𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, February 17, 2025
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Generated Tue 18 Feb 02:49:18 GMT 2025
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/2025/02/17/


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

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QmdLsuRLzrwb58dZaSmJah6oCmNNZ6cW4ick4chqJmHjmY
QmTNR3uqcbMYjPAbbHjBqyNJb3ib8kytQvdFnATzkBFVvo
QmfCHrqMLfMsHXYnQeAvVuNYt91Zw2AmMJ5mx4RqsrWy3b
QmR2rr1yXDANjQBEz2oGtd2UMgy9U37FHdjpUhPfAk7h5z
QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3
QmaoEDiALTYYZdaq3SQ86aQpMwUji1nqCeLbXAoszFRYvJ
QmSTkZUY74BcgbgqS6JKwwNbVnbzY5uqwpgWtYonGJua8s
QmXZcp3rXLYa24pYd7jUu6sPDrhziRCNCok875WLJTLysP
QmUE7nd24kx2soZFbSYKDsb1ik1wpirFTRTBhDTj6w9sjh
QmdKeWBhfnjgQLYU48wto7DdStpXsB5mE1yEEnWcxQ53vu
QmfSnnTnjcAe3YvtRsVgAwUJfpcEk1dM5J5yjJLyv7MxqM
QmQ16CkpxBbMzPZ6wZcuKBUcxH1RZ8uAEhcvdBsPRpVZe9
QmT3gTQRv33wEDtJveL8DiqiacGeRaxEbRFDUyVSJEAvDL
QmTs9qcwghZPs5oBh9qzsu8a11T4s6xHrJjVNyk5miFy3X
Qmdqd6mb8mj27qVvQZRR7sjshrXYYirWm9vRttLkNB5rW6
QmSjY85vxbu9nNFHUMmuK7CxRame2VYuhb523CJaK5zRkj
QmZwah9nZHVvSzbJWEAMxumYDpanFPqTahnqoNP83tuZbx
QmQWSrGfeYwgf6HE9N3742DJrJwq8uNSCUAz469CnuUFGe
QmcgTTyseF5zFd4MLquM4PtJZzkFcBEqaUbqDe4eaUx6Na
QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu


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

⦿ Techrights  -  Back From a Short Break

⦿ Techrights  -  GeekWire: Microsoft Bribes Us While We Cover Microsoft Affairs (Spin Doctoring), Hence We Are "Independent"

⦿ Techrights  -  IBM Going International (and India)

⦿ Techrights  -  IBM's Chronic Neglect Won't Save Anything and It Might Even Get IBM Sued

⦿ Techrights  -  In Europe and in India Richard Stallman Need Not Duck Anymore, People Trying to Cancel His Talk Have No Sway

⦿ Techrights  -  IRC Proceedings: Sunday, February 16, 2025

⦿ Techrights  -  Microsoft Lunduke Belongs in 4Chan

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  The Attacks on LinuxQuestions.org

⦿ Techrights  -  The "Cool Kids" Are Already Using GNU/Linux, Microsoft is Just Cheating

⦿ Techrights  -  The GNU Manifesto Turns 40 Next Month

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2025/02/17/Back_From_a_Short_Break.shtml
https://techrights.org/n/2025/02/17/GeekWire_Microsoft_Bribes_Us_While_We_Cover_Microsoft_Affairs_S.shtml
https://techrights.org/n/2025/02/17/IBM_Going_International_and_India.shtml
https://techrights.org/n/2025/02/17/IBM_s_Chronic_Neglect_Won_t_Save_Anything_and_It_Might_Even_Get.shtml
https://techrights.org/n/2025/02/17/In_Europe_and_in_India_Richard_Stallman_Need_Not_Duck_Anymore_P.shtml
https://techrights.org/n/2025/02/17/IRC_Proceedings_Sunday_February_16_2025.shtml
https://techrights.org/n/2025/02/17/Microsoft_Lunduke_Belongs_in_4Chan.shtml
https://techrights.org/n/2025/02/17/Over_at_Tux_Machines.shtml
https://techrights.org/n/2025/02/17/The_Attacks_on_LinuxQuestions_org.shtml
https://techrights.org/n/2025/02/17/The_Cool_Kids_Are_Already_Using_GNU_Linux_Microsoft_is_Just_Che.shtml
https://techrights.org/n/2025/02/17/The_GNU_Manifesto_Turns_40_Next_Month.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2025/02/17/Gemini_Links_17_02_2025_Ideal_OS_AuraRepo_Alpha_and_Simple_Code.shtml
https://techrights.org/n/2025/02/17/Links_17_02_2025_Blogroll_Conundrum_Research_Scientists_Under_S.shtml
https://techrights.org/n/2025/02/17/Links_17_02_2025_LLMs_Failing_and_Patreon_Support_Becoming_a_Bu.shtml
https://techrights.org/n/2025/02/17/Links_17_02_2025_War_on_Dissent_and_Bloggers_Nationalism_a_Grow.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 80

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/17/Back_From_a_Short_Break.shtml
    Gemini version at https://techrights.org/n/2025/02/17/Back_From_a_Short_Break.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Back From a Short
Break⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


ASIDE from routinary posts (Daily Links, IRC logs, recent articles being listed
etc.) we've hardly published anything since Saturday. This was intentional;
family time was prioritised (and our birds of course).


Today (in the morning) we also fixed some code, hoping it would speed up core
workflows.


We're glad to say that some sites we called out for harboring Serial Sloppers
(SSs) have taken the issue seriously enough; they seem to understand that LLM
slop doomed one's own site (theirs).


We'd rather take a break and not write much for a couple of days than publish
garbage or bot stuff. We never play with chatbots or publish anything machine-
generated.


We can now resume and try to stick to the usual pace. █




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⢾⠘⡆⠈⠁⠀⢻⡯⠿⠭⣿⣓⠙⣽⣧⡞⣿⣞⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡿⢿⠿⠟⠟⠟⠛⢐⣮⡺⣿⡻⠒⣼⠅⠀⠀⠀⣄⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⢿⣿⠇⠘⢻⠋
⢤⣀⡉⠒⠐⣷⡎⢿⣯⠙⡠⣻⢾⠿⠟⠤⠬⠀⠨⣍⡏⣿⣷⣯⣏⣻⣿⡿⣿⣿⣿⣿⣿⣿⠿⣷⣿⣿⣿⠯⠯⠿⠿⠛⠻⡟⠉⠁⣓⡊⠜⠋⠙⠚⡛⣷⠛⠂⠠⠤⠀⢠⡶⠦⠲⢂⡉⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣟⣿⣦⠄⠈⠁⠘⠇⢞⠹⣦⣾⣔⠌⡔⠀⢀⠴⠃⠐⣻⠿⣿⣿⣓⣻⠛⣫⢯⣝⣿⣿⡋⠚⢻⣿⢛⡃⢮⣳⣑⣈⣯⠀⠀⠠⣈⣍⡀⡢⠀⢄⣀⣵⣎⡄⠀⠀⠍⠈⠁⢀⡀⠻⠏⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠗⠿⣿⡅⠀⠀⢀⣦⣾⣼⣾⡿⢯⠀⠀⠌⣻⣶⣤⡨⣈⡄⢀⠉⣿⣝⣅⡤⣠⢾⣹⣻⣿⣦⣾⠛⣿⢾⣻⡚⢂⠥⡟⡉⠑⡤⠉⠝⠃⢡⡃⠀⠀⠚⠛⠃⠀⣠⣤⢤⢢⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠁⢸⢧⡄⢰⣶⣿⣿⡎⠹⠇⠀⠀⠘⢆⢿⣿⣿⣾⡿⣿⣵⡽⣹⣿⡟⠋⣩⡋⣿⡙⠻⢿⣗⡆⢰⣋⢬⣷⡅⠀⣿⣭⠿⠇⠀⠈⠀⠀⢀⠀⣳⣴⣓⣷⠷⢰⣿⣿⡿⢩⠳⢤⣀⠀⠀⠀⢤⣄⡄⠀⠀⠀⠀⠀⠀
⣤⣀⠠⢬⣦⢠⠀⢿⣿⣿⣏⡀⢀⡷⣶⠺⡓⢺⣿⣥⣿⣿⣷⣿⣿⣞⡿⠅⡒⠋⠉⢛⠂⠀⡒⠳⢏⣾⣻⣷⣿⣿⣿⠿⢏⠡⣾⡷⡄⠀⢸⣷⢡⠿⢁⣣⣳⣴⣿⣿⣿⣀⡟⡀⡀⠈⠑⠒⠦⠀⠉⠋⠀⠀⠀⠀⠀⠀
⠋⠉⢧⢸⡇⢬⠞⠈⠃⠡⣼⣷⢀⣴⡯⢯⠥⢯⡽⢷⣿⣿⣿⣿⡟⣊⠢⠃⣗⣷⣦⣤⠹⢗⡱⠟⢻⢗⣯⣿⣽⣿⣏⡷⣤⣴⡿⢁⡀⠺⢷⣿⣶⢾⣿⣿⣼⣿⣿⣿⣿⣿⡿⠋⠁⠛⠁⠃⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 148

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/17/GeekWire_Microsoft_Bribes_Us_While_We_Cover_Microsoft_Affairs_S.shtml
    Gemini version at https://techrights.org/n/2025/02/17/GeekWire_Microsoft_Bribes_Us_While_We_Cover_Microsoft_Affairs_S.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GeekWire: Microsoft Bribes Us While We
Cover Microsoft Affairs (Spin Doctoring), Hence We Are
"Independent"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


What good is a "journalist" sponsored by the very same company he or she writes
about? What good is a "reporter" salaried to relay lies for the company that
salary comes from?


Welcome_to_GeekWire.


They're doing_it_again_today:


     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Trump_layoffs_hit_Pacific_Northwest_engineers_and
               researchers_at_PNNL,_Hanford_cleanup,_elsewhere⦈_


The top there says "independent" but also bribed by Microsoft. Both cannot be
true. That's mockery of the very concept of journalistic integrity.


One common propaganda theme from GeekWire is that the layoffs aren't quite
'happening', citing some very misleading "headcount" figures [1, 2]. As we
explained and showed some years ago, GeekWire also burns Microsoft
whistleblowers. █


"One thing is for certain, you will reach the ceiling of what you can deliver.
If every year you are expected to produce, do, achieve lets say 10% more than
the previous year, eventually over time you’ll reach the pinnacle of what you
can do. When you reach that apex and there’s no way you can do 10% more, it at
that point you’ll have a very different discussion with your manager as to why
you have failed in your assigned goals. The key at MS is to move around enough,
which seems to start that expectation 10% over somewhat. If you don’t then its
best to leave on your own terms before it gets to that. Even more so since MS
has seemingly turned really ultra cheap on the severance." -One_hour_ago,
anonymous comment.




⣿⢟⣻⠿⢿⠿⡟⠿⢻⠻⠿⠹⠿⠿⣿⣿⠿⠿⢿⣿⣿⠿⠿⣿⠿⠿⠿⢿⣿⡿⠿⠿⣿⣿⠿⢿⠿⠿⢿⣿⡿⠿⠿⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣼⣶⣴⣤⣶⣧⣼⣦⣧⣼⣼⣼⣴⣾⣿⣶⣶⣾⣿⣷⣶⣶⣿⣾⣷⣾⣾⣿⣷⣶⣷⣿⣿⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣛⢛⠛⡛⣿⣿⢟⣟⣿⣻⣿⣿⢻⣿⣿⣿⣟⣿⣟⣻⢿⡿⣿⣿⡿⣿⣿⣿⣟⣟⣿⢿⢿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠿⠿⣿⣿⠿⢿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣀⣀⣿⣿⣀⣸⣿⣇⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⣀⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⣿⡿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⢿⡿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣀⣀⣿⣇⣀⣀⣀⣀⣀⣿⣿⣀⣀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣀⣀⣀⢀⡴⣋⣀⣸⣿⣇⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣿⠿⣿⡿⠿⠿⡿⠿⢿⢿⢿⡿⢿⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⠛⠛⠛⡿⠿⠿⠿⠿⢿⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣀⣁⣀⣀⣀⣇⣋⣀⣛⣓⣸⣘⣃⣀⣀⣀⣀⣛⣛⣛⣛⣸⣈⣁⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣈⣀⣈⣀⣀⣁⣀⣀⣀⣀⣀⣀⣈⣀⣈⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⡿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⢟⠯⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⠒⢲⠒⢲⠒⠚⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣁⣀⣀⣀⣴⣶⣶⣶⣶⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠸⢺⢸⠀⡄⠀⠘⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣤⣏⡋⡈⣉⢝⢉⣁⣩⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣾⣾⣶⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠈⠅⠀⠀⠀⠀⠀⠀⠀⡄⠲⣿⣿⣿⡀⠀⢀⣀⣀⣴⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠈⠀⠈⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠂⠀⠀⠀⠠⠀⠀⠐⠃⠀⠠⠛⢽⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠘⢲⡊⣤⠛⣷⠀⡂⢠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣬⣽⣵⣎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⢠⡘⠀⢁⠀⠓⠞⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⡀⡀⢀⠀⠀⡀⣝⣥⣄⣷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠉⠃⡈⡆⢈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⢉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⢐⣠⣿⣷⡿⠛⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 231

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM Going International (and
India)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025,
updated Feb 17, 2025


Based on new activity in thelayoff.com, IBM isn't waiting until_spring. The
managers made their plans known (the_CEO_talked_about_layoffs_last_month) and
also put staff on notice or threw some PIPs their way. It's not only in north
America; European workers are also "E" (as in, "expensive"):


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


That_was_a_few_hours_ago. 2_hours_earlier:


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


IBM is going "I" (inexpensive, not international):


                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Feb_17_Public_Jobs_listing⦈_


Same time as the above. It's Monday and a national holiday (President's Day).


Cheapening one's workforce might lessen expenses and make income/profit look
good, but that comes at a long-term cost. "Goodwill"_at_IBM_isn't_really_worth
over_60_billion_dollars. That's just fantasy. █




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⣿⣿⣿⣿⡿⢛⢿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢂⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠬⢿⣿⣿⣿⣶⣷⣷⣾⣷⣿⣿⣶⣾⣷⣷⣾⣶⣿⣷⣷⣿⣾⣶⣾⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢾⣾⣿⠉⠉⠉⠉⠉⠉⠉⢩⣽⣿⠭⠭⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣜⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⠒⠒⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢷⠰⠼⠦⡎⠤⠇⠊⠱⠆⣿⠦⡎⠤⡏⠂⡖⠺⠶⡎⠶⠷⠷⠶⠉⠂⣾⡇⠿⠭⠸⢎⢳⢸⣿⠨⠂⣇⢣⡳⠎⡆⡆⡆⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢸⣉⣹⣋⣉⣉⣏⣽⣗⣈⣉⡉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠿⢿⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⡼⣬⣿⣿⣷⣝⡎⢩⡍⣽⠉⣿⠍⢥⡏⢹⡏⢩⠍⠫⠋⢼⡟⢹⠉⣽⠩⡃⠫⢋⣫⡍⣽⠉⣭⠉⢽⠸⢩⢉⢫⢉⠋⢯⣽⠸⢾⠀⢇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣓⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⢻⣿⣿⡿⢛⣛⢛⢛⢛⣿⠛⡛⠛⢟⢟⢫⠛⡟⢛⢟⢟⡟⣟⣿⠙⢻⠻⡛⢻⣛⣛⢟⠿⡛⢛⣻⣛⣛⣻⣟⠛⢻⣟⣙⣛⣻⣛⡻⣟⠟⠛⠛⠛⣛⢿⡟⠟⠛⢟⣛⠿⣻⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣝⣵⣿⣿⡿⠿⢷⢿⣟⣟⣻⠿⠿⠟⡿⠿⡛⡿⠿⣞⠿⠻⣿⠿⠛⣟⡟⠿⠿⠿⡿⢿⢿⡿⢷⠿⡛⠿⢿⠟⠟⢶⠿⠿⠿⠿⢻⠻⢿⠿⠿⡿⠿⠿⠿⠿⠻⢿⡿⠿⠟⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣶⣶⣶⣷⣾⡷⠷⣶⣿⡶⣶⣿⡷⣿⣿⣷⢷⡶⢷⣷⣾⣾⣷⣾⢶⣷⣾⣾⣴⣾⣾⣿⣶⣷⣶⣾⣾⣾⣿⣧⣷⣷⢶⣶⣶⣶⣾⣷⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣬⣵⣤⣥⣤⣥⣭⣤⣀⣬⣿⣭⣤⣼⣬⣥⣤⣤⣧⣤⣤⣼⣥⣤⣤⣬⣇⣤⣴⣤⣤⣤⣧⣤⣬⣤⣼⣬⣠⣧⣤⣥⣤⣼⣼⣭⣴⣤⣤⣯⣬⣮⣬⣿⣧⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣊⣽⣋⣑⣳⣓⣉⣙⣻⣐⣏⣉⣫⣊⣽⣫⣮⣻⣋⣿⣫⣙⣽⣆⣞⣏⣭⣏⣉⣙⣽⣩⣉⣙⣊⣙⣳⣛⣽⣁⣁⣧⣚⣍⣇⣤⣹⣫⣒⣟⣿⣩⣍⣝⣸⣭⣗⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⠹⢹⢝⠏⡫⠩⣯⠍⡉⠙⡯⠙⢙⡿⡍⠩⢿⢹⠩⡻⠋⠭⡭⣽⠍⣽⠝⢉⣽⢝⢯⢽⠿⠉⠍⣯⠭⡏⡏⡫⣟⣋⣉⢹⣍⠍⣽⠭⡟⡏⠋⠩⡋⡽⡏⠉⠉⠹⠹⠽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⠛⣿⡛⡋⣻⣛⢟⣟⢛⡛⣟⡻⡛⢻⢛⡻⣻⣟⡻⡛⣛⡿⣛⣻⠛⢻⣋⠟⠙⢻⢋⠛⠙⢻⠋⠛⠙⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⢿⠻⢿⣿⠿⢿⣿⠋⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣛⣛⣓⣛⣓⣛⣛⣻⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡛⣿⡿⢿⠿⠿⢿⢻⢻⠿⡿⢿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣑⣿⣇⣧⣒⠟⣣⣘⣠⣒⣗⣹⣇⣛⣘⣃⣫⣀⣜⣟⣧⣓⣜⣗⣚⣃⣟⣿⣃⣛⣸⣇⣗⣺⢓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣱⣙⣿⣿⣟⠻⠿⢿⠿⡿⠛⣿⡿⠛⠿⠿⣟⢿⠟⠛⠻⠿⠿⠿⢻⣿⢿⢿⡿⣿⠟⡟⠿⡿⣿⡿⡿⠿⡟⢻⡿⣛⣿⠿⡟⡛⠛⣟⠟⡿⠿⠿⣟⣿⢿⠻⢿⣿⢻⡿⢿⣿⣿⢸⠤⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡷⣿⣿⣿⡷⠾⡷⠾⢽⠷⡶⠶⢶⠶⡶⠶⠷⡾⠶⢶⠶⢶⠷⢶⢶⠷⢷⠶⠿⠶⡶⢷⠾⡾⡶⠷⠷⠶⡶⠶⡦⠾⡶⡶⠷⢶⣾⢿⠷⡷⠶⡽⠷⡾⡾⡶⡶⠷⢾⣶⣾⣿⣿⣮⣭⣭⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠧⢿⣿⣿⣿⣭⣥⣬⣾⣭⣤⣤⣼⣬⣤⣤⣼⣿⣾⣥⣼⣽⣯⣵⣼⣼⣥⣴⣵⣽⣥⣬⣯⣿⣤⣬⣤⣼⣧⣭⣧⣤⣿⣤⣾⣬⣽⣤⣯⣧⣭⣧⣭⣦⣯⣯⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⡸⣨⣿⣿⣧⣴⣴⣶⣦⣧⣵⣴⣮⣤⣤⣤⣽⣦⣶⣧⣇⣴⣵⣠⣵⣼⣷⣾⣮⣮⣤⣴⣦⣷⣦⣤⣦⣥⣴⣮⣤⣤⣶⣷⣬⣼⣷⣬⣤⣴⣵⣿⣦⣿⣽⣬⣦⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣉⣹⣉⣿⣍⢫⣽⣍⣭⣭⣉⣩⣽⣉⣉⣉⣉⣽⣹⣉⣉⣉⣉⣉⣏⣹⣁⣍⣹⣙⣉⣍⣍⣏⣈⣉⣉⣭⣍⣏⣩⣩⣍⡯⣍⣹⣿⣩⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣉⣹⣓⣲⣯⣭⣉⣉⣉⣏⣳⣋⣍⣍⣉⣙⣋⣩⣈⢭⣸⣖⣉⣏⣉⡩⣽⣉⣝⣍⣙⣹⢍⣉⢩⣍⣑⣡⣇⣈⣉⣉⣟⣺⠉⣉⣉⣉⣛⣃⣉⣉⡏⣉⣉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⠹⢿⠛⠿⠛⠿⠭⢹⣉⡉⠟⠻⡿⠙⠿⡯⠙⣙⣟⠝⢿⣛⡿⠛⠛⠫⡟⠛⠛⢹⠛⠽⠟⢹⢛⠻⠛⠛⠏⢻⡟⢻⢟⠻⠟⠋⡟⠻⡛⠋⠙⢹⠉⠛⠻⡟⢻⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣻⠛⠛⣟⡟⢟⣛⢟⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣶⣷⣾⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠛⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣞⣶⣿⣿⣗⣀⣨⣋⣁⣈⣉⣉⣹⣻⣁⣉⣀⣉⣉⣉⣛⢟⣉⣟⣙⣟⣏⣁⣏⣉⢉⣉⣹⣘⣏⣉⣋⣊⣙⣹⣛⣧⣛⣉⢭⣏⣻⣹⣞⣋⣛⣋⣉⣋⣋⣻⣋⣁⣇⣉⣿⣿⣿⡸⠭⠼⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣩⣸⣿⣿⡏⠍⠋⠉⢙⠹⡏⡉⡫⡩⢛⢹⠉⠉⢝⠉⡍⠉⢩⡫⡫⡏⠍⠉⡏⠉⡫⢽⡏⠙⢽⢽⡫⡩⣝⠩⡽⠉⣏⣉⢝⠍⢽⠩⣍⣹⠫⡫⠋⡉⢩⡭⠭⢙⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣹⡹⣿⣿⡟⣛⢟⣛⡟⣛⢻⣋⣛⡛⢛⠋⢿⠻⠛⣛⡛⢻⡙⣿⡟⡟⠟⠛⢛⡛⢛⢿⠟⠛⡟⢙⢛⣟⠛⠛⡛⢻⠛⢛⠛⣟⣛⣻⡛⢛⡟⠛⠋⡟⢟⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣮⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡇⣿⢨⣹⣍⡝⣉⣹⠭⡟⣭⢸⣿⢩⡍⣉⡋⠍⡍⠍⡏⣩⢫⡅⡇⡏⣍⡟⠭⢹⣿⢸⢘⡂⡇⠹⢡⣿⣿⣿⠍⣏⠿⡝⣭⢫⢠⢨⡎⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣾⣾⣾⣿⣮⣶⣵⣷⣬⣾⣿⣾⣷⣽⣆⣍⣱⣵⣷⣿⣦⣶⣷⣷⣿⣇⣨⣹⣿⣾⣾⣷⣷⣷⣿⣿⣿⣷⣵⣟⣲⣷⣵⣾⣾⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⠶⢶⠶⠶⠶⢶⠶⣶⡒⠶⠶⠖⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣿⠉⠉⠉⡉⠉⠉⠉⢹⣿⣿
⣿⣿⣿⠿⠶⠾⠶⠶⠶⠾⠶⠿⠶⠶⠶⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⣿⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡭⠉⢭⢹⣿
⣿⣿⣿⣧⠿⣤⣿⣿⣿⠐⡮⢽⠭⣿⢸⢦⣿⢐⡌⠽⠭⡃⢸⠩⡿⢸⠭⡇⢍⠉⣿⠀⠍⡅⠅⢭⠹⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⣛⣸⢸⣿
⣿⣿⣿⡿⢏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣓⣾⣿⣿⣿⠻⠿⠛⠿⡟⠛⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣛⣴⣿⣿⣿⢶⠶⡶⠶⡷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣯⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣉⣉⣈⣸⣉⣵⣾⢍⣉⣩⣏⣁⣸⢩⣭⣏⣯⣋⣭⣩⣸⣍⣹⣈⣉⣩⣉⣽⣉⣍⣍⣉⣹⣭⣽⣽⣧⣉⣨⣭⣍⣽⣍⣼⣀⣔⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠙⠻⢿⡟⠿⠶⠶⠶⠶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⠶⢶⢶⢶⣶⠶⠶⣶⢸⠛⢿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣦⣾⣶⣽⣷⣵⣶⣿⢸⣤⣾⣿
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⡿⠿⠿⠿⠿⢯⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣻⣇⣿⣐⣺⢘⣘⣸⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣛⣛⣛⣛⣛⣚⣛⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⣛⣿
⣿⣿⣿⡟⣭⠻⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢿⣿⡿⣿⠿⠿⠿⠿⡿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡏⣍⢹⢸⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣟⣬⣥⣬⣧⣴⣥⣬⣥⣤⣤⣹⣥⣤⣤⣤⣧⣤⣧⣤⣬⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣓⣒⣚⣸⣿
⣿⣿⣿⣯⣅⣸⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⣿⣿⣿⡿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣷⣭⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿

                    ䷩ 𝚕𝚒𝚗𝚎 397

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/17/IBM_s_Chronic_Neglect_Won_t_Save_Anything_and_It_Might_Even_Get.shtml
    Gemini version at https://techrights.org/n/2025/02/17/IBM_s_Chronic_Neglect_Won_t_Save_Anything_and_It_Might_Even_Get.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM's Chronic Neglect Won't Save Anything
and It Might Even Get IBM Sued⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


According to OBS Studio, Fedora (Red Hat, IBM) does such a shoddy job with
'universal' Flatpaks that it gives a bad name to OBS Studio. That impacts not
only Fedora users; anyone who uses Flatpaks (e.g. GNOME users, increasingly KDE
too) is affected. It's so bad that OBS_Studio_is_willing_to_take_legal_action.
We've often heard developers complaining about Canonical's packaging (for
Ubuntu), but never heard of threats to take legal action/s over it. There are
already videos about this, e.g. [1, 2]. Some vloggers use OBS Studio (on GNU/
Linux) to make their videos; I too use OBS Studio.


The problem is likely a lack of manpower, not deliberate shoddiness.


As a reminder, over a year ago IBM commanded that some key Fedora contribution
team ("staff") simply stops compiling things for Fedora/Red Hat (it wasn't so
hard or expensive) because IBM does_not_care_about_Free_software_or_Fedora. IBM
does not give an F.


Of course IBM's manic rush to adopt Wayland contributes to this problem. Having
to cater for X and Wayland is a_bit_like_the_"Rust_dilemma"_in_Linux. There's
an_overlap_between_the_Wayland_and_Rust_pushers and it should be noted that
Linus_Torvalds_reserves_backlash_for_people_who_really_deserve_it. █




⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣮⣕⡨⠛⢿⡆⠙⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⣄⡠⠈⠻⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣇⢰⣶⡄⢤⣥⠈⣉⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣆⢻⣿⣶⣌⠣⡙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⡇⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣙⠣⠈⡙⢿⣧⠀⣈⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⠁⣿⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠷⣄⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⢺⡆⢻⣿⣦⣌⠐⢌⡀⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠀⣿⣿⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⣿⣷⡀⢿⣿⣿⣿⣦⣌⠢⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⠰⣿⣿⣿⣆⠹⡿⠿⠟⠛⠛⣛⣋⡉⠉⠉⠉⠉⠉⠛⣛⣛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠘⣿⣇⠸⣿⣿⣿⣿⣿⡆⠂⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠸⣿⡇⣿⢘⣿⠿⡿⣿⡄⠐⠀⠉⠁⣀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⣀⠀⠀⠀⠀⣀⠀⠂⣛⡛⣿⢛⣛⣛⠻⢛⣛⣛⣉⡉⣭⣭⣭⣭⣭⣝⣂⠀⠘⣻⡄⢩⢼⣿⣿⣿⣗⠀⠀⢿⣿⣿⣿
⠛⠛⠿⠿⠟⠇⠸⣟⠇⣿⠀⢻⠠⠈⢻⠗⢰⢻⠾⣤⣽⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠙⠂⣀⣀⡀⠋⠀⢸⡿⠇⡋⣨⡅⣶⡏⠬⢙⣛⡋⣥⣭⣭⣷⣶⣶⣶⣭⣭⣂⠹⣷⠈⢿⣿⣿⣿⣿⡦⠀⠘⣟⡻⢿
⠀⠭⠁⠀⠀⠀⠀⢑⠀⣿⠐⠃⠀⠀⠈⡅⢨⢰⣤⠃⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢟⣛⠃⠇⠀⢠⡶⠇⡃⣩⢥⢲⣆⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⠄⠨⣿⡟⠛⠿⢿⡀⠀⠩⠑⠟
⠐⠂⠀⠀⠀⠀⠀⢸⠀⣙⠀⠀⠀⠀⠀⠆⠘⠀⣤⠌⠎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⢠⡆⣿⣿⡇⠀⠀⣠⣶⡏⢳⣿⣬⣼⣿⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠡⠀⢻⣇⠍⠀⠄⠋⠀⠀⠌⠉
⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣣⣿⣿⡇⠀⠄⡿⠿⢇⠸⠿⢰⡸⠿⢼⡿⠿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠿⠿⡿⢡⣶⣦⣭⣭⠭⠭⣍⣉⣍⢻⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣿⡏⢿⣿⡧⣬⣥⣶⣶⣶⡾⠿⣛⣫⣭⡌⣿⣿⣿⣿⡿⠟⢕⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢸⣿⡸⣿⡇⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣇⢻⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣇⠻⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣜⠻⣷⣮⡙⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠛⠦⠻⠿⢿⣿⣿⣿⣿⡿⢟⡕⣿⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣾⣿⣷⢻⡟⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢿⣿⣿⣿⣿⣿⣿⣿⢸⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⠈⣿⣿⣿⣿⣿⣿⣿⣇⠀⠠⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠰⡣⠻⣛⣭⣵⣶⣶⣶⣶⡔⡱⡣⢢⢕⡪⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣌⠱⢸⣿⣿⣿⣿⣿⣿⣿⣷⢘⡵⣱⢟⡜⡡⣓⢌⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⣿⣿⣦⣝⡻⠿⣿⣿⣿⣿⣿⣇⠞⡵⣫⢞⡴⣡⢆⢡⢹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣿⢰⣿⣶⣬⣭⣛⣛⠿⠎⠵⠡⠫⠾⠵⢟⣼⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⣣⣾⣿⣿⡀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡟⣵⣿⣿⣿⣿⡧⠻⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⠏⣼⣿⣿⣿⣿⢋⣼⡜⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣍⡻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⡏⣾⣿⣿⣿⡿⣡⣿⣿⣇⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠿⣿⡀⣭⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣋⣥⡆⠀⡙⣼⣿⣿⣿⡟⣰⣿⣿⣿⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡎⣁⡻⢿⣿⣿⣶⣶⣮⣭⣭⣭⣶⣶⣿⣿⣿⡿⠃⠀⡇⢹⣿⣿⡟⣸⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣿⣿⣷⣦⣭⣝⣛⣛⣛⣛⣛⣛⣛⣫⣭⣴⣾⡆⠀⢸⢀⢻⣿⢱⣿⣿⣿⣿⣿⣿⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣁⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⢸⣎⢃⣿⣿⣿⣿⣿⣿⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡌⣿⣿⢰⣶⣭⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⢸⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣤⠉⢩⠁⣿⣿⡜⣿⣿⣿⣿⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⢸⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣮⣕⡨⠛⢿⡆⠙⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣄⡠⢈⠻⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣧⢰⣶⡄⢤⣥⠈⣉⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣆⢻⣿⣶⣌⠣⡙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⡇⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣙⠣⠈⡙⢿⣧⠀⣈⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⠁⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠷⣄⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⢺⡆⢻⣿⣦⣌⠐⢌⡀⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⠀⣿⣿⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⣿⣷⡀⢿⣿⣿⣿⣦⣌⠢⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣿⣆⠹⡿⠿⠟⠛⢛⣛⣋⡉⠉⠉⠉⠉⠉⠛⣛⣛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠘⣿⣇⠸⣿⣿⣿⣿⣿⡆⠂⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⠠⣿⠿⣿⣿⣆⠐⠈⠉⠁⣀⠐⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠉⠀⣀⠀⠀⠀⠀⣀⠀⠂⣛⡛⣿⢛⣛⣛⠻⢛⣛⣛⣉⡉⣭⣭⣭⣭⣭⣝⣂⠀⠘⣹⡄⢻⣿⣿⣿⣿⡟⡀⠀⢿⣿⣿⣿
⠛⠻⠿⠿⠿⠇⠸⣟⠇⣿⢈⠻⠠⠈⢻⡟⢰⡿⢾⠠⠩⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠙⠂⣀⣀⡀⠉⠀⢸⡿⠗⡋⣨⡅⣶⡏⠬⢙⣛⡋⣥⣭⣭⣷⣶⣶⣶⣭⣭⣂⠹⣷⠈⢾⣿⣿⣿⣷⡧⠀⠘⣟⣟⣿
⠠⠭⠁⠀⠀⠀⠀⢁⠀⣿⠐⠃⠠⠀⠈⡅⢸⢋⠄⣴⠵⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⢟⣛⠃⠇⠀⢠⡶⠗⡃⣩⢥⢲⣆⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠄⢨⣿⡿⡿⢿⢿⡄⠀⠹⠁⢧
⠐⠂⠀⠀⠀⠀⠀⢸⠀⠋⠀⠀⠀⠀⠀⡆⠘⠥⣥⠄⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡆⣿⣿⡇⠀⠀⣠⣶⣯⢳⣿⣬⣼⣿⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠡⠀⢻⣯⡈⠄⠀⠛⠀⠀⠰⠩
⠀⠀⠀⠀⠀⠁⠀⠸⠀⠆⠐⠀⠐⠀⠀⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣣⣿⣿⡇⠀⠄⡿⠿⢏⠸⠿⢰⡸⠿⢼⡿⠿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠂⠸⠈⠀⠀⠀⠀⠀⠀⠠⡄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠿⠿⡿⢡⣶⣦⣭⣭⠭⠭⣍⣉⣍⢻⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣿⡏⢿⣿⡧⣬⣥⣶⣶⣶⡾⠿⣛⣫⣭⡌⣿⣿⣿⣿⡿⠟⢕⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢸⣿⡸⣿⡇⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣇⢻⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣧⠻⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣜⠻⣷⣮⡙⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠛⠦⠻⠿⢿⣿⣿⣿⣿⡿⢟⡕⣿⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣾⣿⣷⢻⡟⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢿⣿⣿⣿⣿⣿⣿⣿⢸⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⠈⣿⣿⣿⣿⣿⣿⣿⣇⠀⠠⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠰⡃⠻⣛⣭⣵⣶⣶⣶⣶⡔⡱⡣⢢⢕⡪⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣌⠱⢸⣿⣿⣿⣿⣿⣿⣿⣷⢘⡵⣱⢟⡜⡡⣓⢌⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⣿⣿⣦⣝⡻⠿⣿⣿⣿⣿⣿⣇⠞⡵⣫⢞⡴⣡⢆⢡⢹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣿⢰⣿⣶⣬⣭⣛⣛⠿⠎⠵⠡⠫⠾⠵⢟⣼⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⣣⣾⣿⣿⡀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡟⣵⣿⣿⣿⣿⡧⠻⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⠏⣼⣿⣿⣿⣿⢋⣼⡜⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣍⡻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⡏⣾⣿⣿⣿⡿⣡⣿⣿⣇⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠿⣿⡀⣭⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣋⣥⡆⠀⡙⣼⣿⣿⣿⡟⣰⣿⣿⣿⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡎⣁⡻⢿⣿⣿⣶⣶⣮⣭⣭⣭⣶⣶⣿⣿⣿⡿⠃⠀⡇⢹⣿⣿⡟⣸⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣿⣿⣷⣦⣭⣝⣛⣛⣛⣛⣛⣛⣛⣫⣭⣴⣾⡆⠀⢸⢀⢻⣿⢱⣿⣿⣿⣿⣿⣿⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣁⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⢸⣎⢃⣿⣿⣿⣿⣿⣿⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡌⣿⣿⢰⣶⣭⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⢸⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣤⢉⢩⠁⣿⣿⡜⣿⣿⣿⣿⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⢸⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠀⢨⣵⡦⣤⡄⢿⡘⣿⣿⣿⣿⢿⣿⡀⣌⡓⢌⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢇⠌⠻⢇⣵⡾⠎⢷⡹⣿⣿⣿⡎⣿⣧⢣⠨⣄⣁⠢⡢⢬⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠈⠀⠉⢰⢠⣤⡈⢷⡹⣿⣿⣷⢸⣿⡄⢧⢹⣿⣿⣦⡀⢤⣍⡒⠦⣍⠛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣤⣴⡖⢸⣿⣿⣿⡆⠳⣜⢿⣿⣇⣿⣧⠈⢆⢻⣿⣿⣿⣆⠻⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢛⣿⢿⡽⠸⢹⣿⣿⣇⠘⢮⡢⡹⢿⡸⣿⡆⠈⠀⢿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣧⠠⣉⠒⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣐⣾⣿⣽⠃⣠⣿⣿⣿⣿⣶⡈⢿⣮⡪⢁⠹⣿⡀⠀⠈⢿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡆⢻⣿⣦⣍⡒⢌⡂⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢠⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⡧⣄⠻⣿⣷⡄⠉⠣⠀⠓⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣦⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣆⠻⣿⠿⠿⠛⣛⣛⣛⣋⣭⠭⠭⠭⢝⣛⠀⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⡈⢿⣷⠀⠈⠢⠀⠀⣀⡀⢻⠋⠄⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣀⡠⣤⢀⣀⣀⡀⠏⣭⣭⣍⣃⠸⢿⣿⢋⣭⡝⢋⣭⡝⣿⢩⣤⣌⠣⠀⣀⢀⣈⡍⣷⠈⣇⠀⠱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠄⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⡅⠁⣿⡏⡝⣿⡇⢀⣻⢸⣿⡇⢸⣿⣇⡅⣿⡏⣿⡇⠈⢹⣿⡏⣥⣿⡄⢻⡀⢀⢍⣍⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠀⠘⣿⣿⣿
⠭⠭⠭⠅⠀⠀⠀⣿⡇⣿⢸⣿⠠⠌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡷⣞⡋⣼⢸⣿⣾⡇⠀⣿⡇⡇⣿⡇⠟⣁⣬⣿⣷⣾⣿⣿⣇⣿⣷⢿⡇⢠⢸⣿⡇⣿⣧⡅⠸⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣿⠐⠀⡄⣿⡇⡇⣿⡇⣾⣿⣿⣿⡇⣿⣿⣿⢿⣿⣯⣼⣿⠘⢸⣿⡇⢹⢻⣿⡄⠻⣦⣤⣤⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡀⠈⣿⣿
⠂⠀⠀⠀⣼⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡄⣿⠸⠿⢿⠸⠿⢠⠸⠿⠿⠆⠀⠿⠷⠾⠟⢃⣿⣿⠿⠿⢇⡻⠯⢭⠸⠿⢰⠼⠿⢬⡼⠿⠇⢸⣼⣿⣽⡀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡄⠄⣿⣷⢰⣶⣶⣶⢠⢈⡭⠶⣛⣛⣭⣭⣵⣶⣶⣶⣿⣿⣿⣷⣶⣎⢿⣦⡈⣉⣤⣤⡘⣿⣿⣿⣿⣿⣿⡟⠙⠈⠺⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢀⢹⣿⢘⣿⣭⡝⡀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣧⠈⣭⣭⣄⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⢿⠀⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⠀⡈⠏⣾⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢰⣿⣿⢿⡎⢿⣿⣿⣿⣿⣿⡆⠐⠠⠀⣿⣿⣿⣿⣿⡀⠀
⣷⠀⠀⠀⠀⣿⡇⢸⡇⢸⠀⠿⢿⣿⣿⣿⢀⣿⡇⠇⢸⣿⣿⣿⣿⣿⣿⣿⡇⢁⣾⣿⡿⡟⠬⢄⣉⡭⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⣿⣿⢸⠈⢿⣮⠿⡜⣿⣿⣿⣿⣿⣷⣾⠀⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⡇⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣘⣍⢵⣾⢘⣛⣭⣵⣾⣆⢿⣿⣿⣿⣿⣿⡟⣡⣬⣿⣿⣿⣿⣿⢸⣿⣿⡀⠀⡜⡔⠀⡇⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣷⠀⠀⠀⠀⣿⣿⠀⣧⢀⡀⠠⠀⣶⣶⣮⠀⣿⣇⢀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠇⣿⢸⣏⢾⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⡆⢀⠀⠀⠁⣸⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⠀
⡿⠀⠀⠀⢈⢽⣿⠀⣿⠈⡄⢀⠴⣇⡍⠉⡇⣿⣿⠈⠈⣿⣿⣿⣿⣿⣿⣿⣷⠸⡸⣦⣝⠢⡹⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⢰⠿⣿⣿⣻⠈⠀⢀⣏⣼⣿⣿⣿⣫⣿⣿⣷⡄⣿⣿⠿⣿⡿⢻⢄
⣿⠀⠀⠀⠰⣽⠸⠀⠀⠀⡆⠠⠁⠃⡀⣸⠁⢹⣿⠀⠀⠍⠹⠋⠻⠿⠿⠿⣿⢗⠀⠀⠬⠙⢨⣭⣭⣭⣵⡜⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⠃⢂⡐⠿⢖⢗⠀⠀⠸⢰⠿⠙⠋⠋⠽⠖⠒⢲⠃⢨⠁⠑⠄⠈⠀⠄
⠩⠀⠀⠀⠐⠧⠲⠀⠠⡀⢀⠀⠐⠀⠀⠁⠁⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠸⠀⠃⠸⠷⠸⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⢰⠀⢑⠀⠀⠀⡀⠀⠀⠊⠄⠢⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀
⠤⠀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠃⠃⠀⠀⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠸⣿⠿⣛⣛⡃⡻⣿⣿⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠃⣾⣿⣿⣿⣿⢐⡔⢍⠈⣿⣿⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠹⢿⣿⣿⣿⣇⠼⣣⠣⣹⣿⣿⣿⢟⣥⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣝⡻⢿⣿⡜⡵⣃⡇⣿⡿⣱⣿⡿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⣿⣿⣿⣷⣶⣥⣬⣵⡇⠟⣼⣿⢟⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⢣⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢪⣛⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⡇⠀⢠⢖⣬⣵⠶⣒⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢪⣛⠿⣶⣭⣭⣯⣭⣭⣶⠾⠀⠀⠸⣿⣿⣿⣧⠀⡇⣿⡟⣵⣿⣿⣿⡿⢟⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⣿⣶⣮⣭⣭⣭⣽⣶⣷⠀⠀⠀⢫⣵⠶⠶⠀⣿⡟⣼⣿⣿⡿⣫⡾⢟⣵⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⣽⣿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⢈⣷⣿⣿⠆⠛⡇⣿⣿⡿⣴⡟⣵⡿⡫⢑⣤⣶⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣷⣶⣭⣭⣶⣧⠀⠀⠀⠘⢏⣴⣾⣿⣧⠱⢨⡻⡇⣿⢹⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⠿⣟⣫⣝⣛⠀⠀⠀⡤⣸⣿⣿⣿⣿⣧⢱⣝⠆⣍⢨⡻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⢿⣿⣵⣾⣿⣿⣿⣿⣿⡆⠀⢳⣿⣿⢟⣫⠭⣽⣇⣿⡷⠎⠀⠙⢮⡻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣨⣶⣿⣿⣿⣿⣿⠿⣛⣯⣭⣤⣬⣗⣙⠵⣫⣶⣿⡿⠃⠁⠀⠀⠀⠀⠈⠻⣦⡻⣿⣿⢇⣿⣿⣿⣿⣿⡿⠿⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣿⣿⣿⡿⢛⢍⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡝⠜⠿⣛⣻⣭⣶⣾⣷⣮⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣞⢟⣥⡾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠀⣀⣠⣤⣴⣶⣶⣾⣿⣶⣍⡻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⢸⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⣋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠀⢨⣵⡦⣤⡄⢿⡘⣿⣿⣿⣿⢿⣿⡀⣌⡓⢌⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢇⠌⠻⢇⣵⡾⠎⢷⡹⣿⣿⣿⡞⣿⣧⢳⠨⣄⣁⠢⡢⢬⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠈⠀⠉⢰⢠⣤⠈⢷⡹⣿⣿⣷⢸⣿⡄⢧⢹⣿⣿⣦⡀⢤⣍⡒⠦⣍⠛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣤⣴⣶⢸⣿⣿⣷⡆⠳⣜⢿⣿⣇⣿⣧⠈⢆⢻⣿⣿⣿⣆⠻⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢛⣾⣻⡿⠸⢹⣿⣿⣇⠘⢮⡢⡹⢿⡸⣿⡆⠈⠀⢿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣧⠠⣉⠒⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣰⣾⣿⣿⠃⣠⣿⣿⣿⣿⣶⡈⢿⣮⡪⢁⠹⣿⡀⠀⠈⢿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡆⢻⣿⣦⣍⡒⢌⡂⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢠⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⠁⢠⣿⣿⣿⣿⣿⣿⡷⣄⠻⣿⣷⡄⠉⠣⠀⠓⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣦⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣆⠻⣿⠿⠿⠛⣛⣛⣛⣫⣭⠭⠭⠭⢝⣛⠀⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤⡈⢿⣷⠀⠈⠢⠀⠀⣁⡀⢻⠋⠄⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣦⠐⠋⠭⢉⣐⢒⣒⣒⣀⡠⣤⢀⣀⣀⡀⡏⣿⣽⣍⣃⠸⠿⣿⢛⣽⡝⢛⣿⡟⣿⢩⣤⣍⡣⢀⣀⣀⣈⡍⣧⠈⣇⠀⢱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠄⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⡅⠁⣿⡏⡝⣿⡇⢀⣿⢸⣿⡇⢸⣿⣇⡅⣿⡏⣿⡇⠈⢹⣿⡏⣥⣿⡄⢻⡀⢀⢍⣍⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠀⠘⣿⣿⣿
⠭⠭⠭⠅⠀⠀⠀⣿⡇⣿⢸⣿⠠⠌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡷⣞⡋⣼⢸⣿⣾⡇⠀⣿⡇⡇⣿⡇⠛⣉⣬⣿⣷⣾⣿⣿⣇⣿⣷⣿⣇⢠⢸⣿⡇⣿⣧⡅⠸⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣿⠐⠀⠄⣿⡇⡇⣿⡇⣾⣿⣿⣿⡇⣿⣿⣿⢿⣿⣯⣼⣿⠘⢸⣿⡇⢹⢿⣿⡄⠻⣦⣤⣤⣄⣀⣀⣽⣻⠈⣿⣿⣿⣿⣿⣿⡀⠈⣿⣿
⠂⠀⠀⠀⣼⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡄⣿⠸⠿⢿⠸⠿⢠⠸⠿⠿⠆⠀⠿⠷⠾⠟⢃⣿⣿⠿⠿⢇⡻⠯⢭⠸⠿⢰⠼⠿⢬⡼⠿⠇⢸⣾⣿⣯⡀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡄⠄⣿⣷⢰⣶⣶⣶⢠⢈⡭⠶⣛⣛⣭⣭⣵⣶⣶⣶⣿⣿⣿⣷⣶⣎⢿⣦⡈⣉⣤⣤⡘⣿⣿⣿⣿⣿⣿⡟⠙⠈⠺⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢀⢹⣿⢘⣻⣭⡝⡀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣧⠈⣭⣭⣄⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⢿⠀⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⠀⡈⠏⣾⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢰⣿⣿⢿⡎⢿⣿⣿⣿⣿⣿⡆⠐⠠⠀⣿⣿⣿⣿⣿⡀⠀
⣷⠀⠀⠀⠀⣿⡇⢸⡇⢸⠀⠿⢿⣿⣿⣿⠀⣿⡇⠇⢸⣿⣿⣿⣿⣿⣿⣿⡇⢁⣾⣿⡿⡟⠬⢄⣉⡭⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⣿⣿⢸⠈⢿⣮⠿⡜⣿⣿⣿⣿⣿⣿⣿⠀⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⣇⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣘⣍⢵⣾⢘⣛⣭⣵⣾⣆⢿⣿⣿⣿⣿⣿⡟⣡⣬⣿⣿⣿⣿⣿⢸⣿⣿⡀⠀⡜⡔⠀⡇⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣷⠀
⣿⠀⠀⠀⠀⣿⣿⠀⣧⢀⡀⠠⠀⣶⣶⣮⠀⣽⣇⢀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠇⣿⢸⣏⢾⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⡆⢀⠀⠀⠡⢸⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⠀
⡟⠀⠀⠀⢈⣭⣿⠀⣿⠈⡄⢀⠴⡇⢩⡝⡇⣿⣿⠈⠈⣿⣿⣿⣿⣿⣿⣿⣷⠸⡸⣦⣝⠢⡹⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⢰⠿⣿⣿⣲⠈⠀⢀⣏⣾⣿⣿⣿⣿⣿⠿⣷⡄⣿⣿⠿⠿⠿⢻⢄
⡿⠀⠀⠀⠰⣾⠬⠀⠀⠀⡆⠠⠦⠷⠀⢸⡁⢹⣿⠀⠀⠉⠹⠋⠻⠿⡿⠻⣿⢗⠀⠀⠬⠙⢨⣭⣭⣭⣵⡜⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⠃⢂⢉⠟⢶⣳⠀⠀⢸⠳⠂⠿⠋⠉⠀⠾⢲⢶⠇⢨⠁⠅⠀⠒⠀⠐
⠩⠀⠀⠀⠐⠿⠖⠀⠠⡂⢀⠀⠑⠈⠈⠂⠁⢸⠊⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠸⠀⠃⠸⢳⠸⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⢰⠀⠁⠀⠀⢘⡄⠀⠀⠁⠆⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⢤⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠸⣿⠿⣛⣛⡃⡻⣿⣿⢹⣿⣿⣿⣿⣿⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠃⣾⣿⣿⣿⣿⢐⡔⢍⠈⣿⣿⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠹⢿⣿⣿⣿⣇⠼⣣⠣⣹⣿⣿⣿⢟⣥⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣝⡻⢿⣿⡜⡵⣃⡇⣿⡿⣱⣿⡿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⣿⣿⣿⣷⣶⣥⣬⣵⡇⠟⣼⣿⢟⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⢣⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢪⣛⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⡇⠀⢠⢖⣬⣵⠶⣒⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢪⣛⠿⣶⣭⣭⣯⣭⣭⣶⠾⠀⠀⠸⣿⣿⣿⣧⠀⡇⣿⡟⣵⣿⣿⣿⡿⢟⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⣿⣶⣮⣭⣭⣭⣽⣶⣷⠀⠀⠀⢫⣵⠶⠶⠀⣿⡿⣼⣿⣿⡿⣫⡾⢟⣵⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⣽⣿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⢈⣷⣿⣿⠆⠛⡇⣿⣿⡿⣴⡟⣵⡿⡫⢑⣤⣶⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣷⣶⣭⣭⣶⣧⠀⠀⠀⠘⢏⣴⣾⣿⣧⠱⢨⡻⡇⣿⢹⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⠿⣟⣫⣝⣛⠀⠀⠀⡤⣸⣿⣿⣿⣿⣧⢱⣝⠆⣍⢨⡻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⢿⣿⣵⣾⣿⣿⣿⣿⣿⡆⠀⢳⣿⣿⢟⣫⠭⣽⣇⣿⡷⠎⠀⠙⢮⡻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣨⣶⣿⣿⣿⣿⣿⠿⣛⣯⣭⣤⣬⣗⣙⠵⣫⣶⣿⡿⠃⠁⠀⠀⠀⠀⠈⠻⣦⡻⣿⣿⢇⣿⣿⣿⣿⣿⡿⠿⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣿⣿⣿⡿⢛⢍⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡝⠜⠿⣛⣻⣭⣶⣾⣷⣮⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣞⢟⣥⡾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠀⣀⣠⣤⣴⣶⣶⣾⣿⣶⣍⡻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⢸⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⣋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠀⢨⣵⡦⣤⡄⢿⡘⣿⣿⣿⣿⢿⣿⡀⣌⡓⢌⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢇⠌⠻⢇⣵⡾⠎⢷⡹⣿⣿⣿⡞⣿⣧⢣⠨⣄⣁⠢⡢⠬⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠈⠀⠉⢰⢠⣤⡈⢷⡹⣿⣿⣷⢸⣿⡄⢧⢹⣿⣿⣦⡀⢤⣍⡒⠦⣍⠛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣤⣴⡆⢸⣿⣿⣿⡆⠳⣜⢿⣿⣇⣿⣧⠈⢆⢻⣿⣿⣿⣆⠻⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣯⣿⡽⠸⢹⣿⣿⣇⠘⢮⡢⡹⢿⡸⣿⡆⠈⠀⢿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣧⠠⣉⠒⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣰⣾⣿⣿⠃⣠⣿⣿⣿⣿⣶⡈⢿⣮⡪⢁⠹⣿⡀⠀⠈⢿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡆⢻⣿⣦⣍⡒⢌⡂⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢠⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⠁⢠⣿⣿⣿⣿⣿⣿⡧⣄⠻⣿⣷⡄⠉⠣⠀⠃⣤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣦⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣆⠻⣿⠿⠿⠛⣛⣛⣛⣫⣭⠭⠭⠭⢝⣛⠀⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⡘⢿⣷⠀⠈⠢⠀⠀⣁⠀⢻⠋⠄⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣦⠐⠋⠭⢉⣐⢒⣒⣒⣀⡠⣤⢀⣀⣀⡀⠏⣿⣯⣍⣃⠸⠿⣿⢛⣿⡝⢛⣿⡝⣿⢡⣤⣌⡣⠀⣀⣀⣈⡍⣧⠈⣇⠀⢱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠄⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⡅⠀⣿⡏⡝⣿⡇⢀⣻⢸⣿⡇⢸⣿⣇⡅⣿⡏⣿⡇⠈⢹⣿⡏⣥⣿⡄⢻⡀⢀⢍⣍⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠀⠘⣿⣿⣿
⠭⠭⠭⠅⠀⠀⠀⣿⡇⣿⢸⣿⠠⠌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡷⣞⡋⣼⢸⣿⣾⡇⠀⣿⡇⡇⣿⡇⠟⣁⣬⣿⣷⣾⣿⣿⣇⣿⣷⢿⣇⢠⢸⣿⡇⣿⣧⡄⠸⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣿⠐⠀⡄⣿⡇⡇⣿⡇⣾⣿⣿⣿⡇⣿⣿⣿⢿⣿⣯⣼⣿⠘⢸⣿⡇⢹⢻⣿⡄⠻⣦⣤⣤⣄⣀⣀⣽⣻⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣼⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡄⣿⠸⠿⢿⠸⠿⢠⠸⠿⠿⠆⠀⠿⠷⠾⠟⢃⣿⣿⠿⠿⢇⡻⠯⢭⠸⠿⢰⠼⠿⢬⡼⠿⠇⢸⣼⣿⣭⡀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡆⠄⣿⣷⢰⣶⣶⣶⢠⢈⡭⠶⣛⣛⣭⣭⣵⣶⣶⣶⣿⣿⣿⣷⣶⣎⢿⣦⡈⣉⣤⣤⡘⣿⣿⣿⣿⣿⣿⡟⠙⠈⠺⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢀⢹⣿⢘⣻⣭⡝⡀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣧⠈⣭⣭⣄⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⢿⠀⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⠀⡈⠏⣾⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢰⣿⣿⢿⡎⢿⣿⣿⣿⣿⣿⡆⠐⠠⠀⣿⣿⣿⣿⣿⡀⠀
⣷⠀⠀⠀⠈⣿⡇⢸⡇⢸⠀⠿⢿⣿⣿⣿⠀⣿⡇⠇⢸⣿⣿⣿⣿⣿⣿⣿⡇⢁⣾⣿⡿⡟⠬⢄⣉⡭⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⣿⣿⢸⠈⢿⣮⠿⡜⣿⣿⣿⣿⣿⣷⣿⡀⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⣇⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣘⣍⢵⣾⢘⣛⣭⣵⣾⣆⢿⣿⣿⣿⣿⣿⡟⣡⣬⣿⣿⣿⣿⣿⢸⣿⣿⡀⠀⡜⡔⠀⡇⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠀⣧⢀⡀⠠⠀⣶⣶⣾⠀⣽⡇⢀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠇⣿⢸⣏⢾⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⡆⢀⠀⠀⠡⢸⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⠀
⡿⠀⠀⠀⢨⢩⣿⠀⣿⠈⡄⢀⠴⣏⠍⡋⡇⣿⣿⠈⠈⣿⣿⣿⣿⣿⣿⣿⣷⠸⡸⣦⣝⠢⡹⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⢰⠿⣿⣿⣲⠈⠀⢀⣏⣾⣿⣿⣿⣿⡿⢍⣷⡄⢿⣿⠿⡿⣿⢿⢀
⡿⠀⠀⠀⠰⣚⠭⠀⠈⠀⠆⠠⠦⠤⠀⢸⡃⢹⣿⠀⠀⠉⠩⠉⠑⠁⠻⠫⣿⢗⠀⠀⠬⠙⢨⣭⣭⣭⣵⡜⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⠃⢂⠑⠿⢢⣳⠀⠀⢸⠨⠠⠿⠟⠋⠁⠛⠲⢶⠇⢨⠃⠙⠆⠀⠀⠀
⠩⠀⠀⠀⠐⠗⠐⠀⢠⡀⢀⠀⠋⠀⠀⠁⠁⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠸⠀⠃⠸⠷⠸⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⢰⠈⠀⢂⠀⠐⡀⠀⠀⠁⠆⠈⠀⠀⠀⠀⠀⠊⠃⠐⠁⠀⠂⠀⠀⠀
⠄⠀⠀⠈⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠠⠀⠀⠐⠀⠀⢻⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠸⣿⠿⣛⣛⡃⡻⣿⣿⢹⣿⣿⣿⣿⣿⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠃⣾⣿⣿⣿⣿⢐⡔⢍⠈⣿⣿⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠹⢿⣿⣿⣿⣇⠼⣣⠣⣹⣿⣿⣿⢟⣥⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣝⡻⢿⣿⡜⡵⣃⡇⣿⡿⣱⣿⡿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⣿⣿⣿⣷⣶⣥⣬⣵⡇⠟⣼⣿⢟⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⢣⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢪⣛⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⡇⠀⢠⢖⣬⣵⠶⣒⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢪⣛⠿⣶⣭⣭⣯⣭⣭⣶⠾⠀⠀⠸⣿⣿⣿⣧⠀⡇⣿⡟⣵⣿⣿⣿⡿⢟⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⣿⣶⣮⣭⣭⣭⣽⣶⣷⠀⠀⠀⢫⣵⠶⠶⠀⣿⡿⣼⣿⣿⡿⣫⡾⢟⣵⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⣿⣿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⢈⣷⣿⣿⠆⠛⡇⣿⣿⡿⣴⡟⣵⡿⡫⢑⣤⣶⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣷⣶⣭⣭⣶⣧⠀⠀⠀⠘⢏⣴⣾⣿⣧⠱⢨⡻⡇⣿⢹⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⠿⣟⣫⣝⣛⠀⠀⠀⡤⣸⣿⣿⣿⣿⣧⢱⣝⠆⣍⢨⡻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⢿⣿⣵⣾⣿⣿⣿⣿⣿⡆⠀⢳⣿⣿⢟⣫⠭⣽⣇⣿⡷⠎⠀⠙⢮⡻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣨⣶⣿⣿⣿⣿⣿⠿⣛⣯⣭⣤⣬⣗⣙⠵⣫⣶⣿⡿⠃⠁⠀⠀⠀⠀⠈⠻⣦⡻⣿⣿⢇⣿⣿⣿⣿⣿⡿⠿⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣿⣿⣿⡿⢛⢍⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡝⠜⠿⣛⣻⣭⣶⣾⣷⣮⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣞⢟⣥⡾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠀⣀⣠⣤⣴⣶⣶⣾⣿⣶⣍⡻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⢸⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⣋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡿⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⡘⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣔⢦⠀⠀⠸⣿⢹⣿⣿⣿⡿⣷⠉⣴⣿⣿⣆⢣⠨⣍⣙⡒⠦⢬⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠈⡃⣀⠀⣿⢸⣿⣿⣿⣧⢻⣧⠹⣿⣿⣿⡄⢧⢹⣿⣿⣷⣶⣤⣍⡒⠦⣍⠛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟⢡⣧⡻⢷⠁⢿⢸⣿⣿⣿⣿⣧⡻⣷⡙⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⢸⣿⠟⠐⠋⡸⡏⣿⣿⣿⣿⣧⢷⡝⢷⡜⢿⣿⣷⠘⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠞⢡⣶⣷⢀⢃⢻⡹⣿⣿⣿⣿⢸⣿⡎⠻⣎⢿⣿⣇⢱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⠸⣿⡄⠣⠻⣿⣿⣿⢸⣿⢣⠀⠌⢂⠙⠻⡄⢧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣆⢻⣿⠿⠿⠛⣛⣛⣛⣫⣭⡭⠭⠭⢝⣛⠃⣾⣿⣿⡟⢀⣿⡇⢱⣕⠹⣿⣿⢸⣿⢠⡀⢫⣦⠀⢠⣈⠘⡆⢻⣿⣿⠋⠤⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣀⡠⣤⢠⣤⣀⡄⡟⣿⣿⣇⣘⢿⣿⡈⣟⣷⡌⢻⣸⡇⣾⣣⣨⣿⡂⢨⣿⣶⣌⡈⣿⣿⣇⠐⢱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠄⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⠩⣥⡇⣿⡏⠙⣿⡇⣿⣷⢸⣿⡇⣿⣿⡇⠋⣿⡏⣿⡇⠈⢹⣿⡏⠁⢹⣿⣿⡀⢀⢭⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⠥⠀⠀⠀⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡻⣼⢸⣿⣶⡎⡇⣿⡇⢠⣿⡇⣿⣿⢸⣿⣷⣾⣿⡇⠇⣿⡇⢻⣧⢄⢸⣿⡇⣧⡄⢿⣿⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣿⠀⠶⡇⣿⡇⢀⣿⡇⠿⠋⣘⣿⡇⣶⣿⣷⢴⣿⣤⣼⣿⢸⢸⣿⡇⣿⣷⡈⢿⣿⣦⣤⣤⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡄⣿⠸⠿⢿⠸⠿⢰⠸⠿⠷⠗⠀⠿⠷⠾⢿⣣⣾⣿⣿⣿⣇⡿⠿⠿⠼⠿⢠⠸⠿⠞⠸⠿⠇⣿⣿⣷⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⠄⡯⠀⣿⣿⣿⠀⣸⡿⢟⣛⣭⣭⠶⠶⢿⣿⣿⣷⠦⠻⣿⣿⣿⣿⣆⠛⠟⣛⣉⡘⣿⣿⣿⣿⣿⣿⣿⡟⠙⠈⠺⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢀⢹⡄⣩⣭⣭⢠⠵⣞⣫⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣷⡘⣟⣛⣥⡹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠈⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡇⣭⣭⡍⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡇⢿⣷⣝⢿⣌⢻⣿⣿⣿⣿⣿⡇⠐⠠⠀⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠈⣿⡇⢸⡇⢸⡀⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⣰⣿⣿⢑⡘⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⡘⡎⠻⡟⢈⠆⣿⣿⣿⣿⣿⣿⣿⡀⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⣇⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠠⢟⣭⡏⢶⣛⣫⣥⣸⣿⣿⣿⣿⠿⠫⢽⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣷⠁⢤⢀⠁⠄⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠈⣧⢀⡀⠰⠀⣶⣶⣾⠀⣿⣧⢠⢸⣿⣿⣿⣿⣿⣿⣿⣇⢈⣿⢸⣇⢿⣿⣿⣿⡇⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡄⠀⣼⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⡄
⣿⠀⠀⠀⣬⣿⣿⠀⣿⠘⡇⢠⣴⣿⣿⡿⡇⣿⣿⠘⠈⣿⣿⣿⣿⣿⣿⣿⣿⠸⡘⢷⡙⢦⢻⣿⣿⡟⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣾⠈⠆⢫⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⢆
⣿⠀⠀⠀⠸⣿⣿⠀⠹⠀⣇⠸⣿⣿⣿⣿⡇⢹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⣉⢃⣬⣭⣽⣾⡸⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⢹⣿⡿⣿⣿⣿⣿⣿⣿⡀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⢸⣏⣿⣿⣿⣿⣿
⣾⠀⠀⠀⢰⣿⣿⡂⢸⡆⢡⠀⣿⣿⣿⣿⡇⢸⡿⠄⡀⡟⣿⣛⡿⢿⠭⣿⣿⡿⠆⠃⠻⡂⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠰⠈⣿⣿⣿⠿⠿⠿⢿⡿⠿⠧⠸⣻⣿⡿⣿⣿⣿
⣧⡀⢄⠌⠌⠜⠍⠇⠘⡇⠸⡂⠋⠉⠍⣫⡳⠈⠠⡀⠀⠡⣽⣿⡯⡙⣙⢾⢿⣿⢀⠀⠰⣃⢸⣿⣿⣿⣇⢿⣿⣿⡇⣿⣿⣿⣿⣿⠸⠛⠛⠛⠩⠉⠙⠛⠛⠛⠃⢀⠀⠿⠋⠓⠁⠁⠐⠀⠑⠀⠀⠀⠉⠯⠿⠤⠢⠨
⠋⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠜⠛⠓⠍⠂⠙⠒⠃⠐⠈⢠⡘⡌⣵⣶⣶⣶⢐⠙⢿⡇⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣷⡀⣿⣿⣿⣿⣇⢦⢪⠇⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣝⠿⣿⣿⢩⠇⡇⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⣿⣷⣾⣶⣶⡇⣿⣿⣿⡿⣱⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡻⢸⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⣫⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⣨⣝⡻⢿⣿⣿⣿⠿⣫⣀⢾⣿⢟⣵⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣮⣝⣻⠿⠶⠶⠾⢟⣭⢺⡬⣵⣿⡿⠀⠀⢀⡴⣪⣵⡾⣫⣭⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢛⢿⣿⣿⣿⣿⣿⣿⣿⢇⡅⣿⣿⡇⠀⠀⢸⢸⣿⢋⣾⣿⣿⣿⡿⣛⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣭⣟⡻⠿⠟⣩⠸⣿⢘⣛⡃⠀⠀⠸⢸⡏⣾⣿⣿⣿⣫⡾⣫⣾⡿⣣⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⡿⢟⣛⣛⠞⣮⢘⣛⠁⠀⠀⠀⢃⢇⢮⡻⣿⢣⣟⣾⠟⡁⣰⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⢛⣭⣾⣿⣿⣿⣿⢸⣮⣭⡄⠀⠀⠀⢸⢸⣮⡻⢦⢘⣨⣋⢾⢹⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣾⣿⣿⠿⣛⣭⣶⣶⣶⣥⣛⡃⠀⠀⠀⠀⢸⣿⡏⣷⣬⠈⠛⢷⡙⢿⡿⣻⡿⠿⣛⣛⣫⣭⣭⣥⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣿⣿⡿⡋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠈⠛⠃⠋⠁⠀⢀⡀⢙⣣⣥⣷⣾⣿⣮⡻⢿⣿⣿⣿⣿⣿⣶⣕⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡼⢏⡞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣥⣶⣾⣿⣿⣿⣿⣶⣝⢻⣿⣿⣿⣿⣿⣶⣝⢿⣿⣿⣿⣿⣿⣷⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣼⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣣⣿⣿⣿⣿⣿⣿⠿⠿⢛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⠿⣛⣭⣶⣿⣿⣿⣿⠿⢛⣩⣵⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡿⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⡸⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣔⢦⠀⠀⠸⣿⢹⣿⣿⣿⡿⣷⢉⣴⣿⣿⣆⢣⠨⣍⣙⡒⠦⢬⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠈⡃⣀⠀⣿⢸⣿⣿⣿⣧⢻⣧⠹⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡒⠦⣍⠛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟⢡⣧⡻⢷⠁⢿⢸⣿⣿⣿⣿⣧⡻⣷⡙⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⢸⣿⠟⠐⠋⡸⡏⣿⣿⣿⣿⣧⢷⡝⢷⡜⢿⣿⣷⠘⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠞⣁⣶⣷⢀⢃⢻⡹⣿⣿⣿⣿⢸⣿⡎⠻⣎⢿⣿⣇⢱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⠸⣿⡄⠣⠻⣿⣿⣿⢸⣿⢃⠀⠌⢂⠙⠻⡄⢧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣦⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣆⠻⣿⠿⠿⠛⣛⣛⣛⣫⣭⡭⠭⠭⢝⣛⠃⣾⣿⣿⡏⢀⣿⡇⢱⣕⠹⣿⣿⢸⣿⢠⡀⢫⣦⠀⢠⣈⠘⡆⢻⣿⣿⠋⠤⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣀⡠⣤⢠⣤⣀⡄⡟⣿⣿⣇⣘⢿⣿⡈⣿⣷⡌⢻⣸⡇⣾⣣⣨⣿⡂⢨⣿⣶⣌⡈⣿⣿⣇⠐⢱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠌⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⣥⡇⣿⡏⠹⣿⡇⣿⣷⢸⣿⡇⣿⣿⡇⠃⣿⡏⣿⡇⠈⢹⣿⡏⠁⢹⣿⣿⡀⢀⢭⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⠥⠀⠀⠀⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡛⣼⢸⣿⣶⡏⡇⣿⡇⢠⣿⡇⣿⣿⢸⣿⣷⣾⣿⡇⠇⣿⡇⢻⣧⢄⢸⣿⡇⣧⡄⢿⣿⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣿⠀⠶⡇⣿⡇⢀⣿⡇⠿⠛⣘⣿⡇⣾⣿⣷⢴⣿⣤⣼⣿⢸⢸⣿⡇⣿⣷⡈⢿⣿⣦⣤⣤⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡔⣿⠸⠿⢿⠸⠿⢠⠸⠿⠷⠧⠀⠿⠷⠾⢿⣣⣾⣿⣿⣿⣇⡿⠿⠿⠸⠿⢠⠸⠿⠎⠸⠿⠇⣿⣿⣷⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⠄⣯⠀⣿⣿⣿⠀⣸⡿⢟⣛⣭⣭⠶⠶⢿⣿⣿⣷⠦⠻⣿⣿⣿⣿⣆⠛⠛⣛⣉⡘⣿⣿⣿⣿⣿⣿⣿⡟⠙⠈⠺⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢀⢹⡄⣩⣭⣭⢠⠵⣞⣫⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣷⡘⣟⣛⣥⡹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠈⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡧⣭⣭⡍⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡇⢿⣷⣝⢿⣌⢻⣿⣿⣿⣿⣿⡇⠐⠠⠀⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠈⣿⡇⢸⡇⢸⡀⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⣰⣿⣿⢑⡘⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⡘⡎⠻⡟⢈⠆⣿⣿⣿⣿⣿⣿⣿⡀⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⣇⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠠⢟⣭⡏⢶⣛⣫⣥⣸⣿⣿⣿⣿⠿⠫⢽⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣷⠁⢤⠀⠁⠄⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠈⣧⢀⡀⠰⠀⣶⣶⣾⠀⣿⣧⢀⢸⣿⣿⣿⣿⣿⣿⣿⣇⢈⣿⢸⣇⢿⣿⣿⣿⡇⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡄⠀⣼⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⠄
⣿⠀⠀⠀⣬⣿⣿⠀⣿⠘⡇⢠⢴⣿⣿⡿⡇⣿⣿⠘⠈⣿⣿⣿⣿⣿⣿⣿⣿⠸⡘⢷⡙⢦⢻⣿⣿⡟⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⠆⢫⣾⣾⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣆
⣿⠀⠀⠀⠸⣿⣿⠀⠹⠀⣇⢸⣿⣿⣿⣿⡇⢹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⣉⢃⣬⣭⣽⣾⡸⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⢽⣿⡿⣿⣿⣿⣿⣿⣿⡀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⢷⡇⢸⣏⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢰⣿⣿⡀⢸⡆⢡⠀⣿⣿⣿⣿⡇⢸⠿⠄⠀⡿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠃⠻⡀⣿⣿⣿⣿⡇⣿⣿⣿⡗⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠰⠈⣿⣿⣿⣿⣿⢿⠿⣿⠿⠧⠸⣻⣿⣿⢿⣿⣿
⣧⡀⠄⠈⠌⠈⠻⠇⠘⡇⠸⡂⠯⠙⠽⢭⠳⠈⡠⡀⠀⠁⣿⣿⡟⣱⣨⣿⣿⣿⢀⠀⠰⣃⢸⣿⣿⣿⣇⢿⣿⣿⡇⣿⣿⣿⣿⣿⠸⠛⠛⠛⠫⠙⠙⠙⠛⠛⠃⢀⠀⢻⠉⠻⠁⠁⠀⠀⠚⠀⠀⠀⠙⠻⠛⠋⠉⠻
⠋⠁⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠝⠛⠹⠞⠉⠋⠒⠁⠘⠈⢠⡘⡌⣵⣶⣶⣶⢀⠙⢿⡇⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣷⡀⣿⣿⣿⣿⣇⢦⢪⠇⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣝⠿⣿⣿⢩⠇⡇⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⣿⣷⣾⣶⣶⡇⣿⣿⣿⡿⣱⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡻⢸⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⣫⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⣨⣝⡻⢿⣿⣿⣿⠿⣫⣀⢾⣿⢟⣵⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣮⣝⣻⠿⠶⠶⠾⢟⣭⢺⡬⣵⣿⡿⠀⠀⢀⡴⣪⣵⡾⣫⣭⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢛⢿⣿⣿⣿⣿⣿⣿⣿⢇⡅⣿⣿⡇⠀⠀⢸⢸⣿⢋⣾⣿⣿⣿⡿⣛⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣭⣟⡻⠿⠿⣩⠸⣿⢘⣛⡃⠀⠀⠸⢸⡏⣾⣿⣿⣿⣫⡾⣫⣾⡿⣣⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⡿⢟⣛⣛⠞⣮⢘⣛⠁⠀⠀⠀⢃⢇⢮⡻⣿⢣⣟⣾⠟⡁⣰⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⢛⣭⣾⣿⣿⣿⣿⢸⣮⣭⡄⠀⠀⠀⢸⢸⣮⡻⢦⢘⣨⣋⢾⢹⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣾⣿⣿⠿⣛⣭⣶⣶⣶⣥⣛⡃⠀⠀⠀⠀⢸⣿⡏⣷⣬⠈⠛⢷⡙⢿⡿⣻⡿⠿⣛⣛⣫⣭⣭⣥⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣿⣿⡿⡋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠈⠛⠃⠋⠁⠀⢀⡀⢙⣣⣥⣷⣾⣿⣮⡻⢿⣿⣿⣿⣿⣿⣶⣕⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠼⢏⡞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣥⣶⣾⣿⣿⣿⣿⣶⣝⢻⣿⣿⣿⣿⣿⣶⣝⢿⣿⣿⣿⣿⣿⣷⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣼⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣣⣿⣿⣿⣿⣿⣿⠿⠿⢛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⠿⣛⣭⣶⣿⣿⣿⣿⠿⢛⣩⣥⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡿⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⡘⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣔⢦⠀⠀⠸⣿⢹⣿⣿⣿⡿⣷⠉⣴⣿⣿⣆⢣⠨⣍⣙⡒⠦⢬⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠈⡃⣀⠀⣿⢸⣿⣿⣿⣧⢻⣧⠹⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡒⠦⣍⠛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟⢡⣧⡻⢷⠁⢿⢸⣿⣿⣿⣿⣧⡻⣷⡙⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⢸⣿⠟⠐⠋⡸⡏⣿⣿⣿⣿⣧⢷⡝⢷⡜⢿⣿⣷⠘⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠖⣁⣶⣷⢀⢃⢻⡹⣿⣿⣿⣿⢸⣿⡎⠻⣎⢿⣿⣇⢱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣦⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⠸⣿⡄⠣⠻⣿⣿⣿⢸⣿⢃⠀⠌⢂⠙⠻⡄⢧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣆⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠭⢝⣛⠃⣾⣿⣿⡏⢀⣿⡇⢱⣕⠹⣿⣿⢸⣿⢠⡄⢫⣦⠀⢠⣈⠘⡆⢻⣿⣿⠋⠤⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣀⡠⣤⢠⣤⣀⡄⡟⣿⣿⣇⣘⢿⣿⡈⣟⣷⡌⢻⣸⡇⣾⣣⣨⣿⡂⢨⣿⣶⣌⡈⣿⣿⣇⠐⢱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠄⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⣥⡇⣿⡏⠹⣿⡇⣿⣷⢸⣿⡇⣿⣿⡇⠋⣿⡏⣿⡇⠈⢹⣿⡏⠁⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⠥⠀⠀⠀⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡛⣼⢸⣿⣶⡏⡇⣿⡇⢠⣿⡇⣿⣿⢸⣿⣷⣾⣿⡇⠇⣿⡇⢻⣧⢄⢸⣿⡇⣧⡄⢿⣿⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣟⠀⠶⡇⣿⡇⢀⣿⡇⠿⠋⣘⣿⡇⣾⣿⣷⢴⣿⣤⣼⣿⢸⢸⣿⡇⣿⣷⠈⢿⣿⣦⣤⣤⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡔⣿⠸⠿⢿⠸⠿⢠⠸⠿⠿⠷⡀⠿⠷⠾⢿⣣⣾⣿⣿⣿⣇⡿⠿⠿⠸⠿⢠⠸⠿⠞⠸⠿⠇⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⠄⡯⠀⣿⣿⣿⠀⣸⡿⢟⣛⣭⣭⠶⠶⢿⣿⣿⣷⠦⠻⣿⣿⣿⣿⣆⠛⠟⣛⣉⡘⣿⣿⣿⣿⣿⣿⣿⡟⠙⠈⠺⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢀⢹⡄⣩⣭⣭⢠⠵⣞⣫⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣷⡘⣟⣛⣥⡹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⢿⠈⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡧⣭⣭⡍⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡇⢿⣷⣝⢿⣌⢻⣿⣿⣿⣿⣿⡇⠐⠠⠀⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠈⣿⡇⢸⡇⢸⡀⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⣰⣿⣿⢑⡘⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⡘⡎⠻⡟⢈⠇⣿⣿⣿⣿⣿⣿⣿⡀⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⣇⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠠⢟⣭⡏⢶⣛⣫⣥⣸⣿⣿⣿⣿⠿⠫⢽⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣷⠁⢤⠀⠁⠄⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠈⣧⢀⡀⠰⠀⣶⣶⣾⠀⣿⣇⢀⢸⣿⣿⣿⣿⣿⣿⣿⣇⢈⣿⢸⣇⢿⣿⣿⣿⡇⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡄⠀⣼⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⡄
⣿⠀⠀⠀⣬⣿⣿⠀⣿⠘⡇⢠⣴⣿⣿⡿⡇⣿⣿⠘⠈⣿⣿⣿⣿⣿⣿⣿⣿⠸⡘⢷⡙⢦⢻⣿⣿⡟⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣾⠈⠂⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢆
⣿⠀⠀⠀⠸⣿⣿⠀⠹⠀⣇⢸⣿⣿⣿⣿⡇⢹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⣉⢃⣬⣭⣽⣾⡸⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⢽⣿⡿⣿⣿⣿⣿⣿⣷⡀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⢸⣏⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢰⣿⣯⡀⢸⡆⢡⠀⣿⣿⣿⣿⡇⢸⡿⠄⡀⡿⣿⣿⣿⣿⣽⣿⣿⡿⠆⠃⠹⡀⣿⣿⣿⣿⡇⣿⣿⣿⡯⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⠈⣿⣿⣿⠿⣿⢿⠿⣿⠿⠧⠸⣻⣿⡿⢿⣿⣿
⣧⡄⠄⠈⠌⠨⠋⠇⠘⡇⠘⡂⠯⠙⠭⢭⠷⠈⡰⡀⠀⠫⣿⣿⡟⣘⣤⣻⣿⣿⢀⠀⠰⣃⢸⣿⣿⣿⣇⢿⣿⣿⡇⣿⣿⣿⣿⣿⠸⠛⠛⠙⠫⠙⠙⠛⠛⠻⠃⢀⠀⢻⠉⠓⠉⠀⠀⠃⠊⠀⠀⠀⠙⠛⠛⠛⠙⠻
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠛⠛⠉⠙⠋⠑⠁⠐⠈⢠⡘⡌⣵⣶⣶⣶⢀⠙⢿⡇⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣷⡀⣿⣿⣿⣿⣇⢦⢪⠇⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣝⠿⣿⣿⢩⠇⡇⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⣿⣷⣾⣶⣶⡇⣿⣿⣿⡿⣱⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡻⢸⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⣫⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⣨⣝⡻⢿⣿⣿⣿⠿⣫⣀⢾⣿⢟⣵⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣮⣝⣻⠿⠶⠶⠾⢟⣭⢺⡬⣵⣿⡿⠀⠀⢀⡴⣪⣵⡾⣫⣭⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢛⢿⣿⣿⣿⣿⣿⣿⣿⢇⡅⣿⣿⡇⠀⠀⢸⢸⣿⢋⣾⣿⣿⣿⡿⣛⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣭⣟⡻⠿⠟⣩⠸⣿⢘⣛⡃⠀⠀⠸⢸⡏⣾⣿⣿⣿⣫⡾⣫⣾⡿⣣⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⡿⢟⣛⣛⠞⣮⢘⣛⠁⠀⠀⠀⢃⢇⢮⡻⣿⢣⣟⣾⠟⡁⣰⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⢛⣭⣾⣿⣿⣿⣿⢸⣮⣭⡄⠀⠀⠀⢸⢸⣮⡛⢦⢘⣨⣋⢾⢹⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣾⣿⣿⠿⣛⣭⣶⣶⣶⣥⣛⡃⠀⠀⠀⠀⢸⣿⡏⣷⣬⠈⠛⢷⡙⢿⡿⣻⡿⠿⣛⣛⣫⣭⣭⣥⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣿⣿⡿⡋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠈⠛⠃⠋⠁⠀⢀⡀⢙⣣⣥⣷⣾⣿⣮⡻⢿⣿⣿⣿⣿⣿⣶⣕⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡼⢏⡞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣥⣶⣾⣿⣿⣿⣿⣶⣝⢻⣿⣿⣿⣿⣿⣶⣝⢿⣿⣿⣿⣿⣿⣷⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣼⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣃⣿⣿⣿⣿⣿⣿⠿⠿⢛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⠿⣛⣭⣶⣿⣿⣿⣿⠿⢛⣩⣥⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡘⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⡛⠁⠀⢸⣿⣿⣿⣿⣿⣧⢹⡿⣋⣴⣿⣿⣆⢣⠨⣍⣙⡒⠦⢬⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⡙⣆⠀⢸⣿⣿⣿⣿⣿⣧⢆⢼⣿⣿⣿⣿⣿⡄⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⡇⣮⣦⢸⣿⣿⣿⣿⣿⣿⡜⡎⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⠁⣬⡛⠘⣿⢸⣿⣿⣿⣿⢱⡹⡜⢿⣿⣿⣿⣿⣷⠘⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢰⠟⢀⡁⣿⢸⣿⣿⣿⣿⢸⣷⠹⡄⠙⠿⣿⣿⣿⣇⢱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢡⣾⣿⡇⢸⡟⣿⣿⣿⣿⢸⣿⢨⠌⠂⠀⣈⠻⣿⣿⡄⢧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⠻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠭⣙⡛⢠⣿⣿⣿⠃⡀⢧⢿⣿⣿⡟⣿⡏⢸⣿⠀⣄⠘⢦⣈⠻⢿⠘⡆⢻⣿⣿⠋⠤⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣀⡠⣤⢠⣤⣠⡜⡟⣿⣏⣄⣛⠘⡼⣿⣿⣻⡟⢇⣿⡟⠀⢨⣤⣀⠙⢳⣤⣁⣹⡈⣿⣿⣇⠐⢱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠌⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⣥⡇⣿⡏⣽⣿⡇⠀⢻⣿⣿⡇⢸⣿⡇⡀⣿⡏⣿⡇⢨⢹⣿⡏⣅⢸⣿⣿⡀⢀⢽⣍⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⠥⠀⠀⠀⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡻⣼⢸⣿⣾⡎⡇⣿⡇⠿⣿⡇⣄⢂⠹⣿⣷⣾⣿⡇⢇⣿⣇⢿⣇⢠⢸⣿⡇⠸⡄⣿⣿⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣿⠰⠶⡇⣿⡇⠢⣿⡇⠟⠀⠳⣿⡇⢸⣿⡇⢸⣿⣮⣼⣿⠈⢸⣿⡇⡀⢧⠸⣿⣿⣦⣤⣤⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⠸⠿⢿⠸⠿⢰⠸⠿⠿⠷⠀⠿⠷⠾⢿⣣⣾⣿⣿⣿⣇⣾⣿⣧⠸⠿⢱⠸⠿⠞⠸⠿⠇⣷⡈⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡄⢸⣿⣿⣇⢀⠀⣿⣿⠿⢟⣛⣻⣭⣭⣭⣭⣥⠹⣿⣿⣿⣿⣇⠸⠿⠿⠟⢀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠈⠺⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢀⠘⣙⣉⡉⠐⢘⣭⠶⣛⣭⣭⣷⣶⣶⣶⣶⣶⣦⠹⣿⣿⣿⣿⣷⡆⢶⡿⢇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠘⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣛⣿⠣⠀⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⠰⣾⣝⢷⡌⢿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠠⠀⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢸⡀⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⡟⠀⠂⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣆⢳⠙⣷⡝⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⣇⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠰⢿⣻⢑⡺⠭⢖⣃⢿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣎⢰⡌⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠈⣧⢀⡀⠰⠀⣶⣶⣾⠀⣿⣇⢠⢸⣿⣿⣿⣿⣿⣿⡇⡎⡇⣿⢰⣾⣿⣿⣿⡼⣿⣿⣿⣿⢰⣶⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⣿⣿⣿⣿⣿⣿⡄
⣿⠀⠀⠀⣬⣿⣿⠀⣿⠘⡇⢠⡴⣿⣿⡿⡇⣿⣿⠘⠈⣿⣿⣿⣿⣿⣿⣇⠡⡻⢬⠳⣹⣿⣿⣿⡇⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⢿⢅
⣿⠀⠀⠀⠸⣿⣿⠀⠹⠀⣇⠠⣿⣿⣿⣿⡇⢹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⡰⠀⠑⠠⣿⣛⣭⡆⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡇⢿⣿⢼⣟⣿⣿⣿⢿⣿⣿⡀⡇⢸⣿⣿⣿⣿⣿⣿⡿⢿⣷⡇⢸⣏⣿⣿⣿⣿⣿
⡻⠀⠀⠀⠰⣿⣏⡀⢰⡂⢠⠀⡿⣿⢛⣻⠃⢸⡿⠀⠀⡟⣿⠿⠏⠙⡻⣿⣿⡿⡇⠃⠀⣿⣿⣿⣇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢃⣿⣿⡿⡿⣿⡻⢿⣿⣿⢿⡇⠠⠀⣿⠟⡛⠛⢻⡿⡛⠛⡿⠧⠸⣹⣿⠿⣻⣿⣯
⢦⡀⠄⠌⠘⠉⠬⠇⠐⠇⠘⡀⠔⠈⠞⢢⠳⠈⢺⡀⠀⠁⣝⣹⣅⠘⡠⡙⠟⣿⢀⠀⠀⢻⡿⠿⠿⠸⣿⣿⣿⣿⢸⣿⣿⣿⣿⠸⠈⠀⠋⠐⠉⠎⠈⠘⠚⠫⠃⢀⠀⠻⠀⠁⠀⠂⠀⠐⠘⠀⠀⠀⠘⠋⠹⠅⠉⠍
⠂⠁⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠕⠀⠀⠀⠀⠄⠀⠀⠀⠗⠛⠰⠊⠒⠁⠀⠃⠀⠀⡇⢰⣾⣿⣿⡦⠨⡻⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣿⣿⣇⠵⡐⡹⣿⢸⣿⣿⣿⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣞⠻⣿⣿⡜⡵⢵⢻⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⣿⣶⣭⣥⣴⣿⢸⡼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠣⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⢹⡿⣫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⣬⡻⢿⣿⣿⣿⣿⢟⡃⣿⡎⣾⣿⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⣮⣝⡻⠶⠶⠶⢞⣫⡅⣝⢷⢙⣵⠀⠀⢀⡔⣫⣶⡿⣟⣣⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢛⣿⣿⣿⣿⣿⣿⣿⢇⣿⣷⡜⡏⠀⠀⢸⢸⣿⢏⣾⣿⣿⣿⡿⣛⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣿⣷⣮⣭⣛⣛⣡⡰⣭⡻⢧⠃⠀⠀⠈⡞⡟⢺⣿⣿⣿⢏⠞⣵⣿⠿⡓⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⢟⣫⣭⣧⣻⣿⣶⡀⠀⠀⠀⠁⣷⠱⣝⠻⢣⣏⣾⣿⣧⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⢟⣯⣶⣿⠿⢿⣛⣛⠿⢟⣃⠀⠀⠀⢸⢿⡗⣬⡻⢨⢠⣭⢻⣿⣾⣿⣿⣿⡿⠿⠿⠿⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢏⣿⣿⢟⢉⣴⣾⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠸⢇⠿⠟⠀⠀⠙⠷⠬⣋⣫⣵⣦⣝⢿⣿⣿⣿⣷⣶⣄⡀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⣟⣵⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣀⣠⣤⣤⣶⣶⣮⣙⢿⣿⣿⣿⣿⣷⣍⡻⣿⣿⣿⣿⣿⣮⡲⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⢸⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣉⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⡳⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⠿⣛⣭⣶⣾⣿⣿⣿⠿⠿⢟⣛⣛⣛⣛⣛⣛⡛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⡿⢟⣭⣶⣿⣿⣿⣿⠿⣋⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡘⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⡛⠁⠀⢸⣿⣿⣿⣿⣿⣷⢹⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⡙⣆⠀⢸⣿⣿⣿⣿⣿⣧⢆⢼⣿⣿⣿⣿⣿⡄⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⡇⣮⣦⢸⣿⣿⣿⣿⣿⣿⡜⡎⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⠁⣬⡛⠘⣿⢸⣿⣿⣿⣿⢱⡹⡜⢿⣿⣿⣿⣿⣷⠘⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢰⠟⢀⡁⣿⢸⣿⣿⣿⣿⢸⣷⠹⡄⠙⠿⣿⣿⣿⣇⢱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢡⣾⣿⡇⢸⡟⣿⣿⣿⣿⢸⣿⢨⠌⠂⠀⣈⠻⣿⣿⡄⢧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠭⣝⡛⢠⣿⣿⣿⠁⡁⢧⢿⣿⣿⡟⣿⡏⢸⣿⠀⡄⠘⢦⣈⠻⢿⠘⡆⢻⣿⣿⠋⠤⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣂⡠⣤⢠⣤⣠⡜⡟⣿⣏⣄⣛⠘⡼⣿⣿⣻⡟⢇⣿⡟⠀⢨⣦⣀⠹⢱⣤⣁⣹⡈⣿⣿⣇⠐⢱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠌⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⣥⡇⣿⡏⣽⣿⡇⠀⢻⣿⣿⡇⢸⣿⡇⡀⣿⡏⣿⡇⢨⢹⣿⡏⣅⢸⣿⣿⡀⢀⢽⣍⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⡥⠀⠀⠀⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡻⣼⢸⣿⣾⡎⡇⣿⡇⠿⣿⡇⣆⢂⠻⣿⣷⣾⣿⡇⠇⣿⣇⢿⣇⢠⢸⣿⡇⠸⡄⣿⣿⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣿⠰⠶⡇⣿⡇⠢⣿⡇⠿⠀⠳⣿⡇⢸⣿⡇⢸⣿⣮⣼⣿⠈⢸⣿⡇⡀⢧⠸⣿⣿⣦⣤⣤⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⠸⠿⢿⠸⠿⢠⠸⠿⠿⠷⠀⠿⠷⠾⢿⣣⣾⣿⣿⣿⣇⣾⣿⣧⠸⠿⢱⠸⠿⠞⡸⠿⠇⣷⡌⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡄⢸⣿⣿⣇⢀⠀⣿⣿⠿⢟⣛⣻⣭⣭⣭⣭⣥⠹⣿⣿⣿⣿⣇⠸⢿⠿⠟⢀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠈⠺⣿⣿⣿⣿⣿⡄⡀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢀⠘⣙⣉⡉⠐⢘⣭⠶⣛⣭⣭⣷⣶⣶⣶⣶⣶⣦⠹⣿⣿⣿⣿⣷⡆⢶⡿⢇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠘⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣛⣿⠃⠀⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⠰⣾⣝⢷⡌⢿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠀⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢸⡀⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⡟⠀⠂⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣆⢣⠙⣷⡝⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠰⢿⣻⢑⡺⠭⢖⣃⢿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣎⢰⡌⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠈⣧⢀⡀⠰⠀⣶⣶⣾⠀⣿⣧⢠⢸⣿⣿⣿⣿⣿⣿⡇⡎⡇⣿⢰⣾⣿⣿⣿⡼⣿⣿⣿⣿⢰⣶⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⡄
⣿⠀⠀⠀⣬⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⡿⡇⣿⣿⠘⠈⣿⣿⣿⣿⣿⣿⣇⠡⡻⢬⠳⣹⣿⣿⣿⡇⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢇
⣿⠀⠀⠀⢸⣿⣿⠀⢹⠀⣇⢸⣿⣿⣿⣿⡇⢹⣿⠀⠀⣻⣿⣿⣿⣿⣿⣿⣶⡰⠀⠑⠠⣿⣛⣭⡆⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡇⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⢸⣏⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠰⣿⣯⡇⢰⡂⢑⠀⣿⣿⣿⢯⡇⢸⣿⠄⡄⡿⣿⢿⣏⢟⣿⣿⣿⡿⠇⠃⠀⣿⣿⣿⣇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⢃⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⡇⠰⠈⣿⣟⣿⠿⠏⠽⠙⣿⠿⠧⠸⣹⣿⣹⣿⣿⡿
⢧⡤⢄⠌⠝⠟⠻⠇⠘⠇⠸⡀⠵⢘⠯⣾⡳⠈⢷⡀⠀⠣⣯⣿⡶⣶⣸⠿⣿⢿⢀⠀⠀⢻⡿⠿⠿⠸⣿⣿⣿⣿⢸⣿⣿⣿⣿⠘⠃⠉⠈⠑⠐⠃⠘⠹⠻⠺⠃⢀⠀⠿⠊⠗⠁⠃⠂⠄⠀⠃⠀⠀⠈⠋⠿⠹⠗⠗
⠋⠓⠉⠀⠀⠀⠀⠐⠀⠂⠀⠀⠐⠜⠀⠀⠁⠀⡆⠀⠀⠐⠟⠙⠳⠚⠚⠒⠛⠂⠐⠀⡇⢰⣾⣿⣿⡦⠨⡻⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣿⣿⣇⠵⡐⡹⣿⢸⣿⣿⣿⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣞⠻⣿⣿⡜⡵⢵⢻⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⣿⣶⣭⣥⣴⣿⢸⡼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠣⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⢹⡿⣫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⣬⡻⢿⣿⣿⣿⣿⢟⡃⣿⡎⣾⣿⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⣮⣝⡻⠶⠶⠶⢞⣫⡅⣝⢷⢙⣵⠀⠀⢀⡔⣫⣶⡿⣟⣣⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢛⣿⣿⣿⣿⣿⣿⣿⢇⣿⣷⡜⡏⠀⠀⢸⢸⣿⢏⣾⣿⣿⣿⡿⣛⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣿⣷⣮⣭⣛⣛⣡⡰⣭⡻⢧⠃⠀⠀⠈⡞⡟⢺⣿⣿⣿⢋⠞⣵⣿⠿⡓⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⢟⣫⣭⣧⣻⣿⣶⡀⠀⠀⠀⠁⣷⠱⣝⠻⢣⣏⣾⣿⣧⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⢟⣯⣶⣿⠿⢿⣛⣛⠿⢟⣃⠀⠀⠀⢸⢿⡗⣬⡻⢨⢠⣭⢻⣿⣾⣿⣿⣿⡿⠿⠿⠿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢏⣿⣿⢟⢉⣴⣾⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠸⢇⠿⠟⠀⠀⠙⠷⠬⣋⣫⣵⣦⣝⢿⣿⣿⣿⣷⣶⣄⡀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⣟⣵⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣀⣠⣤⣤⣶⣶⣮⣙⢿⣿⣿⣿⣿⣷⣍⡻⣿⣿⣿⣿⣿⣮⡲⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⢸⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣉⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⡳⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⠿⣛⣭⣶⣾⣿⣿⣿⠿⠿⢟⣛⣛⣛⣛⣛⣛⡛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⡿⢟⣭⣶⣿⣿⣿⣿⠿⣋⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡘⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⡛⠁⠀⢸⣿⣿⣿⣿⣿⣷⢹⡿⣋⣴⣿⣿⣆⢣⠨⣍⣙⡒⠦⢬⣙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⡙⣆⠀⢸⣿⣿⣿⣿⣿⣧⢆⢼⣿⣿⣿⣿⣿⡄⢧⢹⣿⣿⣷⣶⣤⣍⡒⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⡇⣮⣦⢸⣿⣿⣿⣿⣿⣿⡜⡎⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣉⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⠁⣬⡛⠘⣿⢸⣿⣿⣿⣿⢱⡹⡜⢿⣿⣿⣿⣿⣷⠘⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢰⠟⢀⡁⣿⢸⣿⣿⣿⣿⢸⣷⠹⡄⠙⠿⣿⣿⣿⣇⢱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢡⣾⣿⡇⢸⡟⣿⣿⣿⣿⢸⣿⢨⠌⠂⠀⣈⠻⣿⣿⡄⢧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣆⠻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠭⣝⡛⢠⣿⣿⣿⠁⡀⢧⢿⣿⣿⡟⣿⡏⢸⣿⠀⡄⠘⢦⣈⠻⢿⠘⡆⢻⣿⣿⠋⠤⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣀⡠⣤⢠⣤⣠⡜⡟⣿⣏⣐⣛⠘⡼⣿⣿⣻⡟⢃⣿⡟⠀⢨⣦⣀⠙⢳⣤⣁⣹⡈⣿⣿⣇⠐⢱⠐⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠌⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⣥⡇⣿⡏⣽⣿⡇⠀⢻⣿⣿⡇⢸⣿⡇⡀⣿⡏⣿⡇⢨⢹⣿⡏⣅⢸⣿⣿⡀⢀⢽⣍⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⠥⠀⠀⠀⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡻⣼⢸⣿⣾⡎⡇⣿⡇⠿⣿⡇⣄⢂⠻⣿⣷⣾⣿⡇⢇⣿⣇⢿⣇⢠⢸⣿⡇⠸⡄⣿⣿⣇⠈⠈⠉⣈⣄⠌⣿⡇⢹⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠘⢸⣿⠰⠶⡇⣿⡇⠢⣿⡇⠿⠀⠳⣿⡇⢸⣿⡇⢸⣿⣮⣼⣿⠈⢸⣿⡇⡀⢧⠸⣿⣿⣦⣤⣤⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡔⣿⠸⠿⢿⠸⠿⢠⠸⠿⠿⠷⠀⠿⠷⠾⢿⣣⣾⣿⣿⣿⣇⣾⣿⣧⠸⠿⢱⠸⠿⠞⠸⠿⠇⣷⡈⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡄⢸⣿⣿⣇⢀⠀⣿⣿⠿⢟⣛⣻⣭⣭⣭⣭⣥⠹⣿⣿⣿⣿⣇⠸⠿⠿⠟⢀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠈⠺⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢀⠘⣙⣉⡉⠐⢘⣭⠶⣛⣭⣭⣷⣶⣶⣶⣶⣶⣦⠹⣿⣿⣿⣿⣷⡆⢶⡿⢇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⡇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠘⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣛⣿⠃⠀⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⠰⣾⣝⢷⡌⢿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠠⠀⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠈⣿⡇⢸⡇⢸⡀⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⡟⠀⠂⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣆⢳⠙⣷⡝⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⢶⣿⣿⣿⣿⣿⡇⠀
⣿⠀⠀⠀⠀⣿⣇⢸⡇⠘⠃⠐⣀⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠰⢿⣻⢑⡺⠭⢖⣃⢿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣎⢰⡌⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠈⣧⢀⡀⠰⠀⣶⣶⣾⠀⣿⣇⢠⢸⣿⣿⣿⣿⣿⣿⡇⡎⡇⣿⢰⣾⣿⣿⣿⡼⣿⣿⣿⣿⢰⣶⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⡄
⣿⠀⠀⠀⣬⣿⣿⠀⣿⠘⡇⢠⡴⣿⣿⡿⡇⣿⣿⠘⠈⣿⣿⣿⣿⡿⣿⣇⠡⡻⢬⠳⣹⣿⣿⣿⡇⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⢿⢇
⣿⠀⠀⠀⠸⣿⣿⠀⠸⠀⣇⠠⣿⣿⣿⣿⡇⢹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⡰⠀⠑⠨⣿⣛⣭⡆⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡇⢸⣿⣿⣿⣿⣟⣯⣿⠿⢷⠇⢸⣏⣿⣿⣿⣿⣿
⣻⠀⠀⠀⠰⣯⣧⡄⢰⡂⢁⠀⠿⣿⠻⣿⠃⢸⠿⠀⠀⡟⡿⠿⢷⣷⣿⣿⣿⡿⡇⠃⠀⣿⣿⣿⣇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢃⡷⢧⢾⣿⠿⢿⡿⣿⣿⢿⡇⠠⠈⣿⢟⡛⠙⠻⡷⠚⡀⠹⠧⠸⣹⣿⠉⢻⡿⣿
⠦⡀⠄⠌⠛⠉⠹⠇⠀⠇⠘⡀⢐⠉⠞⠧⠳⠈⢘⠀⠀⠁⣿⣭⣮⠉⡣⢛⢻⢿⢀⠀⠀⢻⡿⠿⠿⠸⣿⣿⣿⣿⢸⣿⣿⣿⣿⠘⠑⠰⠮⠦⠋⠉⠨⠻⠛⠺⠃⢀⠀⠟⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠂⠀⠸
⠂⠉⠀⠁⠀⠀⠀⠐⠀⠂⠀⠀⠀⠄⠀⠀⠁⠀⡆⠀⠀⠀⠟⠛⠰⠀⠃⠙⠛⠀⠀⠀⡇⢰⣾⣿⣿⡦⠨⡻⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣿⣿⣇⠵⡐⡹⣿⢸⣿⣿⣿⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣞⠻⣿⣿⡜⡵⢵⢻⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⣿⣶⣭⣥⣴⣿⢸⡼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠣⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⢹⡿⣫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⣬⡻⢿⣿⣿⣿⣿⢟⡃⣿⡎⣾⣿⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⣮⣝⡻⠶⠶⠶⢞⣫⡅⣝⢷⢙⣵⠀⠀⢀⡔⣫⣶⡿⣟⣣⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢛⣿⣿⣿⣿⣿⣿⣿⢇⣿⣷⡜⡏⠀⠀⢸⢸⣿⢏⣾⣿⣿⣿⡿⣛⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣿⣷⣮⣭⣛⣛⣡⡰⣭⡻⢧⠃⠀⠀⠈⡞⡟⢺⣿⣿⣿⢏⠞⣵⣿⠿⡓⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⢟⣫⣭⣧⣻⣿⣶⡀⠀⠀⠀⢁⣷⠱⣝⠻⢣⣏⣾⣿⣧⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⢟⣯⣶⣿⠿⢿⣛⣛⠿⢟⣃⠀⠀⠀⢨⢿⡗⣬⡻⢨⢠⣭⢻⣿⣾⣿⣿⣿⡿⠿⠿⠿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢏⣿⣿⢟⢉⣴⣾⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠸⢇⠿⠟⠀⠀⠙⠷⠬⣋⣫⣵⣦⣝⢿⣿⣿⣿⣷⣶⣄⡀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⣟⣵⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣀⣠⣤⣤⣶⣶⣮⣙⢿⣿⣿⣿⣿⣷⣌⡻⣿⣿⣿⣿⣿⣮⡲⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⢸⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣉⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⡳⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⠿⣛⣭⣶⣾⣿⣿⣿⠿⠿⢟⣛⣛⣛⣛⣛⣛⡛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⡿⢟⣭⣶⣿⣿⣿⣿⠿⣋⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣿⣼⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣿⣿⡇⣿⣿⣿⣿⡝⡎⢿⣿⣿⡿⢋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⠻⠟⠃⣿⣿⣿⣿⣷⢹⡜⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡕⣆⠀⠀⢻⣻⣿⣿⣿⣏⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⡎⢀⡀⢸⣿⣿⣿⣿⣿⡸⡌⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⡇⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⢈⡋⢸⣿⣿⣿⣿⣿⣇⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠜⣁⢸⣿⣿⣿⣿⡿⣿⢸⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠭⣛⠋⢠⣿⡿⠸⣿⣿⣿⣿⡇⣿⡇⡆⠸⠄⢻⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠋⠤⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣂⡠⣤⢠⣄⣤⡟⡟⣅⣀⣏⣻⢿⣿⡇⣿⣇⡐⢀⣠⡄⠙⢻⣿⣿⣻⢻⣿⣇⣹⡈⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣧⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⣥⠃⣿⡏⠉⣿⡏⣿⡇⢹⣿⡇⢸⣿⡇⡇⣾⡏⣿⡏⣬⣹⣿⡏⣥⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⡥⠀⠀⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡻⡞⢸⣿⣶⡏⠀⣿⡇⡀⣿⡇⣿⡇⠘⣿⣷⣾⣿⡇⢇⣿⡇⢿⣧⢿⣸⣿⡇⠸⡄⣿⣿⣇⠈⠈⠉⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠒⠂⠐⠂⠈⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠀⢸⣿⠰⠆⠀⣿⡇⣷⣿⡇⢻⡇⢰⣿⡇⢸⣿⡇⢸⣿⣧⣼⣿⢸⢸⣿⡇⡆⢧⠸⣿⣿⣦⣤⣤⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⠸⠿⢿⠸⠿⢰⠸⠿⠿⠇⠀⠿⠷⠾⠿⠃⣂⣙⠨⣿⣇⡸⠿⠇⠸⠿⢱⠸⠿⠞⡸⠿⠇⣷⠘⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⠁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⠛⢁⣤⣶⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⡀⣿⣿⡄⢻⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠈⠾⣿⣿⣿⣿⣿⡄⠀⠁
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣇⠀⢛⡛⠃⢠⠆⡾⢟⣛⣯⣭⣭⣿⠶⠶⠶⣦⠹⣿⡇⢺⣿⣷⠈⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡿⠃⢀⣼
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⡈⢟⣛⠃⢼⠠⢞⣛⣭⣭⣷⣶⣶⣿⣿⣿⣿⣦⢹⣧⡈⣉⣩⡄⣿⣿⣿⣿⣿⡄⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⡿⠁⢀⡾⣳
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢸⡂⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣿⣿⡟⣰⣿⣿⠀⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⢻⣭⣅⢻⣿⣿⣿⣿⣿⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢶⣿⡿⠁⢠⡟⠝⠋
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⡍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⡿⢱⡿⠿⡇⠥⢄⣉⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⢼⠱⣝⢧⠻⣿⣿⣿⣿⡄⢧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡟⠁⢠⠿⠀⠀⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⠀⣿⣧⢠⢸⣿⣿⣿⣿⡇⠩⣦⢿⡇⣭⣵⣶⣿⡼⣿⣿⣿⣿⢋⣱⣿⣿⣿⣿⡇⣿⣿⡈⠆⡙⡀⡇⣿⣿⣿⣿⣇⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠁⠀⠎⠀⠀⠀⠀
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠘⠘⣿⣿⣿⣿⣷⢠⢻⣜⢷⡹⣿⣿⣿⡇⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡇⢹⣿⣿⣾⣷⡔⠅⣿⣿⣿⣿⣿⠘⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⡀⢻⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣿⣿⣿⣿⣦⣅⣌⡑⠀⣛⣛⣻⣥⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⡄⢧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⡄⢸⡇⢻⠀⣿⣿⣿⣿⣧⢸⣿⠆⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣤⡼⣿⣿⣿⣇⠘⡇⢸⡆⣿⣿⣿⣿⣿⠈⣿⡇⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⠱⢸⣿⣿⣿⡏⢿⣿⣿⡇⣿⣿⣿⣿⣿⢡⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⢿⡿⠋⢹⠿⠀⢇⠘⡁⠹⡟⡿⡟⣑⠀⣟⡠⠀⠘⠟⠿⠿⠟⠛⠛⠛⠃⡎⢘⣭⣷⣶⡆⡪⡻⣿⡇⢻⣿⣿⣿⡿⢘⣇⠈⣛⡇⡙⣛⠉⠉⢋⠛⡛⠝⠋⠀⡅⠠⠹⡛⡷⡱⡁⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠍⠀⠀⠁⠘⡀⠈⠀⠀⢨⡜⠿⠿⠀⠇⠠⠀⠀⠂⠀⠂⠀⠈⠉⠈⠀⠁⣿⠀⣿⣿⣿⣿⢘⡜⡜⠇⠘⣿⣿⣿⡇⡈⢡⠀⠌⡈⠈⠀⢀⣄⠲⠀⠀⠂⠔⠀⢡⢈⠠⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⢃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣷⣝⢿⣿⣿⡏⢞⢸⠀⠀⣿⣿⣿⣷⡐⠐⡀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡇⣿⣿⣷⣭⣟⣓⣩⣾⠀⠀⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⠤⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢑⢿⣿⣿⣿⣿⣿⣿⣿⡈⢸⣿⣿⡿⣣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⠳⣭⣛⡿⠿⠿⢿⣛⡅⠀⡿⣫⣾⡿⠃⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⣿⣶⣭⣛⣛⣛⣫⣭⡆⠁⢺⡿⢫⣴⡇⠀⢠⢚⣵⣾⠟⣛⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣯⣛⡻⠿⣿⡿⣋⡁⠀⠨⣾⣿⣿⠃⠀⠋⣿⡿⣱⣿⣿⣿⡿⢟⣣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⡶⠾⢿⣇⠀⠀⠻⠿⠿⠀⠀⠘⢹⡇⢿⣿⣿⢏⡴⣫⡶⠿⣛⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⢟⣭⣾⣿⣷⣮⣤⠀⠘⠿⣟⠁⠀⠀⢸⣧⡢⣝⢏⡞⢼⣿⢢⣾⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣵⣾⣿⡿⠟⣛⣭⣭⣭⣤⣄⡙⠛⣥⠀⠀⢸⣿⣧⣮⡑⠖⠳⣮⠛⠿⠛⣯⣭⣭⣭⣭⣭⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡹⣿⢟⡵⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠄⣀⣉⣭⣭⣐⠶⣶⣾⣿⣿⣿⣾⣝⡻⢿⣿⣿⣿⣿⣷⣄⢄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢱⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠵⣾⣿⣿⣿⣿⣿⣿⣿⣮⣝⠿⣿⣿⣿⣿⣿⣷⣝⣿⣛⣻⣭⣭⣥⣽⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣮⠱⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣷⣌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⡿⣛⣭⣶⣿⣿⣿⣿⣿⠿⢛⣛⣭⣭⣥⣶⣶⣶⣦⣭⣅⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⣛⣵⣾⣿⣿⣿⣿⡿⢛⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣿⣼⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣿⣿⡇⣿⣿⣿⣿⡝⡎⢿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣽⠻⠟⠃⣿⣿⣿⣿⣷⢹⡜⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡕⣆⠀⠀⢻⣻⣿⣿⣿⣏⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⡎⢀⡀⢸⣿⣿⣿⣿⣿⡸⡌⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⢈⡋⢸⣿⣿⣿⣿⣿⣇⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠜⣁⢸⣿⣿⣿⣿⡿⣿⢸⠈⡙⢿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠭⣛⠋⢰⣿⡿⠸⣿⣿⣿⣿⡇⣿⡇⡆⠹⠄⢻⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠋⠤⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⠃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣒⣒⣂⡠⣤⢠⣄⣤⡟⡟⣅⣀⣏⣻⢿⣿⡇⣿⣇⡐⢀⣠⡄⡙⢻⣿⣿⣻⢻⣿⣧⣹⡈⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠌⢿⣿⣿⣿
⠛⠿⠿⠿⠿⣇⢸⣿⡇⣿⢸⣿⠰⠙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣯⢹⣿⢸⢸⣿⢩⣥⠇⣿⡏⠉⣿⡏⣿⡇⢹⣿⡇⢸⣿⡇⡇⣾⡏⣿⡏⣬⣹⣿⡏⣥⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⡥⠀⠀⠀⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⣿⣞⡻⡞⢸⣿⣾⡏⠀⣿⡇⠀⣿⡇⣿⡇⠘⣿⣷⣾⣿⡇⢇⣿⡇⢿⣧⢿⣾⣿⡇⠸⡄⣿⣿⣇⠈⠈⠉⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠒⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⠀⢸⣿⠰⠆⠀⣿⡇⣧⣿⡇⢻⣇⢰⣿⡇⢸⣿⡇⢸⣿⣧⣼⣿⢸⢸⣿⡇⡆⢧⠸⣿⣿⣦⣤⣬⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⠸⠿⢿⠸⠿⢰⠸⠿⠿⠇⠀⠿⠷⠾⠿⠃⣂⣙⠨⣿⣇⡸⠿⠇⠸⠿⢱⠸⠿⠞⡸⠿⠇⣷⠘⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⡇⠀⠛⢁⣤⣾⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⡀⣿⣿⡀⢻⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠈⠾⣿⣿⣿⣿⣿⡄⠀⠁
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣇⠀⢛⡛⠃⢠⠆⡾⢟⣛⣯⣭⣭⣿⠶⠶⠶⣦⠹⣿⡇⢻⣿⣷⠈⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠃⢀⣼
⡇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠈⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣿⣿⣿⣿⣿⡘⢟⣛⠃⢼⠠⢞⣛⣭⣭⣷⣶⣶⣿⣿⣿⣿⣦⢹⣧⡈⣉⣩⡄⣿⣿⣿⣿⣿⡄⢷⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠀⣿⣿⡿⠁⢀⡾⣳
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢸⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣿⣿⡟⣰⣿⣿⠀⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⢻⣭⣅⢻⣿⣿⣿⣿⣷⠸⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢶⣿⡿⠁⢠⡟⠝⠋
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢙⢿⠘⣿⡇⠀⢸⣿⣿⣿⣿⡿⢱⡿⠿⡇⠥⢄⣉⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⢼⠳⣝⣧⠻⣿⣿⣿⣿⡄⢣⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡟⠁⢠⠿⠀⠀⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣧⢠⢸⣿⣿⣿⣿⡇⠩⣦⢿⡇⣭⣵⣶⣿⡼⣿⣿⣿⣿⢋⣱⣿⣿⣿⣿⡇⣿⣿⡘⠆⡙⡀⡇⣿⣿⣿⣿⣇⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠁⠀⠎⠀⠀⠀⠀
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠘⠘⣿⣿⣿⣿⣷⢠⢻⣜⢷⡹⣿⣿⣿⡇⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡇⢸⣿⣿⣾⣷⡔⠅⣿⣿⣿⣿⣿⠘⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⡀⢻⠀⣷⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣿⣿⣿⣿⣦⣅⣌⡑⠀⣛⣛⣻⣥⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠨⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⡀⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⡆⢸⡇⢿⠀⣿⣿⣿⣿⡇⢸⣿⡆⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣤⣼⢿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡅⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⠣⢸⣿⣿⣿⡏⢿⣿⣿⡇⣿⣿⣿⣿⣿⢡⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠿⡿⣿⡟⠵⣾⡵⠻⠀⢟⠘⡀⠹⡿⣿⢛⠳⠀⣿⡡⠀⠘⠿⠿⠿⠟⠛⠛⠛⠃⡎⢘⣭⣷⣶⡆⡪⡻⣿⡇⢻⣿⣿⣿⡟⠸⡇⠀⢹⣬⡟⢛⢍⠌⠉⠉⡕⠉⠝⠀⡄⠠⡛⣿⣿⠛⢲⢟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠊⠀⠉⡀⠀⠀⡀⢐⠔⠑⠈⢛⡇⠠⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⣿⠀⣿⣿⣿⣿⢘⡜⡜⠇⠘⣿⣿⣿⡇⠈⢇⠀⠌⠉⠉⠁⠠⠽⠀⠁⠀⠀⡀⠀⢱⢀⡌⠈⠁⠁⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣷⣝⢿⣿⣿⡏⢞⢸⠀⠀⣿⣿⣿⣷⡰⠙⡀⠈⠁⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡇⣿⣿⣷⣭⣟⣓⣩⣾⠀⠀⣿⣿⣿⣿⠇⠀⡀⠀⠀⠀⠤⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢑⢿⣿⣿⣿⣿⣿⣿⣿⡈⢸⣿⣿⡿⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⠳⣭⣛⡿⠿⠿⢿⣛⡅⠀⡿⣫⣾⡿⠃⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⣿⣶⣭⣛⣛⣛⣫⣭⡆⠀⢺⡿⢫⣴⡇⠀⢠⢚⣵⣾⠟⣛⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣯⣛⡻⠿⣿⡿⣋⡁⠀⠨⣾⣿⣿⠃⠀⠋⣿⡿⣱⣿⣿⣿⡿⢟⣣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⡶⠾⢿⣇⠀⠀⠻⠿⠿⠀⠀⠘⢹⡇⢿⣿⣿⢏⡴⣫⡶⠿⣛⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⢟⣭⣾⣿⣷⣮⣤⠀⠘⠿⢟⠁⠀⠀⢸⣧⡢⣝⢏⡞⢼⣿⢢⣾⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣵⣾⣿⡿⠟⣛⣭⣭⣭⣤⣄⣙⠛⣥⠀⠀⢸⣿⣇⣮⡑⠖⠳⣮⠛⠿⠛⣯⣭⣭⣭⣭⣭⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡹⣿⢟⡵⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠄⣀⣩⣭⣭⣐⠶⣶⣾⣿⣿⣿⣾⣝⡻⢿⣿⣿⣿⣿⣷⣄⢄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢱⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠵⣾⣿⣿⣿⣿⣿⣿⣿⣮⣝⠿⣿⣿⣿⣿⣿⣷⣝⣿⣛⣻⣭⣭⣥⣽⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣮⠱⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣷⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⡿⣛⣭⣶⣿⣿⣿⣿⣿⠿⢛⣛⣭⣭⣤⣶⣶⣶⣦⣭⣅⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⣛⣵⣾⣿⣿⣿⣿⡿⢛⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣅⢨⣭⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢷⠩⣍⣙⡒⠶⢭⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⡆⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣷⣿⣿⣿⣏⣧⢻⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣼⣿⠿⢻⣿⣿⣿⣿⢸⡏⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣙⠲⢍⡛⢿⣷⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⢸⣿⡇⣿⣇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣏⣆⠀⢸⢻⣿⣿⣿⡆⡇⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡲⢌⡃⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣎⠃⡎⣿⣿⣿⣿⡇⡇⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⡬⢲⢹⣿⣿⣿⣿⡇⡇⢿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⡘⣿⣧⢸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⢸⣿⡇⣿⢸⣿⢿⣿⣿⣧⠐⠋⠭⣉⣐⢒⣲⣒⣒⡠⠀⣸⣸⣿⣟⣟⣏⣹⣁⣂⠌⠻⣿⣟⣈⡟⢻⣿⡟⣿⣻⣿⣿⣻⢻⣿⣧⣹⡘⣿⣿⣇⠐⢱⠒⠨⡔⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⢹⣿⢀⢿⣿⢻⣿⣿⣿⡏⢹⣿⡇⢀⢻⣿⣿⡇⢸⣿⡇⡟⣿⡏⣿⡏⣬⣽⣿⡏⣥⢹⣿⣿⡀⢁⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠸⣿⣿⣿
⠭⠭⢭⣭⠄⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⣿⣞⡛⠘⢸⣿⣾⣿⡏⣿⡇⢸⣿⡇⢸⠘⣿⣿⣷⣾⣿⡇⣇⣿⣧⢿⣧⣿⣿⣿⡇⠸⡄⣿⣿⣇⠘⡌⢩⣘⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⢸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⢸⣿⡟⢸⣿⠀⢸⣿⢸⣿⠁⣿⡇⢸⣿⡇⢸⣆⢹⣿⡇⢸⣿⡇⢻⣿⣯⣼⣿⢸⣿⣿⡇⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⡘⣿⣿⣿⣿⣿⠿⠌⠈⠛⠛
⠂⠀⠀⠀⣿⣿⠈⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⠸⠿⠇⠸⠿⠀⠸⠿⢿⠇⠀⠿⠷⠾⠿⣣⠀⣿⡶⠿⠇⡸⠿⠇⠸⠿⢱⡸⠿⠾⡿⠿⠇⣷⠸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣧⢸⣿⡇⠀⠀⢀⡾⠀⢞⣛⣓⣈⡛⠀⣿⣇⠘⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⠸⣿⣿⠀⢩⣶⣶⣿⣿⣿⣿⣿⣷⡀⣿⣿⠀⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⢟⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⣸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⠀⠿⠿⠇⢸⢟⣛⣯⣭⡿⠶⠶⠶⢶⡌⠿⠀⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⢋⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢻⡇⠿⢿⣿⣿⣿⢠⣿⡇⡇⢹⣿⣿⣿⣇⠾⣛⠃⢘⣯⣽⣶⣾⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣠⣿⡿⣣⠖⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣇⠘⠃⠘⣈⣍⢝⢿⠸⣿⡇⠁⢸⣿⣿⣿⡏⣾⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⢿⠏⡴⠟⠀⠀⠀⠀⣴⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⣿⢰⡛⣽⢸⣒⡢⢴⢹⣿⣿⡿⣏⣿⣿⣿⣿⡇⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠞⠉⠀⠀⠀⠀⠀⠀⢀⣾⡻⡲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⣾⣿⣿⠀⣿⠘⣇⢠⣶⣿⣿⣿⡇⣿⣿⢸⠸⣿⣿⣿⢠⢻⡹⡜⣶⣾⣿⡞⣿⣿⢰⣾⣿⣿⣿⣿⣷⢸⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⠁⠘⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢹⣿⣿⡆⢿⡀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠈⠀⣿⣿⣿⣦⣑⡙⠎⠼⢿⡿⡃⣿⣿⠈⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⣿⠘⣿⣿⣿⣿⣷⢸⣿⡇⡆⣿⣿⣿⣿⣿⣿⢠⢸⣿⣿⣿⢿⡇⣴⢸⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀
⣿⣦⣥⣾⣿⣿⣿⣧⢸⡇⢸⡇⣿⣿⣿⣿⣿⠸⣿⡇⡇⣿⣿⣿⣿⣿⣿⡐⣏⣿⣿⣿⣸⢡⣿⣆⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⣷⢠⠸⠿⠿⠿⠿⠟⠃⡱⢘⣭⣭⣅⢌⢉⣉⠜⣿⣿⣿⣿⡇⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇⠀⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⠀⣷⢸⣿⣿⣿⣿⡇⢠⣴⣶⣶⣶⣶⣿⣿⣿⡇⣷⢸⣿⣿⣿⡀⢂⢻⣧⢹⣿⣿⣿⡇⢿⣿⣿⣿⣿⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣻⣭⣀⣠⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢿⠘⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣷⡙⢿⣿⣧⠠⡸⣿⡇⣿⣿⣿⣿⡌⢿⢿⡟⡿⡇⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⣿⣿⣿⡿⣿⡇⢸⡇⢈⡆⣟⢿⣿⣿⡿⡀⣿⣿⠿⠿⣛⣿⣿⣿⢐⠇⣿⣿⣷⣶⣷⣾⡄⣿⣧⢸⣿⣿⣿⡿⢈⣈⣅⣁⡁⠀⢀⡀⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠍
⡙⠟⠁⠉⠩⠿⡗⠨⠛⠀⡰⠈⡁⠸⢀⢐⠉⡙⠁⣟⣽⠀⣘⠉⠝⠟⢿⠌⠡⣝⠿⣿⣿⣿⡿⡃⢿⣿⡄⢿⡿⣫⣾⡇⣭⢺⣿⣿⣟⡁⡀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣀
⠃⠀⠨⠈⠁⠈⠈⠀⠤⠀⠁⠀⡂⠘⠇⠈⡁⠀⠈⠀⠁⠀⠈⠀⠀⠀⠫⠀⣳⣮⣛⣶⠶⠶⣚⡅⠊⠀⢐⠘⣼⣿⢋⣄⡨⢅⣢⣤⣤⡅⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣃⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡿⢿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣱⣿⣿⢸⣿⡿⣫⣶⣿⡿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⢸⣿⣷⣾⠭⣲⠇⠀⠀⠁⠀⠀⣿⣿⣿⢸⡿⣼⣿⡿⣫⢎⣵⠖⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡼⢟⣭⣶⣿⣿⡿⢀⡀⠃⠄⠀⢨⣽⣾⡾⡇⣿⣿⢱⢣⣿⡕⢼⣛⣛⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣾⣿⡿⡛⣩⣵⣾⣿⣿⣿⣶⣶⣤⡥⠖⠂⣓⣙⡛⢸⣬⣷⣶⣭⣽⣛⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡬⢯⡞⣽⣿⣿⣿⣿⣿⣿⢟⢯⣶⣿⣿⣿⣿⣿⣿⣷⣮⣛⢿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⢸⣿⣿⣿⣿⣿⣟⣵⣿⣿⣶⣝⡿⣿⣿⣿⢿⣛⣭⣶⣾⡿⠿⣛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣾⣿⣿⡿⢟⣭⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣍⠖⡽⣛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣮⣕⡫⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⣿⣿⣿⣿⣿⡟⣴⡿⣸⣿⣿⠏⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣛⢿⣿⣿⡟⣸⡟⠇⣿⣿⠋⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣽⣻⢣⡿⢸⢸⣿⡏⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⣳
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢷⠩⣍⣙⡒⠶⢭⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⡆⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣧⣿⣿⣿⣏⢧⢻⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣼⣿⠿⢻⣿⣿⣿⣿⢸⡎⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣷⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣏⣆⠀⢸⢻⣿⣿⣿⡆⡇⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡲⢌⡃⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣎⠃⡎⣿⣿⣿⣿⡇⡇⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⡬⢲⢹⣿⣿⣿⣿⡇⡇⢿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⡘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⢸⣿⡇⣿⢸⣿⢿⣿⣿⣧⠐⠋⠭⣉⣐⢒⣒⣒⣒⡠⠀⣸⣸⣿⣟⣟⣏⣹⣁⣂⠌⠻⣿⣟⣈⡟⢻⣿⡟⣿⣻⣿⣿⣻⢻⣿⣧⣹⡘⣿⣿⣇⠐⢱⠒⠨⡔⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⢹⣿⢀⢿⣿⢹⣿⣿⣿⡏⢹⣿⡇⢀⢻⣿⣿⡇⢸⣿⡇⡏⣿⡏⣿⡏⣬⣽⣿⡏⣥⢹⣿⣿⡀⢁⣿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠸⣿⣿⣿
⠭⠭⢭⣭⠄⠐⢂⣿⡇⣿⢸⣿⠰⣌⡈⣿⢸⣿⣿⣿⣿⢸⣿⣿⣞⡛⠘⢸⣿⣾⣿⡏⣿⡇⢸⣿⡇⢸⠘⣿⣿⣷⣾⣿⡇⡇⣿⣧⢿⣧⢿⣿⣿⡇⠸⡄⣿⣿⣇⠘⡈⢩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⢸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⢸⣿⡟⢸⣿⠀⢸⣿⢸⣿⠁⣿⡇⢸⣿⡇⢸⣆⢹⣿⡇⢸⣿⡇⢹⣿⣯⣼⣿⢸⣿⣿⡇⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⡘⣿⣿⣿⣿⣿⠿⠈⠈⠛⠛
⠂⠀⠀⠀⣿⣿⠈⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⠸⠿⠇⠸⠿⠀⠸⠿⢿⠇⠀⠿⠷⠾⠿⣣⠀⣿⡴⠿⠇⡸⠿⠇⠸⠿⢱⡸⠿⠞⡿⠿⠇⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣧⢸⣿⡇⠀⠀⢀⡾⠀⢜⣛⣓⣈⡛⠀⣿⣇⠘⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⠘⣿⣿⠀⢩⣶⣶⣿⣿⣿⣿⣿⣷⡀⣿⣿⠀⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⢟⣡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⣸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⠀⠿⠿⠇⢸⢟⣛⣯⣭⡿⠶⠶⠶⠶⡌⠿⠀⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠘⢋⣴⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢻⡇⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⣿⣇⠾⣛⠃⢘⣯⣽⣶⣾⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣠⣿⡟⣣⠖⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣇⠘⠃⠘⣈⣍⢝⢿⠸⣿⡇⠁⢸⣿⣿⣿⡏⣾⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⢿⠏⡴⠟⠀⠀⠀⠀⣴⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣶⣶⣾⡀⣿⣷⢨⢸⣿⣿⣿⢰⡛⣽⢸⣒⡢⢴⢹⣿⣿⡿⣏⣿⣿⣿⣿⡇⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠞⠉⠀⠀⠀⠀⠀⠀⢀⣾⡻⡲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⣇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠸⣿⣿⣿⢠⢻⡹⡜⣶⣾⣿⡞⣿⣿⢰⣾⣿⣿⣿⣿⣷⢸⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⠁⠘⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣿⣿⣦⣑⡙⠎⠼⢿⡿⡃⣿⣿⠈⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⣿⠘⣿⣿⣿⣿⣷⢸⣿⡇⡆⣿⣿⣿⣿⣿⣿⢠⢸⣿⣿⣿⢿⡇⣴⢸⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀
⣿⣦⣥⣾⣿⣿⣿⣧⢸⡇⢸⡇⣿⣿⣿⣿⣿⠸⣿⡇⡇⣿⣿⣿⣿⣿⣿⠐⣏⣿⣿⣿⣸⢡⣿⣆⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⣷⢠⠹⠿⠿⠿⠿⠟⠃⡱⢘⣭⣭⣅⢌⢉⡁⠜⣿⣿⣿⣿⡇⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇⠀⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⠀⣧⢸⣿⣿⣿⣿⡇⢠⣤⣶⣶⣶⣶⣿⣿⣿⡇⣷⢸⣿⣿⣿⡀⢂⢻⣧⢹⣿⣿⣿⡇⢿⣿⣿⣿⣿⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣻⣭⣀⣠⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢿⠘⣽⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⣷⡙⢿⣿⣧⠠⡸⣿⡅⣿⣿⣿⣿⡌⠿⢿⡟⡿⡇⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠟⣿⣿⣿⣿⡇⢸⡇⢈⡆⣞⡿⢿⢿⡿⡀⣿⣿⠏⠿⠻⣿⣿⣿⢐⠇⣿⣿⣷⣶⣷⣾⡄⣿⣧⢸⣿⣿⣿⡿⢈⣈⣁⣁⣀⢀⢀⣀⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠍
⡓⢨⠁⠌⠙⠛⠉⠀⠊⠀⡡⠈⡅⠈⡈⡈⠈⡘⠁⠙⣻⠛⠃⠀⠘⠛⢻⠈⠣⣝⠿⣿⣿⣿⡿⡃⢿⣿⡄⢿⡿⣫⣾⡇⣏⢸⣿⣿⢿⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠁⠀⡂⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣮⣛⣶⠶⠶⣚⡅⠈⠀⢀⠘⣼⣿⢋⣄⡨⢅⣢⣤⣤⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣃⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡿⢿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣱⣿⣿⢸⣿⡿⣫⣶⣿⡿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣷⣾⠭⣲⠇⠀⠀⠀⠀⠀⣿⣿⣿⢸⡿⣼⣿⡿⣫⢊⣵⠖⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡼⢟⣭⣶⣿⣿⡿⢀⡀⠂⠀⠀⢨⣽⣾⡾⡇⣿⣿⢱⢣⣿⡕⢼⣛⣛⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣾⣿⡿⡛⣩⣵⣾⣿⣿⣿⣶⣶⣤⡥⠖⠂⣓⣙⡛⢸⣬⣷⣶⣭⣽⣛⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡬⢯⡞⣽⣿⣿⣿⣿⣿⣿⢟⢭⣶⣿⣿⣿⣿⣿⣿⣷⣮⣛⢿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡞⢸⣿⣿⣿⣿⣿⣟⣵⣿⣿⣶⣝⡿⣿⣿⣿⢿⣛⣭⣶⣾⡿⠿⣛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣾⣿⣿⡿⢟⣭⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣍⠖⡽⣛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣮⣕⡫⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⣿⣿⣿⣿⣿⡟⣴⡿⢸⣿⣿⠏⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣛⢿⣿⣿⡟⣸⡟⠇⣿⣿⠋⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣽⣻⢣⡿⢸⢸⣿⡏⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⣳
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢷⠩⣍⣙⡒⠶⢭⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⡆⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣷⣿⣿⣿⣏⢧⢻⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣼⣿⠿⢻⣿⣿⣿⣿⢸⡎⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣙⠲⢍⡛⢿⣷⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣏⣆⠀⢸⢻⣿⣿⣿⡆⡇⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡲⢌⡃⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣎⠃⡎⣿⣿⣿⣿⡇⡇⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⡬⢲⢹⣿⣿⣿⣿⡇⡇⢿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⡵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⢿⣿⣿⣧⠐⠋⠭⣉⣐⢒⣒⣒⣒⡠⠀⣸⣸⣿⣟⣟⣏⣹⣁⣂⠌⠻⣿⣟⣈⡟⢻⣿⡟⣿⣻⣿⣿⣻⢻⣿⣧⣹⡘⣿⣿⣇⠐⢱⠒⠨⡔⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⢹⣿⢀⢿⣿⢹⣿⣿⣿⡏⢹⣿⡇⠀⢻⣿⣿⡇⢸⣿⡇⡏⣿⡏⣿⡏⣬⣽⣿⡏⣥⢹⣿⣿⡀⢃⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠸⣿⣿⣿
⠭⠭⢭⣭⠄⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⣿⣞⡛⠘⢸⣿⣾⣿⡏⣿⡇⢸⣿⡇⢸⠘⣿⣿⣷⣾⣿⡇⣇⣿⣧⢿⣧⣿⣿⣿⡇⠸⡄⣿⣿⣇⠘⡈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⢸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⢸⣿⡟⢸⣿⠀⢸⣿⢸⣿⠁⣿⡇⢸⣿⡇⢸⣆⢹⣿⡇⢸⣿⡇⢹⣿⣯⣼⣿⢸⣿⣿⡇⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⡘⣿⣿⣿⣿⣿⠿⠌⠈⠛⠛
⠂⠀⠀⠀⣿⣿⠈⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⠸⠿⠇⠸⠿⠀⠸⠿⢿⠇⠀⠿⠷⠾⠿⣣⠀⣿⡰⠿⠇⡸⠿⠇⠸⠿⢱⡸⠿⠞⡿⠿⠇⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣧⢸⣿⡆⠀⠀⢀⡾⠀⢜⣛⣓⣈⡛⠀⣿⣇⠘⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⠸⣿⣿⠀⢩⣶⣶⣿⣿⣿⣿⣿⣷⡀⣿⣿⠀⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⢟⣡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⣸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⠀⠿⠿⠇⢸⢟⣛⣯⣭⡿⠶⠶⠶⠶⡌⠿⠀⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⢋⣴⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢻⡇⠿⢿⣿⣿⣿⢠⣿⡇⡇⢻⣿⣿⣿⣇⠾⣛⠃⢘⣯⣽⣶⣾⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣠⣿⡟⣣⠖⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣇⠘⠇⠘⣈⣍⢝⢿⠸⣿⡇⠁⢸⣿⣿⣿⡏⣾⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⢿⠏⡴⠟⠀⠀⠀⠀⣴⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⣿⢰⡛⣽⢸⣒⡢⢴⢹⣿⣿⡿⣏⣿⣿⣿⣿⡇⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠞⠉⠀⠀⠀⠀⠀⠀⢀⣾⡻⡲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⣇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠸⣿⣿⣿⢠⢻⡹⡜⣶⣾⣿⡞⣿⣿⢰⣾⣿⣿⣿⣿⣷⢸⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⠁⠘⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢹⣿⣿⡆⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣿⣿⣦⣑⡙⠎⠼⢿⡿⡃⣿⣿⠈⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⣿⠘⣿⣿⣿⣿⣷⢸⣿⡇⡆⣿⣿⣿⣿⣿⣿⢠⢸⣿⣿⣿⢿⡇⣴⢸⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀
⣿⣦⣥⣾⣿⣿⣿⣧⢸⡇⢸⡇⣿⣿⣿⣿⣿⠸⣿⡇⡇⣿⣿⣿⣿⣿⣿⠐⣏⣿⣿⣿⣸⢡⣿⣆⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⡇⢻⣿⣿⣿⣿⡀⣿⣷⢠⠸⠿⠿⠿⠿⠟⠃⡱⢘⣭⣭⣅⢌⢉⡁⠜⣿⣿⣿⣿⡇⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇⠀⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⠀⣇⢸⣿⣿⣿⣿⡇⢠⣴⣶⣶⣶⣶⣿⣿⣿⡇⣷⢸⣿⣿⣿⡀⢂⢻⣧⢹⣿⣿⣿⡇⢿⣿⣿⣿⣿⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣻⣭⣀⣠⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡅⢿⠘⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⣷⡙⢿⣿⣧⠠⡸⣿⡅⣿⣿⣿⣿⡌⢿⢿⡟⡿⡇⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⠿⣿⣿⢻⡿⣿⡇⢸⡇⢈⡆⣟⢿⣿⠿⠿⡀⣿⣿⠿⠿⠿⠿⠟⣿⢐⠇⣿⣿⣷⣶⣷⣾⡄⣿⣧⢸⣿⣿⣿⡿⢈⣈⣁⡁⡁⠀⢀⠀⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠍
⠍⢀⡉⠤⠌⠉⠨⠅⡈⠀⠠⠈⠁⠈⠃⢁⠠⡘⠁⠉⠙⠿⠇⠀⠈⠈⢻⠌⠡⣝⠿⣿⣿⣿⡿⡃⢿⣿⡄⢿⡿⣫⣾⡇⢏⢸⣿⡽⢿⡃⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠁⠀⠂⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣮⣛⣶⠶⠶⣚⣅⠈⠀⢑⠘⣼⣿⢋⣄⡨⢅⣢⣤⣤⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣃⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡿⢿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣱⣿⣿⢸⣿⡿⣫⣶⣿⡿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣷⣾⠭⣲⠇⠀⠀⠀⠀⠀⣿⣿⣿⢸⡿⣼⣿⡿⣫⢊⣵⠖⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡼⢟⣭⣶⣿⣿⡿⢀⡀⠂⠀⠀⢨⣽⣾⡾⡇⣿⣿⢱⢣⣿⡕⢼⣛⣛⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣾⣿⡿⡛⣩⣵⣾⣿⣿⣿⣶⣶⣤⡥⠖⠂⣓⣙⡛⢸⣬⣷⣶⣭⣽⣛⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡬⢯⡞⣽⣿⣿⣿⣿⣿⣿⢟⢭⣶⣿⣿⣿⣿⣿⣿⣷⣮⣛⢿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⢸⣿⣿⣿⣿⣿⣟⣵⣿⣿⣶⣝⡿⣿⣿⣿⢿⣛⣭⣶⣾⡿⠿⣛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣾⣿⣿⡿⢟⣭⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣍⠖⡽⣛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣮⣕⡫⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⣿⣿⣿⣿⣿⡟⣴⡿⢸⣿⣿⠏⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣛⢿⣿⣿⡟⣸⡟⠃⣿⣿⠋⣼⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣽⣻⢣⡿⢸⢸⣿⡏⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⣳
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣭⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢷⠩⣍⣙⡒⠶⢭⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣥⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣸⣿⣿⣿⢧⢻⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣷⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⣇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣩⣿⡿⢿⣿⣿⣿⠸⡎⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡲⢌⡃⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⠌⠀⢸⣿⣿⣿⣦⢳⢹⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⡃⡏⢨⣂⣸⡏⣿⣿⣿⡞⡎⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⡘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⢸⣿⡇⣿⢸⣿⢿⣿⣿⣧⠐⠋⠭⣉⣐⢒⣶⣆⣁⡠⢑⢸⣇⣿⡟⣟⣇⣇⣟⣛⢿⣿⣿⣟⣈⡟⢻⣿⡟⣿⣻⣿⣿⣻⢻⣿⣧⣹⡘⣿⣿⣇⠐⢱⠒⠨⡔⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⢹⣿⠀⢸⣿⢹⣿⣿⣿⡏⢩⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⡏⣿⡏⣿⡏⣬⣽⣿⡏⣥⢹⣿⣿⡀⢁⣿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠸⣿⣿⣿
⠭⠭⠭⣭⠄⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡛⠄⢸⣿⣾⣿⣿⣿⡇⠎⣿⡇⣿⣿⣿⣿⣷⣾⣿⡇⣇⣿⣧⢿⣷⢿⣿⣿⡇⠸⡄⣿⣿⣇⠘⡈⢩⣘⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠒⠂⠘⢻⢸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⢸⣿⡇⢸⣿⠀⢸⣿⠠⢸⡟⣿⡇⣆⣿⡇⢻⣿⣿⣿⡇⢸⣿⡇⢹⣿⣯⣼⣿⢸⣿⣿⡇⡆⢧⠸⣿⣿⣦⣤⣭⣅⣀⣀⣽⣿⡘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠈⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⠸⠿⢷⠸⠿⠀⠸⠿⠿⠇⠇⠿⠷⠾⠿⣣⣆⢻⡿⠿⠇⡸⠿⠇⠸⠿⢱⡸⠿⢞⡿⠿⠇⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⠀⣿⣿⣇⠠⠀⣿⣿⠇⠀⠀⠰⣿⡄⠙⣿⢈⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠘⠿⣿⣿⣿⣿⣿⡌⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡄⣿⣿⣿⠠⠤⢛⣩⣤⢰⣆⣶⣦⠁⣼⠃⣎⢹⠖⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⣸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣧⢸⣿⣿⠐⢲⣿⠿⢿⣛⣛⣻⣯⣇⠉⠰⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠷⠸⠿⠿⠿⠿⣿⣿⣿⣿⡇⠔⠰⠈⣿⣿⣿⣿⣿⡄⠈
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢻⡇⠿⢿⣿⣿⣿⢠⣿⡇⡇⢹⣿⣿⡄⣉⣉⠡⠨⣖⣫⣭⣷⣶⣶⣶⣶⣦⡀⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡆⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣇⠘⠃⠘⣈⣍⢝⢿⠸⣿⡇⠁⢸⣿⣿⣷⢩⣽⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⠸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢸⣿⣿⣿⣿⣿⣿⠐
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⡏⣾⣿⢀⣛⣛⠻⢿⣿⣿⡿⣻⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⡀⢋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⣇⢠⣶⣿⣿⣿⡇⣿⣿⢸⠸⣿⣿⠣⢹⢺⠸⣖⣚⣭⡜⣿⡇⣶⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡟⣰⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⢠⡈⢿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⡀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠈⠀⣿⣿⡇⠜⢮⡫⢻⣿⣿⡇⣿⢃⢹⣿⣿⣿⣿⣿⠘⣿⣿⣿⡏⣰⠟⠋⠁⠀⣰⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⣤⡀⠀⢨⢿⡈⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠘⣿⣿⣿⣿⣧⢸⣿⡇⡆⣿⣿⣿⣷⣶⡀⣭⣟⣫⣦⢿⢸⣆⢻⣿⣿⣿⣿⠀⣿⣿⡿⠀⠁⠀⠀⠀⠰⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠼⣿⣷⡀⠀⠈⠃⠸⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣧⢸⡇⢸⡇⣿⣿⣿⣿⣿⠸⣿⡇⡇⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⠈⢸⣿⣎⢿⣿⣿⣿⡆⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠃⢀⣾⣷⣾⣛⣷⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⣷⢠⠸⠿⠿⠿⠿⠃⠁⢙⣻⣭⡄⠀⣉⣉⡘⣿⣿⣿⣧⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⠀⣷⢸⣿⣿⣿⣿⡇⢠⣶⣶⣶⣶⣶⣿⣿⣿⢰⣸⣿⣿⣷⢀⠘⣿⣿⢸⣿⣿⣿⣆⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣥⣤⣶⣿⣿⣟⣯⣭⣻⣿⣿⣿⣿⣿⣿⠶⠾⠿⡇⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢿⠘⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⡏⢸⢰⣝⠿⠿⢆⡅⣿⣿⡌⣿⣿⣿⣿⡄⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠉⠀⠀⢙⣿⣿⣿⣿⣿⣿⣤⣤⣤⣥⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢈⡆⣿⣿⣿⣿⣿⡀⣿⣿⡯⣿⡿⣽⣿⡇⢎⢸⣿⣿⣿⣿⡇⢸⣿⠇⢹⣿⡿⣫⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣃⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⡆⠀⠀⠀⢐⣿⣿
⠤⢇⣉⢟⢇⠈⢾⠿⠈⠀⡱⠈⠅⠘⠃⠙⠂⡽⠅⢿⣽⠶⠎⠉⠛⣛⢏⠠⡳⢽⣛⣟⣛⠅⠀⠈⠀⠀⠻⣵⡿⣫⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⠀⠀⠀⠈⠉⢁
⠁⠂⠑⠐⠄⠈⠠⠚⠢⠀⠁⠀⡃⠘⠈⠞⡈⠀⠀⠈⠀⠀⢅⠈⢛⠅⡰⠀⢽⣷⢮⣭⣷⠟⠀⠀⠀⠀⠂⠻⣱⣿⡆⡾⡂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⡛⢗⢻⣿⣿⡏⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⣿⠶⣒⡃⠀⠀⠀⠀⠀⠀⢿⣿⠧⢺⡟⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣤⣂⠞⡵⢻⣿⡟⠁⠀⠀⠀⠈⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣶⣾⣿⠿⣟⣃⣀⣀⠀⠂⠀⠈⠵⣟⣂⣭⣔⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣷⣠⣿⠏⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⢟⡭⣴⣾⣿⣿⢟⢫⣽⣶⣿⣿⣷⣮⠻⣿⠿⠁⠀⠀⠀⠀⠀⠀⢨⡢⢝⡻⠿⣿⣿⣿⣼⣛⣛⣿⣭⣿⣿⢏⣾⣷⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢨⢛⣾⣿⣿⣿⣵⣿⣷⣝⣿⠿⣻⡭⠒⣉⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣬⡱⠶⣩⢛⡻⠿⠿⠿⠿⢟⣋⣼⣿⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡹⣿⣿⣿⣿⣿⣿⣿⣶⡿⣫⢂⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⡍⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢿⣿⣿⣿⣿⣿⡿⣱⢃⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣟⣥⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢿⣿⣿⣿⢱⡟⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢟⣸⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣽⡻⡟⢸⠃⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢡⡿⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡇⣼⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⢪⣾⣿⣿⣿⣿⠿⢟⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢣⡀⠘⣿⣿⣿⣿⠏⢴⡿⠟⣛⣩⣥⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣛⡻⠿⢿⣿⣿⣿⣿⣷⢀⣀⠈⠻⣷⣦⣄⡀⠀⠀⠀⣛⣂⠨⢉⣿⠟⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣷⣭⡛⢿⣿⡟⢸⣛⠻⠤⣤⠱⡶⣆⣤⢄⠀⠉⠭⠦⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣅⢨⣭⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢷⠩⣍⣙⡒⠶⢭⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣥⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣸⣿⣿⣿⢧⢿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣙⠲⢍⡛⢿⣷⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⣇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣩⣿⡿⢿⣿⣿⣿⠸⡎⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡲⢌⡃⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⠌⠀⢸⣿⣿⣿⣦⢳⢹⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⡃⡏⢨⣂⣸⡏⣿⣿⣿⡞⡎⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⡘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⢸⣿⡇⣿⢸⣿⢿⣿⣿⣧⠐⠋⠭⣉⣐⢒⣶⣦⣁⡠⢑⢸⣇⣿⡟⣟⣇⣇⣟⣛⢿⣿⣿⣟⣈⡟⢻⣿⡟⣿⣻⣿⣿⣻⢻⣿⣧⣹⡘⣿⣿⣇⠐⢱⠒⠨⡔⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⢹⣿⠀⢸⣿⢹⣿⣿⣿⡏⢩⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⡏⣿⡏⣿⡏⣬⣽⣿⡏⣥⢹⣿⣿⡀⢁⣿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠸⣿⣿⣿
⠭⠭⢭⣭⠄⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⡿⣞⡛⠄⢸⣿⣾⣿⣿⣿⡇⠆⣿⡇⣿⣿⣿⣿⣷⣾⣿⡇⣇⣿⣧⢿⣷⢿⣿⣿⡇⠸⡄⣿⣿⣇⠘⡈⢩⣘⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠋⠐⠂⠘⢻⢸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⢸⣿⡇⢸⣿⠀⢸⣿⠠⢸⡟⣿⡇⣆⣿⡇⢻⣿⣿⣿⡇⢸⣿⡇⢻⣿⣯⣼⣿⢸⣿⣿⡇⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⡘⣿⣿⣿⣿⣿⣿⡌⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠈⣿⡇⣿⢸⣿⣿⣷⣦⣿⠨⠭⠄⡖⣿⠸⠿⢷⠸⠿⠀⠸⠿⠿⠇⠇⠿⠷⠾⠿⣣⣆⢻⡿⠿⠇⡸⠿⠇⠸⠿⢱⡸⠿⢾⡿⠿⠇⣷⠸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⠀⣿⣿⣇⠠⠀⣿⣿⠇⠀⠀⠰⣿⡄⠙⣿⢈⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠘⠿⣿⣿⣿⣿⣿⡌⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡄⣿⣿⣿⠠⠤⢛⣩⣤⢰⣆⣶⣦⠁⣼⠃⣎⢹⠖⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⣸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣧⢸⣿⣿⠐⢲⣿⠿⢿⣛⣛⣻⣯⣇⠉⠰⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠷⠸⠿⠿⠿⠿⣿⣿⣿⣿⡇⠔⠰⠈⣿⣿⣿⣿⣿⡄⠈
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢻⡇⠿⢿⣿⣿⣿⢠⣿⡇⡇⢹⣿⣿⡄⣉⣉⠡⠨⣖⣫⣭⣷⣶⣶⣶⣶⣦⡀⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡆⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣇⠘⠃⠘⣈⣍⢝⢿⠸⣿⡇⠁⢸⣿⣿⣷⢩⣽⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⠸⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⡏⣾⣿⢀⣛⣛⠻⢿⣿⣿⡿⣻⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⡀⢋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⣇⢠⣶⣿⣿⣿⡇⣿⣿⢸⠸⣿⣿⠣⢹⢺⠸⣖⣚⣭⡜⣿⡇⣶⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡟⣰⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⢠⡈⢿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⡀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠈⠀⣿⣿⡇⠜⢮⡫⢻⣿⣿⡇⣿⢃⢹⣿⣿⣿⣿⣿⠘⣿⣿⣿⡏⣰⠟⠋⠁⠀⣰⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⣤⡀⠀⢨⢿⡈⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠘⣿⣿⣿⣿⣧⢸⣿⡇⡆⣿⣿⣿⣷⣶⡀⣭⣟⣫⣦⢿⢸⣆⢻⣿⣿⣿⣿⠀⣿⣿⡿⠀⠁⠀⠀⠀⠰⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠼⣿⣷⡀⠀⠈⠃⠸⣿⣿⣿
⣿⣦⣥⣾⣿⣿⣿⣧⢸⡇⢸⡇⣿⣿⣿⣿⣿⠸⣿⡇⡇⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⠈⢸⣿⣎⢿⣿⣿⣿⡆⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠃⢀⣾⣷⣾⣛⣷⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⣷⢠⠸⠿⠿⠿⠿⠃⠁⢙⣻⣭⡄⠀⣉⣉⡘⣿⣿⣿⣧⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⠀⣷⢸⣿⣿⣿⣿⡇⢠⣶⣶⣶⣶⣶⣿⣿⣿⢰⣸⣿⣿⣷⢀⠘⣿⣿⢸⣿⣿⣿⣆⢛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣥⣤⣶⣿⣿⣟⣯⣭⣻⣿⣿⣿⣿⣿⣿⠶⠾⠿⡇⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢿⠘⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⡏⢸⢰⣝⠿⠿⢆⡅⢿⣿⡌⣿⣿⣿⣿⡄⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠉⠀⠀⢙⣿⣿⣿⣿⣿⣿⣤⣤⣤⣥⠀⠀⠀⠀⢸⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⡇⢈⡆⣟⣿⣿⣿⣿⡀⣿⣿⠽⢿⣟⣿⣿⡇⢎⢸⣿⣿⣿⣿⡇⢸⣿⡇⢹⣿⡿⣫⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣃⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⡆⠀⠀⠀⢘⢿⣽
⠟⢃⡙⠶⣞⡛⠿⡥⠋⠀⡱⠈⠅⠸⠈⢀⠤⡾⠅⢟⣙⢄⡔⠚⠃⡀⠎⠠⡳⢽⣛⣟⣛⠅⠐⠈⠀⠀⠻⣵⡿⣫⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⠀⠀⠀⠈⠉⢁
⠀⠩⠉⠀⠄⠌⠉⠍⠠⠀⠁⠀⡃⠈⠈⠉⡂⠀⠀⠉⠄⠁⠘⠀⠓⢯⠰⠀⢽⣷⢮⣭⣷⠟⠀⠀⠀⠀⠂⠻⣱⣿⡆⡾⡂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⡛⢗⢻⣿⣿⡏⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⣿⠶⣒⡃⠀⠀⠀⠀⠀⠀⢿⣿⠧⢺⡟⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣤⣂⠞⡵⢻⣿⡟⠁⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣶⣾⣿⠿⣟⣃⣀⣀⠐⠂⠀⠈⠵⣟⣂⣭⣔⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣷⣠⣿⠏⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⢟⡭⣴⣾⣿⣿⢟⢫⣽⣶⣿⣿⣷⣮⠻⣿⠿⠁⠀⠀⠀⠀⠀⠀⢨⡢⢝⡻⠿⣿⣿⣿⣼⣛⣛⣿⣭⣿⣿⢏⣾⣷⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢨⢛⣾⣿⣿⣿⣵⣿⣷⣝⣿⠿⣻⡭⠒⣉⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣬⡱⠶⣩⢛⡻⠿⠿⠿⠿⢟⣋⣼⣿⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡹⣿⣿⣿⣿⣿⣿⣿⣶⡿⣫⢂⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⡍⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢿⣿⣿⣿⣿⣿⡿⣱⢃⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣟⣥⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢿⣿⣿⣿⢡⡟⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢟⣸⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣽⡻⡟⢸⠃⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢡⡿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡇⣼⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⢪⣾⣿⣿⣿⣿⠿⢟⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢣⡀⠘⣿⣿⣿⣿⠏⢴⡿⠟⣛⣩⣥⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣛⡻⠿⢿⣿⣿⣿⣿⣿⢀⣀⠈⠻⣷⣦⣄⡀⠀⠀⠀⣛⣂⠨⢉⣿⠟⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣷⣭⡛⢿⣿⡟⢸⣛⠻⠤⣤⠱⡶⣆⣤⢄⠀⠉⠭⠦⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⡛⢿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡃⣿⣿⣎⢿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣵⣿⡇⣿⣿⡿⣆⣽⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡾⣿⠇⣿⣿⣇⢻⡜⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⡉⣼⡧⡀⠀⣿⣿⣿⢁⣿⢸⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⢒⣶⣆⣛⡡⢑⣀⣏⣿⡟⣟⣸⣇⣟⣛⢿⣿⣿⣟⣌⡟⢻⣿⡟⣿⣻⣿⣿⣻⢻⣿⣧⣹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⢹⣿⠑⢸⣿⢹⣷⣿⣿⡏⠹⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⡏⣿⡏⣿⡏⣬⣽⣿⡏⣥⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⢸⣿⣿⣞⡋⣴⢸⣿⣦⣿⣿⣿⡇⠀⣿⡇⣿⣿⣿⣿⣷⣾⣿⡇⡇⣿⣧⢿⣧⢿⢿⣿⡇⠸⡄⣿⣿⣇⠘⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⢸⣿⡏⢸⣿⠀⢸⣿⠀⠄⠻⣿⡇⣇⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⢹⣿⣯⣼⣿⢸⢽⣿⡇⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⠸⠿⢧⠸⠿⢀⠸⠿⠿⠷⡀⠿⠷⠾⠿⣃⡙⣿⡿⠿⠇⡸⠿⠇⠸⠿⢱⠸⠿⠞⡸⠿⠇⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣿⡿⠃⢻⠀⠘⣿⣧⠘⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡄⣿⣿⡇⠢⣹⣧⠼⢋⣉⣨⣤⡀⠀⣬⣿⠀⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⢸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣧⢹⣿⡇⠙⢩⣴⣾⣿⣿⣿⣿⠷⠀⢿⡇⣼⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠔⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡇⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⡇⠸⣿⣧⢸⢘⣫⡭⠷⣶⣚⣛⣛⣛⡈⠀⢿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⣿⣿⡄⣤⠦⠀⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣧⠸⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⡟⣰⣿⠀⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠀⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⣿⣿⡇⠟⣻⣸⠭⢵⡊⣿⣿⢰⣾⣿⣿⣿⣿⠀⢹⣿⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣿⡇⠸⡹⣜⢿⣿⣷⣿⣿⠘⣿⣿⣿⣿⣿⡇⠘⡟⣴⡧⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡄⣿⣿⣿⣤⣈⡓⣘⣛⡋⣿⡏⣤⢻⣿⣿⣿⣿⡇⡀⠸⠋⠁⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣤⡀⠀⠰⠻⡄⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠸⣿⡇⡇⣿⣿⣿⣿⣿⡇⢿⣿⣧⣿⠃⠁⡘⣿⣿⣿⣿⡇⠇⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⣠⣞⢿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⠀⣿⢿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⡿⣿⡿⠀⡏⠸⡆⢻⣿⡟⣿⣟⠀⣿⣳⠠⠘⠿⠿⠿⠿⠀⢸⣭⣭⠈⡈⣈⡁⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣀⣴⣿⣿⣥⣾⣿⠿⣷⣯⣥⠀⠀⠀⣼⢿⣿⣿⣿⣿⣟⡄⢿⡗⣿⡿⣿⣷
⠛⢑⡹⣻⡙⣟⣉⢻⡀⢩⠀⣄⢘⣗⣧⢿⣻⠇⢠⡀⡤⣶⡄⡢⢠⡯⢸⠸⣿⣿⡇⣐⢸⣈⡘⣿⣿⢿⣃⠀⠀⠀⠀⠀⠀⠀⣠⣥⣴⡾⠭⢙⣿⣿⣿⣿⡯⠉⠛⠻⣿⠀⠀⠀⡡⠙⢛⠟⠻⡞⣿⠃⢠⣗⢻⣥⢿⡟
⠛⡠⠵⠝⠚⢣⠉⢳⠃⢠⡀⢗⠈⢀⡩⡉⡻⠇⢸⣇⠒⠖⠂⠤⠴⠁⠸⣷⣬⣛⣿⣠⠈⡍⠢⠹⣿⣿⣿⡧⠀⠀⠀⠀⠀⢰⣿⡟⢁⣠⣤⣴⣾⣿⣿⣿⣿⣿⣷⣶⣾⠀⠀⢸⡷⠀⠀⠖⠦⠭⠑⢄⢠⠙⠤⠈⠀⠒
⠀⠘⠃⠋⠃⠀⠐⠀⠀⠀⠁⠈⠀⡐⠉⠃⠈⠃⠀⠝⠡⠒⠀⠐⠐⠂⠐⢘⠿⣿⣿⠿⠀⠠⠀⠀⠹⣿⡟⣼⡧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⠀⠀⠀⠀⠂⠀⠊⠁⠉⠑⠯⠈⠀⠐⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢭⣶⣮⣭⠈⠉⠀⠀⠀⠹⢹⡟⣼⡆⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾⢭⡵⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢫⣾⣷⣦⡀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣶⡿⠟⣻⣥⣄⣀⠤⠀⠀⣀⣘⣯⡅⠒⠀⠀⠀⠀⠈⠛⢿⣿⣿⣛⣛⣻⣿⣵⣿⢋⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢬⢕⣴⣿⣿⡿⢫⣵⣾⡿⢿⡊⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠿⢿⣿⡿⠟⣱⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢻⣿⣿⣿⣿⣷⣝⣫⠾⢋⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⠉⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⣿⣿⣿⣿⡿⡣⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⡦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠆⣴⣤⣤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣿⣿⢱⢃⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡟⣸⡟⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⢣⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡅⠌⣸⣿⣿⣿⣿⣿⣿⣧⡀⠀⣀⠀⠀⠀⠀⠀⠘⣦⡀⢻⣿⣿⣿⣿⣿⠱⢋⣾⣿⣿⣿⠿⢟⣋⣭⡄⣶⣿⣿⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣭⣶⣶⣮⣝⠿⣿⣿⡇⢀⠘⢷⣄⡀⠀⠀⠀⠘⣷⡄⢻⣿⣿⣿⠃⠰⠿⠟⢋⣭⣶⣾⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣿⣿⣛⢿⣿⣷⡙⣿⢰⣿⠿⠆⠉⠻⠷⠄⠀⠀⢙⣥⠬⣉⣽⠋⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣷⢸⣿⣿⢰⣶⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣮⢻⣷⠈⣸⣿⣿⣶⢊⣹⠯⠕⠮⠥⠄⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⢻⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⠆⠛⠛⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⡛⢿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡃⣿⣿⣎⢿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣵⣿⡇⣿⣿⡿⣆⣽⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡾⣿⠇⣿⣿⣇⢻⡜⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⡉⣼⡣⡀⠀⣿⣿⣿⢁⣿⢸⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣂⣿⢡⢑⡀⡏⣿⣿⣿⣸⡇⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⡗⠠⢹⢹⣿⣿⣇⣧⢻⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢁⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⠆⣡⣶⡆⡜⡇⢿⣿⣎⢸⠀⠹⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠘⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⠟⣸⣿⠏⣰⡇⠇⣄⢻⣿⠀⡇⢦⠹⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⡏⢠⣿⡟⢠⣾⣷⠀⣿⣆⠻⢠⠈⢸⣧⡘⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣿⡿⠁⠻⠀⠘⣿⣧⠘⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡄⣿⣿⡇⠢⣹⣧⠼⢋⣉⣨⣤⡀⠀⣬⣿⠀⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣇⢹⣿⡇⠙⢩⣴⣾⣿⣿⣿⣿⠷⠀⢿⡇⣼⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡇⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⡇⠸⣿⣧⢸⢘⣫⡭⠷⣶⣚⣛⣛⣛⡈⠀⢿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢙⢿⠘⣿⡇⠀⢸⣿⣿⡆⣤⠦⠀⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣧⠸⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⡟⣰⣿⠀⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠀⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⣿⣿⡇⠛⣻⣸⠭⢵⡊⣿⣿⢰⣾⣿⣿⣿⣿⠀⢹⣿⡟⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣿⡇⠸⡹⣜⢿⣿⣷⣿⣿⠘⣿⣿⣿⣿⣿⡇⠘⡟⣴⡧⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢻⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⣿⡆⡄⣿⣿⣿⣤⣈⡓⣘⣛⡋⣿⡏⣠⢻⣿⣿⣿⣿⡇⡀⠸⠋⠁⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣤⡀⠀⠰⠻⡄⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⠇⢿⣿⣧⣿⠃⠁⡘⣿⣿⣿⣿⡇⠇⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⣠⣞⢿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⠀⣟⠸⡇⢻⣿⣿⣿⣿⡀⣿⣴⠀⠸⠿⠿⠿⠿⠀⢸⣭⣭⠈⡀⣈⡁⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣀⣴⣿⣿⣥⣾⣿⠿⣷⣯⣥⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⢿⣿⣿
⢻⠟⣿⣛⣽⡟⣛⠻⡀⢹⠀⡅⢸⣿⣿⣿⡿⡇⢠⡄⡔⡦⢴⣶⡀⡫⢸⠸⣿⣿⡇⣐⢸⠉⠘⣿⣿⢿⣃⠀⠀⠀⠀⠀⠀⠀⣠⣥⣴⡾⠭⢙⣿⣿⣿⣿⡯⠉⠛⠻⣿⠀⠀⠀⠿⡙⣿⠟⢿⠻⣟⠇⢠⣯⠹⣿⣿⣿
⠪⠎⠋⠖⠺⢩⠃⢿⠇⠠⠀⠏⠈⢀⠃⠂⡖⠅⢘⠄⠀⠄⡓⣥⢈⠁⠸⣷⣬⣛⣿⣠⠈⢵⠣⠹⣿⣿⣿⡧⠀⠀⠀⠀⠀⢰⣿⡟⢁⣠⣤⣴⣾⣿⣿⣿⣿⣿⣷⣶⣾⠀⠀⢰⣛⠴⠏⡙⠏⡉⠉⡄⢠⡰⡀⠁⠠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠁⠁⠀⠀⡉⡁⠀⠀⠀⠀⠀⠐⢘⠿⣿⣿⠿⠀⠘⠀⠀⠹⣿⡟⣼⡧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⠀⠀⠀⠀⠂⠀⠀⠀⠉⠁⠏⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢭⣶⣮⣭⠈⠁⠁⠀⠀⠹⢹⡟⣼⡆⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾⢭⡵⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢫⣾⣷⣦⡀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣶⡿⠟⣻⣥⣄⣀⠄⠀⠀⣀⣈⣯⡅⠒⠀⠀⠀⠀⠈⠛⢿⣿⣿⣛⣛⣻⣿⣥⣿⢋⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢬⢕⣴⣿⣿⡿⢫⣵⣾⡿⢿⡊⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠿⢿⣿⡿⠟⣱⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢻⣿⣿⣿⣿⣷⣝⣫⠾⢋⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⠉⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⣿⣿⣿⣿⡿⡣⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⡦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠆⣴⣤⣤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣿⣿⢱⢃⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡟⣸⡟⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⢣⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡅⡌⣸⣿⣿⣿⣿⣿⣿⣧⡀⠀⣀⠀⠀⠀⠀⠀⠘⣦⡀⢻⣿⣿⣿⣿⣿⠱⢋⣾⣿⣿⣿⠿⢟⣋⣭⡄⣶⣾⣿⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣭⣶⣶⣮⣝⠿⣿⣿⡇⢀⠘⢷⣄⡀⠀⠀⠀⠘⣷⡄⢻⣿⣿⣿⠃⠰⠿⠟⢋⣭⣶⣾⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣿⣟⣛⢿⣿⣷⡙⣿⢰⣿⠿⠆⠉⠻⠷⠄⠀⠀⢙⣥⠬⣉⣽⠋⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣷⢸⣿⣿⢰⣶⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣮⢻⣷⠈⣸⣿⣿⣶⢊⣹⠯⠕⠮⠥⠄⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⢻⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⠆⠛⠛⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⡛⢿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡃⣿⣿⣎⢿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣵⣿⡇⣿⣿⡿⣆⣽⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡾⣿⠇⣿⣿⣇⢻⡜⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⡉⣼⡣⡀⠀⣿⣿⣿⢁⣿⢸⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣂⣿⢡⢑⡀⡏⣿⣿⣿⣸⡇⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⡗⠠⢹⢹⣿⣿⣇⣧⢻⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⠇⣡⣶⡆⡜⡇⢿⣿⣎⢸⠀⠹⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠘⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⠟⣸⣿⠋⣰⡇⠇⣄⢻⣿⠀⡇⢦⠹⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⡏⢠⣿⡟⢠⣾⣿⠀⣿⣆⠻⢠⠈⢸⣧⡘⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⠀⣿⣿⠀⣾⣿⡟⠀⣿⡿⠀⠻⠀⠘⣿⣧⠘⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡄⣿⣿⡇⠢⣹⣧⠼⢋⣉⣨⣤⡀⠀⣬⣿⠀⢹⠖⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⡧⢹⣿⡇⠙⢫⣴⣾⣿⣿⣿⣿⠷⠀⢿⡇⣼⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⡇⠸⣿⣧⢸⢘⣫⡭⠷⣶⣚⣛⣛⣛⡈⠀⢿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢙⢿⠘⣿⡇⠀⢸⣿⣿⡆⣤⠦⠀⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣧⠸⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⡟⣰⣿⠀⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠀⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⣿⣿⡇⠛⣻⣸⠭⢵⡊⣿⣿⢰⣾⣿⣿⣿⣿⠀⢹⣿⡟⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣿⡇⠰⡹⣜⢿⣿⣷⣿⣿⠘⣿⣿⣿⣿⣿⡇⠘⡟⣴⡧⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⣿⡇⡄⣿⣿⣿⣤⣈⡓⣘⣛⡋⣿⡏⣠⢻⣿⣿⣿⣿⡇⡀⠸⠋⠁⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣤⡀⠀⠰⠻⡄⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠸⣿⡇⡇⣿⣿⣿⣿⣿⠇⢿⣿⣧⣿⠃⠁⡘⣿⣿⣿⣿⡇⠇⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⣠⣞⢿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⢿⠀⣟⠸⡇⢻⣿⣿⣿⣿⠀⣿⣶⠀⠸⠿⠿⠿⠿⠀⢸⣭⣭⠈⡀⣈⡁⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣀⣴⣿⣿⣥⣾⣿⠿⣷⣯⣥⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⡄⢿⣿⡿⣿⣿⣿
⣻⢻⢟⢛⣿⣙⠋⠻⡀⠝⠀⡅⢘⣟⣿⣿⣿⡇⢠⡄⡔⡆⠤⣒⡄⡏⢸⠸⣿⣿⡇⣐⢸⠉⡘⣿⣿⠿⣃⠀⠀⠀⠀⠀⠀⠀⣠⣥⣴⡾⠭⢙⣿⣿⣿⣿⡯⠉⠛⠻⣿⠀⠀⠀⠽⡛⣿⣻⠫⡻⣿⠇⢸⡿⠟⣿⣿⣿
⠥⠛⠛⠋⠾⣛⠻⢾⡇⢨⠀⢇⠈⢁⢢⡲⠄⠅⢘⠄⡐⣈⡐⡑⠎⠁⠸⣷⣬⣛⣿⣠⠈⡥⠢⠹⣿⣿⣿⡧⠀⠀⠀⠀⠀⢰⣿⡟⢁⣠⣤⣴⣾⣿⣿⣿⣿⣿⣷⣶⣾⠀⠀⢰⣗⢼⠈⠩⢀⡊⠉⠄⢠⠆⠅⠀⠹⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠀⡉⠡⠀⠀⠀⠀⠀⠐⢘⠿⣿⣿⠿⠀⠀⠁⠀⠹⣿⡟⣼⡧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⠀⠀⠀⠀⠃⠈⠀⠀⠉⠁⠏⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢭⣶⣮⣭⠈⠙⠀⠀⠀⠹⢹⡟⣼⡆⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾⢭⡵⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢫⣾⣷⣦⡀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣶⡿⠟⣻⣥⣄⣀⠄⠀⠀⣀⣈⣯⡅⠒⠀⠀⠀⠀⠈⠛⢿⣿⣿⣛⣛⣻⣿⣥⣿⢋⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢬⢕⣴⣿⣿⡿⢫⣵⣾⡿⢿⡊⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠿⢿⣿⡿⠟⣱⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢻⣿⣿⣿⣿⣷⣝⣫⠾⢋⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⠉⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⣿⣿⣿⣿⡿⡣⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⡦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠆⣴⣤⣤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣿⣿⢱⢃⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡟⣸⡟⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⢣⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡅⡌⣸⣿⣿⣿⣿⣿⣿⣧⡀⠀⣀⠀⠀⠀⠀⠀⠘⣦⡀⢻⣿⣿⣿⣿⣿⠱⢋⣾⣿⣿⣿⠿⢟⣋⣭⡄⣶⣿⣿⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣭⣶⣶⣮⣝⠿⣿⣿⡇⢀⠘⢷⣄⡀⠀⠀⠀⠘⣷⡄⢻⣿⣿⣿⠃⠰⠿⠟⢋⣭⣶⣾⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣿⣟⣛⢿⣿⣷⡙⣿⢰⣿⠿⠆⠉⠻⠷⠄⠀⠀⢙⣥⠬⣉⣽⠋⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣷⢸⣿⣿⢰⣶⣬⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣮⢻⣷⠈⣸⣿⣿⣶⢊⣹⠯⠕⠮⠥⠄⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⢻⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⠆⠛⠛⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⢸⣿⣿⣇⠻⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣻⡄⣫⣿⢸⣿⣿⣸⡜⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⢰⡏⡉⢸⣿⣿⣇⡝⡀⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡜⡇⠡⢸⡿⣿⣿⡰⡱⠈⢿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⠎⠁⣇⢻⣿⣿⢳⠣⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⠗⣀⣶⢠⠸⠘⣿⣿⡜⣧⠀⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⣿⣿⡿⢰⣿⠇⢾⣧⡁⠘⣿⣧⢹⡀⢀⢻⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⠁⣾⣿⠀⣾⣿⣧⠀⠹⣿⠀⠇⠈⣄⠻⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⠃⣸⣿⠃⠸⣿⣿⣿⡇⢠⡹⡆⠀⡀⢿⣦⠉⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⡆⢻⣿⡆⣁⠹⢟⣋⣥⣬⣥⡀⠀⢁⢸⣿⡀⡈⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⡇⢸⣿⠀⡄⣾⣿⠿⢿⣛⣛⣓⡸⡆⡀⢻⡇⢹⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⣿⣧⠘⠻⠃⠠⢖⣺⣭⣭⣽⣶⣶⣶⡄⠀⠘⠟⠀⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⢇⣭⠡⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⡭⡅⠿⠛⠛⠛⠉⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⣿⣿⢸⣿⢐⡚⠍⣿⣿⣿⡟⣱⣿⣿⣿⡇⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣷⠀⡽⡰⣿⣿⢹⣿⣿⠃⣿⣿⣿⢟⣼⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠛⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡄⣿⣿⣦⣙⠊⣙⣛⢸⣿⣿⠀⢻⣿⡏⠎⠁⢠⡾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⠀⠈⠳⠸⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠘⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⡃⣿⣿⡾⣿⡟⠀⠈⣿⠁⠀⠀⠈⠀⠀⡀⠀⠀⢀⣠⣾⡿⢀⣴⣿⠇⠀⠀⠀⣿⣿⢿⣿⣷⢸⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⡿⡿⣿⣷⣿⡿⣿⢿⠀⣟⠘⡇⢻⣿⣿⣻⣿⠀⣿⣲⠀⠸⠿⠿⠟⠀⢨⣽⡅⠻⢃⠀⠀⢹⠀⠀⠀⠀⢀⣞⣁⣤⡶⢿⣿⣿⣷⣿⣯⣿⡇⣠⠀⠀⢹⢿⣞⣿⢿⠀⡇⢸⡿⢿⣿⣿⢿⠿⣿⣿⣿⡄⢿⡿⣶⣿⢿⡟
⡒⢙⠛⠛⡿⣿⡟⠙⡀⢙⠀⡅⢸⣟⣿⡛⡟⡃⠠⢄⡠⡦⢀⢒⣍⢸⢈⢿⣿⡀⢂⢛⡇⠂⠀⠀⠀⠀⢸⣿⡿⠛⢉⣑⣻⣿⣿⣯⣤⣤⣁⠆⠀⠀⡞⣟⡚⠯⠻⠄⢧⢸⣏⣻⠛⠿⣙⣻⣻⡯⣷⠃⢠⢻⠿⡺⢿⢍
⠁⠘⢛⠱⠮⠅⢤⢚⡅⠠⠀⠋⠈⢀⠸⢋⡁⠀⢸⢊⠁⣂⠁⠨⠃⠘⢸⣿⣾⣥⣼⠀⢻⣠⠄⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠀⠀⠀⠀⢀⢦⠈⡠⠀⢠⠈⠇⠄⣛⢶⢐⠔⠫⠉⠉⠄⢰⠆⡂⠑⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠡⠃⠀⠀⠀⠀⠨⠨⢝⣛⣛⡫⠂⠃⠊⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡟⠀⠀⠀⠁⠈⠉⠐⠔⠀⠐⢄⠀⠀⠁⠂⠐⠀⠀⠀⠀⠏⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡬⣟⡲⠶⢟⠸⠃⢸⣿⠟⠧⠀⠀⠀⠘⢿⣿⣿⣑⣛⣳⣬⣿⠎⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢁⣟⣋⣽⡯⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⠀⣈⠟⠻⠻⠿⣛⣱⡿⣰⢰⣬⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡜⡿⢋⣵⣮⣔⣛⢋⣵⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠔⢸⣯⢻⣾⠻⣾⣿⣄⣿⡆⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣫⣾⣿⣿⣿⠃⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⠶⢞⣱⣿⢸⣿⠀⣿⡿⡟⣿⣧⣿⣿⠏⣾⣷⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢝⢿⡿⠡⠵⢮⣽⣅⠀⠀⠀⠀⠀⠀⠀⣦⡀⠨⣽⣽⣮⣭⣦⣭⢡⢇⣭⣭⣿⡿⠸⣿⣿⣸⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠴⠾⢿⣶⣮⡙⣆⠀⠀⠀⠀⠀⠀⣿⣿⣦⡈⢻⣿⣿⣿⠏⣰⡿⠟⣋⣥⣶⠸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣮⡻⣷⠘⢠⡘⠆⠀⠀⠀⠸⠿⠿⣛⣤⡭⢉⡽⠀⠉⠀⠉⠛⠻⠿⡇⣿⣿⢸⣷⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢠⢹⢠⣿⣿⣦⣤⡭⣀⠨⠕⠋⠋⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠙⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⣼⠀⠈⠉⠛⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣴⢸⣿⣿⣇⠻⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣻⡄⣻⣿⢸⣿⣿⣸⡜⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⢰⡏⡉⢸⣿⣿⣇⡝⡀⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡜⡇⠡⢸⡿⣿⣿⡰⡱⠈⢿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣥⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⠎⠁⣇⢻⣿⣿⢳⠣⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⠗⣀⣶⢠⠸⠘⣿⣿⡜⣧⠀⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⣿⡿⢠⣿⠇⢾⣧⡁⠘⣿⣧⢻⡀⢀⢻⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⠁⣾⣿⠀⣾⣿⣧⠀⠹⣿⠀⠇⠈⣆⠻⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⠃⣸⣿⠃⠸⣿⣿⣿⣧⢠⡹⡆⠀⡀⢿⣦⠉⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⡆⢻⣿⡆⣁⠹⢟⣋⣥⣬⣥⡀⠀⠁⢸⣿⡀⡈⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⡇⢸⣿⠀⡄⣾⣿⠿⢿⣛⣛⣓⡸⡆⡀⢻⡇⢹⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢙⢿⠘⣿⡇⠀⢸⣿⣧⠘⠻⠃⠠⢖⣺⣭⣭⣽⣶⣶⣶⡄⠀⠘⠟⠀⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⢇⣭⠡⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⡭⡅⠿⠛⠛⠛⠉⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⣿⣿⢸⣿⢐⡒⠍⣿⣿⣿⡟⣱⣿⣿⣿⡇⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⣷⠀⡽⡰⣿⣿⢹⣿⣿⠃⣿⣿⣿⢟⣼⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠻⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢷⠀⣿⣿⣿⣿⣇⢸⣿⡆⡄⣿⣿⣦⣙⠊⣙⣛⢸⣿⣿⠀⢻⣿⡏⠎⠁⢠⡾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⠀⠈⠳⠸⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣷⣦⣥⣼⣿⢿⣿⣇⠘⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⣿⣿⣿⣿⡇⣿⣿⡾⣿⡟⠀⠈⣿⠁⠀⠀⠈⠀⠀⡀⠀⠀⢀⣠⣾⡿⢀⣴⣿⠇⠀⠀⠀⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⡯⣿⣿⣿⣻⣿⣿⢻⠀⣟⠘⡅⢻⣿⣻⣿⣗⡀⣿⣒⠀⠘⠿⠿⠟⠀⢨⣽⡅⠻⢃⠀⠀⢹⠀⠀⠀⠀⢀⣞⣁⣤⡶⢿⣿⣿⣷⣿⣯⣿⡇⣠⠀⠀⢻⣿⢟⣷⣿⠀⡇⢸⢿⣿⣿⣟⣿⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⠹
⠐⠘⣾⡫⢩⣸⠭⠉⡀⠝⠀⡅⢘⣞⡿⢟⡟⡇⠠⡠⡄⢂⣀⠲⣝⢸⢈⢿⣿⡀⢂⢻⡇⠂⠀⠀⠀⠀⢸⣿⡿⠛⢉⣑⣻⣿⣿⣯⣤⣤⣁⠆⠀⠀⡜⠗⣘⡸⠻⠄⢦⠸⡛⣻⣗⢛⠩⠨⢨⠹⣿⠃⢠⠞⠸⡿⣿⡿
⠑⠊⡱⢁⡊⢬⠌⠲⡇⠰⠀⠇⠘⢀⠏⡱⠌⠀⠘⣍⠠⡉⠁⠄⠀⠘⢸⣿⣾⣥⣼⠈⢔⣁⠄⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠀⠀⠀⠂⠨⡢⡆⠣⠀⢠⠀⢅⣔⠐⠈⠀⠀⠔⡈⠍⠄⢠⠘⠔⠕⠁⠝
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠨⠨⢝⣛⣛⡫⠀⠁⠂⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡟⠀⠀⠀⠁⠀⠉⠐⠔⠐⠈⢄⠈⠀⠀⠀⠐⠀⠀⠀⠀⠍⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡬⣟⡲⠶⢟⠸⠁⢸⣿⠟⠧⠀⠀⠀⠘⢿⣿⣿⣑⣛⣳⣬⣿⠎⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢁⣟⣋⣽⡯⠀⠐⠸⢿⠀⠀⠀⠀⠀⠀⠀⣈⠝⠻⠻⠿⣛⣱⡿⣰⢰⣬⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡜⡿⢋⣵⣮⣔⣛⢋⣵⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠔⢸⣯⢻⣾⢻⣾⣿⢄⣿⡆⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣫⣾⣿⣿⣿⠁⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⠶⢞⣱⣿⢸⣿⠀⣿⡿⡟⣿⣧⣿⣿⠏⣾⣷⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢝⢿⡿⠡⠵⢮⣽⣅⠀⠀⠀⠀⠀⠀⠀⣦⡀⠨⣭⣽⣮⣯⣦⣭⢡⢇⣭⣭⣿⡿⠸⣿⣿⣸⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠴⠾⢿⣶⣮⡙⣆⠀⠀⠀⠀⠀⠀⣿⣿⣦⡌⢻⣿⣿⣿⠏⣠⡿⠟⣋⣥⣶⠸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣮⡻⣷⠘⢠⡈⠆⠀⠀⠀⠸⠿⠿⣛⣤⡭⢉⡽⠀⠉⠀⠉⠛⠻⠿⡇⣿⣿⢸⣷⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢠⢹⢠⣿⣿⣦⣤⡭⣀⠨⠕⠋⠋⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠛⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⣼⠀⠈⠉⠛⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢰⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣷⣮⢻⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⠍⣩⣾⣿⣿⣿⣧⢛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⢘⣿⣿⣿⣿⣿⡞⡄⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⠌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡸⡱⡁⢸⢻⣿⣧⣷⠘⡌⢿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠀⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⠱⢡⣸⢸⣿⣿⢸⠀⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⢸⣿⣿⣿⠘⡄⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣥⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⣿⣿⢁⣾⡟⡘⢸⣿⣿⢹⢠⠘⠘⠌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢀⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⠏⣸⣿⠁⡆⠀⢿⣿⠸⢘⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⢠⣿⠏⢸⣿⡄⠊⢿⡄⠈⡆⠻⠈⡆⢻⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣧⢸⣿⠀⣈⠿⢇⣀⣀⣃⠀⠀⣄⢲⣷⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⢸⣿⢠⠄⣿⠿⢿⣛⣛⣓⡐⣿⡄⠙⣧⡙⢿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢙⢿⠘⣿⡇⠀⢸⣿⡇⠸⠿⠀⢠⣚⣯⣭⣷⣶⣶⣶⡌⡡⠀⠛⣁⢸⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⠰⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⢩⡀⠀⣗⡎⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠸⣿⡟⣼⡟⣀⡻⣿⣿⣿⡿⠛⣿⣿⡿⢸⠇⠂⠊⠈⠈⠉⠉⠻⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣯⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⠐⡯⣵⣬⣥⢻⣿⣿⡇⣿⣿⡿⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢻⠈⣿⣿⣿⣿⣇⢸⣿⡆⡄⣿⣆⠱⠇⠻⢿⢸⣿⣿⡇⣿⡟⠞⠃⢀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠽⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠘⡇⢸⡆⣿⣿⣿⣿⡿⠘⣿⡇⠇⢿⣿⣷⡆⢿⣿⡿⣿⣿⠷⣿⠀⠀⠀⠞⠁⠀⠀⠀⣠⣴⠇⣀⣶⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢿⢿⢷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⡿⣿⣿⢿⡻⣿⣿⢻⠀⢟⠘⡆⢻⣿⣿⢿⣷⡀⣟⣳⠀⠘⠿⠿⠁⢨⣿⣧⠙⢿⠀⣿⠀⠀⠀⢀⣔⣀⣔⣺⣿⣯⣾⠫⠷⡇⠄⠀⢸⠟⡿⣿⢿⢿⣿⣿⠟⢾⢺⠀⡇⠰⠟⣿⣿⡿⠿⢿⣿⣿⡿⡀⢿⡳⣿⣿⣿⠷
⡒⠛⠿⡏⠹⠉⡫⠋⡀⠈⠀⡁⢘⢜⡟⡿⡿⡃⠠⠀⠠⠂⢄⡖⡄⣥⣙⠿⠆⢊⠀⢻⡄⠀⠀⠘⣿⣋⣤⣤⣿⣿⡟⣶⣶⡖⠀⠀⠘⡛⢸⡻⢛⣻⠙⠹⠘⢛⡍⡆⠧⢸⢽⠛⠛⠏⣽⠙⢹⠯⣿⠃⢀⠻⣹⠿⠿⠾
⠁⠠⠁⠠⠀⠀⠈⠢⡅⠠⠀⠃⠈⠀⠈⠁⠔⠀⠠⠀⠰⠀⠐⠆⠀⡁⢿⣿⣿⣿⠃⠈⣶⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠂⠂⠴⡴⢲⠐⢆⠮⠨⠀⠂⠀⠠⠈⢄⣚⠑⠁⠀⠂⠔⠈⠁⡄⢠⠀⠄⠔⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠤⠀⢕⣒⣒⣒⢘⠀⢰⣷⡄⠀⠈⠻⣿⣿⣽⣶⣶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠈⠈⠀⠀⠀⠀⢄⠈⠀⠀⠈⠈⠐⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡿⠿⣉⣍⢻⠸⠈⠉⠁⠀⠀⠠⣄⡉⠛⠛⢻⣥⢲⢰⣶⠆⢍⡂⠀⢀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢗⢋⣥⡶⣦⢂⠀⠀⠀⠀⠀⠀⣻⠿⠿⠂⢸⣿⢸⢸⣿⣄⣼⡿⣰⢠⣭⢈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢜⢿⣿⡿⠣⢿⡄⠀⠀⠀⠀⠀⠈⢻⣿⣩⢸⣿⢸⢸⣿⠃⢻⣾⠻⡾⢙⣻⢹⣿⣿⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⠱⢊⣚⡿⣷⣍⠀⢄⠀⠀⠀⠀⠸⣿⣟⣼⡿⣸⢸⣿⠈⠸⣋⠀⣾⢸⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⣿⣿⣿⠷⠹⡆⠈⢤⡀⠀⠀⠄⠸⠭⣉⣚⠋⣨⠏⠀⠀⠉⠀⠉⠈⠿⠨⡏⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢶⡇⠃⠸⢦⣿⡄⣨⠩⠖⠊⠁⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⡿⣟⡯⢶⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠛⠻⢾⣯⣟⠿⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠈⠙⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡻⠿⠿⠿⠿⢿⠁⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣿⠇⣿⡏⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢋⣴⠟⢁⣾⠏⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣼⠏⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣷⣮⢻⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⠍⣩⣾⣿⣿⣿⣧⢛⠻⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣂⢘⣿⣿⣿⣿⣿⡞⡄⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡸⡱⡁⢸⢻⣿⣧⣷⠘⡌⢿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠀⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⠱⢡⣸⢸⣿⣿⢸⠀⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠉⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⢸⣿⣿⣿⠘⡄⢇⢹⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⣿⣿⣿⢁⣶⡟⡘⢸⣿⣿⢹⢠⠘⠘⠌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⠏⣸⣿⠁⡅⠀⢿⣿⠸⢘⠀⡀⠀⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡿⢠⣿⠏⢸⣿⡄⠊⢿⡀⠈⡆⠹⠈⡆⢻⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣯⢘⣿⠀⣈⠿⢇⣀⣀⣃⠀⠀⣄⠲⣷⡘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⢸⣿⢠⠄⣿⠿⢿⣛⣛⣓⡐⣿⡆⠙⣧⡙⢿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⣿⡏⠸⠿⠀⢠⣚⣯⣭⣷⣶⣶⣶⡌⡡⠀⠛⣁⢸⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣧⢠⢸⣿⣿⠰⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⢨⡀⠀⣗⡆⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠘⠘⣿⡟⣼⡟⣀⡻⣿⣿⣿⡿⠛⣿⣿⡿⢸⠇⠂⠊⠈⠈⠉⠉⠻⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⠐⡯⣵⣬⣥⢻⣿⣿⡇⣿⣿⡿⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡄⣿⣆⠱⠇⠻⢿⢸⣿⣿⡇⣿⡟⠞⠃⢀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠘⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⣿⣿⣷⡆⢿⣿⡿⣿⣿⠷⣿⠀⠀⠀⠞⠁⠀⠀⠀⣠⣴⠇⣀⣶⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⠀⣿⠸⡇⢹⢿⣿⣿⣿⠀⣿⣶⠀⠸⠿⠻⠁⢨⣿⣧⠙⢿⠀⣿⠀⠀⠀⢀⣔⣀⣔⣺⣿⣯⣾⠫⠷⡇⠄⠀⢸⣿⣷⣿⣿⢿⢿⣿⢾⣿⡿⠀⡇⠸⣿⣿⡿⡿⣿⣿⣿⣿⡿⡀⢿⣿⣿⣿⣿⠿
⠙⢏⠻⠛⠯⠟⠛⠛⡀⠝⠀⡄⢘⠻⣿⡟⡿⡇⠠⠀⠠⡂⠀⠒⡀⣥⣙⠿⠆⢊⠀⢻⡄⠀⠀⠘⣿⣋⣤⣤⣿⣿⡟⣶⣶⡖⠀⠀⢸⣿⡟⣛⢟⡋⠻⢟⠻⢻⠻⠂⠧⠨⣝⣟⠝⠛⢿⠿⢻⢿⣟⠇⢈⣿⡿⡿⣿⣿
⠀⠊⠭⠉⠚⢉⠎⠠⡃⠠⠀⢇⠘⠀⢟⠁⠎⡅⠸⠀⠐⠀⠀⠁⠀⡁⢿⣿⣿⣿⠃⠈⣶⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠂⠁⠈⢁⠞⣰⣼⡕⠬⠀⠑⠀⢠⠈⠍⢢⠽⣜⠼⡧⠄⠈⠉⡀⠰⠈⠈⠏⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠅⠀⠀⠀⠄⠀⢕⣒⣒⣒⢘⠀⢰⣷⡄⠀⠈⠻⣿⣿⣽⣶⣶⡾⠃⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠠⠐⠀⠈⠄⢈⠁⠈⠈⠙⠑⠁⠁⠀⠄⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣉⣍⢻⠸⠈⠉⠁⠀⠀⠠⣄⡉⠛⠛⢻⣥⢲⢰⣶⠆⢍⡂⠀⢀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢗⢋⣥⡶⣦⢂⠀⠀⠀⠀⠀⠀⣻⠿⠿⠆⢸⣿⢸⢸⣿⣀⣼⡿⣰⢠⣭⢈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢜⢿⣿⡿⠣⢿⡄⠀⠀⠀⠀⠀⠈⢻⣿⣭⢸⣿⢸⢸⣿⠃⢻⣾⠻⡾⢙⣻⢹⣿⣿⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠱⢊⣚⡿⣷⣌⠀⢄⠀⠀⠀⠀⠸⣿⣟⣼⡿⣸⢸⣿⠈⠸⣛⠀⣾⢸⣟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠷⠹⡆⠈⢤⡀⠀⠀⠄⠸⠭⣉⣚⠋⣨⠏⠀⠀⠉⠀⠉⠈⠿⠨⡏⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢶⡇⠃⠸⢦⣿⣄⣈⠩⠖⠊⠁⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⡿⣟⡯⢶⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⠛⠻⢾⣯⣟⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠈⠙⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡻⠿⠿⠿⠿⢿⠁⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣿⠇⣿⡏⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢋⣴⠟⢁⣾⠏⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣼⠏⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣷⣮⢻⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⠍⣩⣾⣿⣿⣿⣧⢛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣂⢘⣿⣿⣿⣿⣿⡞⡄⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡸⡱⡁⢸⢻⣿⣧⣷⠘⡌⢿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⠱⢡⣸⢸⣿⣿⢸⠀⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠉⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⢸⣿⣿⣿⠘⡄⢇⢹⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⣿⣿⣿⢁⣾⡟⡘⢸⣿⣿⢹⢠⠘⠘⠌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⠏⣸⣿⠁⡇⠀⢿⣿⠸⢸⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡿⢠⣿⠏⢸⣿⡄⠊⢿⡀⠈⡆⠻⠈⡆⢻⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⣯⢸⣿⠀⣈⠿⢇⣀⣀⣃⠀⠀⣄⠲⣷⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡂⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⣿⢸⣿⢠⠄⣿⠿⢿⣛⣛⣓⡐⣿⡆⠙⣧⠙⢿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢙⢿⠘⣿⡇⠀⢸⣿⡇⠸⠿⠀⢠⣚⣯⣭⣷⣶⣶⣶⡌⡡⠀⠛⣁⢸⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⣿⠰⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⢨⡀⠀⣗⡎⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⣿⡟⣼⡟⣀⡻⣿⣿⣿⡿⠛⣿⣿⡿⢸⠇⠂⠊⠈⠈⠉⠉⠻⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢸⣿⣿⡄⢻⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⣿⠐⡿⣵⣬⣥⢻⣿⣿⡇⣿⣿⡿⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡄⣿⣆⠱⠇⠻⢿⢸⣿⣿⡇⣿⡟⠞⠃⢀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠷⡌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠘⡇⢸⡆⣿⣿⣿⣿⡿⠘⣿⡇⠃⣿⣿⣷⡆⢿⣿⡿⣿⣿⠷⣿⠀⠀⠀⠞⠁⠀⠀⠀⣠⣴⠇⣀⣶⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣟⢿⣿⢿⠀⢟⠘⡂⢻⣿⠿⢿⠻⠀⣟⣷⠀⠸⠿⠻⠁⢨⣿⣧⠙⢿⠀⣿⠀⠀⠀⢀⣔⣀⣔⣺⣿⣯⣾⠫⠷⣇⡀⠀⢸⣿⣷⣿⢗⣿⣺⠿⠿⡟⢿⠀⡇⠰⠿⣿⣿⣿⣿⣳⣾⣿⣿⡀⠟⡞⣻⢿⣻⡚
⠛⠹⡙⡉⡝⠝⠭⠙⡀⠈⠀⡀⠈⣟⣿⡷⢟⡃⠀⠀⠄⠂⢀⡀⠄⣥⣙⠿⠆⣊⠀⢻⡄⠀⠀⠘⣿⣋⣤⣤⣿⣿⡟⣶⣶⡖⠀⠀⠘⠟⡟⠻⢏⠫⠭⣑⠚⣚⡾⠄⠧⠨⢝⢿⡽⢟⡍⠩⡋⠫⡟⡃⢀⣛⡲⠿⣿⣉
⠀⠀⠠⠍⠀⠀⠀⠢⠃⠠⠀⢇⠘⠀⠉⠋⠊⠁⠸⠀⠐⠀⠂⠀⠀⡁⢿⣿⣿⣿⠃⠈⣶⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠂⠢⠠⠄⠂⢦⡤⡃⡢⠐⠔⠀⢀⠈⠅⠠⠐⠮⠅⢀⠠⠄⠁⠀⠐⠀⠙⢹⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠄⠀⢕⣒⣒⣒⢘⠀⢰⣷⡄⠀⠈⠻⣿⣿⣽⣶⣶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⠀⠀⠈⢄⠈⠁⠀⠀⠙⠒⠁⠁⠀⠂⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣉⣍⢻⠸⠈⠉⠁⠀⠀⠠⣄⡉⠛⠛⢻⣥⢲⢰⣶⠆⢍⡂⠀⢀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢗⢋⣥⡶⣦⢂⠀⠀⠀⠀⠀⠀⣻⠿⠿⠆⢸⣿⢸⢸⣿⣀⣼⡿⣰⢠⣭⢈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢜⢿⣿⡿⠣⢿⡄⠀⠀⠀⠀⠀⠈⢻⣿⣭⢸⣿⢸⢸⣿⢃⢻⣾⠻⡾⢙⣻⢹⣿⣿⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠱⢊⣚⡿⢷⣌⠀⢄⠀⠀⠀⠀⠸⣿⣟⣼⡿⣸⢸⣿⠈⠸⣛⠀⣾⢸⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⣿⣿⣿⠷⠹⡆⠈⢤⡀⠀⠀⠄⠸⠭⣉⣚⠋⣨⠍⠀⠀⠉⠀⠉⠈⠿⠨⡏⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢦⡇⠃⠸⢦⣿⣄⣈⠩⠖⠊⠁⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⡿⣟⡯⢶⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⠛⠻⢾⣯⣟⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠈⠙⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡻⠿⠿⠿⠿⢿⠁⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣿⠇⣿⡏⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢋⣴⠟⢁⣾⠏⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣼⠏⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠍⣯⡛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⡀⣢⣴⢾⣿⡿⡄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣧⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣏⢞⣿⣿⣞⣿⣧⢿⡘⡘⡌⢿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠀⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⢨⠉⠉⢸⣿⣿⣼⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠉⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⡎⡇⡤⢸⢿⣿⣧⣿⠆⠄⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⣿⣿⣿⡿⠄⠒⢸⢸⣿⡟⣿⠀⠰⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⡟⢠⣿⢃⠘⢸⣿⡇⡿⠐⠀⠃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⢿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⠁⣿⡟⢠⠀⢸⣿⢸⢣⡀⠀⢧⡈⠆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⡏⣸⡏⠀⠹⣇⠈⠏⠈⠼⠇⢀⠈⣿⡆⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠀⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⡇⣿⡇⠐⢊⣥⣶⣦⣦⣿⡠⣾⣇⢹⣇⠀⢿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⣿⠇⣿⠀⡏⢾⣛⠯⢭⣭⣭⣥⠐⢨⠸⣿⠀⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⡀⠛⠃⢡⣷⣾⣿⣿⣿⣿⣿⣧⢳⡆⣒⡆⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠸⣿⠇⣭⠁⢸⣿⣿⣿⣿⠟⣻⣿⡟⣸⡇⠏⡾⠀⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢻⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⡟⠸⡏⠲⢥⡸⣿⣿⡟⣿⣿⣿⡇⠋⠁⠀⠀⠀⠀⠉⢻⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡄⣷⡸⣕⠝⣿⠇⣿⣿⡇⢿⣿⢯⠞⡁⠀⠀⠀⠀⠀⠀⠀⢉⠻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⢿⣿⣶⡀⣶⣧⢿⣿⠇⢸⡏⠀⠸⠃⠀⠀⠀⢀⣴⢁⡴⠀⠃⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠿⣿⣿⡿⣿⣷⣿⢾⠀⢟⠘⡇⢹⣿⣿⣿⣿⠀⣿⡲⠀⠸⠿⠻⢁⢸⣶⡌⠻⠘⠘⡇⠀⠀⢀⣀⡤⢼⣿⣿⠋⠻⢀⠀⢸⣿⣧⠘⣿⣿⢿⣿⣿⢿⢿⣷⢿⣿⣿⠀⡇⠰⡿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠿⣿⣿⣿⣿⣿
⠾⡟⡛⢛⡻⡻⠻⠙⡀⠉⠀⡅⢸⠺⣾⢯⣿⡇⠠⠀⡀⠂⠀⠢⢸⣶⣝⣃⣡⠆⠀⣇⠀⠀⠈⣷⣶⣶⣿⣿⣺⣿⡎⠀⢘⣿⣯⠀⣽⡹⡻⢛⠿⠙⠻⣿⠟⣿⣿⠀⢧⢈⣿⣻⠏⢋⠛⡽⢿⠻⣿⡇⢈⣿⡿⣿⣿⡟
⠉⠂⠈⠢⠰⠆⠺⠠⡇⠠⠀⢇⠈⠀⠹⠁⢁⠄⠸⠀⢄⠄⠀⠈⠀⢝⠿⠿⠿⠰⠀⣭⠄⠀⠀⠹⣿⣿⣛⣿⣿⡿⠁⠀⠨⠙⠻⠀⠀⠀⠡⠄⠀⠠⠕⠑⢀⠀⠁⠀⢀⠈⠩⠇⢬⠖⠀⠍⠠⠑⠋⡀⢰⠈⢘⠭⠸⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠪⠃⠀⠀⠀⠆⠐⡭⢭⠭⣸⠀⡵⠋⠀⠀⠀⢈⠛⠿⠿⠟⠄⠀⣀⠀⠉⠭⠠⠄⠀⠀⠀⠁⠈⠁⠀⠀⠠⠑⠀⠀⠄⢈⠁⠀⠈⠙⠐⠁⠁⠀⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⢖⡨⢄⠢⠁⠀⠀⠀⠀⡹⣷⣾⠆⢾⣟⢿⣮⢀⢰⣦⢌⢉⡂⠀⠀⠽⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢢⣾⣶⠟⢼⡀⠀⠀⠀⠀⢨⣓⠶⢚⣼⣿⢸⣿⠈⢸⣿⢀⣿⣼⣿⣿⣿⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡙⢝⣥⣭⡻⣮⢀⠀⠀⢸⢸⣿⣿⢸⣿⣿⢸⡿⠈⠘⣭⠀⣿⢨⢙⠻⢿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢢⣿⣿⣿⡏⡸⠇⢸⣠⡘⣼⣟⣛⠸⣟⣛⢈⠇⠀⠐⡐⠀⠈⠊⠀⢼⡖⠒⣯⠁⠙⠛⠻⠿⣿⣿⣿⣿⡶⣖⢄⡤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⠟⠉⠁⠰⠮⣭⣧⠬⠡⠓⠈⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠀⠀⠀⠀⢸⣏⠉⠳⢾⣝⡳⠾⢭⣗⡂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠈⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣫⡶⣯⠟⣿⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⠋⣰⠏⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠋⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⠇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠍⣯⡛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⡀⣢⣴⢾⣿⡿⡄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣧⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣏⢞⣿⣿⣎⣿⣧⢿⡘⡘⡌⢿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠀⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⢨⠉⠉⢸⣿⣿⣼⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠉⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠄⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⡌⡇⡤⢸⢿⣿⣧⣿⡆⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⣿⣿⣿⡿⠄⠒⢸⢸⣿⡟⣿⠀⠰⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⡟⢠⣿⢃⠈⢸⣿⡇⡿⠐⠀⠃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⢿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⠁⣿⡟⢠⠀⢸⣿⢸⢣⡀⠀⢦⡈⠆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⡏⣸⡟⠀⠹⣇⠈⠏⠈⠼⠇⢀⠈⣿⡆⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠈⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⡇⣿⡇⠐⢊⣥⣶⣦⣦⣿⡀⣿⣇⢹⣇⠀⢿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⣿⡇⣿⠀⡏⢾⣛⠯⢭⣭⣭⣥⠐⠨⠸⡿⠀⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⣿⡀⠛⠃⢠⣷⣾⣿⣿⣿⣿⣿⣧⢻⡆⣒⡆⡀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠸⣿⠇⣭⠁⢸⣿⣿⣿⣿⠟⣻⣿⡟⣸⡇⠏⡾⠀⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢻⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⡟⠸⡏⠲⢥⡸⣿⣿⡟⣿⣿⣿⡇⠋⠁⠀⠀⠀⠀⠉⢻⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡄⣷⡸⣕⠝⣿⠇⣿⣿⡇⢿⣿⢯⠞⡅⠀⠀⠀⠀⠀⠀⠀⢉⠻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠘⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⣿⣿⣶⡀⣶⣧⢿⣿⠇⢸⡏⠀⠸⠃⠀⠀⠀⢀⣴⢁⡴⠀⠃⢹⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⢸⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠿⣿⣿⡿⢿⣻⣿⢿⠀⢟⠘⡂⢹⠿⢿⣿⣿⠀⣿⣶⠀⠸⠿⠿⢁⢸⣾⡌⠻⠘⠘⡇⠀⠀⢀⣀⡤⢼⣿⣿⠋⠻⢀⠀⢨⣽⢧⠘⣿⡿⡿⣿⣿⣿⡿⡿⠿⣿⢿⠀⡇⠰⣿⣿⢿⣿⢿⢿⣿⣿⣷⡄⢟⣿⣷⣾⣿⢿
⠚⠻⡛⣿⠛⠛⣟⠙⡀⠘⠀⡁⠘⡻⠟⡻⠟⠃⠀⠀⡀⠂⠤⠒⢸⣶⣝⣃⣡⠆⠀⣇⠀⠀⠈⣷⣶⣶⣿⣿⣺⣿⡎⠀⢘⣿⣯⠀⢽⠻⢟⠛⠋⢿⣋⠹⠿⢛⢿⠆⢧⢨⣿⡟⢿⠿⠏⡛⣩⠛⡟⠇⠀⡿⢿⣻⣿⠿
⠁⠂⠉⠑⠅⠔⠁⢐⠇⢀⠀⢇⠈⠀⠇⠀⠔⠀⠸⠐⠐⠂⠐⠈⠀⢝⠿⠿⠿⠰⠀⣭⠄⠀⠀⠹⣿⣿⣛⣿⣿⡿⠁⠀⠨⠹⠋⠀⠀⠀⠠⠄⠄⠀⠚⠂⠀⠀⠆⠀⢀⠈⠩⠀⡊⡆⠐⠑⠂⠀⠁⠄⢠⠀⠕⠠⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠆⠐⡭⢭⠭⣸⠀⡵⠋⠀⠀⠀⢈⠛⠿⠿⠟⠄⠀⣀⠀⠉⠩⠠⠄⠀⠀⠀⠁⠈⠁⠀⠀⠰⠀⠰⠀⢄⡈⠁⠀⠀⠉⠁⠁⠁⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡽⢖⡨⢄⠢⠁⠀⠀⠀⠀⡹⣷⣾⢆⢾⣟⢿⣮⢀⢰⣦⣍⢉⡂⠀⠀⠿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢢⣾⣶⠟⢼⡀⠀⠀⠀⠀⢨⣓⠶⢚⣼⣿⢸⣿⠈⢸⣿⢁⣿⣼⣿⣿⣿⣰⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡑⢝⣥⣭⡻⣮⢀⠀⠀⢸⢸⣿⣿⢸⣿⣿⢸⡿⠈⠘⣭⠄⣿⢨⢙⠻⢿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⢢⣿⣿⣿⡏⡸⠇⢸⣠⡘⣼⣟⣛⠸⣟⣛⢈⠇⠀⢐⠖⠀⠈⠊⠀⣼⡖⠒⣯⢅⠉⠛⠻⠿⣿⣿⣿⣿⡶⣖⢄⡤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⠟⠉⠁⠠⠬⣭⣥⠬⠡⠓⠈⠊⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠀⠀⠀⠀⢸⣏⠉⠳⢾⣝⡳⠾⢭⣗⡂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠈⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣫⡶⣯⠟⣿⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⠋⣰⠏⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠋⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣻⣭⡭⠭⠭⢟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣰⡤⢁⢸⣷⡠⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⣫⣾⣏⢸⣿⣱⢹⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⡇⡽⠿⠛⢸⢿⣇⣇⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⡇⡧⠀⠀⢸⣸⣿⢹⠈⠂⠄⢇⢻⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠀⡖⣿⣿⣿⣷⠃⠝⠥⡌⣿⣿⣾⢸⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⡿⢁⣴⠀⠁⣿⣿⢸⠀⠙⣃⠃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⢁⣾⡟⢀⠄⣿⡏⡞⠈⣷⡐⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⠇⣸⡿⠀⢸⢁⠏⠀⠀⠀⡹⢿⡄⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⣿⢰⣿⠁⠀⠄⣂⣤⣤⣤⠀⣧⢸⡧⠀⡀⡆⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⣿⢸⣿⠀⠏⢼⣛⡿⠯⠭⠥⠀⡀⢻⡄⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⡀⣶⣶⣾⡀⣿⣷⢠⢸⣟⠸⡿⠂⢥⣷⣶⣿⣿⣿⣿⣧⢡⡈⡁⠈⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠸⣿⢐⡒⢸⢸⣿⣿⣿⠟⢫⣿⣿⢸⢱⠟⡀⠀⠃⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⡟⠼⠇⠲⢌⢿⣿⡿⢸⣿⣿⡿⠘⠀⠘⠘⠀⠨⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⣿⡆⡄⣷⡰⢃⢻⡿⢸⣿⠇⡸⡿⡫⢂⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⣿⣿⣶⠸⣿⡾⡿⣸⡄⠙⠁⡇⠀⠀⠀⢀⡄⠀⡄⠸⠘⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⡶⢀⠸⠿⠟⠄⢶⣧⠀⠛⠃⠀⠀⠀⣀⣠⣴⣿⣥⡚⠇⠀⠀⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿
⣿⣟⢟⠿⣟⢻⣟⢻⡀⢙⠀⡁⢸⣻⣿⣿⣿⡇⠀⠀⣠⡖⣄⠲⠀⣷⣯⣴⡇⡖⠀⠀⠈⣿⣴⣶⣼⣿⢲⣶⠀⠀⣿⣿⣿⣿⣿⠀⡿⡿⣿⣿⣿⡿⣿⣿⠿⣿⣿⡆⠧⢨⣿⣿⢟⡟⣝⠯⣻⣹⣟⡇⢸⣻⣿⣿⣿⣿
⠭⡉⢙⠃⠙⠹⠫⢸⡅⠠⡄⢇⠘⢁⢊⠠⡞⠁⠸⣕⠀⠂⠈⠒⢠⢊⡭⢭⡁⢐⠂⠀⠀⠻⣿⣿⡟⡻⣹⠏⠀⠀⠉⠙⠟⠉⠛⠅⠹⠁⠚⢽⢇⢍⣝⣱⣽⡧⣏⠀⢠⠈⠏⣑⢧⣍⢢⣋⡾⡈⡍⡀⢠⠸⢌⡋⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠐⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠅⠸⢏⡩⠕⡈⠀⠀⠀⠀⠈⡙⠛⠛⣣⣿⡇⠰⢶⣶⣶⣶⠆⣿⢻⣹⣿⣆⠁⠈⠉⠀⠀⠸⠂⠲⠈⢄⡈⠁⠀⠈⠙⠒⠁⠀⠊⠇⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣫⣾⣫⢎⣥⠀⠀⠀⠀⢩⣿⡧⣹⢫⣾⣎⢿⣮⠛⢨⣅⣿⢘⡸⣿⣿⣮⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢟⡿⢣⣟⡻⣛⠀⠀⠀⠀⢰⣶⣿⢸⣿⡿⠘⠙⠈⢨⣤⣁⡸⠿⠈⠹⣿⣰⣶⣴⢆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⣵⣾⣿⣮⢳⠹⠄⢠⡄⠀⣘⡛⡫⠬⣡⠀⢰⣿⠀⢸⣿⠉⢱⣦⠀⢰⡸⣟⠛⠳⣽⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠜⣀⠌⠰⠧⠗⠐⡈⠈⠀⣤⣄⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡗⠊⣃⣅⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⠁⠁⠈⠁⠈⠉⠉⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢫⠟⣱⠆⡿⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⠭⠭⠭⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣀⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣝⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⢟⣵⠆⣿⣏⠎⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⡧⣻⡿⢇⣿⣿⡞⡜⠛⠉⠀⠄⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⡇⡇⠀⢸⢹⣿⣿⣣⢿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣧⢰⠉⡘⢸⣿⣿⣿⢸⣿⠛⣁⠃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⠏⣠⡆⢀⡜⣿⣿⣿⠘⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⡟⢠⡿⢀⠸⣷⢹⡿⠸⢠⡘⢿⣬⣅⢁⢡⠘⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡇⣿⡁⠈⡄⡽⠘⠁⠀⠘⣿⠈⣿⣿⡄⡀⡆⢿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⡇⣿⡇⣀⣶⠾⢾⣾⡆⠀⣿⠀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⡁⠻⠃⣐⣾⣭⣿⣶⣶⡄⠿⢀⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⡇⣭⠁⢿⣿⣿⡿⢻⣿⣷⢩⢰⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⢸⠇⣤⡞⣿⣿⠁⣿⣿⣿⠘⠈⠉⠀⠀⠀⠀⠨⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⣿⡆⡄⣧⡁⣚⣧⢿⡟⡔⢸⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⣿⣟⢸⣛⣸⠱⣿⠃⠁⡯⠀⠀⠀⠀⣠⡆⣠⡂⠙⠸⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣟⠸⡇⢻⣿⣿⣿⣿⡀⣿⡶⠀⠸⠇⢎⡿⡇⠀⠛⠀⠀⠀⢠⣤⢀⣈⣻⣾⣥⣦⠀⢮⣪⡻⢿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⡿⠻⡀⠟⠀⡅⢸⢟⣿⣿⣿⡇⠠⢀⣴⣂⣂⠀⣿⣿⡿⠸⠄⠀⠀⠈⣿⣿⣿⢟⣍⠙⣿⢰⣆⢇⣿⡆⣴⣬⠙⠀⣿⣿⣿⣿⣿⣿⣿⣿⢟⢿⣿⡆⢷⢨⣿⣿⡿⡿⣿⣿⣿⣿⣟⡇⢸⣿⣿⣿⣿⣿
⠛⡋⣉⡟⢹⠿⠹⣼⡇⠠⡄⢗⠈⢁⢉⡋⣋⡇⢸⠍⣽⠲⠈⠄⢩⡭⠵⠀⣇⠀⠀⠀⠘⠻⢿⣜⣟⡧⣣⣿⠏⢰⡙⣿⠿⠴⣖⠄⢡⠏⣩⣍⡻⢻⢻⣫⡇⣿⣙⡀⢠⠈⢝⣿⣽⣿⡛⡙⣫⣝⠫⡀⢈⡻⢻⣿⡟⡍
⠁⠈⠀⠀⠀⠀⠀⠀⠁⠀⠁⢈⠀⡀⠀⠀⠈⠀⠀⢻⠆⠀⠀⠀⡎⡵⣚⡥⠨⠅⠀⠀⠀⠀⠲⡤⠰⣾⣿⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠄⠁⠈⠁⠂⠉⠳⠈⠰⠀⢄⣈⡁⠈⠈⠙⠓⠉⠁⠂⠇⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⡿⠾⠋⣵⣄⠀⠀⠀⠀⠚⢳⣶⠹⢨⣾⡎⢻⣦⠀⢸⣿⠛⢿⣆⠀⢀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣮⣻⣦⢻⣿⣻⣦⠀⡀⠀⢜⠕⠀⢘⣯⠁⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠗⠹⢋⠭⢵⣤⢸⠿⠂⢰⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢳⣦⠀⢸⡏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⣿⣧⣤⡄⢰⣾⣀⣼⣿⠀⠘⣿⣄⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠿⠿⡗⢦⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣵⠋⣿⠘⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⠇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣻⣭⠭⠭⠭⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣀⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣝⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⢟⣵⠆⣿⣏⠎⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⡧⣻⡿⢇⣿⣿⡞⡜⠛⠉⠂⠄⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⡇⡇⠀⢸⢹⣿⣿⣣⢿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣧⢰⠉⡘⢸⣿⣿⣿⢸⣿⠛⣁⠃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⠏⣠⡆⢀⡜⣿⣿⣿⠘⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⡟⢰⡿⢀⠸⣷⢹⡿⠸⢠⡘⢿⣬⣅⢁⢡⠘⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡇⣿⡁⠈⣄⡽⠘⠁⠀⠘⣿⠈⣿⣿⡄⡀⡆⢿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⡇⣿⡅⣀⣶⠾⢾⣾⡆⠀⣿⠀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⡁⠻⠃⣐⣾⣭⣿⣶⣶⡄⠿⢀⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⡇⣭⠁⢿⣿⣿⡿⢻⣿⣷⢩⢰⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⢸⠇⣤⡞⣿⣿⠁⣿⣿⣿⠘⠈⠉⠀⠀⠀⠀⠨⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⣿⡆⡄⣧⡁⣚⣧⢿⡟⡔⢸⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⣿⣟⢸⣛⣸⠱⣿⠃⠁⡯⠀⠀⠀⠀⣠⡆⣠⡂⠙⠸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⠀⣟⠘⡆⢻⣿⣿⣿⣿⠀⣿⣶⠀⠸⠇⢎⡿⡇⠀⠓⠀⠀⠀⢠⣤⢀⣈⣻⣾⣥⣦⠀⢮⣪⡻⢿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣾⣿⣿⡄⢿⣿⣿⣿⣿⣿
⣟⢻⡟⣿⣿⡻⠿⡻⡀⢝⠀⡁⢸⢟⣿⣿⣿⡇⠠⣀⣔⢆⣆⠀⣿⣿⡿⠰⢄⠀⠀⠈⣿⣿⣿⢟⣍⠙⣿⢰⣆⢇⣿⡆⣴⣬⠙⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⢟⢿⡆⢧⢨⣿⣿⢟⣿⣿⡿⡟⢿⣿⡇⢨⣿⣿⣿⣿⣿
⠈⠩⠁⠹⠁⠻⠱⢴⡇⠠⡄⢗⠈⢁⠇⠋⠑⠇⠸⠔⢞⠲⠊⠄⢩⡭⠵⠀⣇⠀⠀⠀⠘⠻⢿⣜⣟⡧⣣⣿⠏⢰⠙⣿⠿⠴⣖⠄⠱⡍⠉⡭⢿⡿⣵⡹⠆⠐⠒⡁⠰⠈⠍⠏⢓⣉⢹⣎⡋⢊⠉⠀⠀⠫⠻⡻⠭⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠈⡀⡐⠀⠀⠀⠀⠀⠹⡏⠀⠐⠀⡎⡵⣚⡥⠨⠅⠀⠀⠀⠀⠲⡤⠰⣾⣿⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠂⠈⠑⠄⠰⠀⢄⡈⡁⠀⠈⠙⠓⠁⠑⠂⠊⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⡿⠾⠋⣵⣄⠀⠀⠀⠀⠚⢳⣷⠹⢨⣾⡎⢻⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣮⣻⣦⢻⣿⣛⣢⠀⡀⠀⢜⠕⠀⢘⣯⠁⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠗⠹⢋⠯⢥⣤⢸⠿⠂⢰⣾⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢱⣦⠀⢸⡏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⣿⣥⢤⡄⢠⣾⢀⣼⣿⠀⠘⣿⣀⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠿⠿⡗⢦⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣵⠋⣿⠘⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣻⣭⡭⠭⠽⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣂⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣝⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⢟⣵⠆⣿⣏⠎⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⡧⣻⡿⠇⣿⣿⡞⡜⠛⠉⠂⠄⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⡇⡇⠀⢸⢹⣿⣿⣣⢿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣧⢰⠉⡘⢸⣿⣿⣿⢸⣿⠛⣁⠃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⠏⣤⡄⢀⡜⣿⣿⣿⠘⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⢸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⡟⢰⡿⢀⠸⣷⢹⡿⠸⢠⡘⢿⣬⣅⢁⢡⠘⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡇⣿⡁⠈⣄⡽⠘⠁⠀⠈⣿⠈⣿⣿⡄⡀⡆⢿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⡇⣿⡅⣀⣶⠾⢾⣾⡆⠀⣿⠀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⡁⠻⠃⣐⣾⣭⣿⣶⣶⡄⠿⢀⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⡇⣭⠁⢿⣿⣿⡿⢻⣿⣷⢩⢸⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⢸⠇⣤⡞⣿⣿⠁⣿⣿⣿⠜⠈⠉⠉⠈⠁⠀⢨⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⣿⡆⡄⣧⡁⣚⣧⢿⡟⣼⢸⡿⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⣿⣟⢸⣛⡸⢱⣿⡇⠜⢸⠄⠀⠀⠀⣀⡴⢀⣔⠈⠁⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⢿⢿⣿⣿⣿⣿⣿⣿⠀⣟⠘⡇⢻⣿⣿⣿⣿⠀⣿⣳⠀⠸⠇⠆⡻⣇⠀⠛⠃⠀⠈⠀⣤⢀⣈⣻⣷⣧⣶⡄⢰⡮⡹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⡟⡿⣻⣟⣿⣿⡻⡛⡀⢙⠀⡁⢸⢿⣿⣿⣿⡇⠠⠀⢠⣆⢲⠀⢿⣿⡿⠸⠃⠀⠀⠀⢻⣿⣿⡿⣫⡉⢻⡇⣦⠃⣿⡎⣴⣬⠙⠀⣽⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⡆⢧⢨⣿⡿⡿⠿⣿⢟⣻⣿⣿⡇⢘⣿⣿⣿⣿⣿
⠉⠘⠩⠿⡕⠟⠻⣼⡅⠠⡄⢗⠈⢁⢛⠩⢱⠁⠸⣸⠸⠞⠋⠂⢩⡭⠵⠀⠀⠀⠀⠀⠀⠻⠿⣧⣻⣛⢜⣼⡟⢰⠘⣿⠿⠴⣖⠄⢱⢬⡹⡍⡯⢽⣿⡯⣼⡻⣿⠂⢨⠈⠭⡏⡻⠁⣿⡩⣻⡛⠁⡀⠰⡟⡽⠏⠽⠙
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⡀⡐⠀⠀⠀⠈⠀⢹⠆⠀⠘⡂⡎⡵⣚⡥⠀⢅⠀⠀⠀⠀⠲⣤⠌⣶⣿⡏⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠄⠁⠈⠉⠂⠈⠱⠁⠲⠀⢄⡈⡁⠈⠈⠙⠒⠀⠑⠀⠎⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠿⢟⠉⣵⣶⠄⠀⠀⠀⠒⢪⣶⡹⠃⣾⡧⢹⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡝⣷⣹⣿⣛⣷⠀⡆⠀⠸⡫⠂⢨⣭⠁⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠸⣃⠩⢵⣤⢰⡷⠂⢠⣦⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢳⣦⠀⢸⡏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⠁⠀⠀⣗⣢⣤⡄⢰⡶⣀⣼⣿⠀⠘⣿⣀⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡭⣟⢛⡏⠳⡄⠀⠁⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠈⠁⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⠭⠭⠽⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣝⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⢟⣵⠆⣿⣏⠎⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⡧⣻⡿⠇⣿⣿⡞⡜⠛⠉⠂⠄⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⡇⡇⠀⢸⢹⣿⣿⣣⢿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣧⢰⠉⡘⢸⣿⣿⣿⢸⣿⠛⣁⠃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⠏⣠⡆⢀⡜⣿⣿⣿⠘⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⡟⢠⡿⢀⠸⣷⢹⡿⠸⢠⡘⢿⣬⣅⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡇⣿⡁⠈⣄⡽⠘⠁⠀⠘⣿⠈⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⡇⣿⡅⣀⣶⠾⢾⣾⡆⠀⣿⠀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⡁⠻⠃⣐⣶⣭⣿⣶⣶⡄⠿⢀⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠘⡇⣭⠁⢿⣿⣿⡿⢻⣿⣷⢩⢸⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⠀⢸⠏⣤⡞⣿⣿⠁⣿⣿⣿⠜⠈⠉⠁⠈⠁⠀⠨⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡄⣧⡁⣚⣧⢿⡟⣴⢸⡿⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⣿⣟⢸⣛⡸⢱⣿⡇⠜⢸⠄⠀⠀⠀⣀⡴⢀⣔⠈⠁⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⢿⠀⣟⠸⡇⢻⣿⣿⣿⣿⡀⣿⣳⠀⠸⠇⠆⡻⣇⠀⠛⠃⠀⠈⠀⣤⢀⣈⣻⣷⣧⣶⡄⢰⡮⡹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⡿⡽⣻⣟⢻⣛⡿⠟⡀⢙⠀⡁⢸⢟⣿⣿⣿⡇⠠⠀⠰⣦⢲⠀⢿⣿⡿⠸⠃⠀⠀⠀⢻⣿⣿⡿⣫⡉⢻⡇⣦⠃⣿⡆⣴⣬⠙⠀⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⡆⢧⢸⣿⣿⠿⣿⣿⣿⣿⡿⣿⡇⢸⣿⣿⣿⣿⣿
⠉⠙⠬⠝⠹⠙⠞⡸⡁⠠⡀⢗⠈⢁⠙⠳⠑⠁⠸⣧⠅⡚⠊⠂⢩⡭⠵⠀⠀⠀⠀⠀⠀⠻⠿⣧⣻⣛⢜⣼⡟⢰⠘⣿⠿⠴⣖⠄⠉⠍⢽⡿⠹⢭⣯⡥⡿⠚⢟⠂⢨⠈⣽⡧⣛⢶⢹⡋⣡⠊⠍⡀⠘⡻⡽⠫⢽⢉
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠈⠀⢀⡀⡀⠀⠀⠀⠈⠀⢻⠆⠀⠘⠂⡎⡵⣚⡥⠀⢅⠀⠀⠀⠀⠲⣤⠌⣶⣿⡏⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠤⠉⠈⠁⠂⠉⠳⠁⠰⠈⢄⡈⡁⠈⠈⠙⠒⠀⠁⠢⠎⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠿⢟⠉⣵⣶⠄⠀⠀⠀⠒⢪⣶⡹⠃⣾⡧⢹⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡝⣷⣹⣿⣛⣳⠀⡆⠀⠸⡫⠂⢨⣭⠁⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠸⢃⠩⢵⣤⢰⡷⠇⢠⣦⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢱⣦⠀⢸⡇⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⠁⠀⠀⡿⣦⣤⡄⢰⡶⣀⣼⣿⠀⠘⣿⣀⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡭⣟⢛⡏⠳⡄⠀⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣻⣭⠭⠭⠽⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡔⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⡿⢛⣇⣿⢎⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠉⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⡫⣶⣿⣼⣿⣏⡜⠛⠛⠉⠂⠄⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⡇⡅⠉⠸⣿⣿⢹⡸⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⡇⣡⢒⠂⣿⣿⣼⢱⢻⣿⠛⣁⠃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡗⢡⠀⡀⢹⣿⣿⠟⢸⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⢃⣿⢀⠀⢸⣧⣿⠀⢸⣿⣿⣬⣅⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡏⣼⡃⡈⢰⡜⠸⡏⠀⢸⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⠃⣿⠀⢐⣭⣥⣰⡡⠘⠘⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⠘⠿⢠⢸⣛⣓⣺⣯⣅⠂⢿⣿⣿⣟⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠸⢨⡏⡋⣿⣿⣿⣿⢿⣿⡆⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⡄⠾⢧⡄⣿⣿⣿⢰⣿⣿⣧⠀⠉⠁⠀⠀⠀⠀⠨⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡌⡈⢉⣟⢿⣿⣿⠀⣿⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⢿⡸⢿⡺⣿⡇⡾⡘⡏⣦⠀⠀⠀⠀⣠⡆⣠⠃⠈⠸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣟⠘⡇⢻⣿⣿⣿⣿⠀⣿⣶⠀⢸⢠⣛⠿⡐⡃⠙⠂⠀⠀⢀⣤⢀⣉⣻⣿⣴⣶⠀⢦⡨⡻⣻⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⠿⣟⢟⠟⣛⣛⣛⠟⡀⢛⠀⡁⢸⣻⣿⣿⣿⡇⠠⡀⢄⣖⠆⠸⣿⣿⠧⠹⡃⠀⠀⠀⢿⣿⣿⣟⣭⡉⣿⢰⣧⠇⣿⡆⣴⣬⠉⠀⣟⠛⡻⡿⣻⣿⣿⣟⣛⣿⣛⡆⢧⢸⡟⡛⣿⣻⣿⡿⣿⡟⣟⡇⢸⣿⣿⣿⣟⣿
⠉⠉⠙⠈⡫⢟⠟⢹⡃⠠⡀⢧⠘⢀⣝⠃⡁⠁⠸⠌⣢⠋⠑⠀⢩⡭⠗⠀⠀⠀⠀⠀⠈⠛⠿⣼⣿⡵⣡⣿⠟⢰⠘⢿⠿⠴⣖⠄⢁⣐⣎⣕⠳⢡⣫⣗⣰⣽⣍⡆⢠⠈⡅⣀⣜⣔⣘⡟⠝⣐⠁⠀⢈⠝⢽⢽⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢈⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠄⢊⡫⢒⡤⠠⢕⠀⠀⠀⠀⠰⡦⡐⣾⣿⡏⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠉⠈⠁⠃⠀⠹⠉⠰⠈⢄⣈⡁⠀⠉⠈⠙⠀⠁⠂⠏⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣴⠿⣛⠉⣷⣦⠀⠀⠀⠀⠘⢥⣷⠹⢡⣿⡗⢹⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣝⢷⡽⣿⣻⠳⢀⢄⠀⢈⠕⠁⢨⣴⠀⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠋⠈⣫⠔⠒⠶⠸⠛⠁⢰⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢱⣦⠀⢸⡇⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡀⠀⠀⣿⣧⣤⡄⢸⣿⣀⣸⣿⠀⠘⣿⣀⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⡾⣩⠩⡅⠙⠆⠀⠁⠉⠁⠁⠈⠁⠉⠉⠀⠀⠀⠈⠈⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⠈⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣻⣭⠭⠭⠽⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠐⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⡿⢛⣇⣿⢎⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⡫⣶⣿⣼⣿⣏⡜⠛⠛⠉⠂⠄⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⡇⡅⠉⠸⣿⣿⢹⡸⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⡇⣡⢒⠂⣿⣿⣼⢱⢻⣿⠛⣁⠃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡗⢡⠀⡀⢹⣿⣿⠟⢸⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⣿⢃⣿⢀⠀⢸⣧⣿⠀⢸⣿⣿⣬⣅⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡏⣼⡃⡈⢰⠜⠸⡏⠀⢸⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⢸⠃⣿⠀⢐⣭⣥⣰⡡⠘⠐⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⠘⠿⢠⢸⣛⣓⣺⣯⣅⠂⢿⣿⣿⣟⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠸⠸⢨⡏⡋⣿⣿⣿⣿⢿⣿⡆⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⣿⠀⡄⠾⢧⡄⣿⣿⣿⢰⣿⣿⣧⠀⠉⠁⠀⠀⠀⠀⠨⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣇⢸⣿⡆⡌⡈⢉⣟⢿⣿⣿⠀⣿⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣿⡇⠇⢿⡸⢿⡺⣿⡇⡶⡘⡏⣦⠀⠀⠀⠀⣠⡆⣠⠃⠈⠸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⠘⡇⢻⣿⣿⣿⣿⠀⣿⣶⠀⢸⢠⣛⠿⡐⡃⠙⠂⠀⠀⢀⣤⢀⣉⣻⣿⣴⣶⠀⢦⣨⡻⣻⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⢿⣿⣿
⢿⣟⣟⣟⣟⣛⣻⠟⡀⢟⠀⡁⢸⣟⣿⣿⣿⡇⢠⠀⢰⣖⠆⠸⣿⣿⠧⠙⠇⠀⠀⠀⢿⣿⣿⣟⣭⡉⣿⢰⣧⠇⣿⡆⣴⣬⠉⠀⡟⡛⡻⡿⣿⣿⣿⣿⢛⣛⣛⡂⠧⢘⡿⣿⣿⣿⣿⣿⣿⡟⣿⡇⢸⣿⣿⣿⣿⣿
⠊⠙⠙⠙⠍⠳⠉⣺⡃⠀⡄⢧⠈⢀⠝⠣⡑⠅⠸⠵⠰⠫⠑⠀⢩⡭⠗⠀⠀⠀⠀⠀⠈⠛⠿⣼⣿⡵⣡⣿⠏⢰⠘⢿⠿⠴⣖⠄⢡⣴⣸⡂⢽⣩⡯⡃⢆⢳⠩⡄⢠⠈⠝⣉⢇⣿⢙⠐⡙⣙⢳⠄⢨⠙⠻⣯⡮⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠐⠀⠫⠯⠁⢈⠇⢊⡫⢒⡤⠠⢕⠀⠀⠀⠀⠰⡦⡐⣾⣿⡏⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠉⠈⠁⠂⠈⠱⠁⠰⠈⢄⡈⡁⠉⠈⠈⠘⠘⠁⠂⠎⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣴⠿⣛⠉⣷⣦⠀⠀⠀⠀⠘⢥⣶⠹⢡⣿⡇⢹⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣝⢷⡽⣿⣻⠳⢀⢄⠀⢈⠕⠁⢨⣴⠀⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠋⠈⢫⠔⠒⠶⠸⠛⠁⢰⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢱⣦⠀⢸⡇⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡀⠀⠀⢿⣣⣤⠄⢸⣿⢀⢘⣻⠀⠘⣿⣀⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⡾⣩⠩⡅⠙⠆⠀⠁⠁⠈⠁⠈⠉⠉⠁⠁⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⠈⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣻⣭⠭⠭⠽⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠎⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⡿⢿⢰⣦⡹⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⡿⣫⣾⣿⢸⣿⡵⡙⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⢚⡛⠋⠹⣿⣷⢣⢻⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⡎⡎⡤⠀⡏⣿⣾⠀⣿⣿⠛⣁⠃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡏⣀⠈⣤⠀⢿⣿⠇⢹⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⡿⢠⡿⢀⣿⡄⠸⣿⡀⢸⣿⣿⣬⣅⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡇⣸⡇⠘⣿⡇⡇⠏⠇⢸⣿⣿⣿⣿⡄⡌⡆⢿⣷⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠁⢸⠃⣿⡇⣐⣚⣿⣅⠀⡄⠈⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⠀⣿⠁⠭⣽⣓⣒⣂⠀⠇⢿⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠘⠘⣰⠆⣼⣿⣿⣿⣿⣿⠆⢠⢸⣿⣿⣿⡿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⠟⠀⠰⢿⢁⣿⣿⣿⢩⣼⣿⡏⠀⠀⠉⠁⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⣎⡻⠀⢟⣙⣾⣿⡿⢸⣿⣿⡇⣡⢀⠀⠀⠀⠀⠀⡀⢀⠰⡌⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠸⣿⡇⡆⡘⡿⣜⣿⡇⡇⣿⡿⡃⠃⠸⠀⡀⢀⣠⣾⣣⠮⠄⠀⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠀⣿⣷⢀⠁⡸⢿⣆⠙⠃⢹⣾⡇⠀⠀⢰⣆⣭⣬⣿⣷⣶⣇⠰⡨⡙⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡀⢿⠀⣁⢸⣿⣿⣿⣿⡇⢠⣤⣤⣦⠐⢻⣶⡾⠘⡥⡹⣽⡂⠀⠘⢿⣿⡿⣡⣤⡈⡟⣦⠃⣿⡎⣴⡬⠙⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣾⡇⠸⡅⢿⠘⢹⣿⣿⣿⡇⠸⣿⣿⢿⠂⠘⣭⠷⠆⢳⡾⡀⠁⠀⠀⠈⠙⠳⠽⠯⢏⣼⠏⢰⡙⣿⠿⠴⣖⠄⢹⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⡆⢠⠈⣿⣿⣿⣿⣿⣿⣿⣿⣽⡆⢸⣿⣿⣿⣿⣿
⠭⠋⢉⠙⠛⠿⠟⢿⡇⠀⠃⢈⡀⡑⠛⠉⠉⠛⠀⣿⡿⡚⣯⠀⢻⡫⢖⡦⠡⠁⠀⠀⠀⠀⢙⠷⣆⢿⣿⡏⣀⠀⠈⠈⠭⠀⠄⠄⠀⠀⠀⠄⠉⠈⠉⠛⠛⠛⠏⠳⠈⢄⣉⡁⠉⠉⠙⠛⠛⠛⠣⠎⠈⠨⢀⠁⠀⠙
⠀⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠈⠈⠀⠈⠠⠘⣦⡳⣮⡀⣿⣦⠀⠀⠀⢰⣟⢷⣶⠹⠃⣿⠗⢹⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠈⠉⠀⠀⠀⠀⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠚⣷⠻⠟⠛⢀⠀⢘⡩⢈⠱⠁⢠⣶⠀⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⠀⠀⣦⡍⠙⠚⢘⣈⠁⢰⣾⠀⢸⣽⠀⢸⣿⠀⢸⣿⠉⢳⣦⠀⢸⣏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢞⣻⣻⡟⡳⡄⠀⣿⣧⣤⡄⢸⣿⣀⣸⣿⠀⠘⣿⣄⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠋⢸⠀⣳⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠈⠈⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠭⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⡿⢿⢱⣮⡹⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⡿⣫⣾⣿⢸⣿⡵⡙⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⢚⡛⠋⠹⣿⣷⢣⢻⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⡎⡎⡤⠀⡏⣿⣾⠂⣿⣿⠛⣁⢃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡏⢀⠈⣤⠀⢿⣿⠇⢹⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⡿⢠⡿⢈⣿⡀⡸⣿⡀⢸⣿⣿⣬⣅⢁⢡⠘⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡇⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡇⣸⡇⠘⣿⡇⡇⠏⠇⢸⣿⣿⣿⣿⡄⡌⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠸⣿⡇⠁⢸⠃⣿⡇⣐⣛⣿⣇⠀⡄⠈⣉⣀⣐⣨⣧⠀⢱⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⠀⣿⠁⠭⣽⣓⣒⣂⠀⠇⢿⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠘⠘⣰⠆⣼⣿⣿⣿⣿⣿⠆⢠⢸⣿⣿⣿⡿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⠟⡀⠰⢿⢁⣿⣿⣿⢩⣼⣿⡇⠀⠈⠉⠁⠀⠀⠀⠀⠘⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠘⣿⣿⣿⣿⣧⢸⣎⡻⠀⢟⣙⣾⣿⡿⢸⣿⣿⡇⣡⢀⠀⠀⠀⠀⠀⡀⢀⠰⡌⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠸⣿⡇⠆⡘⡿⣜⣿⡇⡇⣿⡿⡃⠃⠸⠀⡀⢀⣠⣾⣣⠮⠄⠀⢿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠀⣿⣷⢠⠁⡸⢿⣆⠙⠃⢹⣾⡇⠀⠀⢰⣆⣭⣬⣿⣷⣶⣇⠰⡨⡙⣿⣿⣿⡧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡀⢻⠀⣅⢸⣿⣿⣿⣿⡇⢠⣤⣴⣦⠰⢿⣶⡾⠘⢥⡹⣽⡂⠀⠘⢿⣿⡿⣡⣤⡈⡟⣦⠃⣿⡎⣴⣬⠙⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⡄⢿⠘⢿⣿⣿⣿⡇⢸⣿⣿⣿⡆⠘⣭⠷⠆⢻⣿⡀⠁⠀⠀⠈⠙⠳⠽⠯⢏⣼⠏⢰⡙⣿⠿⠴⣖⠄⢹⣿⣿⣿⣿⣿⣿⣿⡻⣿⢿⡇⢸⠘⣿⣛⣿⣿⣿⣿⣿⣿⣻⡆⢸⣿⣿⣿⣿⣿
⡛⠛⠛⠛⠏⠉⠉⢟⠃⠘⡃⢈⡀⡘⣿⡋⠹⠟⠀⣿⡿⡻⣯⠀⢻⡯⢖⡦⠡⠁⠀⠀⠀⠀⢙⠷⣆⢿⣿⡏⣀⠀⠀⠈⠭⠤⠠⠠⠀⢀⠀⠬⠉⠉⠉⠋⠛⠛⠟⠳⠨⢄⢈⡁⠋⠉⠛⠛⠛⠛⠻⠏⠈⠑⠙⣑⣹⢿
⠁⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠁⠀⠁⠀⠀⠀⠀⠈⠡⠘⣦⡳⣮⡀⣿⣦⠀⠀⠀⢰⣟⢷⣶⠹⠃⣿⠗⢹⣦⠀⢸⣿⠟⢿⣦⠀⢠⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⢁⠀⠀⠂⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠚⣷⠻⠿⠛⢀⠀⢘⠩⢈⠵⠁⢠⣴⠀⢸⣿⠀⢸⣿⣀⣸⡿⠀⢸⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⠀⠀⣦⡍⠙⠚⢘⣘⠁⢰⢶⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢳⣦⠀⣸⡏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢞⣻⣻⡟⡳⡄⠀⣿⣧⡤⡄⢸⣿⠀⣼⣿⠀⠘⣿⣄⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠋⢸⠀⣳⠁⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠽⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠎⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⡿⢿⢱⣮⡹⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⡿⣫⣾⣿⢸⣿⡵⡙⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⢚⡛⠋⠹⣿⣷⢣⢻⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⡎⡎⡤⠀⡏⣿⣾⠀⣿⣿⠛⣃⢃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⢿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡏⢀⠈⣤⠀⢿⣿⠇⢹⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⡿⢠⡿⢈⣿⡆⠸⣿⡀⢸⣿⣿⣬⣅⢁⢡⠘⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⡇⣸⡇⠘⣿⡇⡇⠏⠇⢸⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠁⢸⠃⣿⡇⣐⣛⣿⣅⠀⡄⠈⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⢸⠀⣿⠀⠭⣽⣓⣒⣂⠁⠇⢿⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠘⠘⣰⠆⣼⣿⣿⣿⣿⣿⠆⢠⢸⣿⣿⣿⡿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⠟⡀⠰⢿⢁⣿⣿⣿⢩⣼⣿⡇⠀⠈⠉⠁⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⣎⡻⠀⢟⣙⣾⣿⡿⢸⣿⣿⡇⣡⢀⠀⠀⠀⠀⠀⡀⢀⠰⡜⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠸⣿⡇⠆⡘⡿⣜⣿⡇⡇⣿⡿⡃⠃⠸⠀⡀⢀⣠⣾⣣⠮⠄⠀⢿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⣷⠀⠁⡸⢿⣆⠙⠃⢹⣾⡇⠀⠀⢰⣆⣭⣬⣿⣷⣶⣇⠰⡨⡙⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡀⢻⠀⣅⢸⣿⣿⣿⣿⡇⢠⣤⣴⣦⠰⢻⣶⡾⠘⢥⠹⣽⡂⠀⠈⢿⣿⡿⣡⣤⡈⡟⣦⠃⣿⡎⣴⣬⠙⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⡅⢿⠘⢻⣿⣿⣿⡇⠸⣿⣿⣿⡆⠘⣭⠷⠆⢻⣿⡀⠁⠀⠀⠈⠙⠳⠽⠯⢏⣼⠏⢰⡙⣿⠿⠴⣖⠄⢹⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⡇⢸⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣟⣻
⠉⠁⠀⠉⠉⠉⠙⠛⡃⠀⠃⢈⡀⡘⠫⠙⠙⠛⠀⣿⡿⠱⣯⠀⢻⡫⢖⡦⠡⠁⠀⠀⠀⠀⢙⠷⣆⢿⣿⡏⣀⠀⠀⠈⠉⠤⠠⠀⠄⢀⠀⠬⠉⠉⠉⠉⠛⠛⠟⠳⠨⢄⢈⡉⠉⠉⠙⠛⠛⠛⠳⠏⠈⠩⢉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠡⠘⣦⡳⣮⡀⣿⣦⠀⠀⠀⢰⣟⢷⣶⠹⠃⣿⠗⢹⣦⠀⢸⣿⠛⢿⣦⠀⢠⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⢀⠀⠀⠂⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠚⣷⠹⠿⠛⢀⠀⢘⠩⢈⠱⠁⢠⣲⠀⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⠀⠀⣦⡍⠙⠚⢘⣈⠁⢰⣷⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢳⣦⠀⢸⡏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢞⣻⣻⡟⡳⡄⠀⢾⣧⣤⡄⢸⣿⣀⣼⣿⠀⠘⣿⣄⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠋⢸⠀⣳⠀⠀⠀⠉⠁⠉⠁⠈⠁⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢭⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⣛⢿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⢟⣩⣶⠇⣿⡇⢛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣧⢻⠿⠟⠂⣿⣧⢂⢺⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⡜⣖⢀⠀⢻⢿⣯⣧⡻⣿⣿⠛⣃⢃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⡌⠈⢛⠘⠸⣿⣏⡆⢹⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⢿⠏⣰⠀⣿⣇⠀⠹⣿⢡⠈⣿⣿⣬⣅⢁⢡⠘⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⢸⢀⣿⠀⣿⣿⣧⠀⢸⠘⢰⣿⣿⣿⣿⡄⡀⡆⣿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠀⠈⢸⡟⠀⠿⠿⠿⢀⠄⠀⠈⣉⢀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⢠⠀⣸⡇⣛⡿⠯⠥⠈⢈⡇⠇⢿⣿⣿⣿⣿⡈⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠘⢀⣉⢠⣾⣿⣿⣿⡇⣾⣧⢠⢸⣿⣿⣿⣿⡇⠂⠇⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⠀⣿⢸⣿⣿⣿⣿⡇⢻⢛⡀⣴⡶⠟⣿⣿⢩⣼⣇⣿⣿⠈⠀⠟⠉⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢸⡘⠷⠓⠀⡇⣿⣿⣾⡟⣸⣿⣿⡇⣱⢀⠀⠀⠀⠀⠀⡠⢀⠐⡌⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠸⣿⡇⠆⢹⢿⡹⣧⣿⣑⢿⣿⣿⡃⠉⠸⠀⡀⢀⣤⣾⣧⠾⠀⠀⣹⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⣷⠠⠀⡻⢷⡈⢻⡿⣠⠘⢛⣃⠀⠀⢰⣯⣥⣤⣿⠿⢿⣇⢐⢎⢿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡀⢻⠀⣅⢸⣿⣿⣿⣿⡇⢠⣤⣴⣆⠋⢿⣿⡧⢳⢧⡆⢘⡿⠆⠀⠈⢿⣿⣿⣱⣦⠂⡏⡌⢾⡇⣴⣬⠙⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⡅⢿⠘⢫⣿⣿⣿⡇⠸⣿⣿⣟⡔⢸⡭⠷⠈⢸⣟⠌⠁⠀⠀⠀⠀⢙⠻⠾⠭⣊⡾⢃⡘⣿⠿⠴⣖⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⠅⢸⣿⣿⣿⣿⣿
⠃⠘⠁⠊⠭⠋⠛⣻⠃⠀⠃⠀⡀⡘⡻⠛⠍⠛⠀⣟⣿⠿⢿⠀⠿⢖⠵⣖⢠⠥⠄⠀⠀⠀⠀⢘⣿⡂⣿⣿⢀⠀⠁⠈⠍⠤⠤⠀⠄⠀⠀⠬⠉⠉⠉⠉⠛⠛⠟⠱⠨⢄⣈⡉⠉⠉⠙⠛⠙⠛⠃⠏⠈⠉⢁⠉⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠁⠙⠀⠈⠀⣨⣾⡷⡽⣆⣿⣿⠄⢀⠀⠀⣖⢶⣶⠹⠋⠸⠘⢻⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠂⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠂⡿⠸⢛⡛⠚⢠⣀⡅⢐⠅⠁⢰⣾⠀⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣌⠓⠀⣷⡖⠈⠈⢘⣛⠁⢰⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢳⣦⠀⢸⣟⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡝⢱⡆⢾⠀⠑⠀⣿⣧⣤⡄⢸⣿⣀⣼⣿⠀⠘⣿⣄⣸⡿⠀⢸⣿⠀⢸⢿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠸⠀⠈⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⢿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⡿⣛⣽⡃⣷⡜⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡔⣺⢿⣿⡄⣿⣏⡰⢁⢺⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⡸⡀⠁⠀⣿⣿⣴⠈⡌⣿⣿⣿⠛⣁⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⢿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣝⢀⣀⠤⢏⢿⣿⢂⠁⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⠋⣤⠀⣷⡘⡈⠻⣯⠣⠈⠿⣿⣿⣬⣥⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⣿⡇⡇⠀⣿⢸⣿⣿⠀⠠⠈⠃⠀⢰⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣿⡇⠁⢀⡟⠈⢿⠿⢀⠀⡄⢂⠐⠈⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⠠⢘⡇⣶⣒⠳⠸⣇⠈⠈⡇⠇⢿⣿⣿⣿⣿⡈⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠀⠤⢰⣶⣾⣿⡇⣿⣤⡥⢣⢠⢸⣿⣿⣿⣿⡇⠂⠇⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⠻⠟⢰⣿⠘⢿⡏⣽⢱⣿⣧⣄⠁⡈⠀⠟⠉⠉⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢀⡛⠆⠋⢘⢸⣇⡟⣼⣿⣿⣿⣿⡇⠡⠇⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠸⣿⡇⢨⠿⣏⢹⢡⣿⣿⣿⣿⣿⡇⠀⠘⠀⡀⠀⠀⣀⠀⣠⠀⠃⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠀⣿⣷⠈⢈⢻⠷⢈⠛⠛⠛⠛⢛⡂⠀⠀⣾⡴⢖⣿⣷⡞⠶⠀⡴⡝⢿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⣿⣿
⢛⡿⣟⡟⢿⢛⠻⠿⡀⢛⠀⡁⢸⣿⣿⢿⡿⡇⢠⣤⢴⡊⠚⠿⣿⠆⣿⣿⡿⠋⠀⠀⠀⢻⣿⣶⣾⣿⣷⡏⣦⠃⣿⡎⣤⣤⠙⡀⣿⣿⣿⠿⡟⠛⣻⣿⣿⡿⣿⡆⢧⢸⡿⣿⣿⠿⣟⢻⢛⢻⣿⡇⢸⣿⣿⣿⣿⣿
⡿⠸⢉⠁⣚⠋⠚⣻⡇⠀⡀⢟⠘⢙⡉⠁⠍⠅⢸⣿⣩⡝⡄⢺⣿⠆⠊⢙⣡⣤⠀⠀⠀⠀⠙⠿⠶⠦⢫⡾⠃⢀⡘⣿⠿⠼⣖⠄⢩⢹⡯⣦⣄⠹⣼⡽⠙⣝⡱⡁⢰⠈⣝⣾⣧⣺⣼⣫⡷⣛⣽⡀⢘⠛⢻⣻⢿⢭
⠠⠀⠀⠀⠀⠀⠈⠀⠁⠀⠅⢈⡀⡐⠐⠀⠀⠐⠀⡧⡾⠨⣊⢠⣓⣍⢶⣜⢿⣿⣷⡄⠀⠀⠈⠤⢸⡿⠿⢁⠂⠀⠀⠈⠉⠀⠄⠀⠀⠀⠀⠤⠁⠈⠁⠊⠉⠀⠈⠰⠀⢄⣈⡁⠈⠈⠙⠑⠙⠘⠫⠎⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣿⣿⡇⠻⡆⢟⣫⠵⢆⢠⡈⠈⠡⢐⠀⢠⣾⠟⢻⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣿⣿⢁⢀⠀⣶⣆⣈⠉⢨⣥⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⣀⣸⡿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⠿⠿⣿⠮⡋⠀⣿⡟⠛⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢱⣦⠀⢸⣏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⡞⢹⡏⢻⠀⠑⠀⣿⣧⣤⡄⢸⣿⣀⣼⣿⠀⠘⣿⣀⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠈⠈⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⢿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠎⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⡿⣛⣽⡃⣷⡝⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡔⣺⢿⣿⡄⣿⣏⡰⢁⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⡸⡀⠁⠀⣿⣿⣴⠈⡌⣿⣿⣿⠛⣃⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⢿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣜⢀⣂⠤⢏⢿⣿⢂⠁⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⡇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⠋⣤⠀⣷⡘⡈⠻⣯⠣⠈⠿⣿⣿⣬⣅⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡂⠿⢿⣿⣿⣿⢠⣿⡇⡇⠀⣿⢸⣿⣿⠀⠠⠈⠃⠀⢰⣿⣿⣿⣿⡄⡀⡆⣿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠸⣿⡇⠀⠀⡏⠈⢿⠿⢀⠀⣄⢆⠐⠈⣉⢀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣶⣶⣾⡀⣿⣷⠠⢸⡇⣶⣒⠲⠸⣇⠈⠈⡇⠇⢿⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⣿⠀⠤⢰⣶⣾⣿⡇⣿⣤⣥⢣⢠⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⠻⠟⢰⣿⠘⢿⡏⣽⢱⣿⣧⣄⠁⠈⠀⠟⠉⠉⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢀⡛⠆⠋⢘⢸⣇⡟⣼⣿⣿⣿⣿⡇⠡⠇⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠸⣿⡇⢨⠿⣏⢹⢡⣿⣿⣿⣿⣿⡇⠀⠘⠀⡀⠀⠀⣀⠀⣠⠀⠃⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⣶⠈⢈⢻⠷⢈⠛⠛⠛⠛⢛⡂⠀⠀⣾⡴⢖⣿⣷⡞⠶⠀⡴⡝⢿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⢿
⣻⣿⣿⣟⢟⣻⠟⡿⡀⢟⠀⡃⢸⣿⣿⣿⣿⡇⢠⢄⣔⡊⠺⠿⣿⠆⣿⣿⡿⠋⠀⠀⠀⢻⣿⣶⣾⣿⣷⡏⣦⠃⣿⡎⣤⣤⠙⡀⣿⣿⣿⣿⣿⢛⣿⢿⣿⣿⡟⡆⢧⢸⣿⢿⣿⣿⣻⣟⡟⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠊⠋⡋⡃⠚⠉⠙⣿⡇⠀⡀⢟⠘⢁⠌⢩⣿⠅⢸⣱⢽⡟⠄⢺⣿⠆⠈⢙⣡⣤⠀⠀⠀⠀⠙⠿⠶⠦⢫⡾⠃⢀⡘⣿⠿⠴⣖⠄⢉⢹⣷⣱⡯⣽⠩⣍⡽⣹⣿⠃⢰⠈⣥⣼⣽⣟⢼⢟⡗⣟⢹⡀⢰⠻⢫⢻⡽⡻
⠐⠀⠐⠀⠀⠀⠁⠈⠁⠀⠃⠈⡀⡐⠀⠀⠀⠀⠀⣳⡓⡨⣋⢠⣓⣍⢶⣜⢿⣿⣷⡄⠀⠀⠈⠤⢸⡿⠿⢁⡂⠀⠀⠈⠉⠀⠄⠀⠀⠀⠀⠤⠁⠈⠁⠃⠘⠑⠈⠰⠨⢄⢈⡁⠈⠈⠉⠚⠘⠑⠫⠏⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠌⠀⣿⣿⡇⠻⡆⢟⣫⠵⢆⢠⡈⠈⠁⢐⠀⢠⣾⠟⢻⣦⠀⢸⣿⠛⢿⣦⠀⢀⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣿⣿⢁⣀⠀⣶⣆⣈⠉⢨⣥⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⣀⣸⠿⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⠿⠿⣿⠮⡛⠀⣿⡟⠛⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢳⣦⠀⢸⣏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⡞⢹⡏⢻⠀⠑⠀⡻⣧⣤⡄⢸⣿⣀⣼⣿⠀⠘⣿⣄⣸⡿⠀⢸⣿⠀⢸⣿⠀⣿⡟⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠈⠈⠀⠀⠀⠁⠈⠉⠁⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠽⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⣉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠎⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⡿⠿⣿⣏⣯⢻⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⣠⣾⣿⣶⡈⣿⣎⢿⣷⢁⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⠀⡏⠛⠛⠃⡟⣿⢈⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⢿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡰⠳⢀⠀⣴⣱⣿⣏⣎⢇⢁⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⢃⡈⢩⣤⡀⠘⣿⣎⠣⠈⡈⣿⣿⣿⣬⣅⢁⢡⠘⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⡿⠁⢻⡇⢻⣿⡇⣄⠈⠻⣎⠆⠀⢻⣿⣿⣿⣿⡄⡄⡆⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣧⠈⢈⡇⢸⣿⡇⡌⢦⡈⣶⣥⠘⠈⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠐
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣶⣶⣾⡀⣿⡄⢸⡇⣬⠭⠰⣿⡌⠧⠘⣟⡇⠇⢿⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⣇⢠⣶⣿⣿⣿⡇⣿⠃⠤⢡⣽⣷⡆⣿⣷⣐⣂⢻⣣⢠⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⠀⣿⢸⣿⣿⣿⣿⡇⠛⠸⠿⢘⣿⣽⢃⣿⣿⡎⠘⡅⣿⡈⠀⡋⠉⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠘⣿⣿⣿⣿⣧⢘⡀⢋⣘⣿⡏⣾⣿⣿⣿⣿⣾⣿⠇⠞⢢⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣷⠨⢻⣄⠸⢻⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⡀⠀⢀⡀⢀⡄⠸⢸⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡃⢻⣿⣿⣿⣿⡀⣿⢰⡱⠲⣾⡆⠺⠿⠛⠛⠛⠋⠀⠀⢠⣾⠒⠶⣾⡷⠿⠁⢠⣨⠻⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡀⢿⠀⣃⢸⣿⣿⣿⣿⡇⢠⠨⢵⡔⡰⣴⣶⣾⡼⣇⢦⠀⠀⠀⠈⠻⡟⡛⠛⡻⢣⣴⠇⣣⣧⢩⡍⡭⢫⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⢸⣿⣿⣿⣿⣟⡿⣿⣿⣿⡃⢸⣿⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⡇⢿⠘⢿⣿⣿⣿⡃⢸⢸⠿⢀⡀⣿⣿⣯⡁⢿⠼⠧⠀⠀⠀⠀⠈⢩⣭⣶⠟⠁⠀⢦⠻⣞⠳⠥⠂⠁⢻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⢰⣿⣿⣿⣿⣿
⢟⠛⠹⠽⣟⡛⡛⠿⡇⠸⡇⢈⡀⡞⠿⠿⠿⢿⠠⣜⣛⢸⡇⣿⣿⣘⡃⣶⣿⣿⣷⠆⢀⡀⠀⠙⠛⠁⠄⠀⠀⠀⠁⠠⠭⠤⠤⠠⠄⢀⠀⠬⠉⠉⠉⠛⠛⠓⠟⢳⠨⢄⣈⡉⠉⠉⠛⠛⠛⠛⠣⠏⠈⡹⢛⠙⢻⣿
⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠀⠈⠉⠀⢰⣿⣿⡐⡦⠭⠀⣭⣝⠛⠃⢠⣤⠕⢴⣶⠀⢠⣾⠟⢻⣦⠀⢸⣿⠛⢿⣦⠀⢠⣿⢿⣧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⢟⠹⡀⣀⠀⣿⣿⣀⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⣀⣸⡿⠀⢸⣿⠸⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⢹⢸⠈⡇⡂⠛⠀⣿⡟⠛⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠉⢳⣦⠀⣸⣟⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠥⡇⠀⠀⣿⣧⣤⡄⢸⣿⣄⣼⣿⠀⠸⣿⣄⣘⡻⠀⢸⣿⠀⢸⣻⠀⣿⡟⠛⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠁⠈⠉⠈⠈⠁⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠈⠉⠀⠈⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⣉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠎⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⡿⠿⣿⣏⣯⢻⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⣠⣾⣿⣶⡈⣿⣎⢿⣷⢁⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⠀⡏⠛⠛⠃⡟⣿⢌⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡰⠳⢀⠀⣴⣱⣿⣏⣎⢇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⢃⡈⢩⣤⡀⠘⣿⣎⠣⠈⡈⣿⣿⣿⣬⣅⢁⢱⠸⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⢠⡿⠁⢻⡇⢻⣿⡇⣄⠈⠻⣎⠆⠀⢻⣿⣿⣿⣿⡄⡈⡆⣿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠘⣧⠈⠈⡇⢸⣿⡇⡌⢦⡈⣶⣥⠘⠈⣉⣀⣐⣨⣧⠀⢱⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠐
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣶⣶⣾⡀⣿⡄⢸⡇⣬⠭⠰⣿⡌⠧⠘⣞⡇⠇⢿⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣿⠃⠤⢡⣽⣷⡆⣿⣷⣐⣂⢻⣣⢰⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⠛⠸⠿⢘⣿⣽⢃⣿⣿⡏⠘⡅⣿⡈⠀⡛⠉⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢘⡀⢋⣘⣿⡏⣾⣿⣿⣿⣿⣾⣿⠇⠞⢢⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣧⠸⡇⢸⡆⣿⣿⣿⣿⣿⠘⣷⠨⢻⣄⠸⣻⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⡀⠀⢀⡀⢀⡄⠸⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡀⣿⢰⡱⠲⣾⡆⠺⠿⠟⠛⠛⠋⠀⠀⢠⣾⠒⠶⣾⡷⠿⠁⢠⣨⠻⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⢿⠿⡀⢿⠀⣅⢸⣿⣿⣿⣿⡇⢠⠨⢵⡔⡰⣴⣶⣾⡼⣇⢦⠀⠀⠀⠈⠻⡟⡛⠛⡻⢣⣴⠇⣣⣧⢩⡍⡭⠫⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⣿⡻⢿⣿⣿⣿⣿⣾⡇⠨⡄⢿⠘⢻⣿⣿⣿⡇⠸⢸⠿⢀⡁⣿⣿⣯⡁⢿⠼⠧⠀⠀⠀⠀⠈⢩⣭⣶⠟⠁⡀⠦⠻⣞⠳⠥⠂⠁⢺⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠇⢰⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⣿
⠓⠉⠊⠚⠉⠒⠀⠛⠇⠀⠇⢈⡀⡐⠌⠋⠟⢁⠠⣜⣋⠨⠇⣿⣿⣘⡃⣶⣿⣿⣷⡆⢀⡀⠀⠙⠋⠁⠄⠀⢀⠀⣁⠠⠭⠤⠄⠤⠄⢀⠀⠬⠁⠈⡁⠛⠛⠓⠟⠱⠨⢄⢈⡁⠈⠉⠙⠑⠙⠛⠣⠏⠘⠰⠉⠈⠑⠿
⠁⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠉⠀⢰⣿⣿⡀⠀⠈⠉⠉⠉⠛⠃⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⢟⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡆⢹⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⠭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠘⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⡿⢟⢿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⣈⠭⢥⣿⡼⣿⣿⣿⣿⣿⣷⢡⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿⣷⢔⣿⣷⢻⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠐⠀⡸⢻⣿⢎⣿⣿⣿⣿⣿⣇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠠⠀⠁⠏⢿⡎⠈⢿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣅⢁⢡⠸⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⣿⣿⣿⠀⢸⡆⠈⠠⠻⡜⣦⣽⣿⣿⣿⡇⠁⢻⣿⣿⣿⣿⡄⡈⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣈⣍⢝⢿⠀⢸⡇⠀⢠⡙⣮⡘⢿⣿⣿⣿⣷⠘⠈⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣶⣶⣾⠀⣘⠁⣧⢸⣿⣿⣿⣾⣿⣿⣿⣾⡇⠇⢿⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⡯⣅⢻⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠈⠀⠀⠉⠙⠃⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⣿⣿⢰⡀⢟⣛⠿⢿⣿⣿⣿⠃⠚⢁⠄⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⡧⢙⣫⣴⣿⣿⠿⢿⣴⣉⡛⠋⠀⠀⠀⢀⠀⠀⢀⠀⠀⢠⠀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣧⣿⣿⡩⡳⡄⢦⠰⢸⣿⡃⠀⠀⠀⣾⣖⠲⣿⣷⠶⠇⠀⠄⠃⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⠸⣿⢿⠱⣘⢿⡶⢕⣈⣘⠃⠀⠀⠀⠘⢿⢟⢛⢻⢞⣤⣶⢱⣷⡸⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡀⢿⠀⣧⢸⣿⣿⣿⣦⠁⣏⢇⠠⠻⣿⣟⣻⢱⣷⣦⣀⠀⠠⠀⠉⣭⣵⡟⠙⡃⠋⠻⢿⣨⣭⡍⣀⣉⠫⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⡄⢿⠘⣿⣿⣿⣿⣷⠈⡂⠰⠷⡄⡉⠙⠘⢿⡿⠿⣧⠄⠂⠨⠁⠀⠐⠁⠀⠀⠀⡀⡻⢟⠋⠥⠄⢠⡃⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿
⠟⠛⠛⠻⠿⠿⠿⣿⡇⠀⠃⢈⡀⡚⠛⠛⠿⢿⠀⣮⡔⡃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠂⠆⠀⢀⢀⡀⣀⢨⣩⣉⢄⠀⢀⠀⠬⠉⠉⠉⠛⠛⠛⠟⠱⠨⢄⣉⡉⠉⠉⠙⠛⠛⠛⠣⠏⠘⣻⠉⠉⢿⣿
⠀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡜⣿⣿⣿⣿⣿⣿⣷⢁⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⣷⢜⠇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠹⣷⡡⠃⣿⣿⣿⣿⣿⣿⣿⣇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⢮⡻⡄⢻⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣅⢁⢱⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⠟⣭⡛⠛⢠⣤⡁⠄⢰⣿⣿⣿⣿⣿⣿⣿⡇⢁⢻⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣀⡄⢹⣿⣆⢻⡇⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠘⠘⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣬⣛⣛⡛⣷⣌⡀⢸⣿⣿⡿⢋⠅⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣎⢻⣿⣮⡻⣿⠁⠁⠚⠀⠀⠀⠀⠀⠀⡉⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢹⣷⠙⢿⣷⠙⠀⠀⢀⠄⢀⣠⣂⣰⠇⠃⣿⣿⣿⣷⠠⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⠸⣿⡆⡆⡌⠀⠀⠀⢸⣷⣬⣿⣿⡭⠀⢸⣿⣿⣿⣿⡀⠀⡀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠠⣊⠃⠇⠈⠀⠀⠀⠈⠛⠽⠶⠜⠥⠀⠸⠿⠿⢿⣿⡇⠁⠁⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠘⣿⣥⣶⣶⢆⠀⠀⠀⢀⢀⣼⣿⣿⣿⢸⡼⣿⣷⣮⡀⢀⠸⠸⠛⠛⢻⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣹⡟⢛⣟⣿⢹⡿⠟⡀⢟⠀⡁⢸⣟⡏⠹⣛⡇⠈⠛⠿⠿⡸⢿⣷⡄⠨⢔⠋⣈⠉⠙⠃⠓⠀⠝⡛⠿⣷⣿⣿⣔⣒⡒⠹⣽⣿⠀⡻⡟⢻⡟⠿⢛⣟⣿⡿⣻⣟⡆⠷⢸⣿⡿⣿⣿⣿⣿⣟⣟⣿⡇⢸⣿⣿⡻⣿⣿
⠊⡣⢛⠑⠕⠹⠖⣼⡇⠈⡄⢟⠘⢁⢅⣉⡉⢃⠐⠀⠀⠀⠀⠂⠌⠩⠴⢶⣶⠇⠀⠀⠀⠀⠀⠀⠈⠁⠈⠯⠉⠓⠢⠀⠄⢙⠟⡅⢫⠩⠞⡻⣀⣸⡩⢽⣽⣷⣏⠃⢨⠈⣍⣯⣴⣇⣱⣏⡱⣿⡯⡁⢨⠉⠋⠟⡯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡀⡐⠀⠀⠀⠘⠘⢈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠈⠁⠉⠀⠀⢀⠀⠤⠁⠈⠁⠂⠈⠓⠌⠱⠈⢄⠈⡁⠁⠉⠙⠒⠑⠀⠃⠎⠘⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡔⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡜⣿⣿⣿⣿⣿⣿⣷⢁⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⣷⢝⠇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠻⣷⡡⠃⣿⣿⣿⣿⣿⣿⣿⣇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⢮⡻⡄⢻⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣥⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⠟⣭⡛⠛⢠⣤⡁⠄⢰⣿⣿⣿⣿⣿⣿⣿⡇⢁⢻⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣀⡄⢹⣿⣆⢻⡇⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠘⠘⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣬⣛⣛⡛⣷⣌⡀⢸⣿⣿⡿⢋⠅⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣿⡇⣎⢻⣿⣮⡻⣿⠁⠁⠚⠀⠀⠀⠀⠀⠀⡉⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⢹⣷⠙⢿⣷⠙⠀⠀⢀⠄⢀⣠⣆⣰⠇⠃⣿⣿⣿⣷⠀⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⠸⣿⡆⡆⡌⠀⠀⠀⢹⣷⣬⣿⣿⡭⠀⢸⣿⣿⣿⣿⡀⠀⡀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠠⣊⠃⠇⠈⠀⠀⠀⠈⠛⠽⠶⠜⠥⠀⠸⠿⠿⢿⣿⡇⠀⠁⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠘⣿⣥⣶⣶⢆⠀⠀⠀⢀⢀⣼⣿⣿⣿⢸⡼⣿⣷⣮⡀⢀⠸⠸⠛⠛⢻⣿⣿⣧⠘⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⡱⡏⠚⠻⠛⠋⡯⠻⡀⢛⠀⡁⢸⣟⣿⡟⢟⡇⠈⠛⠿⠿⡸⢿⣷⡄⠨⢔⠋⣉⠉⠙⢃⢓⡀⠝⠛⠿⣷⣿⣿⣔⣒⡒⠹⣽⣿⠀⣛⡿⣿⡿⡟⠿⣿⣟⠟⢻⠛⡆⠷⢸⣿⡿⣿⣿⣿⣿⠻⡻⡿⡇⢸⣿⡟⢿⣻⣿
⠂⢫⢛⠐⠜⣛⠂⣸⡁⠠⡀⢟⠘⢉⠄⡁⠁⢃⠐⠀⠀⠀⠀⠂⠌⠩⠴⢶⣶⠇⠀⠀⠐⠀⠐⠀⠈⠁⠈⠯⠉⠓⠢⠀⠄⢙⢿⡅⠫⣏⡕⠀⡢⢈⣅⡉⣿⡛⡗⠃⢠⠈⠍⣫⡉⣍⡴⡝⡱⢗⠾⡀⢠⠘⠍⢩⠽⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢈⡀⡐⠀⠀⠀⠘⠘⢈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠤⠁⠈⠁⠀⠈⠐⠌⠱⠈⢄⠈⡁⠈⠈⠘⠓⠁⠀⠣⠇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡜⣿⣿⣿⣿⣿⣿⣷⢁⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⢿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣥⢁⢱⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⡿⠿⣿⠠⣿⡇⡇⢻⣿⣿⣿⣿⣿⣿⣿⡇⢁⢻⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣀⣌⢙⣎⠀⣿⡇⠀⢸⣿⣿⠿⠛⠛⠛⠻⢿⠘⠘⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣦⣛⢻⣆⢻⣷⢰⢸⢛⠅⠠⠀⠀⡀⠀⠀⠂⠃⢻⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣌⢿⣷⡹⠘⠈⠈⠀⣠⢤⣾⣷⣼⣇⠘⢠⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡎⠻⡇⠌⠀⠀⢸⣧⣶⣾⣿⣦⡄⠀⠀⠀⣿⣿⣿⣿⣷⠀⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⠀⠜⡸⠂⠀⠈⣿⣹⠿⠉⣿⠇⢀⡆⠇⢿⣿⣿⣿⣿⡀⠀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⢰⡂⠁⠀⠀⠀⢈⠙⣛⣛⣥⣤⣉⡁⠀⠸⣿⣿⣿⣿⡇⡆⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠸⢀⡄⠀⣀⠅⠐⡲⢿⠟⠉⠻⣿⢇⣏⣾⣶⣦⣭⣉⣡⣤⡞⢒⠂⢹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣹⣟⣛⡟⠟⡛⡛⠟⡀⢛⠀⡁⢸⣿⣿⣿⡿⠇⠘⢇⢰⣷⣥⢡⠜⡁⠌⣩⣲⣦⡬⠁⠨⣭⣭⢉⣝⢻⠛⠙⠃⣀⣨⣿⣿⣽⣿⠀⣿⣿⣿⣿⡿⢿⡟⢿⣿⣿⣿⡆⢷⢸⣿⣿⣿⣿⣿⣿⣿⡟⣻⡇⢸⣿⣿⣿⣿⣿
⠊⡋⠙⡫⡳⠘⠘⣸⡅⠨⡄⢟⠘⢉⠏⢛⣏⠄⢘⡦⣙⠛⠃⠀⠀⠂⢤⢉⣋⡟⣱⠙⠹⠉⠑⠘⠁⠁⠀⠀⠀⠱⠻⣻⣿⢻⢿⡄⢻⡻⢒⣷⢧⢦⣋⣽⡟⣯⣯⡀⢠⠘⣭⣿⡹⠧⣲⡳⣿⣻⡯⡄⢨⠹⢻⢙⡫⠽
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⢈⡀⡘⠀⠀⠀⠈⠈⠘⡳⡅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢀⠀⠤⠁⠈⠁⠂⠋⠒⠄⠳⠈⢄⠈⡁⠈⠈⠛⠚⠁⠙⠫⠏⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠽⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣥⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡜⣿⣿⣿⣿⣿⣿⣷⢡⢺⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⢿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣅⢁⢱⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⡿⠿⣿⠠⣿⡇⡇⢻⣿⣿⣿⣿⣿⣿⣿⡇⢁⢻⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣀⣌⢙⣎⠀⣿⡇⠀⢸⣿⣿⠿⠛⠛⠛⠛⢿⠘⠘⣉⢀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣦⣛⢻⣆⢻⣷⢰⢸⢛⠅⠠⠀⠀⡀⠀⠀⠂⠁⢻⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⡌⢿⣷⡹⢘⠈⠈⠀⣠⢤⣾⣷⣬⣇⠘⢠⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡎⠻⡇⠌⠀⠀⢸⣧⣶⣾⣿⣦⡄⠀⠀⠀⣿⣿⣿⣿⣷⠀⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⠀⠜⡸⠂⠀⠈⣿⣩⠿⠉⣿⠇⢀⡆⠇⢿⣿⣿⣿⣿⡀⠀⡀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⢰⡂⠁⠀⠀⠀⢈⠙⣛⣛⣥⣤⣉⡁⠀⠸⣿⣿⣿⣿⡇⡇⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠸⢀⡄⠀⣀⠅⠐⡲⢿⠟⠉⠻⣿⢇⣏⣾⣶⣦⣭⣈⣡⣤⢞⢒⠂⢹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠛⠛⡟⠟⡀⢟⠀⡁⢸⣟⢿⠿⣿⠇⠘⢇⢰⣷⣧⢡⠜⡁⠈⠭⣲⡦⣬⠁⢨⣭⣍⢉⣝⢻⠛⠙⠃⡀⣨⣿⣿⣽⡿⠀⣻⣿⠿⠿⣿⣿⡟⣿⣿⢿⢿⡆⠷⢸⣿⣿⣿⢿⣿⡿⣝⣿⢿⡇⢸⢿⢿⣻⢿⣿
⠚⠙⢒⡋⠈⠔⠙⡸⡅⠠⡀⢷⠘⢉⠰⠣⢋⠀⢘⡤⢙⠛⠃⠀⠀⠀⢀⠈⣯⠙⠓⠑⠋⠉⠐⠁⠁⠁⠀⠀⠀⠡⠓⣪⣿⢛⢿⡄⠫⠿⢔⢠⢪⣦⣧⣭⢛⠅⣢⠁⢠⠘⢅⣚⣏⣍⢁⣲⠆⠾⡶⡀⢠⠿⠌⠫⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢈⠀⡐⠁⠀⠀⠈⠈⠈⠲⢁⡂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠄⠁⠈⠁⠃⠉⠂⠌⠳⠈⢄⠈⡁⠀⠈⠙⠓⠑⠀⠣⠏⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠭⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠎⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣷⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢁⢽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠘⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡔⣿⣿⣿⣿⣿⣿⣷⢁⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠻⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣅⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⡿⢿⣿⠠⣿⡇⡇⢻⣿⣿⣿⣿⣿⣿⣿⡇⠁⢻⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣀⣌⢙⣎⠀⣿⡇⠀⢸⣿⣿⠿⠛⠛⠛⠻⢿⠘⠘⣉⣀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣦⣛⢻⣆⢻⣷⢰⢸⢛⠅⠠⠀⠀⡀⠀⠀⠃⡃⢻⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⡌⢿⣷⡹⢸⠈⠈⠀⣠⢤⣾⣷⣬⣇⠘⢠⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡎⠻⡇⠌⠀⠀⢸⣧⣶⠾⢿⣦⡄⠀⠀⠀⣿⣿⣿⣿⣷⢠⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⠀⠜⡸⠂⠀⠈⣿⣽⣷⡀⣹⠇⢀⡆⠆⢿⣿⣿⣿⣿⡀⠀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⢰⡂⠁⠀⠀⠀⢈⠙⢛⣓⣥⣤⣈⡃⠠⠸⣿⣿⣿⣿⡇⡆⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠸⢀⡄⠀⣀⠅⠐⡲⢿⠟⠉⠻⣿⢇⣏⣾⣶⣦⣭⣈⣡⣤⣞⢒⠂⢹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡀⢿⠀⡇⢸⣿⣿⣿⣿⠇⠘⢇⢰⣷⣧⢡⠜⡡⣬⣯⣶⣦⣬⣁⣨⣭⣍⣉⣝⢻⠛⠙⠃⣀⣨⣿⣿⣽⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⡄⢿⠘⣹⣿⣟⣛⠄⢸⣦⣙⠛⠃⠀⢠⣵⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⠻⣻⣿⢟⢿⡅⢻⣿⣿⢿⣯⢿⣿⣿⣿⣟⣭⠂⢠⠘⣿⣿⣿⣿⡿⣻⢟⣿⡻⡄⢘⣿⣿⣿⢯⣉
⡋⠭⢭⠭⢯⠭⠯⢻⡇⠈⠃⢈⡀⡘⠿⠛⠉⠁⠈⠊⢾⣿⣶⣶⣿⣿⠓⠻⣿⡟⠫⠉⠉⠉⠉⠩⠁⠈⠀⠀⠀⠀⠀⡈⠉⠍⠉⡀⠀⢀⠀⠤⠉⠈⠉⠂⠛⠛⠞⠰⠨⢄⢈⡉⠙⠉⠙⠛⠙⠙⠢⠎⠈⢈⠙⡉⠱⢶
⠁⠁⠉⠈⠈⠀⠀⠘⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠛⠛⠛⠉⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⠭⠭⠭⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠙⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡔⣿⣿⣿⣿⣿⣿⣷⢁⢺⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢁⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣅⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⡿⠿⣿⠠⣿⡇⡇⢻⣿⣿⣿⣿⣿⣿⣿⡇⢁⢻⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣀⣌⢝⣎⠀⣿⡇⠀⢸⣿⣿⠿⠛⠛⠛⠛⠛⠘⠘⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣦⣛⢻⣦⡻⣷⢰⢸⡟⡱⠀⠂⠀⢀⡀⠀⠀⠁⢻⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣧⡻⣿⣮⠘⠘⠀⠀⢀⡢⢴⣾⣶⣽⡂⠘⢸⣿⣿⣿⣿⡇⠂⠁⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⠈⠻⡆⣄⠀⠀⣿⣴⣶⣿⣷⣦⡆⠀⠀⣿⣿⣿⣿⣷⠠⢸⠘⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢠⡘⢱⡇⠀⠀⠹⡟⣵⣆⠎⣿⠃⠀⠇⢿⣿⣿⣿⣿⡀⠀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠐⢗⠈⠁⡀⠀⠀⠉⠛⢩⣛⣵⢾⣦⣤⢘⢛⠿⣿⣿⡇⠇⠃⠸⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡘⣿⠀⣴⡇⠀⠀⢈⡱⢿⠿⠋⠈⠹⠇⡏⢿⣿⣶⣤⣤⣶⢿⢒⠂⢹⣿⣿⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣙⣿⣿⠟⡿⣻⡿⠟⡀⢿⠀⡁⢸⢟⣿⣿⢻⡇⢛⡘⠟⠁⣠⡴⢰⡴⠀⠂⣿⣾⣷⡶⣄⣠⡦⣩⣭⢻⠟⠘⠃⣀⣨⣿⣿⣽⣿⠀⡋⡟⡿⣿⣻⣿⣟⢿⢿⣿⣿⠆⠷⢸⡿⣿⢻⣿⠿⣿⠛⢹⣿⡇⢸⣿⣯⣾⣿⣿
⠭⠓⠀⠃⠟⠙⡕⣸⡃⠠⡀⢟⠘⠈⠡⠕⠈⠁⢀⠻⠕⠌⡛⠁⠔⠀⠐⠔⠉⢹⠫⠉⠁⠟⠏⢩⠀⠁⠀⠀⡀⠡⠹⣻⣿⢟⢯⡅⠃⣟⣡⣾⠀⠊⣡⢮⡋⣐⢺⡁⢠⠈⢏⣿⣿⣿⣄⢸⢶⢋⢉⡅⢘⠙⠙⣿⢡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡀⡐⠀⠀⠀⠀⠈⠈⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠀⠀⢀⠀⠤⠁⠈⠁⠂⠘⠓⠂⠱⠈⢄⠈⡉⠐⠉⠙⠘⠘⠙⠣⠎⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⢭⠭⠭⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣠⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡔⣿⣿⣿⣿⣿⣿⣷⢁⢻⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣃⢃⢡⠸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣅⢁⢡⠘⣿⡘⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⡿⠿⣿⠠⣿⡇⡇⢻⣿⣿⣿⣿⣿⣿⣿⡇⠁⢻⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣀⣌⢝⣎⠀⣿⡇⠀⢸⣿⣿⠿⠛⠛⠛⠛⠛⠘⠘⣉⣀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣷⢀⡀⢰⡀⣦⣛⢻⣦⡻⣷⢰⢸⡟⡱⠀⠂⠀⢀⡀⠀⠀⠁⢿⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣧⡻⣿⣮⠘⠘⠀⠀⢀⡢⢴⣾⣶⣽⡂⠘⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⠈⠻⡆⣄⠀⠀⣿⣴⣶⣿⣷⣦⡆⠀⠀⣿⣿⣿⣿⣷⠠⢸⠘⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢠⡘⢱⡇⠀⠀⠹⡟⣵⣆⠎⣿⠃⠀⠇⢿⣿⣿⣿⣿⡀⠀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠐⢗⠈⠁⡀⠀⠀⠉⠛⢩⣛⣵⢾⣦⣤⢘⢛⠿⣿⣿⡇⠆⠃⠹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⠸⣿⠀⣴⡇⠀⠀⢈⡱⢿⠿⠋⠈⠹⠇⡏⢿⣿⣶⣤⣤⣴⢿⢒⠂⢹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⡞⣿⣻⣻⢻⣿⣻⡟⡀⢻⠀⡁⢸⣿⣿⣿⣛⡇⢛⡘⠟⠁⣠⡴⢰⡴⠀⠠⣽⣿⣷⣶⣤⣤⡆⣩⣭⢻⠟⠘⠃⣀⡸⣿⣿⣽⣿⠀⡻⣻⣿⠿⣿⣻⣿⢻⢿⣿⣟⡆⢷⢸⣿⣿⣿⣿⢿⣟⣟⢻⣿⡇⢸⡿⣿⣻⡿⣿
⠋⠙⠙⠷⢛⠋⢟⣺⡅⠀⡄⢿⠘⢉⠗⠜⡇⠁⢀⢳⠑⢌⣛⠁⠔⠀⡄⡒⠙⣏⡣⠉⠛⠟⠏⣝⠀⠁⠀⠀⡀⠡⠹⣻⣷⢟⢯⡆⠙⡽⡘⣦⡎⡁⣽⣿⣿⣿⣿⡁⢠⠈⣯⡟⣿⣯⣀⠀⣲⢾⣫⣅⢘⠑⡈⢏⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠃⢈⡀⡀⠀⠀⠀⠀⠈⠈⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⠀⠄⠉⠈⠉⠂⠘⠙⠌⠲⠈⢄⢈⡉⠀⠉⠉⠘⠙⠈⠣⠏⠘⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⢻⣿⠿⠿⢛⣛⣛⣛⣫⣭⡭⠭⠭⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠵⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣤⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢿⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⢂⣿⡇⣿⢸⣿⠰⢌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⠩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⠛⠛⠉⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⣿⣿⣿⣿⣷⢡⢺⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣃⢃⢡⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣇⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢻⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣅⢁⢡⠘⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⡿⠿⣿⠠⣿⡇⡇⢻⣿⣿⣿⣿⣿⣿⣿⡇⠁⢻⣿⣿⣿⣿⡄⡀⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣇⠘⠃⠘⣀⣌⢝⣎⠀⣿⡇⠀⢸⣿⣿⠿⠛⠛⠛⠛⠛⠘⠘⣉⣀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⡀⣦⣛⢻⣦⡻⣷⢰⢸⡟⡱⠀⠂⠀⢀⡀⠀⠀⠁⢻⣿⣿⣿⣿⡌⠈⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⠘⡇⢠⣶⣿⣿⣧⡻⣿⣮⠘⠘⠀⠀⢀⡢⢴⣾⣶⣽⡂⠘⢸⣿⣿⣿⣿⡇⠂⠃⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡇⠈⠻⡆⣄⠀⠀⣿⣴⣶⠿⣷⣦⡆⠀⠀⣿⣿⣿⣿⣷⠠⢸⠘⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⢠⡘⢱⡇⠀⠀⠹⡟⣴⣦⠊⣿⠃⠀⠇⢿⣿⣿⣿⣿⡀⠀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⠐⢗⠀⠁⡀⠀⠀⠉⠻⢩⣛⣵⢿⣦⣤⢘⢛⠿⣿⣿⡇⠆⠃⠹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣿⡸⣿⠀⣴⡇⠀⠀⢈⡱⢿⠿⠋⠈⠹⠇⡏⢿⣿⣶⣤⣤⣶⢿⢒⠂⢹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⡞⣿⣿⡟⡟⢻⡟⠟⡀⢻⠀⡃⢸⢿⣿⡿⢛⡇⢛⡘⠟⠁⣠⡴⢰⡴⠠⢠⣽⣿⣷⣶⣤⣤⣆⣩⣭⢻⠟⠘⠃⣀⣸⣿⣿⣽⣿⠀⣿⣟⣿⣿⣿⣻⡿⣻⣿⣿⣟⡆⠷⢸⣿⣿⣿⢿⢿⠾⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠋⠹⢛⠋⢛⡝⠻⣽⡅⠀⡄⢿⠘⢉⢗⠠⢏⠁⢀⠳⠑⢌⡛⢁⠔⢀⠀⡐⠙⠩⠝⠁⠙⠻⠯⣉⠀⠁⠀⠀⡀⠹⠙⣻⣿⢟⢯⡅⢋⣿⣗⣴⡮⠉⣖⣿⢿⡾⣣⡃⢠⠈⠏⠹⣋⣯⠚⠋⡭⣟⣫⡅⢘⠐⠋⠏⡁⣟
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠃⠈⡀⡐⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⠀⠌⠉⠈⠁⠂⠉⠒⠅⠰⠈⢄⠈⡉⠀⠉⠙⠓⠙⠘⠣⠏⠘⢸⠃⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⡏⢸⡇⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢸⣿⡇⣿⡇⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⣿⣿⣦⠻⣿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠭⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⡘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⢸⣿⠿⣿⣿⣧⠐⠋⠭⢉⣐⣒⣒⣒⣦⣤⣬⣭⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⡇⣿⢸⣿⠰⡙⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢁⣽⣭⣱⠀⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⡇⣿⢸⣿⠰⣌⡈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⢩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⢂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⡇⣿⢸⣿⣄⠌⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⠛⠛⠋⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣷⣤⣿⠨⠭⠄⡖⣿⣿⣿⣿⣿⣿⣷⢡⢺⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢣⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠘⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⡇⣿⠸⣿⣿⣿⣿⣿⠀⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣥⢁⢱⠸⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⡇⢹⡆⠿⢿⠿⠿⣿⢠⣿⡇⡇⢻⣿⣿⣿⣿⣿⣿⣿⡇⢃⢻⣿⣿⣿⣿⡎⡈⡆⢿⣷⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⡇⠘⠃⠘⣀⡍⢙⣎⠘⣿⡇⠀⢸⣿⣿⠿⠛⠛⠛⠛⢿⠘⠘⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠐
⣿⠀⠀⠀⠀⣿⣿⠘⣿⢀⡀⢰⠀⣦⡛⢻⣦⢻⣷⢰⢸⢟⠅⠠⠀⠀⡀⠀⠈⠃⠇⢿⣿⣿⣿⣿⡌⠘⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣾⣿⣿⠀⣿⠸⡇⢠⣶⣿⣿⣎⢿⣧⡙⠸⠈⠈⠀⡠⢤⣾⣷⣬⣃⠘⢰⢸⣿⣿⣿⣿⡇⠃⠇⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡄⢿⠀⣿⢸⣿⣿⣿⣿⡎⠻⡇⠌⠀⠀⢸⣧⣶⠾⢿⣦⡄⠀⠀⠀⣿⣿⣿⣿⣿⢀⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⡇⢿⠈⣿⣿⣿⣿⣧⠀⠜⡸⠂⠀⠈⣿⢵⣶⡀⣻⠇⢀⡆⠃⢿⣿⣿⣿⣿⡀⡀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⡇⢸⡆⣿⣿⣿⣿⣿⢘⡀⠁⠀⠀⠀⠈⠑⢚⣓⣥⣤⣘⡁⠀⠸⢿⣿⣿⣿⡇⠂⠇⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠸⡇⢻⣿⣿⣿⣷⠸⢀⡄⠀⡀⠄⠐⡒⢿⠟⠉⠻⣿⢇⣏⣾⣶⣦⣬⣉⣡⣤⡿⢒⠂⢹⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣟⣿⢿⣻⢻⣻⡟⡀⢿⠀⡅⢸⣿⣿⣿⣛⡆⠘⢇⢰⣵⣦⢡⠜⡀⠟⠟⡷⣶⠈⠁⣈⣭⣭⠭⣙⢻⠟⠘⠃⢀⣸⣿⣿⣿⣿⠀⡻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡆⠷⢸⣻⣿⣿⡿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠉⠙⠘⠙⣋⣟⣟⣽⡅⠠⡄⢿⠘⣿⣫⢸⡿⡇⢸⣲⣝⡛⡃⠤⠀⣀⡹⠽⢘⡱⠈⠛⠍⠻⠃⠀⠀⠅⠀⠀⡀⠣⠻⣻⣿⢻⢿⡇⠋⣝⣫⡻⢙⣭⣙⢿⣎⡮⣿⡂⢠⠈⡿⣝⣯⣗⣿⣽⣿⣿⣻⡅⢘⠯⡛⡟⠘⢛
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠃⢈⡀⡈⠀⠁⠁⠀⠈⠈⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠈⠀⠈⠉⠉⠉⠀⠀⢀⠀⠄⠉⠉⠁⠃⠙⠃⠆⠵⠈⢄⠈⡀⠀⠉⠙⠘⠙⠈⠣⠋⠈⣸⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⡆⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⢹⣷⢰⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡆⣿⡆⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⢻⣇⢻⣿⡜⢿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠭⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⡘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⢸⣿⠸⣿⣿⠀⠋⠭⢉⣐⣒⣒⣒⣦⣤⣭⣭⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⣿⣿⣿⡆⣿⡇⣯⢉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢁⣽⣭⣱⠁⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠸⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⣿⣿⣿⡇⣿⣷⢻⢸⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⢩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⢂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⣿⣿⣿⣇⢸⣿⢸⡌⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⠛⠛⠋⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⢸⣿⡀⣿⣦⠨⠄⡖⣿⣿⣿⣿⣿⣿⣷⢡⢺⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⠈⣿⡇⣿⣿⢸⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢣⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⣿⣿⣿⣿⡆⣿⡇⣿⣿⡀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⡇⣿⣧⢸⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣥⢁⢱⠸⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⢸⠿⡇⠃⡇⢹⣿⣿⣿⣿⣿⣿⣿⡇⢃⢻⣿⣿⣿⣿⡎⡈⡆⢿⣷⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣿⣿⡟⠛⡃⠛⡛⠀⢃⣁⣛⢳⡌⣿⣿⣿⣿⣿⣿⣿⣿⠸⠘⣉⣀⣒⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠐
⣿⠀⠀⠀⠀⣿⣿⠘⣿⣿⣷⣶⡆⣠⣅⠀⡄⣦⢒⢚⢃⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⢿⣿⣿⣿⣿⡌⠘⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣾⣿⣿⠀⣿⣿⣿⣿⡇⣸⣿⢰⣾⣾⠰⡂⠀⠉⢻⣿⣿⣿⣿⣿⣿⣧⢰⢸⣿⣿⣿⣿⡇⠃⠇⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⣿⣿⣿⡇⢸⣿⢸⣿⣿⠀⠀⠀⠀⠀⠝⢿⣿⣿⣿⣿⣿⡈⠀⣿⣿⣿⣿⣿⢠⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⢸⣿⢸⣿⣿⢠⣶⠂⠀⢀⣄⠘⢿⣿⣿⣿⣿⡇⠃⢿⣿⣿⣿⣿⡀⡀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⣿⣿⣿⡇⢸⣿⢸⣿⣿⠀⠀⠀⠨⠉⣙⢑⣀⡙⠿⠿⠿⠇⣀⣈⣍⠙⠉⢙⡇⠂⠇⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⡟⢸⣿⣿⠀⠀⠀⠑⢬⢋⠻⠿⠿⠿⠿⠿⣿⣿⣧⣓⣂⠀⢀⣠⠀⠰⠸⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣸⣿⡇⣿⡇⢸⣿⣿⠀⣤⣤⣴⣶⣦⣼⣿⣿⣿⣿⣷⣶⣭⣓⣠⡲⡕⣿⣿⠠⠈⠀⢹⣿⣿⣿⣽⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠿⢿⣿⣿⣿⣿⣿⣿⡇⠨⣿⣿⡇⣾⡇⢸⣿⣿⡆⣿⣿⣿⣿⣿⡿⠿⠛⠻⠿⡫⡛⡻⠿⠿⡿⠉⢹⣋⠀⠀⡄⡘⢻⣿⣿⢿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿
⠌⠀⠀⠈⠙⠀⠘⡟⡇⠈⣿⣿⡇⣿⠆⠈⠍⠙⠀⠏⡟⠉⠈⠉⠡⠀⠀⠀⠀⠈⠁⠀⠈⠀⠈⠀⠀⠀⠄⠂⠀⠀⠀⡈⠉⠉⠉⠀⠀⢀⠀⠌⠉⠉⠉⠛⠛⠛⠟⠳⠈⢄⠈⡉⠉⠉⠙⠛⠛⠋⠣⠏⠈⣿⡟⡛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠁⢧⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠉⠀⠀⠀⠂⠀⠠⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣤⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⡆⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⢹⣷⢰⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡆⣿⡆⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⢻⣇⢻⣿⡜⢿⠿⠿⢛⣛⣛⣛⣫⣭⣭⠭⠭⣟⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⡘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⢸⣿⠸⣿⣿⠐⠋⠭⣉⣐⣒⣒⣒⣦⣤⣭⣥⣤⣤⣄⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⣿⣿⣿⡆⣿⡇⣯⢉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢁⣽⣭⣱⠁⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⣿⣿⣿⡇⣿⣷⢻⢸⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⢱⠸⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⢩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⢀⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⣿⣿⣿⣇⢸⣿⢸⡌⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⠛⠛⠋⠂⠆⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⢸⣿⡀⣿⣦⠨⠄⡖⣿⣿⣿⣿⣿⣿⣷⢡⢺⣿⣿⣿⣿⡐⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⠈⣿⡇⣿⣿⢸⡇⡇⣿⣿⣿⣿⣿⣿⣿⡎⡌⣿⣿⣿⠛⣁⢃⢣⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⣿⣿⣿⣿⡆⣿⡇⣿⣿⡀⡇⡇⣿⣿⣿⣿⣿⣿⣿⣧⢡⢹⣿⣿⣇⢱⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⡇⣿⣧⢸⣿⡇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡌⡈⣿⣿⣿⣬⣥⢁⢱⠸⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⢸⠿⡇⠃⡇⢹⣿⣿⣿⣿⣿⣿⣿⡇⢃⢻⣿⣿⣿⣿⡎⡈⡆⢿⣷⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣿⣿⡟⠛⡃⠛⡛⠀⢃⣁⣛⢳⡌⣿⣿⣿⣿⣿⣿⣿⣿⠸⠘⣉⣀⣐⣨⣧⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠐
⣿⠀⠀⠀⠀⣿⣿⠘⣿⣿⣷⣾⡆⣠⣅⠀⡄⣦⢒⢚⢃⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⢿⣿⣿⣿⣿⡌⠘⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣾⣿⣿⠀⣿⣿⣿⣿⡇⢼⣿⢰⣾⣾⠰⡂⠀⠉⢻⣿⣿⣿⣿⣿⣿⣧⢰⢸⣿⣿⣿⣿⡇⠂⠇⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢿⣿⣿⣿⡇⢸⣿⢸⣿⣿⠀⠀⠀⠀⠀⠝⢿⣿⣿⣿⣿⣿⡈⠀⣿⣿⣿⣿⣿⢠⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⢺⣿⢸⣿⣿⢠⣶⠂⠀⢀⣄⠘⢿⣿⣿⣿⣿⡇⠃⢿⣿⣿⣿⣿⡀⡀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⣿⣿⣿⡇⢸⣿⢸⣿⣿⠀⠀⠀⠨⠉⣙⢑⣀⡙⠿⠿⠿⠧⣀⣈⣍⠙⠉⢙⡇⠃⠇⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⡿⢸⣿⣿⠀⠀⠀⠑⢬⢋⠻⠿⠿⠿⠿⠿⣿⣿⣧⣓⣂⠀⢀⣠⠀⠰⠸⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣸⣿⡇⣾⡇⢸⣿⣿⠀⣤⣤⣴⣶⣦⣼⣿⣿⣿⣿⣷⣶⣭⣓⣠⣮⣵⣿⢿⠀⠈⠀⢹⣿⣿⣿⣽⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠿⢿⣿⣿⣿⡿⢻⣿⡇⠠⣿⣿⡇⣾⡇⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⠛⠛⠛⠟⠙⠛⢿⡿⣿⢿⠿⣹⡻⠀⠀⡄⡜⢿⣿⣿⢿⣿⡇⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿
⠂⠀⠀⠈⠌⠌⠙⠋⡃⠈⣿⣿⡇⣿⡆⠈⢉⠍⠀⠏⡿⠉⠁⠉⠁⠋⠁⠈⠈⠀⠀⠈⠀⠀⠈⠀⠀⠀⠄⠂⠀⠈⠈⡈⠉⠉⠉⠀⠀⢀⠀⠌⠉⠉⠉⠛⠛⠛⠟⢳⠈⢄⠈⡉⠉⠉⠙⠛⠛⠋⠣⠍⠈⣿⡟⡛⠛⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⠇⠇⠩⠨⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠈⠉⠀⠀⠀⠂⠀⠠⠈⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣿⣶⣦⣍⡓⠦⣍⡻⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣶⣶⠦⣤⣤⣬⣭⣉⣙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣉⠙⣛⠷⢶⣬⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢍⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠻⠿⢷⣮⡙⣧⡚⣭⣍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢐⣶⣾⣿⣿⡜⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣩⣥⣬⣟⣛⣻⠿⠿⣷⡘⣿⣆⢛⣛⠻⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡏⡍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠤⠘⣛⣆⠆⢇⢻⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⣿⢃⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢾⣿⡌⡘⡌⢿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢁⣽⣭⣱⠁⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣷⠀⢱⠸⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠘⠈⢩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠂⢻⣿⣿
⠛⠃⠐⠂⠘⢻⠸⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠧⢻⣿⣆⠀⢇⢻⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣭⣄⣀⣀⣽⣿⡈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⡇⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⣿⣿⡈⠘⡌⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⡇⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⡇⢁⢣⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢹⣿⡀⣿⣿⣿⣿⣿⡇⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠈⡈⡆⢿⣏⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⡇⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣛⣋⡙⡆⣿⠿⠀⢁⢱⠸⣿⡘⡶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠈⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⣿⣿⣿⣿⡇⢸⢸⣿⣿⣿⣿⣿⡿⠿⠿⡛⠛⠛⠛⢘⣛⡛⠃⡇⡄⣶⠀⠀⡈⡆⢿⣷⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣿⣿⣿⣿⣷⢸⢸⣿⣿⣷⡖⠚⠋⠁⢒⣀⣒⣚⣩⠁⣤⣶⡆⡇⢡⣤⡆⢠⠀⢡⢸⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠐
⣿⠀⠀⠀⠀⣿⣿⠘⣿⣿⣿⣿⣿⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣀⣉⣩⣭⡵⢸⣿⡇⢸⡌⠘⡀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⡇⠂⠇⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢻⣿⣿⣿⣿⡄⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⢸⣿⢠⢸⠘⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⡇⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣵⣶⣶⣾⣿⢸⣿⡇⢸⣿⡀⡀⡄⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣼⣿⣿⣿⣇⠸⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⡇⠃⠇⢹⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢘⣿⡇⠈⢉⣤⠀⠰⠸⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣸⣿⣿⣿⡄⠂⢸⣿⣿⣿⣿⣿⡿⠿⢛⣛⣉⣥⣤⠴⠔⠀⢸⣿⠀⣶⣾⣿⠀⠘⠀⢻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠿⢿⣿⢿⣿⡿⠟⣿⡇⠨⣹⣿⣿⣿⣇⢰⠈⠹⠿⠻⠿⠍⠉⠛⢋⣉⣩⢄⣰⣶⣶⠀⣾⡿⠀⠊⠉⠁⠀⠀⡄⡸⣯⣾⣿⢿⣿⡇⢛⡙⣿⣯⣿⣿⣿⣿⣿⣿⣿⡂⢰⠈⣟⢿⣿⣿⣿⣿⣿⣿⡿⣇⢸⣿⡿⣯⣿⣿
⠀⠀⠀⠈⠉⠀⠀⠛⠃⠀⡿⠏⠹⢭⠻⠀⠀⠨⠀⠀⠦⠀⠈⠁⠻⠷⠿⠯⠉⠋⠙⠀⢹⠄⠀⠀⠀⠀⠄⠂⠀⠈⠈⡈⠉⠉⠉⠀⠀⢀⠀⠌⠉⢈⠁⠋⠛⠛⠟⠳⠈⢄⢈⡉⡀⠉⠛⠛⠙⠙⠣⠉⠈⣿⠃⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⡀⠀⠀⠁⠘⠂⠈⠨⠀⠀⠙⠃⠀⠈⠐⠀⠁⠀⠈⢐⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠉⠀⠀⠀⠀⠀⠠⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣅⢨⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣆⢳⠨⣍⣙⡒⠦⢬⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⡌⢧⢹⣿⣿⣷⣶⣤⣍⡓⠦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⢻⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⠦⣍⠻⢿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣉⠲⢌⡛⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣶⣍⡒⢌⡃⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢣⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣶⣍⠢⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠿⣛⣫⣭⡥⠶⠶⠖⢛⢛⣛⣛⣛⣛⣛⣛⡳⠶⣌⢻⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⢻⣿⣿⠛⠥⠂⠂⠀⠘⣿⣧⠸⣿⣿⣿⣿⣿⣇⢃⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢁⠟⣩⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢦⠹⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡘⣿⣿⣇⠐⢱⠒⠈⡄⠸⣿⡆⢿⣿⣿⣿⣿⣿⡄⡌⣿⣿⣿⣿
⠛⠿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⡏⣼⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢧⠙⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣇⢹⣿⣿⡀⢀⢽⣭⣱⠁⢻⣿⠘⣿⣿⣿⣿⣿⣷⠰⠘⣿⣿⣿
⠭⠭⠭⣭⠀⠐⠂⣿⣿⣿⣿⣿⢡⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣧⠸⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡄⣿⣿⣇⠈⠈⢩⣈⣅⠌⣿⣇⢻⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿
⠛⠂⠐⠂⠘⢻⠸⣿⣿⣿⣿⡟⢸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣇⢹⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⠸⣿⣿⣦⣤⣬⣄⣀⣀⣽⣿⠈⣿⣿⣿⣿⣿⣿⡈⠈⣿⣿
⠂⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⡇⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡄⢿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⢁⢸⣿
⡇⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⡇⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠘⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠈⠿⣿⣿⣿⣿⣿⡄⠀⣿
⡇⠀⠀⠀⢸⣿⡀⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣇⢹⠖⡈⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣧⢀⢸
⣇⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⠈⠶⠇⢻⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠰⠀⣿⣿⣿⣿⣿⡀⠀
⣿⠀⠀⠀⠘⣿⡇⢸⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠰⠒⠀⠸⡇⢻⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣇⠀
⣿⠀⠀⠀⠀⣿⣧⢸⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠶⠆⠀⣿⠸⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠐
⣿⠀⠀⠀⠀⣿⣿⠈⣿⣿⣿⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡀⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⣼⣿⣿⠀⣿⣿⣿⡄⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡇⢿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣇
⣿⠀⠀⠀⢹⣿⣿⡀⢻⣿⣿⡇⢸⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⢸⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⠈⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿
⣿⣤⣥⣼⣿⣿⣿⣇⠸⣿⣿⣿⡀⢇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣇⢈⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⢸⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡿⣿⣿⣿⣿⣿
⣻⢝⡟⢛⣿⡟⠛⠿⡀⠍⠸⠿⢿⡀⠐⠸⣿⢻⠻⢻⢟⣿⣿⢿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣻⣿⠀⣿⠸⢿⣿⣿⣽⣿⠀⡻⣻⢿⢿⡿⠿⢿⠿⣿⣿⠿⠂⠷⢸⣝⢛⢻⡟⠿⡿⡻⣿⢿⡃⠘⠿⠿⠿⢿⣿
⠀⠐⠉⢉⠟⠀⠨⣽⡁⠀⡁⠰⠁⠃⠈⡆⢩⡋⠈⠸⠗⠓⠂⢰⢠⠲⠒⠎⠋⠉⠩⢟⢭⢉⠹⠋⠉⠉⠹⠁⠙⠀⠠⠇⠛⢻⢟⠅⠑⠀⠁⠄⢓⡀⢀⠂⠈⢀⡄⡂⢠⠈⠍⠁⠟⠠⠎⡡⢩⡙⢫⡅⠀⡐⢋⢀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠹⠈⢥⠄⠀⠀⠀⠀⠀⠀⠂⠀⠔⠀⠃⠈⠈⠀⠑⢉⣁⣀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠄⠉⠈⠁⠃⠈⠐⠀⠰⠀⢄⠈⡀⠀⠉⠉⠐⠘⠀⠁⠈⠈⢱⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠐⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2779

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

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    Gemini version at https://techrights.org/n/2025/02/17/In_Europe_and_in_India_Richard_Stallman_Need_Not_Duck_Anymore_P.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ In Europe and in India Richard Stallman
Need Not Duck Anymore, People Trying to Cancel His Talk Have No
Sway⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


ONE week from now (minus 1 hour) Richard Stallman will deliver a talk about
Software Freedom (the University_of_Bozen-Bolzano_hosts_this_event). Yesterday
another Italian site published yet_another_article_about_Dr._Stallman - the
third one in Italy and in Italian by our count (certainly there are more out
there).


From what we can gather, the last time a talk by Dr. Stallman got canceled was
about a year ago. Trying to silence an innocent_person generally doesn't work.
At the end, Dr. Stallman will tell a lot of people what really happened and how
GNU/Linux_started_more_than_40_years_ago_in_Boston, not in the 1990s. This past
week we saw Linus Torvalds being subjected_to_brigading_as_well. Torvalds and
Stallman share this problem. █




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣛⣛⣛⣛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣐⣒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⠀⣿⣯⣵⡖⣦⣼⡇⠀⠀⢿⣷⠀⠀⠀⠀⠀⣿⠃⠀⠴⠶⠎⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠛⠛⡓⠀⠙⠾⠯⣿⣿⣿⡄⠀⠤⢴⣤⡄⣄⠀⠀⠀⣿⠀⣤⣤⣶⣶⣽⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠂⠀⠀⠀⠈⢦⠀⠀⠀⡀⠉⢉⣧⠈⠚⣿⣿⣷⣿⣿⠄⠀⣿⣧⡍⠙⠻⢿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣠⠊⠉⠀⠈⠙⠀⠀⠀⠀⠻⠿⣿⣿⣤⡿⠁⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⣀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠁⠀⠉⠛⠻⡛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⢀⣶⣾⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⠀⠀⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠘⣜⡿⢿⡿⢿⡀⢰⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⣗⠿⠄⠇⠨⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣥⣤⣦⣶⢧⣼⣿⣿⡿⠦⢄⠀⠀⠀⠀⠠⣤⢰⡀⢠⣄⢠⢄⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⠗⠿⣿⢿⠐⠀⠀⠀⠀⠀⠀⠃⠘⠙⠙⠋⠈⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⡀⠀⠀⠙⢿⣿⣿⣿⢿⢠⢰⣾⠈⠁⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢡⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠁⠷⡸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠌⠃⠸⣦⡀⠆⠀⠀⠀⠀⠀⠀⠙⠀⠀⢻⢣⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⡟⠞⠈⣦⣀⠁⢡⡀⠄⠀⠀⠀⠀⠀⠀⡀⠁⢸⣮⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⠃⡀⢰⢿⠏⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠄⠾⠛⠛⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⣷⠈⠀⣠⣶⠄⠀⠻⣷⣄⠀⠀⠀⠀⡦⢀⣠⣤⣴⡞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠵⠟⠈⠃⠀⡀⠀⠉⠁⠀⡀⠰⡌⠙⣦⡀⠄⠀⠀⠛⠫⡏⠁⠙⠃⠀⠂⠀⠀⢀⡆⠀⠀⠀⠀⠻⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠸⠄⢨⡀⠘⠀⠀⢤⣤⡘⠷⠀⢰⣮⠛⠈⠀⠀⣰⣶⠟⠁⠁⢢⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2849

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/17/IRC_Proceedings_Sunday_February_16_2025.shtml
    Gemini version at https://techrights.org/n/2025/02/17/IRC_Proceedings_Sunday_February_16_2025.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Sunday, February 16,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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The corresponding text-only bulletins for_Tux_Machines and for_Techrights
contain all the text.


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣴⣾⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⡿⠰⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⣶⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠉⢁⣠⣤⣶⣾⣿⣿⣾⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣀⣥⣴⣾⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⢠⣀⣀⣀⣬⣤⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠋⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣸⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠛⠁⠉⠙⠛⠛⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⠀⠀⣀⣴⣶⣿⣧⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣧⣽⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣷⡌⣿⣿⣿⣿⣿⡉⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣮
⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣼⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⡿⠋⢻⣿⣿⢀⣾⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⠛⣥⣾⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡄⠀⠀⠀⠀⠀⣞⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠛⠁⠙⣿⣿⣿⢃⣿⣿⣿⡇⠀⠀⠀⠀⠀⣃⣼⣿⠟⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⢉⠯⠍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠁⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠈⠉⠁⢸⣿⣿⣿⠇⠀⠀⠀⢀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⣀⣤⣀⣀⣀⣼⣿⣿⠟⠀⠀⣠⣾⣿⣿⣿⠛⠻⣿⠟⠉⠉⠉⢁⣼⣿⣿⣿⣿⣷⡀⢶⣿⡀⣿⣦⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡌⠛⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⠀⠀⠹⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿
⢛⣤⣶⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣍⠉⠉⠉⢉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⣿⣿⣿⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠀⣠⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠻⠿⠏⠉⣠⣾⣿⣿⣿⣿⡿⠋⠀⢠⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⡁⢀⣹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠟⠀⠀⠀⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣴⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠋⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠋⢹⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣤⣀⣤⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⣿⣿⣿⣿⢿⡿⠛⠉⢠⣤⡀⠀⢹⣿⣿⣏⣴⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣆⠀⢈⣿⣟⠁⠀⠀⠀⠀⠀⠙⠁⠀⣾⣿⣿⣿⢛⠿⢿⣿⣿⠋⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⡈⠛⠿⣿⠿⠉⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⠀⣠⣿⣿⣿⣿⡀⣷⡶⠋⢀⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛
⣿⣿⣿⣮⣉⠁⠀⠀⠙⢿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⢻⣿⣿⣿⡷⠀⠀⣠⣤⣤⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣄
⣿⣿⣿⣈⠻⠿⠿⢿⣿⡅⣼⡏⠉⠉⠁⠀⠘⣿⣿⠿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⣿⡿⠋⢻⣿⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣶⣤⡼⢟⣿⣿⣷⠶⠷⣶⣄⣀⣼⣿⣤⣀⣽⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠈⠉⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿
⡀⢹⣿⣿⣿⣿⣿⣿⣏⣤⣯⣙⣂⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠻⢷⣦⡀⢀⣴⣿⣁⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⠀⠀⠀⣾⠛⠛⠿⣷⣶⣦⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⠆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠙⢷⣶⡼⣿⣀⣀⣴⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⡿⣿⣿⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 3108

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/17/Microsoft_Lunduke_Belongs_in_4Chan.shtml
    Gemini version at https://techrights.org/n/2025/02/17/Microsoft_Lunduke_Belongs_in_4Chan.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Lunduke Belongs in
4Chan⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025,
updated Feb 17, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Putin_Facepalm:_His_trolling_isn't_even_subtle;_What_a_Loon-
                                    dick⦈_


Microsoft Lunduke (yes, he had worked for Microsoft before he became a supposed
"expert" in "Linux") is becoming_a_major_liability or somewhat of a "facepalm
moment" lately; we're all for free speech [1, 2], but calling_my_wife_and_many
others_n***** is hardly a matter of freedom of expression per se. The UK has
laws about this type of stuff and the EU (or Germany), where Codeberg is based,
also has relevant laws. Some hours ago Microsoft Lunduke published PostmarketOS
Joins_Codeberg's_Fight_Against_"Right_Wing_Forces" and days ago he published
Codeberg_Announces_"Fight_Against_Far-Right" (without specifying the causes).


"Lunduke is barking," one person told us. "I sure hope his position on the
incident is not based on having read anything about it. Such a position is not
excusable, especially if he knows the background of it."


We already known from direct experience that people spewing out words like
n***** in our communication channels are vandals_and_extremists. Provocation
and destruction are the sole goal/intention. Letting them 'off the hook' is
suicide. Hiding behind the 'veil' of free speech might be OK as long as one is
frank rather than deliberately provocative (building an online identity around
being an oppressed "target" of those who are deliberately hurt).


Assuming Microsoft Lunduke is aware of the full context, he is now trolling not
one but two decent organisations merely because they oppose racism; this_is
worse_than_trolling. Microsoft Lunduke sometimes makes a good point about
something, then he_associates_that_point_with_all_that_other_"baggage"_of_his,
in turn associating that point with bigotry or worse*; it's good to never
associate or give a dime to him; he's a prick, not contrarian. He actively
tries to annoy people. He's seeking a new kind of audience that he would be
luckier to find in 4Chan (or similar). █


_____


* 4 years ago he associated criticism of the Linux_Foundation with rejection of
vaccines [1, 2, 3].


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




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠙⠻⡄⠀⠀⠀⠀⠀⠀⠉⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⣽⡂⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣝⠻⣿⣿⣿⠁⠀⠂⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣮⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⡀⠑⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⢄⠊⠀⠀⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⡠⡀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠈⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢀⢪⠂⠀⠀⢄⠈⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣝⠛⠁⠠⠁⠀⠀⠪⠀⠀⢀⢄⠊⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⡠⡑⠁⠀⠠⡢⠁⠀⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠇⢐⠊⠀⠀⡐⠕⠀⠀⡠⡑⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠀⠀⠀⠀⢀⢌⠊⠀⠀⢔⠌⠀⠀⡠⢠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢳⡀⠠⡑⠁⠀⢀⠪⠂⠀⠀⢌⠊⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣄⠀⠈⠀⠀⡐⠑⠁⠀⢀⡪⠀⠀⢀⢿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣀⢄⠈⠀⠀⡐⠑⠀⠀⠀⠢⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠀⠀⡐⠑⠁⠀⢻⣿⣿⣛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠀⡐⠹⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠁⠀⠀⢀⠈⠀⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠁⠀⢀⢸⣿⣿⣿⣿⣿⡝⢿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠐⠉⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⠤⢤⣄⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡟⢱⡶⢤⡈⣿⢻⠛⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣽⣿⣹⣿⣽⣿⣾⣿⣿⣏⣽⣸⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿
⠈⣧⠸⠷⠞⢁⣿⣦⣶⣴⣿⠃⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⣟⢿⢿⡿⣿⣿
⠀⠈⠙⠒⠚⠋⠉⠛⠛⠛⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣟⣿⣿⣿⣇⣿⣿⣿⣿⣿⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢸⣝⣿⣿⣿⢳⣧⣭⣩⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢾⣭⣿⣿⣿⣿⣿⣿⣿⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⣿⡿⠛⠛⢛⣿⣿⣿⡇⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣄⣦⣾⣿⣔⣤⣦⣶⣿⣿⣿⢼⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣀⡀⠙⠿⣿⣿⠿⠋⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢨⣥⣶⡶⠦⡀⠁⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⠆⠈⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢒⣤⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠊⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣹⠙⠛⠿⠿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣱⣿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣦⣌⣨⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠙⠿⡏⡀⠀⠀⠀⠀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠁⠁
⠀⢰⢚⣓⢢⠀⢀⡶⠶⠄⣶⠶⢦⡀⣴⠶⣦⢠⡴⢶⡄⣠⠶⢦⠀⣧⠶⣆⠀⠀⣿⢸⡇⣿⢠⡶⢠⡶⢶⡄⠀⢰⡶⢶⡄⣠⠶⢦⡀⠀⢠⡶⢶⡄⢾⡷⢸⡷⢶⡄⣠⠶⢦⡀⣶⠶⠛⢉⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠬⠉⠆⠀⠠⣍⣻⡆⣿⣄⣼⠇⢿⣉⣭⠸⣏⣩⡅⢿⣄⣤⠄⡇⠀⣿⠀⠀⣿⣸⡇⣿⠹⣆⠸⣍⣩⠅⠀⢸⡇⢸⡇⢿⣄⣼⠃⠀⠹⣄⣠⠏⠸⣇⢸⡇⢸⡇⢻⣍⣩⠅⣿⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3249

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/17/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2025/02/17/Over_at_Tux_Machines.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Over at Tux
Machines...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ No_More_Snakes:_Serpent_OS_Rebrands_as_AerynOS⠀⇛


           Ikey Doherty, the leader of the Serpent OS project


      ⚓  New⠀⇛


   2. ⚓ Operating_Systems_and_Hardware_Leftovers⠀⇛


           for end of Sunday


   3. ⚓ Free,_Libre,_and_Open_Source_Software_Leftovers⠀⇛


           FOSS links, DB focus


   4. ⚓ Firefox_Add-on_Reviews_and_February_patch_set_for_TenFourFox⠀⇛


           Some Firefox news


   5. ⚓ Security_Leftovers⠀⇛


           Security links, not many


   6. ⚓ Events:_FOSDEM_2025_and_PyCon_Italia 2025,_I_Love_FS⠀⇛


           some special picks


   7. ⚓ Fedora_/_Red_Hat_/_IBM_Leftovers⠀⇛


           Red Hat etc.


   8. ⚓ Applications:_TLP_1.8.0,_gThumb_Released_3.12.7,_and_More⠀⇛


           GNU/Linux software in focus


   9. ⚓ today's_howtos⠀⇛


           many howtos for day's end


  10. ⚓ A_Call_for_Unity⠀⇛


           For forty years, the free software movement has been a beacon
           of user freedom


  11. ⚓ This_Week_in_GNOME_#187_Triple_Buffered_Notifications⠀⇛


           Update on what happened across the GNOME project in the week
           from February 07 to February 14


  12. ⚓ Programming_Leftovers⠀⇛


           releases and more


  13. ⚓ FreeBSD_13.5-BETA2_Now_Available⠀⇛


           from Distro Watch also


  14. ⚓ today's_howtos⠀⇛


           many howtos for now


  15. ⚓ Open_Hardware:_FPGA,_Raspberry,_and_More⠀⇛


           Hardware picks


  16. ⚓ GNOME_48_Beta_Is_Now_Available_for_Public_Testing_with_Adwaita_Fonts,
      More⠀⇛


           Today, the GNOME Project announced the general availability of
           the beta version of the upcoming GNOME 48 desktop environment
           series for public testing, bringing more new features and
           improvements.


  17. ⚓ GNOME_47.4_Released_with_Performance_Improvements_for_Nautilus,_Bug
      Fixes⠀⇛


           The GNOME Project announced today the official availability of
           GNOME 47.4, the fourth maintenance update to the latest GNOME
           47 “Denver” desktop environment series with more bug fixes and
           improvements.


  18. ⚓ Android_Leftovers⠀⇛


           Google confirms Android XR will give apps access to your
           headset's cameras


  19. ⚓ These_are_the_13_Linux_distros_optimized_for_gaming_in_2025⠀⇛


           Relatively speaking, gaming in Linux has matured


  20. ⚓ 8_Weird_and_Wacky_Linux_Hardware_Devices⠀⇛


           You can stick Linux in just about anything, and that's a big
           part of what makes it special


  21. ⚓ Free_and_Open_Source_Software⠀⇛


           This is free and open source software


  22. ⚓ KolibriOS_–_tiny_Linux_distribution⠀⇛


           KolibriOS is a tiny yet incredibly powerful and fast operating
           system


  23. ⚓ GNU/Linux_and_Free_Software_Leftovers⠀⇛


           today's leftovers


  24. ⚓ Open_Hardware:_CrowPi,_ESP32,_3-D_Printing,_and_More⠀⇛


           on the physical side


  25. ⚓ Programming_Leftovers⠀⇛


           Development related links


  26. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


      =========================================================================
      The corresponding text-only bulletin for Sunday contains all the text.
      Top-read articles (excluding bot/crawler visits):


                         Span from 2025-02-10 to 2025-02-16
      885 /n/2025/02/11/
          KDE_Plasma_6_3_Desktop_Environment_Officially_Released_This_Is_.shtml


      836 /n/2025/02/04/
          Someone_got_Linux_running_inside_a_PDF_file_because_its_users_a.shtml


      674 /n/2025/02/10/
          Arch_Linux_Based_EndeavourOS_Mercury_Lands_with_Linux_Kernel_6_.shtml


      660 /n/2025/02/06/
          Mixing_Rust_and_C_in_Linux_likened_to_cancer_by_kernel_maintain.shtml


      648 /n/2025/02/13/openSUSE_Tumbleweed_Moves_to_SELinux.shtml


      647 /n/2025/02/11/Best_Free_and_Open_Source_Software.shtml


      577 /n/2025/02/11/GNOME_Project_Launches_Revamped_Website.shtml


      515 /n/2025/02/10/today_s_howtos.shtml


      505 /n/2025/01/13/Kdenlive_24_12_1_and_KDE_in_Tech_Over_Tea.shtml




⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⣄⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠈⠳⣦⡀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿
⣤⣤⣤⣘⠉⢀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⢿⣿
⣿⣿⣿⣿⣿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠙⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⣿
⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠃⠈⠀⠀⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⡷⢠⣿
⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⢯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠠⡦⠈⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣼⣿
⠛⠁⠀⢸⣿⣿⣿⣿⣿⣿⣷⡟⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢉⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠙
⣤⡄⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣮⡠⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣀⣌⢽⣇⠻⠿⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼
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⠠⣦⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢤⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠀⠈⢟⣿⣿⡏⢐⣿⣓⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠹⣿⣿⣿
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⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠁⠙⣿⣿⣿⣿⣷⣍⠿⣿⣿⣿⣿⣿⣆⠀⠀⡀⠀⠀⠀⠀⠙⠻⠓⣿⣿⣿⣟⠙⡖⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣷⡽⠿⠈⠿⠟⠛⠓⠈⠀⠀⠦⣶⣾⣶⣦⣤⣀⡉⠉⠙⠛⠃⢰⡿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⣤⣀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣄⣴⡄⢤⠀⠀⠀⠀⠀⠁⠀⠹⢟⣿⣿⡿⢷⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⠀⡈⡀⠀⢾⣷⡄⠀⡀⠀⠈⠉⠉⠃⠃⠀⠻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠘⠄⠀⠈⠙⠉⠀⠱⡀⠀⣤⣤⣴⣤⣄⢠⣾⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⠉⣯⠀⠑⣤⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⠀⢳⠘⢿⠿⣻⣿⣿⡀⢹⡟⡟⠋⠁⢸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿
⣿⡿⠟⠀⠀⠀⠈⠁⢹⣿⣷⣤⣀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠻⣆⠈⣷⣁⣾⣿⣿⣿⣷⠞⠿⢿⣶⣄⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿
⠉⣷⠀⠾⠿⠀⠀⠓⠺⣿⣿⣿⣿⣿⣦⣄⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠓⠀⠙⢅⠈⣿⣿⠿⠿⠿⠀⠀⢠⣴⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿
⡿⠿⠀⠀⣀⡀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣄⡙⢾⣷⣦⡀⢀⠀⠀⠀⠋⣨⣤⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⡀⠀⢻⣿⣿⣿⣿
⣷⡀⠀⠠⠿⠗⠀⢾⣿⣿⣿⣿⡿⠿⡿⢿⡿⠷⠄⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⢸⢿⣧⠉⠿⠛⠃⠈⠀⠀⣠⠃⠀⠈⠁⠀⠀⠀⣀⣰⡿⠟⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⠗⠀⠀⠉⠉⠛⠛
⣿⠟⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⢛⣠⣤⠃⠀⠀⠀⠀⠀⠀⠺⠟⠀⠀⠀⠀⢠⣴⣿⣿⡉⠀⠀⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠠⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠚⢿⡁⡀⠀⠀⠀⠀⠀⠈⠠⠀⠀⢀⣴⣿⣌⠻⣿⣿⡿⠀⠀⠀⠀⣶⡻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠰⠄⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠉⠟⠃⠀⣠⣿⣷⠀⠀⠋⠀⢨⠳⢄⡀⠀⠀⠀⣰⠀⠘⢶⣟⣿⣿⡿⠃⠈⠀⠀⠀⠀⣤⣬⣿⣿⣿⣿⣿⣿⡏⣻⡿⢿⣿⣿⡧⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3507

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/17/The_Attacks_on_LinuxQuestions_org.shtml
    Gemini version at https://techrights.org/n/2025/02/17/The_Attacks_on_LinuxQuestions_org.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Attacks on
LinuxQuestions.org⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


The site/forum was created by Jeremy_Garcia 25 years ago. He was about 22 at
the time.


LOOKING around the Web for reliable information about DDoS attacks is not
simple. The term is broadly used, there's plenty of SEO SPAM (companies trying
to sell something by misframing facts), there's plenty of LLM slop (trained on
marketing SPAM), and there are misleading technical synonyms, even buzzwords
with "cyber" (seeding vagueness, confusion). Look for "ddos linuxquestions" and
you might only find people asking about DDoS mitigation in some old thread at
LinuxQuestions.org, the "friendly and active Linux Community." (So says the
homepage)


Recently, and as recently as last year in fact, LinuxQuestions.org was being
hammered by bots (or botnets), so it needed to embrace some method/s of
protection. Sadly it chose proprietary Clownflare; that meant some users with
certain browsers could no longer access the site and those who rightly refuse
to run some proprietary JavaScript simply refused to go there. As a result,
participation and visibility decreased, traffic probably declined (as a
function of the participation), and we're told that some sub-forums pushed
"crypto"_(scams) and bigotry. We cannot prove the the latter was some sinister
plot to discredit the site; some rather old accounts were posting those things,
but it's possible that those were abandoned decades ago and merely grabbed for
reuse by malicious actors/purposes. Maybe yes, maybe not.


Regarding the DDoS attacks, that's an open secret.


LinuxQuestions.org might not survive this 'hybrid' attack. Jeremy seems to have
mostly stopped caring (or stopped acting). The site LinuxQuestions.org has
close to a million threads, so maybe the DDoS boils down to very greedy
spiders, maybe LLM harvesters (i.e. plagiarism bots). It's a shame because
there_are_still_many_good_posts_and_posters_in_there. Social control media
sites sometimes ban similar discussions.


Maybe the site LinuxQuestions.org needs better caching or maybe all the
inactive threats can be turned into millions of static pages* (caches can be
bypassed). Going to Clownflare only worsens the problem; GNU/Linux users have
good reasons to be angry at Clownflare [1, 2, 3, 4]. The company now
intentionally ignores bug reports about users of Pale Moon being effectively
blocked by sites using Clownflare. █


______


* Sure, it's a very big job, but it can pay off in the long term. We converted
Tux Machines from Drupal to static (about 200,000 pages) and it has been like
10 times more pleasant to run since then.




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣶⣴⣾⡷⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⣦⣴⣿⠇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣦⣶⣿⠆⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠠⣶⣴⣾⡷⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠹⣿⣿⣿⣦⠀⠀⢹⣿⣿⣿⣿⣿⣿⠃⠀⠘⢿⣿⣿⣷⡆⠀⠀⢻⣿⣿⣿⣿⣿⡿⠁⠀⢸⣿⣿⣿⣷⡄⠀⠈⣿⣿⣿⣿⣿⣿⠏⠀⣾⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡏⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠻⣿⠁⠀⠀⠘⢿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠸⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⠀⢻⣿⣿⣿⠉⠁⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣟⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⡶⠶⢶⣾⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡄⢠⣾⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢁⣤⣶⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⢸⣿⣿⣿⡛⢹⡛⠉⢋⡉⢻⣋⠙⣿⡉⠙⣏⠉⢹⠉⣹⠀⢸⣿⣿⣿⡇⠈⡉⠙⣿⡉⢹⡿⠋⣉⠛⡟⢉⡙⢻⡋⢈⣙⠋⢹⡿⠋⡉⠻⡟⠉⢋⡉⢻⡿⠋⡙⠹⣿⣿⣿⠟⢉⠙⢿⠋⠙⠉⡛⢋⡉⠋⣻⣿
⣿⣿⠇⢸⣿⡿⠋⡅⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⠀⣿⠇⡀⠸⣿⡀⠘⣿⣿⡿⠁⣰⡇⠀⣿⡇⢸⡇⠰⣶⡶⡗⢄⡈⠘⡇⢸⣿⡇⢸⡀⢸⣿⠀⣹⠀⣿⡇⢸⡗⢠⣈⠐⣿⢿⡇⠀⣿⡇⢈⡇⢸⣿⡇⢘⣃⣠⣿⣿
⣿⣧⣤⣤⣤⣤⣴⣤⣤⣥⣤⣼⣤⣤⣽⣦⣤⣤⣤⣤⣤⣯⣤⣬⣿⣦⣄⠀⠤⠶⢿⣿⣤⣤⣤⣤⣽⣦⣤⣴⣧⣤⣤⣴⣿⣤⣤⣤⣤⣷⣤⣤⣴⣧⣤⣼⣤⣤⣵⣤⣤⣴⣷⣤⣿⣦⣤⣤⣾⣤⣤⣿⠃⢠⣤⠈⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3602

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/02/17/The_Cool_Kids_Are_Already_Using_GNU_Linux_Microsoft_is_Just_Che.shtml
    Gemini version at https://techrights.org/n/2025/02/17/The_Cool_Kids_Are_Already_Using_GNU_Linux_Microsoft_is_Just_Che.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The "Cool Kids" Are Already Using GNU/
Linux, Microsoft is Just Cheating⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025,
updated Feb 17, 2025


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


Related: Good_Reason_to_Delete_Windows,_Not_Dual-Boot,_and_Call_Out_the
Microsofters_Who_Worked_to_Impose_'Secure'_Boot,_Undermining_Antitrust
Complaints


Desktops and laptops have long been the sole area where Windows could dominate
(owing to rogue play, not technical merit), but Microsoft now has less_than_70%
of_that_"market". In Mail_(MX)_Servers Microsoft has less than 0.2% of "the
market" and Azure_seems_like_a_zombie (Microsoft almost stopped talking about
it; it now talks of "hey hi" instead of "clown_computing"). Putting aside some
phony controversy (Asahi_brigading the manager), many people and sites now talk
about Linux running_in_a_PDF_file (after DoomPDF and Pdftris). Watch who's
accomplishing this.


A lot of today's young hackers are not interested in Windows, not just because
it's "uncool" but because it's a bloated mess with technical debt going back to
the 90s if not 80s.


The future and the present are Linux. But the OEMs are signing secret deals
with Microsoft. Desktops and laptops get shipped with Windows to prevent choice
and impose NSA_back_doors_on_billions_of_people_worldwide. █




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣤⣤⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⣴⠆⣠⣄⣤⣠⣤⣄⣠⡀⠀⣤⣄⣄⠀⠀⢹⠀⣾⠉⣉⡉⡉⢉⢉⡉⠉⢉⣋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡺⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠀⣀⢀⡉⠃⠙⠋⠛⠛⠛⠃⠛⠃⠀⠻⠛⠗⠀⠀⢸⡀⣿⠰⠟⠻⠿⠿⠽⢿⠀⢸⣿⣿⣿⣿⣿⠃⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣀⣉⣠⣄⣀⢸⣿⣯⠍⠁⠀⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠐⢯⠽⢿⢾⣿⢾⣿⣾⣿⣶⣷⣶⢲⣶⠀⣾⣷⣷⢸⠃⣿⠀⠂⠀⠀⣶⣦⣤⣤⣤⣤⣤⠀⠀⢀⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣬⣿⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠁⠀⠉⠉⠉⣼⠀⣿⢰⣆⠐⡀⣛⣛⣛⣛⣻⣟⣛⡀⢀⣠⣝⣉⣹⣷⣄⡀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⠀⣄⣄⣿⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⣿⣿⣯⣽⣷⣦⣥⣖⡸⣦⣿⡇⠀⠀⠀⡀⠀⠀⠀⢰⣿⢰⣿⡆⣿⡇⠀⢰⣷⣶⡆⢸⡇⠀⠀⢀⣠⡤⠔
⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢀⣠⣾⣿⣶⣿⢹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⡇⣟⡀⣨⣿⣿⡿⠀⠈⠁⣈⣩⢀⡉⣁⣀⠈⠉⠈⠁⢸⣧⠶⠞⠋⠁⠀⠀
⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣀⣶⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣯⢟⠹⠀⠀⠀⠿⠿⠻⠿⠿⠹⠿⠿⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀
⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣋⣾⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⣿⣷⣦⣤⣤⣤⣤⣤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣠⠸⠿⠿⠿⢿⠿⠿⠿⠟⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛
⣘⣳⢶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣯⣭⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣛⣛⣛⣛⣒⣒⣂⣀⣀⣘⣀⣀⣀⣀⣀⣀⣿⡀⠀⠀⠀⠀⠂⠀
⠉⢩⣿⣯⠭⠭⢽⡏⢹⣿⣾⣿⣼⣷⣿⣿⣷⣿⣿⣿⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣴⣿⣿⣿⠉⠉⠉⣭⣽⡏⠉⣋⣛⠿⣹⡿⠏⢭⣽⡍⡙⠁⠀⡄⠀⠀⠀⠀⠀
⢈⠛⢻⡟⠋⠉⠙⣿⣟⣿⡿⠟⠿⠟⠻⠟⢻⣿⣿⣿⣿⣷⡶⣤⣬⣿⣿⣿⣿⣿⣤⢛⣿⣿⣿⣿⣴⣷⣾⣾⡏⠀⢸⡇⠀⠀⠈⠁⠀⠈⠙⣿⣿⠀⠀⠀⠀⠙⢳⣆⡈⠈⠂⣿⠐⠀⠈⠉⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀
⡷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣦⣤⠀⢀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⠃⠈⣸⣿⣿⣿⣿⣽⣯⠟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⡀⣀⡐⢦⠀⢸⠟⣿⣿⣿⣿⡿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⣼⡧⡀⠀⠀⠀⠀⠀⢠⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠻⠿⠄⠂⢸⠿⠿⠿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠻⠿⢿⣿⣿⢿⣿⣿⣟⣋⣩⣭⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠤⢤⣤⡀⣶⠆⢤⣤⣤⡀⢉⣀⢈⣻⣶⣿⡇⠐⢂⣾⠶⢿⣿⣼⣿⣿⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠉⢹⡏⠁⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡶⢻⣖⠃⠹⢀⣾⣭⣉⣉⣹⣤⣤⣴⣿⣯⣄⣴⡶⢿⠶⡾⣿⣿⠟⡛⣋⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢉⡿⢀⣠⣏⣼⠛⠛⠛⠿⢿⣿⣿⣵⣾⣾⣿⣿⣿⣷⣾⣴⣤⠟⣃⣀⡾⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣤⣤⡦⢀⣸⣷⠶⠶⢶⣶⣶⣄⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣿⠈⠉⢉⡵⠶⠴⢶⡶⠾⣿⣽⣿⣴⣾⣾⣿⢿⣿⠿⠿⢷⣐⣫⣿⠷⠶⢶⣶⣶⣶⣿⣿⣿⣿⣧⣿⣯⣽⣷⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣒⣒⣒⣒⢐⣶⣿⣀⠀⠀⠀⠀⣠⣴⠀⠀⢀⠀⠀⠀⠀⠀⠀
⣤⠷⡾⢿⡏⠄⠀⠀⠛⠀⠱⠸⡿⢿⣿⣿⣿⣷⣾⣿⣶⣦⣼⣿⣿⣿⡚⠛⠛⠻⠳⡾⣻⣿⣿⣿⣿⠿⠿⢿⣿⠿⢿⣟⣛⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⢶⣶⣾⣷⣾⣿⣷⣧⣼⣷⣬⣭⣭⣵⣺⡗⣄⢀⣀⡀⠀
⠃⠀⠙⣿⠛⠰⢸⣿⣿⣿⣻⠿⣇⣴⣾⣁⣀⣰⣞⣣⣤⣀⠈⢻⣿⣿⣿⣶⣶⣶⣶⣦⣽⣿⣿⣿⣿⡟⠛⠛⠻⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⡾⠋⠛⠀⠀
⣦⣤⣤⠏⠀⠀⠈⠉⠿⠿⠿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣥⣥⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠶⣦⣼⠋⠛⣩⡄⠛⠀⠶⠆⠀⢀⣰⣆
⣿⡛⠋⠀⠀⠀⠀⠐⠒⠢⠤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⢻⡐⠯⡥⠒⠳⣷⡏⢀⠜⡁⠀⢀⠀⠈
⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠛⠛⠛⠛⠻⠿⠟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠿⠿⠿⠿⠿⠿⠿⠧⣴⣻⠏⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠈⠛⠀⠠⠀⠓⠆⢀⡑⡦⠈⠁⠄
⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣯⣭⣍⣀⣀⣘⣛⣛⣛⣛⣛⣓⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣒⣚⣛⣛⡿⠷⠦⠀⢻⣿⣿⣾⣝⣲⣿⡟⠋⣭⡉⠉⢭⣽⣛⡛⢻⡿⣶⣶⣶⣝⣦⢀⡐⠀⢠⣄⢨⡇⠀⠀⠯
⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠻⣿⣿⣿⡿⠿⠿⠿⡿⣿⡟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠈⠛⠻⢶⣈⠉⠋⠀⣷⣄⠉⠛⠿⢿⣿⣶⣥⣽⣿⣿⣷⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠀⠀⠀⠀⢻⣛⣛⣛⣛⣓⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠿⣿⣏⣿⢷⣿⣿⣿
⠿⠿⠿⠿⠿⠯⠟⠉⡉⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⣭⣭⣭⣭⣍⣍⣉⣩⣍⡙⢿⣯⣤⣤⣬⣧⣤⣤⣤⣤⣤⣷⡈⢿⢋⠀⠀⠹⠛
⣾⣷⣶⣶⣦⣤⢤⣤⣤⣶⡁⠀⠀⠀⠀⢀⣀⣀⣀⣐⣾⣿⣿⣿⣿⣟⣿⢻⢿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⡿⣿⡿⢸⣷⣿⣷⣆⣤⣠⣬⣭⣶⣶⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣎⣽⣿⣿⣿⠃⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⡟⠻⠛⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣭⣶⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⢻⣿⡿⠿⢿⣿⣿⢿⡿⣿⠛⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣿⣧⣀⣠⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣤⣀⡀⠀
⣿⣿⣷⣀⡀⠙⠻⠏⠁⠿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠬⠥⠤⠤⠄⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣬⣭⣭⣭⣽⣭⣭⣨⣭⣿⣿⠍⠘⠉⠉⠉⠉⠹⠉⢉⡉⠉⠉⠙⠃⣿⣿⣿⣶
⢻⣿⣿⣽⣿⣿⣿⠆⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠲⣶⠒⠺⠟⠛⠛⠛⠂⠀⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣬⣭⣍⣉⣉⡉⠙⠉⠙⠛⠛⠛⠉⠀⠀⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣯
⠸⣿⣿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⢻⡿⠙⠉⠉⠉⠉⠉⠉⠉⠉⠩⣭⣭⡍⠉⠉⡍⠛⠛⠛⠛⠛⠻⣿⣆⠀⠀⠈⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠙⠛⠛
⡀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣀⣀⣀⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⡇⣿⣿⡇⣽⣧⣀⡀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⢴⡞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⣀⡀⠀⠀⠀
⠃⣿⣿⣧⠀⠙⠹⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣶⡦⠙⠘⠛⠓
⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣷⣤⡄⢀⡴⢦⣤⣤⡀⠀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠐⢀⣤⣿⠀⠀⠀⠀⠀
⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣀⣐⣲⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣬⣥⣤⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠀⠈⣿⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⣬⣭⣬⣭⣭⣍⣍⣛⣛⣿⣛⠛⣿⣿⣿⣿⣿⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⡟⠋⠙⢻⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⣿⣿⣿⠏⢿⠻⠿⠀⠤⠤⢤⡄⠤⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢐⠛⠉⠉⠛⠛⠻⣿⣏⠈⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠰⠤⠤⠤⠤⠤⠤⠴⣿⡦⠤⢤⠤⠤⠄⠛⠁⠒⢸⣿⣿⣿⠛⠀⠀⠀⠀⢪⣄⣀⠠⡾⠁⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 3707

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The GNU Manifesto Turns 40 Next
Month⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇In_1985_Richard_Stallman_published_the_GNU_Manifesto⦈_


I've embraced and actively promoted Free software for a majority of my lifetime
(relentlessly promoted for about half the lifetime so far). I'm of the "DOS
generation" and I was introduced to computers around the time the FSF was
founded (and GNU's development had already begun). GNU didn't have a kernel
(yet) and the Internet was not a residential thing; you only had it in some
particular places of employment and there was nothing like IRC or the Web. They
didn't exist yet.


So much has changed since I promoted Free software in the 90s. Many people are
now 'hooked' on "apps" and "stores". They depend not so much on Microsoft but
on giants like Google and Apple. That means that to promote Free software we
need to speak about issues bigger than Microsoft alone. Some days ago in Torino
Richard_Stallman_explained_that_the_Free_Software_Movement_isn't_about
combating_just_one_person_or_company (after someone had asked about Bill
Gates). Companies change, not just by means of renaming, morphing, or being
replaced by bigger (or lesser) evils. Unless we can keep track of the
fundamental issues, the 'audience' will lose touch (or get fed up) with the
solutions. Many people falsely assume that some proprietary software is "open"
or somehow a victory for "Linux" (a new article says_that_"Valve_officially
recommends_re-installing_your_operating_system_if_you_played_this_game").


As we explained months ago, digital freedom-fighting is a perpetual goal and a
battle that will never be "won". However, "being in the game" means more people
will (over time) participate and emancipate themselves.


The_GNU_Manifesto_is_about_to_turn_40 and its_author_turns_72_on_the_very_same
month.


Judging by his recent "marathon of talks" (in Europe and India, not the US
where he lives), he can still articulate his positions/stances as well as ever,
his hair grows back (after treatment for cancer), and perverts who attempt to
cancel his talks cannot_succeed_anymore. His right-hand man, Alex (Alexandre)
Oliva, has just upped_his_digital_autonomy, and the FSF keeps adding_new_staff
(this_one_is_the_latest). The FSF's board has grown, the budget has_apparently
improved, and there are big celebrations later this year, even some_auctions.


The guardian of Free software (definition, licences, philosophy, hosting and so
on) has managed to endure and persevere for 40 years. Very few others can say
the same. █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣈⣛⣛⣓⣓⣛⣛⣛⠛⠛⠿⠿⠿⠿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣀⣀⣘⣀⠀⠁⠉⠉⢛⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢟⢛⣿⠿⢿⡟⣿⠟⡛⡻⠿⡻⡛⡛⡻⡻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣴⣶⠶⠶⠶⠶⠿⠿⣿⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⠾⠷⢶⠾⢾⢿⠶⠷⡶⠶⣶⣿⣶⣷⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⡅⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣦⣮⣦⣶⣾⣶⣦⣥⣾⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠉⣀⣀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⠀⠐⡗⠒⣀⠰⡶⠶⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣯⣤⣤⣤⣤⣠⣤⣤⣄⡠⠶⣦⣤⣤⣤⣤⣤⣤⢤⣀⡡⢤⣈⣿⣭⣽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⣄⡀⠀⠀⠀⠁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3798

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 17/02/2025: Ideal OS, AuraRepo
Alpha, and Simple Code⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Technology_and_Free_Software
                # Internet/Gemini
                # Programming
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ A_Somewhat_Brutal_Bongusta_Cleanup⠀⇛


                       It's the second half of February, the new year is
                       not so new anymore, and that means it's time for
                       the usual Bongusta list cleanup.


                       This time, it was a bit brutal. At the start, the
                       list contained 78 phlogs. Even though I removed
                       only phlogs with broken links and those with no
                       activity at all in 2024, I ended up with 64
                       remaining. After adding eight fresh new phlogs, the
                       counter stopped at 72.


                       I hope this was the last decrease in 2025 and that,
                       from now on, gopherspace activity will only grow.
                       And yes, I know, I need to start contributing
                       myself again. My own phlog has been silent since
                       August. What a shame.


                # ⚓ Fickle_Dreams⠀⇛


                       Once one of my designs is completed, I submit it to
                       my master for his review and approval. If it
                       satisfies him - and there is need for it - I often
                       see my templates take form in stone and marble.


                       I should be extremely grateful for my master to
                       continue selecting my templates, and seeking out
                       contracts for which they can be put to good use.
                       Unfortunately, the template - my template - that he
                       selected, had not undergone his review.


          o § Technology and Free Software⠀➾


                # ⚓ Graphical_Mode_Links2_on_Mac⠀⇛


                       I consider myself a happy links2^ user. I tend to
                       just use links2 in text mode but recently, I wanted
                       to see the magic of graphical mode links2. There's
                       just one issue: I wanted to set this up on my work
                       computer and my work computer is a Mac.


                # ⚓ My_ideal_operating_system⠀⇛


                       I’ve been watching fairly alternative OSs like
                       Haiku (the BeOS clone) and I wanted to really clear
                       the slate and assume multiple orders of magnitude
                       of work done just for this OS. Otherwise an
                       operating system is just a way to run stuff that
                       people can already run on a Linux distribution or
                       macOS.


                       Originally, here I said “This is a desktop
                       operating system” but increasingly I’m coming
                       around to the notion that all great modern
                       computing platforms are entire ecosystems and not
                       just a pile of bits that one throws on commodity
                       hardware. Because of this, I’m also specifying
                       stock peripherals like monitors and keyboards and
                       thinking about ways to have peripherals — like
                       wireless headphones — shared between all your
                       devices without an Apple Account coordinating
                       permissions behind the scenes.


                # ⚓ note_browsing_with_fzf⠀⇛


                       Since I now keep updated directories for tags and
                       titles in my notes, I can just straight up call fzf
                       instead of that complicated mechanism I was using
                       for browsing notes by title and tag before.


                # ⚓ Started_a_new_web_project⠀⇛


                       Some of the more exciting news since my last week
                       notes is that I’ve been working on a new web
                       project. The idea is a searchable, curated
                       directory of high quality and user-respecting web
                       apps.


                       I’m taking a pretty loose definition of “web app”,
                       meaning almost any website that has a function
                       beyond “hey here’s a document”. Basically I’ve
                       found that search engines do a pretty terrible job
                       of helping users find quality tools, so this is
                       hopefully a remedy to that.


                       I’ve got several dozen sites already in the
                       directory, and I’m hoping to get that built up a
                       lot through user submissions if this gains any
                       traction.


                       I’ll have more details to share later I’m sure. I’m
                       pretty close to launching it. The main thing left
                       is to clean up the code organization a bit, and
                       there’s not very much so that should go quickly. In
                       the meantime if you have any sites you’d like me to
                       add or know of anywhere I could find more, feel
                       free to let me know.


                # § Internet/Gemini⠀➾


                      # ⚓ AuraRepo_Alpha⠀⇛


                             I am almost ready to release a beta of
                             AuraRepo! I have an alpha running on my
                             server right now. I'd appreciate if people
                             can browse it and provide any feedback on the
                             UI.


                # § Programming⠀➾


                      # ⚓ Why_I_like_simple_code_(1)⠀⇛


                             So I was randomly browsing and found this
                             talk by Peter van Hardenberg, “Why Can’t We
                             Make Simple Software?”. [1] This YouTube
                             comment summarizes it well: «This
                             presentation is basically the talk I have
                             with every stakeholder at some point but most
                             of it just gets dismissed as “nerd shit”» -
                             JordanManfrey


                      # ⚓ Why_I_like_simple_code_(2)⠀⇛


                             In the last post I focused deeply on the
                             presentation itself, without much reflexion
                             of my own. It is a long presentation, after
                             all. But I'd like to introduce the topic of
                             the title: why make simple code? Simple code
                             is boring, like a game of checkers or tic-
                             tac-toe, where the rules are simple, the
                             number of states limited, and the
                             straightforwardness of it is almost numbing.
                             It's no surprise that people are more and
                             more captivated by the concept of super tic-
                             tac-toe, where you play 10 simultaneous games
                             with extra restrictions. [1]


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





                    ䷩ 𝚕𝚒𝚗𝚎 4003

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 17/02/2025: Blogroll Conundrum;
Research, Scientists Under Siege⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Standards/Consortia
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Pseudo-Open_Source
                # Openwashing
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
    * Internet_Policy/Net_Neutrality
    * Monopolies/Monopsonies
          o Patents
          o Trademarks
          o Copyrights
    * § Leftovers⠀➾


          o ⚓ The Register UK ☛ DoomPDF_dev_stuffs_a_Linux_system_into_a_PDF⠀⇛


                 First came Tetris, then Doom – and now a bare-bones Linux
                 instance that boots inside a PDF.


                 Yes, the humble PDF – thanks to its ability to run
                 limited JavaScript – has been coaxed into booting a
                 stripped-down 32-bit RISC-V Linux buildroot environment
                 in a suitable PDF viewer. This is made possible by
                 compiling the C-based TinyEMU emulator into JavaScript,
                 and then embedding that into a PDF so that it is executed
                 by the document viewer, and it in turn runs the included
                 small Linux distribution.


          o ⚓ MJ Fransen ☛ Blog_Questions_Challenge:_Technology_Edition⠀⇛


                 I built my first electronics project when I was twelve
                 years old. This was a crystal radio. It required very few
                 components, but I still needed to save money for a while
                 before I could afford the purchase.


                 For the antenna I used a very long wire, probably 10
                 meter or longer. The reception was of course terrible,
                 but it felt like an adventure, listening secretly under
                 the blankets during the night to the stations that it was
                 able to receive.


          o ⚓ Amit Gawande ☛ Blogroll_Conundrum⠀⇛


                 I haven't yet created a blogroll. They are simple, but
                 somehow, I am caught in a conundrum: What's the purpose?


          o § Standards/Consortia⠀➾


                # ⚓ Smithsonian Magazine ☛ Dial_Up_the_Story_of_the_First_911
                  Call,_Which_Was_Placed_on_This_Day_in_1968⠀⇛


                       For proponents of 911, this “first” was a huge
                       milestone. But it would take several more decades
                       for most of the country to gain access to the
                       service. In 1976, the emergency number served just
                       17 percent of the population. Even by 1987, that
                       figure had only risen to 50 percent.


          o § Science⠀➾


                # ⚓ New York Times ☛ As_Convicted_Felon_Targets_Research,
                  Scientists_Share_Grief_and_Resolve_to_Fight⠀⇛


                       At a conference in Boston, the nation’s scientists
                       commiserated and strategized as funding cuts and
                       federal layoffs throw their world into turmoil.


                # ⚓ Wired ☛ This_New_Algorithm_for_Sorting_Books_or_Files_Is
                  Close_to_Perfection⠀⇛


                       This problem was introduced in a 1981 paper, and it
                       goes beyond simply providing librarians with
                       organizational guidance. That’s because the problem
                       also applies to the arrangement of files on hard
                       drives and in databases, where the items to be
                       arranged could number in the billions. An
                       inefficient system means significant wait times and
                       major computational expense. Researchers have
                       invented some efficient methods for storing items,
                       but they’ve long wanted to determine the best
                       possible way.


                       Last year, in a study that was presented at the
                       Foundations of Computer Science conference in
                       Chicago, a team of seven researchers described a
                       way to organize items that comes tantalizingly
                       close to the theoretical ideal. The new approach
                       combines a little knowledge of the bookshelf’s past
                       contents with the surprising power of randomness.


                # ⚓ NYPost ☛ Researchers_took_a_whiff_of_Egyptian_mummies_for
                  science_—_they_‘were_surprised_by_the_pleasantness_of_them’⠀⇛


                       At first whiff, it sounds repulsive: sniff the
                       essence of an ancient corpse.


                # ⚓ The Conversation ☛ 2025-02-14_[Older]_‘Myrrh,_conifer_oil
                  and_…_breakfast_tea’:_my_sniffer_team’s_surprise_findings_on
                  what_mummified_bodies_smell_like⠀⇛


                # ⚓ The Conversation ☛ 2025-02-12_[Older]_How_our_team_spotted
                  the_most_energetic_neutrino_detected_to_date⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-12_[Older]_High-Energy
                  Cosmic_Neutrino_Detected_Under_Mediterranean_Sea⠀⇛


          o § Career/Education⠀➾


                # ⚓ Kansas Reflector ☛ USAID_shutdown_would_halt_research
                  grants_to_state_universities⠀⇛


                       For decades, USAID has turned to experts at state
                       colleges and universities to help it improve
                       agriculture, education and public health in foreign
                       countries — and in the process build goodwill
                       toward the United States.


                # ⚓ Crooked Timber ☛ Small_is_beautiful_–_and_other_thoughts
                  about_university_governance⠀⇛


                       If one had to choose one reason for why things are
                       not going well in academic life, the managerial,
                       top-down style of governance that reigns in many
                       universities would be a top candidate (with budget
                       cuts as a close competitor). But what is a better
                       way of running universities? For me, this is a
                       question in which theoretical and practical-
                       professional interests intersect.* I’ve long been a
                       defender of workplace democracy, and since 2023,
                       I’m on the board of a small faculty – so the
                       question became: What does it mean for a faculty to
                       be a democratic workplace? Especially if the
                       official rules do not allow for, say, an election
                       of the faculty board by the faculty members…


          o § Hardware⠀➾


                # ⚓ The Conversation ☛ 2025-02-12_[Older]_Sofas_that_self-
                  assemble_when_you_heat_them_up?_How_4D_printing_could
                  transform_manufacturing⠀⇛


                # ⚓ PC World ☛ 8_mistakes_that_will_kill_your_SSD_early⠀⇛


                       SSDs are finely tuned, blazing-fast storage devices
                       that can take more advantage of the high bandwidth
                       of PCIe 5.0 than even the fastest graphics cards.
                       But like all instruments of performance, you can’t
                       treat them poorly and expect them to last forever.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ The Conversation ☛ 2025-02-10_[Older]_How_the_brain_can
                  miraculously_switch_off_pain⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-09_[Older]_Some_US
                  Health_Clinics_Grapple_With_Federal_Funding_Squeeze⠀⇛


                # ⚓ Simone Silvestroni ☛ Outside_the_Wall⠀⇛


                       I call, I message, I write emails, sometimes I meet
                       them in person and have real discussions without
                       taking my phone out of any pocket or bag.


                # ⚓ The Straits Times ☛ Covid-19,_influenza_vaccination
                  mandatory_for_high-risk_Malaysian_haj_pilgrims⠀⇛


                       Eligible haj pilgrims can obtain the Covid-19
                       vaccine for free at 247 selected health clinics.


                # ⚓ New York Times ☛ On_a_Mission_to_Heal_Gila_Monsters⠀⇛


                       After years in Big Pharma, a chemist pivoted to
                       help save the species that made Ozempic possible.


                # ⚓ New York Times ☛ Medicare_Doesn’t_Pay_for_Everything:_How
                  to_Bridge_the_Cost_Gap⠀⇛


                       Older Americans have ways to protect against high
                       out-of-pocket health care costs, but it’s important
                       to understand the trade-offs.


                # ⚓ New York Times ☛ She’s_Trying_to_Stay_Ahead_of_Alzheimer’s,
                  in_a_Race_to_the_Death⠀⇛


                       In the Netherlands, doctors and dementia patients
                       must negotiate a fine line: Assisted death for
                       those without capacity is legal, but doctors won’t
                       do it.


                # ⚓ Federal News Network ☛ HHS_is_losing_thousands_of_workers
                  under_Convicted_Felon_administration_probationary_job_cuts⠀⇛


                       Department of Health and Human Services officials
                       expected most of the agency’s roughly 5,200
                       probationary employees to be fired. That’s
                       according to a recording of a staff meeting shared
                       with The Associated Press. Included in that tally
                       are nearly 1,300 employees at the Centers for
                       Disease Control and Prevention. The moves are part
                       of the Convicted Felon administration’s bid to get
                       rid of nearly all probationary employees.


          o § Proprietary⠀➾


                # ⚓ Google,_From_Layoffs_to_Voluntary_Exits [Ed: So many
                  layoffs that they try to call them something else]⠀⇛


                       In a move that has sent ripples across the tech
                       industry, Google recently announced a voluntary
                       exit program for its employees. This initiative,
                       which allows employees to opt for a severance
                       package and leave the company, has sparked a mix of
                       reactions — ranging from curiosity to concern. As
                       an IT professional, I can’t help but wonder what
                       this means for the future of work at Google, the
                       broader tech landscape, and the employees who are
                       now faced with a life-altering decision.


                # ⚓ Metro UK ☛ Why_Xbox_will_never_beat_PlayStation_with_its
                  multiformat_plans_–_Reader’s_Feature⠀⇛


                       A reader explains why he thinks Microsoft embracing
                       multiformat publishing with Xbox will only make it
                       harder to compete with PlayStation.


                # ⚓ Josh Betz ☛ Cloudflare_as_a_Free_CDN_for_WordPress_Assets⠀⇛


                       A Content Delivery Network (CDN) helps speed up a
                       website by caching static assets (like JavaScript
                       and CSS) on servers distributed around the world.
                       This reduces latency and offloads traffic from the
                       origin server, improving load times and user
                       experience.


                       Cloudflare has a WordPress plugin that will help
                       you cache everything, including dynamic content, on
                       the Cloudflare edge. I didn’t want to do that,
                       preferring more control over caching HTML content
                       and less complexity around invalidating the
                       Cloudflare cache. However, I still want to take
                       advantage of Cloudflare’s CDN to cache my site’s
                       static assets. I’ve found that you can still get
                       great performance without proxying dynamic content
                       through Cloudflare. (I do cache full HTML pages in
                       Nginx.)


                # ⚓ Jason Tucker ☛ Here_WeGo_-_Google_Maps_alternative?⠀⇛


                       HERE is a mapping platform with a long history,
                       originally developed by Nokia and now owned by a
                       consortium of major automakers, including BMW,
                       Audi, and Mercedes-Benz. It's widely used in
                       commercial fleets, logistics, and even built into
                       some car navigation systems. I used it way back
                       when the Nokia n95 came out and I was testing it
                       for review.


                       Their mapping technology powers navigation systems
                       for major car manufacturers, and their app, HERE
                       WeGo, is designed to offer a robust alternative to
                       Google Maps and Apple Maps.


                # ⚓ Business Insider ☛ How_to_avoid_being_labeled_an
                  'underperformer,'_according_to_the_ex-VP_of_HR_at_Microsoft⠀⇛


                       The lesson from these layoffs is that simply doing
                       your job well isn't enough. You can toil away for
                       decades doing a fine job and still get caught up in
                       these layoffs.


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ IP Kat ☛ 2025-02-11_[Older]_[Guest_Post]_In_too_deep?
                        Considering_the_legal_risks_when_using_DeepSeek⠀⇛


                      # ⚓ The Register UK ☛ Zypher's_speech_model_can_clone
                        your_voice_with_5s_of_audio⠀⇛


                             The results are actually two Zonos models:
                             One that uses a fully transformer-based
                             architecture, and the other, a hybrid that
                             combines transformer and Mamba state space
                             model (SSM) architectures. The latter, Zyphra
                             claims, makes it the first TTS model to use
                             this arch. While transformer-based models are
                             without a doubt the most commonly used in
                             generative AI today, alternative
                             architectures like Mamba are gaining
                             traction.


                             From a practical standpoint, both models
                             behave similarly to other text-to-speech
                             models. But unlike those developed by
                             ElevenLabs and others, Zyphra has elected to
                             release its model weights on Hugging Face
                             under a permissive [sic] Apache 2.0 license.


                      # ⚓ Unmitigated Risk ☛ The_Fallacy_of_Alignment:_Why_AI
                        Safety_Needs_Structure,_Not_Hope⠀⇛


                             This raises a deeper question: If we now view
                             ourselves as the existential threat, can we
                             truly build AI that serves us? Or will our
                             fears—whether of AI or of our own
                             past—undermine the future we once dreamed of?


                      # ⚓ Robin Sloan ☛ Reasons-ing_models⠀⇛


                             In the warmup to my recent post about the
                             foun­da­tional ques­tion of lan­guage models,
                             I wrote about what the models are doing. I
                             think “mod­eling text” under­sells the
                             mech­a­nism. The sys­tems I tinkered with
                             back in the late 2010s “modeled text”; these
                             new ones, while mechan­i­cally very similar,
                             are qualitatively, viscerally dif­ferent.


                      # ⚓ Idiomdrottning ☛ The_Dystopian_Hellscape_of_Apple's
                        1987_Knowledge_Navigator_Concept_Video⠀⇛


                             For his actual work, the lecture, he throws
                             something together in three seconds with the
                             LLM and mooches off a friend, asks her to
                             come do the lecture. Actual thinking: nadita.
                             I’m not denying that an LLM like he has could
                             help him come up with some great insights and
                             ideas, that’s not one of the problems with
                             LLMs, they can be great. But that’s not what
                             he’s doing. He’s just pasting some maps
                             together…


                             And he’s tasked to do the remembering part
                             while the LLM does the thinking.


                      # ⚓ Pivot to AI ☛ El_Salvador_finds_the_use_case_for_AI:
                        handouts_to_the_government’s_pals⠀⇛


                             Bukele has recently set himself up as
                             effective President for Life — however long
                             that life might be. But his big problem is
                             that the country is out of money, because he
                             spent it to get re-elected — hence the
                             bitcoin gamble, which was finally abandoned
                             to secure a $1.4 billion loan from the
                             International Monetary Fund.


                      # ⚓ BoingBoing ☛ Fake_AI_"true_crime"_documentaries_are
                        taking_over_YouTube⠀⇛


                             Part of the way this scam was discovered was
                             that a resident of one of the towns where one
                             of the supposed crimes took place began to
                             investigate. "Why wasn't this on the local
                             news?" they wondered. "Why is nobody talking
                             about this?"


                      # ⚓ 404 Media ☛ A_‘True_Crime’_Documentary_Series_Has
                        Millions_of_Views._The_Murders_Are_All_AI-Generated⠀⇛


                             Hernandez called several law enforcement
                             officials and quickly confirmed her
                             suspicions. The murder was fake, and the
                             video was made using generative AI.


                             The video was uploaded to a YouTube channel
                             called True Crime Case Files. Before the
                             channel was terminated while I was working on
                             this story in January, it posted more than
                             150 similar videos over the past year. This
                             one was the most popular.


          o § Pseudo-Open Source⠀➾


                # § Openwashing⠀➾


                      # ⚓ The Conversation ☛ 2025-02-12_[Older]_DeepSeek:_how
                        China’s_embrace_of_open-source_AI_caused_a_geopolitical
                        earthquake [Ed: It's not "open-source"]⠀⇛


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ International Business Times ☛ 2025-02-14_[Older]_UK
                        To_Fine_£100,000_For_Misuse_Of_Ring_Doorbell_Camera_-
                        Here's_What_You_Should_Know⠀⇛


                      # ⚓ India Times ☛ New_downloads_of_DeepSeek_suspended_in
                        South_Korea:_Data_protection_agency⠀⇛


                             The service of the app will be resumed once
                             improvements are made in accordance with the
                             country's privacy law, the Personal
                             Information Protection Commission (PIPC) said
                             in a media briefing.


                      # ⚓ The Register UK ☛ YouTube_ID_exploited_to_find_Gmail
                        deests,_says_researcher⠀⇛


                             It all started when Brutecat was digging
                             through Google's People API and found out
                             that a function that allows blocking a
                             YouTube user relied on an obfuscated “Gaia”
                             ID. Gaia is the ID management system for all
                             Google products. Brutecat pointed out that,
                             per a Google support page, blocking someone
                             on YouTube extends to other Google services,
                             meaning it's their Gaia ID that's blocked,
                             not their YouTube account.


                      # ⚓ Rlang ☛ Burn_Notice⠀⇛


                             Your Phone and Watch have a lot of data about
                             you. I mean, like, a lot. Someone should
                             really write a book all about the general
                             issues for society that this raises.
                             Yesterday I decided I wanted to take a look
                             specifically at the health data on my iPhone.
                             I’m not a huge user of the iPhone’s or the
                             Apple Watch’s health features. I don’t use or
                             subscribe to Apple Fitness+, for example. I’m
                             not in any studies. But I do have a bathroom
                             scale that records data and I allow the Watch
                             to keep an eye on my activity. This means
                             that, like so many people, I have grown to
                             heartily despise the blandly affirming
                             Californian inside those devices who
                             periodically encourages me to take a walk, or
                             stand up, or be mindful, and so forth.


          o § Defence/Aggression⠀➾


                # ⚓ NYPost ☛ Family_gives_heartbreaking_update_on_sole_survivor
                  of_Wyoming_mom’s_murder-suicide_rampage_that_left_3_sisters
                  dead⠀⇛


                       Olivia Blackmer was shot in the head by her mother
                       Tranyelle Harshman at the family home in Byron
                       Wyoming.


                # ⚓ New Yorker ☛ We_Might_Have_to_“Shut_Down_the_Country”⠀⇛


                       Anthony Romero, the A.C.L.U.’s executive director,
                       talks about what he thinks could happen if the
                       Convicted Felon Administration defies the authority
                       of the courts.


                # ⚓ New York Times ☛ The_Republican_Party’s_NPC_Problem_—_and
                  Ours⠀⇛


                       What happens when ambition no longer checks
                       ambition?


                # ⚓ El País ☛ Salman_Rushdie:_‘Musk_does_not_defend_freedom_of
                  expression;_he_curates_the_discourse_of_the_extreme_right’⠀⇛


                       During his conversation with EL PAÍS, Rushdie — who
                       was threatened with death in 1989 for his book The
                       Satanic Verses — points out that, at the time,
                       literary critics forgot to read between the lines
                       of the humor that he sprinkled his books with.


                       The recent attack against him took away his desire
                       to go to public events, but he has returned as an
                       act of resistance, with the love of his family in
                       one hand and laughter in the other. He spoke to El
                       PAÍS about the poetry that Netflix lacked while
                       adapting One Hundred Years of Solitude, and about
                       his new relationship with death. He also discussed
                       the ongoing immigration crisis in the United
                       States.


                # ⚓ CS Monitor ☛ Finland_urges_rearming_Ukraine_as_U.S.
                  excludes_Europe_from_peace_talks⠀⇛


                       On the final day of the Munich Security Conference,
                       Mr. Stubb and other European leaders sought to plot
                       how the European Union can move from talk to more
                       action and stay relevant as Washington pushes to
                       stop the fighting. He laid out three phases: “pre-
                       negotiation,” ceasefire, and long-term peace
                       negotiation.


                       “The first phase is the pre-negotiation, and this
                       is a moment when we need to rearm Ukraine and put
                       maximum pressure on Russia, which means sanctions,
                       which means frozen assets, so that Ukraine begins
                       these negotiations from a position of strength," he
                       said.


                # ⚓ The Guardian UK ☛ Europeans_are_right_to_be_angry_with
                  Donald_Trump,_but_they_should_also_be_furious_with
                  themselves⠀⇛


                       The betrayal of Ukraine is a final warning to the
                       UK and its continental allies to put a lot more
                       energy and money into rebuilding their defences


                # ⚓ New York Times ☛ Knife_Attack_Suspect_in_Austria_Was
                  Inspired_by_ISIS,_Official_Says⠀⇛


                       In July, the singer Taylor Swift was forced to
                       cancel three concerts in Vienna, Austria’s capital,
                       after the authorities learned of a plan to attack
                       the venue by two teenagers who had become
                       radicalized Islamists online. Neither was a
                       refugee.


                # ⚓ Deutsche Welle ☛ 2025-02-15_[Older]_Austria:_One_dead,_four
                  injured_in_knife_attack⠀⇛


                # ⚓ Deutsche Welle ☛ Austria_stabbing_'Islamist_attack,'
                  interior_minister_says⠀⇛


                       "It is an Islamist attack with IS connections,"
                       Karner told reporters, adding that the suspect was
                       radicalized online "in a short space of time."


                # ⚓ The Record ☛ Estonian_spy_chief:_‘Hybrid_schmybrid,_what’s
                  happening_is_attacks’⠀⇛


                       In a late panel discussion on Saturday at the
                       Munich Security Conference, Kaupo Rosin protested
                       the use of the word which has been applied to a
                       range of hostile activities that are deemed to be
                       deniable or below the threshold justifying an armed
                       response.


                       “Hybrid schmybrid,” he said. “I think the word
                       ‘hybrid’ is misleading and soft… What’s happening
                       is attacks, cyberattacks, assassination plots,
                       maybe in some parts it’s actually state-sponsored
                       terrorism what is going on.”


                # ⚓ US News And World Report ☛ 2025-02-09_[Older]_'No_Thanks',
                  White_South_Africans_Turn_Down_Cheeto_Mussolini's_Immigration
                  Offer⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-08_[Older]_Cheeto
                  Mussolini_Says_Some_White_South_Africans_Are_Oppressed,_Could
                  Be_Resettled_in_the_US._They_Say_No_Thanks⠀⇛


                # ⚓ TruthOut ☛ 2025-02-10_[Older]_Cheeto_Mussolini_Cuts_Off
                  South_Africa_Aid_in_Push_to_Further_Interests_of_White
                  Landowners⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-11_[Older]_Cheeto
                  Mussolini's_Accusations_Against_South_Africa_Spark_'White
                  Privilege'_Self-Mockery⠀⇛


                # ⚓ Scheerpost ☛ 2025-02-11_[Older]_‘The_PayPal_Mafia’:_Meet
                  the_South_African_Oligarchs_Surrounding_Cheeto_Mussolini,
                  from_Elon_Musk_to_Peter_Thiel⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-11_[Older]_China_Builds
                  Space_Alliances_in_Africa_as_Cheeto_Mussolini_Cuts_Foreign
                  Aid⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-08_[Older]_African
                  Leaders_Call_for_Direct_Talks_With_Rebels_to_Resolve_Congo
                  Conflict⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-09_[Older]_Sam_Nujoma_battled
                  South_Africa_and_led_a_freed_Namibia⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-09_[Older]_Namibia's_'founding
                  father'_Sam_Nujoma_dies_at_95⠀⇛


                # ⚓ The Verge ☛ 2025-02-14_[Older]_Apple_and_Google_Both_Return
                  TikTok_to_App_Stores,_After_Letter_of_‘Assurance’_From
                  Attorney_General_Pam_Bondi⠀⇛


                # ⚓ Citizen Lab ☛ 2025-02-10_[Older]_The_TikTok_ban_is_already
                  dead_in_the_water:_Jon_Penney_writes_for_the_Globe_and_Mail⠀⇛


                # ⚓ Make Tech Easier ☛ 2025-02-10_[Older]_TikTok_Returns_to
                  Android,_Sort_Of⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-08_[Older]_TikTok_to_Let
                  US_Android_Users_Download_App_Via_Kits_on_Its_Website⠀⇛


                # ⚓ The Straits Times ☛ Off-limits_to_humans_for_70_years,_S.
                  Korea’s_border_zone_becomes_sanctuary_for_rare_cranes⠀⇛


                       The strip of land has turned the area into a
                       sanctuary for many endangered plants and animals.


                # ⚓ The Straits Times ☛ Trump’s_impending_tariffs_loom_large_in
                  South_Korea’s_‘steel_city’⠀⇛


                       South Korea was the fourth-largest exporter of the
                       metal to the US in 2024.


                # ⚓ The Straits Times ☛ Speculation_mounts_in_South_Korea_over
                  Yoon_Suk_Yeol’s_resignation⠀⇛


                       However, his legal team has denied any notion of
                       the suspended President’s resignation.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]
                        Ammunition_Initiative_for_Ukraine_to_Continue,_Czech
                        President_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_China
                        Calls_for_All_Stakeholders_in_Ukraine_War_to_Be_in
                        Peace_Process⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]
                        Zelenskyy_Calls_for_'European_Army'_as_EU_Leaders
                        Bristle_at_New_US_Policies_on_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_Europe
                        Needs_Its_Own_Plan_for_Security_and_Ukraine,_Says
                        Poland's_Tusk⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_France
                        and_Allies_Discuss_Holding_Informal_Ukraine_Summit⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_UK's
                        Foreign_Minister:_US_and_Ukraine_Should_Deepen
                        Partnership⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_US_Asks
                        Europeans_for_Contributions_to_Ukraine_Guarantees⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]
                        Zelenskiy_Says_Draft_US_Minerals_Deal_'Does_Not
                        Protect'_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]
                        Zelenskiy:_Ukraine_Won't_Accept_Deals_Reached_Behind
                        Our_Backs⠀⇛


                      # ⚓ Latvia ☛ 2025-02-14_[Older]_Nordics,_Baltics_say_they
                        will_stand_by_Ukraine⠀⇛


                      # ⚓ Counter Punch ☛ 2025-02-14_[Older]_Why_Cheeto
                        Mussolini_Shouldn’t_Negotiate_With_Putin_on_Ukraine⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-14_[Older]_Ukraine:_Kyiv's
                        reaction_to_Cheeto_Mussolini's_phone_call_with_Putin⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_A_Drone
                        Strike_at_Chernobyl_Has_Raised_Ukraine's_Nuclear
                        Ghosts._What_Are_the_Dangers?⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Europe
                        Quietly_Works_on_a_Plan_to_Send_Troops_to_Ukraine_for
                        Post-War_Security⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_New
                        Traces_of_Tear_Gas_Found_on_Ukraine_Battlefield_by
                        Chemical_Weapons_Watchdog⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Cheeto
                        Mussolini's_Apparent_Concessions_on_Ukraine_NATO_Ties,
                        Territory_'A_Mistake',_German_Defence_Minister_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_UK,_US
                        Agree_Zelenskiy_Must_Be_Part_of_Ukraine_Peace_Talks,
                        Says_UK's_Lammy⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_At_NATO_meeting,
                        Europe_demands_part_in_Ukraine_peace_talks⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_Ukraine_peace
                        talks:_Germany_calls_for_European_involvement⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_What_is_known_of
                        Donald_Cheeto_Mussolini's_'peace_plan'_for_Ukraine?⠀⇛


                      # ⚓ The Age AU ☛ 2025-02-13_[Older]_Australia_news_LIVE:
                        Crossbench_rages_as_electoral_reforms_pass;_Cheeto
                        Mussolini_and_Putin_agree_to_negotiate_end_of_war_in
                        Ukraine⠀⇛


                      # ⚓ The Age AU ☛ 2025-02-13_[Older]_Cheeto_Mussolini_and
                        Putin_begin_talks_to_end_Ukraine_war⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]_Kyiv,
                        EU_Alarmed_by_Prospect_of_'Dirty_Deal'_After_Cheeto
                        Mussolini-Putin_Call⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]_UAE
                        Offers_to_Host_Talks_Aimed_at_Ending_Ukraine_War,
                        Sources_Say⠀⇛


                      # ⚓ NL Times ☛ 2025-02-12_[Older]_Dutch_Defense_Min.
                        calls_for_calm_after_U.S._hints_at_limiting_Ukraine
                        support⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-12_[Older]_Cheeto_Mussolini
                        says_Putin_agreed_to_Ukraine_war_talks_'immediately'⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-12_[Older]_US_says_Ukraine
                        regaining_pre-2014_borders_'unrealistic'⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]_Former
                        Ukraine_President_Poroshenko_Says_Sanctions_Imposed_on
                        Him⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]_Putin
                        Invited_Cheeto_Mussolini_to_Moscow_to_Discuss_Ukraine,
                        Kremlin_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]
                        Zelenskiy,_Cheeto_Mussolini_Discuss_'Opportunities_to
                        Achieve_Peace'_by_Phone⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]_UK_Says
                        It_Supports_Cheeto_Mussolini's_Desire_to_End_Ukraine
                        War,_Focused_on_Boosting_Kyiv's_Position⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]
                        Zelenskiy_Says_Ukraine_Will_Need_US_Help_to_Boost_Army
                        if_It_Can't_Join_NATO⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-11_[Older]_Ukraine:
                        Zelenskyy_plans_to_meet_Cheeto_Mussolini_officials_in
                        Germany⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-11_[Older]_Kremlin
                        Says_There_Is_Nothing_New_to_Report_on_Discussions
                        Around_Ukraine_With_the_US⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-11_[Older]_U.S.
                        Treasury_Secretary_Bessent_to_Visit_Ukraine_for_Talks
                        on_Rare_Earth_Minerals,_Source_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-11_[Older]_U.S.
                        Will_Not_Send_Troops_to_Ukraine,_Pentagon_Chief_Hegseth
                        Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-10_[Older]_Ukraine
                        Imposes_Power_Supply_Restrictions_Amid_Frosty_Weather,
                        Lack_of_Generation⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-09_[Older]_Ukraine's_rare
                        earths_are_key_to_its_bargaining_power⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-09_[Older]_US_updates:
                        Cheeto_Mussolini_says_he's_spoken_with_Putin_about
                        Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-09_[Older]_Cheeto
                        Mussolini_Says_He_Has_Spoken_to_Putin_About_Ending_the
                        Ukraine_War⠀⇛


                      # ⚓ The Independent UK ☛ 2025-02-15_[Older]_The_Art_of
                        the_Deal?_Bitcoin_fraudster_tied_to_2016_hacking_of
                        Democrats_is_Russian_released_in_exchange_for_U.S
                        teacher⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-15_[Older]_A_year_after
                        Navalny's_death,_Russian_opposition_demoralized⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_Russian
                        Court_Orders_US_Citizen_Suspected_of_Drug_Smuggling
                        Held_in_Custody⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_G7
                        Ministers_Link_Future_Russia_Sanctions_to_Good_Faith
                        Talks⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_Russian
                        Court_Puts_US_Citizen_in_Custody_Suspected_of_Drug
                        Smuggling⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_Lavrov,
                        Rubio_Agree_on_Contacts_to_Prepare_for_Putin-Cheeto
                        Mussolini_Meeting,_Russia_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_Cheeto
                        Mussolini_Team_to_Start_Russia-Ukraine_Peace_Talks_in
                        Saudi_Arabia⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_Ukraine
                        Destroys_33_Russian_Drones_During_Overnight_Strike:_Air
                        Force⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_UK
                        Tracks_Russian_Ships_Carrying_Ammunition_From_Syria⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]_Europe
                        Will_Not_Be_Part_of_Ukraine_Peace_Talks,_US_Envoy
                        Says⠀⇛


                      # ⚓ CBC ☛ 2025-02-14_[Older]_Cheeto_Mussolini_says_Russia
                        and_Ukraine_can_reach_a_peace_deal._Will_Ukrainians_buy
                        what_he's_selling?⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-14_[Older]_Russia_detains_US
                        traveler_with_cannabis-laced_gummies⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-14_[Older]_Why_Russia_is
                        seeing_a_rise_in_demand_for_second-hand_goods⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-14_[Older]_Why_Russia_is
                        seeing_a_rise_in_demand_for_secondhand_goods⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_The
                        Latest:_Zelenskyy_Says_Cheeto_Mussolini_Is_Key_to
                        Ending_Russia-Ukraine_Conflict⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Italy
                        President's_'Third_Reich'_Comments_on_Russia_Spark
                        Rome-Moscow_Dispute⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Kremlin
                        Says_G7_Has_Lost_a_Lot_of_Relevance_After_Cheeto
                        Mussolini_Calls_for_Russia_to_Be_Readmitted⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Russia
                        Calls_Zelenskiy_Accusation_Over_Chornobyl_Plant_Stage-
                        Managed_'Nuclear_Blackmail'⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Russia
                        Confirms_It_Has_Detained_a_U.S._Citizen_Suspected_of
                        Drug_Offences,_Ifax_Reports⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Russian
                        Suspected_of_Sabotage_Against_Poland,_US,_Deported_From
                        Bosnia,_Tusk_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Saudi
                        Arabia_Welcomes_Idea_of_U.S._and_Russian_Presidents
                        Meeting_in_Kingdom⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_Two
                        Russians_Jailed_in_Poland_for_Espionage_and_Wagner
                        Membership⠀⇛


                      # ⚓ Latvia ☛ 2025-02-13_[Older]_Saeima_to_look_at_tourism
                        ban_to_Russia,_Belarus⠀⇛


                      # ⚓ International Business Times ☛ 2025-02-13_[Older]
                        David_Beckham's_Russia_Trademark_Sparks_Controversy
                        Amidst_His_Support_for_Ukraine⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]_Kremlin
                        Says_a_Russian_Citizen_Will_Be_Returned_Within_Days
                        From_the_U.S⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]_Russia
                        Rejoices_at_Cheeto_Mussolini-Putin_Call_as_Zelenskyy
                        Rejects_Talks_Without_Ukraine_Present⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]
                        Russia's_Sibur_Set_to_Restart_Drone-Hit_Petchem_Plant
                        in_March⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]_Cheeto
                        Mussolini’s_Call_With_Putin_Ends_U.S._Efforts_to
                        Isolate_Russia⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]_Ukraine
                        Drones_Hit_Russia's_Andreapol_Oil_Pumping_Station,_Kyiv
                        Source_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]_Ukraine
                        Says_It_Will_Not_Accept_US-Russia_Peace_Deal_Reached
                        Without_Kyiv⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]
                        Ukrainians_Worry_About_Cheeto_Mussolini_Effort_to_End
                        War_With_Russia,_Though_Some_Hope_for_the_Best⠀⇛


                      # ⚓ CBC ☛ 2025-02-12_[Older]_Cheeto_Mussolini_confirms
                        Putin_call_as_U.S._defence_secretary_dismisses_prospect
                        of_Ukraine_NATO_membership⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]_Things
                        to_Know_About_Russia's_Release_of_American_Marc_Fogel
                        and_the_Impact_on_Ending_Ukraine_War⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]
                        Exclusive-Russian-Linked_Bots_Sow_Fear,_Distrust_Ahead
                        of_German_Vote,_Researchers_Find⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]_Cheeto
                        Mussolini_Makes_First_Big_Foray_Into_Ukraine_Diplomacy,
                        Speaking_to_Putin,_Zelenskiy⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]_UK
                        Defence_Minister_Healey:_Ukraine_Should_Decide_When_to
                        Start_Russia_Negotiations⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]_Who_Is
                        Alexander_Vinnik,_the_Russian_Prisoner_Being_Traded_for
                        American_Marc_Fogel?⠀⇛


                      # ⚓ Vox ☛ 2025-02-12_[Older]_Cheeto_Mussolini’s_peace
                        talks_with_Putin⠀⇛


                      # ⚓ CPJ ☛ 2025-02-11_[Older]_Russia_preps_to_block_income
                        of_‘foreign_agent’_journalists⠀⇛


                      # ⚓ CPJ ☛ 2025-02-11_[Older]_Russia’s_repression_record⠀⇛


                      # ⚓ Latvia ☛ 2025-02-11_[Older]_Real_estate_purchase_ban
                        for_Russians,_Belarusians_being_considered_in_Latvia⠀⇛


                      # ⚓ Ruben Schade ☛ 2025-02-11_[Older]_Baltic_states
                        disconnect_from_Russian_grid⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-11_[Older]_Russia-Ukraine:
                        Indian_recruits_share_'frightening'_ordeal⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-11_[Older]_Russian
                        Cybercrime_Network_Targeted_for_Sanctions_Across_US,_UK
                        and_Australia⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-11_[Older]_UK
                        Sanctions_Russia's_Zservers_Over_Cyber_Crimes⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-11_[Older]_Four
                        Russians_Arrested_in_Phobos_Ransomware_Crackdown,
                        Europol_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-11_[Older]_Russia
                        Offers_India_Its_Most_Advanced_Su-57_Stealth_Fighter
                        Jet⠀⇛


                      # ⚓ CBC ☛ 2025-02-10_[Older]_They_welcomed_Canada's_open
                        arms._Now_Ukrainians_worry_about_future_as_Russian
                        invasion's_3rd-year_mark_nears⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-10_[Older]_Germany:_Russian
                        on_trial_after_deadly_attack_on_Ukrainian_soldiers⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-10_[Older]_Russia
                        Yet_to_Receive_Satisfactory_Proposals_to_Start_Talks_on
                        Ukraine,_RIA_Reports⠀⇛


                      # ⚓ Modern Diplomacy ☛ 2025-02-09_[Older]_Determining_the
                        Endgame_for_Russia_in_Ukraine⠀⇛


                      # ⚓ CBC ☛ 2025-02-09_[Older]_Ground_drones_are_the_next
                        wave_of_offence_in_Ukraine's_battle_with_Russia⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-09_[Older]_Ukraine's_metals
                        the_US,_EU_and_Russia_want_access_to⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-09_[Older]
                        Governor_Puts_Parts_of_Russia's_Sakhalin_on_High_Alert
                        After_Cargo_Ship_Runs_Aground⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-09_[Older]_Russia
                        Says_It_Sees_No_Positive_Steps_From_US_on_Disarmament,
                        RIA_Reports⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-09_[Older]_Russia
                        Awaits_Appropriate_Signals_From_US_on_Contacts,_Senior
                        Diplomat_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-09_[Older]_Russia
                        Launches_Drone_Attacks_on_Kyiv,_Sumy,_Ukrainian
                        Officials_Say⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-09_[Older]
                        Ukraine's_Military_Says_It_Shot_Down_70_Out_of_151
                        Drones_Launched_by_Russia_Overnight⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-09_[Older]_Cheeto
                        Mussolini_Plan_to_End_Ukraine_War_Must_Prevent_New
                        Russian_Aggression,_Zelenskiy_Says⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-08_[Older]_Ukraine
                        Says_Russia_Launched_139_Drones_Overnight⠀⇛


                      # ⚓ France24 ☛ Navalny's_widow_Navalnaya_calls_for_fight
                        for_'free,_peaceful'_Russia⠀⇛


                             Russian opposition figure Yulia Navalnaya,
                             widow of the late Alexei Navalny, on February
                             16 urged supporters to fight for a 'free,
                             peaceful' Russia, a year after her husband's
                             prison death.


                      # ⚓ France24 ☛ Navalny_supporters_mark_first_anniversary
                        of_his_death_as_Russian_opposition_falters⠀⇛


                             Supporters of Russian opposition leader
                             Alexei Navalny marked the first anniversary
                             of his death on Saturday, risking retaliation
                             from President Vladimir Putin. The opposition
                             has been badly weakened since Navalny’s death
                             as many members have fled into exile while
                             those who remain face fines or imprisonment.


                      # ⚓ France24 ☛ US_cuts_Europe_from_Ukraine_peace_talks:
                        It_'has_caused_extreme_alarm'⠀⇛


                             Dictator shocked European allies this week by
                             calling Russian President Vladimir Putin
                             without consulting them or Kyiv beforehand
                             and declaring an immediate start to peace
                             talks. 'The idea the Europe is going to be
                             excluded from talks to reach an agreement has
                             caused extreme alarm in European capitals',
                             France 24's Nick Holdworth reports.


                      # ⚓ RFERL ☛ U.S._Officials_Heading_to_Saudi_Arabia_For
                        Russia-Ukraine_Peace_Talks⠀⇛


                             Amid a flurry of dramatic diplomatic
                             discussions, U.S. President The
                             Insurrectionist is sending a senior team to
                             Saudi Arabia to begin negotiations with
                             Russia and Ukraine with an eye on ending the
                             nearly 3-year-old war, U.S. officials told
                             multiple media outlets.


                      # ⚓ New York Times ☛ Ukraine_Won’t_Accept_a_Deal_It
                        Didn’t_Help_Negotiate,_Zelensky_Says⠀⇛


                             Volodymyr Zelensky, the president of Ukraine,
                             told NBC News that he’d warned President
                             Convicted Felon that Russia’s president,
                             Vladimir Putin, is a “liar.”


                      # ⚓ New York Times ☛ Putin_Has_Long_Wanted_More_Power_in
                        Europe._Convicted_Felon_Could_Grant_It.⠀⇛


                             Remarks by Vice President JD Vance and
                             Defense Secretary Pete Hegseth are fueling
                             concerns that the U.S. will move away from
                             Europe and align with Moscow.


                      # ⚓ France24 ☛ Vance-Zelensky:_'This_meeting_was_more
                        successful_than_we_expected'⠀⇛


                             US Vice President JD Vance held a meeting in
                             Munich with Ukraine's leader Volodymyr
                             Zelensky to discuss The Insurrectionist's
                             push for a deal with Moscow. Olena
                             Prokopenko, senior fellow at the German
                             Marshall Fund of the United States, was our
                             guest. 'I would say that this meeting was
                             more successful than we expected,' she said.


                      # ⚓ France24 ☛ French_President_Emmanuel_Macron_to_host
                        European_leaders'_meeting_on_Ukraine⠀⇛


                             French President Emmanuel Macron will host a
                             meeting of European leaders on February 17 to
                             discuss the situation in Ukraine. What can we
                             expect to come out of this meeting? France/
                             Europe correspondent for the Swiss daily
                             Blick Richard Werly tells us more.


                      # ⚓ France24 ☛ Former_PM_of_Ukraine_Arseniy_Yatsenyuk:
                        'No_talks_about_Ukraine_without_Ukraine'⠀⇛


                             Europe won't have a seat at the table for
                             Ukraine peace talks, The Insurrectionist's
                             Ukraine envoy said on February 15, after
                             Washington sent a questionnaire to European
                             capitals asking what they could contribute to
                             security guarantees for Kyiv.


                             Former Ukrainian Prime Minister Arseniy
                             Yatsenyuk was our guest. 'In order to achieve
                             peace, we need to craft and hammer out a
                             strong, bold, joint action plan, agreed upon
                             by the United States, the European Union, and
                             Ukraine. No talks about Ukraine without
                             Ukraine,' he said.


                      # ⚓ France24 ☛ Europe_will_not_be_part_of_Ukraine_peace
                        talks,_US_envoy_says⠀⇛


                             Europe won't have a seat at the table for
                             Ukraine peace talks, The Insurrectionist's
                             Ukraine envoy said on February 15, after
                             Washington sent a questionnaire to European
                             capitals to ask what they could contribute to
                             security guarantees for Kyiv.


                      # ⚓ RFERL ☛ Ukraine_Not_Invited_To_U.S.-Russia_Talks_In
                        Saudi_Arabia,_Zelenskyy_Says⠀⇛


                             Ukrainian President Volodymyr Zelenskyy said
                             Kyiv has not been invited to attend U.S.-
                             Russia talks in Saudi Arabia over ending
                             Moscow's war on Ukraine.


                      # ⚓ CS Monitor ☛ Finland_urges_leaders_to_rearm_Ukraine
                        as_U.S._hints_Europe_excluded_from_peace_talks⠀⇛


                             At Munich Security Conference, Finland's
                             president says Europe should put "maximum
                             pressure on Russia" as U.S. prepares to
                             negotiate deal without them.


                      # ⚓ The Straits Times ☛ White_House_envoy,_national
                        security_advisor_head_to_Saudi_Arabia_for_Russia
                        talks⠀⇛


                             White House Middle East envoy Steve Witkoff
                             on Sunday said he would travel to Saudi
                             Arabia later in the day with National
                             Security Advisor Mike Waltz for talks on how
                             to end Russia's war on Ukraine.


                      # ⚓ The Straits Times ☛ Four_killed_in_Ukrainian_drone
                        attacks_in_Russia's_Belgorod_region,_governor_says⠀⇛


                             Ukrainian drone attacks killed four people in
                             two incidents in Russia's Belgorod border
                             region on Sunday, the regional governor said.


                      # ⚓ New York Times ☛ Left_Out_of_Ukraine_Talks,_Europe
                        Races_to_Organize_a_Response⠀⇛


                             The Convicted Felon administration’s push for
                             direct negotiations with Russia without
                             Ukraine’s involvement leaves the European
                             allies with no clear role.


                      # ⚓ New York Times ☛ Zelensky_Rejects_Convicted_Felon
                        Administration_Demand_for_Half_of_Ukraine’s_Mineral
                        Resources⠀⇛


                             President Volodymyr Zelensky publicly faulted
                             the American proposal because it did not
                             include security guarantees.


                      # ⚓ New York Times ☛ A_Pro-Ukraine_Activist_Is_Accused_by
                        Slovakia’s_Leader_of_Trying_to_Topple_Him⠀⇛


                             A woman who runs a pro-Ukraine group has been
                             accused by Prime Minister Robert Fico of
                             Slovakia of plotting to topple him as part of
                             his campaign against organizations he says
                             are funded from abroad.


                      # ⚓ RFERL ☛ U.S._Officials_In_Rare_Belarus_Visit_Seeking
                        Deal_On_Political_Prisoners,_Sanctions⠀⇛


                             Three senior U.S. officials traveled to
                             Belarus to negotiate the possible release of
                             a large number of political prisoners in
                             return for an easing of sanctions, The New
                             York Times reported, following the release of
                             three detainees earlier in the week


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_EU's
                        Kallas:_Listening_to_Vance_Speech_Felt_Like_United
                        States_Was_Trying_to_Pick_Fight_With_Us⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-14_[Older]_In
                        Munich,_Vance_Accuses_European_Politicians_of_Censoring
                        Free_Speech⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-15_[Older]
                        Germany's_Scholz_Rebukes_Vance,_Defends_Europe's_Stance
                        on_Hate_Speech_and_Far_Right⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The Telegraph UK ☛ Letby_hospital_forced_whistleblower_out
                  of_her_job,_tribunal_rules⠀⇛


                       She claimed she was “harassed and intimidated” by
                       Mr Haythornthwaite, whom she accused of putting the
                       financial security of the hospital before patient
                       care.


                       She later “blew the whistle” about her concerns
                       about him and was suspended before she eventually
                       resigned from her job in 2022.


                       Now her claim of unfair dismissal has been upheld.
                       Judge Dawn Shotter, who chaired the tribunal, ruled
                       that Mr Haythornthwaite and three other senior
                       figures at the hospital worked together to remove
                       Dr Gilby from her post.


          o § Environment⠀➾


                # ⚓ Counter Punch ☛ 2025-02-14_[Older]_Climate_Upheaval,_Mild
                  or_Severe,_Who_Really_Cares?⠀⇛


                # ⚓ Counter Punch ☛ 2025-02-14_[Older]_Two_Books_on_Climate
                  Change_and_Beyond⠀⇛


                # ⚓ Vox ☛ 2025-02-14_[Older]_Why_the_US_is_freezing_as_the
                  planet_reaches_record_warmth⠀⇛


                # ⚓ Modern Diplomacy ☛ 2025-02-13_[Older]_The_Vatican’s_Path_on
                  Fiji’s_Climate_Change_Policy⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_What's_next_for
                  Germany's_climate_movement?⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-13_[Older]_EPA_Chief
                  Seeks_to_Claw_Back_$20_Billion_in_Climate_Funding⠀⇛


                # ⚓ TruthOut ☛ 2025-02-12_[Older]_Cheeto_Mussolini’s_Climate
                  Funding_Freeze_Leaves_Tribes_and_Community_Groups_in_Limbo⠀⇛


                # ⚓ Jacobin Magazine ☛ 2025-02-11_[Older]_Colombia’s_Receding
                  Coastline⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-11_[Older]_Climate_versus_economy:
                  Does_Germany_need_to_choose?⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-11_[Older]_Transparency
                  International:_Corruption_is_a_climate_issue⠀⇛


                # ⚓ HRW ☛ 2025-02-11_[Older]_Panama_Needs_to_Expedite_Efforts
                  Toward_Climate_Relocation_Policy⠀⇛


                # ⚓ New Yorker ☛ 2025-02-11_[Older]_The_Second_Cheeto_Mussolini
                  Administration_Takes_Aim_at_the_Climate⠀⇛


                # ⚓ International Business Times ☛ 2025-02-10_[Older]_Jeff
                  Bezos'_£8B_Fund_Cuts_Funding_to_Climate_Group_As_Amazon
                  Secures_£670K_Military_Contract_In_Britain⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-10_[Older]_Most
                  Countries_Miss_UN_Deadline_for_New_Climate_Targets⠀⇛


                # ⚓ Modern Diplomacy ☛ 2025-02-08_[Older]_U.S_Withdrawal_and
                  Politics_of_Paris_Climate_Agreement⠀⇛


                # ⚓ TruthOut ☛ 2025-02-08_[Older]_DOGE_Ransacks_NOAA,_Raising
                  Fears_About_Privatization_of_Climate_Data⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-12_[Older]_Extreme_weather_has
                  killed_almost_800,000_people_in_30_years,_says_report⠀⇛


                # § Energy/Transportation⠀➾


                      # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_Germany:_Porsche
                        set_to_slash_jobs_by_2029⠀⇛


                      # ⚓ New York Times ☛ Prominent_Cryptocurrency_Investor
                        Faces_Senate_Tax_Inquiry⠀⇛


                             A Senate committee is investigating whether a
                             prominent cryptocurrency investor violated
                             federal tax law to save hundreds of millions
                             of dollars after he moved to Puerto Rico, a
                             popular offshore tax haven, according to a
                             letter reviewed by The New York Times.


                      # ⚓ Modern Diplomacy ☛ 2025-02-14_[Older]_South_Africa’s
                        G20_Presidency_for_2025:_A_Catalyst_for_Energy
                        Investment_in_Africa⠀⇛


                      # ⚓ Truthdig ☛ 2025-02-13_[Older]_Mayors_Across_U.S._Urge
                        Congress_Not_To_Repeal_Clean_Energy_Tax_Credits⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]
                        Democratic_US_Lawmakers_Ask_Energy_Department_About_Any
                        DOGE_Access_to_Nuclear_Data⠀⇛


                      # ⚓ Vox ☛ 2025-02-10_[Older]_The_tiny_lizard_that_will
                        test_Cheeto_Mussolini’s_“drill,_baby,_drill”_agenda⠀⇛


                # § Wildlife/Nature⠀➾


                      # ⚓ The Conversation ☛ 2025-02-11_[Older]_Most_animals
                        have_their_own_version_of_tree_rings_–_here’s_how_we
                        biologists_use_them_to_help_species_thrive⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-12_[Older]
                        Brazil's_Lula_to_Meet_With_Agency_on_Petrobras'_Bid_to
                        Drill_Near_Mouth_of_Amazon_River⠀⇛


                      # ⚓ TwinCities Pioneer Press ☛ Business_People:_Joy_King
                        named_CEO_of_Animal_Humane_Society⠀⇛


                             NONPROFITS Animal Humane Society, Golden
                             Valley, announced it has named Joy King as
                             CEO. King previously served as chief
                             advancement officer of NMDP, formerly Be The
                             Match, a national bone marrow donation
                             registry, and executive director of the NMDP
                             Foundation.


                      # ⚓ NYPost ☛ Doctor_reveals_the_truth_about_nondairy_milk
                        options_—_and_if_any_of_them_are_healthier_than_cow’s
                        milk⠀⇛


                             Is plant-based milk really better than good
                             old cow’s milk? Is it all hype? Or are people
                             onto something?


          o § Finance⠀➾


                # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_Commerzbank_plans_job
                  cuts,_new_goals_to_fend_off_UniCredit⠀⇛


                # ⚓ The Age AU ☛ 2025-02-11_[Older]_Banks_told_to_ignore
                  student_debt_when_weighing_up_home_loans⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-10_[Older]_Sanctions_on
                  Syrian_Banks_Choke_Recovery_Hopes,_Investment_Chief_Says⠀⇛


                # ⚓ Jacobin Magazine ☛ 2025-02-13_[Older]_Cheeto_Mussolini’s
                  New_Consumer_Finance_Regulator_Loves_Pleasing_Banks⠀⇛


                # ⚓ Counter Punch ☛ 2025-02-14_[Older]_Funding_the_Revolution,
                  Beating_the_Banks⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-14_[Older]_Nigeria_approves_$200M
                  to_offset_shortfall_from_US_aid_cuts⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-14_[Older]_German_parties_consider
                  taking_on_more_debt⠀⇛


                # ⚓ Digital Camera World ☛ What_Monty_Python_taught_me_about
                  the_art_of_haggling_over_a_price_of_a_camera⠀⇛


                       In order to successfully haggle, you’ll want to
                       decide what’s a fair price for the tech gear you
                       want to buy. So, research the cost of that product
                       and use it to determine what you’re willing to pay.
                       A helpful tip is to print out or take screen shots
                       of website pages. You might also get quotes from
                       competitors (but make sure they’re in writing and
                       print those out, too). Once you do that, contact
                       the store to confirm that it will match the lowest
                       price you’ve found. If you can’t get a better
                       price, you could try asking them about free
                       shipping or delivery.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Silicon Angle ☛ Why_Intel_must_stay_independent,_spin_out
                  its_foundry_and_rebuild_its_iconic_brand⠀⇛


                       Today, Intel finds itself in a precarious position.
                       Its once-vaunted manufacturing machine has fallen
                       behind Taiwan Semiconductor Manufacturing Corp.,
                       which dominates advanced process nodes. Meanwhile,
                       Intel’s core central processing unit design
                       business — a substantial, if bruised, revenue
                       engine — remains overshadowed by the mounting
                       losses and capital burn in its foundry operations.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Hong Kong Free Press ☛ Chinese_animated_blockbuster
                        breaks_records,_prompts_patriotism⠀⇛


                             Some fans have speculated that the film also
                             contains hidden geopolitical symbolism,
                             suggesting the villain’s palace is a
                             reference to the US Pentagon or White House,
                             though the filmmakers haven’t commented on
                             these rumours.


          o § Censorship/Free Speech⠀➾


                # ⚓ EFF ☛ 2025-02-13_[Older]_First_Cheeto_Mussolini_DOJ
                  Assembled_“Tiger_Team”_To_Rewrite_Key_Law_Protecting_Online
                  Speech⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_Nepal's_social_media
                  bill_raises_free_speech_concerns⠀⇛


                # ⚓ ANF News ☛ Iranian_Writers'_Association_calls_for_annulment
                  of_death_sentences_for_Warisha,_Pakshan_and_Sharifa⠀⇛


                       The Iranian Writers' Association has called for the
                       death sentences of Warisha Moradi, Pakshan Azizi
                       and Sharifa Mohammadi to be annulled.


                       The Iranian Writers' Association pointed out that
                       the Iranian regime has been burying the bodies of
                       executed individuals in unmarked graves for years,
                       adding: “This horrible punishment is still
                       continuing.”


                # ⚓ YLE ☛ Helsinki_proposes_Navalny_memorial_site_near_Russian
                  Embassy⠀⇛


                       Confirming the news, Jussi Luomanen, the city's
                       head of urban space and landscape planning, said
                       the memorial was proposed by Russian activists
                       opposing Vladimir Putin's policies from an
                       organisation called the Initiative for Resistance
                       and Dialogues.


                       "This group wants to honour the memory of Aleksei
                       Navalny by installing a memorial bench. Helsinki is
                       granting permission for the bench to be placed in a
                       public park," Luomanen said in an email.


                # ⚓ Meduza ☛ ‘History_is_not_written_only_by_the_victors’
                  International_readers_of_Alexey_Navalny’s_memoir_reflect_on
                  the_late_politician’s_life_and_legacy⠀⇛


                       Patriot was translated into over 20 languages,
                       including ones spoken in countries where Alexey
                       Navalny is far from a household name. Meduza found
                       several people from around the world who read the
                       book and published their own reviews online, and
                       invited them to share their impressions of the
                       memoir and their thoughts on Navalny himself.


                # ⚓ The Moscow Times ☛ One_Year_After_His_Death,_Allies_and
                  Supporters_Remember_Navalny_in_Berlin_Memorial⠀⇛


                       In a wide-ranging 90-minute conversation, Navalny’s
                       widow Yulia shared memories of her husband,
                       discussed life without him and called on Russians
                       abroad to protest the regime “for those in Russia
                       who can’t.”


                # ⚓ VOA News ☛ Navalny_supporters_risk_reprisals_with_memorial
                  events_a_year_after_death⠀⇛


                       Remembrance events will take place as Russia's
                       opposition movement -- driven into exile by
                       unprecedented repression -- has been plagued by
                       infighting and badly weakened since the loss of its
                       figurehead.


                       Exiled in various countries, its leading members
                       have tried to revive the fight against Vladimir
                       Putin's long reign, including in Russia where
                       criticism of authorities is severely punished.


                # ⚓ JURIST ☛ Committee_to_Protect_Journalists_urges_Taliban_to
                  lift_broadcast_ban_on_political_and_economic_content⠀⇛


                       The ban reflects a trend of heightened media
                       censorship under Taliban control, which has greatly
                       restricted press and expression freedoms in
                       Afghanistan. The UN Assistance Mission in
                       Afghanistan has noted a significant decline in
                       media freedoms since the Taliban takeover in 2021.
                       Human Rights Watch has documented several incidents
                       where journalists were harassed, detained, and
                       physically abused for attempting to cover sensitive
                       issues. Amnesty International has also detailed the
                       Taliban’s arbitrary detention of journalists and
                       the closure of media outlets as part of a broader
                       crackdown on freedom of expression.


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


                # ⚓ TruthOut ☛ 2025-02-12_[Older]_White_House_Revoked_Access_to
                  AP_for_Refusing_to_Comply_With_Censorship⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ Deutsche Welle ☛ 2025-02-12_[Older]_Google_Calendar_removes
                  Black_History_Month_and_Pride_Month⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-10_[Older]_Amazon_Faces
                  Union_Vote_at_North_Carolina_Warehouse⠀⇛


                # ⚓ TruthOut ☛ 2025-02-11_[Older]_Workers_Resist_Amazon’s
                  Attempts_to_Divide_Them_by_Race_Ahead_of_NC_Union_Vote⠀⇛


                # ⚓ Scheerpost ☛ 2025-02-15_[Older]_Amazon_Stokes_Racial
                  Divides_in_Lead-Up_to_North_Carolina_Union_Vote⠀⇛


                # ⚓ Jacobin Magazine ☛ 2025-02-15_[Older]_Ahead_of_Workers’
                  Union_Vote,_“Amazon_Mobilized_an_Army”⠀⇛


                # ⚓ Project Censored ☛ 2025-02-10_[Older]_Is_This_the_Best_We
                  Can_Do?_Hope_and_Limitations_in_International_Law⠀⇛


                # ⚓ [Old] EFF ☛ Van_Buren_is_a_Victory_Against_Overbroad
                  Interpretations_of_the_CFAA,_and_Protects_Security
                  Researchers⠀⇛


                       The decision is a victory for all Internet users,
                       as it affirmed that online services cannot use the
                       CFAA’s criminal provisions to enforce limitations
                       on how or why you use their service, including for
                       purposes such as collecting evidence of
                       discrimination or identifying security
                       vulnerabilities. It also rejected the use of
                       troubling physical-world analogies and legal
                       theories to interpret the law, which in the past
                       have resulted in some of its most dangerous abuses.


                       The Van Buren decision is especially good news for
                       security researchers, whose work discovering
                       security vulnerabilities is vital to the public
                       interest but often requires accessing computers in
                       ways that contravene terms of service. Under the
                       Department of Justice’s reading of the law, the
                       CFAA allowed criminal charges against individuals
                       for any website terms of service violation. But a
                       majority of the Supreme Court rejected the DOJ’s
                       interpretation. And although the high court did not
                       narrow the CFAA as much as EFF would have liked,
                       leaving open the question of whether the law
                       requires circumvention of a technological access
                       barrier, it provided good language that should help
                       protect researchers, investigative journalists, and
                       others.


                # ⚓ [Old] Los Angeles Times ☛ Opinion:_Violating_a_website’s
                  terms_of_service_is_not_a_federal_crime⠀⇛


                       At any rate, Barrett’s opinion should help contain
                       the CFAA within its intended boundaries. She was
                       joined in the ruling by two other textualists on
                       the court — Justices Neil Gorsuch and Brett
                       Kavanaugh — and the court’s three liberals, but not
                       by three of their fellow conservatives: Chief
                       Justice John G. Roberts Jr. and Justices Clarence
                       Thomas and Samuel A. Alito Jr.


                       The two sides disagreed on what the law meant by
                       “exceeds authorized access.” Writing for the
                       dissenters, Thomas argued that “Van Buren never had
                       a ‘right’ to use the computer to obtain the
                       specific license plate information.” But that’s
                       just another way of saying that the law governs
                       what computer users do with the information they
                       are authorized to access on a site, which
                       eradicates the act’s boundaries. The majority
                       rightly held that the law prohibits people from
                       getting into computers or files that the computer
                       owner hasn’t opened to them, not those who violate
                       the terms the computer owner has imposed.


    * § Internet Policy/Net Neutrality⠀➾


          o ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_YouTube:_From_failed_dating
            site_to_pop_culture_juggernaut⠀⇛


          o ⚓ Tom's Hardware ☛ Meta_plans_50,000_km_undersea_cable_to_connect
            the_U.S.,_Brazil,_Africa,_India,_and_Australia⠀⇛


                 Meta just announced an ambitious new undersea internet
                 cable project that spans over 50,000 km to connect North
                 and South America, Africa, Asia, and Australia. The
                 Facebook parent company is part-owner of several undersea
                 communications cables, but this new plan, called Project
                 Waterworth, will apparently be the first that it will
                 solely own and operate. Meta says it will be the longest
                 cable deployed so far and will likely cost the company
                 over $10 billion.


§ Monopolies/Monopsonies⠀➾


    * ⚓ IP Kat ☛ 2025-02-10_[Older]_Urban_places_as_a_stage_and_the_CGI_and_VFX
      trend:Using_buildings_in_videos_to_make_the_ordinary_extraordinary⠀⇛


    * § Patents⠀➾


          o ⚓ The Age AU ☛ 2025-02-16_[Older]_Dupe_culture_and_patent_costs
            threaten_the_next_great_Australian_inventions⠀⇛


          o § Kangaroo Courts⠀➾


                # ⚓ IP Kat ☛ 2025-02-12_[Older]_EBA's_preliminary_opinion_in
                  G1/24:_"the_description_and_the_figures_can_be_referred_to_in
                  the_course_of_claim_interpretation"⠀⇛


    * § Trademarks⠀➾


          o ⚓ IP Kat ☛ 2025-02-11_[Older]_AG_Biondi:_extending_patent_rights
            through_trade_marks_is_not_bad_faith_per_se_(but_the_“line_is
            blurry”) [Ed: Well, patents and trade marks are totally different;
            more of a reason to avoid terms like "IP"]⠀⇛


          o ⚓ IP Kat ☛ 2025-02-12_[Older]_GTI_v_GTA:_Too_short_to_be
            confusingly_similar?_Not_according_to_the_German_Patent_Court [Ed:
            Trademarks or patents? Are the courts mislabeled?]⠀⇛


          o ⚓ IP Kat ☛ 2025-02-10_[Older]_[Guest_post]_Retromark_Volume_XV:_the
            last_six_months_in_trade_marks⠀⇛


    * § Copyrights⠀➾


          o ⚓ IP Kat ☛ 2025-02-11_[Older]_Sony_still_can’t_get_no_relief_in
            claim_over_Jimi_Hendrix_Experience_recordings⠀⇛


          o ⚓ IP Kat ☛ 2025-02-12_[Older]_[Guest_post]_Copyright_in_fictional
            universes⠀⇛


          o ⚓ US News And World Report ☛ 2025-02-12_[Older]_Thomson_Reuters
            Scores_Early_Win_in_AI_Copyright_Battles_in_the_US⠀⇛


          o ⚓ Torrent Freak ☛ TorrentGalaxy_Drama_Continues_With_Days_of
            Downtime⠀⇛


                 Trouble continues for popular torrent site TorrentGalaxy.
                 The site, which is seen as a notorious piracy market by
                 the Office of the U.S. Trade Representative, has been
                 unreachable for days. While some believe that the end has
                 come for the site, technical troubles certainly can't be
                 ruled out.


          o ⚓ Torrent Freak ☛ Real-Debrid_Traffic_Falls_16%_in_3_Months,_Anti-
            Piracy_Action_Painful_But_Non-Fatal⠀⇛


                 At least on paper, Real-Debrid's November 2024
                 announcement detailing new anti-piracy measures,
                 suggested a tough time ahead for the popular platform.
                 Under pressure from dozens of powerful rightsholders,
                 Real-Debrid's position looked precarious to put it
                 mildly; not precarious enough for the service to throw in
                 the towel, however. Three months later, a 16% drop in
                 traffic is painful but non-fatal.


          o ⚓ [Old] Ruboss Technology Corp ☛ Why_Don’t_I_Use_Leanpub?._
            (Originally_published_Aug_28,_2014…⠀⇛


                 Today Jurgen Appelo wrote a very well-written post
                 entitled “Why I Don’t Use Leanpub”.


                 Go read it now. Seriously.


                 Now that you’re back, you’ll know that Jurgen essentially
                 makes the following arguments: [...]





                    ䷩ 𝚕𝚒𝚗𝚎 6049

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 17/02/2025: LLMs Failing and Patreon
Support Becoming a Burden to Bloggers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Technology_and_Free_Software
                # Internet/Gemini
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ On_the_back_foot⠀⇛


                       The climate aware intersectional justice movement
                       is on the back foot, and the fascists have (for
                       now) won the propaganda war.


                       The vast majority of folks outside of the ivory
                       towers have no idea of what we’re going on about.
                       They get their misinformation and fake news from
                       group threaads on WhatsApp, Facebook and X. The
                       right wing owns media right now.


                       And it’s not about “our team vs theirs”; the stakes
                       are the survival of the world. We wanna save it for
                       everyone, they wanna end it, for everyone. And why
                       they wanna end it, nobody knows but I’d bet it’s a
                       triumvirate of weird religious “accelerate
                       Revelation” nonsense joining forces with good old
                       “fuck you I’ve got mine, après moi le déluge, I can
                       cash in on the apocalypse and then die rich”
                       joining forces with just plain uninformed.


                # ⚓ 🔤SpellBinding:_ADILMPU_Wordo:_VOCAL⠀⇛


                # ⚓ Stirling_Who?_🏁⠀⇛


                       It came to my attention that young people don't
                       know who Stirling Moss was. Fair enough, I suppose,
                       because his fame as a racing driver was in the 50s
                       and 60s. He came up when discussing falling down a
                       lift shaft with a colleague at work. Moss had a
                       lift in his house, and fell down the shaft while in
                       his eighties. He broke bones, but survived, and was
                       quite light hearted about it. The incident
                       highlights two things about him. First, he was
                       someone who wasn't overly concerned with risk, and
                       second he was the sort of person who had a lift
                       installed in his house just because it's a fun
                       gadget.


                       I've seen archive clips of him being interviewed
                       about being a racing driver. He calmly explains
                       driving on a knife edge of grip as if he were
                       talking about growing begonias, when in fact making
                       a mistake would involve a high speed crash and
                       probable death, not missing out on a prize at a
                       village show. He retired from racing when he had
                       just such a crash that put him in a coma for a
                       month. He'd finished second in the drivers'
                       championship four times, and is often called the
                       greatest driver never to win it. He also drove and
                       won in many other categories, sometimes driving
                       over 50 races in a year.


                # ⚓ Lantashi_Dance_-_Kingdom_of_Joy⠀⇛


                       Below is my latest log for my Cosmic Voyage story
                       Lantashi Dance. It has been a long time since I've
                       done one of these logs. I forgot how much fun it is
                       to write these! I definitely need to create more
                       adventures for the crew of Lantashi Dance!!


          o § Technology and Free Software⠀➾


                # ⚓ The_Dystopian_Hellscape_of_Apple’s_1987_Knowledge_Navigator
                  Concept_Video⠀⇛


                       He has a ton of message notifications.


                       He also gets a few appointments and is expected to
                       remember them himself. The appointments are pretty
                       big deals but they’re completely last minute shocks
                       to him, like having to prepare a lecture that he’s
                       supposed to have in a few hours or getting a cake
                       for a family gathering.


                       For his actual work, the lecture, he throws
                       something together in three seconds with the LLM
                       and mooches off a friend, asks her to come do the
                       lecture. Actual thinking: nadita. I’m not denying
                       that an LLM like he has could help him come up with
                       some great insights and ideas, that’s not one of
                       the problems with LLMs, they can be great (and the
                       "What was his name, Fleming something" and the LLM
                       understanding that certainly rings true to a lot of
                       us). But that’s not what he’s doing. He’s just
                       pasting some maps together...


                       And he’s tasked to do the remembering part while
                       the LLM does the thinking.


                # ⚓ Perplexity's_Deep_Research_is_a_Hallucinating_Mess⠀⇛


                       Perplexity (perplexity.ai) loosely is a ChatGPT
                       competitor that focuses on incorporating online
                       search into its responses. This supposedly helps
                       with reducing hallucinations and allows the LLM to
                       have up to date information. Very recently they
                       lunched "Deep Research" which instead of basically
                       querying (I suppose) Bing then RAG on the search
                       result. They use some Chain-of-Though and iterative
                       refining to dig deeper into the search results.
                       Interesting but how well that actually works?


                       I happen do have a subscription that give me access
                       to the Deep Research feature. I use Perplexity from
                       time to time as it is genuinely helpful solving
                       difficult questions. Let's try. I also happen to be
                       quite familiar with what Tenstorrent is doing, so
                       let's ask Deep Research about Tenstorrent:


                # § Internet/Gemini⠀➾


                      # ⚓ Blog_activity_for_2025⠀⇛


                             First, I decided to stop the Patreon page for
                             multiple reasons. It was an interesting
                             experimentation and helped me a lot in 2023
                             and a part of 2024 as I went freelance and
                             did not earn much money. Now, the business is
                             running fine and prefer my former patrons to
                             support someone else more active / who need
                             money.


                      # ⚓ Blog_activity_for_2025⠀⇛


                             The way I implemented Patreon support was
                             like this: people supporting me financially
                             had access to blog posts a 2 or 3 days
                             earlier than the public release, the point
                             was to give them a little something for their
                             support without creating a paywall for some
                             content. I think it worked quite well in that
                             regard. A side effect of the "early access
                             publishing" was that, almost every time, I
                             used this extra delay to add more content /
                             fix issues that I did not think about when
                             writing. As a reminder, I usually just write
                             then proofread quickly and publish.


                             Having people paying money to have early
                             access to my blog posts created some kind of
                             expectations from them in my mind, so I tried
                             to raise the level higher in terms of content
                             at the point that I came to procrastinate
                             because "this blog post will not be
                             interesting enough" or "this will just take
                             too long to write, I'm bored".


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





                    ䷩ 𝚕𝚒𝚗𝚎 6261

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 17/02/2025: War on Dissent and
Bloggers, Nationalism a Growing Theme⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 17, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Axel_Rose⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
                # Artificial_Intelligence_(AI)
                # Social_Control_Media
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
    * § Leftovers⠀➾


          o ⚓ Ruben Schade ☛ Coffee_shop_chatter,_week_7_2025⠀⇛


                 Some fun random things I overheard this morning:


                 These phones don’t make sense anymore. I’m barely 30, and
                 I don’t understand what half this crap does.


          o ⚓ Ruben Schade ☛ A_question_about_aviation_ESG_plans⠀⇛


                 I read a few blogs and sites for transport insiders. I’m
                 clearly not the target audience, but I still find them
                 really interesting.


          o ⚓ New York Times ☛ She_Was_the_Female_Lead_in_His_Film._Now_She’s
            His_Leading_Lady.⠀⇛


                 When Alan Yang, known for “Parks and Recreation” and
                 “Master of None,” directed his first film, Christine Ko’s
                 audition tape stopped him in his tracks. Once the film
                 wrapped, romance emerged.


          o ⚓ US News And World Report ☛ 2025-02-11_[Older]_How_Photos_Lost_in
            American_Disasters_Find_Their_Way_Home,_With_a_Little_Help_From
            People_Who_Care⠀⇛


          o § Science⠀➾


                # ⚓ Hackaday ☛ Using_Antimony_To_Make_Qubits_More_Stable⠀⇛


                       One of the problems with quantum bits, or “qubits”,
                       is that they tend to be rather fragile, with a high
                       sensitivity to external influences. Much of this is
                       due to the atoms used for qubits having two
                       distinct spin states of up or down, along with the
                       superposition. Any disturbing of the qubit’s state
                       can cause it to flip between either spin, erasing
                       the original state. Now antimony is suggested as a
                       better qubit atom by researchers at the University
                       of New South Wales in Australia due to it having
                       effectively eight spin states, as also detailed in
                       the university press release along with a very
                       tortured ‘cats have nine lives’ analogy.


                # ⚓ Science Alert ☛ Materials_Can_Form_'Memories'_in_New_And
                  Unexpected_Ways,_Study_Shows⠀⇛


                       Remember, remember.


                # ⚓ Science Alert ☛ A_Psychologist_Explains_a_Simple_Technique
                  to_Declutter⠀⇛


                       This can make it a lot easier.


                # ⚓ Science Alert ☛ Afternoon_Naps_Boost_Your_Problem-Solving,
                  Study_Finds⠀⇛


                       Sleep on it.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ SPOKE_capacitive_touch_sensor_board_targets
                  interactive_computer_interfaces_(Crowdfunding)⠀⇛


                       SPOKE is a Raspberry Pi RP2040-based capacitive
                       touch sensor board for interactive computer
                       interfaces. It is designed to simplify the
                       integration of touch-based control into various
                       projects. SPOKE features up to 27 sensor inputs and
                       can “turn almost any conductive material into a
                       sensor” to control almost any computer input.
                       Potential applications include music making, video
                       game controlling, typing, and general software
                       controlling.


                # ⚓ Tom's Hardware ☛ Intel_8th,_9th_and_10th_Gen_processors
                  removed_from_Microsoft's_backdoored_Windows_11_24H2_CPU
                  support_list⠀⇛


                       Intel's 8th, 9th, and 10th Gen processors are
                       absent from the backdoored Windows 11 24H2 official
                       support list.


                # ⚓ Tom's Hardware ☛ AMD_exec_sarcastically_teases_RX
                  90700.05XTXT_Max_GPU_with_320GB_of_VRAM_and_'1.2_Gigawatts'
                  power_supply_requirement [Ed: Not funny because they do ruin
                  the planet with wasteful CPUs that help run Ponzi schemes]⠀⇛


                       AMD's Frank Azor commented on a recent 32GB RX 9070
                       XTX rumor but didn't outright deny it.


                # ⚓ Tom's Hardware ☛ TSMC_and_Broadcom_explore_deals_to_split
                  Intel's_foundry_and_chip_design_wings,_says_report⠀⇛


                       Intel is reportedly the target of acquisition
                       interest from TSMC and Broadcom, with both
                       companies exploring deals that could divide the
                       struggling chipmaker’s operations.


                # ⚓ Hackaday ☛ [Quinn_Dunki]_Makes_A_Screw_Shortener_Fit_For
                  Kings⠀⇛


                       It’s common problem when you’re building anything
                       with screws: this one is too long, this one is too
                       short. While she can’t teach you how to fix the
                       latter, [Quinn Dunki] has made herself an
                       absolutely deluxe screw shortening jig. And while
                       that’s cool and all, the real value here is the
                       journey; watching over [Quinn]’s shoulders while
                       she’s in the machine shop is always illuminating.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Science Alert ☛ Your_Risk_of_Cancer_Could_Fluctuate_Even
                  Born_You're_Born⠀⇛


                       It's not just bad luck.


                # ⚓ Hackaday ☛ Graphene_Tattoos:_The_Future_Of_Continuous
                  Health_Monitoring?⠀⇛


                       In the near future, imagine a world where your
                       health is continuously monitored, not through bulky
                       devices but through an invisible graphene tattoo.
                       Developed at the University of Massachusetts
                       Amherst, these tattoos could soon detect a range of
                       health metrics, including blood pressure, stress
                       levels, and even biomarkers of diseases like
                       diabetes. This technology, though still in its
                       infancy, promises to revolutionize how we monitor
                       health, making it possible to track our bodies’
                       responses to everything from exercise to
                       environmental exposure in real-time.


                # ⚓ The Straits Times ☛ ‘Bullet_recycling_plant’_found_in_raid
                  on_illegal_e-waste_factory_in_Malaysia⠀⇛


                       Bullet casings, fired and live bullets were found
                       during the raid.


                # ⚓ Deutsche Welle ☛ 2025-02-12_[Older]_STIs_in_Europe:
                  Gonorrhea_and_syphilis_hit_record_highs⠀⇛


          o § Proprietary⠀➾


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ Science Alert ☛ ChatGPT's_Deep_Research_Is_Here._But
                        Can_It_Really_Replace_a_Human_Expert? [Ed: Falsely
                        marketed garbage]⠀⇛


                             "It promises to do the heavy lifting of
                             research in minutes."


                      # ⚓ NYPost ☛ Lonely_men_are_creating_Hey_Hi_(AI)
                        girlfriends_—_and_taking_their_violent_anger_out_on
                        them⠀⇛


                             Experts say that the abusive behavior could
                             be detrimental to their real life
                             relationships.


                # § Social Control Media⠀➾


                      # ⚓ Deutsche Welle ☛ 2025-02-10_[Older]_To_fight_dissent,
                        Kenya_clamps_down_on_social_media,_AI⠀⇛


          o § Defence/Aggression⠀➾


                # ⚓ France24 ☛ Rally_against_Germany's_resurgent_far_right
                  draws_thousands_in_Berlin⠀⇛


                       One week out from Germany's general election, tens
                       of thousands of people gathered in Berlin to
                       protest the growing support for the far-right
                       Alternative for Germany (AfD) party. A quarter of a
                       million people joined a similar rally in Munich
                       last weekend.


                # ⚓ JURIST ☛ State_attorney_generals_challenge_MElon-led_DOGE
                  control_over_US_federal_agencies⠀⇛


                       Fourteen US state attorney generals filed a lawsuit
                       in a New York federal court against MElon, his
                       Department of Government Efficiency (DOGE), and
                       President The Insurrectionist on Thursday.


                # ⚓ The Strategist ☛ China_is_exporting_its_model_of_political
                  authoritarianism_to_Africa⠀⇛


                       To expand its influence in Africa, China has
                       stepped up its elite capture programs from hosting
                       delegations and training to exporting its
                       authoritarian model of governance.


                # ⚓ France24 ☛ Panama_Canal_caught_in_power_struggle_as_US_and
                  China_vie_for_trade_dominance⠀⇛


                       The Panama Canal is one of several territories that
                       US President The Insurrectionist says he wants the
                       US to take control of, amid concerns about China's
                       influence over the waterway. What worries the US is
                       a Hong Kong-based company that manages the two
                       ports of entrance. Back in 2017, Chinese President
                       Pooh-tin Jinping integrated the canal into his Belt
                       and Road Initiative. But under US pressure,
                       Panama's government has now backed out of that
                       project. The canal finds itself caught in a
                       struggle between two major world powers. Our France
                       2 colleagues report, with FRANCE 24's Lauren Bain.


                # ⚓ Hong Kong Free Press ☛ Philippines’_Marcos_puts_China_at
                  centre_of_election_campaign⠀⇛


                       President Ferdinand Marcos put Beijing firmly
                       centre stage on the campaign trail on Saturday,
                       saying his predecessor’s administration was all too
                       happy for the Philippines “to be a province of
                       China”.


                # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_Why_Ghana_faces_a
                  growing_jihadist_threat⠀⇛


                # ⚓ Defence Web ☛ 2025-02-12_[Older]_Atalanta_on_high_alert_as
                  possible_pirate_attack_reported⠀⇛


                # ⚓ Jacobin Magazine ☛ 2025-02-12_[Older]_South_Africa’s_Worst
                  State-Sponsored_Massacre_Since_Apartheid⠀⇛


                # ⚓ Defence Web ☛ 2025-02-13_[Older]_Sandu_names_units_of
                  soldiers_killed_in_the_DRC,_MPs_lay_wreaths⠀⇛


                # ⚓ Defence Web ☛ 2025-02-12_[Older]_Lamola_dismisses_proposal
                  to_withdraw_SA_troops_from_the_DRC⠀⇛


                # ⚓ Defence Web ☛ 2025-02-13_[Older]_EU_Parliament_hears_DR
                  Congo_crisis_is_an_“escalation”⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-12_[Older]_Protests
                  After_2_Sudden_Deaths_Force_Closure_of_Hospital_Trauma_Unit
                  in_Central_African_Republic⠀⇛


                # ⚓ Vox ☛ 2025-02-14_[Older]_The_roots_of_Donald_Cheeto
                  Mussolini’s_fixation_with_South_Africa⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-15_[Older]_White_South
                  Africans_Gather_in_Support_of_Cheeto_Mussolini_and_His_Claims
                  That_They_Are_Victims_of_Racism⠀⇛


                # ⚓ Counter Punch ☛ 2025-02-14_[Older]_The_Commercial_Impetus
                  Behind_Cheeto_Mussolini’s_Targeting_of_South_Africa⠀⇛


                # ⚓ Defence Web ☛ 2025-02-14_[Older]_al-Shabaab_to_face_renewed
                  military_operations_in_Somalia⠀⇛


                # ⚓ Defence Web ☛ 2025-02-14_[Older]_Yemeni_dhow_hijacking_ends
                  without_loss_of_life⠀⇛


                # ⚓ Defence Web ☛ 2025-02-14_[Older]_Mapping_South_Africa’s
                  arms_exports:_trends,_key_markets,_and_regional_demand⠀⇛


                # ⚓ Modern Diplomacy ☛ 2025-02-15_[Older]_The_US’s_Boycott_of
                  the_G20_Meeting_in_South_Africa:_Implications_and_Underlying
                  Factors⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-15_[Older]_African
                  Leaders_Elect_Djibouti's_Foreign_Minister_as_New_Leader_of
                  the_African_Union_Commission⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-15_[Older]_Djibouti's
                  Foreign_Minister_Elected_to_Top_African_Union_Post⠀⇛


                # ⚓ CBC ☛ 2025-02-07_[Older]_Cheeto_Mussolini's_threat_to_annex
                  Canada_'real'_and_motivated_by_access_to_critical_minerals,
                  Trudeau_tells_crowd⠀⇛


                # ⚓ JURIST ☛ UN_denounces_Israel_offensive_in_West_Bank_amid
                  violence_and_mass_displacement⠀⇛


                       The United Nations Human Rights Office (OHCHR) on
                       Friday condemned Israel’s continuing offensive
                       operation in the West Bank, urging Israel to
                       immediately halt the “alarming wave of violence and
                       mass displacement.” The OHCHR noted a resumption of
                       unlawful killings of Palestinian civilians
                       beginning on January 21, 2025.


                # ⚓ The Straits Times ☛ US-made_Typhon_missiles_to_bolster
                  security,_deter_‘repressive’_China:_Philippine_Defence
                  Secretary⠀⇛


                       Mr Gilberto Teodoro Jr said the Philippines’ plans
                       to acquire the missile system were an “internal
                       matter”.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ France24 ☛ European_countries_to_meet_in_Paris_to
                        discuss_security:_France_FM⠀⇛


                             France's President Emmanuel Macron will host
                             envoys from the 'main European countries' on
                             February 17 to discuss security on the
                             continent, Foreign Minister Jean-Noel Barrot
                             said. 'The president will bring together the
                             main European countries tomorrow for
                             discussions on European security,' Barrot
                             told the France Inter radio broadcaster on
                             February 16, without saying which nations
                             would participate.


                      # ⚓ CS Monitor ☛ Vice_President_Vance_tells_Europe's
                        leaders:_Stop_building_a_'firewall'_to_block_far
                        right⠀⇛


                             At the Munich Security Conference, Vice
                             President Vance said German political
                             coalitions that refuse to work with far right
                             parties violate democracy.


          o § Environment⠀➾


                # § Energy/Transportation⠀➾


                      # ⚓ Deutsche Welle ☛ 2025-02-10_[Older]_Can_Japan_solve
                        its_growing_over-tourism_crisis?⠀⇛


                      # ⚓ Hackaday ☛ Scrapyard_Vacuum_Dehydrator_Sucks_The
                        Water_From_Hydraulic_Oil⠀⇛


                             Anyone who has ever had the misfortune of a
                             blown head gasket knows that the old saying
                             “oil and water don’t mix” is only partially
                             true. When what’s coming out of the drain
                             plug looks like a mocha latte, you know
                             you’re about to have a very bad day.


                      # ⚓ Deutsche Welle ☛ 2025-02-08_[Older]_Alaska:_Missing
                        plane_found,_all_10_on_board_believed_dead⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-11_[Older]_US:_Private_jet
                        collision_in_Scottsdale,_Arizona,_kills_1⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-11_[Older]_Germany:_Train
                        collides_with_truck_in_Hamburg,_killing_1⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-09_[Older]_Mexico:_Dozens
                        killed_in_bus-truck_collision⠀⇛


                      # ⚓ CBC ☛ 2025-02-07_[Older]_Montreal_businessman
                        sentenced_to_3_and_a_half_years_in_U.S._prison_for
                        laundering_bitcoin⠀⇛


                      # ⚓ Arena Group ☛ Trump_Administration_Lays_Off_Hundreds
                        Of_FAA_Employees_Despite_Recent_Plane_Crashes⠀⇛


                             The Federal Aviation Administration has
                             officially begun the process of laying off
                             hundreds of probationary employees despite
                             recent plane crashes that have impacted areas
                             across the country.


                             Over the past several weeks, since Donald
                             Trump took office, the nation has seen plane
                             crashes impact cities across the country
                             including in Scottsdale, Arizona, Noem,
                             Alaska, and of course, Washington, D.C. where
                             just two weeks ago an American Airlines
                             commercial jet collided with a military
                             helicopter killing more than sixty people.


                      # ⚓ GeekWire ☛ Trump_layoffs_hit_Pacific_Northwest
                        engineers_and_researchers_at_PNNL,_Hanford_cleanup,
                        elsewhere [Ed: The_top_says_"independent"_but_also
                        bribed_by_Microsoft._Both_cannot_be_true.]⠀⇛


                             The Trump administration’s government-wide
                             layoffs are hitting engineers and researchers
                             at agencies in Washington state including the
                             Pacific Northwest National Laboratory (PNNL),
                             the Hanford Nuclear Reservation, the National
                             Oceanic and Atmospheric Administration
                             (NOAA), the Bonneville Power Administration
                             and elsewhere.


                      # ⚓ 100s_Of_FAA_Probationary_Employees_Summarily
                        Terminated_By_Trump_Administration⠀⇛


                             Many federal employees continue to get pink
                             slips under the Trump Administration, which
                             is looking to trim down the federal workforce
                             significantly. This is part of a larger plan
                             in which the Department of Government
                             Efficiency (DOGE) is carefully examining
                             several government departments in an effort
                             to reduce federal staffing numbers.


                             Layoffs have now also affected the Federal
                             Aviation Authority, as new reports have
                             surfaced about hundreds of probationary
                             employees being asked to leave.


                # § Wildlife/Nature⠀➾


                      # ⚓ New York Times ☛ Shark_Bites_Tourist_Who_Was_Trying
                        to_Take_Photo_With_It⠀⇛


                             The woman was flown off the island to receive
                             medical care, according to the Turks and
                             Caicos government.


                      # ⚓ Deutsche Welle ☛ 2025-02-14_[Older]_Conservation
                        efforts_double_India's_tiger_population⠀⇛


                      # ⚓ US News And World Report ☛ 2025-02-13_[Older]_Man
                        Whose_Wife_Was_Killed_in_a_Hippo_Attack_in_Africa_Sues
                        the_US_Company_That_Booked_the_Trip⠀⇛


                      # ⚓ Deutsche Welle ☛ 2025-02-09_[Older]_Caribbean_hit_by
                        7.6_magnitude_earthquake⠀⇛


          o § Finance⠀➾


                # ⚓ New York Times ☛ Argentina’s_Milei_Orders_Investigation
                  After_Promoting_Crypto_That_Cratered⠀⇛


                       Javier Milei posted about the coin on social
                       control media, then deleted it and announced an
                       investigation into whether any laws were broken.


                # ⚓ New York Times ☛ How_Convicted_Felon’s_One-for-One_Tariff
                  Plan_Threatens_the_Global_Economy⠀⇛


                       In starting a process to impose reciprocal tariffs
                       on American trading partners, the White House is
                       sowing uncertainty and risking inflation.


                # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_Why_Europe's_southern
                  periphery_props_up_eurozone_growth⠀⇛


                # ⚓ BIA Net ☛ 2025-02-10_[Older]_Turkey’s_unemployment_rate
                  drops_to_8.5%_in_December⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-08_[Older]_Canada_Seeks
                  Stronger_EU_Trade_Ties_as_Both_Regions_Threatened_by_Cheeto
                  Mussolini_Tariffs⠀⇛


                # ⚓ Modern Diplomacy ☛ 2025-02-07_[Older]_How_Can_Canada_+_USA
                  +_Mexico_Combine_the_Balance_of_Power_Against_China_on_the
                  Global_Stage?⠀⇛


                # ⚓ US News And World Report ☛ 2025-02-08_[Older]_Canada_Task
                  Force_Says_Ex-Finance_Minister_Freeland_Target_of_China-
                  Linked_Campaign⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ BIA Net ☛ 2025-02-10_[Older]_Turkey's_main_opposition_party
                  investigated_over_vote_buying_allegations_during_congress⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_Should_you_trust_hotel
                  and_restaurant_reviews? [Ed: AstroTurf and slop ruin
                  everything online]⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-13_[Older]_Germany:_Scholz_warns
                  of_lawsuit_over_'racist_lapse'_claim⠀⇛


                # ⚓ The Straits Times ☛ Malaysia’s_DAP_election_heats_up,_with
                  Lim_Guan_Eng_at_risk_of_losing_chairman’s_post⠀⇛


                       His aggressive tactics in the 2023 state poll had
                       backfired, and he is seen as overstaying his
                       welcome.


                # ⚓ Deutsche Welle ☛ 2025-02-15_[Older]_Jay-Z,_Sean_'Diddy'
                  Combs_accuser_drops_sexual_assault_case⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-08_[Older]_How_the_far_right_is
                  expanding_its_international_network [Ed: Social_control
                  media]⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-08_[Older]_Germany's_Left_Party
                  wants_to_halve_billionaires'_wealth⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-08_[Older]_German_conservatives
                  insist_they're_the_anti-AfD_'firewall'⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-09_[Older]_Germany:_Refugees
                  stigmatized_as_anti-migrant_wave_swells⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-12_[Older]_Thousands_sign_petition
                  for_Denmark_to_buy_California⠀⇛


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Deutsche Welle ☛ 2025-02-07_[Older]_Fact_check:
                        Cheeto_Mussolini's_team_targets_USAID_with_false
                        claims⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ Deutsche Welle ☛ 2025-02-08_[Older]_Libya's_cultural
                  crackdown_silences_popular_rap_music⠀⇛


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


                # ⚓ IP Kat ☛ 2025-02-13_[Older]_Blow_up:_Claim_against_BBC_ends
                  in_civil_restraint_order⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-14_[Older]_Czech_opposition_leader
                  eyes_state_funding_for_public_media⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ JURIST ☛ Human_rights_groups_urge_EU_to_engage_with_Bahrain
                  authorities_over_release_of_two_arbitrarily_detained_men⠀⇛


                       31 human rights organizations issued a joint letter
                       on Friday, urging the European Union (EU) to engage
                       with Bahraini authorities to secure the release of
                       Danish-Bahraini Abdulhadi Al-Khawaja and Swedish-
                       Bahraini Sheikh Mohammed Habib Al-Muqdad.


                # ⚓ NYPost ☛ Son_of_British_banking_bigwig_gets_forgiving
                  Manhattan_plea_deal_on_charges_of_beating_comedian
                  girlfriend:_‘Slap_on_the_wrist’⠀⇛


                       The son of a British banking bigwig was allowed to
                       take a forgiving plea deal after he was charged
                       with beating and strangling his up-and-coming
                       comedian girlfriend in Manhattan, The Post has
                       learned.


                # ⚓ BIA Net ☛ 2025-02-11_[Older]_Thousands_of_KFC,_Pizza_Hut
                  workers_in_Turkey_unpaid_amid_debt_restructuring⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-11_[Older]_Is_Bangladesh_plunging
                  into_political_chaos_once_again?⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-10_[Older]_Bangladesh_arrests
                  1,300_in_crackdown_on_pro-Hasina_protests⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-12_[Older]_UN:_Up_to_1,400_killed
                  in_Bangladesh_protests_crackdown⠀⇛


                # ⚓ Deutsche Welle ☛ 2025-02-12_[Older]_US_updates:_Cheeto
                  Mussolini_sued_by_inspectors_general_over_firing⠀⇛


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Ruben Schade ☛ Feedback_rules [Ed: Being trolled and
                  bullied over E-mail]⠀⇛


                       Hi! This will be the third and final instalment in
                       my “trolls get to Ruben” series, fun as it has been
                       to live it since last Thursday.


                       Sadly, it’s become clear some ground rules are
                       required for people who want to send me messages.
                       These will do nothing to deter the dregs, but I’m
                       going to codify and link to this anyway so there’s
                       no ambiguity.


                       You can have constructive criticism, disagree with
                       an opinion, or have an alternative technical
                       solution to a problem. You cannot be a dick,
                       douchebag, or other metaphor. I reserve the right
                       to define what those mean.


                # ⚓ Data Swamp ☛ Blog_activity_for_2025⠀⇛


                       Hello, you may have wondered why the blog has not
                       been really active this year, let's talk about it :
                       -)

      § Monopolies/Monopsonies⠀➾


          o ⚓ IP Kat ☛ 2025-02-13_[Older]_[Guest_Post]_CJEU_weighs_in_on
            supplementary_protection_certificates_in_Merck_v_Teva/Clonmel
            decision⠀⇛




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