𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, September 10, 2022
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Generated Sun 11 Sep 02:44:09 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
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Gemini index for the day: gemini://gemini.techrights.org/2022/09/10/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ On the World Wide Web, 25 Years is an Eternity | Techrights

⦿ [Meme] Time to Take Away the EPO’s Diplomatic Immunity | Techrights

⦿ Never Let Courts Be Controlled by Those Who Ignore Court Rulings (European Patent Office, European Patent Organisation, or EPO) | Techrights

⦿ IRC Proceedings: Friday, September 09, 2022 | Techrights

⦿ [Meme] Mozilla Does Not Trust Web Sites, But It Trusts the CIA Enough to Hire Managers From It | Techrights

⦿ [Meme] We’re Back to Medieval Times: The Case of EPO | Techrights

⦿ Mozilla Hired Top-Level Managers Directly From the Central Intelligence Agency (CIA), Can They Be Trusted on Privacy? | Techrights

⦿ Mozilla’s Strategy: More Lawyers and Spam, Not More Engineers | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/09/10/25-for-techdirt/#comments
		http://techrights.org/2022/09/10/diplomatic-immunity-a-mistake/#comments
		http://techrights.org/2022/09/10/ignoring-court-rulings/#comments
		http://techrights.org/2022/09/10/irc-log-090922/#comments
		http://techrights.org/2022/09/10/man-in-the-mozilla/#comments
		http://techrights.org/2022/09/10/medieval-epo/#comments
		http://techrights.org/2022/09/10/mozilla-three-letter-agencies/#comments
		http://techrights.org/2022/09/10/moz-pr-spam/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/09/10/keepass2-2-52-released/#comments
		http://techrights.org/2022/09/10/tor-browser-12-0a2/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 69

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/10/25-for-techdirt/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/10/25-for-techdirt/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ On_the_World_Wide_Web,_25_Years_is_an_Eternity⠀✐


Posted in Site_News at 8:30 pm by Dr. Roy Schestowitz


I only built my first site in 1997/1998 (Geocities); some had already made much
bigger things


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Last_Chance_To_Join_Us_For_The_Techdirt_25th_Anniversary
                                   Party!⦈_


Summary: TechDirt turns 25 and we too expect to reach 25 (we’ve future-proofed
everything)


Governing a country (or “commonwealth”) as a “monarch” for over 70 years is a
lot, today it’s_9/11, but one milestone you likely did not hear of is TechDirt
turning_25. Earlier this year my personal site turned 20, Tux Machines turned
18 (to be clear, I’m not that site’s founder!), and this site, Techrights,
turns 16 in about 8 weeks from now. The site is as active as ever and it
produces code like never before (thousands of lines of code per month in some
months).


“I’m rather certain this site too will turn 25, even if the World Wide Web
isn’t its primary protocol anymore. We’re constantly adapting.”We’re not joking
or provoking when we say that the future of the World Wide Web isn’t bright.
There are several factors contributing to this demise and many data points
proving the demise.


Thankfully, as far as Techrights is concerned, we’re no longer dependent on the
World Wide Web. While working on the new Tux Machines we’ve made a Content
Management System (CMS) that treats Gemini like a first-class citizen, not
merely a by-product. Later this year we’ll deploy the same here, whereupon this
site will be “natively” more than just the World Wide Web. In recent months
we’ve been busy behind the scenes (the back end) working to make this a
reality.


I’m rather certain this site too will turn 25, even if the World Wide Web isn’t
its primary protocol anymore. We’re constantly adapting.


Happy birthday to TechDirt and long live activism/citizen journalism online. We
recently passed 34,500 blog posts (now 34,513) and we expect 50,000 one day,
even if WordPress is trying_to_herd_people_into_bloatware with a universal_back
door (we’ll probably have a new CMS in place by the end of the year). As a
matter of full disclosure (on the record), my health is OK, we have additional
people capable of running Techrights, and financially we’re secure for at least
a decade. █


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣷⣷⣿⣾⣷⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣼⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 162

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/10/diplomatic-immunity-a-mistake/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/10/diplomatic-immunity-a-mistake/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Time_to_Take_Away_the_EPO’s_Diplomatic_Immunity⠀✐


Posted in Europe, Patents at 10:11 am by Dr. Roy Schestowitz


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


Summary: It was a huge mistake to give the EPO any immunity; instead of
upholding the law the EPO breaks the law, and moreover it violates conventions
and constitutions with impunity


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

                    ䷩ 𝚕𝚒𝚗𝚎 1198

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/10/ignoring-court-rulings/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/10/ignoring-court-rulings/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Never_Let_Courts_Be_Controlled_by_Those_Who_Ignore_Court_Rulings_(European
Patent_Office,_European_Patent_Organisation,_or_EPO)⠀✐


Posted in Europe, Patents at 9:58 am by Dr. Roy Schestowitz


Video_download_link | md5sum cb73d03748fcbc6b5bb0843f0317e373
EPO Laughing at the Courts
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-ignores-judges-from-iloat.webm


Summary: Not only is Europe’s second-largest institution exceedingly corrupt;
when taken to court it refuses to obey rulings against it and at the same time
it_calls_monarchs_"role_models"; to make matters yet worse, the EPO tries to
replace_courts_that_are_answerable_to_the_population with kangaroo courts
answerable to corrupt EPO management


THE truly absurd EPO is still trying to replace patent courts with a bunch of
kangaroo courts while shamelessly ignoring the rulings (against EPO) regarding
unlawful actions from Benoît_Battistelli. Battistelli’s friend António_Campinos
not only refuses to execute the latest judgement; he also keeps lying about it!


That the EPO is run by a bunch of criminals is hardly news, but the following
letter is new:


     European Patent Office | 80298 MUNICH | GERMANY


     Mr António Campinos
     President of the EPO


     By email


     OPEN LETTER


     Reference: sc22117cl
     Date: 06.09.2022


     Execution of ILOAT Judgment No. 4551 (mass emails)


     Dear Mr President,


     In a letter of 29 July 2022, the CSC demanded the immediate execution
     of Judgment No. 4551 issued on 6 July 2022 and reinstating the former
     rules on mass emails in force prior to 31 May 2013.


     To this day, this letter remains unanswered and Staff Committees and
     their members still cannot send an email to more than 50 addresses.


     We note that mailing lists for sending mass emails to more than 50
     staff members, e.g. DDL-ALL-STAFF(-XX), already exist in the EPO
     standard email system. Such mailing lists can be easily selected from
     the available address book and inserted into the recipient field.
     However, when the sender is a Staff Committee or one of its members,
     sending of the email is technically blocked. The same applies upon
     inserting more than 50 individual addresses as recipient from the
     available address book.


     The above confirms that the EPO has not executed Judgment No. 4551
     two months after the ruling of the Tribunal.


     As already explained in the letter of 29 July 2022, we see no legal
     or technical requirements preventing the EPO from granting
     authorisation to Staff Committees and their members to use the EPO
     mailing lists. In fact, granting authorisation is technically a
     matter of seconds for the EPO internal IT services (BIT) and could
     have been easily done already immediately after the Judgment was
     issued.


     Therefore, we repeat the demand for the immediate execution of
     Judgment No. 4551 and no_later_than_30_September_2022.


     Yours sincerely,


     Thomas Czogalla
     Chairman LSC Berlin


     Jutta Haußer
     Deputy Chairwoman LSC Vienna


     Michael Kemény
     Chairman LSC Munich


     Jorge Raposo
     Chairman LSC The Hague


     Alain Dumont
     Chairman Central Staff Committee


I did a video about the prior_letter along with a bunch_of memes about this
non-presidential behaviour from Campinos, who insisted (in his own words): “I
am the f***ing president” (how do people who talk like this manage to make it
into positions of great power???)


Corruption prevails and thrives at today’s EPO while politicians simply look
the other way. As noted in the video above, the EPO is attempting to paint
itself_as_a_lover_or_art, a sympathetic_lover_of_life_(or_a_monarch,_which_it
calls_“a_public_service_role_model“). At the same time the EPO says “Unitary
Patent & UPC” (illegal & unconstitutional) “Coming this winter”, which is a
lie. We recently mentioned back_room_deal_with_monarchs. The EPO’s is Europe’s
pinnacle of corruption, intended to benefit and protect the rich (and their
lawyers). █



                    ䷩ 𝚕𝚒𝚗𝚎 1342

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/10/irc-log-090922/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/10/irc-log-090922/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_September_09,_2022⠀✐


Posted in IRC_Logs at 2:49 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-090922.gmi
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    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-090922.gmi
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Over HTTP:


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§ Bulletin for Yesterday⠀➾


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                    ䷩ 𝚕𝚒𝚗𝚎 1469

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/10/man-in-the-mozilla/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/10/man-in-the-mozilla/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Mozilla_Does_Not_Trust_Web_Sites,_But_It_Trusts_the_CIA_Enough_to_Hire
Managers_From_It⠀✐


Posted in Deception, Security at 1:27 pm by Dr. Roy Schestowitz


Related: Mozilla_Hired_Top-Level_Managers_Directly_From_the_Central
Intelligence_Agency_(CIA),_Can_They_Be_Trusted_on_Privacy?


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇This_site_signs_its_certificates?_Instead_of_outsourcing
           'trust'_to_Mozilla's_corporate_patrons_and_government?⦈_


Summary: Who do you trust more? Mozilla or yourself? Or the so-called ‘Linux’
Foundation, which outsourced Let’s Encrypt to Microsoft?


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⢿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠹⠇⠀⠛⢻⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣼⣤⣤⣾⣿⣼⣿⣤⣾⣤⣾⣤⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⡿⡿⢿⣿⢿⡿⢿⣿⠿⣿⣿⣿⣿⡿⠿⣿⠿⠿⢿⡿⠿⣿⠿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣤⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⣟⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣾⣾⣷⡷⣾⣿⣿⣿⣶⢷⣷⠿⣿⣾⡶⢿⣿⣷⢾⢶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣾⣿⣿⣷⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢛⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⢟⣿⣿⣻⠿⣛⣛⠿⣛⣿⣟⣻⣿⣛⡿⣟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣿⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⣷⣭⡇⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢹⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⡜⠿⣿⣶⡰⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣾⣿⡟⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣾⢹⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣧⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣹⣡⣬⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣍⣧⣧⣯⣹⣼⣜⣉⣍⣩⣼⣭⣮⣟⣛⣯⣤⣯⣿⣷⣽⣿⣽⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣽⢻⣭⣭⣽⡟⣻⣭⣭⣟⣿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡙⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣽⡿⣛⣭⣭⣟⢿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡇⣸⣿⣿⣧⣾⣽⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠿⣿⣮⢻⣿⢸⣿⡇⣉⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢈⣉⡃⣿⣿⢹⣿⢻⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⡇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⡿⢸⣿⣧⣬⢸⣿⡇⣿⣿⢹⢸⣿⣿⡇⣿⣿⢸⣿⡇⣷⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣬⡏⣿⣧⣼⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣵⣿⣮⣭⣭⣽⣿⣿⣷⣭⣭⣭⣷⣮⣭⣭⣭⣬⣭⣵⣭⣭⣿⣮⣭⣿⣷⣭⣭⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣿⣯⣭⣽⣿⣯⣭⣭⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠹⠇⠀⠛⢻⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣼⣤⣤⣾⣿⣼⣿⣤⣾⣤⣾⣤⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⡿⡿⢿⣿⢿⡿⢿⣿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⢿⡿⠿⣿⠿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢛⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣾⣾⣷⡷⣾⣾⣿⣿⣶⢷⣷⠿⣿⣾⡶⢿⣿⣷⢾⢶⢶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣿⣿⣿⣷⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢛⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⢟⣿⣿⣻⠿⣛⣛⠿⣛⣿⣟⣻⣿⣛⡿⣟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣿⢸⣿⡏⠿⠷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⣷⣭⡇⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⡜⠿⣿⣶⡰⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣾⣿⡟⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣾⢹⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣇⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣹⣡⣬⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣍⣧⣧⣯⣹⣼⣜⣉⣍⣩⣼⣭⣮⣟⣛⣯⣤⣯⣯⣷⣽⣿⣽⣿⣾⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢻⣭⣭⣽⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡛⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣽⡿⣛⣭⣭⣟⢿⢿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡇⣸⣿⣿⣧⣾⣽⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠿⣿⣮⣻⣿⢸⣿⡇⣉⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢈⣉⡃⣿⣿⢹⣿⢻⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⠛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⡇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⡿⢸⣿⣧⣬⢸⣿⡇⣿⣿⣸⢸⣿⣿⡇⣿⣿⢸⣿⡇⣷⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣬⡏⣿⣧⣼⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣮⣭⣭⣽⣿⣿⣷⣭⣭⣭⣷⣮⣭⣭⣭⣬⣭⣥⣭⣭⣿⣮⣭⣿⣷⣭⣭⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣿⣯⣭⣽⣿⣯⣭⣭⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⢿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠹⠇⠀⠛⢻⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣼⣤⣤⣾⣷⣼⣿⣤⣾⣤⣾⣦⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⡿⣿⢿⣿⢿⡿⢿⣿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⡿⠿⣿⠿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣦⣤⣶⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢟⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⢽⡶⢿⢶⣶⣾⣾⣷⡷⣾⣿⣿⣿⣶⢷⣷⠿⣿⣾⡶⢿⣿⣷⣾⢶⢶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣾⣿⣿⣷⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⣟⣿⣿⣻⠿⣛⣛⠿⣛⣿⣟⡻⣿⣛⡿⣟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣿⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣭⡇⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡰⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣾⣿⡟⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣾⢹⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣇⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣻⣡⣬⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣍⣧⣧⣯⣹⣼⣜⣉⣉⣩⣼⣭⣬⣟⣛⣯⣤⣯⣯⣷⣽⣿⣽⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢻⣭⣭⣽⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡙⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣽⡿⣛⣭⣭⣟⢿⢿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡏⣸⣿⣿⣧⣮⣽⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠿⣿⣦⣻⣿⢸⣿⡇⣉⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢈⣉⡃⣿⣿⢹⣿⢻⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⡇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⣿⢸⣿⣧⣬⢸⣿⡇⣿⣿⣹⢸⣿⣿⡇⣿⣿⢸⣿⡇⣷⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣟⣿⣿⣬⡏⣿⣧⣼⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣮⣭⣭⣽⣿⣿⣷⣭⣭⣭⣷⣮⣭⣭⣭⣬⣭⣵⣭⣭⣿⣮⣭⣽⣷⣭⣭⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣽⣿⣭⣵⣿⣯⣭⣭⣷⣾⣭⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠹⠇⠀⠛⢻⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣼⣤⣤⣾⣯⣼⣿⣤⣾⣤⣾⣦⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⡿⡿⢿⣿⢿⡿⢿⣿⠿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⡿⠿⣿⡿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣦⣦⣤⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢟⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣾⣾⣷⡷⣶⣿⣿⣿⣶⢷⣷⠿⣿⣾⡶⢿⣿⣷⣾⢶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣾⣿⣿⣷⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢛⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⢟⣿⣿⣻⠿⣛⣛⠿⣛⣿⣟⡻⣿⣛⡿⣟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣿⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣭⡇⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡴⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣶⣿⠝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣾⢹⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣧⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣹⣡⣬⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣉⣧⣧⣯⣩⣼⣜⣉⣉⣩⣼⣭⣬⣟⣛⣯⣤⣯⣯⣷⣿⣿⣽⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢻⣭⣭⣭⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡙⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣽⡿⣛⣭⣭⣟⢿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡏⣸⣿⣿⣧⣮⣹⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠿⣿⣾⣻⣿⢸⣿⡇⣉⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢈⣉⡃⣿⣿⢹⣿⢻⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⡿⢸⣿⣧⣬⢸⣿⡇⣿⣿⣹⢸⣿⣿⡇⣿⣿⢸⣿⡇⣷⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣏⣿⣿⣬⡍⣿⣧⣼⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣮⣭⣭⣽⣿⣿⣷⣭⣭⣭⣷⣮⣭⣭⣭⣬⣭⣵⣭⣭⣿⣮⣭⣽⣷⣭⣭⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣽⣿⣭⣵⣿⣯⣭⣭⣵⣾⣭⣭⣽⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⢿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠹⠇⠀⠛⢻⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣼⣤⣤⣾⣿⣼⣿⣤⣾⣤⣾⣦⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⡿⣿⢿⣿⢿⡿⢿⣿⠿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⡿⠿⣿⡿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣦⣴⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢛⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣾⣾⣷⡷⣶⣾⣿⣿⣶⢷⣷⠿⣿⣾⠶⢿⣿⣷⣾⢶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⢟⣿⣿⣻⠿⣛⣛⠿⣛⣿⣟⡻⣿⣛⡿⣟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣿⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣭⡇⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡲⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣶⣿⠝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣾⢹⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣇⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣿⣥⣬⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣉⣧⣧⣯⣹⣼⣜⣉⣉⣩⣼⣭⣬⣟⣛⣯⣤⣯⣯⣷⣿⣿⣽⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢻⣭⣭⣭⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡛⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣽⡿⣛⣭⣭⣟⢿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠭⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡏⣸⣿⣿⣧⣮⣹⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠻⣿⣮⣻⣿⢸⣿⡇⣋⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢘⣉⡃⣿⣿⢹⣿⢻⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⣿⢸⣿⣧⣬⢸⣿⡇⣿⣿⢸⢸⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣏⣿⣿⣬⡍⣿⣧⣸⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣾⣭⣭⣵⣿⣿⣷⣭⣭⣭⣷⣮⣭⣭⣭⣬⣭⣥⣭⣭⣿⣮⣭⣿⣷⣭⣽⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣽⣿⣭⣵⣿⣯⣭⣭⣵⣾⣭⣭⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⢿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠹⠇⠀⠛⢹⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣼⣤⣤⣾⣯⣼⣿⣤⣾⣤⣾⣦⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⡿⣿⢿⣿⢿⡿⢿⣿⠿⣿⣿⢿⢿⡿⠿⣿⠿⠿⣿⡿⠿⣿⡿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣶⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢛⠻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣶⣾⣷⡷⣶⣿⣿⣿⣶⢷⣷⠿⣿⣾⡶⢿⣿⣷⣾⢶⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⢟⣿⣿⣻⠿⣛⣛⠿⣛⣿⣟⣻⣿⣛⡿⣟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣿⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣭⡇⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡲⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣶⣿⡝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣾⢹⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣧⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣻⣥⣬⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣍⣧⣧⣯⣹⣼⣜⣉⣉⣩⣼⣭⣬⣟⣛⣯⣤⣯⣿⣿⣿⣿⣽⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢻⣭⣭⣽⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡙⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣽⡿⣛⣭⣭⣟⢿⢿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡏⣸⣿⣿⣧⣾⣹⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠿⣿⣾⣻⣿⢸⣿⡇⣋⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢈⣉⡃⣿⣿⢹⣿⢻⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⣿⢸⣿⣧⣬⢸⣿⡇⣿⣿⢸⢸⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣏⣿⣿⣬⡍⣿⣧⣸⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣾⣭⣭⣵⣿⣿⣷⣭⣭⣭⣷⣮⣭⣭⣭⣬⣭⣵⣭⣭⣿⣮⣭⣽⣷⣭⣭⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣽⣿⣭⣵⣿⣯⣭⣭⣵⣾⣭⣭⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠹⠇⠀⠛⢹⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣴⣤⣤⣾⣿⣼⣿⣤⣼⣤⣾⣤⣧⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⡿⡿⢿⡿⢿⡿⢿⣿⠿⣿⣿⢿⢿⡿⠿⣿⠿⠿⣿⡿⠿⣿⡿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣦⣦⣶⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢛⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣶⣾⣷⡷⣶⣾⣿⣿⣶⢷⣷⠿⣿⣾⡶⢿⣿⣷⣾⢶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣿⣿⣿⣷⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⣟⣿⣿⣻⠿⣛⣛⠿⣛⣿⣟⡻⣟⣛⡿⣟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣿⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣭⡇⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡶⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣶⣿⡝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣶⢹⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣧⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣿⣥⣮⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣉⣧⣧⣯⣩⣼⣜⣉⣉⣩⣼⣭⣬⣟⣛⣯⣤⣯⣯⣴⣽⣿⣽⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢫⣭⣭⣭⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡛⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣽⠿⣛⣭⣭⣟⢿⢿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠭⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡏⣸⣿⣿⣧⣮⣹⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠿⣿⣾⣻⣿⢸⣿⡇⣋⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢈⣉⡃⣿⣿⢹⣿⢻⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⡿⢸⣿⣧⣬⢸⣿⡇⣿⣿⢹⢸⣿⣿⡇⣿⣿⢸⣿⡇⣷⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⡟⣿⣿⣬⡏⣿⣇⣸⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣾⣭⣭⣽⣿⣿⣷⣯⣭⣭⣷⣮⣭⣭⣭⣬⣭⣵⣭⣭⣿⣮⣭⣿⣷⣭⣽⣮⣭⣵⣿⣯⣭⣿⣾⣭⣭⣵⣮⣭⣵⣮⣭⣽⣿⣭⣽⣿⣯⣭⣭⣷⣾⣭⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠹⠇⠀⠛⢺⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣴⣤⣤⣼⣷⣼⣿⣤⣾⣤⣬⣤⣥⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⠿⡿⢿⣿⢿⡿⢿⡿⠿⣿⡿⢿⢿⡿⠿⡿⠿⠿⣿⡿⠿⣿⣿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣶⣶⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢟⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣾⣾⢷⡷⣾⣿⣿⣿⣷⢿⣷⠿⣿⣿⡷⢿⣿⣷⢾⢶⢶⣷⣶⣾⣶⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣾⣿⣷⣾⣿⣿⣷⣷⣶⣾⣾⣿⣾⣿⣷⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣛⣿⣿⢟⣿⣿⣻⡿⣛⣛⠿⣛⣿⣟⡻⣟⣛⡻⢟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣯⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣥⡅⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡴⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣶⣿⠝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣶⢸⣿⣿⣿⣿⢨⡻⢿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣇⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣻⣥⣮⣝⣛⣯⣭⣯⣥⣍⣛⣛⣥⣼⣉⣧⣧⣯⣽⣼⣜⣉⣉⣩⣼⣭⣬⣟⣛⣯⣤⣯⣯⣵⣽⣿⣭⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢫⣭⣭⣭⡟⣻⣭⣭⣟⣿⣿⡿⣫⣭⣭⡛⢫⣭⣭⣭⢩⣭⣭⣭⡙⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣭⠿⣛⣭⣭⣝⢿⢿⣯⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⢿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡇⣸⣿⣿⣧⣮⣹⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠿⣿⣾⣻⣿⢸⣿⡇⣋⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢘⣉⡃⣿⣿⢹⣿⢹⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⡿⢸⣿⣧⣬⢸⣿⡇⣿⣿⣸⢸⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣬⡏⣿⣧⣸⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣾⣭⣭⣽⣿⣿⣷⣯⣭⣭⣷⣮⣭⣭⣭⣬⣭⣥⣭⣭⣿⣮⣭⣿⣷⣭⣽⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣾⣭⣵⣮⣭⣽⣿⣭⣿⣿⣯⣭⣭⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⢿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠹⠇⠀⠛⢻⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣴⣤⣤⣼⣿⣼⣿⣤⣾⣤⣬⣤⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠿⡿⠿⠿⠛⡿⠟⠿⡿⢿⣿⢿⠿⢿⡿⠿⣿⣿⢿⢿⡿⠿⡿⠿⠿⣿⡿⠿⣿⣿⣿⡿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣦⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢛⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣾⣾⢷⡷⢾⣿⣿⣿⣷⢿⣷⠿⣿⣿⡷⢿⣿⣷⢾⢶⢶⣷⣶⣾⣶⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣾⣿⣷⣾⣿⣿⣿⣷⣶⣾⣾⣿⣾⣿⣷⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣛⣿⣿⢟⣿⣿⣻⡿⣛⣛⠿⣛⣿⣟⡿⣟⣛⡻⢟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠇⣯⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣥⡅⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡰⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣶⣷⠝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣶⢸⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣇⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣿⣥⣮⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣉⣧⣧⣯⣹⣼⣜⣉⣉⣩⣼⣭⣬⣟⣛⣯⣤⣯⣯⣴⣽⣿⣭⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣯⣭⢫⣭⣭⣭⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡙⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣭⠿⣛⣭⣭⣟⢿⢿⣯⣽⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡇⣸⣿⣿⣧⣮⣹⣿⣏⣥⣿⣿⠩⡵⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⠝⠿⣿⣾⣻⣿⢸⣿⡇⣋⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢘⣉⡃⣿⣿⢹⣿⢹⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⣿⢸⣿⣧⣬⢸⣿⡇⣿⣿⣹⢸⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣬⡏⣿⣧⣼⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣾⣭⣭⣽⣿⣿⣷⣯⣭⣭⣷⣮⣭⣭⣭⣬⣭⣥⣭⣭⣿⣮⣭⣽⣷⣭⣽⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣿⣿⣭⣿⣿⣯⣭⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠹⠇⠀⠛⢻⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣴⣤⣤⣼⣿⣼⣿⣤⣾⣤⣬⣤⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⠿⡿⢿⣿⢿⡿⢿⣿⠿⣿⣿⢿⢿⡿⠿⣿⠿⠿⣿⡿⠿⣿⣿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣦⣦⣴⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢛⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣾⣾⢷⡷⢾⣿⣿⣿⣷⢿⣷⠿⣿⣿⡷⢿⣿⣷⢾⢶⢶⣷⣶⣾⣶⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣾⣿⣷⣿⣿⣿⣿⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣛⣿⣿⢟⣿⣿⣻⡿⣛⣛⠿⣛⣿⣟⡻⣟⣛⡻⢟⣻⠿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣯⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣥⡅⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡰⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣶⣿⠝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣶⢸⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣇⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣿⣥⣮⣝⣛⣯⣬⣯⣥⣍⣛⣛⣥⣼⣉⣧⣧⣯⣹⣼⣜⣉⣍⣩⣼⣭⣬⣟⣛⣯⣤⣯⣯⣴⣽⣿⣭⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢫⣭⣭⣭⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡙⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣭⠿⣛⣭⣭⣟⢿⢿⣯⣽⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡇⣸⣿⣿⣧⣮⣹⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣷⡝⠿⣿⣾⣻⣿⢸⣿⡇⣋⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢘⣉⡃⣿⣿⢹⣿⢹⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣯⣸⣿⢿⣿⣸⣿⣇⣿⡿⢸⣿⣧⣬⢸⣿⡇⣿⣿⣸⢸⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣬⡏⣿⣧⣼⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣾⣭⣭⣽⣿⣿⣷⣯⣭⣭⣷⣮⣭⣭⣭⣬⣭⣥⣭⣭⣿⣮⣭⣽⣷⣭⣽⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣿⣿⣭⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⢿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠹⠇⠀⠛⢹⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣴⣴⣤⣤⣾⣿⣼⣿⣤⣼⣤⣼⣤⣥⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⡿⡿⢿⣿⢿⠿⢿⣿⠿⣿⣿⢿⢿⡿⠿⣿⠿⠿⣿⡿⠿⣿⡿⢿⠿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣦⣦⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢛⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢷⣶⣾⣾⣷⡷⣾⣾⣿⣿⣷⢷⣷⠿⣿⣾⡶⢿⣿⣷⢾⢶⣶⣷⣶⣾⣶⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⣾⣾⣿⣾⣿⣷⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⢟⣿⣿⣻⡿⣛⣛⠿⣛⣿⣟⡻⣟⣛⡻⢟⣻⢿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣯⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢷⣥⡅⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡰⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣾⣿⠝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣶⢸⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣇⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣻⣥⣮⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣉⣧⣧⣯⣩⣼⣜⣉⣍⣩⣼⣭⣬⣟⣛⣯⣤⣯⣯⣴⣽⣿⣽⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢫⣭⣭⣭⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡛⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣭⠿⣛⣭⣭⣟⢿⢿⣭⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠭⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡏⣸⣿⣿⣧⣮⣹⣿⡏⣥⣿⣿⠩⡵⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⡝⠿⣿⣦⣻⣿⢸⣿⡇⣋⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢘⣉⡃⣿⣿⢹⣿⢹⣿⣿⡿⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⡿⢸⣿⣧⣬⢸⣿⡇⣿⣿⣸⢸⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣬⡏⣿⣇⣼⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣾⣭⣭⣵⣿⣿⣷⣯⣭⣭⣷⣮⣭⣭⣭⣬⣭⣥⣭⣭⣿⣮⣭⣿⣷⣭⣽⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣿⣿⣭⣽⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕⠹⠇⠀⠛⢻⣿⣧⣧⣤⣤⣧⣧⣤⣤⣤⣤⣤⣴⣤⣤⣾⣿⣼⣿⣤⣼⣤⣬⣤⣥⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡿⠿⠟⠿⠿⡿⠿⠿⠛⡿⠟⠿⡿⢿⣿⠿⠿⢿⣿⠿⣿⣿⢿⢿⡿⠿⣿⠿⠿⣿⡿⠿⣿⣿⢿⡿⢿⡿⢿⠿⣿⠿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣴⣾⣿⣟⠛⠟⠛⠛⢛⡟⢛⢛⡻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣷⢶⢷⡿⢶⠷⣾⢵⡦⢿⣽⡶⢿⢶⣶⣶⣾⢷⡷⢶⣾⣿⣿⣶⢷⣷⠿⣿⣾⡶⢿⣿⣷⢾⢶⣶⣷⣶⣾⣶⣿⣿⣿⣿⣿⣷⣷⣾⣾⣵⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣾⣧⣶⣾⣾⣾⣿⣾⣶⣶⣾⣶⣾⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣾⣾⣿⣾⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠙⢛⠿⠉⠛⠛⠋⢻⢻⠫⡛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢛⣛⡛⣛⣛⢟⣛⡻⢟⣻⣿⣛⢿⣿⡿⣛⣿⣟⡻⢟⣛⡛⣛⣛⣛⣛⢛⣛⣛⣻⣿⣿⢟⣿⣿⣻⡿⣛⣛⠿⣛⣿⣟⡻⣟⣛⡻⢟⣻⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⢛⢸⣿⡇⣿⣿⢸⣿⡇⣾⣿⠹⠿⠧⣯⢸⣿⡏⠿⢷⢸⣿⡇⡛⣿⣿⠛⢸⣿⡟⢳⣥⡅⣿⣿⠹⢿⡄⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⢸⣿⢸⣿⡏⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡿⣿⣿⢸⣿⡇⠜⠿⣿⣶⡰⣾⣮⠻⢿⣷⣌⢸⣿⡇⡆⣿⣿⢸⢸⣿⡿⢷⣶⣷⠝⢿⣿⣮⡃⣿⣿⢸⣿⣧⣶⣶⢸⣿⣿⣿⣿⢨⡻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⣿⢸⣿⡇⢿⣿⣸⣿⡇⣹⡹⣿⣇⣿⣿⢸⣿⡇⡃⣿⣿⢘⢸⣿⣇⣭⢋⡁⣿⣿⣸⣿⡇⣿⣿⢸⣿⣇⣿⣿⢸⣿⡟⣿⣿⢸⣿⣇⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣧⣿⣿⣬⣿⣥⣮⣝⣛⣫⣬⣯⣥⣍⣛⣛⣥⣼⣉⣧⣧⣯⣹⣼⣜⣉⣍⣩⣼⣭⣮⣟⣛⣫⣤⣯⣯⣵⣽⣿⣭⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣯⣭⢫⣭⣭⣭⡟⣻⣭⣭⣟⢿⣿⡿⣫⣭⣭⡙⢫⣭⣭⣭⢩⣭⣭⣭⡛⣭⣭⣭⣭⡟⣭⣽⢻⣭⣭⣽⣯⣭⠿⣛⣭⣭⣝⢿⢿⣭⣽⡿⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢨⢹⣿⡏⡅⣿⣯⡹⠿⣼⣿⢸⣿⡇⣿⣿⢸⣿⡏⠩⢸⣿⡏⣿⣷⣩⢹⣿⣏⡅⣿⣿⢸⣿⡏⠍⣿⣿⠀⣿⣿⢸⣿⡇⣸⣿⣿⣧⣮⣹⣿⡏⣥⣿⣿⠩⡷⣿⣏⡿⣿⣴⡿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣿⠝⠿⣿⣮⣻⣿⢸⣿⡇⣉⣉⢸⣿⡿⠿⢸⣿⡟⣿⣅⣿⢸⣿⣿⡇⣿⣿⢸⣿⡿⠇⣿⣿⠀⣿⣿⢘⣉⡃⣿⣿⢹⣿⢹⣿⣿⡇⣿⣿⣿⢿⣷⡟⠿⣿⣾⡛⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡇⣇⣿⣧⣸⣿⢿⣿⣸⣿⣇⣿⡿⢸⣿⣧⣬⢸⣿⡇⣿⣿⢸⢸⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⣿⣿⣸⣿⢇⣿⡿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣬⡏⣿⣧⣼⣿⠇⣭⡥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣭⣾⣮⣭⣽⣿⣾⣭⣭⣵⣿⣿⣷⣭⣭⣭⣷⣮⣭⣭⣭⣬⣭⣥⣭⣭⣿⣮⣭⣽⣷⣭⣽⣮⣭⣵⣿⣯⣭⣿⣮⣭⣭⣵⣮⣭⣵⣮⣭⣽⣿⣭⣿⣿⣯⣭⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⠿⠯⠁⠉⠀⠉⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠶⠇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣶⠷⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢛⡏⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣷⣄⡀⢁⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡀⠀⠀⠀⠀⠀⠂⠸⠛⢛⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣟⣷⡄⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢿⣿⣿⠀⠀⠀⢠⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠈⢴⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⢀⡀⣀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⣿⣾⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢻⣿⣿⣿⣿⣿⠁⠈⣿⡙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡦⠀⠹⣿⣷⣄⣂⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄⣠⣿⣿⣷⣿⣿⣿⣿⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⡀⣀⣀⢀⣀⡀⢀⣠⣤⣀⠀⠀⠀⣠⣤⣄⡀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣿⣟⣿⣿⣿⡿⣟⣙⠻⣋⣽⣅⡘⢋⣀⡀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⠛⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⡇⠀⢸⣿⣏⣿⣿⢸⣿⡇⠛⣿⣿⠛⢻⣿⡟⠻⢿⡏⣿⣿⣿⣿⡆⣿⣿⢸⣿⡏⣿⣿⢸⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⣿⣿⢸⣿⡇⠙⢿⣿⣶⡄⠀⠈⠻⣿⣷⣆⢸⣿⡇⠀⣿⣿⠀⢸⣿⣿⡿⠀⠀⠛⢿⣿⣦⡀⣿⣿⢸⣿⣷⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣸⣿⡇⠀⢸⣿⣇⣿⣿⢸⣿⡇⠀⣿⣿⠀⢸⣿⣧⣤⠀⠀⣿⣿⣹⣿⡇⣿⣿⣸⣿⣇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠘⠛⠃⠛⠛⠘⠛⠃⠈⠛⠛⠋⠁⠀⠀⠙⠛⠛⠁⠘⠛⠃⠀⠛⠛⠀⠘⠛⠛⠛⠀⠀⠈⠛⠛⠋⠀⠛⠛⠉⢿⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣤⢠⣤⣤⣤⡤⣠⣤⣤⣄⠀⠀⢀⣤⣤⣤⣀⢠⣤⣤⣤⢠⣤⣤⣤⡀⣤⣤⣤⣤⡄⣤⣤⢠⣤⣤⣤⣤⣤⡄⣠⣤⣤⣄⠀⢠⣤⣬⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠈⢹⣿⡏⠱⣿⣿⡻⠿⠀⠀⢸⣿⡏⣿⣿⢸⣿⡏⠉⢸⣿⡏⣿⣿⠉⢹⣿⡏⠁⣿⣿⢸⣿⡏⠉⣿⣿⣇⣿⣿⢹⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⢧⣙⣿⣿⣶⡀⠀⢸⣿⡇⣉⣉⢸⣿⡿⠿⢸⣿⡿⣿⣧⠀⢸⣿⡇⠀⣿⣿⢸⣿⡿⠇⣿⣿⣿⣿⣿⢈⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⡀⣿⣿⣼⣿⠇⠀⢸⣿⣇⣿⣿⢸⣿⣧⣤⢸⣿⡇⣿⣿⠀⢸⣿⡇⠀⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⣼⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⢀⣈⣩⣥⣶⣬⣟⡛⠉⠀⠀⠀⠉⠛⠋⠁⠈⠉⠉⠉⠈⠉⠁⠉⠉⠀⠈⠉⠁⠀⠉⠉⠈⠉⠁⠀⠉⠉⠁⠈⠙⠛⠉⠈⠉⠁⠈⠉⠹⢿⣿⣿⡿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠏⢷⠶⠴⢿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣼⣿⣿⣷⠂⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠙⠟⠙⠋⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠒⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠓⢾⠗⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⠷⣦⡀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⠀⠈⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡿⠏⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⢹⣷⣄⡀⣩⣦⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⡄⠀⠀⠀⠀⠀⡇⣾⣿⣟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣤⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⡉⠓⠘⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠁⠀⠀⠈⠙⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠛⠁⣀⣀⣠⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠛⠛⠛⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⢻⣿⣿⣿⣿⣿⠿⢿⣿⣟⠏⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠿⣿⣿⣿⣿⣶⡿⢿⣿⣿⣶⣶⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⣹⣿⣿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⡆⣀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⢅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣤⣤⣤⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠛⠛⠛⠋⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⠿⠿⣿⡿⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢷⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣠⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣁⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣹⣝⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠿⢷⠶⠾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠀⣶⣾⣦⣠⣾⣿⣿⣿⠇⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠉⠙⠁⠈⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠲⣶⠆⢀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣶⣦⣄⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟⠀⠙⣧⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢹⣧⣀⠀⢋⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠐⡆⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠀⢀⣠⣠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⠋⠫⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠘⢛⣿⣮⣯⣽⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⠀⠀⠀⢀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠋⠁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠺⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣤⣿⣿⣿⣾⣴⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⢿⣿⣿⣿⣁⣋⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠴⣷⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣤⣤⣤⣤⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠿⡿⢿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣄⣠⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠰⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⢘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢇⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠀⠀⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠛⠉⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠧⣤⡦⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣄⡀⠀⠈⠁⠘⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠙⢳⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢺⣇⠀⠠⣿⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣷⣤⣾⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡀⠀⠀⠀⠀⠈⢲⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⠿⠿⠖⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠁⠡⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠏⢁⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣋⣽⣿⣿⣏⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⠿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡟⣤⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠛⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⢠⣤⣤⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣍⠉⣉⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠙⠛⠛⠛⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣉⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣮⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⢀⣴⣦⣤⣴⣿⣿⣿⣿⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠀⠈⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠛⠉⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠧⣤⡦⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣄⡀⠀⠈⠁⠈⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠉⢳⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢸⣇⠀⠠⣿⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣷⣤⣾⣿⡄⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡀⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⠿⠿⠖⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠁⠡⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠏⢁⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣋⣽⣿⣿⣏⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡟⣤⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠛⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢠⣤⣤⣤⣴⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣍⠉⣉⣁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠋⠙⠛⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⢀⣶⣦⣤⣴⣿⣿⣿⣿⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠟⠿⠛⠻⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⢀⡀⢀⣀⣀⠀⣀⣀⣀⢀⣀⡀⠀⣀⣀⠀⣠⣄⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣧⢸⡇⣿⣏⠿⠈⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⣇⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡛⣷⡄⢺⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠻⠇⠿⠇⠙⠷⠿⠳⠺⠿⠀⠸⠿⠶⠿⠏⢹⠧⢿⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣂⣰⠀⣀⣀⡀⠀⣀⢀⣀⠀⣀⣈⡻⣿⣿⣿⣿⡿⣃⡀⣀⠀⣀⠀⢀⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢸⣷⢸⣿⢸⣿⠈⣿⡏⡁⣿⣝⠛⢰⣿⢹⣿⠀⣿⢸⣿⠀⣿⣿⣿⣰⣿⣿⣿⡅⣿⡇⣿⣧⣿⠀⣿⡏⠿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠛⣬⠻⣷⢸⣿⣼⣿⣆⣿⢸⣿⣴⣿⣿⣷⣿⣿⢹⣿⠷⣿⡇⣿⢹⣿⠀⣿⡟⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠁⠘⠃⠀⠀⠈⠛⠚⠋⠈⠛⠚⠃⠀⠛⠃⠀⠛⠛⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠆⠛⠃⠛⠀⠛⠀⠙⠓⠛⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⣀⣀⠠⣉⣙⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠈⣿⡏⠁⣿⣏⣿⠀⣿⠃⣿⠀⣿⣙⠛⠉⢻⡏⣅⣛⣙⠉⠀⢹⣿⠉⢸⣿⢹⣷⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡏⣷⠀⣿⠁⣿⠀⣬⠻⣷⠀⢸⡇⠿⣿⠟⠡⠀⢸⣿⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠃⠛⠀⠛⠻⠛⠀⠛⠾⠛⠀⠘⠃⠀⠘⣿⣶⣀⠘⠛⠀⠈⠻⢾⣫⣶⡖⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⣀⡀⣀⡀⠀⣀⣠⣼⣿⣿⣿⣷⠿⣗⣚⡛⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡇⣿⡇⠀⣿⡿⡟⣿⢻⣿⣿⡾⣿⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡏⠀⣿⡇⣿⡇⠀⣿⡇⢸⣿⣼⣏⠻⣁⣭⢻⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠛⠀⠛⠛⠃⠛⠃⠛⠛⠃⠛⠛⠘⠛⠘⠛⠀⠉⠻⠾⣻⣖⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⢀⣀⣀⡀⢀⣀⣀⠀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⡀⣀⣀⡀⠀⢀⣀⣀⡀⢀⣀⡀⢀⣀⣉⣛⢃⣀⣐⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⢹⡇⢸⣏⣿⡇⢸⣇⣹⡇⣿⡇⣿⡇⣿⣇⣿⠀⣾⢿⣇⠈⢹⡏⠁⣿⣏⡁⠀⢸⣿⣸⡇⣸⡟⣿⠈⢹⣿⠁⢸⣟⣿⣿⣿⡏⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣤⡆⢿⡇⣸⡇⢸⡏⣿⡆⢸⡏⠉⠀⣿⡇⣿⡇⣿⡏⣿⠀⣿⣬⣿⠀⢸⡇⠀⣿⡏⠁⠀⢸⣿⠉⠁⣿⣧⣿⡄⢸⣿⣄⢸⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠘⠃⠙⠃⠘⠃⠀⠀⠙⠛⠋⠀⠛⠃⠛⠘⠛⠀⠛⠂⠘⠃⠀⠛⠛⠃⠀⠘⠛⠀⠀⠛⠃⠛⠃⠘⠛⠙⣸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣄⡀⠀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣀⡀⣀⣀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣷⢸⣷⣸⡟⢸⣿⣁⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢸⣿⣙⢿⣿⣟⣿⡿⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⢹⣿⡇⣿⡇⣿⡇⠀⢸⣿⢹⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⠉⢸⣿⢿⣿⠁⢸⣿⣿⠿⢟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠴⠰⠶⠶⠶⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠁⠀⠛⠛⠁⠘⠛⠛⠘⠛⠘⠃⣘⣃⣙⠃⠘⠃⠛⠘⠛⠘⠛⠛⠘⠛⠘⠛⠀⣘⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⠛⠛⠛⠋⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⡦⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⢀⡀⢀⣀⣀⠀⣀⣀⣀⢀⣀⡀⠀⣀⣀⠀⣀⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣧⢸⡇⣿⣏⠿⠈⢹⣿⠉⢸⣿⠉⢸⣿⣿⡸⣿⡏⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡛⣷⣔⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⣇⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠻⠇⠿⠇⠙⠷⣿⠋⠸⠿⠀⠸⠿⠶⠿⠏⢹⣷⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣉⣀⠀⣀⣀⡀⠀⣀⢀⣂⠈⣛⣿⣿⣿⣿⣿⣟⠀⣀⡀⣀⠀⣀⠀⢀⣀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢸⣷⢸⣿⢸⣿⠈⣿⡏⣵⣿⣝⠛⢰⣿⠙⣿⠀⣿⢸⣿⠐⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⣿⣇⣿⠀⣿⡏⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠟⣬⠻⣷⢸⣿⢸⣿⠄⣿⢸⣿⢠⣿⣿⣷⢿⣿⣿⣧⠀⣿⡇⣿⢹⣿⠀⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠘⠓⠛⠁⠘⠃⠀⠀⠈⠛⠚⠋⠈⠛⠚⠋⠀⠛⠃⠀⠛⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⠆⠛⠃⠛⠀⠛⠀⠙⠓⠛⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⡀⣛⠻⣿⣻⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣧⡤⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠈⣿⡏⠁⣿⣏⣿⠀⣿⡗⣿⠐⣿⣟⢛⣿⢻⡿⠷⠛⠛⠙⠳⢿⣿⠙⢹⣿⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡏⣷⠀⣿⠂⣿⠀⣬⠻⣷⠉⢸⣧⣶⣿⠀⠀⠀⢸⣿⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠃⠛⠀⠛⠿⠛⠀⠛⠾⠛⠀⠘⠃⢻⣥⣀⠀⠀⠘⠛⠀⣈⠻⠾⣋⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⣀⡀⣀⡀⠀⣀⣠⣿⣿⣶⣀⣀⠀⣀⣙⡲⠿⠿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡇⣿⡇⠀⣿⣿⣟⣿⢻⣿⣟⡸⣿⣙⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡏⠀⣿⡇⣿⡇⠀⣿⡟⢻⣿⣾⣯⠿⢃⣭⢻⣷⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠛⠀⠛⠛⠃⠛⠃⠛⠛⠃⠛⠛⠘⠛⠘⠛⢢⣤⣻⣾⣛⡀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⠀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⡀⣀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣈⢉⣻⣷⣄⢀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⢹⡇⢹⣏⣿⡇⢸⣇⣹⡇⣿⡇⣿⡇⣿⣇⣿⠀⣾⢿⣇⠈⢹⡏⠁⣿⣏⡁⠀⢸⣿⣸⡇⣸⡟⣿⠈⢹⣿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡄⢿⡇⣸⡇⢸⡏⣿⡇⢸⡏⠉⠀⣿⡇⣿⡇⣿⡏⣿⠀⣿⣬⣿⠀⢸⡇⠀⣿⡏⠁⠀⢸⣿⠉⠁⣿⣧⣿⡄⢸⣿⢾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠘⠃⠙⠃⠘⠃⠀⠀⠙⠛⠋⠀⠛⠃⠛⠘⠛⠀⠛⠂⠘⠃⠀⠛⠛⠃⠀⠘⠛⠀⠀⠛⠃⠛⠃⠘⠻⣌⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣄⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣀⡀⣀⣀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣷⢸⣷⣸⡟⢸⣿⡁⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢸⣿⣿⣿⣿⣟⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⢹⣿⡇⣿⡇⣿⡇⠀⢸⣿⢹⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠁⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⠉⢹⣿⢿⣿⠈⢸⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠿⢶⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠋⠈⠛⠛⠁⠀⠛⠛⠁⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠘⠛⠘⠛⠛⠘⠛⠛⠛⠀⣘⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠋⠉⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⣤⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⢀⡀⢀⣀⡀⠀⣀⣀⣀⢀⣀⡀⠀⣊⣉⠂⣀⣀⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣧⢸⡇⣿⣏⠿⠈⢹⣿⠉⢸⣿⠉⢸⣿⣿⠀⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡛⣷⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠻⠇⠿⠇⢙⣷⠿⠃⠸⠿⠀⠸⠿⠶⠿⠏⣹⣧⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡈⣋⣀⣀⠀⣀⣀⡀⠀⣀⢘⣻⢿⣿⣿⣿⣿⣇⣀⣀⠀⣀⡀⣀⠀⣀⠀⢀⣙⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢸⣷⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⠛⢰⣿⢹⣿⠀⣿⢸⣿⠈⣿⣿⣿⣿⣿⠉⣿⠀⣿⡇⣿⣇⣿⠀⣿⡏⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⡇⣬⠻⣷⢸⣿⢸⣿⠀⣿⢸⣿⠀⣿⣿⣿⣿⣿⠀⣤⠀⣿⡇⣿⢹⣿⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⠓⠛⠁⠘⠃⠀⠀⠈⠛⠚⠋⠈⠛⠚⢫⣾⡛⠃⠀⠛⠛⠛⣀⣛⣟⣛⣀⣿⣿⣿⣆⣿⣻⣿⣿⣟⠟⠛⠀⠛⠃⠛⠀⠛⠀⠙⠓⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠿⠿⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⣀⡀⣈⣉⣀⠀⣀⣾⣿⣾⣿⣻⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⣿⣿⠗⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠈⣿⡏⠁⣿⣏⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣷⣽⣿⠉⢸⣿⢹⣷⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡏⣷⠀⣿⡇⣿⠟⣿⢻⣿⢻⣿⡿⡿⠻⠿⠿⠿⢿⣿⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠃⠛⠀⠛⠿⠛⠀⠛⠾⢛⣾⣸⣇⠀⠀⠀⠀⠀⠘⠛⠀⠈⠻⠞⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⣀⡀⣈⡛⠛⣃⡀⠀⣀⣀⡉⣀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡇⣿⡇⠀⣿⣿⡆⣿⢻⡇⢙⡸⣿⣙⢛⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡏⠀⣿⡇⣿⣇⣾⣿⣿⣿⣿⣼⣧⡿⢆⣭⢻⣷⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠛⠀⠛⠛⠃⠛⠃⠛⠛⠃⢿⣿⣸⣟⡞⠟⠀⠀⠻⠾⠛⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⢀⣀⣀⡀⢀⣀⣀⠀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⡀⣀⣀⡀⠀⢀⣀⣉⡀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⢹⡇⣼⣏⣿⡇⢸⣇⣹⡇⣿⡇⣿⡇⣿⣇⣿⠀⣾⢿⣇⠈⢹⡏⠁⣿⣏⡁⠀⢸⣿⣸⡇⣸⡟⣿⣿⣿⣿⠁⢸⣇⣽⣿⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣤⡄⢿⡇⣸⡇⢹⡏⣿⡇⢸⡏⠉⠀⣿⡇⣿⡇⣿⡏⣿⠀⣿⣬⣿⠀⢸⡇⠀⣿⡏⠁⠀⢸⣿⠉⠁⣿⣧⣿⡌⢸⣿⣼⣼⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠘⠃⠙⠃⠘⠃⠀⠀⠙⠛⠋⠀⠛⠃⠛⠘⠛⠀⠛⠂⠘⠃⠀⠛⠛⠃⠀⠘⠛⠀⠀⠛⠃⢛⠃⣸⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣄⡀⠀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣀⡘⣳⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣷⢸⣷⣸⡟⢸⣿⡁⢸⣿⣹⡇⢸⣿⣸⡇⢸⡿⣇⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⢹⣿⡇⣿⡇⣿⡇⠀⢸⣿⢹⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠁⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠆⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠋⠈⠛⠛⠁⠀⠛⠛⠁⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠘⠛⠙⢻⣿⣿⡟⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⠛⠻⠛⠟⠻⠿⠿⠻⠛⠋⠉⠉⠉⠻⠍⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⠿⠛⠛⠛⠛⠅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡧⠴⠾⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⡩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⡋⠀⠐⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⠀⣀⣀⣀⢀⣀⡀⠀⣀⣀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠻⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣧⢸⡇⣿⣏⠿⠈⢹⣿⠉⢸⣿⠉⢸⣿⣿⡸⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣌⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡛⣷⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣴⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠙⠷⠿⠃⠸⠿⠀⠸⠿⠷⠿⠏⢹⣷⣿⣷⣿⣳⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣻⡆⣀⣀⡀⠀⣀⢀⣀⢘⣁⣀⣰⣿⣿⣿⣿⡄⣀⡀⣀⡀⣀⡀⢀⣀⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⠛⢰⣿⢹⣿⠀⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⠄⣿⡇⣿⣧⣿⡇⣿⡏⠿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⡞⣮⢻⣷⢸⣿⢸⣿⠀⣿⢸⣿⠈⣿⣿⣷⣿⣿⣿⣿⠇⣿⡇⣿⢻⣿⡇⣿⡟⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠳⠛⠁⠘⠃⠀⠀⠈⠛⠞⠋⠈⠛⠞⠋⠀⠛⣷⣷⣿⠿⠛⠀⠛⠿⠛⠀⠛⣿⣿⣖⣿⣛⣿⣿⣿⣿⣿⣷⠛⠃⠛⠀⠛⠃⠙⠗⠛⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣾⣿⣟⣋⣀⠀⣀⣀⡀⢀⣀⣀⡈⣛⣻⣿⡿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣿⣿⠀⣿⣏⣿⣶⣿⣝⣿⣾⣿⣿⣷⣿⣿⣿⣷⣿⣿⢹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡏⣷⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠃⢿⣠⣛⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣙⠛⣛⣛⡐⣛⡿⣿⣿⣿⣿⣿⣿⣛⣛⡛⣛⠻⣛⣛⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡇⣿⡇⢻⣿⣿⣿⣿⢻⡇⠙⠸⣿⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡏⠀⣿⡇⣿⡇⠈⣿⣿⣿⣿⣼⣧⠀⢠⣯⢻⣷⢠⣴⣤⣤⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠛⠀⠛⠛⠃⠛⠃⠛⠛⠃⢿⢿⣸⣟⣾⣿⣠⣬⣻⣾⣻⣿⣿⣿⣿⠟⠀⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⡀⣠⣠⡀⣾⣾⣿⣟⣿⣿⣿⣟⣟⣿⣧⣄⢠⣿⣛⡀⢀⣤⣄⡀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣏⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠂⣿⢿⣇⠈⢹⡏⠁⣿⣏⡙⠻⢿⣿⣿⣇⣿⡿⣿⠻⢹⣿⠉⢸⣏⣽⡇⣿⡇⣿⡇⣸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣾⡇⣿⣯⣿⡇⢸⡏⠉⠁⣿⡇⣿⡇⣿⡏⣿⣄⣿⣼⣿⠀⢸⡇⠀⣿⡏⠁⠀⢸⣿⠉⠉⣿⣧⣿⡆⢸⣿⠀⢸⡏⢻⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠛⠋⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠘⠛⠀⠛⠂⠘⠃⠀⠛⠛⠃⠀⠘⠛⠀⠀⠛⠃⠛⣿⡾⣿⣶⠘⠃⠘⠃⠘⠛⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣄⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣀⡀⣀⣀⢙⣻⣷⢀⣀⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣷⢸⣿⣼⡟⢸⣿⣁⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢸⣿⣉⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⢻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢹⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠆⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠁⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠘⠛⠘⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠛⠀⠈⠙⠟⠋⠉⠉⠈⠀⠁⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠐⠿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⢠⠹⡿⠋⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⠀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠐⠀⠳⠿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠭⣿⣿⣿⣄⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⢫⢹⣇⣿⡿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠛⠷⠿⠃⠸⠿⠀⠸⠿⢿⣿⣏⠹⠷⢿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⣀⣰⠀⣻⢛⣿⢿⣿⣿⣿⣷⣀⣀⣀⠀⣀⡀⣀⡀⣀⡀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣬⣿⣿⡷⣿⣝⠛⢰⣿⢹⣿⢘⣿⢸⣿⢸⣿⣿⣿⣿⣿⠹⣿⠀⣿⡇⣿⣧⣿⡇⣿⡏⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⣙⣿⡇⡟⣮⢻⣿⢸⣿⣼⣿⢼⣿⢸⣿⢸⣿⣿⣿⣿⣿⣠⣤⠀⣿⡇⣿⢻⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠞⠋⠈⠻⣿⣻⣿⣻⡇⠀⠛⠿⢛⣤⣻⡿⢻⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠛⠃⠛⠈⠛⠃⠛⠗⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣻⣿⣿⣟⠁⣀⡀⣀⠀⣈⣁⣠⣶⣶⣾⡿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡔⣿⣝⢛⣨⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣼⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡿⣿⡏⣷⣤⣿⣿⣿⣟⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢻⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⡟⣿⡏⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠻⢻⣿⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡟⠉⣿⣿⣿⣿⣿⣿⡇⢸⣿⣼⣧⣤⢠⣭⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠟⠙⠿⠻⠃⠿⠻⠿⣿⣟⣿⣿⣸⠟⠸⢿⣹⣮⢻⣾⣿⣤⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢠⣤⣤⡄⣠⣽⣿⣿⣿⣷⣄⣠⢨⣭⣟⣟⣿⣿⣟⢻⣿⣀⣀⢀⣤⣄⡀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠂⣿⣿⣇⠈⢹⣯⠁⣿⣏⣿⣿⣿⣿⣿⣇⣼⡿⣿⢻⢹⣿⣿⢸⣏⣽⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣾⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⡄⣿⣬⣿⠀⢸⣿⢶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡦⢸⣿⣿⢸⣯⢻⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠛⠋⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠋⠀⠛⠛⠋⢿⡿⣿⣿⣿⠛⠃⠛⢣⡜⢛⣿⣘⡋⢘⣃⠘⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡟⢳⣦⣀⣠⣦⢚⣾⣯⢁⣟⠁⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣿⢸⣿⣼⡟⢸⣿⣉⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣏⣿⣿⣼⣿⣉⢸⣿⣆⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⢻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢹⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢹⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠷⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠛⣘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⠟⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠸⠟⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠾⣟⣿⣿⣿⠟⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢰⠘⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⠀⣀⣀⣀⢀⣓⣀⣴⣟⣳⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⣿⣿⣿⡈⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣷⡄⢸⣿⠀⢸⣿⠃⢽⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⡿⢿⣿⣿⣿⣷⣿⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⣀⣀⣿⡿⣀⣀⣀⠀⣀⣀⣀⠁⣘⢋⣉⢹⣿⣿⣿⣿⣿⣆⣀⠀⣀⡀⣀⡀⣀⡀⢀⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⢹⣿⡿⡷⣿⣝⠛⢰⣿⣹⣿⣰⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⣿⣧⣿⡇⣿⡏⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⣿⣿⡇⠁⣬⢻⣿⢸⣿⢻⣿⢻⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣧⠀⣿⡇⣿⢻⣿⡇⣿⡟⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠞⠋⠈⠻⣿⣯⣿⣿⠃⠀⠛⠿⠛⠀⠛⠿⣻⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠛⠃⠛⠈⠛⠃⠛⠗⠛⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣰⣿⣿⣿⣋⠀⣀⣀⣀⠀⣀⣀⣈⢛⣛⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⣿⣿⣿⣏⣿⢀⣿⣿⣿⣷⣿⣟⣿⣾⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠁⣿⡏⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⢙⣿⣿⣿⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⡇⣿⡏⣿⡇⢩⣿⠛⣿⣿⣿⣿⣿⣿⡿⠁⣿⢻⡏⡛⢸⣿⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡟⠀⣿⡿⣿⣿⣿⣿⣿⢾⣿⣼⣷⣿⣷⣭⢻⣷⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠟⠉⠿⠿⠃⠟⠃⠻⠿⣿⣿⣿⣸⡟⠘⠿⡹⣯⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢠⣤⣤⡄⣠⣶⣾⣿⣿⣿⣗⣶⣿⣿⣟⣟⣿⣿⣟⢻⣯⣀⡰⢆⣤⣄⡀⢀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣻⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠂⣿⢿⣇⠈⢹⣿⣅⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⣿⢋⢹⣿⣿⢸⣏⣽⡇⣿⡇⣿⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣼⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⡄⣿⣼⣿⠀⢸⣿⠈⣿⡏⠿⣿⣿⣿⣿⣿⣿⣧⣿⣆⢸⣿⣿⢸⡟⢻⡏⣿⡇⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠛⠋⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠋⠀⠛⠛⠃⠈⠙⠛⠙⢯⣛⣃⠛⠃⢘⣛⣟⣘⠃⠘⠃⠘⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡈⢻⣿⡻⣿⣿⣟⣷⣿⢛⣏⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠣⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣿⢹⣿⣼⡟⢸⣿⣉⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢻⣿⣉⢼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢧⠄⠀⠀⠀⠀⠀⠀⠈⠐⠀⣿⣧⣿⡇⣿⢻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢹⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠷⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⣘⡛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⡿⡿⠿⣿⣿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣰⣌⣿⣤⡻⠟⣷⠯⠣⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠉⠋⠉⠉⠉⠁⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡬⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⠋⠉⠁⠀⠉⠙⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⣾⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⣴⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠸⡟⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⠀⣀⣀⣀⢀⣰⣇⠸⣃⣀⠀⣀⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⣤⣿⡏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣧⣊⡻⣷⡄⢸⣿⠀⢸⣿⠃⢼⣇⣿⡟⣿⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⢧⣿⣿⣿⣷⡿⠃⠸⠿⠀⠸⣿⢿⣿⣯⣿⣷⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣂⣲⣾⣟⡙⣉⣀⣀⠀⣀⣐⣻⠟⣛⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣀⡀⣀⡀⣀⡀⢀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣿⣿⡏⠁⣿⣝⠛⢰⣿⢻⣿⠀⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⣿⣧⣿⡇⣿⡏⠿⠇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⣿⣿⡇⠀⣬⠻⣷⢸⣿⢸⣿⣷⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⣿⢻⣿⡇⣿⡟⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠁⠘⠃⠀⠀⠈⠻⠞⠋⣨⣿⣿⣿⠟⠛⠃⠀⠛⠿⣛⣀⣻⣿⣛⣠⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣟⠀⠛⠃⠛⠈⠛⠃⠛⠗⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣻⣛⡛⣋⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢹⢻⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣦⣿⣟⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠛⠿⠛⠿⠳⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣟⠿⠸⠟⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⣙⣻⣿⣿⣿⣿⣟⠀⣀⣀⣺⣃⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡟⣿⣿⣿⣿⣿⣇⣿⢻⡟⠻⣹⣿⣙⢛⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡟⠀⣿⡇⣿⡇⣿⣿⣿⣿⣿⣼⣧⣌⣹⣯⣻⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠟⠀⠛⠿⠃⠿⠃⢿⣿⣿⣿⣿⣸⣿⣾⣿⣿⣯⣻⢾⠛⣻⣿⡿⠀⠘⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢀⣈⣽⡜⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⢇⣤⣽⣞⢻⣧⣄⡀⢀⣤⣄⡀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠀⣿⢿⣇⠈⢹⡏⠁⣿⣏⡛⢿⣿⣿⣿⡇⣽⡿⣿⢨⢹⣿⣻⢸⣏⣽⡇⣿⡇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⠀⣿⣼⣿⠀⢸⡇⠀⣿⡏⠁⠀⢸⣿⠉⠷⣿⣧⣿⣆⢸⣿⣿⢸⡏⢻⡏⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠋⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠘⠛⠀⠛⠂⠘⠃⠀⠛⠛⠃⠀⠘⠛⠀⠀⠛⠻⣛⣿⣿⣟⠙⠘⠃⠘⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣤⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣠⡀⣩⣝⢛⣦⣠⣺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣿⢹⣿⣼⡟⢸⣿⣉⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⢻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢹⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠷⠶⣶⠏⢶⠄⠰⠶⠶⠖⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣟⡿⣿⡿⠿⠿⠿⠇⠈⠋⠉⠈⠈⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠉⠉⠈⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣾⣿⣾⣿⣲⣟⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠻⠋⠉⠉⠘⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠆⠦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠖⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⣀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣀⣠⡾⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠽⣿⠁⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠟⡀⠀⠀⠸⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣾⣿⣦⣄⣠⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⠀⣀⣀⣀⢀⣀⣀⠀⣀⣸⠟⣛⣛⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢾⣇⣿⣏⢿⡊⢹⣿⠉⢸⣿⠉⢸⣿⣿⣴⣿⡏⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣏⣛⡻⣿⡅⢸⣿⠀⢸⣿⣃⢼⣇⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⣧⣿⣿⣿⡷⠿⠃⠸⠿⢀⣸⡿⡿⢿⣏⣻⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣐⣿⣿⣿⡋⣁⣀⣀⠀⣀⣘⣛⠙⣛⢈⣉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣿⣿⡟⠅⣿⣝⠛⢰⣿⢹⣿⠀⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣧⣿⡇⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⣼⣿⣿⣿⡇⠀⣬⢻⣷⢸⣿⣼⣿⣧⣿⢸⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⢻⣿⡇⣿⡟⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠞⠋⠈⠻⠿⠋⠁⠛⢃⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⠃⠛⠗⠛⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠅⣿⣯⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⠙⣿⣿⣿⣟⣿⢻⣿⢿⣿⣿⣿⣿⣿⡿⠟⢻⣿⠹⢻⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠃⠛⠀⠛⠿⠛⠀⠛⠿⠛⣾⣻⣿⣿⣿⣿⣅⠀⠘⢿⣰⣼⣻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⣀⡀⣀⡘⠿⣻⣿⣿⣛⣛⡁⣓⠀⣛⣛⡻⣀⣀⣶⣦⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡇⣿⡇⠀⣿⣿⣿⣿⢿⣧⡙⣸⣿⣙⢛⣿⣿⣿⣿⣿⣿⡿⠀⢀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡟⠀⣿⡇⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣷⣿⠟⠿⡿⣿⣿⠃⠀⠛⠓⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠟⠁⠛⠛⠃⠛⠃⠿⢿⣿⣿⣿⣸⣿⣾⣿⣿⣿⣿⣾⣿⠇⢀⣸⣿⣾⣷⣠⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⡀⣀⣈⡙⠛⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣅⢲⣷⣊⡻⢟⣿⣍⡁⣠⡀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠀⣿⣿⣇⠈⢹⡏⠁⣿⣏⡁⠀⢸⣿⣹⡇⣸⡿⣿⢈⢹⣿⠉⢸⣏⣽⡇⣿⡇⣿⡇⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣄⣿⣼⣿⠀⢸⡇⠀⣿⡏⠁⠀⢸⣿⠉⠁⣿⣧⣿⡾⣿⣿⣿⣸⡏⢻⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠘⠛⠛⠁⠛⠋⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠃⠀⠛⠛⠃⠀⠘⠛⠀⠀⠛⠃⠛⠃⠘⠛⠟⠙⢻⣞⠃⢸⣟⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣀⡀⣀⣀⢀⣤⣄⢀⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣿⢸⣿⣼⡟⢸⣿⣉⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢸⣿⣉⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⢻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢹⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠏⢶⠄⠰⠶⠶⠖⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠘⠛⠘⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⢻⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠟⠛⠊⠋⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠈⠩⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⢠⣶⠄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⠟⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢻⠇⠀⠀⠈⣳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⣀⠀⠀⠀⠙⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣤⣴⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⣤⣄⣀⢀⣀⣀⣀⢀⣀⣀⠀⣰⣿⠛⣛⣛⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢿⣿⣿⣏⢿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⣴⣿⣯⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣋⡻⣿⡄⢸⣿⠀⢸⣿⣯⣼⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⣿⣿⣿⣟⡻⠷⠿⠃⠸⢿⣈⣸⡿⣿⣿⣏⣻⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢲⣿⣿⣿⣋⡁⣀⣀⣀⠀⣈⣛⣉⢉⣉⢉⣤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⡀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⣼⣿⣿⣿⡏⠁⣿⣝⠛⢰⣿⢹⣿⠀⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣿⡇⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⣸⣿⣿⣿⠟⣿⡇⠀⣬⢻⣷⣸⣿⣼⣿⣶⣿⣸⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⢻⣿⡇⣿⡟⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠾⠋⠛⠻⠿⠋⠀⢛⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⠃⠛⠗⠛⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⣯⣧⣿⣯⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠛⣿⡟⣷⠽⣿⣿⣿⣟⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢹⢻⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠃⠛⠀⠛⠿⠛⠀⠻⠿⣿⣿⣻⣿⣿⣿⣟⠀⠀⠘⢿⣠⣌⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⣀⡀⣙⡿⣿⣿⣿⡿⣛⣛⡀⣂⠺⣟⣛⡣⣀⣠⣤⣄⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡇⣿⡇⠘⣿⣿⣿⣿⢿⡇⠹⢸⣿⣙⢛⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡟⠀⣿⡇⣿⡇⣠⣿⣿⣿⣿⣾⣷⣾⣿⣯⣻⣷⣿⢿⡿⣿⣿⣿⠃⢀⣾⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠟⠁⠛⠛⠃⢿⣧⠿⣿⣿⣿⣿⣸⣟⣿⣿⣿⣿⣿⣾⣿⠃⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣖⢺⣿⣟⣻⢗⣿⣗⡂⣠⡀⢀⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠀⣿⣿⣇⠈⢹⡏⠁⣿⣏⡁⠈⢹⣿⣻⡏⣿⡿⣿⠫⢹⣿⢙⢸⣏⣽⡇⣿⡇⣿⡇⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⢀⣿⣼⣿⠀⢸⣇⠀⣿⡏⠁⠀⢸⣿⠉⠁⣿⣧⣿⣶⣼⣿⣭⢸⡏⢻⡇⣿⡇⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⡀⠘⠛⠛⠁⠈⠛⠛⠁⠛⠋⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠃⠀⠛⠛⠃⠀⠘⠛⠀⠀⠛⠃⠛⠛⠙⣻⣿⣾⣧⡘⠃⠘⠛⠛⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⡄⠀⠀⠀⠀⠛⠒⠀⠈⠃⢀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣀⡀⣠⣄⢂⣭⣭⢛⣷⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣿⢹⣿⣼⡟⢸⣿⣉⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢸⣿⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⢻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠏⢷⠄⠰⠶⠶⠖⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠘⠛⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠀⠩⠽⠶⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠙⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⣄⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⢹⡏⠀⠀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠘⣡⡀⠀⠀⠘⠋⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⣿⣿⣷⣦⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣶⣤⣄⣀⣀⣀⢀⣀⣀⠀⣀⣁⢠⣿⣛⣛⢋⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣿⣿⣿⣟⢿⣯⢹⣿⠉⢸⣿⠉⢸⣿⣿⣠⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣏⣚⡻⣿⡿⢺⣿⠀⢸⣿⣋⣸⣇⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⣿⣧⣿⣿⣿⣷⠿⠃⠸⠿⢰⣸⣿⣿⣿⣏⣻⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣛⣿⣿⣿⡿⣟⣀⣀⠀⣀⣀⣻⢟⣛⢛⣉⢉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣿⣿⣿⡷⣿⣝⠛⢰⣿⢹⣿⢀⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⣾⣿⣿⣿⡏⠁⣬⢻⣷⢸⣿⣸⣿⣼⣿⢸⣿⢸⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠾⠋⠸⢿⣿⡿⠏⠛⠃⣤⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⠃⠛⠷⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⣥⣿⣏⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠛⣿⣿⣷⡽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠃⠛⠀⠛⠿⠟⠛⠻⠿⢿⣿⣻⣿⣿⣿⣿⣿⡿⠛⠻⢨⣼⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⣀⡀⣀⡹⣿⣿⣿⣿⣿⣟⣿⣒⡰⣈⣛⣿⣿⣆⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡇⣿⡇⠙⣿⣿⣿⣿⢿⡿⡻⢹⣿⣙⢛⣿⣿⣯⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⣿⡇⣿⡇⣿⡇⣾⡟⠀⣿⡇⣿⡇⠀⣿⡏⢿⣿⣿⣷⣷⣦⣭⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣶⣀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠘⠃⠛⠃⠙⠷⠟⠑⠛⠛⠃⢿⣇⣿⠿⢃⣿⣿⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣟⡛⣽⣿⡿⡿⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣀⣀⡀⢠⣄⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⣀⣀⡀⢀⣀⣈⡉⣻⣷⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⢻⣤⣞⣻⢟⣿⣏⣡⣠⡄⣠⡄⢀⣤⣄⣀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠀⣿⣿⣇⠈⢹⣿⠁⣿⣏⡉⠛⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣇⣿⡇⣿⡇⣿⣿⣸⡇⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣄⣿⣼⣿⠀⢸⣿⠀⣿⡏⠁⠀⢸⣿⠉⠉⣿⣧⣿⣾⣽⣿⣀⢸⡏⢻⡇⣿⡇⣿⡇⣿⡟⣿⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡄⠘⠛⠛⠁⠈⠛⠛⠁⠛⠋⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠋⠀⠛⠛⠃⠀⠘⠛⠀⠀⠛⠃⠛⠋⠻⣿⣿⢘⣿⣿⡃⠾⠛⠛⠵⠛⠃⢛⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⢀⡄⠀⢰⣿⠫⠚⠉⠁⢀⣄⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣠⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣀⡀⣀⣀⢈⣿⣿⢛⣿⢿⣤⢀⣠⣤⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣩⠒⠃⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣿⢹⣿⣼⡟⢸⣿⣉⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢸⣿⣩⢾⣿⣇⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠿⠒⠐⠚⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⢻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⠉⢸⣿⢿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠖⠰⠶⠶⠖⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠛⠘⠛⠛⣾⣟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⢿⣿⣿⣿⣿⣿⡏⣽⠽⠿⣿⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⢸⣟⡯⡿⢉⣴⣷⡴⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠉⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠀⢻⠿⠿⠻⢙⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡷⠙⠛⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠋⠙⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⢻⡏⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⢙⣧⣄⠀⠀⠘⣛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠸⣃⣀⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣿⡇⣿⣏⢿⣮⣽⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣷⣚⣻⣿⣿⣿⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⣇⣿⣇⣿⣿⣿⣻⣿⣿⣴⡸⠿⢿⣿⣏⣻⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣾⣿⣿⣿⡿⣿⣿⣻⠏⣐⣷⣲⣖⣻⢛⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣿⣿⣿⣷⣿⣝⠛⢰⣿⢹⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣯⢻⣿⢸⣿⢸⣿⢹⣿⢸⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠞⠋⠈⣻⣿⣿⣿⣿⣿⣿⠻⠿⠟⠀⠛⠿⢛⣀⣻⣿⣟⣞⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣿⣿⣿⣿⣿⠟⣀⣀⣂⣴⣾⣓⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠉⣿⣏⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣄⣿⣟⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠙⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡈⢉⣉⣉⠙⣛⣛⡛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣛⣛⡿⣿⣿⢏⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⡇⣿⡏⣿⡆⢩⣿⠃⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣝⢛⣿⣿⣿⣷⣄⣽⣡⣄⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⡇⣿⡇⣾⡟⠃⣿⡇⣿⡇⠹⣿⡿⣿⣿⣽⣿⣿⣿⣯⢻⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠟⠙⠻⠿⢇⣿⣧⠿⠿⠃⠿⠿⢸⣟⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⣷⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⣀⣀⡀⢀⣤⣽⡄⣤⣤⡄⢠⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣿⢟⣿⣿⣿⣻⡇⢠⡟⢛⣯⣄⡀⠀⠀⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠆⣿⣿⣧⠈⢹⣿⠓⣿⣏⣳⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡇⣿⡇⣿⣿⣸⣇⢿⣧⡛⠃⠀⢀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠀⢸⣿⠀⣿⡏⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡏⣿⡇⣿⡇⣿⡿⣿⣏⣧⡝⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠛⠀⠛⠛⠃⠀⠘⠛⠉⠻⠛⠛⠛⢻⣟⠛⠟⠘⠋⠙⢣⣾⣛⣛⣵⣛⣣⡟⠻⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢀⡀⢀⡀⢀⣀⡀⣈⣿⢳⣾⣿⢒⣶⣿⣿⢻⣿⣿⡟⣞⣤⣄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠀⢀⣤⣶⣦⣀⣀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡇⢸⣿⣸⡇⢸⣿⣇⣿⣿⢸⣿⣙⢾⣿⣿⣿⣿⢹⣿⣁⣛⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣮⣿⡟⠂⠀⣿⣧⣿⡇⣿⣻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⢸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⠩⢾⣿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⢿⣿⣿⢿⠿⠿⠷⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠛⠘⠛⠛⠘⠛⠘⢛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠁⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠋⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⠟⢿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣷⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⣿⠃⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠼⠟⡀⠀⠀⠀⢽⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣘⠏⣀⣰⣾⣿⣦⣤⣀⣤⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣿⡇⣿⣏⢿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⣆⣿⡏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣧⣛⣻⣿⡆⢸⣿⠀⢸⣿⠋⣸⣏⣿⡟⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⣿⣿⣿⣿⣿⣿⣷⣸⠿⠀⠸⠿⠿⠿⢏⡻⡷⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣠⢤⣄⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣛⣖⣾⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣿⣿⣿⣷⣿⣝⢛⣴⣿⣿⣿⣾⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣮⢻⣿⣹⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠁⠘⠛⠀⠀⠈⠻⠿⢋⣸⣿⣿⣿⣿⣿⣟⠁⠛⠿⠛⠀⠻⠿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣾⣿⣿⣿⣿⣿⣿⣟⣓⣂⣀⡀⣀⣀⣀⢀⣀⣚⡛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣛⣿⣿⣿⣿⣿⣿⣿⢲⣿⣿⣿⣿⣿⣝⣛⣼⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⡟⠋⣿⣟⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣤⣀⣻⣇⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢙⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⡟⣿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣛⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⡇⣿⡇⣾⡟⠉⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣷⣿⣿⣿⣆⣠⠛⣷⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠻⠃⠛⠿⢟⣝⢿⡿⠇⠿⠃⢿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣠⣀⣀⠀⣠⣴⡾⢣⣤⣤⡄⣨⣽⡟⣿⣿⣿⣟⣿⣿⣿⣟⣿⣯⣿⣿⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣻⡟⣇⣤⣄⡀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣿⣟⢹⣿⠁⣿⣏⣡⣾⣿⣿⣿⣏⣿⣿⣿⣻⣿⣿⣿⣼⣿⣿⣿⣿⡇⣿⡿⣿⣿⣸⣿⢿⣧⡛⠃⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢹⢸⣿⣇⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡇⣿⡟⣿⡿⣿⡇⣤⡝⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⠛⠀⠛⠋⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣣⣿⣛⣻⣽⣛⣣⣿⣷⣿⡛⠛⠁⠀⣠⣤⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣤⡀⣠⡀⣠⣤⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢹⣿⣟⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⢟⣿⢻⣿⣿⡟⣟⣿⣟⢿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠹⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡗⢹⣿⣿⡇⢹⣿⣿⣿⣿⢻⣿⣉⢺⣿⣟⣿⢸⣿⣿⣷⠛⠃⣿⡟⠂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⣾⣿⠩⣼⣿⣿⣿⠾⢿⣿⠿⠿⠟⠿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡰⣶⡶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠛⣜⣛⣛⣛⣻⣿⣿⣄⠘⠛⣀⣛⣣⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋⠁⠀⠈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠠⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⢿⡿⠂⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠙⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⣿⡇⢸⣿⠇⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠃⠛⣫⣤⡀⠀⠀⠸⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⢸⣇⣀⣸⢿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣿⡟⣿⣏⢿⡎⢹⣿⠉⢸⣿⠉⢸⣿⣿⣼⣿⡏⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣻⣻⣿⣇⢸⣿⠀⢸⣿⠋⣸⣇⣿⡏⣿⡇⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣀⣸⡿⠿⠿⣏⣻⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣶⢶⣶⣿⣿⣿⡿⣿⣿⣟⢿⣟⣿⣻⣕⣿⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣿⣿⣿⣷⣿⣝⢛⣴⣿⣿⣿⣾⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⣸⣿⣿⣿⣿⣿⣯⢻⣿⣹⣿⣿⣿⣿⣿⢼⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠘⠛⠀⠀⠈⠻⠿⢋⣸⣿⣿⣿⣿⣿⣿⡃⠛⠿⠛⠀⠻⠿⠛⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣟⣓⣈⣀⡀⣀⣀⣀⢀⣀⣘⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣝⣟⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⡟⠋⣿⣟⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⢛⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⡿⣿⣿⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⡇⣿⡏⣾⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣗⣀⡴⣷⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠻⠃⠛⠿⢟⣝⣿⡿⠇⠿⠃⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣠⣀⣀⠀⣨⣥⡾⢣⣤⣤⡄⣨⣿⡟⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣽⣟⢻⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⡟⢛⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣷⡟⢹⣿⠁⣿⣏⣡⣿⣿⣿⣿⣏⣿⣿⣿⢻⣿⣿⣿⣼⣿⣿⣿⣿⡇⣿⣯⣿⣿⣻⡇⢿⣧⣻⡇⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢱⢸⣿⡂⣿⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⣿⡇⣿⡧⣿⡿⣿⡇⣭⡝⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⠛⠀⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⣛⣻⣵⣿⣷⣛⣃⣽⣛⠛⠁⠀⠀⠀⢀⣠⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣤⡀⣠⡀⣤⣤⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣝⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⡟⣟⣿⣟⢿⣿⡆⠀⠀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠟⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡗⢻⣿⣿⡟⢻⣿⣿⣿⣿⢿⣿⣹⢾⣿⣟⣿⢾⣿⣿⣷⣟⠃⣿⣿⡿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⣇⢸⡟⣿⡇⢸⡇⣿⣿⣿⣼⣿⢩⣼⣿⢿⣿⣸⣿⣿⣿⠿⢿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⠶⢶⣶⡿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠋⠘⠃⠙⠃⠘⠃⠛⠙⠛⣛⣛⣛⣿⣿⣿⣿⡍⠙⠛⠉⠛⠋⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢫⣋⠌⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠬⠘⠛⠁⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠛⠙⢃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠙⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⣄⣀⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠉⠉⠻⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣿⠉⢙⣿⡇⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣰⣿⣀⣘⣟⡀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣾⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⣿⣶⣤⣄⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣧⣿⣿⣿⣿⡿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠷⣿⣷⣿⣣⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣘⢿⣿⣿⣿⣿⡿⣿⣿⣂⠀⣀⣀⣀⢀⣀⢀⣀⢀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⣸⣿⢸⣿⣿⣿⣿⣷⣿⣝⢛⣰⣿⣿⣿⣼⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢻⣿⢸⣿⣿⣿⣿⡟⣮⢻⣿⣹⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠿⣯⣿⣻⣿⣿⣿⣿⣿⣇⣻⠿⢟⣄⣻⣿⣿⣿⣿⣿⣿⣟⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣻⣿⣿⣿⣿⣿⣿⠟⣛⣋⣀⡘⣛⣛⡛⢛⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣧⣟⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡐⣿⣝⠛⢈⣿⣿⣧⣟⣿⣻⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡀⣿⣿⣿⣇⣭⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠙⠿⣿⣿⣿⠏⠁⣿⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⣀⣀⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢻⡿⣿⡿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠘⠃⠻⢃⠛⠷⠟⠙⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣸⣟⣿⣿⣻⣯⣻⣿⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣤⣍⣀⣠⣠⣴⡄⢠⣤⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣟⣿⣿⣟⢻⣤⣄⣴⣿⣷⣞⣿⣳⣶⣠⡄⢀⣤⣄⡀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣷⠈⢹⣿⠷⣿⣟⣿⣿⣿⣿⣽⡏⣼⡿⣿⢋⢹⣿⣿⢼⣿⣿⣧⣿⡇⣿⡧⣿⣿⣸⡇⣿⣧⡛⠃⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣦⣿⣾⣿⠀⢸⣿⠀⣿⡏⢿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣾⣿⣿⢸⣿⣿⣯⣿⡇⣿⡇⣿⡿⣿⣿⣧⡝⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⣈⣛⡿⡘⠛⢀⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⡋⣿⣛⣿⣽⠟⠃⠛⠃⠙⠛⠛⠁⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⡀⣠⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡙⢻⣿⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⢛⣿⢻⣿⣿⡗⣄⣤⣄⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢾⣿⣟⣿⣼⣹⣿⡷⠛⠓⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⣿⣿⣟⣿⡏⢻⡏⣿⣿⣿⢹⣿⠩⢾⣿⢿⣿⣿⣼⣿⣄⠿⢿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠆⠰⠶⠶⠖⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠋⠙⠃⠙⠃⠘⠃⣻⣝⣛⣜⣛⣛⣘⣛⣜⣛⣼⣝⣛⣧⣛⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣼⠼⢿⠟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⡿⢿⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠯⣽⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠿⠷⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠋⠉⠉⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣴⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢠⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⡿⠿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⢀⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣶⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢻⡿⠿⣿⡿⠀⠀⠈⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⣿⣇⣰⣿⠃⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣻⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡟⣿⡏⣿⣷⣄⠀⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢇⣿⣧⣿⣧⣿⣷⡿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⣷⢿⣷⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣒⢲⣿⣿⣿⣿⡿⣿⣿⣀⠀⣀⣠⣀⢀⣀⢀⣀⠀⣃⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣿⣿⣿⣷⣿⣟⣛⣰⣿⣿⣿⣼⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⣼⣿⢸⣿⣿⣿⣿⣟⣾⢻⣿⣹⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠿⣫⣿⣿⣿⣿⣿⣿⣿⡗⠻⣿⣿⡦⣻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣟⣚⣃⡉⣛⣻⣿⣿⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣛⣽⣿⣿⣿⣿⣿⣿⠚⣿⣿⣿⡟⣿⣝⠛⠈⣿⣿⣧⣟⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡭⣿⣿⣿⣇⣭⢻⣷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠿⢛⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⢙⣛⡛⢋⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠘⠇⠻⠋⠛⠿⠟⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣻⣯⣻⣿⣿⣿⣿⡉⠛⢓⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣤⣶⣋⢀⣠⣤⡄⢠⣤⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⢻⣧⣆⣠⣽⣿⣿⣿⣲⣤⣠⡄⢀⣤⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⢟⣿⣿⣷⠈⢹⣿⢷⣿⣿⣿⣿⣿⣿⣹⣏⣿⡿⣿⢻⢹⣿⣿⢼⣿⣿⣧⣿⡇⣿⣧⣿⣿⣹⡇⢿⣧⡛⠃⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣦⣿⣼⣿⠁⢸⣿⠀⣿⡏⠿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣾⣿⣿⢸⣿⣿⣟⣿⡇⣿⡏⣿⡿⣿⣷⣧⡝⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⠛⣝⣛⣣⣜⠛⠀⢛⣿⣣⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣼⣿⣿⣻⣿⣛⣻⣽⣟⠃⠛⠋⠙⠛⠛⠁⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⡀⣠⡀⣤⣄⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣠⡟⢻⣿⢻⣶⣔⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⢟⣿⢻⣿⣿⡆⣀⣤⣄⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠗⢸⣿⢸⣿⢹⣿⣼⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢾⣿⣟⣿⣼⢿⣿⣷⠿⠳⣿⡏⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⣿⣿⣿⣿⡏⢿⡏⣿⣿⣿⢹⣿⠩⣾⣿⢿⣿⣿⣼⣿⣅⠿⢿⣿⠇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠋⠙⠋⠙⠃⠘⠃⢛⣝⣛⣘⣛⣛⣙⣛⣜⣛⣼⣟⣛⣯⣛⠋⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠙⠈⠈⠉⠉⠙⠛⠻⠏⠩⠛⠿⠿⠿⠿⠛⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡹⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠛⠛⠛⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠛⠉⡉⠙⢳⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣆⠀⢻⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣇⠀⠈⠻⠿⠃⠀⠈⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣈⣓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣐⣂⢀⣀⣀⠀⣀⣀⣿⣛⣛⣿⠇⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣿⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⣿⣿⡏⣿⡇⠀⠀⠀⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡏⣿⡇⣿⣿⣦⣄⣀⣠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⢧⣿⢇⣻⡷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⢻⡷⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣒⣾⣿⣿⣿⣿⣧⣀⠀⣀⣀⣀⢀⣀⢀⣁⢘⣗⣰⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣟⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣿⣿⣿⣷⣿⣝⢛⢰⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⣸⣿⢸⣿⣿⣿⣿⣟⣼⢻⣿⣹⣿⣿⣿⢿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠛⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣙⣿⣿⣿⣟⣿⣿⣿⣇⣘⣛⡻⣉⣻⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⣩⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣝⠛⠻⣿⣿⣷⣿⣿⣿⣷⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡽⣿⣿⣿⡇⣭⢻⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣃⣛⣿⣟⣀⣻⣿⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⢟⣋⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⣤⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠺⠟⠿⠻⠿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣀⣀⣀⡀⢀⣀⣀⡀⣀⣤⣄⠀⣤⣴⣀⠀⣠⣬⡍⢻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣟⣿⣿⣿⣿⢳⣤⣝⣻⢇⣤⣄⡀⣠⡄⢠⡄⢀⣤⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠷⣿⣿⣷⠈⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⣼⡿⣿⢛⢻⣿⣿⢸⣿⣿⣿⣿⡇⣿⡇⣿⣿⣸⡇⢿⣧⡛⠃⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣶⣿⣾⣿⠀⢸⣿⠛⣿⡯⣿⣿⣿⣿⣽⣿⣿⣧⣿⣎⢸⣿⣿⣾⣿⣿⣿⣿⡇⣿⡷⣿⡿⣿⣇⣤⡝⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⣿⣟⠛⢃⠘⠛⠀⣛⣛⣻⣿⣿⣿⣿⣿⣿⣣⣻⣿⣿⣿⣿⣼⣿⣿⣧⣿⣿⣿⣽⡛⠃⣛⣃⣽⡛⠛⠁⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣤⣤⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣨⣟⢳⣿⢣⣤⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⢟⣿⢿⣿⣿⡅⢀⣬⣄⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠟⢸⣿⢸⣿⢹⣿⣼⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣟⣿⣿⣿⣿⣧⣿⣧⣿⡇⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠛⢻⣿⣻⣿⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣿⠩⢾⣿⢿⣿⢿⢿⣿⠟⠿⢿⣿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠙⠻⠿⠛⠛⠃⢝⣿⣛⡝⠛⠙⡛⢛⣙⠛⢛⣛⣿⣟⣛⣦⣛⠻⠟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠙⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠙⠛⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣩⣶⣤⠍⢿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢿⣿⣿⣿⣆⢸⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠈⠛⠛⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡇⠀⠈⠛⠋⠁⢴⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣤⣬⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠉⠛⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣚⠂⣀⣀⠀⣀⣀⣀⢿⡟⢻⣿⡇⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣿⡇⣿⣏⠿⠎⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡿⠇⡻⣿⣀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡆⢸⣿⠀⢸⣿⠋⣸⣇⣿⡇⣿⡇⣿⡇⠀⣿⣿⣿⣶⣤⣤⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⢷⣿⣃⣸⣿⠀⠸⠿⠿⠿⠏⠻⠷⢿⡷⣿⡇⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⣀⣰⣺⡿⣿⣿⣿⣿⣿⣧⣀⢀⣀⢀⣀⢀⣀⣀⣁⠸⣇⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢼⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠉⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣸⣿⢸⣿⢸⣿⣿⣿⢰⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢼⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⣴⣿⣷⣿⣯⢻⣿⣻⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠃⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣻⣿⣿⣞⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣻⣿⣿⣿⣿⣿⣿⣿⣇⣺⣋⢛⣛⣻⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⣁⣿⣿⣿⣿⣿⣿⣿⡿⣿⣝⠛⠸⣿⣿⠇⠟⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⢻⣷⠀⣿⣿⣀⣠⣬⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣭⣿⣿⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⣀⡈⢛⣻⡿⣿⣛⣁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠸⠇⠿⠛⠛⠿⠟⠟⠿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣤⣤⣀⠀⣠⣾⡄⢠⣤⣤⡍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢻⣿⣟⣿⣟⣯⣍⣻⣻⣶⣲⣆⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡏⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣿⣛⢹⣿⠁⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⡇⣿⡿⣿⣿⣻⣿⣿⣧⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢛⢸⣿⡄⣿⡏⠉⠛⢹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⡟⣿⡿⣿⣿⣿⡝⣿⡿⣠⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⠛⠈⠛⠻⣼⣛⣁⣛⡛⠃⢠⣜⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣤⣤⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣠⢺⣿⣿⣿⣶⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡟⣟⣿⣏⠄⠀⠀⠘⠇⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣷⣿⡇⣿⡏⣿⡇⠀⢸⣿⠹⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡿⢻⣟⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⡿⢛⣿⣿⡟⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠛⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠋⠘⠃⠙⠃⠛⠋⠛⠙⠛⣿⣛⣛⣛⣛⡞⢛⣿⣙⣛⣿⣻⣻⣿⣿⣿⠟⠃⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⢉⢉⠛⣷⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣄⡘⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⠿⠿⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡏⠉⠙⠿⠟⠉⣃⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣤⠀⠒⠂⠉⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣈⣻⣿⣿⣿⣿⣿⠛⠻⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠍⢸⣿⣿⡀⣿⡏⣿⡟⢿⣿⡇⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⡇⢸⣿⡃⠀⠀⠀⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠷⠿⢷⡿⠃⢹⣾⣿⣦⣀⣀⣸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⣀⣀⣀⡀⣟⣯⣀⡀⣀⣀⣀⢀⣀⢀⣀⢀⣀⣀⣸⡇⣀⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣟⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣩⣿⣯⣵⣿⣝⣿⣷⣿⣽⣿⢸⣿⢸⣿⢠⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⢹⣿⣿⣿⣿⣻⣿⣽⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣷⢹⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⢿⣫⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣞⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣟⣛⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠛⣩⣿⣿⣧⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣿⣿⣷⣿⣿⣿⣿⣟⣯⢻⣷⠻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⣿⣿⣟⣭⡻⠿⠛⠀⠻⠟⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣀⣠⣀⣰⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⢸⣿⣿⣿⣿⡿⣿⡏⣿⣧⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⢻⣿⣿⡇⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣀⣀⡀⣀⣤⣄⠙⣿⣿⣛⠿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⢟⣿⣏⡀⣠⡄⢠⡄⢀⣤⣄⡀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣧⠈⢹⣿⠛⣿⣟⣿⣿⣿⣿⣿⣏⣿⣿⣿⢻⣿⣿⣿⢸⣿⣿⣏⣿⡇⣿⡇⣿⣿⣸⡇⢿⣧⡛⠃⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢱⢸⣿⠀⣿⡏⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⢸⣿⣿⡟⣿⡇⣿⣷⣿⡿⣿⣿⣷⡝⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⠛⣟⣛⣻⣘⣛⡀⠛⠛⠋⠟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣥⡆⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣠⣤⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡈⢹⣿⢻⣭⣄⢠⣤⣄⣰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣟⢻⣿⠿⣿⠇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠟⢸⣿⢸⣿⢹⣿⣼⡿⢾⣿⣿⣸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣼⣽⣿⣷⣟⡃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣶⣷⡄⠀⢀⣴⣶⣾⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣞⣻⣿⣿⣛⣿⣛⡻⠽⢿⣿⡿⠀⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠀⠀⠀⠉⠛⠛⠛⠛⠿⠿⠿⠛⠉⠉⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠉⠉⠉⢛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣦⡎⠹⣧⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⢀⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠿⢿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠈⠛⠋⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡧⠀⠀⠈⣃⣠⠟⠿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣠⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣘⢿⣿⣿⣿⣿⠋⠙⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢻⣿⣿⡀⣿⡏⣿⡟⡟⠙⣿⡿⠀⠀⠀⢨⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⣿⡷⢈⣿⣧⡀⠀⠀⠸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⣿⣃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠷⠿⠷⢿⡃⠀⢸⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⣀⣀⣀⡀⣐⣿⣃⣠⣄⣤⣀⢀⣀⢀⣀⠀⣀⣀⣀⢨⣿⣤⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣩⣿⣯⣷⣿⣝⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⢰⣿⢹⣿⠅⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠉⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣾⣿⢸⣿⢸⣿⣿⣷⢸⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠁⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⣿⣫⣶⣿⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣿⣿⣾⣿⣿⣿⣿⣿⣝⣛⢉⣿⣿⣷⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡀⣿⣿⣿⣿⣿⣿⣿⣟⣭⢻⣷⠸⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠻⠟⢀⣠⣶⣿⣿⣟⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣀⣸⣿⣿⣿⣿⡿⣿⡟⣿⣧⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢻⣿⣿⣧⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠘⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣀⣀⡀⣀⣤⣄⠀⣤⣭⣉⠉⣻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣿⣟⣿⣟⣷⣠⡄⢠⡄⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣷⣈⢹⣿⡇⣿⣟⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣇⣿⣿⣻⣧⣿⣧⡛⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢹⢸⣿⠀⣿⡏⠽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡇⣿⣟⣿⡿⣿⣿⣿⡝⣿⡇⡂⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⠛⠈⠛⣻⣼⣟⣧⠛⡛⠃⠉⢙⣻⣿⣿⣿⣿⣿⣿⣿⣛⣿⣼⣛⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣛⣻⣿⣾⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣠⣤⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣽⢻⣿⣥⣴⣦⣄⣰⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣟⠿⠿⠿⢛⡿⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣷⣿⣧⣿⣇⣀⣀⣇⠀⠀⠀⢀⣀⣀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠂⠀⣰⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠋⠙⠳⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣛⣿⣿⣿⣿⣛⣻⣏⣼⣿⣿⡏⠀⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠉⠉⠉⠛⠛⠿⠿⠿⢿⠿⠿⠛⠋⠉⠉⠀⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣩⣯⣭⠻⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣰⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠙⠿⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⠀⠀⠙⠿⠉⢹⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠲⠦⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣄⣀⣀⠀⣀⣀⣀⢻⣿⣿⣿⣿⠃⠀⠈⠛⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢹⣿⣿⡀⣿⡏⣿⣯⣿⠀⣿⣿⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⡿⠟⠐⣿⣿⣦⡀⠀⠀⣹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⣿⣧⠸⠿⠀⠸⠿⠿⠿⠏⠻⠷⠿⠷⠿⢧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⣀⣀⣀⡀⣀⣿⣻⣶⣿⣶⣀⢀⣀⢀⣀⢀⣀⣀⣒⠀⣿⣧⣸⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⣽⣿⣿⣷⣿⣟⣿⣿⣿⣿⣿⣸⣿⢸⣿⢸⣿⣿⣿⢰⣿⢹⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⣟⣛⣿⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣷⣾⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⣿⣫⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣐⡛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣻⣿⣛⡟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⠛⠈⣿⣿⣷⣟⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣤⣿⣿⣿⣿⣿⣿⣿⣟⣯⢻⣷⠀⣿⣿⠉⠉⢙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣄⣻⣟⣤⣤⣾⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⢀⣀⡀⢻⣿⣿⣿⣿⣿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣏⣿⡏⣿⣧⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠇⠿⠻⢿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣄⣀⡀⣀⣤⣄⠀⣠⣄⣀⠀⣠⣴⡖⢠⣤⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣿⣿⣿⣟⣹⣻⣷⣰⣖⣆⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣷⣾⢹⣿⡗⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⡇⣿⡇⣿⣿⣻⣿⣿⣷⣻⠃⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢻⢸⣿⣧⣿⡏⠽⠿⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⣿⡷⣿⡿⣿⣿⣿⡟⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠋⢼⣟⣯⣛⣛⠃⠀⣘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⢿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣠⣄⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢠⣿⣿⣻⣯⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⣟⣿⣟⢯⡀⠀⠀⡎⠁⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠹⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣷⣻⣛⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡏⢻⡟⣿⡷⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⠟⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⡛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠼⠟⠛⠙⠛⠟⣿⣛⣛⣛⣞⠛⣿⣝⣛⣿⣿⣿⣿⣿⣿⣿⠟⠀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⠁⠀⠀⠉⠉⠙⠻⠿⠿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⣀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⢿⣿⠟⠛⠂⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢯⠤⠚⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣈⣙⣛⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠛⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⠀⢸⣿⠻⣿⣿⠀⠀⠀⢈⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⣹⣿⣰⣿⣟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⣀⡸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠀⣿⠃⢈⣿⣿⣷⣤⣀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⣿⣿⣅⣀⢀⣀⢀⣀⣀⣀⠀⣀⣠⣀⠀⣙⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠱⣿⣝⢛⣰⣿⣿⣿⣿⣿⣾⣿⢸⣿⣿⣿⢰⣿⢹⣿⠄⣿⣧⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠘⣬⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿⢸⣿⣿⣷⢸⣿⢠⣤⠄⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⠿⠋⠀⠛⣇⣠⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣿⣾⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣘⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣻⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⠀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣟⣻⣻⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠉⠙⠿⠿⠿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠻⠇⠀⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⠀⠀⠀⠀⠀⢘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⡀⢀⣀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣥⣴⣾⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣏⣿⣿⢯⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠛⠿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣠⣀⣀⠀⣠⣥⡄⢰⣿⣭⡄⣩⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣿⣿⣿⣿⣿⣻⡟⣻⡇⣖⣶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠆⣿⣿⣧⠈⢹⣿⣗⣿⣏⡃⢠⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡏⣿⡇⣿⣿⣻⣿⣿⣷⣿⣿⣦⢄⡠⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠈⢸⣿⣿⣿⡏⠕⠀⢸⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⣿⣷⣿⡿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣯⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠛⢿⣿⣟⣃⣮⡘⠛⣠⣖⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣟⣻⣽⣿⣿⣿⣿⣿⣟⣛⣽⣿⣿⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣠⣄⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣘⢻⣿⣟⣣⣨⣴⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⢿⣿⣉⠉⠋⢿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠹⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⢳⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡏⢿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⢿⣿⣿⡏⠀⣴⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⡛⡃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠻⠿⠟⠛⠛⠛⣿⣟⣛⣞⠛⡿⣙⣛⣻⣻⣿⣿⣿⣷⣾⣿⠿⢃⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⠦⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⢁⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣶⡾⠿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣋⣨⣍⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⣸⣿⠙⣿⣿⠁⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠀⠀⣼⡿⣀⣿⣿⡀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⣤⣠⣄⣀⢀⣀⠀⣀⣀⣀⠀⣀⣠⣀⠀⣀⡛⣁⡈⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⠛⣰⣿⣹⣿⣾⣿⣸⣿⢰⣿⣿⣿⢰⣿⠹⣿⠄⣿⣧⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠀⣬⢻⣿⣹⣿⣿⣿⣿⣿⢿⣿⢸⣿⣿⣷⢸⣿⢠⣤⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠛⠛⠀⠀⠈⠻⠾⠋⠈⠻⠾⠋⠀⠛⠃⠀⠛⠿⢿⣗⣿⣿⣿⣿⣿⣿⣿⣞⣿⣛⣿⣩⣻⡿⣛⣄⣿⣃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⣠⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣻⣿⣷⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣽⡿⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⠃⠀⠛⠃⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡅⠀⠈⠛⠛⠛⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡃⢀⣀⡀⢈⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡃⣀⣀⣀⣀⣀⡲⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡏⣿⣷⣿⣿⣾⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⣨⣽⡍⢩⣽⣿⡟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣻⡇⣀⣤⣄⡠⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣧⠈⢹⣿⣥⣿⣏⡣⠉⢹⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⣿⣿⣻⣷⣿⣷⣿⣿⣧⣀⡀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠀⢸⣿⣷⣿⡏⠥⡤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⣿⣧⣿⡿⣿⣿⣿⣿⣿⡿⢟⣷⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠛⣿⣿⣛⠃⢵⡞⠛⠉⣉⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣧⣿⣿⣻⣿⣟⣻⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣠⣤⣀⠀⠀⢀⣤⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣈⢻⣿⣖⣿⣫⣆⣾⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣟⣿⣿⡟⠛⠿⢿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠹⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⣷⣿⣿⣿⣿⣶⣶⣿⡇⠀⢀⣰⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢹⡟⣿⡟⢻⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⣛⣛⣃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠻⣿⣿⢿⠟⣿⣿⣿⣿⣟⡛⡿⢙⡛⢿⣿⣿⣿⣿⣿⣶⣿⣿⠟⣠⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠿⠛⠻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠉⢰⣶⣶⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠠⣿⠏⠉⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⠿⠿⠋⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣷⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣷⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠁⠈⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⢠⣿⡏⢉⣿⡇⠀⠀⠀⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠀⠀⣴⣿⠃⣼⣿⣧⡀⠀⠀⣻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⣠⣰⣖⣀⢀⣀⠀⣀⣀⣀⠀⣀⣀⣀⠀⣀⡸⣃⡀⣸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣟⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⢛⣰⣿⣽⣿⣿⣿⣼⣿⢰⣿⣿⣿⢰⣿⠹⣿⠄⣿⣷⣿⣧⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠀⣬⢻⣿⣹⣿⣿⣿⣿⣿⣻⣿⢸⣿⣿⣷⣸⣿⢠⣤⠄⣿⡏⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠛⠀⠀⠈⠻⠞⠋⠈⠻⠾⠋⠀⠛⠃⠀⠛⣿⣟⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣨⣻⣿⣛⣄⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⢀⣾⣶⣿⣿⣿⣻⣿⣿⣿⣿⡿⣿⣿⣻⡿⣻⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⣻⣿⡷⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⡿⠋⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡻⠃⠀⠻⠃⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⠀⠀⠈⠉⠙⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡃⢀⣀⡀⢀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣠⣀⣀⣠⣠⣠⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⡏⣿⣿⢯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⣠⣤⡆⢠⣶⣯⡍⣩⣽⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣻⡏⣹⡗⣔⣶⣖⣄⡈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣧⠈⢹⣿⡷⣿⣏⡓⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⣿⣿⣻⣿⣿⣷⣿⣿⣿⣷⣢⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠀⢸⣿⣿⣿⡏⢥⡀⢸⣿⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⣿⣷⣿⡿⣿⣿⣿⣿⣿⡿⣧⣼⣿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠛⠻⣛⣟⣃⣠⡜⠛⢀⣄⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣠⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢙⣿⣟⣿⣡⣅⣾⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⢿⣿⣏⠉⠉⣸⡿⠁⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠹⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡿⢿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⢸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡏⢹⡏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⣿⣿⣿⠀⣰⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⣛⢃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠿⠛⠛⠛⠛⠛⣟⣛⢟⡛⠘⢘⣛⣻⣛⣻⣿⣿⣿⣿⣿⠟⢉⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢀⣾⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠘⠟⠁⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⠟⢛⠟⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⠏⠉⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠷⠿⠷⠿⠃⠀⠀⠀⣼⡟⠙⣿⡿⠀⠀⠀⣰⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠠⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⡀⠀⣀⣀⣀⠀⣿⡿⣈⣿⣇⡀⢀⣀⣹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣟⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⠛⢰⣿⣿⣿⢰⣿⢸⣿⠀⣿⣿⣿⢰⣿⠹⣿⠀⣿⡇⣿⣿⣿⣷⣿⣯⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠀⣬⢻⣿⣸⣿⣿⣿⣾⣿⢸⣿⠀⣿⣿⣷⢸⣿⢠⣤⠄⣿⡇⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠁⠘⠋⠀⠀⠈⠻⠞⠋⠈⠻⠾⠋⠀⠛⠃⠴⢛⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠘⠛⣛⡟⠀⣻⠿⠛⠀⣿⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⠀⣀⣘⣻⡻⣿⣿⣿⣿⣿⣿⡿⣷⣒⣰⡛⣓⣐⣛⢲⣓⣀⡅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣷⣿⣿⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⡽⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠿⠃⠿⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣀⡀⢀⣀⣠⣖⣚⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣀⡀⠈⣛⣛⡛⣛⡻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣾⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣀⣿⢿⣇⣻⣻⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⡿⣿⣿⣿⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠻⣻⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣀⣀⡀⣀⣤⣄⠀⣠⣬⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⢠⡄⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠏⣿⣿⣿⠋⢹⣿⡓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣻⣧⣿⣧⣛⢃⣠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢹⢸⣿⡟⣿⡏⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⡿⣿⣿⣿⡟⣿⣏⣯⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⢻⣼⣿⣿⡟⢛⠃⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⣠⡀⣠⡀⣠⣀⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢹⣿⣏⢠⣾⣄⡀⣰⣞⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⠿⢿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠷⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣙⢾⣿⣽⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣧⣴⣵⣿⠇⠀⢀⣴⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢻⣿⣿⣿⣿⣟⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⡟⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⣌⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠋⠙⠳⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣿⣿⣛⣿⣛⣻⣛⣽⣿⣿⢃⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠛⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢐⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠸⠟⠁⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠿⠿⡟⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠾⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣽⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠀⠀⢹⣿⠿⣿⣿⠇⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⣤⣀⢀⣀⢀⣀⠀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣸⣿⡀⣺⣻⣀⣀⣀⢺⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⠛⢰⣿⢽⣿⣸⣿⢸⣿⠀⣿⣿⣿⢰⣿⠹⣿⠀⣿⡟⣿⣧⣿⣿⣿⣯⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠀⣬⢻⣿⣸⣿⢸⣿⣿⣿⢸⣿⠀⣿⣿⣷⢸⣿⢠⣤⠀⣿⣇⣿⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠓⠀⠀⠈⠻⠞⠋⠈⠻⠾⠋⠀⠛⠃⠀⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡔⠛⠛⠛⠀⠻⠿⠛⠀⠻⣻⢻⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⠀⣀⣈⣀⡿⣟⣻⣿⣿⣿⣿⡿⣿⣷⣠⡀⣚⣓⣀⠾⣀⣀⡀⣙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢠⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣧⣿⣿⣿⣷⣿⣿⢹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⠙⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠢⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠟⠃⠿⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⡀⢀⣀⡀⢀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠉⣘⣛⡿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⡇⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⡿⣿⣿⡇⢀⣿⢿⡇⣻⣹⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠻⠓⣿⣿⣿⣟⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣄⣀⡀⣀⣤⣄⠀⣠⣄⣘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⢡⡄⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣷⠛⢹⣿⡓⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⣿⣿⣸⣧⣿⣧⣛⡃⡀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢠⢸⣿⣿⣿⡏⠡⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⡇⣿⡇⣿⡿⣿⣿⣿⣿⣿⡏⣿⣴⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠛⢘⣿⣿⣿⡟⢃⠁⠜⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⠀⣠⡀⣠⡀⣠⣄⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢨⣿⣿⣫⣤⣞⡀⢠⣔⣾⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⡿⢿⣿⠏⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣽⣷⣿⣿⣽⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣧⣶⣤⣾⡿⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡿⢿⣿⣿⡏⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⠇⢀⣼⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⣛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠋⠛⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣟⣛⣿⣛⣻⣻⣻⣿⣿⡟⣠⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⡜⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⣫⣥⣤⡄⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡏⢸⣿⡿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠿⢴⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠘⠛⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣬⣭⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⠟⠛⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠀⠀⠀⣻⡿⠻⣿⡿⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⣤⣀⢀⣀⢀⣀⠀⣀⣀⡀⠀⣀⣀⣀⠀⣀⡀⣻⣷⣐⣿⣇⣀⣀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣟⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⠛⢰⣿⣻⣿⣼⣿⢸⣿⠀⣿⣿⣿⢰⣿⠹⣿⠀⣿⡏⣿⣧⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠀⣬⢻⣿⢸⣿⣸⣿⣿⣿⣸⣿⢀⣿⣿⣷⢸⣿⢠⣤⠄⣿⡇⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠘⠛⠀⠀⠈⠻⠞⠋⠈⠻⠿⠋⠀⠛⠃⠀⠻⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⣟⠿⠛⠛⠀⠻⠿⣛⠀⠛⠃⣿⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⠀⣀⣁⣁⡺⣿⣻⣿⣿⣿⣿⡿⣿⣿⣷⡄⣘⣛⣂⢸⣛⣒⣤⣀⡉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢠⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣧⣿⣿⣿⣷⣿⣿⢹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⠙⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠿⠃⠿⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣆⡀⢀⣀⡀⢀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠋⣉⣛⡻⣛⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⡇⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣿⢿⡇⣻⣹⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠻⠃⢻⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣠⣀⣀⠉⣻⣿⡿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣳⡄⣄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣷⠈⢹⣿⣅⣿⣏⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⣿⣿⣻⣿⣿⣷⣿⣇⣀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠘⢸⣿⣿⣿⡏⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⡿⣿⣿⣿⣿⣿⣟⣿⣾⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⢿⣿⡛⠛⢃⠀⠘⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣛⣫⣿⣟⣻⣽⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⠀⣠⡀⣠⡀⣠⣄⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣸⣟⢻⣿⣏⡀⣠⣟⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⢿⠛⠙⣿⣿⠁⠀⢀⣤⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡏⢹⡟⣿⡏⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⢛⣛⣇⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⣽⣿⠟⡿⠟⢿⣿⣛⣛⣛⡞⢛⣿⣙⣛⣿⣿⣿⣾⣿⣿⠟⢻⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⡁⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣛⣩⣟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠰⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠘⠿⠃⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⡈⣛⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠛⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠧⠿⣷⠿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⠀⠀⠙⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣀⣠⣀⢀⣀⢀⣀⠀⣀⣀⡀⠀⣀⣀⣀⠀⣀⡸⣿⡀⣸⣻⣀⣀⣀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣟⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⠛⢰⣿⢹⣿⢸⣿⢸⣿⠀⣿⣿⣿⢰⣿⠹⣿⠀⣿⡿⣿⣧⣿⣿⣿⣏⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠀⣬⢻⣿⢸⣿⣸⣿⣿⣿⢸⣿⠀⣿⣿⣷⢸⣿⢠⣤⠀⣿⡇⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠘⠛⠀⠀⠈⠻⠞⠋⠈⠻⠿⠋⠀⠛⠃⠀⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡜⠛⠛⠛⠀⠻⠿⠛⠀⠻⣻⡿⣨⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⠀⣒⣛⣁⣻⣿⣿⣿⣿⣿⣿⡿⣿⣇⣀⠀⣰⣂⣀⢾⣂⣀⡀⠸⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢀⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣧⣿⣿⣿⣷⣿⣿⢹⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⠽⣿⣿⣿⣟⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠿⠃⠿⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣀⡀⢀⣀⡀⢀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣾⣿⡇⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⢿⡇⡻⣹⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠻⢳⣿⣿⣿⣟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣀⣠⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⣠⡄⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣿⢋⢹⣿⡓⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⣿⣿⣻⣿⣿⣧⣻⢇⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⢻⢸⣿⡟⣿⡏⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⡟⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠛⣸⣿⣿⣛⠛⡃⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣛⣻⣿⣿⣿⣿⣟⣿⣿⣿⣿⢛⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⣠⡀⣠⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢠⣿⣷⢲⣾⣇⡀⣰⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣟⠿⠛⣟⣿⠏⠀⠀⣠⣤⣀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣽⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣷⣿⣷⣿⣏⣴⣿⣿⠀⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡿⣿⣿⣿⣏⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⠿⢿⣿⣿⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⢈⣛⣛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠛⣫⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⠜⣛⣿⣛⣛⣿⣿⣿⣿⣿⡿⠻⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠿⠿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⠷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⣠⣶⣶⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠋⠉⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⡟⠛⢻⣿⠟⠘⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⣤⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠁⠉⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠀⠀⠠⣿⡉⢉⣿⠇⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣀⣀⠀⣐⣦⣀⢀⣀⢀⣀⠀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣰⣿⡃⣘⣻⣄⣀⣀⢈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣟⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⠛⢰⣿⢹⣿⣾⣿⢸⣿⠀⣿⣿⣿⢰⣿⠹⣿⠀⣿⡇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠀⣮⢻⣿⣸⣿⣾⣿⣿⣿⣾⣿⢠⣿⣿⣷⢸⣿⢠⣤⠄⣿⣷⣿⢻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠓⠀⠀⠈⠻⠞⠋⠈⠻⠾⠋⠀⠛⠃⠠⠻⡿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣞⠟⠛⢻⣀⡻⣿⡛⢀⡟⠻⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣳⣿⣟⣛⣿⣿⣿⣿⡟⣿⣿⣿⡄⣋⣿⣗⢻⣉⣻⣷⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣟⣿⣻⣿⣿⣿⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠻⠃⠀⠛⠃⠿⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣀⡀⢀⣀⡀⢐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡃⠀⣀⣉⡉⣙⡻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣧⣤⣿⢿⣧⣿⣻⣿⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠻⠋⠻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣄⣀⡀⣀⣤⣄⠀⣀⣀⣀⠘⣻⣿⡟⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⡄⣲⣖⣄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠆⣿⣿⣷⣾⢹⣿⡷⣿⣏⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣻⣿⣿⣧⣻⣧⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠹⢸⣿⣧⣿⡏⠁⠨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⣿⡇⣿⡿⣿⣿⣿⣝⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⢘⣿⣯⣛⣻⠃⠀⢘⣛⣿⣿⣿⣿⣿⣿⣿⣟⣿⣼⣿⣿⣯⣿⣟⣿⣽⣿⣿⣿⣯⣽⣛⣿⣽⡏⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣜⢿⣧⣄⣰⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡟⣟⣿⣏⠁⣘⣼⡟⠀⠀⣠⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣹⣿⣷⠿⢿⣿⣿⣿⣿⠇⠀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡏⢻⡟⣿⡏⣿⡏⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣷⠿⢟⣿⣿⣿⡏⢀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⡫⠛⠃⠛⠙⠛⠛⢛⡛⠘⣛⣘⣛⣹⣛⣻⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣄⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⢀⣤⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⡛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠝⠛⠻⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡅⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠲⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠋⠉⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⣼⡏⠈⣹⡏⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢠⣿⠗⠐⢿⣧⡀⠀⠀⢹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⠀⠸⢿⣿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣤⣀⣀⣔⣧⣠⣞⣻⢿⣿⢶⣀⣀⣀⠀⣀⣀⣀⠀⣂⡀⣰⡦⣀⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣏⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠁⣿⣝⢛⣰⣿⣿⣿⣿⣿⣾⣿⢸⣿⣿⣿⢰⣿⠹⣿⠄⣿⡇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡟⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠀⣬⢻⣿⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣸⣿⣤⣬⠅⣿⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠁⠘⠃⠀⠀⠈⠻⠞⠋⠈⠻⠾⠋⠀⠛⠃⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣛⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⠀⣀⣀⣻⣿⣿⣻⣿⣿⣿⣿⡿⣋⣻⣻⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠻⠳⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠉⢹⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢇⣄⣿⡃⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣏⣥⣤⣄⣠⣜⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢈⣛⡛⢇⣐⣻⣿⣿⣿⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⡇⣿⡟⣿⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⡇⣿⡟⣿⡟⠿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠘⠃⠛⠃⠙⠷⠟⠙⠻⠿⢇⠿⠇⡿⠿⠋⠿⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣽⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣀⣀⣀⠀⣀⣀⡀⢠⣬⣤⣎⣥⣤⡄⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣿⣿⣿⣟⣿⣻⣿⣿⣿⣟⣿⣟⣿⣤⣤⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠆⣿⣿⣧⠈⢹⣿⡗⣿⣏⣡⠀⢸⣿⣹⡏⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣟⣿⡏⣿⡟⣿⣿⣻⣿⣿⣿⣿⣧⣿⣿⡾⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣄⣿⣼⣿⠀⢸⣿⠈⣿⡏⠅⠀⢸⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡇⣿⡇⣿⡿⣿⣿⣿⡝⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠁⠛⠋⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⠛⠀⠛⠂⠘⠛⠀⠛⠛⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣵⣿⣿⣿⣿⣿⣛⢛⣵⣿⡇⠀⠀⢀⣤⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣠⡀⢀⣀⢀⣀⣀⢀⣀⣀⡀⢻⡟⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⣟⣿⣟⢿⣿⣿⣿⡿⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠟⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡇⢸⣿⣸⡇⢼⣿⣟⣿⣿⢿⣿⣿⢿⣿⣟⣿⠸⢹⣿⣷⣛⣃⣿⡏⣼⣿⣿⡁⣀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⢸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡇⣿⣿⣿⢸⣿⠉⢼⣿⢿⣿⢰⣼⣿⠟⠿⠟⠿⠃⠛⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠛⠃⠛⠃⠛⠀⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠛⠘⠛⠛⢘⣛⣜⣛⡸⠙⢻⣆⠛⠃⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⣛⠛⣻⣿⣿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⢷⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣼⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠉⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⡟⠛⠛⣿⠟⠻⡧⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⣤⣀⠐⠀⠒⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣛⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠋⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠈⣻⡿⠿⣿⡿⠀⠀⠈⠛⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⢿⠀⠸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠀⠀⣻⡆⢰⣿⡇⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣠⣀⠀⣀⣤⣀⣀⣀⢀⣀⠀⣀⣀⣀⠀⣀⣠⣀⠀⣘⡛⣁⣈⣻⣷⣄⣀⣀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠑⣿⣝⢛⣰⣿⣿⣿⣼⣿⢸⣿⢠⣿⣿⣿⢰⣿⢹⣿⠀⣿⡇⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣺⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⢀⣬⢻⣿⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⢸⣿⢠⣤⠄⣿⡇⣿⣻⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠃⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⠿⠋⠀⠛⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡿⠛⣿⡈⢻⣿⡛⠀⠻⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣶⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣿⣻⣷⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⣷⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠿⣇⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣻⠟⠉⠙⠿⠿⠿⢟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⣀⣀⡀⣀⡺⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣾⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⣿⣿⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠘⠃⠻⠃⠛⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣄⡀⢠⣤⣀⡀⣀⣤⣄⠀⣤⣄⣀⠀⣠⣬⡄⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣻⣿⣻⣗⣖⣶⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡏⣿⡇⣿⣿⣿⡇⢸⣏⣿⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣧⠈⢹⣿⠃⣿⣏⡁⠙⢻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡏⣿⡇⣿⣿⣻⣿⣿⣷⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠀⢸⣿⣁⣿⡏⠅⠀⢸⣿⠉⣿⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⣟⣿⡇⣿⡿⣿⡿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠛⠛⠀⠛⠂⠘⠛⠉⠛⢛⣣⢃⡘⣛⣴⣟⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣟⣻⣽⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⡀⣠⡀⣠⣄⣀⠀⠀⢀⣤⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣠⣀⢠⣾⣟⣊⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⣿⣤⣄⣸⣿⡏⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠹⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⢃⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢹⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⣿⣿⠿⢿⣿⣻⣫⣿⣿⡏⠀⣰⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢶⠆⠰⠶⠶⠖⠛⠃⠛⠃⠛⠃⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠋⠛⠙⠛⠙⠛⠛⠛⣛⣘⠛⢀⣙⣛⣤⣛⣻⣿⣿⣿⡟⠉⢀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠋⠉⢛⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⢷⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠠⠼⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⡟⠛⠛⣿⠛⠻⠅⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣦⣬⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⠀⠀⣹⠛⠛⣿⡏⠀⠀⠀⢉⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⢠⣿⠄⢸⣿⡃⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⣴⣸⠿⠿⠿⠏⠻⠷⠿⠷⠿⠃⠀⠀⠀⠈⠉⠀⢰⣿⣿⣦⣤⣤⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣠⣰⣄⣐⣿⣻⣶⣦⣀⣀⠀⣀⣀⣀⠀⣀⣠⣀⠀⣀⡀⣀⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠱⣿⣝⣛⣴⣿⣿⣿⣿⣿⢼⣿⢰⣿⣿⣿⢰⣿⠹⣿⠀⣿⡇⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⢀⣮⢻⣿⣹⣿⣿⣿⣿⣿⢾⣿⢸⣿⣿⣷⢸⣿⢠⣤⠄⣿⣇⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠁⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⠾⠋⠀⣻⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣾⣿⣛⣿⣾⣿⣿⣿⣦⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡟⣲⣿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣟⣻⣻⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣷⣽⣿⣿⣿⣟⣿⣿⣿⢻⣿⣿⠀⠘⠛⠙⠛⢻⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠻⣟⣠⠀⢀⣀⣀⣘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⣶⣆⡀⢛⣛⣿⣿⣿⣟⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠟⠙⠿⠿⠏⠿⠋⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣰⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣠⣀⣀⠀⣀⣤⡀⢠⣴⣦⡄⣩⣤⡌⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⢿⣿⣟⣿⣻⣿⣿⣿⣟⣿⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣧⠈⢹⣿⣥⣿⣏⡁⠀⢸⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⣿⡧⣿⣿⣻⣿⣿⣿⣛⢫⣿⣇⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠀⢸⣿⠁⣿⡏⡥⡀⢸⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡇⣿⡗⣿⡿⣿⣿⣿⡟⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠛⠀⠛⣛⣃⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣵⣛⣳⣿⣛⣛⡛⠛⠹⠏⠃⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⡀⣠⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣤⣟⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡝⣟⣿⣟⢿⣾⣶⣷⡇⠀⠀⣰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡇⢸⣿⣹⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣸⣻⣿⣷⠛⠓⣿⡏⢻⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡏⣿⣿⣿⢻⣿⠿⢿⣿⢿⣿⠸⣿⣿⣛⠿⢿⣿⣷⣾⡿⠿⢰⣾⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠘⠛⠘⠛⠛⣛⣛⣜⣛⣼⣿⣿⡟⠛⠛⠟⠛⠋⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣶⣤⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠉⢉⣉⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⡉⡙⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠠⠿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⡀⠀⠙⠃⠀⠉⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠈⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡄⣿⡏⣿⡇⠀⠀⢻⣿⣿⣿⣿⠃⠀⠀⠛⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⢸⣇⠀⣽⣿⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠋⠸⠿⠀⠸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠿⠏⠠⣻⣿⣦⡀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣤⣀⢰⣟⣾⣀⢀⣀⢀⣀⠀⣀⣀⣀⠀⣀⣀⣀⠀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠑⣿⣝⢛⣴⣿⣿⣿⣾⣿⢸⣿⠀⣿⣿⣿⢰⣿⠹⣿⠄⣿⣯⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡏⢓⣾⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣷⢸⣿⢠⣤⠅⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⠿⠋⠀⣻⣇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣛⣿⣨⣻⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⣿⣛⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢾⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣷⠟⢻⣻⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣟⣷⣽⣿⣿⣿⣟⣿⣿⣿⠻⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠻⠛⠀⠀⠀⠀⢉⡛⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣁⣴⣆⣠⣤⣶⣶⣿⣿⣹⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⢯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠻⠃⠛⠿⢟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣠⣀⣀⠀⣠⣤⡌⢡⣤⣤⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣿⣟⣿⣿⣷⣻⣮⣻⣿⣟⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣹⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣧⠈⢹⣿⡁⣿⣏⡁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⡏⣿⣿⣻⣿⣿⣧⣛⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠀⢸⣿⠟⣿⡏⠁⠀⢸⣿⣽⣿⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⣏⣿⡇⣿⣇⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠛⢠⣻⣟⡣⢤⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢽⣛⣻⣿⣿⣿⠛⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⣠⡀⣠⡀⣀⣀⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣈⢻⣿⣗⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⡟⣟⣿⣗⢖⣢⣰⣿⠋⠀⠀⣴⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡇⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣷⢛⣃⣿⣿⣿⣿⣿⠀⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡏⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⢻⣿⣿⠿⢿⣿⣃⣿⣿⡇⣀⣾⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠆⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠌⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠛⠙⠛⣛⣙⣛⣘⣛⣽⣟⣛⣿⣛⣻⣿⣿⡟⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠿⢿⣷⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⣾⣿⡷⢦⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⣀⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄⡙⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠙⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⡿⠛⠻⢿⣿⠿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢀⣀⡠⠅⠀⠂⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣌⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡤⣿⡏⣿⡇⠀⠀⢙⡿⠛⢿⣿⠇⠀⠀⠈⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⣄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⣸⣷⠀⣾⣿⠀⠀⠀⠠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⣿⣀⡸⠿⠿⠿⠏⠻⠧⠿⠷⠿⠃⠀⠀⠛⠋⠀⣽⣿⣷⣤⣀⣠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣠⣀⠸⣿⣿⣡⣄⣀⢀⣀⠀⣀⣀⣀⠀⣀⣠⣀⡀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⣯⡵⣿⣝⣻⣴⣿⣿⣿⣿⣿⢸⣿⢠⣿⣿⣿⢰⣿⠹⣿⠍⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⢀⣾⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣷⢸⣿⢠⣤⠄⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⠿⠋⣠⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣿⣨⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⡙⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣛⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣷⣽⣿⣿⣿⣟⣿⣿⣿⢻⣿⣿⠹⠿⠿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠻⠟⠀⠀⠀⠀⢠⣜⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣾⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣿⣯⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠛⠿⠟⠙⢿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢇⣀⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣀⡀⢠⣤⣀⡀⣀⣤⣄⠀⣠⣀⣀⠀⣠⣤⡄⢠⣤⣤⡜⣿⣯⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣷⠈⢹⣿⣅⣿⣏⡁⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣿⣧⣻⣿⣿⣣⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠀⢸⣿⠋⣿⡏⠅⠀⢸⣿⣽⣿⣿⣿⣿⣾⣿⣿⣿⣸⣿⣿⣿⣿⡇⣿⣧⣿⡿⣿⣿⣿⡟⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠛⢠⣿⣿⡃⢫⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣛⣽⣟⣿⣿⣿⠿⠛⢛⣽⡿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⡀⣠⡀⣀⣀⣀⡀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢹⣿⣟⣿⣿⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⡟⣟⣿⣟⢯⣥⣼⣽⡁⠀⢀⣼⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢾⣿⣿⣷⢿⣧⣿⡿⣿⣿⣿⠃⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣻⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢿⡏⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣻⣿⣿⠿⢿⣿⣧⣿⣿⡧⣠⣾⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠆⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠛⠘⠛⣛⣟⣛⣜⣛⣼⣟⣛⣿⠛⢿⣿⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣤⡤⣠⣤⠀⠀⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈⠛⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠁⠀⠀⠙⠛⣩⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠤⠌⠛⠛⢿⠟⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢸⡇⣿⣏⠿⠊⢹⣿⠉⢸⣿⠉⢸⣿⣿⡀⣿⡏⣿⡇⠀⠀⠀⢈⣿⠛⢿⣿⠃⠀⠀⠀⣹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣈⡻⣿⡄⢸⣿⠀⢸⣿⠃⢸⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⣸⣿⡄⢸⣿⡀⠀⠀⠀⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇⠿⠇⠻⠷⠿⠃⠸⠿⣀⣸⡿⠿⠿⠏⠻⠷⠿⠷⠿⠃⠀⠀⠀⠙⠁⠀⣽⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⢀⣀⢀⣀⢀⣀⣀⡀⣀⣄⣀⡄⣀⣿⣿⣄⣀⢀⣀⠀⣀⣀⣀⠀⣀⣠⣀⠀⣀⡀⣐⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⡇⢸⣿⡉⠀⢸⣿⢹⣿⢸⣿⢸⣿⠈⣿⡏⠱⣿⣝⣛⣴⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⢰⣿⠹⣿⠀⣿⡇⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⣿⠁⠀⢸⣿⢸⣿⢸⣿⢸⣿⠀⣿⡇⠉⣬⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⢸⣿⢠⣤⠄⣿⡇⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠁⠘⠛⠀⠀⠈⠻⠾⠋⠈⠻⠿⠋⠀⣻⣷⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣿⣿⣿⣿⣿⣦⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⣀⣀⣙⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣖⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠉⣿⡏⠁⣿⣏⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣻⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠉⠙⠿⠟⠿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⠟⣀⡀⠀⣀⣀⣘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⢀⣀⣀⢘⣛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⡏⣿⣯⣿⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡿⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠃⠙⠷⠟⠙⠿⠿⠟⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢀⣤⣄⡀⣠⣤⣄⡀⢠⣤⣀⡀⣀⣤⣄⠀⣠⣀⣀⠀⣠⣤⡄⢠⣤⣴⡆⣤⣿⡅⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣟⣷⣤⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠇⣾⡇⣿⡇⣿⣿⣿⡇⢸⣏⣽⡇⣿⡇⣿⡇⣿⣏⣿⠇⣿⣿⣧⠈⢹⣿⢓⣿⣏⡁⠀⢸⣿⣹⡏⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⣿⣧⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⡆⣿⡇⣿⡇⣿⣿⣿⡇⢸⡟⠉⠁⣿⡇⣿⡇⣿⡏⣿⣆⣿⣼⣿⠀⢸⣿⣟⣿⡏⢹⡖⢸⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣧⣿⡿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠛⠛⠁⠛⠛⠛⠃⠘⠃⠀⠀⠙⠛⠛⠀⠛⠃⠛⠙⠛⠀⠛⠂⠘⠛⠉⠛⣿⣣⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣽⣛⣻⣿⣿⣿⡛⠛⠙⣿⡿⠁⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⡀⣀⡀⣀⣀⣀⠀⠀⢀⣠⣤⡀⢀⣠⣤⡀⣀⡀⢀⣀⢀⣀⣀⢀⣀⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⣟⣿⣟⢿⣿⣿⣿⣿⡄⠀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⣿⣧⣿⡇⣿⡏⣿⡇⠀⢸⣿⠸⠿⢸⣿⢸⣿⢹⣿⣼⡿⢸⣿⣉⢸⣿⣹⡇⢸⣿⣹⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣷⣿⠗⣿⡿⠿⣿⣿⣿⠀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⡇⣿⣿⣿⡇⣿⡇⣿⡇⠀⢸⣿⢻⣿⢸⣿⢸⣿⠸⣿⣿⡇⢸⣿⠉⢸⣿⢹⡇⢸⡟⣿⡇⢸⡏⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⢹⢿⣿⣏⠿⢿⣿⣷⣶⡿⠿⢻⣶⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠆⠰⠶⠶⠖⠛⠃⠛⠃⠛⠁⠛⠃⠛⠛⠛⠁⠀⠈⠛⠋⠛⠈⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠘⠛⠘⠃⠘⠃⠙⠃⠘⠃⠛⠙⠛⠘⠛⠛⣛⣛⣞⣛⣴⣾⣿⣿⠛⠛⠻⠛⠛⠇⢀⣸⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3491

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/10/medieval-epo/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/10/medieval-epo/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_We’re_Back_to_Medieval_Times:_The_Case_of_EPO⠀✐


Posted in Europe, Patents at 9:18 am by Dr. Roy Schestowitz


Yesterday in the EPO’s official site:


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


This is the_EPO’s_“role_model”:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇'Are_the_British_public_ultimately_paying_for_Andrew_to
avoid_appearing_in_court?'⦈_


Summary: The EPO’s management thinks that it is the royal family or the Queen
of England; is the EPO aware that this is not how patent offices are meant to
work? The EPO became_a_for-profit_corporation that views itself as entirely
above the law.


⠀⠀⠀⠀⠲⣜⢦⡀⠀⠀⠐⠐⡐⣀⡐⠒⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿
⠀⠀⠀⣠⣝⣎⡏⡇⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⡇⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⢰⣇⢏⣏⣇⡇⠀⠀⠐⠀⠀⠐⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠻⠛⠛⠇⡄⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢠⣓⣒⡯⠎⠈⠀⠀⠀⡉⡀⠀⠐⠐⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡠⠀⠀⠠⠀⢠⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⠀⠠⢄⡀⠀⠀⠀⠀⠀⢸⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⢠⠀⠸⣿⠄⡀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠼⠀⠀⠀⠋⠁⠐⠃⠀⠀⡄⠀⠀⠸⠄⠀⠠⠃⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠃⠀⠀⠂⠀⠀⠀⠀⠑⠂⠀⠀⠒⠂⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠂⠀⠀⠘⠒⠂⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿
⣯⣽⣭⣭⣿⣽⣭⣭⣭⣿⣽⣽⣭⣯⣭⣿⣿⣭⣭⣭⣽⣯⣧⣭⣼⣿⣯⣿⣿⣿⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⡟⡛⢿⠛⢻⢻⡻⠛⢻⡟⠛⢻⣻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⢛⡛⢛⢻⢻⡿⣙⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠿⣯⣵⣟⣿⣸⣿⣶⣶⣇⣅⣷⣯⣺⣬⣻⣇⣷⣇⣨⣼⣿⣇⣇⣯⣽⣬⣻⣇⣇⣷⣿⣨⣸⣿⣾⣅⣇⣗⣇⣸⣀⣗⣿⣪⣊⣥⣇⣧⣣⣸⣺⣃⣥⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡱⢾⢈⠤⣿⣷⣶⣾⡰⣸⠶⣈⠤⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⡿⢿⡟⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣟⣿⢿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⢻⣛⣿⣿⣿⣿⣿⣿⡟⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠇⣒⠹⡇⣾⢐⡂⣿⡆⢰⡇⣶⢸⠑⡂⣹⣿⢨⡥⢺⢰⡆⣷⢰⡇⣇⡒⠇⣴⡌⣿⡇⢴⠌⡁⡿⢸⠀⡶⢹⢸⢸⠡⡦⣿⡇⢸⠇⡇⣷⢰⡇⡇⣶⠀⣦⠹⢒⠈⡆⣾⢑⡂⡃⣧⠹⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣷⣿⣷⣶⣿⣿⣶⣷⣿⣾⣷⣶⣿⣿⣶⣶⣿⣾⣷⣿⣶⣷⣷⣶⣷⣿⣷⣿⣧⣶⣾⣷⣶⣾⣶⣶⣿⣾⣾⣷⣶⣿⣿⣶⣶⣷⣿⣶⣷⣷⣿⣶⣿⣾⣶⣶⣷⣶⣷⣶⣷⣏⣥⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⡿⣿⡿⠭⡿⠿⢿⡿⠿⢿⡿⠋⠽⠿⢿⠿⢿⣿⡟⡻⣿⠿⠿⣿⠿⠏⡿⠿⡿⠿⡿⣿⠿⣿⢿⡿⠻⡿⠿⣿⣿⠿⠿⠿⣿⢿⠿⢿⡯⣿⠿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠺⢃⡋⠅⢰⡘⣰⠀⡇⣿⢸⡐⢓⢸⣿⠀⣇⠿⢠⠀⣿⡿⢠⣥⠹⢰⡇⢀⠸⠇⡇⢸⡀⠭⣴⡘⣤⢃⣾⣿⠸⡄⠿⣸⣿⠩⠅⣧⠉⣄⠸⢇⡇⣇⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⢻⠛⡛⢿⢛⡛⠿⢛⠻⣛⡛⡟⢛⡗⡟⢛⠻⠟⣛⢻⣿⠒⡟⣛⢻⣿⠟⣛⡿⢛⠻⠛⣿⢻⠛⣛⢙⣭⡍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣒⣸⢈⣋⣼⢈⣋⣤⣐⣲⣔⣂⣇⣸⣇⣇⣿⣀⡤⠉⢸⣿⣀⣇⣿⣸⣿⣌⣋⣧⣙⣡⣆⣋⣸⣸⣿⣘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⢿⣿⡟⡏⠻⣿⡏⢿⡿⡻⡻⣿⡛⣿⢹⣻⢿⣿⢙⣿⣹⣿⢻⡟⣿⣿⣿⡛⡟⡻⣟⣿⡟⢻⣿⡟⡟⠹⣿⡟⣟⣿⣿⢹⣿⣿⠋⣿⢹⣿⣿⣻⣹⣿⣿⢿⣿⡟⣟⡟⡻⢹⡿⡟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣀⡕⣸⣸⣿⣨⣨⣄⣇⣿⣗⣷⣩⣸⣇⣧⣸⣢⣧⣄⣷⣶⣩⣸⣶⣗⣿⣈⣰⣷⣺⣇⣷⣾⣨⣯⣺⣶⣇⣡⣿⣺⣈⣔⣅⣅⣿⣒⣗⣺⣦⣇⣇⣿⣒⣷⣸⣕⣗⣺⣋⣿⣂⣿⣒⣅⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⠿⢻⠿⣿⡿⡿⣿⣿⡿⡿⣿⡿⣿⣿⣿⢿⣿⣻⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣾⣷⣿⣾⣶⣿⣷⣿⣷⣿⣷⣿⣾⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣠⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣭⣽⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣴⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⡟⢡⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⢀⢀⣀⠤⠤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣿⣟⠻⢟⠙⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⡟⠕⢡⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠏⠽⠟⠉⠹⠄⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢸⠏⠀⠀⠈⠩⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣆⡀⢀⣤⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠐⠋⠉⠉⠉⠙⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠹⠛⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⠤⠦⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢙⣛⠀⠀⠀⠸⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠜⡇⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣧⣸⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⢠⡆⢠⣤⣤⣾⣿⣿⣿⣿⠟⣔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣴⠿⠿⢛⣷⠃⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣯⢈⣴⣿⣿⣿⣿⠿⢿⣟⣎⣼⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠿⡷⠾⠉⠉⠁⠄⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣟⢛⡛⣛⢛⡛⣈⠛⠛⠛⠛⢍⢭⡩⠌⠬⠉⠉⠁⠉⢭⡩⣍⢭⣩⢭⠳⣄⣮⡁⣀⢦⡪⣍⢍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠒⠋⠀⠀⠘⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⠏⠳⠝⠮⠳⠝⠮⠁⠔⠋⠑⠊⠓⠑⠂⠀⠀⠀⠂⠀⠀⠙⠊⠓⠘⠓⠛⠈⠘⠙⠊⠓⠙⠊⠋⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡛⠋⢛⣿⢻⣿⠏⢻⣏⠙⡛⣿⡻⢻⢻⠛⠛⡿⡛⢻⠛⡟⣿⢙⣿⠛⡟⣛⠛⠛⡛⢿⡛⠛⡛⡏⠻⠻⢻⡻⡟⣟⠛⠻⡛⣿⡟⣟⠹⣻⡻⡟⢙⡟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 3600

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/10/mozilla-three-letter-agencies/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/10/mozilla-three-letter-agencies/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Mozilla_Hired_Top-Level_Managers_Directly_From_the_Central_Intelligence
Agency_(CIA),_Can_They_Be_Trusted_on_Privacy?⠀✐


Posted in Deception at 1:06 pm by Dr. Roy Schestowitz


This article from yesterday leaves out a key part or key fact:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Mozilla's_CSO⦈_


He joined 7-8 years ago (article from 20 months ago):


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


After he had worked for the CIA :


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


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


Don’t worry, he doesn’t call it CIA, it’s just “intelligence community”.


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


His career also started_there [PDF]


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


Summary: Mozilla’s composition of managers is a parade of spies and monopolies;
the message (or promise) does not match the actions


THIS post will be followed up by a video quite soon. This is just to note who
we’re expected to trust with Firefox security.


Mozilla also hired_managers_from_Facebook_while_promising_us_"privacy"_and
bagging_money_from_Google (surveillance giants). Microsoft_is_in_Mozilla's
Board and the VPN is about as trustworthy as DNS_partners. Wake up, people,
Mozilla isn’t woke. It’s just pretending like the Linux_Foundation. They
destroy entire countries. They bomb_and_ban_people_based_on_nationality_alone.
That’s racist. Would you trust Mozilla to decide which sites are trustworthy
and which ones are not? Would you like this company to turn Firefox into a
censorship machine based on some criteria of “misinformation”? Do you trust
Mozilla when it tells you some site isn’t to be trusted because it uses a self-
signed certificate instead of outsourcing to a US-centric cabal of CAs? The
latter begets censorship. Anybody can request and receive a ‘free’ certificate,
but a shadowy group of American firms can revoke_these_at_any_time, denying
access to sites/services.


“The CA model they use facilitates MitM,” an associate of ours noted,
“especially with their antipathy_towards_self-vouched_for_certificates. They
are especially state, then after that Google specifically though pandering to
Microsoft a lot.” █


⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⡀⠠⡄⣠⣀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⡇⣿⢉⢧⡟⡝⡯⣹⠃⡇⢯⢳⡆⣦⢤⣒⠟⣵⢙⡿⣽⡟⣝⢻⢩⠻⡍⡏⡝⢫⢸⣩⢿⡇⡇⢻⢹⢫⣛⡽⣿⢹⢫⢻⡟⣽⢻⢻⢩⢸⢹⡏⣒⢹⠚⡍⣿⡆⡞⣍⡟⣽⢨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣫⢿⡿⡏⣍⠏⣏⣹⠀⡇⣯⢹⢩⠛⣭⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣝⣿⣟⣿⣿⣿⣟⣟⣟⣿⣿⣿⣿⣛⣟⣿⣿⣿⣻⣛⣿⣟⣿⣿⣿⢻⡻⣟⣻⣻⣟⣿⣿⣿⣟⣿⣿⣟⣟⣻⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁
⠁⠉⠀⠈⠉⠉⢱⣙⣛⣻⣛⣛⣛⣻⣛⣟⣛⣛⣟⣛⣛⣛⣛⣟⣛⣛⣟⣏⡟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⢹⣍⡇⠐⣉⡉⠱⣟⣛⡟⣛⣟⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⠛⠛⡟⠙⠛⡛⣟⠟⢻⠛⠛⢹⢛⢻⠉⡟⢻⠛⠛⠻⡟⠋⠛⡟⢛⠙⠛⡟⠟⠛⣻⠛⠛⣻⡟⣿⠙⠛⡛⢹⠙⢻⣛⠻⠛⠛⠛⠛⡟⢻⠛⠛⢛⠛⠛⣻⠙⢻⢻⠙⠛⡏⠙⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⡿⣿⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣯⣤⣭⣤⣥⣧⣼⣵⣥⣤⣬⣽⣥⣤⣽⣥⣦⣤⣧⣭⣼⣥⣠⣤⣬⣧⣤⣤⣥⣧⣽⣼⣤⣤⣧⣤⣭⣤⣤⣤⣽⣽⣤⣤⣼⣧⣥⣴⣽⣧⣤⣥⣤⣤⣧⣬⣼⣤⣬⣯⣤⣯⣼⣯⣥⣧⣤⣼⣥⣼⣯⣽⣿⣿⣿
⣿⡿⠿⠋⢹⠿⠛⢻⠹⡿⡟⠛⠻⠛⠛⢹⡿⡛⠟⢿⢻⣿⠻⠛⢻⢻⡿⡛⡿⠙⠛⡛⠏⠋⠛⡏⠻⡟⠛⠿⡿⠟⣻⠹⠟⠛⠫⢿⠏⢿⠹⡽⠛⠛⡿⡋⠟⠛⣻⠹⡏⢉⠏⡿⣙⠉⡽⢿⠟⠛⠉⡏⢛⠹⠻⠛⢻⣿
⣿⡿⣿⣿⣿⡿⡿⣿⡿⣿⣿⡟⡿⡻⣿⡟⢾⢿⢿⣿⠻⡿⣿⢿⠿⡿⣿⣿⠿⡿⣿⢿⡿⡿⢿⡿⡿⡿⡿⡿⢿⣿⡿⠿⡿⣿⢿⢿⡿⣯⣭⢭⢭⠭⣬⣭⢭⣥⢭⢭⠍⢭⡭⡭⡭⣭⢭⢭⣭⣭⣭⢩⣭⣭⣭⣭⣭⣿
⣿⣧⠜⠃⠀⠀⠊⠂⠘⠀⠀⠀⠃⠋⠂⠃⠑⠈⠙⠀⠀⠀⠀⠘⠈⠊⠂⠘⠒⠊⠋⠀⠃⠉⠀⠀⠀⠀⠁⠘⠐⠀⠈⠐⠃⠀⠀⠙⠋⠀⠀⠑⠀⠀⠋⢹⣧⣼⣭⣤⣥⣼⣽⣧⣥⣯⣿⣼⣅⣤⣤⣼⣿⣿⣿⣿⣿⣿
⣿⡏⠙⠙⠉⢽⡋⣯⠭⢻⠹⡍⠙⠉⡿⣉⠯⠋⠍⠸⡏⡟⢹⠉⡽⠝⠋⠉⠟⠙⠩⠏⡟⢉⡛⠉⣽⠅⠙⢹⠘⠙⠉⡏⡊⡝⢫⡟⡉⡏⠯⠙⢿⡽⡏⣏⣙⠛⠉⠉⡍⣿⠹⡟⢩⠩⢻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡷⡿⡿⡷⡿⠿⠿⢿⢿⠟⢿⢿⡿⡿⢿⢿⠿⡿⣿⢿⠿⡿⠿⠿⠿⢟⣿⢻⢿⢿⣿⢿⠿⢿⠿⣻⢿⡿⡿⡿⠿⣿⢿⢿⢿⠿⣾⣿⡿⡿⡿⡿⠻⢿⠿⠿⠛⣿⢿⢻⢿⢿⢿⢟⢷⣿⢿⠟⢿⠿⢿⡿⠻⢿⣿⣿⣿
⣿⣧⣬⣯⣮⣦⣤⣬⣿⣵⣥⣤⣬⣯⣄⣼⣤⣬⣮⣿⣤⣤⣎⣦⣤⣧⣼⣭⣼⣤⣼⣿⣽⣬⣤⣤⣵⣽⣧⣤⣴⣦⣿⣵⣴⣼⣤⣽⣯⣿⣤⣦⣦⣧⣾⣼⣥⣤⣧⣼⣴⣽⣽⣵⣼⣧⣼⣵⣤⣾⣮⣵⣯⣤⣼⣿⣿⣿
⣿⡏⠉⣯⡍⡯⠩⣽⢹⡫⣥⡯⠈⣉⡫⢩⠩⣧⢉⠩⣽⠩⡯⠈⡫⣯⣙⡫⡫⢈⢥⢝⢙⢝⠽⣇⢭⢿⢽⠱⣽⢝⢙⢽⡋⠨⡏⣯⠉⣏⠅⡨⡫⡙⣩⢹⣮⡏⠝⡩⣟⢽⢽⡼⠉⢭⠍⡇⢉⡏⢉⠩⣽⢽⣿⣿⣿⣿
⣿⡿⡿⠿⠿⡿⡿⣟⢿⠿⣿⡟⡿⢿⢿⣿⢟⠿⡿⠿⠿⣾⢿⢿⢿⢿⣿⢿⢿⡿⡟⡿⠿⢿⢿⠿⡿⡿⢿⡿⢿⡟⠿⠿⡻⡟⠿⡿⠿⢿⠿⢿⠻⢿⠿⠟⠿⠿⣿⠻⠿⡿⡿⣿⠿⠿⠿⠿⠿⡗⠿⠿⡿⡿⠿⣿⣿⣿
⣿⣧⣴⣾⣬⣼⣷⣿⣵⣤⣿⣼⣤⣶⣽⣿⣽⣴⣷⣴⣶⣿⣵⣼⣽⣾⣽⣴⣽⣮⣾⣷⣦⣷⣽⣯⣶⣿⣾⣮⣯⣧⣤⣼⣿⣧⣼⣧⣤⣼⣿⣿⣤⣿⣼⣥⣶⣾⣽⣾⣮⣯⣧⣽⣽⣵⣤⣼⣿⣧⣼⣿⣯⣿⣴⣿⣿⣿
⣿⣇⣩⣍⣉⣹⣹⣍⣩⡏⣉⢭⣟⢝⣉⣉⣉⣽⣷⣷⣜⣩⣙⣽⣉⣏⣉⣇⣁⣿⣾⣈⣽⢈⣭⣯⣉⣍⣸⣹⣝⣩⡯⣫⣋⣉⢩⣋⣭⡋⣽⢩⣏⣭⢩⢙⣹⡉⣹⣹⠩⣉⢿⣉⣉⣫⣿⣍⣍⣉⡫⣭⣽⣉⣩⣩⣹⣿
⣿⡿⣿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠟⠻⢿⢿⣿⢿⠿⠿⠿⠿⠿⠟⠿⠿⡿⢿⠟⠿⣿⠿⢿⠻⢿⡿⠻⠿⡿⠿⠿⣿⡿⡿⠿⡿⡿⠿⡿⠿⠿⠿⠿⡿⡿⠿⠟⡿⠿⡿⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣶⣶⣿⣷⣿⣶⣶⣶⣶⣷⣶⣾⣿⣾⣿⣾⣬⣬⣶⣷⣶⣶⣶⣾⣷⣷⣶⣾⣿⣷⣿⣾⣿⣿⣶⣾⣷⣷⣶⣿⣼⣧⣿⣷⣿⣶⣷⣾⣶⣶⣼⣶⣿⣾⣶⣷⣾⣾⣷⣶⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠄⠄⢨⠀⢀⠀⡆⠀⠀⡌⡈⡀⠀⠠⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⣿⣿⣀⣁⣁⣈⣀⣀⣀⣁⣈⣀⣀⣁⣀⣀⣈⣈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣉⣉⣉⣉⣉⣉⣉⡉⣉⣉⡉⣉⣉⡉⣉⣉⢉⣉⣉⢉⢉⣉⣉⣉⡉⣉⣉⣉⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⣉⣉⢉⢉⣉⣉⢉⢉⣉⣉⣉⡉⢉⡉⢉⣉⣉⣉⣉⣉⢉⣉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⢉⣉⣉⣉⣉
⣿⣿⣇⣄⣠⣢⣹⣶⣀⣜⣧⣶⣇⣅⣇⣶⣬⣺⣆⣸⣔⣅⣼⣠⣄⣀⣰⣿⣀⣦⣰⣱⣰⣠⣇⣀⣸⣖⣢⣻⣠⣵⣀⣸⣼⣾⣀⣸⣠⣸⣔⣅⣤⣀⣀⣤⣠⣎⣿⣆⣠⣼⣖⣆⣄⣧⣀⣪⣠⣠⣪⣠⣢⣆⣿⣿⣿⣿
⣿⣿⡏⢙⠛⡋⣟⡛⠛⣏⠟⠋⠛⢻⠛⢹⣏⠋⠛⠛⠉⠙⢻⠛⢛⠛⢻⣉⠙⠛⣉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⣿⣿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣄⣆⣀⣰⣸⣀⣄⣄⣄⣴⣀⣎⣀⣤⣇⣤⣄⣄⣀⣾⣄⣄⣇⣀⣄⣄⣂⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⡝⡿⡟⠋⡏⠛⡟⢻⠙⢻⠛⠛⠋⠛⢛⡟⠛⠛⡛⠛⠛⠛⢹⡏⢙⠛⣟⣿⠻⠛⠛⠛⢋⡹⢛⣿⣭⠛⠟⢻⢿⠙⢻⠛⠛⠛⠛⠛⠹⠟⡏⡛⣿⠉⠛⢻⠙⢻⠛⠛⡏⢙⠟⡋⡏⠋⡟⠛⠋⢹⢻⣿⣿⣿⣿
⣿⣿⡿⠿⠿⢿⢿⡿⣿⠿⡿⢿⢿⢿⠿⣿⠿⢿⠿⠿⡿⠿⠿⡿⢾⡿⢿⠿⡿⢿⠿⡿⢿⡿⠿⠿⠿⡾⣿⠿⡿⠿⠿⣿⢿⢻⠿⡿⡿⢿⢿⡿⡿⠿⢶⠿⢿⢿⢿⠿⡿⠿⡿⠿⢿⢿⡿⢿⠿⠿⠿⡿⠿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣼⣢⣬⣮⣼⣧⣵⣴⣭⣬⣽⣬⣦⣦⣤⣿⣥⣿⣤⣬⣷⣦⣤⣧⣷⣼⣴⣤⣧⣤⣤⣬⣦⣾⣤⣧⣤⣤⣷⣥⣼⣬⣧⣮⣭⣼⣮⣾⣤⣼⣤⣧⣼⣽⣼⣬⣯⣧⣤⣿⣢⣇⣵⣧⣼⣥⣮⣥⣿⣿⣿⣿⣿
⣿⣿⡏⣉⢉⢋⣽⢉⢉⡉⡉⢩⡭⢉⣏⢉⣽⡏⣿⠁⠉⢉⣛⢈⢽⣋⢙⢩⢫⡏⡉⢉⠁⢉⡇⢉⢋⢽⠉⠈⡉⣹⡉⡋⣩⡉⠉⢩⡉⡩⡍⢁⡉⣹⠀⣍⢩⢹⣉⡉⢹⠉⢩⢉⡏⣩⢉⢩⠁⡉⣹⡩⣡⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⣿⠿⠻⢟⢿⣿⠿⣿⠿⣿⠿⠿⠟⣿⢿⢿⠿⠿⢿⢻⢿⠿⢻⠿⠿⢿⠿⣿⠿⡿⢿⠿⠿⢿⠿⠿⠿⡿⠛⠿⠿⣿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⠻⠿⢿⠿⡿⠿⠿⣿⢿⡿⠿⢿⠻⠿⠿⠿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣾⣶⣶⣶⣾⣷⣶⣾⣾⣾⣶⣶⣶⣿⣶⣿⣶⣾⣿⣾⣷⣶⣾⣶⣶⣾⣶⣿⣶⣷⣾⣾⣶⣾⣶⣶⣾⣷⣶⣾⣷⣿⣶⣶⣶⣧⣶⣾⣷⣼⡷⣶⣶⣶⣾⣶⣧⣶⣶⣾⣷⣶⣾⣾⣶⣶⣷⣶⣿⣿⣿⣿⣿
⣿⣿⣇⣰⣃⣀⣸⣀⣾⣕⣟⣀⡇⣪⣆⣀⣺⣫⣚⣀⣸⣀⣰⣑⣿⣁⣄⣀⣀⣿⣂⣸⣘⣁⣁⣷⣂⣀⣀⣶⣿⣏⣄⣀⣇⣾⣠⣡⣨⣇⣸⣀⣀⣸⣕⣅⣏⣚⣸⣂⣸⢐⣳⣋⣆⣑⡪⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⣻⣻⣛⣟⠋⠛⠛⡏⢛⣿⠛⠛⠙⠛⢻⡿⠛⢻⡟⠛⠛⢻⡻⣛⠛⢻⠛⠛⢛⣿⣻⠛⠟⠛⡏⣛⠟⠛⢹⣻⡛⠛⢹⣟⣹⠛⡛⢻⠛⠛⠉⠛⢛⣛⡿⠛⠛⠛⣻⡋⠛⠹⢻⡿⠛⠛⣟⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⡶⣶⣶⣶⢶⣶⣶⡿⣷⣿⣶⣶⣾⣾⣾⡷⢷⣷⣷⣶⣾⣾⣷⣷⣷⣾⣷⣶⣾⣿⣿⣶⣿⣾⣿⣿⣶⣾⣾⣿⣷⣶⣿⣿⣿⣾⣷⣿⣷⣷⣷⣷⣷⣷⣷⣷⣷⣶⣿⣶⣶⣿⣾⣷⣾⣾⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣴⣽⣀⣤⣤⣶⣹⣧⣤⣧⣬⣤⣤⣤⣤⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⡟⠛⠟⠛⢹⠛⠛⢻⢻⡛⠛⠛⠛⡟⢛⢛⠛⠛⢛⠋⠛⠟⢻⠛⢻⠙⠛⠛⠋⠉⠛⠛⢛⠛⠛⢻⠛⢛⠟⢹⠛⠛⢿⠛⠛⠛⠛⡛⠛⢛⠛⠛⡋⠛⠛⢻⣿⠉⠛⢛⢛⠛⠛⠛⡟⡛⠋⢹⠛⠛⢻⣿⣿⣿⣿
⣿⣿⣷⣷⣷⣷⣶⣾⡴⣶⣷⣾⣷⡶⢷⣶⡿⠶⣷⣶⣶⣾⣶⣷⣷⣿⣶⣾⣶⣶⣶⣶⣶⣶⣷⣿⣶⣶⣾⣶⣾⣷⣾⣶⣶⣷⣶⣶⣶⣷⣷⣶⣾⣷⣶⣷⣶⣶⣾⣿⣶⣶⣾⣾⣾⣶⣶⣿⣶⣶⣾⣶⣾⣾⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣤⣧⣤⣤⣤⣬⣦⣧⣴⣤⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⡏⠋⠙⢙⣽⢽⢙⢝⠏⠉⠉⢉⢻⡭⡙⠉⡏⡝⡍⠋⡏⣭⢛⢙⡟⡉⠋⠋⠋⣟⢝⢹⠉⢉⢻⠫⠏⣯⠉⠋⢩⡟⡝⡏⢩⡋⢻⠩⠹⡉⠋⡟⠝⢝⢿⡝⠙⠉⡍⠋⢫⠙⠝⡝⢹⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠷⠿⠿⠿⣿⡛⡿⠿⠶⠿⠷⢿⠿⡿⡿⢿⡿⢿⠿⢿⠿⠻⢿⠷⡿⠿⠿⣿⠿⢿⠿⢿⠷⡟⠿⠻⣿⠿⣿⠟⠿⢿⡿⡿⢿⠿⠿⡿⠿⠿⠿⠿⠿⡿⠻⠿⠿⡿⢿⢿⠿⠿⠿⢿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⣿⣿⣧⣥⣤⣷⣥⣤⣽⣧⣿⣤⣤⣦⣧⣼⣤⣧⣤⣿⣮⣤⣤⣼⣤⣴⣴⣿⣦⣤⣤⣿⣥⣼⣼⣿⣤⣧⣤⣬⣿⣼⣿⣥⣴⣼⣮⣮⣮⣤⣤⣦⣾⣾⣴⣧⣮⣾⣤⣤⣤⣷⣵⣴⣧⣤⣤⣿⣤⣿⣤⣤⣧⣾⣿⣿⣿⣿
⣿⣿⣇⡏⢉⣩⣹⣈⣹⣏⣙⡉⡉⣉⣉⣅⣿⣽⣋⣹⣉⣉⣉⣉⣍⣍⣈⣉⣉⣁⣯⣉⣉⣩⣈⢻⣨⣉⡏⣹⣯⡉⢹⣈⣹⣧⣈⣉⣹⣩⣽⣉⣉⣁⣉⣙⣍⣹⣉⣠⣏⣁⣽⡂⣉⣋⣉⣈⡙⣇⣩⣯⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⠻⠛⢛⣟⠟⠻⣿⠻⠛⢟⣿⡟⠻⠟⠟⢟⠻⠻⠻⡻⡛⠛⠟⢻⣻⠻⠻⣟⣟⡟⠟⠟⣛⢻⣟⢛⠟⣛⡟⢛⠟⠿⣻⠛⠟⠟⠟⢟⢻⡟⢛⣿⡛⡻⢻⡟⡟⡟⠻⠻⣟⣿⣛⠟⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⢾⣷⣶⣶⣾⣶⣶⣶⣿⣶⣶⡶⡶⣿⣶⣶⣶⣷⣶⣾⣦⣼⡷⣷⣶⣿⣿⢿⣶⢶⣷⣶⣷⣾⣶⣷⣷⣾⣷⣦⣿⣴⣶⣶⣶⢶⣶⣷⣷⣾⣶⣷⣾⣷⣶⣿⠶⣶⡿⣾⡿⣶⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣤⣀⣈⣠⣺⡗⣀⣀⣿⣂⣸⣐⣕⣽⣀⣆⣰⡕⣀⣼⣧⣔⣸⣏⣰⣆⣨⣸⣗⣀⣠⣰⣾⣆⣀⣀⣇⣔⣷⣇⣶⣀⣸⣀⣰⣨⣀⣕⣀⣀⣶⣺⣂⣸⣇⣕⣖⣀⣀⣀⢤⣇⣢⣆⣀⣸⣖⣆⣀⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⡛⠛⠛⠋⠛⢛⣻⣿⠛⡛⠛⡟⡋⠛⡟⠛⢙⠛⣛⡟⠛⠛⡟⠛⠛⡿⡟⢻⡟⠙⠛⠛⢻⣻⠛⠛⡟⠛⢻⢛⡻⠛⡛⢻⠛⢛⠟⡏⢛⠉⠛⡟⠛⠛⢛⠙⢿⠩⠛⡛⠛⠛⠋⡏⢹⡟⢛⠛⠛⣿⣿⣿⣿⣿
⣿⣿⡷⡿⢿⡿⢿⣿⢿⢿⢿⢿⢿⢿⡿⢿⡿⡿⡿⢿⠿⢿⢿⢿⣿⢿⢿⢿⢿⠿⣿⡿⡿⡿⢿⡿⠿⡿⣿⠿⣿⢿⠿⠿⢿⢿⡿⠿⡿⡿⢿⣿⠾⠿⣿⢿⡿⠿⠿⡿⢿⡿⣿⠿⠿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣾⣤⣦⣤⣴⣤⣥⣤⣤⣼⣤⣥⣨⣤⣤⣤⣤⣧⣥⣤⣽⣼⣤⣤⣤⣼⣼⣧⣼⣤⣤⣰⣤⣤⣿⣿⣄⣿⣤⣤⣧⣼⣧⣴⣤⣼⣤⣽⣤⣧⣼⣤⣇⣥⣧⣤⣿⣸⣯⣴⣤⣤⣬⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⡍⠉⠁⡩⠏⠁⠉⢩⣿⠅⠉⢩⣿⣿⡋⡉⠉⢩⡋⡫⢸⠉⡇⠩⡭⡇⢩⢝⡍⠹⣏⡉⢨⡉⣫⠉⡇⣏⡉⠉⠉⡏⢹⢝⡋⣹⢉⢽⡫⡯⣩⠉⣯⡏⠉⠉⡋⣻⠍⢽⡫⡻⢩⡏⢉⢙⢍⢿⡅⢩⢻⣿⣿⣿⣿
⣿⣿⡟⠿⡿⢿⠿⡿⠛⠿⠿⠿⠿⢻⠿⠿⠿⣿⡿⠻⠿⠿⣿⡿⠿⠿⡿⡿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣷⣷⣾⣶⣿⣷⣶⣾⣶⣷⣾⣷⣶⣾⣼⣷⣾⣶⣿⣿⣷⣶⣶⣿⣷⣶⣶⣮⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⢀⠀⡇⢠⠀⠀⡀⡆⠀⠀⡘⠰⢠⠠⢠⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣀⣁⣀⣈⣀⣀⣀⣈⣀⣁⣁⣁⣀⣀⣀⣁⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠘⠄⠣⠾⠍⠉⠫⠈⠉⠉⢫⣇⡏⠉⠉⠉⠙⢅⡇⠋⠋⢫⠉⠈⠋⠫⡟⢹⣇⢉⠉⢹⣇⠉⠁⠩⣉⢛⡋⠏⢝⡏⠉⢏⢙⢉⠉⠩⢫⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⢿⡿⡿⣿⣿⠿⠿⡿⢿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿
⣿⣿⣷⣆⣠⣁⣸⣀⣄⣄⣆⣆⣀⣌⣄⣼⣀⣀⣀⣄⣀⣆⣀⣀⣄⣄⣸⣠⣀⣄⣀⣧⣂⣠⣸⣄⣀⣡⣸⣀⣦⣀⣀⣄⣇⣀⣠⣠⣀⣇⣀⣀⣄⣀⣸⣄⣌⣄⣀⣠⣆⣠⣀⣄⣌⣇⣄⣆⣀⣸⣄⣀⣀⣿⣿⣿⣿⣿
⣿⣿⡟⡛⠛⢿⡟⠛⠛⠛⠛⢻⠙⡛⠛⣛⢻⠛⠛⡟⠛⠛⠛⢛⠛⠛⢻⠙⡛⠛⡛⡏⠛⠛⣛⢻⠙⠛⠛⠛⠛⠛⣟⡙⠛⣻⠙⡛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⢻⠛⢛⠛⢹⠛⠛⠛⠛⠛⡛⠛⠛⠛⣟⠙⢻⣿⣿⣿
⣿⣿⣷⣿⣾⣾⢿⢶⣷⣷⡷⣿⣾⡷⡷⢿⣿⣶⠾⣿⡶⢶⣷⣿⣷⣷⣾⣿⣷⣶⣷⣿⣾⣾⣿⣾⣷⣾⣷⣷⣿⣾⣿⣷⣷⣿⣶⣷⣶⣾⣶⣾⣶⣾⣾⣾⣷⣷⣿⣶⣾⣷⣾⣷⣶⣷⣷⣿⣷⣷⣷⣷⣿⣾⣾⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣤⣤⣦⣀⣧⣤⣤⣧⣤⣤⣤⣤⣤⣥⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⡛⠻⠻⢛⢻⡟⢿⠻⠛⡟⡿⢿⡿⠻⠻⠛⠟⠟⣿⠻⢻⢻⠛⠟⠟⠿⠛⠟⣿⠻⢻⡟⡟⠿⠻⢿⡿⢻⢛⠛⠟⢿⠟⠛⢻⡟⠛⢿⠿⠟⢿⡟⠟⠟⠟⡟⠛⢻⡟⠛⠛⠿⢻⡟⠟⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣾⣾⣶⣷⣾⣶⣶⣿⣷⣼⣶⣶⣶⣶⣶⣾⣿⣶⣾⣿⣴⣶⣶⣦⣶⣶⣿⣶⣾⣿⣶⣶⣷⣦⣷⣾⣷⣷⣶⣶⣦⣴⣿⣿⣶⣾⣶⣶⣶⣿⣶⣶⣾⣷⣶⣶⣶⣶⣾⣶⣾⣷⣶⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣉⣀⣆⣁⣁⣌⣈⣰⢹⣇⣉⣈⣊⣸⣃⣈⣀⣿⣊⣈⣸⣎⣇⣑⣹⣈⣘⣇⣑⣕⣙⣀⣹⣁⣷⣿⣈⣈⣊⣈⣈⣲⣀⣀⠁⣿⣈⣀⣑⣁⣁⣈⣇⣤⣀⣠⣾⣇⣠⣇⣽⣀⣾⣄⣈⣠⣂⣹⣀⣎⣈⣸⣿⣿⣿
⣿⣿⡿⠟⠛⡟⠛⢻⣋⠻⡛⠛⣿⢻⣿⣟⠛⠻⠻⡛⠛⡟⣟⠛⢻⣛⠛⠛⣛⡟⠻⠻⡻⠛⠛⢻⢟⠛⠛⣛⣻⡟⠛⠛⡛⠛⢻⠛⢟⣛⠛⡟⣛⠏⠛⢛⠟⣟⡛⠻⠻⣟⡛⡟⢻⢛⠟⡟⢿⠛⢟⢟⠟⢻⣿⢛⣿⣿
⣿⣿⡷⣾⣶⣷⣶⢾⣿⣶⣶⡶⣾⣾⣷⣿⣶⣾⣶⣷⡶⣶⣿⣶⣾⣷⣶⣶⣷⣷⣶⣾⢶⣴⣶⡾⣷⣶⣶⣿⣿⡷⡦⡴⣷⣶⣾⣷⣾⣷⣷⣷⣾⣶⣶⣤⢶⣿⣶⣶⡾⣷⣶⣾⣾⣾⡶⣷⣾⣶⣶⣾⣶⣶⣿⣾⣿⣿
⣿⣿⣇⣀⣐⣖⣻⣸⣐⣗⣅⣰⣸⣀⡕⢠⣀⣅⣽⣠⣀⣸⣾⣇⣁⣀⣶⣁⣽⣂⣸⣇⣰⣅⣽⣂⣎⣷⡑⢀⣸⣐⣀⣠⣻⣆⣀⣀⣏⣪⣂⣀⣁⣿⣿⣇⣰⣇⣾⣐⣇⣀⣸⣰⣅⣀⣀⣐⣶⢡⣇⣑⣽⣿⣿⣿⣿⣿
⣿⣿⡿⠛⡛⢛⢛⡏⢛⢟⡟⠛⣛⠛⠛⡋⡟⠛⣛⠙⠛⡻⢻⡿⠛⡛⢙⣿⠟⣛⠋⢛⠙⣟⢟⡛⠛⡟⠛⡛⣛⠛⢛⡛⣛⠛⠛⢻⢛⠛⠻⠻⠛⢛⠻⠛⣿⠉⢿⠛⣿⡛⣛⣿⡛⠛⡛⡟⢛⣿⡛⢹⣛⠙⠛⣿⣿⣿
⣿⣿⣷⣾⣶⣾⣷⡷⣶⡿⣷⣶⣧⣴⣶⣷⣶⣶⣷⣶⣶⣷⣾⣷⣾⣷⢾⣿⡶⣿⣶⣶⣶⣿⢾⡶⢶⣷⣾⣾⣿⣶⡾⢶⣿⡶⣶⣾⣷⣶⣾⣶⣤⣾⢾⣶⣾⢶⣷⣶⣿⣷⣿⣿⣶⣾⣾⣶⣶⣿⣶⣾⣷⣶⣶⣿⣿⣿
⣿⣿⣏⣠⣂⣰⣔⣇⣇⣀⣐⣿⣀⣺⣗⣴⣔⣖⣀⣐⣖⡇⣀⣨⣢⣀⣀⣸⣶⣆⣪⣶⣸⣀⣨⣅⣡⣀⣀⣐⣅⣘⣿⣇⣪⣂⣀⢠⣷⣳⣀⣢⣫⢂⣀⣻⣖⣀⣀⣿⣶⣀⣀⣰⣿⣨⣀⣰⣔⣜⣀⣸⣰⣇⣤⣂⣿⣿
⣿⣿⡿⠛⠛⡏⠙⢟⠛⢻⡟⠛⢻⣽⡛⠋⠙⠋⠛⣿⠛⠋⠛⡟⠛⡛⡋⡟⠛⠛⡛⠛⡋⠛⣿⠛⣟⠛⡟⡋⣟⠋⠙⠋⣟⡋⠛⡛⠛⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣶⣷⣷⣷⣷⣶⣷⣾⣾⣿⣷⣶⣾⣷⣶⣷⣶⣶⣶⣷⣶⣿⣶⣷⣶⣾⣾⣷⣷⣾⣾⣶⣿⣶⣿⣾⣧⣶⣶⣶⣿⣶⣶⣷⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⡿⢻⡟⢻⣿⣿⠟⣽⡟⣿⣿⡟⣻⡟⣿⡟⣿⣿⡟⣿⡟⣿⢛⣿⢻⣟⢻⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢰⢣⢸⣩⡌⣷⣆⣟⠾⡁⣶⣾⢣⣅⡇⠿⡇⠿⣿⡇⠶⠇⣦⢺⡀⣇⣸⢸⢸⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠿⣿⣿⠿⣿⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣶⣾⣿⣷⣷⣾⣿⣶⣷⣿⣶⣶⣶⣶⣶⣶⣷⣾⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠙⠉⠛⠙⠉⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣙⣟⣏⣏⣉⣛⣹⣹⣿⣯⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⢿⠿⡿⢿⡿⢿⢿⢿⢿⠿⠿⢿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣾⣷⣶⣶⣶⣾⣾⣾⣶⣶⣶⣶⣾⣿⣿⢿⣾⠿⣿⣿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⣷⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣟⣩⣍⣿⣹⣿⣯⣭⣯⣽⣿⣿⣿⣯⣯⣽⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿
⣿⣿⠟⠿⡿⠻⠿⢻⣻⠿⡿⢿⢿⣿⠿⣿⠿⢿⠿⡟⠿⡿⣻⡿⢿⣟⠻⢿⠿⡿⢿⢟⢿⢿⠿⢿⠿⡟⠿⣿⡟⡿⣿⠿⡿⠿⠿⣿⠿⣿⣿⣿⣿⠩⠤⠤⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⢿⣿⢿⡿⣿⠿⣿⠿⣿⣿⢿⢿⡿⢟⢿⣿⠿⠿⢿⡿⡿⢿⠟⡿⠿⠿⠿⠟⢿⡿⣿⣿⠛⢿⣿⡿⢿⢿⠿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣥⣭⣯⣬⣭⣼⣯⣝⣯⣭⣭⣭⣯⣯⣭⣯⣽⣽⣧⣬⣽⣽⣬⣥⣝⣭⣯⣯⣿⣿⣭⣭⣯⣭⣥⣹⣯⣥⣭⣭⣽⣯⣽⣭⣯⣯⣭⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⣽⣼⣽⣿⣿⣭⣽⣯⣽⣯⣽⣯⣽⣭⣾⣥⣽⣿⣯⣽⣭⣽⣭⣽⣯⣯⣬⣿⣯⣽⣯⣽⣌⣯⣽⣭⣬⣯⣿⣼⣽⣿⣼⣭⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣀⡀⠀⠀⣿⣿
⠀⣿⣤⣷⣥⣶⣯⣴⣧⣬⣾⣼⣤⣴⣤⣶⣷⣤⣤⣾⣴⣾⣬⣦⣼⣤⣤⣧⣥⣼⣮⣶⣧⣴⣦⣧⣼⣷⣤⣿⣵⣤⣾⣤⣾⣯⣷⣵⣤⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣿⣿
⠀⣿⢽⣵⣤⣤⣧⣴⣧⣤⣽⣬⣴⣯⢤⣽⢴⣦⣶⣦⢥⣤⣼⣧⣦⣴⣤⣴⣾⣥⣤⣷⣽⣵⣮⣤⣴⣷⣤⣼⣵⣤⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⡠⠛⠻⣿⣿⣿⣿⣿⣿
⠀⣿⣽⣷⣶⣿⣾⣷⢶⣷⣶⣷⣾⣾⢶⣾⣶⢾⣴⣶⡾⣶⣴⣿⣶⢷⣷⣾⣶⣷⣶⣷⣶⣷⡷⣶⣶⣶⣶⡽⣾⣶⣾⣶⣾⣿⣿⣶⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠐⢁⣤⠀⠠⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⠀⣿⣷⢶⠶⣿⣾⢷⣿⣶⡷⣿⢶⣾⣷⢶⣮⡶⢾⣶⢷⣿⣷⡿⣿⣶⣶⣶⣷⢶⣷⣶⣾⣼⢷⠾⡶⣾⣷⣶⣷⣶⢷⡿⣷⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣯⣡⣄⣤⣄⣀⣀⣿⣷⣿⡀⡀⣀⣤⣿⣿⣿⣿⣿⣿
⠀⣿⡶⠾⡶⡦⠾⣷⠿⢿⠾⣾⡷⢿⡾⠾⣾⢷⢿⠿⡾⠶⡷⣴⠾⢾⢷⠾⠶⠾⣿⠿⡾⢶⡿⢶⢿⠾⠾⡶⡷⠿⡾⢾⠶⡶⠷⢼⠿⡿⠿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣷⡶⡿⡿⢶⢾⡶⠷⣶⣿⣿⣾⣶⣾⣾⣷⣿⣶⣾⣾⣷⣷⣷⣾⣾⣶⣾⣾⣷⣶⣷⣿⣶⣿⣾⣾⣶⣷⣶⣶⣶⣿⣿⣾⣶⣾⣿⣾⣶⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠁⠈⠁⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 3831

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/10/moz-pr-spam/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/10/moz-pr-spam/

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Gemini_version_available_♊︎


✐ Mozilla’s_Strategy:_More_Lawyers_and_Spam,_Not_More_Engineers⠀✐


Posted in Deception, Law, Marketing at 11:23 am by Dr. Roy Schestowitz


They send me stuff before even asking me if I accept an embargo (I do not; we
reject NDAs and information embargoes from greedy corporations)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇moz-spam⦈_


Summary: Mozilla has been contacting a load of people, asking them to generate
inane hype over a useless hire by a notoriously_wasteful_CEO


They’re hiring lawyers from firms that attack programmers, just like they hire
managers_from_Facebook_while_they_promise_us_privacy:


     Hi Roy,


     Hope you’re well. I am writing with


embargoed news for Monday


, September 12, 2022 @ 9:00 a.m. ET to give you a heads up that Mozilla has
hired a new Chief Legal Officer:


Carlos Torres will lead Mozilla’s global legal and public policy teams,
developing legal, regulatory and policy strategies that support Mozilla’s
mission. He will also manage all regulatory issues and serve as a strategic
business partner helping Mozilla accelerate its growth and evolution.


Carlos comes to Mozilla from Flashbots where he led the company’s legal and
strategic initiatives. Prior to that, he was General Counsel for two start-ups
and spent over a decade at Salesforce in a variety of leadership roles
including VP, Business Development and Strategic Alliances and VP, Associate
General Counsel, Chief of Staff. He also served as senior counsel of a biotech
company and started his legal career at Orrick, Herrington & Sutcliffe.


Let me know if you’d be interested in mentioning this in your newsletter on
Monday? For your convenience, here_is_a_link to our blog with the announcement
(Note: the blog post will go live when the embargo lifts on Monday). I’ve also
shared a draft of the announcement below.
Thanks,


Cherie


===============================================================================
DRAFT UNDER EMBARGO UNTIL 9 am ET 9/12


Announcing Carlos Torres, Mozilla’s new Chief Legal Officer


Mitchell Baker


I am pleased to announce that starting today, September 12, Carlos Torres has
joined Mozilla as our Chief Legal Officer. In this role Carlos will be
responsible for leading our global legal and public policy teams, developing
legal, regulatory and policy strategies that support Mozilla’s mission. He will
also manage all regulatory issues and serve as a strategic business partner
helping us accelerate our growth and evolution. Carlos will also serve as
Corporate Secretary. He will report to me and join our steering committee.


Carlos stood out in the interview process because of his great breadth of
experience across many topics including strategic and commercial agreements,
product, privacy, IP, employment, board matters, investments, regulatory and
litigation. He brings experience in both large and small companies, and in
organizations with different risk profiles as well as a deep belief in
Mozilla’s commitment to innovation and to an open internet.


“Mozilla continues to be a unique and respected voice in technology, in a world
that needs trusted institutions more than ever,” said Torres. “There is no
other organization that combines community, product, technology and advocacy to
produce trusted innovative products that people love. I’ve always admired
Mozilla for its principled, people-focused approach and I’m grateful for the
opportunity to contribute to Mozilla’s mission and evolution.”


Carlos comes to us most recently from Flashbots where he led the company’s
legal and strategic initiatives. Prior to that, he was General Counsel for two
start ups and spent over a decade at Salesforce in a variety of leadership
roles including VP, Business Development and Strategic Alliances and VP,
Associate General Counsel, Chief of Staff. He also served as senior counsel of
a biotech company and started his legal career at Orrick, Herrington &
Sutcliffe.


–
Cherie Crosby


she/her/hers
518.321.2144


cherie.crosby@berlinrosen.com


It’s worth noting that the email itself contained surveillance; Mozilla
Thunderbird warned about it. So the PR firm chosen by Mozilla is spying. This
is where Mozilla’s money goes.


“Notice that their links is to AWS and not to Mozilla,” an associate noted.
“More can be said about the embargo or lack thereof.”


I never spoke to Mozilla, so they’re clearly mass-mailing hundreds if not
thousands of people with this (without following the correct protocol; you must
first verify an embargo is accepted by the recipient).


Only they know the extent of the distribution and notice the screenshot at the
top. Even Mozilla’s own email client does not like it.


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                    ䷩ 𝚕𝚒𝚗𝚎 3991

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

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Gemini_version_available_♊︎


✐ Links_10/09/2022:_New_Debian_Builds_and_KeePass2_2.52_Released⠀✐


Posted in News_Roundup at 3:10 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o BSD
          o Fedora_Family_/_Red_hat_/_IBM
          o Debian_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Chromium
          o Content_Management_Systems_(CMS)
          o Programming/Development
    * Leftovers
          o Security
                # Fear,_Uncertainty,
                  Doubt/Fear-mongering/Dramatisation
                # Privacy/Surveillance
          o Finance
          o AstroTurf/Lobbying/Politics
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
                # Announcements
                # Programming
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ StormD_StormOS_Debian_Variant_–_Invidious⠀⇛


                       In this video I will be taking a look at StormD a
                       variant from the distro creators of StormOS which
                       is an Arch based distro, StormD is based on Debian.
                       The ISO I have downloaded is an XFCE build which
                       also comes with the same Maintenance Utilities
                       Program as StormOS. Besides being based on Debian
                       there are slight differences with applications out
                       of the box, theming and layout, I don’t believe
                       plank was available in the original StormOS. StormD
                       also comes with Gnome Software with Flatpak
                       available out of the box, also being Debian you
                       would also be able to boost software availability
                       by installing Snap Packages if that’s your
                       preference. Hope you enjoy the video.


                # ⚓ MakuluLinux_Max_(_Debian_)_Dev_Build_2022.09.10_–
                  MakuluLinux⠀⇛


                       We take a look at the many new changes over the
                       last few weeks, Development is speeding along. This
                       is one HOTLY anticipated Debian release of 2022.
                       Keep up with the latest updates…


                # ⚓ Video ☛ This_Tool_Converts_Arch_Linux_Packages_To_AppImage
                  –_Invidious⠀⇛


                       I love Arch Linux. I love AppImages. And I love
                       this Python script that easily converts any Arch
                       Linux package (either in the standard repos or the
                       Chaotic AUR) to an AppImage. This tool is so simple
                       to use that I think it will greatly increase the
                       number of AppImages and their usage.


                # ⚓ Video ☛ Top_7_New_Games_to_Play_on_Linux_with_Proton_|
                  August_2022_–_Invidious⠀⇛


                       I looks at the latest data dumps from ProtonDB to
                       give you a quick list of new games that work
                       perfectly with Proton since they were released in
                       August 2022 – all of them work out of the box or
                       well enough with tweaks.


                # ⚓ Video ☛ Saint_Kotar_|_Linux_Game_–_Invidious⠀⇛


                       Saint Kotar is a psychological horror detective
                       game set in a cursed valley in rural Croatia.
                       Investigate the disappearance of your relative in
                       the occult-ridden town of Sveti Kotar as you switch
                       between conflicting realities through the eyes of
                       two godly men.


                # ⚓ Video ☛ Reasons_Not_to_Use_Linux_–_Invidious⠀⇛


                       This is a highlight reel from the longer discussion
                       on when not to use Linux.


          o § Applications⠀➾


                # ⚓ Ubuntu Handbook ☛ KeePass2_2.52_Released!_PPA_Updated_for
                  Ubuntu_22.04_|_20.04
                  ⠀⇛


                       KeePass2 password manager released version 2.52 a
                       day ago. Here’s how to install it in Ubuntu 22.04,
                       Ubuntu 20.04, & Ubuntu 18.04 via PPA.


                       The new release now allows importing 1Password 8.7
                       1PUX, and Key Folder 1.22 XML files, as well as
                       groups and expiry dates when importing Sticky
                       Password XML.


                       There are also other password manager files
                       compatibility, such as support for the new encoding
                       of double quotes when importing Steganos Password
                       Manager CSV, and automatically convert time-based
                       one-time password generator settings on Bitwarden
                       JSON import.


                # ⚓ Ghacks ☛ Password_Manager_KeePass_2.52_is_out⠀⇛


                       Check out my review of KeePass if you are new to
                       the application. It has been my password manager of
                       choice for a long time. Main reasons for that are
                       that it is a local application with optional cloud
                       syncing support, extensible through a ton of
                       extensions and apps, well designed and more secure
                       than online password managers.


                       KeePass 2.52 is available as a download from the
                       official project website. You may get an update
                       notification in the program itself, but need to
                       download and install the update manually.


          o § Instructionals/Technical⠀➾


                # ⚓ Trend Oceans ☛ Use_Apt_or_Apt-Get_Command_to_Install_a
                  Specific_Version_of_a_Package_on_Ubuntu_–_TREND_OCEANS⠀⇛


                       Do you want to install a specific version of a
                       package using the apt or apt-get command without
                       using modern sandboxing tools like Snap or Flatpak?


                       Then check your package for all available versions
                       that you want to install by using the below
                       command.


                # ⚓ TecAdmin ☛ cURL_–_How_to_display_request_headers_and
                  response_headers_–_TecAdmin⠀⇛


                       The request headers contain the information about
                       the resource that is required to be fetched. The
                       response headers contain information about the
                       response sent by the server. It’s something like
                       server details and other information.


                       cURL is a command line utility used to transmit
                       data over the different-2 protocols. It is a quick
                       tool for developers to view the request header and
                       response header values of a website.


                # ⚓ peppe8o ☛ MAX7219_LED_Matrix_with_Arduino⠀⇛


                       To control the dot matrix with MAX7219 using
                       Arduino and display different patterns/characters
                       on a dot matrix


                       In this tutorial, we will learn how to interface
                       MAX7219 LED Dot matrix display with Arduino. We
                       will familiarize you with the MAX7219 dot matrix
                       display and program Arduino to show various
                       demonstrations of displaying texts and symbols.


                # ⚓ Tried_implementing_FUSE_cpiofs.⠀⇛


                       Tried implementing FUSE cpiofs. I thought it might
                       be fun to implement a file system that can mount
                       initrd file systems. I’ve implemented symlinks and
                       regular files handling and then I realized that it
                       is kind of annoying that I need to implement hard
                       links.


                # ⚓ uni Toronto ☛ The_history_of_sending_signals_to_Unix
                  process_groups⠀⇛


                       All (Unix) processes are members of some process
                       group. Process groups go very far back in Unix;
                       they’re present at least as far back as Fourth
                       Edition (V4) Unix. However, they aren’t really
                       “process groups” in the modern sense, as we can see
                       from the relevant proc struct field being called
                       p_ttyp. Instead they were used primarily to send
                       signals to your terminal processes when various
                       things happened (see dmr/tty.c and dmr/dc.c), and
                       the ‘process group number’ was the address of the
                       ‘struct tty’ for your terminal.


                       In V7, h/proc.h changed the p_ttyp field to p_pgrp
                       and now called it the ‘process group leader’.
                       However, there’s (still) no way to send a signal to
                       a process group from user code, although various
                       tools know about the idea of process groups and
                       will report them to user level (for example
                       pstat.1m, which gets this information in the
                       traditional Unix approach of reading kernel memory,
                       per cmd/pstat.c). V7 is also where the ‘process
                       group’ number becomes the process ID of the first
                       process to open a (serial) tty after it’s been
                       closed.


                # ⚓ H2S Media ☛ Install_or_Uninstall_add-ons_on_Mozilla_Firefox
                  –_Here_is_How?⠀⇛


                       Want to install add-ons like Adblocker in Mozilla
                       Firefox? Here is this tutorial where we will learn
                       how to install the extensions for this open-source
                       browser on Windows, Linux, or macOS.


                       To extend the functionality and feature of the
                       browser we use extensions and the same goes for
                       FireFox as well. For example, if you want to block
                       advertisements in FireFox completely, then we can
                       use extensions such as Adblocker that need to be
                       installed separately in Mozilla Firefox. The so-
                       called add-ons/extensions make it easier for us to
                       surf or enable you to use new functions.


          o § Games⠀➾


                # ⚓ Positech Games ☛ Democracy_4_DLC_now_available_to_add_to
                  wishlist!_–_Cliffski’s_Blog⠀⇛


                       All the cool kids these days are trying to get
                       people to add their upcoming games to their
                       wishlist. Its literally the coolest game in town.
                       You wouldn’t want to not be cool right?


                       In all seriousness, the reason indie devs do all
                       that is because its widely believed that steams
                       algorithm internally keeps track of what new games
                       are ‘hot’ by how many people are following them or
                       adding them to their wishlists, and this helps to
                       determine how much visibility those games get at
                       launch. I suspect the effect is much reduced with
                       DLC because it sells to a smaller audience anyway,
                       and perhaps steam prioritizes new IP over
                       expansions and DLC anyway. We have no way of
                       knowing.


                # ⚓ Daniel Miessler ☛ Metagaming:_An_Interview_With_Andrew
                  Ringlein_–_Daniel_Miessler⠀⇛


                       In today’s standalone episode I’m going to talk
                       about some new gaming ideas I’ve not seen anywhere
                       else, and have their creator, Andrew Ringlein, come
                       on and talk about them. Andrew was also on a
                       previous episode where we talked about crypto and
                       how it changes incentives in business.


                       So I’ve been a steady, casual gamer since junior
                       high school, and Andrew actually introduced me to
                       Role Playing Games way back then. Andrew is a die-
                       hard gamer, a super close friend, and quite simply
                       the smartest game designer I’ve ever met. And now
                       he’s actually built a game studio and is in the
                       middle of launching two games.


                       But before I bring him on I want to talk about why
                       I thought these ideas warranted a UL episode. He’s
                       a close friend, but I have lots of friends, and I
                       only create UL content around ideas that I think
                       will be interesting to the audience.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Liliputing ☛ GNOME_Shell_for_mobile_Linux_reimagines
                        how_a_smartphone_UI_can_work⠀⇛


                             The GNOME desktop environment is one of the
                             most popular user interfaces and suites of
                             apps available for desktop Linux
                             distributions. Now a team of developers have
                             been working to bring GNOME to mobile devices
                             running Linux-based operating systems.


                             GNOME Shell for mobile provides a touch-
                             friendly user interface optimized for
                             smartphones and tablets. And while it looks a
                             bit like Android or iOS at first glance,
                             there are a few key differences. The GNOME
                             team have outlined some of them in an article
                             about recent updates to GNOME Shell on
                             mobile.


                      # ⚓ Make Use Of ☛ GNOME_43_Is_Almost_Here!_Here’s_What
                        You_Can_Expect⠀⇛


                             GNOME 43 has almost arrived, with the beta
                             already released on August 6, 2022. Although
                             it is not a finished product, it provides a
                             glimpse of what to expect from the stable
                             release which is due in September 2022.


                             GNOME 43 brings a number of cool features and
                             updates with a focus heavily on visual
                             enhancements making the UI more user-friendly
                             and efficient.


    * § Distributions and Operating Systems⠀➾


          o § BSD⠀➾


                # ⚓ Liam Proven ☛ liam_on_linux_|_A_fresh_look_at_FreeBSD⠀⇛


                       It went easier than I expected, so I thought I’d
                       have a go on my sacrificial half-decent Thinkpad.


                       (It is only a Core i5, it has a wobbly screen
                       hinge, and until recently it had a tiny decade+ old
                       SSD. Recently, I pulled the SSD that was giving
                       errors from my X220, replaced it with a new bigger
                       one — that’s only been waiting for a couple of
                       years — and bunged the old, possibly-flakey one
                       into the sacrificial T420. I tried it with Ubuntu
                       Kylin, the international remix. Worked well
                       although there are glitches.)


                       This machine’s primary SSD has ChromeOS Flex on it.
                       I rather like it. It’s slick, it’s fast, it does
                       its one job very well. I am using a Debian
                       container to run Firefox ‘cos I am perverse like
                       that. Slow to start, issues with maximisation, but
                       works well.


                       Tonight, because the radio has gone Very Very
                       Solemn And Dull And Worthy, I spent a while faffing
                       with DR-DOS VMs and then I decided on something
                       that might be more educational.


                       I nuked Kylin and put FreeBSD 13.1 on it.


                       Now recently I tried GhostBSD on my multiboot
                       testbed. It was a nightmare. Hard, fiddly, falls
                       over in its own install process, and the end result
                       has an ugly theme. Not impressed.


                       So I went with the vanilla version.


                       First boot: it finds the wifi card, but can’t see
                       any WLANs. That is not much cop.


                       Tried again. Found a hint online on my phone,
                       switched vconsoles, did `ifconfig wlan0 down` and
                       then `ifconfig wlan0 up`. Went back to the
                       installer, and lo! It sees WLANs! Pick mine,
                       connect, and now I can install stuff.


                       So, violating the recommended process, since it’s
                       booted off a DVD image via Ventoy, I figure that if
                       I reboot, I won’t be able to readily mount and
                       install stuff off that. So let’s do it while I’m
                       booted off the install medium. It leaves you in a
                       `chroot` console so it should be installing stuff
                       onto the hard disk.


                # ⚓ November_2022_FreeBSD_Vendor_Summit⠀⇛


                       Join us for the online November 2022 FreeBSD Vendor
                       Summit. The event will consist of virtual, half day
                       sessions, taking place November 3-4, 2022. It’s
                       free to attend, but we ask that you register with
                       the Eventbrite conference system to gain access to
                       the meeting room. In addition to vendor talks, we
                       will have discussion sessions and a separate
                       hallway track. The vendor summit is sponsored by
                       the FreeBSD Foundation.


          o § Fedora Family / Red hat / IBM⠀➾


                # ⚓ [Test-Announce]_Fedora_Linux_37_Beta_is_GO⠀⇛


                       The Fedora Linux 37 Beta RC5 compose[1] is GO and
                       will be shipped live on Tuesday, 13 September 2022.
                       For more information please check the Go/No-Go
                       meeting minutes[2] or logs[3]. Thank you to
                       everyone who has and still is working on this
                       release! The Final Freeze begins on Tuesday 4
                       October.


                # ⚓ Red Hat Official ☛ Compiler:_The_Fractious_Front_End⠀⇛


                       Front-end development can be complex—and that means
                       a front-end developer’s skills are essential,
                       albeit constantly shifting. But a humble web search
                       can produce various memes and jokes about how the
                       front end isn’t as much of an endeavor as other
                       parts of an application can be.


                # ⚓ The Next Platform ☛ Managing_Infrastructure_At_Cloud_Scale
                  Without_The_Hyperscaler_Propellerheads⠀⇛


                       As more enterprises embrace hybrid and multicloud
                       strategies and begin to extend their IT reach out
                       to the edge, scale becomes an issue. Red Hat, a
                       longtime player in the datacenter thanks to its
                       Linux distribution and related systems software,
                       has worked hard over the past decade to establish
                       itself in the hybrid cloud world. It was an effort
                       that worked well enough to compel IBM to spend $34
                       billion in 2019 to buy it to try to change its own
                       future.


                # ⚓ Red_Hat_OpenShift_Certified_and_Supported_for_the_Public
                  Cloud_with_NVIDIA_AI_Enterprise⠀⇛


                       Red Hat OpenShift, the industry’s leading
                       enterprise Kubernetes platform with integrated
                       DevOps capabilities, is now certified and supported
                       for the public cloud in addition to bare-metal and
                       VMware vSphere-based deployments, following
                       NVIDIA’s announcement of general availability of
                       NVIDIA AI Enterprise 2.1.


          o § Debian Family⠀➾


                # ⚓ Debian_—_News_—_Updated_Debian_11:_11.5_released⠀⇛


                       The Debian project is pleased to announce the fifth
                       update of its stable distribution Debian 11
                       (codename bullseye). This point release mainly adds
                       corrections for security issues, along with a few
                       adjustments for serious problems. Security
                       advisories have already been published separately
                       and are referenced where available.


                       Please note that the point release does not
                       constitute a new version of Debian 11 but only
                       updates some of the packages included. There is no
                       need to throw away old bullseye media. After
                       installation, packages can be upgraded to the
                       current versions using an up-to-date Debian mirror.


                # ⚓ Debian_—_News_—_Updated_Debian_10:_10.13_released⠀⇛


                       The Debian project is pleased to announce the
                       thirteenth (and final) update of its oldstable
                       distribution Debian 10 (codename buster). This
                       point release mainly adds corrections for security
                       issues, along with a few adjustments for serious
                       problems. Security advisories have already been
                       published separately and are referenced where
                       available.


                # ⚓ Linuxiac ☛ Debian_10.13_and_Debian_11.5_Are_Available_as
                  Bugfix_Releases⠀⇛


                       The Debian Project has announced 10.13 and 11.5
                       updates to its “Buster” and “Bullseye” series,
                       which mainly address security issues.


                       Debian is one of the oldest GNU/Linux distributions
                       in active development. However, it does not follow
                       a strict release schedule, making it difficult to
                       predict when a new release will be available.


                # ⚓ FLOSSLinux:_202209101115_Debian_release_day_–_Cambridge_–
                  Bullseye_and_Buster_testing_starting⠀⇛


                       And I’m over here with the Debian images/media
                       release team in Cambridge.


                       First time together in Cambridge for a long time:
                       several of the usual suspects – RattusRattus,
                       Sledge, Isy and myself. Also in the room are Kartik
                       and egw – I think this is their first time.


                # ⚓ FLOSSLinux:_202209101602_Debian_release_day_–_Cambridge_–
                  post_2⠀⇛


                       Definitely settling into a rhythm – we’ve been
                       joined by smcv in person (and bittin on line).
                       Bullseye testing is now well beyond the standard
                       image testing into the live images.


                       Buster images are gradually being built so there’s
                       the added confusion of two sets of wiki editing,
                       two sets of potential edit conflicts …


          o § Open Hardware/Modding⠀➾


                # ⚓ Prusa_Mini⠀⇛


                       In June I caved and bought a Prusa Mini 3D printer
                       for home. I bought it just before an announced
                       price hike. I went for a Prusa because of their
                       reputation for “just working”, and the Mini mostly
                       as its the cheapest, although, the print area (7″³)
                       is large enough for most of the things I am likely
                       to print.


                       To get started, at the same time I bought some
                       Prusament recycled PLA to print with which,
                       unfortunately, I’ve been a little disappointed
                       with.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Ubuntu Pit ☛ Top_20_Best_Video_Recording_Apps_for_Android
                  Devices_in_2022⠀⇛


                # ⚓ Android Central ☛ AGM_H5_Pro_rugged_phone_review:_An_ideal
                  outdoor_companion_|_Android_Central⠀⇛


                # ⚓ The Verge ☛ Google_Pixel_foldable_and_a_‘Pro’_tablet_hinted
                  at_in_Android_13_code_–_The_Verge⠀⇛


                # ⚓ 4_Ways_to_Control_Android_TV_Without_Remote⠀⇛


                # ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss_this
                  week_–_Android_Apps_Weekly⠀⇛


                # ⚓ Make Use Of ☛ How_to_Draw_on_Your_PC_Screen_With_Your
                  Android_Phone⠀⇛


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


          o § Web Browsers⠀➾


                # § Chromium⠀➾


                      # ⚓ Ghacks ☛ Google_releases_Chrome_105_emergency_update
                        to_address_security_issue⠀⇛


                             Google released an emergency update for the
                             company’s Chrome web browser on September 2,
                             2022. The update addresses a security issue
                             in the browser that is rated high and
                             exploited in the wild.


                      # ⚓ Medevel ☛ Turn_your_Google_Chrome_into_a_DICOM_Viewer
                        with_These_Free_Extensions⠀⇛


                             Google Chrome is a web browser that holds
                             65.21% of the web browser market, according
                             to Statista. It has a vast marketplace of
                             extensions and themes that allows users to
                             extend its functionality for free.


          o § Content Management Systems (CMS)⠀➾


                # ⚓ Linux Links ☛ 5_Best_Free_and_Open_Source_Lisp_Static_Site
                  Generators_–_LinuxLinks⠀⇛


                       LinuxLinks, like most modern websites, is dynamic
                       in that content is stored in a database and
                       converted into presentation-ready HTML when readers
                       access the site.


                       While we employ built-in server caching which
                       creates static versions of the site, we don’t
                       generate a full, static HTML website based on raw
                       data and a set of templates. However, sometimes a
                       full, static HTML website is desirable. Because
                       HTML pages are all prebuilt, they load extremely
                       quickly in web browsers.


                       There are lots of other advantages of running a
                       full, static HTML website.


          o § Programming/Development⠀➾


                # ⚓ Grantlee_version_5.3_now_available_|_Steveire’s_Blog_
                  (Stephen_Kelly)⠀⇛


                       I previously announced the end of new Qt5-based
                       Grantlee releases. The Grantlee template system is
                       to find new life as part of KDE Frameworks 6 in the
                       form of KTextTemplate. The Grantlee textdocument
                       library will probably become part of another KDE
                       library with similar scope.


                       Meanwhile, some changes have accumulated since the
                       last Grantlee release, so I’ve made a new release
                       to make them available to users. Many of the
                       changes are small, but with a few new features
                       which were cherry-picked from the Cutelee repo.


                       The other significant change is that Grantlee 5.3.0
                       can be built with Qt 6. This is not a change of
                       plan regarding migration to KDE Frameworks, but is
                       intended to assist with porting existing code to Qt
                       6.


                # ⚓ Rlang ☛ Financial_Industry_Supports_Robust_Vienna_R
                  Community⠀⇛


                       R Consortium recently talked to Mario Amau, co-
                       organizer of the Vienna<-R about the lively R
                       community in Vienna. The group is committed to
                       providing its members with valuable talks and
                       networking opportunities. The group is looking
                       forward to restarting their live events, now
                       hybrid, in September!


                # ⚓ Joachim_Breitner:_rec-def:_Behind_the_scenes⠀⇛


                # ⚓ Make Use Of ☛ Using_the_Subversion_Version_Control_System
                  on_a_Server⠀⇛


                       Subversion is an open-source version tracking
                       system. It keeps files in a central repository and
                       provides version control over directories or files.
                       As a developer, you can pull project files from a
                       repository, make changes to them, and push them
                       back again.


                       Subversion also has a server component that you can
                       use to host your projects. It works much like an
                       ordinary file server.


                # ⚓ zstd_compressed_debug_sections_|_MaskRay⠀⇛


                       In January I wrote Compressed debug sections. The
                       venerable zlib shows its age and there are
                       replacements which are better in every metric
                       except adoption. The obvious choice was Zstandard,
                       but I was not so confident about solving the
                       ecosystem issue if we adopted it for ELF compressed
                       debug sections. At any rate, I slowly removed some
                       legacy .zdebug support from llvm-project so that a
                       new format could be more easily introduced.


                       In June, Cole Kissane posted [RFC] Zstandard as a
                       second compression method to LLVM on LLVM discourse
                       forums. I learned that other folks were
                       investigating a better compression format for ELF
                       compressed debug sections and told myself: it’s
                       high time to propose ELFCOMPRESS_ZSTD to the
                       generic System V Application Binary Interface
                       (generic ABI).


                       ELF is an elegant format which has passed the test
                       of time. Many things created by the forefathers
                       from 30 years ago carry over and are still used
                       today. Every new feature, even a small addition
                       like introducing a new constant has to pass a
                       significant high bar for acceptance. There were
                       many discussions on Add new ch_type value:
                       ELFCOMPRESS_ZSTD.


                # ⚓ Multiple_studies,_one_chart⠀⇛


                       I redesign a grouped-bar chart to attempt to better
                       align the logic of the display with the logic of
                       the argument. The redesigned chart provides better
                       visual access to year-by-year comparisons by
                       different combinations of categories and reveals
                       nuances in the data not obvious in the original
                       chart.


                # ⚓ Tracking:_announcing_new_R_package_TrackMateR⠀⇛


                       TrackMate is a plug-in for ImageJ which ships with
                       Fiji. It’s essential for single particle tracking
                       work, particularly for microscopy movies. For
                       example, tracking the movement of fluorescent
                       vesicles inside cells.


                       A tracking session generates a TrackMate XML file.
                       The idea was to write something for R that could
                       load these XML files and do some analysis.


    * § Leftovers⠀➾


          o ⚓ 4.2_Gigabytes,_or:_How_to_Draw_Anything⠀⇛


                 Watching a vibrant Seattle sunset the other day, my
                 imagination started running. The otherworldly hue of the
                 sky evoked something from science fiction. The hazy
                 orange-purple was mesmerizing.


                 I envisioned a massive, alien object hovering over a
                 long-abandoned Seattle, with a burning orange sky, and
                 buildings overgrown as nature reclaimed the city.


          o ⚓ Andy Baio ☛ Exploring_12_Million_of_the_2.3_Billion_Images_Used
            to_Train_Stable_Diffusion’s_Image_Generator_–_Waxy.org⠀⇛


                 One of the biggest frustrations of text-to-image
                 generation AI models is that they feel like a black box.
                 We know they were trained on images pulled from the web,
                 but which ones? As an artist or photographer, an obvious
                 question is whether your work was used to train the AI
                 model, but this is surprisingly hard to answer.


                 Sometimes, the data isn’t available at all: OpenAI has
                 said it’s trained DALL-E 2 on hundreds of millions of
                 captioned images, but hasn’t released the proprietary
                 data. By contrast, the team behind Stable Diffusion have
                 been very transparent about how their model is trained.
                 Since it was released publicly last week, Stable
                 Diffusion has exploded in popularity, in large part
                 because of its free and permissive licensing, already
                 incorporated into the new Midjourney beta, NightCafe, and
                 Stability AI’s own DreamStudio app, as well as for use on
                 your own computer.


          o § Security⠀➾


                # ⚓ 20220910-youngest-LUKS-user⠀⇛


                       So I’m in Berlin currently to attend the fourth
                       Qubes OS Summit, also to discuss the future of the
                       reproducible-builds.org mirror of
                       snapshot.debian.org and in the evening I’ve met an
                       old Debian friend who told a lovely story about his
                       5 year old daughter, who since recently is a Debian
                       user using an old laptop with LUKS encryption,
                       knowing her data will be lost when she forgets her
                       passphrase… 😀


                # § Fear, Uncertainty,
                  Doubt/Fear-mongering/Dramatisation⠀➾


                      # ⚓ Security Week ☛ New_‘Shikitega’_Linux_Malware_Grabs
                        Complete_Control_of_Infected_Systems [Ed: Those systems
                        need to be infected in the first place, and not the
                        fault of "Linux"]⠀⇛


                      # ⚓ The Register UK ☛ Shape-shifting_cryptominer_savaging
                        Linux_endpoints_and_IoT [Ed: Well, better find out the
                        actual cause of breach, and it's not likely to be
                        Linux]⠀⇛


                             AT&T didn’t say how the initial infection
                             occurs…


                # § Privacy/Surveillance⠀➾


                      # ⚓ Bert Hubert ☛ On_my_resignation_as_regulator_of_the
                        Dutch_intelligence_and_security_services_–_Bert
                        Hubert’s_writings⠀⇛


                             I’ve seen some mediocre automated
                             translations of my Dutch language resignation
                             statement go round. To prevent any confusion,
                             please find the story here in English:


                             Until today I was one of the three members of
                             the board that checks warrants for the Dutch
                             intelligence and security services. This
                             board is called “Toetsingscommissie Inzet
                             Bevoegdheden” or TIB.


                             If either of the civil or the military
                             intelligence and security services of The
                             Netherlands want to use their lawful
                             intercept, SIGINT or hacking (& some other)
                             legal powers, they have to first convince
                             their own jurists, then their ministry and
                             finally the TIB. The TIB then studies if the
                             warrant is legal, and that decision is
                             binding.


          o § Finance⠀➾


                # ⚓ Michael West Media ☛ Lufthansa_paid_back_its_debt,_Qantas
                  bought_its_own_shares_–_Michael_West⠀⇛


                       As the Spirit of Stuff-Ups continues, nothing puts
                       the Qantas conundrum in starker relief than rival
                       airline, Germany’s national carrier Lufthansa,
                       which paid back its Covid debt to the German people
                       last November.


                       “On behalf of all Lufthansa employees, I would like
                       to thank the German government and the German
                       taxpayers,” declared Carsten Spohr, CEO of Deutsche
                       Lufthansa. “In the most serious financial crisis in
                       our company’s history, they have given us a
                       perspective for the future. This has enabled us to
                       save more than 100,000 jobs.”


                       What’s the scam? The German government lent the
                       money (1m euros), jobs were saved, service
                       standards preserved. The Australian government gave
                       billions in public subsidies instead of loans,
                       standards plummeted and 9,400 lost their jobs while
                       management banked the JobKeeper.


                # ⚓ Military-Industrial_Complex_Clinches_Nearly_450,000%_Return
                  on_Investment_–_Public_Citizen⠀⇛


                       Every year, the defense industry donates millions
                       of dollars to the campaigns of members of Congress,
                       creating pressure on the legislative branch to fund
                       specific weapons systems, maintain an extremely
                       high Pentagon budget, and add ever more military
                       spending. This upwards pressure is a constant, no
                       matter what figure is requested by the president
                       for the Pentagon, even though nearly 50% of the
                       current Pentagon budget already goes to private
                       contractors each year.


                       Members of the House and Senate Armed Services
                       Committees are especially targeted by defense
                       contractors. These committee members determine the
                       amount of money authorized for the Pentagon when
                       the committee marks up the annual Pentagon policy
                       bill, the National Defense Authorization Act.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ TomDispatch ☛ Steve_Fraser,_The_Rogue_Court,_Then_and_Now⠀⇛


                       Once upon a time, such a donation would have been
                       inconceivable. However, thanks to a series of court
                       decisions, chiefly the Supreme Court’s 5-4 2010
                       Citizens United one that wiped out century-old
                       campaign finance restric­tions, corpor­a­tions and
                       other outside — or as they’re known, “dark-money” —
                       groups can now essentially sink unlim­ited funds
                       into elec­ting those they believe will benefit them
                       most. In this case, that money will assumedly help
                       Leo and his nonprofit further reshape both American
                       politics and our courts.


                # § Misinformation/Disinformation⠀➾


                      # ⚓ Antipope ☛ London_Bridge⠀⇛


                             If you can find any other news that’s being
                             buried under the royal succession whoopsie?
                             This is your thread.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ EUKLNQI_Wordo:_SABRA⠀⇛


                       This is a wordlog for the SpellBinding puzzle (in
                       which you construct words using the specified
                       letters; each word must contain the anchor letter).


                # ⚓ Star_Log_2022-09-10_01:50_AKDT_(Fairbanks,_AK,_US)⠀⇛


                       This, alas, must be a rather brief and pathetic
                       post. For the last two weeks, I have been reading
                       books on astronomy and star gazing, and I have been
                       very eager to do more star gazing. But that whole
                       time we have had, here in Fairbanks, an almost
                       unbroken continuance of overcast cloud conditions.
                       That, coupled with the fact that, in my location,
                       one must currently get up at about 1am or 2am for
                       workable light conditions, has made stargazing near
                       impossible for the working man.


                       [...]


                       Of course, here in Alaska we have plenty of
                       darkness once we get deep into winter, but the
                       benefit is offset somewhat by the sub-zero
                       temperatures.


          o § Technical⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ Welcome_to_snonux.land⠀⇛


                             This is yet another Gemini capsule and
                             interweb site. This is more of an experiment
                             and I don’t know yet if it will roll. Let’s
                             see! I will take bets!


                # § Announcements⠀➾


                      # ⚓ GemiNotes_source_code_available⠀⇛


                             It’s a very simple app I made with Python and
                             sqlite with no proper coding standards
                             applied, but hopefully the code would be
                             useful for other people trying to learn more
                             about Gemini and cgi scripts in general.


                # § Programming⠀➾


                      # ⚓ Porting_*Space_Station_13*_with_Transpilation⠀⇛


                             I’ve been working on *Donk Project* for the
                             past three months or so. It was one of those
                             projects that I couldn’t help but try out, to
                             see how far I could get.


                             [...]


                             There’s decades worth of solid libraries in
                             the ecosystem, as well as a new generation of
                             modern, C++17-and-above-supporting libraries.


                      # ⚓ progress_in_design⠀⇛


                             I’ve slowly made progress in the cluster
                             design. I have started setting up what could
                             be called the hashi stack. It’s been an
                             interesting, if sometimes frustrating,
                             process.


                             I’ve also worked on getting some network kit.
                             I ended up looking at ibm rackswitch
                             equipment, ebay found me some ibm 8264
                             switches for cheap, one had ethernet, the
                             cables of course were a fortune.


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



                    ䷩ 𝚕𝚒𝚗𝚎 5126

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_10/09/2022:_diaspora*_0.7.18.1,_Tor_Browser_12.0a2,_and_Wine_7.17⠀✐


Posted in News_Roundup at 7:02 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o Licensing_/_Legal
          o Programming/Development
                # Perl_/_Raku
                # Python
          o Standards/Consortia
    * Leftovers
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o ⚓ Its FOSS ☛ Traditional_Linux_Packaging_is_not_Suitable_for_Modern
            Applications_[Opinion]⠀⇛


                 The fundamental issue with traditional packaging is that
                 it does not leverage containers. Many graphical
                 applications are inherently complicated and require very
                 specific dependencies to run as intended. Many
                 distributions build the same application in different
                 environments by making use of workarounds, such as
                 patching the application or disabling build options. This
                 leads to different variants of one application and
                 suffers from inconsistent behavior and user experience.
                 Of course, distribution maintainers can’t realistically
                 rewrite their package managers and make use of containers
                 in 10 days. These rewrites will break many scripts,
                 features, and more and will also take a long time to be
                 production-ready.


                 My personal recommendation would be to use and promote
                 Flatpak, as it is solely intended to extend an existing
                 distribution rather than replace it. Packagers won’t have
                 to worry about packaging applications and resorting to
                 workarounds, as Flatpak will already be taking care of
                 that.


          o ⚓ Linux Links ☛ Linux_Around_The_World:_Estonia_–_LinuxLinks⠀⇛


                 We cover events and user groups that are running in
                 Estonia. This article forms part of our Linux Around The
                 World series.


          o § Audiocasts/Shows⠀➾


                # ⚓ Hackaday ☛ Hackaday_Podcast_184:_What_Is_Art,_Bulk_Tape
                  Eraser_Go_Brr,_And_The_Death_Of_Email⠀⇛


                       This week, Editor-in-Chief Elliot Williams and
                       Assignments Editor Kristina Panos had a lot of fun
                       discussing the best of the previous week’s hacks in
                       spite of Elliot’s microphone connectivity troubles.
                       News-wise, we busted out the wine and cheese to
                       briefly debate whether a Colorado man should have
                       won an art competition by entering an image created
                       by AI. Afterward, we went around a bit about
                       floppies, which are being outlawed in Japan.


          o § Applications⠀➾


                # ⚓ diaspora*_version_0.7.18.1_released!_–_The_diaspora*
                  Project⠀⇛


                       We just released diaspora* version 0.7.18.1 which
                       fixes an issue when multiple bundler versions were
                       available that results in diaspora* being unable to
                       start.


                # ⚓ WINE Project (Official) ☛ WineHQ_–_Wine_Announcement_–_The
                  Wine_development_release_7.17_is_now_available.⠀⇛


                       The Wine development release 7.17 is now available.

                       What's new in this release:
                         - High Unicode planes support in DirectWrite.
                         - Some work towards Wow64 support in the Vulkan
                       driver.
                         - Various bug fixes.

                       The source is available at:

                       https://dl.winehq.org/wine/source/7.x/wine-
                       7.17.tar.xz

                       Binary packages for various distributions will be
                       available from:

                       https://www.winehq.org/download

                       You will find documentation on https://
                       www.winehq.org/documentation

                       You can also get the current source directly from
                       the git
                       repository. Check https://www.winehq.org/git for
                       details.

                       Wine is available thanks to the work of many
                       people. See the file
                       AUTHORS in the distribution for the complete list.
          o § Instructionals/Technical⠀➾


                # ⚓ UNIX Cop ☛ How_to_change_network_interface_name_to_eth0_on
                  CentOS_9/8⠀⇛


                       In this post, you will learn How to change network
                       interface name to eth0 on CentOS 9/8 and RHEL 9/8


                       When on a Linux system, you show the name of the
                       network interfaces, usually, the Ethernet
                       connection is shown with eth0 but if you do it on
                       CentOS, you will get an ens33 or an enp0s3 and how
                       to reverse this? Well, let’s go for it.


                # ⚓ Linux Made Simple ☛ How_to_install_Scribus_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Scribus 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.


                # ⚓ Matt Rickard ☛ The_Lost_Art_of_System_Administration⠀⇛


                       I spent a good chunk of my adolescence learning
                       Linux systems administration. I attribute some of
                       my success as a software engineer to the scripting
                       and systems knowledge I picked up while installing,
                       maintaining, and tinkering with Linux distros.


                       Now, one rarely needs to know things like that –
                       runtimes are “serverless,” and ssh is disappearing.
                       Macbooks are the developer machine. Init systems
                       and daemons have been replaced by single-process
                       containers. General-purpose operating systems have
                       been replaced with small (e.g., alpine) or even
                       smaller ones (e.g., microkernels). Hardware


                       This is the natural progression of things. Here are
                       a few things I learned from tinkering over the
                       years.


                # ⚓ BSDly ☛ The_Things_Spammers_Believe_–_A_Tale_of_300,000
                  Imaginary_Friends⠀⇛


                       It finally happened. Today, I added the three
                       hundred thousandth (yes, 300,000th) spamtrap
                       address to my greytrapping setup, for the most part
                       fished out of incoming traffic here, for spammers
                       to consume.


                       A little more than fifteen years after I first
                       published a note about the public spamtrap list for
                       my greytrapping setup in a piece called Hey,
                       spammer! Here’s a list for you!, the total number
                       of imaginary friends has now reached three hundred
                       thousand. I suppose that is an anniversary of
                       sorts.


                # ⚓ Digital Music News ☛ How_To_Record_Vocals_at_Home_(for
                  Beginners)⠀⇛


                       Most indie artists are recording music from their
                       bedrooms. It’s amazing we have that opportunity,
                       but it also requires knowing more about how to
                       properly record. And the quality of the vocals is
                       one of the things that can make or break a track.
                       So here’s the basic process for how to record
                       vocals at home…


                # ⚓ Terence Eden ☛ What’s_the_cheapest_domain_you_can_register
                  for_10_years?⠀⇛


                       I’m concerned about the longevity of the domains I
                       register. I want my domains to be available for as
                       long as possible. But it seems that every year
                       prices rise – and the discount often provided for a
                       new domain rarely continues into subsequent years.


                       So I recently started renewing them for as long as
                       possible. It turns out that most domains can be
                       registered for a maximum of 10 years1.


                # ⚓ Chris Hannah ☛ How_I_Set_Up_My_Ghost_Blog_to_Support_Micro
                  Posts⠀⇛


                       Yesterday, I configured my blog to support micro
                       posts, and I had a lot of feedback asking,
                       essentially, how I did it. So, I’ve decided to
                       write exactly what I did to enable micro posts on
                       my Ghost blog.


                       As a side note, my blog is a self-hosted instance
                       of Ghost on Digital Ocean. This is the only way
                       I’ve ever used Ghost, so if you pay for a Ghost
                       instance directly on Ghost.org, then I’m not sure
                       if you will have access to everything a self-hosted
                       instance does.


                # ⚓ James G ☛ TIL:_Fixing_the_author_card_on_my_home_page_h-
                  feed⠀⇛


                       Assumed knowledge: This post assumes technical
                       knowledge with microformats. This post is most
                       useful for someone debugging authorship relations
                       on their h-feed or for community members who want
                       to discuss documenting this pattern.


                # ⚓ James G ☛ Hosting_a_fun_DNS_server_with_Go_and_a_DNS
                  library⠀⇛


                       I had a lot of fun building this project. Projects
                       like this keep me thinking about how joyful
                       computing can be (as well as how you can do some
                       really fun things with protocols!). Now that I have
                       the shell of a DNS server and some utilities, I can
                       add new functionalities at any time as I think of
                       them. I don’t have any ideas just yet, but I think
                       there’s more I can do with my personal website.


                       Let me end by extending a big thank you to miekg
                       and everyone who worked on the aforementioned DNS
                       library in Go. This library (which also powers
                       dns.toys that I mentioned at the beginning of the
                       article) let me build this project without having
                       to implement a whole DNS server myself.


                # ⚓ IT Pro Today ☛ How_To_Create_an_Ubuntu_Virtual_Machine_on
                  Windows_10 [Ed: Too much Windows, but this is at least not as
                  bad as WSL]⠀⇛


                # ⚓ Trend Oceans ☛ How_to_Run_Shell_Scripts_in_Linux_[with
                  Detailed_Explanation_for_Beginners]_–_TREND_OCEANS⠀⇛


                       What is a shell script? A shell script is a
                       sequence of commands written inside a text file
                       with a “.sh” extension that is intended to be run
                       on Unix-based operating systems like Linux.


                       Any person skilled in the Linux command line and
                       possessing a decent knowledge of shell and bash
                       scripting languages can create their own shell
                       script to automate certain tasks like backing up
                       the system.


                       Standard users like you and me, who don’t have any
                       knowledge about this technicality and use Linux
                       just for media or office work, soon you might
                       encounter this shell file and you should know what
                       are the different ways to execute this shell file
                       are and how to choose the relevant one, including
                       which shell interpreter is recommended by the
                       developer.
                       Stick with this article till the end to learn about
                       them, including bonus tips.


                # ⚓ Linux Hint ☛ CORS_Nginx⠀⇛


                       “Cross-origin resource sharing is known by the
                       acronym CORS. When someone is operating on a
                       different domain, the server will use this method
                       to control access to its services. It happens in
                       the middle of a server and a browser. With the help
                       of HTTP Access-Control-Request-* headers, the
                       browser transmits some data. Based on the received
                       headers, the server decides what to send back as
                       Access-Control-Allow-* headers. The browser is now
                       aware of its ability or inability to access server
                       resources. The browser may occasionally perform a
                       pre-flight, which is a validation, before making
                       the actual request. The headers cannot be changed
                       by front-end code in the browser. The headers can
                       be modified by the server-side code. However, it
                       must be performed by a downstream service that the
                       application cannot see, such as an API gateway or
                       the HTTP server.


                       Cross-origin HTTP queries made by scripts are
                       restricted by browsers for security concerns. The
                       same-origin principle, for instance, is adhered to
                       both the Fetch API and XMLHttpRequest. This implies
                       that a web application utilizing those APIs can
                       only make requests for resources from the origin
                       from which it was loaded unless the response from
                       other sources has the appropriate CORS headers.”


                # ⚓ OpenSource.com ☛ 5_ways_to_resize_and_optimize_images_for
                  the_web_on_Linux_|_Opensource.com⠀⇛


                       There was a time when 5 MB was the reasonable
                       maximum size for an email attachment. Today, it’s
                       easily possible for a single photo to be 5 MB.
                       Accordingly, the maximum attachment size has
                       increased to, say, 25 MB. But of course file sizes
                       are getting bigger and bigger too, and so
                       eventually the attachment limit will go up too.
                       It’s an endless cycle, common in the digital world:
                       the tools are built for today’s data, and today’s
                       data increases in complexity and size until the
                       tools are revised and improved. You have to contain
                       data, preferably in the smallest packaging
                       possible, so that sharing it online goes faster for
                       everyone. Here are five ways to optimize images for
                       the Internet.


                # ⚓ Linux Hint ☛ Nginx_Block_Geo_Location⠀⇛


                       “Nginx is known to be a lightweight open-source
                       software (Linux). It proves to be a high-
                       performance web server by providing high-
                       performance stability, HTTP capabilities, improved
                       application-based deliveries, and security of the
                       websites with the reduction of the long waiting
                       times for the busiest web pages by acting as load
                       manager/balancer for the websites. In comparison
                       with other lightweight web servers, Nginx offers a
                       tremendous variety of features, and one of these
                       features includes the GeoIP module.


                       GeoIP module helps to know about the geo-location
                       of the client; sometimes it happens that the
                       organization/websites aren’t interested in
                       providing their services, or they want to keep
                       their information confidential from certain clients
                       coming from specific geo-location, in such
                       situation GeoIP maps the IP address belonging to
                       the clients’ location and blocks it to avoid any
                       visitor from that location.”


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Valve_opens_official_Steam_Deck_repair
                  centers⠀⇛


                       Need to get your Steam Deck fixed up? Well, you no
                       longer have to do it yourself as Valve have
                       officially opened up some repair centers. If you
                       need to send off your Steam Deck for any reason, it
                       will now go to one of their specialized repair
                       shops.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Nate Graham ☛ This_week_in_KDE:_Getting_Plasma_5.26
                        ready⠀⇛


                             While in Touch mode in the Plasma Wayland
                             session, you can now force the Maliit Virtual
                             Keyboard to appear even if it didn’t appear
                             automatically (Aleix Pol Gonzalez, Plasma
                             5.26. Link)


                             In System Monitor and the Plasma widgets of
                             the same name, you can now query sensors for
                             your CPUs’ minimum, maximum, and average
                             temperature and frequency (Alessio Bonfiglio,
                             Plasma 5.26. Link)


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ 9to5Linux ☛ GNOME_Shell_on_Mobile_Is_Shaping_Up
                        Nicely,_Gets_New_Navigation_Gestures,_Quick_Settings⠀⇛


                             In my previous report, I told you that GNOME
                             developers are working on a native port of
                             GNOME Shell, the main UI of the GNOME desktop
                             environment, for mobile devices (a.k.a. Linux
                             phones and tablets), since the release of
                             GNOME 40.


                             Now, developer Jonas Dreßler shares that
                             “there’s been a huge amount of progress”
                             since the last update in May 2022, and that
                             GNOME Shell on mobile received a
                             sophisticated 2D navigation gesture system
                             similar to what Android and iOS offer, but
                             with a single overview for both launching and
                             switching. Here it is in action!


                      # ⚓ GNOME_Shell_on_mobile:_An_update_–_GNOME_Shell_–
                        Mutter⠀⇛


                             It’s been a while since the last update on
                             GNOME Shell mobile, but there’s been a huge
                             amount of progress during that time, which
                             culminated in a very successful demo at the
                             Prototype Fund Demo Day last week.


                             ​The current state of the project is that we
                             have branches with all the individual patches
                             for GNOME Shell and Mutter, which together
                             comprise a pretty complete mobile shell
                             experience. This includes all the basics we
                             set out to cover during the Prototype Fund
                             project (navigation gestures, screen size
                             detection, app grid, on-screen keyboard,
                             etc.) and some additional things we ended up
                             adding along the way.


                             The heart of the mobile shell experience is
                             the sophisticated 2D gesture navigation: The
                             gestures to go to the overview vertically and
                             switch horizontally between apps are fluid,
                             interruptible, and multi-dimensional. This
                             allows for navigation which is not only quick
                             and ergonomic, but also intuitive thanks to
                             an incredibly simple spatial model.


    * § Distributions and Operating Systems⠀➾


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Make Use Of ☛ 5_Reasons_Ubuntu_Is_the_Ideal_Linux_Distro
                  for_Software_Developers⠀⇛


                       Ubuntu is one of the most widely used Linux
                       distros; it’s stable, reliable, well maintained,
                       and has a huge community of followers.


                       According to a recent survey by HackerEarth, Ubuntu
                       is the preferred Linux OS for software development,
                       making it the most used open-source OS for the
                       development and deployment of code. But why is this
                       so?


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ $60_Raspberry_Pi_Mini_Tower_NAS_kit_takes
                  one_M.2_SATA_SSD⠀⇛


                       52Pi appears to have noticed and liked the design,
                       as they created something similar with the
                       Raspberry Pi Mini Tower NAS kit taking one M.2 SATA
                       SSD instead of using the UPS module. There are also
                       a few tweaks to the mechanical design with the OLED
                       display at an angle for easier reading.


                       There’s also a user manual, but some people
                       complained it’s not detailed enough. You’ll also
                       find installation instructions on the Wiki, where
                       we also learn that 2.4GHz WiFi may not work that
                       well with the kit, so using 5GHz is recommended
                       (But it looks to be a copy/paste from another
                       section of the Wiki for a metal case…).


          o § Open Hardware/Modding⠀➾


                # ⚓ Starting_CPUs_on_ARM64_|_Adam_Young’s_Web_Log⠀⇛


                       The systems I am working with have 80 or more cores
                       in them. I’ve recently had to investigate processes
                       around core start up. Here are my notes.


                # ⚓ Jeff Geerling ☛ A_YouTuber_built_a_tool_that_beat_Snap-On⠀⇛


                       The LTT Screwdriver’s shaft is thinner than the
                       other ratcheting drivers, the ratchet mechanism has
                       the least amount of force required to use it, and
                       the bit storage mechanism—licensed from Megapro—is
                       a pleasure to use, especially in comparison to the
                       stone-age ‘unscrew a cap and dump out a bunch of
                       bits’ method the Snap-On employs.


                       That’s not to say it’s perfect. The smooth plastic
                       grip is fine for lighter work, but requires a lot
                       more finesse if you need high torque, like when
                       screwing into wood. The shaft is in the middle of
                       the pack when it comes to wobble and slop. And
                       little niceties like pre-installed bits (which even
                       the cheap $13 Amazon Basics Screwdriver had) aren’t
                       present with the LTT experience.


                # ⚓ Hackaday ☛ The_Filamentmeter:_For_When_You_Absolutely_Want
                  To_Count_Every_Meter_Used⠀⇛


                       [ArduinoNmore] took an interesting approach to
                       designing a counter intended to accurately display
                       how many meters of filament a 3D printer has used.
                       The Filamentmeter looks a little bit like a 3D
                       printed handheld tally counter (or lap counter) but
                       instead of a button to advance each digit, the
                       readout represents how many meters of filament have
                       gone through the extruder.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Android Police ☛ The_best_Android_apps_for_photographers_in
                  2022⠀⇛


                # ⚓ Liliputing ☛ Android_code_hints_at_unannounced_Pixel_Tablet
                  Pro_and_a_foldable_Pixel_phone_–_Liliputing⠀⇛


                # ⚓ Android Police ☛ Quick_settings_toggles_get_some_cute_new
                  animations_in_Android_13_QPR1_Beta_1⠀⇛


                # ⚓ Android Central ☛ LG_Wing_flew_under_the_radar_with_the_new
                  Android_12_update_in_the_US_|_Android_Central⠀⇛


                # ⚓ Android Central ☛ Google_Fi_expands_its_global_5G_coverage
                  for_select_Android_phones_|_Android_Central⠀⇛


                # ⚓ Make Use Of ☛ 6_iPhone_14_Pro_Features_That_Android_Phones
                  Introduced⠀⇛


                # ⚓ 9to5Google ☛ Google_Keep_gets_dual_pane_view_on_Android
                  tablets_–_9to5Google⠀⇛


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


          o ⚓ Unicorn Media ☛ FOSS_News_Quiz_for_September_9,_2022⠀⇛


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Tor ☛ New_Alpha_Release:_Tor_Browser_12.0a2_(Android,
                        Windows,_macOS,_Linux)⠀⇛


                             This marks our first alpha on the Firefox ESR
                             102 series, and our first Android released
                             based on the Firefox ESR (Extended Support
                             Release) series.


          o § Licensing / Legal⠀➾


                # ⚓ Alexandru Nedelcu ☛ Open_Source_vs_Free_Software⠀⇛


                       The Open Source definition exists because
                       businesses wanted to release products as Free
                       Software, but either wanted a more clear social
                       contract, or wanted nothing to do with its
                       politics, or the organization behind it. It’s still
                       about freedom though, but from a slightly different
                       perspective.


          o § Programming/Development⠀➾


                # ⚓ Do_we_need_an_office?⠀⇛


                       Apple first announced their return-to-office
                       policy, which resulted in their Director of ML
                       leaving, then retracted it, then re-introduced it,
                       resulting in a petition against the change.


                       [...]


                       When thinking about the most efficient work setup,
                       it’s necessary to first define the parameters which
                       we are optimizing our setup for. In general,
                       knowledge work in software consists of using our
                       cognitive and logical capabilities to produce
                       solutions to problems. The nature of these problems
                       can vary greatly – how to implement a feature using
                       a certain programming language, how to structure &
                       resource a project to fulfill customer’s schedule
                       requirements, how to solve interpersonal issues in
                       a team, how to improve the flow of important
                       information within a company, the list goes on and
                       on.


                # ⚓ Good_Interviewer/Bad_Interviewer⠀⇛


                       This post outlines what separates good and bad
                       interviewers, inspired by Ben Horowitz’s timeless
                       post about what distinguishes good product managers
                       from those that are bad.


                # ⚓ Visually_impaired,_blind_children_benefit_from_new_coding
                  project⠀⇛


                # ⚓ Matt Rickard ☛ Materializing_Results⠀⇛


                       Cache invalidation is hard. Even if it’s not really
                       “cache invalidation.” The problem is that you often
                       want denormalized data from your relational
                       databases. But complex joins and large amounts of
                       data can make those queries expensive (in terms of
                       both time and dollar cost).


                       The answer is often an incremental approach. A
                       materialized view provides an up-to-date cached
                       table of the denormalized data. They’ve been around
                       in some form since 1998 (Oracle 8). You can
                       manually implement them with triggers and state
                       functions, but those solutions aren’t
                       generalizable.


                # ⚓ Data Swamp ☛ Git_–_How_to_prevent_a_branch_to_be_pushed⠀⇛


                       I was looking for a simple way to prevent pushing a
                       specific git branch. A few searches on the Internet
                       didn’t give me good results, so let me share a
                       solution.


                # ⚓ Geshan ☛ 101_software_engineering_realities_you_must_be
                  aware_of_(especially_as_a_junior_engineer)⠀⇛


                       I have been writing code in some form for more than
                       20 years now. I have been a software engineer by
                       trade since 2007. Repeatedly, I find myself
                       discussing the same points with multiple people
                       interested in software engineering and web
                       development, mostly junior engineers. So, in this
                       post, I am going to list 101 software engineering
                       realities (experiences moreover) that you can read
                       and possibly learn from, here it goes.


                # ⚓ Alexandru Nedelcu ☛ Scala_isn’t_fun_anymore⠀⇛


                       Many Scala libraries are really well maintained and
                       stable (e.g., Cats), and we’ve got the tools to do
                       it, such as sbt being awesome at conditional/cross
                       compilation, checking versioning schemes, or the
                       availability of Mima, a plugin meant to check for
                       breakages of binary compatibility. It’s a useful
                       case study in communities adapting to their sins.
                       But being the user, and having to deal with all the
                       breakage, is still painful as hell, and I feel that
                       in general many libraries have no respect for
                       downstream users suffering from breakage.


                # ⚓ Jay Little ☛ All_Hail_the_Tech_Magicians_and_their
                  Cantrips⠀⇛


                       My fear here is that we have built a world in which
                       nobody understands how anything actually works.
                       That applies to both the economic priests that we
                       have been serving along with the tech priests that
                       we will inevitably end up serving instead. This
                       idea scares me because it means that on the day
                       things really begin to break, nobody will be in a
                       position to fix it. Right now the end users bet on
                       me being able to fix broken things and I’m betting
                       on the proprietary application / cloud service
                       developers (e.g. Microsoft) being able to fix them.


                # § Perl / Raku⠀➾


                      # ⚓ Stack Overflow ☛ This_is_not_your_grandfather’s
                        Perl⠀⇛


                             All of this meant that for almost twenty
                             years, Perl had no next version number to
                             use. And this has, unsurprisingly, led to a
                             large part of the industry assuming that Perl
                             hasn’t changed much over that time. This is
                             unfortunate as Perl has undergone massive
                             changes in the new millennium. The Perl 5
                             team have developed an annual release cycle,
                             where a new version is released in about May
                             of every year. Version 5.36 was released in
                             May 2022 and is very different to version
                             5.6.0, which was current back in the summer
                             of 2000. In this article, we’ll look at some
                             of the new Perl features that you might have
                             missed.


                # § Python⠀➾


                      # ⚓ Accelerate_Python_code_100x_by_import_taichi_as_ti_|
                        Taichi_Docs⠀⇛


                      # ⚓ You_Can_Build_Portable_Binaries_of_Python
                        Applications⠀⇛


                      # ⚓ AIM ☛ Pycharm_Extends_Support_for_Python_3.11_with
                        Improved_HTTP_Client_and_UX_Enhancements⠀⇛


                             JetBrains’ Pycharm has released a new update
                             2022.2 with a range of features like
                             providing code insight for Python 3.11, run-
                             environment selection in HTTP client, new UI
                             for setting up remote interpreters and
                             support for PyScript framework.


                             The Python version 3.11 has code insight for
                             exception groups, for marking individual
                             TypedDict items and initial support for
                             variadic generics. In the new version, with a
                             click of an icon in the gutter, developers
                             may select a “run environment” before “run”.


          o § Standards/Consortia⠀➾


                # ⚓ NPR ☛ Apple_CEO_Tim_Cook’s_fix_for_those_pesky_green_text
                  bubbles?_‘Buy_your_mom_an_iPhone’⠀⇛


                       Apple CEO Tim Cook seemed to reject the idea of
                       adopting a new messaging protocol on the company’s
                       devices that would make communicating with Android
                       users smoother.


    * § Leftovers⠀➾


          o ⚓ Mark Dominus ☛ Pope_Fibonacci⠀⇛


                 When Albino Luciani was crowned Pope, he chose his papal
                 name by concatenating the names of his two predecessors,
                 John XXIII and Paul VI, to become John Paul. He died
                 shortly after, and was succeeded by Karol Wojtyła who
                 also took the name John Paul. Wojtyła missed a great
                 opportunity to adopt Luciani’s strategy. Had he
                 concatenated the names of his predecessors, he would have
                 been Paul John Paul. In this alternatve universe his
                 successor, Benedict XVI, would have been John Paul Paul
                 John Paul, and the current pope, Francis, would have been
                 Paul John Paul John Paul Paul John Paul. Each pope would
                 have had a unique name, at the minor cost of having the
                 names increase exponentially in length.


          o ⚓ The Conversation ☛ Seven_times_people_discovered_the_Americas_–
            and_how_they_got_there⠀⇛


                 When Columbus landed in 1492, the Americas had been
                 settled for tens of thousands of years. He wasn’t the
                 first person to discover the continent. Instead, his
                 discovery was the last of many discoveries.


                 In all, people found the Americas at least seven
                 different times. For at least six of those, it wasn’t so
                 new after all. The discoverers came by sea and by land,
                 bringing new genes, new languages, new technologies. Some
                 stayed, explored, and built empires. Others went home,
                 and left few hints they’d ever been there.


                 From last to first, here’s the story of how we discovered
                 the Americas.


          o ⚓ Hackaday ☛ Motorcycle_Builder_Makes_Downhill_Mountain_Bike⠀⇛


                 [Allen Millyard] is a premier British motorcycle builder.
                 In these circles he is widely regarded and his custom
                 motorcycles are nearly world-famous. But when his son
                 took up downhill mountain biking, he decided to put his
                 skills building a different type of vehicle. This is the
                 Millyard MR001, one of the most unique mountain bikes
                 ever built thanks to some design choices that solve many
                 problems otherwise inherent in bicycles.


          o ⚓ Hackaday ☛ The_Internet_Without_The_Computer:_1990s_Style⠀⇛


                 We think of the Internet extending to small devices as a
                 modern trend, but it actually is a good example of how
                 everything makes a circle. Today, we want the network to
                 connect to our thermostat and our toaster. But somewhere
                 between the year 1990 and the year 2010, there was a push
                 to make the Internet accessible to the majority of people
                 who didn’t own a computer. The prototypical device, in
                 our mind, was Microsoft’s ill-fated WebTV, but a recent
                 video from [This Does Not Compute] reminded us of another
                 entry in that race: The Audrey from 3COM. Check out the
                 video, below.


          o ⚓ Counter Punch ☛ Boris_Kagarlitsky⠀⇛


          o § Education⠀➾


                # ⚓ Jeff Geerling ☛ Short_is_good⠀⇛


                       I watched TheOdd1sOut’s How to Find Inspiration and
                       remembered the most important lesson I learned from
                       my high school English teacher:


                       Short is good. Short is hard.


                       The teacher didn’t exactly put it like that. But he
                       harped on something nobody else did: writing
                       concisely.


                # ⚓ RTL ☛ Voice-operated_smartphones_target_Africa’s
                  illiterate⠀⇛


                       In Ivory Coast, a so-called “Superphone” using a
                       vocal assistant that responds to commands in a
                       local language is being pitched to the large
                       segment of the population — as many as 40 percent —
                       who are illiterate.


                       Developed and assembled locally, the phone is
                       designed to make everyday tasks more accessible,
                       from understanding a document and checking a bank
                       balance to communicating with government agencies.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Bootstrapping_The_Old_Fashioned_Way⠀⇛


                       The PDP-11, the Altair 8800, and the IMSAI 8080
                       were some of the heroes of the computer revolution,
                       and they have something in common — front panel
                       switches, and a lot of them. You probably have a
                       fuzzy idea about those switches, maybe from reading
                       Levy’s Hackers, where the painful process of
                       toggling in programs is briefly described. But how
                       exactly does it work? Well thanks to [Dave Plummer]
                       of Dave’s Garage, now we have a handy tutorial. The
                       exact computer in question is a reproduction of the
                       IMSAI 8080, the computer made famous by a young
                       Matthew Broderick in Wargames. [Dave] managed to
                       score the reproduction and a viewer saved him the
                       time of assembly.


                # ⚓ Hackaday ☛ Ultra-Thin_Rubber_Parts_Made_With_A_3D_Printed
                  Plug⠀⇛


                       We generally think of 3D printed components as
                       being hard bits of plastic, because for the most
                       part, that’s what we’ve got loaded up in our
                       desktop machines. But outside of the normal PLA,
                       PETG, and ABS, you can also print with various
                       flexible filaments such as TPU. This can be handy
                       for producing custom seals, or rugged enclosures.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Scheerpost ☛ LA_Ended_a_Zero-bail_COVID_Rule,_and_Now_the
                  Jail_Population_Is_Growing⠀⇛


                       In June, a judge ended an emergency order to slow
                       the spread of COVID-19 in LA’s jails, enraging
                       civil-rights advocates.


                # ⚓ The Conversation ☛ Psychedelic_drugs_can_be_almost_as_life
                  altering_as_near-death_experiences⠀⇛


                       In the study, people described both drug and NDE
                       experiences that brought a more positive attitude
                       to death, with less fear. People reported
                       significant increases in psychological insight,
                       welfare and meaning in their lives.


                # ⚓ Common Dreams ☛ Opinion_|_Jackson,_Mississippi_Must_Reject
                  Water_Privatization⠀⇛


                       What’s happening in Jackson, Miss., where residents
                       remain under a boil-water advisory after having
                       little to no access to safe water for all of last
                       week, is horrifying. If it weren’t happening in a
                       poor city with a majority Black population, it
                       would be getting the 24/7 news coverage it
                       deserves.


                # ⚓ Common Dreams ☛ Opinion_|_As_New_Covid_Boosters_Move
                  Forward,_Better_Outreach_Is_Needed_to_Save_Lives⠀⇛


                       This week––nearly ten months after the emergence of
                       the Omicron variant––the United States is rolling
                       out Covid-19 booster vaccines that specifically
                       target newer, now-dominant strains of the virus.
                       The CDC has estimated that 209 million Americans
                       over the age of 12, or 74 percent of that
                       population, will be eligible for the shots.


                # ⚓ Common Dreams ☛ Locals_Celebrate_‘Tremendous_Victory’
                  Against_South_Louisiana_Methanol_Petrochemical_Complex⠀⇛


                       “It took hundreds of residents banding together to
                       force LDEQ to recognize how overburdened the
                       community is with industrial pollution, and to show
                       polluters that we will not accept another plant
                       moving in.”


          o § Proprietary⠀➾


                # ⚓ [Old] ABC ☛ Oracle_joins_in_FBI,_CIA_database_plans⠀⇛


                       Oracle Corporation is working with the CIA and the
                       FBI on plans to create a national database which
                       will capture information on all Americans and quite
                       possibly, people in the rest of the world.


                # ⚓ [Old] SFGate ☛ Oracle’s_coziness_with_government_goes_back
                  to_its_founding_/_Firm’s_growth_sustained_as_niche
                  established_with_federal,_state_agencies⠀⇛


                       The CIA was not just Oracle’s first customer.
                       Founded in May 1977, the firm’s name came from a
                       CIA project code-named “Oracle.” Company co-
                       founders Larry Ellison, Robert Miner and Ed Oates
                       worked on Project Oracle at a consulting firm,
                       before striking out on their own.


                       A quarter century later, close to a quarter of the
                       company’s revenue — $2. 5 billion a year — still
                       comes from selling software to federal, state and
                       local agencies.


                # ⚓ [Old] Gizmodo ☛ Larry_Ellison’s_Oracle_Started_As_a_CIA
                  Project⠀⇛


                       Oracle has pulled in billions of dollars each year
                       working for governments at all levels for all
                       manner of projects, the most high-profile of late
                       being the disaster that was the Oregon health
                       insurance exchange. But it’s the company’s
                       philosophy behind how national security databases
                       should work which would surprise someone who’d only
                       read about them on Vox.


                       Ellison has always been a big believer in the
                       federal government maintaining large national
                       databases. And he was able to be much more public
                       about it in the months after the September 11th
                       attacks. In fact, Ellison argued that we needed
                       just one large national security database, one with
                       national ID cards and mandatory iris scans,
                       naturally.


                # ⚓ Kev Quirk ☛ iCreep⠀⇛


                       At this point, pretty much all of my computing is
                       done on an Apple device, but I never intended for
                       it to be this way.


                       Back when I ditched Android my plan was to only
                       ditch Android because I feel that Apple is the
                       lesser of the two evils.


                # ⚓ Klara ☛ Deploying_FreeBSD_on_Oracle_Cloud:_Why_Leverage
                  FreeBSD_for_Oracle_Cloud’s_new_Arm_Instances⠀⇛


                       Although most people associate ARM processors with
                       small personal devices, ARM64 servers have grown by
                       leaps and bounds in the last few years. For
                       example, Ampere Altra machines are available in 80
                       and 160 core variants and can support up 512GB of
                       RAM. These machines are core to Oracle Clouds ARM
                       server offering.


          o § Security⠀➾


                # ⚓ New_Linux_malware_combines_unusual_stealth_with_a_full
                  suite_of_capabilities [Ed: Microsoft-funded sites keep
                  pushing this narrative; Linux typically has nothing to do
                  with the malware, which gets put there some other way.]⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ Video ☛ The_Police_Are_Watching_Us_All_–_Invidious⠀⇛


                             This week in the Weekly News Roundup, police
                             bypass warrants with big tech, Apple takes a
                             swipe at passwords, and scientists are trying
                             to assist memory.


                      # ⚓ Video ☛ The_Police_Are_Watching_Us_All_–_Invidious⠀⇛


                      # ⚓ Help Net Security ☛ Researchers_publish_post-quantum
                        upgrade_to_the_Signal_protocol⠀⇛


                             PQShield published a white paper that lays
                             out the quantum threat to secure end-to-end
                             messaging and explains how post-quantum
                             cryptography (PQC) can be added to the Signal
                             secure messaging protocol to protect it from
                             quantum attacks.


                      # ⚓ EDRI ☛ New_EU_law_amplifies_risks_of_state_over-reach
                        and_mass_surveillance⠀⇛


                             What this means for us is that the sensitive
                             data of up to 10% of the population – such as
                             people’s DNA and fingerprint data – are being
                             collected in national policing databases
                             which can be searched automatically by each
                             Member State. The system currently allows
                             police authorities to compare a DNA profile –
                             in theory, taken from a criminal suspect or
                             found at a crime scene – and use it to run a
                             search against all other participating member
                             states’ DNA databases. The new proposal would
                             allow searches on the basis of people’s
                             facial images, too.


                             Since entering into EU law in 2008 (between
                             2005 and 2008, it was a treaty between
                             several governments only) the Prüm framework
                             has proven unfit for purpose. For example, in
                             Slovenia, investigations have revealed that
                             victims and their family members have been
                             included in criminal databases, and other
                             examples show that non-suspects, acquitted
                             people, victims and witnesses are routinely
                             included in criminal databases without a
                             legal basis in many EU countries. Our
                             research has also shown a patchwork of rules
                             (or lack of rules) and systemic data
                             protection failings across these national
                             databases. When plugged into supranational
                             systems like Prüm, the risks skyrocket.


                      # ⚓ [Old] Austin Gil ☛ TIL:_You_Can_Access_A_User’s
                        Camera_with_Just_HTML⠀⇛


                             The interesting thing about the capture
                             attribute is for users coming to your website
                             on a mobile device. If they interact with
                             that input, instead of opening up the default
                             file picker, it will actually open up one of
                             their cameras. It could be the front facing
                             camera or the back facing camera, depending
                             on the value.


                      # ⚓ I Cringely ☛ What_yesterday’s_Apple_satellite
                        announcement_really_means⠀⇛


                             I took the summer off to move with my family
                             from California to Virginia, thus escaping
                             the inevitable fires of doom. I deliberately
                             left my Apple/Globalstar column up so it
                             would be still staring at readers when Apple
                             made its eventual announcement, which was
                             yesterday. That was a gutsy move on my part,
                             but clearly I was correct. Today’s column —
                             my first from our new home in Virginia —
                             looks at specifics of the Apple satellite
                             announcement, placing it in a more informed
                             context.


                      # ⚓ Techdirt ☛ Yet_Another_Data_Broker_Found_To_Give
                        Massive_Amounts_Of_Location_Info_To_Law_Enforcement⠀⇛


                             The Supreme Court may have extended
                             constitutional protection to historical cell
                             site location info, but that’s not going to
                             stop our public servants — and the private
                             companies that serve them — from finding ways
                             to elude the ramifications of the Carpenter
                             decision.


                      # ⚓ Common Dreams ☛ Coalition_Tells_FTC_to_Curb_Amazon
                        ‘Surveillance_Empire’_by_Blocking_Purchase_of_iRobot⠀⇛


                             “The deal will further entrench Amazon’s hold
                             on the smart home technology ecosystem,
                             eliminate competition in that sector, and
                             enhance the company’s monopoly power.”


          o § Defence/Aggression⠀➾


                # ⚓ Scheerpost ☛ Zelensky_Rings_New_York_Stock_Exchange_Bell_as
                  Euro_Dips_Below_Dollar⠀⇛


                       As the Ukraine proxy war triggers economic crisis
                       across the West. Zelensky kicks off a campaign
                       inviting foreign investors to plunder his country
                       while he crushes the labor rights of its citizens.


                # ⚓ France24 ☛ Shelling_at_Zaporizhzhia_nuclear_power_plant
                  poses_a_growing_problem⠀⇛


                       Shelling has destroyed power infrastructure at the
                       Ukrainian city of Enerhodar where staff operating
                       the Russian-held Zaporizhzhia nuclear power plant
                       live, posing a growing threat to the plant, the UN
                       nuclear watchdog said on Friday. Meanwhile Russian
                       forces have killed two staff members.


                # ⚓ CBC ☛ Ukrainian_nuclear_plant_operating_in_emergency_mode,
                  state_operator_says⠀⇛


                       The six-reactor Zaporizhzhia nuclear power plant
                       came under the control of Russian forces early in
                       the war that started in February, but is being
                       operated by Ukrainian staff. The plant and
                       surrounding areas have been repeatedly hit by
                       shelling that Russia and Ukraine blame on each
                       other’s forces.


                       The last power line connecting the plant to the
                       Ukrainian electricity grid was cut on Monday,
                       leaving the plant without an outside source of
                       electricity and receiving power for its own safety
                       systems from the only one of the six reactors that
                       remains operational.


                # ⚓ Jacobin Magazine ☛ Michigan_GOP_Election_Officials_Are
                  Attempting_to_Subvert_Democracy_in_Plain_Sight⠀⇛


                       The Board of State Canvassers decision is part of a
                       broader, more disturbing trend with the potential
                       for much more serious consequences. Earlier this
                       year, Michigan Republicans nominated Kristina
                       Karamo to run for secretary of state, Michigan’s
                       top election administrator. An unhinged election
                       denier who was among the pro-Trump mob that
                       gathered to intimidate Detroit election workers in
                       2020, Karamo has called public schools “government
                       indoctrination camps” and likened abortion to
                       “child sacrifice,” deeming it a “satanic practice.”
                       Karamo also allegedly threatened and attempted
                       violence against her family. It is hard to imagine
                       fair elections in Michigan with Karamo running the
                       show.


                # ⚓ The Strategist ☛ Al-Qaeda,_the_Taliban_and_the_tragedy_of
                  Afghanistan⠀⇛


                       The Taliban don’t have the field to themselves.
                       They are neither prone to change nor united among
                       themselves to embrace an enlightened Islam. It is
                       imperative that the West support the anti-Talban
                       resistance until they can negotiate for a
                       nationally and internationally legitimate and
                       participatory system of governance and a sovereign
                       united Afghanistan with respect for human rights
                       and the rights of women. Whatever the
                       circumstances, the struggle for the soul of
                       Afghanistan is set to continue.


                # ⚓ The Gray Zone ☛ Chain_of_corruption:_how_the_White_Helmets
                  compromised_OPCW_investigations_in_Syria⠀⇛


                # ⚓ TruthOut ☛ Fascism_Has_Gone_Mainstream⠀⇛


                # ⚓ FAIR ☛ NYT_Scolds_China_for_Not_‘Learning_to_Live’—or
                  Die—With_Covid⠀⇛


                       Four and a half million people.


                # ⚓ Scheerpost ☛ Ukraine_and_the_Triumph_of_Militarism⠀⇛


                       “What [Tierney] is saying about liberals who once
                       protested the Iraq invasion now supporting U.S.
                       proxy warfare in Ukraine is broadly
                       true, including throughout the Bernie Sanders/AOC
                       “progressive” wing of the Democratic Party.”


                # ⚓ Common Dreams ☛ Jayapal_Shares_Threatening_Voicemails_Weeks
                  After_Stalking_Incident⠀⇛


                       “From the Big Lie to January 6 to a man with a gun
                       at my door, it is clear how much is at stake.”


                # ⚓ Meduza ☛ Russian-controlled_occupation_authorities_in
                  Kharkiv_region_report_that_they_have_started_evacuating
                  people_from_Izyum_—_Meduza⠀⇛


                       According to TASS, the Russian-controlled
                       administration of the occupied part of Kharkiv
                       Region announced that it had started “evacuating”
                       civilians from the town of Izyum, which is
                       controlled by Russian troops.


                # ⚓ Meduza ☛ Elections_have_begun_in_Russia._Moscow_election
                  observers_say_hundreds_of_cyber_attacks_have_been_stopped._—
                  Meduza⠀⇛


                       On September 9 a three-day voting for various
                       levels of government began in 82 Russian regions.
                       The main and final election day will be September
                       11.


                # ⚓ Common Dreams ☛ Opinion_|_The_Lasting_Impacts_of_Mikhail
                  Gorbachev’s_Squandered_Legacy⠀⇛


                       Mikhail Gorbachev, who died at the age of 91 on
                       August 30, was “perhaps the most radical thinker
                       about security to ever lead a major power,” writes
                       Katrina vanden Heuvel in The Nation, the
                       progressive magazine where the journalist serves as
                       editorial director and publisher. In the deeply
                       moving piece, where vanden Heuvel describes her
                       personal relationship to the man who called both
                       her and her late husband—the unparalleled scholar
                       of Russian history, Stephen Cohen—his “true
                       friends,” she considers the former Russian leader’s
                       legacy as “a great reformer in his country’s
                       tormented history.”  Vanden Heuvel, who is not only
                       fluent in Russian and studied Russian history at
                       Princeton University but has lived in the Soviet
                       Union and Russia, joins Robert Scheer on the latest
                       edition of “Scheer Intelligence” to expand on her
                       Nation piece and the consequences of the
                       squandering of Gorbachev’s legacy. 


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Common Dreams ☛ ‘Huge_Win’_for_Civil_Liberties_as_Judge
                  Blocks_Arizona_Law_Limiting_Filming_of_Police⠀⇛


                       “Recording law enforcement interactions is one of
                       the best tools to hold police accountable.”


          o § Environment⠀➾


                # ⚓ The Nation ☛ Paving_Paradise⠀⇛


                # ⚓ Democracy Now ☛ Appalachians_Protest_Manchin’s_Mountain
                  Valley_Pipeline_Plan;_Sanders_Decries_“Disastrous_Side
                  Deal”⠀⇛


                       Climate activists from as far away as Alaska,
                       Indigenous peoples and Appalachians rallied in
                       Washington, D.C., Thursday against the construction
                       of the Mountain Valley Pipeline. The protest — No
                       Sacrifice Zones! — spoke out against concessions to
                       West Virginia Senator Joe Manchin included in the
                       Inflation Reduction Act that would expedite the
                       pipeline slated to cut through Appalachia, as
                       Senator Bernie Sanders gave an address on the
                       Senate floor calling it a “disastrous side deal” to
                       the Inflation Reduction Act that undermines climate
                       activism. We speak with two environmental activists
                       in D.C. who helped organize the protest, Crystal
                       Cavalier-Keck and Russell Chisholm. “We do not want
                       this dirty deal that Senator Joe Manchin is pushing
                       forward,” says Cavalier-Keck. “This project must be
                       stopped, and these extractive industries that
                       create sacrifice zones must also be stopped,” says
                       Chisholm.


                # ⚓ TruthOut ☛ Appalachians_Protest_Manchin’s_Mountain_Valley
                  Pipeline_Plan⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Decolonization:_A_Crucial
                  Prerequisite_for_Environmental_Justice_in_Africa⠀⇛


                       All across the African continent a colonial
                       approach of extraction and exploitation continues
                       to plague and paralyse economies. It pushes
                       ecosystems to the edge and puts pan-Africanism on a
                       back burner. 


                # ⚓ Common Dreams ☛ ‘Climate_Denial’:_Forest_Service_Sued_for
                  Approving_Crude_Oil_Railway_in_Utah⠀⇛


                       “Forest Service just dismissed this staggering
                       amount of new oil production as insignificant…
                       That’s climate denial.”


                # § Energy⠀➾


                      # ⚓ DeSmog ☛ How_Biden_Could_Use_the_Tennessee_Valley
                        Authority_to_Address_the_Climate_Crisis⠀⇛


                             “Climate change threatens the basic
                             foundations of society. It is the very
                             definition of a whole-of-government problem,
                             which means every single federal agency
                             should apply its existing powers creatively
                             and aggressively toward the problem,”
                             Revolving Door Project Research Director Max
                             Moran said in a statement. “Alone, these
                             executive branch policies are wildly
                             insufficient to the task of getting America
                             to meet its climate goals. But all of these
                             policies are necessary components of the
                             puzzle, and represent the lowest-hanging
                             fruit in terms of climate action.”


                      # ⚓ DeSmog ☛ Liz_Truss_Campaign_Funded_by_Donors_From
                        Pro-Fracking_Groups_and_Climate_Denier⠀⇛


                             Two days after taking office, Truss gave the
                             green light for new fracking projects,
                             putting her at odds with the Conservatives’
                             2019 manifesto pledge and in advance of a
                             much-awaited report by the British Geological
                             Survey on the safety of fracking.


                # § Wildlife/Nature⠀➾


                      # ⚓ Suff NZ ☛ Giant_squid_returns_to_Timaru_for_new
                        exhibition⠀⇛


                             An exhibition in honour of the colossal squid
                             caught by a Timaru fishing vessel in
                             Antarctica has landed in the district.


                             Parts of the squid make up a travelling
                             exhibition by The Museum of New Zealand Te
                             Papa Tongarewa, which is now on display at
                             the South Canterbury Museum and its director
                             Philip Howe is excited by its “Timaru-link”.


                             “It shows locals that big discoveries can be
                             made anywhere,’’ Howe said.


          o § Finance⠀➾


                # ⚓ Krebs On Security ☛ Transacting_in_Person_with_Strangers
                  from_the_Internet⠀⇛


                       I recently stumbled upon one of these designated
                       exchange places by accident, hence my interest in
                       learning more about them. The one I encountered was
                       at a Virginia county sheriff’s office, and it has
                       two parking spots reserved with a sign that reads,
                       “Internet Purchase & Exchange Location: This Area
                       is Under 24 Hour Video Surveillance”.


                       According to the list maintained at
                       Safetradestations.com, there are four other such
                       designated locations in Northern Virginia. And it
                       appears most states now have them in at least some
                       major cities. Safeexchangepoint.com also has a
                       searchable index of safe trading locations in the
                       United States and Canada.


                # ⚓ Dhole Moments ☛ Should_You_Delete_Your_Patreon_Account
                  After_They_Laid_Off_Their_Entire_Security_Team?⠀⇛


                       Last night, the Internet learned that Patreon fired
                       their entire security team, abruptly.


                       [...]


                       We also learned that the primary motivation was
                       outsourcing.


                # ⚓ Xe’s Blog ☛ Developing_Situation:_Something_is_up_with
                  Patreon⠀⇛


                       Hey, I don’t usually write these kinds of posts,
                       but I have been made aware of a post on twitter
                       that seems fairly credible. It seems that the
                       Patreon security team has been let go.


                # ⚓ TruthOut ☛ Wall_Street_Giants_Set_to_Smash_Profit_Records
                  Off_Energy_Crisis,_Global_Hunger⠀⇛


                # ⚓ FAIR ☛ Media_Summon_Inflation_Specter_to_Oppose_Student
                  Debt_Forgiveness⠀⇛


                       President Joe Biden’s student debt cancellation
                       plan may not be full forgiveness, but it can still
                       have a life-changing impact on millions of people.
                       Almost 20 million may see their debts wiped clean,
                       and more than 40 million are directly affected. The
                       plan is a step forward for debtors and activists
                       who have spent decades struggling to abolish
                       student debt and make higher education, long
                       promised as the path out of poverty, affordable for
                       everyone.


                # ⚓ Scheerpost ☛ US_Announces_$2.8_Billion_in_Military_Aid_for
                  Ukraine,_Allies_in_the_Region⠀⇛


                       Blinken announced $2.2 billion during an
                       unannounced visit to Kyiv.


                # ⚓ Common Dreams ☛ Wall_Street_Giants_Set_to_Smash_Profit
                  Records_Off_Global_Hunger,_Energy_Crisis⠀⇛


                       “We’re in a market where speculators are driving
                       prices up.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Silicon Angle ☛ White_House_releases_six_proposals_for
                  reforming_tech_industry_regulation⠀⇛


                       The White House has released six proposals for
                       reforming tech industry regulation that span areas
                       such as privacy, algorithmic decision-making and
                       market competition.


                       The proposals were published Thursday following a
                       listening session held at the White House about the
                       tech industry. The session included the
                       participation of more than a dozen experts and
                       practitioners.


                       The first of the six proposals published by the
                       White House is designed to promote competition in
                       the tech sector. “A small number of dominant
                       Internet platforms use their power to exclude
                       market entrants, to engage in rent-seeking, and to
                       gather personal information,” the proposal stated.
                       To remedy the situation, the White House is calling
                       for the implementation of new rules capable of
                       ensuring “small and mid-size businesses and
                       entrepreneurs can compete on a level playing
                       field.”


                # ⚓ New York Times ☛ Twitter_Reached_$7_Million_Settlement_With
                  Whistle-Blower⠀⇛


                       “They’re paying the guy $7 million and making sure
                       he’s quiet,” Alex Spiro, an attorney for Mr. Musk,
                       said during the hearing.


                # ⚓ Techdirt ☛ Elon_Musk,_Once_Again,_Fails_To_Get_His_Big_Asks
                  From_Delaware_Chancery_Court⠀⇛


                       Chancellor Kathaleen McCormick, who is overseeing
                       the Twitter v. Musk case in the Delaware Chancery
                       Court, has a bit of a reputation as a no-nonsense
                       judge who isn’t one to put up with much crap. And
                       so far, that’s definitely been clear from how she’s
                       handled the case. She isn’t showing favoritism, but
                       every time big decisions come in regarding the
                       case, she seems to shut down Musk’s ridiculous
                       asks, while granting him just small concessions. It
                       happened in the original fight over when the trial
                       would be, in which McCormick scheduled the trial to
                       be just a month after Twitter requested, but three
                       months earlier than Musk had hoped for. It happened
                       again a few weeks ago in a fight over how much data
                       Twitter needed to hand over to Musk in his silly
                       quest to find out how much spam is in the mDAU
                       (something that doesn’t really matter). The judge
                       gave him a much smaller segment of the data he
                       requested, but still gave him some.


                # ⚓ Axios ☛ TikTok_unites_tech_factions_against_it⠀⇛


                       Be smart: It’s not what TikTok is doing today that
                       has people most concerned, but rather what it could
                       do with millions of users, many of them young
                       people, and a powerful algorithm that seems
                       perfectly tuned to reach their hearts and minds.


                # ⚓ Democracy Now ☛ Roundtable:_Amid_Tributes_to_Queen
                  Elizabeth,_Deadly_Legacy_of_British_Colonialism_Cannot_Be
                  Ignored⠀⇛


                       We host a roundtable on the life and legacy of
                       Britain’s Queen Elizabeth II, who died Thursday at
                       the age of 96. She was the country’s longest-
                       reigning monarch, serving for 70 years and
                       presiding over the end of the British Empire. Her
                       death set off a period of national mourning in the
                       U.K. and has thrown the future of the monarchy into
                       doubt. “The monarchy really has come to represent
                       deep and profound and grave inequality,” says
                       Cambridge scholar Priya Gopal, author of “Insurgent
                       Empire: Anticolonial Resistance and British
                       Dissent.” We also speak with Harvard historian Maya
                       Jasanoff, Novara Media editor Ash Sarkar and Pedro
                       Welch, former chair of the Barbados Reparations
                       Task Force, who says the British monarchy’s brutal
                       record in the Caribbean and other parts of the
                       world must be addressed. “The enslavement of our
                       ancestors has led to a legacy of deprivation, a
                       legacy that still has to be sorted out,” says
                       Welch.


                # ⚓ Common Dreams ☛ After_Queen’s_Death,_Victims_of_British
                  Imperialism_Share_Why_‘We_Will_Not_Mourn’⠀⇛


                       “Her legacy is colonialism, slavery, racism, loot,
                       and plundering.”


                # ⚓ The Dissenter ☛ Decolonizing_Memories_Of_The_Queen—Plus,
                  EU’s_Self-Inflicted_Energy_Crisis⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Mourn_the_Queen,_But_God_Save_the
                  People⠀⇛


                       Every human death is a loss. But Queen Elizabeth
                       lived a long and, from most accounts, good life.
                       The people close to her have lost a mother, a
                       friend, a real person. They shouldn’t be dismissed.
                       Neither should the British citizens who mourn her.
                       The grief people feel for a public figure is real,
                       even if what they’re really mourning are the
                       passing days of their lives.


                # ⚓ Scheerpost ☛ The_Queen_and_Her_Legacy:_21st_Century_Britain
                  Has_Never_Looked_So_Medieval⠀⇛


                       In this moment there is no public room for
                       ambivalence or indifference, for reticence, for
                       critical thinking…The British establishment expects
                       every man, woman, and child to do their duty by
                       lowering their head.


                # ⚓ TruthOut ☛ Election_Workers_Brace_for_Violence_Around_the
                  Midterms⠀⇛


                # ⚓ The Nation ☛ How_the_Democrats_Got_Their_Groove_Back⠀⇛


                       Just a few months ago, both Joe Biden and the
                       Democratic Party were facing grim prospects—not
                       just for the midterms but for the foreseeable
                       future. Biden’s presidency seemed adrift, with all
                       his promised Build Back Better agenda roadblocked
                       by Senators Joe Manchin and Kyrsten Sinema.
                       Starting with the botched withdrawal from
                       Afghanistan—a move that had majority support but
                       was accompanied by dismal images of American
                       defeat—Biden’s reputation for competence had been
                       badly tarnished.


                # ⚓ Meduza ☛ Police_draw_up_reports_of_‘discrediting’_the_army
                  against_St._Petersburg_deputies_who_accused_Putin_of_treason
                  —_Meduza⠀⇛


                       In St. Petersburg seven deputies from the
                       Smolninskoye municipal council were summoned by the
                       police for “discrediting” the Russian army. Deputy
                       Dmitry Palyuga spoke to Mediazona about it.


                # ⚓ Scheerpost ☛ Putin_Sees_Future_With_Asia_and_Claims_Western
                  Economic_Decline_in_New_Speech⠀⇛


                       Speaking at the Eastern Economic Forum, Putin
                       addressed Western sanctions, Russia’s growing
                       relationship with Asia and an update on Ukraine.


                # ⚓ TruthOut ☛ DOJ_Appeals_Ruling_Granting_Trump_a_Special
                  Master_in_Classified_Docs_Inquiry⠀⇛


                # ⚓ Common Dreams ☛ 72_House_Democrats_Tell_Pelosi_to_Keep
                  Manchin’s_Dirty_Deal_Out_of_Must-Pass_Legislation⠀⇛


                       In a new letter signed by an ideologically diverse
                       array of House Democrats—including members of both
                       the Congressional Progressive Caucus (CPC) and the
                       New Democrat Coalition—lawmakers warn that the
                       “destructive provisions” negotiated behind closed
                       doors by Manchin and Senate Majority Leader Chuck
                       Schumer (D-N.Y.) “will allow polluting
                       manufacturing and energy development projects to be
                       rushed through before the families who are forced
                       to live near them are even aware of the plans.”


                # ⚓ TruthOut ☛ Majority_of_Americans_Say_MAGA_Movement_Is_a
                  Threat_to_Democracy,_Poll_Finds⠀⇛


                # § Misinformation/Disinformation⠀➾


                      # ⚓ Scheerpost ☛ John_Pilger:_Silencing_the_Lambs._How
                        Propaganda_Works⠀⇛


                             Having soaked for 82 years in a deep bath of
                             righteousness that is the official version of
                             the last world war, isn’t it time those who
                             are meant to keep the record straight
                             declared their independe…


          o § Censorship/Free Speech⠀➾


                # ⚓ Carl Svensson ☛ King_Charles_III_and_the_Swedish_General
                  Election:_On_metapolitics_and_impending_doom⠀⇛


                       Western ideals have now deteriorated to arresting
                       citizens for posting online, and laughing at urgent
                       warnings simply for being delivered by the wrong
                       flavor of representative. This has been long in the
                       making. Those who warned about Sweden’s current
                       problems during the last few decades – and they
                       were many – were effectively silenced with
                       accusations of fascism, alarmism, communism, racism
                       or denialism.


                       Despite being right, they will have no vindication.
                       There’s no reason to concede when the effects of
                       term upon term of mismanagement can be blamed on
                       belligerent foreign autocrats – or on the decisions
                       of a supranational union it was so important to
                       join, all those years ago. Curiously, there’s been
                       very few accusations of opportunism.


                # ⚓ The Atlantic ☛ Where_the_Hatred_Comes_From:_What_I_learned
                  in_the_space_between_death_threats_and_bodyguards⠀⇛


                       Those who have denounced the attack in printed
                       newspapers—most of which are directly or indirectly
                       controlled by the state—rarely do so in the name of
                       free speech, claiming instead that it must have
                       been a false-flag operation staged by the West,
                       maybe by America itself, to put Muslim countries
                       and Islam in a bad light. Even among the Turkish
                       writers and intellectuals who I know value free
                       speech, few have been eager to protest or even draw
                       attention to the matter.


                       I’ve had many long conversations with writers who
                       have received death threats, especially from
                       “Islamists” or “Islamic extremists,” and with
                       writers and journalists who—for various
                       reasons—live under threat in Muslim countries such
                       as Egypt and Turkey. The threats I face in Turkey
                       are primarily not from Islamic extremists, but
                       rather from nationalists who take issue with my
                       comments on the Armenian genocide and think I am
                       insulting Turkish history—though, in truth, these
                       two groups are not too distant from each other, and
                       Turkey is currently governed by an Islamic-
                       nationalist coalition.


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


                # ⚓ Observer Research Foundation ☛ Is_Mainstream_Media_Dead?⠀⇛


                       This question delivered a number of affirmatives,
                       denials, and up-to-a-points, and yet, there was a
                       clear and definite consensus: Corporate news
                       outlets will not be destroyed by more democratised
                       news content, but will certainly adapt to their
                       reduced market share. Print media and major news
                       outlets will survive, but only if they adapt.


                # ⚓ BIA Net ☛ Journalists_Sadiye_Eser,_Sadık_Topaloğlu
                  sentenced_to_six_years_in_prison⠀⇛


                       Lawyer Kılıç said the prosecution’s allegation was
                       based on Ögür Baran, a witness who had not attended
                       any hearing. He cited Court of Cassation decisions
                       that the allegations of a witness who was not heard
                       face to face should not be taken into account.


                       He also noted that a Kurdish song on Eser’s phone
                       was cited as evidence in the case file.


                # ⚓ BIA Net ☛ Journalist_investigated_after_report_on_vehicles
                  rented_for_Erdoğan_rally⠀⇛


                       Two and a half million lira (1.37 million US
                       dollars) was paid for the cars rented for two days,
                       according to his report.


                       The prosecutors opened the investigation after a
                       complaint by Çetin Can, an executive of Erdoğan’s
                       justice and Development Party (AKP) in Van, who got
                       the contract for the car rental.


                       The journalist is under investigation for “slander
                       and insult.”


                # ⚓ BIA Net ☛ Journalist_Ziya_Ataman_says_strip_searched_in
                  prison⠀⇛


                       Ataman was a reporter for the Dicle News Agency
                       (DİHA), which was shut down by a statutory decree
                       during the period of State of Emergency after the
                       July 2016 coup attempt.


                # ⚓ BIA Net ☛ European_Federation_of_Journalists_head_protests
                  Erdoğan_in_Zagreb⠀⇛


                       “The problem is not the blocked streets, it is
                       Erdoğan. In Türkiye, 38 journalists are currently
                       in prison. According to a RSF report, 90 percent of
                       the national media is under the control of the
                       government,” she later wrote on Twitter.


                # ⚓ Techdirt ☛ Politico’s_New_Owner_Signals_He’s_Doubling_Down
                  On_Feckless_‘He_Said,_She_Said’_Journalism⠀⇛


                       New Politico owner and Axel Springer CEO Mathias
                       Döpfner has been craving U.S. press attention, and
                       got more of it than he wanted this week. Döpfner
                       was the focus of a not particularly flattering
                       profile in the Washington Post showing, among other
                       things, that the German billionaire was excited by
                       the prospect of a second Trump term and really
                       liked a lot of the stuff Trump was up to…


          o § Civil Rights/Policing⠀➾


                # ⚓ Jacobin Magazine ☛ Eugene_V._Debs:_In_a_Just_Society,_Every
                  Day_Would_Be_Labor_Day⠀⇛


                       On Labor Day, there’s perhaps no one better to read
                       than Eugene V. Debs. Here’s his 1903 Labor Day
                       message, never before republished, in which he
                       declares, “The struggle in which we are now engaged
                       will end only when every day is Labor Day.”


                # ⚓ France24 ☛ For_Qatar’s_foreign_workers,_protesting_can_lead
                  to_deportation⠀⇛


                       As Qatar prepares to host the FIFA World Cup in
                       November, the country is once again drawing
                       criticism from human rights organisations. For
                       several months, a construction company’s workers
                       have been protesting to claim unpaid wages. But on
                       August 14, the Qatari government arrested some of
                       them and deported them.


                # ⚓ RFA ☛ Authorities_free_Tibetan_sentenced_in_connection_with
                  burning⠀⇛


                       Authorities in Tibet have released a man serving a
                       12-year prison term for “murder” in connection with
                       the death of a fellow Tibetan who self-immolated in
                       protest of Chinese rule, according to sources
                       living in exile from the region with knowledge of
                       the situation.


                       “Pema Dhondup has been under constant scrutiny
                       since his release from prison on Aug. 31,” the
                       source told RFA Tibetan, speaking on condition of
                       anonymity citing security risks.


                # ⚓ TruthOut ☛ Michigan_Supreme_Court_Puts_Abortion_Rights
                  Initiative_on_the_Ballot⠀⇛


                # ⚓ Common Dreams ☛ OB-GYNs_Warn_of_Abortion_Threat_Dr._Oz
                  Poses_in_Latest_Fetterman_Ad⠀⇛


                       In Fetterman’s latest ad, obstetrician and
                       gynecologist Dr. Lisa Perriera is seen speaking at
                       a podium about Oz’s pro-forced pregnancy beliefs.


                # ⚓ Common Dreams ☛ Medical_Associations_Warn_of_‘Irreparable
                  Harm’_Without_Clear_Guidance_on_State_Abortion_Laws⠀⇛


                       “As physicians and pharmacists, we view patient
                       wellbeing as paramount and are deeply troubled that
                       continuity of care is being disrupted.”


                # ⚓ Common Dreams ☛ Opinion_|_DOJ_Will_Appeal_Judge_Cannon’s
                  Widely_Criticized_Decision_to_Appoint_Special_Master⠀⇛


                       In 2018, Chief Justice John Roberts said, “We do
                       not have Obama judges or Trump judges, Bush judges
                       or Clinton judges.”


                # ⚓ TruthOut ☛ Life_Expectancy_for_Indigenous_Americans_Drops
                  by_6.6_Years⠀⇛


                # ⚓ FAIR ☛ Matt_Gertz_and_Eric_K_Ward_on_White_‘Replacement’
                  Theory⠀⇛


                # ⚓ TruthOut ☛ Elizabeth_Warren_Introduces_Bill_to_Ban_Anti-
                  Union_“Right-to-Work”_Laws⠀⇛


                # ⚓ EFF ☛ U.S._Federal_Employees_Can_Take_A_Stand_for_Digital
                  Freedoms⠀⇛


                       U.S. federal employees and retirees can give to EFF
                       by going to GiveCFC.org and clicking the DONATE
                       button to give via payroll deduction, credit/debit,
                       or an e-check! If you have a renewing pledge, you
                       can increase your support as well. Be sure to use
                       EFF’s CFC ID #10437. Scan the QR code below to
                       easily make a pledge!


                # ⚓ Common Dreams ☛ Opinion_|_Corporate_Media_Has_Failed_to
                  Report_Accurately_on_the_Threats_to_Women’s_Reproductive
                  Rights⠀⇛


                       In the weeks since the Supreme Court overturned Roe
                       v. Wade, the corporate media has been saturated
                       with analyses and reports about the implications of
                       the ruling for women’s lives and health. Legal
                       observers have weighed in on the conservative
                       majority’s reasoning in the case. The impact of the
                       ruling on the 2022 midterm elections has been
                       discussed endlessly. The state-by-state battles
                       over legislation and state-level constitutional
                       amendments banning abortion have been covered
                       exhaustively, as have efforts by women’s rights
                       groups and medical providers to ensure that women
                       get the reproductive health services they need.


                # ⚓ The Nation ☛ Labor_Day⠀⇛


                # ⚓ Common Dreams ☛ ‘Great_News’_for_Ball_Players_as_MLB_to
                  Voluntarily_Recognize_Minor_League_Union_Drive⠀⇛


                       “With 5,000 members, this is one of the largest
                       union organizing victories in years.”


                # ⚓ TruthOut ☛ Senators_Are_Optimistic_That_Marriage_Equality
                  Bill_Will_Pass_This_Month⠀⇛


                # ⚓ Common Dreams ☛ Analysis_Shows_‘Quiet_Fleecing’_of_US
                  Workers—Not_‘Quiet_Quitting’—Is_the_Real_Problem⠀⇛


                       “The reality is workers have long been going ‘above
                       and beyond’ and not getting paid for it.”


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ Sender_pays⠀⇛


                       So, the entire issue of network neutrality,
                       interconnection and settlements, termination
                       monopolies, cost allocation, and infrastructure
                       investment economics is back again. This time, it’s
                       not under the banner of network neutrality but
                       under a more directly confronting title of ‘sender
                       pays’. The principle is much the same — network
                       providers want to charge both their customers and
                       the content providers to carry content to users.


                # ⚓ RIPE ☛ Towards_a_Sanctions_Solution_Space⠀⇛


                       As the RIPE NCC manages its compliance with
                       relevant sanctions, we are also looking at how to
                       ensure that sanctions don’t jeopardise the global
                       Internet.


                       In recent years, the RIPE NCC has been very
                       publicly managing the challenge of complying with
                       EU sanctions while fulfilling our remit as the
                       Internet number registry for our service region.
                       These EU sanctions, levied primarily against
                       individuals and legal entities in Syria, Iran and
                       Russia, have resulted in the RIPE NCC freezing the
                       accounts of a small number of members, but they
                       have also consumed significant organisational
                       resources as we work to ensure full compliance with
                       the law. Our Chief Legal Officer, Athina Fragkouli,
                       provided details in presentations and in past RIPE
                       Labs articles, and our Managing Director has
                       reported on these issues at recent RIPE Meetings
                       and RIPE NCC events.


                # ⚓ Perifèries Urbanes ☛ Zero_rating_and_the_infrastructure_of
                  political_(mis)communication_in_Brazil_–_Raquel_Rennó_and
                  Juliana_Novaes⠀⇛


                       Given these conditions, in which fixed broadband
                       Internet connectivity, where there is generally no
                       data cap, is unavailable, insufficient, or
                       unaffordable, users from lower socioeconomic
                       backgrounds develop a dependency on zero-rated
                       services and applications included in mobile
                       Internet plans. Zero-rating is a term that refers
                       to a specific practice in telecommunications,
                       whereby consumers are offered plans that enable the
                       use of certain services and applications without
                       being charged as part of the data cap. Normally,
                       this offer is provided as part of prepaid plans,
                       where the user gets a limited amount of data to use
                       in a certain period of time. Zero-rating plans are
                       usually the outcome of negotiations between
                       technology companies that develop applications and
                       services and network operators that offer mobile
                       Internet plans to users. Given the scale of this
                       negotiation, these zero-rating agreements are
                       generally made between multinational technology
                       companies and network operators that have already
                       achieved market dominance. In a recent study on
                       Internet users in Brazil, 40% of low-income
                       individuals reported having their connection
                       recently restricted exclusively to zero-rated
                       applications due to the impossibility of buying
                       more mobile data. Among them, 80% mentioned they
                       would prefer to have the possibility to have access
                       to other platforms and websites on the Internet,
                       rather than being limited to one zero-rated
                       application (Instituto Brasileiro de Defesa do
                       Consumidor & Instituto Locomotiva, 2021).


                # ⚓ [Old] uni Stanford ☛ Facebook,_Google_&_Big_Telecoms_Want
                  to_Keep_Violating_Net_Neutrality_in_Europe._Regulators_Should
                  Stop_Them.⠀⇛


                       The E.U.’s top telecom regulator BEREC is set to
                       issue new net neutrality rules, after the European
                       Court of Justice found that discriminatory zero-
                       rating plans such as T-Mobile’s StreamOn and
                       Vodafone’s Pass violate Europe’s net neutrality
                       law.


                       In a proceeding that has gotten almost no press
                       attention, BEREC is deciding what the new rules
                       should be for carriers that “zero-rate” some
                       applications by exempting them from customers’
                       monthly data caps. These discriminatory schemes
                       almost invariably favor the carrier’s own services
                       or those of giant platforms like Facebook and
                       YouTube.


                # ⚓ [Old] uni Stanford ☛ European_Regulators_Just_Stopped
                  Facebook,_Google_and_Big_Telecoms’_Net_Neutrality
                  Violations⠀⇛


                       BEREC’s previous net neutrality guidelines did not
                       categorically ban selective zero-rating programs or
                       category-based ones that, e.g., offer to zero-rate
                       all music or video apps. So carriers across the EU
                       took advantage and collectively launched hundreds
                       of zero-rating programs. These often exempted the
                       carriers’ own services and disproportionately
                       benefited big platforms like Apple, Google, and
                       Facebook, while small companies and European
                       startups were left out.


                       BEREC has now banned those.


                # ⚓ [Old] uni Stanford ☛ Zero-rating_in_Africa,_Reconsidered⠀⇛


                       Throughout the world, people access the Internet
                       via various zero-rated offers. Over the years,
                       policy debates about zero-rating have primarily
                       focused on cases of zero-rating taking place across
                       the Global South and involving US tech companies or
                       organizations, from Facebook (Internet.org/Free
                       Basics) to Wikipedia (Wikipedia Zero). Most
                       famously, in 2015, digital rights activists in
                       India led a spectacular year-long campaign that led
                       to a regulatory ban on zero-rating. Across the
                       world, however, zero-rating remains a practice
                       rarely regulated and widely used in the industry.


                # ⚓ [Old] Data-Pop Alliance ☛ The_High_Cost_of_“Free”_Data:
                  Zero-Rating_and_its_Impacts_on_Disinformation_in_Brazil⠀⇛


                       Last but certainly not least, one of the fastest
                       growing concerns related to zero-rating is how it
                       can facilitate the spread of disinformation.
                       Focusing on Brazil, (although similar situations
                       are playing out all over Latin America and the
                       world), the popularity of WhatApp has grown so much
                       that nearly every business, institution, hospital,
                       school and other public and private facility uses
                       it to communicate with their consumers or clients.
                       It’s even more popular here than in the US (where
                       it was created), with 93% of Brazilians being
                       active users. This statistic is directly related to
                       the fact that many mobile plans, offered by the
                       largest telephone companies in the country, sponsor
                       the data “caps” that fuel the demand for this type
                       of “free” application.


                       Herein lies the problem, for example, when someone
                       receives a WhatsApp message with shocking news and
                       clicks on the link, they cannot access the full
                       website because they don’t have enough mobile data.
                       Subsequently, they are left only with a biased
                       title and no ability to confirm whether the
                       information is true or false. It becomes almost
                       impossible for low-income populations to verify
                       information they consistently receive, due to their
                       lack of access to mobile data. Additionally,
                       sharing unverified content becomes more and more
                       common, which contributes to the spread of fake
                       news.


                # ⚓ Techdirt ☛ White_House_Releases_Performatively_Ridiculous
                  ‘Principles’_For_‘Tech_Platform_Accountability’_That_Include
                  Removing_Section_230⠀⇛


                       During the 2020 campaign, there were a few times
                       when candidate Joe Biden insisted he wanted to get
                       rid of Section 230 entirely, though he made it
                       clear he had no idea what Section 230 actually did.
                       When I wrote articles highlighting all of this, I
                       had some Biden supporters (even folks who worked on
                       his campaign) reach out to me to say not to worry
                       about it, that Biden wasn’t fully briefed on 230,
                       and that if he became President, more knowledgeable
                       people would be tasked to work on stuff, and the
                       230 stuff wouldn’t be an issue. I didn’t believe it
                       at the time, and it turns out I was correct.


                # ⚓ Self-Hosted_email_is_the_hardest_it’s_ever_been,_but_also
                  the_easiest.⠀⇛


                       The top page on HN had an interesting post on it
                       titled “After self-hosting my email for twenty-
                       three years I have thrown in the towel. The
                       oligopoly has won.”.


                       Before you write off the post as just another self-
                       hoster complaining, read it. Carlos has been at it
                       a LONG time, and he’s tried everything. Carlos
                       makes excellent points, and they’re all about the
                       centralization of email services.


                       It’s true – Big, concentrated email services are
                       elbowing out people who run their own servers in
                       the name of “spam protection”. While the attacks
                       may not be targeted to one individual or another,
                       kafka-esque systems that often just don’t work are
                       being employed to make it harder to land in user’s
                       inbox.


                       Even if you you set up all the “acronyms” (i.e.
                       DKIM, DMARC, SPF), emails from your self-hosted
                       email server may go to spam.


          o § Monopolies⠀➾


                # ⚓ [Old] USDOJ ☛ 1854._Copyright_Infringement_—_First_Sale
                  Doctrine⠀⇛


                       The first sale doctrine, codified at 17 U.S.C. §
                       109, provides that an individual who knowingly
                       purchases a copy of a copyrighted work from the
                       copyright holder receives the right to sell,
                       display or otherwise dispose of that particular
                       copy, notwithstanding the interests of the
                       copyright owner. The right to distribute ends,
                       however, once the owner has sold that particular
                       copy. See 17 U.S.C. § 109(a) & (c). Since the first
                       sale doctrine never protects a defendant who makes
                       unauthorized reproductions of a copyrighted work,
                       the first sale doctrine cannot be a successful
                       defense in cases that allege infringing
                       reproduction.


                # ⚓ [Old] American Library Association ☛ Copyright_for
                  Libraries:_First_Sale_Doctrine⠀⇛


                       The “first sale” doctrine (17 U.S.C. § 109(a))
                       gives the owners of copyrighted works the rights to
                       sell, lend, or share their copies without having to
                       obtain permission or pay fees. The copy becomes
                       like any piece of physical property; you’ve
                       purchased it, you own it. You cannot make copies
                       and sell them—the copyright owner retains those
                       rights. But the physical book is yours. First sale
                       has long been important for libraries, as it allows
                       them to lend books without legal hurdles. (Jenkins,
                       Jennifer. 2014. “Last Sale? Libraries’ Rights In
                       The Digital Age”. College & Research Libraries News
                       75 (2): 69-75.)


                # ⚓ uni Massachusetts ☛ First_Sale_(or_Exhaustion)_Doctrine_in
                  Copyright⠀⇛


                       “First Sale” (also called the “exhaustion
                       doctrine”) is the name in US copyright law for the
                       idea that owners of copies of copyrighted works
                       have the right to re-sell, lend, give away, or even
                       destroy their personal copies of works. The
                       copyright holder’s right to control the
                       distribution of their work goes away after the
                       “first sale” of the work. The “First Sale Doctrine”
                       is codified in U.S. copyright law at 17 U.S.C.
                       Section 109.


                       In other areas of law, such as patent law, this
                       principle is called the “exhaustion” principle.


                # ⚓ Techdirt ☛ Sony_Claps_Back_At_Microsoft_Over_Limited
                  Promise_For_‘CoD’_Cross-Platform_Plans⠀⇛


                       And here we are again, with more exclusivity drama
                       coming out of the recent acquisitions Microsoft has
                       undertaken in the video game space. After the
                       announcements of the Zenimax/Bethesda and
                       Activision Blizzard acquisitions, which are still
                       going through review, Microsoft came out with a
                       bunch of conflicting statements on what those buys
                       would mean for exclusivity of games. Then the
                       company said some games, mostly from the Bethesda
                       acquisition, would be “first/best” on Xbox. Then
                       one title from Bethesda was announced as an Xbox
                       exclusive. And then, after all of that, came Xbox
                       chief Phil Spencer talking about how exclusives
                       weren’t the future, as everyone listening realized
                       that they certainly seem to be Xbox’s present.


                # § Copyrights⠀➾


                      # ⚓ Digital Music News ☛ Hipgnosis_Songs_Fund_Has_‘Burned
                        Through_Its_Funds_and_Is_Unable_to_Raise_More,’
                        Financial_Times_Reports⠀⇛


                             Moreover, Hipgnosis will reportedly need to
                             achieve a 20 percent revenue boost (assuming
                             that costs remain steady) to fund its
                             dividend for the fiscal year ending in March
                             of 2023, and “raising new equity would dilute
                             existing shareholders and, in the words of an
                             HSF spokesperson, ‘destroy value,’” per FT
                             once again.


                      # ⚓ Digital Music News ☛ Led_Zeppelin_Bootleg_Concert
                        Footage_From_the_’70s_Appears_on_YouTube⠀⇛


                             The film was taken at the Inglewood Forum on
                             September 4, 1970 – then sat in a drawer for
                             50 years. After it was rediscovered, the
                             footage was matched to audio from another Led
                             Zeppelin bootleg recording, On Blueberry
                             Hill. The footage gives fans a previously
                             unseen look at the group performing songs
                             like “Since I’ve Been Loving You,” “Thank
                             You,” “What Is And What Should Never Be,”
                             “Whole Lotta Love,” “Some Other Guy,” and
                             “Lemon Song.”


                      # ⚓ Future Publishing Limited ☛ Seven_minutes_of_unseen
                        Led_Zeppelin_film_gathered_dust_for_50_years:_now_it’s
                        online⠀⇛


                             The footage was despatched to another
                             collector, a French Led Zeppelin expert and
                             audio synchroniser named Etienne Marchand,
                             who was able to identify the exact moments in
                             the 106-minute set that Vincent had filmed,
                             and match them to the relevant parts of the
                             On The Blueberry Hill audio. And that’s the
                             footage that has been released today, on the
                             50th anniversary of the original show.


                      # ⚓ CBC ☛ Rings_of_Power_could_cost_$1B._What’s_making_TV
                        so_expensive?⠀⇛


                             Amazon CEO Jeff Bezos, a noted Tolkien fan,
                             had his company acquire the rights to Lord of
                             the Rings’ appendices for a reported $250
                             million US. The appendices are additional
                             information Tolkien included at the end of
                             his books, and because of that Amazon does
                             not even have the ability to include
                             information from the books’ main story or its
                             prequels like The Hobbit.


                             And with the first season of a five-season
                             run costing an estimated $465 million US
                             (subsequent seasons, though still wildly
                             expensive, could require slightly reduced
                             budgets as producers will be able to use
                             existing construction and costumes), Rings of
                             Power may conservatively cost the studio in
                             excess of $1 billion US.


                      # ⚓ Torrent Freak ☛ US_Piracy_Blocking_Lawsuit_Enters_New
                        Phase_–_Part_Public,_Part_Hidden⠀⇛


                             This April, a coalition of entertainment
                             companies convinced a judge to sign a pirate
                             site blocking injunction that affected every
                             ISP in the United States. This document was
                             later found to be unenforceable but it was
                             public access to court records that first
                             pushed it into the public eye. As the case
                             enters a new phase to block more domains, a
                             level of secrecy had been requested by the
                             plaintiffs.


                      # ⚓ Techdirt ☛ 🚨🚨🚨Twitch_Decides_A_Siren_Sound_Effect_Is
                        Covered_By_Copyright_And_Silences_Stream⠀⇛


                             Alongside death and taxes, one of life’s
                             great certainties is a constant flow of
                             absurd copyright claims. Here’s one from the
                             world of live videogame streaming on the
                             popular Twitch platform, owned by Amazon.  A
                             group of Spanish-speaking streamers organized
                             a gaming event featuring “Project Zomboid“, a
                             zombie survival role-playing game.
                             TorrentFreak explains how copyright spoilt
                             their fun:


                      # ⚓ The_New_Numbers_on_Music_Consumption_Are_Very_Ugly⠀⇛


                             There’s a widespread view that only tech
                             industries need to innovate. Yet nothing
                             could be further from the truth.


                             Even arts and entertainment businesses
                             require constant infusions of fresh talent
                             and new ways of thinking. It’s their
                             lifeblood and oxygen. And if they can’t (or
                             won’t) find it, stagnation sets in. At that
                             juncture, even major artistic endeavors start
                             to feel anachronistic and backward-looking.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ What_I_look_forward_to_in_the_fall⠀⇛


                # ⚓ Replaying_Hatsune_Miku:_Project_Diva_F⠀⇛


                       When I’ve had free time in the evenings this week,
                       I’ve been playing Hatsune Miku: Project Diva F on
                       my PlayStation 3. Project Diva F is a rhythm game
                       featuring the popular Japanese Vocaloid character
                       Hatsune Miku, in which the player hits the four
                       action buttons and tilts the control sticks in time
                       to music.


          o § Technical⠀➾


                # ⚓ Freezr_“P.E.B.C.A.K.”⠀⇛


                       All the morning trying to figuring out why I
                       couldn’t run the `vncsever` through a crontab
                       @reboot job…
                       Let me say this is a shared P.E.B.C.A.K. with
                       hundreds and hundreds off people with the same
                       problem and without a clear solution… And this is
                       one of the reason why Linux sometimes pisses me off
                       very, very, badly… There is a shared problem and
                       nobody has solution but you can find countless of
                       fake solutions and useless workarounds that never
                       work… But those are there to create mess,
                       confusion, clickbait, for whatever anyother reason
                       but not solve the problem, I refer all these
                       bullshi


                # § Science⠀➾


                      # ⚓ Hackaday ☛ Frank_Drake’s_Legacy,_Or:_Are_We_All_Alone
                        In_The_Universe?⠀⇛


                             When Frank Drake began his astronomy career
                             in the late 1950s, this was an incredibly
                             exciting time for the field. Humanity was
                             beginning to unlock the secrets of the
                             Universe using ever more powerful radio
                             frequency and optical telescopes, including
                             the tantalizing prospect of space-based
                             telescopes. Amidst the ramping up Space Race
                             between the US and USSR, there was an ever-
                             growing excitement about humankind’s future
                             among the stars.


                # § Internet/Gemini⠀➾


                      # ⚓ Gemini_Radio_—_Episode_44⠀⇛


                      # ⚓ I’ve_been_enjoying_a_couple_of_Gemini_puzzle_games.⠀⇛


                # § Programming⠀➾


                      # ⚓ LZR’s_button_rebinding_menu⠀⇛


                             Hey! I took a few hours to work on a small
                             input rebinding system for LZR.


                             Pressing F1 in any LZR project will open a
                             new (small) window, asking for directions.


                             The user will then have the ability to press
                             the keys they want to bind to (in order)
                             left/right/up/down/O/X. They have the ability
                             to cancel anytime with Escape.


                      # ⚓ Zig_programming_language⠀⇛


                             I heard about Zig programming language
                             before, and was quite dismissive about it as
                             “yet another C replacement”. Short-sighted of
                             me.


                             Couple days ago I stumbled upon it again, and
                             decided to at least glance at documentation.
                             Folks, it is really awesome. I am excited. Go
                             read documentation yourself.


                             The most awesome feature is ability to
                             execute code at compile time, and have this
                             compile-time code access to all functions
                             that will also be used at runtime. Power of
                             Lisp macros or Template Haskell in C. In
                             particular, this power allows implementing
                             “printf” better than in C.


                             In C, format string argument to “printf”,
                             while 99% of time is literal, is treated no
                             different than any other “const char *”
                             argument to any other function, so format
                             string is parsed at runtime and code that
                             handles something obscure, like %A, is
                             compiled in no matter whether you use it or
                             not. Also, vardaic functions in C are very
                             easy to misuse and pass argument type
                             mismatching format string.


                      # ⚓ Praising_automatic_code_formatters⠀⇛


                             I believe Go language was first that came
                             with source formatter built into compiler.


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


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