𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, May 12, 2021
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Generated Thu 13 May 02:40:21 BST 2021
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/2021/05/12/


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

⦿ Personal Thoughts About the EPO ’Kangaroo Court’ Scandal | Techrights

⦿ The European Campinos Award | Techrights

⦿ The EPO’s War on Justice and Assault on the Law  -  Part 2: Just Another Pro Forma Rubber-Stamping Exercise? | Techrights

⦿ IBM is Destroying Red Hat, Squeezing Red Hat’s Work for Cash, Laying Off Staff, and Asking Staff to Resign | Techrights

⦿ [Meme] Longing for the Original IP Kat... | Techrights

⦿ IRC Proceedings: Tuesday, May 11, 2021 | Techrights

⦿ The EPO’s War on Justice and Assault on the Law  -  Part 1: Rumours of a Kangaroo Court at EPOnia | Techrights

⦿ Why I’m Using Just a Landline and Recalling My Richard Stallman (RMS) Interview on Working Locally or How the Signal Processor in Phones is a De Facto Back Door | Techrights

⦿ Doing Justice by Reporting Injustice | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/05/12/attacks-on-justice-itself/#comments
		http://techrights.org/2021/05/12/campinos-award/#comments
		http://techrights.org/2021/05/12/epo-pro-forma-rubber-stamping/#comments
		http://techrights.org/2021/05/12/ibm-squeezing-red-hat/#comments
		http://techrights.org/2021/05/12/ip-kat-memes/#comments
		http://techrights.org/2021/05/12/irc-log-110521/#comments
		http://techrights.org/2021/05/12/kangaroo-court-at-eponia/#comments
		http://techrights.org/2021/05/12/mobile-phones-or-cellphones-issues/#comments
		http://techrights.org/2021/05/12/reporting-injustice/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/05/12/jedi-risk/#comments
		http://techrights.org/2021/05/12/mousepad-0-5-5/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 72

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/attacks-on-justice-itself/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/attacks-on-justice-itself/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Personal_Thoughts_About_the_EPO_‘Kangaroo_Court’_Scandal⠀✐


Posted in Europe, Patents at 5:38 am by Dr. Roy Schestowitz


Video_download_link


http://techrights.org/videos/epo-lawless-boa.webm


Summary: Some unscripted and unedited thoughts about the current EPO scandal/
series, which shows intervention such as stacking by António_Campinos,
continuing the tradition of Benoît_Battistelli with his attacks on justice
itself


THE VIDEO above is just a quick and offbeat interjection. I’ll likely do these
every now and then when wishing to express an opinion (as in personal view)
about the current series, which will run until late May.


“Part 2 of the series will be published this evening.”As a side note, I wasn’t
able to focus on this video. I regret this deeply. About 3 minutes into the
video one can hear the music in the background, which could not be removed by
NoiseTorch though it came from a separate (very different) room and was
extremely distracting to me. It was very loud, but NoiseTorch did a good job
‘torching’ most of it. My wife wasn’t aware I was recording. I never redo
videos, except in very unusual circumstances, so I kept on recording
regardless. It seems like the talk is audience anyway. That’s what’s important.
Part 2 of the series will be published this evening. Maybe then we can produce
another (and much better) video. There’s so much left to be said… █


Related/contextual items (in order of appearance in the video above):


   1. Doing_Justice_by_Reporting_Injustice
   2. The_EPO’s_War_on_Justice_and_Assault_on_the_Law_—_Part_1:_Rumours_of_a
      Kangaroo_Court_at_EPOnia
   3. EPO_and_Microsoft_Collude_to_Break_the_Law_—_Summing_Up:_EPO
      Administrative_Council_Still_Asleep_at_the_Wheel

                    ䷩ 𝚕𝚒𝚗𝚎 126

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/campinos-award/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/campinos-award/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ The_European_Campinos_Award⠀✐


Posted in Europe, Patents at 6:41 am by Dr. Roy Schestowitz


                    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I'm from Portugal!⦈
                          He’s from Portugal, honest!


Summary: The campinos (peasants) of Europe shall gather around for another
ceremony championing farmers and nurses… or not


TYRANNOSAURUS Theranos


Open your thesaurus
Prepare the abacus
Don’t be quite so raucous


Professor Campinos in a tux
The media he has paid $15 million bucks
Because investigative journalism sucks
Corruption evidence filling up trucks


Patents are inventions
Those were the intentions
Of those who live in mansions
Societal_aberrations


Inventions are patent monopolies
For those who govern the metropolis
Patents on tomatoes and broccolis
Invented by humans like syphilis


“The media shall be bombarded in May”Everything deemed a patent
For those without a talent


Trolling as a “right”
Creators the trolls must fight
Eternally eager to bite
Even just for spite


A ceremony at stakeholders’ expense
To cover up the mess
Just a bunch of webstreams or less
Can receive an award naked, without a dress


“European” it’s called
But recipients are walled
US tech giants mulled
European programmers appalled


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇António Campinos said what?!?!⦈ Diversity championed aplenty
French,_French,_English,_French_presidents all about identity
Blind obedience for legal certainty
Certainty they will shield their immunity


Striking staff escorted away
The camerapeople are here today
Dissent is not OK
The media shall_be_bombarded_in_May █


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⡣⡆⠀⠀⠒⠃⠀⣿⣿⣿⣿⣿⢛⣛⣛⡻⢟⣻⣟⡻⢛⣛⣛⡛⣛⣛⣛⡛⣛⡛⣛⡛⢟⣯⣟⡻⢟⣛⣛⠻⣛⣛⡿⣛⡛⣿⣿⣿⣿⣿⠄⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠙⠉⠉⠻⣟⣅⣀⠄⠀⠀⠀⢹⣿⣿⣿⣿⢸⣿⢹⣿⣾⣿⢹⣷⢸⣿⣹⣿⡉⣿⡏⡅⣿⡇⣿⡇⣿⡏⠿⠇⢸⣿⣿⡆⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠉⠉⠀⠀⢀⢠⣾⣿⣿⣿⣷⠀⠀⠀⠈⣿⣿⣿⣿⢸⣿⢛⣅⣿⣿⢸⣿⢸⣿⢹⣷⠁⣿⡇⡇⣿⡇⣿⡇⣿⡇⣿⡇⣸⣧⣿⡇⣿⡿⠷⢿⡇⣿⣿⣿⣿⠏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡷⢒⠀⠀⠁⠀⢸⣿⣿⣏⠉⠉⠀⢄⠀⠀⠈⢿⣿⣿⣘⣻⣸⣿⣜⡿⢿⣣⣘⣻⣘⣻⣤⣛⣃⣷⣛⠷⢟⣣⣝⠷⣛⣃⣛⣃⣙⣛⣛⣛⣃⣛⣃⣿⣿⣿⠋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⠁⠀⢀⣀⣤⣤⣿⣿⠟⠋⠀⠀⠀⠀⠀⠠⠄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠊⠀⠀⠀⠀⠀⢀⣠⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣥⣦⣼⣿⣾⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠙⠻⢿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⡀⠀⠿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣦⡀⠀⠀⠀⠀⠀⠀⠀⣇⠐⠁⠀⠀⠀⠀⠀⣠⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣄⠈⠙⠷⠀⠠⣤⣤⣤⣬⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠰⠀⠀⠂⠄⠠⠆⠀⠀⠀⢀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⡙⣻⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⢿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣿⡇⢀⣶⣬⣿⣿⡿⢿⡏⣿⣿⣿⠹⣿⣿⡟⢹⣿⣿⢹⣿⣿⢹⠋⢿⣿⣿⣿⣧⢹⡟⢙⣿⣿⠉⣿
⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣤⣿⣿⣿⡇⠐⣿⣿⣿⣿⠇⢾⣿⣿⣿⣿⢇⢾⠇⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⠈⣿⣿⡿⣤⡀⢹⣿⣹⡃⣸⡇⢸⣿⠇⡇⠿
⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠃⠀⣿⡿⠛⠁⠀⠀⠻⣟⢿⣫⠋⠀⠀⣿⣿⣿⠀⢸⣿⠁⢸⣿⡟⠀⣿⡇⡇⠋⠁⠈⢏⣻⠉⣸⡇⠀⣿⠀⡇⠘
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠁⠀⠀⠀⠀⠀⠹⡧⢢⠀⠂⠀⣿⣿⣏⣼⣾⣿⠀⠈⣿⡇⠀⠿⠇⠀⠀⣧⣄⠀⣙⡄⠀⠀⠀⠙⠰⣷⠀
⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⢀⡀⠀⢿⣿⢻⣿⠏⢸⠀⢠⣾⠃⠀⠀⠀⠀⠀⢿⣿⢛⣾⣧⠀⠀⠀⠀⠀⢹⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⡇⠀⢸⣿⡿⠀⠀⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣿⠀⠀⠀⠀⠀⠸⠀
⣿⠋⠃⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠏⠀⢠⣆⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠠⡆⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣆⠀⣀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢧⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣀⣤⣼⣶⣶⣶⣶⣶⣿⣿⡆⢸⣿⣄⣴⣤⣤⣶⠀⠀⠀⠀⠸⡏⠀⠀⢡⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⣤⡦⠛⣀⠶⠻⣷⣴⡄⠛⢸⠀⠀⣸⣿⠿⢿⣿⣶⣄⣀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣷⣀⣤⣤⣿⣶⣶⣿⡇⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣅⠀⠈⠙⠻⠿⣿⣶⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⢛⣉⣩⣭⣥⣤⣤⣤⣤⣤⣤⣌⣛⣻⣿⣿⣿⣿⣶⣄⡀⠀⠀⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠶⠦⢤⣈⡉⠛⠿⣿⣿⣿⣿⣦⡀⠀
⣿⢿⣿⣿⣿⣿⣶⣦⠀⠀⠀⣚⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⡉⠻⢿⣿⣿⣄
⠈⠀⠙⠛⠛⢿⣿⡏⠀⠀⢠⡅⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡙⢿⣿
⢀⣴⣦⠀⠀⠀⠘⠁⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣻
⣾⣿⣿⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣇⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣋⠉⠁⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠷⣾⣿⠿⠋⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⣰⣿⣿⡟⣵⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⠿⠀⠈⠉⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠰⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⣿⣿⡟⢰⡿⠟⠁⠀⠀⠀⠀⠀⠀⢠⠟⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⢻⡟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⠋⠒⠛⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀
⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⡄⣀⡀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀
⠻⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⣤⡄⣤⣤⣤⣼⣽⣯⣠⣿⣯⣄⣤⣤⡀⣤⡄⣤⣄⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢸⣷⡄⠀⠀⠀
⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⣿⠉⣿⣿⠉⣿⣿⣿⣿⢸⣿⣧⣿⡇⣿⡇⣿⣿⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⡋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⡇⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣷⠀⣠⡀⠀⣿⣿⡆⠀⠀
⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠿⠧⠿⠏⠿⠿⠀⠿⠿⠀⠻⣿⣿⣿⡸⠿⠸⠿⠇⠿⠇⠹⢿⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠘⢿⣾⣿⠃⢠⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⡀⢀⣀⣀⢀⣀⡀⣀⣘⣿⣿⣟⣀⢀⣀⡀⣀⡀⢀⣀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣶⣾⣿⣿⡯⠻⣦
⠀⠐⠀⠀⠀⠀⣰⠁⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⣷⢸⣿⣿⡇⢸⣿⣿⣾⣿⡇⣿⣿⢻⣿⢹⣿⢸⣿⣧⣿⡇⣿⣿⣿⣿⢸⣿⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⠿⠿⠿⠋⠀⠀⠁
⠀⠀⠀⠀⠠⠾⠚⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠐⣿⡇⣉⣉⣼⣿⣿⣷⢸⣿⣿⣿⣿⡇⣿⣿⠿⠟⢸⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⢈⣻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⣿⣧⣿⡟⣿⣿⢻⣿⣸⣿⢻⡿⣿⡇⣿⣿⠀⠀⢸⣿⢸⣿⢸⣿⡇⢿⣿⣿⡿⢸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠸⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⢀
⡄⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣰⣿⢿⣷⠀⣿⣿⣷⢸⣿⡇⣿⣿⢿⣷⠀⠘⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡇⢸⣿⣿⡇⠿⣿⣿⠿⣼⣿⣿⣷⢸⣿⢰⣿⣿⣿⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡉
⠃⣴⣦⣄⠙⠻⠿⠇⠀⠀⠀⠀⠸⢿⣷⣦⢰⣿⣿⣿⣸⣿⡇⣿⣿⢸⣿⠀⠀⣿⣷⣿⣿⣾⣿⢹⣿⣿⣿⡇⣾⣿⣿⣧⠀⣿⣿⠀⣭⣭⣿⣿⢸⣿⢨⣭⣽⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠛⠛⠂⠀⠀⠘⢿⠶⠀⠀⢸⣿⣹⣿⣿⣿⢿⣿⣿⣿⡇⣿⣿⣼⣿⠀⠀⢻⣿⣿⢿⣿⣿⢸⣿⡇⣿⡇⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⠛⠉⢸⣿⢸⣿⡟⠋⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠉⠈⠉⠉⠉⠁⠉⠉⠉⠉⠀⠀⠈⠉⣉⣬⣭⣭⣬⣭⣅⠉⠉⠉⠉⠉⠉⠀⠉⠉⠀⠉⠉⠀⠀⠈⠉⠈⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣻⣿⢿⣿⣿⣿⣿⣿⣷⣴⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣾⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠻⠻⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⢻⣿⣿⣿⣿⣿⣿⣟⡙⠛⠻⢅⡋⠋⠁⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 285

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/epo-pro-forma-rubber-stamping/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/epo-pro-forma-rubber-stamping/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ The_EPO’s_War_on_Justice_and_Assault_on_the_Law_—_Part_2:_Just_Another_Pro
Forma_Rubber-Stamping_Exercise?⠀✐


Posted in Courtroom, Europe, Law, Patents at 11:38 am by Dr. Roy Schestowitz


Previously in this series:


    * The_EPO’s_War_on_Justice_and_Assault_on_the_Law_—_Part_1:_Rumours_of_a
      Kangaroo_Court_at_EPOnia
    * You are here ☞ Just Another Pro Forma Rubber-Stamping Exercise?
                   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇The kangaroo judges⦈
    G 1/21 is likely to be just another pro forma rubber-stamping exercise.


Summary: Half a decade after Benoît_Battistelli ‘kidnapped’ and then defamed
judges (it started in 2014) António_Campinos has done nothing to restore
lawfulness at the EPO, as controversial referral case G 1/21 shows; in fact,
they recently approved European_software_patents after pressure from Campinos
himself


This time the story is connected to the “new normal” at the EPO and plans of
the management to impose oral proceedings by videoconference, in particular in
circumstances where the parties don’t consent to the use of such a procedure.


The case is G_1/21 (warning: epo.org link) and the crucial referral question
reads as follows:


     “Is the conduct of oral proceedings in the form of a videoconference
     compatible with the right to oral proceedings as enshrined in Article
     116(1) EPC if not all of the parties to the proceedings have given
     their consent to the conduct of oral proceedings in the form of a
     videoconference?”


Back in February of this year, IPKat began reporting on the case under the
headline


“BREAKING:_The_legality_of_Board_of_Appeal_oral_proceedings_by_video_conference
has_been_referred_to_the_EBA”.


This was followed up by two further posts in March:


“BREAKING:_Board_of_Appeal_in_T1807/15_continues_with_ViCo_oral_proceedings
referral”; and


“Chairman_and_Enlarged_Board_criticised_for_lack_of_impartiality_in_ViCo_oral
proceedings_referral_(G1/21)”.


It seemed like the blog was finally starting to show signs of awakening from
its Kat-atonic torpor and recovering some of its long-lost critical faculties
vis-à-vis the already deeply entrenched and ongoing erosion of the rule of law
at the EPO.


“Even the normally censorious Rose from AstraZeneca has been allowing EPO-
critical comments to filter through.”In particular, IPKat recognised that the
“hasty scheduling of the oral proceedings with limited time for third parties
to comment, and (…) the potential conflicts of the appointed members of the
Enlarged Board” had given rise to a significant amount of legitimate public
criticism.


Even the normally censorious Rose from AstraZeneca has been allowing EPO-
critical comments to filter through.


Much of the criticism in the comments following the articles has been directed
at Carl Josefsson.


“It should be noted that the decision adopted by the EBA in such a case is a
final decision which is not subject to review by any further instance.”In his
capacity as President of the Boards of Appeal, Josefsson was directly involved
in the introduction of the disputed amendments to the Rules of Procedure. His
involvement in the amendment procedure is foreseen under Rule_12c(2)_EPC
(warning: epo.org link).


It seems that Josefsson is now insisting on playing a key role as Chairman of
the Enlarged Board in deciding whether or not the amendments which he himself
proposed are compatible with the European Patent Convention.


It should be noted that the decision adopted by the EBA in such a case is a
final decision which is not subject to review by any further instance.


As things stand, the procedure in G 1/21 is unlikely to be anything more than
another pro forma rubber-stamping exercise.


“But even if the outcome seems like a foregone conclusion at this stage, the
case has generated a significant amount of public interest and controversy and
will, in all likelihood, continue to do so in the lead-up to the hearing
scheduled to take place on 28 May.”The only useful purpose which it is likely
to serve is to provide a further “exhibit” in the mounting pile of evidence of
a serious erosion of the rule of law at the EPO and a failure by the
organisation’s main judicial body to comply with even the most elementary
standards of judicial independence and procedural fairness.


But even if the outcome seems like a foregone conclusion at this stage, the
case has generated a significant amount of public interest and controversy and
will, in all likelihood, continue to do so in the lead-up to the hearing
scheduled to take place on 28 May.


In the next part we will present the composition of the judicial panel
entrusted with deciding the controversial referral case G 1/21. █


⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⢸⡇⣿⣿⣿⣸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⣿⣿⣿⢸⠀⣿⡇
⡆⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⢸⡇⣿⣿⣿⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢸⣿⣿⣿⡇⣿⠀⣿⣿⣿⢸⠀⣿⣷
⡇⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⠀⣿⣿⣿⢸⠀⢻⡟
⡇⢸⣿⣿⣿⡇⠸⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢀⣿⣿⣿⢸⡀⠸⡇
⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠈⣿⣿⣿⢸⡇⠀⡇
⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢠⣿⣿⣿⢸⡇⢸⣿
⠁⣸⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢸⣿⣿⣿⣸⡇⢸⡏
⠀⢻⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⡇⣿⡿⠿⠛⢹⣿⣿⠋⠙⠿⡟⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⢿⣿⣿⣿⣿⣿⢻⣿⡿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⢸⣿⣿⣿⣿⡇⢠⡇
⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⡏⠇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⠛⠉⠀⠈⢿⡿⠃⠀⠉⠙⣿⣿⣿⡇⣿⠸⣿⣿⣿⣿⡇⢸⣿
⠀⢸⣿⣿⣿⣧⠀⣿⣿⣿⣿⢸⡇⠀⡀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠈⣿⣿⡿⠛⠉⠈⣿⣿⡏⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡗⠟⣿⣿⣿⠛⢿⣿⢸⣿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⡇⠈⣿
⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣸⣷⣾⠃⠀⠀⠀⠀⠀⠈⢿⣷⣄⣴⣿⡿⠁⠀⠀⠀⠈⠋⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠉⠀⠀⠙⠿⠋⠀⠀⠈⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠉⣿⣿⣿⣿⡇⠀⣿
⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢀⣤⣤⣤⣤⡄⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⡏
⠀⢸⣿⣿⣿⣿⠀⢻⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⠃⠀⠀⠀⠫⣿⣏⠄⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠐⣿⣿⣿⣿⡇⠀⡇
⠀⣸⣿⣿⣿⣿⡀⢸⡿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⢼⣌⠹⠇⠀⠀⠀⠈⣿⣿⡿⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁⠀⠈⠛⠫⣿⡇⠀⠀
⠀⣿⣿⣿⡟⠋⠁⠀⠀⠹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⢀⡌⠀⠀⣠⠀⠀⠀⢺⡇⠀⠀
⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀
⠀⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣴⣶⠶⠦⠀⠀⠀⠀⠀⠀⠀⢶⣦⣄⠀⠀⠀⠀⣀⣠⣶⡶⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⣴⣾⡐⠆⠀⠔⠀⠀⠀⢀⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⠝⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠛⠀⠀⠀⠀⠘⣟⡿⠇⠀⠀⠀⠀⢰⣿⡟⠦⠀⠀⠀⠚⢿⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⡿⠄⠀⠀⠀⠀⠰⠟⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡷⠀⠀⠛⠫⡃⠀⠀⠀⠀⠀⠀⠸⠹⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣲⠖⠀⠀⠀⣬⣵⢿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠃⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⡄⠀⣀⠐⠛⠛⠻⠀⠀⠈⠁⠀⠧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢸⠃⠀⢠⠀⠀⠀⣀⣀⣀⣤⣴⢀⣴⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⣀⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⣀⣀⣡⡀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠃⠀⠀⣀⣼⠀⠼⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠤⠀⠀
⣿⣯⣅⡀⠀⢀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣭⣴⣿⣿⣧⣉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⣠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣆⣄⣴⣶⣾⣶⣦⣤⣤⣤⣄⣐⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 445

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/ibm-squeezing-red-hat/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/ibm-squeezing-red-hat/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ IBM_is_Destroying_Red_Hat,_Squeezing_Red_Hat’s_Work_for_Cash,_Laying_Off
Staff,_and_Asking_Staff_to_Resign⠀✐


Posted in Deception, IBM, Red_Hat at 2:44 pm by Dr. Roy Schestowitz


Video_download_link


http://techrights.org/videos/ibm-layoffs.webm


Summary: Layoffs are not a new thing at IBM (hardly so in the past couple of
decades or more), but they’re oversensitive about the Red Hat agenda


THIS video regarding_layoffs_at_IBM is based on weeks upon weeks of research.
We’ve been trying to study what’s going on inside IBM, not based on media that
IBM is paying and manipulating but based on insiders, some of whom are Red Hat
employees (or former employees; there_were_layoffs and resignations_at_Red
Hat). IBM is extremely sensitive about this subject being brought up in the
same way Microsoft is paranoid about people pointing out Azure failures and
layoffs.


The video isn’t easy to make, mostly for sentimental reasons. I spent a lot of
my life promoting Red Hat and pushing for stuff like OpenDocument Format along
with IBM. In the SCO case, IBM was on our side. █



                    ䷩ 𝚕𝚒𝚗𝚎 487

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/ip-kat-memes/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/ip-kat-memes/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ [Meme]_Longing_for_the_Original_IP_Kat…⠀✐


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Can't_pretend_EPO_is_OK⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Any_objections?_IP_Kat's_Rose⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Animated_Judge_Judy:_She_thinks_we're_independent⦈_


Summary: It would be nice to see more posts critical of injustice at the EPO,
as we've_just_noted


⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⢀⣀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⣷⢀⣿⣿⣿⠀⣿⣿⣸⣿⢸⣿⠛⣿⣿⠛⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢸⣿⡇⠛⠛⢸⣿⢿⣿⡀⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡸⣿⣇⣿⣿⣸⣿⢿⣿⡇⣿⡏⣿⣿⠀⠀⠀⣿⣿⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣭⣿⣯⣷⣯⣭⣶⣭⣥⣭⣥⠬⣭⣴⣾⣶⣭⣭⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠟⢹⠛⢻⣿⠿⠋⠀⢀⣼⣿⠟⠻⠿⠛⠿⠛⠛⠿⠿⣿⣉⣙⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣟⠍⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⡋⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠉⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣛⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⣹⣿⠟⠀⠀⠀⠀⢰⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣧⠀⣰⣿⠗⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠆⢿⣧⡬⣄⡀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠈⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢶⣾⣿⣻⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣶⣷⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⠑⠶⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣷⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠿⢿⡏⠀⠀⠉⠛⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠋⠁⠀⠐⠙⠙⠀⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣯⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⡍⣷⣶⣶⣦⢰⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⡆⣶⣦⢰⣶⠀⣶⣶⣶⣤⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⡇⣿⣿⣼⣿⢸⣿⣧⡾⣶⣿⣿⢰⢸⣿⣇⡄⣿⣿⣾⣿⠀⣿⡇⣿⣿⢸⣿⢿⣿⢫⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⡅⣿⣿⢹⣿⢸⣿⡏⢣⡇⣿⣿⢰⢸⣿⡏⠁⣿⡿⣿⣿⠀⣿⡇⣿⣿⠸⣿⣿⣿⣿⠓⢞⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢧⣿⣇⠿⠿⠸⠿⠸⠿⠿⠿⠀⠿⠿⠈⠸⠿⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠀⠀⠀⠉⠻⠷⠖⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣭⡍⠙⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣹⣿⠟⠁⠀⠀⠀⠀⢰⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⡀⢀⣼⣿⠷⠔⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣮⣽⣷⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠀⠤⠀⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡧⠼⣿⣦⡦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠁⠀⠈⠙⠻⢾⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣲⣭⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣮⣟⢿⣿⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⣽⣷⣿⣿⣿⣿⣿⣿⣿⣟⠷⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣭⣦⣤⣤⣤⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⣋⣉⠉⠛⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠙⢿⣿⣿⣿⣿⣅⠰⠂⠀⠀⠀⠀⠀⠀⠀⣔⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢨⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣿⣿⣯⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠛⢿⣿⣿⣧⠀⢀⣴⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⣍⣛⣿⣷⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⠖⠐⠶⠦⠒⠒⠶⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠿⠟⠛⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣙⣙⢛⣀⣀⣀⠀⢀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⡀⠀⠀⢂⣀⣀⡀⠀⣀⡀⢀⣈⢻⣿⣿⣿⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⠛⢸⣿⡟⣿⡇⣿⣿⢹⣿⡄⠀⢸⣿⡇⣿⣏⠿⠷⠀⠀⣿⣿⢹⣿⠀⣿⣧⣿⡟⠼⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⠀⣿⣿⠿⢸⣿⡷⠿⠇⣿⣿⢸⣿⡇⠀⢸⣿⡇⠙⢿⣷⣆⠀⠀⣿⣿⢸⣿⠀⣿⣿⣿⡅⣶⣬⣟⡻⢿⠧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡆⣿⣿⣤⣼⣿⡇⠀⠀⢿⣿⣼⣿⠃⠀⢸⣿⡇⣿⣇⣿⣿⠀⠀⢿⣿⣼⣿⠀⣿⡏⣿⣷⢹⣿⣿⡿⣷⡦⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣭⣭⣭⣭⣭⣥⣤⣀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠈⠉⠉⠁⠀⡀⣀⠉⣭⣥⣬⣭⣥⣌⣩⣵⣽⡻⢿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⢠⣤⡀⣤⣤⣤⢠⣤⠄⠀⣠⣤⣤⡄⢠⣤⣤⣄⠀⣤⣤⢠⣤⣤⢀⣤⣤⣤⣠⣤⣤⣤⣤⣤⡄⣠⣤⣤⡀⣤⣤⢠⣤⢠⣤⣤⣄⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⢰⣿⢿⣧⢸⣿⣧⣿⡇⣿⣿⡿⠀⠀⣿⡇⣿⣿⢸⣿⣸⡿⠀⣿⣿⢸⣿⣉⢸⣿⡿⣿⡇⢹⣿⡏⢹⣿⡇⣿⡇⣿⣷⣿⣿⣾⣿⢸⣿⣜⡛⠘⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⢸⣿⣼⣿⢸⣿⢿⣿⡇⢸⣿⡇⠀⠀⣿⡇⣿⣿⢸⣿⢹⣿⠀⣿⣿⢸⣿⠉⢸⣿⣧⣶⡆⢸⣿⡇⢸⣿⡇⣿⡇⣿⡿⣿⡿⣿⣿⢠⣭⢻⣿⠸⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠸⣿⡇⠀⢀⡄⠀⠀⠚⠛⠘⠛⠛⠻⠘⠛⠃⠘⠛⠃⠀⠀⠙⠿⠿⠃⠘⠛⠛⠛⠘⠛⠋⠸⠛⠛⠋⠻⠿⠟⠁⠘⠻⠃⠘⠛⠃⠛⠿⠟⠃⠛⠃⠙⠛⠘⠻⠿⠛⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⢿⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠃⠀⠀⠀⢀⠔⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠈⠄⣸⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⢰⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⡄⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣗⡀⠠⢒⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⠀⠀⠀⠀⠀⠈⣼⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣾⣿⣿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⠀⠀⠀⠀⢡⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⣀⣤⡴⠾⠓⠻⠿⠿⠿⣿⣷⣶⣶⣶⣶⠆⢤⣤⣶⠆⠀⠀⠀⡄⠀⣼⣿⣿⣿⣿⣿⠯⠍⠛⣻⣿⣿⠿⠛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣰⡇⠀⠀⠀⠀⠀⠈⠀⠀⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢘⣧⢰⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣤⣄⣀⣠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠟⢁⣀⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⣏⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠸⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣭⣉⣉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠈⢿⣿⠇⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⣶⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠰⣠⠤⠀⠈⣻⣿⣿⣿⣿⣿⣿⣏⣁⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⠿⠿⠿⠻⠿⣿⡿⠿⠿⠿⠿⠧⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣠⣴⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠈⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢹⣶⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⣴⣿⣿⢻⣿⣿⣿⣿⡏⣽⡶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣸⣾⣿⣷⣾⣧⢿⣷⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣷⣿⡟⣿⣿⣿⣿⡟⣷⡏⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⢟⣽⣿⣯⡛⣿⣿⣯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡿⢸⣿⣿⣿⡇⣿⣧⣟⠃⣿⣿⣤⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠙⠋⠉⠉⠉⠛⠉⠉
⣷⣴⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⢹⣿⢸⣿⣿⣿⡇⣶⡟⣿⡇⣿⣿⣉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠋⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠘⠛⠘⠛⠈⠛⠛⠛⠁⠙⠛⠛⠃⠛⠛⠛⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣤⣵⣿⣿⣿⣦⣤⣼⣿⣿⣿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠭⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⠛⠛⠛⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⢿⣿⣿⣿⣿⡿⣟⣻⠟⠂⠀⢀⣤⣴⣶⣤⣄⢹⣿⣿⣿⣿⣾⡶⠟⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⢯⢛⣛⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠻⣿⣿⣿⣿⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡊⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠻⡇⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠻⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡗⣶⣤⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀
⠀⢀⣧⣀⣤⣴⣾⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠻⠷⢟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⢰⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠷⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢡⠀⠀⣠⣤⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⠋⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⣿⠿⠟⢛⣿⣤⣾⠿⠛⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⡄⠀⠀⡛⠋⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠄⢀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠙⣿⣿⠛⢸⣿⣄⠀⠀⠀
⠀⠀⣀⣨⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠟⠉⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠀⠀⠀⠀⠀⠀⠘⣿⣴⠟⢛⣻⣦⠀⠀
⢠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣿⣿⣿⣷⡀
⠸⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢋⣁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠟⠋⠉⢻⣿⡟⠁⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠇⠰⣶⠀⠰⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣬⣷⣿⣿⣿⣤⣤⣼⣿⣿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⠛⠛⠛⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⢻⣿⣿⣿⣿⡿⣟⣻⡟⠃⠀⢀⣤⣶⣶⣤⣌⢻⣿⣿⣿⣿⣶⡶⠚⡚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣇⢀⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⢿⢙⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⣿⣿⣿⣿⣿⣿⣥⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡊⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠈⢿⡇⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠹⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡷⣶⣠⣿⣿⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀
⠀⢠⣧⣀⣤⣴⣾⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠛⠷⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⢸⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢶⣤⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⢡⠀⠀⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⣿⠿⠟⢛⣷⣤⣾⠾⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣶⠀⠀⣩⡿⠋⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⢀⣠⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠄⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠹⣿⣿⠛⣻⣷⡄⠀⠀⠀
⠀⠀⣀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠉⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠉⠛⠗⠀⠀⠀⠀⠀⠀⠹⣿⣼⠟⢛⣻⣆⠀⠀
⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣼⣿⣿⣿⣷⡀
⠸⠛⠛⠋⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢋⣁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠟⠋⠉⢿⣿⡟⠁⠙⠻⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠆⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣤⣷⣿⣿⣿⣤⣤⣽⣿⣿⣿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠹⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⢿⣿⣿⣿⣿⡿⣟⣻⡟⠃⠀⢀⣤⣴⣶⣤⡌⢹⣿⣿⣿⣷⣶⡶⠚⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⡇⢀⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⡿⢏⢛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⣿⣿⣿⣿⣿⣯⣁⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣶⡈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠈⢿⡄⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣶⣰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⡀⠀⠀⠀⠀⠀⠀
⠀⢸⣇⣀⣤⣴⣾⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠷⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⢸⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⣡⠀⠀⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⣿⠿⠛⢻⣷⣴⣶⠾⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣶⠀⠀⠈⠛⠋⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠄⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠹⣿⣿⠃⣿⣷⡄⠀⠀⠀
⠀⠀⣠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠉⠛⠓⢀⠀⠀⠀⠀⠀⠹⣿⣼⠟⣛⣿⣄⠀⠀
⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣼⣿⣿⣿⣧⡀
⠸⠛⠋⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢋⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠉⠉⢿⣿⡟⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠆⠰⣶⠀⠶⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣧⣷⣿⣿⣿⣤⣤⣼⣿⣿⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⡛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣟⣻⡟⠗⠀⢀⣤⣶⣶⣦⣬⢹⣿⣿⣿⣿⣶⡶⠒⡛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣷⣷⣿⣿⡿⠿⢛⣓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠻⣿⣿⣿⣿⣿⣿⣿⣥⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡊⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠘⢿⡄⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣦⣰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣄⡀⠀⠀⠀⠀⠀⠀
⠀⢸⣇⣀⣤⣴⣾⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠷⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⢸⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢶⣤⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡋⣠⠀⠀⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⣿⠿⠛⢻⣷⣼⣷⠿⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⠀⠀⠸⠟⠃⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣀⣀⠀⣠⡀⠀⠀⠀⠀⠀⠻⣿⣿⠋⣿⣷⡄⠀⠀⠀
⠀⢀⣠⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠉⠛⠃⢀⠀⠀⠀⠀⠀⠹⣯⣼⠟⣛⣿⣄⠀⠀
⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣼⣿⣿⣿⣧⡀
⠘⠛⠛⠙⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢋⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠉⠉⢿⣿⡟⠀⠙⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠰⣶⠀⠲⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣾⣛⣿⣿⣶⣶⣿⣿⣾⣿⣿⣅⣤⣾⣿⣿⣦⣤⣤⣿⣿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣟⡋⢛⣿⣿⣽⣷⣾⣿⣿⣿⣆⠀⠙⠉⠈⠉⠛⠛⠿⣿⣿⣏⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠩⠿⠛⣿⣿⣿⣿⡿⠛⣋⡉⠀⠀⠀⢠⣤⣶⣄⠄⠈⢿⣿⡿⢷⣶⡖⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⠀⣼⣿⣿⣿⣶⣶⣿⣿⠿⠀⢀⣿⣿⣿⣿⣿⣷⣶⣶⣾⣕⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⣿⣿⣿⣿⣧⣄⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢽⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⠃⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡠⣄⠀⣿⣿⣯⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣤⣴⠾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠃⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠉⠀⠀⠀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⢛⣧⣠⡶⠞⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⢷⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣏⡛⠃⠿⣷⡀⠀⠀⠀
⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠹⣧⡼⠛⢛⢳⣄⠀⠀
⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⣿⣿⣿⣦⠀
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢉⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⢿⣿⡿⣻⢿⣿⣟⣛⣛⣛⣛⣻⢿⣛⣻⣿⣿⡿⣿⢿⡿⣟⣀⡀⢀⣀⣀⣀⣀⢀⣀⡀⣀⢀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⣹⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡈⢸⣿⣿⣿⣿⣽⠛⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠂⠰⢰⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣎⣻⣿⣷⣶⣾⣿⣷⣿⣿⣿⣤⣶⣿⣿⣷⣶⣤⣼⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⠛⠛⣻⣿⣿⣿⣶⣾⣿⣿⣿⡄⠀⠉⠁⠁⠉⠛⠛⠿⣿⣿⣆⡉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⢛⣿⣿⣿⣿⡿⢉⣭⡍⠀⠀⠀⢠⣴⣦⣆⠀⠘⢿⣿⠻⣶⣶⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⢠⣿⣿⣿⣿⣶⣾⣿⡿⠟⠀⣰⣿⣿⣿⣿⣿⡿⢷⣶⣯⡁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⣿⣿⣿⣿⣿⣿⣇⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣅⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⠃⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡄⣄⠀⣸⣿⣿⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⢜⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⢀⣀⣤⣴⠾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠃⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠈⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡉⠀⠀⠀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⢙⣧⣠⣶⠞⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⢷⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣟⡛⠃⠿⣷⡀⠀⠀⠀
⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠹⣇⣼⠛⢛⢻⣄⠀⠀
⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⣿⣿⣿⣦⠀
⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢉⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⢿⣿⡿⣻⢿⣿⣟⣛⣛⣛⣛⣻⢿⣛⣻⣿⣿⡿⣿⢿⡿⣟⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⢹⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢹⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠛⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣶⣘⣿⣿⣶⣶⣿⣿⠿⣿⣿⣿⣴⣿⣿⣿⣶⣶⣶⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣙⠛⠛⢛⣿⣿⣿⣷⣶⣿⣿⣿⣿⡄⠀⠈⠁⠀⠉⠛⠛⢿⣿⣧⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠛⣻⣿⣿⣿⠿⠯⣉⣭⣍⠀⠀⢀⣴⣶⣶⣖⠀⠻⢿⡿⠛⣿⡇⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣴⣿⣿⣿⣿⣶⡾⠿⠿⠟⢀⣸⣿⣿⣿⣿⣿⠿⢿⣿⣯⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢸⣿⣿⣿⣿⣿⣿⣧⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡔⣄⣀⢰⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣴⣮⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⣀⣤⣴⠾⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠓⠈⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡉⠀⠀⠀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⢛⣧⣠⣶⠞⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠈⠁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣷⣿⣿⣧⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣟⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣟⣛⠃⠿⣷⡀⠀⠀⠀
⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠹⣧⣼⠛⢛⣳⣄⠀⠀
⠀⢰⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⣿⣿⣿⣦⠀
⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⢋⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⢿⣿⡿⣿⢿⣿⣟⣛⣛⣛⣛⣻⢿⣛⣻⣿⣿⡿⣿⢿⡿⣟⣀⡀⢀⣀⣀⣀⣀⢀⣀⡀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⢹⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⣹⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠛⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣹⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣬⠿⢿⣶⣶⣿⣿⠿⢿⣿⣯⣾⣿⣿⣿⣶⣶⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢉⣙⠛⠛⢉⣽⣿⣽⣷⣶⣿⣿⣿⣿⣄⠀⠉⠉⠀⠉⠛⠻⣿⣿⣤⣀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠿⠛⣻⣿⣿⣿⠿⠿⣉⣥⣌⠀⠀⣠⣶⣶⣶⣆⠈⠿⣿⡿⡛⣶⠊⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠀⢀⣴⣿⣿⣿⣿⣶⡾⠿⠟⠛⢁⣤⣿⣿⣿⣿⣿⠿⢿⣿⣎⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠺⣿⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣆⢧⡀⠀⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣄⣀⣤⣴⠾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠘⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡉⠀⠀⠀⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⢛⣧⣠⣶⠞⠙⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠈⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣷⣾⣿⣧⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⣰⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣛⣿⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣟⣛⠃⠻⣷⡀⠀⠀⠀
⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠠⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠹⣇⣼⠛⠛⣻⡄⠀⠀
⠀⢦⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⣿⣿⣿⣦⠀
⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢋⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠿⣿⡿⣿⢿⣿⣟⣛⣟⣛⣛⣻⢿⣛⣻⣿⣿⡿⣿⢿⡿⣟⣀⡀⢀⣀⣀⣀⣀⢀⣀⡀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⢹⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⣽⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠛⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣼⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢦⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣤⣼⠿⢿⣶⣶⣿⣿⠿⢿⣿⣧⣾⣿⣿⣿⣶⣶⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣹⡛⠙⠉⣩⣿⣿⣿⣶⣶⣿⣿⣿⣿⣄⠀⠉⠁⠀⠉⠙⠻⣿⣿⣦⣀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⠿⠟⣉⣭⣤⠁⠀⣠⣶⣾⣶⣆⠀⠿⣿⠿⢿⣇⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣠⣾⣿⣿⣿⣿⣶⡾⠿⠿⠋⢀⣠⣿⣿⣿⣿⡿⠻⢿⣿⣌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢐⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⡈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠲⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⠃⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⡰⣄⠀⢰⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⢄⣀⣤⣴⠾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠃⠉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠳⠠⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡉⠀⠀⠀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⢙⣧⣠⣶⠞⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⣷⣾⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣛⣛⣛⣛⣻⣟⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣟⣛⠃⠻⣷⡀⠀⠀⠀
⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠹⣇⣼⠛⢛⣷⣄⠀⠀
⠀⢶⣺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣸⣿⣿⡿⣦⠀
⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠻⣿⡿⣿⢿⣿⣟⣻⣟⣛⣛⣻⢿⣟⣻⣿⣟⡿⣿⢿⡿⣟⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⠸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠹⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠛⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⣿⣿⣶⣤⣽⠿⢿⣶⣶⣿⣿⠿⢿⣿⣷⣾⣿⣿⣷⣶⣾⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢩⣽⣋⠉⠉⣩⣿⣿⣿⣷⣶⣿⣿⣿⣿⣄⠀⠉⠉⠀⠉⠛⠿⣿⣿⣄⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⠿⠿⣋⣭⣄⠀⢀⣠⣶⣶⣶⡂⠛⠿⣿⢛⣻⡚⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣴⣾⣿⣿⣿⣿⣶⡾⠿⠿⠛⣦⣼⣿⣿⣿⣿⡟⠻⣿⣷⣁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣤⡘⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⡿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⠃⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣄⢧⡀⠀⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣤⣴⠾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠨⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠓⠦⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡉⠀⠀⠀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⢙⣧⣠⣶⠞⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠈⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⢷⣾⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠀⠀⠀⢰⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣛⢛⣛⣛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣛⠃⠻⣷⡀⠀⠀⠀
⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠹⣇⣼⠛⢛⣳⡄⠀⠀
⠀⢒⣳⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣸⣿⣿⡿⣦⠀
⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⣀⣘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠙⣿⡿⣿⢿⣿⣟⣛⣟⣛⣛⣻⢿⣛⣻⣿⣟⡿⣿⢿⡿⣟⣁⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠹⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠉⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⣬⡿⠿⣷⣶⣾⣿⡿⠿⣿⣿⣷⣿⣿⣿⣷⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣩⣍⠉⠉⠉⣹⣿⣿⣿⣶⣾⣿⣿⣿⣧⡀⠀⠉⠉⠉⠙⠻⢿⣿⣶⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠊⠛⠛⣛⣿⣿⣿⡿⠿⠿⣉⣤⣌⠀⢀⣰⣶⣶⣶⠀⡿⣿⡟⣗⣶⠊⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀⣴⣿⣿⣿⣿⣿⣶⡾⠿⠿⠋⣤⣼⣿⣿⣿⣿⠛⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⡄⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⢿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⡿⠸⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⡰⣆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⣀⣠⣴⠾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡉⠀⠀⠀⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⢛⣧⣠⣶⠞⠙⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠈⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⣷⣾⣾⣧⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣟⡛⣛⣛⣛⡛⢛⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣛⠃⠻⣷⡀⠀⠀⠀
⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⣇⣼⠛⠛⣳⣄⠀⠀
⠀⠢⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣸⣿⣿⣿⣦⠀
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠘⣛⡿⣿⢿⣿⣟⣛⣿⣛⣛⣻⢿⣛⣻⣿⣟⡿⣿⢿⡿⣟⣁⡀⢀⣀⣀⣀⣀⢀⣀⡀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⣽⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠉⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣼⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣤⣬⠿⠿⣷⣶⣿⣿⠿⢿⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢉⣭⣉⣉⠉⣩⣽⣿⣽⣶⣶⣿⣿⣿⣷⣤⡀⠈⠉⠉⠉⠛⠻⣿⣷⣎⡁⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠛⢛⣻⣿⣿⣿⠿⠿⠋⣩⣤⡁⠀⣀⣶⣶⣶⡆⠈⢿⣿⣟⣶⡂⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⣴⣾⣿⣿⣿⣿⣷⣶⠿⠿⠟⢃⣤⣿⣿⣿⣿⡟⠿⣿⣷⡄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣄⣿⡢⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⣀⣤⣴⠾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠉⠀⠀⠀⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⢻⣧⣰⡶⠞⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠈⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡔⣷⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⡯⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣛⢛⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡛⠃⠿⣧⡀⠀⠀⠀
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡼⠛⢛⣷⡄⠀⠀
⠀⢲⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣸⣿⣿⡿⣆⠀
⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢉⣀⣘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠈⣛⡿⣿⢿⣿⣟⣛⣿⣛⣛⣻⢿⣛⣻⣿⣟⡿⣿⢿⡿⣟⣃⡀⢀⣀⣀⣀⣀⢀⣀⡀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡁⣿⣷⣿⣹⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠈⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣹⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣤⡽⠿⢿⣷⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠏⢠⣍⣉⡉⢉⣭⣿⣷⣷⣿⣿⣿⣿⣿⣧⣄⠀⠉⠉⠉⠛⠛⢿⣿⣷⣋⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠛⣻⣽⣿⣿⡿⠿⠟⢉⣡⣍⠀⢀⣴⣶⣶⣶⠘⠿⣿⣿⢖⡂⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⣠⣶⣿⣿⣿⣿⣿⣶⡾⠿⠿⠛⣦⣼⣿⣿⣿⣿⠿⢿⣿⣇⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⡀⢹⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡟⠸⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣄⢻⣞⢲⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣀⣀⣤⡶⠾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⢀⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠟⠛⢻⣦⢰⡶⠞⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⢁⣠⣴⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡾⣷⣷⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⢨⣿⣿⣿⣿⣿⣛⡛⡛⢛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡛⠁⠿⣧⠀⠀⠀⠀
⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡾⠛⢛⣷⡀⠀⠀
⠀⢠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣸⣿⣿⣿⣆⠀
⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢉⡀⡙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠈⣛⡿⣿⢿⣿⣟⣻⣿⣟⣛⣻⢿⣛⣻⣿⣟⡿⣿⢿⡿⣟⣃⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣽⣿⣿⡉⣿⣿⣿⣽⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣼⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢦⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⡼⠿⠿⣷⣶⣿⣿⠿⢿⣿⣯⣿⣿⣿⣿⣶⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢤⣴⣄⢀⣀⣭⣾⣿⣶⣿⣿⣿⣿⣿⣷⣄⠀⠉⠉⠉⠙⠛⢿⣿⣷⣂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣛⣭⣿⣿⡿⠿⠿⢉⣡⣌⡀⠀⣠⣶⣶⣶⡀⠻⣿⣿⡗⣖⠒⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣠⣶⣿⣿⣿⣿⣿⣷⡶⠿⠿⠟⣠⣬⣿⣿⣿⣿⠿⢿⣿⣯⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⡄⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡇⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⠸⣶⠐⣾⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣀⣠⣤⡶⠾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠀⠀⢀⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠟⠛⢻⣆⢰⡶⠞⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠈⢀⣠⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡺⣶⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣛⣛⡛⣛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡛⠁⠿⣧⠀⠀⠀⠀
⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⡾⠛⢛⣷⡀⠀⠀
⠀⣐⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣸⣿⣿⣿⣄⠀
⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⡀⠝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣙⡻⣿⢿⣿⣟⣻⣿⣟⣛⣻⢿⣛⣻⣿⣟⡿⣿⢿⡿⣟⣃⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢰⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⣬⠿⠿⣷⣶⣿⣿⠿⣿⣿⣯⣿⣿⣿⣿⣤⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠠⣴⣅⢁⣀⣥⣿⣿⣶⣿⣿⣿⣿⣿⣷⣄⠀⠉⠉⠉⠛⠛⢿⣿⣷⣍⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢉⣭⣿⣿⡿⠟⠟⢍⣉⣉⠀⠀⣀⣴⣶⣦⡀⢽⣿⣿⣷⣴⡀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⣠⣾⣿⣿⣿⣿⣿⣷⡶⠿⠿⠛⣀⣼⣿⣿⣿⣿⠿⢿⣷⣏⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⣶⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠇⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣸⣧⠀⣾⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣠⣤⡶⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠈⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠁⠀⠀⢀⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠛⢻⣆⣴⡶⠚⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⢀⣠⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡺⣶⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣛⣛⣛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⡛⠀⢿⣆⠀⠀⠀⠀
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣥⡿⠛⢛⣧⡀⠀⠀
⠀⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣿⣿⣿⣷⣄⠀
⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⡀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣙⡻⣿⢿⣿⣟⣻⣿⣟⣛⣻⢿⣛⣻⣿⣟⡿⣿⢿⡿⣟⣃⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⡬⠿⢿⣷⣶⣿⡿⢿⣿⣿⣧⣾⣿⣿⣿⣤⣭⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣶⢦⢀⣀⣤⣾⣷⣶⣾⣾⣿⣿⣿⣦⡀⠈⠙⠛⠛⠛⠻⢿⣿⣯⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣩⣽⣿⣿⡿⠿⠿⢉⣉⡉⠀⠀⣠⣤⣶⣄⠠⣿⣿⣿⢤⠤⠄⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠄⣠⣾⣿⣿⣿⣿⣷⣶⣾⠿⠿⠿⣀⣼⣿⣿⣿⣿⣶⣶⣿⣟⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠇⠿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣦⣤⣤⣤⡸⣿⣲⣾⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣠⣤⡶⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⠁⠀⠀⢠⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠛⠛⣻⣆⣴⡶⠛⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠈⢀⣤⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣺⣶⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣟⣛⣛⡛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⠛⠘⢿⣄⠀⠀⠀⠀
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡟⠛⢻⣦⡀⠀⠀
⠀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣿⣿⣿⣷⡄⠀
⠈⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⡀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣙⡻⣻⢿⣿⣟⣻⣿⣛⣛⣻⢿⣛⣻⣿⣿⡿⣿⢿⡿⣛⣁⡀⢀⣀⣀⣀⣀⢀⣀⡀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⠸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣤⡽⠿⢿⣶⣾⣿⡿⣿⣿⣿⣷⣿⣿⣿⣯⣄⣉⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢾⣧⢀⣀⣴⣿⣷⣶⣿⣿⣿⣿⣿⣄⠀⠙⠛⠛⠛⠿⠿⣿⣿⣏⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢉⣭⣿⣿⣿⠿⠿⠯⢉⣉⠀⠀⠀⣤⣤⣤⡀⢈⣿⣿⣿⣦⡤⡄⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⣤⣾⣿⣿⣿⣿⣶⣶⣾⣿⡿⢇⣀⣿⣿⣿⣿⣷⣶⣾⣿⡛⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢽⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠻⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠇⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣼⣿⣦⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣀⣠⣤⡶⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠁⠀⠀⢠⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠛⠋⣿⣄⣶⠶⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠈⢀⣴⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢿⣶⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣛⣛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⡀⠀⠀⠀⠀⠀⠈⢿⣛⠛⠸⢿⣄⠀⠀⠀⠀
⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⠟⠛⣻⣦⠀⠀⠀
⠀⣢⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣿⣿⣿⣷⡄⠀
⠈⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢁⣀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣙⡛⣻⢿⣿⣟⣻⣿⣛⣛⣻⢿⣛⣻⣿⣿⡿⣿⢿⡿⣛⣁⡀⢀⣀⣀⣀⣀⢀⣀⡀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⢿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣽⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢦⠀⠰⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⣿⣿⣿⣤⡽⠿⣿⣶⣾⣿⣿⣽⣿⣧⣀⣾⣿⣿⣯⣀⣘⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠧⠤⣠⣴⣿⣷⣶⣷⣿⣿⣿⣯⡀⠉⠛⠛⠛⠻⠿⢿⣿⣿⣟⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣭⣿⣿⣿⠿⠿⠟⡛⡓⠀⠀⢀⣠⣤⣄⠀⠙⣿⣿⣶⣄⢤⠤⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⣴⣿⣿⣿⣿⣷⣶⣶⣿⡿⡗⠀⣰⣾⣿⣿⣿⣦⣤⣬⣿⠏⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣅⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡉⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢘⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠃⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣠⣴⠾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠁⠀⠀⣠⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠛⠛⣿⣄⣶⠶⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⢿⣾⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠂⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣛⣛⡛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⠋⠸⢿⣄⠀⠀⠀⠀
⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣰⠟⢛⣻⣦⠀⠀⠀
⠀⡾⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⣿⣿⣿⢷⡀⠀
⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢀⣀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣉⡻⣿⢿⣿⣟⣛⣿⣛⣛⣻⢿⣛⣻⣿⣿⡿⣿⢿⡛⣋⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⠿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⣿⣿⣿⣿⣿⡤⠿⢿⣷⣶⣾⣿⣿⣿⣿⡇⣀⣿⣿⣿⣅⡀⠘⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠧⢄⣠⣴⣿⣿⣶⣶⣿⣿⣿⡏⠉⠻⠿⠛⠛⢿⣿⣿⣿⣿⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣿⣿⣿⣿⣿⡿⠿⠿⠄⠀⠀⢀⣀⣀⡀⠈⠻⣿⣷⣦⣀⣀⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠀⣶⣿⣿⣿⣿⣧⣤⣴⣾⣿⠄⠀⣴⣾⣿⣿⣿⣄⣀⣿⣿⡟⠙⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠉⢉⣡⣶⣾⣿⣿⣿⣿⣿⡟⠛⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢸⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡊⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⡿⠙⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣭⣤⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣄⣀⣤⣴⡾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠀⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠘⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠁⠀⠀⣠⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢂⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠛⠙⣿⣄⣶⠿⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢿⣾⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣛⠃⠸⣿⡄⠀⠀⠀⠀
⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣼⠟⢛⣻⣆⠀⠀⠀
⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣔⣿⣿⣿⢷⡀⠀
⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣐⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣈⡻⣿⢿⣿⣟⣻⣿⣛⣛⣻⢿⣛⣻⣿⣿⡿⣿⢛⡛⣉⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⠿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⣿⣿⣿⣿⣬⣿⣿⣷⣤⣾⣿⣿⣿⣷⠄⠀⣸⣿⣿⡂⠀⠘⣿⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⣷⣤⣠⣼⣿⣯⣶⣼⣿⣿⣿⡛⠛⣿⡿⠶⢿⣿⣿⣿⣿⣷⠶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⣿⣿⣿⣿⣿⢿⣿⣗⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣦⣄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⢠⣾⣿⣿⣿⣿⣍⣉⣥⣶⡆⠀⢠⣤⣾⣿⣿⣷⠂⢸⣿⣿⠟⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠛⠛⣷⣶⣾⣿⣿⣿⣿⣿⡿⢿⣿⣯⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⡿⠹⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣆⣀⣤⣴⡾⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡍⠀⠀⠀⣠⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣂⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⠙⣿⣄⣾⠿⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢿⣾⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⠋⠸⣿⡄⠀⠀⠀⠀
⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⠟⢛⣻⣆⠀⠀⠀
⠰⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣔⣿⣿⡿⣷⡀⠀
⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡻⣿⢿⣿⣟⣻⣿⣛⣛⣛⢻⣛⣻⣿⣿⡿⣟⢛⡋⣁⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⠿⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⢸⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣸⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⣿⣿⣿⣿⣷⣙⣿⣿⣦⣀⣶⣿⣿⣿⣧⡀⠀⢸⣿⣿⡇⠀⠠⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣷⣄⣈⣽⣿⣟⣧⣽⡿⣿⣿⠿⣿⣿⣿⣤⣶⣿⣿⣿⣷⣦⣤⣽⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠉⠀⠀⠈⠙⠛⠻⣿⣿⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⢠⣾⣿⣿⣿⣟⡛⠛⣩⣭⠉⠀⢀⣠⣶⣶⣶⡤⠀⢹⣿⣿⠟⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⢿⣅⣠⣿⣿⣿⣿⣿⣿⣶⣶⣿⣟⠂⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣾⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣧⣴⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣆⣀⣤⣴⠾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣖⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡉⠀⠀⠀⣠⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢀⣢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⢙⣷⣤⣾⠞⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢿⣾⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣛⠃⠸⣷⡀⠀⠀⠀⠀
⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣼⠛⣛⣻⣆⠀⠀⠀
⢰⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣜⣿⣿⡿⣧⡀⠀
⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣘⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡻⣿⢿⣻⣟⣛⣟⣛⣛⣛⢛⣛⣻⣿⣟⡿⣛⢛⡉⣀⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⠛⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣿⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⣮⡻⣿⣦⣀⢀⣤⣿⣿⣿⡟⠀⠘⢻⣿⣿⡏⠀⢈⣿⣿⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣯⣍⣙⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣟⣀⣤⣼⣿⣿⣧⣄⣀⣻⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠙⠛⠋⠉⠛⠿⠿⣿⣿⣿⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⢠⣴⣾⣿⣿⣿⠿⠟⠛⡛⠒⠀⠀⠀⣤⣤⣤⣀⠈⢿⣿⣿⣦⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣶⣶⣿⣷⠀⢀⣾⣿⣿⣿⣿⣧⣤⣼⣿⡿⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠂⠀⣿⣿⣿⣿⣿⣿⣿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣆⣀⣤⣴⡾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠘⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡉⠀⠀⠀⣤⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⢙⣷⣤⣾⠟⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢿⣾⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⠃⠺⣷⡄⠀⠀⠀⠀
⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⢹⣿⣿⣷⣶⣮⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣼⠛⣛⣻⣆⠀⠀⠀
⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣼⣿⣿⡿⣧⡀⠀
⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡛⣿⢿⣿⣛⣛⣛⣛⣛⣛⢛⣟⣻⣿⣿⡿⣋⢉⡁⣀⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⠛⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣧⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣿⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣝⢿⣷⣄⠀⠈⠁⣹⣿⣿⣿⠋⠹⢿⣿⣿⡿⠀⠛⢻⣿⣞⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⣦⣿⡛⠛⢿⣿⣖⡛⣿⣿⣶⣿⣿⣻⣿⣦⠀⢀⣠⣿⣿⣇⠀⠀⣻⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⣿⣾⣿⣿⣿⣿⣿⣟⣻⣟⠛⢻⡯⠟⠾⢿⣿⣿⣿⣿⣿⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣿⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣀⣁⣤⣄⠀⠀⣠⣴⣿⣿⣿⡇⠀⣸⣿⣿⠉⠭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⢰⣄⣀⣤⣶⠾⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡉⠀⠀⠀⣤⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⣨⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⢙⣷⣰⡾⠟⠛⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣆⠀⠀⠀⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣾⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣛⠃⡿⣷⡀⠀⠀⠀⠀
⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⢻⣿⣿⣮⣭⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣼⠛⣛⣿⣄⠀⠀⠀
⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣸⣿⣿⡿⣦⠀⠀
⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡛⣿⢿⣛⣛⣛⣛⣛⣛⣋⢙⣛⣻⣿⣟⡿⣋⢉⡀⣀⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠉⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣹⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⡏⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣿⣇⣿⢸⣿⣅⣿⢿⣇⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⢈⣁⣭⣬⣵⣯⣧⣭⣤⣭⣁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠈⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⣢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡻⢿⣿⠉⠛⠻⠟⠻⣿⣿⣿⣿⢿⣿⣿⣿⣷⠀⠨⢿⣿⡤⣎⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣯⣿⡿⢿⣿⣿⣬⣿⣿⣦⣄⣤⣤⣽⣿⡟⠁⠀⠈⢿⣿⡟⠀⠀⢶⣿⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠙⢻⣳⣤⣼⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣷⣤⣤⣬⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡙⠛⠿⣿⣿⣿⣿⣿⣶⣿⡆⠉⠛⠊⠉⠙⠻⠿⢿⣿⣿⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠘⠉⢡⣿⣿⣿⣿⣿⠿⠿⠿⠿⠂⠀⠀⢀⣤⣶⣦⣄⠀⢙⣿⣿⠻⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣧⣤⣶⣶⡄⢀⣼⣿⣿⣿⣿⣷⣴⣾⣿⣟⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣄⣠⣤⣶⡾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠃⠘⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡉⡄⠀⢀⣤⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢀⣬⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⢹⣷⣰⡾⠟⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠁⣿⣷⡀⠀⠀⠀⠀
⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢻⣿⣿⣟⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡾⠛⣛⣷⣄⠀⠀⠀
⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣸⣿⣿⡿⣦⠀⠀
⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣈⡛⡿⣛⡻⣛⢿⣛⣋⣉⣛⣛⣛⣋⢙⣛⣻⣿⣿⡿⣋⢉⡀⣀⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⣤⢿⣿⣿⣾⡟⣿⣏⠙⢻⣿⣿⢿⣿⣉⠉⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣽⣿⣿⡉⣿⣿⣿⣻⡏⣿⢸⣿⡁⣿⣿⣯⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⣸⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣻⣇⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠈⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⣬⣷⣿⣾⣷⣿⣷⣿⣾⣿⣷⣿⣿⣿⣶⣿⣷⣿⣭⣴⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠁⠉⠀⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠰⢶⠀⠐⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⡀⠛⢿⣿⣟⢙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢿⣿⣿⣿⣿⣝⢿⣧⣀⠉⠉⠋⠹⣿⣿⣿⠏⠻⣿⣿⣿⣷⠀⠘⣛⣋⣉⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠻⢿⣿⡙⠻⣿⣷⡾⢿⣿⣷⣶⣾⣿⣿⣿⡇⠀⠀⠈⣿⣿⡃⠀⠐⣻⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⢶⣷⣾⣿⣿⣾⣷⣿⣿⠿⣿⣿⣿⡿⣿⣶⣾⣿⣿⣿⣿⣿⢶⠞⠉⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣴⠷⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠋⠀⠀⠈⠛⠛⠻⣿⣷⣤⡄⢀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠀⠀⣀⣴⣾⣿⣶⡦⢀⣽⣿⡏⠻⢿⡏⠀⠀⠀⠀⠀⠀⣰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⡴⠁⢰⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡟⠸⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣇⣠⣤⣶⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠘⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣆⣤⣀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡉⡄⠀⢀⣤⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣀⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⠟⠛⢻⣷⣴⡾⠟⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣷⣿⣿⣧⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠻⣿⡟⠃⡿⣷⡀⠀⠀⠀⠀
⢀⣠⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣾⠛⣛⣷⣄⠀⠀⠀
⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⢿⣿⣿⣶⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣸⣿⣿⡿⣦⠀⠀
⠘⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣀⣚⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣈⣛⢟⣛⡻⣿⣟⡿⣛⢿⣛⣛⣛⣟⣟⣛⣻⢿⣛⣻⣿⣟⡿⣛⢉⡀⣀⣀⡀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢸⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⣿⢿⣿⣿⣾⡿⣿⣏⢹⢻⣿⣿⢿⣿⣉⠉⣿⡇⣿⣾⡇⣿⣿⣿⢸⣏⣹⣿⣽⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣯⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⣹⢸⣿⣿⣿⡇⣿⣯⣿⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⢸⣯⣽⣿⠉⢸⣿⣅⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠠⣭⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣬⣅⠉⠈⠁⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉⠉⠉⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣻⣿⣯⣭⣉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣮⢿⣿⣦⣀⠈⣁⣙⣿⣿⡿⠏⠛⢿⣿⣿⣿⠈⠙⣿⣧⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠙⠛⣿⣌⣙⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢈⣿⣿⣇⡀⠈⣿⠿⠟⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠐⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠉⠀⢀⣈⠙⠛⠻⣿⣿⣶⣄⣴⡶⠞⠃⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣠⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⠀⠀⣠⣶⣿⣿⣿⣷⣤⣿⣿⣟⠛⠻⠇⠀⠀⠀⠀⠀⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠄⢀⣀⣤⣴⣾⣿⡏⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣴⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣧⣠⣤⣶⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠟⠃⠘⠟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠸⠻⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣋⣄⠀⢀⣴⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢀⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠉⠂⠀⠀⠀⠀⠸⣿⠟⠛⢻⣷⣼⡿⠟⠛⠉⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠂⠀⠋⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠄⠀⠀⠀⠀⠀⠀⢻⣿⣟⢋⣿⣷⡀⠀⠀⠀⠀
⢀⣰⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠻⣧⡾⢛⣛⣷⣄⠀⠀⠀
⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣾⣿⣿⣿⣦⠀⠀
⠘⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⢠⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡘⣛⢿⣻⣟⣻⣿⣿⣛⣻⢿⣛⣻⣿⣟⡻⣛⢟⡉⣀⣀⡀⣀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⣹⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣯⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⣿⢺⣿⣿⣿⣿⣽⣿⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⠉⢸⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠹⢿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣾⣷⣿⣭⣅⠈⠉⠁⠉⠀⠈⠉⠉⠉⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠄⠲⣶⠀⠰⠄⠠⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣻⣿⣿⣿⣷⣿⣿⡟⠻⢿⣿⣿⣿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣟⢻⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣙⣿⣿⢶⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⣿⣿⡿⠿⣿⣿⣓⡹⣿⣷⣄⠀⠈⣨⢻⣿⣿⠟⠉⠻⣿⣿⣿⠃⠉⣹⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣦⣤⣽⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣯⣀⡀⠙⠿⠋⠉⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⡀⠘⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠉⠛⠃⠀⣀⣉⠛⠛⢿⣿⣷⣦⣤⣾⡟⠁⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠇⠀⢠⣴⣿⣿⣿⣷⣶⣿⣿⡿⠉⠛⠋⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠁⠀⠀⠀⠀⠀⠙⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠄⢀⣀⣤⣴⣾⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣠⣔⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⡿⠓⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣤⣤⣴⣶⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠟⠃⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠸⠻⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠉⣄⠀⢠⣴⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠊⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⣠⣤⣿⢀⣨⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠛⣻⣧⣼⡿⠟⠛⠁⠀⠀
⠀⠀⠀⠀⣀⣤⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠂⠛⠉⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀⠀⠀⠀⠀⠀⢿⣿⡟⢛⣿⣧⡀⠀⠀⠀⠀
⢀⣼⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡿⢛⣛⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣿⣿⣿⣿⣆⠀⠀
⠸⠛⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⢠⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣛⢿⣿⣟⣛⣛⣻⣛⣻⢿⣛⣻⣿⣟⡻⣻⢿⡻⣛⣛⡻⢃⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⣿⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣽⣿⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⠉⢸⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠻⢿⣷⣿⣾⣷⣿⣿⣷⣾⣿⣧⡉⠀⠈⠉⠉⠉⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠆⠲⣶⠀⠴⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⡋⠛⢿⣿⣿⡿⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣏⢿⣿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⣩⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠛⠿⣿⣛⠻⢿⣿⣭⣻⣿⣷⣄⣀⣀⣎⢿⣿⡿⠋⠁⠛⣿⣿⣿⠀⢀⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣿⣿⣷⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣿⣿⣧⣀⣀⡻⠏⠁⠀⢹⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⡀⣠⠌⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⡘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⢃⣀⣉⡛⠛⠻⣿⣿⠷⣶⣾⡿⠋⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢾⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠂⠀⣴⣿⣿⣿⣿⣿⣿⣿⡝⠃⠙⡛⠀⠀⠀⠀⠙⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⡄⢀⣀⣤⣴⣾⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣠⣀⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⢀⣤⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣤⣤⣴⣶⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠃⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠛⠛⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠛⠙⠉⠀⠀⠀⠀⠀⠀⢀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢩⣤⠀⢠⣴⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠈⠀⠈⠑⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣴⣿⠀⢸⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠛⣻⣧⣼⡿⠟⠛⠁⠀⠀
⠀⠀⠀⢀⣤⣤⡮⠚⠘⠉⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⡿⠟⠛⠛⠁⢠⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣭⣽⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⢠⣶⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠀⠀⠀⠀⠈⢿⣿⡟⢛⣿⣧⡀⠀⠀⠀⠀
⢠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡿⢛⣻⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣿⣿⣿⣿⣦⠀⠀
⠘⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣙⢿⣿⣿⣛⣛⣛⣛⣛⢿⣛⣻⣿⣟⡿⣻⢿⡻⣟⣛⡿⣟⣛⣃⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⢿⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡄⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⠉⢸⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⢺⣷⣿⣿⣷⣾⣿⣿⣿⣾⡌⠉⠉⠉⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡉⠙⢿⣿⣿⣟⡋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⠙⠻⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢠⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠻⣿⣍⡹⢿⣶⣧⣿⣿⣷⣦⣤⣦⣬⢿⣿⠿⠋⠉⠻⣿⣿⡿⠀⢠⣿⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣀⣿⣿⣧⣀⣈⠿⠉⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⢀⣠⣼⠍⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⣃⣨⣙⡻⡛⣿⣿⡟⣷⣶⣿⠿⠁⠀⠻⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀
⢨⠀⠀⠀⠀⡆⢀⣀⣤⣴⣾⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣼⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂⢠⣾⣿⣿⣿⣿⣿⣿⣿⡻⠉⠉⠋⠀⠀⣠⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣤⣤⣴⣾⣿⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠙⠛⠻⠿⠿⠿⠿⠿⠿⠃⠙⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⣠⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠻⠟⠛⠀⠀⠀⣿⣿⣿⣿⣿⢩⣄⠀⣠⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠏⠀⠙⠱⠄⠀⢀⣀⣀⣀⣄⣀⣠⣠⣤⣾⡿⠀⢻⣯⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠛⣿⣧⣾⡿⠟⠛⠁⠀⠀
⠀⠀⠀⢀⣤⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠟⠛⠃⠀⣸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⢭⣭⣽⣿⣿⣿⣿⣿⣧⣤⣦⠀⡀⠀⠀⠀⠀⠈⢿⣿⡟⢻⣿⣧⡀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠁⠀⠀⠀⠀⠈⢿⣷⡿⢛⣻⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣿⣿⣿⣿⣆⠀⠀
⠸⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢰⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢻⣿⣿⣻⣟⣛⣛⣛⢿⣛⣻⣿⣟⡿⣿⢿⡻⣟⣛⡿⣟⣛⣛⣋⣀⢀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣿⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠈⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡄⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⢸⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠉⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⣿⣿⣷⣾⣿⣿⣿⣿⣿⡍⠉⠉⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠂⠲⣶⠀⠶⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠑⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⡉⠙⢿⣿⣿⣟⣃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⢿⣿⣿⡷⡽⣿⣿⡈⠛⠻⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢠⣬⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣨⣿⣷⣌⣿⣿⣷⣿⣿⣿⣦⣤⣶⣦⢻⣿⠛⠁⠈⠙⣿⣿⡿⠀⢠⣽⣿⡟⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠂⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣆⣀⣀⣀⣿⣿⣦⣀⣘⠛⠉⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣤⣾⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⢠⠂⣀⣠⣤⣶⣿⣿⠇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣾⣿⡄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⣅⣬⣙⠛⠻⣿⣿⠛⣶⣾⡿⠻⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣤⣤⣴⣾⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠛⠛⠻⠿⠿⠿⠿⠃⠙⠛⠛⠿⢿⣿⣷⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⠁⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⢠⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⣦⠀⠀⢠⣿⣿⣿⢩⣤⠀⣠⣶⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⠏⠀⠉⠉⠀⠀⢀⣀⣤⣤⣤⣀⣀⣠⣤⣾⡟⠀⢻⣟⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⠋⠉⠁⠀⠀⡾⠟⢛⣿⣧⣿⠿⠛⠋⠁⠀⠀
⠀⠀⠀⣀⣴⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⢀⣼⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⣠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⢹⣿⣧⠀⠀⠀⠀⠀
⢠⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣰⣶⣽⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠈⢿⣷⡿⣛⣻⣷⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣿⣿⢿⣆⠀⠀
⠸⠛⠛⠛⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢘⣿⣿⣿⣿⣿⣟⣛⢿⣛⣻⢿⣟⡿⣿⢿⡿⣟⣛⡿⣟⣛⣻⣛⣃⢀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⢉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠀⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡄⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣸⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⣿⣷⣾⣿⣿⣿⣿⣿⣿⡍⠉⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡜⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⡟⢿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡨⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣄⠈⠻⠿⢿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠙⣿⣯⡟⢿⣯⣟⡻⣿⣷⣀⠀⠉⢀⢻⣿⣿⣿⠿⢿⣿⣿⣿⡗⠒⢶⣾⡿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⣘⣿⣿⣿⣾⣿⣿⣿⡛⢿⣿⣿⣿⣿⣆⣹⣿⠁⠀⠀⢙⣿⡿⠃⠀⢾⡿⠟⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣿⣶⣤⡀⠀⠀⢸⠿⠁⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⢰⣀⣀⣤⣴⣶⣿⡿⠇⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡦⣶⣤⣶⣶⣶⣶⣿⣆⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡋⠀⣠⣴⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣤⣴⣶⣿⡿⠿⠛⠋⠁⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠟⠿⠛⠛⠁⠉⠛⠛⠛⠿⠿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⣽⣶⣶⣿⣉⣹⢿⣏⠙⠿⡿⠋⠃⣼⡇⠀⠀⠀⠀⠀⠀⠀
⠸⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣤⠸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣣⣤⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣴⣯⠱⣄⡀⣴⣷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠀⠀⠉⠋⠃⠀⣤⣀⣤⣠⣤⣤⣀⣠⣴⣿⡏⠀⢿⡿⣋⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⡿⠀⠀⢀⣉⣿⣷⠿⠟⠋⠉⠀⠀⠀
⠀⠀⢀⣤⣶⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⢠⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠀⠀⠀⢀⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⣹⣿⣧⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠙⠙⠻⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠈⢿⣾⡟⣩⣿⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⢿⣆⠀⠀
⠸⠛⠛⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣛⣿⣿⣿⣿⣿⣿⢿⣛⣻⣿⣟⡿⣿⢿⡿⣟⣛⡿⣟⣛⣿⣛⣻⢇⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣿⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠀⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⢿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣸⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠉⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⢹⣷⣾⣿⣿⣿⣿⣿⣿⣯⠉⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡞⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⡘⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠻⢿⣿⣿⢿⣿⣿⢧⣻⣿⣿⠉⠛⠻⠿⢻⣿⣿⣿⣿⣿⣿⣭⣿⣦⣈⣉⣉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠠⣾⣿⣷⣭⣿⣿⣶⣽⣿⣷⣤⣤⣤⡎⢻⣿⣿⠛⠉⠿⣿⣿⣿⠁⣩⣿⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⢿⣷⣫⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣼⣿⡄⠀⠀⠀⣾⣿⣅⠀⠘⠋⠁⠘⣿⡆⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⢸⣀⣠⣴⣶⣿⣿⠿⠃⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣶⣶⣶⣶⣶⣿⣿⣿⣄⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣦⡏⠀⠀⠀⠀⠀⠀⠀
⢸⣦⣶⣾⡿⠟⠛⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠀⠉⠉⠙⠛⠛⠛⠻⣿⣿⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠻⣿⣟⣛⠿⠿⢿⣿⡿⠷⣤⣼⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠋⠉⠀⠀⠀⠀⠀⠀⢀⣀⡤⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣄⣀⢀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⣠⣿⣿⣿⣿⣷⣶⣏⠉⠀⠘⠉⠀⢀⡰⣆⣀⣴⣷⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⡿⠀⠀⠈⠃⣒⣰⣤⣤⣤⣦⣤⣤⣤⣶⣶⣿⡇⠀⢿⣿⢟⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⢠⣼⣷⠿⠟⠉⠉⠀⠀⠀
⠀⠀⣤⣴⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠙⠛⠋⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢾⣿⣉⣽⣿⣧⡀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠈⢿⣾⢋⣭⣽⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣭⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡿⢿⣆⠀⠀
⠸⠛⠛⠋⠛⠛⢑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣈⣻⣿⣿⣿⣟⣿⢟⣛⣻⣿⣟⡿⣿⢿⡿⣟⣛⡿⢟⣛⣿⣛⣻⢿⣂⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠁⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡄⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢹⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⣷⣾⣿⣿⣿⣿⣿⣿⣿⡍⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡇⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⡿⠻⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣽⣿⡿⢿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠻⢿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⡿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⡿⣦⡀⠙⠻⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⢀⣈⣻⣿⣭⠿⣿⣿⣗⣻⣿⣧⡀⠈⠉⡈⢿⣿⣿⣿⡿⢿⣷⣿⣿⡖⠲⢶⡾⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡵⣏⣿⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⣌⣿⡛⠁⠀⠈⢹⣿⡿⠉⠻⣿⠷⠸⣿⡀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⣸⣤⣤⣶⣾⡿⠿⠟⠉⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣿⣿⣷⣦⣤⠀⠀⣀⡿⠃⠀⠀⠀⠀⠀
⢸⣶⣾⣿⡿⠟⠛⠉⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠉⠋⠛⠛⠛⠛⠛⠉⠀⠉⠉⠉⠛⠛⠋⠙⢻⣿⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀
⠘⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡇⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣤⣄⡀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⣻⣷⣤⣭⡍⣉⡻⠿⠉⢻⠿⠋⠀⣀⣀⣾⣷⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⣾⣾⣿⠟⠀⠀⠈⠙⠡⢴⣶⣶⣶⣶⣶⣦⣶⣶⣶⣿⠃⠀⢿⣿⠿⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⣸⠿⠛⠉⠁⠀⠀⠀
⠀⣀⣤⣴⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⡿⠁⠀⣼⣿⣆⠀⠀⠀⠀⠀⠀
⢰⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣾⢉⣽⣿⣧⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⢋⣭⣿⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠛⢛⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⠟⢿⣆⠀⠀
⠘⠋⠉⠉⠛⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣛⣿⣿⣿⣿⣿⢿⣛⣻⣿⣟⡻⣻⢿⡿⣟⣛⡿⣟⣛⣿⣛⣻⢿⣓⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣿⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠋⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢹⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠉⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣯⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⣿⣿⡿⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣯⣉⠙⢻⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣥⠈⠙⠻⣿⣿⡻⣿⣿⡿⣼⣿⣿⡍⠙⠛⠟⠙⣿⣿⣿⣿⣿⣿⣅⣽⣷⣤⣤⣤⣾⡿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢴⣤⣤⣤⣤⣤⣄⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣶⣷⣲⣿⣿⣿⣮⣿⣿⣿⣮⣿⣿⣶⣤⣴⣦⠙⣿⢿⠞⠉⠸⢿⣿⣿⠓⣶⣾⣮⢹⣧⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣯⣤⣶⣾⣿⠿⠿⠛⠘⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣤⣿⣧⠀⠀⠀⣾⣿⣧⣀⡈⠁⠀⢸⡿⠀⠀⠀⠀⠀
⢰⣶⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋⠉⠀⠈⠉⠉⠛⠋⠋⠉⠉⣿⣿⣦⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣠⣿⠀⢀⡀⠀⠀⠀
⠈⠉⠀⠀⠀⠀⠀⠀⢠⣤⣰⡇⠹⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣤⣄⡀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠙⣿⣯⣙⣻⡿⠿⢿⣟⠛⣦⣿⠏⠃⣴⣿⡷⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⠏⠀⠀⠈⠋⠂⢠⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⠁⠀⢿⣿⡿⢫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⢠⣾⣿⣿⣿⣿⣾⣧⡉⠀⠁⠁⠀⠘⠋⠀⠀⠀⠀⠀
⠀⣠⣤⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣶⠀⠀⣶⣆⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠉⠉⠁⢀⣤⣿⣿⣧⡀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣡⣾⣿⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠈⠛⠿⠟⢿⣆⠀⠀
⠘⠉⠉⠉⠙⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠀
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣘⣻⣿⣿⣻⣿⢿⣛⣻⣿⣟⡻⣛⢿⡻⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣃⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠇⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡄⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠉⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣯⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣶⣾⣿⣿⣿⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⣿⣿⡇⠹⣿⣿⣿⣿⣄⣻⣿⣿⣿⣿⣿⣿⣵⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣉⡋⠛⠻⢿⣿⣿⣿⣿⣿⣯⣻⣿⣿⠛⢿⢿⡟⢿⣷⣾⣿⣿⣿⣿⠉⣷⣄⣀⣉⣩⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣤⣴⢲⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⣿⣿⣷⣶⣦⣪⣿⣿⣮⣻⣿⣾⣯⣻⣿⣧⣄⣀⣠⡈⢿⣿⣿⠿⠋⣿⣿⣿⣿⣭⣭⣯⡽⣾⡄⠀⠀⠀⠀
⠀⠀⢀⣀⣷⣴⣶⣿⡿⠿⠟⠋⠈⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣗⣬⣿⡉⠀⠀⠀⣼⣿⡁⠀⠙⠋⠁⣿⡇⠀⠀⠀⠀
⢸⣿⣿⠿⠿⠋⠉⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠹⣿⣷⣹⢫⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⡿⠆⠀⣰⡿⢁⡀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⢀⣤⡶⠆⠹⠥⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠄⢰⣦⣄⡀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⡿⠿⣿⣿⣿⣿⠟⢡⣠⣿⠻⢱⣿⠷⠀⠀⠀
⠀⠀⠀⠀⣠⣤⣴⣿⣿⡿⠃⠀⠀⠀⠁⠀⠲⣾⣿⣿⣾⣷⣶⣿⣿⣿⡿⠀⠈⢿⣿⠿⢫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⢠⣿⣿⣿⣾⣵⣬⡉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣶⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡦⡤⠀⢠⣆⠀⠀⠀⠀⠀⠀
⢨⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠋⠋⠀⣠⣼⣿⣦⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣴⣶⣿⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠛⠻⢛⣿⣆⠀⠀
⠈⠉⠉⠈⠙⠹⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⠀
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣈⣻⣿⣿⣿⣿⢿⣛⣻⣿⣟⡻⣛⢟⡻⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣃⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠇⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠱⣾⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⢠⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣴⣶⣾⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣟⠙⢿⣿⣿⣿⣇⡹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣶⡾⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣏⠛⠿⢿⣿⡿⣿⡛⣿⣿⠻⣿⣿⡿⢿⣿⣿⣿⣷⣬⣿⣿⣿⣿⡟⢳⣤⠈⠙⠛⣻⣿⡇⠀⠀⠀⠀
⠀⠀⠀⢀⡄⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣾⣧⣿⣷⣦⣤⣿⣿⣿⡿⣿⣯⣳⡻⣿⣷⣀⠉⠉⢁⢹⣿⣿⣿⡿⢿⣷⣾⣿⣟⣻⣿⣏⣿⡇⠀⠀⠀⠀
⠀⢀⣀⣬⣷⣶⣿⡿⠿⠛⠛⠁⠈⠙⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣾⣿⡆⢹⡟⠃⠀⠀⢙⣿⡟⠁⠙⠟⠛⢻⣿⠀⠀⠀⠀
⢸⣿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠙⠁⠀⠉⠀⠀⣿⣿⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣤⣤⣼⣿⣿⣷⡶⠀⢀⣼⢋⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡾⠆⠻⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠀⢰⣶⣤⣀⡀⠀⠀⢀⣀⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣰⡿⡏⠿⠇⠀⠀⠀
⠀⠀⠀⣀⣤⣶⣿⣿⡿⠟⠁⠀⠀⠈⠒⠐⡻⣿⣿⣿⣷⣿⣿⣿⣿⣿⠏⠀⠘⢿⣿⠿⢫⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣿⣷⣿⣯⣭⣟⠋⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀
⢠⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⣄⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⠛⠟⠁⣰⢿⣦⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣦⣾⣿⣿⣷⡄⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⣿⣆⠀⠀
⠈⠀⠀⠈⠉⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣈⣻⣿⣿⣿⣿⢿⣟⣻⣿⣟⡻⣛⢟⡻⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣃⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⢩⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣿⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⡇⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢸⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡄⢸⣿⣿⣿⣿⣭⠁⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢹⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠉⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣯⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣷⣾⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣝⣿⣿⣿⠛⢿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣧⣨⣿⣿⣿⣿⣷⣿⡷⠿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢻⠻⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⠧⣄⡈⠝⠛⢛⣿⡇⠀⠀⠀⠀
⠀⠀⠀⢠⠀⠀⢀⣠⣤⣶⣶⡏⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣷⣿⣷⣤⣭⣻⣿⣿⣿⣾⣿⣳⡿⣿⣿⡈⠉⠙⠋⠹⣿⣿⣿⣹⣿⣳⣴⣿⣿⣻⣻⣟⣿⣧⠀⠀⠀⠀
⢀⣀⣤⣼⣶⣿⡿⠿⠛⠛⠉⠀⠈⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⠏⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣾⡗⠙⣿⠿⠉⠀⠙⣻⣿⠏⠙⠿⠛⢻⣿⠀⠀⠀⠀
⢸⣿⠟⠛⠉⠉⠀⠀⠀⠀⢀⢰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣦⣀⣀⣸⣿⣿⣶⣤⠀⠀⣼⡟⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⠿⠀⠻⠷⣲⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣷⠀⣿⣶⣦⣀⣀⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣾⡿⠛⠃⠀⠀⠀
⠀⠀⢀⣠⣴⣿⣿⣿⠿⠛⠀⠀⠀⠈⠁⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠙⢿⣿⠿⢫⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⣿⣿⣽⣿⢟⣿⠛⠁⠘⠿⠁⠀⠀⠀⠀⠀⠀
⢠⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⣿⣿⣿⣧⣤⡄⠀⣠⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠛⢀⣿⣦⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢶⣿⣿⣿⣷⡀⠀⠀⠀
⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠋⠩⣿⣆⠀⠀
⠀⠀⠀⠀⠉⠹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣀⣛⣿⣿⣟⣿⢿⣟⣻⣿⣟⡻⣛⢟⡻⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣃⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣿⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⡏⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠁⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢹⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠉⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣯⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣤⣴⣶⣷⣾⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠅⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣬⣙⣿⣿⣿⠛⢿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣷⣿⣇⣈⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⢻⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⠷⣤⡈⠙⢛⢛⣿⡇⠀⠀⠀⠀
⠀⠀⠀⢴⡀⢀⣠⣤⣴⣾⣿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣧⣿⣶⣌⣉⣿⣷⣽⣿⣾⣿⡷⣼⣿⣿⡉⠙⠛⠟⠹⣿⣿⣿⣻⣿⢧⣴⣿⣿⣻⣻⣿⣿⣷⠀⠀⠀⠀
⢀⣤⣴⣿⣿⣿⠟⠛⠋⠉⠁⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠿⢿⠿⠿⠿⠈⠻⠿⠿⣿⣿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⣤⣶⡦⠙⣿⠿⠙⠁⠘⣻⣿⠏⠙⠿⠛⢻⣿⠀⠀⠀⠀
⠸⠟⠋⠉⠁⠀⠀⠀⠀⢀⡄⢸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣤⣾⣦⣀⣀⣀⣿⣿⣷⣤⠄⠀⣸⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣶⣾⣿⠃⠈⠿⣿⣶⣀⣀⣄⣀⣠⣀⣠⣀⣤⣴⣿⡇⠀⣿⣷⣦⣄⣀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣾⠿⠋⠀⠀⠀⠀
⠀⢀⣠⣴⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠙⠻⠿⠛⢱⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣿⣽⣿⣿⣿⠛⠋⠈⠻⠋⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣷⣤⣴⠂⣀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠛⣠⣿⣆⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠼⣿⣿⣿⣷⡀⠀⠀⠀
⠸⠿⠿⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠁⠸⢿⣄⠀⠀
⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣀⣛⣿⣿⣟⣿⢿⣛⣻⣿⣟⡻⣛⢟⡻⣛⣛⡿⣟⣛⣿⣛⣻⢿⣛⣃⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣿⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⡇⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢹⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠉⠉⠈⠁⠉⠈⠁⠉⠁⠉⠈⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣯⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡤⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣿⣶⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀
⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣄⡙⢿⣿⣿⡟⢻⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣾⣧⣀⢹⣿⣿⣿⣷⣺⣷⠾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣍⠻⣿⣿⣿⣿⠷⣤⡀⠙⠛⢛⣿⡷⠀⠀⠀⠀
⠀⠀⠀⠆⣀⣀⣤⣴⣾⣿⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⢤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣷⣼⣦⣌⣉⢻⣿⣽⣿⣮⣿⣷⣌⢿⣿⡏⠙⠻⠿⠛⢿⣿⣿⡟⣿⡏⣀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⢠⣤⣶⣿⡿⠿⠛⠋⠉⠁⠀⡀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠛⠈⠛⠛⠻⠿⠿⠿⠿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣮⣿⣿⣶⣤⣤⣶⠘⢻⡿⡏⠋⠀⠛⣿⡿⠉⠟⠛⠛⣿⠀⠀⠀⠀
⠘⠛⠉⠀⠀⠀⠀⠀⠀⣀⡆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣿⣿⣿⣿⣦⣠⣷⣄⣀⣀⣸⣿⣿⣦⡄⠀⣰⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⣶⣿⡟⠁⠈⠳⠄⠆⠀⣀⣄⣤⣠⣀⣀⣀⣤⣴⣿⠃⠸⣿⣷⣦⣤⡀⠄⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣼⡿⠁⠀⠀⠀⠀
⠀⢀⣤⣦⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⠻⠿⠛⢱⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣯⣿⣿⣿⡟⠛⠁⢻⠋⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣼⣿⣿⣿⣿⣾⣿⣄⣠⡏⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠟⣰⣿⣆⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠸⣿⣿⣿⣧⡀⠀⠀⠀
⠘⠿⠿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠁⠿⢷⡄⠀⠀
⠀⠀⠀⠀⠀⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣀⣛⣿⣿⣟⣿⢿⣛⣻⣿⣟⡻⣛⢟⡻⣛⣛⡿⣟⣛⣿⣛⣻⢿⣛⣛⣀⣀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⡇⣿⡇⣿⣿⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⣿⣿⣿⡇⣿⣭⠀⢀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢹⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣿⣶⣾⣿⣿⣿⣿⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣯⣿⣿⣿⣿⣿⣿⣿⣯⣻⣷⣌⠙⣿⣿⣿⠛⢿⣿⣿⣿⣿⠘⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣷⣾⣄⠀⣻⣿⣿⣿⣦⣾⡷⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⡿⢧⣀⡉⠙⢛⣻⣿⠀⠀⠀⠀
⠀⠀⠀⣆⣀⣤⣴⣶⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣴⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣰⣷⣦⣄⢙⢿⣧⣽⣷⣬⣿⣧⣝⣿⣿⡏⠛⠻⠿⠙⣿⣿⣿⠝⣿⢇⣠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⢠⣶⣿⣿⠿⠟⠋⠉⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣾⣽⣿⣿⣦⣀⣠⡄⠘⢿⣿⡘⠉⠐⢻⣿⠟⠉⠛⠛⣻⡇⠀⠀⠀
⠈⠋⠀⠀⠀⠀⠀⠀⡀⣠⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣯⣀⣸⣤⣀⣀⣀⣿⣿⣷⣤⠠⢀⡿⠁⠀⠀⠀
⠀⠀⠀⠀⢀⣤⣴⣾⣿⠏⠀⠀⠀⠀⠀⢀⣤⣤⣤⣠⣄⣀⣀⣠⣼⡿⠀⢸⣿⣷⣤⣄⠀⢀⣀⣤⣶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⣿⠃⠀⠀⠀⠀
⠀⣀⣴⣶⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠉⠿⠟⠋⣾⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⢿⣿⠛⠁⢘⡟⠁⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢤⣿⣿⣿⣿⣖⣿⣦⣠⡌⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣷⣿⣄⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠰⣿⣿⢿⣦⡀⠀⠀⠀
⠘⠛⠻⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⠐⠻⢷⡄⠀⠀
⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣘⣻⣿⣿⣻⣛⢿⣛⣻⣿⣟⡻⣿⢿⡻⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣛⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠇⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⢿⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢹⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀
⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣌⣿⣧⣌⣹⣿⢿⡃⠙⣿⣿⣾⣿⡁⠻⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣙⢿⣿⣿⣿⣶⣦⣀⠘⣿⣿⣿⡿⢠⣷⠾⣿⣿⣿⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠉⠃⠙⠿⣿⣿⡿⣿⣿⢿⣷⡽⢿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠿⣿⡿⣿⠳⢤⣀⠈⢛⣻⣿⠂⠀⠀⠀
⠀⠀⢀⣀⣠⣴⣶⣾⣿⠿⠃⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡦⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣽⣤⣿⣷⣦⣄⡻⢿⣶⣿⣷⣼⣿⢦⣹⣿⣿⠈⠛⠛⠋⢻⣿⣿⡇⣹⠇⣀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀
⢰⣾⠿⠿⠛⠋⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠋⠀⠈⠙⠛⠛⠛⠙⠛⠛⠛⠛⠉⢙⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣷⡭⣿⣷⣤⣠⣦⠀⠻⣿⠇⠋⠀⢛⣿⡟⠉⠛⠛⣻⡇⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⢀⣤⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣄⣐⣧⣤⣀⣀⣬⣿⡿⣶⠄⢀⡾⠁⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣶⣿⡿⠀⠀⠈⠁⠀⠀⣀⣄⣤⣤⣤⣤⣤⣤⣶⣿⠇⠀⢿⣿⣷⣤⡀⢀⣀⣤⣴⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣠⡿⠃⠀⠀⠀⠀
⢀⣠⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠛⠙⢰⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡯⠙⢻⣿⣶⣻⡛⣛⠛⠁⠀⡟⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣾⣿⣿⣿⣇⣿⣦⣠⡔⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠛⣳⣷⣄⠀⠀⠀⠀⠀
⢺⣿⣿⣿⣀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠸⣿⡿⢿⣦⠀⠀⠀⠀
⠈⠛⠛⠟⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣫⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⠻⢧⡀⠀⠀
⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣙⣻⣿⣿⣛⣛⢛⣛⣻⣿⣛⡻⣿⢟⡻⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣛⣃⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠀⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢹⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠴⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀
⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⠸⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡟⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣦⣽⣷⣤⣹⣿⠿⠇⠉⢿⣿⣿⣿⡇⠙⠻⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣿⣍⣻⣿⣿⣿⣷⣷⣄⠈⣿⣿⣿⣿⢀⣷⠚⢿⣿⣿⣿⣿⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⠁⣁⠈⠛⢿⣿⡿⠿⣿⠿⣷⣎⠻⣿⣿⣿⣿⣿⣿⣿⣦⣉⡛⣿⡿⣿⠓⢤⣄⣈⣛⣭⣿⠃⠀⠀⠀
⠀⠀⣀⣤⣤⣶⣿⡿⠿⠟⠘⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣔⣿⣿⣶⣤⡙⣿⣶⣽⣿⣾⣿⣷⡹⣿⣿⠀⠉⠉⠃⠹⣿⣿⡆⣸⠇⣀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀
⢸⡿⠿⠛⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠉⠁⠀⠈⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⢈⣿⣿⣿⣿⣿⣿⣊⣿⣿⣿⣿⣷⣿⣿⣿⣷⠬⢿⣿⣦⣤⣦⠀⠹⡿⠇⠁⠀⢛⣽⡟⠀⠉⠉⢹⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣦⣴⣶⣦⣀⣤⣬⣿⡿⣶⠂⢀⡾⠁⠀⠀⠀
⠀⠀⠀⢀⣀⣤⣶⡿⠏⠀⠀⠀⠁⠀⠀⢤⣤⣦⣤⣤⣤⣤⣴⣾⣿⠁⠀⢿⣿⣷⣄⠄⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢽⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢋⣴⡿⠁⠀⠀⠀⠀
⢀⣤⣾⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠐⠋⠁⣾⣿⣿⣿⣿⣿⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⠉⢻⣿⣶⣽⡛⣛⠋⠁⠈⠏⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⣿⣿⣿⣇⣿⣦⣠⡎⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢙⣽⣷⡀⠀⠀⠀⠀⠀
⢸⣿⣿⣧⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠺⢿⠟⢿⣄⠀⠀⠀⠀
⠈⠉⠛⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠻⢧⠀⠀⠀
⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣀⣛⣻⣿⣿⣛⣛⢛⣛⣻⠿⣛⡻⣿⢿⡿⣟⣛⡿⢟⣛⣿⣛⣻⢿⣛⣛⣃⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠀⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣯⢹⣿⠁⠀⠀
⠀⠀⢰⣮⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣼⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠂⠲⣶⠀⠴⠄⠠⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀
⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣿⣿⣟⣿⣿⣿⣿⠘⣿⡙⠻⣿⣿⣿⡿⣿⣿⣷⢻⣿⡟⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣷⣦⣼⣿⠻⠃⠈⢻⣿⣿⣿⣇⠙⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⡿⣿⣿⣝⣻⣿⣿⣿⣿⡿⣷⣬⣙⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⢠⣷⠚⢿⣿⣿⣿⣿⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠀⣄⣈⠙⠻⣿⣟⠻⣿⡻⢿⣎⠻⣿⣿⣿⢿⣿⣿⣿⣦⣈⣛⠿⣟⡿⠓⢤⣄⣈⣛⣩⣿⠂⠀⠀⠀
⠀⢀⣤⣤⣴⣾⣿⠿⠟⠋⠙⠻⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢺⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣾⣿⣿⣷⢦⣌⣿⣿⣮⠿⣾⣿⣷⠼⣿⣧⡀⠉⠉⠁⠹⣿⣿⠆⣸⠇⣤⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀
⠸⠿⠛⠛⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⢿⣿⣦⣴⡇⠀⠹⡟⠁⠁⠀⢋⣽⡋⠈⠋⠉⣿⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣷⣦⣤⣶⣦⣀⣤⣬⣿⠗⣶⠀⣀⡞⠀⠀⠀⠀
⠀⠀⠀⡀⣠⣴⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣴⣾⡟⠀⠘⠿⣷⣦⡤⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢃⣴⠟⠀⠀⠀⠀⠀
⢠⣴⣶⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠘⠉⢰⣿⣿⣿⣿⣿⡏⠙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠉⢻⣿⣧⡝⢉⡉⠉⠀⢘⠋⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣗⣠⣿⣿⣿⣿⣸⣷⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⢋⣼⣦⡀⠀⠀⠀⠀⠀
⢸⣿⣿⣆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠿⢿⠟⣷⡄⠀⠀⠀⠀
⠈⠉⠙⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠉⠻⢦⠀⠀⠀
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣈⣛⣻⣿⣿⣛⣛⢻⣛⣛⠟⣛⡿⣿⢿⡿⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣛⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠀⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣯⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣸⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣯⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠄⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀
⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⢹⣿⣿⣯⣿⣿⣿⣿⠸⣿⠙⠿⣿⣿⣿⡿⣿⣿⣿⢻⣿⡿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣦⣽⣷⣦⣼⣟⠻⠀⠈⢿⣿⣿⣿⡅⠈⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⡝⢿⣿⣽⣻⣿⣿⣿⣿⡻⣷⣬⣹⣿⣿⣿⣿⣷⣄⠈⣿⣿⣿⡗⣰⡗⠛⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣶⢀⣤⣌⠉⠹⣿⣏⠻⣯⡛⣿⣌⠻⣿⣿⡿⣿⣿⣿⢿⣆⣉⡛⠿⢻⡟⠳⣤⡀⠈⢋⣹⣿⠀⠀⠀⠀
⠀⣨⣤⣤⣶⣿⡿⠿⠛⠁⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣼⣾⣿⣿⣷⣦⣬⣿⣿⣾⢿⣿⣯⣶⠹⣿⣇⡀⠉⠙⠀⢻⣿⣿⢀⣿⢁⣠⣿⣿⣿⣻⡿⣿⠆⠀⠀⠀
⠸⡟⠛⠋⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⣸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⠚⣿⣷⣤⣶⠀⠀⠻⠉⠀⠀⠘⣫⣽⠋⠈⠛⠃⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣶⣤⣴⣶⣤⣠⣤⣼⡿⢷⡄⠀⣠⠏⠀⠀⠀⠀
⠀⠀⠀⡀⣤⡶⡿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣴⣾⠇⠀⠸⠿⢷⣤⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⢁⣼⠟⠀⠀⠀⠀⠀
⢠⣷⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⠋⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢙⣿⣿⣬⡛⢫⡋⠉⠀⠚⠁⠀⠀⠀⠀⠀⠀
⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣅⣾⣿⣿⣿⣇⢸⣧⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠙⢃⣾⣦⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠿⠿⠛⣷⡀⠀⠀⠀⠀
⠈⠉⠙⢗⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⣄⠀⠀⠀
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣘⣛⣻⣿⣟⣛⣛⢿⣛⣛⠟⣛⡿⣿⢿⡿⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣃⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠀⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣿⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣸⣿⣥⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⢵⣾⣿⣿⣿⣿⣿⣿⣿⡯⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣏⣹⣿⣿⣿⣿⣿⣿⡟⠘⣿⡉⠻⣿⣿⣿⡿⣿⣿⣷⢻⣿⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣿⣿⣦⣾⣟⠛⠀⠈⣿⣿⣿⣿⡀⠛⠻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠘⢿⣿⣿⣿⣿⣿⣿⣿⡹⢷⣤⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣿⡇⣸⡖⠛⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⢴⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣴⣿⢰⣶⣄⠉⠹⣿⣍⣻⣯⡙⣿⣌⢻⣿⣿⠿⣿⣿⣿⣿⣄⣙⠻⢿⣻⡟⠣⣤⡀⠈⢋⣹⣿⠀⠀⠀⠀
⢀⣠⣤⣶⣾⡿⠿⠟⠛⠈⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢷⣼⣿⣿⣟⣿⣿⣿⣇⠻⣿⣄⠀⠀⠉⠈⢿⣿⡗⢠⡿⢀⣴⣿⣿⣟⣿⠿⣿⠀⠀⠀⠀
⠸⠟⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠀⠀⣿⣧⣿⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⣿⣷⣴⡶⠀⠈⠗⠁⠀⠀⠘⣩⡿⠋⠙⠛⠀⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⣦⣬⣵⣦⣄⣤⣤⣽⠿⢦⠄⠀⣠⠏⠀⠀⠀⠀
⠀⠀⢀⣠⣴⢾⠿⠃⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣾⣿⠁⠀⠻⠿⣷⣄⠄⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡸⣟⣿⣿⣿⠿⣿⣿⣿⣿⣿⠋⣀⣾⡏⠀⠀⠀⠀⠀
⢠⣼⣿⡧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠉⠁⣾⣿⣿⣿⣿⣿⢉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⢹⣿⣧⣌⠉⣋⠉⠁⠀⠋⠁⠀⠀⠀⠀⠀⠀
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣰⣿⣿⣿⣿⣀⣿⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠘⣱⣾⣆⠀⠀⠀⠀⠀⠀
⢸⣿⣷⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⠿⠟⢻⣧⡀⠀⠀⠀⠀
⠈⠉⠙⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠙⠷⡄⠀⠀⠀
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢀⣙⣛⣻⣿⣛⣛⣛⢿⣛⣛⠛⣿⡿⣿⢿⡿⣟⣛⡿⣟⣛⣿⣛⣻⢿⣛⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠀⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣯⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢻⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣸⣿⣅⣿⢻⣿⣿⣇⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠁⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⠉⣷⣾⣿⣿⣿⣿⣿⣿⣿⡍⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣠⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣏⣹⣿⣿⣿⣿⣿⣿⡟⠸⣿⡉⠻⣿⣿⣿⠿⣿⣿⣷⢻⣿⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⡷⢿⣿⣶⣾⣟⡋⠀⠘⣿⣿⣿⣿⡀⠛⡻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠹⠘⢿⣿⣯⣿⣿⣿⣿⣿⡙⢿⣦⣿⣿⣿⣿⣿⣧⡀⢼⣿⣿⣿⣃⣸⠖⠻⣿⣿⣿⣿⣶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣾⣿⣰⣶⣄⡀⠹⣿⣌⡻⣮⣹⣷⡌⢻⣿⣿⠻⢿⣿⡿⣷⣄⡉⠻⢿⣿⠛⢢⣄⠀⠘⢋⣹⡿⠀⠀⠀⠀
⢀⣤⣴⣶⣿⠿⠿⠛⠋⠈⠙⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢶⣾⣿⣿⣯⣿⣿⣾⣇⠻⣿⣤⠀⠀⠁⠈⣿⣿⡇⣰⠟⣀⣴⣿⣿⣛⢿⠿⡿⠀⠀⠀⠀
⠘⠛⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣯⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢻⣿⣷⣴⡇⠀⠘⠏⠁⠀⠀⢉⣭⡟⠉⠙⠛⠀⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡴⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣷⣶⣮⣷⣦⣤⣤⣤⣽⠿⣤⠀⠀⣤⠃⠀⠀⠀⠀
⠀⠀⢀⣄⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣦⣤⣠⣴⣾⡟⠀⠈⠻⢿⣷⡤⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣺⢟⣿⣿⣿⠿⣿⣿⣿⣿⡿⠋⣀⡾⠇⠀⠀⠀⠀⠀
⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠈⠉⢀⣿⣿⣿⣿⣿⡏⢉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣹⣿⣆⣍⠙⡍⠉⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀
⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧⣼⣿⣿⣿⣿⣈⣿⣄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠁⠛⣠⣿⣄⠀⠀⠀⠀⠀⠀
⢸⣿⣧⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⠿⠟⣻⣧⠀⠀⠀⠀⠀
⠈⠉⠙⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⡀⠀⠀⠀
⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⢀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⢀⣀⡀⠀⣀⡀⣀⢈⣛⣟⣻⣟⣛⣛⣛⢿⣛⣛⠛⣿⡿⣿⢿⡿⣟⣛⡿⣟⣛⣿⣛⣻⢿⣃⣀⣀⢀⣀⣀⣀⡀⢀⣀⡀⣀⢀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣯⣛⢺⣿⣿⡇⣿⣉⠀⠉⣿⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢿⣿⡛⠀⢿⣿⣿⣾⡿⣿⣏⠙⢻⣿⣿⢿⣿⣉⠀⣿⡇⣿⣾⡇⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⡉⣿⣿⣿⣿⡏⣿⢸⣿⡁⣿⣿⣯⢹⣿⠁⠀⠀
⠀⠀⢰⣎⣿⢾⣿⣿⡇⣿⣭⠀⠀⣿⠀⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣷⢶⣿⣿⠀⢸⣿⣿⣿⡇⣿⣯⡀⢸⣿⣿⣿⣿⣭⠀⣿⡇⣿⢿⡇⣿⣿⣿⣿⣯⣽⣿⢩⣸⣿⣅⣿⢻⣿⣿⣧⣿⢸⣿⣅⣿⢿⣿⢸⣿⠀⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠀⠀⠉⠀⠉⠈⠉⠈⠁⠉⠈⠁⠉⠁⠉⠀⠉⠁⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠀⠈⠁⠉⠈⠁⠉⢹⣷⣾⣿⣿⣿⣿⣿⣿⣿⠉⠈⠉⠈⠉⠁⠈⠉⠁⠉⠈⠁⠈⠉⠀⠀⠀
⠀⠀⠲⣶⠀⠰⠄⠠⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣶⣷⣦⣤⣤⣤⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⣠⢰⣿⣧⢾⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⡇⠹⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠠⡀⠀⠀⢀⣀⣤⣴⡶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⢀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣿⣿⣿⣿⣾⣍⣿⣿⣿⣿⣿⣽⣿⣍⢿⣿⣿⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⢷⣤⣘⣻⣿⣿⣿⠀⠀⠀⠀
⣸⣷⣶⣿⣿⡿⠿⠟⠁⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢈⣯⡸⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀
⠹⠟⠛⠉⠀⠀⠀⡀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠙⠋⠉⠉⠉⠉⠉⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣙⣿⠟⠉⠘⢿⣿⡿⠋⠻⠛⢻⣿⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣴⣿⣿⠘⢿⣿⣦⣤⣀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣶⠀⣿⣶⣤⣀⡀⠀⠀⣀⠀⢀⣠⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣶⠆⣠⣼⡟⠀⠀⠀⠀
⢠⣴⣿⣿⣿⣿⠟⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠸⣿⣿⣿⣿⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣿⡏⠀⠀⠀⠀⠀
⢸⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠘⠛⠉⣹⣿⣿⣿⣿⣿⣏⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⠛⠁⢸⠟⠁⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀
⢺⣿⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⣟⣷⣿⣄⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠿⢿⢛⣿⣦⠀⠀⠀⠀⠀
⠘⠻⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠄⠀⠀⠈⠙⠻⢷⡄⠀⠀⠀
⠀⠀⠘⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠿⠛⠛⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠙⠻⠿⠿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣤⣁⣱⣿⣶⣤⣤⣤⣤⣾⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣠⣶⣾⣵⣷⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⠠⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣘⣟⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣟⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣠⣴⣶⢶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⣽⣿⣍⢿⣿⣿⠻⣿⣿⡿⣿⣯⣿⣿⣿⣿⠻⢶⣤⣹⣿⣛⣿⣿⠀⠀⠀⠀
⣸⣶⣾⣿⡿⠿⠟⠛⠈⠙⠛⠛⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢈⣯⢸⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠸⠟⠋⠁⠀⠀⣀⡄⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠙⠉⠉⠉⠉⠉⠉⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣹⡿⠏⠁⠘⣻⣿⡿⠋⠻⠛⢻⣿⠀⠀⠀⠀
⠀⠀⢀⣤⣤⣾⣿⠇⠹⣿⣷⣦⣄⣄⠀⠀⠀⣀⣀⢀⣀⣠⣴⡇⠀⣷⣦⣤⣀⣀⣀⣀⣀⠤⢀⣠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣶⠀⣤⣾⠏⠀⠀⠀⠀
⢰⣾⣿⣿⣿⡿⠋⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠻⣿⣿⣿⣿⣯⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⡿⠋⠀⠀⠀⠀⠀
⢸⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠚⠛⠉⣽⣿⣿⣿⣿⣿⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣟⠋⠁⢺⠏⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠙⢛⣼⣷⡄⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⢿⢛⣿⣆⠀⠀⠀⠀⠀
⠘⠿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⡀⠀⠀⠀
⠀⠀⠛⠃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠿⠛⢻⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠈⠛⠿⠿⠿⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⣵⣿⣶⣤⣤⣤⣤⣾⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣦⣰⣿⡮⣣⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⠀⠒⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣿⡅⠸⣿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣏⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⣀⣠⣤⣶⣶⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣷⣷⣿⣿⣾⣿⣷⣽⣷⣌⣿⣿⣿⠻⣿⣿⡿⣿⣾⣿⣿⣿⣿⠛⢶⣤⣸⣿⣛⣿⣿⠀⠀⠀⠀
⣰⣿⣿⣿⠿⠟⠛⠁⠈⠙⠛⠛⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣈⣧⡹⣿⣿⣿⣿⣯⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠸⠛⠉⠀⠀⢀⣀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣹⣿⠋⠀⠘⣻⣿⡟⠙⠿⠛⢻⣿⠀⠀⠀⠀
⠀⠀⢀⣤⣴⣼⡿⠃⢻⣿⣶⣦⣠⣀⠀⢀⠀⣀⠀⢀⣀⣠⣾⡇⢸⣿⣷⣤⣄⣀⣠⣀⡀⠀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣿⣿⣿⣶⠀⢄⣾⠏⠀⠀⠀⠀
⢠⣾⣿⣿⣿⡿⠁⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠿⣿⣿⣿⢟⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃⣰⣿⠋⠀⠀⠀⠀⠀
⢸⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠐⠟⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠚⠉⢁⣿⣿⣿⣿⣿⣿⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣿⣿⣿⣟⠉⠁⢻⠏⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠛⠛⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠛⠹⢋⣾⣷⡀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠿⡟⣻⣿⣆⠀⠀⠀⠀⠀
⠘⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠛⠻⢧⡀⠀⠀⠀
⠀⠈⠛⣡⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⠟⠛⢻⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠁⠀⠈⠛⠿⠿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢴⣀⣵⣿⣶⣶⣶⣶⣴⣾⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣦⢔⣽⣟⣶⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠄⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣜⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣘⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⢀⣀⣤⣶⣶⡞⣷⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣄⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣿⣷⣌⣿⣿⡟⠻⢿⢿⡿⣿⣿⣿⡿⣿⣿⠛⢶⣤⣘⣟⣟⣿⣿⠀⠀⠀⠀
⢴⣿⣿⡿⠿⠛⠋⠁⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣧⢹⣿⣿⣿⡿⢧⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠘⠋⠁⠀⠀⢀⣀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀⠀⢀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣹⣛⠃⠀⠈⣿⣿⠟⠉⠻⠛⢻⡇⠀⠀⠀⠀
⠀⠀⣠⣶⣾⣾⡿⠈⢿⣿⣷⣶⣄⣄⣀⢀⢀⣀⡀⣠⣀⣴⣿⠀⢸⣷⣶⣤⣀⣀⣠⣀⡀⢄⣂⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣿⣿⣿⣤⠀⢠⣾⠃⠀⠀⠀⠀
⢰⣿⣿⣿⡿⠟⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⢿⣿⣿⣿⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣸⣿⠃⠀⠀⠀⠀⠀
⢸⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠐⠛⠉⢡⣿⣿⣿⣿⣿⣿⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣟⠉⠀⣻⠏⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣧⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠙⣛⣾⣷⡀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⠿⢟⣹⣿⣄⠀⠀⠀⠀⠀
⠘⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⠀⠀⠀⠀
⠀⠘⠋⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠟⠛⢻⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠀⠀⠈⠻⠿⠿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⣤⣠⣿⣿⣷⣶⣶⣶⣶⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣴⣿⢭⣱⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⡤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣯⣿⣄⠸⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣍⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⣀⣤⣴⣶⣾⢾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣷⣿⣿⣌⣿⣿⡟⠛⠿⢿⡿⣿⣿⣿⡿⣿⣿⠛⢶⣤⣘⣛⣿⣿⣿⠀⠀⠀⠀
⢾⣿⡿⠿⠟⠛⠉⠀⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣧⢹⣿⣿⣿⡿⢷⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠈⠁⠀⠀⠀⢀⡄⣾⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣄⣽⣟⠃⠀⢈⣿⣿⡟⠉⠛⠛⢻⣷⠀⠀⠀⠀
⠀⢀⣰⣾⣿⣿⠇⠘⢿⣿⣶⣤⣠⣀⣀⢀⣀⣠⣀⣀⣄⣶⣿⠀⣿⣿⣶⣤⣄⣀⣠⣤⠄⢒⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣶⠀⢠⣾⠃⠀⠀⠀⠀
⢸⣿⣿⣿⠿⠃⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⢿⣿⣿⡿⣫⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣴⡿⠁⠀⠀⠀⠀⠀
⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠐⠉⠉⣸⣿⣿⣿⣿⣿⣏⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣏⠉⠀⢻⠋⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣤⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠛⣋⣾⣷⡀⠀⠀⠀⠀⠀⠀
⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⠿⢟⣹⣿⣄⠀⠀⠀⠀⠀
⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⢦⠀⠀⠀⠀
⠀⠛⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠟⠛⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠙⠻⢿⠿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠀⣠⣤⣬⣿⣷⣶⣶⣶⣶⣶⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⡦⢶⡿⣬⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣻⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣯⣿⡀⠸⣿⣿⣿⣿⣌⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣬⣿⣟⠿⣿⣿⣿⢿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣿⠛⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣀⣄⣀⣀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣿⣿⣌⣿⣿⡏⠙⠿⢿⡿⣿⣿⣿⡿⣿⣿⠛⢲⣦⣘⣛⣿⣿⣿⠀⠀⠀⠀
⢾⣿⡿⠟⠛⠋⠁⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣧⠹⣿⣿⣿⡿⢧⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠈⠀⠀⠀⠀⣀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣹⣛⠃⠀⢈⣿⣿⡟⠉⠛⠛⢹⣗⠀⠀⠀⠀
⠀⢀⣠⣶⣾⡿⠃⠻⣿⣗⣦⣀⣀⣀⣀⣀⢀⣀⢀⣀⣠⣾⡇⠀⣿⣿⣶⣤⣀⣀⣠⢀⠀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣶⠀⢄⣾⠃⠀⠀⠀⠀
⢸⣿⣿⣿⠟⠁⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠹⢿⣿⣿⣿⣫⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⣼⣿⠁⠀⠀⠀⠀⠀
⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠐⠋⠉⣸⣿⣿⣿⣿⣿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⡏⠁⠀⣺⠋⠀⠀⠀⠀⠀⠀⠀
⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠛⢋⣾⣷⡀⠀⠀⠀⠀⠀⠀
⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⠿⢟⣹⣿⣄⠀⠀⠀⠀⠀
⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⢦⠀⠀⠀⠀
⠀⠛⣁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠟⠛⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠙⠻⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⣤⣤⣿⣿⣷⣶⣾⣶⣾⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⣄⣲⣽⣡⣬⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠌⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣹⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣯⣿⡀⠘⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣨⣿⣟⠿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⠛⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⣀⣤⣴⣶⣿⡟⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣠⣄⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣿⣿⣌⣿⣿⡏⠙⠿⢿⡟⣿⣿⣿⡟⣿⡿⠙⢳⣦⣘⣛⣛⣿⣿⠀⠀⠀⠀
⢻⣿⠿⠛⠛⠉⠁⠀⠉⠉⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣦⠻⣿⣿⣿⡿⢷⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⢸⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣹⡘⠁⠀⢈⣽⣿⡟⠈⠛⠛⢻⣟⠀⠀⠀⠀
⢀⣠⣤⣶⣿⡟⠀⢻⣿⣟⣦⣤⣀⣀⣀⣀⣀⣀⢀⣀⣴⣾⡇⢸⣿⣷⣤⣄⣀⣀⣀⡤⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣶⠀⢀⣾⠃⠀⠀⠀⠀
⢸⣿⣿⡿⠟⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠻⢿⣿⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⣼⣿⠁⠀⠀⠀⠀⠀
⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠉⠉⣸⣿⣿⣿⣿⣿⣇⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⣿⣿⣿⡍⠉⠀⣻⠋⠀⠀⠀⠀⠀⠀⠀
⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠙⢋⣼⣧⡀⠀⠀⠀⠀⠀⠀
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠰⠿⢟⣹⣿⣄⠀⠀⠀⠀⠀
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⣦⠀⠀⠀⠀
⠘⠋⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠟⠛⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠙⠿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⡀⠀⠒⠠⢤⣤⣴⣿⣶⣿⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣰⣿⣌⣴⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⠌⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣹⣿⣿⡿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣾⣿⣀⣹⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣼⣿⡟⠿⣿⣿⣟⣿⣿⢿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀
⢀⣠⣤⣶⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣿⣷⣼⣿⣿⡏⠛⠟⢿⡻⣿⣿⣿⡿⣿⡟⠉⢳⣦⣘⣛⣫⣿⣿⠀⠀⠀⠀
⢻⠿⠟⠛⠋⠉⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⠏⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣦⣠⣼⡦⢻⣿⣿⣻⠿⢳⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡄⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡙⠀⠀⢉⣿⣿⡋⠈⠛⠛⢹⣇⠀⠀⠀⠀
⢀⣠⣴⣿⣿⠟⠘⢿⣿⣖⣄⣠⣀⡀⣀⣀⠀⢀⢀⣀⣶⣿⠀⢸⣿⣷⣦⣀⣀⣀⣄⡤⢄⣀⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⡶⠀⢠⣾⠃⠀⠀⠀⠀
⢸⣿⣿⠟⠋⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠛⢿⣿⣿⢟⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣼⢿⠁⠀⠀⠀⠀⠀
⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠚⠉⢁⣿⣿⣿⣿⣿⣿⣏⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⡉⠁⠀⡻⠃⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠛⢃⣾⣧⡀⠀⠀⠀⠀⠀⠀
⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠰⠿⢟⣹⣿⣄⠀⠀⠀⠀⠀
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⣦⠀⠀⠀⠀
⠘⢁⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠟⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠀⠈⠛⢿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠀⢤⠄⠀⢲⣤⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢒⣔⣾⣂⣳⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣬⣿⣿⣿⡿⠻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣾⣷⣄⣹⣿⣿⣿⣷⣼⣿⣻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣼⣿⡛⠿⢿⣿⣟⣿⣟⢿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣟⠉⠻⢿⣿⣿⣿⣷⠀⠀⠀⠀
⣠⣤⣶⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⣶⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⠈⠛⠛⢿⠻⣿⣿⣿⢻⣿⡏⠉⣷⣦⣭⣹⣭⣿⣿⠀⠀⠀⠀
⢹⠿⠛⠉⠉⠀⠀⠀⠁⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⣿⡿⠿⠃⠙⠻⠿⢿⣿⣿⡿⡿⠿⠿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣾⡄⢻⣿⣿⠿⠟⣰⣿⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡄⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣤⣿⡉⠀⠀⢩⣿⣿⡁⠈⠙⠛⢹⣗⠀⠀⠀⠀
⢠⣴⣶⣿⡿⠃⠙⠿⣿⣶⣤⣄⣀⣀⣀⣀⡀⣀⣀⣤⣶⡿⠀⢻⣿⣷⣤⣀⣀⣀⣀⠤⢄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡖⠀⣠⡾⠁⠀⠀⠀⠀
⢸⣿⠿⠛⠁⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠘⠻⣿⣿⣿⣋⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠫⣤⣾⠿⠁⠀⠀⠀⠀⠀
⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠉⢁⣿⣿⣿⣿⣿⣿⣠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣴⣿⣿⣿⣿⣿⣿⡉⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠛⣡⣿⣧⡀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⢋⣹⣿⣄⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣦⠀⠀⠀⠀
⠈⡁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠛⢻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠋⠀⠈⠻⢿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢠⡀⢀⡀⠀⣒⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣻⣄⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠠⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⡟⠻⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣷⣼⣟⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣿⣯⣛⠻⣿⣿⣻⣿⡛⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⡏⠉⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣠⣴⣶⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⠈⠛⠻⡏⢻⣿⣿⣿⢻⣿⠋⢙⣷⣤⣍⣩⣭⣿⡿⠀⠀⠀⠀
⠹⠛⠋⠉⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⢿⠿⠿⠿⠁⠻⠻⠿⢿⡿⣿⣿⠿⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣦⡘⢿⣿⣿⠿⠛⣾⣿⣿⣿⣿⣿⣿⢿⡷⠀⠀⠀⠀
⠀⠀⠀⢀⣤⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣏⡉⠀⠀⣼⣿⣟⠁⠈⠉⠉⢸⡧⠀⠀⠀⠀
⢠⣾⣾⣿⡟⠀⠙⢿⣿⣧⣤⣤⣀⣀⣀⣀⣀⣀⣠⣴⣿⡏⠀⣿⣿⣷⣤⣀⣀⣀⡀⠤⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⠖⠀⣰⣾⠁⠀⠀⠀⠀
⢸⣿⠿⠋⠀⠀⠀⠀⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠘⠛⣿⣿⡿⣫⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣠⣾⠿⠁⠀⠀⠀⠀⠀
⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠉⢠⣿⣿⣿⣿⣿⣿⣠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣯⠁⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠛⣡⣿⣧⡀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⠻⠋⣽⣿⣄⠀⠀⠀⠀⠀
⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢦⠀⠀⠀⠀
⠀⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠛⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠋⠀⠈⠻⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡶⡀⢠⡄⠢⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠟⣿⣴⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⢠⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡔⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⠛⢿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣤⣸⣿⣿⣿⣿⣦⣿⣟⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣿⣿⡙⢿⣿⣟⣿⣿⡻⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⣿⡏⠙⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣤⣶⣾⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⢤⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠙⠛⢿⠟⣿⣿⣿⡟⣿⡿⠉⢹⣶⣤⣹⣩⣽⣿⡿⠀⠀⠀⠀
⠙⠛⠉⠉⠀⢀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⢿⡿⠿⠛⠈⠛⠛⠿⣿⣿⣿⣿⡿⡿⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣶⠻⣿⣿⡿⠿⢳⣾⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀
⠀⢀⢀⣠⣦⢸⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣉⠁⠀⢈⣽⣿⡏⠀⠉⠛⠋⣿⡇⠀⠀⠀⠀
⢠⣿⣿⣿⠋⠀⠻⣿⣿⣷⣶⣄⣀⣀⣄⣠⣄⣠⣤⣾⣿⠇⠈⣿⣿⣷⣦⣤⣄⣀⡤⠔⣚⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⠂⢀⣴⡿⠁⠀⠀⠀⠀
⢸⡿⠛⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠙⢿⣿⣿⡿⣫⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢅⣠⣿⠟⠀⠀⠀⠀⠀⠀
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠉⠁⢠⣿⣿⣿⣿⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣏⠁⠀⢈⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠛⣡⣿⣧⡀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠻⠋⣽⣿⣄⠀⠀⠀⠀⠀
⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠠⠀⠀⠀⠈⠛⠻⢦⠀⠀⠀⠀
⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠛⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠈⠻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2126

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/irc-log-110521/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/irc-log-110521/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ IRC_Proceedings:_Tuesday,_May_11,_2021⠀✐


Posted in IRC_Logs at 2:25 am by Needs Sunlight


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇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
 QmUx9AH1SnGs4JGjbxqZ3hKJgeDeFV7dZHLCS22C8n6gxL #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 #boycottnovell
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                                                 as plain/ASCII
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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmY1nEtvC6N6tNSxkwj8Tw653B51CPx3PDFFgdZ8WdY6uP



                    ䷩ 𝚕𝚒𝚗𝚎 2240

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/kangaroo-court-at-eponia/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/kangaroo-court-at-eponia/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ The_EPO’s_War_on_Justice_and_Assault_on_the_Law_—_Part_1:_Rumours_of_a
Kangaroo_Court_at_EPOnia⠀✐


Posted in Europe, Law, Patents at 1:15 am by Dr. Roy Schestowitz


             🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Carl Josefsson's kangaroo court⦈
              Is Carl Josefsson presiding over a kangaroo court?


Summary: EPO‘s President Benoît_Battistelli viciously attacked judges and
slandered judges; António_Campinos adopts a more ‘soft power’ approach, but
nevertheless the_impact_is_the_same


Almost two years have passed since Techrights published the mini-series "EPO
Looney_Tunes" which explored the “difficult_legacy” of Battistelli’s Boards of
Appeal “reform”, in particular the banishment of the Boards to Haar.


That mini-series reported on the referral case G 2/19 in which the Enlarged
Board had to deal with the question as to whether or not oral proceedings could
lawfully be held in the municipality of Haar adjoining Munich.


As predicted, the Enlarged Board ended up confirming that the holding of oral
proceedings in Haar was in compliance with the EPC, thereby effectively rubber-
stamping the exile of the Boards from Munich in accordance with controversial
scheme conjured up by Battistelli in 2016.


Since then the Enlarged Board under Josefsson’s management has cemented its
reputation for “legal_fudge” and “cakeism”, most notably following its decision
in case no. G 3/19 in May of last year.


On the surface, case no. G 3/19 was about the rules governing biotech patenting
but the decision of the EBA has far more general and wide-reaching legal and
political implications which extend beyond any specific field of patenting.


“Hence, the decision of the Enlarged Board in case no. G 3/19 implies that the
mechanism for amending the Implementing Rules can now be (mis)used by the
Council as a convenient – but legally questionable – means for avoiding the
bother of convening a diplomatic conference to revise the Articles of the
EPC.”According to informed commentators, the doctrine of “dynamic
interpretation” on which G 3/19 relied, basically opens the door to the EPO’s
Administrative Council to change the EPC by amending the Implementing Rules.


It should be recalled that – in contrast to the Articles of the EPC which can
only be changed by a diplomatic conference and the unanimous consent of all
contracting states – the Implementing Rules can be changed at the drop of a hat
by a simple majority of the Administrative Council.


Hence, the decision of the Enlarged Board in case no. G 3/19 implies that the
mechanism for amending the Implementing Rules can now be (mis)used by the
Council as a convenient – but legally questionable – means for avoiding the
bother of convening a diplomatic conference to revise the Articles of the EPC.


This is because the Enlarged Board has effectively taken the position that the
primary law of the EPC can be “dynamically re-interpreted” in the light of
amendments to the subordinate Implementing Rules.


“Even IP Kat – which had been more or less neutered by Battistelli from about
2016 onwards – showed visible signs of discomfort at this development…”Such a
position is completely at odds with the generally recognised principle of the
hierarchy_of_legal_norms – but this is EPOnia we are dealing with here, the
realm of “legal anarchy”.


Even IP_Kat – which had been more or less neutered_by_Battistelli from about
2016 onwards – showed visible signs of discomfort at this development and
warned that “the fudging by the EBA to reach its decision in G3/19 will raise
questions as to its functioning as an independent body, free from the political
influence of the President and AC.”


The Enlarged Board has been back in the news again recently and once again
questions are being raised about its compliance with fundamental legal
principles such as judicial independence.


“As the date for the hearing approaches it seems like a good time to take a
fresh look at the EPO’s Enlarged Board of Appeal to get a better idea about
what is really going on behind the scenes in this landmark case.”This time the
case number is G_1/21 (warning: epo.org link) and the IP blogosphere is buzzing
with rumours of a “kangaroo court” procedure.


An oral hearing is due_to_take_place_on_28_May. [PDF]


As the date for the hearing approaches it seems like a good time to take a
fresh look at the EPO’s Enlarged Board of Appeal to get a better idea about
what is really going on behind the scenes in this landmark case.


Stay tuned for more… █


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


⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⡤⣬⣹⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⡆⣰⣧⣻⣻⣻⣿⢿⣿⣿⣮⣛⡻⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⡟⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣮⣹⣛⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠟⣟⣛⣯⣹⣋⣿⣶⣷⣿⡿⣡⣿⠦⣤
⣙⡟⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣫⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣯⣿⣿⣿⣿⣿⣿⣟⣛⣫⣽⣽⣿⣦⣷⢍⠽⣵⣿⣿⣟⣻⣿⣿⢪⣽⣩⣍⡄⡦⠀⡉
⣈⣇⣉⣿⣘⣏⣻⢽⣿⠛⡿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣞⣻⢻⣿⣻⣽⣭⣻⣿⢸⠀⡇⠀⣬⣿⡏⡟
⣀⡏⣉⣿⣿⣿⣿⣿⣿⠛⠛⡟⠻⠿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣺⣟⣻⣩⣯⡉⢋⣸⣄⣧⡂⣈⢷⣿⣿
⠭⢿⠿⠯⢭⠿⠶⠤⢿⢤⡴⡿⣧⢦⣮⠶⠿⢿⢽⣿⣿⡿⣿⣿⣿⡿⣷⣷⣦⣼⣷⣶⣦⣿⣇⣥⣾⣶⢲⣶⣷⣶⣿⣯⢍⡉⣹⣉⡉⣿⡉⢉⣽⣿⣿⣹⢹⣿⣿⣻⣿⣯⣹⣼⣧⣤⣤⣄⠀⣦⢸⠀⡇⠀⢼⡻⣿⡇
⡀⠒⠂⠀⡉⠋⠂⡠⠊⡀⡹⠁⢘⢠⠱⠠⡁⠨⢾⠣⢹⡧⢊⡿⣃⣗⣁⣿⣿⣿⣿⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣷⣦⣭⣤⣤⣽⣧⣜⣈⣗⣀⣀⣐⢐⣶⣿⣿⣿⣿⣿⣿⣽⣬⣤⣤⣤⢧⠉⠉⠁
⠈⠀⠀⣈⣃⣂⣆⣦⣤⣧⣵⣴⣤⣵⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⢀⣀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⡀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢻⣿⣇⣸⣿⠃⢀⣤⣶⣿⣿⣿⣿⣦⣀⠀⠀⠀⢸⣿⣶⣻⡕⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠈⠛⠛⠛⠛⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡋⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣦⣠⣄⣾⣟⣻⣿⣧⠒⠚⢂⣸⣿⣼⣀⠀⣤⡄⠀⠐⠒⠀⠀⠀⠀⠠⠤⠀⣰⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠚⣏⡟⠋⣽⣿⡻⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣾⣿⣿⣿⣿⣿⡍⢈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⢸⡼⠽⣿⣿⣽⣿⢏⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⠶⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⠆⢹⣿⣿⣿⣽⣿⣿⣷⣾⣿⣿⠇⠀⠀⠀⢉⠀⣙⡿⣿⣿⣿⢟⣻⡿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠈⠑⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⡇⠁⣴⡞⠋⠀⠰⣼⠏⢹⣿⣿⣿⡁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣖⢦⡀⠀⠀⠀⢀⣶⠀⣿⣿⣯⣙⣿⣿⣿⣿⡿⣿⠢⢶⡀⠀⠀⡆⠀⠘⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⡧⠊⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢿⣆⣠⣶⣿⠃⢀⣿⣿⠿⡿⢻⣿⣿⣿⠇⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⢿⡿⠿⡇⢀⣾⣟⠅⠀⠀⠻⠿⣿⣿⡇⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⢸⣿⡧⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⢂⣿⣷⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠀
⠀⣀⣠⣤⣤⣤⣤⣤⣤⣼⣧⢺⣿⣾⣿⣿⣿⡿⠃⠀⠀⠶⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⡟⠈⢷⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀
⠛⠛⠛⠙⠋⠉⠉⠛⠛⠛⡿⠯⢸⣿⣿⣯⡁⣀⣀⡀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠉⠁⠀⠀⣿⡇⠀⠘⢿⣿⣿⠿⠿⠿⠿⠷⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⣄⣀⣀⣠⡿⠀⣴⣿⣿⣿⣷⠤⠴⠤⢤⢤⣤⣤⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣼⣿⣧⡤⢀⡀⠀⠀⠒⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀
⠠⠶⠾⠿⠿⠿⠿⠿⠿⡿⠁⣰⣻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠛⢿⠿⠻⠻⠿⠷⠾⠧⠀⠀⠉⠉⠉⠁⠀⠈⠈⠉⠉⠉⠉⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢿⢹⣿⣿⣿⡄⠀⠀⢀⣀⠀⠈⣹⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣶⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⢻⣄⢀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⢿⣟⣩⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠁⠰⠶⠶⢶⠶⠒⠒⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⡤⠀⠛⠧⠀⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠠⢩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⢤⡶⢼⠟⣩⣯⡿⡂⢀⣰⣾⣿⣿⣷⣍⡈⣀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠿⠿⠿⠦⠀⠩⠈⠛⠛⠒⢄⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠀⠀⢸⣠⣿⠟⣿⣷⣷⣽⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠁⠑⢄⢀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡑⠙⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⡀⠀⠀⠈⣻⣿⣿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢋⣤⢶⣸⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢷⣄⢀⣾⣟⠍⠁⠀⠀⡀⡀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⡁⠀⢀⣦⣷⣶⣷⣶⣾⡿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠁⠙⢿⡇⠉⠩⠩⠭⢭⣿⡇⣿⣿⣿⣏⠈⢩⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠙⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣒⠒⢒⣂⢒⣒⡂⣀⡒⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡟⡁⠀⠀⢸⡇⠉⠉⢉⠉⠿⢿⡇⣿⣿⣿⡏⠉⠛⠙⠛⠛⠛⠛⢹⠉⠙⠛⠛⠛⢹⠛⢩⠋⠛⠛⠛⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⣤⣤⣦⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⡟⠂⠀⠀⣀⣼⡇⣒⡒⢚⡒⣒⣛⡃⣿⣿⣿⡿⡒⠶⠶⠶⠗⠶⡗⣚⠲⠷⠷⠖⠳⠾⢾⠞⠺⠶⠶⠾⠾⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡤⠤⠤⠴⠿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣘⣒⣀⣐⣚⣛⣛⣃⣒⣒⣒⣒⣚⣛⣃⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣉⣁⣀⣉⣀⣀⣅⣉⣉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢹⠉⠉⠉⢹⠉⠉⠉⡏⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠙⠉⠉⠉⡏⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡸⠀⠀⠀⢸⠀⠀⠀⠇⠀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣠⣀⣀⣀⣇⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣀⣠⣀⣈⣸⣀⣁⣁⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠳⠂⠶⠔⠽⠞⠲⠰⡖⠠⠞⠿⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣸⣄⣀⣠⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡖⠒⠒⠒⠲⡶⠒⠒⠛⠒⠒⠒⠒⠒⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⡛⠛⠛⠙⠛⠛⠛⠏⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣋⣉⡉⣉⡩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣉⣈⣉⣏⣁⣉⣉⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⢿⣿⠛⡟⠻⠻⠟⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣣⣘⣘⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠖⣶⠚⠟⢷⠛⠒⢲⠖⠖⠒⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣾⣶⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣿⣿⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠹⠇⠂⠄⠄⠀⠮⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠠⠭⠭⠌⠩⠉⠤⠥⠌⠡⠭⠡⠭⠤⠹⠤⠩⠍⠍⠭⠥⠤⠌⠭⠽⠬⠧⠌⠭⠽⠬⠥⠬⠩⠁⠭⠿⠿⠇⠅⠀⠀⠀⠀⠇⠸⠿⠳⠿⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢠⣭⣭⣬⣭⣤⣉⣤⣭⣥⣬⣭⣭⣥⣭⣥⣤⣭⣭⣬⣭⣬⣥⣬⣍⣭⣬⣥⣤⣥⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠘⡉⡋⡉⠛⣏⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣌⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣄⣄⣄⣀⣇⣈⣠⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠿⠿⠿⠿⠿⠿⠇⠸⠌⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠟⠟⠟⠛⠛⠛⠿⠻⠛⠛⡟⠻⠿⠿⠟⠿⠿⠿⠛⠿⠿⠿⠟⠻⠿⠿⠿⠟⠟⠿⠿⣿⣿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣶⣶⣴⣶⣶⣷⣷⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣴⣿⣿⣒⣚⣒⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⠀⡠⣄⣀⣄⡀⣀⢈⣸⣀⣠⣀⢆⣀⢤⣇⣀⡀⣀⢀⣀⠀⢀⣸⡤⣀⣄⣀⣠⣁⡀⣀⣀⣀⣀⠀⣀⡀⣀⢄⣀⣠⣠⣀⣀⣀⣀⣀⣀⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⠀⠄⠤⠠⠄⠤⠄⠴⠨⠤⠸⠤⠤⠤⠤⠼⠠⠤⠤⠠⠆⠠⢠⠄⠤⠠⠦⠥⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠿⠿⢿⠻⠿⠿⠿⠿⠟⠿⠿⠿⠿⠟⠖⠶⡖⠂⠲⠖⠶⠶⢶⠲⢶⠲⠒⣶⠒⠒⠲⡒⠔⠖⠶⣲⡞⠒⡒⠶⠶⠖⡶⠾⠿⠟⠿⢿⠿⠻⠟⠻⠿⠟⠿⠿⠿⠻⠿⠿⠻⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠒⠒⠒⠚⠒⠒⠒⠀⠒⠒⠒⠒⢲⠒⡚⢲⠒⠓⠒⠒⠒⡒⠒⠘⠲⠞⠒⠒⠚⠒⠚⢲⠓⠒⠒⠛⠒⠓⠒⠚⠓⠒⡖⠂⢖⠒⠲⠒⠒⠒⡖⠒⠒⠖⠒⠲⠃⠐⠒⠒⠒⣲⣶⣶⣤⣶⣧⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠶⠷⠶⠶⠷⠾⠶⠾⡶⠶⠾⠿⠶⠿⠾⠾⢿⠷⠷⠷⢷⠶⠶⠶⡿⠷⠶⠷⠶⡾⠿⠾⡷⠾⠶⡶⠶⢶⠶⠿⠷⠷⠾⠷⠷⠾⡶⠾⠿⡷⠶⠷⡷⠷⠶⡷⠾⢷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠲⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⢲⠒⡒⠒⠒⠒⠒⡖⠒⠒⠚⠒⠖⠒⠓⡖⣲⠓⠖⡗⠒⠓⢨⠐⠒⠓⠒⠚⠒⠂⠒⢲⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣦⣴⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣿⣷⣶⣾⣿⣿⣿⣿⣾⣿⣿⣾⣷⣶⣷⣿⣾⣿⣷⣾⣿⣷⣷⣾⣾⣷⣷⣿⣷⣿⣿⣿⣿⣾⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⣨⣆⣠⣦⣀⢤⣀⣴⣸⣀⣸⣠⣠⢆⣀⣁⣠⣀⣀⣅⢀⣀⣸⣀⣸⣠⣢⣔⣄⣀⣇⢦⣀⢄⣄⣣⣀⣆⣺⣠⣀⣀⣇⣄⣀⣇⣠⣄⣕⣆⠄⣠⡀⣄⢸⠀⠀⠧⣸⣄⣄⣀⣀⣀⣅⣇⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣴⣧⣬⣧⣤⣤⣥⣤⣤⣤⣥⣤⣤⣄⣠⣤⣼⣤⣧⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣴⣤⣤⣤⣼⣤⣤⣤⣧⣼⣾⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣿⣿⢉⢉⣉⡋⣉⢹⢉⣉⣉⡉⣙⢉⡉⠉⢉⡉⡏⡉⡉⡏⣉⣉⡋⠉⡉⣏⣫⡉⠋⣉⡉⢉⡉⣉⣉⣏⡉⣉⣉⣏⣉⢉⠉⣫⡉⢉⢉⠉⢉⣹⠉⣉⢉⣏⣉⢉⣉⣉⡉⡉⢉⣉⢉⠉⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⢈⣉⣉⣉⣍⣉⣇⣉⣀⣠⣐⣇⣌⣉⣉⣇⣀⣈⡀⣧⢉⣉⣹⣉⣉⣉⣉⣉⣈⣉⣉⣏⣉⣇⡈⣉⣉⣁⣉⣇⣐⣀⣀⣉⣉⣉⣈⣉⣸⣉⣉⡉⣁⣈⣉⡇⣁⣉⣉⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣡⣀⣄⣤⣢⣠⣠⣦⣠⣀⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣭⣿⣿⣠⣀⣇⣄⣠⣧⣄⣠⣦⣀⣈⣆⣀⣴⣄⣀⣠⣄⣠⣨⣤⣄⣇⣀⣠⣀⣤⣀⣄⣤⣥⣄⣠⣸⣠⣬⣤⣠⣇⣄⣀⣄⣇⣄⣠⣅⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣉⣈⣩⣉⣉⣅⣌⣉⣸⣌⣉⣇⣉⣏⣉⣁⣧⣍⣉⣉⣉⣍⣉⣉⣉⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⡿⢿⢿⠿⠿⡿⡿⠿⡿⠿⣿⠿⢿⠿⣿⡿⠿⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣾⣤⣶⣷⣷⣤⣤⣤⣴⣤⣴⣤⣤⣧⣤⣬⣤⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡗⠀⠀⠀⠀⠐⠄⠠⠀⠀⠠⡀⠀⠀⠀⠀⠆⠀⠈⠀⢤⠀⠜⠀⠃⠀⢄⠛⢻⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣴⣶⣤⣴⣴⣶⣤⣼⣤⣤⣴⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡆⠃⠀⠀⢠⠨⠆⠀⠁⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⠿⠷⠶⠶⠶⠾⠶⠶⠶⠶⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠲⠗⠒⠶⠚⠲⠶⠶⠲⠶⠞⠖⠖⠲⠖⠒⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠉⠙⠛⠙⠛⠛⠋⠛⢛⠛⢋⠉⠋⠛⠋⠛⠋⠛⠛⠛⠛⢹⠛⠛⠛⠙⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡗⠲⠲⠖⠖⠖⢲⠖⠲⠲⠲⠖⠒⠲⠒⠖⠖⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣍⣉⣉⣉⣉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣏⣁⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣭⣩⣭⣩⣭⣭⣉⣭⣭⣍⣩⣭⣍⣍⣭⣭⣭⣩⣭⣩⣭⣭⣉⣽⣿⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣏⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣯⡛⡝⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣟⡉⡛⣿⣟⣛⣛⣻⣙⣟⣛⣛⡿⡟⣋⡟⣛⣛⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡟⡍⡎⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠛⣟⠛⡟⢻⢻⢟⠛⠛⣟⣿⡻⢻⠿⠟⠛⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣣⣑⢜⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡿⠿⠿⣿⡿⣻⠻⡿⢿⣿⡿⠿⢿⢿⣿⣷⡷⠿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣷⣶⣿⣿⣾⣶⣶⣾⣿⣿⣷⣾⣿⣿⣿⣷⣶⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣷⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢾⣯⣶⣽⣷⣵⣽⣾⣿⣶⣿⣿⣴⣯⣷⣶⣿⣧⣶⣯⣧⣤⣿⣵⣧⣤⣯⣶⣼⣿⣷⡬⣿⡷⠶⡿⣧⣦⣧⢾⣿⡾⢽⣵⣶⢿⣷⣧⣽⢿⣶⣼⣯⣾⣷⣴⢽⣾⡷⢿⣿⣧⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡾⣿⡿⣷⡿⢾⣶⣿⡿⢿⣷⣿⣷⣾⣶⣿⣿⣿⣴⣷⣿⣿⣶⣿⣷⣾⣿⣿⣾⣿⣷⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣿⣷⣿⣾⣿⣾⣷⣾⣿⣷⣾⣿⣷⣶⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠁⠙⢿⡇⠩⠩⠭⠭⣭⣿⡇⣿⣿⣿⣏⠍⢩⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⡩⠉⠋⠉⠉⠉⠉⠙⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣒⣒⣒⣂⣒⣒⣆⣀⣒⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡟⡁⠄⠀⢸⡇⠉⠉⢉⠙⠿⢿⡇⣿⣿⣿⡏⠉⠛⠙⠛⠛⠛⠛⢹⠉⠛⠛⠛⠛⢹⠛⢩⠏⠟⠛⠛⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢠⠂⠀⣤⣤⣦⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⡟⠂⠀⠀⣀⣾⡇⣓⡒⣛⣚⣛⣛⡃⣿⣿⣿⡿⡒⠶⠾⠷⠗⠶⡗⣛⠳⠿⠷⠖⠳⠿⢾⠞⠺⢶⠶⠾⠾⠾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡤⠤⠤⠶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣘⣓⣀⣒⣚⣛⣛⣃⣒⣒⣒⣒⣚⣛⣃⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣩⣍⣁⣉⣩⣀⣈⣭⣍⣉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⡿⠛⠻⢿⠿⠟⠻⠿⠛⠿⠿⠟⠿⠻⠛⠟⠿⢻⠿⠻⠿⠻⠿⠿⠟⠿⡟⠛⠿⠿⠟⠿⢿⠿⠟⢻⠿⠿⠟⠿⠿⠛⠿⠿⢻⠻⢿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣶⣷⣶⣶⣾⣶⣷⣶⣶⣷⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣾⣿⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢛⠿⠟⠿⠟⠿⠻⠻⠻⠻⠟⡿⢻⠻⠻⠟⠿⠻⠿⠻⠻⠿⠟⠟⡟⠻⠿⠿⠟⢟⠻⢟⠿⢟⠟⠟⠻⢿⡛⡻⠻⢛⠿⠟⠿⠛⠛⠿⢻⡿⠛⠻⠟⠟⠛⠻⢻⢛⢿⠿⠻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠒⠒⠒⠒⠒⠒⡖⠐⠒⠒⠒⠒⠒⠒⠐⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢐⣨⣠⣼⣤⣐⣄⡨⣔⣅⣠⣥⣈⣥⣐⠈⣨⣠⡅⣗⣆⣄⡨⣤⢆⣯⣸⡸⣠⣨⣩⣨⣨⣀⣅⣀⣏⣐⡅⣨⣀⡵⣀⢥⣀⣔⡠⢁⣇⢤⣔⣔⡄⣑⣀⣀⢨⣦⣼⣨⢄⣐⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠤⠤⠧⠤⠤⠤⠤⢤⠤⡧⢴⡠⡤⢤⢤⢤⢤⢼⠤⠧⠦⠤⡤⢼⠴⡧⠴⠤⡦⢤⠼⠤⡦⡦⠤⢤⠤⠤⠤⠧⢤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣴⣶⣶⣵⣵⣶⣶⣾⣶⣶⣶⣶⣶⣴⣼⣴⣾⣵⣦⣶⣦⣦⣧⣴⣶⣷⣶⣦⣦⣴⣶⣦⣶⣧⣶⣵⣶⣦⣶⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⡟⡿⠛⠿⢻⠟⡟⠻⢻⡻⠛⠟⠻⠟⠻⠛⠿⠛⢛⠛⠛⠟⠛⠛⠻⡛⡟⠟⠛⠿⠻⠛⠻⠛⠿⠛⢟⠛⡛⠛⠿⠛⠛⠿⠛⠟⡟⠟⡻⠛⠟⡿⢻⠛⠻⠛⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⡛⠛⠓⠙⠓⠛⠛⠑⢳⠉⢉⠩⡇⠓⠚⠃⠓⠂⠚⠚⠑⠒⠓⠒⠛⠂⢺⠓⠓⠘⠚⠓⠚⠚⠚⢱⠛⡖⠛⠚⠛⠒⠙⢻⠒⠃⠛⠒⠓⠓⠘⠒⢓⠛⠺⡖⢁⠀⠚⢺⠓⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣈⢉⣉⢉⣉⣉⣹⣏⡍⣋⣉⣋⢹⣉⡋⡉⣋⣏⢹⣉⢍⢉⢉⡉⣋⣙⣉⣉⡉⢈⣏⣉⣈⣉⣎⣙⢉⣉⣉⡎⣈⣉⣉⣉⣘⢉⡻⣉⣋⣉⢉⢉⡍⣉⣉⣉⣹⣉⣝⣉⢍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣉⣉⣀⣉⣉⣏⣉⣁⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠻⠿⠿⢿⠿⠿⢿⠿⡿⠿⢿⠻⡿⠿⠿⠿⠿⢟⠿⠿⠿⢿⠿⢿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⢿⠿⠿⠿⢿⠿⠿⠿⠿⡿⠿⠿⠿⡿⠟⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠻⠒⠖⠴⡲⢶⡰⠲⠔⠖⠺⢖⠖⠲⠾⠖⠶⠺⠒⠗⡖⣺⠒⠖⡖⠖⠶⠒⠒⡲⠒⢶⠒⠶⣸⠶⠢⠖⠶⠗⠶⠲⠒⠂⠲⡖⠲⢰⠲⠲⠶⡺⠶⠒⠾⢲⠲⠲⠖⠶⡓⢒⣲⡖⠖⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠚⠒⠛⢶⠛⠚⠒⠒⠛⡞⠓⠒⠓⠛⠂⡒⢲⠚⠓⠓⠓⠚⠒⠓⠃⠒⠒⠓⢲⠒⣲⠚⠒⠒⠓⡆⠚⠊⡗⢲⠒⠚⡆⠀⡢⢱⠐⠚⠚⣆⡚⠓⠒⠒⠚⠚⠂⠲⠑⠒⠙⠒⠒⣿⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠙⠛⠛⠋⡙⠛⠛⠻⠛⠓⠛⠛⠛⠙⠙⠓⠚⠓⠛⠙⠉⠛⠛⠋⠋⠛⡛⠛⠛⠛⠋⠛⣛⠛⠛⢙⠛⡓⡛⠛⠻⠙⠛⢻⢫⠛⡛⠛⠛⠛⠙⠛⡏⢻⠛⠛⠛⠛⠛⢛⢻⠙⢻⢙⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢉⣉⣉⣉⣉⣙⣍⣉⣏⣩⣉⣏⣈⣉⣏⣉⣩⣉⣉⣉⣉⣏⣩⣏⣉⣹⣉⣉⣉⣙⣉⣏⣉⣉⣉⣍⣋⣉⣹⣉⣏⣉⣙⣉⣉⣉⣉⣉⣏⣩⣉⣁⣉⣉⣉⣉⣉⣉⣉⡙⣏⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣠⣉⣇⣀⣔⣰⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢉⢙⡉⢙⡝⢻⠋⠉⠛⡟⠛⠙⠛⠝⠋⢛⠙⢹⠝⣋⠉⢙⠉⢉⡩⡋⢙⡍⠙⢙⠛⠟⠉⢙⠙⣛⠉⡋⠛⠋⠋⠉⢩⠛⡏⡙⡋⠛⡋⠛⢻⠛⡩⠛⢙⠉⠙⠋⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣠⣉⣍⣉⣉⣉⣉⣁⣉⣉⣉⣁⣉⣹⣉⣹⣉⣉⢉⣉⣉⣉⣉⣉⡉⣏⣁⢉⣉⣉⣉⣍⣉⣁⣉⣉⣏⢉⣃⣉⣉⣉⣏⣹⣈⣹⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⢉⣉⣉⣉⣉⣉⣩⣉⣁⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣠⣅⣴⣀⣤⡅⣑⣠⣀⢠⣄⣠⣅⣄⣐⣅⣢⢰⣢⣤⡜⡠⣠⣨⡤⣄⣨⣁⣻⣠⣀⣥⣼⣠⣨⣄⣍⣀⣡⣀⡥⣄⣵⢄⣥⣤⣠⣅⣠⣧⣅⣇⣨⣮⣔⡬⣑⣄⣍⡔⣄⣄⣅⣬⣀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣠⣦⣴⣤⣤⣤⣤⣤⣼⣤⣤⣤⣠⣤⣤⣤⣤⣤⣄⣧⣴⣤⣤⣤⣧⣤⣧⣤⣤⣦⣤⣤⣄⣤⣄⣤⣤⣤⣼⣤⣦⣤⣦⣤⣴⣠⣤⣤⣤⣤⣤⣧⣼⣤⣦⣤⣦⣤⣧⣤⣦⣆⣤⣤⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿⠟⠿⠟⠛⠻⡻⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠟⠿⡟⠻⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⢿⠻⠿⠿⠿⡿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠻⠻⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠚⠒⡖⢒⡗⠖⡖⠖⠳⠚⠒⠂⢲⠒⠖⠒⠲⠒⠞⠒⡒⠃⠞⠖⠒⣖⠒⠲⠐⠖⡖⠒⠒⠓⠒⠒⣲⠂⠒⡖⠒⢒⠲⠒⠲⠚⡚⠒⠲⠒⠗⡖⠚⠒⠒⠒⠲⠒⠲⠒⠲⠚⠺⠚⠒⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠙⢻⠛⠓⠓⢳⠓⡗⠚⢹⠊⠛⠚⢻⠛⠛⡚⠛⠓⠙⠙⢓⠉⠊⡛⠓⠚⡞⠋⠓⠓⡟⠚⠃⠛⠓⠚⠛⠛⠙⠛⠓⢛⠛⠙⠛⠛⠛⠙⠓⡏⠕⠛⠚⢷⢀⠛⡗⠛⠚⠛⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣉⣉⣻⢉⣉⣉⣉⣉⣉⣉⣱⣉⣋⣉⣹⣉⣉⣉⣏⣏⣉⣉⣉⣉⣹⣉⣉⣉⣉⣉⣉⣈⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⡿⡿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣥⣤⣴⣄⣤⣄⣤⣄⣤⣴⣤⣦⣴⣤⣤⣤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣠⣴⣤⣤⣤⣤⣤⣴⣠⣥⣤⣤⣤⣤⣬⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣍⣉⣹⣉⣉⣉⡏⣉⣙⣉⣉⣉⣙⣹⣉⢩⣉⣉⣉⣉⣏⣉⣩⣉⣉⡏⣉⡉⣉⣉⣉⣏⣉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⠉⣉⣉⣹⡉⡉⣉⣉⣹⣉⢹⣉⣉⣉⣹⣉⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣈⣁⣈⣉⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣿⣟⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⠿⠿⠿⠿⠿⡿⠿⠿⡿⡿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠷⠿⢿⠿⠿⠿⠿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⠿⢿⠟⡿⠿⠿⠿⠿⠿⠿⠿⣿⠿⡿⢟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⠲⠒⠲⠲⠖⣶⡒⠳⠲⡶⠒⠷⠶⢲⠚⢲⠒⠚⠒⠒⢲⠖⠶⠞⡲⢶⠶⠲⢲⡗⠾⠲⠗⠲⠲⠶⠶⠷⠒⠶⠖⠶⡲⢶⠣⠗⠲⠖⠾⠶⠾⢾⠷⠲⢲⡒⠒⠶⡶⠎⠾⠶⠶⢶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⣾⣶⣶⣶⣷⣶⣿⣶⣾⣶⣾⣶⣶⣶⣾⣶⣷⣾⣶⣶⣾⣾⣾⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣿⣷⣶⣾⣶⣿⣶⣷⣾⣶⣷⣶⣾⣷⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠿⠻⠿⡿⠻⠿⡿⡿⠿⠿⠿⢿⠟⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠟⢿⠻⠿⠿⢿⠻⠿⠟⠿⠿⢿⠛⡿⠿⠿⠿⡿⠟⠿⠿⠿⠟⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣷⣶⣶⣴⣾⣶⣷⣾⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣾⣶⣶⣶⣶⣾⣴⣶⣶⣦⣶⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣷⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣷⣦⣶⣶⣶⣶⣧⣶⣶⣶⣶⣶⣷⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣶⣦⣼⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⡛⠛⠛⠛⠛⠛⡿⠛⠛⢻⠛⢻⢛⠛⡟⠛⠛⠛⠛⠛⠛⠛⢻⠛⡛⠛⢻⠻⠛⠛⠻⢻⠻⠛⠛⠛⠻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⠄⠤⢤⣤⠤⠧⢤⡤⠼⠤⠤⢤⡤⠤⡤⢤⢤⣤⠤⣤⡼⡤⢦⠤⣤⡴⡤⡤⡧⣤⠤⠤⠄⠤⣼⠤⣤⣯⢤⠤⡀⢥⣤⢤⢤⠧⡤⡦⠤⣤⡼⡠⢤⡨⠧⠤⣤⡤⡧⡶⢤⠤⢄⠧⢤⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠵⠤⠤⠴⠥⠦⠴⠦⠄⠦⠰⠕⣤⣴⣧⣶⣼⣵⣤⣶⣴⣦⣴⣴⣤⣤⣧⣼⣤⣧⣦⣴⣶⣦⣤⣤⣶⣴⣼⣭⣴⣤⣷⣾⣥⣤⣦⣧⣦⣶⣤⣦⣼⣴⣴⣤⣧⣶⣦⣯⣾⣬⣵⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣉⣏⣉⣉⣻⣿⣿⣿⣿⣿⣿⣏⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣯⡛⡝⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣟⡉⡛⣿⣟⣛⣛⣻⣙⣟⣛⣛⡿⡟⣋⡟⣛⣛⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡟⡍⡎⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠛⣟⠛⡟⢻⢻⢟⠛⠛⣟⣿⡻⢻⠿⠟⠛⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣣⣑⢜⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡿⠿⠿⣿⡿⣻⠻⡿⢿⣿⡿⠿⢿⢿⣿⣷⡷⠿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣷⣶⣿⣿⣾⣶⣶⣾⣿⣿⣷⣾⣿⣿⣿⣷⣶⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣽⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣾⣿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠁⠙⢿⡇⠩⠩⠭⠭⣭⣿⡇⣿⣿⣿⣏⠍⢩⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⡩⠉⠉⠉⠉⠉⠉⠙⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⣒⣒⣒⣂⣒⣒⣂⣀⣒⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡟⡁⠀⠀⢸⡇⠉⠉⢉⠉⠿⢿⡇⣿⣿⣿⡏⠉⠛⠙⠛⠛⠛⠛⢹⠉⠙⠛⠛⠛⢹⠛⢩⠋⠟⠛⠛⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢠⠀⠀⣤⣤⣦⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⡟⠂⠀⠀⣀⣼⡇⣒⡒⣚⣚⣒⣛⡃⣿⣿⣿⡿⡒⠶⠶⠶⠗⠶⡗⣚⠲⠷⠷⠖⠳⠾⢾⠞⠺⠶⠶⠾⠾⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡤⠤⠤⠶⠿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣘⣒⣀⣒⣚⣛⣛⣃⣒⣒⣒⣒⣚⣛⣃⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣨⣍⣁⣉⣉⣀⣈⣅⣍⣉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣈⣉⡍⣉⣉⣉⣉⣉⣈⡉⢉⣁⣉⣉⢉⢉⣉⣁⣉⣉⣈⣈⣉⣉⣹⣁⣁⣉⣉⣉⣉⣀⣉⣉⣉⣉⣉⣁⣇⣈⣹⣀⣉⣉⣁⣉⣏⣡⣁⢉⢉⣉⣁⣉⣸⣀⣉⣁⣈⣉⣉⢉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣄⣤⣤⣄⣄⣤⣤⣀⣭⣇⣠⣠⣤⣤⣀⣤⣀⣀⣄⣄⣤⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⣉⣉⣉⡉⣉⣉⣉⣉⣏⣉⣉⣉⣉⣉⣉⣉⣙⣉⢉⣹⢉⣉⣉⡏⣙⣹⣉⡏⡉⡉⣉⣉⣉⣉⣍⣹⢉⡉⡉⡉⣋⣉⢹⣉⢉⣉⣉⢙⣉⣉⣉⢉⡏⣉⢉⡉⣉⢉⣉⢉⣉⣉⣉⣹⢉⣙⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⣈⣈⣉⣉⣩⣈⣩⣉⣉⣉⣏⣹⣉⣉⣉⣉⣏⣉⣉⣁⣈⡉⣉⣉⣉⣁⣈⣉⣉⣉⣉⣇⣅⣉⣉⣉⣁⣁⣈⣉⣏⣉⣁⣉⣹⣉⣉⣉⣍⣸⣉⣉⣈⣉⣻⣀⣉⣉⣉⣈⣉⣉⣉⣁⣉⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣼⡤⣤⣤⣄⣸⣤⣤⣤⡧⡤⢤⣠⣤⣤⣤⣤⣤⣄⣠⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣸⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⢿⢿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡧⢦⣤⠤⠴⡦⣴⣼⣴⣤⣤⢤⡤⣴⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢿⣿⣿⣿⡿⣿⡿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡧⠤⠤⡤⠴⡬⡤⠤⠠⡠⠤⠤⠤⠤⠤⠤⠤⢼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣴⣤⣤⣠⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣼⣠⣦⣤⣤⣤⣤⣄⣤⣤⣬⣄⣤⣤⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣦⣧⣤⣧⣶⣶⣦⣦⣶⣴⣶⣴⣶⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⠉⠛⠛⣻⠋⠛⠛⠙⠛⡟⠉⠛⠋⠙⠛⠙⠉⠋⠙⠛⡟⠛⡏⢉⠛⠋⠛⠛⢻⠙⠙⠛⡫⠉⠙⡛⠛⠛⠛⠛⡋⠏⠫⠉⠉⣽⠋⠉⠉⢹⠛⡏⠛⠋⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⢿⠿⠿⠻⠻⠿⠻⠿⠟⠿⠟⢛⠛⡟⠿⠿⠟⠿⢿⠟⠟⡟⠟⠛⠛⠛⡟⠛⠟⠛⠻⠿⡿⠻⠿⠿⠿⠿⢿⠻⠿⠻⠿⠟⡟⠿⠿⠟⠿⢿⢻⠛⠛⠛⢻⠻⡛⠛⠟⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⠒⠒⠒⠛⠲⣶⣶⣶⣶⣧⣶⣶⣶⣷⣶⣶⣧⣶⣶⣶⣶⣿⣶⣶⣶⣧⣶⣶⣶⣶⣶⣶⣶⣴⣶⣿⣦⣶⣶⣷⣶⣾⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢿⡿⣶⡿⡿⣾⢿⣿⢿⣿⠿⡿⢿⣿⠿⡿⣿⢿⠿⢿⢿⣿⣿⠿⣿⢿⣿⢿⣿⢿⣿⡿⡿⡿⢿⠿⠿⣿⡿⣿⣿⢿⢿⢿⢿⢿⡿⢿⠿⣿⡿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡧⠼⠤⢤⠧⠤⠴⠴⠤⠦⢶⠤⠃⢤⠴⠤⡄⠆⢔⢤⠤⠤⠤⠤⠄⠄⢴⠴⠅⠼⠤⢤⠧⢠⠤⠴⠤⠰⠤⡷⠤⠼⢼⠤⠄⠤⠤⠤⠤⠤⠤⠧⡤⠬⠤⠾⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠒⠲⠚⠶⢰⢂⡖⠒⠚⠞⠒⠒⠞⡖⠲⠓⢞⡒⠒⠐⡖⠒⢒⡖⠖⠘⠒⢲⣶⣶⣾⣿⣾⣶⣶⣶⣶⣤⣷⣶⣴⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣧⣾⣶⣶⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⠺⠾⠶⠾⠾⠶⠷⡶⠶⠷⠶⠶⢷⠷⠞⠶⡟⠷⠶⠶⠷⠲⠾⠷⠷⠶⠿⠾⠿⡿⠿⢿⠛⠿⠿⢿⠟⠻⠻⡿⠻⠿⠿⠻⡿⠿⢿⠿⠟⠿⠿⠿⡿⢿⠿⠿⠿⠟⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⠗⠒⠖⠲⡒⠲⠒⠗⠲⠖⠲⡲⠚⢲⠒⠖⠓⠒⠲⢲⠒⠒⠞⠒⠒⠞⠖⠶⢰⠓⠒⠚⠒⠒⠖⠺⠒⢶⠒⠓⠖⠒⠶⢲⡳⠒⠞⠲⠒⠒⠒⢲⢓⡞⠒⠶⠚⠒⠗⠒⢖⠛⢟⠻⠟⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⠉⠒⠓⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣷⣾⣶⣾⣾⣷⣶⣶⣶⣶⣶⣾⣾⣶⣷⣶⣶⣷⣶⣷⣶⣶⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠙⠛⠛⠛⠋⢛⠛⠛⠋⡋⠛⠋⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⡟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⡀⠁⠋⠚⣏⠉⢛⠙⡋⠛⡉⡏⢽⠉⠙⢛⢹⢙⠉⠛⠉⡙⢙⠍⢋⠉⠻⠉⢫⣋⠉⢫⠉⠋⡏⠋⠋⠙⠉⢹⣉⡉⡉⠩⡉⠋⢟⠉⣏⡉⠩⢉⡙⠉⠉⡯⠉⢙⡉⠉⡙⢙⠙⡋⠉⠉⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣩⢉⣉⣍⣉⣁⣯⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣈⣹⣉⣉⣃⣈⣉⣉⣏⣉⣁⣉⡉⣹⣁⣉⣉⣉⣉⢉⣈⣉⣁⣉⣙⣆⣈⣉⣉⣉⣉⣩⣉⡉⣁⣉⣙⣈⡩⣉⣉⣹⣍⣉⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣄⣤⣄⣨⣠⣠⣠⣸⣀⣈⣄⣇⣸⣠⣀⣅⣀⣄⣄⣨⣤⣠⣀⣄⣧⣁⣀⣧⣀⣧⣢⣠⣅⣸⣄⣬⣠⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠈⠉⠁⡉⡈⠀⡈⢿⡿⣿⠿⡿⡿⢿⣿⠿⡿⠿⠿⠿⠿⢿⢿⠿⠿⠿⠿⠿⢿⠿⡿⠿⠿⠿⠿⠿⣿⠿⠿⢿⠿⡿⠿⠿⡿⡿⠿⢿⢿⡿⢿⠿⢿⠿⠿⢿⢿⢿⠿⡿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡧⠦⠄⠤⠤⠷⠄⠴⠤⢢⠤⠦⠧⠶⠠⠀⢤⡆⡤⠤⠠⠠⠜⠤⠤⠬⠦⠄⠤⠼⠤⠧⠶⠤⠤⠤⠠⡽⠴⠄⠼⠤⠨⠤⡦⠧⠤⠶⠼⠤⠥⠄⠤⠾⡤⠦⠤⠥⠴⠀⠧⢦⣤⣦⣤⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣧⣶⣶⣶⣶⣶⣶⣷⣶⣶⣷⣾⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⡟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⠈⠁⡂⡶⡉⢙⠉⡏⣉⢙⢹⠉⠉⢉⠙⡏⠋⡩⡉⠉⣉⡋⣋⢍⣍⠉⠉⢹⢍⡏⠩⣉⢋⠉⠏⢉⢉⡉⡉⠉⡙⡏⢉⣩⡉⢹⢍⡉⣉⣋⣉⢙⢉⠉⣉⡉⣏⡉⡩⡉⣹⣉⡉⡉⢙⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣉⣍⣉⣍⣈⣉⣸⣨⣉⣈⣉⣉⣁⣈⣉⣀⣍⣹⣉⣁⣉⣉⣉⣉⣏⣈⣏⣉⣸⣉⣁⣩⣉⣇⣉⣹⣉⡉⣉⣉⣉⣈⢉⣉⣀⢩⣉⣉⣸⣈⣉⣀⣁⡈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⡟⠙⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣄⣉⣁⣉⣟⣉⡸⣉⣈⢈⣈⣗⣉⡁⠀⣹⢈⣉⣈⣹⢂⠉⡈⡉⢻⣘⣉⣏⣉⣉⣅⣉⣈⣉⣁⣏⣩⣁⡇⢉⣉⡁⣉⣉⣍⣉⣇⣇⣁⡉⣀⣉⡼⣉⣀⣹⣉⣈⣉⢊⣉⣩⢉⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡧⡤⠄⠤⢤⢤⠼⢤⠧⢼⠤⢤⠤⠧⠥⢤⠷⠤⠧⡼⢾⠤⠤⢤⠧⢤⠹⠤⢤⠼⢤⢼⢤⠤⢤⠥⠤⢤⠤⠤⠴⠀⠦⠤⠤⠤⠤⠼⢠⠤⣤⠤⡤⠤⢰⢤⢦⠤⠤⡤⠤⠤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡧⠢⠤⠤⠴⢼⠨⠼⠈⠵⠄⠰⠤⠤⡄⡰⠴⠠⠤⠤⠄⠃⠤⠥⠀⣮⣤⣤⣤⣴⣤⣴⣤⣴⣤⣦⣥⣴⣴⣴⣤⣦⣤⣴⣤⣦⣤⣤⣴⣤⣤⣤⣬⣤⣤⣵⣮⣤⣤⣦⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣶⣾⣶⣶⣷⣶⣶⣶⣷⣶⣶⣶⣶⣴⣷⣶⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⡇⠀⢉⡁⣈⡉⢀⣉⣉⣉⣉⣿⡿⣿⣿⣿⡿⣿⣿⠿⢿⣿⠿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⠿⡿⡿⢿⣿⣿⡿⢿⢿⣿⣿⣿⣿⡿⢿⣿⢿⡿⢿⣿⠿⣿⡿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣦⣤⣤⣤⣧⣤⣤⣤⣤⣤⣦⣧⣤⣤⣤⣤⣦⣤⣤⣤⣴⣤⣤⣦⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣬⣤⣤⣧⣤⣤⣤⣧⣤⣼⣤⣤⣤⣤⣴⣤⣴⣤⣤⣤⣴⣦⣤⣦⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⠦⠚⠶⢆⠲⠴⠶⢶⠰⠗⠦⡦⠦⠶⠣⠦⣴⣦⣦⣶⣶⣦⣴⣤⣴⣧⣴⣾⣴⣶⣤⣶⣶⣦⣴⣤⣴⣴⣴⣶⣴⣶⣶⣶⣴⣶⣶⣦⣶⣦⣦⣶⣦⣶⣦⣤⣶⣶⣴⣶⣴⣼⣦⣷⣴⣴⣧⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣴⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣉⣏⣉⣉⣹⣿⣿⣿⣿⣿⣿⣏⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠁⠈⢿⡇⠈⠩⠉⠉⢭⣽⡇⣿⣿⣿⣏⠈⢉⠉⠈⠉⡏⠈⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⡒⠒⢒⣂⠒⣒⡂⣀⠒⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⠟⡁⠀⠀⢸⡇⠉⠉⢉⠉⠿⢿⡇⣿⣿⣿⡏⠉⠛⠙⠛⠛⠛⠛⢹⠉⠙⠛⠛⠛⢹⠛⢩⠋⠛⠛⠛⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⣤⣤⣦⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⡟⠂⠀⠀⣀⣼⡇⢒⡒⠚⠒⠒⠛⡃⣿⣿⣿⡗⠒⠶⠶⠶⠖⠶⠖⡚⠲⠷⠖⠖⠳⠾⢶⠞⠚⠶⠶⠾⠾⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠠⡤⠤⠤⠔⠿⠛⠛⠟⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣘⣒⣀⣐⣚⣛⣛⣃⣒⣒⣒⣒⣚⣛⣃⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣉⣁⣀⣉⣀⣀⣁⣉⣉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣀⣀⣸⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣀⣀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣃⣈⣀⣀⣇⢀⣸⣀⣠⣀⣀⣀⣸⡀⣂⣀⣀⡀⣰⣐⣇⣀⣡⣐⣀⢀⣇⣁⣀⣀⣊⣀⣀⣇⣈⣁⣀⢈⣺⣀⠀⢁⡇⣀⡀⢰⣀⣸⣰⣁⣇⣀⣀⣸⣀⡠⣀⣀⢇⣀⣀⣈⣀⣇⣀⣀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⡄⣠⣠⣀⡠⡄⣀⣌⢌⣠⣧⣀⣇⠠⡀⡧⣇⣤⣤⢀⣀⣤⣀⡇⣀⢀⣠⣄⣸⣀⣠⡄⢰⡄⡠⢽⣠⡤⠸⠀⢠⠄⢤⣀⣀⡤⠸⣀⣀⣅⣀⣄⣄⢄⣄⣄⡸⢄⢴⣠⣀⣔⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠤⢤⠤⢧⢤⣧⢤⢤⠤⠤⢄⣤⣦⣼⡴⠤⠤⠄⣤⣤⣠⣤⣤⣄⣤⣤⣤⣠⣼⣤⣤⣦⣤⣤⣤⣤⣤⣤⣧⣤⣦⣴⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣸⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣵⣤⣼⣴⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⡿⡿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⢌⣤⣀⣄⣄⣀⣼⠠⣀⢼⠠⣠⣄⠀⠀⠀⡠⠀⣸⣀⣸⠠⢀⣄⣀⣀⣠⣀⡇⣀⣠⣄⠤⡆⣸⣀⣠⠄⡄⡀⡤⣤⡨⠄⡀⡧⡤⣀⣀⣄⣠⠨⠀⠸⣴⢤⣀⢀⡄⣇⡠⣤⣀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣤⣄⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣴⣤⣧⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣄⣧⣤⣤⣼⣵⣤⣤⣧⣤⣧⣤⣤⣬⣤⣤⣤⣤⣼⣤⣤⣥⣹⣤⣰⣤⣤⣄⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⢿⣿⡿⣿⡿⢿⣿⣿⡿⠿⣿⡿⣿⣿⢿⢿⣿⣿⠿⠿⣿⡿⣿⣿⢿⣿⡿⢿⡿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⠿⣿⢿⣿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠤⠶⠥⠧⠤⠤⠤⢤⠤⠤⠤⠧⡤⠤⢤⠤⡦⡤⠤⠤⣼⣤⣥⣤⣧⣤⣤⣤⣤⣤⣧⣤⣤⣧⣤⣤⣤⣤⣾⣤⣤⣤⣤⣤⣤⣼⣰⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣼⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣼⣤⣤⣦⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⠻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡗⠒⠦⠶⠶⢶⠲⠲⠿⠿⠟⠻⠿⡟⠛⠛⡻⠿⠛⠻⠿⡟⡿⠻⠻⠿⠟⠿⡟⠻⢿⠿⠿⠿⠟⠟⠿⠟⡟⠻⢿⠟⠟⠿⠛⠿⢻⠻⠻⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⠿⢻⠻⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡷⠗⠲⠲⠖⠞⠖⠒⠖⠲⠲⠖⠶⠓⠖⠗⠾⠒⠒⠖⠖⠶⠗⠖⢲⠂⠗⠶⠳⠶⠚⠲⢲⠲⠲⠓⢲⠲⠓⠳⠚⠖⠒⠖⠲⠒⠚⠶⠲⠖⠖⠖⠶⠒⠖⣶⣶⣶⣶⣶⣾⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠒⠒⠲⠒⢲⠒⠖⡞⠒⠲⡖⠓⠒⡺⠒⠒⠒⠒⠒⠖⠒⣖⠖⡞⠒⠒⢲⠒⢶⠒⠒⡚⡐⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣾⣶⣶⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣷⣷⣶⣶⣾⣶⣾⣷⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣏⣉⣩⣉⡉⢹⢉⠉⣉⣉⡏⣉⣉⣉⡉⣉⣉⢉⣉⣉⣏⣹⣉⢉⣩⣉⣉⡉⣉⣏⣉⣉⣍⣉⣙⢉⣉⡉⣉⢉⡉⣉⣉⣉⢉⡉⢉⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣏⣉⣉⠉⠉⠈⣇⣠⣐⣈⣂⣁⣈⣉⣇⣈⣉⣉⣉⣉⡁⣉⣉⣈⣉⣈⡈⢸⣉⣅⣈⣙⣀⣉⣫⣹⣀⣸⢀⢸⣀⣈⣀⣀⣀⣀⣀⣀⣁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠻⠛⠛⢻⠉⠛⠛⢛⠛⠛⠛⠋⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠉⠙⠛⠋⠋⡏⠙⠛⡟⠛⠛⠙⠛⢻⠙⢛⠉⠛⠛⠛⠛⠛⠛⢹⠛⠛⠛⠛⠛⠋⠙⠛⠛⢻⠙⠛⠛⠛⠛⢫⢩⠉⠉⠉⡉⢹⠉⠙⠛⠙⠛⠛⡏⡝⠛⠙⠛⠙⠛⢹⠉⠛⠛⠛⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⠉⡙⡙⠙⠙⠙⠉⡏⠁⠹⠉⠉⠋⠋⠉⠙⠉⠉⢉⠃⠁⠉⡏⠉⠊⠉⠙⠙⠉⠉⠉⠑⠈⠋⠉⠉⠉⡏⠉⠙⡏⠉⠋⠉⠉⠋⠉⡏⠙⠉⠉⠉⡏⠉⠋⡏⠙⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⡉⢙⠉⠉⡏⠉⠉⢉⠉⣝⠉⢉⠉⢉⠉⢉⢹⠉⢉⢩⠉⣙⠉⠉⠉⠉⢹⠉⠉⣉⠉⡉⢹⠉⢉⠉⠉⡉⡉⠉⠉⠁⠙⡉⠉⠉⠉⣙⠉⠉⢉⢉⠉⡉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣉⣉⣉⡉⢉⣉⣸⣉⣙⣉⡏⣉⣉⣉⣉⣉⣈⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣉⣹⣁⣉⣈⣁⣉⣇⣁⢨⡀⣇⣀⣀⣀⣈⣈⢫⣁⣉⠉⣏⣉⣉⣈⣉⣁⣈⣉⣨⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣉⣀⣉⣉⣹⣀⣉⣹⣀⣉⣈⣩⠉⣉⣸⣀⣉⣉⣉⣸⣉⣉⣉⣉⣉⣈⡉⢁⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⣇⣀⣀⣸⢠⣀⢀⣈⣅⣃⡀⣀⣀⣀⣀⣀⣇⣀⣠⣀⣁⣇⣀⣀⣀⣀⣨⣀⣆⣀⣀⣄⣄⣀⣀⣠⣀⣸⣀⣸⣀⣀⣅⣀⣄⣀⣀⣀⣀⣸⣀⣀⣀⣀⣸⣨⣠⣀⣀⣇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣤⣦⣤⣄⣤⣄⣸⣄⣄⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢩⠉⢙⢉⠉⠉⠉⠉⠉⢹⣿⡏⠹⡏⠉⠉⡙⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣤⣴⣾⠛⠙⢦⣠⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢩⠛⠟⡏⠋⠋⡟⡏⠋⠋⠙⡿⠋⠋⠙⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⢸⣿⡏⠀⠀⢸⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣷⢷⣷⢿⣿⠓⠻⣾⠿⣷⡿⣿⣾⡿⢿⣿⣿⢿⣿⣿⡿⣿⡿⢿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢯⣀⣠⣶⡿⠣⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣠⣤⣠⣿⣃⣂⣷⣥⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣠⣤⣦⣤⣤⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡈⢹⢡⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⡟⠝⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠙⠋⠋⠛⡋⠉⡉⢹⠛⡙⠙⢻⠉⠛⠛⠻⠛⠉⡙⠛⠛⠛⠙⠛⠛⠋⡋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⣏⢉⠉⢉⠉⢙⠉⢏⠋⠉⠙⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠄⣯⠉⠛⠙⠛⠛⠋⡟⠛⠙⠛⠙⠛⠛⠏⠙⠛⠛⢹⠉⡙⠍⠋⠛⠛⡟⠛⠋⠛⠋⠛⠛⠛⠛⠋⠛⠛⠛⡏⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣀⣸⣄⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⣩⣏⣹⣿⣿⣏⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⡿⡿⣿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠁⠙⢿⡇⠩⠩⠭⠭⣭⣿⡇⣿⣿⣿⣏⠍⢩⠉⠉⠋⡏⠉⠉⠉⠉⠉⡉⠉⠉⡩⠉⠋⠉⠉⠉⠉⠙⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣒⣒⣒⣂⣒⣒⣦⣀⣒⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡟⡁⠄⠀⢸⡇⠉⠉⢉⠙⠿⣿⡇⣿⣿⣿⡏⠉⠛⠙⠛⡛⠛⠛⢹⠉⠛⠛⠛⠛⢹⠛⢹⠏⠟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢠⡂⠀⣤⣤⣦⣴⣦⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⡟⠂⠀⠀⣀⣾⡇⣓⡚⣛⣚⣛⣛⡃⣿⣿⣿⡿⡚⠿⠿⠿⠗⠶⡿⣛⠳⠿⠷⠗⠳⠿⢾⠟⠺⢶⠶⠾⠾⠾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⡤⠤⠤⠶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣘⣓⣀⣒⣚⣛⣛⣃⣒⣒⣒⣒⣚⣛⣃⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣩⣍⣁⣉⣩⣈⣉⣭⣍⣉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠿⠿⢿⠿⡿⠿⠻⠿⠿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⡟⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣇⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣒⣓⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡍⡩⡛⡋⠉⡉⡏⠉⠉⠉⠉⠉⠉⢉⡉⣹⡉⣋⣉⢉⡉⠉⠉⡏⣋⡍⣙⢹⢉⠉⠉⡙⠉⠉⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⡿⡿⣿⣿⡿⡿⣿⢿⢿⡿⢿⣿⣿⣿⢿⡿⣿⣿⣿⢿⣿⡿⡿⣿⠿⢿⣿⣿⡿⢿⣿⡿⡿⣿⣿⠿⣿⢿⢿⠿⡿⣿⣿⢿⣿⢿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⠴⡤⠧⠤⡼⠥⡧⠤⠤⢾⠧⠤⠴⡥⡤⠴⠶⠤⠤⢼⠤⢥⠤⠤⠬⠤⠤⢤⠦⠼⡤⠦⠼⠤⠤⡮⠤⠤⠥⠤⠤⠼⡤⠤⠤⠧⠼⠤⢥⡦⠤⢮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠶⠶⠶⠧⠆⠦⠶⢼⠼⠷⠶⡵⠵⠧⠴⠴⠦⠶⠾⠦⠾⠶⠦⠄⠦⠶⡼⠶⠴⠦⢾⠲⡦⠼⡷⡖⠔⠶⠶⡕⠐⠨⡲⣴⣶⣴⣶⣴⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠔⠖⠲⠲⢶⠲⠒⠔⢺⠒⠶⠱⠷⡶⢖⠒⠶⠶⠾⠶⠶⠶⠶⡶⠖⡶⠶⢶⠒⠶⠸⠾⠷⠶⠒⠳⠷⠶⠔⡦⢗⠖⠷⠦⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣾⣶⣷⡾⣶⣶⣶⣶⠷⣾⣾⡶⣶⢶⣶⣶⣶⣶⣷⣶⣷⣷⢾⣶⣶⢶⣶⣴⣶⣶⣶⣶⣶⣶⢷⣾⣾⣴⣴⣶⢶⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣼⣠⣤⣤⢤⣤⣤⣤⢠⠼⡤⣤⡤⡤⠤⠼⣤⡴⠠⣤⣤⠠⣤⣤⣤⣼⢤⠤⣤⣤⣷⡤⣤⣤⣤⣼⡤⠬⣼⣠⠤⣦⣼⣤⣴⣧⡤⢤⣤⣤⡼⣿⢿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣼⣤⣤⣤⣧⣤⣤⣤⣤⣧⣦⣬⣤⣧⣼⣤⣤⣼⣦⣤⣤⣤⣮⣼⣴⣤⣤⣤⣤⣤⣦⣤⣧⣴⣦⣤⣼⣤⣦⣤⣤⣤⣤⣧⣤⣤⣴⣤⣮⣼⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣉⡉⣉⣉⣉⣹⣀⣨⡉⣏⣙⣁⣉⣉⣈⣉⣀⣉⣉⣹⣈⣹⣉⣉⣩⣉⣉⣩⣉⣁⣈⣉⣉⣉⣹⣉⣉⣉⢉⣉⡭⣹⣉⣍⢉⣈⢍⣉⣉⣙⣏⣉⣉⣇⣈⣉⣈⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⢤⣤⡧⣦⡨⣠⣠⣠⢄⣇⠵⣤⣄⡼⡸⣴⣄⠧⢄⣁⡠⣸⣼⡰⣦⠇⡖⠄⠶⡗⢥⠇⢤⠨⢤⡤⡄⠸⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣧⣤⣤⣤⣴⣧⣤⣬⣧⣴⣥⣵⣤⣵⣮⣼⣤⣥⣬⣮⣧⣥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣁⣉⢹⣀⣉⣉⣉⣉⢉⣉⡉⣉⣍⣁⣏⣍⣹⢉⣉⣉⣉⣉⣁⣉⢉⣙⣏⣉⣉⣉⣉⣉⣹⣈⣏⣈⣉⣉⣉⣉⣹⣀⣉⣈⣍⣸⣀⣠⣑⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣅⣠⣊⣸⡂⣤⣨⣾⢀⣁⣆⣀⣈⣤⣇⡀⢧⡀⣠⣸⣅⡠⡇⣇⣢⣄⢸⣨⢠⢅⣀⣸⣰⢅⣇⣴⣀⣧⣎⣀⣈⣮⣀⣭⣀⣷⣅⣸⣡⣀⣔⣇⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣤⣤⣤⣤⣠⣼⣤⣤⣤⣤⣼⣴⣤⣧⣤⣤⣤⣄⣤⣤⣧⣤⣤⣤⣼⣤⣦⣆⣄⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⢉⣹⣉⣹⣉⣉⣩⣉⣏⣉⣉⣉⣁⣈⡉⣏⣉⡉⣹⣈⣹⣉⣉⣉⣉⣏⣁⣋⣉⢩⢉⣉⣉⣏⣹⣁⣉⣉⣉⣉⣸⣉⣉⣉⣉⣉⣀⣍⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⠛⡛⠛⢻⠛⡛⢻⠛⡛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⡟⠛⡟⠛⠋⢫⢻⠛⠛⠛⠟⠛⠛⡛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⠛⠃⠚⣛⠛⢻⠘⢻⠛⡏⠙⠋⢻⠈⠙⡏⠉⡉⠽⡖⡛⠋⠟⠉⡛⢻⠛⠛⢙⠛⠋⠛⠋⠙⠛⠛⡟⠛⠛⠛⡏⠓⠛⠉⠛⢺⠘⢛⠛⠛⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⠛⠛⠛⠛⠛⢹⠛⡛⠛⠛⠛⠉⠛⠛⠻⡟⠙⠛⠟⠛⠛⠛⠛⡟⠛⠟⠊⡟⠛⡟⠛⠛⢹⠙⡋⠙⠛⡛⠛⠛⠋⡟⠛⠙⠛⠛⠛⡏⡚⠋⠛⠋⠛⠋⠙⣛⡏⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠙⡩⢿⣉⠋⠉⣋⢹⠋⢙⢍⠉⡊⠉⠉⢻⡋⢙⠝⠋⣙⠙⡉⢙⠋⠙⠋⣹⠉⡉⠉⡏⡋⡏⡋⣋⢹⠉⣋⠉⠙⡏⡋⠉⢉⡏⠉⠩⢛⠉⡋⡋⢙⡏⠉⢙⠉⠋⢙⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢻⣉⣉⣛⣉⣉⣉⡍⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣉⣉⣇⣈⣉⣉⣉⣉⣹⣉⣌⣈⣉⣧⣭⣉⣁⣁⣉⣉⣏⣡⣁⣉⣹⣐⣋⣉⢉⣉⣉⣹⣠⣉⣉⣩⣹⣐⣁⣈⣉⣏⣈⣉⣉⣸⣽⣸⣈⣈⡉⣇⣐⣁⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣁⣉⢹⣀⣉⣁⣀⣉⣉⣏⣱⣁⣉⣉⣉⣉⣉⣅⣉⣍⣉⣁⣉⢹⣈⣁⣉⣁⣉⣩⣉⣏⣉⣉⣉⣃⣈⣉⣉⣉⣹⣉⣉⣹⣁⣉⣍⣍⣹⣨⣈⣉⣩⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣮⣸⣉⣄⣹⣁⣀⣕⣅⣉⣂⣁⣈⣸⣀⣨⣄⣇⣉⣯⣭⣈⣀⣑⣅⣁⣄⣡⣈⣀⣅⣇⣈⣑⣩⣀⣁⣅⣁⣰⣁⣨⣔⣅⣀⣵⣨⣀⣀⣽⣐⣋⣕⣁⣨⣈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣤⣤⣼⣤⣤⣤⣥⣧⣴⣥⣧⣤⣬⣴⣥⣤⣤⣤⣧⣤⣧⣅⣰⣤⣤⣼⣜⣄⣧⣦⣤⣣⣧⣤⣤⣤⣯⣬⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡯⠛⠉⣫⡙⠋⢛⠉⠫⠋⠙⡯⠋⠙⠉⠉⠛⡝⢹⠹⢫⢉⠛⢹⠉⡋⠙⣙⠛⠉⡏⣙⠉⠛⠫⠉⢙⣝⢹⠙⣝⢹⢙⠝⠉⠙⠍⡏⠉⡛⠉⠉⡏⣉⠉⢍⢍⡏⠙⡻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⡉⣁⣉⣉⣉⣯⣉⣉⣉⣉⣙⣏⣉⣉⣁⣈⣉⣈⣨⣉⣉⣙⣉⣈⣱⣭⣉⣀⣏⣉⣏⣈⣉⢉⣉⣉⣈⣉⣹⣉⣸⣨⣉⣇⣉⣉⣉⡃⠉⠉⠏⠉⠉⠩⠉⣏⣉⣈⣉⣉⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣧⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣦⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⣿⠛⠻⠟⠟⠿⡟⡻⠿⠿⢛⠿⢻⠿⡿⠻⠟⢿⠛⠟⡟⠻⠻⠿⠛⢻⠿⢻⠻⡻⡻⠿⢿⠟⠿⠟⠿⠻⣻⠿⠻⠟⠿⠻⠛⠛⠿⡿⠟⢛⡟⠻⠿⡟⠛⢛⠿⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⡒⠒⠒⠒⡗⠓⠒⢲⠒⠚⣺⠒⠒⡒⠒⠚⠒⠖⠓⣞⠒⠒⡲⠚⠒⢚⠗⡖⢒⠒⢺⠒⠒⠓⡲⠚⠛⠒⠚⠒⠒⡲⢲⠚⠒⠓⢒⣺⣷⣶⣶⣿⣶⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠶⠾⢿⢷⡾⠾⡷⠿⢾⠿⠿⢾⠿⠷⠶⢷⠿⡷⠷⠿⢾⠾⠿⠿⢶⢷⠷⠿⠿⠿⢿⠿⠾⠾⡿⠿⠾⢿⠿⠾⠾⡾⠿⡿⢷⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠤⠬⠥⠤⠤⠤⠤⡥⠤⢬⠥⠤⠤⠥⠤⠅⠤⢬⠄⠤⠤⠀⢬⣤⣤⣤⣤⣤⣬⣥⣥⣤⣬⣤⣤⣬⣤⣤⣤⣤⣤⣥⣥⣤⣬⣤⣤⣬⣤⣤⣥⣤⣥⣭⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣬⣥⣤⣤⣥⣤⣤⣤⣥⣤⣬⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣇⣀⣀⣈⣀⢘⣂⣃⢀⣈⢐⢀⢀⠐⣀⣁⣂⣀⣀⣀⣐⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣁⣘⣀⣈⣘⣀⣘⣀⣀⣈⣂⣀⣀⣊⣂⣀⣀⣂⣀⣀⣘⣀⣀⣊⣀⣀⣘⣊⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣐⣀⣀⣀⣃⣀⣀⣋⣃⣁⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣇⢍⣉⣹⣉⣉⣁⣉⣉⣉⣉⣏⣁⣏⣈⣈⣉⣉⣉⣁⣉⣉⣹⣉⣉⣍⣉⣉⣉⣉⣉⣩⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⣉⡉⠉⣉⢙⣝⢹⣉⢏⣉⣉⢙⣽⣉⡉⡉⡉⣉⡉⢹⢍⠉⣉⣉⡍⡏⢫⡋⡏⢉⢙⢹⣉⢝⢉⠹⡯⣹⣉⡉⡉⢉⢝⢉⣉⢙⡉⣉⢙⢹⢉⠹⡋⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⠻⠛⠛⠛⠛⠛⡟⡻⠛⡟⠛⢻⠛⠙⢛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠙⠛⢻⠋⠛⠛⢻⡛⠛⡟⠛⠛⠛⢛⠛⡟⠻⠛⠙⠋⢛⠛⢛⠛⠙⠛⠙⢻⠛⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠛⠋⢹⠙⠙⢻⠻⠋⠛⠋⠛⠛⠛⠋⡟⠙⠛⠛⣛⠛⠛⠻⠛⠛⢹⡛⠋⡟⠛⠛⠋⠙⠛⣛⠛⠉⢻⠛⡓⠛⠛⠛⠛⠚⠙⠛⡏⠛⠛⠛⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠛⠋⠛⠋⠛⠛⠻⡏⠙⠛⠛⠛⠛⣻⠙⢻⢹⠛⢹⠙⠛⠛⡛⡻⠛⠛⠛⠙⢻⠚⠛⠙⡟⠻⠙⠛⠛⠛⠛⠛⠛⢿⠛⠉⠉⠛⡿⠋⠛⠋⠛⠙⡏⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⠉⣹⠉⣹⢉⡋⡏⡻⡉⢙⠍⢻⠉⢙⠍⡉⡋⡩⡉⢹⣉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣉⣉⣏⣉⣁⣊⣉⣩⣏⣹⣿⣿⣏⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠁⠈⢿⡇⠉⠩⠉⠍⢭⣿⡇⣿⣿⣿⣏⠈⢉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠙⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⡒⠒⢒⣂⢒⣒⡂⣀⠒⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡟⡁⠀⠀⢸⡇⠉⠉⢉⠉⠿⢿⡇⣿⣿⣿⡏⠉⠛⠙⠛⠛⠛⠛⢹⠉⠙⠛⠛⠛⢹⠛⢩⠋⠛⠛⠛⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⣤⣤⣦⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⡟⠂⠀⠀⣀⣼⡇⢒⡒⢚⠒⠒⠛⡃⣿⣿⣿⡗⡒⠶⠶⠶⠖⠶⡖⡚⠲⠷⠶⠖⠳⠾⢶⠞⠺⠶⠶⠾⠾⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠠⡤⠤⠤⠴⠿⠛⠛⠟⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣘⣒⣀⣐⣚⣛⣛⣃⣒⣒⣒⣒⣚⣛⣃⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣉⣁⣀⣉⣀⣀⣅⣉⣉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠀⠀⣸⡀⠀⠀⠃⠀⢠⣼⣤⣤⣤⣼⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠙⠊⠛⠛⠙⠘⡏⡐⠋⠛⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣍⣉⣉⣙⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡈⢉⢉⣉⡉⢈⣉⣉⣉⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡤⢤⠴⠤⡤⠤⠦⠤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣬⣤⣤⣴⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣉⣉⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣙⣉⢙⣉⣹⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣉⣉⣉⣉⣉⣉⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠲⠒⠲⠒⠖⠒⠒⠒⠒⢲⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡻⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⡉⠉⠉⠉⠉⠉⠉⢉⣉⡉⣉⠉⠉⠈⠁⠀⣁⣁⣀⣀⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠥⠠⠤⠤⠤⠥⠠⠤⠤⢤⣤⣤⣤⣤⣭⣭⣥⣤⣤⣤⣤⣬⣤⣬⣭⣭⣭⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⢶⡶⣶⣶⡾⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣤⣤⣤⣤⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⡖⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⢒⡒⠒⠒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣤⣤⣤⣤⣤⣴⣼⣿⣿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠤⠦⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠛⠛⠛⠛⠛⢻⠛⢻⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⢻⠛⠻⠛⡛⢻⠛⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠶⡾⢿⢾⢿⠾⠾⠾⠾⡶⠾⠶⠿⠾⡾⡶⠶⡾⢿⠶⠾⣶⠶⠶⢶⠶⠾⠷⢷⢾⠿⢷⠿⢾⠿⡿⢶⢷⡾⠶⠾⡷⢿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣃⠠⢤⠤⠤⠼⠤⠤⠄⠤⠴⠤⠤⠴⢤⠤⠤⠤⠤⠧⠵⠤⡤⠴⠥⠄⠼⡤⠆⠤⠤⢤⣤⣤⣠⣼⣤⣧⣤⣴⣤⣤⣴⣤⣼⣥⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣤⣦⣦⠦⠴⠶⠤⠴⠦⠤⠾⠴⠴⠦⠦⠤⠦⠦⠧⠴⠶⠴⠤⠦⠤⠤⠤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⠛⢻⠙⠹⠉⠹⢙⢹⠛⠛⠛⠛⠛⠛⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⡉⣭⣁⣁⣉⣉⣉⣉⣈⣉⣉⣉⣉⣉⢎⣌⣂⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠛⠿⠿⠟⠿⠟⠟⠻⠿⡻⠛⡛⠛⡿⠟⠛⠻⠿⡿⠿⠻⠻⢿⠻⢿⠻⠛⢿⠿⠿⠿⠿⠿⠿⢿⠛⠿⠟⢟⢛⢛⢻⠻⠿⠿⠻⠿⡿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠒⠲⠖⠒⠲⠂⡖⠲⡒⠒⠒⠒⠧⠰⠒⠲⠒⢶⠒⠘⠗⠓⠲⠖⠓⠲⠒⠒⡒⠓⠲⠒⠖⠚⠀⠒⠒⠒⠺⠒⢲⠒⠖⡖⠓⠚⠖⡒⢺⠚⠲⠲⠚⠒⠖⠒⣶⣦⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣾⣶⣷⣶⣶⣾⣶⣾⣶⣷⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⠿⢿⠿⡿⠿⡿⠿⠿⠿⠿⠿⡿⢿⢿⠿⠿⠿⠿⡿⠿⠿⠿⠿⣿⠿⡿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣤⡤⣤⣤⡤⢧⣤⣥⢤⡤⣤⡤⡼⣤⣦⢤⣴⣤⢤⣤⣥⣤⣧⠧⣼⣶⣤⣤⣵⡤⠴⣤⢤⣤⡤⣤⣧⠤⣤⡬⣧⣤⢦⣤⢤⣤⣤⣤⡼⣿⣿⡿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡧⢤⡤⠤⡤⠧⠤⠼⣤⣤⣤⣧⣤⣦⣤⣼⣤⣤⣤⣤⣄⣼⣤⣴⣤⣤⣤⣢⣤⣤⣦⣬⣦⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣄⣦⣤⣼⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 2833

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/mobile-phones-or-cellphones-issues/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/mobile-phones-or-cellphones-issues/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Why_I’m_Using_Just_a_Landline_and_Recalling_My_Richard_Stallman_(RMS)
Interview_on_Working_Locally_or_How_the_Signal_Processor_in_Phones_is_a_De
Facto_Back_Door⠀✐


Posted in Free/Libre_Software at 10:44 am by Dr. Roy Schestowitz


Video_download_link


http://techrights.org/videos/danger-of-phones.webm


Summary: A longer-than-expected rant about what mobile phones have turned into
and a look back at (or listen to) what Richard Stallman (RMS) told me way back
in 2013


THE thing many people have dubbed “a phone” isn’t really a phone but an
artificially-crippled computer that can — among many other things — make or
receive calls.


The video above explain what I use (in 2021) instead of mobile phones. They’re
rarely needed, except for few people with very particular occupations that
require a lot of travel.


“The recording also mentioned torture whistleblower Craig Murray, who has just
been arrested.”While recording this I recalled an old conversation that I had
with Richard Stallman (RMS), whom I’ve been in touch with for many years. He
has been observing technology for a lot longer than many of us. At around 4
minutes from the start of this old interview with RMS (TechBytes_episode_84;
very low quality, recorded over landline with a microphone next to it; direct
download_as_Ogg; 00:14:31 in total duration; 8.2 MB in size) he mentioned
FirefoxOS and OpenMoko. Later he also suggested using Replicant, if anything at
all. The recording also mentioned torture_whistleblower_Craig_Murray,_who_has
just_been_arrested. Dark week…


The main point though is, it’s far too difficult to secure any mobile phone
from privacy violations and therefore they’re rarely worth the trade-offs. █



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Download:


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


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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/05/12/reporting-injustice/#comments
    Gemini version at gemini://gemini.techrights.org/2021/05/12/reporting-injustice/

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✐ Doing_Justice_by_Reporting_Injustice⠀✐


Posted in Europe, Patents at 4:14 am by Dr. Roy Schestowitz


       🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Can I see what goes on in EPOnia? No, GTFO!⦈
    The EPO’s management still prevents about 7,000 workers from accessing
                                  Techrights


Summary: Europe’s second-largest institution, helped_by_Europe's_largest, is
engaging in a massive attack on the very concept of the Rule of Law and
incredibly enough the so-called ‘press’ (or ‘media’) doesn't_report_on_it


THIS morning we started a new series about the EPO. Expect this series to go on
for well over a fortnight. There’s lots more to come. Readers of ours, many of
whom work for the EPO, are paying close attention.


Associate of ours (at Techrights) has stated: “The EPO has been one of the many
multifaceted scandals willfully ignored (and thus condoned) by the press.”


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇They trusted me to assess patent applications, but they
created a monster⦈ We’re making use of IPFS and Gemini to reduce prospects of
censorship — either by technical means or intimidation. The EPO did try this
several times in the past. We’re moreover still blocked by the EPO. It also
targeted IP Kat, which has never been the same (never since a lot of writers
stepped down in quick succession). Speak to the old (original) Kats and they
might have some stories to tell…


“By the way,” the associate has added, “so many newspapers are covering some
aspects of Bill’s [Gates] scumminess. However, they all still are loyal to him
in that they refuse to cover the damage he has done to business, industry,
government, and education through his crap products and his bribing of media to
shut up about it. How, many have exposed that he has influence over media and
uses it to keep FOSS out of the news? The goal is Software Freedom…”


To our EPO readers this may seem off-topic, but it’s not. We assure you! It’s
all connected, not just through Gates obsessing over patents, Microsoft
grabbing_the_EPO's_data, and the lobbying for European_software_patents
(nowadays it’s just fashionable to call them all “Hey Hi” patents because
buzzwords beget ambiguity). What Gates and the EPO have in common, for
instance, is their “above the law” status (de facto immunity) and control_of
the_media_by_means_of_funding.


          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇EPO violates the EPC? Remind me later⦈
   “Remind me later” (maybe after the EPO is totally and completely defunct)


What’s at stake here isn’t just European sovereignty but the sovereignty of
every software developer and computer user. Do we want to be policed or at
least governed by patent offices in the pockets of large corporations that ban,
censor, manipulate and spy on people?


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇'Judge' António Campinos and Carl Josefsson⦈ Certainly not,
right?


Techrights was always about patents (since the very beginning in 2006), but it
often explains the connection to software freedom, which is increasingly
connected to personal freedom and societal justice. The more “digital” society
gets, the more pronounced this correlation will become.


Later today we shall post Part 2 of the series, to be entitled “Just Another
Pro Forma Rubber-Stamping Exercise?”


Remember that this case pertains to proprietary software, privacy, outsourcing,
and many other aspects of digital or “tech” rights. █


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

                    ䷩ 𝚕𝚒𝚗𝚎 3180

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Links_12/5/2021:_New_Audacity_and_Musescore_Owner_Named,_Microsoft_May_Lose
“JEDI”_(Trump’s_‘Bailout_Package’)⠀✐


Posted in News_Roundup at 2:22 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⠀➾


                # ⚓ mintCast_360.5_–_What’s_a_Distro?⠀⇛


                       2:11 Bi-Weekly Wanderings
                       43:58 The News
                       1:05:46 Security Update
                       1:07:29 Announcements & Outro


                       In our Innards section, what makes a distro a
                       distro? It’s Elementary, my dear Watson.


                # ⚓ Distro_in_the_Rough_|_LINUX_Unplugged_405⠀⇛


                       We’re taking a look at an underdog distro. We may
                       have found a diamond in the rough with a few tricks
                       up its filesystem.


                       Plus our review of the ODROID-Go Super an Ubuntu-
                       powered handheld, and our tools for laptop battery
                       health.


                # ⚓ This_YouTuber_now_runs_the_Audacity_project⠀⇛


                       Tantacrul is a designer and musician who has been
                       running Musescore for years. Now he’s set his
                       sights on Audacity.


                # ⚓ Endeavour_OS_Review_|_Why_THIS_Is_The_Best_Linux_Distro_For
                  Intermediate_Users_In_2021?_(NEW!)⠀⇛


                       Tried ALL the Linux distros and Ready to take the
                       NEXT STEP? Endeavour OS is a POWERFUL and FLEXIBLE
                       Arch-Based Distro that really puts the POWER in
                       your hands. Endeavour OS gets the newest
                       technologies, advanced features and latest package
                       updates before anybody else. It also gives you a
                       lean system that you can build according to your
                       needs.


                # ⚓ Termite_Is_Dead,_Go_Install_Alacritty_Right_Now⠀⇛


                       Recently the Termite maintainer decided that he has
                       had enough dealing with the VTE library and rather
                       than handing the project off to someone else has
                       decided to just kill the project and suggest that
                       people move to Alacritty instead. He also calls out
                       GNOME for creating a really hostile environment for
                       developers who want to use their libraries.


          o § Kernel Space⠀➾


                # ⚓ Latest_Linux_kernel_introduces_preliminary_Apple_M1
                  support⠀⇛


                       The latest version of the Linux kernel, Linux 5.13,
                       introduces support for Apple’s M1 system-on-chip
                       and is now available as a release candidate.


                       Apple M1 support was previously reported for Linux
                       5.13, though no release date was mentioned at the
                       time. On Tuesday, however, Linux kernel principal
                       developer Linus Torvalds announced that the release
                       candidate version is now available for public
                       testing.


                       Although security researchers have successfully
                       booted Linux on Apple Silicon in the past, it
                       required some fairly technical workarounds. With
                       preliminary support in Linux 5.13, Linux
                       distributions and systems will have a much easier
                       time running on Apple’s SoC.


                # ⚓ Linux_Kernel_‘Linux_5.13′_Will_Support_Apple_M1_System-on-
                  Chip_|_Now_Available_for_Public_Testing⠀⇛


                       The Apple M1 chip has recently started to gain much
                       traction and is now fully recognized as another
                       possible processor to choose for high-end
                       performance. It seems like the recognition now
                       stems past Apple as the latest version of the
                       popular Linux kernel known as the Linux 5.13 would
                       introduce support for Apple’s M1!


                       Apple M1 on Linux


                       Apple made headlines for deciding to step away from
                       their long-time chip supplier, Intel, as the
                       company decided to manufacture their own CPUs.
                       Apple made headlines with their M1 chip and are now
                       spreading the chip to other units that they own.
                       Aside from Apple, it now looks like Linux is
                       recognizing its power.


                       According to the story by AppleInsider, the Linux
                       5.13 reportedly introduces support for Apple’s
                       popular M1 system-on-chip and is currently
                       available as a certain release candidate. The Apple
                       M1 support was also previously reported for the
                       Linux 5.13 but there was no release date given
                       during that time.


                # § Graphics Stack⠀➾


                      # ⚓ AMD_Releases_ROCm_4.2_Compute_Stack⠀⇛


                             Just over one month has passed since the
                             release of Radeon ROCm 4.1 and it’s now been
                             succeeded by the ROCm 4.2 feature release.


                             The Radeon Open eCosystem 4.2 release comes
                             with changes such as:


                             - HIP target platform macros were added for
                             easily targeting HIP_PLATFORM_AMD /
                             HIP_PLATFORM_NVIDIA code differences such as
                             including different header files.


          o § Applications⠀➾


                # ⚓ Kodi_19.1_Matrix_software_update_brings_Xbox_support_and
                  more⠀⇛


                       Kodi formerly XBMC the free and open-source media
                       player software application developed by the XBMC
                       Foundation, a non-profit technology consortium, has
                       this week released a new update in the form of the
                       Kodi 19.1 Matrix providing a wealth of bug fixes,
                       tweaks and enhancements to the software. Kodi is
                       available for a wide variety of different operating
                       systems and hardware platforms and comes with a 10-
                       foot user interface for use with large screen
                       televisions and the like.


                       Thanks to its open source and cross-platform
                       design, with its core code written in C++, modified
                       versions of Kodi-XBMC together with a JeOS have
                       been used as a software appliance suite or software
                       framework in a variety of devices including smart
                       TVs, set-top boxes, digital signage, hotel
                       television systems, network connected media players
                       and embedded systems based on arm platforms such as
                       the Raspberry Pi and similar.


                # ⚓ Jakub_Kadlčík:_A_year_with_Emacs⠀⇛


                       Why would I commit such a heinous crime? After ten
                       years, I came close to hitting my peak knowledge
                       about VIm. Of course, nobody can claim to truly
                       know Vim in its full depth but I got to the point
                       where the learning curve slowed to a deadly pace
                       and new tricks just slightly adjust your approach
                       when solving obscure scenarios. The only real game-
                       changer yet to be conquered was plugins
                       development. I tried but I dislike VimL as a
                       language for writing code and thus I have no
                       intention of doing so.


                       On the other hand, I am fascinated by the
                       functional programming paradigm and Lisp in
                       particular. This alone, was a strong enough impulse
                       for migrating to Emacs. I won’t hit the ceiling
                       regarding custom package development.


                       Also, I came to realize, that my Vim workflow is
                       different than for most other users (at least in my
                       social circle). Everyone seems to have a shell-
                       centric approach, find-ing, grep-ing, cat-ing their
                       way through a project, and then opening the
                       intended file in Vim, editing, and closing. I do
                       the same thing when it comes to searching within a
                       project but I do it in a separate terminal. When it
                       comes to Vim, I start it once, do everything from
                       within, and then close it after six months when a
                       new Fedora is released and I need to upgrade. If it
                       reminds you of something, it’s Emacs.


                       There is also a couple of tempting Emacs features
                       but about them later.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_Minecraft_Bedrock_on_a_Chromebook⠀⇛


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


                # ⚓ How_To_Install_Samba_on_CentOS_8_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       the Samba on CentOS 8. For those of you who didn’t
                       know, Samba is a free and open-source software that
                       can be used to share files, folders, and printers
                       between Linux and Windows systems.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you through the step-by-
                       step installation of the Samba on a CentOS 8.


                # ⚓ How_to_Mount_Partitions_using_UUID_in_Linux⠀⇛


                       If you use lots of disks that regularly changed or
                       moved, it’s preferred to mount the partition using
                       UUID. This is because OS may change device names in
                       some situations like adding another disk. This may
                       end with issues with booting. UUID is unique and
                       independent from the actual device names.


                       In this tutorial, we are going to learn how to
                       mount partitions using UUID in a Linux system.


                       Firstly, find the UUID of the device partition that
                       is going to be mounted. You can use the following
                       command to find the UUID of the partitions.


                # ⚓ Raspberry_Pi_Articles⠀⇛


                       Fresh off publishing a bunch of articles on
                       learning tmux yesterday, I finally took the time to
                       also migrate my older Raspberry Pi articles. Given
                       the timeline, they’re mostly about RPi4 release and
                       thoughs on Raspberry Pi 4 platform.


                # ⚓ How_to_Create_Virtual_Machine_with_Vagrant_and_VirtualBox⠀⇛


                       This article shows how to create a Vagrant project
                       to install a vagrant box, configure a guest
                       machine, and understand important configurations
                       and commands.


                # ⚓ How_to_generate_and_backup_a_gpg_keypair_on_Linux⠀⇛


                       Gnu Privacy Guard (gpg) is the Gnu project free and
                       open source implementation of the OpenGPG standard.
                       The gpg encryption system is called “asymmetric”
                       and it is based on public key encryption: we
                       encrypt a document with the public key of a
                       recipient which will be the only one able to
                       decrypt it, since it owns the private key
                       associated with it. Gpg allows us also to sign
                       documents using our private key and let others
                       verify such signature with our public key. In this
                       tutorial we will see how to generate and create a
                       backup of a gpg keypair.


                # ⚓ How_to_run_a_NYM mixnode_·_Pablo_Iranzo_Gómez’s_blog⠀⇛


                       Some time ago I’ve started running a NYM mixnode.
                       NYM is a project that targets improving privacy by
                       decomposing network packages from different hosts,
                       so that origin and target cannot be traced.


                # ⚓ How_to_run_a_NYM Validator_·_Pablo_Iranzo_Gómez’s_blog⠀⇛


                       As said in the article about mixnodes, NYM is a
                       technology aiming for providing privacy for the
                       communications.


                       Apart of the mixnodes, other key piece in the
                       infrastructure are the validators.


                       As said, the project uses Open Source technology to
                       run, and they have a nice docs with details on how
                       to run a node at https://nymtech.net/docs/, and the
                       one relevant for mixnodes at https://nymtech.net/
                       docs/run-nym-nodes/validators/.


                       In this case, we can follow the instructions for
                       compiling, but I faced some issues (compiling went
                       fine, but initial sync failed), so in this case, we
                       will use the pre-compiled version provided with the
                       0.10.0 release.


                # ⚓ How_to_check_if_a_system_is virtual_·_Pablo_Iranzo_Gómez’s
                  blog⠀⇛


                       I was improving a playbook in Ansible and wanted to
                       find a way to find if a system was virtual or not
                       to decide about some tunning like setting tuned-adm
                       profile virtual-guest or disable the power off when
                       the lid is closed.


                # ⚓ How_to_install_Krita_on_Deepin_20.2⠀⇛


                       Today we are going to look at how to install the
                       latest version of Krita on Deepin 20.2. As seen in
                       the video, a person updates the repositories of our
                       system, install flaptak, add the flathub
                       repository, install Flowblad, and then reboot your
                       computer. Enjoy!


                # ⚓ How_to_cast_video_from_Android_to_Linux_|_FOSS_Linux⠀⇛


                       There are many apps and tools out there that will
                       help you cast your Android screen to your Linux PC.
                       However, the main problem is that it only mirrors
                       what’s on the screen and not the audio. This can be
                       an issue if you are trying to cast video from
                       Android, which requires you to forward both video
                       and audio.


                       Also, the tools that do let you effectively cast
                       video (including its audio) from your Android
                       device to your Linux PC either require a rooted
                       Android phone or suffers from latency issues. And
                       if not that, then it’s a premium tool and requires
                       you to pay money.


                       But it’s Linux we are talking about! Ain’t there a
                       free and open-source tool that will help us cast
                       video and forward audio from Android to Linux?


                # ⚓ What_is_the_OSI_model?⠀⇛


                       Today I tweeted something about how the OSI model
                       doesn’t correspond well to the reality of how TCP/
                       IP works and it made me think – what is the OSI
                       model, exactly?


                # ⚓ How_to_set_up_an_MP4_video_player_on_Ubuntu⠀⇛


                       Are you new to Ubuntu? Trying to figure out how to
                       play an MP4 video on your Ubuntu desktop but don’t
                       know what video player to use or how to do it? We
                       can help! Follow along as we show you how to set up
                       an MP4 video player on Ubuntu!


                # ⚓ How_to_Fix_Bluetooth_Connectivity_Issues_in_Ubuntu_Linux⠀⇛


                       Although Ubuntu Linux is a stable and robust
                       operating system, sometimes Bluetooth connections
                       with external devices do not work properly.


                       If you have been using Bluetooth devices on your
                       computer, you might have noticed that you need to
                       reconnect your Bluetooth devices whenever the
                       computer wakes up from sleep or hibernation. And
                       that’s just one problem to speak of.


                       This guide will show you how to fix common
                       Bluetooth connectivity issues on Ubuntu Linux so
                       that you do not have to reconnect Bluetooth devices
                       whenever you want to work on your PC.


                # ⚓ How_To_Use_Nmap_–_A_Comprehensive_Guide:_Basics_To
                  Advanced⠀⇛


                       Nmap is a free and open-source network discovery
                       and security audit tool. Nmap stands for “Network
                       Mapper“.


                       Whether you are a network engineer or a penetration
                       tester, Nmap is one of the most important tools in
                       your arsenal.


          o § Games⠀➾


                # ⚓ Godot_Engine_–_Announcing_Go_Godot_Jam⠀⇛


                       Meet Adrian, a game developer from Stockholm,
                       Sweden. He co-organises Go Godot Jam, a one-month
                       long community festival with a game jam included.
                       Adrian answered a few questions.


                       [...]


                       Godot is a great game engine that unlocks
                       possibilities for game developers. It is a free,
                       open-source 2D and 3D engine that provides many
                       features so that you can focus on your game.


                       Yet most people start developing games with
                       proprietary engines such as Unity or Unreal. They
                       are solid engines with a proven track record and a
                       vibrant ecosystem. One advantage having experience
                       with more than one engine can enable people to
                       create better games. In the end, it’s up to each
                       individual to pick the one that they’ll be most
                       comfortable with to fulfil their creative vision.


                       I know that Godot has a lot to offer to new
                       developers, with a distinctive approach to game
                       development which enables more people to express
                       their creativity. It’s open, focused on user-
                       friendliness, easy to learn, yet feature-packed and
                       a great fit for many types of games. As such, I
                       want to increase awareness of the engine so that
                       more users decide to try it out and add it to their
                       toolset.


                # ⚓ Try_out_the_new_teaser_for_Drova_–_Forsaken_Kin,_an
                  upcoming_2D_action_RPG⠀⇛


                       After already being available on itch.io, the free
                       teaser for Drova – Forsaken Kin is now available on
                       Steam and it’s been upgraded for the new release.


                       “Drova – Forsaken Kin is an Action Based RPG filled
                       with handcrafted open world adventures inspired by
                       the much renowned Gothic game series. A society has
                       discovered the power of a dead empire: to capture
                       the spirits that govern nature and rule over them
                       instead. However, the anger of the remaining
                       spirits divided them. Where will you stand?”


          o § Distributions⠀➾


                # § Reviews⠀➾


                      # ⚓ Bodhi_Linux_6.0_livestream_Distro_Review⠀⇛


                             In this live stream, we took a look at the
                             new release of Bodhi Linux – live! There were
                             some technical difficulties, and some rough
                             edges, but it was a fun experience for sure.
                             Check out Bodhi Linux, it’s an interesting
                             distribution for sure.


                # § New Releases⠀➾


                      # ⚓ Bodhi_Linux_6.0_Released,_This_is_What’s_New⠀⇛


                             A new version of Bodhi Linux is available to
                             download, based on the Ubuntu 20.04.2 point
                             release.


                             As well as offering a newer version of the
                             Linux kernel, Bodhi Linux 6.0 carries a
                             commendable crop of changes. This includes
                             several major improvements to distro’s
                             distinctive Moksha desktop, plus important
                             bug fixes, theme tweaks, and more.


                             Keep reading for more more detail on what’s
                             new in Bodhi 6.0, or skip straight to the
                             download section to grab one of the three
                             .iso images that are available so you can
                             road-test the system for yourself.


                # § BSD⠀➾


                      # ⚓ NomadBSD_130R-20210508_is_now_available!⠀⇛


                             We are pleased to present the release of
                             NomadBSD 130R-20210508.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ IBM_leapfrogs_everyone_with_its_2nm_chips⠀⇛


                             As TSMC charges to 5nm transistor designs and
                             Intel struggles for 7nm, IBM has topped them
                             all with the world’s first 2-nanometer node
                             chip.


                             OK, it won’t come to market for four years,
                             according to IBM, and they might not be the
                             first name that comes to mind when you think
                             of processor design, but they are the quiet
                             power in the semiconductor world.


                      # ⚓ IBM_Exec:_‘There’s_Never_Been_A_Better_Time_To_Be’_A
                        Partner [Ed: CRN seems to have been reduced to pure
                        marketing, not news]⠀⇛


                             IBM GMs David La Rose and Evaristus Mainsah
                             told CRN about channel partner-focused
                             announcements at the tech giant’s Think 2021
                             conference, including a new competency
                             framework for partners, message acceleration
                             workshops to help partners with marketing and
                             expansion of Cloud Engagement Funds for
                             multiple partner types.


                      # ⚓ What_CIOs_and_CMOs_can_learn_from_each_other⠀⇛


                             It used to be that CIOs were strictly
                             concerned with the technical nuts and bolts
                             of product development. That’s no longer the
                             case. With IT becoming more of a revenue
                             driver for organizations, CIOs are asking
                             their teams to take a customer-first approach
                             to application development and design.


                             What customers want and how they get it can
                             change quickly.
                             The problem is, what customers want and how
                             they get it can change quickly. For example,
                             a person’s buying patterns during the
                             holidays are probably different in the
                             spring. How they buy can change, too,
                             sometimes during a single transaction – for
                             instance, a person might start a purchase on
                             their desktop PC but eventually click “buy”
                             on their mobile device.


                             Customers are complicated. Your team needs
                             help developing applications that meet
                             customers wherever they are on their buying
                             journey. And you need help creating a truly
                             customer-centric IT organization.


                      # ⚓ Digital_transformation:_4_ways_to_build_in_security⠀⇛


                             But just because it’s essential doesn’t mean
                             it’s easy. Change is hard, and successful
                             digital transformation takes a village – from
                             the IT partners and internal staff who help
                             implement the tools to executives
                             communicating the efforts to the team members
                             interfacing with the new technology each day.


                             While migrating to new systems and following
                             new protocols is hard enough, there’s another
                             vital part of digital transformation strategy
                             that often gets overlooked. While setting up
                             infrastructure and training employees is
                             typically the main focus, securing these new
                             and exciting projects can sometimes take a
                             back seat.


                # § Debian Family⠀➾


                      # ⚓ Mirror_in_USA⠀⇛


                             There is a new repo mirror available for
                             Sparkers, located in Chicago, USA.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ You_Can_Now_Upgrade_Ubuntu_20.10_to_Ubuntu_21.04,
                        Here’s_How⠀⇛


                             Upgrades from Ubuntu 20.10 to Ubuntu 21.04
                             were blocked until today (May 11th) due to a
                             bug that made some systems to end up in an
                             unbootable state if they use EFI 1.10. An
                             updated shim version was released today,
                             which is compatible with EFI 1.10, to make
                             upgrades from Ubuntu 20.10 to Ubuntu 21.04
                             possible.


                             Dubbed Hiruste Hippo, Ubuntu 21.04 introduces
                             numerous new features and improvements, such
                             as a newer kernel (Linux 5.11), the Wayland
                             session enabled by default, GNOME 40 apps,
                             and updated internals to some of the most
                             recent GNU/Linux technologies.


                      # ⚓ Ubuntu_21.04_(Hirsute_Hippo)_Gets_Its_First_Kernel
                        Security_Patch,_Update_Now⠀⇛


                             Ubuntu 21.04 was released three weeks ago and
                             ships with the Linux 5.11 kernel series by
                             default, which has now been patched by the
                             Ubuntu Kernel Team against three recently
                             discovered security vulnerabilities.


                             These include CVE-2021-3489 and CVE-2021-
                             3490, two vulnerabilities discovered by Ryota
                             Shiga and Manfred Paul respectively in Linux
                             kernel’s eBPF implementation. Both of these
                             security issues could allow a local attacker
                             to crash the system by causing a denial of
                             service (DoS attack) or execute arbitrary
                             code.


                      # ⚓ Kubuntu_and_Other_Ubuntu_18.04_Flavours_Reached_End
                        of_Life⠀⇛


                             Ubuntu 18.04 LTS is supported until April
                             2023, but the flavours finally reached the
                             end of life in May 2021.


                             This includes popular flavors like Kubuntu
                             18.04, Ubuntu MATE, and others.


                             In case you do not know, usually, the Ubuntu
                             flavours get 3 year support in a row while
                             Ubuntu’s official release gets 5 years of
                             support.


                             [...]


                             While you can already find bleeding edge
                             versions available for some flavors like
                             Ubuntu MATE 21.04, the next best option for
                             users with Ubuntu 18.04 flavors is to upgrade
                             to another flavor based on Ubuntu 20.04 LTS.


                             Of course, considering this is already 2021,
                             you will have two more years of support for
                             them.


                             If you are aiming for something with a long
                             term support cycle, you may want to stick to
                             the official Ubuntu release, or you can
                             choose Linux Mint over Ubuntu for a similar
                             support cycle.


                             If you have a 32-bit installation, you will
                             have to opt for a fresh installation of any
                             latest Ubuntu release/Ubuntu-based distro of
                             your choice.


                             If you have a 62-bit installation on board,
                             you can choose to upgrade your flavor to
                             Ubuntu 20.04 LTS base release.


          o § Devices/Embedded⠀➾


                # ⚓ Guest_Post:_In_Linux_smartphones_we_trust⠀⇛


                       What would have been inconceivable just a few years
                       ago is now a reality – there are two mainline Linux
                       phones on the market. The PinePhone from Pine64 and
                       Librem 5 from Purism don’t use old and SoC-specific
                       Android kernels, nor do they rely on binary blobs
                       to enable core device functionality.


                       While PINE64 and Purism may have been the first to
                       the market with their respective devices, I have
                       reasons to believe they won’t be the last. Interest
                       in these devices is steadily growing and people
                       outside the Linux community are now taking notice.
                       To me it looks like something more than a temporary
                       fad – I don’t want to jinx it, but I think Linux
                       smartphones are here to stay.


                # ⚓ Automotive_–_A_bumpy_ride_ahead.⠀⇛


                       Automotive is going through one of the biggest
                       transformations among all industries. Since its
                       inception, for decades, it focused on hardware and
                       horsepower. Now, the entire sector needs to
                       reconsider the supply chain ties, the relationships
                       with customers and the way vehicles are being
                       produced. Not too dissimilar to what we witnessed
                       with mobile telephony moving from handset form-
                       factors to user interfaces, the battleground in
                       automotive is becoming defined by software.


                # ⚓ Embedded_MXM_modules_are_first_to_load_Nvidia_Turing_GPUs⠀⇛


                       Adlink announced the first MXM 3.1 modules with
                       Nvidia Turing GPUs, ranging from the Quadro T1000
                       to the RTX5000. Aimed at edge AI applications, the
                       modules are only a fifth the size of a PCIe card.


                       Adlink announced three PCIe graphics expansion
                       modules that adopt the compact, PCIe x16-enabled
                       MXM 3.1 form-factor: the EGX-MXM-T1000 with
                       Nvidia’s Quadro Embedded T1000, the EGX-MXM-RTX3000
                       with the Quadro Embedded RTX3000, and the EGX-MXM-
                       RTX5000 with the Quadro Embedded RTX5000. The
                       Nvidia collaboration represents the first time such
                       high-level graphics have been available on MXM
                       (Mobile PCI Express Module).


                       [...]


                       Linux and Windows drivers are available.


                # ⚓ MontaVista_Launches_a_Migration-Free_Support_Program_for
                  Yocto_Baselines⠀⇛


                       MontaVista® Software, LLC, a leader in commercial
                       Embedded Linux® products and services, today
                       announced the availability of “MVShield for Yocto,”
                       a professional services offering to support
                       customer’s Linux distribution created with Yocto
                       Project software, giving access to industry-leading
                       support and maintenance services without any
                       migration effort to commercial Linux baselines.
                       MontaVista will maintain and support the customer’s
                       specific Yocto Project created Linux distribution.


                # ⚓ Gateworks_GW7200_Dual_Gigabit_Ethernet_industrial_SBC,_also
                  supports_WiFi,_Cellular,_and_GPS⠀⇛


                       Gateworks GW7200 is a versatile dual Gigabit
                       Ethernet industrial single board computer with an
                       NXP i.MX8M Mini processor, 1GB to 4GB of RAM, mini
                       PCIe expansion sockets for wireless connectivity,
                       serial interfaces, industrial temperature range,
                       wide range input voltage, and long-term supply.


                       The board should be a better match to projects with
                       industrial requirements, for example, an industrial
                       IoT gateway than lower-cost dual GbE alternatives
                       such as NanoPi R2S or Raspberry Pi CM4 IoT Router
                       Carrier Board Mini.


                       [...]


                       The company provides an Ubuntu Linux Board Support
                       Package (BSP) for the board. The made-in-the-USA
                       single board computer is part of the Gateworks 7th
                       generation Venice family of rugged and industrial
                       single board computers and targets small embedded
                       applications such as IoT Gateways, Machine
                       Learning, digital signage, and robotics. You’ll
                       find hardware and software documentation in the
                       Wiki.


                # § Open Hardware/Modding⠀➾


                      # ⚓ This_pendulum_POV_clock_uses_a_Nixie_tube_to_plot_the
                        time_as_it_swings_|_Arduino_Blog⠀⇛


                             Clock pendulums are generally mechanical
                             devices that time each second as it ticks
                             away, but do little else. Jason Oeve’s
                             concept, however, places the face itself – a
                             single IN-12B Nixie tube – onto its large
                             wooden pendulum. As it swings back and forth,
                             four digits are progressively displayed on
                             the tube for a unique timepiece.


                             An Arduino Nano is the brains of the
                             operation, along with an RTC module and an
                             accelerometer that senses the pendulum’s
                             position. When it’s straight up and down, an
                             electromagnetic coil gives it a boost,
                             keeping it ticking along “forever.”


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Why_Android_12_(Not_iOS_15)_Will_Be_The_Best
                        Smartphone_Update_Of_2021⠀⇛


                      # ⚓ Nokia_Android_11_schedule_slips_and_pushes_back
                        devices_–_9to5Google⠀⇛


                      # ⚓ OnePlus_7,_7T_series_plagued_with_problems_after
                        Android_11_update⠀⇛


                      # ⚓ Samsung_Galaxy_A12,_Galaxy_A02s_Receiving_Android_11-
                        Based_One_UI_3.1_Update:_Reports_|_Technology_News⠀⇛


                      # ⚓ Samsung_issues_warning_to_all_Galaxy_owners_–_check
                        for_this_update_NOW_|_Express.co.uk⠀⇛


                      # ⚓ PUBG_Mobile_1.4_update_for_Android:_APK+OBB_download
                        link_for_worldwide_users⠀⇛


                      # ⚓ Best_Android_Operating_System_in_2021?_–_Android_OS⠀⇛


                      # ⚓ 5_best_free_Android_games_like_GTA_5_for_2_GB_RAM
                        smartphones_in_May_2021⠀⇛


                      # ⚓ What_Is_RCS_Messaging_on_Android_and_How_Do_I_Use
                        It?⠀⇛


                      # ⚓ How_to_change_the_default_Android_Home_Screen
                        launcher_–_Phandroid⠀⇛


                      # ⚓ Meet_The_Android_Automotive_OS_–_PC_Perspective⠀⇛


                      # ⚓ Sunyard_i80_Android_Mobile_Payment_Terminal⠀⇛


                      # ⚓ Google_Assistant_Could_Be_Soon_Summoned_With_Power
                        Button_in_Android_Phones_|_Technology_News⠀⇛


                      # ⚓ Webinar_on_Introduction_to_Android_Studio_to_be_held
                        on_Wednesday⠀⇛


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


                # ⚓ ‘I’m_Possibly_Alive_Because_It_Exists:’_Why_Sleep_Apnea
                  Patients_Rely_on_a_CPAP_Machine_Hacker⠀⇛


                       Christy Lynn was tired all the time, and, after
                       months of trying to diagnose the problem, one of
                       her doctors thought they’d figured out why.


                       “I didn’t fit any of the descriptions for sleep
                       apnea,” she told me on a phone call. “I’m a woman,
                       I wasn’t overweight. No one would have thought to
                       test me, except I was seeing a doctor who had a
                       similar medical history.”


                       Lynn, who lives in rural Arizona, did an at-home
                       oximetry test, which tests blood oxygen levels, and
                       then a sleep study. She was diagnosed with a
                       difficult-to-treat form of sleep apnea, a disorder
                       in which patients suddenly stop breathing for
                       periods of time while they sleep that most often
                       affects overweight men. She was given a continuous
                       positive airway pressure (CPAP) machine and face
                       mask—which blows air down a patient’s windpipe to
                       keep the airways open—and sent home.


                       But a year-and-a-half and three sleep doctors
                       later, her symptoms hadn’t improved. Her Apnoea-
                       Hypopnea Index (AHI), which refers to the number of
                       times she stopped breathing per night, was
                       “horrible.”


                # ⚓ AV1_Decoder_dav1d_Lands_10-bit_AVX2_Assembly_For_Big_Speed-
                  Up,_Thanks_Facebook_+_Netflix⠀⇛


                       For those making use of 10-bit AV1 content and
                       using dav1d as the performant CPU-based decoder,
                       the performance on modern Intel and AMD processors
                       is about to be a heck of a lot better.


                # ⚓ 6_start-to-finish_guides_to_deploying_open_source
                  technology_at_your_organization⠀⇛


                       There are a lot of reasons to deploy open-source
                       operating systems and software: A large community
                       of people helping to constantly improve it, it’s
                       free, and you can even participate in its
                       improvement.


                       Open source does come with a bit of a catch,
                       though: You’ll need to do a lot of legwork yourself
                       that is often automated when using paid products.
                       When done correctly, however, open source operating
                       systems like Linux, database software like MariaDB,
                       and automation software like Kubernetes can be
                       invaluable to an organization.


                       These TechRepublic Premium start to finish guides
                       by TechRepublic’s open-source expert Jack Wallen
                       will help you get started with invaluable open-
                       source tools without the headache.


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Peace_of_mind_browser_add-ons_for_Firefox⠀⇛


                                   The web can be as wonderful as it is
                                   overwhelming. Fortunately there are
                                   ways you can customize Firefox with
                                   add-ons to achieve a more harmonious
                                   browsing experience. Here are a few
                                   examples—from soothing visual
                                   enhancements to great tools for mental
                                   clarity and peace of mind.


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ insideBIGDATA_Latest_News_–_5/11/2021⠀⇛


                             Percona, a leader in open source database
                             software and services, announced a preview of
                             its 100% open source Database as a Service
                             (DBaaS), which eliminates vendor lock-in and
                             enables users to maintain control of their
                             data. As an alternative to public cloud and
                             large enterprise database vendor DBaaS
                             offerings, this on-demand self-service option
                             provides users with a convenient and simple
                             way to deploy databases quickly. Plus, using
                             Percona Kubernetes Operators means it is
                             possible to configure a database once, and
                             deploy it anywhere.


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ GNU_Guix_1.3.0_released⠀⇛


                                   We are pleased to announce the release
                                   of GNU Guix version 1.3.0!


                                   The release comes with ISO-9660
                                   installation images, a virtual machine
                                   image, and with tarballs to install the
                                   package manager on top of your GNU/
                                   Linux distro, either from source or
                                   from binaries. Guix users can update by
                                   running guix pull.


                                   It’s been almost 6 months since the
                                   last release, during which 212 people
                                   contributed code and packages, and a
                                   number of people contributed to other
                                   important tasks—code review, system
                                   administration, translation, web site
                                   updates, Outreachy mentoring, and more.


                                   There’s been more than 8,300 commits in
                                   that time frame, which we’ll humbly try
                                   to summarize in these release notes.


                            # ⚓ Request_to_reinstate_project:_m4-1.4.18b.pot⠀⇛


                                   The following beta release includes a
                                   new m4.pot, where we would like to
                                   reinstate the m4 translation domain
                                   with disclaimers required (since FSF
                                   owns M4 copyright):

                                   file m4-1.4.18b/po/m4.pot within

                                   https://alpha.gnu.org/gnu/m4/m4-
                                   1.4.18b.tar.xz

                                   announced at

                                   https://lists.gnu.org/archive/html/m4-
                                   discuss/2021-05/msg00001.html

                                   Notice of translations can be sent to
                                   m4-patches@gnu.org; a mere URL of
                                   the available translation would be
                                   sufficient (no need to send
                                   translations themselves, since m4's
                                   bootstrap is designed to download
                                   the .po files prior to release, the
                                   list posts are just a courtesy
                                   rather than a patch to be applied
                                   manually).

                                   See also [1], where the m4 package was
                                   removed, because at the time
                                   there had never been a released build
                                   of m4 that used m4.pot.  More than
                                   10 years ago, when m4.pot was first
                                   uploaded, it was for a version
                                   number 1.9.x in preparation for an
                                   experimental 2.0 release; that
                                   release is nowhere near close, but in
                                   the meantime, the stable branch
                                   for m4 1.4.x has finally enabled the
                                   use of translations [2].  The set
                                   of strings for 1.9.x are probably
                                   dissimilar enough from 1.4.18b that it
                                   is not worth trying to revive the old
                                   translations, rather, you can
                                   treat this request as a new project,
                                   even if you are able to reinstate
                                   the m4 package name (and if you must
                                   pick a different package name, I
                                   need to know, as that will introduce
                                   its own wrinkles into how m4's
                                   bootstrap script downloads available
                                   .po files).

                                   [1] https://lists.gnu.org/archive/html/
                                   bug-m4/2021-03/msg00002.html
                                   [2] https://git.savannah.gnu.org/
                                   gitweb/?p=m4.git;a=commit;h=610290de87f

                                   Given comments at [3], I may still need
                                   to make some tweaks to what
                                   strings are offered for translations
                                   between now and 1.4.19, but we've
                                   got to start somewhere, and I want to
                                   get 1.4.19 out the door this month.

                                   [3] https://lists.gnu.org/archive/html/
                                   bug-m4/2021-03/msg00006.html
                # § Programming/Development⠀➾


                      # ⚓ Paul_E._Mc_Kenney:_Stupid_RCU_Tricks:_Which_tests_do
                        I_run???⠀⇛


                             The rcutorture test suite has quite a few
                             options, including locktorture, rcuscale,
                             refscale, and scftorture in addition to
                             rcutorture itself. These tests can be run
                             with the assistance of either KASAN or KCSAN.
                             Given that RCU contains kernel modules, there
                             is the occasional need for an allmodconfig
                             build. Testing of kvfree_rcu() is currently a
                             special case of rcuscale. Some care is
                             required to adapt some of the tests to the
                             test system, for example, based on the number
                             of available CPUs. Both rcuscale and refscale
                             have varying numbers of primitives that they
                             test, so how to keep up with the inevitable
                             additions and deletions? How much time should
                             be devoted to each of locktorture,
                             scftorture, and rcutorture, which, in
                             contrast with rcuscale and refscale, do not
                             have natural accuracy-driven durations? And
                             finally, if you do run all of these things,
                             you end up with about 100 gigabytes of test
                             artifacts scattered across more than 50 date-
                             stamped directories in tools/testing/
                             selftests/rcutorture/bin/res.


                             Back in the old days, I kept mental track of
                             the -rcu tree and ran the tests appropriate
                             to whatever was queued there. This strategy
                             broke down in late 2020 due to family health
                             issues (everyone is now fine, thank you!),
                             resulting in a couple of embarrassing
                             escapes. Some additional automation was
                             clearly required.


                      # ⚓ Linux_X86_Assembly_–_How_to_Build_a_Hello_World
                        Program_in_GAS⠀⇛


                      # § Rust⠀➾


                            # ⚓ The_Rust_Programming_Language_Blog:_The_Plan
                              for_the_Rust_2021_Edition⠀⇛


                                   We are happy to announce that the third
                                   edition of the Rust language, Rust
                                   2021, is scheduled for release in
                                   October. Rust 2021 contains a number of
                                   small changes that are nonetheless
                                   expected to make a significant
                                   improvement to how Rust feels in
                                   practice.


                                   What is an Edition?


                                   The release of Rust 1.0 established
                                   “stability without stagnation” as a
                                   core Rust deliverable. Ever since the
                                   1.0 release, the rule for Rust has been
                                   that once a feature has been released
                                   on stable, we are committed to
                                   supporting that feature for all future
                                   releases.


                                   There are times, however, when it is
                                   useful to be able to make small changes
                                   to the language that are not backwards
                                   compatible. The most obvious example is
                                   introducing a new keyword, which would
                                   invalidate variables with the same
                                   name. For example, the first version of
                                   Rust did not have the async and await
                                   keywords. Suddenly changing those words
                                   to keywords in a later version would’ve
                                   broken code like let async = 1;.


                                   Editions are the mechanism we use to
                                   solve this problem. When we want to
                                   release a feature that would otherwise
                                   be backwards incompatible, we do so as
                                   part of a new Rust edition. Editions
                                   are opt-in, and so existing crates do
                                   not see these changes until they
                                   explicitly migrate over to the new
                                   edition. This means that even the
                                   latest version of Rust will still not
                                   treat async as a keyword, unless
                                   edition 2018 or later is chosen. This
                                   choice is made per crate as part of its
                                   Cargo.toml. New crates created by cargo
                                   new are always configured to use the
                                   latest stable edition.


    * § Leftovers⠀➾


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Pseudo-Open Source⠀➾


                            # § Entrapment (Microsoft GitHub)⠀➾


                                  # ⚓ Microsoft_brings_Threat_and_Vulnerability
                                    Management_capability_to_Linux⠀⇛


                                  # ⚓ Porting_Linux’s_eBPF_to_Windows_10_and
                                    Windows_Server⠀⇛


                                         In Linux circles, eBPF has
                                         evolved into a powerful tool for
                                         running sandboxed userspace
                                         programs inside the kernel. Now,
                                         Microsoft is working on porting
                                         eBPF to Windows as well.


                                  # ⚓ Making_eBPF_work_on_Windows_(Microsoft
                                    Open_Source_Blog)⠀⇛


                                         The Microsoft Open Source Blog
                                         takes a look at implementing eBPF
                                         support in Windows


                                  # ⚓ Microsoft_embraces_Linux_kernel’s_eBPF
                                    super-tool,_extends_it_for_Windows⠀⇛


                                         Microsoft on Monday launched an
                                         open source project to make a
                                         Linux kernel tool known as eBPF,
                                         short for Extended Berkeley
                                         Packet Filter, work on Windows.


                                         Inspired by network packet
                                         filtering and capture software
                                         dubbed Berkeley Packet Filter,
                                         eBPF is a register-based virtual
                                         machine designed to run custom
                                         64-bit RISC-like architecture via
                                         just-in-time compilation inside
                                         the Linux kernel. As such, eBPF
                                         programs are particularly well-
                                         situated for debugging and system
                                         analysis, such as tracing file
                                         system and registry calls.


                      # § Security⠀➾


                            # ⚓ ISTIO-SECURITY-2021-006⠀⇛


                                   Istio contains a remotely exploitable
                                   vulnerability where an external client
                                   can access unexpected services in the
                                   cluster, bypassing authorization
                                   checks, when a gateway is configured
                                   with AUTO_PASSTHROUGH routing
                                   configuration.


                            # ⚓ ISTIO-SECURITY-2021-005⠀⇛


                                   Istio contains a remotely exploitable
                                   vulnerability where an HTTP request
                                   path with multiple slashes or escaped
                                   slash characters (%2F or %5C) could
                                   potentially bypass an Istio
                                   authorization policy when path based
                                   authorization rules are used. Related
                                   Envoy CVE: CVE-2021-29492.


                            # ⚓ Announcing_Istio_1.9.5⠀⇛


                                   This release fixes the security
                                   vulnerabilities described in our May
                                   11th posts, ISTIO-SECURITY-2021-005 and
                                   ISTIO-SECURITY-2021-006.


                            # ⚓ Announcing_Istio_1.8.6⠀⇛


                                   This release fixes the security
                                   vulnerabilities described in our May
                                   11th posts, ISTIO-SECURITY-2021-005 and
                                   ISTIO-SECURITY-2021-006.


                            # ⚓ Six_cyber_security_tips_to_keep_your_workspace
                              safe [Ed: Neglects to say you should reject
                              proprietary software, lots of which contains back
                              doors]⠀⇛


                                   It’s not a secret to anyone that
                                   maleficent software is very prevalent
                                   across the Internet these days, and
                                   navigating with your guard down is
                                   cyber suicide. Although there may not
                                   be such a thing as 100% protection,
                                   there are plenty of useful measures you
                                   can take to reduce the risk of getting
                                   your computer hacked.


                            # ⚓ The_13_Most_Essential_Books_for_Data_Protection
                              Officers [Ed: How many of these "Officers" are
                              themselves tech-savvy and not just imposers and
                              posers?]⠀⇛


                                   Data protection is a broad field
                                   encompassing backup and disaster
                                   recovery, data storage, business
                                   continuity, cybersecurity, endpoint
                                   management, data privacy, and data loss
                                   prevention. Data protection software
                                   becomes more crucial as the amount of
                                   data an enterprise creates and stores
                                   continues to grow at ever-increasing
                                   rates. This makes the role of a data
                                   protection officer essential in today’s
                                   technological landscape.


                                   There are plenty of free resources
                                   available online (such as Solutions
                                   Review’s Data Protection Buyer’s Guide,
                                   Backup and Disaster Recovery Guide,
                                   DRaaS Buyer’s Guide, Data Protection
                                   Vendor Comparison Map, and best
                                   practices section), but sometimes it’s
                                   best to do things the old-fashioned
                                   way. There are few resources that can
                                   match the in-depth, comprehensive
                                   detail of a book targeted specifically
                                   at data protection officers.


                            # ⚓ Mac,_Linux_and_Windows_machines_need_to_update
                              Google_Chrome⠀⇛


                                   Google has pushed out a new update for
                                   Chrome, its browser, again. The update,
                                   90.0.4430.212, went live on May 10, and
                                   typically these new systems are
                                   automatically installed, or Google
                                   lights up your browser with a color-
                                   coded indicator at the top right.


                                   This update, however, is not
                                   necessarily showing up that way, and
                                   instead right now may


          o § Monopolies⠀➾


                # ⚓ Bill_and_Melinda_Gates_divorce:_Split_in_the_works_since
                  2019,_one_factor_was_Epstein_connection,_WSJ_reports⠀⇛


                # ⚓ Pentagon_May_Axe_Microsoft_JEDI_Contract_Amid_Amazon
                  Litigation:_WSJ⠀⇛


                # § Patents⠀➾


                      # ⚓ [Older]_Report_reveals_a_dip_in_patent_applications
                        in_Europe,_but_a_rebound_is_likely [Ed: There is no
                        rebound in what really matters, namely patent quality
                        and validity]⠀⇛


                      # ⚓ Introducing_our_EP_Validations_Portal [Ed: Many
                        European Patents (EPs) are bunk as quality is lowered,
                        legal certainty reduced, EPC ignored (unlawful patents
                        knowingly granted to game the numbers), and some law
                        firms wish to profit from that chaos, too]⠀⇛


                             The management of EP validations requires
                             expertise in both European patent law and
                             associated formalities, including
                             translations. Novagraaf’s EP validation
                             services give customers peace of mind that
                             their patent portfolios are being safely and
                             cost-effectively maintained, while our new EP
                             Validations Portal provides customers of
                             Novagraaf and NovumIP with a single access
                             point for all EP data.


                      # ⚓ IP_legal_expert_Roche_to_lead_Secerna_Dublin_office
                        [Ed: Standing Advisory Committee before the European
                        Patent Office (SACEPO) [1, 2] and the revolving door?
                        EPO does not attract experts in law but experts in ways
                        to break the law and then get away with it, sometimes
                        using personal connections rather than a valid legal
                        argument (they lie, too).]⠀⇛


                             A member of numerous patent advisory boards
                             and panels, including the Standing Advisory
                             Committee before the European Patent Office
                             (SACEPO) working parties on Guidelines and e-
                             Patent Process, Dermot Roche also sits on the
                             European Patent Institute (EPI) Council and
                             EPI Harmonisation Committee.


                      # ⚓ Fed._Circ._Appeal_Dropped_Challenging_Albright’s
                        Comments [Ed: Texas isn't following patent law; it's
                        just following the money of patent trolls and other
                        radical elements that distorted the system...]⠀⇛


                             Vulcan Industrial Manufacturing and Kerr
                             Machine Co. have resolved a yearlong patent
                             dispute, dropping their appeal in the Federal
                             Circuit over Western District of Texas Judge
                             Alan D. Albright’s refusal to pause…


                      # § Software Patents⠀➾


                            # ⚓ $1,250_Awarded_for_FireNet_Technologies_prior
                              art⠀⇛


                                   Unified is pleased to announce PATROLL
                                   crowdsourcing contest winner, Euclid
                                   Woo, who received a cash prize of
                                   $1,250 for his prior art submission for
                                   U.S. Patent 7,739,302. The patent is
                                   owned by FireNet Technologies, LLC, an
                                   NPE and entity of IPinvestments Group.
                                   The ’302 patent relates to firewalls
                                   for protecting network attached devices
                                   and was being asserted against Kemp
                                   Technologies, Fortinet, Citrix, A10
                                   Networks, and Fujitsu.



                    ䷩ 𝚕𝚒𝚗𝚎 4752

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Links_12/5/2021:_HAProxy_Data_Plane_API_2.3_and_Mousepad_0.5.5⠀✐


Posted in News_Roundup at 4:03 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Huawei_is_reportedly_working_on_a_Linux_laptop⠀⇛


                 Chinese tech giant Huawei is apparently set launch a
                 Linux laptop that sports a custom Arm-based chip.


                 While Huawei hasn’t officially announced the device,
                 dubbed the Huawei Qingyun L410, some keep-eyed scribes
                 found it listed on a Chinese ecommerce website, where it
                 was apparently only available for enterprises and
                 government agencies.


                 Arm-based laptops aren’t a novelty anymore, but this one
                 from Huawei is important since it will be the first non-
                 Intel, non-AMD powered laptop in the company’s stable.


          o § Desktop/Laptop⠀➾


                # ⚓ System76,_Higher_Prices_and_GPU_Supply_Problems⠀⇛


                       How is the ongoing COVID-19 pandemic affecting
                       System76 Linux PC prices and GPU supply? Jason and
                       Jeremy also reflect back on the recent Radeon RX
                       6000 launches.


          o § Audiocasts/Shows⠀➾


                # ⚓ Full_Review:_Ubuntu_Cinnamon_Remix_21.04⠀⇛


                       In this video, I decided to install Ubuntu Cinnamon
                       Remix 21.04, and check it out. Ubuntu Cinnamon
                       Remix is not an official flavor of Ubuntu (at least
                       not yet) but maybe it will be recognized as being
                       official if all goes well.


                # ⚓ Painpoints_to_Profits_|_Coder_Radio_413⠀⇛


                       Chris struggles with his nature, while Mike shares
                       some sage developer advice that everyone should
                       hear before using a platform like AWS.


                       Then we react, strongly, to Docker charging to skip
                       updates.


                # ⚓ Breeze_Redesign_and_Blue_Ocean⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Linux_5.12.3⠀⇛


                       I'm announcing the release of the 5.12.3 kernel.

                       All users of the 5.12 kernel series must upgrade.

                       The updated 5.12.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.12.y
                       and can be browsed at the normal kernel.org git web
                       browser:

                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s...

                       thanks,

                       greg k-h
                # ⚓ Linux_5.11.20⠀⇛


                # ⚓ Core_Scheduling_Looks_Like_It_Will_Be_Ready_For_Linux_5.14
                  To_Avoid_Disabling_SMT/HT⠀⇛


                       It looks like the years-long effort around CPU core
                       scheduling that’s been worked on by multiple
                       vendors in light of CPU security vulnerabilities
                       threatening SMT/HT security will see mainline later
                       this summer with Linux 5.14.


                       Linux core scheduling has been worked on by pretty
                       much all of the hyperscalers and public cloud
                       providers to improve security without disabling
                       Hyper Threading. Core scheduling is ultimately
                       about what resources can share a CPU core and
                       ensuring potentially unsafe tasks don’t run on a
                       sibling thread of a trusted task.


          o § Applications⠀➾


                # ⚓ 4_Linux_terminal_multiplexers_to_try⠀⇛


                       Linux users generally need a lot of virtual visual
                       space. One terminal window is never enough, so
                       terminals have tabs. One desktop is too
                       constraining, so there are virtual desktops. And
                       sure, application windows can stack, but how much
                       better is it when they tile? Heck, even the back-
                       end text console has F1 to F7 available for
                       flipping back and forth between tasks.


                       With this much multitasking going on, it’s no
                       surprise that somebody invented the concept of a
                       terminal multiplexer. This is admittedly a
                       confusing term. In traditional electronics, a
                       “multiplexer” is a component that receives several
                       input signals and forwards the selected one to a
                       single output. A terminal multiplexer does the
                       opposite. It receives instructions from one input
                       (the human at the keyboard typing into one terminal
                       window) and forwards that input to any number of
                       outputs (for example, a group of servers).


                # ⚓ Kodi_Media_Center_19.1_Released!_How_to_Install_in_Ubuntu
                  21.04⠀⇛


                       Kodi 19.1, the first update for the “Matrix”
                       series, was released with various bug-fixes.


                       The new release of the media player and
                       entertainment hub contains mainly bug-fixes. It
                       fixed HDR metadata detection issue, playback of
                       optical DVDs in Linux, and BD-J Blu-ray chapter
                       skipping via remotes/keyboard.


                       System fonts and use fonts detection for ASS
                       subtitles, as well as rendering of semi-transparent
                       ASS subtitles on Wayland are now fixed in the
                       release.


                       Kodi 19.1 also enabled filecaching by default for
                       network filesystems, improved reliability for HTTP
                       and NFS network filesystems, and added support for
                       WS-Discovery protocol to locate SMB servers and
                       browse shared folders via SMBv3.


                # ⚓ The_Future_of_Open-Source_Firmware_on_Server_Systems⠀⇛


                       Open-Source Firmware for Host Processors is already
                       quite prominent in the embedded world – we do have
                       a lot of systems running on u-boot or nearly every
                       Chromebook which is not older than 5 years is
                       running on coreboot (Surprise, Surprise!). In
                       addition Intel does officially support coreboot and
                       their Firmware Support Package (FSP) in API mode,
                       which is mandatory to be supported in coreboot. So
                       future is looking bright for the embedded world –
                       But what does the server market looks like?


                # ⚓ Netboot.xyz_is_now_Part_of_LinuxBoot⠀⇛


                # ⚓ Announcing_HAProxy_Data_Plane_API_2.3⠀⇛


                       HAProxy Data Plane API version 2.3 is now available
                       and you will find it in the 2.3 version of the
                       Alpine Docker image. It does much to simplify the
                       complexity exposed to users, as well as expand its
                       set of features in areas like service discovery,
                       logging, and validation.


                       The most obvious change is moving the command-line
                       arguments needed to start the API into a YAML
                       configuration file. This change, which outwardly
                       looks cosmetic, is an indication of the maturity of
                       the API. New features that require their own
                       command-line arguments, such as the new Syslog
                       support, make it clear that this API has grown
                       bigger than its initial role that was focused on
                       generating an HAProxy configuration. It is fast
                       becoming the interface between HAProxy and the
                       services that surround it. Managing that complexity
                       will be crucial going forward.


                       [...]


                       The HAProxy Data Plane API version 2.3 adds service
                       discovery capabilities with a native AWS EC2
                       integration. It also adds a new configuration file
                       that supports HCL and YAML, an Inotify
                       configuration watcher, and Syslog support. The
                       HAProxy Data Plane API continues to get better
                       thanks to the active community surrounding it. If
                       you’d like to get involved, head over to our GitHub
                       repository to learn more!


                # ⚓ Mousepad_0.5.5_Is_Released_With_Client_Side_Decorations_And
                  Spellchecking⠀⇛


                       Mousepad is a really simple and light-weight text
                       editor made primarily with the Xfce desktop
                       environment in mind. The latest version comes with
                       client side decoration support and it is enabled by
                       default. That’s bad news if you want a light-weight
                       text editor you can use to copy some text from an
                       e-mail client on one virtual desktop into a web
                       browser on another virtual desktop then mousepad is
                       no longer for you since there is no button for
                       making it sticky between virtual desktops anymore.
                       You can also forget about maximizing it vertically
                       or horizontally by clicking the maximize button
                       with the middle or right mouse buttons; that’s also
                       gone since those “client side decorations” on the
                       “header bar” don’t support those.


                       The only good news about this new client side
                       decoration “feature” is that it can be turned off.
                       There is a setting in the xfce4-settings-editor
                       under xsettings titled DialogsUseHeader. Mousepad
                       0.5.5 does, of course, not care if you disable that
                       setting. And there is, of course, now way to turn
                       it off from in Edit ▸ Preferences from within
                       Mousepad. However, our close-up inspection of
                       mousepad/mousepad-settings.h, mousepad/mousepad-
                       util.c and mousepad/org.xfce.mousepad.gschema.xml
                       reveals that Mousepad developer Gaël Bonithon put a
                       secret client-side-decorations into the setting
                       schema. No, it can’t be changed by opening some
                       text file in mousepad, the actual settings are
                       stored in the a binary blob file $HOME/.config/
                       dconf/user. The trick to adding a setting to that
                       file so mousepad understands it is to open a
                       terminal and run:


                       dconf write /org/xfce/mousepad/preferences/window/
                       client-side-decorations false
                       The header bar on other GTK “apps” can be somewhat
                       fixed by installing gtk3-nocsd, but that’s not a
                       elegant solution: It leave you with the window
                       manager title bar and the header bar. Setting that
                       configuration key using dconf makes mousepad look
                       as it should with all the window manager
                       functionality intact.


                # ⚓ Qt5_Markdown_Editor_Ghostwriter_2.0.0_Released_With_New
                  Markdown_Processor,_New_Sidebar_And_Revamped_Theming⠀⇛


                       Ghostwriter, a Qt5 Markdown editor, has been
                       updated to version 2.0.0. The new release comes
                       with revamped theming, the HUDs have been replaced
                       with a sidebar, and there’s a new default Markdown
                       processor.


                       Ghostwriter is a free and open source Markdown
                       editor for Linux and Windows (macOS is not
                       officially supported, but it mostly works as long
                       as you compile it from source). The application
                       comes with a clean interface, with a distraction-
                       free writing experience in mind. You can easily
                       disable the sidebar, go full-screen, and show a
                       live HTML preview, either from its View menu or
                       using keyboard shortcuts


          o § Instructionals/Technical⠀➾


                # ⚓ How_Do_I_Change_My_Desktop_Background_in_Ubuntu?_–_Linux
                  Hint⠀⇛


                       The first step after having installed Ubuntu is to
                       personalize it according to your preferences, to
                       give it a “homier feel”. One way to get started
                       with customizing your new Linux setup is to change
                       the desktop background. In this guide, we will show
                       you different ways you can do just that.


                # ⚓ How_Do_I_Remove_Files_from_Trash_on_Ubuntu?_–_Linux_Hint⠀⇛


                       You can delete unnecessary files and folders by
                       selecting them and pressing the “Delete” button on
                       your keyboard. These deleted files then go to
                       Trash, a system directory designated for deleted
                       files. Deleted files stay in “Trash” until you
                       decide to empty the directory or restore the files.
                       We will be discussing the first option in this
                       guide – how you can remove files from Trash?


                       Method 1: Using Ubuntu’s File Manager


                       Let us start off with a simple way to clear the
                       trash folder. This and the next method are going to
                       be implemented using the user interface, so people
                       who do not feel comfortable using the terminal
                       often should go this one.


                       First, open Ubuntu’s file manager through the
                       sidebar. On the left side, you will see a list of
                       accessible directories. Click on the one that says
                       “Trash”.


                # ⚓ How_To_Install_HandBrake_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       HandBrake on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, Handbrake is a video transcoder for
                       converting video from one format to another format
                       and available for Linux,macOS X, and windows. The
                       open-source, multi-threaded HandBrake can be
                       effectively used for the conversion of DVD-Videos
                       into other formats. This program (HandBrake)
                       supports major video formats like MP4, MKV, H.264,
                       MPEG-4, or other formats.


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


                # ⚓ How_to_Access_Another_Computer_on_the_Same_Network_with
                  Linux_–_Linux_Hint⠀⇛


                       There are many reasons for accessing another
                       computer on the home/office network from your
                       laptop/desktop. For example,


                       1. Using Graphical Software Remotely: There are
                       many software that needs high-spec computers to run
                       (i.e., Autodesk Maya, AutoCAD, Blender). Your
                       laptop/desktop may not have the required specs to
                       run it. At times, a particular software may run on
                       a specific operating system that you don’t want to
                       install on your laptop/desktop just for that one
                       piece of software. In these cases, you can install
                       the required graphical software on other computers
                       and access them remotely from your laptop/desktop
                       and use the required graphical software from your
                       laptop/desktop.


                       2. Solving Problems Remotely: If you’re the tech
                       guy of your office, at times, you may need to solve
                       problems on the computers of your colleagues or
                       show them how to do something. You can remotely
                       connect to your colleague’s computer and solve his/
                       her problem. This will save you a lot of your time
                       that you would otherwise spend on walking or in the
                       lift or stairs to go to your colleague’s room.


                       3. Remote Graphical/Command-Line Administration:
                       You may be a system administrator of a company. The
                       company may have a lot of computers that you need
                       to administer. Going from desk to desk or room to
                       room to administer every single computer of your
                       company will be many hassles for you. Instead, you
                       can sit and relax on your desk and remotely connect
                       to the computers you need to administer from your
                       laptop/desktop. This will save you a lot of time
                       and extra work.


                       4. Accessing Virtual Machines: You may want to run
                       virtual machines on your server using Type-
                       I hypervisors like Proxmox VE, VMware vSphere, KVM,
                       etc. In that case, to use the virtual machines, you
                       need to remotely connect to the virtual machines
                       from your laptop/computer as these virtual machines
                       won’t have any physical display, keyboard, or
                       mouse.


                       This article will show you different methods of
                       accessing other computers and virtual machines on
                       the same network with Linux. So, let’s get started.


                # ⚓ How_to_install_Xubuntu_21.04⠀⇛


                       In this video, I am going to show how to install
                       Xubuntu 21.04.


                # ⚓ How_to_Add_a_Git_Commit_Message?_–_Linux_Hint⠀⇛


                       Documentation is very useful for any type of
                       programming. It helps us understand the code
                       easily. The coder may forget the function of the
                       code written by himself/herself after a long time.
                       But if the code is well documented, then the coder
                       or anyone can easily understand the function of the
                       code anytime from the documentation. The
                       information about the particular file and folder of
                       GitHub can be set like the documentation using Git
                       commit message. When a git repository is published
                       in GitHub, a default commit message is added with
                       each file and folder of which function of the
                       particular file or folder is not defined clearly.
                       The git user can add the custom commit message for
                       each file or folder that defines the purpose of
                       that file or folder clearly. The way to add the git
                       commit message has been explained in this tutorial.


                # ⚓ Hidden_gem_–_Show_failures_only_in_external_results⠀⇛


                       Certain tests like ltp perform a series of tests
                       within a test run and show the results as “External
                       results”. This is useful, because it allows to show
                       more details about which substeps are being perform
                       within a test. It allows to show a passing or
                       failing state of those substeps directly in the
                       WebUI. For instance, in the Tumbleweed JeOS ltp-
                       syscalls test case, it shows all running syscalls
                       tests and you are able to identify the failaing
                       syscalls, instead of just the whole ltp-syscalls
                       test failing.


                       In a nutshell: openQA will show certain substeps as
                       individual test cases in the WebUI with their
                       corresponding passed/failed state.


                # ⚓ How_to_Check_Dependencies_of_a_Package_in_Ubuntu_20.04⠀⇛


                       In the Ubuntu system, installing the packages using
                       the command-line is popular among beginners as it
                       seems quite easy. There are various ways to get the
                       dependencies of a package in Ubuntu 20.04. But we
                       need to know about the “package dependencies” for
                       the folks who are unaware of it.


                       While installing software packages in the Linux
                       operating system, some packages depend on other
                       packages to function correctly. Sometimes they are
                       already installed on the system, but, in other
                       cases, they installed with the package
                       automatically. These dependent packages are termed
                       package dependencies.


                       There are multiple approaches to get dependencies
                       details, such as using apt package manager, dpkg
                       command, or installing a tool.


                       Let’s begin with the APT package management system
                       to get the dependencies of a package.


                # ⚓ How_to_Check_Fail2banLogs?_–_Linux_Hint⠀⇛


                       In today’s post, we are going to explain how to
                       check Fail2ban logs. We will also explain what are
                       the log levels and log targets and how we can
                       change them.


                       [...]


                       What is a Log File?


                       Log files are automatically generated files by an
                       application or OS that have a record of events.
                       These files keep track of all events linked with
                       the system or application which generated them. The
                       purpose of log files is to maintain a record of
                       what happened behind the scene so that if something
                       occurs, we can see a detailed list of events that
                       have happened before the problem. It is the first
                       thing administrators check when they encounter any
                       issue. Most log file ends with .log or .txt
                       extension.


                # ⚓ How_to_Create_a_Simple_Shell_Script_in_Linux_–_Linux_Hint⠀⇛


                       In Unix System, Shell provides an environment to
                       connect the Linux user and operating system. It
                       helps to get input from the user through commands,
                       operate the function based on input and return the
                       output on the terminal.


                       Shell scripts are the list of simple commands to
                       perform operations. You can also create your own
                       commands to perform functions in a system.


                       How to Create a Simple Shell Script in Linux:


                       Shell scripting can be added in a Linux system
                       using multiple text editors. This guide will create
                       a shell script with Linux by default text editor
                       and the “Vim” text editor tool.


                # ⚓ Display_Linux_Kernel_Module_Information_With_Modinfo
                  Command_–_OSTechNix⠀⇛


                       This brief guide explains what is Linux Kernel
                       module, how to list the currently loaded Kernel
                       modules using lsmod, and how to display Linux
                       Kernel module information with modinfo command in
                       Linux.


                       [...]


                       Some examples of Kernel modules are firmware and
                       device drivers, which allows the Linux Kernel to
                       access and control hardware connected to the
                       system. Generally, the Kernel modules are used to
                       add support for new hardware (as device drivers),
                       and/or filesystems, or for adding system calls.


                       Without Kernel modules, we have to rebuild and
                       reboot the kernel every time we want a new
                       functionality. We also need to build bigger
                       monolithic kernels and add new functionality
                       directly into the kernel image without Kernel
                       modules. With the help of a Kernel modules, we can
                       simply avoid these problems.


                # ⚓ Ethernet_Switch_vs._Hub_vs._Splitter:_What’s_the
                  Difference?_–_Make_Tech_Easier⠀⇛


                       You’re short on Ethernet ports and want to
                       transform one Ethernet cable into two. The first
                       thing that springs to mind is probably Ethernet
                       splitting. You have a few options: hub, splitter,
                       or switch. Each solution has something different to
                       offer, so before purchasing any gadget, it’s
                       important to identify which one has the most to
                       offer you. Here we show you the differences between
                       an Ethernet switch vs. hub vs. splitter so you can
                       make the right choice.


                       [...]


                       A major downside of an Ethernet splitter is that it
                       reduces the number of utilized wires in a Cat 5e
                       Ethernet cable and reduces the data throughput from
                       1000Mbps to 100Mbps, which is barely on par with
                       most home Internet connections. This enables you to
                       utilize one cable for two Ethernet connections.


                       While Ethernet splitters are cheap and appear to
                       offer a good solution, they do result in a slower
                       speed for network traffic. This is likely to affect
                       the performance of your Ethernet-connected devices.
                       Ethernet splitters are also limited to a maximum of
                       two devices per cable.


                       For some limited situations, Ethernet splitters are
                       a good option. However, it’s almost always better
                       to opt for an Ethernet switch or hub.


                # ⚓ How_to_Delete_a_Git_Branch_Locally?⠀⇛


                       One of the important features of GitHub is the
                       branch that contains the copy of the project from a
                       particular point. It helps manage the project work
                       properly. When all project works are done and
                       approved, then it is necessary to combine the works
                       from the different branches to the main branch.
                       After merging the project work, it is required to
                       delete the unnecessary branches. The GitHub server
                       contains the main files and folders for the user.
                       The owner of the GitHub account can access the file
                       and folders of the different repositories at any
                       time and if any file is changed locally, then the
                       owner can publish the updated content from the
                       local system to the main server. The branches of
                       the main server are called remote branches and the
                       branches of the local system are called local
                       branches. GitHub Desktop has used it in this
                       tutorial to create, access, and update the
                       repositories of the local drive and GitHub server.
                       The branch of the repository can be deleted by
                       executing commands in the terminal or by using the
                       GitHub Desktop. These two ways of deleting any
                       local git branch have been shown in this tutorial.


                # ⚓ How_to_Download_and_Install_TeamViewer_on_Linux⠀⇛


                       Need to remotely access another computer or accept
                       remote access to your Linux PC? Here’s how to use
                       TeamViewer on Linux.


                       TeamViewer is no doubt one of the most popular
                       remote computing clients available on the internet.
                       Like Windows and macOS, Linux users can also
                       install TeamViewer on their system to remotely
                       access other devices and computers.


                       In this article, we will discuss how you can
                       download and install TeamViewer, a remote control
                       and access software, on your Linux machine.


                # ⚓ How_to_Enable_Dark_Mode_on_Ubuntu_20.04_LTS_–_Linux_Hint⠀⇛


                       There are many remarkable advantages of enabling
                       the dark mode on the system.


                       By default, the system offers the Standard mode
                       (light/white mode), but there are two more modes:
                       light and dark.


                       Most of the PC users preferred to select the dark
                       mode, as working continuously in front of a sharp
                       white background for a longer period makes the eyes
                       tired and burdened.


                       Using the dark mode helps to clear visibility for
                       the users having low vision. It also saves the PC
                       energy and adjusts the screen light according to
                       the environmental light condition.


                       And the interesting thing is that it looks amazing
                       while using the system with the dark mode. As
                       everything looks catchy, especially all icons/
                       folders can be differentiated easily.


                # ⚓ How_to_Find_and_Delete_Broken_Symlinks_on_Linux_–_Linux
                  Hint⠀⇛


                       Symlink or a.k.a symbolic link is a file containing
                       the address of some file or directory and points
                       towards that directory or file. But, when you move
                       or delete the original file, then the symlink gets
                       broken, and it does not work anymore. Although the
                       broken symlinks do not work, they consume the space
                       on your system, and over some time, you realize
                       that you need to get rid of them and free up some
                       storage space.


                       This post will provide you with a complete and in-
                       detail guide on finding and deleting a broken
                       Symlink on the Ubuntu 20.04 LTS system. So, let’s
                       start with learning how to verify a symbolic link
                       file.


                # ⚓ How_to_Install_Scribus_on_Ubuntu_–_Linux_Hint⠀⇛


                       Scribus is an open-source, multi-platform desktop
                       publication application. It is used for designing
                       and publishing brochures, newspapers, magazines,
                       posters, books, and even newsletters.


                       If you are familiar with the Adobe InDesign app,
                       then Scribus is a free alternative to it. Scribus
                       has all the features that a premium application
                       offers, such as layout designing, typesetting,
                       vector drawing, and image manipulation. The
                       projects created in Scribus can be published in
                       digital and print formats.


                # ⚓ How_to_Manage_Startup_Programs_on_Ubuntu_Linux_–_Linux
                  Hint⠀⇛


                       Startup programs are the programs or applications
                       that get executed automatically when an Operating
                       system boots up. The programs can be any regular
                       program like Skype, Discord, Torrent Client, etc.
                       They help save time and enhance the usability
                       experience but at the same time, running too many
                       programs leads to the Operating system’s slow and
                       poor performance because the whole memory gets busy
                       in running all those programs.


                       This post’s purpose is to get you aware of those
                       programs and help you in learning how to manage
                       startup Programs on Ubuntu 20.04. We will learn all
                       about adding and removing the applications from the
                       startup list in the Ubuntu 20.04 system. So, let’s
                       jump in and start learning.


                # ⚓ How_to_Merge_Two_Branches_in_Git_–_Linux_Hint⠀⇛


                       Any git repository contains one or more branches.
                       The git user creates different branches for storing
                       files and folders based on the different topics. It
                       helps the user to manage the code easily. In the
                       development process, sometimes it requires
                       combining one branch with the other branch of the
                       repository for the project purpose. `git merge`
                       command is used for this task. This command finds
                       out the common base commit command by examining the
                       two commit pointers of the merging branches and
                       generates a new merge to combine the changes after
                       running the command. Both local and remote
                       repositories are required to be updated before
                       running the merge command. The way of merging two
                       branches locally has shown in this tutorial.


                # ⚓ How_to_Search_in_Vim_Editor_–_Linux_Hint⠀⇛


                       We have heard several times the “Vim” editor tool
                       in Linux distributions. It the most commonly used
                       multiplatform tool that comes up with several
                       modes. Each of its modes has different editing
                       functionality; some are used to perform commands
                       (code editor), and some for the text editor.


                       It is simple to work with the “Vim” editor but
                       giving more attention to this tool help to learn to
                       explore more.


                       This guide will focus on the search feature of the
                       “Vim” editor, which is quite handy. We need to
                       understand this because searching for the specific
                       word/string from large file data is not easy.


                       Let’s start with the “Vim” editor, but keep in mind
                       your mode should be in the command mode.


                # ⚓ How_to_convert_video_to_GIF_in_Linux_–_Linux_Hint⠀⇛


                       While using social media, we always see animated
                       GIFs everywhere. If adding a picture on blogs would
                       tell you 100 words about the story, GIF would come
                       up with 1000 words.


                       Animated GIFs are used to make the blogs
                       interesting and a great alternative for demo
                       purposes short videos. It is a quick way to display
                       anything that could not be expressed in images, or
                       you don’t need to insert long videos all the time.


                       GIFs are also used in software documentation and
                       media and make everything a part of the fun.


                # ⚓ How_to_install_the_Delft_icon_theme_in_Linux⠀⇛


                       The Delft icon theme is a fork of the famous Faenza
                       icon theme. It’s incredibly stylish and fits right
                       at home on any Linux desktop. If you’d like to try
                       out the Delft icon theme on your system, follow
                       along with the instructions in this guide!


                # ⚓ How_to_print_command_output_in_Ansible?_–_Linux_Hint⠀⇛


                       Ordinarily, when you run an Ansible playbook, you
                       get execution details printed on the terminal.
                       These include the name of the play and task and a
                       play recap indicating if the playbook has made any
                       changes on the managed host or remote system


                       But, suppose you want to print the command output
                       of the command being executed on the remote target.
                       How do you go about this? In this tutorial, you
                       will learn how to print the command output in
                       Ansible.


                # ⚓ How_to_run_a_shell_script_as_a_different_user_–_Linux
                  Hint⠀⇛


                       Sometimes you might find yourself required to run a
                       shell script as a different user other than the
                       active user on the shell. This is quite easy and
                       can be done in a few simple steps So how do you go
                       about this? Let’s find out.


                       [...]


                       Before getting started, ensure that you have access
                       to the shell of a Linux system; any Linux
                       distribution will do just fine. In this guide, we
                       are running Ubuntu 18.04.


                       Equally crucial is to make sure that you have a
                       shell script with execute permissions. We have a
                       simple shell script called welcome.sh that requests
                       a user’s name and prints it out to the terminal.


                # ⚓ Kali_Linux_2021.1_–_Fresh_Installation_Guide⠀⇛


                       Kali Linux is arguably one of the best out-of-the-
                       box Linux distributions available for security
                       testing. While many of the tools in Kali can be
                       installed in most Linux distributions, the
                       Offensive Security team developing Kali has put
                       countless hours into perfecting their ready-to-boot
                       security distribution.


                       Kali Linux is a secure Debian-based Linux
                       distribution that comes pre-loaded with hundreds of
                       well-known security tools and has gained quite a
                       name for itself.


                       Kali even has an industry-respected certification
                       available called “Pentesting with Kali”. The
                       certification is a rigorous 24-hour challenge in
                       which applicants must successfully compromise a
                       number of computers with another 24 hours to write
                       up a professional penetration test report that is
                       sent to and graded by the personnel at Offensive
                       Security. Successfully passing this exam will allow
                       the test taker to obtain the OSCP credential.


                # ⚓ Compress_a_PDF_with_ghostscript⠀⇛


                       This days I had to send a multiple page PDF with a
                       bunch of pictures on it, but requirements said that
                       it needed to be smaller than 5Mb. With Ghostscript
                       I was able to transform a 10.9MB file into a 1.2Mb
                       without loosing quality, since it was mandatory
                       that the small letters contained on the PDF were
                       completely readable.


                # ⚓ What_is_the_Meaning_of_127.0.0.1?_–_Linux_Hint⠀⇛


                       Internet Protocol or IP uses a 32-bit IPv4 or 128-
                       bit IPv6 address for identifying a device on a
                       network. This is analogous to our physical home
                       address which is used for delivering our mails and
                       online shopping items, for reaching to us, etc. Our
                       physical home address is a mix of numbers and
                       words, but in the case of computers, they only
                       understand numeric addresses in a specific format.
                       Even if we type an address like “www.domain.com”,
                       computers will resolve it into a numerical format
                       using the DNS mechanism.


                # ⚓ VRChat_on_Linux_PC_–_Install_&_Play_online_virtual_reality
                  game⠀⇛


                       Online VRChat is a popular virtual parallel world
                       for the player in which he can interact with others
                       using a 3D avatar. The game is available to play
                       using Steam, Quest, Rift, and Viveport. In VRChat,
                       the users can create their own worlds and chat
                       rooms to meet friends and the community. The best
                       part is the developers have given the community
                       almost complete freedom. However, leaving the
                       moderation largely to the community, sometimes have
                       negative consequences such as numerous trolls
                       cavort in the chat rooms and offensive memes kind
                       of things emerge.


                       Nevertheless, to counter this VRchat developers
                       have already introduced a panic button. Using which
                       the player can replace all participants’ avatars
                       that are not in the friend list with gray schemes
                       and also mute the corresponding players.


                # ⚓ Linux_for_Starters:_Your_Guide_to_Linux_–_Install_Ubuntu
                  from_your_USB_stick_–_Part_4_–_LinuxLinks⠀⇛


                       This is a series that offers a gentle introduction
                       to Linux for newcomers.


                       In this article we show you how to install Ubuntu
                       21.04 on your hard disk. It’s a slick process.


          o § Games⠀➾


                # ⚓ Valheim_gets_a_small_patch_with_a_large_creature_visual
                  overhaul⠀⇛


                       While we wait on the first major update to the co-
                       op survival game Valheim, the team at Iron Gate
                       have released a small patch to keep us going.


                       This is part of the update they teased recently,
                       which includes a nice overhaul to some of the
                       bigger creatures in the game including the Troll
                       and the second and third boss. The Troll, for
                       example, has more hair, nails and more defined
                       muscles making it a bit scarier. Can’t imagine
                       meeting it for the first time again now, it was
                       scary enough with the original model when you’re
                       quite new to it.


                       [...]


                       I’m personally very excited by the upcoming Hearth
                       and Home update which will bring in lots of new
                       goodies. Once there’s a date for it, we will let
                       you know.


                # ⚓ The_fan_remaster_Sonic_3_–_Angel_Island_Revisited_has_a_big
                  new_stable_release_out⠀⇛


                       Ready for more epic Sonic fan games? Following on
                       from the Doom-powered Sonic Robo Blast 2, we also
                       have Sonic 3 A.I.R (Angel Island Revisited) a
                       remaster of Sonic 3 & Knuckles which has a big new
                       release.


                       This has been in development for 9+ months, during
                       which Linux support was hooked up in a previous
                       preview version which is now properly live for
                       everyone. So now Linux users can enjoy one of the
                       best Sonic fan games around. As a reminder, we
                       spoke to the developer of this previously who
                       mentioned they built it “directly on top of SDL2,
                       OpenGL and Ogg Vorbis”.


                # ⚓ Oddventure_RPG_smashes_Kickstarter_goal_and_puts_out_a
                  Linux_demo_|_GamingOnLinux⠀⇛


                       Oddventure is a crazy turn-based RPG about the
                       misadventures of Charlie, a girl trapped in a
                       cursed fairy-tale world.


                       We previously covered the launch of the
                       Kickstarter, which at the time did not have a Linux
                       build of the demo available. After asking the
                       developer, they promptly put one up. As it turns
                       out, it’s using the open source Godot Engine too
                       which we weren’t aware of before! Wonderful to see
                       more excellent looking games use it.


                       “Oddventure is a JRPG about the misadventures of
                       Charlie – a nihilistic and rebellious teenage girl
                       with anger issues and social awkwardness. Charlie
                       searches for her troublesome brother Bonzo and
                       ultimately for a way back home. The setting is the
                       Kingdom of Luxia, a land straight from original
                       Grimm Brothers’ fairy tales with a dark,
                       Nietzschean twist.”


                # ⚓ Dota_2_–_The_International_10_returns_in_August_with_the
                  biggest_esport_prize_pool_ever⠀⇛


                       Ready for some intense Dota 2? The Aegis of
                       Champions is in play once more! Valve has confirmed
                       that The International 10 shall return officially
                       begin in August.


                       In a fresh blog post Valve mentioned The
                       International 10 will take place this August in
                       Stockholm, Sweden. Beginning with the Group Stage
                       which takes place between August 5 – 8 with the big
                       main event kicking off on August 10 and lasts until
                       August 15.


                # ⚓ Hobo:_Tough_Life_is_an_urban_co-op_survival_game_where
                  you’re_on_the_streets_|_GamingOnLinux⠀⇛


                       The Linux version seems to run reasonable well too,
                       with it running mostly smoothly on Max settings but
                       it does stutter here and there when entering new
                       areas as it loads bits in. Overall though,
                       perfectly playable. You can play it solo or online
                       in co-op with friends.


                # ⚓ Siege_Up!_is_an_upcoming_full-featured_RTS_in_low-poly
                  style⠀⇛


                       Asking the developer about Linux support, they
                       confirmed: “This is not going to be a problem for
                       me, because of using Unity3d that supports Linux. I
                       myself was using Linux exclusively during my
                       student times, so having more than enough
                       experience of Linux platform for supporting it.”


          o § Distributions⠀➾


                # ⚓ Bodhi_Linux_is_a_beautiful_nod_to_the_old_school_ways⠀⇛


                       Bodhi Linux has become an absolutely fascinating
                       intersection on what Linux was and what it can be.
                       It’s both old and new, out-of-date and ahead of its
                       time. Because of that, I believe (for the first
                       time) I could honestly suggest this Linux desktop
                       distribution for just about any type of user. If
                       you’re new to the Linux desktop, Bodhi Linux would
                       be a fine first experience. If you’re an old hat
                       with Linux, Bodhi will offer up plenty of
                       customization options. With the latest Moksha
                       desktop, you won’t be missing out on anything found
                       on your current desktop of choice.


                       Give Bodhi 6.0 a try and see if it doesn’t wind up
                       your desktop of choice.


                # § Reviews⠀➾


                      # ⚓ MX_Linux_Package_Installer_review_–_Nice_but_can_be
                        nicer⠀⇛


                             MX Package Installer is not a bad idea. But
                             it’s a workaround to the horrible mess that’s
                             Linux packaging. If anything, it just makes
                             the problem more prominent, and puts it into
                             the user’s hands really. And, when we
                             integrate over the problem space, the fault
                             ends up at the MX doorsteps, because it’s an
                             MX Linux component that created the
                             possibility for the user to try a program,
                             all hopeful, and then to have it crash.


                             Ideally, every software component would have
                             a clearly defined, rigorous test procedure.
                             Every system would have a chain of these
                             tests, declared, defined, interlinked. No
                             application would be allowed for inclusion or
                             publication without successful testing that
                             proves the components work great on their own
                             and as part of the overall complex system.
                             The responsibility can be shared, if needed,
                             whatever works the best. But to rely on third
                             parties for your own success means gaps and
                             problems and issues and tons of
                             blameshifting. It’s Debian, no it’s MX, no
                             it’s KDE, no it’s the user, and so on. Who
                             cares? The Linux desktop isn’t growing. Well,
                             I do. I want it to grow.


                             So this would be the conclusion of this
                             review. MXPI is a nice thing, but it’s still
                             90% nerdy, 10% friendly, and the equation
                             needs to be flipped. Over the years, the MX
                             team has done pretty cool stuff, and I
                             believe and hope they will be able to polish
                             up MXPI. After all, they did it with their
                             distro, and really transformed it from a
                             nerdbox into a cool, accessible system. But
                             the journey is far from over.


                # § New Releases⠀➾


                      # ⚓ Kali_Linux_2021.1_Released_–_Download_DVD_ISO
                        Images⠀⇛


                             Kali Linux (formerly known as BackTrack
                             Linux) announced the release of Kali Linux
                             Version 2021.1 on February 24th, 2021. Kali
                             Linux is a Debian-based distribution
                             specially focused on penetration testing and
                             digital forensics use.


                             The latest version of Kali Linux ships with
                             both feature and cosmetic changes as we shall
                             see later on in this guide. In summary, here
                             are some of the improvements included in Kali
                             2021.1.


                      # ⚓ CyberOS_–_A_New_QT_Based_Arch_Linux_Distribution_that
                        Looks_Like_Deepin_DE⠀⇛


                             So, I stumbled upon a fairly new Linux
                             distribution called CyberOS based on GNOME +
                             Arch Linux. And I thought to do a test drive.
                             Here’s how it is.


                # § BSD⠀➾


                      # ⚓ DragonflyBSD_6.0_Released⠀⇛


                             On May 10th, the DragonflyBSD team released
                             version 6.0. Let’s take a look at what
                             changes make up this release.


                             For those of you who are not aware of what
                             DragonflyBSD is, let me enlighten you. The
                             DragonflyBSD project began in 2004. It was
                             created by Matthew Dillon after a falling out
                             with the FreeBSD developers. Dillon disagreed
                             with the development path they chose for
                             FreeBSD 5, so he forked FreeBSD 4.


                             One of the biggest changes made to
                             DragonflyBSD was an overhaul of the kernel.
                             This included “inter-process communication
                             via message passing.” Many of the changes
                             were inspired by Dillon’s work on Amiga. “The
                             Amiga kernel was designed around small but
                             powerful APIs and messaging. Having a small,
                             well defined API for a subsystem results in
                             fewer bugs, easier to find bugs, and code
                             sustainability.”


                      # ⚓ NetBSD:_aiomixer,_X/Open_Curses_and_ncurses,_and
                        other_news⠀⇛


                             aiomixer is an application that I’ve been
                             maintaining outside of NetBSD for a few
                             years. It was available as a package, and was
                             a “graphical” (curses, terminal-based) mixer
                             for NetBSD’s audio API, inspired by programs
                             like alsamixer. For some time I’ve thought
                             that it should be integrated into the NetBSD
                             base system – it’s small and simple, very
                             useful, and many developers and users had it
                             installed (some told me that they would
                             install it on all of their machines that
                             needed audio output). For my particular use
                             case, as well as my NetBSD laptop, I have
                             some small NetBSD machines around the house
                             plugged into speakers that I play music from.
                             Sometimes I like to SSH into them to adjust
                             the playback volume, and it’s often easier to
                             do visually than with mixerctl(1).


                             However, there was one problem: when I first
                             wrote aiomixer 2 years ago, I was intimidated
                             by the curses API, so opted to use the Curses
                             Development Kit instead. This turned out to
                             be a mistake, as not only was CDK inflexible
                             for an application like aiomixer, it
                             introduced a hard dependency on ncurses.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Using_Red_Hat’s_single_sign-on_technology_with
                        external_databases,_Part_1:_Install_and_configure_SSO
                        with_MariaDB⠀⇛


                             Red Hat’s single sign-on (SSO) technology,
                             based on the Keycloak open source project, is
                             Red Hat’s solution for securing web
                             applications and RESTful web services. The
                             goal of Red Hat’s single sign-on technology
                             is to make security simple, so that it is
                             easy for application developers to secure the
                             apps and services they have deployed in their
                             organization.


                             Out of the box, single sign-on uses its own
                             Java-based embedded relational database,
                             called H2, to store persistent data. However,
                             this H2 database is not viable in high-
                             concurrency situations and should not be used
                             in a cluster. So, it is highly recommended to
                             replace this H2 database with a more
                             production-ready external database.


                      # ⚓ Mostly_harmless:_An_account_of_pseudo-normal_floating
                        point_numbers⠀⇛


                             Floating point arithmetic is a popularly
                             esoteric subject in computer science. It is
                             safe to say that every software engineer has
                             heard of floating point numbers. Many have
                             even used them at some point. Few would claim
                             to actually understand them to a reasonable
                             extent and significantly fewer would claim to
                             know all of the corner cases. That last
                             category of engineer is probably mythical or,
                             at best, optimistic. I have dealt with
                             floating-point related issues in the GNU C
                             Library in the past, but I won’t claim to be
                             an expert at it. I definitely did not expect
                             to learn about the existence of a new kind of
                             number, as I did a couple of months ago.


                             This article describes new types of floating
                             point numbers that correspond to nothing in
                             the physical world. The numbers, which I dub
                             pseudo-normal numbers, can create hard-to-
                             track problems for programmers and have even
                             made it into the dreaded Common
                             Vulnerabilities and Exposures (CVE) list.


                      # ⚓ How_to_install_Virtual_hosts_on_apache_(Centos8)_–
                        Unixcop⠀⇛


                             The Apache webserver is an opensource and
                             popular HTTP web server that continues to
                             enjoy a massive market share in the hosting
                             industry. It ships with loads of features
                             including module enhancements, multi-protocol
                             support, simplified configuration, and multi-
                             language support to mention just a few.


                      # ⚓ IT_leadership:_How_to_spot_a_collaboration_superstar
                        in_interviews⠀⇛


                             As a collaborative leader, I recognize the
                             importance of using job interviews to find
                             the right people for a successful
                             collaborative team. In the book, Good to
                             Great, Jim Collins said, “People are not your
                             most important asset. The right people are.”


                             To that end, consider these questions that I
                             ask candidates regarding cross-team
                             collaboration. This list isn’t exhaustive:
                             I’ve selected the questions with the highest
                             impact on my decisions.


                      # ⚓ Automating_RHEL_for_Edge_image_rollback_with
                        GreenBoot⠀⇛


                             With the release of Red Hat Enterprise Linux
                             (RHEL) 8.3, Red Hat announced an rpm-ostree
                             version of RHEL targeted for Edge use cases
                             called RHEL for Edge.


                             One of the unique features of rpm-ostree is
                             that when you update the operating system, a
                             new deployment is created, and the previous
                             deployment is also retained. This means that
                             if there are issues on the updated version of
                             the operating system, you can roll back to
                             the previous deployment with a single rpm-
                             ostree command, or by selecting the previous
                             deployment in the GRUB boot loader.


                             While this ability to manually roll back is
                             very useful, it still requires manual
                             intervention. Edge computing use case
                             scenarios might be up in the tens or hundreds
                             of thousands of nodes, and with this number
                             of systems, automation is critical. In
                             addition, in Edge deployments, these systems
                             might be across the country or across the
                             world, and it might not be practical to
                             access a console on them in the event of
                             issues with an updated image.


                             This is why RHEL for Edge includes GreenBoot,
                             which can automate RHEL for Edge operating
                             system rollbacks.


                             This post will cover an overview of how to
                             get started with GreenBoot and will walk
                             through an example of using GreenBoot.


                      # ⚓ Using_Ansible_to_configure_Podman_containers⠀⇛


                             In complex IT infrastructure, there are many
                             repetitive tasks. Running those tasks
                             successfully is not easy. Human error always
                             presents a chance of failure. With help of
                             Ansible, you perform all of the tasks through
                             a remote host and, as the tasks are executed
                             with playbooks, and those playbooks can be
                             reused as many times as you need. In this
                             article you will learn how to install and
                             configure Ansible on Fedora Linux and
                             describe how to use it to manage and
                             configure Podman containers.


                             Ansible


                             Ansible is an open source infrastructure
                             automation tool sponsored by Red Hat. It can
                             deal with all the problems that come with
                             large infrastructure, like installing &
                             updating packages, taking backups, ensuring
                             specific services are always running, and
                             much more. You do this with a playbook which
                             is written in YAML. Ansible playbooks can be
                             used again and again, making the system
                             administrator’s job less complex. Playbooks
                             also eliminate repetitive tasks and can be
                             easily modified. But we have many automation
                             tools like Ansible, why use it? Unlike some
                             other configuration management tools, Ansible
                             is agentless: you don’t have to install
                             anything on managed nodes. For more
                             information about Ansible, see the Ansible
                             tag in Fedora Magazine.


                      # ⚓ Getting_better_at_counting_rpm-ostree_based_systems⠀⇛


                             Since the release of Fedora 32, a new
                             mechanism has been in place to better count
                             the number of Fedora users while respecting
                             their privacy. This system is explicitly
                             designed to make sure that no personally
                             identifiable information is sent from counted
                             systems. It also insures that the Fedora
                             infrastructure does not collect any personal
                             data. The nickname for this new counting
                             mechanism is “Count Me”, from the option
                             name. Details are available in DNF Better
                             Counting change request for Fedora 32. In
                             short, the Count Me mechanism works by
                             telling Fedora servers how old your system is
                             (with a very large approximation). This
                             occurs randomly during a metadata refresh
                             request performed by DNF.


                      # ⚓ Cockpit_244⠀⇛


                             Cockpit is the modern Linux admin interface.
                             We release regularly.


                             Here are the release notes from Cockpit
                             version 244 and Cockpit Machines 244.


                      # ⚓ A_brief_introduction_to_Ansible_Vault⠀⇛


                             Ansible Vault is an Ansible feature that
                             helps you encrypt confidential information
                             without compromising security.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Ubuntu_Touch_OTA-17_Released_for_Ubuntu_Phones_with
                        NFC_Support,_Many_Improvements⠀⇛


                             As reported last week, the biggest new
                             feature of the Ubuntu Touch OTA-17 software
                             update is support for NFC hardware, which is
                             available for all devices running with
                             Android 9 compatibility, such as the Google
                             Pixel 3a and Volla Phone.


                             According to UBports, NFC support can allow
                             app developers to implement the ability to
                             read and write NFC tags in their apps, as
                             well as to communicate with another device
                             that supports the NFC protocol.


          o § Devices/Embedded⠀➾


                # ⚓ Environmental_multi-sensor_device_runs_on_Raspberry_Pi
                  CM4⠀⇛


                       Sfera Labs has launched a $276 “Exo Sense Pi”
                       multi-sensor computer based on an RPi CM4 with
                       sensors for air quality, temp, humidity, light, and
                       motion plus RS-485, an open collector output, 2x
                       digital inputs, a mic, and an RTC.


                       In 2019, Sfera Labs launched an Exo Sense Py
                       environmental monitoring system that runs
                       MicroPython on an ESP32. Now, the company, which is
                       known for Raspberry Pi Compute Module 3+ (CM3+)
                       based devices such as the Iono Pi Max industrial
                       controller, has launched an Exo Sense Pi that
                       advances to running Raspberry Pi OS Linux on a quad
                       -A72 Raspberry Pi Compute Module 4.


                # ⚓ i.MX8M_Mini_SBC_offers_dual_GbE_with_PoE⠀⇛


                       Gateworks has launched a “Venice GW7200” SBC that
                       runs Ubuntu on an i.MX8M Mini with up to 4GB RAM
                       and 64GB eMMC. Highlights include 2x GbE with PoE,
                       2x mini-PCIe, MIPI DSI/CSI, and -40 to 85°C
                       support.


                       Last year when Gateworks announced its 105 x 100mm
                       GW7300 SBC based on NXP’s i.MX8M Mini, the company
                       said there would be three more Mini-based Venice
                       SBCs, including a 140 x 100mm GW7400, 100 x 70mm
                       GW7200, and 100 x 35mm GW7100. The GW7200 has now
                       arrived with the same dual GbE with PoE capability
                       as the GW7300, but with one less mini-PCIe slot and
                       no standard USB host port.


                # ⚓ Digi_IX15_IoT_Gateway_&_Cellular_Router_features_a_Zigbee_&
                  BLE_XBee_module⠀⇛


                       Digi International has just announced the Digi IX15
                       IoT gateway and cellular router with Ethernet and
                       4G LTE connectivity as well as support for Zigbee,
                       Bluetooth 5.0, 2.4 GHz proprietary via an XBee
                       module.


                # ⚓ The_Zigbee_Alliance_renames_to_the_Connectivity_Standards
                  Alliance_(CSA),_Project_CHIP_becomes_“Matter” [Ed: Pretending
                  one failed because of one's choice of name and not something
                  else]⠀⇛


                # ⚓ What_is_an_SBC?⠀⇛


                       Most of the under-$200 SBCs offer varying degrees
                       of open hardware support. Schematics and other open
                       hardware files are typically available, and most
                       offer community resources like forums and online
                       tech support.


                       Customized Linux and Android images are typically
                       available, which are increasingly tied to mainline
                       Linux. There is a lot of sloppy work out there in
                       OS support, especially on the lower-cost models,
                       but OS reliability is improving.


                       The most popular OS choices for Linux SBCs are
                       Ubuntu and Yocto Project, which is not a
                       distribution but a standardized collection of
                       components and libraries. Other desktop distros
                       such as Fedora are sometimes supported on higher-
                       end x86 SBCs.


                       Linux continues to dominate the Arm SBC world and
                       increasingly competes with Windows 10 in the larger
                       market for commercial x86 SBCs. Low-power
                       microcontroller-driven boards that run real-time
                       operating systems such as FreeRTOS, tend to be more
                       like SOMs (see the new Raspberry Pi Pico). Many
                       Arduino boards, however, are more like SBCs.


                       In both the Linux and RTOS MCU board markets, the
                       open source RISC-V architecture has begun to make
                       inroads, with new Linux-driven SBCs such as
                       SiFive’s HiFive Unmatched. We will examine RISC-
                       V in a future article.


                # ⚓ A_Raspberry_Pi-powered_platform_for_remote_play
                  experiences⠀⇛


                # ⚓ MontaVista_Launches_‘MVShield_For_Yocto’_Migration-Free
                  Support_Program_For_Yocto_Baselines⠀⇛


                       MontaVista Software has announced the availability
                       of MVShield for Yocto, a professional services
                       offering to support customer’s Linux distribution
                       created with Yocto Project software, giving access
                       to support and maintenance services without any
                       migration effort to commercial Linux baselines.


                       MontaVista will maintain and support the customer’s
                       specific Yocto Project created Linux distribution.


                # ⚓ IAR_Systems_extends_product_portfolio_for_streamlined
                  Linux-based_automated_workflows⠀⇛


                       IAR Systems®, the future-proof supplier of software
                       tools and services for embedded development, today
                       presented the latest addition to its powerful build
                       tools for Linux, which are based on the well-known
                       build tools in the development toolchain IAR
                       Embedded Workbench®. The extended tools now support
                       deployment in Linux-based frameworks for Renesas’
                       low-power RL78 microcontrollers (MCUs), enabling
                       organizations to streamline building and testing
                       workflows.


                # § Open Hardware/Modding⠀➾


                      # ⚓ Portenta_Machine_Control:_Add_a_powerful_brain_to
                        your_machines⠀⇛


                             Arduino Pro is introducing a powerful new
                             member of the Portenta product family, the
                             Portenta Machine Control. It’s a fully-
                             centralized, low-power, industrial control
                             unit able to drive equipment and machinery.
                             Plus, you can program it using the Arduino
                             framework or other embedded development
                             platforms.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Nokia’s_Android_11_Rollout_May_Get_Delayed_as_Company
                        Pulls_Roadmap_Announcement_Tweet:_Report_|_Technology
                        News⠀⇛


                      # ⚓ Android_11_now_available_in_beta_for_Realme_X7_5G,
                        C15,_and_C12_in_India_–_Technology_News⠀⇛


                      # ⚓ SDMC-3SS_Android_TV_Solution_Goes_Live_in_Uruguay⠀⇛


                      # ⚓ Mecool_Now_Android_TV_device_with_video_calling
                        review_–_The_Gadgeteer⠀⇛


                      # ⚓ Poll:_Are_you_logged_into_an_OEM_account_on_your
                        Android_phone?⠀⇛


                      # ⚓ TeaBot_Trojan_Targets_Banks_via_Hijacked_Android
                        Handsets_|_Threatpost⠀⇛


                      # ⚓ Fascinating_Features_Offered_By_Bitcoin_Wallet_For
                        Android!_|_TechBullion⠀⇛


                      # ⚓ Lenovo_May_Be_Launching_An_Android_Tablet_With_HDMI⠀⇛


                      # ⚓ Asus_Zenfone_8_review:_The_best_small_Android_phone,
                        hands-down_|_Tom’s_Guide⠀⇛


                      # ⚓ Samsung_Galaxy_A02s,_Galaxy_A12_receive_Android_11
                        update⠀⇛


                      # ⚓ Rivals_start_following_Samsung’s_lead_with_Android
                        updates_–_or_so_they_say_–_SamMobile⠀⇛


                      # ⚓ Gboard_for_Android_Will_Make_Sharing_Screenshots
                        Easier⠀⇛


                      # ⚓ Why_is_Android_more_popular_globally,_while_iOS_rules
                        the_US?_–_TechRepublic⠀⇛


                      # ⚓ POCO_has_no_plans_to_launch_Android_One_smartphones⠀⇛


                      # ⚓ An_Ultimate_Guide_To_Android_Bitcoin_Mining._|
                        TechBullion⠀⇛


                      # ⚓ You_Can_Now_Cast_Files_From_the_OneDrive_Android
                        App⠀⇛


                      # ⚓ Google_Discover_redesign_rolling_out_on_Android_12_–
                        9to5Google⠀⇛


                      # ⚓ Android_12:_Release_date,_new_features_and_everything
                        else_we_know_–_CNET⠀⇛


                      # ⚓ OnePlus_7_and_7T_Android_11_update_is_reportedly_very
                        buggy_–_SlashGear⠀⇛


                      # ⚓ Oppo_A5_&_A9_3GB_RAM_models_won’t_get_(Android_11)
                        ColorOS_11⠀⇛


                      # ⚓ OneDrive_for_Android_gets_casting_support_with_latest
                        update⠀⇛


                      # ⚓ PUBG_Mobile_1.4_update_APK_download_link_for
                        Android⠀⇛


                      # ⚓ How_to_Make_a_Slideshow_on_Android_Phone⠀⇛


                      # ⚓ Magisk_v23.0_brings_along_SafetyNet_API_fixes_but
                        drops_legacy_Android_support⠀⇛


                      # ⚓ Freeview_Play_viewers_get_Android_TV_interface_update
                        in_UK_–_Telecompaper⠀⇛


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


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ Percona_Announces_Preview_Of_Open_Source_Database_as
                        a_Service⠀⇛


                             As an alternative to public cloud and large
                             enterprise database vendor DBaaS offerings,
                             this on-demand self-service option provides
                             users with a convenient and simple way to
                             deploy databases quickly. Plus, using Percona
                             Kubernetes Operators means it is possible to
                             configure a database once, and deploy it
                             anywhere.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ LibreOffice_Adds_A_Command_Popup_/_HUD,_Inspired_By
                        Half-Decade_Old_Microsoft_Office_Feature⠀⇛


                             Adding to the changes building up for
                             LibreOffice 7.2 ahead of its debut in August
                             is a “Command Popup” or a heads-up display
                             (HUD) of sorts for easily running LibreOffice
                             commands.


                             For a half-decade now Microsoft Office has
                             offered a “Tell Me” feature whereby it’s a
                             text field that the user can enter words/
                             phrases about what they want to do while
                             editing/creating a document. That Tell Me
                             feature can allow quickly accessing different
                             commands that otherwise are tucked away
                             within different menus, etc.


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ GNU_Guix_1.3.0_released_[LWN.net]⠀⇛


                                   GNU Guix, the transactional package
                                   manager and distribution, has released
                                   version 1.3.0. This released adds new
                                   features, refines the user experience,
                                   and improves performance. Support for
                                   the POWER9 platform is now offered as
                                   technological preview.


                            # ⚓ GNU_Guix_1.3_Released_With_Better_User
                              Experience,_Initial_POWER9_Support_–_Phoronix⠀⇛


                                   GNU Guix as a cross-platform package
                                   manager based on Nix and also being the
                                   package management solution for the
                                   Linux-based GNU Guix system
                                   distribution is out with a new version.


                # § Programming/Development⠀➾


                      # ⚓ AMD_Releases_ROCm_4.2_Compute_Stack_–_Phoronix⠀⇛


                             Just over one month has passed since the
                             release of Radeon ROCm 4.1 and it’s now been
                             succeeded by the ROCm 4.2 feature release.


                             The Radeon Open eCosystem 4.2 release comes
                             with changes such as:


                             - HIP target platform macros were added for
                             easily targeting HIP_PLATFORM_AMD /
                             HIP_PLATFORM_NVIDIA code differences such as
                             including different header files.


                             - Stream Memory Operations now allow direct
                             synchronization between network nodes and
                             GPUs.


                      # ⚓ GCC_12_Adds_Support_For_New_#elifdef_#elifndef
                        Directives_–_Phoronix⠀⇛


                             With C2X and potentially a future version of
                             C++, there is finally the #elifdef and
                             #elifndef directives. The GNU Compiler
                             Collection is preparing its support.


                             There has long been #ifdef, #else, #elif and
                             similar directives for controlling
                             conditional compilation in C/C++. While there
                             has been #ifdef, until the upcoming C2X there
                             hasn’t been #elifdef for else if defined or
                             #elifndef for else if not defined… Short of
                             pairing “#elif defined()” or so. With C2X the
                             #elifdef and #elifndef pre-processor
                             directives are finally there and it’s being
                             looked at for C++ as well.


                      # ⚓ Can’t_the_Compiler_Do_That?⠀⇛


                             Good static analysis can save a lot of effort
                             and time. With customized static code
                             analysis, the project code can be checked not
                             only for general programming errors but also
                             for project-specific conventions and best
                             practices. The Clang Compiler Framework
                             provides the ideal basis for this.


                             The programming language C++ manages the
                             balancing act between maximum performance,
                             which is essential in the embedded sector, on
                             the one hand, and maximum code correctness
                             through a high level of abstraction on the
                             other. The balancing act is achieved by
                             focusing on compile-time checks and
                             opportunities for optimization. Calculations
                             that could be carried out more efficiently by
                             low-level code should not, where possible, be
                             rewritten by the developer, but by the
                             compiler. Additionally, errors should already
                             be excluded during compilation, instead of
                             taking up valuable computing time for checks
                             at runtime.


                             Clang has become very popular in recent years
                             and has long since established itself as one
                             of the most important C and C++ compilers.
                             This success is due not least to the
                             architecture of Clang itself. Clang is not
                             just another compiler, but a compiler
                             framework. The essential parts of the
                             compiler are a carefully designed library,
                             thus enabling the diverse landscape of
                             analysis and refactoring tools that has
                             already emerged around the framework based on
                             the LLVM project.


                             The command-line tool, clang-tidy, offers
                             static code analysis and checks compliance
                             with coding conventions, among other things,
                             but can also refactor code independently. The
                             clang-format tool can automatically
                             standardize the coding style. The Clazy tool,
                             which was developed by the author’s company,
                             supplements the compiler with a variety of
                             warnings around the Qt software framework and
                             warns of frequent anti-patterns in the use of
                             the same. Many other useful tools exist in
                             the Clang universe, as well. Even integrated
                             development environments, such as Qt Creator
                             or CLion, rely on the Clang Compiler
                             Framework for syntax highlighting, code
                             navigation, auto-completion, and refactoring.


                             Anyone who knows the tools of the Clang world
                             in their entirety is well positioned as a C
                             or C++ developer. But if you want to get
                             everything out of the technology, that is not
                             the end of the story. The LibTooling library,
                             on which most Clang tools are based, also
                             allows you to create your own customized code
                             analysis and refactoring tools, with little
                             effort.


                             I’ll give you an example. A small but
                             recurring piece of the puzzle of embedded
                             software is the exponentiation of real
                             numbers, mostly with static, natural
                             exponents. Of course, the std::pow function
                             would be used for this, had it not been
                             determined in extensive profiling that on-
                             the-target architecture std::pow(x, 4) is
                             many times slower than x*x*x and forms a
                             bottleneck in particularly performance-
                             critical code. The senior developer of the
                             project has therefore created a template
                             function, usable as utils::pow<4>(x). And
                             thanks to compiler optimizations, it’s just
                             as nimble as the manual variant1.
                             Nevertheless, since then the usual std::pow
                             variant has crept in again at various places
                             in the code, and even several hundred
                             thousand lines of code have not been ported
                             consistently.


                             The first attempt to automate the refactoring
                             is, of course, the search and replace with a
                             regular expression. std::pow\((.*), (\d+)\)
                             already finds the simplest cases. But what
                             about the cases where the “std::” is omitted
                             or the second parameter is more complicated
                             than an integer literal?


                      # § Qt⠀➾


                            # ⚓ Qt_introduces_a_new_customer_support_system⠀⇛


                                   We are making some significant
                                   enhancements in our customer support to
                                   make it even better. A new upcoming
                                   support system allows us to streamline
                                   processes and respond to support
                                   tickets quicker than ever before.


                            # ⚓ Commercial_LTS_Qt_5.15.4_Released⠀⇛


                                   We have released Qt 5.15.4 LTS for
                                   commercial license holders today. As a
                                   patch release, Qt 5.15.4 does not add
                                   any new functionality but provides bug
                                   fixes and other improvements.


                                   Compared to Qt 5.15.3, Qt 5.15.4
                                   contains about 100 bug fixes and
                                   security updates. The list of fixes and
                                   the overview of all important changes
                                   in Qt 5.15.4 can be found from the Qt
                                   5.15.4 release note. It is available
                                   via Qt Account Downloads.


                            # ⚓ Qt_for_Python:_details_about_the_6.1_release⠀⇛


                                   Last week, we announced Qt 6.1, and
                                   with that, we wanted to announce the
                                   new release of our official set of
                                   Python bindings: Qt for Python.


                      # § Python⠀➾


                            # ⚓ Ensemble_Learning_in_Python_by_Example_–_Linux
                              Hint⠀⇛


                                   There is no secret that machine
                                   learning is getting better with time
                                   and the predictive models. Predictive
                                   models form the core of machine
                                   learning. It is good to improve the
                                   accuracy of the model for better
                                   results in the machine learning model.
                                   A technique called “ensemble machine
                                   learning” is used for increasing the
                                   performance and accuracy of a model.


                                   Ensemble learning uses different models
                                   of machine learning for trying to make
                                   better predictions on the dataset. A
                                   model’s predictions are combined in an
                                   ensemble model for making the final
                                   prediction successful. However, many
                                   people are not familiar with ensemble
                                   machine learning. Read below; we
                                   explain everything about this machine
                                   learning technique using Python with
                                   appropriate examples.


                                   Suppose you are participating in a
                                   trivia game and have good knowledge of
                                   some topics, but you don’t know
                                   anything other few topics. A team
                                   member would be required to cover all
                                   of the game topics if you wish to
                                   achieve a maximum score in the game. It
                                   is the basic idea behind ensemble
                                   learning in which we combine the
                                   predictions from different models for
                                   accurate output.


                      # § Rust⠀➾


                            # ⚓ William_Brown:_Compiler_Bootstrapping_–_Can_We
                              Trust_Rust?⠀⇛


                                   Recently I have been doing a lot of
                                   work for SUSE with how we package the
                                   Rust compiler. This process has been
                                   really interesting and challenging, but
                                   like anything it’s certainly provided a
                                   lot of time for thought while waiting
                                   for my packages to build.


    * § Leftovers⠀➾


          o ⚓ Planting_Caltrops_in_the_Dawn⠀⇛


                 What have you got A hole in your head? Too? Four? Six,
                 eyes umbrellas shouldn’t just snap, right?


                 It really oughtta be a crime Or, it is! In the true light
                 of the true law Although it’s unenforced Haha! Or, we
                 don’t recognize — Complex as it is, as it were — The
                 mechanism Spread across the scales beyond


          o ⚓ Vircadia_Web_Interface_Announced⠀⇛


                 According to the announcement, Vircadia has partnered
                 with Linux Professional Institute (LPI) on this project
                 and will be adding support for Vircadia’s servers to
                 communicate with web browsers over WebRTC.


          o § Education⠀➾


                # ⚓ Universities’_humanities_provision_should_never_become
                  history⠀⇛


                       There are other histories we should confront, each
                       of them with insights that have relevance to our
                       own lives and times. That includes even the ancient
                       past. Consider one of the biggest threats to
                       democracy of our day, disinformation and fake news.
                       Think that’s a new problem? Not at all. Historians
                       have discovered that the famous monuments
                       commemorating the celebrated Pharaoh Rameses the
                       Great’s victories and skills as a warrior are
                       little more than ancient propaganda, often belying
                       the reality of defeat.


                       Historians are the fact-checkers of our accounts of
                       civilisations and power. They ask how we know what
                       we know, what we can trust and who we should
                       believe. They sort through conflicting narratives,
                       the prominent and the unsung, in the search for
                       understanding. They are the detectives
                       investigating not only crimes but also the rise and
                       fall of powers and the life stories that those
                       vicissitudes shape – of both the victors and the
                       vanquished.


          o § Health/Nutrition⠀➾


                # ⚓ Air_Pollution_From_Livestock_and_Fertilizers_Kills_Nearly
                  18,000_People_Yearly⠀⇛


                # ⚓ Parking_Lot_Crematoria_Burn_Through_the_Night_as_Covid-19
                  Overwhelms_Delhi⠀⇛


                       New Delhi—A son stood near his father’s funeral
                       pyre with folded hands and asked for forgiveness.
                       About three dozen burning pyres and mounds of ashes
                       surrounded him. As the flames rose from the corpse
                       and the smoke thickened, he had to take a few steps
                       back. Next to him, a Hindu priest chanted prayers.


                # ⚓ Opinion_|_It_Is_Imperative_We_Fix_the_Gaping_Holes_in
                  Medicare⠀⇛


                       Since its inception in 1965, Medicare has not
                       covered such basic health-care needs as hearing,
                       dental care, and vision.


                # ⚓ Covid’s_Spread_Ignores_All_Borders⠀⇛


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Nearly_all_Microsoft_365_customers_have_suffered
                        email_data_breaches⠀⇛


                             Using Microsoft 365, the software giant’s
                             cloud-based communications and collaboration
                             platform, could be a security liability for
                             many organizations, a new report from Egress
                             seems to suggest.


                             The data security company’s new Outbound
                             Email: Microsoft 365’s Security Blind Spot
                             paper, based on a poll of 500 IT leaders and
                             3,000 remote-workers in the UK and US, claims
                             businesses who use Microsoft 365 suffer more
                             email data breaches and have to deal with
                             more difficult consequences in the aftermath.


                             Were it not for the pandemic, however, things
                             would probably have been different.


                      # ⚓ Microsoft_patches_three_zero-days_in_May_2021_Patch
                        Tuesday_update⠀⇛


                             Security update includes patches for Windows,
                             Internet Explorer, Exchange Server, Office,
                             .NET Core, Visual Studio, SharePoint Server,
                             Hyper-V, Skype for Business and Lync


                      # ⚓ Microsoft_Patch_Tuesday,_May_2021_Edition_–_Krebs_on
                        Security⠀⇛


                      # ⚓ A_Closer_Look_at_the_DarkSide_Ransomware_Gang_–_Krebs
                        on_Security⠀⇛


                      # ⚓ Microsoft’s_LinkedIn_Accused_by_Noted_China_Critic_of
                        Censorship⠀⇛


                             A prominent critic of China based in the U.K.
                             said Microsoft Corp.’s LinkedIn froze his
                             account and removed content criticizing the
                             country’s government, the latest in a series
                             of allegations that the networking website
                             had censored users — even outside of the
                             Asian nation — to appease authorities in
                             Beijing.


                             Peter Humphrey, a British corporate
                             investigator and former journalist who
                             accesses LinkedIn from his home in Surrey,
                             England, said he received notification from
                             LinkedIn last month that comments he had
                             published on the platform had been removed.
                             The comments, seen by Bloomberg News, called
                             the Chinese government a “repressive
                             dictatorship” and criticized the country’s
                             state media organizations as “propaganda
                             mouthpieces.”


                      # ⚓ Feds_eye_more_oversight_of_pipelines_after_Colonial
                        attack [iophk: Windows TCO]⠀⇛


                             Some officials have indicated that the
                             ransomware attack on a pipeline that provides
                             almost half of the East Coast’s energy may
                             have unfolded as it did due to the relative
                             lack of federal oversight of pipelines
                             compared to other utilities.


                      # ⚓ FCC_approves_$7_billion_to_get_better_equipment_to
                        remote_learners⠀⇛


                             The new fund will use processes already in
                             use by the E-Rate program, which currently
                             helps schools and libraries pay for broadband
                             internet. Qualifying schools and libraries
                             will be able to purchase hotspots, routers,
                             tablets, and computers, among other devices
                             necessary for remote learning (though
                             smartphones don’t qualify). Students and
                             patrons can take them home and use them,
                             rather than huddle outside of a Taco Bell in
                             order to finish their homework.


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ Linux_Foundation_and_NGMN
                                          collaborate_on_5G⠀⇛


                                               The Linux Foundation and
                                               the Next Generation Mobile
                                               Network Alliance (NGMN),
                                               today announce the signing
                                               of a Memorandum of
                                               Understanding (MoU) for
                                               formal collaboration
                                               regarding end-to-end 5G and
                                               beyond.


                                               NGMN’s mission is to
                                               provide impactful industry
                                               guidance to achieve
                                               innovative and affordable
                                               mobile telecommunication
                                               services for the end user,
                                               placing a particular focus
                                               on Mastering the Route to
                                               Disaggregation,
                                               Sustainability and Green
                                               Future Networks, as well as
                                               on 6G and the continuous
                                               support of 5G’s full
                                               implementation.


                                        # ⚓ Hyperledger_Announces_2021_Brand
                                          Study [Ed: When the so-called 'Linux'
                                          Foundation says "research" it means
                                          marketing/branding]⠀⇛


                                               The debate is no longer
                                               about deploying blockchain
                                               technology, but rather
                                               about building production
                                               networks that will scale
                                               and interoperate. In 2020,
                                               the focus shifted from
                                               proving the value of
                                               blockchain to scaling,
                                               governance, and managing
                                               blockchain networks. COVID-
                                               19 has given the
                                               digitization of trust-based
                                               processes a new urgency,
                                               driving more profound
                                               interest in identity,
                                               interoperability, and
                                               supply chain use cases.


                                               Together with Linux
                                               Foundation Research,
                                               Hyperledger is conducting a
                                               survey to measure the
                                               market awareness and
                                               perceptions of Hyperledger
                                               and its projects,
                                               specifically identifying
                                               myths and misperceptions.
                                               Additionally, the survey
                                               seeks to help Hyperledger
                                               articulate the perceived
                                               time to production
                                               readiness for products and
                                               understand motivations for
                                               developers that both use
                                               and contribute to
                                               Hyperledger technologies.


                            # § Entrapment (Microsoft GitHub)⠀➾


                                  # ⚓ Microsoft_wants_eBPF_tools_for_Linux
                                    kernel_running_on_Windows_10⠀⇛


                                  # ⚓ GitHub_restores_a_fork_of_the_cross-
                                    platform_reverse-engineered_GTA_III_and
                                    Vice_City_code⠀⇛


                                         Remember recently we had a
                                         release of the reverse-engineered
                                         GTA III and Vice City code that
                                         worked well on Linux? Which was
                                         then promptly taken down by a
                                         DMCA notice? Well, it’s back.


                                         Not the original mind you, one of
                                         the forks on GitHub has returned
                                         as the forker issued a DMCA
                                         Counter Notice and intends to
                                         actually fight it. According to
                                         TorrentFreak, New Zealand-based
                                         developer named Theo is taking a
                                         stand against this DMCA behaviour
                                         and has managed to get GitHub to
                                         restore their fork.


                                  # ⚓ One_Developer_Gets_GTA3_And_Vice_City
                                    Source_Code_Un-DMCAd_On_GitHub⠀⇛


                                         The strange flip-flop by Rockstar
                                         Games on being open and cool with
                                         its fans continues. By way of
                                         context and a bit of throat
                                         clearing, recall that Rockstar is
                                         both the company that whipped out
                                         the ban-hammer on Grand Theft
                                         Auto 5 players over the use of
                                         mods, and the company that paid
                                         out money to a modder that fixed
                                         that same games long loading
                                         times. In addition, Rockstar is
                                         both the company that happily
                                         used intellectual property to try
                                         to silence a documentary while
                                         also being the company that
                                         enthusiastically embraced gamers
                                         making short films out of GTA
                                         footage.


                      # § Security⠀➾


                            # ⚓ All_WiFi_devices_are_vulnerable_to_“frag
                              attacks”,_here_is_how_to_protect_yourself_–
                              Techzim⠀⇛


                                   A well known Belgium security
                                   researcher, Mathy Vanhoef, who
                                   specialises in WiFi security has
                                   discovered a series of flaws that
                                   affect all WiFi devices and in
                                   particular all WiFi routers out there.
                                   Due to the nature of these
                                   vulnerabilities, he has christened them
                                   frag attacks aka fragmentation and
                                   aggregation attacks.


                            # ⚓ FragAttacks:_New_Security_Vulnerabilities
                              Affecting_WiFi_Devices,_12_CVEs_Issued_–
                              Phoronix⠀⇛


                                   FragAttacks was made public on Tuesday
                                   as a set of new security
                                   vulnerabilities affecting WiFi devices.
                                   These are just not some driver-level
                                   bugs but rather three of the
                                   vulnerabilities are attributed as
                                   design flaws in the WiFi standard
                                   itself and in turn most devices on the
                                   market.


                                   The FragAttacks researchers believe,
                                   “experiments indicate that every Wi-Fi
                                   product is affected by at least one
                                   vulnerability and that most products
                                   are affected by several
                                   vulnerabilities.” WEP through WPA3 WiFi
                                   security is believed to be impacted but
                                   the researchers did also acknowledge
                                   “the design flaws are hard to abuse”.


                            # ⚓ FragAttacks⠀⇛


                                   This website presents FragAttacks
                                   (fragmentation and aggregation attacks)
                                   which is a collection of new security
                                   vulnerabilities that affect Wi-Fi
                                   devices. An adversary that is within
                                   radio range of a victim can abuse these
                                   vulnerabilities to steal user
                                   information or attack devices. Three of
                                   the discovered vulnerabilities are
                                   design flaws in the Wi-Fi standard and
                                   therefore affect most devices. On top
                                   of this, several other vulnerabilities
                                   were discovered that are caused by
                                   widespread programming mistakes in Wi-
                                   Fi products. Experiments indicate that
                                   every Wi-Fi product is affected by at
                                   least one vulnerability and that most
                                   products are affected by several
                                   vulnerabilities.


                            # ⚓ Security_updates_for_Wednesday⠀⇛


                                   Security updates have been issued by
                                   Debian (composer, hivex, lz4, and
                                   rails), Fedora (chromium, community-
                                   mysql, djvulibre, dom4j, firefox, php,
                                   php-phpmailer6, python-django, and
                                   redis), Mageia (mariadb, nagios, and
                                   pngcheck), openSUSE (opera, syncthing,
                                   and vlc), SUSE (kernel, openvpn,
                                   openvpn-openssl1, shim, and xen), and
                                   Ubuntu (flatpak, linux, linux-aws,
                                   linux-aws-5.4, linux-azure, linux-
                                   azure-5.4, linux-gcp, linux-gcp-5.4,
                                   linux-gke, linux-gke-5.4, linux-gkeop,
                                   linux-gkeop-5.4, linux-hwe-5.4, linux-
                                   kvm, linux-oracle, linux-oracle-5.4,
                                   linux, linux-aws, linux-azure, linux-
                                   gcp, linux-hwe-5.8, linux-kvm, linux-
                                   oracle, linux-raspi, linux, linux-aws,
                                   linux-azure, linux-gcp, linux-kvm,
                                   linux-oracle, linux-raspi, linux,
                                   linux-aws, lnux-aws-hwe, linux-azure,
                                   inux-azure-4.15, linux-dell300x, linux-
                                   gcp, linux-hwe, linux-gcp-4.15, linux-
                                   kvm, linux-oracle, linux-raspi2, linux-
                                   snapdragon, linux-oem-5.10, linux-oem-
                                   5.6, and mariadb-10.1, mariadb-10.3,
                                   mariadb-10.5).


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Australian_Crime_Commission:_Only
                                    Criminals_Use_Encrypted_Communications⠀⇛


                                         Well, someone finally said the
                                         quiet part loud: some government
                                         officials actually believe the
                                         only people who need, want, or
                                         use encryption are criminals.
                                         Here’s Asha Barbaschow with the
                                         “encryption is for criminals”
                                         news at ZDNet.


                                  # ⚓ Japan’s_Rikunabi_Scandal_Shows_The
                                    Dangers_of_Privacy_Law_Loopholes⠀⇛


                                         A recent data privacy scandal in
                                         Japan involving Rikunabi—a major
                                         job-seeking platform that
                                         calculated and sold companies
                                         algorithmic scores which
                                         predicted how likely individual
                                         job applicants would decline a
                                         job offer—has underscored how
                                         users’ behavioral data can be
                                         used against their best
                                         interests. Most importantly, the
                                         scandal showcases how companies
                                         design workarounds or “data-
                                         laundry” schemes to circumvent
                                         data protection obligations under
                                         Japan”s data protection law (Act
                                         on the Protection of Personal
                                         Information (APPI)). This case
                                         also highlights the dangers of
                                         badly-written data protection
                                         laws and their loopholes.
                                         Japanese Parliament adopted
                                         amendments to the APPI, expected
                                         to be implemented by early 2022,
                                         intended to close some of these
                                         loopholes, but the changes still
                                         fall short. 


                                         Rikunabi is operated by Recruit
                                         Career (at the time of the
                                         scandal. It’s now Recruit Co.,
                                         Ltd.), a subsidiary of a media
                                         conglomerate Recruit Group, which
                                         also owns Indeed and Glassdoor.
                                         Rikunabi allows job-seekers to
                                         search for job opportunities and
                                         mostly caters to college students
                                         and others just beginning their
                                         careers. It hosts job listings
                                         for thousands of companies. Like
                                         many Internet platforms, Rikunabi
                                         used cookies to collect data
                                         about how its users search,
                                         browse, and interact with its job
                                         listings. Between March 2018 and
                                         February 2019, using Rikunabi’s
                                         data, Recruit Career—without
                                         users’ consent—was calculating
                                         and selling companies algorithmic
                                         scores that predicted how likely
                                         an individual job applicant would
                                         decline a job offer or withdraw
                                         their application.


                                         Thirty-five companies, including
                                         Toyota Motor Corporation,
                                         Mitsubishi Electric Corporation,
                                         and other Japanese corporate
                                         giants, purchased the scores. In
                                         response to a public outcry,
                                         Recruit Career tried to excuse
                                         itself by saying that the
                                         companies who purchased the job-
                                         declining scores agreed not to
                                         use them for the selection of
                                         candidates. The company claimed
                                         the scores were intended only for
                                         clients to have better
                                         communication with their
                                         candidates, but, there was no
                                         such guarantee that’s how they
                                         would be used. Because of Japan’s
                                         dominant lifetime employment
                                         system, students feared such
                                         scores could limit their job
                                         opportunities and career choices,
                                         potentially affecting their whole
                                         professional life. 


                                  # ⚓ Privacy_concerns_cause_tensions_over_data
                                    localization_and_data_transfers_to_rise⠀⇛


                                         Microsoft is doing this, it says,
                                         as “another step toward
                                         responding to customers that want
                                         even greater data residency
                                         commitments”. A key question is
                                         what happens if the US government
                                         demands access to data held
                                         within the EU. A FAQ about
                                         Microsoft’s new “EU Data
                                         Boundary” explains: “We will
                                         challenge every government
                                         request for an EU public sector
                                         or commercial customer’s personal
                                         data – from any government –
                                         where there is a lawful basis for
                                         doing so.” However, as privacy
                                         expert Alexander Hanff points
                                         out: “Even when the new EU Data
                                         Boundary is completed it doesn’t
                                         make any difference from a legal
                                         perspective because FISA 702 and
                                         US Cloud Act still gives the US
                                         government unfettered access to
                                         the data (despite being stored in
                                         the EU)”. For this reason, back
                                         in October last year, the French
                                         data protection authority ruled
                                         that US companies can’t be
                                         trusted with personal data about
                                         EU citizens, even if it is kept
                                         within the EU. Microsoft’s
                                         announcement of the EU Data
                                         Boundary notes: “Many of our
                                         services put control of customer
                                         data encryption in customers’
                                         hands through the use of
                                         customer-managed keys”. But that
                                         doesn’t help if the keys are
                                         available to Microsoft, as they
                                         must be when the latter is
                                         performing computational tasks on
                                         customers’ data. It’s irrelevant
                                         whether the keys are “customer-
                                         managed”: if Microsoft has access
                                         to them, so does the US
                                         government.


                                  # ⚓ How_to_Unblock_YouTube:_a_guide_to
                                    unblocking_YouTube_videos⠀⇛


                                         Makes you want to watch the video
                                         even more, doesn’t it? The
                                         forbidden fruit of YouTube.


                                  # ⚓ 3_ways_to_gain_control_of_your_Twitter
                                    feed⠀⇛


                                         Aral’s post Hell site reminded me
                                         that, while I’ve talked about
                                         deactivating and reactivating my
                                         Twitter account several times, I
                                         haven’t mentioned ways in which
                                         I’ve found to battle the
                                         algorithmic timeline.


                                  # ⚓ Democrats_urge_Facebook_to_reverse
                                    WhatsApp_privacy_update⠀⇛


                                         But the Democrats wrote in a
                                         letter Tuesday that WhatsApp’s
                                         failure to commit to the same
                                         privacy policy for the messages
                                         with businesses is a “potential
                                         misuse of data,” and could lead
                                         to the use of that information
                                         for targeted advertising.


                                         The key concern the lawmakers
                                         highlighted is the fact that
                                         “this policy may not provide an
                                         option to opt out.”


                                  # ⚓ Helsinki_launches_smartphone-based_crowd
                                    tracking_system⠀⇛


                                         In an aim to help people avoid
                                         areas that are highly congested
                                         in the pandemic age, the City of
                                         Helsinki is rolling out an
                                         anonymous people-tracking system
                                         around Esplanadi park, one of the
                                         city’s most crowded summertime
                                         tourist areas.


                                         In a cooperative project with
                                         tech firms IBM and Hypercell, the
                                         city is installing bluetooth
                                         signal sensors on both sides of
                                         the leafy esplanade and park,
                                         which is usually packed with
                                         people whenever the sun is
                                         shining.


                                  # ⚓ Facebook_has_been_told_to_stop_processing
                                    German_WhatsApp_data⠀⇛


                                         Mark Zuckerberg’s social media
                                         giant has been looking for new
                                         ways to monetize WhatsApp, which
                                         is used by around 60 million
                                         people in Germany, ever since it
                                         acquired it for $19 billion in
                                         2014.


                                  # ⚓ Texas_Attorney_General_Unblocks_Twitter
                                    Users_Who_Sued_Him;_Still_Blocking_Others⠀⇛


                                         It seems by now that public
                                         officials should know that they
                                         cannot block critics on social
                                         media if they are using their
                                         social media accounts for
                                         official business. This was
                                         thoroughly established the Knight
                                         v. Trump case, where the court
                                         made it clear that if (1) a
                                         public official is (2) using
                                         social media (3) for official
                                         purposes (4) to create a space of
                                         open dialogue (and all four of
                                         those factors are met) then they
                                         cannot block people from
                                         following them based on the views
                                         those users express, as it
                                         violates the 1st Amendment. Yet
                                         over and over again elected
                                         officials seem to ignore this.


                                  # ⚓ Twitter_Loses_Lawsuit_Seeking_to_Stop
                                    Texas_Probe⠀⇛


                                         “Unlike the defendants in the
                                         cases on which Twitter relies,
                                         the Office of the Attorney
                                         General has no authority to
                                         impose any sanction for a failure
                                         to comply with its
                                         investigation,” writes Chesney.
                                         “Rather, the Office of the
                                         Attorney General would be
                                         required to go to court, where
                                         the only possible consequence
                                         adverse to Twitter would be a
                                         judicial finding that the CID,
                                         contrary to Twitter’s assertion,
                                         is enforceable. Accordingly, as,
                                         to date, no action has been taken
                                         to enforce the CID, the Court
                                         finds Twitter’s lawsuit is
                                         premature, and, as such, is
                                         subject to dismissal.”


                                  # ⚓ Judge_dismisses_Twitter’s_lawsuit_against
                                    Texas_attorney_general⠀⇛


                                         A federal judge in California on
                                         Tuesday dismissed a lawsuit
                                         brought by Twitter that had
                                         sought to block Texas Attorney
                                         General Ken Paxton’s (R) office
                                         from allegedly retaliating
                                         against the company for its
                                         decision to ban former President
                                         Trump from the platform.


                                         In a 7-page ruling, the judge
                                         said Twitter’s lawsuit was
                                         premature because Paxton has not
                                         sought to enforce his January
                                         records request related to the
                                         company’s content moderation
                                         policies.


                                  # ⚓ Attorneys_General_Fight_Launch_of
                                    Instagram_Kids⠀⇛


                                         Social media can be very alluring
                                         to kids, but few will argue that
                                         it’s a healthy environment for
                                         them. This led several state
                                         attorneys general in the U.S. to
                                         press Facebook CEO Mark
                                         Zuckerberg to not launch
                                         Instagram Kids. It’s unknown at
                                         the time of writing whether he
                                         was successfully persuaded.


          o § Defence/Aggression⠀➾


                # ⚓ Balancing_interests_After_the_Kerch_school_shooting_in
                  2018,_Russia_promised_to_tighten_its_gun_laws_—_but_ended_up
                  easing_restrictions⠀⇛


                       Immediately after a fatal shooting at a Kazan
                       school on May 11, the Russian authorities started
                       talking about tightening gun ownership laws, along
                       with other legal measures and regulations. Vladimir
                       Putin instructed the Russian National Guard chief
                       to conduct an audit of the types of weapons
                       available to ordinary citizens. The Federation
                       Council called for “strengthening controls over the
                       content of computer games” once again. And State
                       Duma lawmakers suggested creating “a criminal
                       intent tracking system” for the Internet and social
                       media, or even introducing the death penalty as
                       punishment for killing children. Russia’s Human
                       Rights Commissioner, Tatyana Moskalova, proposed
                       raising the age requirement for purchasing firearms
                       to 21 years old for those who haven’t served in the
                       army. Since none of these initiatives have been put
                       down on paper, Meduza decided to look into what
                       happened to similar proposals that were put forward
                       after the 2018 mass shooting in Kerch — where a
                       student massacred his classmates using the exact
                       same weapon as the Kazan shooter. 


                # ⚓ The_Humanity_of_a_Bombardier⠀⇛


                       He told me that after one month as a student at
                       City College, he received a letter saying that he
                       had been drafted into the army and was sent to camp
                       Upton in New Jersey for training. He was 18 years
                       old. He stayed there for a couple of months until a
                       friend of his, whose father was a lieutenant in the
                       Air Force, recommended him, and he was transferred
                       there, where he was trained as a bombardier. “I
                       disliked being in the army,” he told me, “but I
                       hated even more to lose a war that would have
                       submerged the world into darkness.”


                       Allied forces had conducted many air raids on
                       Japan, causing widespread destruction and the loss
                       of hundreds of thousands of lives. By some
                       estimates, more lives were lost during those
                       bombing raids than by the two atomic bombs that
                       were dropped in Hiroshima and Nagasaki. Strategic
                       air raids began in 1944 and continued until the end
                       of the war in 1945. Although plans for attacking
                       Japan by air had been drawn much earlier, they
                       couldn’t start until the B-29 Superfortress bomber
                       was ready for combat.


                # ⚓ Spending_More_on_Nukes:_STRATCOM’s_Nuclear_Death_Wish⠀⇛


                       Much of his address as part of the Posture
                       Statement Review should be treated as the
                       conventional lunacy that comes with that cretin-
                       crusted field known as nuclear deterrence.  “Peace
                       is our profession” remains the somewhat obscene
                       motto of STRATCOM, and it is a peace kept by
                       promising the potential extinction of the human
                       species.


                       For the Admiral, strategic deterrence is the holy
                       of holies.  If it fails, “we are prepared to
                       deliver a decisive response, decisive in every
                       possible way.”  This decisiveness will be achieved
                       “with a modern resilient, equipped, and trained
                       combatant-ready force.”  To avoid the failure of
                       such deterrence also required revisiting “a
                       critical forgotten lesson that deterrence operates
                       continuously from peacetime, through the gray zone,
                       worldwide, across all domains, and into conflict”
                       [Richard’s emphasis].


                # ⚓ Opinion_|_Why_the_Pentagon_Budget_Keeps_Rising⠀⇛


                       Joe Biden’s first 100 days were a Pentagon prize.


                # ⚓ Putin_submits_bill_to_Russian_parliament_on_withdrawing
                  from_Open_Skies_treaty⠀⇛


                       President Vladimir Putin has submitted a bill to
                       the Russian State Duma on withdrawing from the Open
                       Skies Treaty.


                # ⚓ The_True_Meaning_of_the_Afghan_‘Withdrawal’⠀⇛


                       Many of us have had a recurring nightmare. You know
                       the one. In a fog between sleeping and waking,
                       you’re trying desperately to escape from something
                       awful, some looming threat, but you feel paralyzed.
                       Then, with great relief, you suddenly wake up,
                       covered in sweat. The next night, or the next week,
                       though, that same dream returns.


                # ⚓ Opinion_|_Art_Against_Drones⠀⇛


                       Bilal, Durant and other artists who help us think
                       about U.S. colonial warfare against the people of
                       Iraq and other nations should surely be thanked.


                # ⚓ Will_Biden_Have_Blood_on_His_Hands_in_Afghanistan?⠀⇛


                       That’s a good thing. And it is long overdue. 


                       But there is one big problem with Biden’s
                       timetable: It violates an agreement that the U.S.
                       government entered into with the Taliban to exit
                       the country by May 1 of this year.


                # ⚓ “Harm_Is_Still_Being_Done”:_36_Years_After_MOVE_Bombing,
                  Misuse_of_Children’s_Remains_Reopens_Wounds⠀⇛


                       This week marks the 36th anniversary of the day the
                       city of Philadelphia bombed its own citizens. On
                       May 13, 1985, police surrounded the home of MOVE, a
                       radical Black liberation organization that was
                       defying orders to vacate. Police flooded the home
                       with water, filled the house with tear gas, and
                       blasted the house with automatic weapons, all
                       failing to dislodge the residents. Finally, police
                       dropped a bomb on the house from a helicopter,
                       killing 11 people, including five children. The
                       fire burned an entire city block to the ground,
                       destroying over 60 homes. But the tragedy didn’t
                       end on that day. We look at how Princeton and the
                       University of Pennsylvania have used bones from one
                       or two of the murdered children in their classes
                       for years. “We still don’t know all the details
                       about what happened in terms of the chain of
                       custody,” says Abdul-Aliy Muhammad, an organizer
                       and writer in West Philadelphia who helped bring
                       the revelations to the public. “You can’t even
                       begin to heal because the harm is still being
                       done,” adds Mike Africa Jr., a second-generation
                       MOVE member. “Everybody is just retraumatized.”


                # ⚓ Nine_dead_in_Russian_school_shooting._Attacker_now_in
                  custody.⠀⇛


                       Nine are dead and more than 20 are injured after a
                       school shooting in the Russian city of Kazan on the
                       morning of May 11. Though initial reports stated
                       that two armed men entered the building and opened
                       fire on students and teachers, police officials
                       detained just one culprit and have denied reports
                       of a second gunman. According to media reports,
                       police units were also sent to the shooter’s
                       apartment, where he allegedly planted a bomb.
                       Russia’s Republic of Tatarstan has declared
                       Wednesday, May 12, a day of mourning.


                # ⚓ Colombian_Protesters_Are_Ready_for_the_Long_Haul⠀⇛


                       Bogotá—On May 9, after multiple days of widespread
                       unrest and police violence, demonstrators in
                       Colombia’s capital city gathered, with candles
                       cradled in their hands, for an evening of mourning.
                       On the cracked cement floor of a public park lay
                       sheet after sheet of paper with the typewritten
                       names of demonstrators killed during recent
                       protests. One read: “Jeisson García, 13 years old,
                       Suspect: ESMAD”—one of the youngest alleged victims
                       of the country’s notorious riot control police.


                # ⚓ Corporate_Media_Oppose_Afghan_Control_of_Afghanistan⠀⇛


                       When President Joe Biden announced the “withdrawal”
                       of US troops from Afghanistan after almost 20 years
                       of occupying the country in violation of
                       international law, corporate media not only misled
                       their audiences on what the US is actually planning
                       to do in Afghanistan, but also somehow made it seem
                       as if withdrawing from the longest overseas war in
                       US history would be premature (FAIR.org, 9/11/19).


                # ⚓ In_Blow_to_NRA,_Federal_Judge_Dismisses_Group’s_Bankruptcy
                  Case⠀⇛


                       “The NRA’s bankruptcy was deemed to be bad faith,
                       much like every promise and statement the
                       organization has made for decades,” said one group
                       working to end gun violence. “The NRA cannot escape
                       justice.” 


                # ⚓ In_Exclusive_Jailhouse_Letter,_Capitol_Riot_Defendant
                  Explains_Motives,_Remains_Boastful⠀⇛


                       In a letter sent from behind bars, a key defendant
                       in the Jan. 6 riot at the U.S. Capitol said he and
                       fellow inmates have bonded in jail, and boasted
                       that those attacking the building could have
                       overthrown the government if they had wanted.


                       The letter is signed “the 1/6ers” and expresses no
                       remorse for the assault on the Capitol, in which
                       five people died. While no names appeared on it,
                       ProPublica was able to determine, through
                       interviews with his family and a review of his
                       correspondence from jail, that it was penned by Guy
                       Reffitt, a member of the Three Percenter right-wing
                       militant group accused of participating in the
                       riot. The letter said the inmates arrested for
                       their role in the attack regularly recite the
                       Pledge of Allegiance inside the Washington, D.C.
                       jail and sing the national anthem “all in unison,
                       loud and proud most everyday.”


                # ⚓ Historian:_8-9_May_–_How_and_why_do_we_remember_the_end_of
                  WW2_in_Europe?⠀⇛


                       May 8 marks the anniversary of the German
                       surrendered to Allied forces in 1945, which brought
                       an end to the Second World War in Europe. Some
                       former Eastern Bloc states, including Russia, mark
                       this anniversary instead on May 9, accounting for
                       the difference in time zones between Eastern and
                       Western Europe. For many, May 9 has become a day of
                       celebration, honoring the triumph over the Axis
                       powers. However, writes Estonian historian David
                       Vseviov, it would be more constructive, and more
                       pertinent, to learn from the past rather than
                       venerate it.


                # ⚓ French_army_chief_tells_soldiers_to_quit_over_civil-war
                  letter⠀⇛


                       The letter, published in a right-wing magazine,
                       accused the French government of granting
                       “concessions” to Islamism.


                       It followed a similar letter three weeks ago signed
                       by 20 former generals.


                       Both letters were condemned by the French
                       government but praised by right-wing politicians.


                       On Tuesday, General François Lecointre addressed
                       the latest letter in a message to military
                       personnel.


          o § Environment⠀➾


                # ⚓ Nuclear_reactions_at_Chernobyl_are_spiking_in_an
                  inaccessible_chamber⠀⇛


                       The explosion at Chernobyl in 1986 brought down
                       walls and sealed off many rooms and corridors.
                       Tonnes of fissile material from the interior of a
                       reactor were strewn throughout the facility and the
                       heat it generated melted sand from the reactor
                       walls with concrete and steel to form lava-like and
                       intensely radioactive substances that oozed into
                       lower floors.


                       One chamber, known as subreactor room 305/2, is
                       thought to contain large amounts of this material,
                       but it is inaccessible and hasn’t been seen by
                       human or robotic eyes since the disaster.


                # ⚓ Tide_of_climate_refugees_swells_as_Earth_heats_up⠀⇛


                       Prepare for the arrival of more displaced persons,
                       climate refugees driven from their homes by global
                       heating.


                # ⚓ Climate_Experts_Applaud_as_US_Government_Approves_Largest
                  Offshore_Wind_Farm_in_Nation’s_History⠀⇛


                       “A clean energy future is within our grasp in the
                       United States,” said Interior Secretary Deb
                       Haaland.


                # § Energy⠀➾


                      # ⚓ Indigenous_Rights_Groups_Join_Michigan_Gov._Whitmer
                        in_Demanding_Shutdown_of_Enbridge’s_Line_5⠀⇛


                             The governor called the pipeline a “ticking
                             time bomb” as her deadline of Wednesday, set
                             last year for the Canadian company, fast
                             approached.


                      # ⚓ ‘The_Future_of_Energy?_Bright_and_Breezy’:_IEA
                        Forecasts_Huge_Growth_in_Solar_and_Wind⠀⇛


                             Renewable power sources grew at their fastest
                             rate in two decades last year—an increase
                             that is set to become the “new normal.”


                # § Wildlife/Nature⠀➾


                      # ⚓ Give_Turtles_a_Brake⠀⇛


                             Nesting Females: Roads, Roadsides, and
                             Predators


                             What makes it even worse is that a
                             disproportionate amount of the turtles being
                             killed are adult females. They are especially
                             at risk because of the long distance forays
                             they make searching for nest sites in spring
                             and summer. Some turtles are terrestrial,
                             such as Box Turtles and tortoises, some are
                             amphibious, such as Wood Turtles, but most
                             are aquatic — and they all lay eggs and nest
                             on land, such as roadsides. Even aquatic
                             species such as Sliders and Cooters, and Map,
                             Musk, Softshell, and Snapping Turtles may
                             nest 200-600 yards from the water. When they
                             leave their wetlands in search of upland nest
                             sites, they usually will have to cross at
                             least one road.


          o § Finance⠀➾


                # ⚓ Inside_the_April_Jobs_Report [Ed: Fake employment numbers
                  that basically redefine the concept of "unemployment" in a
                  country where only about half of work-able adults have a
                  job]⠀⇛


                       Performance Across Sectors was Very Mixed


                       The leisure and hospitality sector accounted for
                       more than all the gains in April, adding 331,000
                       jobs. Restaurants added 187,000; arts and
                       entertainment added 89,600; and hotels added
                       54,400. State and local government added a
                       surprisingly low 39,000 jobs, almost all in
                       education. Employment in state and local
                       governments is still 1,278,000 below the pre-
                       pandemic level. There should be large employment
                       increases here as more schools reopen in May.


                # ⚓ Warren,_Sanders_Propose_Permanently_Expanding_Food_Stamps
                  to_College_Students⠀⇛


                # ⚓ Opinion_|_CEO_Pay_Skyrocketed_at_Corporations_While_Their
                  Low-Wage_Workers_Suffered_in_the_Pandemic⠀⇛


                       More than half of the country’s 100 largest low-
                       wage employers rigged pay rules in 2020 to give
                       CEOs 29 percent average raises while their
                       frontline employees made 2 percent less.


                # ⚓ Sanders_Blames_“Rigged_Economy”_for_CEO_Pay_Hikes_Amid
                  Worker_Pay_Cuts_in_2020⠀⇛


                # ⚓ We_Can’t_Just_Tell_People_to_“Go_Back_to_Work.”_We_Have_to
                  Improve_Workplaces.⠀⇛


                # ⚓ Opinion_|_We_Don’t_Have_a_Labor_Shortage_in_the_US,_We_Have
                  a_Crisis_of_Low_Wages⠀⇛


                       Don’t easily believe claims that there’s a lack of
                       people to fill jobs. What’s really going on is that
                       employers aren’t offering workers a living wage.


                # ⚓ Despite_Weeks_of_Union-Busting,_Workers_at_Imperfect_Foods
                  Vote_to_Unionize⠀⇛


                # ⚓ The_Cash_Cows_of_Catron_County⠀⇛


                       In 2020, the FSA paid out $588,940.19 under the LIP
                       for livestock lost in 2019 in Catron County, New
                       Mexico because of Mexican wolves. This money went
                       to just eleven livestock owners, for 1130 head.
                       Yes, 1,130 head of “beef.” I confirmed twice that
                       there were only wolf payments in 2019 and no
                       weather-related claims.


                       According to the US Fish and Wildlife Service there
                       were just 87 wolves in New Mexico in 2019. If all
                       the wolves in New Mexico in 2019 were responsible
                       for the loss or injury of 1130 head of livestock on
                       these 11 ranches in Catron County, it would mean
                       that each wolf was responsible for the death or
                       injury of nearly 13 head of cattle in 2019, and
                       that cattle were being killed or injured at the
                       rate of three a day on just these ranches.


                # ⚓ Bill,_Melinda,_and_the_Burden_of_Grand_Fortune⠀⇛


                # ⚓ Report_Reveals_How_Big_Corporations_Rigged_Rules_to_Boost
                  Pandemic_Pay_of_CEOs_as_Workers_Suffered⠀⇛


                       “By inflating executive compensation while their
                       workers struggled during a pandemic, corporate
                       boards have strengthened the case for tax penalties
                       on huge CEO-worker pay gaps.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Rushing_to_Judgment_on_Scott_Stringer⠀⇛


                       On April 28, Jean Kim, a political lobbyist,
                       accused Scott Stringer, New York City comptroller
                       and the leading progressive candidate in the
                       upcoming mayoral primary, of harassing and sexually
                       assaulting her when she was an intern on his
                       unsuccessful 2001 campaign for public advocate.
                       Stringer vigorously denied her allegations. To no
                       avail: Within two days, he had lost endorsements
                       from the Working Families Party, The Jewish Vote,
                       the Sunrise Movement, and individual progressive
                       allies, including US Representative Jamaal Bowman
                       and state Senators Jessica Ramos, Alessandra
                       Biaggi—the latter both Stringer protégés—Julia
                       Salazar, and Gustavo Rivera. Assembly  members Yu-
                       Line Niou, Catalina Cruz, Representative Adriano
                       Espaillat, state Senator Jose Serrano, and others
                       quickly followed. Maya Wiley and Dianne Morales,
                       Stringer’s rivals on the left, called on him to
                       quit the race.


                # ⚓ Opinion_|_GOP:_We_Just_May_Be_the_Lunatics_You’re_Looking
                  For⠀⇛


                       These days, you don’t have to be delusional to be
                       in the Republican leadership, but it helps.


                # ⚓ Decrying_Global_Violence,_Jamaal_Bowman_Says_‘White_House
                  Must_Act’⠀⇛


                       Congressman calls on Biden administration to
                       everything in its power to de-escalate “tensions
                       around the world.”


                # ⚓ Left_Says_Senate_Democrats_Face_Existential_Choice:_Kill
                  Filibuster_or_Watch_Democracy_Die⠀⇛


                       “This is about to move from an abstract
                       conversation about Senate rules to a very clear
                       choice for Senate Democrats: Protect the ‘Jim Crow’
                       filibuster or protect American democracy—they won’t
                       be able to do both.”


                # ⚓ History_Lessons_From_3021⠀⇛


                       Support independent cartooning: join Sparky’s
                       List—and don’t forget to visit TT’s Emporium of
                       Fun, featuring the new book and plush Sparky!


                # ⚓ Biden’s_First_Immigration_Court_Picks_Are_All_Judges
                  Selected_Under_Trump⠀⇛


                # ⚓ GOP_Lawmaker_Claims_Only_5_Republicans_in_the_House
                  Actually_Buy_Trump’s_Lies⠀⇛


                # ⚓ Republicans_Love_Hypocrites,_and_Elise_Stefanik_Is_the
                  Hypocrite_Du_Jour⠀⇛


                       House minority leader Kevin McCarthy announced
                       Sunday that he wants to replace House Republican
                       Conference chair Liz Cheney with Elise Stefanik.


                # ⚓ Opinion_|_The_Far-Right_War_on_History,_Education,_and
                  Thinking⠀⇛


                       Knowing the real history of the United States is
                       essential to advancing the struggles of today.


                # ⚓ Dark_Money_Group_Tied_to_McConnell_Plans_Ad_Blitz_Against
                  Voting_Rights_Act⠀⇛


                # ⚓ Virginia’s_Shrunken_GOP_Electorate_Finally_Picks_a_Nominee
                  for_Governor⠀⇛


                       It took until Monday night, more than 48 hours
                       after the GOP’s jerry-built, 39-site, mostly drive-
                       up Virginia “convention” ended, but former Carlyle
                       CEO Glenn Youngkin, a Donald Trump loyalist, will
                       be the state’s GOP nominee for governor. The only
                       candidate to acknowledge that Joe Biden won the
                       presidency, former House speaker Kirk Cox, was the
                       first of the four major candidates to be eliminated
                       as the ranked-choice votes were hand-tallied—hand-
                       tallied because some candidates didn’t trust the
                       vote-counting software the party proposed using.


                # ⚓ 9_of_9_GOP_Senators_Agree_That_Voters_Waiting_in_Line
                  Should_Not_Be_Given_Food_or_Water⠀⇛


                       “Republicans would rather have you starve than
                       vote,” said one critic.


                # ⚓ ‘What_We’ve_Seen_in_Sheikh_Jarrah_Is_a_Microcosm_of_What
                  We’ve_Experienced_for_the_Last_70+_Years’⠀⇛


                       Janine Jackson interviewed the US Campaign for
                       Palestinian Rights’ Ahmad Abuznaid about Israel/
                       Palestine apartheid for the May 7, 2021, episode of
                       CounterSpin. This is a lightly edited transcript.


                # ⚓ Israel_Condemned_for_‘Unambiguous_War_Crime’_After
                  Destroying_Gaza_Apartment_Tower⠀⇛


                       Resistance fighters retaliated with a barrage of
                       rockets as the death toll during the current
                       conflagration rose to over 30 people—almost all of
                       them Palestinians.


                # ⚓ Three_Children_Are_Reportedly_Among_Those_Killed_by_Israeli
                  Forces_in_Gaza⠀⇛


                # ⚓ Israeli_Forces_Kill_Dozens_in_Gaza,_Including_9_Children⠀⇛


                # ⚓ Biden_Budget_Would_Send_$1.3_Billion_More_to_Israeli
                  Military_Than_to_Global_Climate_Programs:_Analysis⠀⇛


                       A group of anti-war veterans said President Joe
                       Biden’s spending priorities indicate that he thinks
                       “preserving apartheid is more important than
                       fighting climate change.”


                # ⚓ Opinion_|_A_New_Generation_of_Palestinians_Are_Rising_Under
                  Netanyahu’s_Nose_and_Saying_‘Enough_Is_Enough’⠀⇛


                       How Israel is sowing the seeds of a new uprising.


                # ⚓ State_Dept_Spokesperson_Under_Fire_for_‘Spineless’_Refusal
                  to_Condemn_Israel’s_Killing_of_Children_in_Gaza⠀⇛


                       “This unsurprising response is devoid of empathy
                       and concern for human suffering,” said Rep. Ilhan
                       Omar. “He can’t even condemn the killing of
                       children.”


                # ⚓ Human_Rights_Experts_Denounce_Israeli_Violence,
                  Confiscation_of_Homes_in_East_Jerusalem_as_Violation_of
                  International_Law⠀⇛


                       The new statements of condemnation came as Israel
                       launched another round of airstrikes into Gaza,
                       bringing the death tolll toll at least 26 people.


                # ⚓ Israel_Kills_Dozens_in_Gaza_While_Imposing_“Constant_War”
                  on_Palestinian_Residents_of_Jerusalem⠀⇛


                       Israeli airstrikes in Gaza have killed at least 26
                       Palestinians, including nine children, as tension
                       in the region has escalated sharply. Hundreds were
                       also injured by Israeli forces Monday when they
                       stormed the Al-Aqsa Mosque, the third-holiest site
                       in Islam. Hamas responded by firing hundreds of
                       rockets into Israel, which reportedly caused dozens
                       of injuries but no deaths. The tension in Jerusalem
                       has been mounting for weeks as Palestinians have
                       been organizing to block Israel from forcibly
                       evicting dozens of Palestinians in the Sheikh
                       Jarrah neighborhood to give their homes to Jewish
                       settlers. The United Nations has described the
                       planned eviction as a possible war crime. Raji
                       Sourani, award-winning human rights lawyer and
                       director of the Palestinian Center for Human Rights
                       in Gaza, says Israel’s latest assault is
                       compounding the suffering of people in the besieged
                       territory. “We have the occupation. We have the
                       blockade for the last 14 years, which paralyzed our
                       entire lives. We have the pandemic, and now we have
                       this fourth war against Gaza,” he says. We also
                       speak with Orly Noy, an Israeli political activist
                       and editor of the Hebrew-language news site Local
                       Call, who says the latest outbreak of fighting is
                       likely to help Israeli Prime Minister Benjamin
                       Netanyahu cling to power. “Israeli politics is now
                       in a very strange phase,” Noy says. “Extreme right-
                       wingers are controlling both sides of the Israeli
                       map.”


                # ⚓ Sanders_Says_US_Must_Call_for_Cease-Fire_and_End_to
                  ‘Provocative_and_Illegal_Settlement_Activity’_by_Israel⠀⇛


                       The senator joined a growing chorus of global
                       political leaders alarmed by the escalating
                       violence and settler colonialism in the region.


                # ⚓ The_Pursuit_of_National_Liberty_Should_not_be_Handed_Over
                  to_Toxic_Populists_and_Demagogues⠀⇛


                # ⚓ The_Political_Party_of_the_Big_Lie⠀⇛


                       – Hamlet,” Act 1, Scene IV


                       The boy who cried wolf would feel right at home in
                       the Republican Party.


                # ⚓ Andrew_Yang_[kee]:_Champion_of_Memes,_Math_and_Murder⠀⇛


                       Andrew Yang made a name for himself during the 2020
                       Democratic presidential primary, primarily by being
                       nothing like the other candidates. More interested
                       in meme causes than bread and butter political
                       causes, Yang’s name was synonymous with the words
                       “outsider,” “memes,” and “math.”


                # ⚓ Democrats_are_Running_Out_of_Time⠀⇛


                       The window of opportunity is already tiny. And it’s
                       closing fast.


                # ⚓ DHS_establishes_domestic_terror_unit_within_its
                  intelligence_office⠀⇛


                       The Department of Homeland Security (DHS) is
                       establishing a new domestic terrorism branch within
                       its intelligence arm while seeking to rebrand an
                       office criticized under the Trump administration
                       for doing little to address growing extremism.


                       The new, dedicated domestic terrorism branch within
                       the department’s Office of Intelligence and
                       Analysis (OIA) is designed to “ensure DHS develops
                       the expertise necessary to produce the sound,
                       timely intelligence needed to combat threats posed
                       by domestic terrorism and targeted violence,” the
                       agency said in a release.


                # ⚓ The_PRO_Act_would_reshape_the_tech_industry_—_will_it_get
                  the_chance?⠀⇛


                       The National Labor Relations Act (NLRA) of 1935 was
                       meant to defend worker organizing. But the
                       Taft–Hartley Act of 1947 poked holes in many of its
                       protections. The legislation allowed states to pass
                       right-to-work laws, forcing unions to represent
                       workers who don’t pay dues, which weakens their
                       position financially.


                       Now, Congress is considering a law that would
                       dramatically reshape American labor. The Protecting
                       the Right to Organize Act (also known as the PRO
                       Act) would eliminate many of the roadblocks that
                       workers face when they try to unionize. Among other
                       things, it would ban companies from forcing
                       employees to attend captive audience meetings where
                       managers spread anti-union messages; allow unions
                       to collect dues from non-union members — increasing
                       their budgets and their ability to effectively
                       organize; and establish penalties for companies
                       that violate workers’ rights.


          o § Misinformation/Disinformation⠀➾


                # ⚓ Heritage_Minister_Guilbeault_Traffics_in_Misinformation_and
                  Conspiracy_Theory_as_Cause_of_Bill_C-10_Criticism_and_Need
                  for_Government_Speech_Regulation⠀⇛


                       If the public needed yet another reason to be
                       concerned about the government’s motivation for
                       Bill C-10, Guilbeault just provided it. He is set
                       to introduce a bill that purports to deal with
                       misinformation, yet just used his own Twitter feed
                       to traffic in it. Indeed, the government cannot
                       claim to support freedom of expression and at the
                       same time have its lead minister on the file
                       amplify flimsy conspiracy theories and openly
                       support regulating speech based on such theories.
                       Bill C-10 is not designed to address
                       misinformation, but the fact that Guilbeault seems
                       to think it could help address the issue represents
                       a giant red flag that cannot be ignored. The
                       government should start from scratch on Bill C-10
                       and cannot vest responsibility for the online harms
                       bill in Guilbeault.


          o § Censorship/Free Speech⠀➾


                # ⚓ Disgraced_Yale_Law_Professor_Now_Defending_Anti-Vaxxers_In
                  Court_With_His_Nonsense_Section_230_Ideas⠀⇛


                       Back in January, we wrote about a bizarrely bad
                       Wall Street Journal op-ed co-written by disgraced
                       and suspended Yale Law professor Jed Rubenfeld,
                       arguing that Section 230 somehow magically makes
                       social media companies state actors, controlled by
                       the 1st Amendment. This is, to put it mildly,
                       wrong. His argument is convoluted and not at all
                       convincing. He takes the correct idea that
                       government officials threatening private companies
                       with government retaliation if they do not remove
                       speech creates 1st Amendment issues, and then tries
                       to extend it by saying that because 230 gives
                       companies more freedom to remove content, that
                       magically makes them state actors.


                # ⚓ Lyubov_Sobol_handed_fines_in_two_more_Prigozhin_defamation
                  lawsuits⠀⇛


                       Moscow’s Simonovsky Court has partially fulfilled
                       two defamation lawsuits filed by Russian oligarch
                       Evgeny Prigozhin against opposition politician
                       Lyubov Sobol, MBX Media reported on Tuesday, May
                       11, citing the court’s press service.


                # ⚓ Whistleblower_Craig_Murray_Sentenced_To_8_Months_In_Prison
                  Over_His_Reporting_On_Former_Scottish_First_Minister’s
                  Trial⠀⇛


                       The following was originally published as part of
                       The Dissenter Newsletter.Former UK diplomat-turned
                       whistleblower Craig Murray was sentenced to
                       eight months in prison at the High Court in
                       Edinburgh for contempt of court resulting from his
                       coverage of the trial of former Scottish First
                       Minister Alex Salmond.


                       A three-judge panel determined on March 25,
                       2021—following a two-hour trial in January—that
                       information published by Murray in a number of his
                       blog posts was likely to lead indirectly to people
                       being able to identify witnesses in Salmond’s
                       sexual assault trial.This process, known as “jigsaw
                       identification,” refers to the possibility that a
                       person may piece together information from various
                       sources to arrive at the identification of a
                       protected witness.


                # ⚓ Novel_about_Black_boy_shot_by_officer_pulled_from_Florida
                  classes_after_police_union_complaint⠀⇛


                       Complaints from a police union and parents prompted
                       a South Florida school system to temporarily stop
                       teaching a fictional book about a Black boy who was
                       fatally shot by a white police officer, district
                       officials said.


                       A representative for Broward County Public Schools,
                       one of the largest school districts in the country,
                       with more than 260,000 students, confirmed in a
                       statement Monday that the novel, “Ghost Boys,” by
                       Jewell Parker Rhodes, has been pulled, for now,
                       from two fifth grade classrooms.


                       The spokesperson said in a statement that, after
                       the school district received a letter from the
                       Fraternal Order of Police, it determined that
                       proper procedures to make sure the book could be
                       taught in classrooms weren’t followed.


                # ⚓ English_universities_fear_legal_minefield_under_free_speech
                  bill⠀⇛


                       Eric Kaufmann, professor of politics at Birkbeck,
                       University of London and co-author of a report for
                       the Policy Exchange thinktank that was source for
                       the key proposals in the DfE policy paper, said the
                       “most important difference” the legislation would
                       make to life in universities “will be the security
                       the bill will provide to political minorities in
                       the university who wish to dissent from prevailing
                       orthodoxies”.


                       But Smita Jamdar, head of education at law firm
                       Shakespeare Martineau, said that the “introduction
                       of the statutory tort will almost certainly involve
                       universities in more legal action”.


                       “We are not an especially litigious society, but in
                       this area there are likely to be those who are
                       happy to press forward with legal action, either on
                       the grounds of principle or ideology…or simply to
                       support an attack on universities more generally.
                       This will entail resource and expense on the part
                       of universities,” she said.


                # ⚓ U.K._Adds_Anti-‘Censorship’_Clause_to_Online_Safety_Bill⠀⇛


                       The bill also asks U.K. regulator Ofcom to set out
                       how companies should guard “freedom of expression,”
                       such as giving ways to appeal if content is
                       removed. It raises major questions about online
                       debate and will now be scrutinized by lawmakers
                       before being brought to a vote in Parliament.


                       The largest social media platforms have found
                       themselves in a fiery clash about the nature of the
                       digital public square, and their responsibilities
                       as the private businesses that host it. That’s been
                       exemplified in Twitter and Facebook’s decisions to
                       ban former President Donald Trump for breaking
                       their rules around glorifying violence.


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


                # ⚓ Reporter’s_Alert:_Part_V⠀⇛


                       We started an online webpage: Reporter’s Alert.
                       From time to time, we will use Reporter’s Alert to
                       present suggestions for important reporting on
                       topics that are either not covered or not covered
                       thoroughly. Reporting that just nibbles on the
                       periphery won’t attract much public attention or be
                       noticed by decision-makers. Here is the fifth
                       installment of suggestions:


                       1. Jamie Dimon, the CEO of JP Morgan Chase, has
                       just reported staggering quarterly earnings. This
                       achievement, no doubt assisted by policies of the
                       Federal Reserve, makes the following statement by
                       him on January 21, 2021, a wonderful opportunity
                       for reportorial follow up:


                # ⚓ Meduza_challenges_‘foreign_agent’_designation_in_court⠀⇛


                       Meduza has filed a claim in court seeking to
                       overturn the Russian Justice Ministry’s decision to
                       add our news outlet to the list of “foreign agent”
                       media.


                # ⚓ 3_Myanmar_Journalists_Arrested_in_Thailand⠀⇛


                       Three reporters working for a now-banned news
                       broadcaster in Myanmar have been arrested in
                       Thailand on charges of illegally entering the
                       country.


                       The three journalists work for the Democratic Voice
                       of Burma, an online and broadcast news outlet that
                       was recently shut down by the ruling military
                       junta.


          o § Civil Rights/Policing⠀➾


                # ⚓ Appeals_Court_Says_Families_Of_Car_Crash_Victims_Can
                  Continue_To_Sue_Snapchat_Over_Its_‘Speed_Filter’⠀⇛


                       A few years ago, the Georgia Court of Appeals kept
                       a lawsuit alive against Snapchat, brought by the
                       parents of a victim of a car crash — one supposedly
                       encouraged by Snapchat’s “speed filter.” No Section
                       230 immunity was extended to Snapchat, which only
                       made the filter available, but did not actually
                       participate (other than as another passenger) in
                       the reckless driving that resulted in the accident
                       that left another driver permanently brain damaged.


                # ⚓ Russian_court_sentences_activist_Olga_Misik_to_two_years_of
                  restricted_freedom⠀⇛


                       On May 11, a Russian justice of the peace found
                       three activists from the “Termless Protest”
                       movement (“Bessrochny Protest”) guilty of vandalism
                       and sentenced them to restrictions on freedom, OVD-
                       Info reported.


                # ⚓ Republicans_Have_Made_It_Harder_To_Vote_In_11_States_So
                  Far⠀⇛


                       As we wrote in March, Republican state legislators
                       — inspired by Trump’s baseless claims of voter
                       fraud — have introduced hundreds of bills this year
                       that would make it harder to vote. Based on the
                       latest data from the Brennan Center for Justice and
                       our own research, at least 404 voting-restriction
                       bills have now been introduced in 48 state
                       legislatures.1 What’s more, nearly 90 percent of
                       them were sponsored primarily or entirely by
                       Republicans.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Despite_Empty_FCC_Promises,_Broadband_Prices_Jumped_19%
                  During_Trump_Era⠀⇛


                       To justify its decision to effectively lobotomize
                       itself at telecom lobbyist behest, the Trump FCC
                       made all manner of promises. A major one was that
                       if we gutted regulatory oversight of Comcast and
                       AT&T, we’d see a massive boost in broadband
                       investment. Shockingly, that never happened,
                       despite repeated, ongoing claims by Ajit Pai and
                       friends to the contrary.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Why_Biden’s_Vaccine_IP_Waiver_is_Political_Theatre⠀⇛


                             The US statement itself is cautiously worded
                             and is non-committal. It only says, “We will
                             actively participate in text-based
                             negotiations at the World Trade Organization
                             (WTO) needed to make that happen. Those
                             negotiations will take time given the
                             consensus-based nature of the institution and
                             the complexity of the issues involved.”


                             The Biden administration’s emphasis continues
                             to be on “our vaccine supply for the American
                             people.” It is an America First strategy.
                             President Biden has plans to at least
                             partially vaccinate 70% of adults by July 4
                             so that herd immunity develops that will help
                             the level of new infections to drop.


                      # ⚓ Opinion_|_We_Must_Push_Politics_Aside_in_the_Global
                        Race_to_Vaccinate_the_World_Against_Covid-19⠀⇛


                             The pandemic is truly a global threat that
                             requires a global mobilization.


                # § Copyrights⠀➾


                      # ⚓ Triller_Hits_H3_Podcast_With_$50m_Jake_Paul_Piracy
                        Lawsuit,_Judge_Guts_Original_Complaint⠀⇛


                             Triller’s legal campaign against entities
                             that allegedly streamed the Jake Paul boxing
                             match has taken two new and significant
                             turns. After the judge gutted the original
                             lawsuit targeting several sites, dismissing
                             all but one of them from a $100m lawsuit,
                             Triller has now filed a second complaint,
                             demanding $50m from the popular H3 Podcast.


                      # ⚓ The_Pirate_Bay_Suffers_Downtime,_Tor_Domain_Remains
                        Online⠀⇛


                             The Pirate Bay’s main domain has been
                             inaccessible to most people for two days.
                             There is no official word from the site’s
                             operators, but history shows that the outage
                             is likely being caused by a technical issue.
                             Meanwhile, some of the site’s many proxies
                             and its official Tor domain are still working
                             fine.


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