𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Sunday, May 08, 2022
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Generated Mon 9 May 02:40:23 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
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/05/08/


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

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QmSfKUr8nYNDDrrEjYSKeMg1rgZ73NY8Da3ikHMwy9QdiT
QmNYJoJ9Ugk6bzW4kiqNd1XX3pDsY94QQQpPX6zvttdDqD
QmV1eHWHRNxm9DLspjvUjeFdk6NvTiYcLCWvwH1WMxLvmr
QmQqTBNQUDBHwqhe5DXPxQgvUpCPJ3nxybhExga3qmyuSs
QmV9dsXk4xgy3qMWvESny4Qa35XgbLoeAZM7H2FPwKwGvC
Qmdi6KmxktEbkwsxpoVUymukiJMVcBzPGPMGpwRC53dkPc
QmSt9PHdTW5UrpNhxfds5Sa5936A4u7z6WyeEdySKphgiP
QmPEqWRo8KpNpJoaaGc99smHG89yvkWtPpeGmTEGxHf9yk
QmUeQTHKAjJ9v96gsDvCYLFh5GgXDKixWCuPqS4a8BmfQU
QmcShTQ5PvGDVnPhQjNW6G56NoR5mcoFctfN5iZeHGrwb1
QmaBR3fV7zaUgkD5dHU52m9Wb3wWGh1z4676MwhPA7cDXx
QmeQxfBxXEPRvN8SC7GyMDSGuxuPgyw5YGtaYLHZYLYLQQ
QmNYYAtNrZGSDgN96vbFkZNpzAhfBHT7jiw6ETUGeaiNLT
QmeJ3YXwyJcW6kexCygGpKWEiZPC21tTub4dQeBZofT8kC
QmPU61A7yYbdcsRB7yyR25CQVBn6a5AhRwTaJhRsyBhZy6
QmPMrr81hHACq6jy5DSLRHakQJ8gQvqoPtt3FNWbmcZS7j
QmPYCg8CVfzpxnfQVnhNP7m73rJTPrrgEmqd8DvpvJhAoJ
QmV7FAs2sr4jaf6G5j1H1iXz4NWKvsn6vaLidkmk6yE6cH
QmYZarboG9cQGehNWR64pLu2jUMh7JDcDbjFPcqWpvgXg6
QmRQVhGpsKDNmkjNUW1AkVeznhpmY4wAGbjRcBeWH1qdd2


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

⦿ On the Cusp of Widespread Adoption of GNU/Linux in More Countries | Techrights

⦿ Debian is Not Defending Volunteers by SLAPPing Other Volunteers, It Just Tarnishes the Community’s Reputation and Brand | Techrights

⦿ [Meme] He is the EPO’s President | Techrights

⦿ IRC Proceedings: Saturday, May 07, 2022 | Techrights

⦿ The Charade of Fake News and Lobbying (Based on Lies) by Team UPC | Techrights

⦿ UPC: “A Neo-colonialist Plot” | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/05/08/china-and-edge-of-change-gnu-linux-policies/#comments
		http://techrights.org/2022/05/08/debian-slapping-volunteers/#comments
		http://techrights.org/2022/05/08/epo-president-video/#comments
		http://techrights.org/2022/05/08/irc-log-070522/#comments
		http://techrights.org/2022/05/08/team-upc-disinformation/#comments
		http://techrights.org/2022/05/08/unitary-patent-system-neo-colonialist-plot/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/05/08/release-of-linux-5-18-rc6/#comments
		http://techrights.org/2022/05/08/tor-0-4-7/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 63

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/08/china-and-edge-of-change-gnu-linux-policies/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/08/china-and-edge-of-change-gnu-linux-policies/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.08.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ On_the_Cusp_of_Widespread_Adoption_of_GNU/Linux_in_More_Countries⠀✐


Posted in GNU/Linux, Microsoft, Windows at 6:02 am by Dr. Roy Schestowitz


Video_download_link | md5sum 45932bcae1d06970a2c702c721d87a48
China and GNU for Domestic Control
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/china-gnu-linux-policies.webm


Summary: It looks like China may soon migrate 50 million PCs to GNU/Linux,
according to the corporate media controlled by an American oligarch


THE GNU/Linux operating system is a global project. It’s neither a country nor
a company. This means that corporations struggle to just extinguish the thing;
they try to shoot down people, instead. They prop up front groups like the so-
called ‘Linux’_Foundation to achieve that. It’s all about control.


“It’s all about control.”The video above concerns an extended_interpretation of
a paywalled_wall_of_text_from_Wall_Street-leaning_media (the parts about GNU/
Linux are sheltered away behind a paywall). It looks like China may soon
migrate 50 million PCs to GNU/Linux. █



                    ䷩ 𝚕𝚒𝚗𝚎 107

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/08/debian-slapping-volunteers/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/08/debian-slapping-volunteers/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.08.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Debian_is_Not_Defending_Volunteers_by_SLAPPing_Other_Volunteers,_It_Just
Tarnishes_the_Community’s_Reputation_and_Brand⠀✐


Posted in Debian, GNU/Linux, Law at 7:38 am by Dr. Roy Schestowitz


Video_download_link | md5sum 1639f04d8aa93b37596fc72b3d7457c7
Debian Trademarks and SLAPP
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/debian-slapp.webm


Summary: Volunteers of Debian face an unwelcoming gesture not because of
critics online but because it seems clear that Debian leadership misuses very
limited Debian funds to SLAPP disgruntled volunteers; the project is not in
good hands and this needs to be corrected before it gets yet worse


THE video above is an expression of an opinion, not to be taken out of context
by selective quoting (hence the licence). It deals with a couple of blog posts
[1, 2] about Debian — through SPI — doing to a former volunteer what ICBM — via
Fedora and some external law firm — did_to_that_same_former_volunteer*.
Internet tribunals deem that kind of SLAPP a form of “harassment” (to quote
directly) as it’s a slap across to face to the notion of free speech online.


“Some people donate hard-earned money thinking that they help Free software
projects and their money ends up landing in the bank accounts of millionaire
bullies who use Microsoft Windows to type threatening letters to people who
actually develop Free software.”By curious coincidence, Francis_Gurry (WIPO)
comes from the same university as the volunteer and Julian Assange too comes
from there. WIPO has long been a big bully, fronting for corporate bullies.
That they’re now going under the skin of volunteers is a really low blow, even
if their laws get weaponised by opportunistic lawyers who never even used GNU/
Linux and don’t have the most basic understanding of how the Free software
community actually functions. Debian ought not waste its constrained budget
literally paying bullies, as_happened_before. I too have been a victim of such
bullying, even_as_recently_as_months_ago. Some people donate hard-earned money
thinking that they help Free software projects and their money ends up landing
in the bank accounts of millionaire bullies who use Microsoft Windows to type
threatening letters to people who actually develop Free software.


The Debian trademark is now being mishandled by few individuals working for
large corporations, just like the Linux_Foundation misuses_the_"Linux"_brand. █
____
* They just don't_care_about_the_people_who_did_all_the_work_without_being_paid
for_it. How’s that for gratitude?



                    ䷩ 𝚕𝚒𝚗𝚎 174

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/08/epo-president-video/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/08/epo-president-video/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.08.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_He_is_the_EPO’s_President⠀✐


Posted in Europe, Patents at 9:42 am by Dr. Roy Schestowitz


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇European Patent Convention; I am the f***ing president!!⦈
  Stop obstructing the speculation-loving_banker who has no understanding of
   patents (meme template: scene from American_Psycho with investment banker
                               Patrick Bateman)


Summary: EPO President António_Campinos has reached the "let_me_through!"_or
the_"let_me_in!" moment (like Lukashenko_2_years_ago)


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

                    ䷩ 𝚕𝚒𝚗𝚎 1484

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/08/irc-log-070522/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/08/irc-log-070522/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.08.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Saturday,_May_07,_2022⠀✐


Posted in IRC_Logs at 2:32 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-070522.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-070522.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-070522.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-070522.gmi
Over HTTP:


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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


CID                                              Description     Object type


                                                 IRC log for
 QmZhk13Misy1B4xbKqw39MonYXnf3GvaycGJDckgoufoyi #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmV41qjKoimQuXwfJgGPdJqGWuyA7AhdrmjFPB9rVwygtg (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmYysxf2my13YVcefHsNPVFwAmGFv5iHgLRspEp3Wg61Zd social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmPw7p7cjjpFHx8jxyBjPaDfBQcXVkMW5c5WH6nE2Gtg2c social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmcfhjohYfZZMs9Tqc4WiTZLMpiGhnHF6x6W85iZ3r4xCS #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmWHS9eoqQ4pCvMrFfYf6USe74jbnycSX1rR7cFwMD6Q2L (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmTS1Mku3LbfG4roiSLRJbxrdNDP97tH5BXK7unHeMNhK2 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmTY5u2nCGNT7WUSjfwsVL8tTzc3Hsvd3KvT1TLiriCNFB (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmRQVhGpsKDNmkjNUW1AkVeznhpmY4wAGbjRcBeWH1qdd2



                    ䷩ 𝚕𝚒𝚗𝚎 1611

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/08/team-upc-disinformation/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/08/team-upc-disinformation/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.08.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Charade_of_Fake_News_and_Lobbying_(Based_on_Lies)_by_Team_UPC⠀✐


Posted in Deception, Europe, Patents at 9:10 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Rory_O’Neill/UPC_seminar:_in-house_to_ramp_up_plans_in_next
few_months:__Funded_by_litigation_companies;_Lobbying;_Why?_To_fake_process?
But_UPC_neither_exists,_nor_is_it_legal⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Conference_&_CLE_Calendar:_UPC_lobbying_and_sales_calendar⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇D_Young_&_Co_LLP_-_Rachel_Bateman:_UPC_preparations_-_five
actions_to_take_now:_To_help_the_lobbyists_with_self-fulfilling_prophecies...⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Opinion:_UPC_should_look_to_CJEU_on_transparency:_Max
Walters:_Legality;_Illegal;_Compliance_with_the_law;_Kangaroo_court⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇D_Young_&_Co_LLP_-_Alice_Stuart-Grumbar:_UP_&_UPC_-
representation_and_judges:_EPO_kangaroos;_This_does_not_even_exist_and_it's_not
legal⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Bristows_LLC:_Bristows/Gregory_Bacon:_Appointment,_training
and_remuneration_of_UPC_judges;_No_such_thing_exists._Bristows_said_the_same_5+
years_ago!!⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Fake_advice:_D_Young_&_Co_LLP_-_Alice_Stuart-Grumbar:_UP_&
UPC_-_structure,_language_&_where_to_start_a_case:_No_such_system_even_exists!
Advice_on_an_illegal_and_unconstitutional_wishlist⦈_


Summary: The EPO‘s replace-courts-with-kangaroo-courts project is based on
lies, disinformation (worse than misinformation), fabrication, and
glorification of illegal actions, overt violations of constitutions,
conventions being ignored, court-rigging, and even habitual perjury (at the
expense of the EU’s legitimacy), so we continue watching and reporting_the
prominent_culprits


THIS post will be followed by a video. I wish to express my concerns about Team
UPC not only lying but also shamelessly pushing illegal agenda under the guise
of law firms with legal advice (yes, the irony).


We’ve noticed a slowdown — a considerable slowdown in fact — even though the
EPO’s Web site has had lots of dininformation plastered onto its front page a
little over a week ago (epo.org has become rather farcical). It was around the
time António_Campinos was having a breakdown; go read all_these_comments
(especially the comments!) because it looks like a turning point has been
reached. Benoît_Battistelli‘s boy sees no way forward other than bullying and
cursing at those who merely point out facts and tell the truth. That’s the last
step before declaring defeat. █


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

                    ䷩ 𝚕𝚒𝚗𝚎 1935

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/08/unitary-patent-system-neo-colonialist-plot/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/08/unitary-patent-system-neo-colonialist-plot/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.08.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ UPC:_“A_Neo-colonialist_Plot”⠀✐


Posted in Deception, Europe, Patents at 12:01 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 0c08b64f7556fd53968332478203e183
Team UPC Lies Explained
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/upc-lies-2022.webm


Summary: The EPO is harming_the_European_Union because its handlers try to
ratify an_illegal_system under the guise of unity


HAVING just published the_weekly_screenshots_of_UPC_lies (we’ve been doing this
every weekend, usually on Sundays, for quite a while now), I want to comment on
what’s wrong with it. It’s not just immoral; it is illegal.


To make matters worse, those lies and illegalities harm the EU, which I care
deeply for. Benoît_Battistelli and António_Campinos care only about their
personal gain, which relies on destroying the patent system on behalf of
bankers and lawyers, mostly at the expense of science and technology. It’s
crude_financialization.


Meanwhile, the media has quit covering the issue. Dr._Glyn_Moody_asked_the_EPO
about it 6 years ago and then said: “When asked by Ars, the EPO’s spokesperson
mentioned the imminent arrival of the unitary patent system as an important
reason for revising the EPO’s internal rules…”


Notice the choice of words “imminent arrival”. That was 2016! They keep lying*.


Dr. Moody, author of Rebel_Code, has also said that intellectual monopoly is “a
neo-colonialist plot to ensure the continuing dominance of Western nations.”


He’s not fooled by the spiel about “innovation” and other_buzzwords.


Contrariwise, Juve has transformed_itself_into_an_English-speaking propaganda
site (it used to do actual reporting on EPO abuses, albeit in German only). To
give two new examples from Daily Links [1, 2], Mathieu Klos, the chief editor,
speaks of “the potential UPC” without noting that it is illegal. That’s just
more ads/spam disguised as reporting and this publisher profits from promotion
of law firms that sue with patents, so there’s a conflict of interest, too.
Mathieu’s colleague, Konstanze, meanwhile speaks of “the impending UPC” even
though it’s neither legal nor certain. She keeps referring to a “community” (by
which she means people who charge 200-300 euros per hour). There is no such
thing as “Europe’s patent community”; those are parasites and this piece is
lobbying disguised as journalism, citing “tweets” (which aren’t valid sources
and aren’t fact-checked, either). Twitter is curated_by_and_for_billionaires,
nowadays_under_the_guise_of_"news". █
___________
* Whilst using lies about the UPC (as a lobbying tactic) may not be outright
illegal, such lies can be a violation of trust in the context of a legal
profession as they have binding commitments and they cannot mislead politicians
or bribe politicians in this fashion. If clients pay them a lot of money only
to be lied to, then these clients can file formal complaints. So we generally
think that calling them out on their lies certainly helps prevent repetition
(of such lies), sometimes it even helps to passively silence them as they don’t
want to get caught and risk getting disbarred/sanctioned/sacked. They disengage
or retire.



                    ䷩ 𝚕𝚒𝚗𝚎 2020

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.08.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_08/05/2022:_A_Look_at_CrowPI2_and_Release_of_Linux_5.18_RC6⠀✐


Posted in News_Roundup at 5:19 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Desktop/Laptop⠀➾


                # ⚓ CrowPI2:_Reviewing_the_Famous_all-in-one_STEM_Solution⠀⇛


                       Raspberry PI computer boards are famous for
                       learning to code and small electronics projects. By
                       using the beards as is, you will need cabling and
                       buying the needed sensors. CrowPI2 gives a
                       different way of thinking about Raspberry PI with
                       an innovative laboratory layout


                       The CrowPi2 is a device which appears, at a first
                       look, as classic netbooks, that were small and very
                       cheap notebooks spreading the computer market in
                       2010.


                # ⚓ Linuxiac ☛ 4_Major_Distros_in_the_History_of_Linux_That
                  Shaped_the_Linux_World⠀⇛


                       The Linux world is incredibly diverse, but it
                       started with a few major Linux distros. Here’s who
                       they are!


                       There are currently hundreds of active Linux
                       distros, but only a few of them can be described as
                       the mothers and fathers of everything else we know
                       these days as Linux.


                       They are the ones who have laid the foundation that
                       almost every single Linux distro today stands on.
                       Loved by some or disliked by others, they are the
                       shoulders on which the modern Linux world has stood
                       to get where it is today.


                       This article will focus on each of them, giving
                       them all the respect they deserve. They are all
                       distros created from scratch, making them one of
                       the so-called original Linux distros, ones that are
                       not based on anything before them.


                # ⚓ Linux Made Simple ☛ Linux_Weekly_Roundup_#181⠀⇛


                       We had a good week in the world of Linux releases,
                       with Voyager 22.04.1, SparkyLinux 6.3, and Nitrux
                       20220503.


          o § Server⠀➾


                # ⚓ Ubuntu Pit ☛ 20_Best_Linux_Media_Server_Distros_&_Software
                  for_Your_Home_Theater_PC⠀⇛


                       People who love home theater PC are constantly
                       getting interested in Linux since Microsoft made a
                       wall above the Windows Media Center Edition for the
                       users. As an open source operating system, Linux
                       provides more opportunities to create and maintain
                       a home theater PC. But you will need a Linux Media
                       Server software or distro for that. It can help you
                       to set up a cost and resource-effective media
                       server, which ultimately lets you watch, share, or
                       listen to all the media files from a remote
                       location on your Smartphone or desktop.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ MusikCube:_All_In_One_Player,_Library_&_Streaming_–
                  Invidious⠀⇛


                       My personal music player on Linux is MPD + NCMPCPP
                       but if you want a more contained solution then how
                       about you try out musikcube which even has an
                       android app to control it.


          o § Kernel Space⠀➾


                # ⚓ Linus_Torvalds:_Linux_5.18-rc6⠀⇛


                       So 5.18 is looking like it's going to be one of the
                       larger releases in
                       numbers of commits (we'll see where it ends up -
                       it's going to be
                       neck-and-neck with 5.14 right now, but won't be as
                       big as 5.13 was).
                       But despite the merge window being big, the release
                       candidates have
                       generally been quite modest in size, and rc6
                       continues that trend. I
                       keep expecting the other shoe to drop, but 5.18
                       just seems to be quite
                       well-behaved.

                       Let's see if this jinxes it, but nothing looks
                       particularly scary
                       here. rc6 looks to be mostly some driver updates
                       (network drivers and
                       rdma stand out, small random fixes elsewhere), with
                       the usual
                       smattering of architecture updates (x86 kvm fixes,
                       but also a
                       long-standing x86 kernel FP use issue, and a
                       smattering of parisc and
                       powerpc fixes). And some wireguard selftest
                       updates.

                       The rest is mostly some btrfs fixes, some core
                       networking, and just
                       random small one-offs elsewhere.

                       Please do go test it all out - because things may
                       look good now, but
                       continued testing is the only thing that will make
                       sure.

                       Thanks,
                                      Linus
                # ⚓ The_sixth_version_of_patches_for_the_Linux_kernel_with
                  support_for_the_Rust_language⠀⇛


                       Miguel Ojeda, author of the Rust-for-Linux,
                       proposed the release of v6 components for Rust
                       device driver development for Linux kernel
                       developers to consider. This is the seventh edition
                       of the patches, taking into account the first
                       version, published without a version number. Rust
                       support is considered experimental, but is already
                       included in the linux-next branch and mature enough
                       to start working on creating abstraction layers
                       over kernel subsystems, as well as writing drivers
                       and modules. The development is funded by Google
                       and the ISRG (Internet Security Research Group),
                       which is the founder of the Let’s Encrypt project
                       and promotes HTTPS and the development of
                       technologies to increase the security of the
                       Internet.


          o § Applications⠀➾


                # ⚓ UNIX Cop ☛ Deploy_Jellyfin_on_Docker⠀⇛


                       Jellyfin is an Opensource software which can handle
                       all your media requirements by exposing them
                       securely, allowing you to access anywhere as well
                       as features like metadata fetch, transcoding, user
                       access.


                # ⚓ Medevel ☛ HLedger_Web_is_an_outstanding_personal_accounting
                  and_money_tracking_system⠀⇛


                       hledger is released under the GPL-3.0 License.


                # ⚓ Medevel ☛ Contact_Otter_is_your_personal_free,_CRM_and
                  contact_manager⠀⇛


                       Contact Otter is a free open-source personal CRM
                       and contact management solution for individuals and
                       families.


                       It is a simple easy to use contact manager and
                       address box solution, written with Python and
                       Django.


                # ⚓ Medevel ☛ Dillinger_is_a_web-based_feature-rich_Markdown
                  editor⠀⇛


                       Dillinger is a cloud-enabled, mobile-ready,
                       offline-storage compatible, AngularJS-powered HTML5
                       Markdown editor.


                       If you are using Sandstorm ecosystem, you can
                       install Dillinger with one click.


          o § Instructionals/Technical⠀➾


                # ⚓ H2S Media ☛ How_to_install_Podman_on_Ubuntu_22.04_LTS_Jammy
                  Linux_–_Linux_Shout⠀⇛


                       Follow the steps of this tutorial to install the
                       Podman container tool on Ubuntu 22.04 LTS Jammy
                       JellyFish Linux for creating virtual containers.


                       Podman is a container tool for virtualizing
                       applications. It was originally developed by Red
                       Hat and originated in the Cri-O project, which
                       develops a lightweight container runtime
                       environment for Kubernetes as an alternative to the
                       Docker runtime environment.


                       It is compatible with Docker on the command line
                       however doesn’t rely on the Docker daemon. Hence,
                       we can use its Container Engine to provide
                       containers without root access. Buildah is the
                       Image builder used by Podman.


                # ⚓ Linux Made Simple ☛ How_to_install_Eclipse_IDE_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Eclipse IDE
                       on a Chromebook. Please follow the video/audio
                       guide as a tutorial where we explain the process
                       step by step and use the commands below.


                # ⚓ Video ☛ How_to_install_Inkscape_on_Debian_11_–_Invidious⠀⇛


                       In this video, we are looking at how to install
                       Inkscape on Debian 11.


                # ⚓ Ubuntu Handbook ☛ How_to_Create_USB_Installer_for_Windows
                  7/8/10_in_Ubuntu_22.04_Linux⠀⇛


                # ⚓ The New Stack ☛ How_to_Manage_your_Docker_Containers_with
                  DockStation_–_The_New_Stack⠀⇛


                       When you go to find a GUI tool to manage your
                       Docker containers, you’ll find more options than
                       you can imagine. Those tools range from the overly
                       simplistic to the remarkably complicated, and
                       everything in between. Every so often, however,
                       you’ll find a desktop client that does an
                       outstanding job of making container management much
                       easier.


                # ⚓ GNU_Linux_Debian_–_how_to_view_chm_(windows_help)_files⠀⇛


                       chm files are basically html files packed into an
                       archive.


                # ⚓ ID Root ☛ How_To_Install_PostgreSQL_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       PostgreSQL on Ubuntu 22.04 LTS. For those of you
                       who didn’t know, PostgreSQL is a popular and
                       powerful open-source relational database management
                       system that has been adopted for running mission-
                       critical applications. It supports a large part of
                       the SQL standard and is designed to be extensible
                       by users in many aspects. Some of the features are
                       ACID transactions, foreign keys, views, sequences,
                       subqueries, triggers, user-defined types and
                       functions, outer joins, and many more.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the PostgreSQL relational database
                       management on Ubuntu 22.04 (Jammy Jellyfish). You
                       can follow the same instructions for Ubuntu 22.04
                       and any other Debian-based distribution like Linux
                       Mint, Elementary OS, Pop!_OS, and more as well.


                # ⚓ How_To_Download_Ubuntu_in_Step_by_Step⠀⇛


                       This tutorial explains in step by step how you can
                       download Ubuntu computer operating system from the
                       internet. This includes various methods to do so,
                       among them are via torrents and mirrors, and how to
                       further verify the ISO file with the official
                       checksums. This excludes how to create a bootable
                       media, as it’s been covered in a separate tutorial.


                # ⚓ Linux Mint ☛ How_to_upgrade_to_LMDE_5_–_The_Linux_Mint
                  Blog⠀⇛


                       It is now possible to upgrade LMDE 4 to version 5.


                # ⚓ How_to_Install_juffEd_Development_Environment_on_Ubuntu
                  20.04⠀⇛


                       If you are an application developer you are
                       probably already using a text editor or IDE, but if
                       you are a novice you are likely overwhelmed by the
                       sheer number of solutions out there. In any case,
                       it pays to learn about new tools so that you can
                       get the most out of them. Today, you’ll learn how
                       to install juffEd Development Environment on Ubuntu
                       20.04. In addition to this, we’ll tell you a bit
                       about it.


          o § Games⠀➾


                # ⚓ PS4/Switch/Vita/Linux_Release_–_pEMU_6.0_(NES/SNES/Sega/
                  Arcade_emulator_suite)_–_Wololo.net⠀⇛


                       Developer CPasJuste has released pEMU 6.0 for the
                       PS4, Nintendo Switch, Linux, and PS Vita. This new
                       release adds Sega rom (Mega Drive, Master System,
                       Game Gear, Mega CD…) support to the emulator suite.
                       The pEmu suite are pretty stable emulators that can
                       provide a very good alternative to Retroarch.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ KDE_Plasma_5.25:_Top_New_Features_and_Release
                        Details⠀⇛


                             We will give you the feature summary of the
                             KDE Plasma 5.25 desktop environment
                             (upcoming).


                             KDE Plasma 5.25 is the 27th version of KDE
                             Plasma desktop, not an LTS release. This
                             release is followed by the prior 5.24 LTS,
                             released in February. KDE Plasma 5.25 brings
                             several exciting updates on the desktop UI,
                             polished applets, widgets, a good set of
                             gesture updates for touch-based devices and a
                             massive list of bug fixes. Plasma 5.25 is
                             based on Qt 5.15.2 and KDE Frameworks 5.94.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Kevin_Fenzi:_Onlykey_DUO⠀⇛


                             Next, I tried to enroll a otp for our Fedora
                             account system, but found that the TOTP
                             secret wouldn’t work. Further investigation
                             showed that the onlykey NEO only supports
                             sha1 for TOTP secrets and our account system
                             uses SHA512. ;( There’s a old closed ticket
                             about this on the onlykey firmware repo:
                             https://github.com/trustcrypto/OnlyKey-
                             Firmware/issues/101


                             There’s also no way to generate a ssh private
                             key on the device (like you can using the
                             opensc support on a yubikey). You can
                             generate ecdsa sk openssh keys, which is
                             great, but not too useful to me yet as RHEL7
                             and RHEL8 don’t support them.


          o § Devices/Embedded⠀➾


                # ⚓ Linux Gizmos ☛ DIN_Rail_PC_with_four_2.5_GbE_LAN,_dual
                  display_and_PCIe_x4_slot⠀⇛


                       Germany based ICP has launched a compact PC based
                       on Intel’s processors (11th Gen Intel Core &
                       Celeron) for DIN rail use. The DRPC-240-TGL comes
                       with 8GB RAM by default although it can be expanded
                       to 64GB through two DDR4 SO-DIMM slots. ICP ensures
                       to deliver the DRPC-240-TGL in a ready-to-use form,
                       meaning pre-assembled and with an OS installed (Win
                       10 or Linux).


                       The DRPC-240-TGL is offered in three processor
                       variations, Intel Celeron 6305, Intel Core-i5-
                       1145G7E and Intel Core-i7-1185G7E. The PC design
                       allows the user to implement a PCIe expansion box
                       (PCI Express x4) for add-on cards. The device also
                       provides one M.2 2230 A-key and one M.2 3042/52/80
                       B-key for additional add-on cards. Furthermore,
                       there is a 2.5” drive bay for SATA (6Gb/s) storage.


                # § Open Hardware/Modding⠀➾


                      # ⚓ Arduino ☛ The_Root_Commander_is_a_homemade_MIDI
                        controller_ensures_you_never_play_the_wrote_note_|
                        Arduino_Blog⠀⇛


                             After attempting to learn how to play the
                             piano after some previous experience with
                             guitar and music theory in general, YouTuber
                             EvolutionStoneware encountered a few
                             difficulties when trying to learn the keys on
                             a standard MIDI keyboard. Because of this,
                             she created a DIY MIDI controller called the
                             Root Commander that allows for a single note
                             to be played based on the settings of several
                             inputs.


                             Within the controller is an Arduino that
                             reads the values from three potentiometers
                             and determines the corresponding scale, key,
                             and octave. Once stored, the firmware chooses
                             the correct string containing either the
                             scale, key, or octave depending on which
                             range the values fall into. For example,
                             setting the scale potentiometer to between
                             500 and 722 selects the “Dorian” scale. From
                             here, these values are all shown on the
                             integrated I2C OLED display in the center.


                      # ⚓ CNX Software ☛ Canaan_K510_CRB_RISC-V_AI_development
                        kit_ships_with_dual-camera_module_and_LCD_display_–_CNX
                        Software⠀⇛


                             Last summer, Canaan introduced the Kendryte
                             K510 tri-core RISC-V AI processor, now also
                             known as Canaan K510, as an updated version
                             of the Kendryte K210 with a much higher 3
                             TOPS of performance, but at the time, there
                             were no development board and SDK.


                             But I’ve now just been informed of the
                             availability of the Canaan Kendryte K510 CRB
                             (customer reference platform) AI development
                             kit with camera module and LCD display, as
                             well as a software development kit with U-
                             Boot, Linux, and AI tools which can be used
                             to develop smart audio and computer vision
                             applications.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ The_Best_Cyberpunk_Games_for_Android_2022_–_Jydge,
                        Hyperforma_and_More_–_Droid_Gamers⠀⇛


                      # ⚓ Android Police ☛ How_to_unlock_your_Chromebook_with
                        your_Android_phone_using_Smart_Lock⠀⇛


                      # ⚓ Tech Times ☛ Google_TensorFlow_Lite_To_Make_Android
                        Smarter—Leading_To_More_AI-Reliant_Smartphone_Features
                        |_Tech_Times⠀⇛


                      # ⚓ Android Police ☛ What_do_the_Pixel_Buds_Pro_need_to
                        succeed?_Some_advice_from_the_Android_Police_podcast⠀⇛


                      # ⚓ Express ☛ Millions_of_Android_users_told_of_date_they
                        need_to_upgrade_phone_by_|_Express.co.uk⠀⇛


                      # ⚓ 9to5Google ☛ YouTube_Music_testing_big_playlist_UI
                        redesign_on_Android_–_9to5Google⠀⇛


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


                # ⚓ Medevel ☛ mdSilo_is_an_outstanding_open-source_note-taking
                  app_for_the_active_mind⠀⇛


                       mdSilo is a super lightweight knowledge-base and
                       note-taking software for people who constantly
                       taking notes.


                       It leverages Markdown for note-taking, internal
                       tagging and backlinks, and building a connected
                       network between notes for easy browsing.


                       mdSilo is built using Tauri, a revolutionary
                       framework for building desktop applications on top
                       of Rust and HTML/ JavaScript. It also uses React
                       and Slate.


                       You can use mdSilo to organize anything, your
                       personal note, code, tasks, personal projects, and
                       keep track of your educational curve.


                       [...]


                       mdSilo is released under the GNU Affero General
                       Public License v3.0.


                # ⚓ OpenSource.com ☛ How_open_source_leads_the_way_for
                  sustainable_technology_|_Opensource.com⠀⇛


                       There’s a palpable change in the air regarding
                       sustainability and environmental issues. Concern
                       for the condition of the planet and efforts to do
                       something about it have gone mainstream. To take
                       one example, look at climate-based venture
                       capitalism. The Climate Tech Venture Capital (CTVC)
                       Climate Capital List has more than doubled in the
                       past two years. The amount of capital pouring in
                       demonstrates a desire and a willingness to solve
                       hard climate challenges.


                       It’s great that people want to take action, and I’m
                       here for it! But I also see a real risk: As people
                       rush to take action or jump on the bandwagon, they
                       may unwittingly participate in greenwashing.


                       The Wikipedia definition of greenwashing calls it
                       “a form of marketing spin in which green PR and
                       green marketing are deceptively used to persuade
                       the public that an organization’s products, aims,
                       and policies are environmentally friendly.” In my
                       view, greenwashing happens both intentionally and
                       accidentally. There are a lot of good people out
                       there who want to make a difference but don’t yet
                       know much about complex environmental systems or
                       the depth of issues around sustainability.


                # ⚓ Medevel ☛ Magda_is_an_open-source_Big_Data_cataloging
                  system⠀⇛


                       Magda is a data catalog system that will provide a
                       single place where all of an organization’s data
                       can be cataloged, enriched, searched, tracked and
                       prioritized – whether big or small, internally or
                       externally sourced, available as files, databases
                       or APIs. Magda is designed specifically around the
                       concept of federation – providing a single view
                       across all data of interest to a user, regardless
                       of where the data is stored or where it was sourced
                       from.


                       The system is able to quickly crawl external data
                       sources, track changes, make automatic enhancements
                       and make notifications when changes occur, giving
                       data users a one-stop shop to discover all the data
                       that’s available to them.


                       [...]


                       Magda is released under the Apache-2.0 License


                # § Programming/Development⠀➾


                      # ⚓ Linux Links ☛ 7_Top_Free_and_Open_Source_Crystal_Web
                        Frameworks⠀⇛


                             
                             One of the types of software that’s important
                             for a web developer is the web framework. A
                             framework “is a code library that makes a
                             developer’s life easier when building
                             reliable, scalable, and maintainable web
                             applications” by providing reusable code or
                             extensions for common operations. By saving
                             development time, developers can concentrate
                             on application logic rather than mundane
                             elements.


                             A web framework offers the developer a choice
                             about how to solve a specific problem. By
                             using a framework, a developer lets the
                             framework control portions of their
                             application. While it’s perfectly possible to
                             code a web application without using a
                             framework, it’s more practical to use one.


                      # ⚓ lispreading⠀⇛


                             One thing that I would like to understand
                             better is the place of code walking in macro
                             programming. The Raskin paper explains that
                             it is not possible to write a fully correct
                             code walker in ANSI CL. Consfigurator
                             currently uses Raskin’s best-effort portable
                             code walker. Common Lisp: The Language 2
                             includes a few additional functions which
                             didn’t make it into the ANSI standard that
                             would make it possible to write a fully
                             correct code walker, and most implementations
                             of CL provide them under one name or another.
                             So one possibility is to write a code walker
                             in terms of ANSI CL + those few additional
                             functions, and then use a portability layer
                             to get access to those functions on different
                             implementations (e.g. trivial-cltl2).


                             However, both On Lisp and Let Over Lambda,
                             the two most substantive texts on CL
                             macrology, both explicitly put code walking
                             out-of-scope. I am led to wonder: does the
                             Zen of Common Lisp-style macrology involve
                             doing without code walking? One key idea with
                             macros is to productively blur the
                             distinction between designing languages and
                             writing code in those languages. If your
                             macros require code walking, have you perhaps
                             ended up too far to the side of designing
                             whole languages? Should you perhaps rework
                             things so as not to require the code walking?
                             Then it would matter less that those parts of
                             CLtL2 didn’t make it into ANSI. Graham notes
                             in ch. 17 of On Lisp that read macros are
                             technically more powerful than defmacro
                             because they can do everything that defmacro
                             can and more. But it would be a similar sort
                             of mistake to conclude that Lisp is about
                             read macros rather than defmacro.


                      # ⚓ Medevel ☛ TerriaJS_is_an_open-source_web-based
                        geospatial_cataloging_framework⠀⇛


                             TerriaJS is a feature rich open source
                             solution for building amazing spatial data
                             federation web platforms.


                      # ⚓ Thorsten_Alteholz:_My_Debian_Activities_in_April
                        2022⠀⇛


                             This month I accepted 186 and rejected 26
                             packages. The overall number of packages that
                             got accepted was 188.


                      # ⚓ Medevel ☛ revealJS_is_an_open-source_presentation
                        framework⠀⇛


                             reveal.js is an open source HTML presentation
                             framework. It enables anyone with a web
                             browser to create beautiful presentations for
                             free.


                             Presentations made with reveal.js are built
                             on open web technologies. That means anything
                             you can do on the web, you can do in your
                             presentation. Change styles with CSS, include
                             an external web page using an <iframe> or add
                             your own custom behavior using our JavaScript
                             API.


                             You can use Markdown to create a stylish
                             presentation with reveal.js. Developers can
                             easily embed reveal.js in their web projects.


                      # § Perl/Raku⠀➾


                            # ⚓ Perl ☛ Save_the_date_–_Deutscher_Perl/Raku
                              Workshop_2023_in_Frankfurt_am_Main_–_27.02.2023-
                              1.03.2023⠀⇛


                                   Hello everybody,

                                   after a long time of waiting it is
                                   finally time - we cordially invite you
                                   to the German Perl/Raku Workshop 2023.

                                   Next year's workshop will take place
                                   from Monday 28 February to
                                   Wednesday 1. March in the Saalbau
                                   Gallus in Frankfurt am Main.
                      # § Python⠀➾


                            # ⚓ On_forms_of_apparent_progress_«_Paul_Boddie’s
                              Free_Software-related_blog⠀⇛


                                   Over the years, I have had a few things
                                   to say about technological change,
                                   churn, and the appearance of progress,
                                   a few of them touching on the evolution
                                   and development of the Python
                                   programming language. Some of my
                                   articles have probably seemed a bit
                                   outspoken, perhaps even unfair. It was
                                   somewhat reassuring, then, to encounter
                                   the reflections of a longstanding
                                   author of Python books and his use of
                                   rather stronger language than I think I
                                   ever used. It was also particularly
                                   reassuring because I apparently
                                   complain about things in far too
                                   general a way, not giving specific
                                   examples of phenomena for anything
                                   actionable to be done about them. So
                                   let us see whether we can emerge from
                                   the other end of this article in better
                                   shape than we are at this point in it.


                                   Now, the longstanding author in
                                   question is none other than Mark Lutz
                                   whose books “Programming Python” and
                                   “Learning Python” must surely have been
                                   bestsellers for their publisher over
                                   the years. As someone who has, for many
                                   years, been teaching Python to a broad
                                   audience of newcomers to the language
                                   and to programming in general, his
                                   views overlap with mine about how
                                   Python has become increasingly
                                   incoherent and overly complicated, as
                                   its creators or stewards pursue some
                                   kind of agenda of supposed improvement
                                   without properly taking into account
                                   the needs of the broadest reaches of
                                   its user community. Instead, as with
                                   numerous Free Software projects, an
                                   unscrutable “vision” is used to impose
                                   change based on aesthetics and
                                   contemporary fashions, unrooted in
                                   functional need, by self-appointed
                                   authorities who often lack an awareness
                                   or understanding of historical
                                   precedent or genuine user need.


    * § Leftovers⠀➾


          o ⚓ E-mails_Aren’t_Really_Letters⠀⇛


                 Fine. Opening a conversation in a friendly matter similar
                 to an actual letter is okay. It’s polite, I guess, though
                 a little verbose in some attempt to show that thought and
                 time has gone into it. Or maybe just to shift the content
                 to signature ratio a bit.


                 You answer in similar fashion. Probably top posting,
                 which means that you just hit “reply” and start typing
                 without lending a thought to the fact that all previous
                 messages in the conversation will be cited in your
                 response.


                 Then that person replies. Again with the full “Hello,
                 Person” introduction and gigantic signature. Before you
                 know it you have a full conversation where each new
                 message contains more than ten full “Hello, Person”s
                 complete with filler text and automatically appended big
                 signatures that nobody reads (see footnote).


          o ⚓ Response_to_Greenfeld’s_System_to_Stay_in_Touch_with_Hundreds_of
            Peopl⠀⇛


                 A quick summary of it is that Jakob managed to implement
                 Derek Sivers’s method of staying in touch with hundreds
                 of people[2], by which you categorize people into four
                 levels of importance that dictate how often you should
                 contact them. Sort of like MySpace’s top friends feature
                 but even more punishing.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Fix_AMD_driver_keeps_crashing_while_playing_games_on
                        Windows_11 [Ed: Vista 11 is a giant eXPeriment and its
                        users are subjects]⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The_Two-Dimensional_Political_Compass_is_an_Insult⠀⇛


                       One nauseating political meme has survived too long
                       – the two-axis political-compass.


                       “You see”, (someone explains), you might be left or
                       right wing, but you can also be more or less
                       authoritarian or libertarian.


                       I get the idea. People’s political ideas don’t
                       really divide well into Left and Right, so a little
                       nuance wanders in to bandage the oddity.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Eindhoven_continues_to_be_the_innovation_hub [Ed:
                        Conflating patents with "innovation" to help the EPO
                        spread mindless propaganda, supportive of an agenda to
                        grant fake patents in bulk]⠀⇛


                             Phillips rises to the occasion, becoming the
                             company that applied for the most patents.


                      # ⚓ B#_On_Demand_abandons_own_Federal_Circuit_appeal⠀⇛


                             On April 22, 2022, the Federal Circuit
                             granted B# On Demand LLC’s motion to dismiss
                             its Federal Circuit appeal in Case No. 22-
                             1357 (see below). Unified had won on all
                             issues at the PTAB (IPR2020-00995), which
                             resulted in claims 1–10, 13–22, and 25–34 of
                             U.S. Patent 9,553,880 being found
                             unpatentable. The patent is related to on-
                             demand distribution of subscription media and
                             had been asserted against Spotify.


                      # ⚓ PTAB_Discretionary_Denials_Fall;_Board_Time_Spent_on
                        Issue_Rises⠀⇛


                             In 2021, in more than 45% of all IPR
                             institution decisions (420 of 918), the PTAB
                             spent considerable time and resources dealing
                             with the discretionary considerations under
                             the NHK Spring-Fintiv rule. But with more
                             than a year since Director Iancu stepped down
                             from the USPTO, Fintiv and 314(a) denials
                             have plummeted dramatically. In Q1 of 2022,
                             only 37 petitions have been denied on
                             procedural grounds, and such denials on
                             procedural grounds are projected to decrease
                             by 17% year-over-year as seen below.


                      # ⚓ PATROLL_aims_to_shatter_records_in_2022⠀⇛


                             PATROLL, Unified Patents’ only Crowd Sourced
                             Prior Art platform, has hit numerous
                             milestones since being launched in 2018. So
                             far in 2022, there have been 81 contests
                             announced, versus 42 in 2021, and currently
                             34 active contests with $68,000 in total
                             prizes. We are extremely happy to announce
                             that over the last month, 29 contests have
                             ended with over 170 total submissions, and
                             nearly $30,000 paid to winning submissions.
                             That averages nearly 6 submissions per
                             contest.


                      # ⚓ After_Feldges:_Allen_&_Overy’s_patent_team_secures
                        succession [Ed: More ads/spam disguised as reporting;
                        this publisher profits from promotion of law firms that
                        sue with patents, so there’s a conflict of interest,
                        too; Mathieu_Klos speaks of “the potential UPC” without
                        noting that it is illegal]⠀⇛


                             Pharmaceuticals expert Joachim Feldges has
                             left the partnership and the Allen & Overy
                             patent team. The 63-year-old Munich patent
                             litigator had already surpassed the Magic
                             Circle firm’s age-limit for the partnership.
                             Now he has set up his own firm in Munich.
                             With his departure, the patent team has
                             finally completed its long-awaited
                             generational change.


                      # ⚓ “The_CJEU_has_clarified_PI_case_law_for_Europe’s
                        judges” [Ed: There is no such thing as "Europe’s patent
                        community"; those are parasites and this piece is
                        lobbying disguised as journalism, citing "tweets";
                        Konstanze Richter speaks of "the impending UPC" even
                        though it's neither legal nor certain]⠀⇛


                             Social media reaction suggests that Europe’s
                             patent community has met the CJEU’s latest
                             decision on preliminary injunctions with
                             broad approval. However, as is so often the
                             case, the devil is in the detail.


                             Case law that finds only patents that have
                             survived opposition or nullity suits worthy
                             of a PI is discriminatory. Indeed, this case
                             law excludes newly-granted IP rights, such as
                             in the case referred by the Munich Regional
                             Court. Patents never challenged with an
                             opposition or nullity action are also
                             excluded, with patent owners having no
                             influence on either. Nevertheless, patent
                             owners should still be able to access
                             effective protection of their rights for such
                             patents.


                             Tobias Pichlmaier, current presiding judge at
                             the 37th Civil Chamber at the Munich Regional
                             Court, therefore had no choice but to submit
                             the question to the CJEU. Based on
                             established case law, if the Munich Regional
                             Court had granted a preliminary injunction, a
                             second-instance court would almost certainly
                             have overturned the decision.


                             Now, rather than dismissing a PI for an as-
                             yet unchallenged patent, judges must take a
                             closer look at the technology. They must also
                             consider the possible validity of a patent-
                             in-suit. As a result, a further backlog of
                             cases might occur, since proceedings could
                             take longer. But the CJEU has no doubt
                             streamlined the judicial approach.


                             [...]


                             In recent years, both the EPO and national
                             patent offices, lately the French INPI, have
                             worked to improve the quality of granted
                             patents. Many in the patent community have
                             repeatedly criticised the EPO in particular
                             for its long-pursued strategy of increasing
                             efficiency. Stakeholders complained that the
                             desire for high productivity led to problems
                             in patent examinations, and thus to poorer
                             quality. They claimed that patent examiners
                             have insufficient time for the individual
                             applications.


                             The EPO’s strategic plan for 2023, unveiled
                             in 2019, focused on patent quality – but the
                             negative effects of increased efficiency
                             linger. This is specially in the minds of
                             many stakeholders, who still do not trust the
                             quality of patents.


                             Until patent quality visibly increases, as
                             more patents survive oppositions and nullity
                             suits unscathed, the infringement judges must
                             take the matter into their own hands. They
                             must examine patent validity intensively and
                             decide, based on this, whether to grant a
                             preliminary injunction.


                             [...]


                             As a result, the CJEU ruling contributes to a
                             more uniform case law among German courts.
                             This is especially important in view of the
                             impending UPC, where German judges are sure
                             to play an important role.


                      # ⚓ INTA_2022:_Office_heads_tout_pros_of_unified_IP
                        agencies [Ed: There is no such thing as "IP"; they just
                        try to combined totally different things, based on
                        lobbyists' suggestions]⠀⇛


                # § Copyrights⠀➾


                      # ⚓ [Guest_post]_Second_time_is_a_charm:_Danish_design
                        company_wins_plant_box_war⠀⇛


                             On 22 April 2022, the Danish Eastern High
                             Court handed down its decision in yet another
                             dispute concerning applied art and the
                             question of originality and infringement
                             under copyright law. The dispute concerned a
                             plant box created by the Danish design
                             company ferm Living and sold in various
                             colours.



                    ䷩ 𝚕𝚒𝚗𝚎 3129

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.08.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_08/05/2022:_Nextcloud_Hub_24_and_Tor_0.4.7⠀✐


Posted in News_Roundup at 3:58 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ Tux Digital ☛ This_Week_in_Linux_197:_Firefox_100,_WINE
                  Bottles,_Tails_5.0,_Unity_Desktop,_Ubuntu_and_more_Linux
                  news!_–_TuxDigital⠀⇛


                       On this episode of This Week in Linux: Mozilla
                       Firefox 100, Bottles 2022.5.2, Tails 5.0, Deb-Get
                       for 3rd-Party Software, Unity 7.6 For Testing,
                       Trinity Desktop R14.0.12, Open Media Vault 6, GCC
                       12.1, Ubuntu Christian Edition 22.04 and an
                       Unofficial SteamOS 3. All that and much more on
                       Your Weekly Source for Linux GNews!


          o § Applications⠀➾


                # ⚓ A_Critique_of_Lagrange⠀⇛


                       This is not a full review of Lagrange, but rather
                       discussing one specific aspect of it. My intention
                       here is to start a conversation.


                # ⚓ Nextcloud_Hub_24_automates_data_export_and_import_–
                  LinuxStoney⠀⇛


                       Nextcloud Hub 24 is the latest from “the world’s
                       most widespread collaboration platform, used by
                       tens of millions of private users, governments, and
                       Fortune 500 companies alike to reclaim data
                       sovereignty and privacy.” This is how the project
                       introduces the new version of it, the first to see
                       the light this year 2022.


                       Without much fanfare, however, Nextcloud Hub 24 is
                       the new version of the old Nextcloud , renamed
                       Nextcloud Hub a few versions ago to reflect its
                       status as an application suite, something that
                       serves more than one thing – it serves many, in
                       fact – although its basic function as Dropbox to
                       free and self-managed software does not change,
                       because everything continues to revolve around
                       that.


                # ⚓ Tor_0.4.7_Stable_Version_Released_–_LinuxStoney⠀⇛


                       The release of the Tor 0.4.7.7 toolkit used to
                       organize the work of the anonymous Tor network is
                       presented. Tor 0.4.7.7 is recognized as the first
                       stable release of the 0.4.7 branch, which has been
                       in development for the past ten months. The 0.4.7
                       branch will be maintained as part of the regular
                       maintenance cycle – updates will be discontinued 9
                       months later or 3 months after the release of the
                       0.4.8.x branch.


          o § Instructionals/Technical⠀➾


                # ⚓ DJ Adams ☛ Converting_strings_to_objects_with_jq⠀⇛


                       In preparing some data for another upcoming blog
                       post, I needed to convert a list of fully qualified
                       GitHub repository names into a JSON array of
                       single-property objects (to reflect the style of
                       JSON output from GitHub’s gh CLI). I achieved this
                       with a short jq filter. Here’s how, recorded here,
                       with my working thoughts, mostly for my outboard
                       memory.


                # ⚓ DJ Adams ☛ Some_thoughts_on_jq_and_statelessness⠀⇛


                       I came across a great article via lobsters
                       recently: Introducing zq: an Easier (and Faster)
                       Alternative to jq. I posted some brief thoughts on
                       it over on the lobsters thread, and in the spirit
                       of “owning your own words”, I thought I’d write
                       them up here too.


                       I do like articles like this, that show and lay out
                       the thinking behind the conclusion, and along the
                       way, impart knowledge about the topic at hand.
                       Especially when they’re on a subject I’m eager to
                       learn more about.


                       While reading the article a couple of things struck
                       me.


                # ⚓ Linux Hint ☛ Touch_Command_in_Ubuntu_22.04⠀⇛


                       Touch command in Ubuntu 22.04 serves various
                       purposes such as generating files or sets of files,
                       altering the modification or access times of files,
                       etc. Moreover this command can be used to classify
                       files based on their timestamps without causing any
                       changes to the files. Besides this you can set the
                       date and time of modification of a file according
                       to your desire using the touch command.


                       In this blog we have elaborated the usage of a
                       touch command in Ubuntu 22.04 by demonstrating some
                       basic and advanced examples of this command.
                       Without any further ado let’s get started.


                # ⚓ UNIX Cop ☛ Deploy_your_own_personalized_wiki:_Bookstack_on
                  Docker⠀⇛


                       Bookstack is an Opensource self-hosted wiki service
                       which can handle any of your guides, references,
                       flowcharts, Has built in integration of
                       diagrams.net which you can use to create aesthetic
                       diagrams.


                # ⚓ UNIX Cop ☛ Configure_Apache2_to_use_SSL_Client
                  Authentication⠀⇛


                       SSL Client Authentication is a process by which a
                       server checks client provided certificate to make
                       an SSL connection. If the client certificate is
                       trusted, then a successful SSL connection is made
                       with server. Else client is denied access to the
                       website.


                       This is useful when you want only specific clients/
                       people to access your website even by keeping your
                       website public. You can add the SSL Client
                       Authentication in location block as well for Apache
                       to restrict specific paths to allow only SSL
                       Authorized users.


                       Here are the steps to configure this on Apache
                       server


                # ⚓ Linux Hint ☛ Add-Apt-Repository_Without_User_Input_Prompt⠀⇛


                       In Linux OS, a number of packages are installed by
                       default. However, these packages are never enough.
                       You may need several packages over time. The Linux
                       distribution Ubuntu uses apt for installing,
                       updating, and removing the packages. The apt keeps
                       the repositories in the single sources.list file
                       under the /etc/apt/ directory. It also keeps the
                       repositories in separate (.list) files under the /
                       etc/apt/sources.list.d directory. To add a
                       repository in Ubuntu, you need to either edit these
                       files or you can use the add-apt-repository.


                # ⚓ Linux Hint ☛ How_to_Install_and_Use_Webmin_in_Ubuntu
                  22.04⠀⇛


                       Webmin is a web-based interface for Linux-based
                       systems administration. It permits you to operate a
                       server from the console or remotely, eliminating
                       the requirement to change Linux/Unix configuration
                       files manually. You can also utilize the Webmin
                       interface for configuring operating system
                       internals such as disc quotas, services or
                       configuration files, and open source applications
                       like MySQL, PHP, DNS, Apache, or Tomcat.


                       This write-up will discuss the procedure to install
                       and use Webmin in Ubuntu 22.04. So, let’s start!


                # ⚓ Linux Hint ☛ How_to_find_the_IP_address_of_the_Raspberry_Pi
                  operating_system⠀⇛


                       The Raspberry Pi operating system is also a type of
                       Debian-based Linux distribution so the commands of
                       the command-line interface are almost the same so
                       we can find out the IP address of the Raspberry Pi
                       similarly we find in any other Debian based
                       distribution..


                       In this write-up, we will find out about the
                       methods by which we can find out the IP address of
                       the Raspberry Pi operating system, but before
                       proceeding towards these methods, we will explore
                       what the IP address is.


                # ⚓ Linux Hint ☛ How_to_install_and_use_veracrypt_on_Ubuntu
                  22.04⠀⇛


                       VeraCrypt is an open-source data encryption utility
                       to encrypt a drive or the whole system storage.
                       VeraCrypt is the descendent of the obsolete
                       encryption utility named TrueCrypt.


                       VeraCrypt is derived from the source code of
                       TrueCrypt. However, it overcomes the limitations of
                       TrueCrypt. For instance, VeraCrypt is equipped with
                       various encryption algorithms such as AES (Advanced
                       Encryption Standard), Camelia, Kuznyechik, Serpent,
                       and Twofish. Additionally, VeraCrypt provides
                       support to combine various algorithms from the
                       above-mentioned algorithms.


                # ⚓ Linux Hint ☛ How_to_install_Android_Studio_on_Ubuntu
                  22.04⠀⇛


                       Android studio is one of the many tools available
                       that are used for android development. This is a
                       cross-platform tool that works on many operating
                       systems and has numerous built-in features and
                       comes with multiple layouts for generating eye
                       catchy GUI. These features were one reason why this
                       tool replaced the formerly popular tool Eclipse
                       IDE.


                       You can install Android Studio on Ubuntu 22.04
                       using two methods which are either using android-
                       studio repository or Snap. Both of these methods
                       have been discussed here in detail.


                # ⚓ Linux Hint ☛ How_to_Install_Apache_on_Ubuntu_22.04⠀⇛


                       Apache web server is developed by “Robert McCool”.
                       This open-source web server is responsible for
                       accepting the HTTP requests from the users and
                       providing the requested information in the form of
                       web pages and files. It is mainly utilized by
                       programmers for code testing. Apache also offers a
                       secure file-sharing feature that permits users to
                       store their important files in its root directory
                       and share them with other users.


                       This write-up will discuss the method to install
                       Apache on Ubuntu 22.04. So, let’s start!


                # ⚓ Linux Hint ☛ How_to_Install_Discord_on_Ubuntu_22.04⠀⇛


                       Discord is a social application that is used by
                       millions of people to text, video, and voice chat
                       with their friends and social communities. Discord
                       is free and can be utilized on multiple devices.
                       Users can exchange messages, and share media and
                       files either in private chat or in groups called
                       servers. This app was originally developed for the
                       gamers to chat meanwhile playing games.


                       This app is cross-platform compatible and can be
                       used on Windows, Linux Distros, or Mac OS. In this
                       blog, we will teach various ways with which you can
                       install discord on Ubuntu 22.04.


                # ⚓ Linux Hint ☛ How_to_Check_and_Update_Java_Version_on_Ubuntu
                  22.04?⠀⇛


                       Java is a general-purpose client-side programming
                       language that serves several functionalities like
                       android application development, game development,
                       web applications development, and many other
                       software products. To build any application, first,
                       we have to install Java on our computer systems.
                       However, some applications are not capable to run
                       on java’s outdated version. So, it’s essential to
                       know which Java version is installed on our
                       operating system and if our machine is running an
                       outdated version of java, then how to update it.


                       This post will explain how to check and upgrade the
                       Java version on Ubuntu 22.04. So, let’s begin!


                # ⚓ Linux Hint ☛ Install_the_latest_PHP_on_Ubuntu_22.04⠀⇛


                       PHP, which is a scripting language, was designed
                       for building websites. This language can be used on
                       many platforms such Linux, Windows, Mac OS, and
                       Unix. The latest version of PHP which is version
                       8.1 was released on 25th November, 2021 and serves
                       as an extension of PHP version 8.0. This version
                       introduces many features which were not present in
                       the previous one such as enums, read-only
                       properties, never return type, fibers, etc.


                       Here we have summed up steps using which you can
                       with great ease install the latest version of PHP
                       in Ubuntu 22.04.


                # ⚓ Linux Hint ☛ How_to_Install_VLC_Media_Player_on_Ubuntu
                  22.04⠀⇛


                       VLC media player is open-source and free software
                       that works on every platform such as Windows, Mac
                       OS, Linux, etc and is capable of playing all types
                       of multimedia files and audio CDs, DVDs, VCDs, etc.
                       It is a streaming media server that was founded by
                       the VideoLAN project.


                       Since we mentioned that it can work on any
                       platform, therefore, if you are a Linux user and
                       wondering how to install the VLC media player on
                       Ubuntu 22.04 then you are at the perfect place.
                       Here we have summed up the ways with which you can
                       install VLC on Ubuntu 22.04.


                # ⚓ Linux Hint ☛ How_to_Install_Ubuntu_22.04_on_VirtualBox⠀⇛


                       The Canonical developers are about to release their
                       latest version of Ubuntu in April 2022 which will
                       be referred to as Ubuntu 22.04. The beta version of
                       the system has been released and we performed
                       certain steps to install this version on the
                       VirtualBox. Installation of the other stable
                       versions will be similar to the one discussed here.


                       Therefore, if you wish to learn the installation
                       procedure of Ubuntu 22.04 on VirtualBox then read
                       the article till the end.


                # ⚓ Linux Hint ☛ How_to_Create_New_User_on_Ubuntu_22.04⠀⇛


                       The cloud server originally contains a user named
                       system, however, if you wish to create a new user
                       on your system to perform system administrative
                       actions then you can generate one using two
                       possible ways. Both of these methods have been
                       discussed here in this blog.


          o § Wine or Emulation⠀➾


                # ⚓ Wine_Staging_7.8_Released_with_Improved_Alt+Tab_Handling
                  for_Unity_Games_–_LinuxStoney⠀⇛


                       published release of the Wine Staging 7.8 , within
                       which extended builds of Wine are formed, including
                       patches that are not fully ready or risky, not yet
                       suitable for acceptance into the main Wine branch.
                       Compared to Wine, Wine Staging provides 550
                       additional patches.


                       codebase Wine 7.8. 3 patches related to the
                       processing of key states and the refinement of the
                       get/set_key_state functions have been transferred
                       to the main Wine package. updated Four patches :
                       winex11-_NET_ACTIVE_WINDOW , user32-
                       Mouse_Message_Hwnd , user32-rawinput-mouse and api-
                       iteration-tokens .


          o § Distributions⠀➾


                # § Arch Family⠀➾


                      # ⚓ So_I_Installed_Arch_on_My_Work_Mac⠀⇛


                             Ever since I went back to the office I’ve
                             been using a 2018 Mac Mini for work. It’s
                             been… usable. I’ve at least been able to get
                             everything done that I needed to.


                             Recently though we started a big server
                             migration. It’s much needed since we’re in
                             need of more hardware and are still on Ubuntu
                             16, but working on that migration has been
                             the back-breaking straw for me with MacOS.
                             I’ve just had to deal too much with tooling
                             issues, painful package management,
                             uncomfortable workflows despite my best
                             customization efforts, and lots of other tiny
                             things that have piled up which I won’t bore
                             anyone with.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ David Rosenthal ☛ Probabilistic_Fault_Tolerance⠀⇛


                             In our 2003 SOSP “Best Paper” Preserving Peer
                             Replicas By Rate-Limited Sampled Voting (also
                             here, expanded version here) we introduced a
                             number of concepts. The most important was
                             consensus based on sampling the electorate at
                             random, in contrast to the traditional
                             Byzantine Fault Tolerance (BFT), which at
                             every step solicits votes from the entire
                             electorate. The advantages of this mechanism
                             are so significant that, a decade and a half
                             later, it was re-discovered and improved upon
                             in the context of a blockchain protocol.
                             Below the fold I explain our original
                             consensus system, and describe how the basic
                             idea has been adopted and enhanced.


                      # ⚓ Linux Hint ☛ What_is_MQTT_and_how_to_use_it_with
                        Raspberry_Pi⠀⇛


                             The Raspberry Pi is a multi-purpose small
                             size device which has the power to become
                             people’s ideal choice in every aspect. It has
                             started to set its mark into the Internet of
                             Things (IoT) world and has quickly become an
                             excellent source to bring people into the
                             whole new world. When we talk about IoT, the
                             only thing that comes to our mind is the
                             communication of devices over the internet
                             but on the other side some people will also
                             need an answer about how a Raspberry device
                             will be used for communication purposes.


                             If you are the one among those people who
                             don’t have any knowledge then you should
                             follow this guide which will teach you how
                             you may utilize your Raspberry Pi device for
                             communication purposes with the help of a
                             Message Queuing Telemetry Transport (MQTT)
                             protocol. Before proceeding towards its use
                             with Raspberry Pi, it is important for you to
                             acquire the basic understanding of MQTT.


                      # ⚓ Linux Hint ☛ What_is_Raspberry_Pi_Cluster⠀⇛


                             The Raspberry Pi is an excellent little tool
                             that people can have in their pockets. The
                             device has an exceptional feature that drives
                             everyone to go hard on it and performs high
                             computational tasks. Handling complex tasks
                             would be hard for a single Raspberry Pi
                             device, even with 8GB RAM.


                             If you are considering purchasing more
                             Raspberry Pi devices, you will still leave
                             with the unanswered question of how to boost
                             the Raspberry Pi performance. In that
                             situation, cluster technology will come into
                             the business and in this article, we will
                             show you how the Raspberry Pi cluster will
                             help you boost your device performance.


                      # ⚓ Linux Hint ☛ What_is_piwheels_and_how_it_works_on
                        Raspberry_Pi⠀⇛


                             Python wheels are the standard package
                             managing system to download Python packages
                             on Linux based operating systems. The wheels
                             are hosted on a web server platform with the
                             name PyPi and this allows the Linux users to
                             access these wheels pretty easily. However,
                             the Raspberry Pi users don’t have a supported
                             architecture to download Python packages and
                             the packages need to be built from source in
                             order to make it prepare for your Raspberry
                             Pi OS. The installation of these packages
                             requires a lot of time and this excessive
                             execution time is due to the compilation of
                             source codes.


                             If you are looking for a way to speed up your
                             Python packages installation, you should look
                             into this article. It provides a detailed
                             guideline for speeding up your package’s
                             installation using Raspberry Pi wheels called
                             as Piwheels.


                             Before going into the detail how Piwheels
                             works on Raspberry Pi let’s first discuss
                             what are Piwheels.


                      # ⚓ Linux Hint ☛ What_are_different_methods_to_monitor
                        the_temperature_of_the_Raspberry_Pi_4⠀⇛


                             The Raspberry Pi 4 is a single board computer
                             which means it has a processor or a CPU to
                             process the commands and also has the RAM
                             with other peripheral devices that a computer
                             has like a keyboard. When we use the
                             Raspberry Pi 4 to process different tasks it
                             raises the temperature of the CPU of the
                             Raspberry Pi. Temperature rise can damage the
                             CPU. In this write-up, we will find out the
                             methods by which we can monitor the
                             temperature of the Raspberry Pi 4 and protect
                             it from overheating.


                      # ⚓ Linux Hint ☛ Best_Raspberry_Pi_Starter_Kits_in_2022
                        [Ed: Potentially spammy as they try to sell things]⠀⇛


                             The Raspberry Pi device has gained remarkable
                             success in the present era and it’s no
                             surprise that this device will become a
                             valuable tool for people of all ages. The
                             importance of this device among the children
                             and students has increased a lot because they
                             are getting enough learning opportunities
                             from this device. It’s not just a machine to
                             run different operating systems or games on
                             it, but it has some extraordinary features as
                             well.


                      # ⚓ Linux Hint ☛ How_to_make_digital_counter_using_7
                        segment_with_Arduino_Uno⠀⇛


                             A 7-segment display can be used to display a
                             limited amount of data having numeric values
                             and alphabets. Such types of displays are
                             mostly used in banks, hospitals, super
                             markets for displaying token numbers and
                             counter numbers. So, we have also created a
                             digital counter using the 7-segment display
                             with Arduino Uno.


                      # ⚓ Linux Hint ☛ What_are_the_causes_of_Arduino_freeze⠀⇛


                             When working on a project using Arduino
                             students come across a lot of problems and
                             these problems can be either related to the
                             Arduino code or to the Arduino board itself.
                             Sometimes due to errors in the Arduino code
                             that the compiler is unable to recognize or
                             hardware problems the Arduino boards freeze
                             completely and do not show any output. So, we
                             have addressed some of the issues that cause
                             the Arduino to freeze.


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


                # § Web Browsers⠀➾


                      # ⚓ [Old] How_To_Build_an_Absurdly_Backwards_Compatible
                        Website⠀⇛


                             It feels like so much of the web is composed
                             of clickbait, ads, popups, and a toxic amount
                             of JavaScript that you need a modern computer
                             just to get any value out of it. Remember
                             when low-power computers were created for
                             people who were “just browsing the
                             [Internet]?”


                             Half of the sites on the [Internet] are so
                             overloaded with tracking scripts, ads, third-
                             party “analytics” platforms, and other junk
                             that they simply crash in the face of sub-par
                             hardware; and don’t even get me started on
                             what they do to “retro” computers.


                             If the modern web hasn’t been created with
                             aging hardware in mind, what does that mean
                             for the proliferation of e-waste? Is it
                             really so necessary to update your computer
                             every 2-5 years? And, what if you didn’t?
                             What if you couldn’t afford to?


                # § Programming/Development⠀➾


                      # ⚓ Fig_Terminal_Auto-complete_Review⠀⇛


                             At first Fig presents itself as just an auto-
                             complete tool and, don’t get me wrong, if
                             that is all you are looking for, it does a
                             great job. However there is clearly a much
                             larger ambition with this product to expand
                             the idea of terminal auto-completion into
                             making CLIs much more approachable, baking
                             documentation into the terminal and then
                             allowing you to share that among your entire
                             team for public or private tools. While at
                             present the idea is just starting to become
                             fleshed out, there is a lot of promise here.


                             So while Fig is a useful tool today, the
                             promise of where Fig could go is really
                             exciting to me. I’m going to focus mostly on
                             what the product is now, but felt I needed to
                             mention the obvious hooks they are building
                             into the application and the overall
                             framework they are constructing.


                      # § Python⠀➾


                            # ⚓ Linux Hint ☛ Password_Generator⠀⇛


                                   With the continuous advent of
                                   Technology and the great amount of data
                                   floating around, the security data is
                                   of prime importance today.
                                   This is done by the usage of passwords
                                   which keep our data safe and secure
                                   from the world and the internet.


                                   However, an easy password can be hacked
                                   very easily, and our data can become
                                   vulnerable to misuse. To prevent this
                                   from happening, it is extremely
                                   important to use strong passwords.


                                   In this article, we will learn to
                                   create a ‘PASSWORD GENERATOR’ in python
                                   using GUI to generate strong passwords
                                   using Python Tkinter Module. This
                                   application will generate a random
                                   password: with a combination of
                                   letters, numerical values, and some
                                   special characters. The user will
                                   mention the length of the password
                                   based on the requirement and
                                   accordingly, we will get our password.


                                   By the end of this article, you will
                                   get a clear understanding of the
                                   working of the application and the
                                   logic behind the code.


                            # ⚓ Linux Hint ☛ Dice_Rolling_Simulator_–_Python⠀⇛


                                   Dice is a cube-shaped object used in
                                   games like ludo, snakes and ladders,
                                   bunko and Yahtzee, etc. The cube when
                                   spun faces up with a random number
                                   ranging from 1-to 6.


                                   A dice rolling simulator is a digital
                                   computer model that works like normal
                                   dice and shows a random number. It is
                                   developed using a software program that
                                   can be coded in any programming
                                   language.


                                   In this article, we will be coding a
                                   dice-rolling simulator using python
                                   language with GUI using the Tkinter
                                   library.


                                   We will start by importing the modules
                                   and then proceed with the remaining
                                   part.


                            # ⚓ Linux Hint ☛ Pandas_Rolling_Groupby⠀⇛


                                   The Python programming language
                                   provides Pandas library which has many
                                   methods that perform simple to complex
                                   functions. Pandas in Python make data
                                   analysis very simple and easy.
                                   Moreover, it is a very exceptional
                                   language for performing data
                                   investigation while providing an
                                   incredible environment of information-
                                   driven python bundles.


                                   In this article, we will discuss the
                                   pandas rolling groupby function in
                                   Python. Here, we will demonstrate some
                                   useful examples that will help you
                                   learn about the Pandas rolling groupby
                                   function and how to use that function
                                   in python code. So, let us begin with
                                   the definition of the rolling function.


                            # ⚓ Linux Hint ☛ Factorial_in_Python_NumPy⠀⇛


                                   We’ll show you how to employ the NumPy
                                   factorial function, also known as
                                   np.math.factorial, in this article.
                                   We’ll also go through the syntax of the
                                   np.math.factorial function, how it
                                   works, and how to apply it. In
                                   addition, we’ll show you how to compute
                                   factorials element-wise on NumPy arrays
                                   using a different function,
                                   scipy.special.factorial. However, it is
                                   preferable if you read the entire
                                   tutorial to find all the guidelines.
                                   That way, everything will probably make
                                   more sense.


                            # ⚓ Linux Hint ☛ Currency_Converter_Using_Gui_In
                              Python⠀⇛


                                   A ‘Currency converter’ is an app or
                                   tool that enables you to quickly
                                   convert any amount from one currency to
                                   another, anytime and anywhere. Creating
                                   this app in Python language is an
                                   immensely fun and interesting task.


                                   We will have two tabs in this
                                   application. One is going to be our
                                   currency tab where we mention our home/
                                   base currency and the currency we want
                                   to convert our amount into, along with
                                   the rate of conversion. In the second
                                   tab, we define the amount we want to
                                   convert and then we get our desired
                                   result.


                                   Via this article, you will get a clear
                                   understanding of the logic behind the
                                   code and working of this application.


                            # ⚓ Linux Hint ☛ Use_of_the_‘if___name___==
                              __main__’_Statement_in_Python⠀⇛


                                   Some special variables are set when any
                                   Python script executes. The __name__
                                   variable is one of them. The Python
                                   file is saved with the ‘.py’ extension
                                   and each Python file is called a
                                   module. The classes, functions, and
                                   variables are defined by the module.
                                   The __name__ variable is set to
                                   __main__ if the Python interpreter runs
                                   a module in the main program. The
                                   __name__ variable is set to the
                                   module’s name if the Python file is
                                   importing the module from another
                                   module. The ‘if __name__ == __main__’
                                   statement is used to check if the
                                   module is imported or not. Different
                                   uses of this statement have been shown
                                   in this tutorial.


                            # ⚓ Linux Hint ☛ Use_of_the___init__()_Function_in
                              Python⠀⇛


                                   Python supports both structured and
                                   object-oriented programming. The class
                                   and object are used to implement
                                   object-oriented programming. The class
                                   defines the properties of the object.
                                   The constructor method is used in
                                   object-oriented programming to declare,
                                   initialize and manipulate the object,
                                   and this method is called automatically
                                   when an object of the class is created.
                                   The __init__() function works like the
                                   constructor method in Python and it is
                                   declared inside the class.


                            # ⚓ Linux Hint ☛ Use_of_Python_kwargs⠀⇛


                                   Two types of arguments can be passed to
                                   the Python function. These are *args
                                   (Non-keyword arguments) and **kwargs
                                   (Keyword arguments). The wildcard
                                   characters, ‘*’ and ‘**’ are used when
                                   the number of arguments is not defined.
                                   The **kwargs is used in the function to
                                   pass keyword-based variable-length
                                   arguments in the function. Different
                                   uses of kwargs in the Python function
                                   have been shown in this tutorial.


                      # § Shell/Bash/Zsh/Ksh⠀➾


                            # ⚓ [Old] DJ Adams ☛ Bash_notes_3⠀⇛


                                   Another Exercism Bash track exercise,
                                   another opportunity to learn from the
                                   community solutions. This time I came
                                   across a few nice Bash language
                                   features that I’d probably known about
                                   but forgotten due to lack of practice.


                                   The exercise in question is Atbash
                                   Cipher and the features that I wanted
                                   to share with you are from user Victor
                                   Guthrie’s solution.


                            # ⚓ [Old] DJ Adams ☛ Bash_notes_2⠀⇛


                                   I looked at a couple of more solutions
                                   to another Exercism exercise in the
                                   Bash track – Scrabble Score. I was
                                   reminded of one particular feature of
                                   the case statement, and another
                                   solution was rather splendid in its
                                   approach and it reminded me a little of
                                   some functional programming techniques,
                                   or perhaps MapReduce.


                            # ⚓ [Old] DJ Adams ☛ Bash_notes⠀⇛


                                   Here are a few things I learned, or re-
                                   learned, while reading through a neat
                                   solution to a Bash track exercise in
                                   Exercism.


                                   I completed a very basic solution to
                                   the Proverb exercise in the Bash track
                                   on Exercism and proceeded to look at
                                   some of the solutions others had
                                   submitted. A beautifully simple and
                                   succinct solution from user Glenn
                                   Jackman had the most stars, and I
                                   wanted to share a few things I learned
                                   from it.


                            # ⚓ Medium ☛ 5_Types_of_Expansions_on_Linux⠀⇛


                                   Bash has a special mechanism called
                                   expansion, which gives us much
                                   convenience. So we can use some
                                   notations to write a short command that
                                   will be expanded into something complex
                                   before being executed.


                            # ⚓ Lars Wirzenius ☛ Unix_command_line_conventions
                              over_time⠀⇛


                                   This blog post documents my
                                   understanding of how the conventions
                                   for Unix command line syntax have
                                   evolved over time. It’s not properly
                                   sourced, and may well be quite wrong.
                                   I’ve not been using Unix until 1989, so
                                   I wasn’t there for the early years.
                                   Maybe someone has written a proper
                                   essay on this, with citations. I’m too
                                   lazy to dig them up.


                            # ⚓ Linux Hint ☛ Bash_Declare_–a_for_Arrays⠀⇛


                                   Arrays are the must-haves in any
                                   programming language. In Bash, we also
                                   declare the arrays but with different
                                   syntax. Within this article today, we
                                   will be discussing the declare “-a”
                                   option method to declare arrays in the
                                   Bash program. Let’s start with the
                                   examples now. We need a Bash file to
                                   create some Bash code examples in it.
                                   So, we have tried the Bash “touch”
                                   instruction to create one with the name
                                   “array.sh” having a Bash extension.
                                   This file needs to be opened in the
                                   “Gnu Nano” editor of the Ubuntu 20.04
                                   system.


                            # ⚓ Linux Hint ☛ Bash_String_Operators⠀⇛


                                   As we already know that the Bash string
                                   values are the group of words or
                                   characters. To manipulate string
                                   variables and values, Bash provides us
                                   with many functions and operators. If
                                   you are new to Bash programming and
                                   string manipulation, then this simple
                                   article is meant for your help. Within
                                   this guide today, we will be utilizing
                                   and discussing some of the most-used
                                   string Bash operators specially
                                   designed for string manipulation in
                                   Bash programming.


                                   Let’s get started with some of the
                                   examples to see the working of these
                                   operators. Start with the Bash file
                                   creation as we have to code in Bash.
                                   The “touch” instruction can be a plus
                                   to use here in Ubuntu 20.04. We prefer
                                   to use the Gnu Nano editor to open the
                                   Bash file and create code in it. You
                                   can use the text editor or vim editor
                                   as well.


                      # § Java⠀➾


                            # ⚓ Linux Hint ☛ What_does_%_percentage_sign_mean
                              in_Java⠀⇛


                                   There are multiple arithmetic operators
                                   in java such as +, -, /, and so on.
                                   Another useful arithmetic operator in
                                   java is % which divides the two values
                                   and consequently returns the remainder
                                   of these values. In java, there are
                                   multiple use cases of % for example it
                                   can be used to check wheater a number
                                   is even or odd, it can be used to check
                                   if the number is palindrome or not, and
                                   so on.


                            # ⚓ Linux Hint ☛ What_is_a_constructor_in_Java⠀⇛


                                   Classes are the core concept of OOP
                                   (object-oriented programming). Java
                                   offers the concept of constructors that
                                   is directly associated with the classes
                                   as constructors hold exactly the same
                                   name as the class name. In java, the
                                   prime objective of constructors is to
                                   initialize the class objects. A java
                                   class can have several constructors,
                                   but their definition must be different
                                   in terms of parameters.


    * § Leftovers⠀➾


          o ⚓ The_Stars,_From_the_Ground_Up:_While_Supplies_Last_(Part_1)⠀⇛


                 An Urbit meetup is being held in Kansas City, MO this
                 weekend. It began yesterday evening and continues through
                 today. Many users from all over the Midwest, and some
                 employees at Tlon, are in attendance, many from the St.
                 Louis area. This is the first Urbit meetup I’ve ever
                 attended, though I was only able to join yesterday, and I
                 felt like a little kid going to Walt Disney World. While
                 I was there, though, I overheard a spirited (but not
                 heated) discussion about the nature of planets in the
                 network.


          o ⚓ [Old] The Street ☛ Here’s_Why_You_Might_Get_Arrested_For_Renting
            From_Hertz⠀⇛


                 A judge cleared 17 cases against Hertz to move forward
                 last week, joining more than about half of the 230 that
                 are also currently pending. Other claims will be decided
                 at a later date.


                 Francis Alexander Malofiy, the Pennsylvania-based lead
                 attorney for the claimants, indicated to USA Today that
                 “230 is not the majority. … It’s the tip of the iceberg,”
                 and “you’re talking 20,000 people who were stuck in the
                 criminal justice system because they had a dispute or an
                 issue with their rental, or that (Hertz) couldn’t find
                 their car.”


                 According to court documents, the current group of
                 claimants has spent a total of 2,742 days in jail or
                 prison because of false arrests.


          o ⚓ [Old] Los Angeles Times ☛ Column:_Renting_a_car_from_Hertz?_You
            could_wind_up_in_jail⠀⇛


                 Their experiences may be the tip of a large iceberg.
                 Hertz acknowledges that it files some 3,500 theft reports
                 per year on customers; lawyers for the claimants say that
                 figure applies to customers who rented their vehicles
                 legally and for which the company has payment
                 information, such as a credit or debit card number, on
                 file.


                 Lawyers for the claimants say that although it’s not
                 unheard of for other car rental companies to report
                 vehicles stolen, Hertz appears to have systemic problems
                 keeping track of rental extensions and payments.


          o ⚓ [Old] Gannett ☛ After_Hertz_car_rentals_lead_to_some_arrests,
            know_what_to_do_when_you_rent_a_car⠀⇛


                 When talking to rental company, document everything


                 Document any conversations with rental company employees.


                 For example, if you call to extend your rental or report
                 an issue, write down the time of the call, who you spoke
                 with and what was said.


                 “If there is something important that is said verbally,
                 try and write it down,” Bland said. If there is a
                 dispute, your phone records matched up with what you
                 wrote down at that time could be helpful evidence.


                 [...]


                 Bland recommends keeping the paperwork and receipts from
                 your rental for at least a year, although three years is
                 the statute of limitations in most places for the kind of
                 tort case that may arise from a rental car dispute.


          o ⚓ [Old] The Drive ☛ Hertz_Customer_Thrown_in_Jail_for_Rental_Car
            ‘Theft’_a_Year_After_He_Returned_It:_Report⠀⇛


                 In a statement, Hertz said these situations are “very
                 rare” and “happen only after exhaustive attempts to reach
                 the customer.” That doesn’t seem to be the case here. The
                 man’s attorney says, “Hertz refuses to correct a police
                 report when they’ve learned payments [were] made, when
                 they’ve learned the car’s been returned or when they’ve
                 learned there’s inaccuracies.” So according to him, it’s
                 a case of Hertz’s incompetence.


          o ⚓ [Old] CBS ☛ New_Hampshire_man_arrested_aboard_cruise_ship_is
            latest_to_be_accused_of_stealing_Hertz_rental_car:_“Most_horrific
            experience_of_my_life”⠀⇛


                 “Hertz refuses to correct a police report when they’ve
                 learned payments [were] made, when they’ve learned the
                 car’s been returned or when they’ve learned there’s
                 inaccuracies,” he said.


                 Malofiy sent a letter to the company over the weekend,
                 asking Hertz to help get Doucette out of jail. He said
                 unless something changes, Doucette will be in jail for a
                 minimum of 10 days because he is awaiting extradition to
                 Arizona.


          o ⚓ [Old] CNET ☛ US_Senators_Call_for_Investigation_of_Hertz_Stolen
            Vehicle_Reports⠀⇛


                 The issue, which is being investigated by several US
                 senators, including Democratic senators Elizabeth Warren
                 of Massachusetts and Richard Blumenthal of Connecticut,
                 came to light during Hertz’s bankruptcy proceedings in
                 Delaware courts. Documents allege that the company has
                 filed police reports for approximately 3,300 vehicles per
                 year for four years, though it’s unclear how many of
                 those could be considered to have resulted in improper
                 arrests.


          o ⚓ ABC ☛ Al-Qaida_chief_blames_US_for_Ukraine_invasion_in_new
            video⠀⇛


                 Al-Zawahri’s whereabouts are unknown. He is wanted by the
                 FBI and there is a $25 million reward for information
                 leading to his capture.


          o ⚓ I’m_behind.⠀⇛


                 I feel like I’m frequently 3-4 years behind on most
                 mainstream media.


          o § Education⠀➾


                # ⚓ Times Higher Education ☛ Are_corporate_interests_taking
                  over_US_higher_education?⠀⇛


                       Individually, such challenges aren’t necessarily
                       new. But the numbers and types and spread are being
                       taken by experienced advocates of higher education
                       as heralding a worrisome shift in a battleground
                       where they’re winning some victories yet look
                       increasingly outmanoeuvred over the long run.


                       On the one hand, it’s getting easier for activists
                       in academia and beyond to identify a particular
                       company or industry or market behaviour they
                       consider objectionable, and organise effective
                       protest actions, including boycotts, without
                       suffering major financial repercussions.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Web_Emulator_For_The_Kenbak-1_Computer_(If
                  You’ve_Heard_Of_It)⠀⇛


                       Ever heard of the KENBAK-1? Recognized as the first
                       personal computer, created by John Blankenbaker and
                       sold in 1971 in comparatively small numbers, it’s
                       now a piece of history. But don’t let that stop you
                       if you are curious, because of course there is an
                       emulator on the web.


                # ⚓ Hackaday ☛ Reflecting_On_A_Queueing_Prism_Leads_To
                  Unexpected_Results⠀⇛


                       Computers are difficult enough to reason about when
                       there’s just a single thread doing one task. There
                       are dozens of cores in today’s modern processor
                       world, and your program might try to take advantage
                       of using more than just one. Things happening
                       concurrently makes the number of states and
                       interactions explode in to a mess we as humans are
                       likely going to have trouble understanding. So,
                       like [Hillel], you might turn to the computer to
                       try and model those interactions.


                # ⚓ Hackaday ☛ Mods_Make_A_Stock_Keyboard_Your_Own⠀⇛


                       Trust me, you don’t have to build your own keyboard
                       from the deskpad up to be happy or feel like one of
                       the cool kids. Sure, it doesn’t hurt, but not
                       everyone is able to or even wants to start from
                       next to nothing. Take [Roger] for example. [Roger]
                       started with a stock mechanical keeb — the Ultimate
                       Hacking Keyboard (UHK) — which can be outfitted
                       with magnetic add-on modules such as a thumb key
                       cluster, trackball, trackpoint, and touch pad, and
                       made it his own.


                # ⚓ Hackaday ☛ APPLE2IDIOT_Expansion_Card_Lets_Your_Apple_II_
                  (Sort_Of)_Access_The_Internet⠀⇛


                       [Nathanial Hendler]’s Apple2Idiot expansion card
                       for the Apple II family of computers is a nifty mix
                       of modern and vintage, and provides a clever means
                       of allowing the host computer to (indirectly)
                       access the internet over WiFi while keeping things
                       simple from the host computer’s perspective.


                # ⚓ Hackaday ☛ Bee_Motion_Combines_ESP32_With_PIR_Sensor_And
                  USB-C⠀⇛


                       There’s no shortage of ESP32 development boards out
                       there, with many of them offering some “killer app”
                       feature which may or may not align with whatever it
                       is you’re trying to do. But if you’ve got a project
                       that could benefit from the pairing of a powerful
                       WiFi-enabled microcontroller and a passive infrared
                       (PIR) motion sensor, the Bee Motion created by
                       [Paul Price] is certainly worth a close look.


                # ⚓ Hackaday ☛ Learning_Obsolete_Technology⠀⇛


                       Tom Nardi and I were talking about his trip to the
                       Vintage Computer Festival on the podcast, and he
                       admitted to not having been a retrocomputer
                       aficionado before his first trip. But he ended up
                       keying some binary machine code into some
                       collection of archaic silicon, and he got it. In
                       the same episode, the sound of the week was a
                       Strowger switch — the old electromechanical “brain”
                       of telephone switching centers of old. The sample I
                       used was from Sam of Look Mum No Computer on
                       YouTube, who got one for his museum and thinks it’s
                       just awesome.


                # ⚓ Hackaday ☛ This_Spherical_Lamp’s_Pieces_Ship_Flat,_Thanks
                  To_Math⠀⇛


                       [Nervous System] sells a variety of unique
                       products, and we really appreciate the effort they
                       put into sharing elements of their design and
                       manufacturing processes. This time, it’s details of
                       the work that went into designing a luxury lamp
                       shade that caught our eye.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Futurism ☛ Head_Of_FDA_Says_Misinformation_Is_Now_The
                  Leading_Cause_Of_Death⠀⇛


                       Califf’s position could mean the FDA takes a
                       stronger stance on COVID misinformation, although
                       it isn’t clear what form that’ll take. Still, it’s
                       a welcome breath of fresh air after poor official
                       health messaging during the pandemic left Americans
                       across the political spectrum suspicious.


                # ⚓ FDA_Commissioner_Califf_sounds_the_alarm_on_health
                  misinformation⠀⇛


                       But the issue that keeps him up at night, he said,
                       is the proliferation of false and misleading health
                       information, particularly online — and the distrust
                       in institutions, data and expertise that it has
                       wrought.


                       “I believe that misinformation is now our leading
                       cause of death,” he said, naming ongoing COVID-19
                       vaccine hesitancy, the number of people taking
                       Ivermectin and the prevalence of vaping as examples
                       of the problem. “Historically, the FDA has been
                       relatively quiet and puts out definitive
                       information through guidance or labels or
                       regulatory actions … that would be transmitted to
                       consumers and patients through trusted
                       intermediaries. But the world has changed at this
                       point.”


                       All this, he argued, had fueled the drop in life
                       expectancy in the U.S. compared to other wealthy
                       nations, and he urged reporters to avoid clickbait,
                       lean into fact checking, make sure the headline
                       matches the copy and take other steps to
                       responsibly convey news about COVID-19 and other
                       pressing health concerns.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ [Old] Obsolescence_Is_a_State_of_Mind⠀⇛


                             Sometime near the end of this year, every
                             Apple computer in my home will be rendered
                             obsolete and insecure. To be more accurate,
                             every Apple computer released prior to 2013
                             will suffer the same fate, thanks to the
                             impending death of macOS Catalina.


                             Why do I have so many “old” Apple computers,
                             you ask? Because Apple builds exceptionally
                             durable machines, and I don’t see the need to
                             add perfectly good hardware to the gigantic
                             pile of e-waste filling up our landfills. So,
                             come November(ish), these computers will get
                             no more updates, no more security patches,
                             and no more support. Consumers get to make
                             the choice between buying a new machine, or
                             replacing the operating system (I bet you can
                             guess what my choice was).


                      # ⚓ Digital Music News ☛ Google_Is_Shutting_Down_YouTube
                        Go_In_August_—_What_to_Know⠀⇛


                             YouTube Go, an app providing offline video
                             access, will be shutting down in August.
                             Designed with users with intermittent
                             [Internet] access in mind, YouTube Go
                             received more than 500 million downloads in
                             its six years of life.


                      # ⚓ Digital Music News ☛ Facebook_Is_Abruptly_Shutting
                        Down_Podcasts_—_Less_Than_One_Year_After_Launch⠀⇛


                             Parent company Meta confirmed to Bloomberg
                             that it will wind down its podcasting unit in
                             June. Soundbites and its general audio hub
                             will also get the ax, per the report. Live
                             Audio Rooms will be folded into the Facebook
                             Live offering.


                             According to Meta, this move is to help the
                             company “focus on the most meaningful
                             experiences.” Facebook Podcasts launched as
                             an attempt to rival Spotify’s growing
                             relevance in the space. As Spotify has
                             flourished with new podcasts, growing from
                             one million to four million in just a year –
                             Facebook has languished.


                      # ⚓ The_real_reason_that_the_first_version_of_Windows_NT
                        was_called_3.1⠀⇛


                             Real reason: MS had a deal in place with
                             Novell to include some handling of Novell
                             Netware client drive mappings. Novell gave MS
                             a little bit of Novell’s client source code,
                             so that Novell shares looked like other
                             network shares, meaning peer-to-peer file
                             shares in Windows for Workgroups.


                      # ⚓ SANS ☛ What_is_the_simplest_malware_in_the_world?⠀⇛


                             During a malware analysis class I taught
                             recently, one of the students asked me what
                             was “the simplest malware in the world”. Of
                             course, the answer to this question would
                             depend heavily on one’s definitions of
                             ‘simplest’ and ‘malware’, as well as on a
                             target hardware architecture and its
                             operating system (and potentially additional
                             software and other factors), but I thought
                             that it was conceptually interesting enough
                             to devote today’s diary to.


                             If we were to discuss simplicity only in the
                             terms of overall size of the code, and define
                             ‘malware’ (with small help from NIST[1]), as
                             a “program, that is intended to compromise
                             the confidentiality, integrity, or
                             availability of the victim’s data,
                             applications, or operating system or to
                             otherwise annoy or hinder the victim”, then
                             the simplest malware overall would probably
                             be a single instruction of the “Halt and
                             Catch Fire” type[2] for any platform, on
                             which instructions capable (by design or due
                             to a bug) of stopping CPU operations were
                             available and could be executed on their own.
                             Or – to be exact – the simplest malware would
                             probably be such a code on a platform, on
                             which the instruction would be shortest
                             (which would probably come to a single byte).
                             However, this is purely theoretical answer
                             from a historical standpoint.


                             If we were move beyond this case and focus
                             only on code that can run on modern operating
                             systems and current hardware platforms, the
                             situation becomes much more complex. And
                             although I spent some time thinking about
                             what the smallest malware might be, and I do
                             have a potential answer, I’m not completely
                             certain it is the correct one. If you can
                             think of a smaller example of a working
                             malicious code, let us know in the comments.


                      # ⚓ Silicon Angle ☛ UK’s_National_Health_Service_infected
                        by_massive_phishing_campaign⠀⇛


                             The U.K.’s National Health Service has been
                             infected by a massive phishing campaign that
                             resulted in hundreds of accounts on Microsoft
                             365 being compromised.


                             Detailed today by researchers by email
                             security firm INKY Technology Corp., the
                             phishing campaign was first detected in
                             October, then escalated in March. The
                             campaign used compromised NHS accounts to
                             send phishing emails to unsuspecting third
                             parties.


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Krebs On Security ☛ Your_Phone_May_Soon
                                    Replace_Many_of_Your_Passwords⠀⇛


                                         Apple, Google and Microsoft
                                         announced this week they will
                                         soon support an approach to
                                         authentication that avoids
                                         passwords altogether, and instead
                                         requires users to merely unlock
                                         their smartphones to sign in to
                                         websites or online services.
                                         Experts say the changes should
                                         help defeat many types of
                                         phishing attacks and ease the
                                         overall password burden on
                                         Internet users, but caution that
                                         a true passwordless future may
                                         still be years away for most
                                         websites.


                                  # ⚓ NBC ☛ Secret_surveillance,_mining
                                    customer_data:_How_retailers_help_bag
                                    shoplifting_kingpins⠀⇛


                                         Since 2020, an increasing number
                                         of states have launched organized
                                         retail crime task forces that
                                         pair corporate investigators with
                                         police and prosecutors. State
                                         attorneys general have created
                                         teams in Florida, Arizona, Utah,
                                         New Mexico and Illinois. Plans
                                         are in the works in Connecticut
                                         and Michigan.


                                         But the rise of retail
                                         investigators raises civil
                                         liberties and privacy concerns,
                                         experts say.


                                         These corporate cops use many of
                                         the same tactics as law
                                         enforcement officers — they
                                         surveil and question suspected
                                         shoplifters, run license plate
                                         searches, and collect large
                                         amounts of personal data. But
                                         constitutional restrictions that
                                         bind the actions of police and
                                         federal agents don’t apply to
                                         retail investigators, allowing
                                         them to do things like question
                                         people without reading them their
                                         Miranda rights.


                                  # ⚓ I_Hate_My_Smartphone⠀⇛


                                         Without a smartphone, it was
                                         impossible to do basic things
                                         like pay for parking, view a
                                         restaurant menu, drop my kids off
                                         at school, or pick my kids up
                                         from school. It is now taken as a
                                         given that everyone has an iPhone
                                         or Android phone, and while you
                                         can choose not to have one, it is
                                         becoming increasingly unlikely
                                         that you will be able to
                                         effectively participate in modern
                                         society without one.


                                         Now, don’t get me wrong, I’m not
                                         against the existence of
                                         smartphones. They are truly
                                         valuable tools that have the
                                         ability to improve the lives of
                                         many people in many different
                                         ways. What bothers me is the
                                         general lack of choice in the
                                         matter.


                                  # ⚓ Patrick Breyer ☛ Chat_control:_EU
                                    Commission_presents_mass_surveillance_plan
                                    on_May_11⠀⇛


                                         Next week on Wednesday (May 11),
                                         the EU Commission will present an
                                         EU draft law on mandatory chat
                                         control to the public for the
                                         first time. Similar to Apple’s
                                         highly controversial “SpyPhone”
                                         plans, the Commission wants to
                                         oblige all providers of email,
                                         chat and messaging services to
                                         search for suspicious messages in
                                         a fully automated way and forward
                                         them to the police in the fight
                                         against “child pornography”. This
                                         will require them to monitor and
                                         scan the communications of
                                         citizens en masse – even if they
                                         are still securely encrypted end-
                                         to-end so far.


                                  # ⚓ Where_anonymity_on_Twitter_is_a_matter_of
                                    life_or_death⠀⇛


                                         Activists and free speech
                                         advocates in several countries
                                         suggested that Musk needs a more
                                         nuanced understanding of what
                                         free speech is, and needs to be
                                         transparent about how
                                         authentication decisions will be
                                         made.


                                  # [Old]
                                    ⚓ Risks_of_the_Passport_Single_Signon
                                    Protocol [PDF]⠀⇛


                                         Some improvement is possible in
                                         Passport without violating the
                                         system’s goals of supporting
                                         unmodified browsers. Rotating the
                                         keys used to encrypt cookies
                                         would significantly increase the
                                         difficulty of retrieving cookie
                                         contents, as would using the
                                         master key to generate encryption
                                         keys instead of encrypting all
                                         cookies with the same key.
                                         Requiring SSL for all
                                         transactions would eliminate the
                                         possibility of forged redirects
                                         (at the cost of significantly
                                         increased load on merchant
                                         servers). Replacing password-
                                         based authentication with a
                                         challenge-response scheme (such
                                         as HTTP digest authentication)
                                         would make it impossible for an
                                         attacker to reuse passwords to
                                         impersonate a user.


                                         In the end, Passport’s risks may
                                         be inevitable for a system with
                                         its requirements. We believe that
                                         until fundamental changes are
                                         made to underlying protocols
                                         (through standards such as DNSSEC
                                         and IPSec), efforts such as
                                         Passport must be viewed with
                                         suspicion.


          o § Defence/Aggression⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_Who’s_Cashing_in_on_the_War_in
                  Ukraine?_Fossil_Fuel_Firms_and_Agricultural_Traders⠀⇛


                       As Russia continues to inflict untold suffering and
                       devastation in Ukraine, many around the world are
                       profiting amid the horrific bloodshed.


                # ⚓ Common Dreams ☛ Opinion_|_General_Dynamics_Shuts_Out
                  Critics,_‘Radical_Skeptics’⠀⇛


                       On May 4th, General Dynamics held its annual
                       shareholder meeting. This meeting took place
                       virtually, possibly in response to last year when
                       shareholders were able to directly engage with the
                       General Dynamics Board and ask how they justify the
                       destruction and death their weapons cause.


                # ⚓ Common Dreams ☛ Opinion_|_Amid_War_and_Devastation,
                  Ukrainians_Track_Russian_Eco_Crimes⠀⇛


                       On Feb. 24, 2022, Russian President Vladimir Putin
                       declared a full-scale military invasion of Ukraine.
                       The assault, by what’s widely considered the
                       second-most powerful military in the world, was on
                       six fronts across air, land, and sea, spanning
                       3,000 kilometers (1,900 miles) across the Ukrainian
                       border.


                # ⚓ NPR ☛ Georgia_officials_rule_that_Marjorie_Taylor_Greene
                  can_remain_on_the_ballot⠀⇛


                       The plaintiffs had asked the state to disqualify
                       Greene, citing a provision in the Constitution that
                       forbids members of Congress who support an
                       insurrection from serving in office.


                       Later on Friday, Georgia’s secretary of state,
                       Republican Brad Raffensperger, who had final say,
                       announced that he would follow the judge’s
                       recommendation.


                       [...]


                       Greene testified under oath last month, answering a
                       slew of questions about the days leading up to Jan.
                       6 with “I don’t recall” or “I don’t remember.”


                # ⚓ Arab News ☛ Muslim_Brotherhood’s_influence_in_US_should_be
                  confronted_and_defeated⠀⇛


                       Led by the Muslim Brotherhood, these organizations
                       bully anyone who stands against the Islamist
                       ideology and manipulate our system and government
                       using the magical term “Islamophobia.” We ought to
                       remember that they are proud of being anti-Semitic
                       and anti-American and that they sympathize with
                       radical groups, and act accordingly.


                # ⚓ VOA News ☛ Jihadist_Attack_Kills_11_Egypt_Troops:_Army⠀⇛


                       Eleven Egyptian soldiers were killed on Saturday
                       attempting to thwart a “terrorist” attack on the
                       Suez Canal zone abutting the Sinai peninsula, a
                       hotbed of jihadist activity, the army said.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Rolling Stone ☛ Meet_the_YouTube_Scuba_Divers_Solving_Cold
                  Cases_—_And_Racking_Up_Views⠀⇛


                       When Sides pivoted from treasure hunting to
                       searching for missing persons, he saw his views
                       spike. In mid-2021, he gave up his day job as a
                       mobile wheel repairman and went full-time into
                       YouTube, supplementing his ad revenue with
                       merchandise sales, donations, and paid
                       subscriptions. When he found Foster and Bechtel in
                       late 2021, he says his followers tripled. (He now
                       has about 360,000.) His audience has changed, too.
                       Whereas it was once fellow divers and treasure
                       hunters, most people today come for updates or
                       breakthroughs on cases. “The missing-persons
                       community watching these videos are super
                       supportive,” he says.


                       Divers like Sides take their roles as amateur
                       investigators seriously. If Sides finds a car
                       belonging to a missing person, he says, he calls
                       the authorities instead of a tow truck, and he gets
                       out of their way when they arrive. “Police will
                       take over, and we become spectators,” he says. His
                       interactions with law enforcement have been mainly
                       positive so far, though according to other divers
                       who spoke with Rolling Stone, encounters can be
                       rocky. In one instance in 2020, AWP was waiting
                       with the family of missing 17-year-old Nicholas
                       Allen when the cops arrived to pull out the teen’s
                       car. The cops can be heard on the AWP video acting
                       dismissively toward the family, saying there’s “no
                       guarantee” their child’s body was in there. “No,
                       but at least it’s my car, and I asked you guys — I
                       begged you guys to check,” the mother says. Allen’s
                       body was recovered, and the sheriff’s office later
                       issued an apology for acting insensitively toward
                       the family.


          o § Finance⠀➾


                # ⚓ Counter Punch ☛ Banks_Fueling_Global_Warming_is_Business_as
                  Usual⠀⇛


                # ⚓ Counter Punch ☛ The_Solution_to_Homelessness_Is_Not_Death⠀⇛


                       The problem with the homeless is they don’t have
                       anywhere to go. Shoo them out of doorways and they
                       move to the parks. Chase them from the parks and
                       they move to the freeways. Give them bus tickets to
                       other towns and those towns try to send them right
                       back. Give them housing? Don’t be ridiculous; this
                       is America!


                # ⚓ Common Dreams ☛ Sanders_Says_‘No_Corporation_That_Breaks
                  the_Law_Should_Get_a_Federal_Contract’⠀⇛


                       Sen. Bernie Sanders on Friday reiterated his call
                       for the Biden administration to prohibit all union-
                       busting corporations from receiving federal
                       contracts, citing the National Labor Relations
                       Board’s fresh complaints against Starbucks and
                       Amazon over their attempts to crush worker
                       organizing.


                       “This is what oligarchy and corporate greed are all
                       about,” Sanders, the chair of the Senate Budget
                       Committee, tweeted Friday. “Two large and
                       profitable corporations, owned by billionaires,
                       spend millions to illegally deny their workers the
                       right to organize. No corporation that breaks the
                       law should get a federal contract.”


                # ⚓ Common Dreams ☛ Workers_Say_NLRB_Complaint_“Fully_Unmasks
                  Starbucks’_Facade_as_a_Progressive_Company”⠀⇛


                       A regional director of the National Labor Relations
                       Board filed a sweeping complaint Friday alleging
                       that Starbucks violated federal law more than 200
                       times in its campaign to prevent employees in
                       Buffalo, New York from forming a union.


                       “Starbucks has been saying that no union-busting
                       ever occurred in Buffalo. Today, the NLRB sets the
                       record straight.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Common Dreams ☛ Lula_Launches_Campaign_to_Unseat_Far-Right
                  Brazilian_President_Jair_Bolsonaro⠀⇛


                       Speaking to a crowd of supporters and allies
                       gathered in São Paulo on Saturday, Luiz Inácio Lula
                       da Silva officially launched his campaign to unseat
                       far-right Brazilian President Jair Bolsonaro, whose
                       three-year tenure has accelerated the destruction
                       of the Amazon rainforest and intensified the
                       nation’s myriad human rights crises.


                       “Everything that we did is being destroyed by this
                       government,” said Lula, a globally renowned leftist
                       who served as Brazil’s president from 2003 to 2010
                       and departed office with a striking 83% approval
                       rating. Extreme poverty fell sharply during Lula’s
                       presidency, owing in large part to his
                       implementation and expansion of safety-net programs
                       that included cash transfers and unemployment
                       insurance.


                # ⚓ Craig Murray ☛ Some_Off-Beat_Points_on_Thursday’s
                  Elections⠀⇛


                       The Labour Party’s national projected vote share is
                       35%, which is the same as the Labour Party’s
                       national projected vote share in 2018 under Corbyn.
                       The “Starmer surge” is a lie, broadcast by the
                       media to perpetuate the myth that a more radical
                       Labour Party would be uniquely unelectable. Tory
                       switching to Lib Dems, Greens or sitting at home
                       helped Labour, but hardly represents Starmer
                       enthusiasm.


                # ⚓ Futurism ☛ Bill_Gates_Says_It_Was_A_Bad_Idea_To_Pal_Around
                  With_Jeffrey_Epstein⠀⇛


                       In a BBC interview released yesterday, the former
                       world’s richest man and Microsoft co-founder
                       responded to comments by ex-wife Melinda French
                       Gates. In March, she called Gates out for his
                       relationship with Epstein, a wealthy financier and
                       convicted sex offender who died while in prison in
                       2019. Gates met with Epstein multiple times in 2011
                       — after his sex crime conviction in 2008, notably —
                       and stayed late into the night at his home on at
                       least one occasion, according The Week.


                # ⚓ [Old] Suff NZ ☛ Final_Supreme_Court_ruling_clears_path_for
                  decision_on_Kim_Dotcom_extradition⠀⇛


                       A ruling by New Zealand’s highest court has cleared
                       the path for a decision to be made on whether Kim
                       Dotcom and his co-accused should be extradited to
                       the United States, marking the end of a legal
                       battle spanning nearly a decade.


                       A final decision on whether the men will be
                       extradited now sits with Justice Minister Kris
                       Faafoi.


                       But a law professor says that decision can be
                       contested in the courts, and it may be several more
                       years before an outcome is known


                # ⚓ [Old] New Zealand Herald ☛ Empathy_‘critical’_to_role,_says
                  retiring_Supreme_Court_judge⠀⇛


                       The judges don’t always agree either.


                       “There are quite a lot of 3-2 decisions. We try to
                       agree if we can, we try to iron out differences
                       that aren’t consequential and come up, if possible,
                       with a text that we can all sign off on.”


                       Some of the cases he has sat on include Kim
                       Dotcom’s extradition, the ban on prisoners’ right
                       to vote, and an attempt by Kawerau siege shooter
                       Rhys Warren to have his conviction overturned on
                       the basis of Māori sovereignty.


                # ⚓ New Zealand Herald ☛ Kim_Dotcom_set_to_father_sixth_child,
                  first_with_new_wife_Liz⠀⇛


                       Kim Dotcom married Elizabeth Donnelly on January
                       20, 2018 – the anniversary date of the raid during
                       which he was arrested in 2012.


                       The arrests were on behalf of the FBI, which was
                       carrying out a worldwide operation targeting
                       Megaupload. At the time, activity on the site
                       comprised 4 per cent of the globe’s [Internet]
                       traffic.


                       Even though Dotcom was facing claims of criminal
                       copyright violation – something later found to not
                       be a crime in New Zealand – the police used the
                       heavily-armed anti-terrorist Special Tactics Group
                       in a helicopter assault on his Coatesville mansion.


                # ⚓ [Old] Business Insider ☛ New_Footage_Shows_Just_How_Crazy
                  The_Kim_Dotcom_Raid_Was⠀⇛


                       New footage has come out of the raid on Kim’s home,
                       which was conducted in January under warrants that
                       have since been ruled illegal. The scale of the
                       raid is pretty remarkable, with two helicopters,
                       four police vehicles, police dogs and officers
                       armed with semi-automatic Colt Commando 5.56 guns.
                       Kim alleges that he was assaulted during the raid,
                       though officers deny it.


                # ⚓ [Old] New Zealand Herald ☛ Dotcom_wins_settlement_from
                  police_over_the_2012_dawn_raid_which_saw_him_arrested⠀⇛


                       The settlement came after a damages claim was filed
                       with the High Court over what was considered an
                       “unreasonable” use of force when the anti-terrorism
                       Special Tactics Group raided his $30 million
                       mansion in January 2012.


                       The raid was part of a worldwide FBI operation to
                       take down Dotcom’s Megaupload file-sharing website
                       which was claimed to be at the centre of a massive
                       criminal copyright operation.


                # ⚓ Variety ☛ Social_Media_Slowdown_Tests_Investors’_Loyalty⠀⇛


                       But now things are shifting. Usage on social media
                       platforms hasn’t necessarily slowed over time, but
                       other factors such as supply-chain disruptions,
                       conflict in Ukraine, inflation and higher interest
                       rates are causing reduced advertising budgets and
                       spending.


                       In the near term, these issues appear to be far
                       from abating, which means a harder operating
                       environment for the companies that rely so heavily
                       on advertising to fuel their top line. Investors
                       also seemed to realize that putting their money in
                       Twitter, Snap and Meta doesn’t yield the sky-high
                       returns they once did.


                # ⚓ The Wall Street Journal ☛ Facebook_Deliberately_Caused
                  Havoc_in_Australia_to_Influence_New_Law,_Whistleblowers_Say⠀⇛


                       The goal, according to the whistleblowers and
                       documents, was to exert maximum negotiating
                       leverage over the Australian Parliament, which was
                       voting on the first law in the world that would
                       require platforms such as Google and Facebook to
                       pay news outlets for content.


                       Despite saying it was targeting only news outlets,
                       the company deployed an algorithm for deciding what
                       pages to take down that it knew was certain to
                       affect more than publishers, according to the
                       documents and people familiar with the matter.


          o § Misinformation/Disinformation⠀➾


                # ⚓ NPR ☛ 7_persistent_claims_about_abortion,_fact-checked⠀⇛


                       Below, seven popular claims surrounding abortion
                       get fact-checked.


          o § Censorship/Free Speech⠀➾


                # ⚓ TruthOut ☛ ADL_CEO_Misrepresents_Report_on_Antisemitism_to
                  Attack_Palestinian_Groups⠀⇛


                # ⚓ NPR ☛ Opinion:_For_comedians,_safety_is_a_growing_concern⠀⇛


                       Comedy can often challenge our views, or cement
                       them. Jokes can make us grimace and squirm as we
                       laugh…or don’t. These days, anyone who objects to a
                       routine can tweet a response, put a little scowling
                       face on Facebook or post a 5000-word essay on
                       Medium.


                       People in an audience can boo. Or just walk out,
                       without committing assault.


                # ⚓ CBC ☛ ‘Fake_news’_law_forced_many_Russian_journalists
                  abroad._Those_who_remain_must_weigh_truth_against_safety⠀⇛


                       For most of March, the Friday edition of Novaya
                       Gazeta, which until it suspended operation last
                       week, was one of Russia’s last remaining
                       independent news outlets still based within the
                       country, featured a blank two-page spread.


                       There was no text; no pictures; just an
                       explanation.


                       Because the paper wasn’t allowed to publish
                       anything about what is currently happening in
                       Ukraine other than the Russian government’s
                       official version, Novaya Gazeta would rather not
                       publish anything at all, the explanation read.


                # ⚓ The_real_cost_of_[Internet]_shutdowns_in_South_Asia⠀⇛


                       The World Wide Web turned 33 last month, so I spent
                       some time reading the arguments in favor of
                       declaring the [Internet] a basic human right. The
                       ideas seem fantastical to me, sitting in South
                       Asia, where the internet increasingly feels like
                       the personal estate of governments that decide to
                       shut off access whenever it suits them.


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


                # ⚓ Why_has_Julian_Assange_lost_in_the_High_Court,_where_Lauri
                  Love_won,_and_what_could_this_mean_for_Journalism?⠀⇛


                       This article is not about Julian Assange as a
                       person, nor about his political or social
                       attitudes, nor previous criminal allegations.
                       Rather this article is about the consequences of US
                       imperialism and the future of any journalism that
                       intends to hold the decreasingly hegemonic
                       superpower of the United States to account for
                       crimes so vast that one can scarcely keep track of
                       even just those that it has not managed to conceal.


          o § Civil Rights/Policing⠀➾


                # ⚓ TruthOut ☛ Overturning_“Roe”_Would_Immediately_Activate
                  Abortion_Penalties_in_13_States⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_For_My_Body_and_the_Choice_of
                  Millions,_I’m_Going_to_Fight_Like_Hell⠀⇛


                       The personal, as they say, is political. And
                       there’s nothing more personal than the right to
                       control your own body.


                # ⚓ Common Dreams ☛ Opinion_|_The_Right-Wing_Supreme_Court_Is
                  About_to_Unleash_Hardship,_Suffering,_and_Chaos_for
                  Millions⠀⇛


                       The draft opinion in Dobbs v. Jackson Women’s
                       Health Organization infamously decides that
                       pregnant females’ 49-year-old right to obtain an
                       abortion no longer will be constitutionally
                       protected. Writing for the five-justice majority,
                       Justice Samuel Alito offers two reasons for this
                       conclusion: The Constitution does not explicitly
                       protect the right to abortion, and the right to
                       obtain an abortion is neither “deeply rooted in
                       [our] history and tradition” nor “essential to our
                       Nation’s ‘scheme of ordered liberty.’”   


                # ⚓ The Telegraph UK ☛ Taliban_order_women_to_wear_full_veil_as
                  they_reintroduce_burqa_mandate⠀⇛


                       Mariam Solaimankhil, a member of parliament under
                       the ousted Afghan republic, said: “If you ever
                       believed that the Taliban have changed, you’re an
                       idiot.”


                # ⚓ RTE ☛ Taliban_orders_all_Afghan_women_to_wear_burqa⠀⇛


                       “We have been verbally instructed to stop issuing
                       licences to women drivers … but not directed to
                       stop women from driving in the city,” said Jan Agha
                       Achakzai, the head of Herat’s Traffic Management
                       Institute that oversees driving schools.


                # ⚓ Saudi Arabia ☛ Taliban_leader_orders_women_to_wear_all-
                  covering_burqa_in_public:_Decree⠀⇛


                       “Those women who are not too old or young must
                       cover their face, except the eyes, as per sharia
                       directives, in order to avoid provocation when
                       meeting men who are not mahram (adult close male
                       relatives),” the decree said.


                       It added that if women had no important work
                       outside it was “better they stay at home.”


                       During their first regime between 1996 and 2001,
                       the Taliban imposed similar restrictions on women.


                # ⚓ France24 ☛ Taliban_chief_orders_all_Afghan_women_to_wear
                  burqa_in_public⠀⇛


                       Akhundzada’s decree also said that if women had no
                       important work outside it was “better they stay at
                       home”.


                # ⚓ RFERL ☛ Afghanistan’s_Taliban_Orders_Women_To_Wear_Burqa
                  Coverings_In_Public⠀⇛


                       Failure to comply will result in a woman’s father
                       or closest male relative being reprimanded, or
                       imprisoned, or fired from government jobs, the
                       decree said.


                # ⚓ ABC ☛ Afghanistan’s_Taliban_order_women_to_cover_up_head_to
                  toe⠀⇛


                       The decree, which calls for women to only show
                       their eyes and recommends they wear the head-to-toe
                       burqa, evoked similar restrictions on women during
                       the Taliban’s previous rule between 1996 and 2001.


                # ⚓ UPI ☛ Taliban_require_women_to_wear_burqa_in_new_decree⠀⇛


                       The Taliban on Saturday ordered that all Afghan
                       women must wear a full-body covering, including the
                       face, a return to restrictions first implemented in
                       the 1990s.


                # ⚓ New York Times ☛ Labor_regulators_find_merit_in_accusations
                  by_unions_at_Amazon_and_Starbucks.⠀⇛


                       In a sign that federal labor officials are closely
                       scrutinizing management behavior during union
                       campaigns, the National Labor Relations Board said
                       Friday that it had found merit in accusations that
                       Amazon and Starbucks had violated labor law.


                # ⚓ New York Times ☛ Amazon_Abruptly_Fires_Senior_Managers_Tied
                  to_Unionized_Warehouse⠀⇛


                       The firings, which occurred outside the company’s
                       typical employee review cycle, were seen by the
                       managers and other people who work at the facility
                       as a response to the victory by the Amazon Labor
                       Union, three of the people said. Workers at the
                       warehouse voted by a wide margin to form the first
                       union at the company in the United States, in one
                       of the biggest victories for organized labor in at
                       least a generation.


                # ⚓ NPR ☛ Daunte_Wright’s_mother_was_detained_after_recording_a
                  traffic_stop⠀⇛


                       The officer then pulled her out of her vehicle,
                       took her phone and placed it on the roof of her car
                       before leading her toward a grassy median while
                       holding her arm behind her back. Wright said the
                       officer grabbed her so forcefully that he injured
                       her wrist.


                       Wright told him her name and said “you guys killed
                       my son. I’m going to videotape them,” gesturing to
                       the other officers. The officer told Wright he
                       would send her a ticket in the mail and both
                       returned to their vehicles.


                # ⚓ ABC ☛ Canadian_prisoner_attacked_by_convicted_terrorist_now
                  in_legal_fight_with_Victorian_government⠀⇛


                       Shoma, now 29, was remarkably frank and told
                       investigators that she had been hoping to spark
                       international headlines by attacking Mitz, who was
                       a Canadian citizen.


                       She cheered when they charged her with terror
                       offences, and told them that Allah would be pleased
                       with her.


                       How Shoma came to arm herself with the gardening
                       shears and stab her victim in a low-security unit
                       is the crux of a new lawsuit launched in the County
                       Court of Victoria by Mitz, who is suing the state
                       for unspecified damages.


                # ⚓ Christian Post ☛ Sudanese_couple_face_flogging_for
                  ‘adultery’_after_court_nullifies_marriage_over_Christian
                  conversion⠀⇛


                       Shukralah’s family filed a case in a sharia court,
                       which dissolved their marriage, as apostasy was a
                       crime punishable by death at the time, it
                       explained.


                       In 2021, Shukralah also converted to Christianity
                       and returned with their two children to her
                       husband, as Sudan had decriminalized apostasy a
                       year after the end of President Omar al-Bashir’s
                       Islamist regime. Both are members of a Baptist
                       church.


                       However, socially, conversion was still not
                       accepted.


                       Shukralah’s brother charged them with adultery
                       under Article 146 of Sudan’s 1991 criminal law
                       based on the Sharia court’s annulment of their
                       marriage, leading to the couple’s arrest last
                       August.


                # ⚓ Morning Star News ☛ Christian_Couple_in_Sudan_Faces
                  Possible_Flogging_for_‘Adultery’⠀⇛


                       He said the couple, members of a Baptist church,
                       are facing growing threats from hardline Muslims,
                       in particular Shukralah’s brother.


                       In the case of adultery by an unmarried person,
                       Article 146 calls for a sentence of flogging and
                       expulsion from the area. If the convicted is
                       married, adultery is punishable by death by stoning
                       under Article 146.


                       Flogging violates the absolute prohibition against
                       torture and other ill treatment in international
                       human rights law, according to Amnesty
                       International.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Wi-Fi_May_Be_Coming_Soon_to_a_Lamppost_Near_You⠀⇛


                       As Wi-Fi is deployed more widely in cities, and
                       perhaps at higher frequencies, it may depend on an
                       abundant urban asset: streetlight poles.


                       To help ensure these networks work well,
                       researchers at the National Institute of Standards
                       and Technology (NIST) developed and verified a
                       novel model that will help wireless communications
                       providers analyze how high to attach Wi-Fi
                       equipment to light poles.


                       In general, the NIST team found that the optimal
                       height depends on transmission frequency and
                       antenna design. Attaching equipment at lower
                       heights of around 4 meters is better for
                       traditional wireless systems with omnidirectional
                       antennas, whereas higher locations 6 or 9 meters up
                       are better for the latest systems such as 5G using
                       higher, millimeter-wave frequencies and narrow-beam
                       antennas.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ The Verge ☛ An_Xbox_outage_is_preventing_some_players_from
                  launching_digital_titles⠀⇛


                       Although Xbox seemed to resolve these problems, it
                       looks like issues with its store, digital titles,
                       and Cloud Gaming have started to resurface. As my
                       colleague Tom Warren notes, if you’re affected by
                       the outage, you should still be able to play games
                       offline when you have your Xbox set as your “home”
                       console. Xbox Support also says rebooting your Xbox
                       console might help.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ FOSS_Patents:_Ericsson_says_Apple_‘walk[ed]_back_its
                        agreement_to_accept_Ericsson’s_[5G_patent_licensing]
                        offer_if_it_is_confirmed_as_FRAND’_by_Texas_court⠀⇛


                             If both Ericsson and Apple are sincere in
                             this regard, the United States District Court
                             for the Eastern District of Texas–whose Chief
                             Judge Rodney S. Gilstrap decided on the
                             structure of the dispute and the schedule two
                             weeks ago–may become the center of gravity of
                             their patent dispute. While no single court
                             anywhere in the world is going to set a
                             license fee for non-standard-essential
                             patents, it would put the parties much closer
                             to an agreement if the terms on which Apple
                             licenses Ericsson’s SEPs (up to 5G) were set.
                             It’s hard to imagine they couldn’t then
                             easily agree on the rest. A complete
                             agreement on SEPs and non-SEPs would result
                             in the dismissal of roughly three dozen
                             lawsuits in at least half a dozen countries.


                             That’s a big If, though. Not with respect to
                             Ericsson, which says that $5 per device (with
                             Apple probably having missed out on the
                             opportunity to get a $1 per-unit early-
                             signing bonus) is a fair, reasonable, and
                             non-discriminatory (FRAND) rate. The Swedish
                             company undoubtedly wants to conclude a
                             license agreement as soon as that one–a rate
                             it publicized a while ago–has been blessed by
                             the Texas court. What’s unclear here is
                             Apple’s agenda.


                      # § Software Patents⠀➾


                            # ⚓ $2,000_for_Fare_Technologies_prior_art⠀⇛


                                   On May 3, 2022, Unified Patents added a
                                   new PATROLL contest, with a $2,000 cash
                                   prize, seeking prior art on at least
                                   claim 1 of U.S. Patent RE46727, owned
                                   by Fare Technologies, LLC, an NPE. The
                                   ’727 patent generally relates to a taxi
                                   trip meter system that includes a
                                   taximeter and a location sensor
                                   connected to a computer loaded with
                                   street information and driver
                                   evaluation software. It has been
                                   asserted against Lyft and Uber.


                            # ⚓ $2,000_for_prior_art_on_Equitable_IP_entity,
                              Route_Guidance_System_patent⠀⇛


                                   On May 6, 2022, Unified Patents added a
                                   new PATROLL contest, with a $2,000 cash
                                   prize, seeking prior art on at least
                                   claim 1 of U.S. Patent 6,917,876, owned
                                   by Route Guidance Systems, an NPE and
                                   Equitable IP entity. The ’876 patent
                                   relates to a route guidance system for
                                   vehicles. The patent has been asserted
                                   against several companies such as
                                   Honda, Verizon, Salesforce, Grubhub,
                                   and DoorDash.


                            # ⚓ $2,000_for_prior_art_on_IP_Edge_entity,
                              Moxchange_—_Unified_Patents⠀⇛


                                   On May 6, 2022, Unified Patents added a
                                   new PATROLL contest, with a $2,000 cash
                                   prize, seeking prior art on at least
                                   claim 1 of U.S. Patent 7,233,664, owned
                                   by Moxchange LLC, an NPE and IP Edge
                                   entity. The ’664 patent relates to a
                                   dynamic computer system security method
                                   using dynamic encryption and full
                                   synchronization between system nodes
                                   for wireless communication. This patent
                                   has been asserted against companies
                                   like Resideo, ADT, Panasonic, and
                                   Western Digital.


                            # ⚓ Lexology ☛ Part_II_–_Strategies_in_Response_to
                              Non-Obviousness_Requirements_for_Mechanical_and
                              Software_Patents_in_the_United_States,_China,
                              Europe_and_Taiwan [Ed: This crazy world where you
                              can carve yourself a monopoly on maths]⠀⇛


                            # ⚓ Lexology ☛ New_Patent_Examination_Guidelines
                              for_Computer_Software-Related_Inventions [Ed:
                              Taiwan's litigation lobby hobbling and curtailing
                              the country's own industry]⠀⇛


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ IPTV_Pirate_Agrees_to_Pay_Well_Over
                        Half_a_Billion_Dollars_in_Damages⠀⇛


                             Large-scale pirate IPTV operations can
                             generate significant profits but with that
                             comes the chance of significant liability
                             should things go bad. A man from Canada who
                             operated and sold pirate IPTV services is
                             finding just how bad things can get. In
                             response to a lawsuit, he’s asking a US court
                             to find him liable for $585 million in
                             damages. He’ll pay his own legal bills but
                             not those of the plaintiff.


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