀⡀⠀⠀⣰⣿⣿⣿⣷⣾⡿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣟⣿⣽⢻⣿⣿⣇⢻⣿⣿⣛⣽⣟⣽⣿⣿⣿⣿⣯⣿⣟⣙⣿⣧⣛⢻⡻⣿⣿⣛⣸⣿⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⣛⣇⡀⢀⡜⣷⣶⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣶⣿⣿⣷⣷⣶⣷⣶⣾⣦⣿⣿⣾⡿⠶⠴⠶⢾⣿⣿⣿⣿⣿⣶⣷⡿⣵⠶⢷⢷⢶⠶⠶⢶⣽⡍⢹⣿⣿⣿⣯⣩⣦⡀⣀⠀⠀⠈⣿⣷⣾⣟⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣰⣾⣶⣮⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣇⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⠿⠗⠛⠠⢄⡲⠀⢣⡎⣈⣽⣳⣼⣿⣿⣿⣿⣿⣿⣷⣿⣷⣄⣸⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀

⠀⠆⢲⣾⣿⣿⡿⠿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⣿⡿⢿⡿⣺⣴⣄⣶⢶⣿⣷⡿⣿⢰⡏⣝⠿⣿⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠛⠟⠶⠿⣿⣿⢿⢿⢿⠿⣿⡀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⡀⠀⠀⠀⢀⣀⢀⣀⣸⣿⣿⣿⣷⣦⣤⣄⣤⣠⣿⣿⣿⣶⣶⣂⣄⣤⣀⣀⣠⣮⣠⣅⣀⣁⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣹⡏⣀⣈⣿⠋⣨⣿⢩⣽⣿⣿⣿⣿⣯⣾⣿⢫⣽⣿⣿⢸⣷⣿⢡⣾⣾⣿⢰⠏⡭⡆⠀⠴⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣵⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⡚⣿⠈⣿⣿⢼⣟⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣿⢚⣛⣛⣿⢸⣹⣄⡇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠜⠛⠻⠿⠾⠿⠿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣇⠨⣿⣿⣀⣯⣿⣸⣿⣷⣝⣟⣿⣇⢻⡿⣼⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢀⣸⣿⣷⣾⣶⣿⣶⣿⣿⣿⣿⣿⣾⣿⣀⠀⢀⣏⣀⣀⣀⠀⢀⣜⣧⣤⣨⣄⣄⣠⣯⣶⣮⣵⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣷⣄⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠀⣫⡸⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⢹⣯⣿⡬⣠⡸⢸⣠⣾⣪⣶⣶⠇⣾⣿⣻⣿⣿⣿⣻⣿⣿⣬⣾⣏⣿⣺⣿⣯⣿⣿⣿⣿⣿⣷⣷⣿⣷⣸⣶⣶⣣⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣊⡀⠀⣀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠁⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂⢷⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠞⠉⠹⣿⠀⠀⣿⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⣟⣯⡖⠈⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣿⠷⣿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⢠⣶⣼⣷⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠋⢻⡄⣤⡻⣿⣿⠇⣾⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠁⣀⣠⣀⣀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣆⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢾⣿⡿⠿⠿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠳⢄⠀⠀⠀⢀⡀⠀⠀⣴⣿⣿⣿⣿⣾⣿⢷⣶⣤⣄⠀⠀⠀⠀⢀⡀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣛⣿⣽⢻⣿⣿⣯⣿⣿⣿⣛⣽⣟⣽⣿⣿⣿⣿⣯⣿⣟⣉⣿⣧⣻⢻⡫⣿⣿⣛⣸⣽⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⣟⣇⡀⢀⡜⣿⣿⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣦⣶⣿⣿⣿⣿⣶⣿⣿⣷⣷⣶⣷⣾⢾⣆⣷⣿⣿⡿⠶⠶⠶⢾⣿⣿⣿⣿⣷⣾⣷⡿⣵⠶⢶⢷⢶⠶⠶⢶⣝⡅⢹⣿⣿⣿⣏⣱⣶⡄⣀⠀⠀⠈⢿⣷⣾⣟⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣰⣾⣶⣮⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣧⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⠿⠗⠛⠠⢄⡲⠀⢣⡏⢈⣽⣳⣼⣿⣿⣿⣿⣿⣿⣷⣿⣷⣄⣰⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀

⠀⠆⢲⣾⣿⣿⡿⠿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣶⣿⣿⣿⣿⡿⢿⡿⣻⣴⣄⣶⢶⣿⣷⡿⣿⢰⡏⣽⠾⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠛⠛⠲⠶⢿⣿⣿⠿⣿⣿⣿⡄⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⢀⠀⠀⠀⡀⡀⢀⣀⣀⣿⣿⣿⣶⣤⣤⣀⣀⣀⣶⣾⣿⣴⣶⣀⣀⠀⣀⣀⡀⣀⣠⣀⣀⣀⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣽⡏⠀⠈⣿⠋⣈⣿⢩⣭⣿⣿⣿⣿⣯⣾⣿⢋⣵⣾⣿⢸⣶⣿⢡⣾⣾⣿⢰⠏⠬⡆⠀⠰⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠓⣿⠐⣿⣿⢼⣟⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣻⣿⢚⣛⣛⣿⢸⣋⡀⡇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠚⠛⠟⠻⠿⠿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣶⣿⣀⣿⣿⣰⣝⣷⣝⣟⣿⣇⠹⡿⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⣿⣸⣿⣯⡇⠀⠀⠀⠄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢀⣸⢿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣿⣄⠀⢠⣉⠀⢀⣀⠀⢀⣨⣦⣤⡌⠀⣄⣀⣿⣢⣬⣵⣴⣾⣷⣶⣶⣿⣷⣶⣶⣿⣷⣤⣤⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠀⠪⡸⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣻⡻⠿⠬⢤⡸⠸⣄⡾⣪⣴⣶⠇⣾⣿⣳⣿⣿⣿⣻⣾⣿⣨⣾⣇⣾⣸⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣷⣸⣶⣶⣣⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣵⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣅⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⢐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⣟⣯⠖⠈⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⠿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⠷⢿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⢠⣶⣼⣷⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠋⢻⡄⣄⡻⣿⣿⠂⣾⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠁⣀⣀⣀⣀⡀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣆⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢴⡿⡿⠿⠿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠳⢄⠀⠀⠀⢀⡀⠀⠀⣰⣿⣿⣿⣿⣾⣿⢷⣶⣤⣄⠀⠀⠀⠀⢀⡀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣛⣿⣽⢻⣿⣿⣯⣿⣿⣿⣛⣽⣟⣽⣿⣿⣿⣿⣯⣿⣟⣉⣿⣧⣻⢻⡻⣽⣿⣛⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⣛⣇⡀⢀⡜⣿⣿⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣦⣶⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣾⢾⣆⣷⣿⣿⡿⠶⠴⠶⢾⣿⣿⣿⣿⣷⣾⣷⡿⣵⠶⢶⢶⠶⠶⠶⢶⣝⡉⢙⣿⣿⣿⣏⣡⣶⡀⣀⠀⠀⠈⢿⣷⣾⣟⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣰⣾⣶⣮⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣧⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⠿⠗⠚⠠⠀⡢⠀⢣⡏⢈⣽⣳⣼⣿⣿⣿⣿⣿⣿⣷⣿⣷⣄⣰⢿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀

⠀⠆⢲⣾⣿⣿⡿⠿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣶⣿⣿⣿⣿⡿⠿⡿⣻⣴⣄⣶⢶⣿⣧⡟⣿⢰⡏⣽⠾⣽⢝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠛⠛⠒⠶⢿⣿⢿⠻⣿⣿⣿⡄⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⡀⢀⠀⢀⢀⢀⢀⣀⣬⣿⣿⣿⣿⣷⣴⣤⣴⣤⣿⣿⣿⣷⣶⣤⣄⡠⣀⣀⣀⣭⣌⣄⣀⣀⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣿⡏⣽⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣽⡏⣁⢈⣿⠋⣬⣿⢩⣽⣿⣿⣿⣿⣯⣾⣿⢫⣽⣿⣿⢸⣿⣿⢡⣾⣮⣿⢰⢋⣭⡇⠀⠰⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⣛⣿⠀⣿⣿⢼⣟⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣻⣿⢚⣛⣛⣿⢸⣯⣀⡇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣀⣿⣿⣸⣿⣷⣻⣿⣿⣇⢿⡿⣼⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣿⡇⠀⠀⠀⠅⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢀⣸⣿⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⢦⣴⣿⣤⣤⣂⠠⢦⣾⣷⣴⣾⣆⣄⣀⣿⣶⣾⣵⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣤⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢀⠪⡸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠾⢞⣽⣸⣨⣽⣪⣶⣷⠇⣾⣿⣳⣿⣿⣿⣻⣿⣿⣬⣿⣏⣿⣸⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣷⣸⣶⣶⣣⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣭⣃⡀⠀⢀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠁⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢛⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠞⠉⠹⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢿⠀⠀⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⣟⣯⡖⠉⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣿⠷⣿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣀⣼⣧⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠋⢻⡀⣄⠻⠿⡿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡯⠀⣀⣄⣀⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣛⢾⣿⢿⠿⡿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⠳⢄⡀⠀⠀⢀⡀⠀⠀⣰⣿⣿⣿⣷⣾⣿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣿⣛⣿⣽⢻⣿⣿⣏⢻⣿⣿⣛⣽⣟⣽⣷⣿⣿⣿⣯⣿⣟⣉⣿⣧⣛⢻⡋⣿⣿⣛⣸⣽⣿⣿⣿⣿⣿⣿⣟⡏⣧⣉⣛⣇⡀⠀⡜⣷⣶⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣷⣾⣾⣆⣷⣿⣾⡿⠶⠴⠶⢾⣿⣿⣿⣿⣷⣾⣷⡿⣵⠶⢶⠷⠶⠶⠶⢶⣝⡍⢹⣿⣿⣿⣏⣥⣦⡄⢀⠀⠀⠈⣿⣧⣾⣟⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣰⣾⣶⣮⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣇⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⠿⠗⠛⠠⠀⡢⠀⢫⠎⢈⣿⣳⣼⣿⣿⣿⣷⣾⣿⣷⣿⣧⣄⢰⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀

⠀⠆⢲⣾⣿⣿⡿⠿⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⡿⢿⡿⣻⣴⣄⣶⢶⣿⣷⡟⣿⢰⡏⣝⠿⡿⢝⢛⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠙⠛⠒⠶⢿⣿⣿⠿⠻⢿⣿⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣀⠀⢀⠀⢀⣀⣀⢀⣀⣐⣿⣿⣿⣿⣷⣴⣤⣦⣴⣾⣿⣿⣶⣶⣤⣄⣀⣄⣀⡀⣭⣌⣄⣀⣀⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⣏⣽⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣽⡏⣀⣈⣿⠋⣬⣿⢩⣭⣿⣿⣿⣿⣯⣾⣿⢋⣽⣿⣿⢸⣿⣿⢡⣾⣾⣿⢰⠏⣭⡆⠀⠴⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣬⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⣛⣿⠀⣿⣿⢼⣟⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣻⣿⢚⣛⣛⣿⢸⣧⣄⡇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣀⣿⣿⣸⣿⣿⣻⣿⣿⡇⢿⡿⣼⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣟⡇⠀⠀⠀⠄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⣀⣻⣿⣷⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⢤⣴⣿⠤⢄⣀⠠⢠⣾⣷⣤⣼⣆⣄⣀⣿⣶⣮⣥⣶⣾⣷⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣤⣀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠀⣪⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⢲⣹⣸⢤⣾⣪⣾⣷⠇⣾⣿⣳⣿⣿⣿⣻⣿⣿⣬⣿⣏⣿⣸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣶⣶⣣⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣁⡀⠀⢀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠈⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠞⠉⠹⣿⠀⠀⣿⢿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⣟⣯⡶⠈⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣿⠷⣿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣠⣼⣧⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠋⢻⡀⣄⠻⠿⡿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢀⣀⣀⣀⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⢼⣿⢿⠿⠿⠷⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⠳⢄⠀⠀⠀⠀⡀⠀⠀⣰⣾⣿⣿⣷⣾⣿⢷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣿⣛⣿⣽⢻⣿⣿⣏⢻⣿⣿⣛⣽⣟⣽⣷⣿⣿⣿⣿⣿⣟⣉⣿⣧⣛⢻⡫⣿⣿⣛⣘⣽⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⣛⣇⡀⢀⡜⣶⣶⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣷⣾⣾⣆⣷⣿⣾⡿⠶⠴⠶⢾⣿⣿⣿⣿⣷⣶⣷⡿⣵⠶⢶⢶⠶⠶⠶⢶⣝⡍⢹⣿⣿⣿⣏⣥⣦⡄⢀⠀⠀⠈⣿⣧⣾⣇⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣴⣾⣷⣮⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣇⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⠿⠗⠚⠠⠀⡢⠀⢫⡎⢈⣽⣳⣼⣿⣿⣿⣿⣿⣿⣷⣿⣷⣄⢰⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⠄⢲⣾⣿⣿⡿⠻⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⡿⢿⡿⣻⣴⢄⣶⢶⣿⣷⡟⣿⢰⡏⣝⠾⡿⢝⢛⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠛⠛⠒⠶⢿⣿⢿⠿⢿⠿⣿⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣄⣀⠀⠀⠀⣀⡀⢀⣀⣀⣿⣿⣿⣷⣤⣀⣀⣀⣠⣴⣾⣷⣦⣄⣄⣀⠀⣀⣀⣀⣀⣤⣄⣀⣀⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣽⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡏⠁⠈⣿⠋⣈⣿⢩⣭⣿⣿⣿⣿⣯⣾⣿⢋⣽⣿⣿⢸⣶⣿⢡⣼⣾⣿⢰⠋⠤⡆⠀⠰⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⣿⠠⣿⣿⢼⣟⢛⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣻⣿⢚⣛⣛⣿⢈⣋⣄⡇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠚⠳⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣴⣿⣀⣿⣿⣸⣝⣷⣛⣟⣿⡇⢻⡿⣼⣿⣿⣿⢿⣿⣿⣸⣿⣿⣿⣸⣿⣏⡇⠀⠀⠀⠄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢐⣻⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⢀⣉⠀⢀⣀⠀⢀⣌⣒⣄⡈⣄⣄⣀⣹⣶⣮⣥⣶⣾⣷⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣤⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠀⠪⡼⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡬⠀⢸⠸⣀⣼⣪⣴⣶⠇⣾⣿⣳⣿⣿⣿⣻⣿⣿⣬⣾⣏⣿⣸⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣶⣶⣣⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣥⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠞⠉⠹⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣶⣷⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⣟⣯⡖⠈⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣊⡽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠗⢿⣿⣷⣿⠀⠘⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣀⣼⣧⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠋⢻⡀⣄⠻⠿⡿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⣀⣀⣀⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⢾⣿⠿⠿⠷⡶⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⠳⢄⠀⠀⠀⠀⡀⠀⠀⣰⣾⣿⣿⣶⣾⡿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣸⣿⡟⣿⣛⣿⣽⢻⣿⣿⣏⢻⣿⣿⣛⣽⣟⣽⣷⣿⣿⣿⣿⡿⣟⣛⣿⣧⣻⢻⡋⣽⣿⣛⣘⣽⣿⣿⣿⣿⣿⣿⣟⡏⣧⣉⡛⣇⡀⢀⡜⣶⣶⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣷⣾⣾⣆⣷⣿⣾⡿⠶⠴⠶⢾⣿⣿⣿⣿⣷⣶⣷⡿⡽⠶⢶⢶⠶⠶⠶⢶⣽⡉⢹⣿⣿⣿⣏⣵⣦⡄⢀⠀⠀⠈⣿⣧⣾⣇⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣴⣿⣿⣶⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣇⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⠿⠗⠋⠠⠀⡢⠀⢫⠎⢈⣿⣳⢼⣿⣿⣿⣷⣾⣿⣷⣿⣧⣀⢰⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⠄⢲⣿⣿⣿⠿⠻⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⡿⢿⡿⣻⣴⣄⣖⢶⣿⣷⡟⣿⢰⡏⣝⠾⡿⢝⢛⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠛⠛⠒⠶⢿⣿⠿⠿⠟⠻⢿⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣇⢀⠀⠀⠀⢀⣀⢀⣀⣀⣿⣿⣿⣷⣤⣄⣀⣀⣠⣤⣾⣧⣦⣤⣀⣀⠀⣀⣀⡀⣀⣠⣀⣀⣀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣭⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡏⠀⠈⣿⢋⣬⣿⢹⣯⣿⢿⣿⣿⣯⣾⣿⢋⣽⣾⣿⢠⣶⣿⢡⣼⣮⣿⢰⠋⠬⡆⠀⠐⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⣾⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⣿⢸⣿⣿⣿⣟⣛⢼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣻⣿⢚⣛⣛⣿⠘⣁⣀⡇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣈⣿⣿⣸⣿⣷⣵⣋⣿⡇⢙⡿⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⣿⣸⣿⣏⡇⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢀⣻⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣉⠀⢀⣀⠀⢀⣀⢀⠀⡈⠀⣀⣀⣉⣖⢮⣁⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣦⣤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠪⡸⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣀⡸⠰⢀⡸⣪⣴⣶⠇⣼⡿⣳⣿⣿⣿⣻⣾⣿⣨⣿⣇⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣶⣶⣣⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠇⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣀⣀⡀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠞⠉⠹⣿⠀⠀⣿⢳⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣴⣆⣠⢤⠄⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣚⣶⣾⣭⠽⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣟⣯⡖⠈⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣴⣶⣿⠿⠿⠿⠷⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⠷⢿⣿⣷⣷⠀⠙⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣀⣀⣀⣠⣄⣤⣦⣿⣇⠘⠛⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠋⢻⡀⣄⠻⡿⡿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⠢⢀⠀⠀⠀⠀⡀⠀⠀⣰⣿⣿⣿⣷⣾⡿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢈⣿⣿⡟⣿⣙⣿⣽⢻⣿⣿⣏⢻⣿⣿⣛⣽⣟⣽⣷⣿⣿⣿⣿⡿⣟⣋⣿⣧⣛⢻⡋⣽⣿⣛⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⡛⣇⡀⢀⠘⣶⣾⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣆⣷⣿⣾⡿⠶⠴⠶⠺⣿⣿⣿⣿⣷⣶⢷⡿⡵⠶⢶⢶⠶⠶⠶⢶⣝⡍⢹⣿⣿⣿⡏⣥⣦⠀⣀⠀⠀⠈⣟⣤⣾⣇⣹⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣾⣿⣿⣷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣇⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⠿⠗⠋⠠⠀⡂⠀⢣⠎⢈⣿⡳⢼⣿⣿⣿⣷⣶⣿⣶⣿⣦⣀⢰⣿⣿⠟⡿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⠀⣶⣿⣿⣿⠟⠻⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⠿⢿⡿⣺⣔⣄⣖⢶⣿⣵⡏⡿⢰⡇⡕⠾⡿⠜⠛⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠙⠓⠒⠲⢿⣿⣿⠿⢿⠿⣧⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣇⣀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣶⣤⣄⣀⣀⣠⣴⣶⣶⣤⣄⣀⣀⠀⣀⣀⡀⣀⣄⣀⣀⣀⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⣏⣽⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⡏⠀⠈⣿⢻⣾⣿⣽⣿⣿⢿⣿⣿⣯⣾⣿⢋⣵⣷⣿⢘⣗⣿⢡⣬⣮⣿⢰⠂⠤⡆⠀⠰⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠚⣿⢸⣿⣿⣿⣟⣻⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣻⣿⢚⣛⣛⣿⠘⠀⡀⡇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⠳⠓⠲⠶⠿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡰⣼⣿⣸⣿⣿⣻⣿⣿⣿⣟⣿⣇⢹⡿⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⣿⣸⣿⣩⡇⠀⠀⠀⠄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢐⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⠂⢀⣉⠀⢀⣀⠠⢰⣻⠄⠀⠈⠀⣄⣀⢰⣴⣼⣥⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣶⣤⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢀⠪⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡬⠀⣸⠸⣀⣸⡪⣰⣶⢇⣾⣿⣳⣷⣿⣿⣻⣿⣿⣨⣾⣏⣿⣸⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣾⣶⣣⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣧⣿⣵⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣉⣀⡀⠀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠖⠉⠹⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣿⣴⠶⠞⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣈⣽⣿⣶⣒⡹⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⠖⠨⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣴⣶⠿⢿⠟⠛⠉⠉⠛⠁⠀⠀⠀⠀⢀⣠⣤⣿⠿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠷⣿⣿⣷⣿⠀⠙⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠋⢿⠀⣄⠻⠿⡿⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡛⠀⢀⡀⠀⠀⠀⠀⣠⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⢼⡿⠿⠿⠶⡴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⡦⢀⠀⠀⠀⠀⡀⠀⠀⣰⣿⣿⣿⣷⣾⡿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣻⣿⣿⡟⣿⣛⣿⣽⢻⣿⣿⣏⢻⣿⣿⣛⣽⣟⣽⣷⣿⣿⣿⣿⡿⣟⣋⣿⣧⣛⢛⡛⣽⣿⣛⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⡛⣇⡀⢀⠘⣶⣾⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠠⣶⣿⣿⣿⣿⣿⣿⣧⣿⣷⣿⣶⣶⣾⣶⣆⣷⣿⣾⡷⠶⠴⠶⢶⣿⣿⣿⣿⣷⣶⡷⡿⣽⠶⢶⢶⠶⠶⠶⢶⣙⡅⢹⣿⣿⣿⣏⣱⣦⡀⣀⠀⠀⠈⢯⣦⣾⡇⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⣾⣿⣿⣾⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣿⣿⡇⠀⠀⣸⣶⣿⣿⣿⣿⣿⣿⠿⠗⠊⠠⠀⡂⠀⢫⠏⣈⣿⡳⢼⣿⣿⣿⣷⣷⣿⣶⣿⣦⣀⢰⣿⣿⠟⡿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⠂⣶⣿⣿⣿⠟⠹⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⠿⠿⠿⣻⣔⣤⣖⢶⣿⣵⡎⡿⢰⠏⡝⠾⡿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠛⠒⠒⠶⢿⣿⢟⠿⠿⠿⢧⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣽⣿⣿⣿⣷⣧⣴⣿⣿⣿⣿⣀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣷⣤⣀⡀⠀⣀⣤⣴⣦⡀⣀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣉⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⢻⣿⡏⠀⣈⣿⢻⣿⣿⣽⣿⣿⣿⣿⣿⣯⣾⣿⢋⣵⣷⣿⢀⣤⣿⢡⣦⣨⣗⠰⠀⠤⡆⠀⠰⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⢛⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⡋⣿⣿⢿⣿⣟⣿⡟⣻⣿⠚⣛⣛⡯⠀⠀⣶⡇⢰⡀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠒⠖⠒⠢⠴⢾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢻⣿⣸⣿⣿⣿⣿⣿⣿⣏⣿⡀⠻⡻⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⡟⣸⣮⣿⡇⠘⠁⠀⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢐⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣷⣿⣿⣶⠆⢀⣃⠀⢲⣿⠶⢾⣿⠿⠀⢀⠀⣀⣀⢑⣶⢬⣡⣲⣾⣷⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣶⣦⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠪⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠭⠈⡸⠸⢀⠸⢪⣤⣶⠇⣾⣿⣳⣻⣿⣿⣻⣿⣿⣬⣿⣿⣾⣸⣿⣧⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣷⣶⣣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃⡵⣦⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⠏⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣁⣀⡀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠒⠉⠹⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⣚⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢿⠀⠀⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡦⢾⡿⠛⠛⠵⠊⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠛⠛⠿⠿⢿⣿⣿⣿⣿⡿⣟⣯⠆⠈⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⣠⣶⣾⣿⣿⡟⠛⠛⠃⠀⠀⠀⠀⢀⣠⣤⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⠷⣿⣿⣵⣷⠀⠙⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠚⠟⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢀⣀⣀⣀⣀⡀⣀⣹⣆⠘⠛⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠉⢯⠀⣈⠿⠿⡿⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⠦⢀⠀⠀⠀⠀⡀⠀⠀⣴⣿⣿⣷⣷⣾⡿⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⡟⣿⣙⣿⣽⢻⣿⣿⣏⢻⣿⣻⣋⣽⣟⣽⣷⣿⣿⣿⣿⡿⣟⣛⣿⣧⣛⢛⡋⣽⣿⣛⣘⣹⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⡛⣇⡀⢀⠘⣦⣾⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣆⣷⣿⣾⡷⠶⠴⠶⠶⣿⣿⣿⣿⣶⣾⡷⡿⡱⠶⢶⢶⠶⠶⠶⠶⣉⡁⢹⣿⣿⣿⡏⣡⣦⠀⡀⠀⠀⠈⢛⣦⣾⡃⣻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⣶⣿⣷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣿⣿⡇⠀⠀⣸⣶⣿⣿⣿⣿⣿⣿⠿⠃⠚⠠⠀⡂⠀⢣⠊⣈⣟⡲⢼⣿⣿⣿⣿⣶⣿⣶⣿⣦⣀⢠⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⢀⣾⣿⣿⢿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⡿⠿⠿⣻⣔⣄⣖⢶⣿⣵⡎⡿⢰⠇⡕⠾⡿⠜⢿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠈⠙⠒⠒⠲⢿⣿⢟⠿⠻⠻⢣⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣽⣿⣿⣿⣧⣥⣼⣿⣿⣿⣷⣀⡀⠀⢀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣤⣀⡀⡀⣠⣤⣶⣦⣀⣀⣀⣀⠀⣀⣀⡀⣀⣀⣀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣉⣯⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡏⠀⣨⣿⢻⣿⣿⣽⣿⣿⣿⣿⣿⣯⣾⣿⢋⣵⣷⣿⢀⣦⣿⢡⣤⣬⡟⢰⢀⣤⡆⢠⡴⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡗⢚⣛⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⡋⣿⣿⢿⣿⣟⣿⡟⣻⣿⠚⣛⣛⡏⢸⣿⣿⡇⢸⣷⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠠⠖⠶⠶⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠂⢿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣀⢻⡿⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⣇⣸⣿⣿⡇⠸⠟⠀⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢐⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣷⣿⣿⣷⡖⢀⣃⠲⢶⣿⣶⣾⣿⣿⣖⠈⠀⣀⣀⢈⠠⣈⣡⣶⣾⣷⣶⣶⣿⣷⣶⣶⣿⣿⣶⣶⣶⣶⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠪⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠯⠀⠸⠸⢀⣸⣪⣴⣷⠇⣶⣿⣳⣻⣿⣿⣻⣶⣿⣾⣿⣿⣾⣼⣿⣇⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣶⣶⣣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⠇⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣀⡀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠒⠉⠹⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢿⠀⠀⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⠾⠟⠓⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣵⠆⠸⡿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣰⣶⣶⣾⡾⠿⠿⠋⠁⠀⠁⠀⣀⣠⣤⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠿⣿⣿⣼⣇⠀⠉⠈⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠠⠄⠈⠻⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠏⠁⠀⠀⠀⠀⠀⠀⠈⢦⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠙⢧⠀⡈⠿⠿⠟⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣷⣶⣴⡖⠄⠄⠀⠤⣾⡿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣿⣿⠦⣀⠀⠀⠀⠀⡀⠀⠀⣴⣿⣿⣷⣶⣾⡿⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡟⣿⣛⣿⣽⢻⣿⣿⣇⢻⣿⣻⣋⣽⣟⣽⣷⣿⣿⣿⣿⡿⣟⣫⣻⣧⣛⢛⡛⣽⣿⣛⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⡟⣇⡀⢀⠐⣶⣾⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠠⠀⠀⠀⣠⣤⣶⣶⣶⣶⣾⣿⣿⣿⣷⣿⣶⣶⣶⣶⣆⣷⣿⣾⡷⠶⠴⠶⠶⣿⣿⣿⣿⣶⣿⡶⡿⣽⠶⢶⢷⠶⠶⠶⢶⣉⡉⢹⣿⣿⣿⠏⣥⣦⠀⡀⠀⠀⠈⢿⣦⣾⡇⣻⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣿⣿⡇⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⠿⠃⠛⠠⣐⡂⠀⢫⠉⣩⣟⡢⢼⣿⣿⣿⣷⣾⣿⣾⣿⣦⡀⢠⣿⣿⠟⡿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⢆⣶⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⡿⢻⠿⣻⣔⣤⡖⢺⣿⣵⣧⡿⣺⠃⡝⠿⡿⡚⢻⣿⣿⣿⣿⣿⣿⢿⣿⡄⠈⠙⠒⠂⠠⢿⣿⢿⠿⠛⠙⢃⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣽⣿⣿⣿⣧⣯⣼⣿⣿⣿⣿⣄⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⣄⣀⡀⢠⣤⣶⣦⡀⣄⣀⣀⠀⣀⣀⡀⣀⣀⣀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣩⣿⣿⣯⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⡏⢀⣼⣿⢻⣿⣿⣽⣿⣿⣿⣿⣿⣯⣾⣿⢋⣵⣶⣽⠠⣦⣿⢡⣤⣨⣗⢰⣢⣶⡆⢰⣶⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡗⢛⣛⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⡏⣿⣿⢿⣿⣟⣿⡟⣻⣿⠚⣛⣛⣇⣿⣿⣿⡇⢼⣿⣿⣧⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⠐⠢⠚⠷⠮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢧⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢛⡿⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⢏⣿⣿⣿⡇⣸⣿⣿⠉⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢐⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣷⣿⣿⣷⡆⢐⣉⠶⣶⣿⣶⣾⣿⣿⡖⠂⠀⣀⣀⢁⠀⢈⣡⣴⣾⣷⣶⣶⣿⣷⣶⣶⣿⣿⣶⣶⣿⣿⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠪⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⡸⠰⢀⡸⠪⣬⣵⠇⣴⣾⣳⣻⣿⣿⣻⣬⣽⣾⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣷⣶⣣⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣠⣄⠰⣵⣿⣿⣿⣿⣿⣿⣶⣿⡏⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⣶⣼⣿⣿⣿⣿⣿⣿⣯⣿⣟⣻⣴⣯⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣀⣀⡀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣀⡀⠀⠀⠀⠀⢀⡀⢻⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⠟⠻⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣴⣶⠶⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢿⢻⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⠸⠿⠿⠏⠉⠉⠉⠀⠀⣀⣴⣿⠿⠿⠟⠿⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⡿⣿⣧⣿⠀⠈⠀⠉⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠸⠗⠁⠈⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠻⠁⠀⠀⠀⠀⠀⠀⠉⢫⠉⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⠿⠏⢹⡄⠀⠛⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡼⢿⣷⣦⢰⡂⠀⠀⠀⠠⣠⠾⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⣠⣿⣿⣿⣷⢄⠀⠀⠀⠀⠠⣦⠀⠀⣤⣿⣿⣷⣦⣾⡿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⣼⣿⡟⣿⣙⣿⣽⢻⣿⣻⣇⢻⣿⣻⣋⣽⣟⡝⣧⣿⣿⣿⣿⡟⣟⣋⣿⣯⣛⢛⡛⣽⣿⣛⣘⣿⣿⣿⣿⣿⣿⣿⣟⡏⣥⣉⡟⣇⡀⢀⠰⣶⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣦⣤⣾⣿⣿⣿⣷⣿⣶⣶⣶⣶⣆⣷⣿⣾⡷⠶⠴⠶⠶⣾⣿⣿⣿⣿⣿⣷⠿⡽⠶⡶⠷⠶⠶⠶⢶⣉⡉⢹⣿⣿⣿⢿⣷⡖⣀⡀⠀⠀⠈⢿⣦⣾⠃⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⢻⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣽⣿⡇⠀⠀⣼⣶⣼⣿⣿⣿⣿⡿⠟⠓⠑⠠⣐⠂⠈⡹⠉⣩⣟⣦⣼⣿⣿⣿⣷⣿⣷⣿⣷⣄⡀⢠⣿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⢠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⠿⢻⢗⣓⣶⣴⡖⣺⣿⣼⢳⡇⣾⢨⡟⢿⡗⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠒⠀⠢⣿⣿⠟⠻⠛⠻⢃⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣬⣳⣷⣿⣧⢇⣴⣿⣿⣿⣿⣆⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⣀⣠⣤⣤⣀⣀⣀⣀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⡏⣉⣏⣿⡯⣿⣿⣿⣿⣾⢫⣿⣿⣿⣿⣿⡏⢠⣼⣿⢻⣿⣿⣽⣿⣿⣿⣿⣿⢯⣾⣿⢋⣵⣶⣽⠀⡀⣿⢠⣾⣿⣷⣾⣠⣶⡆⢰⣶⣸⡏⢴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣟⣛⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⡗⢛⣛⣿⢸⣿⣿⣿⣟⣿⣾⣿⣿⠉⣿⣿⢾⣿⣟⣿⡖⡓⣿⢚⣛⣛⡇⣿⣿⣿⡇⣿⣿⣿⣷⣌⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠄⢒⣿⣯⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⡿⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⠇⣿⣿⣿⡇⣿⣿⣿⠻⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢐⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣿⣷⠆⢀⣋⢶⣶⣿⣶⣾⣿⣿⣶⠞⠀⣀⣀⢈⠀⢈⣁⣶⣾⣷⣶⣶⣿⣿⣶⣾⣿⣿⣷⣾⣿⣿⣷⣶⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠪⠹⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣟⡿⠿⠀⠸⠸⠈⠹⠫⢹⣿⠇⣼⣷⣳⣳⣿⣿⣻⣤⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣿⣷⣣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣏⢁⢀⠄⢤⣴⣿⣿⣿⣿⣿⣶⣿⠇⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣿⣶⣾⣼⣯⣿⣟⣧⣿⣯⣿⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣀⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣶⣶⣶⣶⣾⣿⣶⣶⣾⣿⣯⣤⣖⠊⣿⢿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⠉⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠸⠿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡿⠁⠀⠀⠀⠈⠙⠻⠏⠉⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠀⠰⠼⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⣴⣾⠛⠉⠉⠉⠉⠉⠉⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢠⣬⣇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠈⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡆⢹⣿⣿⢀⡀⠀⠀⠀⠀⡀⠈⢿⣿⡍⠀⠀⠀⠀⠀⢀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠀⣰⣿⣶⣦⣰⣿⣷⣶⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⢀⢈⣿⡟⣿⣙⣿⢽⢻⣿⣿⣇⢻⣿⣿⣛⣽⣟⡙⣇⣟⣻⣿⣿⡟⣛⣉⣿⣇⣻⢛⡋⣽⣿⣛⣘⣿⣿⣿⣿⡟⣿⣿⣟⡏⣥⣉⡋⣇⡀⢀⠲⣶⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣋⣻⣿⣿⣿⣷⣷⣶⣶⣶⣶⣆⣷⡾⣾⡶⠶⠴⠶⠲⠦⢶⣿⣿⣿⣿⣶⣿⠵⢶⠶⠶⡶⢶⢶⣶⡁⠈⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠘⣷⣤⣾⠃⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣁⣉⣻⣿⣇⠀⠀⣾⣦⣀⣾⣿⣿⣿⠟⠛⠀⠀⣀⡝⠀⣁⠋⣤⡮⣍⣲⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀

⠀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⡿⣟⣟⢞⣴⣢⢯⢪⣿⣷⠇⣟⣸⡇⣮⠛⡞⠫⠋⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠉⠛⠒⠂⠠⢿⣿⠟⠿⠻⠻⠇⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣬⣳⣵⣿⡇⠀⣼⣿⣿⣿⣿⣧⡀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⢀⣤⣤⣤⡀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⡏⣉⣗⣿⡯⣿⣿⣿⣷⣾⢻⣿⣿⣿⣿⣿⡏⣠⣼⣿⢹⣿⣿⣽⣿⣿⣿⣿⣿⢯⣾⣿⢋⣵⣶⣽⠀⢦⣿⢰⣿⣿⡇⣾⣤⣶⡆⣴⣶⣸⡏⢴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣟⣛⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⣛⣿⢸⣿⣿⢿⣟⣻⣾⣿⣿⠚⣿⣿⢿⣿⣟⣿⡖⣻⣿⢚⣛⣛⡅⣿⣿⣿⡇⣿⣿⣿⣷⣌⡙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠠⠴⢴⣿⣯⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣀⠙⡿⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⠅⣿⣿⣿⡇⣿⣿⣿⡻⣿⣿⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢐⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣿⣶⠆⢀⣻⣶⣶⣿⣶⣾⣿⣿⣶⡾⠆⣀⣀⢁⠀⢈⣡⣴⣾⣷⣶⣾⣿⣿⣶⣾⣿⣿⣷⣾⣿⣿⣷⣷⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠪⠹⢻⣿⣿⢯⣿⣿⣿⣿⣿⣿⣻⣝⢿⠯⠀⠸⠰⠈⢹⠫⢻⣿⠇⣹⡿⣳⣳⣿⣿⣻⣴⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣿⣿⣣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣽⣿⢿⣿⣿⣿⣿⡟⣿⣿⡏⠉⢄⡤⢴⣴⣿⣿⣿⣿⣿⣶⣿⠏⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⣴⣿⣶⣮⣿⣟⣻⣿⣿⣯⣿⣬⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣤⣤⣤⣶⣶⣾⣶⣶⣾⣯⣽⣿⣿⣿⣿⠯⣍⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠉⠀⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢹⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠈⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠛⡿⠉⠙⠛⠛⣿⠟⠀⠈⠉⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠠⢐⠀⠠⠀⠀⠋⠀⠀⠀⠀⠀⠉⣩⣽⠿⠟⠛⠉⠉⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⣘⣶⡀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠻⢿⣿⠷⡀⠀⠀⠀⠀⡠⠺⢿⣿⡞⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⣶⣿⣦⣦⣴⣿⣷⣶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⠀⣠⣾⡟⣿⣙⣿⢽⢻⣿⣻⣇⢻⣿⣿⣋⣽⣟⡝⣇⣟⢻⣿⣧⡟⣛⣉⣻⣇⣻⢻⡋⣽⣿⣛⣘⣿⣿⣟⣿⡟⣿⣿⣟⡏⣭⣉⡋⣇⡀⢀⢲⣶⣾⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡟⢿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣆⣷⣿⣶⣷⠶⠴⠶⠶⠦⠶⢾⣾⣿⣿⡷⣿⠵⠶⠶⠶⡶⠶⠶⢶⡁⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠺⣧⣤⣿⠂⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠋⢛⣛⣻⡃⠀⠀⣾⣦⣀⣶⣿⣿⣿⠟⠋⠁⢀⣬⣅⡀⣰⢀⠤⢖⣮⣹⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⢄⢰⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀

⠀⠀⣲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣟⡟⣽⣾⡶⢯⡹⣿⣾⢻⣇⣿⢰⡏⢹⠎⠛⣹⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠉⠛⠚⠒⠾⣿⣿⠿⠿⠛⠻⠇⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣬⣓⣽⣇⡇⠀⣼⣿⣿⣿⣿⣿⣀⠀⢀⣲⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⢀⣠⣤⣤⡀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠿⣿⡿⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⣿⡏⣉⣇⣿⡏⣿⣿⣿⣿⣾⢫⣿⣿⣿⣿⣿⡏⣠⣾⣿⢹⣿⣿⣹⣿⣿⣿⣿⣿⢧⣾⣿⢋⣴⣶⣽⠀⣴⣿⢱⣿⣿⠆⣾⣠⣶⡆⣰⣶⣸⡏⢴⣶⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣷⣿⣿⣿⣗⣛⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⣛⣿⢸⣿⣿⢿⣟⣻⣾⣿⣿⠎⣿⣿⢿⣿⢟⣿⡖⣻⣿⢚⣛⣛⡇⣿⣿⣿⡇⣿⣿⣿⣷⣌⡙⠻⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠄⢆⣿⣯⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⡿⣼⣿⣿⣿⢷⣿⣿⣸⣿⣿⠅⣿⣿⣿⡇⣿⣿⣿⠻⣿⣿⠄⣘⠿⠅⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣿⣶⠂⢀⣹⢶⣶⣿⣶⣾⣿⣿⣶⡿⠂⣀⣀⢚⠒⢊⣡⣴⣾⣷⣶⣾⣿⣿⣶⣾⣿⣿⣷⣾⣿⣿⣷⣷⣶⣾⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠪⠹⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣛⢿⠧⠀⠸⠰⠈⠹⠫⢿⣿⠏⣿⣿⣓⣸⣿⣿⣻⣴⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣿⣿⣯⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣽⢿⣿⣿⣿⣿⣿⡟⣿⣿⣛⠁⢠⡤⢠⣰⣿⣿⣿⣿⣿⣶⣿⡇⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣥⣶⣵⣶⣭⣝⡿⣹⣿⣿⣿⣮⣤⣴⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣀⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠸⣿⡿⢿⣟⣛⣩⠽⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣠⣤⣶⣶⣶⣶⡖⠉⢽⣿⣧⣶⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠛⠉⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢹⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠛⠛⠛⠛⠛⣻⣿⣿⠇⠀⠈⠉⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠀⠀⠀⠠⠀⠀⠂⠈⠙⠻⠿⠟⠉⠉⢿⣿⡿⠟⠋⠉⠀⠉⢹⣿⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡉⠀⠀⠀⠀⠀⢀⡈⠻⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠀⠀⠀⠀⠀⡸⢿⣿⣿⣯⠈⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣴⣾⣦⣤⣶⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⢧⣼⣾⣿⣿⣙⣿⣽⢻⣿⣿⣇⢻⣿⣿⣋⡹⣟⡝⣇⣟⠻⣿⣇⡟⣙⣉⣿⣇⣛⢻⡛⣽⣿⣿⣸⣿⣿⣿⣿⡿⣿⣿⣛⡏⣧⣉⡋⣇⡀⠀⣴⣶⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡻⠿⣾⣿⣿⣿⣷⣶⣶⣶⣶⣆⣷⡾⣶⣶⠶⠴⠶⠲⠦⠶⠾⣰⣿⣷⡶⠶⠱⠶⠶⠶⢶⡶⠶⣶⣁⡸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣶⣦⣤⣗⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠙⠛⢻⡏⠀⠀⣾⣦⢀⣴⣾⣿⣿⠛⠁⠀⣀⣤⢁⢠⡌⣠⠢⣲⣿⣟⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢷⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣲⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣟⣻⠟⣽⣯⡞⠎⡾⡿⡞⢸⢡⣏⢸⡎⠿⠌⡏⣿⣿⣿⣿⣧⡤⠀⠀⠀⠀⠈⠙⠗⠓⠪⣿⣿⡿⣿⣿⠟⠻⠂⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣱⡆⠃⠀⣼⣿⣿⣿⣿⣿⣇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⢀⣠⣄⣤⣀⣀⣲⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⡇⠀⢿⣿⣿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⠉⢉⣇⣿⡏⣭⣭⣿⣄⣾⢫⣿⣿⣿⣿⣿⡏⣰⣿⣿⢹⣿⣿⢹⣿⣿⣿⣿⣿⢣⣶⣾⢋⣵⣶⢽⠰⣶⣿⢰⣿⣿⠀⣾⣠⣶⡆⢰⣶⣸⡏⢴⣶⡄⢽⣋⠢⠀⠉⠛⠛⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣠⣿⣿⣿⡗⣛⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⣛⣿⢸⣿⣿⢼⣟⣻⣾⣿⣿⠘⣿⣿⣾⣿⣟⣾⣟⣿⣿⢚⣛⣛⡀⣿⣿⣿⡇⢸⣿⣿⣷⣌⡙⠻⡯⠻⣧⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢃⣿⣈⢿⣿⣿⣇⣿⣿⣿⢻⣿⣽⣿⣿⣿⣿⣿⣇⣿⣿⣿⣸⣿⣿⣺⣿⣿⣿⣿⣿⡀⣽⣿⣿⣿⣿⣿⢿⣿⣿⣸⣿⣿⠀⣿⣿⣿⡇⣸⣿⣿⠻⣿⣿⠄⠀⠰⠾⡏⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣺⣿⣶⣶⣆⣶⣶⣿⣿⣷⣿⣷⣾⣿⣦⠂⢘⣿⣶⣶⣿⣶⣾⣿⣿⣶⣿⡆⣀⣼⣿⣿⣾⣿⣶⣿⣿⣶⣾⣿⣿⣶⣿⣿⣿⣷⣾⣿⣿⣷⣶⣶⣞⣃⡹⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠪⠹⢪⡿⣽⣾⣿⣿⣿⣿⣿⣿⡻⣙⢻⠮⠀⠸⠰⠈⠻⠯⣿⣿⠏⣿⣿⣳⣰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣿⣿⣧⣻⠓⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢱⡿⣿⣿⣿⣿⣿⣿⣿⠻⠄⠀⠀⠀⠀⣰⣶⣶⣿⣷⣿⣶⣿⠇⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣤⣼⣍⣉⣻⣿⣿⣿⣏⣻⣤⣤⣤⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣀⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡄⠀⠒⠉⢹⣿⢠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⠇⣀⣤⣤⢸⣿⡿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠛⢻⣿⣿⣿⣿⠃⠀⠈⠉⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⠀⠀⠀⣘⣀⠄⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⠟⠋⠉⠙⢿⣿⣿⣇⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠤⠀⠀⡂⠀⠉⠁⠀⠀⠉⠉⠉⠀⠀⣠⣿⡿⠁⠀⠀⠀⣀⡈⠻⣿⣿⣿⢧⠀⠀⠀⠀⢀⣾⡃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⣿⣿⣷⡄⠀⠀⠸⡿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣠⣶⣦⣤⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣼⣿⣿⣿⣙⣿⢽⢻⣿⣻⣇⢻⣿⣿⣋⣹⣟⡙⣇⣟⢻⣿⣇⡟⣙⣋⣿⣇⣛⢻⡛⣿⣿⣿⣾⣿⣿⣿⣿⡟⣟⣻⣟⡟⣧⣉⡋⣇⣀⣤⣾⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⠿⣷⣿⣿⣿⣷⣶⣶⣶⡶⢆⢷⣾⣶⣷⣶⠶⠶⠶⠦⠶⠾⠰⣾⡶⠶⠶⠱⠶⠶⠶⠶⠶⢶⣾⣥⣼⣿⣿⣿⡟⠁⠈⠀⠀⠀⢠⣤⣶⣶⣼⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠛⠻⢻⣿⠃⢀⣾⣦⢠⣶⣆⠸⣿⠁⠀⡀⣠⡴⣠⢠⣇⡔⢻⣿⣿⣏⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢲⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣆⣿⣿⣿⡿⣿⣯⠿⣿⣯⡋⠀⠛⢳⡏⣿⣶⣇⣿⢀⠿⡈⠋⣿⣿⣿⣦⡄⠐⠀⠀⠀⠀⠻⠿⢼⣿⣿⣿⣿⣿⣿⣿⡒⠳⠀⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⣰⡄⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⢀⣠⣤⣀⡀⣨⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣴⣟⡸⣿⣿⣿⣿⣿⣿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⠉⢉⣇⣿⡏⣭⣭⣿⣄⣼⢫⣿⣿⣿⣿⣿⡏⣰⣿⣿⢹⣿⣿⢹⣿⣿⣿⣿⣿⢣⣶⣾⢋⣤⣤⢹⢰⣷⣿⢰⣿⣿⡄⣾⣠⣶⡆⢰⣶⣸⡏⢰⣶⡄⠠⠍⠈⠙⠻⠿⠿⠛⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣢⣿⣿⣿⡗⣛⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⣛⣿⢸⣿⣿⢼⣟⣻⣾⣿⣿⠝⣿⣿⣾⣿⣿⣶⣟⣿⡟⢚⣛⣛⡀⣿⣿⣿⡇⢸⣿⣿⣷⣌⠙⠻⡈⠉⢳⢄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢽⣿⣿⣇⣿⣿⣿⢻⣿⣽⣿⣿⡿⢷⣿⣇⣿⣿⣿⣸⣿⣿⣺⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⢿⣿⡷⢸⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⠹⣿⣿⠄⠉⠀⠶⢿⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣺⣿⣶⣶⣶⣶⣶⣿⣿⣷⣿⣷⣾⣿⣦⠀⢈⣻⣶⣶⣿⣶⣾⣿⣿⣶⣿⠖⣂⣿⣿⣿⣾⣷⣷⣿⣷⣶⣾⣿⣿⣶⣾⣿⣿⣶⣾⣿⣿⣷⣶⣶⣾⠃⠉⢥⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠢⠹⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⠮⠀⠸⠰⠈⠻⢯⣿⣿⠏⣿⡿⣓⣠⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣿⣿⣧⣸⣿⡂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⣴⣶⣶⣷⣿⣶⣿⠇⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣬⣬⣽⣿⣿⣿⣿⣿⣿⣠⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣀⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠠⠒⠉⠸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⡆⠐⠀⣀⣀⢰⣿⣼⠏⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠛⠁⠀⠈⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣀⣀⣀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⠛⠋⢿⣿⣿⣿⣟⣿⠃⠀⠈⠉⠙⠉⠁⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠠⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠟⠂⠘⠻⠿⠿⠿⠟⠋⠁⣹⡟⠁⠀⠀⢀⣌⠙⠻⣿⣿⡿⠧⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣾⣿⣷⣦⠀⠀⣿⣿⣿⣷⣼⣿⣷⣶⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⣰⣿⠟⣟⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣿⣿⣿⣝⣿⢽⢻⣿⣻⣇⢻⣿⣿⣛⡹⣟⡙⣅⣿⣿⣯⣇⡟⣙⣉⣽⣯⣛⢛⡛⣿⣿⣿⣾⣿⣿⣿⣿⡟⣿⣿⣟⡟⣧⣉⡋⣇⣰⣿⣷⣾⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡻⢧⣿⣿⣿⣿⣷⣶⣶⣶⢆⣷⡾⣶⣶⣶⡶⠶⠶⠦⠶⠾⢰⣶⠶⠶⠶⠰⠶⠶⠶⠶⠶⣷⣾⣕⣼⣿⣿⣿⡿⠇⠵⠀⠀⠀⢰⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⡿⠫⠛⣿⣿⠟⢰⣶⣆⢠⣶⡆⠀⡏⠀⠀⠀⣤⡦⡤⣲⢧⡞⡻⣿⡿⣯⣿⣿⣿⡁⠀⠀⠀⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣆⣽⣿⣿⡿⣿⡯⠓⣾⣮⠘⢠⢑⢻⣃⣟⣾⡇⣿⡸⢛⡜⠹⣿⣿⣷⣤⠐⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⣐⡄⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⢀⣠⣄⣀⣀⣸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢡⣟⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⠉⢉⣇⣿⡏⣭⣭⣿⣀⣼⢫⣿⣿⣿⣿⣿⡏⣴⣿⣿⢹⣿⣿⢹⣿⣿⢿⣿⣿⢣⣾⣿⢋⣥⣦⢹⢰⣷⣿⢰⣿⣿⡀⣾⣠⣶⡆⢰⣶⣸⡏⢰⣶⡄⡠⠌⠙⠿⢿⣿⣿⠿⠛⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣢⣿⣿⣿⡗⣛⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⣛⣿⢸⣿⣿⢼⣟⣻⣾⣿⣿⠘⣿⣿⣾⣿⣿⣿⣟⣿⣷⢚⣛⣛⠀⣿⣿⣿⡇⢸⣿⣿⣷⣌⠙⠻⣌⠉⠙⡦⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠿⣿⣿⣇⣿⣿⣿⣻⣿⣽⣿⣿⡿⢷⣾⣇⣿⣿⣿⣸⣿⣿⣺⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⢿⣿⡷⢸⣿⣿⠂⣿⣿⣿⡇⢸⣿⣿⠹⣿⣿⠀⠙⠀⠰⠾⡟⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣬⡭⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣿⣆⠀⢘⣿⣶⣶⣿⣶⣶⣿⣿⣶⣿⡶⣆⣿⣿⣿⣿⣷⣿⣿⣷⣶⣾⣿⣿⣶⣾⣿⣿⣶⣾⣿⣿⣷⣶⣶⣎⠂⠄⢱⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠢⠸⢀⡽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠸⠸⠘⠻⢯⣿⣿⠏⣿⡿⣳⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣿⣿⣧⣰⣾⡧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣰⣦⣶⣾⣶⣿⣶⣿⠇⡍⢹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⣀⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⢕⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠠⠒⠉⠸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⠀⠡⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠒⠐⠁⠀⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢠⣀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⠋⠙⢻⣿⣿⣿⣿⡏⢿⠇⠀⠈⠉⠉⠉⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣷⣠⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⣿⣿⣿⣿⡿⠟⢉⡟⠁⠀⠀⣀⣾⡛⠻⣿⣿⡿⠧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣷⣦⡄⠰⣿⣿⣿⣷⣬⣿⣷⣶⡀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⢠⣾⡿⠻⡇⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣾⣿⣿⣟⣿⢽⢻⣿⣻⣇⢻⣿⣿⣻⡽⣟⡙⣅⣿⣿⣟⣇⡟⣙⣉⣿⣯⣻⢿⡛⣿⣿⣻⣿⣿⣿⣿⣿⡟⣿⣿⣟⡟⣧⣏⡋⣇⣰⣾⣷⣾⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣘⢿⣿⣿⣿⣿⣷⣶⣶⣶⢆⣷⢾⣶⣶⣶⡶⠶⠶⠦⠶⠾⢹⡖⠶⠶⠶⠰⢶⠶⠶⡶⢶⣶⢾⣇⣿⣯⣿⣿⣿⡿⠃⠀⠀⠀⠰⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠟⢰⣶⡄⣠⣶⡀⠰⡋⠀⣀⣀⣶⣦⣖⣾⢵⢟⡽⣿⡿⣽⢿⣿⣿⡋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀

⠀⠀⠰⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣆⣿⣿⣿⡿⣿⡯⠁⣾⡟⠙⣸⠛⣿⣹⣷⣿⣸⣇⡜⣳⢹⢸⢿⣿⣷⣴⡒⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⠀⠈⠐⠀⠀⠀

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⢀⣀⣤⣀⣴⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⡭⣿⠉⠉⠇⣹⡏⣉⢉⡻⢀⣼⢫⣿⣿⣿⣿⣿⡯⣷⣾⣿⢹⣿⣿⢹⣿⣿⣿⣿⣿⢣⣶⣿⢋⣤⣦⣽⢸⣷⣿⢰⣿⣿⠀⣾⣠⣶⡆⢰⣶⣸⡏⢠⣶⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢆⣾⣿⣿⡗⣓⣻⢰⣿⣿⣾⣿⣿⣿⣿⢿⡗⣛⣛⣿⢸⣿⣿⢼⣟⣿⣿⣿⣿⢸⣿⣿⣾⣿⣿⣿⡟⣻⣷⢚⣛⣛⠀⣿⣿⣿⡇⢸⣿⣿⣷⣌⠙⠻⣾⡛⠿⣿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠽⢫⣿⣇⣿⣿⣾⣻⣿⣽⣿⣯⡽⢷⣼⣇⣿⣿⣿⣸⣿⣿⣸⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⢿⣿⡷⣸⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⠙⣿⣿⠀⠹⠃⠀⠀⠽⠛⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠈⢀⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣿⣀⠀⢸⣿⣶⣶⣿⣶⣾⣿⣿⣶⣾⡶⣄⣿⣿⣿⣾⣷⣾⣿⣷⣶⣾⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣷⣶⣶⣾⠳⠀⠐⣂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠢⠸⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠸⠸⠙⢿⣯⣿⣿⠇⣿⣿⣓⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⣿⣿⣧⠀⢀⣦⡀⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⣀⣤⣤⣴⣿⣿⣶⣿⠇⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣀⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⡿⡿⠟⠃⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠠⠒⠉⠸⣿⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⠀⠀⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⡤⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣄⣀⡀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠋⠿⠿⣿⣿⣿⣿⣿⡟⢿⠇⠀⠈⠉⠉⠉⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⣿⣿⣿⣿⣦⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⣿⡻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⣋⡝⠁⠀⠀⢀⣠⣍⠻⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⢿⣿⣿⣾⡶⠰⣿⣿⣿⣿⣮⣿⣿⣶⡄⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⣴⡿⠋⢿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⢽⢻⣿⣻⣏⢻⣿⣿⣻⡽⣟⡙⣅⣿⣿⣏⣇⡟⣙⣹⣿⣯⣿⢻⡛⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣟⡟⣽⣿⣯⣇⡀⢈⣶⣿⣶⣾⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡙⣿⣿⢿⣿⣷⣶⣶⣶⣆⣷⡾⣶⣶⣶⡶⠶⠶⠦⠶⠾⢻⡖⠶⠶⠶⢴⡶⠶⡿⢶⣿⣿⣿⣽⣿⣿⠀⢸⣿⡏⠀⠀⠀⠀⠀⢸⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣶⣦⢀⣴⣦⠀⢼⢋⢁⣀⣴⣶⣴⣶⢧⡎⣿⢿⣿⢿⣿⣿⣾⣿⡿⠧⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀

⠀⠀⠰⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⢟⣿⠿⢽⣿⡟⢫⢛⢻⣅⣿⣾⣇⣿⣼⢹⡞⡝⡿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤

[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⢀⣀⣄⣀⣤⣿⣎⣸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠉⠉⠇⢹⡏⠉⠉⡻⢀⣼⢫⣿⣿⣿⣿⣿⡯⣿⣾⣿⢹⣿⣿⣽⣿⣿⣿⣿⣿⢡⣶⣿⢋⣴⣦⣿⢸⣷⣖⢰⣿⣿⡀⣴⣠⣶⡆⢠⣶⣸⡏⢠⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⠀⣾⣿⣿⡗⣒⣺⢠⣿⣿⣿⣿⣿⣿⣿⢿⡗⣛⢛⣿⢸⣿⣿⣿⣟⣿⣿⣿⣿⢸⣿⣟⣾⣿⣿⣿⡟⣹⣟⢚⣛⣛⠀⢿⣿⣿⡇⢸⣿⣿⣷⣈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠉⠋⣹⣇⣿⣿⣿⣻⣿⣽⣿⣯⡵⠶⣸⣇⣿⣿⣿⣸⣿⣿⣸⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⢿⣿⣯⣸⣿⣿⠀⣾⣿⣿⡇⢸⣿⣿⠙⣿⣿⠀⠸⠏⠉⠛⢿⡿⠟⠋⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠈⢀⣴⣶⣶⣶⣿⣿⣿⣿⣷⣶⣌⣀⠀⢸⣿⣶⣶⣿⣶⣶⣿⣿⣶⣾⣶⣀⣻⣿⣿⣾⣷⣾⣿⣷⣶⣶⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣶⣶⣶⣼⠓⢀⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠢⠨⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠸⠸⢻⣿⣿⣿⣿⠇⣿⣿⣓⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣧⣵⣿⣷⣸⣿⣿⣧⠁⠀⣤⡄⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣲⣾⣿⣿⣿⣿⣶⣿⠏⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃⣀⢀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠭⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠒⠉⠸⣿⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⠀⠀⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣄⣀⡀⠁⠀⠀⠀⣴⣾⣿⣿⠿⢋⠿⣿⣿⣿⣿⣿⣿⡟⣿⠇⠀⠈⠉⠉⠉⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⣿⣿⣿⣿⣦⡄⠀⠀⠈⠉⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣋⡍⠁⠀⠀⢀⣤⣌⠙⣿⣿⡿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢿⣿⣿⣿⣶⠴⣿⣿⣿⣿⣾⣿⣿⣶⡄⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⢀⣼⠿⠋⢿⡿⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⢽⢻⣿⣻⣇⢻⣿⣿⣻⡽⣛⡙⣅⣿⣿⣟⣇⡟⣙⣹⣿⣧⣻⢻⡟⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣟⡏⣥⣿⣯⣇⡀⠈⣶⣿⣷⣶⣾⣶⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡘⣿⡿⢿⣿⣿⣷⣶⣶⣆⣷⡾⣶⣶⣶⡶⠶⠶⠦⠶⠾⢻⢆⣶⠶⠷⣵⠶⠶⡾⣶⣿⣿⣿⣿⣿⣿⠇⢰⣿⡏⠀⠀⠀⠀⠀⢸⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣷⣦⢠⣶⡆⠀⢞⠉⣉⣠⣾⣾⣖⣾⢵⣏⣿⢿⣿⣿⣿⣿⣴⣿⣿⡧⠀⢀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀

⠀⠀⠰⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣟⣿⠿⣿⣿⡟⣿⢹⢿⣵⣿⣿⣼⣿⡎⢻⣺⡸⢻⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤

[22A⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⣘⡀⢀⣀⣼⣳⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⢀⣀⣀⣀⣼⣷⣄⣾⣬⣾⣶⣾⣿⣿⣿⣶⣛⣤⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠉⠇⢹⡏⠉⠉⡻⢀⣼⢫⣿⣿⣿⣿⣿⡏⣟⣺⣿⢩⣿⣿⣽⣿⣿⣿⣿⣿⣳⣶⣾⢋⣤⣴⣽⢨⣃⡇⢰⣿⣾⠀⣴⣀⣴⡆⢠⣴⢨⡏⢠⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠀⣶⣿⣾⡗⣒⣺⢀⣾⣿⣾⣿⣿⣿⣿⣿⡗⣛⣛⣿⢸⣿⣿⣿⣟⣿⣿⣿⣿⢺⣿⣟⣾⣿⣿⣿⡟⣹⡇⢚⣛⣛⠀⢾⣿⣿⡇⢸⣯⣕⣦⣈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠉⣹⣇⣿⣿⣿⣻⣿⣿⣿⣯⡭⠄⣸⣇⣿⣿⣿⣸⣿⣿⣻⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⢴⣿⡇⢸⣿⣿⠀⣾⣿⣿⡇⢸⣿⣿⠉⣻⣿⠀⡸⠟⢻⣿⣿⣿⣿⡿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠈⢀⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣌⣀⠀⢘⣿⣶⣶⣷⣶⣶⣿⣿⣶⣾⣶⣆⣸⣿⣿⣾⣷⣾⣿⣷⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣿⣿⣶⣤⣦⣴⡆⠀⠀⠨⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠪⠨⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠸⢸⣿⣿⣿⣿⣿⡇⢸⣿⣳⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣽⣿⣇⣕⣿⣷⣸⣿⣿⣣⠁⠀⢠⣀⠑⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣸⣿⣿⣿⣿⣿⣶⣿⠏⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⢀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣟⠊⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣾⣿⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣦⠀⠀⠒⠉⠸⣿⠀⠀⣿⢷⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⠀⠀⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠁⠁⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣆⢀⣄⣄⣀⠀⣼⣷⣷⣷⣾⣿⣿⠿⢋⠿⢿⣿⣿⣿⣿⣿⠏⢿⠃⠀⠈⠉⠉⠉⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠋⠉⠙⣿⣿⣿⣿⣷⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣏⠙⠁⠀⠀⢀⣠⣈⠙⣿⣿⡿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢿⣿⣿⣾⣦⢰⣿⣿⣿⣿⣦⣿⣿⣶⡆⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⢀⣼⠿⠋⢿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢽⢻⣿⣻⣏⢻⣿⣿⣻⡽⣛⡙⣅⣿⣿⣿⣇⡟⣙⣿⣿⣧⣻⢻⡛⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣻⣛⡏⣥⣿⣿⣇⡀⠀⢱⣾⣷⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣈⣿⡿⢿⣿⣿⣶⣶⣶⣆⣷⡾⣴⣶⣶⡶⠶⠶⠦⠶⠾⢻⠆⡶⠶⠷⣴⠶⢶⡿⣶⣿⣿⣾⣿⣿⣿⡇⢀⣿⡏⠁⠀⠀⠀⠀⠈⣿⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀

⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣿⣿⣿⣿⣿⣿⣛⣿⣿⢫⣶⣦⢠⣶⡆⠀⢞⡉⣉⣤⣶⣮⣖⡾⣷⢫⡿⣿⡿⣿⣿⣿⣤⣾⣿⣗⠀⡠⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀

⠀⠀⠰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣟⣿⠟⣿⣾⡛⣟⡻⣿⣸⣿⣿⣼⣧⡏⣵⣹⣹⢻⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣶⣦

[22A⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⣘⡀⢀⣀⣔⣵⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣀⣀⣄⣜⣧⣄⣆⣤⣚⣰⣾⣿⣿⣿⣶⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠭⠉⠇⢹⡏⠉⠉⡻⢀⣼⢫⣿⣿⣿⢿⣿⡏⡾⡂⣿⢩⣿⣿⣽⣿⣿⣿⣿⣿⣷⣶⣿⢋⣤⣴⣽⠨⣄⣧⢰⣽⣾⠀⣴⣀⣴⡆⢠⣴⠨⡏⢠⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠘⣆⣾⣿⡗⣒⣺⢠⣾⣿⣾⣿⣿⣿⣿⣿⡗⣛⠓⣿⢸⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⣟⣾⣿⣿⣿⡟⣹⡯⢚⣛⣛⠀⢼⣿⣿⡇⢸⣋⢀⣠⣈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣿⡀⠈⠉⣹⣇⣿⣿⣿⣻⣿⣿⣿⣯⡭⠅⣸⣇⢠⣼⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣈⣿⣿⣿⣿⣿⣿⢿⣿⣟⢸⣿⣿⠀⣾⣿⣿⡇⢸⣿⣻⠉⣛⣿⠀⡽⠿⢻⣟⣿⣿⣿⣷⠹⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠈⢠⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣯⣀⠀⢸⣱⣦⣶⣶⣶⣾⣿⣿⣶⣾⣶⣆⣸⣿⣿⣾⣷⣾⣿⣷⣶⣶⣿⣷⣶⣾⣿⣷⣶⣶⣾⣽⣦⣦⠶⣴⡧⠀⠈⠙⠙⠙⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠢⠨⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠸⢸⣿⣿⣿⣿⣿⠇⣺⣿⣓⣩⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣇⣿⣿⣿⣽⣿⣇⣅⣿⣷⣸⣿⣿⣧⢁⡀⢁⣀⠐⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣶⣿⠇⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⣤⣤⡤⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⢀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡫⢙⡟⠊⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠒⠉⠸⣿⠀⠀⣿⢷⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⢀⣄⣀⣀⠀⠀⢀⣠⣴⣾⣿⣿⡿⢯⠿⣿⣿⣿⣿⣿⣿⡏⣿⠇⠀⠈⠉⠉⠉⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠟⠉⠙⣿⣿⣿⣿⣷⡞⠉⠁⠉⠉⠉⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣏⠙⠁⠀⠀⢀⣤⣉⠻⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⢟⣿⣿⣾⣶⠰⣿⣿⣿⣿⣮⣿⣿⣶⡆⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢀⣼⠿⠋⣿⣿⠃⡀⡀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢽⢻⣿⣿⣏⢻⣿⣿⣻⡽⣛⡙⣅⣿⣿⣿⣇⡟⣙⣿⣿⣧⣻⢻⡿⣿⣿⣿⣿⣿⣛⡋⣿⣿⣟⣻⣟⡏⣥⣻⣿⣷⡄⠀⠘⣶⣿⣦⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣈⡿⣿⡿⣿⣿⣷⣾⣾⣆⣷⡾⣴⣶⣶⡶⠶⠶⠦⠶⠾⢻⢆⣶⢶⠷⣵⠶⢶⡿⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⡏⠁⠀⠀⠀⠀⠀⣸⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀

⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣄⣰⣶⡄⠀⡞⡉⣡⣤⣾⢮⣶⡞⣾⢹⡿⣿⡿⣿⣿⣯⣠⣾⣿⣷⣀⡄⢀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀

⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⠿⣿⣿⠛⡞⡏⣯⣼⣿⣿⣸⣷⡍⣷⣫⢻⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣤⣤

[22A⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣘⠀⢀⡀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣀⣠⣤⣘⣦⣆⣆⣤⣒⣒⣾⣿⣿⣿⣆⣈⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⡇⢹⡏⠉⠉⠻⢀⣼⢫⣿⣿⣿⢿⣿⡏⡞⠈⣿⢩⣿⣿⣹⣿⣿⣿⣿⣿⣿⣾⣿⢋⣤⣴⣽⠈⣆⣖⢰⣿⣾⠀⣴⣀⣤⡆⢠⣴⢀⡏⢠⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⢽⣿⣿⣾⡗⣒⣺⢠⣾⣿⣾⣿⣿⣿⣿⣿⡗⣛⣛⣿⢸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⣻⡿⠚⢛⣛⠀⢸⢯⣿⡇⢸⣃⠀⣠⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⢿⣿⡈⠉⠉⣹⣇⣿⣿⣿⣻⣿⣿⣿⣿⡭⠅⣸⣇⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣈⣿⣿⣽⣿⣿⣿⢿⣿⡧⢸⣿⣿⠀⣼⣿⣿⡇⠸⡿⢉⠉⣛⣿⠀⠹⡿⣿⡿⣿⣿⣿⣧⡋⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠈⢠⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣿⣀⠀⢀⣑⣤⣶⣶⣶⣾⣿⢿⣶⣿⣶⣆⣺⣿⣿⣾⣷⣶⣿⣷⣶⣶⣿⣷⣶⣾⣿⣷⣶⣤⣾⣿⣤⡀⠀⣐⠲⠄⠋⠹⢿⠻⠗⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠢⠨⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠸⢰⣿⣿⣯⣿⣿⢇⣾⣿⣳⢹⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣇⣿⣿⣿⣽⣿⣇⣅⣿⣷⣸⣶⣷⣫⢁⡀⠀⣀⠐⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣶⣿⠇⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣂⣠⣤⣶⣾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣮⣿⣿⣿⡟⠊⠽⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠂⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠐⠈⠸⣿⠀⠀⣿⢷⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠗⠀⠀⠀⠀⢿⠀⠀⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⣄⣀⣀⠀⠀⠀⢐⣴⣿⣿⣿⡿⢯⠿⣿⣿⣿⣿⣿⣿⡏⢿⠃⠀⠈⠉⠉⠉⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠟⠉⠙⣿⣿⣿⣿⣧⣴⠀⠙⠛⠛⠉⠉⠀⠈⠀⢹⣿⣻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣋⠘⠉⠀⠀⢀⣠⣌⠻⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠈⢻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢇⣿⣿⣿⣶⣄⣿⣿⣿⣷⣮⣿⣿⣶⡆⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢠⣾⠟⠙⣿⣿⢃⣀⡀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣄⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢽⢻⣿⣟⣏⢻⣿⣿⣻⡿⣋⡙⣇⣟⣿⣿⣇⡟⣙⣿⣿⣧⣻⢻⡿⣿⣿⣿⣿⣿⣛⡋⣿⣿⣟⣻⣛⡏⣥⣿⣿⣿⣷⠀⠀⢳⣼⣦⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣤⣤⣈⢿⣻⡿⣿⣿⣷⣾⣾⣆⣷⣾⣶⣶⣶⡾⠶⠲⠦⠶⠾⢻⢇⣶⢶⢷⣵⠶⢾⢿⣾⣿⣿⣿⣿⣿⣿⠇⠀⣼⡏⠁⠀⠀⠀⠀⠀⢠⣿⣯⢀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀

⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⡄⣴⣶⠀⠀⡚⣉⣡⣴⣿⣷⣺⣟⡿⣹⣻⣿⢿⣿⣿⣯⣀⣼⣿⣿⣀⡄⢀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀

⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⡿⣻⡿⢷⣾⣿⢻⡏⡿⣯⣾⣽⣧⣿⣽⢩⣇⣇⢻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣆⣀

[22A⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢀⣰⣿⣿⣷⣤⠈⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⢀⠐⠤⠀⠀⠄⠂⠀⢾⣬⣼⡙⠂⠈⢠⢼⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣶⣬⣤⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⡾⣎⡃⠀⣐⣠⣵⣾⣿⣶⣿⣿⣿⠹⠺⣽⢾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣦⣤⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣌⣄⣻⡿⣿⣿⣿⡿⢭⣷⣿⣆⢀⠀⠨⠏⣨⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣟⣫⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠛⠘⠁⠁⠒⠫⣿⢿⡿⣟⡉⠙⣻⣿⡇⠋⣿

⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⡿⠋⠛⠉⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⢈⣀⣀⠀⢀⠈⠀⠵⢠⣿⢧⣩⠂⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣿⣿⣿⣿⣿⢣⣸⡏⡤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣬⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣶⣿⠇⡏⢹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠟⠃⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣀⣀⣀⣀⣤⣴⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⠋⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠐⠈⠸⣿⠀⠀⣿⢷⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡿⠂⠀⠀⠀⢿⠀⠀⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⣀⣀⠀⠀⠀⢠⣾⣿⣿⣿⡿⢫⢿⣿⣿⣿⣿⣿⣿⠟⢿⠃⠀⠈⠉⠉⠉⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⢻⣿⣿⣿⣷⣤⠄⠌⠙⠛⠉⠁⠀⠁⠁⣻⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣫⣬⡉⠀⠀⠀⣀⣌⡙⢿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠈⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⣿⣿⣿⣿⠦⣾⣿⣿⣿⣦⣿⣿⣶⣆⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⣰⡿⠋⠸⣿⣿⣃⣀⣀⠀⠀⠀⠀⣠⣴⣶⣶⠶⣶⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢽⢻⣿⣟⣏⢻⣿⣻⣻⡯⣛⡙⣇⣟⣿⣿⣇⡽⣟⣿⣿⣷⣛⣿⡿⣿⣿⣿⣿⣿⣋⡋⣹⣿⣿⣻⣛⡟⣧⣉⣿⣿⣿⣦⠀⠈⢦⣵⣆⣤⣤⣄⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣄⡈⣿⣿⡿⣿⣿⣷⣶⣾⣆⣷⣾⣶⣶⣶⡾⠶⠲⠦⠶⠾⠻⣗⡶⠶⡷⡵⠶⡿⣿⣿⣿⣿⣿⣽⣿⣿⠇⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⣽⣿⣋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀

⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣶⡆⠀⢀⣋⣉⣤⣴⣿⣟⣿⣻⢏⣟⣿⣟⣿⣿⣿⣏⣠⣾⣿⣿⣇⢄⢀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠐⠀

⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⡿⣿⣿⡟⣿⢹⢹⣵⣯⣿⣾⣿⡇⣿⣽⡘⡿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣶⡆⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⡿⣿⣦⡀

[22A⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣰⣿⣧⣶⣠⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣀⠢⠀⠀⠀⠄⠀⠀⠎⠠⢬⡉⠂⠀⣠⣼⣷⠃⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣦⣾⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡧⠞⣁⠀⣀⣠⣵⣾⣶⣴⣿⣿⣾⠡⠚⡥⣾⣯⠒⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣒⣦⣛⣽⣿⣿⣿⠿⢬⣴⣿⣄⠀⠀⠠⡋⣘⡫⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿

⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠀⠁⠐⠫⣶⣟⠾⠟⠈⠙⢻⣻⡇⠹⢻

⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣄⠀⣀⡀⠠⠀⠘⢀⠱⢀⣾⣦⢉⠄⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⢉⣿⣿⣿⣿⣿⠣⣻⡏⣭⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣴⣼⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢸⣿⣿⣿⣿⣿⣶⣿⠇⡏⢹⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣂⣀⣀⣀⣀⣤⣤⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠸⣿⡟⠹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠈⠸⣿⠀⠀⣿⢵⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⢿⠀⠀⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠁⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣀⣀⡀⠀⠀⢠⣾⣿⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⠏⢿⠃⠀⠈⠉⠉⠁⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠿⠋⠉⢻⣿⣿⣿⣿⣤⠀⠈⠉⠉⠉⠁⠀⠁⠈⣿⣟⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣫⣴⣏⠀⠀⢀⣠⣄⡙⢿⣿⣿⢿⢇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⢏⣾⣿⣿⣿⠶⣾⣿⣿⣿⣦⣿⣿⣶⣦⠀⠀⠀⢀⡀⡀⠀⠀⠀⢀⣴⠿⠋⠺⣿⣿⣃⣤⣀⡀⠀⠀⠀⣠⣴⣶⣶⠶⣶⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢽⢻⣿⣿⣏⢻⣿⣻⣻⡿⣋⡙⣅⣟⣿⣿⣇⡽⣝⣿⣿⣷⣻⣻⡿⣿⣿⣿⣿⣿⣋⡋⣹⣿⣿⣿⣛⡟⣧⣉⣻⣿⣿⣶⠀⠈⢢⣴⣦⣠⣤⣄⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣄⡉⣿⣿⡿⣿⣿⣷⣾⣾⣆⣷⣾⣶⣶⣶⡾⠶⠲⠦⠶⠾⠻⣖⡶⠶⢷⠴⢶⡿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠀⣰⣿⡁⠀⠀⠀⠀⠀⠀⣼⣿⡋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀

⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣶⡄⠀⢐⣋⣩⣤⣾⣿⢷⡟⣾⢹⡟⣿⡟⣿⣿⣿⣧⣠⣾⣿⣿⣧⡄⢀⡀⠀⠀⢴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡁⠀

⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⡿⣷⣿⡟⣾⡍⣿⢼⣽⣿⣸⣿⡅⣿⣹⡹⣻⣿⣿⣿⣿⣿⣿⣿⣿⠹⣤⡄⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⢿⣧⡄

[22A⠀⢀⡒⠂⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠐⢲⣄⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣾⣽⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠛⣹⣿⣿⡟⠻⣿⡿⣗⣶

⠀⠈⠋⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣾⣶⣶⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣴⣿⡏⠀⢤⣿⢻⣿⡿

⠀⠀⠒⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢀⠀⣄⠀⠀⠀⠀⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠰⠇⢸⠓⣿⠓⠙⠿

⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠉⣵⣯⣦⣧⡤⢐⠀⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠿⣿⡯⢉⢹⣦⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠸⠀⠀⠠

⠀⠀⠀⠀⠉⠙⠋⢿⠉⣿⣿⣿⣍⡉⠻⠋⠀⠠⣬⣽⣻⣿⣿⣿⣿⣷⠟⢃⡈⠿⣿⣿⣿⣿⣿⠟⠛⣿⡿⠿⠿⠟⠟⠁⡀⠠⣿⣯⣘⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠘⠙⠙⠛⠀⠀⠀⠀⠀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠈⠉⠉⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⣶⣷⣾⣿⣿⢿⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣤⠄⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣀⣾⣿⣶⣴⣠⠀⡄⢰⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⢀⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⣻⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠐⣶⣶⣶⡿⠉⠹⠦⠘⠛⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⡿⢿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢀⣄⣰⣀⡀⠀⠀⠀⣀⠀⠀⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠘⣿⡏⠙⡿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⡙⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠐⡦⠀⠀⢃⢠⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⣿⣯⣵⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⢒⠀⠀⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠿⣥⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⣿⣹⡏⣿⣿⠻⠃⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣀⣀⠀⠀⠀⢠⣾⣿⣿⡿⠛⠁⢹⣼⣿⣿⣿⣿⡿⠃⠙⠀⠀⠀⠈⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣀⡀⣀⣀⡀⠀⣀⣀⣀⡀⡾⣛⣛⣛⣛⠛⢋⣉⣉⣈⠉⣉⣙⡛⢓⣀⡀⠈⢉⣉⣁⠀⣀⣀⢀⣉⣉⣙⣛⣛⣃⠀⣀⣀⡀⢀⣀⡀⠀⢀⣀⡀⢀⣀⡀⣀⣀⣀⣀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⢀⣀⣀⠀⠀

⠀⠀⣿⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⠁⠀⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⠀⠘⣿⣧⣾⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⣇⠀⣿⣿⡿⣿⣷⠈⣿⣿⠀⠀

⠀⠀⣿⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡏⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⢀⠀⢸⣿⣿⣷⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⠀⠀⢻⣿⣿⡟⠀⣿⣿⣧⣤⢸⣿⡟⣿⣿⠀⣿⣿⣷⣿⠿⠀⣿⣿⠀⠀

⠀⠀⣿⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⢋⡁⣺⣿⡟⢛⣉⣀⢸⣿⣿⢀⡭⡃⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢿⣿⣿⣿⢿⣿⣿⣿⠀⡉⣁⠘⣿⣿⠁⠀⣿⣿⡏⠉⣸⣿⣧⣿⣿⡄⣿⣿⡏⣿⣿⠀⣿⣿⠀⠀

⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⠾⡇⣼⣿⡇⠀⠦⠆⢸⣿⣿⠠⠄⠂⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⠀⠀⣠⡀⣿⣿⠀⠀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⠀⣶⣶⠀⠀

⠀⠀⠈⢉⣵⣬⣭⣥⣭⣭⣶⣭⣍⣥⣭⣭⣶⣦⡜⢮⣭⡁⢀⣁⣀⣀⣉⣩⣦⣠⣶⡀⠉⠁⡀⡉⣡⢬⢩⢩⠉⡅⣠⠉⣭⡱⣤⣩⣭⣁⣠⣾⣿⣓⡍⠉⠀⠀⠉⠉⠉⣁⡉⢉⣤⣬⣭⣅⣉⣉⣤⠉⠉⠠⣉⡉⠀⠀

⠀⠀⣰⣿⣿⣿⢿⣿⣿⣿⣿⣿⡞⠉⠙⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⢛⣿⠛⣳⣶⢈⡎⡉⡇⣾⣽⣧⣿⣾⠀⢇⣃⢱⠹⠽⣯⣿⣿⣿⣿⣷⡀⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⠓⠋⠇⠘⠀⠀⠙⠿⡀⠀

⣄⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⠍⢿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣺⣯⣦⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣯⣇⣠⡀⠤⢶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠿⠷⣀⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⢿⣿⣿⣭⡁⠈⡏⠀⠀⠀⠀⠀⢀⣤⣤⢀⣁⣈⣉⠠⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⢼⣿⡿⣿⣿⣿⣿⣦⡤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠀⢀⣁⣽⣭⠓⠆⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⢿⣿⡯⣄⣴⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⢿⣿⣿⣿⣿⡟⡟⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠈⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡿⢟⣭⣭⣿⣿⣿⠁⠀⣠⣴⣯⣄⣩⣿⣦⣀⠀⣀⣤⣤⠀⣹⠟⠋⠉⠙⠛⠻⣿⣿⡷⠀⠀⡀⠀⠀⣠⣴⣿

⠀⢸⣿⠿⢠⣿⣿⣿⣿⣷⣄⢀⡀⢀⣤⣤⣬⣭⣤⡀⠀⠀⠀⢀⣴⣿⡿⠿⠿⢿⣻⣿⣷⡄⠀⠀⠙⣿⣶⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢿⡄⠀⣀⠀⠀⠀⢹⡇⠀⠀⢸⣿⣿⣷⣍⣿⣷

⠀⣿⣿⣰⣿⣿⣿⣿⣿⠟⣷⣿⠃⢸⣿⣯⣽⡿⢿⣿⣧⣤⣼⣿⣿⣿⣯⣼⣿⣿⣿⣿⡟⠃⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠸⣿⣿⣿⣿⣿⣷⣾⠇⠀⢤⣮⣉⣿⣿⣿⣿⢿

⣶⣿⢿⣿⣿⣿⣿⣿⣿⣮⣁⠀⢀⣾⣿⠟⣛⣭⣭⡏⣿⣿⣿⡏⠙⠛⠛⠛⠛⠻⠿⠁⠀⣾⣇⠀⠀⠀⣸⣷⣿⣿⣿⣿⣿⣿⣯⠩⢩⣩⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣶⣿⡛⠛⠿⢿⣿⠋⢀⣴⣿⣿⣿⣿⣿⣿⠟⠈

⠛⠃⠘⠛⠃⠙⠿⠻⡟⠻⣭⣧⣿⣿⣇⣾⣿⣿⠟⠁⠻⠿⣼⡧⠀⠰⣶⣀⣤⣶⣶⣶⣿⣿⣿⡗⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⣸⣟⠙⠟⠀⠀⠻⣿⣄⠀⠀⠀⢾⡓⣼⢀⢹⣿⠻⢻⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⢻⣿⣿⣿⣿⠄⠀⠀⠀⠀⠹⣟⣠⠄⠀⢸⣿⣿⣿⣷⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠀⢀⣀⡀⣀⣀⡘⠋⣉⣉⣉⡀⠀⣀⣀⣀⣈⠉⢁⣀⣈⣉⠛⣋⣙⡛⢛⣉⡙⢿⢟⣛⣛⠋⣙⣛⢛⣛⣉⣉⣙⣉⣙⠋⣉⣙⡛⢛⣛⡻⣿⢛⣛⡛⢛⣛⡛⣛⣉⣛⣛⠿⣋⣉⣉⡉⠛⣉⣉⣙⣛⠻⢟⣋⣙⣻⣿

⠀⠀⢸⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢁⣾⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠇⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⠀⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡄⢸⣿⡟⣿⣿⠀⣿⣿⣤⣿⠿⠀⣿⣿⠸⣿

⠀⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⢋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣾⣿⢿⣿⣿⣿⠀⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠁⢸⣿⣧⣿⣿⡀⣿⣿⠉⣿⣿⠀⣿⣿⢠⣿

⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣶⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⠰⣿⣿⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡆⣿⣿⢀⡀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⢈⣿

⠀⠀⠀⠀⠀⡀⢠⢤⣤⣀⣠⣠⣤⣥⣤⣬⣾⣿⣿⣦⣤⣠⣿⣿⣿⣷⣥⣼⣾⠿⢿⣦⣤⣥⣤⣀⣤⣤⢤⣤⣤⣵⣦⣠⣤⣵⣤⣤⣤⣵⣿⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣤⣴⣮⣤⣤⣥⣤⣤⣤⣬⣦⣥⢬⣾⣿

⠀⠀⠀⠀⡀⢁⣾⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⣄⣀⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⠭⢿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣷⣇⣠⡀⠤⢶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⣿⡿⠻⣿⡶⣤⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣯⡁⠈⣿⠀⠀⠀⠀⠀⣀⣄⡀⣈⣩⣉⡁⢠⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⢹⣿⡿⣿⣿⣿⣿⣦⡤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⠋⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⢨⣿⣯⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣟⠅⣠⡟⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⢹⣷⣿⣿⣿⣏⡟⠀⠀⠀⠀⠉⢻⣦⡀⠀⠀⠀⠀⠀⠹⠃⣼⣿⡿⣿⡿⠿⢇⡀⠀⠀⠀⣿⣿⣿⢟⣭⣿⣿⣿⣿⠁⠀⣀⣤⣯⣅⠈⢿⣦⣶⣶⡄⠀⠈⠛⣿⠟⠋⠉⠛⠛⠿⣿⣿⡴⠀⠀⣀⠀⠀⣠⣴⣿

⠀⢸⣿⠿⢠⣿⣿⣿⣿⣷⡄⠀⠀⣀⣤⣶⣭⣭⣤⡀⠀⠀⠀⢀⣼⣿⣿⣷⣶⣶⣿⣿⣿⡷⠀⠀⠛⣿⣴⣿⣷⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⣷⡀⠀⣀⠀⡀⠀⣿⡆⠀⠀⢸⣿⣿⣷⣍⣻⣷

⠀⣿⣿⣰⣿⣿⣿⣿⣿⠟⣱⡿⠁⣿⣿⣭⣿⠿⣿⣿⣤⣀⣤⠈⠻⢿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠠⣮⣉⣿⣿⣿⣿⢿

⣶⣿⢿⣿⣿⢟⣿⣿⣿⣿⣭⠀⣰⣿⡿⢟⣫⣭⣽⣻⣿⣿⢿⡄⠀⢀⣀⣈⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣟⣦⠀⣾⣿⣿⣿⣫⣿⣿⣿⣿⣿⣷⣤⣤⣿⡛⠻⠿⢿⣿⠁⢀⣰⣿⣿⣿⣿⣿⡿⠟⠈

⠛⠃⠘⠛⠃⠘⢿⠸⣿⠛⢏⣱⣿⣿⣗⣿⣿⣿⠟⠉⢻⢿⢼⣧⠀⠸⣿⡟⢄⣠⣴⣶⣶⣿⣿⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀

⠁⠀⠀⠀⠀⠀⠀⢀⣆⣄⣀⡟⠉⠻⠀⠀⠻⣿⣄⠀⠈⡘⣾⡯⡧⡤⡉⣰⡿⠿⠿⢻⢿⣿⣿⣿⣾⣿⣿⣧⣤⣤⣤⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠁⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣛⣤⠀⠁⣹⣇⣿⣿⣿⣾⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠀⢀⣀⡀⣀⣁⡘⠋⣉⣉⣉⡃⠀⣀⣀⣀⣀⠉⢁⣀⣀⣈⠙⣋⣙⡛⢛⣉⡛⠿⢛⣉⣛⠟⣉⣛⢛⣛⣋⣉⣉⣉⣉⠋⣉⣉⡛⢛⣉⡻⣯⢟⣛⡛⢛⣛⡛⣛⣛⣛⣛⠿⣋⣉⣉⡙⠟⣛⣛⣛⣛⠻⢟⣛⣛⣻⣿

⠀⠀⢸⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢁⣆⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠇⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⠄⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡄⢸⣿⡟⣿⣿⠀⣿⣿⣤⣿⠿⠀⣿⣿⢸⣿

⠀⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⠁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⢀⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠁⣸⣿⣧⣿⣿⡀⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⢸⣿⣯⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢠⣿⣿⡆⣿⣿⢀⡀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⢸⣿

⠀⠀⠀⠀⠀⡀⢠⣀⣤⣀⣤⣤⣤⣥⣤⣬⣾⣿⣿⣦⣤⣥⣿⣿⣿⣷⣥⣼⣾⠿⣿⣦⣥⣥⣤⣀⣤⣦⣤⣤⣤⣵⣦⣠⣤⣵⣤⣤⣤⣵⣿⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣤⣴⣮⣤⣥⣥⣬⣤⣥⣬⣤⣡⣨⣾⣿

⠀⠀⠀⠀⡀⣴⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[22A⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⠉⢿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠐⣾⣇⣠⡀⠤⢶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⠿⠿⣯⡶⣤⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣯⡀⠉⣿⠀⠀⠀⠀⠀⢀⣄⡀⣈⣉⣍⡁⢦⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⡿⣿⣿⣿⣿⣦⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⣠⣾⣿⣿⣿⣇⠀⠀⠀⠀⢨⣿⣯⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣯⣥⣠⡟⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣾⢻⣿⣿⣿⣿⣏⡟⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠹⠁⣼⣿⡿⣿⡿⠿⢇⡀⠀⠀⠀⣿⣿⡿⢏⣭⣿⣿⣿⣿⠀⠀⣀⣤⣯⣅⠈⣿⣦⣶⣶⡄⠀⠈⠛⣿⠟⠋⠉⠛⠛⠿⣿⣿⡴⠀⠀⣀⠀⠀⣠⣴⣿

⠀⢸⣿⠯⢠⣿⣿⣿⣿⣷⡄⢀⡀⣀⣤⣤⣭⣭⣤⡀⠀⠀⠀⢀⣼⣷⣿⣷⣶⣶⣿⣿⣿⣷⠀⠀⠛⣿⣴⣿⣷⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⣷⡀⠀⣀⠀⣀⠀⣿⡆⠀⠀⢸⣿⣿⣷⣍⣻⣷

⠀⣿⣿⣰⣿⣿⣿⣿⣿⠟⣱⡿⠃⣿⣿⣭⣿⠿⣿⣿⣦⣀⣤⠈⠛⠿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠠⣮⣉⣿⣿⣿⣿⢿

⣶⣿⢿⣟⣿⢿⣿⣿⣿⣿⣭⡀⣰⣿⣿⢟⣫⣭⣽⣸⣿⣿⢻⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣟⣦⠀⣾⣿⣿⣿⣫⣿⣿⣿⣿⣿⣷⣤⣤⣿⡛⠻⠿⢿⣿⠁⢀⣰⣿⡿⣿⣿⣿⡟⠛⠈

⠛⠃⠜⠛⠃⠘⢿⠙⣿⠛⠏⣵⣿⣿⣷⣿⣿⣿⠟⠉⠻⢿⢼⣧⠀⠸⣿⡟⢄⣠⣴⣶⣶⣿⣿⣷⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀

⠃⠄⠀⠀⠀⠀⠀⢀⣆⣄⣀⡟⠉⠻⠀⠀⠻⣿⣄⠀⠀⡘⣾⡯⡧⡠⡉⣰⡿⠿⠿⢻⢿⣿⣿⣿⣾⣿⣿⣧⣤⣤⣤⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠁⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣋⣠⠀⠁⣹⣇⣿⣿⣿⣾⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠀⢀⣀⡀⣀⣁⡘⠋⣉⣉⣉⡃⠀⣀⣀⣀⣀⠉⢁⣀⣀⣈⠙⣉⣙⡛⢛⣉⡛⢿⢛⣉⣛⠟⣉⣛⢛⣛⣋⣉⣉⣉⣉⠋⣉⣉⡛⢛⣉⡻⣯⢟⣛⡛⢛⣛⡛⣛⣛⣛⣛⠿⣋⣉⣉⡙⠟⣛⣛⣛⣛⠻⢟⣛⣛⣻⣿

⠀⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⠁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣾⣿⢿⣿⣿⣿⢀⣿⣿⠈⣿⣿⠁⠀⣿⣿⡏⠁⢸⣿⣧⣿⣿⡀⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣾⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢠⣿⣿⡆⣿⣿⢀⡀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⢸⣿

⠀⠀⠀⠀⠀⡀⢠⣀⣤⣀⣄⣤⣤⣥⣤⣬⣾⣿⣿⣬⣤⣡⣿⣿⣿⣷⣥⣼⣾⠿⣿⣦⣤⣥⡤⣀⣤⣦⣤⣤⣤⣵⣦⣠⣤⣵⣠⣤⣤⣵⣿⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣤⣶⣮⣤⣥⣤⣤⣤⣥⣬⣤⣁⣠⣾⣿

⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣅⣐⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠘⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⠉⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢪⣄⣠⡀⠤⢖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣬⠶⢿⣿⣿⣦⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⡛⠉⠙⣿⠀⠀⠀⠀⠀⢀⣤⡀⣀⣉⣉⡁⢤⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⢽⣿⠿⣿⣿⣿⣿⣦⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢁⣼⣿⣿⣿⣿⡗⠀⠀⠀⠀⢠⣿⣯⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⡿⡁⣠⡟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣾⢹⣿⣿⣿⣿⣟⡟⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠘⠁⢾⡿⠆⠹⠛⣛⣧⣀⠀⠀⠀⣿⣿⡿⢯⣽⣿⣿⣿⣿⠀⠀⢀⣨⣟⡁⠘⠿⣄⣠⣤⠀⠀⠈⠙⣿⠟⠛⠛⠛⠻⢿⣿⣿⡴⠀⠀⡀⠀⠀⣠⣴⣿

⠀⢸⣿⡿⢠⣿⣿⣿⣿⣷⡄⠀⣀⣀⣤⣴⣾⣯⡀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⣿⣾⣿⣿⣿⣿⣿⣿⣠⣶⣿⣿⣿⣿⣆⣿⣿⣿⣿⡇⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣿⣿⣷⣍⣿⣷

⠀⣿⣿⣲⣿⣿⣿⡟⣩⣤⡴⢾⣿⣿⣟⣻⣿⣿⣿⣶⣦⣀⣠⠉⠛⠿⠿⡿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⣮⡉⣿⣿⣿⣿⢿

⣶⣿⣿⣏⠿⢻⣿⣿⣿⢯⠄⢸⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⢻⡄⠀⠀⣄⣀⣀⠀⠀⠀⠀⢸⣷⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣉⢙⣽⣿⣿⣿⢿⣿⣿⣿⣿⣷⣄⣤⣤⣿⡻⠿⠿⢿⣿⠁⢀⣠⣾⣿⣿⣿⣿⡟⠛⠈

⠛⠋⠈⠉⠀⠈⠛⠍⠋⠙⠻⠿⣿⣤⡶⢾⣿⠿⡗⠿⣿⢿⣸⣷⠄⠀⣿⡿⠁⢀⣠⣴⣶⣾⣿⣿⢀⣴⣿⣩⣭⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠉⠉⠄⠀⠈⢿⣆⠀⠈⡸⣾⡿⡸⢦⣅⡀⣿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣬⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷

⠈⠀⠀⠀⠀⠠⡀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢟⣠⠀⡁⣹⣿⣧⣾⣿⣇⣿⣶⣶⣶⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⢀⣀⡀⣀⣁⡀⠋⣉⣉⣉⡋⠀⣀⣀⣀⣀⠉⢁⣀⣀⣈⠙⣉⣙⡛⢛⣉⡙⣿⢛⣉⣙⠛⣛⣛⢛⣛⣛⣉⣉⣉⣉⠉⣉⣙⡛⢛⣋⡻⣟⢛⣛⡛⢛⣛⡛⣋⣛⣛⣛⠿⣋⣉⣉⡙⠟⣛⣋⣉⣉⠻⢟⣛⣛⣻⣿

⠀⠀⢸⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢁⣧⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠇⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⠂⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡇⣼⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡄⢸⣿⡟⣿⣿⠀⣿⣿⣤⣿⠿⠀⣿⣿⢰⣿

⠀⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠋⢉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠁⠀⣿⣿⡏⠁⣸⣿⣧⣿⣿⡀⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⠸⣿⣿⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢈⣿⣿⡀⣿⣿⢀⡄⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⢸⣿

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣤⣠⣤⣥⣤⣬⣾⣿⣿⣮⣤⣥⣿⣿⣿⣷⣥⣼⣾⠿⣿⣦⣤⣤⡤⣀⣤⣦⣤⣤⣤⣥⣶⣠⣤⣵⣤⣤⣤⣵⢸⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣤⣶⣮⣤⡥⣤⣬⣤⣤⣤⣦⣥⣬⣾⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣄⣀⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠘⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⠉⢿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⢾⣂⣠⡀⠤⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠙⣟⡻⣦⡄⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⡿⠿⠛⢻⡇⠀⠀⠀⠀⠀⣀⣄⠀⣈⣉⣉⡁⢤⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⡿⣿⣿⣻⣿⣦⡤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⣰⣿⣿⣿⣿⣵⠀⠀⠀⠀⢠⣿⣯⣿⣿⣿⣿⣿⣷⠀⠀⢿⣿⣿⡷⠂⢸⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⢻⣿⣿⣿⣿⣏⡟⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠘⠃⡸⣿⠟⠟⠛⠛⢋⡀⠀⠀⠀⣿⣿⡿⣯⡭⣽⣿⣿⣿⠃⠀⠀⢙⡿⠃⠰⢿⣀⣤⡀⠀⠀⠈⠛⣿⠟⠛⠛⠛⠻⢿⣿⣿⡴⠀⠀⣁⠀⠀⣠⣴⣿

⠀⢸⣿⣿⢠⣿⣿⣿⣿⣷⣄⠀⠀⣀⣤⣴⣾⣯⣀⠀⠀⠀⠀⢠⣾⣿⣶⣶⣶⣶⣶⣿⣿⣷⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⢀⣴⣾⣿⣿⣷⣠⣿⣿⣿⣷⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣿⣿⣷⣍⣿⣷

⠀⣿⣿⣤⣾⣿⠋⣩⣅⣤⣍⣷⣿⣿⢿⣿⣿⣿⣿⣷⣶⣠⡶⠉⠛⠿⣿⣿⣿⣿⣿⠿⠛⠃⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣮⡉⣿⣿⣿⣿⢿

⣶⣿⣿⣿⣿⣿⣿⠿⠉⠈⠹⣿⡿⠟⠉⠉⠙⢿⣿⣿⣿⣿⢻⡆⠀⠀⣀⣀⡀⠀⠀⠀⠀⢸⣷⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠉⣭⣿⣿⡿⣿⣿⣿⣾⣿⣧⣀⣤⣤⣿⠻⠿⠿⢿⣟⠁⢀⣠⣶⣿⣿⣿⣿⡟⠛⠈

⠛⡟⠑⠈⠯⠁⠐⠒⠶⠦⠤⣽⣧⣠⣤⣤⣤⣤⢿⣿⣿⣿⢸⣿⣆⢀⢹⡿⠃⠀⣀⣤⣾⣶⣿⣿⢀⣴⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠶⠀⠀⢻⡆⠈⠋⠈⢾⣿⡎⣾⢠⢰⣼⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡆⡄⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠷⣀⡀⠀⣸⣿⣱⣧⣿⣿⢿⣷⣶⣶⣮⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⡀⣀⣀⡀⠀⣈⣉⣀⡀⠀⣀⣀⣀⣀⠙⢉⣀⣀⣉⠛⣋⣛⡛⢛⣉⡛⣿⢟⣋⣙⠛⣛⣛⢛⣛⣛⣛⣛⣛⣛⠛⣉⣉⡛⢛⣋⡻⣟⢛⣛⡛⢛⣛⡛⣛⣛⣛⣛⠿⣋⣉⣛⡛⠟⣋⣉⣉⣛⠻⢟⣛⣛⣻⣿

⡄⠀⢸⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣷⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠇⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⠁⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡤⢸⣿⡟⣿⣿⠀⣿⣿⣤⣿⠿⠀⣿⣿⢰⣿

⠀⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣷⣿⣿⠀⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠁⣸⣿⣧⣿⣿⡀⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⠸⣿⣟⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⠀⣿⣿⡄⣿⣿⢀⡀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⢸⡿

⠀⠀⠀⠀⡀⠀⣠⣤⣤⢀⣤⣤⣤⣤⣤⣬⣾⣿⣿⣮⣤⣥⣿⣿⣿⣷⣥⣽⣾⠿⣿⣦⣤⣤⣤⢀⣠⡤⢤⣤⣤⣥⣦⣤⣤⣵⣦⣤⣤⣵⠐⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣤⣶⣮⣤⢥⣤⣤⣤⣤⣤⣤⣥⣬⣾⣷

⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠸⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⢝⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⣿⣇⣠⡀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣫⠴⠀⣛⣛⣶⡄⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣿⡿⠿⠻⢿⡆⠀⠀⠀⠀⠀⣠⣄⠀⣈⣉⣉⡀⢤⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣻⣿⡿⣿⣿⣻⣿⣦⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠋⣰⣿⣿⣿⣿⣽⠂⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⢿⣿⣿⡶⠂⢸⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⢻⢿⣿⢿⣿⣟⡟⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠈⠋⠸⡿⠟⠛⠛⠛⢻⡀⠀⠀⠀⣿⣿⠿⣯⠽⣽⣿⣿⣿⠃⠀⠈⢛⣿⠃⠴⢿⣁⣤⡀⠀⠀⠈⢛⣿⠟⠛⠛⠛⠻⢿⣿⣯⡴⠀⠀⣁⠀⠀⣠⣴⣿

⠀⢸⣿⠿⢠⣿⣿⣿⣿⣷⣤⣄⡀⢀⣀⣤⣾⣯⣀⠀⠀⠀⠀⢀⣴⣿⣦⣴⣶⣶⣶⣶⣿⣷⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⢀⣠⣶⣿⣿⣧⣠⣿⣿⣿⣧⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣿⣿⣿⣍⣿⣷

⠀⣿⣿⣁⣾⣿⠿⢛⡋⢉⡙⢿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣤⡶⠋⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣮⠉⣿⣿⣿⣿⢿

⣶⣿⣿⣿⣿⣿⣶⡿⠟⠋⠙⣿⣿⡿⠋⠉⠛⢿⣿⣿⣿⣿⢿⣆⠀⠀⢉⠉⠉⠉⠉⠁⠀⢸⣷⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣿⣿⣟⣽⣿⣿⣿⣿⣧⣀⣤⣤⣿⠻⠿⠿⢿⣟⠁⢀⣠⣴⣿⣿⣿⣿⡿⠛⠈

⢻⠛⠞⢿⠻⠏⠀⠤⠤⣤⣤⣼⣿⣀⣤⣤⣤⣤⣽⣿⣿⣿⣸⣿⡦⢀⢸⣿⠃⠀⣀⣤⣾⣿⣿⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣧⡀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠗⠀⠀⢿⡄⠉⠋⠙⢿⣿⡇⡞⣤⣤⣸⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡆⡄⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠷⣆⡀⠀⢸⣿⣿⣷⣿⣿⢽⣷⣶⣶⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⡀⣈⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠚⢉⣁⣀⣉⠛⣋⣙⡛⢛⣉⡛⣿⢛⣋⣙⠛⣛⣙⢛⣛⣛⣛⣛⣛⣛⠛⣉⣉⡙⢉⣙⡻⣿⢟⣛⡛⢛⣛⡛⣛⣛⣛⣛⠿⣋⣉⣛⡛⠟⣋⣉⣙⣛⠻⢟⣛⣛⣿⣿

⡔⠀⢸⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣷⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⠁⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡄⢸⣿⡟⣿⣿⠀⣿⣿⣤⣿⠿⠀⣿⣿⢰⣿

⠀⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⠀⣿⣿⠈⣿⣿⠁⠀⣿⣿⡏⠁⢸⣿⣧⣿⣿⡀⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⠸⣿⣟⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢀⣿⣿⡄⣿⣿⢀⡄⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⠈⣿

⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣤⣄⣤⣤⣤⣬⣾⣿⣿⣮⣤⣥⣿⣿⣿⣷⣥⣼⣾⠿⣿⣦⣤⣥⣤⢀⣠⣆⢤⣤⣤⣥⣦⣥⣤⣵⣦⣤⣤⣵⣿⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣤⣶⣮⣤⢥⣤⣬⣤⣤⣨⣤⣥⣬⣾⣆

⠀⠀⠀⢠⠈⢰⣿⣿⣿⣿⢿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠻⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠘⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠈⠉⢿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣾⣇⣤⡀⠤⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢢⠤⢐⣛⣛⣶⣄⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣴⣿⣿⠿⠿⢿⡆⠀⠀⠀⠀⠀⣠⣄⠀⣈⣉⣉⡀⣤⣀⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⡿⣿⣿⣻⣿⣦⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠃⣰⣿⣿⣿⣿⣽⠆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⢿⣿⣿⡶⠂⢸⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⢹⢿⣿⣿⣿⣏⡟⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠛⢸⠿⠇⠛⠛⠛⠻⠀⠀⠀⠀⣿⣿⠿⣯⠽⣿⣿⣿⣿⠃⠀⠈⢻⣿⠧⢴⣿⣁⣤⡀⠀⠀⠈⢛⡿⠟⠛⠛⠛⠻⣿⣿⣯⡴⠀⢀⣀⠀⠀⣠⣴⣿

⠀⢸⣿⢿⢠⣿⣿⣿⣿⣷⣤⣄⡀⢀⣀⣤⣼⣯⣀⢀⠀⠀⠀⢀⣴⣿⣦⣴⣶⣶⣶⣴⣿⣦⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⢀⣠⣴⣿⣿⣦⢰⣿⣿⣿⣇⠀⠀⠀⠸⣆⠀⠀⡀⠀⠀⠈⣿⠀⠀⠀⢸⣿⣿⣷⣍⣿⣷

⠀⣿⣿⣀⣾⣿⠿⢛⣛⠙⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣶⡋⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣮⠉⣿⣿⣿⣿⢿

⣶⣿⣿⣿⡿⣫⣆⠻⠛⠛⠛⣾⣿⣿⠒⠛⠻⢿⣿⣿⣿⣿⢿⣇⠀⠀⠉⠉⠉⠉⠉⠉⠀⢠⣿⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣯⣉⣽⣿⣿⢟⣿⣿⣿⣿⣿⣧⣀⣤⣴⣿⠻⠿⠿⣿⡟⠁⢀⣠⣴⣿⣿⣿⣿⡿⠛⠈

⠻⡿⠿⠛⠘⠃⠀⠀⠦⠤⡄⢸⣿⣠⣤⣤⣤⣤⡽⣿⣿⣿⣸⣿⡦⡀⠸⣿⠃⠀⣀⣤⣶⣷⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣿⣿⣾⣿⣻⣿⣯⣽⣿⣿⣧⡀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⠽⠀⠀⢿⡄⠉⠋⠙⢿⣿⣃⠗⣔⣅⣴⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡷⢂⡀⠀⢸⣿⣿⣼⣿⣿⢽⣷⣶⣷⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⡀⣈⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠚⢋⣁⣀⣈⠛⣋⣙⡛⢛⣉⡛⣿⢛⣋⣙⠛⣛⣛⢛⣛⣛⣛⣛⣉⣉⠉⣈⣉⡛⢛⣉⡻⣿⢟⣛⡛⢛⣛⡛⣛⣛⣛⣛⠿⣋⣉⣛⡛⠟⣋⣉⣙⣛⠿⢟⣛⣙⣻⣿

⡿⠀⢹⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣷⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠇⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⡄⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢰⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣾⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠁⢸⣿⣧⣿⣿⡀⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⠸⣿⣟⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⠀⣿⣿⡄⣿⣿⢀⡄⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⠈⣿

⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⣠⣄⣤⣥⣤⣬⣾⣿⣿⣮⣤⣥⣾⣿⣿⣷⣥⣽⣾⠿⣿⣦⣤⣥⣤⢀⣠⡂⢤⣤⣤⣥⣦⣥⣤⣵⣦⣤⣤⣵⣿⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣤⣶⣮⣤⢥⣤⣤⣤⣅⣬⣤⣥⣬⣶⣠

⠀⠀⠀⢀⠈⠠⣾⡿⣿⣿⢿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀

⣅⣰⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⢝⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠘⣿⣆⣠⡀⠤⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢀⣛⣛⣶⣄⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣴⣿⡿⠿⠿⢿⡆⠀⠀⠀⠀⠀⣠⣄⠀⣈⣉⣉⡀⣤⣀⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣻⣿⡿⣿⣿⣿⣿⣦⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⣰⣿⣿⣿⣷⣭⡆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⡶⠂⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⢻⢿⣿⣿⣿⣏⡟⠀⠀⠀⠀⠙⢻⣦⡀⠀⠀⠀⠀⠀⠀⠋⢸⡿⠗⠛⠛⠛⠻⠀⠀⠀⠀⣿⣿⢿⣿⠾⣿⣿⣿⣿⠃⠀⠈⢻⣿⠳⢶⣿⣡⡀⠀⠀⠀⠘⢛⡿⠟⠛⠛⠛⠻⣿⣿⣯⡴⠀⠀⣁⣀⠀⣠⣴⣿

⠀⢸⣿⣿⢠⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⢀⣭⣭⡀⠀⠀⠀⠀⢀⣴⣿⣦⣴⣶⣶⣶⣴⣿⣦⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣶⣿⣿⣆⢰⣿⣿⣿⣀⠀⠀⠀⠸⣆⠀⠀⡀⠀⠀⠈⣿⠀⠀⠀⢸⣿⣿⣿⣍⣿⣷

⠀⣿⣿⣀⣾⣿⠟⢉⣉⢉⣙⠻⣯⣿⣿⣿⣟⣿⣿⣷⣶⣄⣴⠟⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣮⠉⣿⣿⣿⣿⢿

⣶⣿⣿⣿⢿⡥⠆⠉⠉⠉⠛⣷⣿⡿⠧⠘⠻⠿⣿⣿⣿⣿⣏⣷⡀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣿⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣏⢉⣿⣿⣿⣻⣿⣿⣿⣿⣿⣆⠀⣤⣴⡿⠿⠿⠿⣿⡟⠁⢀⣠⣼⣿⣿⣿⣿⡟⠻⠈

⠛⠿⠛⠉⠉⠁⠀⠀⠲⠤⠄⠸⠿⠁⣤⣤⣤⣤⣼⣿⣿⣿⣭⣿⣶⡀⡀⣿⠟⠀⣀⣶⣶⣿⣾⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣿⣿⣾⡿⣿⣿⣯⣿⣿⣿⣇⡀⠀

⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠁⠵⠀⠀⢻⡀⠛⠟⠿⠟⣿⣷⢠⡇⡁⣴⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⠿⢿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⢳⡄⣀⠀⠀⣿⣷⣼⣽⡿⣿⣿⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⡀⣀⣀⡀⠀⣀⣀⣈⡀⠀⣀⣀⣀⣀⠚⢋⣉⣀⣀⠛⣉⣙⡛⢛⣉⡙⡿⢛⣉⣙⠋⣙⣛⢛⣛⣛⣋⣃⣀⣉⠉⣉⣉⡋⢋⣉⡉⣻⢟⣛⡛⢛⣛⡓⣛⣛⣛⣛⠿⣋⣉⣛⡛⠛⣋⣉⣙⣛⠻⢟⣋⣙⣻⣿

⣽⠀⢸⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣷⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⠉⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡄⢸⣿⡟⣿⣿⠀⣿⣿⣴⣿⠿⠀⣿⣿⢰⣿

⡆⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢰⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⢰⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠁⣸⣿⣧⣿⣿⡀⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡇⢸⣿⡇⢠⣶⣿⢸⣿⣿⠸⣿⣿⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⢀⡄⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⠘⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣤⣤⣤⣥⣠⣬⣾⣿⣿⣮⣤⣥⣿⣿⣿⣷⣥⣽⣾⠿⣿⣦⣤⣥⣤⢁⣠⡂⢠⣤⣤⣵⣦⣥⣤⣵⣦⣤⣤⣅⢸⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣬⣶⣮⣤⣥⣤⣤⣤⣥⣬⣶⣥⣽⡆⢠

⠀⠀⠀⢠⠀⠀⢾⣿⣿⣿⢿⣽⣿⣿⡗⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀

[22A⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣅⣐⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠐⣿⣇⣠⡀⠤⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⣺⣛⣳⣆⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣴⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⣠⣄⠀⣈⣉⣉⡀⣤⣀⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⡿⣿⣿⣻⣿⣦⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⣠⣿⣿⣿⣿⣌⡇⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣷⣦⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⢻⢻⣿⣿⣿⣟⡟⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠛⢸⡿⠟⠚⠛⠛⠻⠁⠀⠀⠀⣿⣿⢟⡵⠾⣿⣿⣿⣿⠃⠀⠈⢻⣿⠷⢷⣟⣁⡀⠀⠀⠀⠘⢛⡿⠟⠛⠛⠛⠻⣿⣿⣯⡴⠀⢀⣁⢀⠀⣠⣴⣿

⠀⢸⣿⣿⢠⣿⣿⣿⣿⣷⣤⣤⣀⠀⢀⣤⣩⣭⣀⡀⠀⠀⠀⢀⣴⣿⣦⣴⣶⣶⣶⣶⣿⣶⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣶⣿⣿⣦⢰⣿⣿⣿⣀⠀⠀⠀⠸⣄⠀⠀⡀⠀⠀⠈⣿⠀⠀⠀⢸⣿⣿⣿⣍⣿⣷

⠀⣿⣿⣀⣾⡿⠋⣩⡉⣉⣙⠻⣏⣴⣿⣿⣿⣿⣿⣷⣦⣄⣰⠟⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣮⠉⣿⣿⣿⣿⢿

⣶⣿⣿⣿⣿⠴⠈⠉⠉⠉⠹⣶⣿⣿⠿⠚⠛⠻⣿⣿⣿⣿⣏⣷⡀⠀⠈⠉⠉⠉⠉⠉⠀⠀⣿⣆⠀⠀⢀⣿⣿⣿⣿⣻⣿⣿⣏⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣤⣴⣿⠻⠿⠿⣿⡟⠁⢀⣠⣼⣿⣿⣿⣿⡿⠻⠈

⠛⠿⠟⠋⠁⠀⠀⠘⠒⠢⠄⠫⠿⣯⣴⣶⡶⣤⣼⣿⣿⣿⣯⣿⣷⡄⡀⣿⠟⠀⣠⣶⣶⣿⣾⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣿⣿⣾⡿⣿⣿⣯⣿⣿⣿⣇⡀⠀

⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠉⠴⠀⠀⢣⣀⠛⠿⠿⡟⣿⣿⢠⡇⡁⣴⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⢿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾

⠀⠀⠀⠀⠀⠀⢆⠄⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⢻⡶⢀⠀⠀⣿⣷⣾⣼⡿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣀⡀⣀⣀⡀⠀⣀⣀⣀⡁⠀⣀⣀⣀⣀⠚⢋⣉⣀⣀⠙⣉⣙⡛⢛⣉⡙⡿⢛⣉⣉⠋⣙⣛⢛⣛⣛⣋⣃⣀⣉⠉⣉⣉⡉⢋⣉⡙⣻⢟⣛⡛⢛⣛⡓⣛⣛⣛⣛⠿⣋⣙⣛⡛⠟⣋⣉⣙⣛⠿⢟⣋⣙⣻⣿

⣿⠀⢸⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣷⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠈⣿

⠀⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡤⢸⣿⡟⣿⣿⠀⣿⣿⣴⣿⠿⠀⣿⣿⢸⣿

⠇⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢰⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⢰⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠁⣸⣿⣧⣿⣿⡄⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⣸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡇⢸⣿⡇⢠⣶⣿⢸⣿⣿⠸⣿⣧⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⢀⡄⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⠘⣿

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⢤⣤⣤⣥⡄⣬⣾⣿⣿⣮⣤⣥⣿⣿⣿⣷⣥⣽⣾⡿⢿⣦⣥⣥⣤⣀⣥⣄⠡⣤⣤⣵⣦⣤⣤⣵⣤⣤⣤⡅⢸⣿⣿⣷⣥⣬⣾⣷⣥⣤⣤⣤⣤⣤⣶⣮⣤⣥⣤⣤⣤⣥⣭⣶⣥⣭⡄⠀

⠀⠀⠐⢢⠄⠀⠰⣿⣿⣿⠾⣻⣿⣿⡇⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀

⣍⣸⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⢝⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠘⣿⣇⣠⡀⠤⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡤⠆⣺⣛⣷⣆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣤⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣠⣄⠀⣈⣉⣉⡀⣤⣀⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⡿⣿⣿⣿⣿⣦⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡎⣠⣿⣿⣿⣿⣬⡷⠀⠀⠀⢀⣼⣿⣿⣿⣾⣿⣿⣿⠀⠘⣿⣿⣯⣁⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⢻⢿⣿⣿⣿⣏⡟⠀⠀⠀⠀⠙⢻⣦⡀⠀⠀⠀⠀⠀⠀⠙⢠⡿⠟⠚⠛⠛⠻⡁⠀⠀⠀⣾⣿⢟⡶⠶⣿⣿⣿⣿⠃⠀⠘⢿⣿⡿⢦⣾⣁⡀⠀⠀⠀⠈⢛⡿⠟⠛⠛⠛⠿⣿⣿⣯⡴⠀⢀⣉⢀⠀⣠⣴⣿

⠀⢸⣿⡿⢠⣿⣿⣿⣿⣿⣦⣄⣄⠀⠀⣤⣭⣩⣤⡀⠀⠀⠀⢀⣴⣿⣶⣴⣶⣶⣶⣶⣿⣶⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣶⣿⣿⣦⢠⣿⣿⣿⣄⠀⠀⠀⠸⡄⠀⠀⡀⠀⠀⠈⣿⠀⠀⠀⢸⣿⣿⣷⣍⣿⣷

⠀⣿⣿⣀⣿⡟⢩⣥⣀⣭⡙⢿⣇⣰⣾⢿⣿⣿⣿⣿⣦⣄⣰⢟⠻⢿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⠀⠀⠀⢿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⣮⠉⣿⣿⣿⣿⢿

⣶⣿⣿⣿⣯⠆⠀⠁⠉⠉⠃⣴⣿⣿⠿⠊⠉⠛⢿⣿⣿⣿⡏⣷⡀⠀⠈⡉⠉⠉⠉⠁⠀⠀⣿⣆⠀⠀⢀⣾⣿⣿⣟⣫⣿⣿⣣⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣤⣴⣟⠻⠿⠿⣿⡟⠁⢀⣠⣼⣿⣿⣿⣿⠿⠿⠘

⠛⠿⠟⠋⠁⠀⠀⠑⠲⠒⠂⠛⠛⣿⠶⢲⡶⢶⡼⣿⣿⣿⣧⣿⣷⡄⡀⣿⠟⠀⣠⣶⣶⣿⣾⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣾⡿⣻⣿⣿⣿⣿⣿⣧⡀⠀

⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠀⠀⢧⣄⠙⠿⠿⡟⣿⣿⢰⢇⡀⣴⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾

⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⢿⣶⢀⡀⠀⣿⡇⣿⣼⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣀⡀⣀⣀⡀⠀⣀⣀⣀⡈⠀⣀⣀⣀⣀⠚⢋⣉⣁⣀⠙⣉⣙⡛⢛⣉⡙⡟⢛⣉⣉⠉⣛⣛⢛⣛⣛⣋⣃⣀⣉⠉⣉⣙⡉⢋⣉⡙⣻⢛⣛⡛⢛⣛⡓⣛⣛⣙⣛⠿⣋⣙⣛⡛⠟⣋⣉⣙⣛⠿⢟⣋⣙⣻⣿

⣿⠀⢹⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣷⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⡇⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⢰⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠁⣸⣿⣧⣿⣿⡄⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⣸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⢸⣿⣷⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⢀⡄⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⠘⣿

⠀⠀⠀⢀⠀⠀⠀⢀⣤⣬⣄⣠⣄⣥⣥⢨⣾⣿⣿⣮⣬⣥⣾⣿⣿⣷⣭⣽⣾⡿⢿⣦⣥⣥⣤⢁⣡⣄⠁⣤⣬⣵⣦⣥⣬⣵⣤⣥⣤⡅⢸⣿⣿⣷⣥⣭⣾⣷⣭⣤⣤⣤⣤⣤⣶⣮⣤⣥⣥⣭⣤⣥⣭⣴⣭⣽⡄⠀

⠀⠀⠐⢢⠄⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⠜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⢹⣿⣻⣿⣿⣿⣿⣿⣿⣇⠀

[22A⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣍⣻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⠛⠛⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠀⠀⠈⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠹⣿⣷⣤⡀⢤⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠂⣺⣛⣳⣦⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⢀⣤⡄⣀⣉⣉⡁⠠⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⡿⣿⣿⣿⣿⣦⡤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣠⣿⣿⣿⣿⣧⣱⠀⠀⠀⢀⣼⣿⡿⣿⣶⣿⣾⣿⠀⠘⣿⣿⣿⠋⠉⢽⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⣿⢿⣿⣿⣿⣟⡟⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⢁⠻⠟⠘⠛⠛⠛⣃⠀⠀⠀⢸⣿⢿⡴⠶⣾⣿⣿⣿⠃⠀⠙⢿⣿⣦⣤⣾⣃⣀⠀⠀⠀⠀⢩⡿⠿⠿⠿⢿⣿⣿⣿⣿⡵⠀⢀⣉⣀⠀⣠⣴⣿

⠀⣸⣿⣿⢠⣿⣿⣿⣿⣷⣶⣤⡄⠀⠀⣤⣭⣍⣤⣤⠀⠀⠀⢠⣶⣿⣷⣶⣶⣶⣶⣾⣿⣷⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢀⣠⣶⣿⣿⣤⢨⣿⣿⣿⣆⠀⠀⠀⢸⣄⢀⣀⣀⣀⠈⢙⣧⠀⠀⠀⢸⣿⣿⣿⣍⣿⣷

⠀⣿⣿⢃⣾⠏⢔⣦⣠⣬⠙⣿⣧⣤⣶⠿⣿⣿⣿⣿⣷⣤⣠⣿⠛⠿⢿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣮⠉⣿⣿⣿⣿⢿

⣶⣿⣿⣾⠟⠈⠀⠀⠀⢁⢹⣿⣿⣿⡟⠉⠉⠛⢿⣿⣶⣿⣹⣽⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⢀⣾⣿⣿⣿⣽⣿⣿⣦⢠⣽⣿⣿⢻⣿⣿⣿⣿⣿⣆⡀⣤⣴⣦⠀⠈⠈⣿⡏⠀⢀⣠⣬⣿⣷⣿⣿⡿⠿⠛

⠻⠿⠿⠅⠀⠀⠀⠉⠙⠉⠉⠁⠉⠹⠿⢛⢳⢶⡾⣿⣿⣿⣷⣾⣷⠄⠀⢻⠟⠀⣠⣶⣶⣶⣶⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣾⡿⣻⣿⣛⣻⣿⣿⣧⡀⠀

⣶⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢧⣀⠉⠛⠿⠟⣿⡟⢰⠂⡀⣤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾

⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣀⡀⠀⢼⣷⢳⣼⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠁⣀⣀⡀⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠒⢋⣉⣉⣀⠘⣉⣀⡋⢉⣉⡙⡟⢋⣉⣉⠉⣛⣛⢛⣛⣛⣙⣋⣀⣀⠈⣉⣋⡛⢋⣉⡉⣻⢟⣛⡛⢛⣛⡓⣛⣛⣛⣛⠿⣋⣛⣛⡙⠛⣋⣉⣙⣛⠿⢟⣋⣙⣻⣿

⠻⠀⢹⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣿⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⡤⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣾⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡤⢸⣿⡟⣿⣿⠀⣿⣿⣴⣿⠿⠀⣿⣿⢠⣿

⡇⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢰⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠉⣸⣿⣧⣿⣿⡄⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠀⠀⣸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⣸⣿⡇⢠⣶⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⢀⡀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⠘⣿

⠀⠀⠈⢉⠁⠈⠉⢀⣭⣭⣴⠈⣉⣁⣩⣭⣾⣿⣿⣮⣭⣥⣿⣿⣿⣷⣭⣽⣾⣿⣿⣦⣭⣥⣤⡭⢁⠀⢭⣭⣭⣵⣶⣭⣭⣵⣤⣭⣭⡅⣿⣿⣿⣷⣭⣭⣾⣷⣭⣭⣭⣥⣭⣭⣷⣮⣭⣥⣭⣭⣤⣭⣭⣴⣭⣭⡄⠀

⠀⠀⠰⢻⠀⠀⠀⠻⣿⣿⣿⣠⣿⣯⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣿⣿⣿⣿⣋⣴⣿⣄⡤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⢙⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀

[22A⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣍⣹⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⠟⠛⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠀⠀⠈⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠹⣿⣷⣤⡀⠤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣺⣟⣻⡦⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⢀⣴⡦⣀⣉⣉⡀⠀⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⡿⣿⣿⣿⣿⣦⣤⠤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢠⣾⣿⣿⣿⣧⣹⠀⠀⠀⢀⣼⣿⣿⣿⣶⣿⣿⣿⠀⠘⣿⣿⡟⠋⠉⣹⡇⠀⠀⠀⠀⠀⢺⣯⣾⣿⣿⣿⣿⣶⣿⣿⣷⠈⠀⠀⠀⠀⠀⠀⣴

⠀⢀⣿⣿⣿⣿⣿⣿⣟⡟⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⢀⡻⠟⠀⠛⠛⠛⣇⠀⠀⠀⢸⡿⢿⡴⢶⣿⣿⣿⣿⡃⠀⠙⢿⣿⣴⣦⣿⣡⣄⠀⠀⠀⠀⢠⡿⠿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣋⣀⡀⣠⣴⣿

⠀⣸⣿⣿⢠⣿⣿⢿⣿⣿⣶⣴⡄⠀⠀⣵⣯⣭⣤⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢇⣤⣶⣿⣿⣦⢸⣿⣿⣿⣇⠀⠀⠀⢸⣄⣀⣀⣀⠈⠙⣻⡇⠀⠀⠀⢸⣿⣿⣿⣭⣿⣷

⠀⣿⣿⣇⣾⠇⢔⠆⣤⡌⠛⣿⣧⣠⣴⠿⣿⣿⣿⣿⣷⣦⣠⣿⠛⠿⠿⣿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⠀⠀⠈⢻⠿⢿⡿⣿⣿⣿⠃⠀⠀⠀⣾⢉⣿⣿⣿⣿⣿

⣶⣿⣿⣾⠿⠂⠀⠀⢨⣅⣻⣿⣿⣿⡟⠉⠉⠛⢿⣿⣶⣿⢹⣽⡇⠀⠀⣀⣀⠀⠀⠀⠀⠀⣸⣧⠀⠀⢀⣾⣿⣿⣿⣽⣿⣿⣦⢠⣽⣿⣿⢻⣿⣿⣿⣿⣿⣧⡀⣤⣴⣦⠀⠀⢠⣿⡇⠀⢀⣠⣬⣿⣷⣿⣿⡿⠿⠛

⠛⠿⠿⠏⠀⠀⠀⠈⠙⠉⠉⠃⠁⠹⠟⠛⢷⣶⠾⣿⣿⣿⣿⣾⣷⠄⠀⢻⠟⠀⣠⣶⣶⣶⣷⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣾⡿⣻⣿⣟⣻⣿⣿⣧⡀⠀

⣶⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠸⣯⣌⠙⠻⠿⠿⣿⡏⢸⢃⡠⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠋⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾

⠛⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣀⡀⠀⢸⣳⠳⣼⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⣀⣀⡀⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠒⢋⣉⣉⣀⠘⣉⣀⡓⢉⣉⡙⡛⢋⣉⣉⠙⣛⣙⢛⣛⣛⣙⣉⣉⣀⠀⣈⣉⡙⢋⣁⡉⣻⢟⣛⡛⢛⣛⡓⣛⣛⣛⣛⠿⣋⣛⣛⡙⠛⣋⣁⣙⣛⠿⢟⣋⣙⣻⣿

⠀⠀⢹⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣷⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣼⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⣶⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⡤⢸⣿⡟⣿⣿⠀⣿⣿⣴⣿⠿⠀⣿⣿⢠⣿

⡇⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠁⣸⣿⣧⣿⣿⡄⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠁⠀⣸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⢸⣿⡇⢠⣶⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⢹⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⢀⡄⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⠀⣿⣿⠀⣶⣶⠘⣿

⠀⠀⠈⣉⠁⠈⠉⢀⣭⣭⣦⠌⢉⣁⣉⣭⣾⣿⣿⣮⣭⣥⣾⣿⣿⣷⣭⣽⣾⣿⣿⣦⣭⣥⣤⣭⠁⠤⣭⣭⣭⣥⣶⣩⣭⣵⣤⣭⣭⡅⣿⣿⣿⣷⣭⣭⣾⣷⣭⣭⣭⣥⣭⣭⣷⣮⣭⣥⣭⣭⣤⣭⣭⣤⣭⣭⡄⠀

⠀⠀⠰⢻⠆⠀⠀⠻⣿⣿⣿⡆⣾⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣿⣿⣿⡿⢋⣵⣦⣄⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⢉⣿⡻⣿⣿⣿⣿⣿⣿⡇⠀

[22A⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣍⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⡟⠛⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠂⢀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⠹⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⠀⠀⠘⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢻⣿⣷⣦⡀⣴⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠔⢘⣿⣛⣷⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣤⣶⣄⣈⣛⠁⠀⣄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠈⣿⣿⡿⣿⣿⣿⣿⣦⣤⡤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣿⣿⣿⣷⣝⠆⠀⠀⠀⣼⣿⡿⢿⣷⣾⣯⣿⡄⠹⣿⣿⣟⠁⠋⣿⡆⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣶⣿⣿⡆⠈⠁⠀⠀⠀⠀⢠⣴

⠀⢀⣿⣿⣿⣿⣿⣿⣟⡿⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣡⣚⣟⣃⣛⣛⣛⣫⡀⠀⠀⢸⣿⢟⡴⠒⣲⣭⣿⣿⡇⠀⠙⣿⣿⣿⣿⣿⣀⣤⡀⠀⠀⠀⢰⠟⠻⠿⢿⣿⣿⣿⣿⣿⡷⠀⣀⣋⣀⡀⣠⣴⣿

⠀⣸⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⡄⠀⠸⣿⣿⣭⣤⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣇⣤⣾⣿⣿⣦⡰⣿⣿⣿⣇⠀⠀⠀⢸⣄⣀⡀⠀⠈⠙⢻⡇⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿

⠀⣿⣿⣿⣿⡇⣴⠄⣠⡝⠻⣿⣷⣰⣵⣿⣿⣿⣿⣿⣿⣦⣄⣿⠍⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣿⣿⣾⣿⣿⠃⠀⠀⠀⣾⣉⣿⣿⣿⣿⣿

⣷⣿⣿⣿⠟⠁⠈⠀⣠⣨⡾⢿⣿⣿⣿⠋⠉⠛⢿⣿⣷⣿⢹⢿⣧⠀⠀⣤⣤⠄⠀⠀⠀⠀⢸⣷⡀⠀⠀⣾⣿⣾⣿⣿⣾⣿⡄⢀⣼⣿⣿⢛⣽⣿⣷⣯⣿⣧⡀⣤⣴⣦⠀⢀⣈⣿⡇⠀⢊⣠⣬⣽⣷⣿⣿⡿⡿⠻

⠻⠿⣿⡏⠀⠀⠀⠀⠈⠀⠉⠉⠀⢹⡿⠓⠖⠦⡮⣿⣿⣿⣿⣾⣷⢖⠀⠹⠟⠀⣤⣶⣶⣶⡔⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⡿⣻⣿⣟⣿⣿⣿⣧⡀⠀

⣶⣀⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⣀⠀⠉⠻⢿⢿⣿⡇⡌⢡⡠⡴⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣛⣛⣋⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾

⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠀⣀⠀⢸⣻⠃⠰⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡙⠛⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣀⡁⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠒⢊⣉⣉⣀⠈⣉⣀⡂⢉⣉⡙⠟⢋⣉⣉⠛⣋⣛⢛⣉⣉⣉⣉⣀⣀⠀⣈⣋⡛⢋⣁⡈⣹⢛⣛⡛⢛⣛⡓⣛⣋⣛⣛⠿⣉⣉⣙⡉⠛⣉⣁⣈⣛⠿⢟⣋⣙⣻⣿

⡀⠀⢻⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⣧⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣾⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⣇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⡿⠀⢸⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢸⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⡿⢸⣿⣿⣷⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⣤⢸⣿⡟⣿⣿⠀⣿⣿⣴⣿⠿⠀⣿⣿⢠⣿

⡇⠀⢸⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⢸⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢻⣿⣿⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠉⣸⣿⣧⣿⣿⡄⣿⣿⠉⣿⣿⠀⣿⣿⢸⣿

⠁⠀⣸⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⣸⣿⡇⢠⣶⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⢀⠀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⡀⣿⣿⠀⣶⣶⠘⣿

⠀⠀⠈⢉⠁⠈⠉⢁⣭⣭⣤⣍⠉⠁⠉⢩⣾⣿⣿⣮⣭⣥⣾⣿⣿⣷⣭⣽⣾⣿⣿⣦⣭⣥⣤⣭⠁⠀⣭⣭⣭⣡⣄⣩⣭⣅⣤⣭⣭⡅⣿⣿⣿⣷⣭⣭⣾⣷⣭⣭⣭⣥⣭⣭⣷⣮⣭⣥⣭⣭⣤⣭⣭⣤⣭⣭⡆⠀

⠀⠀⠰⢿⠦⠀⠀⠻⣿⣷⣿⣷⠀⠀⠀⣾⡏⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠟⢁⣿⣿⣿⡟⢋⣵⣷⣄⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⢩⣽⣛⠛⣪⣽⣿⣿⣿⣇⠀

[22A⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣽⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠂⢀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⠹⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⠀⠀⠘⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢻⣿⣷⣦⡀⣴⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠴⢐⣿⣛⣷⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡆⣠⣾⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⣠⣶⣄⣀⣉⡁⠀⢄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣼⣿⣿⣿⣷⣜⠆⠀⠀⠀⣴⣿⡿⠿⣷⣶⣦⣿⡆⠹⣿⣿⣯⣙⣽⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⢻⣿⣦⢈⠅⠀⠀⠀⠀⢠⣴

⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣟⣃⣛⣛⣛⣫⡀⠀⠀⢸⣿⢿⠰⠒⣲⣯⣿⣿⡇⠀⠙⣿⣿⠿⣿⣯⣀⣤⡀⠀⠀⠀⢰⠛⠛⠛⠿⣿⣿⣿⣾⣿⡷⠀⣀⣋⣀⡀⣠⣴⣿

⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣦⣶⡄⠀⡼⣿⣿⣍⣤⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣇⣤⣾⣿⣿⣦⠸⣿⣿⣿⣧⠀⠀⠀⢸⡄⣀⠀⠀⠀⠙⢿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣯⣿⣇⣶⠄⣠⠙⠻⣿⣷⣰⣥⣿⣿⣿⣿⣿⡿⣶⣤⣾⡍⠙⠛⠛⠋⠛⠛⠛⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣿⣿⣷⣶⣿⠡⠐⢀⠀⣾⣉⣿⣿⣿⣿⣿

⣷⣿⣿⣿⠟⠁⠀⢀⣀⣰⡾⣿⣿⣿⣿⠋⠉⠙⢿⣿⣷⣿⡏⢻⣧⠀⠀⢠⣠⠤⠤⠀⠀⠀⠸⣷⡀⠀⠀⣼⣶⣶⣟⣵⣬⣷⡄⢀⣼⣿⣿⢏⣽⣿⣷⣯⣿⣧⣀⣤⣼⣅⠈⠁⠀⣿⡇⠀⣋⣩⣮⣿⣷⣿⣿⣿⡿⢿

⠻⠿⣿⡏⠀⠀⠀⠀⠁⠀⠉⠁⠈⢽⡿⠛⠛⠒⠾⣿⣿⣿⣿⣾⣿⢆⠀⠘⠏⢀⣴⣶⣶⣦⡀⢽⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⣿⣿⣾⡿⣻⣿⣿⣿⣿⣿⣧⡀⠀

⣶⣀⣤⠍⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⣤⣤⣠⡀⠀⠉⠛⠻⠿⢿⣏⡆⢠⢀⡶⠿⠛⣿⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣔⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣀⠀⠠⣹⠃⠀⠾⣦⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣟⠛⠳⠶⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣯⣿⣿⣿

⠀⠀⣀⣀⡁⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠐⢊⣉⣉⣀⠈⣉⣀⡀⢀⣀⡙⠿⢋⣉⣉⠟⣉⣛⢛⣋⣉⣉⣉⣀⣀⠀⣈⣛⡋⢋⣀⡈⣹⢛⣙⡛⢛⣙⡓⣛⣋⣙⣛⠿⣉⣉⣉⡃⠋⣉⣁⣀⣛⠿⢟⣉⣙⣻⣿

⣄⠀⣿⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⣾⣿⡟⣿⣿⢸⣿⡇⣿⣿⢁⣦⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣿⠘⣿⣧⣾⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⣇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⡿⠀⣿⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⢻⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⡿⢸⣿⣿⣷⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⣤⢸⣿⡟⣿⣿⠀⣿⣿⣴⣿⠿⠀⣿⣿⠀⣿

⡇⠀⣿⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⣻⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣏⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢿⣿⣿⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠉⣸⣿⣧⣿⣿⡄⣿⣿⡉⣿⣿⠀⣿⣿⢸⣿

⠁⠀⣿⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣿⡆⣿⣿⡇⢠⣶⣿⢸⣿⣿⢸⣿⣷⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⢀⡀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⠀⣶⣶⠘⣿

⠀⠀⠈⢉⠁⠈⠉⢁⣭⣍⣦⣉⡍⠁⠉⠉⣼⣿⣿⣮⣩⣥⣾⣿⣿⣷⣭⣭⣾⣿⣷⣦⣭⣥⣤⡭⠁⠀⣭⣭⣭⣡⣌⣩⣭⣁⣤⣭⣭⡁⣾⣿⣿⣷⣭⣭⣾⣷⣭⣭⣭⣭⣭⣭⣷⣮⣭⣥⣭⣭⣤⣭⣭⣤⣭⣭⡆⠉

⠀⠀⠰⢿⠇⠂⠀⠻⣿⣷⣿⣿⡆⠀⠀⢰⣿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⢻⣿⣿⠉⢋⣴⣿⣄⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠉⠀⣭⣭⣙⠛⣪⣭⣾⣿⣿⣿⠀

⣝⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⡹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⠀⠀⠸⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢻⣿⣷⣦⡀⣴⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠴⢐⣿⣛⣷⣆⠀⠀⠀⠈⠻⣿⣿⣿⡿⣿⣿⣿⡇⣤⣿⣿⣿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⣀⣙⡁⠀⢄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣿⣿⣿⣿⣜⡇⠀⠀⠀⣴⣿⡿⠿⢷⣶⣶⣿⡇⠹⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠻⣿⣷⠌⠅⠀⠀⠀⠀⢠⣴

⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢛⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣟⣃⣛⣛⣛⣻⣀⠀⠀⢰⣿⡟⠐⢒⣲⣾⣿⣿⡇⠀⠙⣻⡿⠿⢿⣯⣀⣤⡀⠀⠀⠀⠸⠛⠛⠛⠿⢿⣿⣿⣶⣭⡿⠂⣀⣋⣀⡀⣠⣴⣿

⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⡾⣿⣿⣍⣴⣤⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣇⣴⣾⣿⣿⣦⢨⣿⣿⣿⣷⠀⠀⠀⢰⡄⣀⠀⠀⠀⠙⢿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣟⣿⣅⣤⠀⣬⠙⠻⣿⣿⣠⣄⡾⣿⣿⣿⣽⡿⢷⣦⣼⡍⠙⠛⠛⠉⠉⠙⠋⠉⠁⠁⠀⠀⠀⠙⢿⣿⡿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⣿⣿⣿⣿⣵⣾⣿⠡⠐⢀⡀⣾⣙⣿⣿⣿⣿⣿

⣷⣿⣿⣿⡟⠁⠀⢀⢀⣴⡿⢿⣿⣿⣿⡏⠉⠉⠻⣿⣿⣾⡇⢻⣧⠀⠀⢠⣤⠤⠤⠀⠀⠀⠨⣷⡀⠀⠀⣸⣶⣾⣋⣤⣽⣦⣍⣀⣼⣿⣿⢟⣭⣿⣷⣮⣿⣷⣄⣤⣼⡍⠉⠁⠁⣿⡗⠀⣋⣡⣬⣽⣷⣿⣿⣿⣿⣿

⠿⠿⣿⣿⠀⠀⠀⠀⠁⠀⠁⠀⠈⣿⣿⠏⠉⠙⢶⣿⣿⣿⣿⣷⣿⢇⠀⠈⠏⢀⣴⣶⣶⣦⡄⢼⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⣿⣿⣾⡿⣻⣿⡟⠛⣿⣿⣯⡁⠀

⣷⣄⣤⠍⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⣧⣤⣀⡀⠀⠀⠙⠻⠿⠯⢹⠇⢰⢀⡶⠛⠛⢿⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷

⡿⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠤⢆⣀⠀⠀⣽⠁⠀⠾⣢⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣟⠓⠶⡦⣶⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣯⣿⣿⣿

⠀⠀⣀⣀⡁⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠒⢋⣉⣉⣁⠈⣉⣁⡀⢀⣀⡘⠿⢋⣉⣙⠟⣉⣛⢛⣋⣉⣉⣀⣀⣀⠀⣈⣛⡛⢋⣀⡈⣹⢛⣙⡛⢛⣉⡓⣛⣋⣙⣛⠿⣋⣉⣉⡋⠉⣉⣉⣀⣙⠿⢟⣉⣙⣻⣿

⣄⠀⣿⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢻⣿⡟⣿⣿⢸⣿⡇⣿⣿⢁⡆⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣾⠘⣿⣧⣾⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⣇⠀⣿⣿⠿⣿⣷⠈⣿⣿⠀⣿

⣿⠀⣿⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡇⣾⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⡯⢸⣿⣿⣷⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⣤⢸⣿⡟⣿⣿⠀⣿⣿⣴⣿⠿⠀⣿⣿⠀⣿

⡇⠀⣿⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⣋⡁⣿⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣏⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢿⣿⣿⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠉⣸⣿⣧⣿⣿⡄⣿⣿⡍⣿⣿⠀⣿⣿⢸⣿

⠃⠀⣿⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⣽⡆⣽⣿⡇⢠⣶⣿⢸⣿⣿⢸⣿⡷⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⠀⠀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⠀⣶⣶⠈⣿

⠀⠀⠈⠉⡁⠈⠉⢁⣭⣍⣦⣉⣭⠁⠉⠉⢐⣿⣿⣮⣩⣥⣾⣿⣿⣷⣭⣽⣾⣿⣷⣦⣍⣥⣤⡍⠁⠀⢭⣭⣭⢡⣈⣩⣭⢅⣤⣭⣭⡅⣼⣿⣿⣷⣭⣭⣾⣧⣭⣭⣭⣭⣭⣭⣵⣾⣭⣥⣭⣭⣤⣭⣭⣤⣭⣭⣦⠉

⠀⠀⠀⢾⠇⠂⠀⠻⣿⣷⣿⣿⣿⠀⠀⠀⣼⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⢹⠟⠋⠈⣡⣴⣿⣄⡀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠟⠋⠠⣬⣭⣙⠛⣃⣭⣼⣿⣿⣿⠀

[22A⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠓⢄⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠐⠀⠘⡹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣈⠐⠁⠸⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣶⣾⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢻⣿⣷⣦⡐⣴⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢖⣿⣟⣷⣦⡀⠀⠀⠈⠻⣿⣿⣿⡿⣿⣿⣿⡇⢴⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣔⣀⣙⡁⠀⢄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣴⣿⣿⣿⣿⣄⡳⠀⠀⠀⣰⣿⡟⠙⠿⣾⣷⣽⡇⠈⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣟⣻⣿⣿⣄⢹⣿⣷⢬⠅⠀⠀⠀⠀⢠⣴

⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣋⣙⣛⣛⣻⣅⠀⠀⠀⣿⡏⠐⠉⣓⣶⣿⣿⡏⠀⢀⣹⣿⠛⢻⣷⣀⣠⡀⠀⠀⠀⢸⠋⠙⠛⠻⠿⣿⣿⣶⣿⡿⠂⣤⣿⣀⣀⣠⣴⣿

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⡿⢿⣿⣭⣤⣶⣶⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣧⢸⣿⣿⣿⣷⡀⠀⠀⢸⣄⣀⡀⠀⠀⠉⢻⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣿⣿⣅⣠⠀⡌⠻⢿⣿⣷⣹⣧⣾⣟⣿⣿⣧⣼⠟⣿⣾⡯⠉⠛⠋⠋⠙⠛⠋⠉⠁⠁⠀⠀⠀⠈⢿⣿⡿⢿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣷⣶⣿⠩⠐⢀⡠⣾⣙⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠁⢀⢀⣰⠿⠿⣿⣿⣿⣿⣅⣀⡈⢿⣿⣿⣿⡀⣿⡀⠀⠠⣄⡤⠤⠀⠀⠀⠀⣿⡀⠀⠀⣸⣷⣾⣿⣿⣿⣷⣭⣁⣼⣿⣿⡟⣫⣿⣿⣭⣻⣷⣄⣤⣼⣍⠉⠉⠙⣿⡟⠀⣛⣩⣦⣽⣷⣿⣿⣿⣿⣿

⠿⠿⣿⣿⠁⠀⠀⠈⠁⠈⠁⠀⡌⢿⣿⡟⠈⠉⠹⡿⢿⣿⣿⣷⣯⡷⠀⠀⠉⢀⣴⣶⣶⣦⡆⢼⣿⣠⣾⣿⣿⣿⡿⠿⠿⢿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⡿⣿⣿⡿⣻⣿⠻⠻⣿⣿⣿⡁⠀

⣷⣄⣤⠍⠁⠀⠀⠀⢀⡀⠁⠀⠀⢨⣯⣀⣀⡀⠀⠀⠈⠛⠛⠃⢻⠃⠎⢀⡴⠛⠛⢻⣿⣿⣷⣼⣿⣿⣿⣿⣏⠁⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣧⣶⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷

⣿⠟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠉⠁⠀⠐⣂⣀⡀⠀⠈⠁⠀⠰⢳⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⡏⠛⠻⠿⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠙⣿⣿⣿⣯⣿⣿⣿

⠁⠀⣀⣈⡉⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠚⣉⣉⣁⣀⠀⣈⣁⡀⢀⣀⡙⠿⢋⣉⣙⠟⣉⣙⢛⣉⣉⣉⣀⣀⣀⠀⣈⣛⡛⢋⣀⡉⢛⢋⣉⡛⢛⣉⡁⣘⣋⣙⣛⠟⣉⣉⣉⡛⠃⣈⣉⣀⣈⠻⢟⣉⣙⣻⣿

⣧⠀⣿⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⣿⣿⡟⣿⣿⢸⣿⡇⣿⣿⢡⡆⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣾⠸⣿⣧⣾⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⣇⠀⣿⣿⡿⣿⣷⠘⣿⣿⠀⣿

⣿⠀⣿⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡏⣻⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⡇⢸⣿⣿⣷⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⣇⢻⣿⣿⡟⠀⣿⣿⣧⣤⢸⣿⡟⣿⣿⠀⣿⣿⣷⣿⠿⠀⣿⣿⠀⣿

⡇⠀⣿⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⢋⡁⣿⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣟⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢿⣿⣿⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠉⣸⣿⣧⣿⣿⡄⣿⣿⡏⣿⣿⠀⣿⣿⢰⣿

⠃⠀⣿⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⢴⡆⣿⣿⡇⢠⣶⣿⢸⣿⣿⠰⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⠀⠀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⠀⣶⣶⠈⣿

⠀⠀⠈⠉⠁⠈⠉⢁⣭⣭⣦⣉⣭⣅⠉⠉⠀⢸⣿⣮⣩⣥⣾⣿⣿⣷⣭⣭⣶⣿⣶⣌⡉⠡⡤⠉⢁⠈⠭⣭⣭⢡⣈⡩⣭⢅⣀⣍⣭⣵⢸⣿⣿⣷⣭⣭⣾⣧⣭⣭⣩⣭⣭⣭⣷⣮⣭⢧⣍⣭⣤⡭⣍⡠⣭⣭⣾⡉

⠂⠀⠀⢠⠷⠖⠀⠻⣿⣷⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠘⠋⠀⢀⣠⣶⣿⣶⣄⠀⢾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢿⠉⢱⣦⣭⣍⡙⢁⣭⣴⣿⣿⣿⡇

⠀⠀⠓⢀⣻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣈⠐⠁⠸⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣶⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢻⣿⣷⣦⡐⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢒⣿⣟⣿⣦⡀⠀⠀⠙⠻⣿⣿⣿⡿⣿⣿⣿⡇⠰⣿⣿⣿⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣔⣀⣉⡁⠀⢄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣿⣿⣿⣿⣯⡳⠀⠀⠀⣠⣿⡟⠙⠿⣾⣷⣿⡇⠀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠐⣿⣿⣟⣻⣿⣿⣄⠸⣿⣷⢬⢅⠀⠀⠀⠀⢠⣴

⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣋⣘⣛⣛⣻⣅⠀⠀⠀⣿⣏⠀⠉⣙⣲⣿⣿⡏⠀⣀⣽⣿⠉⢻⣷⣄⣀⡀⠀⠀⠀⢰⠋⠉⠛⠛⠿⣿⣿⣾⣿⡿⠂⣰⣟⣀⣀⣠⣴⣿

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡐⡿⣿⣿⣽⣶⣶⣶⣆⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠹⣿⣿⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣧⢀⣿⣿⣿⣷⡀⠀⠀⢸⣄⣀⡀⠀⠀⠈⢻⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣿⣿⣁⡠⠀⡍⠛⢿⣿⣿⣻⣤⣼⣿⣿⣿⣿⣼⡿⣿⣶⣯⠛⠛⠋⠉⠉⠙⠋⠉⠁⠁⠀⠀⠀⠈⢿⣿⡿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣵⣶⣿⠣⡐⢂⠠⣾⣹⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠟⠈⠀⢀⣀⣴⠿⠿⣿⣿⣿⣿⣧⣀⡈⢹⣿⣿⣿⡀⣿⡄⠀⠀⣤⡤⠤⠀⠀⠀⠀⣿⡀⠀⠀⣸⣷⣶⣿⣿⣿⣶⣭⣀⣸⣿⣿⡿⢛⣿⣭⣭⣻⣷⣆⣤⣼⣍⠉⠉⠙⣿⡟⠀⣛⣩⣦⣿⣷⣿⣿⣿⣿⣿

⠿⠿⣿⣿⠀⠀⠀⠉⠀⠉⠁⠀⡌⢿⣿⣿⠀⠉⠙⠛⠻⣿⣿⣿⣿⡷⠂⠀⠈⢁⣴⣶⣶⣦⡄⢼⣿⣠⣾⣿⣿⣿⣿⠿⢿⣿⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⠿⣿⣿⡿⣻⣿⡟⠻⠿⣿⣿⡁⠀

⣿⣄⣤⡏⠁⠀⠀⠀⠀⡀⠀⠀⠀⢨⣥⣀⣀⡀⠀⠀⠀⠉⠛⠛⠘⠃⠎⢀⡴⠿⠻⢿⣿⣿⣷⣴⣿⣿⣿⣿⣋⢁⣀⣀⣀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣧⣴⣏⣿⣭⣿⣿⣿⣿⣽⣿⣿⣷

⣿⠟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠏⠉⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢳⢶⣲⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠛⠛⠻⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡋⢿⣿⣿⣯⣿⣿⣿

⠁⠀⣀⣈⡉⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠈⣉⣁⣀⣀⠀⣈⣁⡀⢀⣀⡘⠻⢋⣉⣉⠟⣉⣙⢛⣉⣉⣉⣀⣀⣀⠀⣀⣛⡛⢋⣀⡉⠛⢋⣉⡛⢛⣉⡁⣈⣋⣙⣛⠟⣉⣉⣁⡙⠛⣁⣀⣀⣀⠻⢟⣉⣙⣻⣿

⣧⠀⣿⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⣿⣿⡟⣿⣿⢸⣿⡇⣿⣿⢁⡆⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣼⠸⣿⣧⣾⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⣇⠀⣿⣿⡿⣿⣷⠘⣿⣿⠀⣿

⣿⠀⣿⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡏⣻⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⡇⢸⣿⣿⣷⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⡇⢻⣿⣿⡟⠀⣿⣿⣧⣤⢸⣿⡟⣿⣿⠀⣿⣿⣷⣿⠿⠀⣿⣿⠀⣿

⡇⠀⣿⣿⡏⣿⣿⡇⣾⣿⣧⣿⣿⠀⣿⣿⠛⢋⡁⣿⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢿⣿⣿⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠉⣸⣿⣧⣿⣿⡄⣿⣿⡏⣿⣿⠀⣿⣿⢰⣿

⠃⠀⣿⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⠤⡆⣿⣿⡇⢠⣶⣿⢸⣿⣿⠰⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⠀⠀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⠀⣶⣶⢸⣿

⠀⠀⠈⠉⠁⡈⠉⢁⣭⣍⣦⣉⣭⠥⡉⠉⠀⢀⣿⣮⣩⣥⣾⣿⣿⣷⣭⣭⣶⣿⣷⣌⣉⠁⠀⠉⢁⡌⠭⣭⣭⢡⣈⡉⢉⢁⣀⣍⣩⣵⢸⣿⣿⣷⣭⣭⣾⣧⣭⣭⣭⣭⣭⣭⣷⣮⣭⢧⣭⣭⣤⡍⠍⠠⣭⣭⣾⡟

⠟⠀⠀⢀⠐⠶⠀⠻⣿⣷⣿⣿⣿⣿⡁⠀⢀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡘⠉⠀⠀⣠⣶⣿⣷⣤⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢿⢻⣏⢲⣶⣤⣌⣉⣁⣠⣴⣿⣿⣿⡇

⠀⠀⠃⢀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⡹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣈⠐⠁⠸⢽⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢻⣿⣷⣦⡐⣴⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⣻⣿⣻⣶⡀⠀⠀⠙⠻⣿⣿⣿⣿⢿⣿⣿⡇⠸⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣔⣀⣉⡁⠀⢄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣧⣳⠀⠀⠀⣠⣿⡿⠘⠻⢿⣷⣿⡇⠀⠻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠐⣿⣿⣟⣻⣿⣿⡄⢸⣿⣷⢬⢅⠀⠀⠀⠀⢠⣶

⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣿⣛⣘⣛⣛⣛⣅⠀⠀⠀⣿⣏⠀⠉⢉⣱⣾⣿⡏⠀⣠⣼⣿⡉⠹⣿⣄⣀⠀⠀⠀⠀⢰⠋⠉⠛⠛⠿⣿⣿⣶⣿⡿⠂⣰⣟⣀⣀⣠⣴⣿

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⢄⡿⣿⣿⣿⣶⣶⣶⣦⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠀⣿⣿⣿⣷⡄⠀⠀⢸⣄⣀⡀⠀⠀⠈⢻⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣿⣿⣁⡀⠀⡝⠻⢿⣿⣿⢻⣤⣼⣿⢿⣿⣿⣼⣿⣿⣶⣿⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⢿⣿⣿⢿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣷⣤⣶⣾⠫⡒⢂⠠⣾⣙⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠈⠀⣀⠀⣰⠿⠿⣿⣿⣿⣿⣧⣄⡈⠹⣿⣿⣿⡀⣿⡄⠀⠀⣤⡤⠄⠀⠀⠀⠀⣿⡀⠀⠀⣸⣿⣶⣾⣿⣿⣶⣭⣀⣹⣿⣿⡿⢛⣿⣯⣙⣿⣿⣆⣤⣼⣍⠉⠉⠉⣿⡟⠀⣋⣭⣦⣽⣷⣿⣿⣿⣿⣿

⠿⠿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⡬⢿⣿⡿⠉⠉⠙⠍⠻⣿⣿⣿⣿⡷⢂⠀⠘⢀⣴⣶⡶⣦⡆⢼⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⠿⣿⣿⣿⣻⣿⡿⠟⠿⣿⣯⡀⠀

⣿⣄⣤⡍⠁⠀⠀⠀⠀⡀⠀⠀⠀⢠⣥⣀⣀⡀⠀⠀⠀⠈⠙⠛⠘⡃⠎⢀⡴⠟⠻⢿⡿⣿⣿⣤⣿⣿⣿⣿⡛⠛⠋⠉⣉⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣧⣴⣯⣿⢿⣾⣿⣻⣷⣽⣿⣿⣷

⣿⠟⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠏⠉⠁⠀⢀⣀⣄⠀⠀⠀⡁⠀⠀⢳⢖⣲⣶⣶⣶⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠁⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠸⣿⣿⣏⣿⣿⣿

⠉⠀⣀⣈⡉⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠈⣉⣁⣀⣀⡀⣈⣁⡀⢀⣀⡈⠛⢋⣉⣉⠟⣉⣙⢛⣉⣉⣁⣀⣀⣀⠀⣀⣛⡛⢋⣈⡉⠛⢋⣉⡛⢛⣉⡉⣈⣋⣙⣛⠟⣉⣉⣉⡈⠙⣉⣀⣀⣀⠹⢟⣉⣙⣻⣿

⣷⠀⣿⣿⡇⣿⣿⡇⢰⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⣿⣿⡟⣿⣿⢸⣿⡇⣿⣿⢁⡆⢸⣿⣿⡀⣿⣿⢸⣿⣿⠿⠏⣿⣿⢰⣿⣿⡇⣿⣿⡇⣼⠘⣿⣧⣾⣿⠃⣿⣿⡿⠿⠀⣿⣿⣿⣇⠀⣿⣿⡿⣿⣷⠘⣿⣿⠀⣿

⣿⠀⣿⣿⣷⣿⣿⡇⢸⣿⡟⣿⣷⠀⣿⣿⣼⣿⡟⣻⣿⣧⣿⣿⠀⢿⣿⣿⡏⣼⡇⢸⣿⣿⣷⣿⣿⢸⣿⣿⣤⡄⣿⣿⢸⣿⣿⡇⣿⣿⠃⣿⡇⢻⣿⣿⡟⠀⣿⣿⣧⣤⢸⣿⡟⣿⣿⠀⣿⣿⣷⣿⠿⠀⣿⣿⠀⣿

⡇⠀⣿⣿⡏⣿⣿⡇⣿⣿⣧⣿⣿⠀⣿⣿⠛⢋⡁⣿⣿⡟⠛⣉⣀⢸⣿⣿⢠⣿⣏⢸⣿⡟⣿⣿⣿⢸⣿⣿⠉⠁⢿⣿⣿⣿⢿⣿⣿⣿⢠⣿⣿⠘⣿⣿⠁⠀⣿⣿⡏⠉⣸⣿⣧⣿⣿⡄⣿⣿⡏⣿⣿⠀⣿⣿⢰⣿

⠃⠀⣿⣿⡇⣿⣿⡇⣿⣿⠏⣿⣿⡆⣿⣿⠀⠤⡆⣿⣿⡇⢠⣶⣿⢸⣿⣿⠰⣿⡷⢸⣿⡇⢻⣿⣿⢸⣿⣿⣶⡆⢸⣿⣿⡏⢸⣿⣿⡟⢸⣿⣿⡀⣿⣿⠀⠀⣿⣿⣷⣶⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⠀⣶⣶⢸⣿

⠀⠀⠈⠉⠁⡈⠉⢁⣭⣭⣦⣉⣭⣅⡉⠉⠀⠀⣿⣮⣩⣥⣾⣿⣿⣷⣭⣭⣶⣯⣷⣄⡉⠁⠀⠉⢁⡈⠩⣭⢍⢡⣈⡉⢉⣁⣀⣉⣭⡥⢸⣿⣿⣷⣭⣭⣾⣧⣭⣭⣭⣭⣭⣭⣵⣮⡭⠥⣭⣭⣤⡭⠉⠀⢩⣭⣾⡏

⠿⠃⠀⠀⠀⠶⠀⠻⣿⣷⣿⣿⣿⣿⡇⠀⠀⡾⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⡿⠋⡀⠈⠀⠀⣠⣴⡿⡷⣤⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡾⡿⠏⣾⣏⣲⣶⣦⣤⣉⣉⣠⣴⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 5427

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

Gemini_version_available_♊︎

✐ Links_31/12/2021:_7-Zip_21.07_and_Goodbye_to_CentOS_8⠀✐

Posted in News_Roundup at 5:33 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Distributions

      o Devices/Embedded

* Free_Software/Open_Source

* Leftovers

* § GNU/Linux⠀➾

      o § Audiocasts/Shows⠀➾

            # ⚓ Streaming_Until_2021_Is_Finally_Over_–_Invidious⠀⇛

            # ⚓ LsXtended:_Navigate_Your_Terminal_Like_A_Pro_–_Invidious⠀⇛

                   Navigating tour terminal cna be kind of annoying so

                   how we spruce it up a bit with lsx, which basically

                   takes the idea of a terminal file manager and

                   minuses the file manager.

            # ⚓ How_to_install_Godot_3_on_Elementary_OS_6.0_–_Invidious⠀⇛

                   In this video, we are looking at how to install

                   Godot 3 on Elementary OS 6.0.

      o § Kernel Space⠀➾

            # ⚓ Intel_HFI_Code_Revised_For_Improving_Alder_Lake’s_Hybrid

              Support_On_Linux_–_Phoronix⠀⇛

                   Back in late 2020 Intel’s programming manuals

                   detailed the Enhanced Hardware Feedback Interface

                   for the CPU to provide guidance to the kernel’s

                   scheduler on optimal task placement of workloads.

                   While marketed as Thread Director with the new 12th

                   Gen Alder Lake processors, that hardware feedback

                   interface support is getting squared away for the

                   Linux kernel to improve the support for these

                   newest processors.

                   Microsoft Windows 11 already supports the Intel

                   Hardware Feedback Interface as part of its Alder

                   Lake / Thread Director optimizations while only

                   recently has the Linux kernel support been in the

                   works. In November there were some early

                   “intel_hfi” patches published while right before

                   Christmas Intel dropped a second version of the

                   patches with many changes and improvements stemming

                   from the early code review.

            # ⚓ Linux_5.17_To_Replace_SHA1_With_BLAKE2s_For_Faster_&_More

              Secure_“Random”_–_Phoronix⠀⇛

                   Queued today within the Linux’s random.git

                   repository for the /dev/random and /dev/urandom

                   code is support for using BLAKE2s rather than SHA1

                   when hashing the entropy pool. This in turn is a

                   big performance speed-up in addition to being more

                   secure.

                   For Linux 5.17 there are some nice “random”

                   improvements. Jason Donenfeld who is best known for

                   his work on creating WireGuard is also the Linux

                   kernel’s random maintainer. Queued today was the

                   change to remove SHA1 usage from the random.c code

                   and to instead use BLAKE2s.

      o § Instructionals/Technical⠀➾

            # ⚓ How_to_install_Guilded_on_a_Chromebook⠀⇛

                   Today we are looking at how to install Guilded 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.

            # ⚓ How_To_Install_WildFly_on_Debian_11_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   WildFly on Debian 11. For those of you who didn’t

                   know, WildFly formerly known as JBoss is an

                   application server written in Java and developed by

                   Red Hat. WildFly is a flexible, lightweight,

                   managed application runtime that helps you build

                   amazing applications.

                   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 through the step-by-

                   step installation of the WildFly (JBoss) on a

                   Debian 11 (Bullseye).

            # ⚓ Update_on_Linux_hibernation_support_when_lockdown_is

              enabled⠀⇛

            # ⚓ How_to_listen_to_YouTube_Music_on_Linux_with_Ytmdesktop⠀⇛

                   We’ve covered how to listen to YouTube Music on the

                   Linux desktop before using the unofficial YouTube

                   Music app developed by Th-Ch. However, this program

                   isn’t the only way to listen to the service on the

                   Linux platform.

                   If you’ve tried out Th-Ch’s unofficial YouTube

                   Music app and found that it didn’t do what you

                   wanted, a great alternative is Ytmdesktop. It has a

                   very similar UI. However, Ytmdesktop integrates

                   with Discord, Last.fm, and more. Here’s how to use

                   it on your system.

            # ⚓ How_to_Use_Ubuntu_Disk_Utility_for_Better_HDD/SSD

              Management⠀⇛

                   When using Linux, there are times when you may need

                   to manage hard drives, removable media such as USB

                   drives and SD cards, and more. This is especially

                   true if you plan on dual-booting Ubuntu with

                   Windows or a second Linux installation.

                   Therefore, it’s important to know how you can

                   manage your drives and the partitions that are on

                   them. Resizing a partition, reformatting your hard

                   drive, or checking its health are some of the

                   things that you can do with Ubuntu’s built-in disk

                   management tool known as “Disks.”

            # ⚓ How_to_Install_Tripwire_IDS_on_Debian_11_Bullseye_–

              LinuxCapable⠀⇛

                   Tripwire IDS is a reliable intrusion detection

                   system that identifies changes made to specified

                   files and directories. Tripwire IDS Detects

                   intrusions by analyzing operating systems and

                   applications, resource utilization, and other

                   system activity.

                   In the following tutorial, you will learn how to

                   install Tripwire IDS on your Debian 11 Bullseye

                   operating system.

            # ⚓ How_to_Install_PHP_8.1_on_CentOS_9_Stream_–_LinuxCapable⠀⇛

                   PHP 8.1 is a significant update of the PHP language

                   that was “officially” released on November 25,

                   2021. As we advance from the existing PHP 8.0

                   release, this is a standard upgrade. The new PHP

                   8.1 brings enums, fibers, never return type, final

                   class constants, intersection types, read-only

                   properties, and a long list of new features and

                   changes.

                   In the following tutorial, you will learn how to

                   import the REMI Module and install PHP 8.1 on

                   CentOS 9 Stream.

            # ⚓ How_to_Install_Side-Scroller_SuperTux_0.6.3_via_PPA_in

              Ubuntu_20.04/18.04/21.10_|_UbuntuHandbook⠀⇛

                   Many free open-source apps got new releases before

                   new year 2022. The side-scrolling game SuperTux

                   0.6.3 is one of them!

      o § Desktop Environments/WMs⠀➾

            # § GNOME Desktop/GTK⠀➾

                  # ⚓ Arc_Menu_Extension_Adds_a_New_Layout_&_Standalone

                    Runner_Mode_–_OMG!_Ubuntu!⠀⇛

                         I already think Arc Menu is one of the best

                         GNOME extensions out there, and seeing the

                         change-log for its latest release I’m

                         reminded why.

                         Arc Menu v20 is chock-full of enhancements

                         that span the full gamut of development, from

                         bug fixes and code refactoring through to

                         brand menu layouts and even more

                         customisation options.

                         The star attraction in the latest release is

                         the the new “A.Z.” menu layout.

      o § Distributions⠀➾

            # § IBM/Red Hat/Fedora⠀➾

                  # ⚓ Goodbye_CentOS_8_and_Thanks_for_Everything!⠀⇛

                         The day has finally arrived! Today, December

                         31, 2021 CentOS Linux 8 reaches End-of-Life

                         (EOL).

                         For years, a lot of Linux system

                         administrators have been using CentOS for

                         their Linux servers. The majority of web and

                         server hosting companies also offered CentOS

                         as their default operating system. In other

                         words, CentOS has been dominant on the Linux

                         server field in recent years.

                         Back in December 2020, Red Hat announced that

                         it will be discontinuing CentOS based on

                         RedHat releases. This was come as quite a

                         shock for the CentOS community. And this is

                         where history repeats itself. Let me remind

                         you. Back in 2004, Red Hat did the same thing

                         by EOL’ing all versions of Red Hat Linux and

                         forced users to Red Hat Enterprise Linux.

                         Although the news was announced as early as

                         December last year, many Linux system

                         administrators and developers still feel at a

                         loss. Of course, the system running CentOS 8

                         will not crash overnight, but security and

                         other updates will no longer continue from

                         the beginning of next year.

                  # ⚓ Red_Hat_donates_$10,000_and_the_Flatpak_package_will

                    be_official [Ed: IBM uses deep pockets to push itself

                    as the 'standard']⠀⇛

                         OBS Studio is one of the most successful

                         projects of the free software However, it

                         carries an important but, and that is that

                         for many years it has not offered symmetric

                         support between the platforms it supports, so

                         the version for Linux has fewer features than

                         the Windows version. Added to that is the

                         fact that Ubuntu and Linux Mint are the only

                         officially supported distributions, which

                         will thankfully change shortly thanks to

                         Flatpak.

                         There seems to be interest in improving OBS

                         Studio support for Linux, especially when it

                         comes to covering the spectrum that goes

                         beyond Ubuntu, since Red hat has donated

                         $10,000 to the project in charge of the

                         development and maintenance of the popular

                         video recording and streaming software, which

                         is used not only by free software

                         enthusiasts, but also by professionals who

                         publish on platforms such as Twitch and

                         YouTube.

                         In parallel with the Red Hat donation, the

                         ground is being prepared for the Flatpak

                         build of OBS Studio is official, something

                         that should finish materializing with the

                         release of version 27.2 of the application.

                         What’s more, the beta version of OBS Studio

                         27.2 already ships the Flatpak version as an

                         official build.

      o § Devices/Embedded⠀➾

            # ⚓ Mico_–_A_USB_microphone_based_on_Raspberry_Pi_RP2040_MCU_–

              CNX_Software⠀⇛

                   Raspberry Pi RP2040 dual-core Cortex-M0+

                   microcontroller has found its way into Mico, a

                   compact USB microphone with a PDM microphone

                   providing better quality than cheap USB microphones

                   going for one or two dollars or even 5 cents

                   shipped for new Aliexpress users.

                   The project started when Mahesh Venkitachalam

                   (Elecronut Labs) was doing audio experiments with

                   Machine Learning on the Raspberry Pi, and found out

                   USB microphone dongles were extremely noisy with

                   poor (distance) sensitivity, so he completed the

                   project with a high-quality I2S microphone instead.

                   He then had the idea of making his own USB

                   microphone and found out Sandeep Mistry had already

                   developed a Microphone Library for Pico, so he

                   mostly had to work on the hardware that’s how Mico

                   Raspberry Pi RP2040 USB microphone came to be.

            # § Open Hardware/Modding⠀➾

                  # ⚓ CD_Player_Powered_555_Piano_Goes_Accordion_To_Plan_|

                    Hackaday⠀⇛

                         Acordeonador, an 555 accordion powered by a

                         CD player based genrator

                         Ah yes, the 555 piano project. Be it the

                         Atari Punk Console, or some other 555 based

                         synthesizer, Hackers just love to hear what

                         the 555 can do when attached to a few

                         passives and a speaker. It’s a sound to

                         behold. But for [Berna], that wasn’t quite

                         enough! Below the break, you can see his

                         creation, called the Acordeonador.

                         A portmanteau of the Spanish words for

                         “Accordion” and Generator”, the Acordeonador

                         does what no project we’ve seen so far can

                         do: It turns a CD drive into a generator for

                         a 555 based synthesizer.

                  # ⚓ This_gear_turns_only_once_every_346_quintillion

                    years⠀⇛

                         Mechanical advantage is the single most

                         important principle in mechanical

                         engineering. Archimedes is quoted as saying

                         “Give me a lever long enough and a fulcrum on

                         which to place it, and I shall move the

                         world.” We could say the same of gear

                         reductions, but they have the added advantage

                         of fitting into a very compact space. To

                         prove that point, Sunday Robotics’ INFINITY

                         GEARS has a final gear that will only make a

                         single revolution once every 346 quintillion

                         years.

                         To put that time frame into perspective,

                         consider that our universe is roughly 13.8

                         billion years old. You would have to exceed

                         25 billion similar spans of time before the

                         final gear in this device made a full

                         revolution. Thanks to the power of gear

                         ratios, this device achieves that using only

                         41 individual spur gears (plus the motor’s

                         input gear). The input motor spins at 250RPM

                         and each stage has a gear ratio of 1:5. The

                         final gear ratio, from input to output, is 1:

                         5^41. Not only does that mean the output is

                         spinning extremely slow, it also means that

                         it has an incredible amount of torque —

                         though friction losses keep it from reaching

                         insane levels.

                  # ⚓ OpenBikeSensor:_Build_your_own_distance_meter_for

                    cyclists_–_Market_Research_Telecast⠀⇛

                         The road traffic regulations stipulate a

                         minimum distance of 1.5 meters for drivers

                         when overtaking cyclists, and out of town it

                         is even 2 meters. With the OpenBikeSensor,

                         every overtaking maneuver including the

                         distance can be logged at specific GPS

                         coordinates. With enough data, traffic

                         planners have a concrete basis to identify

                         potential accident black spots and perhaps

                         even to eliminate them.

                         The principle in short: If you are overtaken

                         by a car, the handlebar display shows the

                         distance to the left or right of overtaking

                         vehicles. In addition, the sensor saves

                         distances and associated GPS data permanently

                         on the SD card. If you press the record

                         button within five seconds, the sensor saves

                         the information that this button was pressed

                         for the data record; only such data sets are

                         then currently used for the subsequent

                         evaluation.

                  # ⚓ Remoticon_2021:_Uri_Shaked_Reverses_The_ESP32_WiFi_|

                    Hackaday⠀⇛

                         You know how when you’re working on a

                         project, other side quests pop up left and

                         right? You can choose to handle them briefly

                         and summarily, or you can dive into them as

                         projects in their own right. Well, Uri Shaked

                         is the author of Wokwi, an online Arduino

                         simulator that allows you to test our your

                         code on emulated hardware. (It’s very, very

                         cool.) Back in the day, Arduino meant AVR,

                         and he put in some awesome effort on reverse

                         engineering that chip in order to emulate it

                         successfully. But then “Arduino” means so

                         much more than just AVR these days, so Uri

                         had to tackle the STM32 ARM chips and even

                         the recent RP2040.

                         Arduino runs on the ESP32, too, so Uri put on

                         his reverse engineering hat (literally) and

                         took aim at that chip as well. But the ESP32

                         is a ton more complicated than any of these

                         other microcontrollers, being based not only

                         on the slightly niche Xtensa chip, but also

                         having onboard WiFi and its associated binary

                         firmware. Reverse engineering the ESP32’s

                         WiFi is the side-quest that Uri embarks on,

                         totally crushes, and documents for us in this

                         standout Remoticon 2021 talk.

            # § Mobile Systems/Mobile Applications⠀➾

                  # ⚓ postmarketOS_21.12_improves_Firefox_UI_and_support_–

                    itsfoss.net⠀⇛

                         Has recently appeared postmarketOS 21.12,

                         which is based on Alpine Linux 3.15 and comes

                         to expand the number of supported devices and

                         with improvements to the user interface, the

                         support of virtual consoles and the

                         adaptation of Firefox.

                         We have not dedicated an entry to

                         postmarketOS for a long time, that Linux

                         operating system that aims to greatly extend

                         the useful life of smarpthones, a type of

                         device that has ended up in a high percentage

                         crushed by the aggressive policies of

                         programmed obsolescence of the corporations .

                         The first thing that stands out from

                         postmarketOS 21.12 is the addition of support

                         for new devices, among which are the PineBook

                         Pro by PINE64, the tablets Samsung Galaxy Tab

                         A 8.0 and Samsung Galaxy Tab A 9.7, in

                         addition to the smarpthone Xiaomi Pocophone

                         F1. However, there is also one loss to be

                         regretted, that of the Nokia N900, which has

                         been dropped from the list of officially

                         supported devices because most of the people

                         who contribute to postmarketOS are focused on

                         other newer devices.

                         Regarding user interfaces, first of all we

                         find Sxmo 1.6, the latest version of a simple

                         graphical environment that works on mobiles

                         with Linux. It offers sessions on Xorg and

                         Wayland and it seems that since the last

                         version was released it has received major

                         improvements.

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

            # ⚓ 7-Zip_21.07⠀⇛

                   You can use 7-Zip on any computer, including a

                   computer in a commercial organization. You don’t

                   need to register or pay for 7-Zip.

            # ⚓ 2021:_A_year_in_open_source [Ed: Very corporate-leaning

              slant, full of junk, FUD, and deliberate revisionism]⠀⇛

            # § Web Browsers⠀➾

                  # § Mozilla⠀➾

                        # ⚓ Firefox_I_Love_You,_But_Shut_Up_—_How_to

                          Disable_Firefox_Recommendations_–_OMG!_Ubuntu!⠀⇛

                               Before I get going let me say: I think

                               Firefox is a fantastic browser. A ton

                               of great people work on it. It does

                               some amazing things. I’d scare myself

                               if I tried imagining what the modern

                               web landscape would look like without

it.

            # § Content Management Systems (CMS)⠀➾

                  # ⚓ People_of_WordPress:_Collins_Agbonghama⠀⇛

                         In this series, we share some of the

                         inspiring stories of how WordPress and its

                         global network of contributors can change

                         people’s lives for the better. This month we

                         feature a website builder from Nigeria, who

                         uses the open source WordPress platform to

                         support his family and to share learning with

                         others in his home country and beyond.

                         [...]

                         A friend at the school had a simple mobile

                         phone which could browse the internet.

                         Collins had his first introduction to the

                         World Wide Web through access to this device.

                         He became hooked by reading headlines on a

                         sports site about a famous English Premier

                         League Football Club, Chelsea, a soccer team

                         which he has long supported.

                         “Being a very inquisitive person, I wanted to

                         learn how the web works as well as have my

                         own website. I was able to buy a classic

                         mobile phone through the menial jobs I did

                         after school,” he said.

                         His first website was a wapsite or Wireless

                         Application Protocol site optimized for

                         mobile devices.

            # § FSF⠀➾

                  # ⚓ A_message_from_FSF_president_Geoff_Knauth:_Will_you

                    support_user_freedom_by_helping_to_reach_our_membership

                    goal_before_December_31?_—_Free_Software_Foundation_—

                    Working_together_for_free_software⠀⇛

                         Since its founding, the Free Software

                         Foundation (FSF) and thousands of volunteers

                         have worked hard to make computing safe for

                         users, liberating them to learn the best of

                         the arts of computer science from each other

                         and to share freely their creations, while

                         protecting users from exploitative licenses

                         and intrusions of governments and

                         corporations that put their interests ahead

                         of your computing freedom.

                         In 2021, it became very clear that people in

                         the free software community care deeply about

                         the values enshrined in the FSF mission and

                         the four freedoms. And this level of

                         engagement requires improved governance from

                         the Board of Directors in the form of

                         visibility in our decision-making, and

                         mechanisms that encourage members to discuss

                         and advance candidates for selection to the

                         board. The structure up to now has been too

                         opaque. Consequently, the board has worked

                         very hard this year with outside experts to

                         bring FSF associate members more transparency

                         and give them a voice in governance going

                         forward. Besides what we’ve already

                         announced, more details will be coming soon.

                         [...]

                         As 2021 comes to a close, please also

                         consider supporting the FSF, so that our

                         hard-working and dedicated staff may continue

                         the work they do behind the scenes to secure

                         freedom-preserving infrastructure, develop

                         and promote advocacy, and deliver services to

                         you. Along with the developers of free

                         software, our staff are often the unsung

                         heroes. They are dedicated, smart, wise and

                         considerate. I wish them a free and Happy New

                         Year just as much as I do you.

            # § Programming/Development⠀➾

                  # § Perl/Raku⠀➾

                        # ⚓ Do-It-Yourself_Lexical_Pragmas_|_Tom_Wyant_

                          [blogs.perl.org]⠀⇛

                               The phrase “Lexical Pragmas” is

                               probably both redundant and

                               ungrammatical (the correct plural of

                               “pragma” being “pragmata”, I believe).

                               But the use of “pragma” to mean “Perl

                               module with an all-lower-case name” is

                               fairly common, and I wanted to make

                               clear that this was not what I was

                               talking about. This blog entry is about

                               writing Perl code whose configuration

                               changes are limited to a lexical scope,

                               just like built-in pragmata such as

                               strict or warnings.

                  # § Shell/Bash/Zsh/Ksh⠀➾

                        # ⚓ Literate_Korn_Shell⠀⇛

                               This is the first draft of Literate

                               Korn Shell, the unix shell ‘ksh’

                               written with all of its innards exposed

                               and explained.

                               The goal of Literate Programming is to

                               compile source code into two

                               objects—the executable program with

                               which we are familiar and in additional

                               a document presenting the source code

                               in a format suitable for reading in

                               order to, hopefully, understand it.

                               One advantage in particular offered by

                               literate programming is to break up and

                               re-order the code so that its parts can

                               be introduced to the reader in an order

                               and manner which is focussed on the

                               needs of a human reader who may be

                               unfamiliar with the code without the

                               need to bow to the esoteric demands of

                               a compiler.

                               This draft of literate ksh has

                               concentrated mostly on this feature, to

                               order the code so that a narrative can

                               be threaded from start to finish which,

                               piece by piece, introduces all of the

                               components which go towards making ksh

                               work.

                  # § Java⠀➾

                        # ⚓ What_is_Log4j?_The_Latest_Internet

                          Vulnerability⠀⇛

                               So what is this humble piece of

                               internet infrastructure, how can

                               hackers exploit it and what kind of

                               mayhem could ensue?

* § Leftovers⠀➾

      o ⚓ Crimes_Against_Culture⠀⇛

             “Everyone has the right freely to participate in the

             cultural life of the community.” Universal Declaration of

             Human Rights. Crimes against culture include the

             suppression of language, literature, humor, songs,

             cuisine, clothing styles, and social traditions.

             Colonialism, occupation, and alien domination suppress

             native cultures, denigrating local languages, arts, and

             habits. Proselytization disparages native creeds. The

             French steal the Wedding Feast at Cana, and the English

             take away the Rosetta Stone from Egypt and Kohi-Noor from

             the Mughals. After decades of delay, Yale University

             finally agrees to return the artifacts it has

             misappropriated from Machu Picchu. The Taliban destroy

             the Buddhas of Bamiyan. Wars, decay, and poverty damage

             the monuments and structures that constitute world

             heritage. Minority cultures face suppression in

             majoritarian regimes. Even democracies apply legal

             pressure on minorities to speak the language of the

             majority and adopt the culture of the dominant

             population. English-only laws perpetuate cultural

             suppression requiring millions of Spanish-speaking

             citizens to favor English over their mother tongue in

             their ancestral lands taken through wars. Cultures are

             more durable than nationalities.

      o ⚓ Remembering_Harry_Reid,_1939–2021⠀⇛

             The most awkward job interview I ever had was with Harry

             Reid.

      o ⚓ Revenge_of_the_Nerds⠀⇛

             Zafo Ypi was having the hardest day of his life, but the

             30 laid-off Romani workers camped out on his lawn were

             having an even rougher one. They begged their boss to

             save their jobs, appealing to his conscience and his

             politics: “I told them you’re a man of the people.…  You

             won’t let these children go hungry,” one man pleaded with

             him. But they were barking up the wrong tree. There were

             new rules, and Mr. Ypi didn’t make them.

      o ⚓ Remembering_Techdirt_Contributors_Sherwin_And_Elliot⠀⇛

             It’s been a rough year for our community of tech policy

             advocates, with us losing two of our own, Sherwin Siy in

             July and then Elliot Harmon in October. We remembered

             Sherwin here, and the EFF wrote about Elliott over there.

      o ⚓ In_Botswana,_heavy_metal_bands’_fame_and_fortune_grow_online_in

        pandemic⠀⇛

             Mosaka and his band have helped organise an annual heavy

             metal concert in Ghanzi, a town in the west of Botswana,

             called the Overthrust Winter Metal Mania Charity Fest

             since 2010, with 40% of profits donated to local

             charities.

      o § Science⠀➾

            # ⚓ Combination_of_tucatinib_and_neural_stem_cells_secreting

              anti-HER2_antibody_prolongs_survival_of_mice_with_metastatic

              brain_cancer⠀⇛

                   Brain metastases are among the most severe

                   complications of systemic breast cancer, and

                   overexpression of the human epidermal growth factor

                   receptor 2 (HER2) in breast cancer cells increases

                   the incidence of brain metastases in patients. In

                   this study, we engineered the human-derived, tumor

                   cell tropic neural stem cells LM-NSC008 (LM008) to

                   continuously secrete antibodies against HER2. These

                   anti-HER2 antibodies impaired tumor cell

                   proliferation by inhibiting the PI3K-Akt signaling

                   pathway in HER2+ breast cancer cells in vitro.

                   Importantly, our results demonstrate that the

                   therapeutic combinatorial regimen consisting of LM-

                   NSC008 anti-HER2 antibody-secreting cells and the

                   HER2 kinase inhibitor tucatinib provide therapeutic

                   benefit and prolong survival in preclinical models

                   of HER2+ breast cancer brain metastases.

      o § Hardware⠀➾

            # ⚓ Taking_A_Close_Look_At_Hawkeye’s_Workbench_|_Hackaday⠀⇛

                   We don’t have to tell you that the representation

                   hackers and makers get in popular media is usually

                   pretty poor. At this point, we’ve all come to

                   accept that Hollywood is only interested in

                   perpetuating negative stereotypes about hackers.

                   But in scenes were there plot calls for a character

                   to be working on an electronic device, it often

                   seems like the prop department just sticks a

                   soldering iron in the actor’s hand and calls it a

                   day.

            # ⚓ Electric_Wheelchair_Dump_Truck_Hack_Really_Hauls_|

              Hackaday⠀⇛

                   Have you ever looked at a derelict electric

                   wheelchair and thought “I bet I could make

                   something great with that!” Of course you have-

                   this is Hackaday, after all! And so did [Made in

                   Poland], who managed to get a hold of a broken down

                   electric wheelchair and put the full utility of his

                   well equipped metalworking shop to work. The

                   results? Lets just say it hauls.

                   What we really enjoyed about the build was that

                   there wasn’t much that couldn’t be done by an

                   average garage hacker with a drill press, angle

                   grinder, and a stick welder. While it’s definitely

                   nicer to have a lathe and a high quality welding

                   table, plasma cutter, and everything in between,

                   nothing that [Made in Poland] did in the video is

                   such high precision that it would require those

                   extensive tools. There may be some parts that would

                   be a lot more difficult, or lower precision, but

                   still functional.

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ Union_Head_Rejects_CDC_Covid_Guidelines_That_Put_‘Corporate

              Interests’_Over_Pilot_Safety⠀⇛

                   The head of North America’s largest pilots union

                   said Thursday that its members would “follow the

                   science” regarding Covid-19 safety precautions as

                   opposed to new guidance released by the CDC earlier

                   this week which critics say put the needs of

                   corporate profits over worker safety.

                   “We’ve followed the science throughout the pandemic

                   and will not allow corporate interests to replace

                   the good judgment pilots show daily in making

                   decisions about whether they are healthy to fly,”

                   said Capt. Joe DePete, president of the Air Line

                   Pilots Association, which represents pilots at 38

                   airlines in the U.S. and Canada.

            # ⚓ A_(very)_close-knit_circle_Russia’s_Circle_of_Kindness

              Foundation_helps_critically_ill_children_by_purchasing

              expensive_drugs_from_providers_with_personal_connections_to

              top_officials_(including_Putin_himself)⠀⇛

                   The Circle of Kindness Foundation, which helps

                   children with rare illnesses, was created in early

                   2021 at Vladimir Putin’s own initiative. It’s

                   funded by a two percent tax on the income of

                   Russia’s wealthiest citizens. The organization pays

                   for expensive medications — but competition is rare

                   at the auctions where these drugs are procured. One

                   of the foundation’s main suppliers is a company

                   called Irvin — and it’s connected to both the

                   foundation’s head and to the family of Alexey

                   Dyumin, Putin’s former bodyguard. In addition, the

                   husband of the woman responsible for purchasing

                   medications on behalf of the Circle of Kindness

                   works for the owner of the company that supplies

                   the foundation with Zolgensma — the most expensive

                   drug in the world. Meduza correspondents Svetlana

                   Reiter and Maria Zholobova break down how the

                   Circle of Kindness Foundation’s procurement system

                   works and why its board of trustees (which includes

                   well-known actors and philanthropists) believes it

                   lacks transparency.

            # ⚓ Pressure_Grows_on_Biden_to_Shut_Down_Trump-Era_Medicare

              Privatization_Scheme⠀⇛

                   Calls are mounting for President Joe Biden to

                   terminate an under-the-radar Trump-era pilot

                   program that—if allowed to run its course—could

                   result in the complete privatization of traditional

                   Medicare by the end of the decade.

                   “The Biden administration is moving the DCE program

                   forward, threatening the future of Medicare as we

                   know it.”

            # ⚓ Unwelcome_changes_Russia’s_Health_Ministry_plans_to

              overhaul_its_cancer_care_system._Despite_criticism,_the_new

              regulations_take_effect_in_January.⠀⇛

                   On December 20, 2021, Russia’s Health Ministry

                   proposed a series of changes to adult cancer care

                   practices. These new procedures will take effect in

                   the new year. The previous plan to overhaul cancer

                   treatment was received poorly by the medical

                   community, prompting Deputy Prime Minister Tatyana

                   Golikova to order revisions. However, experts say

                   that none of the Health Ministry’s proposed changes

                   address physician’s most substantive criticisms.

            # ⚓ FDA_Expected_to_Authorize_COVID_Booster_Shots_for_12-_to

              15-Year-Olds⠀⇛

            # ⚓ Opinion_|_Vaccine_Apartheid_Shows_Global_Injustice_Is_Very

              Bad_for_Public_Health⠀⇛

                   The reaction by governments in the Global North to

                   the discovery of the Omicron variant of COVID-19 in

                   South Africa has provided further proof—as if any

                   more were needed—of the deeply inequitable response

                   to the coronavirus pandemic. The backlash against

                   African countries was swift and severe, as if

                   barring travelers from the region could somehow

                   keep the rest of the world safe.

            # ⚓ DeSantis_Accused_of_Going_‘Missing_in_Action’_as_Florida

              Faces_Omicron_Explosion⠀⇛

                   Local officials and public health experts are

                   accusing Florida Gov. Ron DeSantis of abdicating

                   his leadership responsibilities as the state faces

                   a record-shattering spike in coronavirus cases, an

                   increase believed to be fueled by the highly

                   contagious Omicron variant.

                   “As Covid surges in Florida again, our governor is

                   absent.”

            # ⚓ After_Years_of_Complaints,_Florida_Improves_Pollution

              Monitoring_Near_Burning_Sugar_Cane_Fields⠀⇛

                   For the first time in nearly a decade, Florida

                   regulators have upgraded their air-monitoring

                   system in the state’s sugar-growing region, where

                   farmers burn crops to harvest more than half the

                   nation’s cane sugar.

                   The move follows an investigation by The Palm Beach

                   Post and ProPublica that found shortcomings in the

                   way authorities police air pollution in Florida’s

                   heartland, including their use of an air monitor

                   that was unfit to enforce the Clean Air Act, the

                   landmark law aimed at protecting the public from

                   harmful pollutants.

            # ⚓ Delta_Cuts_Paid_Sick_Leave_for_Workers_With_COVID_After

              Lobbying_for_CDC_Change⠀⇛

            # ⚓ After_CDC_Change_It_Lobbied_For,_Delta_Slashes_Paid_Sick

              Leave_for_Workers_With_Covid⠀⇛

                   Just a day after the CDC delivered updated Covid-19

                   isolation guidelines that the company’s CEO lobbied

                   for, Delta Air Lines moved to take advantage of the

                   new recommendations by slashing paid sick leave for

                   infected workers, prompting immediate backlash from

                   union leaders and public health experts who warned

                   of such an outcome.

                   “Dear CEOs—your ‘business needs’ are not worth the

                   life of a single worker.”

            # ⚓ TikTok_moderator_sues_over_‘psychological_trauma’⠀⇛

                   A former TikTok moderator is suing the company,

                   claiming it failed to protect her mental health

                   after “constant” exposure to traumatic video

                   content.

                   Candie Frazier says she reviewed videos that

                   featured “extreme and graphic violence” for up to

                   12 hours a day.

            # ⚓ More_than_a_million_Americans_have_died_from_overdoses

              during_the_opioid_epidemic⠀⇛

                   Deaths due to drug overdose have topped a million

                   for the first time since the Centers for Disease

                   Control and Prevention began collecting data on the

                   problem more than two decades ago.

                   A study released Thursday by the National Center

                   for Health Statistics, a division of the CDC, found

                   that 932,364 people died in the U.S. from fatal

                   overdoses from 1999 through 2020.

      o § Integrity/Availability⠀➾

            # § Proprietary⠀➾

                  # ⚓ Shining_a_Light_on_Black_Box_Technology_Used_to_Send

                    People_to_Jail:_2021_Year_in_Review⠀⇛

                         One of the most common forms of forensic

                         programs is probabilistic genotyping

                         software. It is used by the prosecution to

                         examine DNA mixtures, where an analyst

                         doesn’t know how many people contributed to

                         the sample (such as a swab taken from a

                         weapon). These programs are designed to make

                         choices about how to interpret the data, what

                         information to disregard as likely

                         irrelevant, and compute statistics based on

                         how often the different genes appear in

                         different populations—and all of the

                         different programs do it differently. These

                         assumptions and processes are subject to

                         challenge by the person accused of a crime.

                         For that challenge to be meaningful, the

                         defense team must have access to source code

                         and other materials used in developing the

                         software.

                         The software vendors claim both that the

                         software contains valuable secrets that must

                         not be disclosed and that their methods are

                         so well-vetted that there’s no point letting

                         a defendant question them. Obviously, both

                         can’t be true, and in fact it’s likely that

                         neither is true.

                         When a was finally able to access one of

                         these programs, the Forensic Statistical Tool

                         (FST), they discovered an undisclosed

                         function and shoddy programming practices

                         that could lead the software to implicate an

                         innocent person. The makers of FST submitted

                         sworn declarations about how they thought it

                         worked, it had been subject to ‘validation’

                         studies where labs test some set of inputs to

                         see if the results seem right, and so on. But

                         any programmer knows that programs don’t

                         always do what you think you programmed them

                         to do, and so it was with FST: in trying to

                         fix one bug, they unwittingly introduced

                         another serious error.

                  # ⚓ Fortnite_servers_were_down_for_five_hours,_but_now

                    the_game_is_back_online⠀⇛

                         A follow-up tweet at 3:10PM ET from the team

                         said they were “continuing to work on a fix

                         that will bring Fortnite back online and

                         appreciate everyone’s patience.” As of 6PM

                         ET, we hadn’t heard anything since, but at

                         around 6:30PM ET players reported the game

                         was working again, which we have been able to

                         confirm.

                         The Fortnite Status Twitter eventually

                         tweeted to confirm the game is back up,

                         promising that next week (or, next year)

                         there will be details on “what we’re doing to

                         help you make up for lost time.” It also

                         noted some people might see an extra in-game

                         present to open, but said the team is working

                         on that.

                  # § Security⠀➾

                        # § Privacy/Surveillance⠀➾

                              # ⚓ DHS,_ICE_Begin_Body_Camera_Pilot_Program

                                With_Surprisingly_Good_Policies_In_Place⠀⇛

                                     Following protests over killings

                                     by law enforcement officers, the

                                     Department of Justice decided it

                                     might be a good idea to equip

                                     more police officers with body

                                     cameras. In May 2015, it

                                     announced the federal government

                                     would be spending $75 million

                                     over the next three years to

                                     purchase body cameras for local

                                     law enforcement agencies.

                              # ⚓ Internal_Documents_Show_Huawei_Is_Staying

                                On_The_Cutting_Edge_Of_Oppression_Tech⠀⇛

                                     Pretty much exactly a year ago,

                                     the Washington Post obtained

                                     documents that showed Chinese

                                     tech giant Huawei was working

                                     with the government to create

                                     facial recognition on steroids: a

                                     system capable of not just

                                     recognizing faces, but also

                                     certain ethnicities.

                              # ⚓ NordVPN_under_investigation_in_California

                                for_making_it_difficult_to_cancel.⠀⇛

                                     NordVPN is under investigation in

                                     California for potentially

                                     violating the state’s laws

                                     regulating automatic renewal of

                                     subscriptions, and continuing to

                                     bill people even after they’ve

                                     decided to cancel.

      o § Defence/Aggression⠀➾

            # ⚓ Recovering_Conscience:_A_Conversation_with_Carole_Sargent⠀⇛

                   The following edited Zoom conversation took place

                   on December 27, 2021.

                   John Hawkins: I read your article recently, “Nuns

                   Against Nuclear Weapons: Plowshares Protesters have

                   Fought for Disarmament for Over 40 Years, Going to

                   Prison for Peace.” It brought back memories of my

                   Catholic youth in and around Boston in the ‘60s

                   when Jesuits were turning activist and priests were

                   getting excommunicated for leading public protests

                   of outrageous government policies of day,

                   especially against the Vietnam War, as well as

                   opening up concept halfway houses and drop-in

                   centers for drug addicts.

            # ⚓ Why_Trump_May_Face_Criminal_Charges⠀⇛

                   Rep. Liz Cheney, R-Wyo., an avowed Never Trumper

                   who is vice chair of the House committee

                   investigating the siege of the icon of American

                   freedom, first broached such a possibility

                   publicly. The panel’s chair, Rep. Bennie G.

                   Thompson, D-Miss., confirmed it to The Washington

                   Post.

                   The committee, which The Guardian reported has

                   evidence gathered from more than 30,000 records and

                   interviews from more than 300 people, has homed in

                   on how Trump spent his time on Jan. 6. It wants to

                   know why it took three hours and seven minutes

                   before he called off his mob charging the Capitol

                   to halt the certification of Joe Biden as

                   president-elect, as if Biden were the enemy.

            # ⚓ Trump_Sues_January_6_House_Committee_Because_It_Might_Find

              Trump_Wrongdoing⠀⇛

            # ⚓ Opinion_|_Humanity’s_Final_Arms_Race:_UN_Fails_to_Agree_on

              ‘Killer_Robot’_Ban⠀⇛

                   Autonomous weapon systems—commonly known as killer

                   robots—may have killed human beings for the first

                   time ever last year, according to a recent United

                   Nations Security Council report on the Libyan civil

                   war. History could well identify this as the

                   starting point of the next major arms race, one

                   that has the potential to be humanity’s final one.

            # ⚓ ‘Anti-Democratic_and_Cowardly’:_US_Building_New_Secret

              Courtroom_at_Guantánamo⠀⇛

                   Human rights advocates and attorneys representing

                   Guantánamo Bay detainees on Thursday decried a

                   secret new courtroom reportedly being built by the

                   Pentagon at the notorious offshore U.S. prison.

                   “I’ve observed trials in Mongolia that were more

                   transparent than this.”

            # ⚓ Biden’s_“Diplomacy_Is_Back”_Falls_Flat_as_2021_Middle_East

              Policy_a_Miserable_Flop⠀⇛

                   Despite President Joe Biden having claimed earlier

                   this year that “diplomacy is back” and that he

                   would end the war in Yemen, revive the Iran Nuclear

                   Deal and settle several other issues, in reality

                   his Middle East foreign policy has been just as

                   detrimental to the region as was that of his

                   predecessor.

            # ⚓ The_Real_Meaning_of_January_6⠀⇛

                   But even now, almost a year later, Americans remain

                   confused and divided about the significance of what

                   occurred.

            # ⚓ With_fascism_coming,_America_responds:_LOL_who_cares?_Let’s

              Netflix_and_chill⠀⇛

                   In other ways, the Trump regime’s coup attempt was

                   not so unusual. As in other places and times in

                   history, Trump’s loyalists are continuing with

                   their efforts, both through more or less legal

                   means and otherwise. When a coup fails the first

                   time, the second attempt is usually successful. All

                   of this is happening in real time and in plain

                   sight, with minimal attempt at deception. For the

                   American people and their responsible leaders to

                   ignore such threats is a willful choice.

                   What warnings should we be heeding now? In a recent

                   op-ed for the Washington Post, retired U.S. Army

                   generals Paul D. Eaton, Antonio M. Taguba and

                   Steven M. Anderson are sounding the alarm about the

                   possibility of a second civil war in the aftermath

                   of a future presidential election, if Donald Trump

                   or another Republican refuses to accept the

                   results: [...]

      o § Transparency/Investigative Reporting⠀➾

            # ⚓ Florida_Agency_Spent_$200K_on_PR_Firm_After_Being_Accused

              of_Withholding_Aid⠀⇛

      o § Environment⠀➾

            # ⚓ Encampment_Near_Biden’s_Delaware_Home_Calls_for_Declaration

              of_Climate_Emergency⠀⇛

            # ⚓ Chomsky:_Rising_Anti-Science_Rhetoric_Feeds_the_Pandemic

              and_Climate_Crisis⠀⇛

            # ⚓ They_Don’t_Want_Us_Looking_Up…⠀⇛

                   It’s being lauded as a metaphor for how we’re

                   dealing with climate change in the face of

                   petrobillionaire- and corporate-funded

                   disinformation campaigns, but it’s so much more

                   than that:

                   “Conservatives” on the Supreme Court don’t want

                   Americans to look up at how they legalized

                   political bribery with their 1970s Buckley and

                   Bellotti and 2010 Citizens United decisions that

                   have turned politicians into shills for the same

                   billionaires and giant industries that spent

                   millions putting them on the Court.

            # ⚓ Look_Up,_Down_and_Everywhere⠀⇛

                   The many de rigueur comparisons to Kubrick’s

                   masterpiece Dr. Strangelove are just criminal! Not

                   even close. The Ron Perlman character is a pathetic

                   attempt at mimicking a composite Gen. Buck

                   Turgidson, Brigadier General Jack D. Ripper and

                   Maj. T.J. “King” Kong!

                   My main takeaway – now we need something similar

                   with a clearly Democratic President and a

                   Democratic Party pimping endless growth with all

                   the same lies, etc. I think making Meryl Streep’s

                   president an obvious Trumpist narcissist (with

                   Jackson’s and Nixon’s Portraits on the Oval Office

                   wall and her own Donald “Uday” Trump, Jr., son, as

                   Chief of Staff, no less) gives smug Pius-driving

                   liberals the chance to, well, be smug and ignore

                   the message just as much as the 90% stupid people

                   the film seems to think is the ignore ratio. I

                   guarantee there will be little in the way of the

                   film instigating lifestyle corrections from the

                   film’s loudest liberal supporters. They’ll be (and

                   are) jetting around the planet spewing carbon, as

                   usual. (Uday, however, does utter some of the

                   film’s best lines.)

            # ⚓ “Don’t_Look_Up”_at_that_Movie; _At_Least_Not_to_Fight

              Climate_Change!⠀⇛

                   As an angry, anti-war, combat veteran of Vietnam, I

                   quit teaching at MIT’s business school in 1982 to

                   work full-time in the movement for peace and social

                   justice. Over the last 40 years, I have helped

                   found, fund ($30 million worth) and lead local,

                   state and national organizations, mostly pretty

                   radical. We have had some successes, among them,

                   helpng 13,000 people get arrested to stop US

                   nuclear weapons testing, making all state elections

                   in AZ publicly funded and getting my new home

                   County outside DC to declare the first climate

                   emergency in the world.

                   Over those years, like many others, I have come to

                   believe that reversing the already awful climate

                   catastrophe—or making any other significant social

                   change–will require at least four things:

            # ⚓ Near_President’s_Delaware_Home,_Encampment_Calls_on_Biden

              to_‘Declare_a_Climate_Emergency’⠀⇛

                   A small group of climate activists has established

                   an encampment near President Joe Biden’s private

                   home in Delaware where they are demanding he

                   declare a national climate emergency and

                   immediately order the end to fossil fuel

                   development in the United States.

                   Establishing the camp on Christmas Day and sleeping

                   overnight in tents or cars on a roadside area not

                   far from the family’s Wilmington residence, the

                   campaigners operating under the “Occupy Biden”

                   banner say if the president truly recognizes that

                   the world is in a “code red” situation when it

                   comes to soaring global temperatures then he must

                   act accordingly.

            # ⚓ Within_Decade,_Planet’s_Natural_World_Facing_Largest_Mass

              Extinction_Event_Since_Dinosaurs⠀⇛

                   Increasingly dire ecological damage and severe

                   impacts of the climate crisis are pushing the

                   natural world towards a mass extinction event

                   unparalleled since the age of the dinosaurs,

                   conservationists in Germany warned this week, with

                   humanity possibly facing self-annihilation if

                   behaviors do not change.

                   Releasing its annual “Winners and Losers” list on

                   Wednesday, the World Wildlife Fund’s German branch

                   said 40,000 of the 142,500 species listed on the

                   Red List of Threatened Species by the International

                   Union for Conservation of Nature (IUCN) are

                   “threatened with extinction.”

            # § Energy⠀➾

                  # ⚓ ‘A_mix_of_schadenfreude_and_fear’_The_arrest_of_one

                    of_Russia’s_richest_men_following_a_deadly_mine

                    explosion_has_pleased_locals_but_raised_worries_about

                    regional_stability⠀⇛

                         In mid-December, Siberian Business Union

                         (SDS) head Mikhail Fedyayev, one of the

                         richest people in Russia, was arrested. After

                         the Listvyazhnaya mine disaster in November

                         resulted in 51 deaths, Fedyaev was charged

                         with abusing his authority and violating

                         safety standards. Before his arrest, however,

                         Fedyaev enjoyed near-limitless power in the

                         Kemerovo region: the government is full of

                         his former employees, his holding company

                         received state contracts worth millions of

                         dollars, and presidents and federal ministers

                         routinely paid visits to the SDS

                         headquarters. Now, the prospect of Fedyayev’s

                         property going to a new owner has Kemerovo

                         residents worried, although many are pleased

                         that the region’s “shadow governor” has

                         finally been arrested. Meduza special

                         correspondent Andrey Pertsev tells the story

                         of one of Russia’s last regional businessmen

                         whose influence went all the way to the top.

                  # ⚓ Optimising_public_transport:_A_data-driven_bike-

                    sharing_study_in_Marburg⠀⇛

                         Imagine you are running late for your bus and

                         decide to grab a bike-sharing bike to get

                         there in time. More often than not I found

                         myself standing at an empty station only to

                         miss my bus. Here, I present you my data-

                         driven approach to avoid walking to empty

                         bike-sharing stations.

                         I started collecting Nextbike data in Marburg

                         many months back in order to solve my

                         personal issue of facing empty Nextbike

                         stations in Marburg. After collecting more

                         than 1,000,000 data points, I turned towards

                         the analysis to figure out which stations in

                         Marburg to avoid when desperately needing a

                         bike.

                         After finding the data-driven solution to

                         that question, I expanded my study to not

                         only answer questions for Nextbike users but

                         also from the perspective of the city council

                         to make the lives of all of us easier,

                         healthier and eco-friendlier. After those

                         statistical statements, I conclude my study

                         with a more precise machine-learning based

                         prediction of parked bikes to motivate data-

                         driven optimisations in public transport.

            # § Wildlife/Nature⠀➾

                  # ⚓ Start_Treating_Yellowstone_Bison_the_Way_They

                    Deserve⠀⇛

                         Yellowstone’s wild bison were declared our

                         national mammal in 2016 and are of

                         international significance.

                         Yellowstone bison are not the same as other

                         bison scattered around the West. They are the

                         most genetically pure bison left on the

                         continent, largely influenced by natural

                         evolutionary processes.

                  # ⚓ Opinion_|_E.O._Wilson’s_Lifelong_Passion_for_Ants_and

                    Conserving_the_World’s_Biodiversity⠀⇛

                         E. O. Wilson was an extraordinary scholar in

                         every sense of the word. Back in the 1980s,

                         Milton Stetson, the chair of the biology

                         department at the University of Delaware,

                         told me that a scientist who makes a single

                         seminal contribution to his or her field has

                         been a success. By the time I met Edward O.

                         Wilson in 1982, he had already made at least

                         five such contributions to science.

                  # ⚓ A_man_suffered_serious_injuries_after_being_attacked

                    by_a_tiger_at_a_Florida_zoo._The_tiger_was_shot_and

                    killed⠀⇛

                         critically endangered Malayan tiger named Eko

                         was shot and killed by a sheriff’s deputy

                         Wednesday after a man was attacked by the

                         animal at a zoo in Naples, Florida, officials

                         said.

            # § Overpopulation⠀➾

                  # ⚓ Crocodiles_turn_on_humans_amid_Iran_water_crisis⠀⇛

                         The attacks have come at a time when Iran has

                         been suffering acute water shortages and,

                         consequentially, fast-shrinking natural

                         habitats have seen the gandos’ food supplies

                         dry up. The starving animals treat humans

                         approaching their territory either as prey or

                         a menace to their evaporating resources.

      o § Finance⠀➾

            # ⚓ The_Cruel_Failure_of_Welfare_Reform_in_the_Southwest⠀⇛

                   As the 1960s came to their tumultuous end,

                   California Gov. Ronald Reagan convened a summit on

                   the topic of welfare. He was hoping to try out one

                   of his new ideas: that poor single mothers were, in

                   the wake of the civil rights movement, increasingly

                   living idly and defrauding government assistance

                   programs.

                   George Miller, then the welfare director in

                   neighboring Nevada, volunteered to do a dry run for

                   Reagan, proposing to purge his smaller state’s

                   welfare rolls of alleged welfare cheats. It would

                   be the first effort of its kind in the nation, he

                   said.

            # ⚓ ‘That’s_Just_Wrong’:_Sanders_Slams_Buffett_for_Refusing_to

              Side_With_Striking_Steelworkers⠀⇛

                   Sen. Bernie Sanders on Thursday slammed billionaire

                   Warren Buffett for refusing to intervene on the

                   side of West Virginia steelworkers who are striking

                   to demand better pay and benefits from Precision

                   Castparts, a company owned by Buffett’s

                   multinational holding conglomerate Berkshire

                   Hathaway.

                   “When you have an extremely profitable, well-

                   financed corporation owned by one of the wealthiest

                   guys in the world, you know what? You should not be

                   demanding wage cuts from your workers and cuts in

                   their healthcare benefits,” Sanders (I-Vt.) wrote

                   on Twitter. “That’s just wrong.”

            # ⚓ A_Perfect_Storm_Has_Elon_Musk_Paying_$11_Billion_in_Tax⠀⇛

            # ⚓ Opinion_|_Elon_Musk_Only_Paid_$11_Billion_in_Taxes_Because

              He_Had_No_Other_Rational_Choice⠀⇛

                   Elon Musk has had a field day trolling advocates

                   for a fairer tax system on Twitter. They’ve been

                   attacking him for not paying much at all in taxes

                   over recent years. But Musk knew what they didn’t:

                   that in 2021 he was going to be paying plenty in

                   taxes.

            # ⚓ Join_a_Union—but_Also_Join_a_DAO⠀⇛

                   In late November 2021, the writer and venture

                   capital investor Li Jin tweeted, “DAOs

                   (decentralized autonomous organizations) represent

                   the next step forward in the labor movement.” In

                   her 20-tweet thread, Jin gave a brief history of

                   the American labor movement, including issues with

                   declining membership, bureaucracy, and bloat,

                   before pivoting to DAOs as a new paradigm for

                   worker ownership: “Versus unions, transparency of

                   DAOs’ governance and on-chain flows of capital

                   lessens risk of embezzlement and corruption, since

                   there is visibility into how funds are flowing into

                   & out of the treasury. And open rules for member

                   admission mitigate institutional discrimination.”

                   The response from many leftists on Twitter was

                   swift and negative, reacting to the perceived

                   implication that technology—cryptocurrency

                   especially—could be a substitute for political and

                   social change.

      o § AstroTurf/Lobbying/Politics⠀➾

            # ⚓ Bette_Midler’s_Contempt_Fuels_Right-Wing_Populism⠀⇛

                   Last week, Bette Midler tweeted that the people of

                   West Virginia are “poor, illiterate and strung

                   out.” Donald Trump should send her a thank-you

                   note.

            # ⚓ Michigan’s_Nonpartisan-Drawn_Maps_Give_Dems_Chance_to_Win

              State_Legislature⠀⇛

            # ⚓ Greene_Suggests_Blue_State_Residents_Moving_to_Red_Ones

              Shouldn’t_Get_to_Vote⠀⇛

            # ⚓ On_Foreign_Policy,_Biden_Should_Have_Taken_Golf_Lessons⠀⇛

                   The  biggest issue for both was the 20-year US war

                   in Afghanistan, for which Biden’s predecessor,

                   Donald Trump, had negotiated a long-overdue US

                   surrender.

                   Would Biden fulfill the US end of the Afghanistan

                   peace agreement by completing the withdrawal of US

                   troops? We hoped, but doubted, as he hemmed, hawed,

                   and violated the agreed deadline despite ample time

                   to meet it.

            # ⚓ A_Thorn_in_Biden’s_Side:_the_Revolving_Door_Project⠀⇛

                   The revolving door may not have been closed over

                   the last year, but it’s spinning much less quickly

                   than it was. Roles that once would have gone almost

                   exclusively to Wall Street bankers and corporate

                   defense attorneys are now in the hands of committed

                   public servants. Those revolvers who have secured

                   roles must now contend with a previously

                   unimaginable level of scrutiny. Figures from White

                   House coronavirus response coordinator, Jeffrey

                   Zients, to Federal Energy Regulatory Commissioner,

                   Willie Phillips, can expect to have their every

                   move that benefits corporate America at the expense

                   of the public interest pilloried. Perversely, this

                   certain backlash has led some within the Biden

                   administration to try to hide their revolving door

                   hires. RDP, however, has consistently foiled these

                   efforts, making not only the appointees but also

                   the astounding lack of transparency the subject of

                   significant public anger.

                   RDP has also been unyielding in its efforts to push

                   this administration to contend with Trump’s

                   enduring influence throughout the executive branch.

                   Almost as soon as Biden was elected, RDP called on

                   his administration to commit to removing all Trump

                   holdovers whom it was legally empowered to fire.

                   Over a year later, only a small handful remain and

                   critical roles like the Director of Consumer

                   Financial Protection Bureau, the Commissioner for

                   the Social Security Administration, and the General

                   Counsel for the National Labor Relations Board are

                   in the hands of officials committed to advancing

                   this administration’s priorities. But RDP is not

                   letting up anytime soon; it continues to push for

                   the remaining political holdovers to be fired and

                   to uncover additional evidence of Trump’s lasting

                   influence over executive branch personnel. It is

                   also calling out those Biden administration

                   officials, most notably within the Department of

                   Justice, who are keeping Trump’s horrifying legacy

                   alive by defending the previous administration’s

                   policies in court.

            # ⚓ Cop_Out⠀⇛

      o § Censorship/Free Speech⠀➾

            # ⚓ Booked_Up:_Ban_These_Books,_Please_(the_Writers_Need_the

              Money)⠀⇛

                   Flummoxed, I stammered, “Uh. Uh.”

                   “Out with it, Jeffrey. Choose somebody, at least.”

            # ⚓ Oversight_Board_Overturning_Instagram_Takedown_Of_Ayahuasca

              Post_Demonstrates_The_Impossibility_Of_Content_Moderation⠀⇛

                   Congress has been holding lots of “but think of the

                   children online!” hearings over the past couple of

                   months, and one prominent topic that comes up over

                   and over again is the fact that people can find

                   “drug” information online. Fears about kids and

                   drugs goes back decades, but politicians love it,

                   because it always works. And, of course, the media

                   loves to run these overhyped stories. A quick

                   search finds dozens of stories like the following

                   in just the last month or so: Teens have easier

                   access to drugs as illegal trade booms on social

                   mediaInstagram pushes drug content to teensSocial

                   media platforms becoming sites of illegal fentanyl

                   drug sales targeting teens, L.A. officials

                   warnWARNING: Dealers tempt kids with edible drugs

                   via social mediaRecord number of drug overdose

                   deaths brings new scrutiny to social media

                   appsInstagram offers ‘drug pipeline’ to kids, tech

                   advocacy group claims There are many more such

                   stories, but you get the idea. The Instagram

                   stories, in particular, were targeted by the recent

                   Senate hearing which was focused on allowing

                   Senators to grandstand on how bad Instagram

                   supposedly is for kids. Instagram responded to the

                   report by pointing out that it’s doing a ton of

                   stuff to try to block such content:

            # ⚓ Palestinians_raise_alarm_over_Facebook_content

              ‘suppression’⠀⇛

                   Allegations of pro-Israeli bias at Facebook have

                   simmered for years and were renewed in October when

                   Human Rights Watch, a vocal Israel critic, said the

                   platform had “suppressed content posted by

                   Palestinians and their supporters speaking out

                   about human rights issues in Israel and Palestine”.

                   Palestinian reporters have cited multiple incidents

                   they describe as censorship.

                   One popular online news outlet, Maydan Quds News,

                   may even have to fire reporters after its main

                   Facebook page with 1.2 million followers was

                   deleted, a source who requested anonymity told AFP.

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

            # ⚓ Chomsky_Blasts_the_“Torture”_of_Julian_Assange_&_Biden’s

              Provocative_Acts_Against_China⠀⇛

                   Noam Chomsky decries what he calls the torture of

                   imprisoned WikiLeaks founder Julian Assange. He

                   also critiques the Biden administration’s reckless

                   foreign policy. “The trajectory is not optimistic,”

                   Chomsky says. “The worst case is the increasing

                   provocative actions towards China. That’s very

                   dangerous.”

            # ⚓ BBC_calls_in_Met_Police_over_fear_of_attacks_on_journalists

              after_David_Amess_murder⠀⇛

                   BBC chiefs have been in contact with a journalism

                   safety adviser at the Met as they seek to improve

                   procedures and offer better guidance to presenters

                   about how to deal with abuse both out in the field

                   and online.

            # ⚓ Man_charged_after_BBC_journalist_Nick_Watt_chased_into

              Downing_Street_by_lockdown_protesters⠀⇛

                   A 57-year-old man has been charged after a BBC

                   journalist was chased into Downing Street after

                   being mobbed by anti-lockdown protesters.

                   Martin Hockridge was interviewed by police after

                   Nick Watt, the political editor of Newsnight, was

                   forced to run to safety after being subjected to

                   abuse at a protest on Monday.

      o § Civil Rights/Policing⠀➾

            # ⚓ The_Politics_of_Syntax_and_Poetry_Beyond_the_Border⠀⇛

                   “Some men are women too / the way a mountain is

                   land and a harbor is land and a parking lot,”Ari

                   Banias writes in “Oracle,” the opening poem in his

                   new collection, A Symmetry. In Banias’s poems,

                   binary oppositions—of men and women, land and sea,

                   us and them—buckle, as the very idea of borders is

                   made porous. Attending to the entanglements between

                   the material and the metaphorical, Banias

                   interrogates the terms of relation mapped by

                   dominant systems and structures that underpin

                   global capitalist orders. “What is the ‘we’

                   whiteness requires?” Banias’s poems encourage us to

                   ask. What does “elsewhere” mean when immigration

                   severs the material “here” of daily life from the

                   imaginative “here” of home? How might transness

                   point us toward other ways of being?1

            # ⚓ Biden_Administration_Seeks_to_Overturn_Trump-Era_“Remain_in

              Mexico”_Policy⠀⇛

            # ⚓ Sanders_Pushes_Workers_to_Organize_as_Advocates_Celebrate

              “Year_of_the_Worker”⠀⇛

            # ⚓ DC_Metro_PD’s_Powerful_Review_Panel_Keeps_Giving_Bad_Cops

              Their_Jobs_Back⠀⇛

                   After bad cops do bad things, other cops will rush

                   to the defense of the agency employing them,

                   claiming most cops are good and these officers are

                   outliers. These assertions might be more believable

                   if law enforcement agencies (and their unions)

                   didn’t regularly cover for bad officers or, in the

                   case of police unions, work tirelessly to ensure

                   bad cops get their jobs back.

            # ⚓ Noam_Chomsky_on_Rising_Fascism_in_U.S.,_Class_Warfare_&_the

              Climate_Emergency⠀⇛

                   Noam Chomsky warns the Republican Party is

                   “marching” the world to destruction by ignoring the

                   climate emergency while embracing proto-fascism at

                   home. Chomsky talks about the January 6

                   insurrection, how neoliberalism is a form of class

                   warfare and how President Biden’s climate plans

                   fall short of what is needed.

            # ⚓ Missouri_Governor_Still_Expects_Journalists_To_Be

              Prosecuted_For_Showing_How_His_Admin_Leaked_Teacher_Social

              Security_Numbers⠀⇛

                   Missouri Governor Mike Parson is nothing if not

                   consistent in his desire to stifle free speech. As

                   you’ll recall, the St. Louis Post-Dispatch

                   discovered that the state’s Department of

                   Elementary and Secondary Education (DESE) website

                   was programming in such an incompetent fashion that

                   it would reveal, to anyone who knew where to look,

                   the social security numbers of every teacher and

                   administrator in the system (including those no

                   longer employed there). The reporting on the

                   vulnerability was done exactly following ethical

                   disclosure best practices — getting just enough

                   evidence of the vulnerability, alerting the state

                   to the problem and not publishing anything until

                   the vulnerability was fixed. The FBI told Missouri

                   officials early on “that this incident is not an

                   actual network intrusion” and DESE initially wrote

                   up a press release thanking the journalists for

                   alerting them to this.

            # ⚓ Opinion_|_Desmond_Tutu,_Rest_in_Power⠀⇛

                   Archbishop Desmond Tutu died the day after

                   Christmas at the age of 90. The Nobel Peace

                   laureate was a leader in the movement to overthrow

                   apartheid, South Africa’s brutal system of racial

                   segregation. After that historic victory and the

                   election of Nelson Mandela as South Africa’s first

                   Black president in 1994, Tutu led the Truth and

                   Reconciliation Commission, pursuing restorative

                   justice rather than retribution. After that, Tutu

                   continued demonstrating and speaking out around the

                   world for justice, peace, women’s equality, gay

                   rights, in solidarity with Palestinians, and more.

            # ⚓ Desmond_Tutu_Spoke_Truth_in_the_Face_of_Oppression⠀⇛

                   I first met Archbishop Desmond Tutu when I was a

                   seminarian at Duke University in the 1980s, and I

                   will never forget the question he asked us when he

                   preached in the chapel that day: “Will you join

                   God?” Bishop Tutu knew the power of God to bring

                   justice in this world, but he also knew that we

                   must choose to join God in that work. Neutrality in

                   the face of evil, he always insisted, is a choice

                   to stand against God’s love and justice.

            # ⚓ New_Documents_Prove_Tennessee_County_Disproportionately

              Jails_Black_Children,_and_It’s_Getting_Worse⠀⇛

                   Tennessee’s Rutherford County, which has been

                   widely criticized for its juvenile justice system,

                   has been jailing Black children at a

                   disproportionately high rate, according to newly

                   obtained data. And, in a departure from national

                   trends, the county’s racial disparity is getting

                   worse, not better.

                   In an earlier story, ProPublica and Nashville

                   Public Radio chronicled a case in Rutherford County

                   in which 11 Black children were arrested for a

                   crime that does not exist. Four of the children

                   were booked into the county’s juvenile jail.

            # ⚓ Russia_designates_Pussy_Riot_activists,_Holod_Media_chief

              editor,_and_others_as_‘foreign_agents’⠀⇛

                   The Russian Justice Ministry made yet another round

                   of additions to its “foreign-agent media” registry

                   on Thursday, December 30, blacklisting a number of

                   cultural figures, including two Pussy Riot

                   activists and three journalists.

            # ⚓ ACLU_Files_Suit_to_Block_‘Brazen’_Effort_in_Georgia_to

              Thwart_Black_Voters⠀⇛

                   Alleging that Georgia’s new GOP-drawn General

                   Assembly district maps violate the Voting Rights

                   Act and attempt to disenfranchise Black voters,

                   civil rights groups on Thursday filed a federal

                   lawsuit against the Republican secretary of state

                   in a bid to block the maps.

                   “Politicians don’t get to choose their

                   voters—voters get to choose their politicians.”

            # ⚓ Metaverse_is_unsafe_for_women_already!_Reports_of_groping,

              harassment_rising_in_VR_games⠀⇛

                   The world’s largest tech companies — Microsoft,

                   Google, Apple and others — are hurtling headlong

                   into creating the metaverse, a virtual reality

                   world where people can have their avatars do

                   everything from play video games and attend gym

                   classes to participate in meetings. In October,

                   Mark Zuckerberg, Facebook’s founder and chief

                   executive, said he believed so much in the

                   metaverse that he would invest billions in the

                   effort. He also renamed his company Meta.

                   Yet even as tech giants bet big on the concept,

                   questions about the metaverse’s safety have

                   surfaced. Harassment, assaults, bullying and hate

                   speech already run rampant in virtual reality

                   games, which are part of the metaverse, and there

                   are few mechanisms to easily report the

                   misbehavior, researchers said. In one popular

                   virtual reality game, VRChat, a violating incident

                   occurs about once every seven minutes, according to

                   the nonprofit Center for Countering Digital Hate.

            # ⚓ Iran_secretly_executing_dozens_of_children:_Rights_group_|

              Arab_News⠀⇛

                   The Iranian regime is secretly executing dozens of

                   children every year in violation of international

                   law, according to a rights group.

                   More than 85 people are currently on death row for

                   crimes they are accused of having committed as

                   children, according to Human Rights Activists of

                   Iran.

                   In its annual report, it found that 299 citizens

                   were known to have been executed in the year to

                   Oct. 9.

      o § Internet Policy/Net Neutrality⠀➾

            # ⚓ Dish’s_Hyped_5G_Network_(And_‘Fix’_For_T-Mobile/Sprint

              Merger)_Is_Looking_Rather_Skimpy⠀⇛

                   Two years ago the Trump DOJ and FCC rubber stamped

                   the Sprint T-Mobile merger without heeding experts

                   warnings that the merger would likely erode

                   competition, raise rates, and kill jobs. Then,

                   working closely with T-Mobile and Dish, the FCC and

                   DOJ unveiled what they claimed was a “fix” for the

                   problematic nature of the deal: they’d try to

                   cobble together a fourth major replacement wireless

                   carrier in Dish Network.

            # ⚓ Every_State_Has_a_Chance_to_Deliver_a_“Fiber_for_All”

              Broadband_Future:_2021_in_Review⠀⇛

                   Now it’s up to elected officials in states, from

                   governors to state legislators, to work to ensure

                   the federal infrastructure program delivers 21st-

                   century ready infrastructure to all people. Some

                   states are ahead of the curve. In 2021, California

                   embraced a fiber infrastructure for all effort with

                   the legislature unanimously passing a historic

                   investment in public fiber. State Senator Lena

                   Gonzalez led this effort by introducing the first

                   fiber broadband-for-all bill; EFF was a proud

                   sponsor of this bill in Sacramento.

                   Other states are behind the curve by overly

                   restricting the ability for local governments and

                   utilities to plug the gaps that private internet

                   service providers (ISPs) have left for sixteen

                   years and counting. (2005 was when private fiber-

                   to-the home deployment really kicked off.)

                   Maintaining those barriers, even as federal dollars

                   are finally released, guarantees those states’

                   failures to deliver universal fiber; the federal

                   law, while important, isn’t sufficient on its own.

                    Success requires maximum input from local efforts

                   to make the most of this funding.

                   Understanding what progress we’ve made this

                   year—and what still needs to be done—requires

                   understanding the IIJA itself. The basic structure

                   of the law is a collaboration between the federal

                   government’s National Telecommunication Information

                   Administration (NTIA), the Federal Communications

                   Commission (FCC), and the states and territories.

                   Congress appropriated $65 billion in total. That

                   includes $45 billion for construction funds and $20

                   billion for efforts promoting affordability and

                   digital inclusion. This money can be paired with

                   state money, which will be essential in many states

                   facing significant broadband gaps.

      o § Monopolies⠀➾

            # ⚓ AT&T_Gets_“Favorable”_IRS_Ruling_on_Discovery-WarnerMedia

              Merger⠀⇛

                   AT&T has received a “favorable” IRS ruling on the

                   planned tax-free mega-merger of its entertainment

                   unit WarnerMedia with Discovery Inc., the telecom

                   giant disclosed in a regulatory filing on

                   Wednesday.

                   The companies unveiled the big combination in May,

                   saying it would use a rare multi-step structure

                   known as a Reverse Morris Trust, which is designed

                   to ensure deals are tax-free. In the transaction,

                   AT&T will separate WarnerMedia, via one of two ways

                   (a decision on which will be reached at a later

                   stage), into the so-called “SpinCo,” followed by

                   the merger with Discovery.

            # § Patents⠀➾

                  # ⚓ Yle_News’_15_most-read_stories_of_2021⠀⇛

                         3. Yle News’ third-most viewed story was

                         about a Turku firm that patented a [COVID]

                         drug, in the form of a nasal spray, that

                         delivers low, safe doses of

                         hydroxychloroquine, ivermectin and aprotinin.

                  # ⚓ Germany_sees_significant_rise_in_patent_applications

                    for_air_taxis [Ed: Patents for killing this planet, the

                    only planet we have, a lot faster than otherwise, by

                    burning up orders of magnitude more fuel for the same

                    travel]⠀⇛

                         The number of patents granted in Germany for

                         inventions related to urban air mobility

                         increased significantly in 2020, the

                         country’s Patent and Trademark Office (DPMA)

                         said.

                         Including filings with the European

                         Intellectual Property Office (EUIPO), 583

                         patents were published for air taxis in

                         Germany, 29 per cent more than in 2019,

                         Xinhua news agency quoted the DPMA as saying.

                         “A few years ago, air taxis were not taken

                         very seriously by many,” DPMA President

                         Cornelia Rudloff-Schaeffer said, adding that

                         the considerable amount of venture capital

                         pumped into this segment and the rapid pace

                         of innovation showed that this was an

                         “important future market”.

                         In the past five years, more than 40 per cent

                         of urban air mobility patents registered in

                         Germany came from US companies.

                  # ⚓ Turkey:_COVID-19_Vaccine_Patent_Discussions [Ed: No,

                    Özge Özdemir. COVID-19 vaccines do not have

                    "intellectual property rights", they have patents, and

                    those need to be abolished. They're not property and

                    not rights; it's the plunder from researchers funded by

                    taxpayers, to rob the taxpayers two-fold]⠀⇛

                         Discussions of world leaders about the

                         abolishing of intellectual property rights of

                         covid-19 vaccines have brought along

                         differences of opinion on this issue. The

                         world is currently debating whether removing

                         vaccine patent rights will actually work in

                         the fight against the corona pandemic or

                         hinder the development and production of

                         vaccines that are vital to humanity.

                         While America and Russia are in favor of

                         abolishing these rights, Europe argues that

                         the problem of the unequal distribution of

                         vaccines all over the world cannot be solved

                         by abolishing the patent right of vaccines.

                  # ⚓ Noam_Chomsky:_Corporate_Patents_&_Rising_Anti-Science

                    Rhetoric_Will_Prolong_Pandemic⠀⇛

                         Today, a special broadcast: an hour with Noam

                         Chomsky, the world-renowned political

                         dissident, linguist and author, who just

                         turned 93 years old. Chomsky spoke to

                         Democracy Now! prior to the discovery of the

                         Omicron coronavirus variant, but he predicted

                         new variants would emerge. “If you let the

                         virus run rampant in poor countries, everyone

                         understands that mutation is likely, the kind

                         of mutation that led to the Delta variant,

                         now the Delta Plus variant in India, and who

                         knows what will develop,” Chomsky said.

                  # ⚓ Texas_Team_Applauded_for_Giving_What_Big_Pharma

                    Refuses:_A_Patent-Free_Vaccine_to_the_World⠀⇛

                         A small team of Texas researchers is being

                         hailed for developing an unpatented Covid-19

                         vaccine to share with the world without

                         personal profit, with some advocates asking,

                         if they can do it, why can’t Big Pharma?

                         “If we had even a fraction of the support

                         that Moderna had, who knows, maybe the world

                         would be vaccinated by now.”

            # § Copyrights⠀➾

                  # ⚓ India_Expands_Piracy_Blocklist_to_Tackle_‘Hydra

                    Headed_Rogue_Websites’⠀⇛

                         Pirate site blocking is a common practice in

                         many countries and India is no exception. The

                         language used in Indian courts tends to be

                         more colorful though. This is exemplified by

                         a blocking extension several major Hollywood

                         studios requested recently. According to the

                         High Court in Delhi, it targets an

                         alphanumeric variation of a hydra-headed

                         rogue website.

                  # ⚓ LaLiga_Wins_Dynamic_Court_Injunction_to_Block_40

                    Pirate_IPTV_Platforms⠀⇛

                         Spanish football league LaLiga and telecoms

                         company Telefónica have obtained a court

                         judgment allowing them to block more than 40

                         pirate IPTV and card sharing platforms. The

                         country’s leading ISPs are required to

                         implement the blocks while accepting weekly

                         updates designed to frustrate services that

                         attempt to circumvent the measures.

                ䷩ 𝚕𝚒𝚗𝚎 7737

Gemini_version_available_♊︎

✐ Links_31/12/2021:_Libadwaita_1.0_and_Hugin_2021_Released⠀✐

Posted in News_Roundup at 5:25 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Distributions

      o Devices/Embedded

* Free_Software/Open_Source

* Leftovers

* § GNU/Linux⠀➾

      o § Desktop/Laptop⠀➾

            # ⚓ Tired_of_Windows?_It’s_time_to_give_Linux_a_try._|_Windows

              Central⠀⇛

                   I’m a fan of what Microsoft finally brought to the

                   desktop with Windows 11. Our resident Windows

                   expert Zac Bowden gave the OS a positive score in

                   his incredible in-depth review and I agree with the

                   majority of what was written. Where Windows 11

                   falls flat for me, however, is with the

                   installation process. It’s an absolute mess.

                   I have a few test rigs configured for various PC

                   components we review here at Windows Central and

                   installing fresh copies of Windows for Intel’s 12th

                   Gen launch was riddled with issues from the get-go.

                   The installer would either refuse to load or fail

                   to see drives. In fact, one install required a 2.5-

                   inch SATA SSD to be connected to the board in order

                   for Windows 11 to successfully boot from the M.2

                   NVMe drive.

                   Interestingly, I never had an issue with the latest

                   security measures that require trusted platform

                   modules (or TPM) since most motherboards and

                   processors released in the past few years support

                   it out of the box. It was more Windows having

                   trouble with SSDs, sometimes even outright refusing

                   to install Windows on specific drives.

                   For a laugh, I installed Linux Mint on all the

                   machines and didn’t see a single problem. Not one.

                   This is a billion-dollar company going up against

                   average Joe and losing in my anecdotal experiences.

                   But Windows isn’t completely out of my life. I

                   still use it regularly to remain in the loop with

                   all the latest news and because we continue to

                   benchmark products using the OS. For my main PC,

                   Windows isn’t even installed on a secondary drive

                   anymore.

      o § Audiocasts/Shows⠀➾

            # ⚓ A_New_KDE_Web_Browser_Approaches!_–_Kockatoo_Tube⠀⇛

            # ⚓ KDE_Has_A_New_Desktop?_–_Kockatoo_Tube⠀⇛

            # ⚓ Linux_Daddies:_The_Corporations_that_make_the_Linux_world

              go_’round [Ed: Gardiner Bryant should know better. Microsoft

              is still attacking Linux and it's also attacking (or bribing)

              the media to claim the very opposite]⠀⇛

            # ⚓ Blizzard_Battery_Battle_|_Coder_Radio_446⠀⇛

                   Mike finds a new normal and doubles down on what

                   works. Chris meanwhile is stranded in the woods and

                   is having a bit of a panic.

            # ⚓ 3D_Printing_Special_|_Self-Hosted_61⠀⇛

                   Some old friends of JB join Alex to discuss 3D

                   printing.

      o § Kernel Space⠀➾

            # ⚓ Intel_Alder_Lake’s_Thread_Director_Support_Coming_to_Linux

              |_Tom’s_Hardware⠀⇛

                   Intel has published a new patch series for its

                   Linux drivers that promise to improve the

                   performance of its hybrid Alder Lake processors by

                   optimizing usage of (P)erformance and (E)fficiency

                   cores.

                   When Intel released its 12th Generation Core ‘Alder

                   Lake’ processors earlier this year, it quickly

                   turned out that the new CPUs perform better under

                   Windows rather than under Linux. Unlike Windows 11,

                   Linux does not have proper support for Intel’s

                   Thread Director technology based on the Enhanced

                   Hardware Feedback Interface (HFI), which enables

                   the OS to utilize high-performance Golden Cove and

                   energy-efficient Gracemont cores properly.

                   At present, the Linux kernel decides when to use P

                   or E cores using the ITMT/Turbo Boost Max 3.0

                   driver that relies on the information exposed by

                   the firmware, reports Phoronix. Essentially, this

                   means that under Linux, the OS in many cases

                   prefers the fastest cores (i.e., Golden Coves at

                   high clocks) and underutilizes energy-efficient

                   cores.

            # ⚓ ThinkPad_ACPI_Driver_Picking_Up_New_Features_With_Linux

              5.17_–_Phoronix⠀⇛

                   For those running Linux on Lenovo ThinkPad laptops,

                   the upcoming Linux 5.17 cycle is set to bring a few

                   improvements to the “thinkpad_acpi” driver.

                   Thanks to developers Ognjen Galic and Thomas

                   Weißschuh, the ThinkPad ACPI driver is adding

                   support for inhibit charge behavior if wanting to

                   temporarily disable charging support for ThinkPads

                   allowing this behavior through the system’s

                   embedded controller (EC).

                   Similarly, there is also now force discharge

                   support if wanting to force the battery to change

                   and again contingent upon EC support from the

                   ThinkPad.

            # § Graphics Stack⠀➾

                  # ⚓ Mesa’s_Radeon_Vulkan_Driver_Lands_Experimental_Mesh

                    Shaders_–_Phoronix⠀⇛

                         Thanks to Valve engineer Timur Kristóf and

                         other open-source developers involved, Mesa’s

                         Radeon Vulkan driver “RADV” is ending 2021 on

                         a high note: mesh shaders was just merged!

                         As noted back in October, RADV has been

                         working on mesh shaders at least in

                         experimental form and making use of NVIDIA’s

                         NV_mesh_shader extension.

                         Mesh shaders provide a compute-like shader

                         stage to replace the conventional vertex/

                         geometry pipeline. This work though is

                         expected to remain “experimental” until there

                         is a proper Vulkan cross-vendor extension

                         around mesh shaders as NV_mesh_shader is

                         known to perform poorly on AMD hardware for

                         which the extension was not designed.

                         Mesh shaders support requires Radeon RX 6000

                         “RDNA2″ GPUs and newer for support. This

                         experimental mesh shaders support will be

                         part of Mesa 22.0 that will debut as stable

                         by March. This may prove beneficial for

                         VKD3D-Proton in mapping Direct3D 12 mesh

                         shaders atop Vulkan but, again, the

                         performance isn’t expected to be optimal.

      o § Applications⠀➾

            # ⚓ Best_Free_and_Open_Source_Alternatives_to_Intuit_Mint⠀⇛

                   Intuit Inc. is an American corporation that

                   specializes in financial software. Specfically, the

                   company develops personal finance, accounting, and

                   tax return software.

                   The company is headquartered in Mountain View,

                   California. It has more than 10,000 employees.

                   While Intuit has a GitHub presence with over 100

                   repositories for numerous open source projects,

                   none of these repositories offer any substantial

                   desktop software. Instead, the repositories focus

                   on tools and libraries for developers. None of

                   these projects appear to have attracted significant

                   interest from the open source community.

            # ⚓ Best_Free_and_Open_Source_Alternatives_to_Intuit’s

              Products⠀⇛

                   Intuit Inc. is an American corporation that

                   specializes in financial software. Specifically,

                   the company develops personal finance, accounting,

                   and tax return software.

                   The company is headquartered in Mountain View,

                   California. It has more than 10,000 employees.

                   While Intuit has a GitHub presence with over 100

                   repositories for numerous open source projects,

                   none of these repositories offer any substantial

                   desktop software. Instead, the repositories focus

                   on tools and libraries for developers. None of

                   these projects appear to have attracted significant

                   interest from the open source community.

            # ⚓ Hugin_2021_Released!_How_to_Install_via_PPA_in_Ubuntu

              20.04,_21.10_|_UbuntuHandbook⠀⇛

                   Hugin panorama stitcher finally released version

                   2021. Here’s how to install it via PPA in Ubuntu

                   18.04, Ubuntu 20.04, Ubuntu 21.04, Ubuntu 21.10,

                   and Linux Mint 20.

            # ⚓ Hugin-2021.0.0_Release_Notes⠀⇛

            # ⚓ 10_Selfhosting_Ideas_You_Can_Build_with_Yunohost_Server⠀⇛

                   This article is a collection of ideas to practice

                   selfhosting with Yunohost for beginners who are

                   learning system administration. Yunohost is like

                   magic, this server OS allows us to deploy a full,

                   working email server in one click and that works

                   for other kinds of server too. Now, let’s see the

                   ideas!

            # ⚓ Anklang_takes_over_|_Timj’s_bits_and_tests⠀⇛

                   The Anklang project is a digital audio synthesis

                   application for live creation and composition of

                   music or other audio material. It merges several

                   new developments and (Beast) rewriting efforts by

                   Stefan Westerfeld and me.

                   Starting a new project from scratch was the easier

                   and quicker approach, with all the changes involved

                   in moving to a modern file format, recreating the

                   UI in a new language plus new technologies, using a

                   new IPC layer and reinventing the synthesis engine

                   in modern C++.

                   This brought much quicker results, compared to

                   continued work on the aging Beast code base and a

                   conversion tool is being worked on to carry over

                   what is possible from old files. The tool is set to

                   be integrated when the Anklang features set is

                   ripe.

                   This pre-release show cases some of the new

                   technologies, although the code still has alpha

                   quality, others are still in the queue to be

                   integrated soon and unpolished areas are also to be

                   addressed. Currently, it may be an interesting

                   piece for the adventurous to play around with, so

                   feedback or contributions will be very welcome.

      o § Instructionals/Technical⠀➾

            # ⚓ How_to_convert_(and_flatten)_PDF_documents_to_images⠀⇛

                   Say you have a PDF document in your hands. Say this

                   documents needs editing and redacting. You may want

                   to add some bits of information and obscure some

                   other bits of information. Various PDF programs can

                   do this job for you. However, quite often, the new

                   changes are added as layers on top of the original,

                   so people with the right kind of expertise can

                   glean the data from under the redaction markers.

                   Some time ago, I published a tutorial showing how

                   to flatten PDF files, which basically means putting

                   all of the changes into a single layer. Now, I want

                   to show you another trick, and this is how to

                   convert PDF files into images. This will create a

                   similar effect – flattening, plus the ability to

                   use (only) parts of information contained in the

                   PDF documents. Our tool of the trade will be

                   pdftocairo. In Linux. Let’s commence.

            # ⚓ How_to_install_the_latest_version_of_Blender_on_a

              Chromebook⠀⇛

                   Linux is a buffet for different tools and

                   utilities, some last longer, and others are

                   deprecated with better alternatives.

            # ⚓ How_to_install_the_latest_version_of_Blender_on_a

              Chromebook⠀⇛

                   Today we are looking at how to install the latest

                   version of Blender 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.

            # ⚓ How_to_spin_up_virtual_machines_fast_on_Ubuntu_with

              Quickemu⠀⇛

                   Virtualization on Ubuntu is one of its strengths.

                   However, setting up a VM as a new user can be

                   tedious and confusing. That’s where Quickemu comes

                   in. It harnesses the power of QEMU in the Linux

                   kernel and automatically spins up virtual machines

                   fast. Here’s how to use it on your Ubuntu system.

            # ⚓ How_To_Install_Nginx_on_CentOS_9_Stream_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   Nginx on CentOS 9 Stream. For those of you who

                   didn’t know, Nginx (Engine X) is the most popular,

                   powerful web server software that can be used on

                   your server. It is also known for its high

                   performance and low memory usage. In addition to

                   its HTTP server capabilities, NGINX can also

                   function as a proxy server for e-mail (IMAP, POP3,

                   and SMTP) and a reverse proxy and load balancer for

                   HTTP, TCP, and UDP servers.

                   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 Nginx web server on CentOS 9

                   Stream.

            # ⚓ How_to_install_and_uninstall_Discord_on_Linux_|_FOSS

              Linux⠀⇛

                   We have come to a point in history where at-a-

                   distance communication has become an essential part

                   of our daily lives. This applies to jobs and all

                   kinds of areas of day-to-day activities. We require

                   a communication program that works smoothly and has

                   impressive features to go well. Enter, Discord.

                   Discord has made quite a name for itself even among

                   the vast competition in the category that it

                   belongs to. It has excellent features, works

                   without a hassle, is available on various

                   platforms, and gives the users a great experience.

                   Today, we will check how to install and use Discord

                   on Linux.

            # ⚓ Full_Circle_Magazine_#176⠀⇛

            # ⚓ How_To_Install_PyCharm_on_Fedora_35_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   PyCharm on Fedora 35. For those of you who didn’t

                   know, PyCharm is a cross-platform editor developed

                   by JetBrains. Pycharm provides all the tools you

                   need for productive Python development. Many Python

                   programmers enjoy using PyCharm because it can be

                   used to analyze code, debug programs, and is

                   integrated with Git and other version control

                   systems. Pycharm comes with two variants,

                   Professional (Paid) and Community (Free). The

                   professional edition comes with additional web

                   development support.

                   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 PyCharm IDE on a Fedora 35.

            # ⚓ Install_Plex_Media_Server_on_Debian_11_Bullseye_with_Nginx

              Reverse_Proxy⠀⇛

                   Learn the simple commands to install Plex Media

                   Server on Debian 11 Bullseye Linux for creating

                   your streaming server.

                   Plex was started as a hobby project but with time,

                   it developed into a professional streaming server

                   software to manage various types of media files.

                   Users can install and use it to access their

                   videos, music, and images remotely using the

                   internet or locally over a local network; even you

                   can share them with friends while on the move.

                   You will have the same feel as Netflix, as Plex

                   creates matching thumbnails and loads information

                   from film databases. However, Plex can’t keep up

                   with major streaming providers like Netflix, Amazon

                   Prime Video, Apple TV +, and Disney +.

                   Nevertheless, it has not been developed to compete

                   with them. The main goal of its developers is to

                   provide an easy-to-use piece of software to general

                   users or businesses who want to manage their

                   database of films, photos, and songs either on NAS,

                   Cloud, or any PC.

      o § Games⠀➾

            # ⚓ AMD’s_FidelityFX_Super_Resolution_(FSR)_should_be_a_huge

              deal_for_Steam_Deck_based_on_its_Linux_performance_|_Windows

              Central⠀⇛

                   When they were first announced, I, like many

                   others, had hoped to be holding a Steam Deck this

                   Christmas. But it’s a hard time to manufacture tech

                   right now, and so we’re going to have to wait a

                   little longer.

                   But in that time I’ve been spending more energy

                   experiencing PC gaming on Linux, the base for the

                   Steam Deck. Much has been said already about Proton

                   and much more will be said in the months to come,

                   but there’s one bit of ‘special sauce’ that

                   deserves more attention because it should be a huge

                   deal on Valve’s portable gaming PC.

                   AMD FidelityFX Super Resolution (FSR) is, in simple

                   terms, like NVIDIA’s DLSS. It uses witchcraft to

                   intelligently upscale games while preserving as

                   much detail as possible so as to enable higher

                   frame rates thanks to having been rendered

                   initially at a lower resolution. One big difference

                   is that FSR works on both AMD and NVIDIA hardware,

                   and the other is that it’s open-source. This means

                   the Linux gang has been all over it.

            # ⚓ 2021_Brought_A_Convenient_Installer_For_Arch_Linux,

              Powering_The_Steam_Deck_–_Phoronix⠀⇛

                   Arch Linux had a pretty great year with introducing

                   “Archinstall” as part of the official install media

                   as a new, optional installer for conveniently

                   installing the distribution to Valve choosing Arch

                   Linux as their new SteamOS 3.0 base that will power

                   their forthcoming Steam Deck handheld game console.

                   By nearly any indicator, Arch Linux had a pretty

                   great 2021. Arguably most exciting is the Steam

                   Deck / SteamOS switching to Arch Linux where as

                   previously Valve relied upon Debian that fell stale

                   too quickly. Using Arch Linux will allow for more

                   fast-paced updates and ensuring the newest, most

                   optimal experience for their Linux-based handheld

                   slated to start shipping next quarter. Until

                   getting out new SteamOS images, Valve has been

                   encouraging developers to test on the Arch-based

                   Manjaro Linux distribution that is desktop-oriented

                   and easy to use.

      o § Desktop Environments/WMs⠀➾

            # ⚓ Xfce’s_Apps_Update_for_December_2021:_New_Releases_of_Xfce

              Terminal,_Whisker_Menu,_and_More⠀⇛

                   December has been a slow month for Xfce apps

                   development, but we got a new update of the Xfce

                   Terminal modern terminal emulator app to version

                   0.9.1, which adds an overlay-scrolling preference,

                   support for the new Shortcuts editor widget, and a

                   new preference to select the right-click action.

                   In addition, the Xfce Terminal 0.9.1 release

                   improved the scrolling-on-output behavior and the

                   Paste dialog, and addressed several regressions and

                   updated multiple language translations.

            # § GNOME Desktop/GTK⠀➾

                  # ⚓ Using_GNOME_Screenshot_Tool_in_Linux_Like_a_Pro⠀⇛

                         There are several screenshot tools available

                         for Linux. I prefer using Flameshot for

                         screenshots and Shutter for editing the

                         existing screenshots.

                         But Flameshot doesn’t work with 4K screens,

                         unfortunately. And hence I had to resort back

                         to the default GNOME screenshot tool which

                         works perfectly on my Dell XPS with Ultra HD

                         screen.

                  # ⚓ Libadwaita_1.0_Arrives_to_Kickstart_a_New_Era_of_GTK

                    App_Development_–_OMG!_Ubuntu!⠀⇛

                         Libadwaita 1.0 has been released,

                         kickstarting a new era in GTK app

                         development.

                         Now, there’s been a fair bit of controversy

                         and misunderstanding over what libadwaita is

                         and isn’t. It’s pitched as a library that

                         implements the (new) GNOME HIG, and is a

                         GTK4-based successor to the GTK3-based

                         libhandy library that has, over the past few

                         years, given GTK apps lots of cool adaptive

                         capabilities.

                         Libadwaita is set to become tightly intwined

                         with GNOME as, in a break with the past, this

                         library comes with a stylesheet —what we

                         think of as GTK themes are actually just

                         stylesheets— baked in. This means anything

                         built using libadwaita (i.e., like a lot of

                         GNOME 42) should look virtually the same

                         wherever it runs regardless of what GTK theme

                         is set.

                  # ⚓ Alexander_Mikhaylenko:_Libadwaita_1.0⠀⇛

                         Libadwaita 1.0 has been released, just at the

                         end of the year.

                         Libadwaita is a library implementing the

                         GNOME HIG, complementing GTK. For GTK 3 this

                         role has increasingly been played by

                         Libhandy, and so Libadwaita is a direct

                         Libhandy successor.

                         You can read more in Adrien’s announcement.

                         [...]

                         Ever since Adwaita started using SCSS, it

                         couldn’t really be recolored at all without

                         recompiling it. This created big problems for

                         applications that wanted to do that.

                         For example, GNOME Web makes its header bar

                         blue in incognito mode. This may sound

                         simple, but involves copy-pasting large

                         chunks of Adwaita into the app itself and

                         making many small changes everywhere to

                         adjust it, as well as using SCSS for it

                         because the original style is SCSS. More

                         recently, GNOME Console and Apostrophe

                         started doing the same thing – copy-pasted

                         from Web, as a matter of fact. This approach

                         means the style is messy and extremely hard

                         to keep up to date with Adwaita changes – I

                         have updated this style for the 3.32 style

                         refresh and never want to do this again.

                         Another approach applications like Contrast

                         are using (were using with GTK 3, anyway), is

                         copying the whole stylesheet from GTK, and

                         using libsass to recompile it in runtime.

                         This worked – it’s much more maintainable

                         than the first approach, but fell apart when

                         libsass got deprecated.

                         Meanwhile, the elementary OS stylesheet has

                         been doing recoloring just fine with nothing

                         but @define-color – and so Libadwaita does

                         exactly that, it exposes all of the colors it

                         uses (31 as of the moment of writing) as

                         named colors. The new colors are also

                         documented and will be treated as a proper

                         API.

                         It also drops all of the formerly used PNG

                         assets, so the colors can affect the elements

                         that used them.

                         It also reworks the high contrast variant to

                         use the same colors when possible to make

                         sure that changing color for the regular

                         style also works with high contrast.

                  # ⚓ Libadwaita_1.0_Released_For_Kicking_Off_A_New_Year_Of

                    GNOME_App_Development⠀⇛

                         GNOME’s libadwaita 1.0 has been released for

                         this library implementing the GNOME Human

                         Interface Guidelines (HIG) and complementary

                         to the GTK toolkit.

                         Libadwaita 1.0 is the successor to libhandy

                         that complemented GTK3. Libadwaita 1.0 offers

                         a reworked stylesheet now that the Adwaita

                         style has become part of the library rather

                         than within GTK. This new libadwaita style is

                         designed to be more modern, supports runtime

                         recoloring, a more proper dark variant

                         contrast, style classes updates, API to

                         support the new cross-desktop dark style

                         preference, improved notifications, and much

                         more.

                  # ⚓ GNOME_libadwaita_1.0_released⠀⇛

                         Version 1.0 of the GNOME libadwaita library

                         is out; this will be of interest to GNOME

                         application developers. “Libadwaita is a

                         library implementing the GNOME HIG,

                         complementing GTK. For GTK 3 this role has

                         increasingly been played by Libhandy, and so

                         Libadwaita is a direct Libhandy successor.”

      o § Distributions⠀➾

            # § New Releases⠀➾

                  # ⚓ Linux_Lite_5.8_Is_Slated_for_Release_on_February_1st,

                    2022,_Now_Available_for_Testing⠀⇛

                         Still based on the Ubuntu 20.04.3 LTS release

                         of the long-term supported Ubuntu 20.04 LTS

                         (Focal Fossa) operating system series from

                         Canonical, the Linux Lite 5.8 distribution

                         release promises updated components, bug

                         fixes, and many other tweaks and changes.

                         Don’t get too excited because Linux Lite 5.8

                         is an incremental update to the previous

                         releases in the Linux Lite 5 series. As such,

                         it would appear that the major changes of

                         this upcoming update are an updated Papirus

                         icon theme and nine new wallpapers to make

                         your Linux Lite desktop experience more

                         enjoyable.

                  # ⚓ Celebrate_New_Year_2022_by_switching_from_Windows_11

                    to_Linux_Lite_5.8_RC1⠀⇛

                         Windows 11 is a great operating system. In

                         fact, I can confidently say it is the best

                         desktop operating system Microsoft has ever

                         created. Seriously, folks, it is wonderful.

                         If your computer is compatible with it, and

                         you like Windows 10, you should enjoy Windows

                         11 even more.

                         With all of that said, Windows 11 can be a

                         bit polarizing. It features radical changes

                         to the user interface (such as a centered

                         task bar) which I adore, but some users may

                         dislike. Not to mention, the system

                         requirements will leave many still-capable

                         computers unable to upgrade without using

                         unofficial hacks. Even worse, computers

                         deemed incompatible could eventually stop

                         getting updates! These unfortunate computer

                         owners will have to decide whether to

                         continue using Windows 10 or buy a new

                         Windows 11-compatible PC.

            # § SUSE/OpenSUSE⠀➾

                  # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2021/52_–

                    Dominique_a.k.a._DimStar_(Dim*)⠀⇛

                         Dear Tumbleweed users and hackers,

                         The last week of the year, and the last day

                         of the year, are coming to an end. Tumbleweed

                         had a small dip, as the last two snapshots

                         that moved to openQA had to be stopped from

                         being published. Nevertheless, we still

                         managed to publish 6 snapshots before heading

                         out to the new-year celebrations (1223…1228).

            # § IBM/Red Hat/Fedora⠀➾

                  # ⚓ Looking_back_on_2021_and_ahead_to_an_amazing_new

                    year⠀⇛

                         We’ve made it to the end of 2021, and I’m

                         filled with so many emotions. On the one

                         hand, I’m extremely proud of the work we have

                         done this year. But on the other hand… when I

                         wrote last year’s love letter, I thought we’d

                         surely be able to celebrate our successes in

                         person this year. Unfortunately, the global

                         situation doesn’t seem to be getting any

                         better. Our usual European winter events —

                         DevConf.CZ and FOSDEM — are both virtual

                         again. While I continue to hold out hope that

                         we’ll be able to share a meal together soon,

                         there are no clear dates in sight.

                         So, as we close out 2021 and approach the

                         two-year mark of the pandemic, I’d like us

                         all to take a moment to reflect on how we’ve

                         continued to be a thriving community this

                         year. Nest With Fedora brought together over

                         700 Fedorans—nearly twice the size of Nest

                         2020. We expanded our annual Fedora Women’s

                         Day to Fedora Week of Diversity, celebrating

                         the rich diversity that makes Fedora a great

                         community. And we upgraded the way we

                         communicate, bringing more conversation to

                         Discussion and adding a new chat server using

                         the open Matrix protocol. And all of that

                         featured our new logo, introduced this

                         spring.

                         Of course, as much as we love the Friends

                         foundation, this community is about more than

                         just having fun together. We also produce an

                         excellent operating system. Fedora

                         Workstation 34 led the way among major

                         desktop distributions by featuring GNOME 40—a

                         significant improvement to the widely-used

                         desktop environment. We also changed the

                         default audio system to PipeWire. And even

                         though we broke our on-time streak with

                         Fedora Linux 35, that just shows how

                         seriously we take quality — we want to be

                         leading edge, not “bleeding edge”, and we

                         continue to demonstrate that in what we

                         deliver to users.

                  # ⚓ 15_ways_to_advance_your_Kubernetes_journey_in_2022⠀⇛

                         2021 has been an exciting year for

                         Kubernetes, and these articles prove it. From

                         fun interfaces to homelabs to development

                         environments, check out my favorite articles

                         from 2021, K8s style.

                         If you are interested in the fundamentals,

                         this article about containers on Linux

                         clarifies how Linux containers work from the

                         inside out. Are you more interested in having

                         some fun? Install minikube and start managing

                         it using the DOOM video game as an interface.

                         An alternative to DOOM is kubectl, a more

                         traditional Kubernetes control CLI.

                         Even if you only run Kubernetes on your Linux

                         homelab, you can use tools like Terraform and

                         Helm to automate day-to-day operations. This

                         creates an opportunity to get better at

                         Terraform.

                         One of the few things that are certain in

                         life is that computers will fail in weird and

                         interesting ways. Monitor your Kubernetes

                         cluster with Prometheus and Grafana to see

                         how it fails. Monitor the applications

                         running inside it with distributed tracing

                         using Grafana Tempo. Monitor how strong your

                         monitoring is by introducing Chaos Mesh to

                         cause intentional chaos in Kubernetes.

                  # ⚓ Top_21_sysadmin_guides_and_tutorials_of_2021_|_Enable

                    Sysadmin⠀⇛

                         This was an amazing year for the Enable

                         Sysadmin community. In 2021, our site traffic

                         grew to more than 600,000 page views per

                         month, 100,000 per month over 2020. We

                         generated more than 7.2 million page views

                         and 4.2 million unique visitors in 2021.

                  # ⚓ IT_leadership:_3_ways_to_show_gratitude_to_teams⠀⇛

                         When I discussed these challenges with the

                         instructors on our platform, one solution

                         kept coming up again and again: Gratitude.

                         Showing gratitude doesn’t just mean being

                         nice for the sake of being nice. Gratitude

                         has real business value. A ten-year, 200,000-

                         person study by O.C. Tanner found that 79

                         percent of respondents who’d quit their jobs

                         cited lack of appreciation as a key factor in

                         their departure. In addition, 65 percent of

                         North Americans surveyed felt that they had

                         not been recognized even once in the prior

                         year. That’s a dangerous position for any

                         company to be in.

                         This is why CIOs and IT leaders, in

                         particular, must be cognizant of team morale

                         and keep the gratitude flowing. It’s not

                         always easy under pressure, but here are

                         three elements to keep in mind.

                  # ⚓ Irving_Wladawsky-Berger:_The_World_Ahead_2022:

                    Adjusting_to_New_Realities⠀⇛

                         A few weeks ago The Economist published The

                         World Ahead 2022, its 36th annual look at the

                         economic, political, social and cultural

                         trends that will likely shape the coming

                         year. “If 2021 was the year the world turned

                         the tide against the pandemic, 2022 will be

                         dominated by the need to adjust to new

                         realities, both in areas reshaped by the

                         crisis (the new world of work, the future of

                         travel) and as deeper trends reassert

                         themselves (the rise of China, accelerating

                         climate change),” wrote the issue’s editor

                         Tom Sandage.

                  # ⚓ CentOS_Linux_8_Reaches_End-Of-Life⠀⇛

                         Today is the unfortunate day marking CentOS

                         Linux 8 reaching end-of-life status as a free

                         alternative to Red Hat Enterprise Linux 8.

                         It was a year ago CentOS / Red Hat announced

                         their shift in focus on CentOS Stream as

                         being the new upstream of Red Hat Enterprise

                         Linux moving forward. CentOS Stream has been

                         taking shape this year while unfortunately it

                         means the EOL’ing of CentOS Linux 8.

                  # ⚓ CentOS_Linux_8_EOL⠀⇛

                         In December 2020, the CentOS Project

                         announced a series of changes. The three most

                         important are: the creation of CentOS Stream

                         and the consequent rename of CentOS (the

                         classic Linux distribution the project is

                         known for) in CentOS Linux the anticipation

                         to today (31/12/2021) of the End Of Life for

                         CentOS Linux 8 the fact that CentOS Linux 8

                         is going to be the last and that from now on,

                         only CentOS Stream will have new releases

                         That announcement created a lot of different

                         sentiments in the community and even more

                         among the CentOS Linux users.

                  # ⚓ An_Official_Way_To_Migrate_To_AlmaLinux_8_From_CentOS

                    8_–_OSTechNix⠀⇛

                         This step by step tutorial explains how to

                         migrate to AlmaLinux 8 from CentOS 8 using

                         Almalinux-deploy script. Using Almalinux-

                         deploy script, we can easily convert CentOS

                         machines (hopefully other Enterprise Linux

                         systems) to AlmaLinux.

                         It is written in Bash and the source code is

                         available in GitHub. Now let us go ahead and

                         migrate from CentOS to AlmaLinux with

                         almalinux-deploy script.

                  # ⚓ Install_NVIDIA_Drivers_[495.46_/_470.94_/_390.147_/

                    340.108]_on_CentOS_Stream,_RHEL,_Rocky_Linux_–_If_Not

                    True_Then_False⠀⇛

                         This is guide, howto install NVIDIA

                         proprietary drivers (manually using .run

                         files) on CentOS Stream 9/8, Red Hat (RHEL)

                         9.0/8.5, Rocky Linux 8.5 and disable Nouveau

                         driver. This guide works with GeForce 8/9/

                         200/300/400/500/600/700/800/900/10/20/30

                         series cards.

            # § Canonical/Ubuntu Family⠀➾

                  # ⚓ Unitree_Z1_Robotic_Arm_Can_Pour_You_a_Glass_of_Wine

                    or_Open_the_Door_for_You_–_autoevolution⠀⇛

                         With six DOF (degrees of freedom) and

                         consisting of four segments, the Z1 has a

                         maximum speed of 180 degrees per second, uses

                         the Ubuntu operating system, and has a

                         plethora of applications. It is compatible

                         with mobile robots, including Unitree’s

                         Aliengo and B1 quadrupeds.

      o § Devices/Embedded⠀➾

            # ⚓ The_Mico_RP2040_Microphone_Is_Ideal_for_Machine_Learning

              Applications⠀⇛

            # ⚓ Crowdfunded_Astro_Slide_phone_with_slide-out_keyboard,

              Linux_support_should_ship_in_2022⠀⇛

                   The Astro Slide is a smartphone with a 6.5 inch

                   AMOLED touchscreen display, a MediaTek Dimensity

                   800 processor, 8GB of RAM, 128GB of storage, a

                   4,000 mAh battery and support for wireless

                   charging. But those aren’t the features that make

                   this phone unusual.

                   It also has a physical keyboard that slides out

                   from behind the display, allowing you to use the

                   Astro Slide like a tiny laptop computer. And while

                   it will ship with Android, the phone is also

                   working with mobile Linux developers to ensure that

                   it will be able to support GNU/Linux distributions

                   like Ubuntu Touch.

            # § Mobile Systems/Mobile Applications⠀➾

                  # ⚓ Google_changes_its_requirements_for_Android_apps_to

                    avail_its_services_/_Digital_Information_World⠀⇛

                  # ⚓ Top_5_ways_to_use_your_Android_phone_or_tablet_as_a

                    second_screen⠀⇛

                  # ⚓ The_Best_Android_Games_of_2021_–_The_Witcher_Tales:

                    Thronebreaker_–_Droid_Gamers⠀⇛

                  # ⚓ Google_and_Android_13:_Here’s_what_analysts_want_in

                    2022_|_Android_Central⠀⇛

                  # ⚓ The_last_Nokia_smartphone_to_receive_the_Android_12

                    update_in_2021_–_PhoneArena⠀⇛

                  # ⚓ Samsung_Android_12_update:_These_devices_have_One_UI

                    4.0_–_9to5Google⠀⇛

                  # ⚓ Descendant_12_based_on_Android_12_is_here_for_the

                    POCO_F3,_POCO_X3,_and_more⠀⇛

                  # ⚓ Android_Circuit:_Samsung_Galaxy_S22’s_New_AI,_Xiaomi

                    12_Family_Launched,_Surface_Duo’s_Android_Update⠀⇛

                  # ⚓ Malware_removal_on_Android:_how_to_clean_up_your

                    smartphone_|_TechRadar⠀⇛

                  # ⚓ Android_12_hits_the_Galaxy_Note_10_and_original

                    Galaxy_Fold_–_9to5Google⠀⇛

                  # ⚓ Nokia_G50_is_the_latest_HMD_Global_phone_to_get

                    Android_12⠀⇛

                  # ⚓ Google_Pixel_Android_12_bugs,_problems,_&_issues

                    tracker⠀⇛

                  # ⚓ Vivo_Android_12_(Funtouch_OS_12/OriginOS/iQOO_UI_3.0)

                    update_tracker⠀⇛

                  # ⚓ Here’s_what_to_expect_in_2022:_More_options_in_VR/AR

                    headsets,_strong_focus_on_Android_tablets_|_Technology

                    News,The_Indian_Express⠀⇛

                  # ⚓ Ways_to_make_your_Android_TV_run_faster⠀⇛

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

            # ⚓ Intel_To_Ring_In_2022_With_New,_Faster_AV1_Encoder_Release

              –_Phoronix⠀⇛

                   Intel in cooperation with the Alliance for Open

                   Media continues developing SVT-AV1 as the flagship

                   CPU-based AV1 video encoder. With the next SVT-AV1

                   update there are performance optimizations as well

                   as several new preset levels allowing for even

                   greater performance. Here are some early benchmarks

                   of that updated SVT-AV1.

            # ⚓ Open_Source_Trends_for_2022_and_Beyond⠀⇛

                   “There’s nothing magical about open-source

                   methodology and security,” Vaughan-Nichols notes.

                   “Linus’s law is that given enough eyeballs, all

                   bugs are shallow. But, if not enough developers are

                   looking, security vulnerabilities will still go

                   unnoticed.” And, according to what he is calling

                   Schneier’s law, “Security is a process, not a

                   product,” and “constant vigilance is needed to

                   secure all software.”

            # § Events⠀➾

                  # ⚓ Will_Anyone_Actually_Show_Up_at_CES_on_Wednesday?⠀⇛

                         A given at the first of each year is CES.

                         Formally called the Consumer Electronic Show,

                         the event practically takes over Las Vegas

                         for a few days every January, and every

                         company that even dabbles in electronics is

                         on hand to show off their latest offerings.

                         How big is it? In 2019, more than 182,000

                         people attended and more than 4,400 vendors

                         exhibited their wares. How important is being

                         there to vendors? In 2020, Apple made its

                         first appearance at the event in 27 years, if

                         that tells you anything.

                         In 2021, when there was no in-person event

                         due to COVID, organizers pulled out all the

                         stops to create an engaging virtual event,

                         featuring a live digital performance by

                         Billie Eilish as a lead-in to a discussion

                         session on digital performances in whic Ryan

                         Seacrest spoke with Billie Eilish and Dua

                         Lipa.

                  # ⚓ CES_Rolls_the_Dice_and_Gambles_on_Becoming_a

                    Superspreader_Event⠀⇛

            # § Productivity Software/LibreOffice/Calligra⠀➾

                  # ⚓ LibreOffice_Working_On_A_New_Cairo_Graphics_Back-End

                    –_Phoronix⠀⇛

                         Merged yesterday into the LibreOffice code-

                         base was introducing yet another graphics

                         drawing back-end for this open-source office

                         suite.

                         SvpGraphicsBackend is this new VCL (Visual

                         Class Library) back-end for LibreOffice.

                         SvpGraphicsBackend is being used as a new

                         back-end around Cairo. There is already

                         SvpSalGraphics for LibreOffice that uses

                         Cairo for drawing while SvpGraphicsBackend is

                         being worked into the new implementation

                         alongside the various other VCL graphics/

                         drawing back-ends for the cross-platform

                         office suite.

                         Tomaž Vajngerl of Collabora has been working

                         on this new Cairo back-end that was merged on

                         Thursday. So far there have been a few more

                         follow-up commits beginning to move more

                         functionality into SvpGraphicsBackend.

            # § FSF⠀➾

                  # § GNU Projects⠀➾

                        # ⚓ 2021_annual report_–_GIMP⠀⇛

                               With 4 development versions released

                               already, you know that we are working

                               very hard on the future: GIMP 3.0.

                               Some features took a lot of time,

                               mostly when we changed core logics. I

                               am thinking in particular about the

                               code for multi-selection of layers.

                               It’s not that selecting multiple items

                               in a list is hard to implement, it’s

                               that any feature in the whole

                               application has been forever expecting

                               just one layer or one channel selected.

                               So what happens when there are 2, 3 or

                               any number of items selected? Every

                               feature, every tool, every plug-in and

                               filter has to be rethought for this new

                               use case. This is a huge work and it

                               has been 2 years I have been on and off

                               on this one in between porting or

                               developing other code and reviewing

                               contributors’ code. Fortunately this

                               change is nearing the end lately (not

                               completely finished though). So that’s

                               a great progress.

                               By the way, a part of this work has

                               been to get rid of the “link” (chain ⛓

                               icon in the Layers dockable) concept in

                               favor of multi-selection (and layer

                               search and storage as a replacement

                               concept for the ability to save layer

                               links). This part is also done now.

                               I’ll talk more about this in the GIMP

                               2.99.10 release news.

            # § Programming/Development⠀➾

                  # ⚓ The_Kate_Text_Editor_in_2021_–_Kate⠀⇛

                         From Kate’s development perspective this year

                         looks fantastic. If you track a bit the

                         development via our merge requests overview

                         page or even better participate yourself in

                         our projects, you might have already noticed

                         it ;=)

                  # ⚓ Simple_test_if_audio_muted⠀⇛

                         I am working out how to do things in /usr/

                         sbin/mscw (Multiple Sound Card Wizard). A

                         huge issue for me has been moving from alsa

                         to pulseaudio. Here is a link to earlier

                         work:

                         https://bkhome.org/news/202111/how-

                         pulseaudio-is-implemented-in-easyos.html

                         I am still very uncertain about aspects of

                         the interaction between alsa and pa. The

                         single most important feature is /etc/alsa/

                         conf.d/99-pulseaudio-default.conf, that

                         essentially directs alsa output to the pa

                         server.

                         In mscw, I want a quick check of output

                         volume and muted/unmuted status for a

                         particular card. It can be done using ‘pactl’

                         or ‘pacmd’, pa utilities, however, I wanted

                         to do it at the “alsa level”, with an alsa

                         utility…

                  # ⚓ New_front-page_on_cross-compiling⠀⇛

                         I am gradually working toward putting

                         information from blog posts onto the

                         easyos.org front page.

                  # ⚓ Mold_1.0.1_Released_As_Newest_Version_Of_This_High-

                    Speed_Linker_–_Phoronix⠀⇛

                         It was just this month that Mold 1.0

                         premiered as a very promising, high

                         performance linker alternative to GNU’s Gold

                         and LLVM’s LLD linkers. GCC 12 added support

                         for Mold this week and now for ending out the

                         year Mold 1.0.1 has been released.

                         Mold 1.0.1 is just a maintenance release but

                         given the young age of the project there are

                         a number of fixes as well as new features

                         squeezed in. Mold 1.0.1 now optionally

                         includes its own xxHash library for building

                         but can still use a system-wide xxHash

                         library if desired, support for the “–color-

                         diagnostics” option, the “–threads=” option

                         is now supported as an alias of its existing

                         “–thread-count=” option, and support for a

                         number of other options.

* § Leftovers⠀➾

      o ⚓ Strategies_To_Make_2022_Better:_Embrace_the_Folks_Around_Us⠀⇛

             So, 2021 was no 2020, even if it borrowed many of the

             same contours of that wretched year. But it was still the

             calendar equivalent of me walking down the street after I

             rolled my ankle, pretending that everything is OK, even

             though my ankle was telling me otherwise. (I often wince

             when reading descriptions of people rolling their ankles,

             so if that describes you, I apologize in advance.) Many

             folks got vaccinated this year. Some even got boosters.

             But COVID-19 remains an extremely dynamic part of the way

             that we live and experience the world. But even if

             optimism was in short supply (and less so after learning

             that as I was posting this, Betty White died just three

             weeks before her 100th birthday), tedium was in ample

             supply. And with that, let’s do another one of these

             year-end issues (the eighth one!) where we try to look

             forward and back all at once.

      o § Hardware⠀➾

            # ⚓ Cheetah_RAID_Prowler_Addresses_Rugged_Edge_Computing⠀⇛

      o § Integrity/Availability⠀➾

            # § Proprietary⠀➾

                  # § Security⠀➾

                        # ⚓ Security_updates_for_Friday_[LWN.net]⠀⇛

                               Security updates have been issued by

                               Debian (agg, aria2, fort-validator, and

                               lxml), Fedora (libgda, pgbouncer, and

                               xorg-x11-server-Xwayland), Mageia

                               (calibre, e2guardian, eclipse, libtpms/

                               swtpm, nodejs, python-lxml, and

                               toxcore), openSUSE (c-toxcore, gegl,

                               getdata, kernel-firmware, log4j,

                               postrsd, and privoxy), and SUSE (gegl).

                        # ⚓ Reproducible_Builds_(diffoscope):_diffoscope

                          198_released⠀⇛

                               The diffoscope maintainers are pleased

                               to announce the release of diffoscope

                               version 198. This version includes the

                               following changes:

                               [ Chris Lamb ]

                               * Support showing "Ordering differences

                               only" within .dsc field values.

                                 (Closes: #1002002, reproducible-

                               builds/diffoscope#297)

                               * Support OCaml versions 4.11, 4.12 and

                               4.13. (Closes: #1002678)

                               * Add support for XMLb files. (Closes:

                               reproducible-builds/diffoscope#295)

                               * Also add, for example, /usr/lib/

                               x86_64-linux-gnu to our internal PATH.

                               [ Mattia Rizzolo ]

                               * Also recognize "GnuCash file" files

                               as XML.

⚓ This_Week_In_Security:_The_Log4j_That_Won’t_Go_Away,_WebOS,And_More|

Hackaday⠀⇛

 In the past two weeks, Log4j has continued to drive security news,

 with more vulnerable platforms being found, and additional CVEs

 coming out. First up is work done by TrendMicro, looking at electric

 vehicles and chargers. They found a log4j attack in one of the

 published charger frameworks, and also managed to observe evidence of

 vulnerability in the Tesla In-Vehicle Infotainment system. It isn’t a

 stretch to imagine a piece of malware that could run on both a

 charger, and an EV. And since those systems talk to each other, they

 could spread the virus through cars moving from charger to charger.

 Log4j is now up to 2.17.1, as there is yet another RCE to fix, CVE-

 2021-44832. This one is only scored a 6.6 on the CVSS scale, as

 opposed to the original, which weighed in at a 10. 44832 requires the

 attacker to first exert control over the Log4j configuration, making

 exploitation much more difficult. This string of follow-on

 vulnerabilities demonstrates a well-known pattern, where a high

 profile vulnerability attracts the attention of researchers, who find

 other problems in the same code.

 There are now reports of Log4j being used in Conti ransomware

 campaigns. Additionally, a Marai-based worm has been observed. This

 self-propagating attack seems to be targeting Tomcat servers, among

 others.

§ Privacy/Surveillance⠀➾

* ⚓ Apple_AirTags_Are_Being_Used_to_Track_People_and_Cars⠀⇛

* ⚓ Are_Apple_AirTags_Being_Used_to_Track_People_and_Steal_Cars?⠀⇛

       On a Sunday night in September, Ashley Estrada was at a

       friend’s home in Los Angeles when she received a strange

       notification on her iPhone: “AirTag Detected Near You.”

       An AirTag is a 1.26-inch disc with location-tracking

       capabilities that Apple started selling earlier this year as a

       way “to keep track of your stuff.” Ms. Estrada, 24, didn’t own

       one, nor did the friends she was with. The notification on her

       phone said the AirTag had first been spotted with her four

       hours earlier. A map of the AirTag’s history showed the zigzag

       path Ms. Estrada had driven across the city while running

       errands.

       [...]

       The New York Times spoke with seven women who believe they were

       tracked with AirTags, including a 17-year-old whose mother

       surreptitiously placed one on her car to stay apprised of her

       whereabouts.

       Some authorities have begun to take a closer look at the threat

       posed by AirTags. The West Seneca Police Department in New York

       recently warned its community of the tracking potential of the

       devices after an AirTag was found on a car bumper. Apple

       complied with a subpoena for information about the AirTag in

       the case, which may lead to charges, West Seneca police said.

       And in Canada, a local police department said that it had

       investigated five incidents of thieves placing AirTags on

       “high-end vehicles so they can later locate and steal them.”

       Researchers now believe AirTags, which are equipped with

       Bluetooth technology, could be revealing a more widespread

       problem of tech-enabled tracking. They emit a digital signal

       that can be detected by devices running Apple’s mobile

       operating system. Those devices then report where an AirTag has

       last been seen. Unlike similar tracking products from

       competitors such as Tile, Apple added features to prevent

       abuse, including notifications like the one Ms. Estrada

       received and automatic beeping. (Tile plans to release a

       feature to prevent the tracking of people next year, a

       spokeswoman for that company said.)

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